Life of Richard Trevithick by F. Trevithick: Volume 2: Chapter 26
From Graces Guide
CHAPTER XXVI. TUBULAR BOILER, SUPERHEATING STEAM, AND SURFACE CONDENSER.
December 14th, 1828
Sir, -On my return from London five weeks since I was disappointed at not finding you in Cornwall. I have made inquiry into the duty performed by the best engines, and the circumstances they are under, from which it appears to me there is something which as yet has not been accounted for, particularly in Binner Downs engines. A statement was given to me by Captain Gregor, the chief agent and engineer of the mine, which appears so plain that I cannot doubt the facts, though they differ very widely from all former opinions. There are two engines, one of 42 inches diameter, the other of 70 inches diameter, 10-feet stroke.
Formerly those engines worked without cylinder cases, when the 70-inch cylinder burnt 1.5 wey of coal, and performed a regular duty-of forty-one millions; since that time brickwork has been placed round the cylinder and steam-pipes, leaving a narrow flue, which is heated by separate fires. These flues consume about 5 bushels of coal in twenty-four hours: the heat is not so great as to injure the packing, which stands good for thirteen weeks; the saving for several months past has increased the duty to sixty-three millions.
Before the use of this flue 108 bushels of coal were consumed under the boiler, now only 67 bushels are needed, which with the 5 bushels in the flue gives 72 bushels. The coal burnt under the boiler gives a duty of sixty-six millions, or an expansion of 60 per cent. by the heat of 5 bushels of coal in the flues, and a duty of 1,781 millions gained in twenty-lour hours by 5 bushels of coal, which amounts to 350 millions gained by each of these 5 bushels. The 12-inch cylinder is as near as possible under the same circumstances, no other alterations have been made; and to prove this they left out the fires in the flues, and the engines fell back to their former duty, and the condensing water increased in the same proportion.
The surface sides heated by this 5 bushels of coal is about 300 surface feet, the saving effected is 1,781 millions, which is six millions saving for each foot of surface on the castings in the flues. In Wheal Towan engine that did eighty-seven millions, the surface sides of the boiler was 1,000 feet of fire-sides for every bushel of coal burnt in an hour, and the duty performed per minute from each foot of boiler fire-sides was 1,500 lbs. 1 foot high. Now it appears that the heating of Binner Downs 300 surface feet gave a saving of 6,000 lbs. per minute per surface foot; whereas the boiler sides only gave 1,500 lbs. of duty per minute for each foot of boiler fire-sides. Therefore the saving by heating the sides of the cylinder is equal to four times the duty done by each square foot of boiler sides; and further, it appears that the 300 feet, when not heated, though clothed round with brickwork, condensed or prevented from expanding the steam of 41 bushels of coals, which was eight times as much steam condensed as the 5 bushels of coal would raise. Now if this be a report of facts, which I have no reason to doubt (but still I will be an eye-witness to it next week), there must be an unknown propensity in steam above atmosphere strong to a very sudden condensation, and vice versa, to also a sudden expansion, by a small heat applied to the steam-sides; and if by heating steam, independent of water, such a rapid expansion takes place, certainly a rapid condensation must take place in the same ratio, which might be done at sea by cold sides to a great advantage, always working with fresh water.
I shall have a small portable engine finished here next week, and will try to heat steam, independent of water, in small tubes of iron, on its passage from the boiler to the cylinder, and also try cold sides for condensing.
If the above statement prove to be correct, almost anything might be done by steam, because then additional water would not be wanted for portable engines, but partially condensed and again returned into the boiler, without any fresh supply or the incumbrance of a great quantity; and boilers might be made with extensive fire-sides, both to heat water and steam, and yet be very light.
It appears that this engine, when working without the heated flues round the cylinder and pipes, evaporated 20,000 gallons of water into steam, in twenty-four hours, more than when the flues were heated, and the increase of condensing water was in the same proportion. It is so unaccountable to me that I shall not be satisfied until I prove the fact, the result of which I will inform you, and shall be very glad to receive your remarks on the foregoing statement.
The first engine that will be finished here for Holland will be a 36-inch cylinder, and a 36-inch water-pump, to lift water about 8 feet high on the crank-shaft there is a rag-head of 8 feet diameter, going 8 feet per second, with balls of 3 feet diameter passing through the water-pump, which will lift about 100 tons of water per minute. It is in a boat of iron, 14 feet wide, 25 feet long, 6 feet high, so as to be portable, and pass from one spot to another, without loss of time. It will drain 18 inches deep of water (the annual produce on the surface of each acre of land) in about twenty minutes for the drainage of each acre, with one bushel or six pennyworth of coal per year. The engine is high pressure and condensing.
I remain, Sir,
Your very humble servant,
P.S.— Woolf is making an apparatus to throw back from the bottom of the cylinder on to the top of the piston a fluid metal every stroke. He says he proved by an indicator that he raised 18,000 inches of steam from 1 inch of water, of 11 lbs. to the inch pressure on a vacuum, and that the reason why this engine did not do 800 millions, was because the steam passed by the sides of the piston. That an engine at the Consolidated Mines working 10 feet 2 inch stroke, going 7/8ths expansive, beginning with steam of 20 lbs. to the inch above the atmosphere, and ending with 11 lbs. on a vacuum. I doubt this statement; however, there is some hidden theory as yet, because some engines perform double as much as others, under the same known circumstances, and I believe that nothing but practice will discover where this defect is, for, in my opinion, no statement of theory yet given is satisfactory why high-pressure engines so far exceed low-pressure engines. It is facts that prove it to be so, therefore all theory yet laid down must be defective.
At the date of this letter Trevithick had been rather more than a year in England, residing generally at Hayle, within half-a-dozen miles of Mount's Bay, from which he had sailed for America; and after eleven years of wandering in countries where steam-engines were unknown, except those that he himself had constructed was again on his return giving his whole thoughts to the idol of his life.
During that period scientific men in Europe thought and wrote much on the question of relative temperature, pressure, economy, and manageability of steam. Newcomen's great discovery a century before was the avoidance of the loss of heat by the cooling at each stroke of the exterior of the steam-vessel of Savery's engine by injecting cold water into the steam in the cylinder. After fifty years came the Watt improvement, still reducing the loss of heat by removing the cold injection-water from the steam-cylinder to a separate condenser.
The high-pressure steam-engine was perfect without injection-water, though when convenient its use was equally applicable as in the low-pressure engine. Trevithick, on his return to civilized life, read the views of Watt on steam, as given in 'Farey on the Steam-Engine'. On informing Davies Gilbert of his doubts of the accuracy of those views, and of his intention of testing them by comparison with the work performed by Cornish pumping engines, his friend, who had just published his 'Observations on the Steam-Engine',  forwarded a copy, from which the following is an extract:—
One bushel of coal, weighing 84 lbs., has been found to perform a duty of thirty, forty, and even fifty millions, augmenting with improvements, chiefly in the fire-place, which produce a more rapid combustion with consequently increased temperature, and a more complete absorption of the generated heat; in addition to expansive working, and to the use of steam, raised considerably above atmospheric pressure.
Those words gave the result of Trevithick's experience made known to his friend during twenty years of labour,  and yet by a seeming fatality his name is not found in his friend's book.
Sir John Rennie, who in youth had been employed under Boulton and Watt at Soho, and had risen to be a member of the Royal Society, came about that time into Cornwall, at the request of the Admiralty, to make examination into the work performed by Cornish pumping engines, and selected Wheal Towan engine on which to make special experiments.  The subject of Trevithick's note was therefore at that period, and still is, a matter of importance and his practical treatment of the question is more instructive to young engineers than complex rules. Arthur Woolf was at the same time experimenting on steam at the Consolidated Mines, and finding the want of agreement between the rules of low-pressure and the practice of high-pressure engines, imputed the error to the escape of steam by the sides of the piston. Trevithick disbelieved this, "because some engines perform double as much as others, under the same known circumstances," and advocated the observance of general practice to prove why high-pressure engines were more economical than those of low-pressure. Captain Gregor had placed fire-flues around the steam cylinder and pipes, hoping thereby to exceed the duty of the Wheal Towan engine, whose boiler, cylinder, and steam-pipes were carefully clothed with a thick coating of sawdust or other non-conductor of heat, and lifted eighty-seven millions of pounds of water 1 foot high by the heat from a bushel of coal weighing 84 lbs. This was the greatest duty that had ever been recorded from a steam-engine. The Trevithick or Cornish boilers, similar to those in Dolcoath,  measured at the rate of 1,000 superficial feet of heating surface for each bushel of coal burnt in an hour, and in round numbers have a duty of 1,500 lbs. lifted a foot high to each foot of boiler surface. In words not technical, the heat from 1 lb. of coal gave steam that raised 460 tons weight of water 1 foot high.
The cylinder of this engine used the Watt steam-jacket. The Binner Downs engine was doing not one-half this duty, namely, forty-one millions; when brick flues were built around the cylinder, cylinder cover, and steam-pipes, and one or two fire-places, fixed near the bottom of the cylinder, of a size to conveniently burn 5 bushels of coal in twenty-four hours, the heat from which circulated through those flues on its way to the chimney, and increased the duty of the engine by one-half, raising it to sixty-three millions; in other words, during twenty-four hours of working, 67 bushels of coal in the boiler, and 5 bushels in the cylinder flues, did the same work as 108 bushels in the boiler without the cylinder flues, causing a saving of fifty per cent. by their use. Another startling fact was the greater effect for each foot of heating surface in the steam-cylinder flues than in the boiler flues the latter gave a power of 1,500 lbs. raised 1 foot high by a bushel of coal, while the former gave 6,000 lbs. of power from the same amount of coal and heating surface.
