VOL. LXXVl.] PHILOSOPHICAL TRANSACTIONS. A^ 



noticed, must expect a very great degree of rectification of whatever errors 

 might subsist in the wheel after its first cutting. 



What degree of truth it might in reality be capable of, on its first production 

 and adjustment, is not now to be ascertained, he never having used it for the 

 graduation of any capital instrument. Those that he made with a view to an 

 accurate measure of angles, he always made with a screw and wheel, or parts of 

 circles cut by his engine into teeth, and ground together as before-mentioned; 

 but I have reason to think that its performance, if put to a strict test, was never 

 capable of the accuracy that he himself supposed it to have. The method 

 itself however, from its simplicity and ease of execution, seems to be a founda- 

 tion for every thing that can be expected in truth of graduation; and in con- 

 sequence for reducing instruments to the least size that is capable of bringing 

 out all that can be expected from the largest; when it shall, like manual divi- 

 sion, have received those advantages that the joint labours of the most ingenious 

 men can bestow on it. That I may not appear to be without grounds for my 

 expectations, I beg leave to propose, what near 40 years occasional contempla- 

 tion has suggested to me on the subject ; and as I can describe the process I 

 would pursue, where different from Hindley's, in fewer words than I could make 

 out a regular criticism on his letters, I will immediately proceed to the descrip 

 tion of it. 



Proposed Improvements of H'mdleys method. — I would recommend the num- 

 ber of parts into which the circle is to be reduced, to be 1440, that is 4 times 

 360 ; which divisions will therefore be quarters of a degree; the distances of the 

 holes in the chaps will therefore, to a 3-feet radius, be -'iroV o^ ^n inch nearly; 

 that is, between the -^ and 4^ of an inch distance centre and centre. Having 

 provided myself with a stout mandrel, or arbor, for a chock Lathe, properly 

 framed, that would turn a circle of 6 feet diameter, I would prepare a chock, or 

 platform, for the end of it, of that diameter, or a little more, composed of 

 clean-grained mahogany plank, all cut out of the same log; which, when 

 finished, to be about 1-|- inch thick, and formed in sectors of circles, suppose 16 

 to make the circle; the middle line of each sector lying in the direction of the 

 grain of the wood, this will consequently every where point outward: the me- 

 thod of framing this kind of work is well known. 



The way of getting a slip of brass to answer the circumference of this plat- 

 form is suggested in Mr. Bird's Account of constructing Mural Quadrants. 

 Let a parallelogram of brass, of about 3 feet long, and of a competent sub- 

 stance, suppose half an inch, to make it when finished about -^l of an inch 

 in thickness, be cast of the finest brass; and this to be rolled down till it be- 

 comes of sufficient length for the hoop, and about a 5th part more. I would 



