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1794 Born in Alnwick, Northumberland, the son of Thomas Buckle (b.1759), millwright, and Ann (nee Tate). They moved to Hull, and then to London.
At the age of 14, William was apprenticed to Woolf and Edwards of Lambeth. He studied assiduously in his spare time, and attended evening classes in mechanical drawing in Finsbury.
On the completion of his apprenticeship, his employers recommended him for a postion in Memel, Prussia, to superintend the introduction of steam navigation on the rivers and lakes of Prussia, for the Prince of Hardenburg.
1824 After about 4 years he returned to England, and was appointed by Boulton and Watt to install the engines in the 'Ivanhoe', the first steam mail packet between Holyhead and Dublin.
c1824/5 Appointed as works manager at Boulton & Watt's Soho Foundry, in charge of up to 700-800 men, in whose welfare he took a great interest. He also ensured that the education and interests of apprentices were well catered for.
He was said to possess good mechanical knowledge and was always guided by experimental truths rather than trusting to theory. He experimented on fans and fan blasts, under different conditions, on the velocity of water issuing through pipes from different altitudes, and the velocity that water attains when rushing into a vacuum. He constructed a mill for pulverising bones for agricultural purposes and also a machine for sowing turnip or other seeds with fertiliser
He introduced the first large screw-cutting lathe to the works.
1838 Married Miss Williams.
1846 Buckle, of James Watt and Co, was a member of the committee established to draw up rules for a constitution of the Institution of Mechanical Engineers. The othermembers were: Richard Peacock, James Edward McConnell, Archibald Slate, Edward Humphrys, John Edward Clift, and Edward Alfred Cowper.
1851 William Buckle was appointed to the Royal Mint by Sir John Herschel.
1859 William Buckle, Senior Clerk and Assistant Coiner at the Royal Mint.
1863 Died, leaving a widow and two children. His son, Dr Fleetwood Buckle, was a medical man.
The above information is drawn from a detailed obituary in The Engineer 1863/10/16, page 228.
1923 Obituary from 60 years before
"In our issue of October 16th, 1863, the obituary notice appeared of William Buckle, one of the early school of master engineers . Mr. Buckle's father, a Northumberland millwright, born in 1759, devoted considerable attention to the improvement of agricultural machinery, some examples of which, it is recorded, were propelled by steam power, and, coming to London, was associated with the celebrated Earl of Dundonald in the development of his numerous mechanical schemes, notably machinery for the manufacture of rope. His son William was born in 1794, and shortly after attaining his fourteenth birthday was apprenticed to Woolf and Edwards, millwrights and engineers, of Lambeth... Read more here 
'THE LATE MR. WILLIAM BUCKLE, C.E.
The remains of this distinguished mechanical engineer were, on Tuesday, consigned to their last resting-place, in the cemetery at Kensal Green, and followed to the grave by the members of his own family and several intimate friends, among whom were—Mr. F. P. Smith, inventor the screw-propeller Mr. P. R. Hodge, C.E. ; Mr. Dempsey, C.E. ; Mr. Joseph Newton, acting assistant coiner the Royal Mint ; Mr. W. Langdon, of the house of Boulton and Watt. A number of the workmen at the Royal Mint attended at the cemetery during the funeral ceremony, to pay their last respects to the honoured and lamented deceased. Mr. Buckle was the son of the ingenious engineer, Mr. Thomas Buckle, a native of Alnwick, Northumberland, who, among other works, invented several farming implements, to be driven by steam, winnowing and thrashing machines, and jointly with the late Earl of Dundonald, invented a rope-making machine very similar to the one now in use at the royal dockyard. The deceased, Mr. William Buckle, was born at Alnwick Castle, Northumberland, July 29, 1794, and received his early education at Hull, whence he removed London with his parents. He was apprenticed to Messrs. Woolf and Edwards, engineers, of London, and at the close of his service with those gentlemen was recommended by them to go to Memel to superintend the establishment of boats on the rivers and lakes of Prussia, under the direction of Prince Hardenburg. Whilst thus engaged he had the good fortune to rescue from drowning a young lady, a member the prince's family, and for such effectual aid was rewarded with a gold medal. Mr. Buckle remained at Memel and Berlin for about four years, and then returned to England to take charge of the first steam mail packet between Holyhead and Dublin, that service being then under the direction of Sir Francis Freeling, Postmaster-General. This packet had originally been christened the Lightning, but as it was selected to convey George IV. to Ireland on his memorable visit to that country, the name of the vessel was changed, by command of his Majesty, to that of the Royal Sovereign. The same boat and engines were a short time ago employed on the Thames steam-tug, but under another title. Shortly afterwards, about 1820, Mr. Buckle entered the service of Messrs. Boulton and Watt, of the Soho Works, near Birmingham, where he remained, as their faithful friend and manager, for more than thirty years. While engaged in that celebrated establishment, he superintended the construction of the following mints, with other important machinery :—The Soho Mint, 1820 ; Bombay (original mint of Soho, refitted), 1824; Richardson's Mint (South America), 1825 - the Soho Mints for Soho, 1826; Mr. Robert Mushett (South America), 1827 ; Lisbon 1834. Onthe breaking up of the Soho Works, after the demise of the eminent founders of that establishment, Mr. Buckle was solicited by Sir John Herschel then at the head of the Royal Mint, to take charge of the coining department; and he held his important appointment till the time of his death. In 1835, Mr. Buckle invented a pneumatic apparatus preventing the unequal action of steam engines whilst driving millstones; and during his long connection with the Soho Works he was vice-president and an active member the of the Birmingham Institution of Engineers, and also a member of the Institution of Civil Engineers, Westminster. In 1850 he read an interesting paper before the members of the former institution on the “Inventions and Life of William Murdock," exhibiting at the same time a model of the first locomotive ever constructed. This engine, made in 1784, was the product of Murdock’s genius, and to him the world are indebted for the discovery of gas, practically applied. In private Mr. Buckle was distinguished for his suavity of manners and constant kindness, and by all his professional brethren who had the privilege of his acquaintance his death will be deeply lamented.’