Here was a mystery that Trevithick would not believe until he had seen it with his own eyes: he searched for it for a year or two, and overlooking the fact that the more simply arranged engine of his once pupil, Captain Samuel Grose, was doing more duty than the super-heating steam-engine at Binner Downs, he worked at what seemed to be new facts, and converted them into a new engine.
We have traced how succeeding engineers tried prevent loss of heat. Trevithick took the first bold step, and aiming at the same object, made the boiler the steam-jacket for the cylinder, and in his patent of 1802 went still further and protected the boiler from external cold, and thus describes it:-
The steam which escapes in this engine is made to circulate in the case round the boiler, where it prevents the external atmosphere from affecting the temperature of the included water, and affords by its partial condensation a supply for the boiler itself. 
So that a quarter of a century before the date of those Binner Downs experiments he had patented an engine having neither cylinder nor boiler exposed to the cooling atmosphere. The flues around the Binner Downs cylinder were difficult of control. Trevithick says the piston packing had not been injured, showing that observers thought it would be, and even the cylinder was endangered, for the writer, who stoked those heating flues, recollects the fires burning very brightly in them. The ready transmission of heat through thin metal, used by Trevithick in 1802 for heating feed-water, and in the cellular bottom of the iron ship of 1808, serving as a surface condenser,  and his experience in 1812, that "the cold sides of the condenser are sufficient to work an engine a great many strokes without any injection,"  still followed up in 1828 by condensing steam without the use of injection-water, led to what is since known as Hall's surface condenser.
The following letter is in the handwriting of the present writer; it is the only one of Trevithick's numerous letters not written by himself:—
December 30th, 1828.
Sir,— On the 28th inst. I received your printed report on steam, and have examined Farey's publication on sundry experiments made by Mr. Watt, which are very far from agreeing with the actual performance of the engines at Binner Downs. Mr. Watt says that steam at one atmosphere pressure expands 1,700 times its own bulk as water at 212 deg., and that large engines ought to perform eighteen millions when loaded with 10 lbs. to the inch of actual work, the amount of condensing water being one-fortieth part of the content of the steam in the cylinder at one atmosphere strength, the cold condensing water at 50 deg., and when heated 100 deg. This would give for the Binner Downs engine, with a 70-inch cylinder, 10-inch stroke, 11 lbs. effective work on the inch (this load being one-tenth more than in Watt's table, by Farey, for an engine of this size and stroke), 57 gallons of injection-water for each stroke, and when working eight strokes per minute, to do eighteen millions would consume 11.25 bushels of coal per hour.
Now the actual fact at Binner Downs, at the rate of working and power above mentioned, is that 3 bushels of coal per hour were burnt, using 13 gallons of injection-water at each stroke at 70 deg. of heat, which was raised by its use to 104 deg. or an increase of 34 deg., which multiplied by 13 gallons, gives 442. Mr. Watt's table for this engine and work gives 57 gallons of condensing water at 50 degrees, heated by use to 100 degrees. This 50 degrees raised, multiplied by the 57 gallons of water, amounts to 2,850, or six and half times the quantity really used in the Binner Downs engine, and nearly four times the coal actually used at present. Mr: Watt further says that steam of 15 lbs, to the inch, or one atmosphere, from 1 inch of water at 212 degrees occupies 1,170 inches, and that steam of four atmospheres, or 60 lbs. to the inch, gives only 471 inches at a heat of 293 degrees. Now deducting 50 degrees from 212 degrees leaves 162 degrees of heat raised by the fire. Multiply 15 lbs. to the inch by 1,700 inches of steam, and divide it by 162 degrees, gives 138 degrees, whereas if you deduct 50 degrees from 293 degrees, it leaves the increase of heat by the fire 243 degrees. Steam of 60 lbs. to the inch multiplied by 471, being the inches of steam made by 1 inch of water divided by 243 degrees, the degrees of heat raised by the coal, gives a product of 116; therefore, by Mr. Watt's view it appears that low steam would do one-fifth more duty than high steam, and yet Binner Downs engine in actual work performs about four times the duty given by Mr. Watt's theory and practice, with only one-sixth part of the amount of heat carried off by the condensing water, proving that high steam has much less heat, in proportion to its effective force; and this is further proved by the small quantity of condensing water required to extract its heat.
Yesterday I proved this 70-inch cylinder while working with the fire-flues round it, which flues only consumed 5 bushels coal in twenty-four hours. The engine worked eight strokes a minute, 10-feet stroke, 11 lbs. to the inch effective force on the piston; steam in the boiler 45 lbs. above the atmosphere, consuming 12 bushels of coal in four hours, using 13 gallons of condensing water at each stroke. which was heated from 70 to 104 degrees; but when the fires round the cylinder were not kept up, though still having the casing of hot brickwork around it, and performing the same work, burnt 17 bushels of coal in the same time of four hours, and required 15.5 gallons of condensing water, which was heated from 70 to 112 degrees. You will find that the increased consumption of coal, by removing the fire from around the cylinder, was nearly in the same proportion as the increase and temperature of the condensing water, showing the experiment to be nearly correct.
From the general reports of the working of the engines it appears that when the surface sides of the castings are heated, either by hot air or high steam, the duty increases nearly fifty per cent. from this circumstance alone.
A further proof of the more easy condensation of high steam was in the Binner Downs 42-inch cylinder engine 9-feet stroke, six strokes per minute, 11 lbs. effective power on each inch, burning 1.3 bushel of coal an hour. In this engine the proportion of saving by the heating flues was the same as in the large engine. I tried to condense the steam by the cold sides of the condenser, without using injection-water. The water in the condenser cistern was at 50 degrees. After working for twenty-five minutes the small quantity of hot water discharged at the top of the air-pump reached 130 degrees of heat, but then would rise no higher, the cold sides of the condenser being equal to the condensation of all the steam. The eduction-pipe and air-pump, with its bottom and top, gave 60 feet of surface sides of thick cast iron, and about 20 feet more of surface sides of a thin copper condenser; altogether, 80 feet of surface cold sides, surrounded by cold water. About half a pound on the inch was lost in the vacuum, the discharged water being 130 degree of heat instead of 100°. The vacuum was made imperfect by about 12 lb. to the inch.
It is my opinion that high steam will expand and contract with a much less degree of heat or cold in proportion to its effect, than what steam of atmosphere strong will do. I intend to try steam of five or six atmospheres strong, and partially condense it down to nearly one atmosphere strong, and then by an air-pump of more content than is usual to return the steam, air, and water, from the top of the air-pump, all back into the boiler again, above the water-level in the boiler, and by a great number of small tubes, with greatly heated surface sides, to reheat the returned steam; though by this plan I shall lose the power of the vacuum, and also the power required on he air-bucket to force the steam and water back again into the boiler, yet by returning so much heat I shall over-balance the loss of power, besides having a continued supply of water, is which in portable engines, either on the road or on the sea, will be of great value.
I shall esteem it a very great favour if you will be so good as to turn over in your mind the probable theory of those statements, and give me your opinion. If Mr. Watt's reports of his experiments are correct, how is it possible that the high-pressure engine that built at the Herland thirteen years ago, which discharged the steam in open air, did more than twenty-eight millions? If you wish, I will send a copy of the certificate of the duty done by this engine, which states very minutely every circumstance. Now that cylinder, with every part of the engine, was exposed to the cold; had it been heated around those surfaces, as on the present plan, it would have done above forty millions.
Suppose the Binner Downs 70-inch cylinder engine, 1O-feet stroke with full steam to the bottom of the stroke, when by the experiment, the heated flues were again laid on would have worked one-third expansive, by the heat of 5 bushels of coal around the cylinder. Now one-third of the power would make a 3 feet 4 inch stroke, 11 lbs. to the inch effective power, eight strokes a minute, during twenty-four hours, by the consumption of 5 bushels of coal applied on the surface sides of the cylinder, performing a duty of 324 millions with a bushel of coal. Now suppose the cylinder without the heating flues had the steam cut off at two-thirds of the stroke, and that it is possible in a moment to heat the cylinder by the flues; in that case the steam would, by its expansion from the hot sides, fill the last third of the cylinder to the bottom of the stroke; then if that steam be suddenly cooled, so as to contract it one-third, the piston would descend one-third its stroke in the cylinder; and it appears in theory by this plan, that a cylinder once filled two-thirds full of steam, by receiving the heat on its surface sides from 5 hushels of coal, and again suddenly cooling down would continue to work for ever, without removing the steam from the cylinder, and would perform a duty of millions. This never can be accomplished in practice in this way, but the effect may be obtained by partially condensing in a suitable condenser, and again heating by hot sides.
This mystery ought to be laid open by experiment, for what I have stated are plain facts from actual proofs, and have no doubt that time will show that the theory of Mr. Watt is incorrect. Though there were 300 feet of cold sides, yet 200 feet were not condensing steam, because on the return of the piston, what was condensed below, and while the engine was resting, did not make against it more than what was condensed above the piston on its descent; therefore you may count on 150 feet of cold external sides constantly condensing, that made this third-part difference against the expansion of the steam.
