These reflections apply immediately to my present sub ject, as Hindley's method of division proceeds wholly by contact, and that of the firmest kind ; there being scarcely need of magnifying glasses in any part of the operation.
In the year' 1748,1 came to settle in London ; and the first employment I met with was that of making philosophical in struments and apparatus. In this situation, my friend Hind ley, from a principle the reverse of jealousy, fully commu nicated to me, by letter, his method of division ; and though I was enjoined secrecy respecting others, (for the reasons already mentioned), yet the communication was expressly made with an intention that I might apply it to my own purposes.
The following arc extracts from two letters, which con tain the whole of what related to this subject; and since I have things to observe thereon, so that the paraphrase would be much greater than the text, I think it best not to interrupt the description with any commentary, as perhaps his own mode of expression will more bridly and happily convey the general idea of the work, than any I can use in stead of it.
My Dear Friend, " York, 14th Nov, 1748.
" As to what you was mentioning about my brother's knowing how I divided toy engine plate, will describe it as well as I can myself ; but you will want a good many things to go through with it. The manner is this : first choose the largest number you want, and then choose a long plate of thin brass ; mine was about one inch in breadth, and eight feet in length, which I bent like a hoop for a hogshead, and soldered the ends together, and turned it of equal thickness, upon a block of smooth-grained wood, up on my great lathe in the air, (that is, upon the end of the mandrel); one side of the hoop must be rather wider than the other, that it may fit the better to the block, which will be a short piece of a cone of a large diameter : when the hoop was turned, I took it off, cut, and opened it straight again.
The next step was, to have a piece of steel bended into the form as per margin : which had two small holes bored in it, of equal bigness, one to receive a small pin, and the other a drill of equal size. I ground the holes after they were harden ed, to make them round and smooth. The
chaps formed by this steel plate were as near together as just to let the long plate through. Being open at one end, the chaps so formed would spring a little, and Is attic] press the long plate close, by setting in the vice. Then I put the long plate to a right angle to the length of the steel chaps, and bored one hole through the long plate, into which I put the small pin; then bored through the other hole ; and by moving the steel chaps a hole forward, and putting in the pin in the last hole, I proceeded till I had divided the whole length of the plate.
The next thing was, to make this into a circle again. After the plate was cut off at the end of the intended number, I then proceeded to join the ends, which I did thus : I bored two 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 two or three turned screw pins, with flat head and nuts to them, into each end, which held them together till I rivetted two little plates, one on each side of the narrow plate, on the outside of the hoop. Then f 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.
1 need not tell you, that you get as many prime num bers 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 knows so touch as I have told you, though 1 believe they got some know ledge of it in general terms. I desire you to keep the method of dividing to yourself, and conclude with my best wishes. And am, dear sir, yours, &c.