THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



FEBRUARY 1886. 



XIII. Bars and Wires of varying Elasticity. 

 By 0. Chkee, B.A., King's College, Cambridge*. 



IF m and n denote the elastic constants as used in Thomson 

 and Tait's ' Natural Philosophy,' and no bodily forces act 

 on the mass, then the equations of motion or of equilibrium 

 of an elastic isotropic solid referred to cylindrical coordinates 

 may be written in the form f 



, . . d* d€ , dm d\i 



dllk , m + nd8 , d€ d 2 v 

 - n ^ + —T0 +n Tr = PaW> ■ ■■• • W 



dm L d% , , . ds d?w 



- n -dr- +n W + ^^ n >d-z=P r W ' • & 



The displacements being as usual denoted by u, v, w, the 

 symbols used above are given by 



~ dr r r dd dz' ^ ' 



*-?£-£ « 



■-£-£ w 



c ^i<^_i^ 



r dr r do v ' 



* Communicated by tlie Author. 



t Cf. Lame, Lecons d' Elasticity, p. 184, noticing change of notation, and 

 of sign in (5), (6), and (7). 



Phil Mag. S. 5. Vol. 21. No. 129. 2^. 1886. G 