I remain, sir,
Your very humble servant,
The writer's note-book used during those experiments is in his possession, as well as Trevithick's note-book giving particulars of experiments at several mines, from which the following extracts are taken:
CORNWALL, August, 1828.- Wheal Towan 80-inch cylinder, 10-feet stroke, 6.9 strokes per minute, loaded to 9.5 lbs. on the inch of the piston, with three of Trevithick's boilers each 37 feet long, 6 feet 2 inches diameter, with fire-tube feet 9 inches diameter, fire-place 6 feet long, evaporated 13 square feet of water with 1 bushel (84 lbs) of coal, duty 87 millions. Tho heat in the stack was just the same as the heat of the steam in the boiler. Another engine of the same size on the same mine, with similar boilers, but working only 4.06 strokes per minute, loaded to 4.55 lbs. on each inch of the piston, did 50.8 millions.
Wheal Vor 53-inch cylinder, 9-feet stroke, 6.59 strokes per minute, loaded to 19.58 lbs. on each square inch of the piston, did 36.6 millions.
Wheal Damsel 41-inch cylinder, 7 feet 6 inch stroke, 5.52 strokes per minute, loaded to 21.5 lbs. on the inch of the piston, did 33 millions.
It would appear, therefore, that about 10 lbs. to the inch on the piston allows of the best duty, and that a 10-feet stroke exceeds in duty a 7 feet 6 inch stroke.
The Wheal Towan engine, doing 87 millions, had 1,248 feet of tube fire-surface, and a similar amount of external boiler surface in the flues. 2.5 bushels of coal were consumed each hour, giving about 1,000 feet of fire-sides for each bushel of coal consumed per hour, and 50 feet of fire-bars. Those boilers were intended to supply steam for working the engine at ten strokes a minute; a bushel of coal an hour would in that case have had 600 feet of boiler fire-surface.
Binner Downs 70-inch cylinder, 10-feet stroke, d id 41 millions. A fire was then put around the cylinder and steam-pipes, which burnt 5 bushels of coal in twenty-four hours, by which the duty was increased to 63 millions. The surface sides of the cylinder, cylinder-top, and steam-pipes heated by flues was 300 feet, and caused a saving of 41 bushels of coal in twenty four hours. Another engine in the same mine was tried, having a 42-inch cylinder, when the fire was around the cylinder, she worked 100 strokes without injection-water; the expansion-valve was closed at half-stroke, the steam in the boiler 56 lbs. on the inch above the atmosphere.
It is not easy to deal with the important reasoning flowing from those facts, and influencing the form and economy of the steam-engine, nor to show if Trevithick was right in discrediting the laws laid down by Watt. Newcomen's engine had the interior, as well as the exterior of the steam-cylinder exposed to the cooling atmosphere. Watt, by putting a cover on the cylinder, reduced the loss of the heat from the interior, and by his steam-case hoped to reduce the loss from the exterior, though by it he increased the amount of surface exposed to the cold. In Trevithick's early engines the boiler alone exposed heat-losing surface, and this was further reduced by its own comparatively small size, the engine and boiler complete not exposing one-quarter of the surface of a Watt low-pressure engine of equal power. One object of the Binner Downs experiment was to further curtail this loss of power by increasing the heat of the steam while in operation in the cylinder since called super-heating steam.
This principle of giving increased heat to steam, after it had left its state as water, was made practical by Trevithick's boiler at Wheal Prosper in 1810, where the flues having first been carried around the water portion of the boiler, then passed over the steam portion;  and again in the upright boiler of 1815, having the upper end of the fire-tube surrounded by steam above the water line.  Those early beginnings of super-heating steam and surface condensation culminated in the Binner Downs experiments of 1828, one immediate practical result of which was the tubular surface condenser, enabling steamboat boilers to avoid, in a great measure, the use of salt water, facilitating in a marked degree the application of marine boilers and engines with steam of an increased pressure.
The Binner Downs engine, with a cylinder of 70 inches in diameter, and a stroke of 10 feet when working with steam in the boilers of 45 lbs, to the square inch above the atmosphere, and using the heating flues around the cylinder, required 13 gallons of injection-water at each stroke, and consumed at the rate of 3 bushels of coal an hour, to produce a duty equal to eighteen millions; by removing the cylinder super-heating flues, the quantity of injection-water for the same amount of work increased to 15.5, gallons, and the coal to 4.25 bushels. Watt's rule for his low-pressure steam vacuum engine doing a duty of eighteen millions, gave 57 gallons of injection-water, and 11.25 bushels of coal.
On the question of coal, this statement agrees very nearly with Trevithick's letters of sixteen years before, when he used the high-pressure boilers in the Dolcoath pumping engine,  promising that his high-pressure expansive engine would do the work with one-third of the coal required in the low-pressure vacuum engine.
The high-pressure steam required a less amount of injection-water to condense it than the low-pressure steam, in proportion to the work done, showing the Watt rule and the Watt experience to be inapplicable to high-pressure engines; for instead of 57 gallons of injection-water the Binner Downs engine with steam of 45 lbs, to the inch required but 15.5 gallons of injection-water, and this amount was further reduced to 13 gallons by super-heating the steam; this roughly agrees with the coal consumed, or in other words, with the amount of heat to be carried off by injection-water: the Watt rule giving 11.25 bushels as the fair allowance for low-pressure steam vacuum engines, while the high-pressure steam vacuum engine burnt but 4.25 bushels. This was further reduced to 3 bushels by super-heating. Those facts led to the idea that if the steam pressure was sufficiently increased, condensation might be carried out without any injection-water, by the transmission of the heat in the steam through the metal sides of the condenser. An experiment was at once made by removing the Watt condenser and injection-water, as he had done seventeen years before,  using in their stead a thin copper surface-condenser immersed in cold water, producing, within 0.5 lb, on the inch, as good a vacuum as when injection-water was used, leading to the conclusion,—
It is my opinion that high steam will expand and contract with a much less degree of heat or cold, in proportion to its effect, than what steam of atmosphere strong will do. I intend to try steam of five or six atmospheres strong, and partially condense it down to nearly one atmosphere strong, and then by an air-pump of more content than is usual to return the steam, air, and water back into the boiler again, and by a great number of small tubes, with greatly heated surface sides, to reheat the returned steam.
This, in practical words, is the surface condenser by which the used steam is returned to the boiler in the form of water. The more general use of high-pressure steam of 70 or 90 lbs, to the inch, increasing its expansive force on one side of the piston by superheating it on its passage through numbers of small tubes, and decreasing its expansive force on the other side of the piston by cooling it in passage through similar tubes exposed to cold, is partly effected in steamboats, but has not yet been attempted in engines on the road.
After a month's further consideration he wrote: -
Wheal Towan engine is working with three boilers, all of the same size, and the strong steam from the boilers going to the cylinder-case; the boilers are so low as to admit the condensed water to run back from the case again into the boiler: they find that this water is sufficient to feed one of these boilers without any other feed-water, therefore one-third of the steam generated must be condensed by the cold sides of the cylinder-case, and this agrees with the experiments I sent to you from Binner Downs. Wheal Towan engine has an 80-inch cylinder, and requires 72 bushels of coal in twenty-four hours, therefore, the cylinder-case must, in condensing high-pressure steam, use 24 bushels of coal in twenty-four hours. Bolton and Watt's case for a 63-inch cylinder working with low-pressure steam, condensed only 42 bushels of coal in equal time, the proportions of surface being as 190 to 240 in Wheal Towan. Nearly five times the quantity was condensed of high steam than of low steam, proving that there is a theory yet unaccounted for. 
These apparent facts are, in the case of steamboats, more culpably overlooked now than when he wrote forty-two years ago; engines have been examined and reported on by eminent scientific men, but it was left for Trevithick to point out that cold on the surface of the steam-case of a Watt low-pressure steam vacuum engine condensed about one-fifteenth of the steam given from the boilers, and that the loss from exposure to cold was nearly five times more from high-pressure steam than from low-pressure. Within a few more months he determined on constructing an engine for the purpose of more accurately testing those views.
July 27th, 1829.
Sir,— Below you have a sketch of the engine that I am making here for the express purpose of experimenting on the working the same steam and water over and over again, beating the returned steam by passing it in small streams up through the hot water from the bottom of the boiler. The boiler is 3 feet in diameter, standing perpendicular; the interior fire-tube is 2 feet in diameter; there is a steam-case round the outside of the boiler with a 1.5-inch space. This keeps the boiler hot and partially condenses the steam before it is again forced into the boiler.
The boiler is 15 feet high; the cylinder 14 inches diameter, with a 6-feet stroke, single power. The pump for forcing the steam and water back again is 10 inches in diameter, with a 2 feet 9 inch stroke, about one-quarter part of the content of the steam-cylinder. The bottom of the boiler will have a great number of small holes, about 1/16th of an inch in diameter, through which the steam delivered into the boiler will pass up through the hot water, by which I should think it will heat those small streams of steam again to their usual temperature.
The pump for lifting water to prove the duty of the engine is 30 inches in diameter, with a 6-feet stroke, but this may be lengthened to a 12-feet lift, as the trial or load in the experiments may require, giving from 12 to 24 lbs. to the inch in the piston. This machine will be ready before your return to Cornwall, and I intend to prove it effectually before I go to Holland.
The Holland engine lifted on the trial, when they came down to see it, 7,200 gallons of water a minute 10 feet high with 1 bushel of coal an hour; exceedingly good duty for a small engine of 24-inch cylinder, being 34,560,000 of duty.
