oratory 



at St. John's 



College, 



Oxfot 



* 



26 



32 



38 



46 



53 





28 



34 



41 



47 



59 





29 



36 



43 



49 



61 





31 



37 



44 



50 



67 





221 



The number of divisions thus obtainable is very large. If n 



1 80 



be the number desired, then must consist of an integer 



n 



and a proper fraction whose denominator is a factor of one of 

 the numbers of the above table. The integer is the number 

 of whole turns; and the fraction, reduced to one of which the 

 number in the table is the denominator, gives the number of 

 holes which represents the fraction of a turn. 

 Examples. 



74 !?0 



74 37 ' 



125...i^=lH. 

 12o o0 



It is also possible to approximate to prime numbers by a 

 rapidly converging process. 

 Example. 



71...^=2ff; 



72 **> 



38_1_ b_ _1_, 

 71 2 ~ 142 ~" 28-4 ; 

 so that, if we represent 



180 U 914 



we have 



-ji nearl y 2 M- 



In fact 



71x211 = 180^, 

 and the division errs by about ^ of a division. But we 

 should not often get so close as this ; and the strength of the 

 method lies in the next step. 



If by the above process we divide a micrometer-wheel with 

 a number of holes such as 71, there will be a small error dis- 

 tributed about the wheel, having a maximum at one point. 

 Xow, if we use this in turn as a micrometer-wheel, the resulting 

 division will in many cases be sufficiently accurate for all 



