in the Theory qfSmind. 107 



an extremely simple equation, the integration of which is free from all ambi- 

 guity, and gives jp r= g* ; supposing p and ^ to become each equal to unit at 

 the same instant *. It hence follows, that the 'general expression for 7, or 

 for any change which occurs in the quantity of heat contained in the air, 

 is no " arbitrary function," such as we might modify at our whim or fancy, 

 but a determinate function, fixed down by the above condition ; that the pres- 

 sure vary as the k power of the density, in every case whatever, in which the 

 quantity of heat in the mass of air undergoes no change, or when 7 = 0; and 

 this condition will accord with no other form but what I formerly gave, 

 viz. 



y :^ B (logp — Ar log e) + C. 



It is very remarkable, that four of the greatest mathematicians of the age 

 should have been so completely bewildered regarding this integration. 1«/, 

 The Marquis Laplace, Mec. Cel. tome v. p. 127.; 2</, M. Poisson, Annales de 

 Chim. xxiii. 338. ; 3rf, Mr Herapath, Phil. Mag. Ixii. 329. f ; and IMr Ivory 

 even after the only possible form of the function had been clearly pointed out, 

 as I have shewn at length in the Number of this Journal for July last. 



2. On the Theory of the Variations of the Barometer. 



In the Supplement to the EncycloptEdia Britannica, Profes- 

 sor Leslie has proposed a theory of the depressions of the baro- 

 meter, in which he supposes, that the wind describing a curve 

 in passing over the surface of the globe, acquires a centrifugal 

 force sufficient to diminish the pressure of the air on the earth's 

 surface, and consequently to depress the barometer. Mr Da- 

 niel!^ in his Meteorolog^ical Essays^ has endeavoured to contro- 

 vert this theory; but I am not sure that I have caught the 

 meaning of either of these gentlemen in their respective argu- 

 ments, and therefore do not pretend to decide on their merits. 



If we proceed to compute the centrifugal force of air, as if con- 

 sisting of detached particles like sand, revolving in circles about 

 the earth's centre, the result is by no means considerable ; but, to 



* This supposition has nothing to do with the value of the results : it 

 merely gives the formula a neater appearance. 



f It is but justice to M. Poisson to observe, that Mr Herapath, in bis 

 first note, page 328, accuses him of setting out with the hypothesis, that the 

 increments of expansion, under a constant pressure, are jjrojwrtional to the 

 increments of heat ; whereas nothing of the kind is assumed, till he had 

 got to p. 330, after having obtained the " arbitrary function," as they are 

 pleased to call it. 



