Thermometers with Spherical and Cylindrical Bulbs. 143 



Hence by (15), since B = 0, we get 



KG, 



SF ~ hd °> 



* KGc _ Gc 2 

 c ~~ Ma 2 ~ 6a 2 ' 



and so A _ Gc 2 /j£ . 1\" 



a 2 V3c/i 6f 



Thus from (16) we get the mean lag as follows : 



»-£♦*- £(£♦£> • • • <«) 



5. Steady Lag for a Cylinder in a Medium ivhose Temperature 

 changes at a Uniform Rate, the Surface Conductivity 

 being Finite. 



Substituting u = Gt — in (7), we get the following 

 equation for the steady lag ^- vanishing : 



dM 1 d0 G 



dr 2 r dr a 



+"^+- 2 = o, 



which has the solution 



fl = A + BIpgr-|£, (19) 



and, as before, B = 0. The mean lag for the cylinder is 

 found to be 



Qc 2 



From (17) and (19^ the surface lag is obtained : 

 n „ K Gc __ Gc 2 



Hence A _Gc 2 /l K\ 



A -~tf\l + 2hcy 



