VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 45 



off at the end of the intended number, I then proceeded to join the ends, which 

 I did thus: I bored 2 narrow short brass plates* as I did the long one, and 

 put one on the inside, and the other on the outside of the hoop, whose ends 

 were brought together; and put 2 or 3 turned screw pins, with flat heads and 

 nuts to them, into each end, which held them together till I rivetted 2 little 

 plates, one on each side of the narrow plate, on the -outside of the hoop. Then 

 I took out the screws, and turned my block down, till the hoop would fit close 

 on; and by that means my right line was made into an equal divided circle of 

 what number I pleased. The engine plate was fixed on the face of the block, 

 with a steel hole fixed before it to bore through ; and I had a point that would 

 fall into the holes of the divided hoop; so by cutting shorter, and turning the 

 block less, I got all the numbers on my plate. 



I need not tell you, that you get as many prime numbers as you please; nor 

 that the distance of the holes in the steel chaps must be proportioned to the 

 length of the hoop. You may ask my brother what he knows about my method 

 of dividing; but need not tell him what I have said about it; for I think neither 

 he nor John Smith know so much as I have told you, though I believe they 



got some knowledge of it in general terms.-^ 1 desire you to keep the method 



of dividing to yourself, and conclude with my best wishes, &c. 



Henry Hindley. 

 Though the above letter was in itself very clear and explicit, as to the general 

 traces of the method, yet some doubts occurring to me, a further explanation 

 became necessary. A copy of my letter not being preserved, the purport of it 

 may be inferred from the answer, which was as follows : 



DEAR FRIEND, Yovk, March 13, 1748-9. 



I think in your last you seem to be apprehensive of some difficulties in drilling 

 the hoop for dividing: First, that the centre of the hole in the hoop might not 

 be precisely in the centre of the hole of the steel chaps, it was drilled in ; but 

 if I described fully to you the method I used, I can see no danger of error there : 

 for my chaps were very thick, and the two corresponding holes were a little 

 conical, and ground with a steel pin; first one pair, and then the other, alter- 

 nately, till the pin would go the same depth into each. Then for drilling the 

 hoop, I took any common drill that would pass through, and bore the hole. 

 After that I took a five-sided broach, which opened the hole in the brass between 

 the steel chaps, but would not touch the steel; so consequently the centre of 



* These I shall hereafter distinguish by the name of saddle-plates. — Orig. 



f The persons here referred to were both bred with him. His brother, JMr. Roger Hindley, who 

 has many years followed the ingenious profession of a watch-cap-maker in London, was so much 

 younger as to be an apprentice to him. Mr. John Smith, now dead, had some years past the honour 

 to work in the instrument way, under the direction of the late Dr. Demainbray, for his present 

 Majesty. — Orig. 



