EQUILIBRIUM OF AN ISOTROPIC ELASTIC ROD OF CIRCULAR SECTION. 951 



The first group of terms in Art. 25 may be written 



J¥_, ( 1 / 3 \ o ) 1 i«F_, 



u,,= 



U,= -X- 



dz 



where 



^-.W^"2^(^-^''^)- 



. (7)' 



(8)' 



(In the table given below, the terras involving t here are associated for subsequent 

 convenience with Fq.) 



We will now write down the complete results derivable from Art. 25 in this way ; 

 and seeing that the sum of the integrals in (1) symbolised as in (2) does not depend 

 on x\ y', we may drop the accents on these letters. The variables in the functions 

 X, Y, Z which occur below are then x, y, z. 



It is convenient to tabulate separately the results for force perpendicular, and 

 force parallel to the axis of the cylinder. 



Tables of displacements and stresses arising by integration froTn the permanent 

 displacements and stresses oj the point source solutions. 



Force perpendicular to the axis. 



+ cr(.«2 .. y2)_ ___2 + ^zy^ + 1 - yn_,| 



c^F_9 (iG_o 

 ' dz ■' d?? 



1 C^3F_o / 1 \ ^3Q_^ ^n , 



(9) 



2A- = ^ I 0-(.r2 - 7/2) + — .^2 + — y2 _ l^ ^ ^ __y2 | _ 



i.3-+^- + Tf^^ 



-M- 



ffe 



2^ = /xi o- + — ].<;(/ 





F-2 i / ,2 9^ , 1 9 3 9 / 3 \ 2 ) 1 6^3G_9 (^n 



..= -e.^2_e/!«^, 



C^Z2 



CZ22 



(10) 



where 



-2 TrEa* 

 4 



Dr*2x, 

 I 1 



Fo = ^^Dr^S { l{cr.r2 - cr^2 _ ^«2)X + <,,.;y Y } 



G-2 = -4riD7*2Y, 



rEa*" 

 TRANS. ROY. SOC. EDIN., VOL. XLIX. PART IV. (NO. 17). 



(11) 



130 



