40 PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. 



Accordingly, considering the nature of the endless screw, he set about an 

 engine whose divided wheel or plate was of 30 inches diameter ; and though the 

 performance of this first essay was inferior to his expectations and wishes, yet 

 with it he was able to divide theodolites with a degree of precision far superior to 

 any thing of the kind that had been exhibited to the public. This engine I saw 

 in the spring of the year 1768 ; and it appeared to me not only a very laudable 

 attempt towards instrumental divisions, but a very good model for the construc- 

 tion of an engine of the most accurate kind for that purpose. And at the same 

 time he showed me the model or pattern for casting a wheel of a much larger 

 size, which he proposed to make on the same plan, and with considerable im- 

 provements. This being effected some time in or about the year 1774, its 

 accuracy was proved by making a sextant, afterwards subjected to the examina- 

 tion of Mr. Bird ; who in consequence approved the method, not only as fully 

 sufficient for the division of Hadley's sextants and octants for any purpose what- 

 ever, but in fact for dividing any instrument whose radius did not exceed that of 

 the dividing wheel, which was 45 inches in diameter : on which the Board of 

 Longitude very properly and usefully resolved to confer a handsome reward on 

 Mr. Ramsden, for delivering a full explanation of his method of making the 

 said engine ; which, in consequence, was published by order of the Board of 

 Longitude in the year 1777, above-mentioned ; the designs of which are so full 

 and explicit, that whoever could not understand that description, so as to enable 

 him to make it, would be unfit to undertake it on other accounts. 



From what I have said on the works of the different artists above-mentioned, 

 it would seem that the art of graduation was brought to such a degree of excel- 

 lence that nothing material can now be added to it : and I should have been apt 

 to have thought so myself, if I had not happened, in the course of my life, to 

 have had a communication made to me, under the seal of secrecy, which seems 

 to promise yet further light and assistance in perfecting that important art ; and 

 every impediment to the discovery of it being now removed, I shall in the re- 

 mainder of this essay give the clearest description of it that I am able_, with such 

 elucidations and improvements as seem to be naturally pointed out by the me- 

 thod itself. 



In the autum of the year 1741, I was first introduced to the acquaintance of 

 that then eminent artist, Mr. Henry Hindley, of York, clock-maker. He imme- 

 diately entered with me into the greatest freedom of communication, which 

 founded a friendship that lasted till his death, which did not happen till the year 

 1771, at the age of 70. On the first interview, he showed me, not only his 

 general set of tools, but his engine, at that time furnished with a dividing plate, 

 with a great variety of numbers for cutting the teeth of clock wheels, and also, 

 for more nice and curious purposes, furnished with a wheel of about 1 3 inches 



