1.50 HISTORY OF THERMOTICS. 



judgment the conditions of their experiments and comparisons, making 

 one quantity vary while the others remained constant. In this man- 

 ner they found, that the quickness of cooling for a constant excess of 

 temperature, increases in geometrical progression, ivlien the temperature 

 of the surrounding s}Mce increases in arithmetical progression where- 

 ;t-, according to the Newtonian law, this quickness would not have 

 varied at all. Again, this variation being- left out of the account, it 

 appeared that the quickness of cooling, so far as it depends on the ex- 

 cess of temperature of the hot body, increases as the terms of a geome- 

 trical progression diminished by a constant number, when the temperu- 

 tit re of the hot body increases in arithmetical progression. TLe^e two 

 laws, with the coefficients requisite for their application to particular 

 substances, fully determine the conditions of cooling in a vacuum. 



Starting from this determination, MM. Dulong and Petit proceeded 

 to ascertain the effect of the medium, in which the hot body is placed, 

 upon its rate of cooling ; for this effect became a residual phenome- 

 non when the cooling in the vacuum was taken away. We shall not 

 here follow this train of research ; but we may briefly state, that they 

 were led to such laws as this ; that the rapidity of cooling due to 

 any gaseous medium in which the body is placed, is the same, so long- 

 as the excess of the body's temperature is the same, although the tem- 

 perature itself vary ; that the cooling power of a gas varies with the 

 elasticity, according to a determined law ; and other similar rules. 



In reference to the process of their induction, it is worthy of notice, 

 that they founded their reasonings upon Prevost's law of exchanges ; 

 and that, in this way, the second of their laws above stated, respecting 

 the quickness of cooling, was a mathematical consequence of the first. 

 It may be observed also, that their temperatures are measured by 

 means of the air-thermometer, and that if they were estimated on 

 another scale, the remarkable simplicity and symmetry of their results 

 would disappear. This is a strong argument for believing such a 

 measure of temperature to have a natural prerogative of simplicity. 

 This belief is confirmed by other considerations ; but these, depending 

 on the laws of expansion by heat, cannot be here referred to ; and wo 

 must proceed to finish our survey of the mathematical theory of heat, 

 as founded on the phenomena of radiation and conduction, which 

 alone have as yet been traced up to general principle's. 



We may observe, before we quit this subject, that this correction of 



See Phil. IncL Sciences, B. xiii. c. 7, Sect. iv. 



