Numerics of the Elements. 155 



as a physical consequence, the inversion of more or less of 

 the cooling, and therefore of the polymerization. 



The law of free cooling is known to us by the researches 

 of Dulong and Petit.* Its simplest expression is 



v=ma t , 



where v is the number of Centigrade degrees lost per minute, 

 t is the temperature, m is a constant of condition, and 

 a= 1*0075 is a constant! uniformly the same for all matter. 

 The law of heating will of course be the inverse of this, and 

 take the form 



■=HlW5)'="* 9985 ' 6 >' 



Inasmuch, however, as we are now dealing with tempera- 

 ture on some celestial scale, a modification will be required 

 in the numerical value of the universal geometrical factor. 

 This factor and m should be deducible from experiment. On 

 the whole, if the numerics of the elements depend on poly- 

 merization, more or less inverted by heat necessarily developed 

 at the critical points, they must correspond to the equation 



y = (l, 2, 3, . . .^n—ma*. 



The induction given in Part I. (where x is written for t) 

 shows that this is actually and very exactly the case. The 

 values of n and m are the same (15); and there is a universal 

 factor a = *9375 for all elements within the common system. 

 This system may be typically represented as 



an equation which not improbably includes other systems of 

 elementary bodies. 



Scale of Celestial Temperature. — The universal constant a 

 of D along and Petit has an average value of 1*16143 for 

 20° C, or 2 ^ri6143 = T0075 for 1° C. Now the reciprocal 

 of -9375 is 1*06 ; which, when raised to the power 2 "31 73, is 

 equal to 1*16143. Twenty Centigrade degrees, therefore, 

 correspond to 2*3173 degrees on the celestial scale, one degree 

 of which is, consequently, equal to 8°*6307 C. The equation 

 y=— 15('9375)' represents a rate of heating when the con- 

 ditions are supposed to be constant in the unit of time. 



Variable Stars. — When the process of polymerization above 



* Ann. Ch. Phijs. vii. 252 (1817). 



t Dulong and Petit give 1-0077. The above value is calculated from 

 all their determinations. 



