Lags of Thermometers. 53 



As a special case take F(r) =w = constant, and cj)(t)=Gt, ' 

 where G is a constant. Then the solution becomes 



V 2uoKJ o ( H r/c) *) 



u -&w+mm5 B n i 



^ 2aHj (^/ c) r ^ , , • 



+ inA' + H»)Jo^) 1 + aW ( * 1} J J 



To evaluate the series which occur, we equate the expan- 

 sions of #J o '((.?0 -h HJ (.y) as an infinite product and as an 

 infinite series. 



. . . (13) 

 Writing r = c in (10), we get 



9H 



Sffinnr.- 1 . < 14 > 



and with the aid o£ (14) we find, after equating coefficients 

 in (13), 



Taking the mean temperature we find from (12) the value 

 for the mean lag 



GcYl . l\_v 4H 2 g- ffl V^ 2 / Gc 2 \ . 



a* 1 8 + 2Hj ^ &W+ H 2 ) r 0+ aW>! * l 



On writing m = 0, we get the lag given by Dr. Bromwich's 

 formula. 



In the next case to be considered, we have the solution 

 (12) until t = t 1} when the surface condition becomes 



£(*) = G* 1 + G J (* — Jj for t>t L . . . . (16) 

 Writing t f = t — t lz we have, after time £ l5 a new problem 

 in which the conditions are 



* () "S(A 2 + H 2 )Jo(A)L Mo ' 



