Mi; 



, R. V. SOUTHWELL OX THE GENERAL THEORY OF ELASTIC STABILITY. 207 



terms of order 2 '... . We then obtain, as the equations of neutral equilibrium in 

 \j 



cylindrical co-ordinates, 



irv i3i' r \ i av av 3/11-4 i fv * /i av av\ 

 2 ^2^ + 7Tv"~ ?' + ^?^ i " f "a?" m-2 7 5 aT"'"m-2'rarad azaw 



/5+^\I A/ 1 F^-^-^U/SiS^ -( - ) = 0, .... (46) 



l \ icT/rwVrafl a/- r/ 4C /az\az 



?' PV 1 Sr' r' -1 1 3V . aV . m I 3V 



V 

 av 



-4 



4C 



^ + ^-i^-' N )l = o > . .-. (47) 

 * 



and 



av 



av 



m-2 



/ 



1 ? /I a'' 



4C 



Ll_^')l = 0. . . (48) 



Equations (46-48) represent the conditions for neutraUtability in the equilibrium 

 of a body subjected to a stress-system T, W, K, where n is constant, and ri- and 60 

 are functions of r only, which satisfy the condition of equilibrium 



, 



_ j- - 



? r 



(49) 



For comparison with the ordinary equations ot equilibrium in cylindrical 

 co-ordinates they may be written (with LAME'S notation for the elastic constants) in 

 the forms* 



and 



where 



. (50) 



i a / , x , ia-' 

 = ;a7. (nt) + 7.aT + 



* Cf. LOVK, oj>. r<., 199. 