On the 17th August the trial comes on between the two companies about the quays. They are as desperate as possible on both sides, and castings and every other article are thrown down to 30 per cent. below cost price; iron pumps for 6s. 6d, per cwt., and coal sold to the mines for 37s. 3d. per wey, when 48s. per wey on board ship was paid for it. Several thousands lost per year by each party. This never can last long. If you can think of any improvement I shall be very glad to hear in time, before it may be too late to adopt it. At all events, if it is not too much trouble to write, I shall be very glad to hear from you. What effect do you think the water will have in heating the steam on its passage to the top of the water from the false bottom of the boiler?
I have a cistern of cold water, with a proper condenser in it, connected between the bottom of the boiler-case and the force-pump to the bottom of the boiler, therefore I can partially condense by cold water sides, or by cold air sides just as I please, by rising or sinking the water in the cistern.
The boiler is made very strong to try different temperatures, and an additional length to the water-pump makes all very suitable for a great number of experiments, and if there is any good in the thing I will bring it out.
I shall have indicators at different places to prove what advantages can be gained. I hope to have the pleasure of your company during those experiments, which I think will throw more light on this subject than ever has yet been done. Some trials since I last wrote to you make me very confident that much good will arise from these experiments, but to what extent is uncertain.
I remain, Sir,
Your most obedient servant,
Trevithick did not use letters to illustrate his sketch, knowing that Davies Gilbert would comprehend it; but the reader of to-day may not find it so easy, therefore the writer has added them with a slight detail description, he having been Trevithick's daily companion when those drawings and experiments were made. a, top of boiler; b, water line; c, centre of wheel; d, cast-iron wheel and chain; e, chimney, 13 in, in diameter; f, fire-tube, 2 ft. diameter; g, outer boiler-case, 3 ft. diameter, 15 ft. long; h, water space of 6 in.; i, boiler steam-case, 3 ft. 4 in. diameter; j, small holes through which steam and water are forced into the boiler; k, force-pump, 10 in. diameter, 2 ft. 9 in. stroke; l, steam-cylinder, 14 in. diameter, 6-ft. stroke; m, piston-rod, 6-ft stroke; n, fire-door; o, fire-bars; p, pump for testing the power of the engine.
There is a natural tendency in men of genius to unwittingly return, under new forms, to old ideas. The ideas are similar, though in combination with new forms and new acquirements even the outline of this 1828 boiler, with the exception of its outer steam-casing, is very like that in a letter to Davies Gilbert fourteen years before,  of which Trevithick had kept no copy. When in the foregoing letter he wrote "There is a steam-case round the outside with a 1.5-inch space; this keeps the boiler hot and partially condenses the steam before it is again forced into the boiler" he had forgotten that twenty-seven years before, when constructing his first high-pressure steam-engines, he thus specified his invention:— "The steam which escapes in this engine is made to circulate in the case round the boiler, where it prevents the external atmosphere from affecting the temperature of the included water, and affords by its partial condensation a supply for the boiler itself." 
Not one of his numerous patent specifications has been found among his papers, neither do his letters refer to them; probably be never read them after the first necessary examinations.
November 5th, 1829.
Sir,— The engine has been worked. The result is ten strokes per minute, 6-feet stroke, with half a bushel of coal per hour, lifting six thousand pounds weight. This was done with water in the cistern round the condenser, which water came up to 180 degrees of heat, and remained so. The water sides of the condenser covered with this hot water was 50 surface feet. I tried it to work with the cold air sides, but I found that the cold air sides of 120 feet would only work it four strokes per minute. I should have worked the steam much higher than 50 lbs. to the inch, but being an old boiler I thought it a risk. I am now placing an old boiler of 350 feet of cold sides more to the condenser, to give a fair trial to condensing with cold sides alone. The steam below the piston was about 6 or 7 lbs. to the inch above the atmosphere. The force-pump to the boiler was about one-fifth part of the content of the cylinder, and the valve close to the boiler lifted when the force-piston was down about two-thirds of its stroke, at which time the returned steam entered the boiler again. I have no doubt of doing near ten times the duty that is now done on board ships, without using salt water in the boiler, as at present. Our boiler has been working three days and the water has not sunk 1 inch per day. I am quite satisfied the trial will be a great success.
Mr. Praed and Sir John St. Aubyn are anxious to get a high bank carried out from Chapel Angel to 15 feet below low-water mark on the bar, to make Hayle a floating harbour.
I have proposed to make a sand-lifting engine. When I built that engine for deepening Woolwich Harbour, we lifted 300 tons per hour through 36 feet of water, and 20 feet above water, 56 feet above the bottom. This was done with two bushels of coal per hour, therefore it will not cost above one penny per square fathom to lift the sand over this embankment. It is intended to get down Mr. Telford to give his opinion on it. Your remarks on it would be of service. I remain, Sir,
Your humble servant,
The writer having worked at these experiments, knows that their object was to employ high-pressure steam in the boiler, using it very expansively in the cylinder, and by cold surface sides reducing its bulk either to low-pressure steam or boiling water, and then force it again into the boiler.
November 14th, 1829.
Sir, I have both of your letters and sketches, which shall be put in hand. I understand it perfectly well. Since I wrote to you last I have made several satisfactory trials of the engine, and think it unnecessary to make any further experiments. The statement below may be depended on for a future data. The load of the engine was 6,280 lbs., being 20 lbs. to the inch for a 20-inch cylinder with a 6-feet stroke, 12 strokes per minute, with three-quarters of a bushel of coals per hour, giving a duty of 361,728,000 for 1 bushel of coal, a duty far beyond anything done in the county by so small an engine. The cold water sides round the condenser was 60 feet, and the water at 112 degrees temperature, not having a sufficient stream of cold water to supply the cistern. Each foot of cold water sides did 7,536 lbs. per minute, about three times the work done in the county per foot of hot boiler sides; therefore the condenser need not be more than one-third of the boiler sides. By making the condenser of 4-inch copper tubes and of an inch thick, it would stand in one-twentieth part of the space of the boiler.
I put a boiler naked to try cold air sides; it was very rusty, and did not condense as fast as I expected. The engine worked exceedingly well, but slow. The duty performed for each foot of cold air sides was 565 lbs, per minute, about one-thirteenth part of the condensing of cold water sides. We never wanted to get the steam above 60 lbs. to the inch. I have no doubt but that copper pipes of 1/32nd of an inch thick, clean and small, would do considerably more, because the hot water, came out of the boiler from the condensed steam was but 170 degrees, and the external sides the same heat when the steam was 15 lbs. above the atmosphere in the condensing boiler. This boiler was 4 feet 6 inches diameter, and I think that towards the external sides of the boiler there was a colder atmosphere, if I may call it so, than what it was in the middle of this large condensing boiler, because I found by trying a small tin tube, that it would condense 1,500 lbs. for each foot of cold air sides.
However, as it is, it will do exceedingly well for portable purposes.
The duty, I doubt not, will be, both for water and air sides condensing, at least 50 per cent. above our Cornish engines, which will be above four times what is now done with ships' engines, especially when you take into consideration their getting steam from salt water, and letting out so much water from the boiler to prevent the salt from accumulating in the boiler, which will make 30 per cent. more in its favour.
If strong boilers to stand 200 lbs. to the inch are made with small tubes, I have no doubt but that the duty would be considerably more and my engines will not be one-quarter part of the weight, price, or space of others and when every advantage is taken it will be 1,000 per cent. superior in saving of coal to those now at work on board. This engine works well, and returns the steam very regularly every stroke into the boiler.
I am extremely sorry you were not present to see these experiments. Please make your remarks on these statements, with any further information you may judge useful.
I shall now make drawings agreeable to my experiments for actual performance on board ships. In hope of hearing from you soon,
I remain, Sir,
Your very humble servant,
The large old boilers used as surface condensers, in which the steam was partially condensed by the transmission of heat to the external atmosphere, together with its further condensation in a smaller condenser with cold water around it, so reduced its expansiveness, that a large feed-pump drew the hot water and steam from the small condenser, and forced it back into the boiler without any reduction of quantity those temporary contrivances, almost immediately resolved themselves into a condenser made of copper tubes surrounded by cold water.
Having proved by six months' experiment on a working scale the practicability of the plan which in reality he had invented twenty years before in the iron steamship,  he wrote in June, 1830:—
To THE RIGHT HONOURABLE THE LORDS COMMISSIONERS OF THE ADMIRALTY, &c., &c., &c.
About one year since I had the honour of attending, your honourable Board with proposed plans for the improvement of steam navigation, and as you expressed a wish to see it accomplished, I immediately made an engine of considerable power for the express purpose of proving by practice what I then advanced in theory. I humbly request your lordships will grant me the loan of a vessel of about 200 or 300 tons burthen, in which I will fix at my own expense and risk an engine of suitable power to propel the same at the speed required: no alterations whatever in the vessel will be necessary. When under sail the propelling apparatus can be removed, and when propelled by steam alone, the apparatus outside the ship will scarcely receive any shock from a heavy sea. This new invention entirely removes the great objection of feeding the boiler with salt water.
This petition was backed by Mr. Gilbert and Mr. George Rennie. His old friend Mr. Mills took an interest in it, and wrote, "I am going to meet Captain Symonds at Woolwich again to-morrow, and hope to be able to persuade him to use his influence with Sir T. Hardy."
LAUDERDALE HOUSE, HIGHGATE,
August 19th, 1830.
Sir,— The boiler with the fire-place, cold air tubes outside the boiler but within the steam-case, fire-tubes in the boiler from the top of the fire-place to the top of the boiler, the ash-pit close, except a, small door to clear out the ashes.
