Prof. Challis on a new Equation in Hydrodynamics. 281 



same pressure and temperature, will be to one another as 8 to 

 5, as has been shown by Gay-Lussac. Thus we obtain 



S ——- . — c : and A = p + h = p (1+ -^.— V 



At the surface of the earth the tension z<r of the vapour has 

 a maximum value, which is small when compared to p the 

 pressure of the dry air. The tension ct continually decreases 

 in rising above the earth's surface. 



Although the foregoing reasoning seems clear and unex- 

 ceptionable, yet the result is different from that obtained by 

 Poisson* and Biot, who concur in giving this formula, viz. 



It will not be necessary to enter upon any discussion of this 

 point; because both the eminent philosophers assume that, 

 in an atmosphere of dry air and vapour, a volume of the moist 

 air is greater than the volume of di'y air which is one of its 

 constituent parts : whereas it has been shown that a volume 

 so constituted must be variable in its bulk in the moist atmo- 

 sphere. And, moreover, if vapour be added to a dry atmo- 

 spkere, the densities must be increased : but, according to the 

 formula, the densities in the moist atmosphere are less than 

 the densities in the atmosphere of dry air. 



XLII. Discussion of a new Equation in Hydrodynaynics. By 

 the Rev. James Challis, M.A., F.R.A.S., Plumian Pro., 

 fessor of Astronomy and Experimental Philosophy in the 

 University of Cambridge . 

 ''■^HE argument maintained in my communication to the 

 *■ February Number of this Journal (p. 84) may be briefly 

 recapitulated as follows. The two fundamental equations of 

 fluid motion, which, when impressed forces are left out of consi- 

 deration, are the following, 



'^^'^"-''^^--.r=». ('•) 



are available for the determination of the motion whenever 

 u, V, w are the partial diflerential coeflicients with respect to 

 a?, y, j; of a function of x, y, z, and t. That is, if <j> be the func- 

 tion, when 



• Poisson, Mccanujue, 2nd edit, torn, li. p. 634. Biot, Additions a la 

 Con. den Tpns, IH'.i'J, p. 15. 



Phil. Mag. S. ti. Vol. 20. No. 131. April 1842. U 



