Lags of Thermometers. 55 



and since 



f ?! J* («») } 4 <*J = { «» 2 + H (H - 1) } {JjK) } 2 /2«„ 2 , 

 we have, calling the constant coefficient A„, 



Defining ^(V ? t) to be zero for $<0, and 



x (r, = 1- ^A^W^-iJjKr/cJe-W^ t>0, 



71 = 1 



we have for the function ^r(r, £)> when £ > 0, 

 ^(r, = 1- 2 A re (^/c)-^- a2 *>/ c2 fj,(V/c) 



+ H { ~~ Yr J i( a » r / C ' + "nJiiw/c) J J 



And, as before, the function which takes the value </>(t) for 

 r — c is given by 



+ H | ~ £ J *( a » r / C ) + «*J*WA0 } ] jj 0(t)^ 2 V^t. 



The solution for w satisfying (6) is then found to be the 

 second term on the right of (25), and the solution 

 required is 



W = S(? + H(H^1)} W wJo *^<«"«* I (25) 



+ ^cH«n 2 + H(H-l)}J,K) (r/,)* Jo* W ^ 



Taking F(r)=w , and $(<)=GU, we get 



"iiW + HCR-lJjJjK) 6 I (26) 



^ 2GH(r/ f )-iJ t (a,r/ f ) f _« 2 ,,_*. ^*_ 



1) • 



