[ 214 } 
0,68 oz* then is C S = 0,9785090, h S or d =, 
0,2985090, A S. or ^ = 0,2062042, and or 
jj , I / AS* 
7+‘^‘(=ls 
-j- L S) — 
LF = 0,440951 
oz. and ^ ~ ; therefore the greateft 
motion of the index will be when a Ikain of 36 to 
the pound is changed for one of 37, and the largeft 
interval on the graduated arch will be that which lies 
between 36 and 37. 
C A : CL::CF : Ca or i : 0,68 : : 1,120951 : 
0,762247 ounces, the other counterpoife which gives 
the fame maximum. 
Let the maximum be afllimed at 36 Ikains 
to the pound- exadly, or when F L = 
0.4.144444, then is 4 F L or AE = 0 2222222, 
and SE (== /aE^AS ' x AE"irXS ) = 
0,0828404, whence C L (= CS— .A E S E ) 
= 0,8391272, and CL (=CS — AE — S E) =, 
6,6734464 : if this laft quantity be taken for. the 
weight of the fcale, the divifion for 49 in the pound 
would fall -at the top of the arch very nearly, there- 
fore aflume the divifion of 50 in the pound for the 
top, which will make but little alteration in the ma- 
ximum, and the weight of the fcale will be 0,68, 
the maximum between 36 and 37, as before. 
2 A S 0,41 24084, and =,48, 84 19 i 
therefore with the angle of the lever and counterpoife 
as. before, the maximum, cannoty be higher( than at 
48.ikains to the pound. In Mr. Roufe's machine 
the 
