108 



lure at a i^ivi'ii plane in llic wall, in Icrms of timo and in 

 terms of the distance rioni thai plane to the Avarmer side, 

 are deduced from a famous ('(juation establislied by 

 Fourier. Of the various conelusious he arrived at we shall 

 mention here only the following one which is of some im- 

 portance in the ])racli('al ai)i)licati()ns to l)i()thermometry. 

 The time y necessary for the establishment of the steady 

 state is inversely proportional to the coethcient of conduc- 

 tivity c of the material and directly proportional to its 

 specific heat s, to its specific gravity D and to the s(|uare 

 of the thickness d of the wall 



y°^-^ (3) 



So the factor, specific heat, which had no intluence on the 

 amount of heat traversing the wall in the steady state, plays 

 a role in determining the time necessary for the establish- 

 ment of the steady state and, in general, in various prob- 

 lems of the variable state. 



3. The Problem of the Cooling Body. A particular case 

 of the problem of the wall is that in Avhicli a wall at a tem- 

 perature 9 is brought into contact, on its two sides, with a 

 medium at a temperature t different from S. The wall will 

 then warm u]) or cool down at a certain rate ; if it is in con- 

 tact with the medium not only on two sides but all around, 

 the problem becomes that of a body immersed in a warming 

 or a cooling bath. This problem led to the establishment 

 of the '*Law^ of Cooling." 



Newton, in 1701, on the basis of theoretical considera- 

 tions, came to the conclusion that, when a body is exposed to 

 a constant temperatui-e bath, it should lose, during a unit 

 of time, a quantity of heat Q z (z being the time) propor- 

 tional simultaneously to the difference between its tempera- 

 ture 8 and that of the cooling bath t, to the area A of the 

 body, and to a certain coefficient C which indicates the 

 velocity with whicli heat is removed fi-oni the system: 



-^ocAC(S-t) (a) 



