i LOOIUX or FORCES, 10 



rests on a curve surface whose ignarine] 

 s) -0, coso, cos0, and co-7 are known in torn* 



nee the equations (I) and 



y H9 



to the surface will determine x, y, i, and 1: 

 be given* 



<t on a curve line, then, since the direction 

 - tangent to the curve, we 



(*) 



lowing equation frutn Analytical Geometry of 

 three dimensions, 



Since SJ?, g, ;in .l jj! can be expressed, theoretical!/ at 



hast, in terms of x, /, and *, the equation (*) gives a relation 

 , and cos 7, i and*. Thus I, and 



together with > equations to the carve ana the 



botwivn 001 a. 001 



W tO 



co8*a + co**/9 + cos* 7 1, 



are eu mine the seven quantities 7.' 



cos a, cos/9, and 0087. 



may observe that from (1) 



86. vla's proof of the Parallelogram of Force* which 



17. rests on iple of the friiat 



>/ of force; sec A rt. 1 1 . We shall give ani't 



this nroof is Poisson's 



with a sli-ht m -wumc that if tw c|ual 



- act on a \ t* the resulunt bisects 



the angle between the direction* of the 



nKiirnitude of each o: 

 angle between 

 resul :iof/'a: 



- 



. if wo change oar unit of force, the 



it me resnioHH msec** 

 components. Also, if 

 o equal forces, 2* the 



.. : ' ' . 