The design is for the cold air to pass down from the top of the boiler through the air- tubes within the steam-case surrounding the boilers, becoming heated in its passage by condensing the steam in the case, and then to pass up through the fire-bars in the hot state, nearly as hot as the steam in the case; because this air, heated to nearly 212 degrees by condensing the steam in its passage without any of its oxygen being burnt, it will not carry off so much heat from the fire as cold air would, and still have the same oxygen as cold air to consume the coal.
The cold air will be passing down the steam-case in the air-tubes, and up through the fire and fire-tubes in the boiler. I find by experiments I have made here, by placing a tin tube 2.5-inches in diameter, 4 feet long, inside a 4-inch tube of the same length, having boiling water and steam between the tubes, kept hot by a fire round the outer tube, with a smith's bellows blowing in at the bottom of the inside tube, having 2 and 2/3rds surface feet of condensing sides, measuring the inside, where the air is passing up from the bellows, heats from 60 to 134 degrees 15 square feet of cold air per minute. When you compare the effective heat of 74 degrees given to 15 cubic feet of air every minute from 2 and 2/3rds surface feet of tin plate, and the heat contained in 15 cubic feet of air charged with 74 degrees of effective heat, compared with steam of atmosphere strong, you will find that the condensing power of surface sides is very great, and for locomotive purposes might be carried still further, by forcing the air more quickly through the tubes. If the statements on air given in some books that I have read are correct, that there is about three times as much heat in 1 gallon. of steam of atmosphere strong as there is in 1 gallon of air of 212 degrees of heat, in that case 1 surface foot of tin-plate sides of this pipe, by sending off the hot air before described, would take out the heat of 1.5 cubic foot of steam per minute of atmosphere strong, which in the common condensing engine would be equal to a duty of 2,700 lbs. lifted 1 foot high per minute; but in the high-pressure expansive engine, the heat of 1.5 cubic foot of steam would give a duty of 10,800 lbs., or four times the duty of the Boulton and Watt engine.
If you calculate on the air being heated to nearly 212 degrees before it enters the fire, together with the heat given to the sides of the boiler, the fuel saved will be above one-half on what has been done by the high-pressure engines in Cornwall, because at present the coal must for heating the cold air, therefore a less proportion goes through the sides of the boiler and is lost through the chimney; whereas if the heat of the steam, by passing into the cold air, on its way through the condenser tubes, is carried into the fire-place, one-half of the coal must be saved and you will find by calculation that the quantity of air required to burn the coal, and also to condense the steam, goes exactly in proper proportion for each other, and for locomotive engines with a blast will go hand-in-hand almost to any extent, and the size of an engine, for its power, is a mere nothing.
A smoke-jack fan in the ash-pit under the fire-bars, worked by the engine, would draw air down the condensing tubes and force it up through the fire and fire-tubes always with the speed required, as the steam and the condensation would increase in the same ratio.
As it is possible to blow so much cold air into a fire as to put it out, by first heating the air it would burn all the stronger, and whatever heat is taken out of the condenser into the fire-place from the steam that has been made use of, half this extra heat will go into the boiler again, or in other words, but half the quantity of cold will be put into the fire, being the same in effect as saving fuel. Taking heat from the condenser through the boiler sides is an additional new principle in this engine. I find by blowing through tubes that the condensation of a surface foot of air-tube against a surface foot of boiler fire- tube is greater than the fire that passes through the boiler sides, where the common chimney draught is used, by nearly double; but I expect when both air and fire tubes are forced by a strong current of air it will be nearly equal, and the increase of steam and of condensation can be increased by an increased current of air, so as to cause a surface foot of fire and of air sides to do perhaps five times as much and of course the machine will be lighter in proportion. I think air sides condensation preferable to water sides, as so small a space does the work, and is always convenient, and its power uniformly increasing with its speed, by the increased quantity of air, without the weight of water vessels. This kind of engine can be made to suit every place and purpose, and I think such an engine of the weight of a Boulton and Watt engine will perform twenty times the duty.
Air sides condensation will be advantageous on board ship, because there are boles for the passage of water through the bottom and sides of the ship.
I am anxious to have your opinion on this plan of returning the hot air from the condenser to the fire-place, and what you think the effect will be.
The Comptroller of the Navy has not yet returned from Plymouth, therefore no answer has been given to me.
You will see by the sketch how very small and compact an engine is now brought without complication or difficulty; each surface foot of boiler and condenser is equal to one-third of a horse-power, weighing 20 lbs., or 60 lbs. weight for each horsepower. The consumption of fuel is so small when working a differential engine, that I expect it will not exceed 1 lb. of coal per hour for each horse-power.
The cost of erection and required room are so small from is simplicity that it will be generally used. As I am very anxious that every possible improvement should be considered prior to making a specification for a patent, I must beg that you will have the goodness to consider and calculate on the data I have given you. I am sorry to trouble you, but I am satisfied this will be to you rather a pleasing amusement than a trouble. The warming machines will take a very extensive run, and I believe will pay exceedingly well.
I am almost in the mind to take a ride down to see you in a few days, but am now detained here about the American mining concerns.
I remain, Sir,
Your very bumble servant,
The letters and foot-note are them changes made by the writer in Trevithick's original sketch so descriptive of a wonderful application of varied and improved principles of long-known difficulty and importance; the beautifully compact tubular boiler for giving high-pressure superheated steam, surface condensation, absence of feed and condensing water, and return of the heat, in other engines wasted in condensation, to the fire-place; though there is little or no mention of the mechanical or moving parts of the steam-engine, yet its vital principles are grasped with the hand of a master. The sketch in the letter hastily made forty years ago is more ingenious than any portable engine since constructed, though there may be no sufficient proof of its practical success. The propeller to be worked by this novel engine was of course his screw.
Steam Engines, 21st February, 1831.
NOW KNOW YE, that in compliance with the said proviso, I, the said Richard Trevithick, do declare that the essential points in my improved steam-engine, for which I claim to be the first and true inventor, are:—
Firstly, the placing of the boiler within the condenser, in order to obtain the additional security of the strength of the condenser to prevent mischief in case the boiler should burst, and also by the same arrangement to conveniently make the condenser, with a very extensive surface, enabling one to condense the steam without injecting water into it.
Secondly, the enclosing of the condenser in an air or water vessel, by which the intention of safety from explosion is further provided for, and my engine really rendered what I denominate it, a high-pressure safety engine.
Thirdly, the condensing of the steam in the condenser by means of a current of cold air or cold water forced against the outsides of the condenser.
Fourthly, the returning of the condensed steam from the condenser back again into the boiler, to the end that sediment and concretion in the boiler may be prevented; and,
Fifthly, the blowing of the fire with the air after it has been heated by condensing the steam.
