970 Mr. S. Smith on Initial 



narrow stream chiefly in the direction of the axis of e, 



^-? is small compared with ^~ or y~ . 



Hence neglecting ^-* the above equation becomes 



or d*9_ d</> 



where q = (pe aZ - 



The solution is required to satisfy the following boundary 

 conditions: 



(f> = constant from x = '2 to %= —'2 cm 

 <£ = when x>' 2 or <— '2 cm 



*1* = 0. 



Hence it is clear that <p is a quantity which varies with 

 ^ and £ in the same way as the temperature varies with x 

 and the time t, in an infinite heat-conducting solid, whose 

 initial condition is that, when £ = 6 is zero everywhere 

 except in an infinite slab bounded by planes #=*2 cm. and 

 x = — '2 cm., where the temperature has a uniform value. 



Therefore . . f 3 , -^^ 



<£ = A 1 z~z e * z dg, 



inrl /"* 2 y(*-g) 2 



anQ q = Ae«*i z~*e~ * z d%. 



Hence //, may be found by substituting this value of g in 

 the equation 



n-2 /i 2 



j da? 1 <7 ^ 



^=7^^ ( 3 ) 



f dx I ^^ 



Jo Jo 



This ratio is independent of a when ol is small. The ratio 



ii depends on -=- since 7= t= ft Z = 41 . -=-. where Z is ex- 

 k Ilk A; 



pressed in volts per cm. The values of k corresponding to 



