Intelligence and Miscellaneous Articles. 439 



more and more desirable to put the relations between this and the 

 English system of weights and measures in as simple a light as 

 possible. If a screw is to be cut on an ordinary lathe with its 

 pitch a convenient number of teeth to the millimetre, centimetre, 

 or metre, the change-wheels are not adapted to the purpose. The 

 only reference I have ever found to the subject is in Chambers's 

 ' Encyclopaedia/ article " Wheelwork," where the problem is given 

 to compute the gears needed to cut a screw of 200 threads to 

 1 metre on a lathe whose feed-screw has 4 threads to the inch. By 

 continued fractions the number of teeth, beginning with the spindle, 

 is found to be 50, 48, 89, 73; i. e., if 47=number of threads to 



1 inch, x= ^g-^gX 4=5-08, or in 1 metre are 5-08x39-37 = 200 



threads. This requires two gears with a prime number of teeth. 



A simpler method than this I suggested four years ago to Messrs. 

 Buff and Berger, of Boston ; and by it they cut me some very satis- 

 factory screws with 1 thread to the millimetre, using their new 

 lathe with two dead centres. As it was new to them and to all my 

 friends familiar with mechanical work to whom I have spoken of 

 it, I venture to publish it, though it seems too simple to have 

 escaped previous notice. 



The method is based on the fact that 1 inch equals very nearly 

 25-4 millimetres ; it would equal it exactly 



If 1 metre equalled . 39*37008 inches. 

 Clarke's value equals 39-37043 „ 

 Kater's „ „ 39-37079 „ 



This "mechanical" metre differs from the best determination 

 yet made (Clarke's) by no more than that differs from the next best 

 one, viz. one 110,000th part, though in the opposite direction. The 

 form in which the direction was given to Buff and Berger was : — 

 " Gear the lathe so as to cut a screw with 20 threads to the inch 

 with a gear of 100 teeth on the feed-screw ; replace the 100 by 



= -0-), and the pitch will be 1 millimetre, the theoretical 



error being much less than the mechanical error of cutting. Thus, 



127 

 on the lathe above referred to, x= — x 4 = 25-4 to the inch, or 



127 

 1 to the millimetre ; again, a?= — x4 4-25-4=4, i. e. 1 thread 



to 5 millimetres. 



On small lathes it may often be necessary to put the 127 gear on 

 the arm (because the screw and spindle are too near together), and 

 perhaps to get a longer arm than usual ; but neither this nor the 

 calculation for any whole number of threads to the millimetre, 

 centimetre, or decimetre will present any great difficulty to any 

 one familiar with the principle. 



Phvsical Laboratory, University of Michigan, 

 December 15, 1881. 



