48 On Sir J. W. Lubbock's Theory of Heat and Vapours. 



Lubbock makes choice of three elevations observed by Gay- 

 Lussac in his aeronautic ascent from Paris ; and he finds 

 y = 1-4910, E = — 1-1618; 



which he changes to 



y = 1-5, E = — 1'192. 



With these constants, the two equations will, no doubt, verify 

 the observed values of /?', p" ; but, as y and E have been de- 

 duced from three particular observations, there is no evidence 

 to prove that, with any other three assumed observations, the 

 constants will, in every case, retain the same values. Thus if 

 6'" and ja'" be new observed values, the equation 



/"^ = 'f^, •(/-£) + £ 



will not hold with the same values of y and E, as before. 



Such calculations I'etard knowledge by erroneous views. 

 The author applies his equations to barometrical measure- 

 ments, and to the refractions ; but his processes have no 

 foundation whatever in the constitution of the atmosphere. 



We can hardly help noticing how fruitless it must be to 

 attempt solving physical problems by means of algebraic 

 equations containing many arbitrary constants. In such 

 problems the constants are improperly called arbitrai'y : they 

 are indeterminate, and must be found by observation or ex- 

 periment; but as they are mixed with the other quantities in 

 the equations of the problem, they are independent on the 

 will of the calculator. In the Theory of the Moon, the 

 coefficient of the cosine of the mean anomaly in the reciprocal 

 of the radius vector is one of the constants, which must be 

 found by comparing the theoretical with the observed place 

 of the moon. Now this constant varies with the disturbing 

 force; and if any one, not attending to this circumstance, 

 should be rash enough to fix its value by an arbitrary defini- 

 tion, many errors would thereby be introduced in the expres- 

 sion of the moon's motion. 



In Sir Humphry Davy's Chemical Philosophy this pass- 

 age occurs at p. 233 : — " Air analysed in different quar- 

 ters of the globe, in cities and in the country, on sea and land, 

 has been found not perceptibly different in composition : the 

 accurate proportions of oxygen and azote are 21 and 79." Here 

 it must be understood that air is unmixed with aqueous 

 vapour or carbonic acid gas. The experiments of MM. 

 Dumas and Boussingault, recorded in the ComjHes Ren- 

 dus, June 7, 1841, confirm the words of the illustrious 

 chemist. It thus appears that the atmosphere, at different 



