$56 Mr, PowelPs Appendix to ill. Ramond's Instructions [Nov, 



a given pressure, for instance, 29-921 inches, but according as 

 the intensity of gravity is greater or less, a column of mercury 

 of the constant height of 29*92 1 inches will weigh more or less ; 

 consequently air subjected to this pressure will be more or less 

 compressed. Now by experiments with the pendulum in differ- 

 ent latitudes, we find that calling the force of gravity in lat. 45°, 

 unity, in a latitude ^J/, it will be expressed by 1 — 0'0028371 . 

 cos. 2 >J'.* The density ^ being proportional to the weight will 

 vary in the same ratio ; that is to say, calling it 8 in lat. 45°, and 

 under the pressure h, it will become for any other latitude, and 

 under a column of mercury of the same height, 8 [1 — 0*0028371 

 . cos. 2 •»]/]. The coefficient C, which expresses the ratio of the 

 density to the height of the barometric column, ought to vary in 

 the same proportion, and consequently becomes C [1 — 0-0028371 

 . cos. 2 \^], which being substituted in the value of x, gives z = 



III- 



"TTi • ^°S* (h) • ^^ *^^® ^^y ^^ ^^^^ ^^ ^" 



C . [1-000^8371 .COS. 



M 

 cient to find the coefficient ^-^^-^^^^^^^—^ by experiment 



for a given latitude ; for thus, -^ being known, we shall know 



also — ; and the formula becomes applicable to all possible 



latitudes. The formula may be rendered more convenient by 

 causing the denominator to disappear, which is easily done ; 



for the fraction - — ^ ^^^^ 7:=, ttt beinor developed in a series by 



1 — 0*002837 . COS. 2 vf/ ° ^ •' 



division, becomes 1 + 0-002837 cos. 2 ^^ + 0-00000804857, 

 cos.2 2 4-+ or simply 1 + 0-002837 cos. 2 4. by confin- 

 ing ourselves to the first term, which is alone of sensible magni- 



tude. Thus we shall have z = :^ [1 + 0*002837 cos. 2 4.] log. 



(!)• 



(2.) Thus far we have supposed that the value of the coefficient 

 C or - is the same in all the strata of the column of air ; but it 



A 



is not so in nature ; and many causes tend to make this ratio 

 vary. The principal cause is the inequality of the temperature 

 of the strata ; for the elasticity of air is augmented by heat, so 

 that with a less density, it can support an equal column of mer- 



cury, which makes the ratio -, or C, vary. 



This ratio also varies according to the greater or less quantity 

 of aqueous vapour which is found suspended in the different 

 strata ; for this vapour weighs less than dry air of equal elastic 



• Tliis expression is deduced from one given by Laplace, Mec. Cel. b. 10. — (See M. 

 Ramond*8 First Memoir, Fart II. p. 16.) 



