Applications of the Formulas 91 



allow the computation of the quantities of heat transmitted in the 

 different cases which ordinarily present themselves. But before 

 the establishment of the regime, in bodies limited by two surfaces 

 of which one receives the heat and the other emits it, and during 

 the entire duration of heating, for bodies unlimited in one direc- 

 tion, the temperatures of different points vary with their position 

 and with time, according to very complicated laws, which depend 

 at the same time on the form of the body, on the conductivity of 

 the material of which it is constituted, on its specific heat and on 

 its density ; thus bodies formed of materials which are the best 

 conductors of heat are not always those which disperse it most 

 rapidly, because the dispersion depends on the relation between 

 the conductivity of the material and its specific heat. 



897. It results from mathematical calculations, too compli- 

 cated to give here, that if we consider a plane surface of unlimited 

 extent, maintained at a temperature 7, and beneath this surface 

 a homogeneous body, of very great thickness, at the temperature 

 o Centigrade, after one minute the temperatures at distances of 



.04" .4" 4-" 40." 



will be for sand 0.98870. 88y7o. 15470.000 7 



limestone 0.99770.97370.7457 o.ooi7 



iron 0.99970.99270.92470.3397 



coarse grained marble 0.9997*0. 99370. 938?" 0.4397 



plaster 0.99670.96270.62470.0007 



" motionless water 0.99370.93970.39970.0007 



The formula by which these numbers have been com- 

 puted is a rigorous deduction from the fundamental principle of 

 the transmission of heat and this principle has been proven by 

 too great a number of experiments to allow any doubt of its 

 exactitude ; but in establishing this formula the effects of expan- 

 sion and of variation of specific heat with temperature have been 

 neglected; however, since for solid bodies the expansion, varia- 

 tion of specific heat and variation of conductivity are small we 

 may regard the formula as very approximately representing the 

 facts. Thus the numbers which we have given show with what 

 rapidity heat diffuses itself through bodies even when of low con- 

 ductivity, after the establishment of a permanent regime of tem- 

 perature. 



