CHAP. VI., 7.] 



HEAT. DULONG AND PETIT. 



155 



of air was absent, the influence of the latter became 

 less and less perceptible. 



The principal apparatus of Dulong consisted of a 

 l>alloon of thin copper about a foot in diameter, coated 

 internally with, lamp black, and placed in connection 

 with an air-pump, so that any portion of atmospheric 

 air could be extracted up to about f f of the whole, 

 and any other gas could be introduced into it. The 

 temperature of the balloon could be nicely regulated by 

 introducing it entirely into a water trough. Into the 

 centre of the balloon, thermometers of different sizes, 

 or having different kinds of surface, could be intro- 

 duced. The temperature of the balloon having been 

 first regulated, the thermometer under experiment 

 (being itself the radiating and cooling body) was 

 heated nearly to the boiling point of mercury, and 

 inserted in the balloon so as to occupy the centre of 

 it. The exhaustion and other arrangements being 

 made, the observations on the rate of cooling of the 

 thermometer commenced when its temperature was 

 as high as 250 or 300 centigrade, equivalent to 482 

 and 572 Fahrenheit. 



With respect to simple radiation, or when the 

 ^t e ^" ec * ^ a ^ r * n * ne balloon is estimated as nothing, 

 the inaccuracy of the Newtonian law was soon ap- 

 parent. Whilst the excess of temperature of the 

 cooling body above the envelope or balloon remained 

 constant, and the absolute temperature of both was 

 made to vary, the velocity of cooling, instead of 

 being constant, increased rapidly with the tempera- 

 ture. Thus the excess of temperature being in every 

 case 200 centigrade, and the temperature of the 

 balloon being ... 0, 20, 40, 60, 80, 

 the rate of cooling was 7'4, 8-6, 10-0, 11-6, 13-4. 

 The whole of an elaborate series of observations was 

 beautifully and satisfactorily represented by a for- 

 mula admitting of this simple physical interpre- 

 tation, viz., that the cooling of the thermometer is 

 the difference between the heat which it parts with to 

 the envelope and the heat which it receives from the 

 envelope; and that the heat thus parted with, either 

 by the thermometer or the envelope, varies in a geo- 

 metric ratio with its temperature. 1 



The effect of contact of a gas in cooling the ther- 



mome ter is more complex. It is independent of the 

 , ... .. TVIJIJ i 



^ ex ^ ure of the surface, as Leslie had already supposed. 

 The cooling power of a gas is proportional to a cer- 

 tain power of its elasticity, which varies for each ; it 

 takes place more rapidly in hydrogen than in any 

 other known gas, which was likewise discovered by 

 Leslie. It also comes out rigorously, that the ratio 

 of the radiating power of different surfaces is the same 

 at all temperatures. This ratio for glass and silver 



is 5-707 : 1. Assuming this last principle, and also 

 that the cooling due to the contact of air is indepen- 

 dent of the surface, the law of cooling in vacuo may 

 be deduced from the observed cooling of two thermo- 

 meters suspended in air, and having glass and sil- 

 vered surfaces respectively. Dulong and Petit found 

 that, when they analyzed their experiments in this 

 way, they obtained values for the radiation in vacuo 

 almost absolutely coinciding with what direct experi- 

 ment had already given. No more perfect criterion 

 could be desired of the soundness of every link of the 

 chain of experiment and induction. 



We shall not analyze Dulong's other memoirs. (698.) 



They regarded matters in the science of Heat requir- ^ ther me ~ 



Ji i -11 1 T moirsof 



ing the same skill in devising apparatus and in mam- D u i onR on 



pulation, the same caution in eluding errors, and the the laws 

 same just principles of calculation as in the investi- of neat - 

 gations already specified. They did not, however, 

 lead to the discovery of laws so striking and so ge- 

 neral. They included the very delicate and difficult 

 subject of the laws of the thermal expansion of 

 bodies, particularly that of air and of mercury, which 

 were applied to the theory of the thermometer, the 

 very basis of all exact knowledge in the doctrine of 

 heat. Another referred to the specific heat of the Specific 

 gases, an enquiry of the very greatest difficulty, in he 

 which we still find physicists disagreed. Dulong 

 bethought himself of using Laplace's celebrated cor- 

 rection for the velocity of sound due to the heat de- 

 veloped during the compression of an elastic medium 

 (art. 433), and proposed to deduce the heat thus 

 developed, by a comparison of the observed and theo- 

 retical (Newtonian) velocity of sound, and thence to 

 obtain the specific heat. The theoretical velocity is 

 easily obtained from the density of a gas under a 

 given pressure: the observed velocity was ingeni- 

 ously found by sounding one and the same organ 

 pipe with the different gases in succession, and ascer- 

 taining the pitch by the aid of Cagniard de Latour's 

 Sirene. (441.) 



One of Dulong's latest, most elaborate, and most (699.) 

 useful labours, was ascertaining the elasticity of high- jj^ 8 ^* 8 " 

 pressure steam in terms of its temperature. These 8team> 

 experiments were carried as far as 24 atmospheres 

 of pressure. In the course of them the law of Ma- 

 riotte and Boyle was verified up to the same limit. 

 The condensation of air was found to be exactly pro- 

 portional to the pressure. We shall return to the 

 subject of these later experiments of Dulong in men- 

 tioning the still more recent ones of M. Regnault. 



Dulong was unfortunately lost to the world at the (700.) 

 comparatively early age of 54. His was the peculiar '* 

 merit of a well-balanced scientific mind. He felt 



1 Thus symbolically expressed : F = ^ a a ji 



where V is the " velocity of cooling," or depression of the thermometer in centigrade degrees in one minute, supposing it to con- 

 tinue constant for so long; 6 is the temperature of the envelope ; t + t, that of the thermometer ; a is a constant independent of 

 the size and surface of the cooling body, and which is :s 1-0077 ; w is a constant depending on the dimensions and surface of 

 the body. 



