56 Mr. A. R. McLeod on the 



Using the series 



— 11 — l - 2, < 



^ ia?i 2 + H (H-l) ^VW + HCH-l)} 



^ 6H 2 1 



^ ia ./.{a, 2 + H(H-l)} 15 + 3H' 

 we find for the lag in the mean temperature 



^"Il5 + 3HJ ii«.»{«. r +H(H-l)}l Mo+ ivr ^ 



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

 formula. 



In the case of the temperature inversion, in whicli the 

 solution (26) holds until t = t 1 , and new conditions then set 

 In, the initial condition being given by writing t = ti in (2$), 

 and the surface condition by (16), we find without difficulty 



2 



" ~ l + ,s { «,, 2 + h(h - Dyjj( a „) L « v 



The lag of the mean temperature is found to be 



-("• + S> _ ^- • (29) 



4. Numerical Results. 



We consider the same bulbs that were dealt with in the 

 former paper (Phil. Mag. Jan. 1919). These have the same 

 sensitiveness for a given thermometer stem, the expansion 

 of alcohol being taken as six times that of mercury. Par- 

 ticulars are given below. 



The surface conductivity is taken from the same paper 

 and is given (in G.G.S. units) by 



7i= -0000515 V (30) 



The air density for which (30) holds is that near the ground, 

 V being the velocity of the aeroplane in miles per hour. 

 The data on which this value is based were obtained from 

 work on radiators and engine cooling done at the Royal 



