140 Mr. A. R. McLeod on the Lags of 



The mean value of u is 



-«^?^J^.. • (10) 



»=1 



The lag is thus 

 4G< 2 



^r2-.-*-2-.- 4 «-^']. • • • • ai) 



and its steady value is : 



4Gc 2 '^ _ 4 



Computing the series, we find for the sum of the first 

 10 terms the value '031246 which is practically 1/32. 

 Hence 



L = ^ = "8K (12) 



We shall see in § 5, on writing h=~x> in (20), that this 

 value is rigorously correct ; and so 



The temperature of a cylinder with infinite surface con- 

 ductivity, cooling from a uniform initial temperature w , 

 the temperature of the surrounding medium being zero, 

 is given by 



9 y -f^JoOv/c) 



„=! *n J l(«») 



and the mean temperature is 



oo a2«2 





This equation could be used for calculating the value 

 of a 2 from the curve for the cooling of the cylinder. 