In forming my improved steam-engine I employ several or all of these points according to convenience, in combination with the other necessary parts of steam-engines in common use,
These, my essential points, will admit of various modifications as to form and proportions such as must be and are quite familiar to every competent steam-engine manufacturer, and therefore it will be sufficient for the perfect description of my improved steam-engine that I explain some of the modes of forming and combining the essential points of my invention with the other parts of steam-engines in common use. In my most favourite form of engine in which I condense by a current of cold air, the fire-place and flue, the boiler, the condenser, and the air-vessel, are made of six concentric tubes, standing in an upright position. The inner or first tube forms the fire-place and flue, and at the same time the inner side of boiler. This tube is conical, having its small end upwards. The next or second tube is cylindrical, about 6 inches larger in diameter than the lower end of the first tube, and forms the outside of the boiler, leaving a space all round of about 3 inches at the bottom, and so much more at the top, as the flue is taper for holding water and steam between the two tubes. The third tube is about 2 inches larger in diameter than the second, in order to allow a space of about an inch for powdered charcoal or some other slow conductor of heat. This tuLe also constitutes the inner side of the air-vessel. The fourth tube is about 2 inches larger than the third, and forms the inner side of the condenser. The fifth tube, about 2 inches larger than the fourth, forms the outside of the condenser; and the sixth tube, about 2 inches larger than the fifth, forms the outside of the air-vessel, and at the same time the outside of the whole of the generating and condensing apparatus, consisting of fire-place, flue, boiler, condenser, and air-vessel. These tubes are made of wrought-iron plates riveted together, and are all cylindrical, except the first, which is conical, the bottom or fire end being the largest. The first or inner tube is closed at bottom, but has an opening on one side near the bottom, through which the fire-bars are introduced, and the ashes and clinkers taken away. To this opening a neck-piece about 3 inches long is riveted, having a flange to fit against the inside of the second tube, when the two tubes are concentric, through the side of which second tube is au opening corresponding with that in the first tube, and the flanch is screwed to the second tube so as to make one opening through the sides of the two tubes. The second tube extends downwards about 5 inches below the first tube, and has a flanch turning inwards, to which a second round plate of iron is screwed, forming the bottom of the boiler. The first tube has an external flanch at the top, and the second tube an internal flanch, both of the same height, and screwed to a cast-iron circular plate or cap-piece, which extends wide enough around the boiler to form also the cover for the air-vessel. This plate has a hole in the middle as large as the flue. The sides of the condenser and air-vessel are formed of four concentric tubes, each about 2 inches larger than the one within it. The inner and outer of these tubes constitute the sides of the air-vessel, and are each furnished with an external flanch at the top by which they are screwed to the cap-piece. The two intermediate tubes constituting the sides of the condenser are riveted together at the top, leaving a space of about an inch between their upper ends and the cap-piece, so as to allow of a free communication over them between the outer and inner parts of the air-vessel. The inner tube of the air-vessel extends downwards about an inch below the boiler, and is closed by a flat plate screwed on to a flanch projecting inwards from the tube; the two tubes of the condenser descend about 3 inches lower than the boiler. The inner tube has an internal liana, to which a flat circular plate is screwed to close up the tube. The outer tube of the condenser is of the same length with the inner, and is provided with an external flanch about 3 inches broad. The outer tube of the air-vessel has an external flanch 2 inches broad, and is just long enough to come down upon the broad flanch of the condenser last described, and these two flanches are together bolted upon a bottom piece of cast iron, which is a dish of 4 inches deep, and equal with the diameter of the outer tube, and having a flanch the same breadth as the flanch of the outer tube, and the bottom piece is secured to the air-vessel and outer tube of the condenser by bolts going through all the three flanches. An opening is made through the sides of all the four tubes of the condenser and air-vessel opposite to and as wide as the fire-place opening through the sides of the boiler. The upper part of both openings to be of the same height, but the outer opening is made as low as the bottom of the boiler, in order to allow room for a pipe to enter that part of the boiler for forcing the water into it and also another pipe and cock for drawing off the water or sediment, in case foul water be used by accident or carelessness. These two openings through the condenser and air-vessel, and through the boiler, constitute one fire doorway through all the six tubes for access to the fire-place; a ring is placed between the two tubes of the condenser around the fire door- way, so as to cut off all communication of the steam in the condenser with the air in the doorway; another similar ring is placed between the condenser and the outer tube to prevent the escape of air into the fire doorway, and a half ring is placed in the lower part of the fire doorway between the condenser and the inner tube of the air-vessel, to prevent ashes from falling into the air-vessel, and yet allow a free passage for the air from the inner part of the air-vessel into the upper part of the fire doorway. These two rings and the half ring are secured in their places by rivets passing through all of them and through the tubes, and uniting all firmly together, the interstices being filled with iron cement. A ring is also placed between the boiler and the air-vessel around the fire doorway, against the outside of which ring the charcoal powder is tightly rammed, and will hold the ring in its place without the necessity of either rivets or screws. That part of the fire doorway which is above the fire-bars is supplied with an inner door, to shut the fire-place even with the outside of the boiler and exclude all access of air to the fire, except through the grating. The whole of the fire doorway is enclosed by an outer door even with the outside of the air-vessel, to exclude all air, except that which comes through the air-vessel; a pipe is fixed in the bottom or dish-piece leading to a forcing pump to draw the water out of the condenser and force it into the bottom of the boiler through the pipe before described. A blowing cylinder of about ten times the content of the main cylinder is screwed against the outside of the air-vessel, and opposite to the two outlet valves of the blowing cylinder two apertures are made in the air-vessel, through which the air is forced in. The main cylinder of the engine, of the usual dimensions according to power wanted, is also screwed against the outside of the air-vessel high enough above the blowing cylinder to allow room for the main-crank shaft to work between them. The forcing pump before mentioned is also screwed to the outside of the air-vessel, and thus my improved steam-engine becomes more compact and convenient than any preceding steam-engine. For the purpose of supplying the boiler with distilled water, in case there should be a deficiency in it, a small vessel made of two upright tubes, one within the other, is placed on the cap-piece. The inner tube is of the same diameter as the flue, and forms a continuation of it. The outer tube is about 6 inches larger than the inner, and the space at the top and bottom between the two tubes is closed by two ring-shaped pieces. This vessel may be about 18 inches high; a cock is fixed in the top of this vessel, to which a bent pipe is fastened, leading to and united with a pipe which arises from the top of the condenser and passes through a hole in the cap-piece, and thus a communication between the supplying vessel and the condenser may be opened or shut at pleasure; another pipe, also furnished with a stop-cock, arises from the vessel, and communicates with a water-cistern to receive its supply of water when required; a third pipe, having a cock in it, opens into the vessel near the bottom to let out the sediment; a small cock to let the air out is also fixed in the top of the vessel, which cock may also be used for letting air out of the condenser. In order to supply the boiler with water by means of this vessel, the stop-cock leading to the condenser is shut, and that leading to the cistern is opened, and at the same time the air-cock is opened to allow the air to escape that the water may fill the vessel. When the vessel is nearly full of water, the air-cock and the cock from the cistern are shut, and that in the pipe leading to the condenser is opened. The water being then heated by the flue is converted into steam, which, passing into the condenser, is there reduced to water again leaving the sediment or salt in the supplying vessel, which sediment or salt may be occasionally blown out through the bottom pipe by filling the vessel with water, shutting the water, steam, and air cocks, and opening the cock of the outlet pipe at a time when the steam in the vessel is strong. But the supply of water from the condenser being always equal to that converted into steam and used in the engine, there is no tendency to a variation in the height of the water in the boiler, except there be leakage or waste of steam in some part of the engine. An upright glass tube, having an iron tube of communication with the lower part of the boiler and another iron tube of communication to the upper part of the boiler, is conveniently placed against the outside of the, air-vessel to indicate at all times the height of the water in the boiler; as is usual in steam-boilers, a valve is placed on the top of the air-vessel to allow of the escape of a portion of the air in case that the quality of the fuel should not require so much air for perfect combustion as the steam requires for good condensation. The degree of the condensation or the steam may be increased at pleasure, by increasing the velocity of the air passing into and through the air-vessel. The other parts of my improved steam-engine, such as the steam-pipes, the throttle-valve, the safety-valve, the vacuum-valve, the working valves, crank, connecting rods, cross-heads, pistons, piston-rods, and various other minor parts common to engines in general use may be made in the usual forms, and placed in, the most convenient situations; they cannot, therefore, need any description. When it is intended to use water for condensing instead of air, my improved steam-engine must be made as before directed, except that the communication between the air-vessel and the fire-place must be closed, which may be done by a perfect ring of iron surrounding the opening leading to the fire-place, instead of the half ring before described, and a forcing pump must be employed to draw water from a reservoir, and force it into the vessel which I have hereinbefore denominated the air-vessel, but which in this mode of working would more properly bear the name of water-vessel. In this case a blowing cylinder, the dimensions of which must be calculated according to the quality of the fuel to be used may be worked to blow the fire through a pipe leading into the ash pit. This however will not be necessary where there is a chimney high enough to create a strong draught. In respect to proportions, my improved steam-engine admits of considerable latitude, and it will be sufficient direction to any practical engineer to say that for engines working with steam of 120 lbs. to the inch, used expansively till it be nearly reduced to atmospheric strength and then condensed, a 10-horse engine may have a fire-place 20 inches diameter, the flue at the top 10 inches diameter, and a boiler of 20 feet high; a 60-horse engine, a fire-place 36 inches diameter, a flue of 16 inches diameter and a boiler of 20 feet high. In boat-engines; and in other eases where height cannot be allowed, the diameter must be increased. The thickness of the two tubes constituting the boiler sides of a 10-horse engine may be 1/8th of an inch, that of a 60-horse a quarter of an inch, and so in proportion for engines of other power. The tubes constituting the condenser and inner tube of the air-vessel may in all cases be 1/8th of an inch thick. The outer tube may be 3/8ths of an inch thick, to afford stability to the working cylinder, the blowing cylinder, and the forcing pump fastened to this tube, and as an ultimate perfect barrier against explosion. The respective distances of the other tubes constituting the outside of the boiler, the condenser, and air-vessel, will be the same as hereinbefore given, and therefore their diameters will depend upon the diameter of the fire-place, The cap-piece in small engines may be half an inch thick, and in large engines an inch. The bottom of the ash-pit and of the boiler must have about half an inch of thickness for every foot diameter, or they may be cast with ribs to afford equivalent strength. The fuel is supplied through a door in the flue, at the top of the boiler, consisting of coke or coals the least liable to swell with heat. The flue may be filled to about one-third of the height of the boiler, and the water fill about three-fourths of the boiler, leaving one-fourth for steam.
Having clearly explained my improved steam-engine so that any person competent to make a steam-engine can from this into description understand my invention and carry the same effect in as beneficial a manner as myself, I proceed to observe that the extreme safety of my improved steam-engine will be seen, from considering that in case the boiler should explode inwards into the flue, the power of the steam would be first reduced by filling the flue and fire-place, and could not escape through the chimney and fire doorway faster than it would diffuse itself and be condensed by mixing with the surrounding air, and thus lose all its force. But should the outside or the boiler burst, part of the force of the steam would be spent in filling up the interstices between the particles of the charcoal, and would then probably be too weak to effect a breach through the inner tube of the air-vessel; and should such a second breach be effected, the space within the air-vessel would allow the steam to expand and partly condense, and a portion to escape into and through the fire doorway, where it would divide itself, and proceed harmlessly up the flue, and out at the doorway; so that the outer case being a reserve of strength, would to a certainty withstand the force remaining in the steam after the before-mentioned successive reductions of power.
