Law of Cooling. 59 



The bars used to determine f(y) were respectively of copper, 

 iron, and zinc, 26 cms. long, ro, cm. diameter, and were nickel 

 plated. They were heated to ioo° C. in a hot air bath and 

 then suspended by threads horizontally in air to cool. The 

 temperature during cooling was determined thermo-electri- 

 cally by means of iron-German-silver junctions soldered 

 into small holes in each bar. 



Assuming different forms for f(v), taking c v as being 

 approximately a linear function of v, and integrating, we get 

 different forms of v as a function of /. Out of these we can 

 choose that one which, while simple, best expresses the 

 facts observed. The forms / (v) = v* v(i-\-bv)** v n respec- 

 tively were tried. The first two could not be made to 

 correspond with the experiments, but the third for a suitable 

 value of n, generally = 1 *2 1 , expressed them with a very close 

 degree of approximation, over the whole of the range of 

 temperature 30°toioo°C. 



Writing in (3) c v — c{i+c'v), f(v)= v n we have 



cv 

 — mc(l + c'v)- = shvn n . (4) 



which on integration gives 



-"-1/ n-\ , \ sh . ' „ , , 



v (1-^ c'v) = —(n-l)t + C. (5) 



\ 2-n ) rrur ' w 



where C is an arbitrary constant. 



To show the closeness of the approximation of this for- 



mula to the cooling, I give a series of values of 20 — (11— 1), 



deduced from observed values of v at different times during 

 the cooling. 



* Newton's Law. 



** Used byKundtand Warburg, Pogg. Ann., CLVI., to express the cooling 

 of a thermometer in a sphere concentric with its bulb. 



H. F. Weber, Mon. Ber. d. Berlin Akad. 1880, considers some correction 

 of this form to be necessary in dealing with bars. 



