MODE OF AITI.K'ATIO". '' H 



M sequence of the connexion of the sjstetn 

 iiiy of some parts of it, or th? ji; 



4, relations \ I between the eo- 



i of which all of 



them inav U* exj>rr*vl in trrnn nfa r.-rtain numl^r .f t .. m; 

 i nmy be cxpreMcd in terms of certain other 

 Ht co-ordinates and angles. 



Suppose ,, f f , (,$!. ^,t ^ a .... to denote these i 

 . -.T.liii.itcs and -n, if ux ntglc. 



#/uarc4 and product*, and higher power* of &r. t Sy t . ... &,, 

 Sf t , ... o^ lf fy t , ..., we shall obtain equations m 



, -f ... + o, + *,*, 4 



ns of 

 do not cont. incnts Sf |f ${,,... 



leu of &>,, ?v, ... be substituted in the equations 

 of whirh (S) is the type, ai K values of Sp |f f^ 



be .- 1 in 1 ; this equation will take the f 



.f. + ^.+--*-yM + ^M + --o ...... (3). 



editions for the equilibrium of the system are 



C.-O, t -0,... fc-0, ?,-0 ......... (4). 



since 3f lt Sf,,... o^ |f S^ t> ... are by supposition inde- 

 t have given the body such a displacement 





t , fc. hanged; and then (S) 



Qft | - ; therefore <?, - 0. 

 Similarly, we may shew that the other equations of (4) 1 



260. N\ will give n simple example in illustration of the 

 i cding Article. A string of given length has 

 > 1 fixed at a point ii of intersection o: 



planes at right angles to each other, and at the other end 



