PBOFEBTY OP i 



with respect to other displacement* If, for example, 

 we consi : placement* as make 51 -4 



tvrtainly negative when e# uu.l fy arc taken umall 



V. If, a^ain, we r.-i 

 placements as makc-0--ty, thm M i 



?' and fy are taken small enough ; thus 

 of gravr rested I placement and to 



tile equilibrium is unstable. 



26 v 7 n/rref o/*a r/'tvn ^nyU drawn ft lift rim 



W powito in a Jtorizontul ///,-. //< common catenary i'< 

 < /KM to ecu/re o/ gravity furthest from the fruY-//.r ///.< 



s proposition belongs to the Calculus of Variation*, bat 



nn iui|MTiri-t proof of it may be 



preceding princi}>!< s. Sim-.- tiie string which hangs in a com* 

 mon catenary is in cquilibriuin we conclude that tin- ! ; 

 its centre of grarity from tlic horizontal line is a maximum 

 .minimi. (Sec howi . \\.\ we may 



a maximum and not a minimum from tin* 

 ital fact tluit it | sli_rhtlv displai 



will n-turii to its po.- im so that its cquili- 



. (bee Art. 26i. in any other po- 



of tin- .-trin:: thnn that of equilibrium tre of grarity 



will be nearer to the given horizontal line. And as the - 



i lian-s in the common catenary is of u:. 

 and thickm .<- ; of gra ides with thai of the 



oeition is establishaiL 



'. Lamngo has pi von a demonstration of the principle 

 i doe* not assume a knowledge of 

 .! of eouilibrium of any syst- 

 i is ditliriilt and has not bi-. rsally re- 



l. We shall place it here and refer the read 

 Poisson, Art 337, and t- toal Veloeities* in 



for further ii 



We have \r any system of f-nvs may be 



placed by a string in a state ot tension passing round a 



i i-f pullies. 

 T.S. 



