WIIvLIAMSON: STRAESrS IN OPnCAIv GLASS 2x3 



IV. Solid cylinder with temperature distribution symmetrical 



about the axis. — The only change necessary is that C3 in equation 



dPa dd 



(7) vanishes owing to ^r— and -r being zero at r = o. 



V. Slab with temperature gradient through the smallest dimen- 

 sions, symmetrical about the center. — -The same assumption was 

 made as regards planeness as in the axial displacement for the 

 cylinder and the forces along the Hne of the temperature gradient 

 are neglected. (See previous footnote as regards experimental 

 evidence.) 



The equations then are: 



eP — fP + a^ = constant = Ci 

 and I Pdx = o 



^ o 



The integral gives us a method of evaluating the required con- 

 stant, 



Cx-ad 



/ 



•/ a 



e-f 

 or 



dx = o 



J Cidx = a f 



o »/ o 



ddx 



APPLICATION OF THESE EQUATIONS TO SPECIFIC CASES* 



I. Spherical shell. 



(la) . Shell heated linearly on the surface. 



(Jb). Approximate formulae for the sam£ case when the internal 

 diameter is very small. 



(la).^ In this case 



do hr hai^ 

 dr ~ 3K 30-2 



Equation (4) therefore reduces to 



* The temperature gradients ( — ) in all cases are taken from a forthcoming 



paper on temperature distribution in solids, by E. D. Wiluamson and L. H. Adaks. 



* h = rate of heating; k = diffusivity constant. 