The patent of February, 1831, perfects the sketch in his letter of July 27th, 1829, which in its turn made more perfect the plans put into practice in 1815, just before leaving England for America.  The prejudice against the use of high-pressure steam-engine he tried to meet by calling it a “high-pressure safety engine”. The boiler was of six wrought-iron upright tubes, one within the other. The inner one was the fire-tube, surrounded by a tube of larger diameter, forming the water and steam space. This was again surrounded by another tube, 2 inches larger in diameter, the space being filled with charcoal or other non-conductor of heat; another tube, 2 inches more in diameter, formed the inner circle of the condenser, having an inch space for the passage of cold air from the blowing cylinder, carrying the heat from the condensing steam back to the fire-place. Still another tube, 2 inches more in diameter, giving a space into which the used steam from the cylinder passed to be condensed. Then came the outside tube, 2 inches more in diameter, forming a second space for the passage of air, taking heat from the condenser into the fire. The steam-boiler had its heat retained by a coating of charcoal; next to it came a current of cold air an inch thick, carrying back to the fire any heat that had passed through the charcoal coat, and also the heat from the inner surface of the condenser. Then came the inch-thick circle of steam, on its exit from the cylinder, to be condensed; and finally an outside circle of cold air, performing the same functions as the inner circle in condensing the steam and carrying its heat back again to the fire.
The object or principle of this engine was to avoid the loss of heat, and the necessity for either condensing water or feed-water, as described in the letter and drawing of August 19th, 1830, but the detail was changed, mainly to facilitate construction. As in practice it might be impossible to fully attain those objects, preparation was made to get rid of the salt from such water as might be required as feed-water to make good the loss from leakage or other defects in the working of marine steam-engines. The specification states: “For the purpose of supplying the boiler with distilled water, in case there should be a deficiency in it, a small vessel made of two upright tubes, one within the other, is placed on the cap-piece. The inner tube is of the same diameter as the flue, and forms a continuation of it. The water being heated by the flue is converted into steam, which, passing into the condenser, is there reduced to water again, leaving the sediment or salt in the supplying vessel.”
Where water condensation was preferred the surface-air condenser could be converted into a surface-water condenser by a current of cold water in place of the air; in which case the air from the blowing cylinder was taken direct in to the fire-place or other means used for giving the necessary draught. Steam of about 135 lbs. to the inch was to be so expansively worked as at the finish of the stroke, on its escape to the condenser, to be no more than atmospheric pressure, or 15 lbs. to the inch - just the strength with which Watt preferred to commence his work in the cylinder.
The most prominent feature in Trevithick's numerous modifications of the steam-engine was the boiler. In the ‘Life of Watt,' though his commentators have been numerous and eminent, little or nothing is said about the boiler or the steam pressure. He left that all-important part of the steam-engine just as he found it, resisting the increase of steam pressure, which was the mainspring of Trevithick's engine. The boiler of the high-pressure engines of 1796  sheltered the steam-cylinder from cold; and the used steam from the cylinder circulated around the exterior of the boiler, on its way to the blast-pipe, while the condensed portion was returned as feed-water in the patent engine of 1802.  In 1811 he proposed to force air into the fireplace, hoping thereby to reduce the amount of beat lost by the chimney.  His various forms of tubular boilers, as at the Herland Mine,  and at Dolcoath,  and the upright multitubular boilers patented in 1815,  followed up in 1828. “ I shall have a small portable engine finished here next week, and will try to heat steam independent of water, in small tubes of iron, on its passage from the boiler to the cylinder, and also try cold sides for condensing.” In 1829 a simple boiler and condenser composed of three tubes was made, the inner or fire-tube being 2 feet in diameter and 15 feet long, “for the express purpose of experimenting on the working the same steam and water over and over again;”  and on the same subject, “By making the Condenser of 4-inch copper tubes 1/32nd of an inch thick, it would stand in one-twentieth part of the space of the boiler:”  and finally the sketch of the tubular boiler and tubular condenser of 1830, in its boiler portion, similar to the best portable boilers of the present day, and the patent specification of 1831. Surely therefore to him belongs the credit of having invented and perfected the tubular boiler and surface condenser.
Smiles has written: 
For many years previous to this period (1829), ingenious mechanics had been enraged in attempting to solve the problem of the best and most economical boiler for the production of high-pressure steam. Various improvements had been suggested and made in the Trevithick boiler, as it was called, from the supposition that Mr. Trevithick was its inventor. But Mr. Oliver Evans, of Pennsylvania, many years before employed the same kind of boiler, and as he did not claim the invention, the probability is that it was in use before his time. The boiler in question was provided with an internal flue, through which the heated air and flames passed, after traversing the length of the under-side of the boiler, before entering the chimney.
This was the form of boiler adopted by Mr. Stephenson in his Killingworth engine, to which he added the steam-blast with such effect. We cannot do better than here quote the words of Mr. Robert Stephenson on the construction of the ‘Rocket’ engine:- ‘After the opening of the Stockton and Darlington, and before that of the Liverpool and Manchester railway, my father directed his attention to various methods of increasing the evaporative power of the boiler of the locomotive engine. Amongst other attempts, he introduced tubes (as had before been done in other engines) - small tubes containing water, by which the heating surface was materially increased. Two engines with such tubes were constructed for the St. Etienne Railway, in France, which was in progress of construction in the year 1828; but the expedient was not successful; the tubes became furred with deposit, and burned out.
Other engines, with boilers of a variety of construction, were made, all having in view the increase of the heating surface, as it then became obvious to my father that the speed of the engine could not be increased without increasing the evaporative power of the boiler. Increase of surface was in some eases obtained by inserting two tubes, each containing a separate fire, into the boiler; in other cases the same result was obtained by returning the same tube through the boiler; but it was not until he was engaged in making some experiments, during the progress of the Liverpool and Manchester Railway, in conjunction with Mr. Henry Booth), the well-known secretary of the company, that any decided movement in this direction was effected, and that the present multitubular boiler assumed a practicable shape. It was in conjunction with Mr. Booth that my father constructed the ‘Rocket ' engine.
In this instance, as in every other important step in science or art, various claimants have arisen for the merit of having suggested the multitubular boiler as a means of obtaining the necessary heating surface. Whatever may be the value of their respective claims, the public useful, and extensive application of the invention must certainly date from the experiments made at Rainhill. Marc Seguin, for whom engines had been made by my father some few years previously, states that he patented a similar multitubular boiler in France several years before. A still prior claim is made by Mr. Stevens, of New York, who was all but a rival to Mr. Fulton in the introduction of steam-boats on the American rivers. It is stated that as early m 1807 he used the multitubular boiler.
These claimants may all be entitled to great and independent merit; but certain it is, that the perfect establishment of the success of the multitubular boiler is more immediately due to the suggestion of Mr. Henry Booth, and to my father's practical knowledge in carrying it out.’
We may here briefly state that the boiler of the ‘Rocket' was cylindrical, with flat ends, 6 feet in length, and 3 feet 4 inches in diameter. The upper half of the bailer was used as a reservoir for the steam, the lower half being filled with water. Through the lower part twenty-five copper tubes of 3 inches diameter extended, which were open to the fire-box at one end and to the chimney at the other. The fire-box, or furnace, 2 feet wide and 3 feet high, was attached immediately behind the boiler, and was also surrounded with water.
Stephenson knew of Trevithick's patent of 1802,  which a three-tubed boiler is shown; and it was after that time that Oliver Evans and Fulton tried their experiments, and also the numerous engines with single or return double tube, at work in the principal towns of England prior to 1804,  and near his residence childhood and in manhood. 
George Stephenson's Killingworth boiler, to which he added the steam-blast with such effect, was a copy of Trevithick's boiler and blast, working since 1804 in Newcastle-on-Tyne, and was precisely the boiler described by Stephenson; “in other cases the same result was obtained by returning the same tube through the boiler.” This is an admission from Stephenson that Trevithick's patent boiler was the best in use up to about 1828.
A further proof of the indirect public gain from the use of Trevithick's return-tube boiler over a period of thirty years is their having supplied high-pressure ex-pansive steam in the first experiments made with such steam by the Admiralty, at whose request Mr. Rennie and others examined the duty of the Cornish high-pressure expansive engine, and Captain King, R.N., in charge of the Admiralty Department at Falmouth in 1830, gave an order to Harvey and Co. to construct high-pressure steam-boilers for the Government vessel ‘Echo’; in 1831 the machinery was put on board the ‘Echo' in the Government Dockyard at Plymouth, and included three of Trevithick’s return-tube boilers, made of wrought iron, each 5 feet 6 inches in diameter and 24 feet long, with internal return fire-tube 2 feet 2 inches in diameter. The fire-place end of the boiler was 6 feet 9 inches deep by 5 feet 6 inches wide, to give room for the fire-place and ash-pit. The steam pressure was 20 lbs. on the inch above the atmosphere, worked by double-beat valves, 6 inches in diameter, with expansive gear.
This new machinery was fixed under the superintendence of the writer, after which the Government engineers took charge of the vessel, and the writer who had, as the mechanic in charge, worked like a slave, though receiving but 6d. a day and expenses, was not, invited to take any part in the experimental trials, nor ever heard of the result except in the ordinary rumours of Admiralty bungling on board the ‘Echo.'
Those boilers were similar to the Trevithick boiler that had served the locomotive in Newcastle and elsewhere from 1801 to 1828, the first steamboat experiments in England, in Scotland, and in America, and the numerous high-pressure engines then at work.
