3^ 



Let DA, fig. 5, be the m" side, whatever force 

 pulls AD, the same is communicated to AE in- -A, 

 creased by the action of W + half the weight of ©Li 

 AD = W, supposed to be applied at its centre of 

 gravity g. These therefore are the increase of the 

 tension, while Z. ACB = ma increases by z. ACE = ^, or ' 



(;-• 



;vvj,:^ 



'■fii;ftl 



W, sin. (ma), + W. sin, 



Afi = . 



/2m — 1 ' \" 



COS. jjU 



Integrating and determining the constant so that the whole may 

 vanish when m = 0, 



2 sin. 



<» = 



(ma\ 



I ^.,i„. (i!!=±. a.)+ W. sin. (ri=l . a.) } 



sin. a i \ 2 / ■ V 2 



If now we write for ma, ?r — {m — l)a, we get the compression 

 of the wi" side, and their difference is the actual force which affects 

 it, or 



^ \ fi^ — 1«N C ^F+w. cos. 4a 7 

 J-.= 2cos.C---). ^ sin.a 5 



Hence 



« ., /2»«+la\ C W'+w. cos. Aa7 



. P„^, = 2 COS. (-f-). ^ -t^^ \ 



and the resultant of these in the direction of the arm is 



2 COS. (wa). (W ■\- t«r. cos. J a. 



The arm will lengthen or contract a little by the application of 

 this force according, as it is positive or negative, and in proportion 

 to it ; its variation therefore is t. cos. [nid)^ and the equation of 

 the new shape of the circle is 



a focal ellipse, but in an inverted position with respect to that re- 

 sulting from the expansion of the circle. 



