CONVECTION OF HEAT BY AIR CURRENTS. 43 



exceed one-tenth of a division, that is, 0°*2 Centigrade. The interval of time between 

 any two readings was generally chosen, so that the corresponding decrease in deflection 

 was not less than ten divisions. The error in any one estimate of the rate of cooling 

 during a given interval would therefore not exceed 1 per cent. 



5. Fourier's equation for the motion of heat in a solid homogeneous sphere is 



dv _ K /d 2 v 2 dv\ 

 & ~ GT> \dr* + rdr) 



with the condition that at the surface (r = R) 



tt- dv 



K -j- + hv = 

 dr 



The solution for t = must, of course, be satisfied by the function of v and r represent- 

 ing the initial distribution. The solution for the particular case of uniform initial 

 distribution is 



2 



er K 



2/>R \1 sm R- 



' ; = K~ /i -*- 



— ( iY 



CD \r) t 



<;cosece — cose 

 R 



where e 1} e 2 , etc., are the roots of the equation 



!E -1-i-B. 



tan e R K 



After some time has elapsed, the first term in the series for v is the only one of 



practical value. Further, if R be small, or the ratio r^ be small, the temperature 



throughout the sphere will be uniform. To test this, we may take Macfarlane's determi- 

 nation # of the emissivity of a black surface and the value of K (thermal, not thermo- 

 metric, conductivity) for copper to be 0*95 in C.G.S. units. With these assumptions it 

 will be found that the difference between the temperature for r = and r = 1 when 

 t = 600 is within the limits of experimental error. It may, therefore, be assumed that 

 the temperature at the centre of the ball is that of the ball generally. 



6. The experimental results obtained may be regarded in two ways. First, their 

 bearing on the law of cooling, stated by Newton ; second, the rate of cooling for a 

 given excess of temperature with different speeds of the current of air. 



As regards the first of these, Newton gives no details as to the speed of the current 

 -of air in which he placed the cooling body, and merely states that it was placed " in 



* Proc. Roy. Soc, xxxii. 465. 