The enlarging the fire-place end of boilers or fire-tubes has led to many forms. Trevithick's model of 1796  had an oval tube giving a greater spread of fire-bars; the same is seen in the 1808 steamboat;  the Dolcoath boilers of 1811  show the oval and also the bottle-neck fire-tube; the Welsh locomotive of 1804  had the fire-tube contracted at its bend or return portion; the Tredegar puddling-mill fire-tube of 1801  tapered gradually from the fire-bridge to the chimney end; in the London locomotive of 1808  the fire-tube took the bottle-neck shape close to the fire-bridge. The accompanying sketch shows the bottle-neck contraction, only on the top and sides of the fire-tube was to give breadth to the fire-bars d, and thickness to the fire at bridge c, after which the flue portion of the fire-tube was contracted: this boiler was for many years a favourite in Cornwall. The bottle-neck contraction of the ' Echo boiler was similar to the above, except that the enlargement of the fire-place was downwards instead of upwards, and the fire-tube, instead of going through the end of the boiler, returned to near the enlarged fire-place, when it passed out through the side of the boiler to the chimney, just as in the Tredegar puddling-mill boiler all those variations were with the object of increasing the fire-grate, and at the same time keeping down the gross size and weight of boiler and its water.
In 1805, Lord Melville failed to keep his appointment with Trevithick, on his proposal to construct a high-pressure steamboat. Rennie, a pupil and friend of Watt, and familiar with Trevithick's high-pressure steam-dredgers on the Thames, was employed by Lord Melville and the Admiralty on the Plymouth Breakwater, where in 1813 Trevithick proposed the use of his high-pressure steam locomotive and boring engine.  In 1820 Rennie wrote to Watt, that the Admiralty had at last decided upon having a steamer; at that time fifteen years had passed since Trevithick's offer to propel the Admiralty by steam-puffers, and ten years more were to pass before they could make up their minds to venture on high-pressure steam from his boilers. The Steam Users' Association are equally hesitating, judging from words just spoken by an engineer, the son of an engineer:—
Sir William Fairbairn said he had come to the conclusion, after many years' experience, that it was in their power to economize the present expenditure of fuel by a system which might not be altogether in accordance with the views of the members of the association or the public at large, and that was to increase the pressure of steam. He would have great pleasure in stating a few facts which might some day tend to bring about a change, if not a new era, in the use of steam. From the result of a series of experimental researches in which he had been engaged for several years on the density, force, and temperature of steam, he had become convinced that in case we were ever to attain a large economy of fuel in the use of steam, it must be at greatly-increased pressure, and at a rate of expansion greatly enlarged from what it was at present. Already steam users had effected a saving of one-half the coal consumed by raising the pressure from 7 lbs. and 10 lbs. — the pressure at which engines were worked forty years ago — to 50 lbs., or in some cases as high as 70 lbs. on the square inch. 
Dear me! would have been Trevithick's exclamation had he read this; did I devote my whole life to the making known the advantages of high-pressure steam, and did I, seventy years ago,  really work expansive steam of 145 lbs. on the inch in the presence of many of the leading engineers of the day! Of course this short extract of a speech made by a member of a practical society, may not be taken as conveying fully the speaker's views, but it illustrates the immense difficulty Trevithick encountered in making his numerous plans acceptable to the public.
Another modern statement bearing on inventions originating with Trevithick, but wearing new garbs with new names, shows the same tendency to ignore old friends, or, to say the least of it, to pass them by: -
The trial of No. 36 steam-pinnace was made at Portsmouth yesterday. Her peculiarity consists in the arrangement of her propelling machinery, in the adaptation of the outside surface condenser, and a vertical boiler, both patented by Mr. Alexander Crichton. The condenser is simply a copper pipe passing out from the boat on one quarter at the garboard strake, and along the side of the keel, returning along the keel on the opposite side, and re-entering the boat on that quarter. The boiler is designed for boats fitted with condensing engines, and which, therefore, are without the acceleration of draught given by the exhausted steam being discharged into the funnel. It is of the vertical kind, and stands on a shallow square tank, which forms the hot well. The tubes are horizontal over the fire, the water circulating through them. The condensed steam is pumped into the well at a temperature of 100 degrees, and being there subjected to the heat radiating from the furnace, is pumped back into the boilers at nearly boiling point. It is estimated that, under these conditions, the pinnace would run for nearly 48 hours without having to 'blow off' or carry a supply of fresh water, the waste water being made good by sea water. 
The peculiarity of this steam-pinnace of 1871, on which a patent was granted, is stated to be a metal surface condenser exposed to the cold water at the bottom of the boat, returning the condensed steam at about boiling temperature to the boiler, and a vertical boiler with horizontal tubes through which the water circulates, both of which in principle, if not in detail, are seen in the surface condenser of Trevithick's iron-bottom ship of 1809, and his vertical boiler of 1816,  and further illustrated in the inventions spoken of in this and the following chapter and yet on so all-important a subject, dealt with in various ways by Trevithick from 1804 to 1832, his plans are reproduced as discoveries in 1871.
About 1828, Mr. Rennie, Mr. Henwood, and others, reported on the advantages of high-pressure expansive steam in Wheal Towan engine,  on the north cliffs of Cornwall, near Wheal Seal-hole Mine on St. Agnes Head, where in 1797 Trevithick had worked his first high-pressure steam-puffer engine in competition with the Watt low-pressure steam-vacuum engine. Captain Andrew Vivian was then his companion, and the Cow and Calf, two rocks of unequal size, a mile from the land, were from that time called Captain Dick and Captain Andrew, or the Man and his Man, and there they still remain in the Atlantic waves, fit emblems of their namesakes and their still living inventions. The stir made by those expansive trials led to the experiment in the 'Echo,' of which Mr. Henwood  thus speaks:—
Captain William King, RN., Superintendent of the Packet Station at Falmouth, attempted to impress on Viscount Melville, then First Lord of the Admiralty, the advantage of using high-pressure steam expansively in the Royal Navy, to whom Lord Melville replied that he had been taught by his friend, the late Mr. Rennie, that the danger attending such a course was very great, and that it would he difficult, if not impossible, to persuade him to the contrary.
Twenty-five years of precept and example caused the Admiralty to follow suit, and to request Mr. Ward, a Cornish engineer, to construct boilers and expansive valves for the Government steamboat Echo. The writer was entrusted with fixing the machinery in the vessel at the Plymouth Dockyard, and before starting with it from Harvey and Co.'s foundry, waited on Captain King, R.N., at Falmouth, for his instructions, in happy ignorance of the fear of the Lords of the Admiralty to tread on Cornish high-pressure. After eying the applicant as captains in Her Majesty's service are apt to do when dealing with boys in the civil service, he vouchsafed to say, "Mind, young man, what you are about, for if there is a blow up, by -you'll swing at the yard-arm."
- Life of Richard Trevithick by F. Trevithick
- Life of Richard Trevithick by F. Trevithick: Volume 2: Chapter 25
- Life of Richard Trevithick by F. Trevithick: Volume 2: Chapter 27
- 'Observations on the Steam-Engine,' by Davies Gilbert, V.P.R.S., January 25th 1827. See 'Philosophical Transactions'
- See letter, vol. ii., p. 143.
- See vol. ii., p. 185.
- See drawing, vol. ii., p. 169.
- See patent specification, vol. i., p. 132.
- See vol. i., p. 335.
- See Trevithick's letter, 7th December, 1812, vol. ii., p. 18
- See vol. ii., p. 71.
- See vol. i., p. 364.
- See vol. ii., p. 171.
- See Query 3rd, p. 19.
- See Trevithick's letter, January 24th, 1829, vol. ii., p. 368.
- See Trevithick's letter, 7th May, 1815, vol. i., p. 364.
- See patent specification of 1802, vol. i., p. 128.
- Drawing of iron steamship, vol. i., p. 336
- See Trevithick's letters, July 8th, 1815, vol. ii., p. 80, and 7th, vol. i., p. 364; and 16th May, vol. i., p. 370; and patent of 1815, vol. i., p. 375.
- See vol. i., p. 104.
- See patent specification, vol. i., p. 128.
- See Trevithick's letter, 13th Jan., 1811, vol. ii., p. 6.
- See vol. ii., p. 71.
- See chap. xx.
- See Trevithick’s letters, 8th July, 1815, vol. ii., p. 80; and 7th and 16th May, vol. i., pp. 364, 370.
- See vol. ii., p. 336
- See vol. ii., p. 332.
- 'Life of George Stephenson,' by Smiles, p. 279; published 1857
- See vol. i., p. 128.
- See Trevithick's letter, Sept. 23rd, 1804, vol. ii., p. 2.
- Mr. Armstrong's note, vol. i., p. 184.
- See vol. i., p. 104.
- See vol. i., p. 335.
- See vol. ii., p. 169.
- See vol. i., p. 181.
- See vol. i., p. 223.
- See vol. i., p. 207.
- See Trevithick's letter, 10th Jan., 1805, vol. i., 324.
- Ibid., vol. ii., p. 24.
- 'The Engineer,' March 15th, 1872: remarks by the Chairman at a meeting of the Manchester Steam Users' Association.
- See Trevithick's letter, August 20th, 1802, vol. i., p. 154
- 'The Times,' November 24th, 1871.
- See vol. i., pp. 336, 364, 370.
- See Mr. Henwood's report, vol. ii., p. 185.
- Residing at Penzance, 1871.
- Boiler with Fire-Place (See drawing above)
- a, steam-case;
- b, boiler-case;
- c, Space for condensation of steam;
- d, Water and steam space;
- e, fire-tubes;
- f, fire-box;
- g, fire-door;
- h, fire-bars;
- i, ash-box
- j, ash-box door;
- k, air-tubes in condenser;
- l, chimney;
- m, water level; a smoke-jack fan draft