MM. Jamin and Richard on the Cooling of Gases. 245 



is attainable than could be supposed. One then constructs the 

 curves of the values of h, taking the times for abscissae. They 

 differ from one another; and it is immediately seen that the 

 cooling is as much more rapid as the pressure H is less. 



These curves express the phenomenon graphically; we must 

 now find the equation. We thought at first that^ the excess of 

 pressure h being very small, Newton's law A=Me~"^ could be 

 applied. Indeed it differs very little from experience, which it 

 represents well enough for a time not very great ; but it cannot 

 embrace the whole of the observations. We made the compari- 

 son by three operations. First we took, upon the curve, abscissse 

 in arithmetical progression : the successive ordinates were to be 

 in a constant ratio ; they were not found to be exactly so. Then 

 we drew tangents which should satisfy the condition 



dh , , 



that is to say, -7- ought to represent the ordinates of a straight 



line of which h would be the abscissa; but we ascertained that 

 the line thus constructed had a parabolic form. The third and 

 best process is the following. Newton's law gives 

 \ogh=loQm — ax\oQej 



which is the equation of a straight line forming with the axis of 

 ^ an angle whose tangent is —ahge. In reality the line is 

 curved ; Newton's law must therefore be rejected. 



We then thought to express by Dulong's formula the heat 

 which a gas yields to its envelope, which regulates that which the 

 gas takes from the central thermometer, and which would be 



-^=n'H^'^^^', . . . . * (a) 



or else, replacing d6 by its value as a function of A, which is -ry, 

 dh_ri!_ ¥' _ Jf_ 



or else, finally, taking the logarithms of both sides, 



^)= logm + ^'log/i-(^'-c01ogII. . (5) 



Under this form equation (5) has been completely verified; it 

 signifies : — 



(1) That, for any constant values of the pressure H, log ( — j: ) 



represents the ordinates of a first system of straight lines, all 

 parallel, whose abscissse are log A, and which make with the axis 



bg(. 



