98 



that if t represents the G temperature, A the density of a gas or 

 vapour, and p its elastic force, the equation 



represents the well-known laws of Marriotte and of Dalton and Gay- 

 Lussac. He then states that, as the function which expresses a 

 general relation between p and t, in vapours, must include a more 

 simple function expressing a general relation between A and t, the 



proper course seemed to be to tabulate the quotients y- from the 



experiments of the Academy, and to project them in a curve. For 

 reasons connected with the vis viva theory of gases, which repre- 

 sents the G temperature as a square quantity, he projected these 

 quotients or densities as ordinates, to the square root of the G tem- 

 peratures as abscissae ; and found that the curve traced out was of 

 the parabolic kind, but of a high order. Considering the density 

 as a cubic quantity, the cube roots of the densities were set off as 

 ordinates to the same abscissae, and the author was gratified to find 

 that the resulting curve was the Conic Parabola. To ascertain 

 whether this was accurately the case, the square roots of these ordi- 

 nates, corresponding to the sixth roots of the densities, were set off 

 to the same abscissae, that is the square roots of the G temperatures. 

 The result is shown in a chart, in which, as the author observes, the 

 points determined from the observations range with great precision 

 in a straight line, any slight divergence being sometimes to the right 

 and sometimes to the left; precisely as might be expected from 

 small errors of observation. Other series of experiments on steam 

 were projected in a similar manner, and it was found that, although 

 no two exactly agreed with each other, each set ranged in a straight 

 line nearly. The vapours of ether, alcohol and sulphuiiet of carbon, 

 were found to conform to the same law, as were likewise M. Avo- 

 gadro's observations on the vapour of mercury, and Faraday's ex- 

 periments on liquified gases (Phil. Trans. 1845). Of these last 

 defiant gas is remarkably in accordance with the law, as are nitrous 

 oxide, ammonia, cyanogen, sulphurous acid, and carbonic acid at 

 the upper part of its range ; but muriatic acid, sulphuretted and 

 arseniuretted hydrogen, do not show the same regularity. 



The co-ordinates of the points being the square root of the G 

 temperatures and the sixth root of the densities, the equation to the 

 straight line which passes through the points expresses the sixth root 

 of the density in terms of the G temperature. The constants to be 

 determined in this equation are the inclination of the straight line 

 to the axis of x or that on which Vt is measured, and the distance 

 from the origin at which it cuts this axis, calling the cotangent of 

 this angle h, and this distance g, Ai, Ag densities at G temperatures 



The constants g and Ti being thus determined from two observations, 

 the equation for the density at any other G temperature is 



