434 Prof. Wallace on the Invention of the Pantograph, 



" Annex two ciphers to the difference of the numbers which ex- 

 press the proportion, and divide the result by their sura ; the 

 quotient is the number on the scale which must be set opposite 

 to the index on the socket." Thus, to give the proportion of 3 

 to 2, the difference of which, with two ciphers annexed, is 100, 

 divide 100 by 5 ; the quotient 20 on the scale must be set oppo- 

 site to the index. If the proportion be that of 5 to 3, we have 

 for the dividend 200, and for the divisor 8 ; this gives 25 for 

 the division to be set at the index ; and so on. In general, the 

 quotient is a fraction, but the nearest whole number is accurate 

 enough in practice. Thus, if a design is to be reduced in the 

 proportion of 8 to 5, the sum being 13, and the difference, with 

 two ciphers annexed, 300 ; the number on the scale to be set to 

 the index is 3 T V° = 23, nearly. In some instruments a vernier 

 scale has been engraved on the socket, by which each half of the 

 beam was actually divided into 1000 equal parts ; and then, be- 

 tween the proportion of equality and that of 6 to 1, there might 

 be interposed iJ r° — 714 different ratios, namely, those of 1001 

 to 999, of 1002 to 998, &c. 



The wheels ff. These turn on steel axes which pass 

 through vertical bored tubes fixed to the ends of the beam. The 

 diameter of each is about four inches, and they ought to be exactly 

 equal, because on this the accuracy of the instrument mainly de- 

 pends. 



There is a portion of each wheel, about a third of an inch in 

 breadth from its circumference, which is thicker than the part 

 within it. This is shewn in Fig. 5, which is a section of a wheel 

 through its centre c and a part of the beam, of half the actual 

 size. The upper surface of this bounding ring rises higher than 

 the surface it incloses ; and the lower surface also rises higher 

 than the lower central surface. Thus, additional space is given 

 for the groove in the circumference in which the band lies, and 

 the band thus raised is kept quite clear of the arms which pass 

 freely below it. 



