50 Remarks on the Gradation of Heat in the Atmosphere. 
Hyp. log. = = an, 
b ak 
=¢ 
a 
B — 
Sista ciate 
B 
é 
and, by expanding in a series, 
b 
Bio § arg 
Z-petawx git A 
If we allow 90 fathoms of altitude to every centesimal degree 
of decrease of temperature, which is the rate adopted by Pro- 
fessor Leslie himself, we have « = 90 x ¢; wherefore, 
+ &e. 
— 5 =180.at x {142 x (90.at)*+ &e. 
But 180@ = 57> = 0414 = < nearly; and 90a = -0207 
2 
= jp nearly; and hence, 
25(2-+)=4 x fl4— x (55)? + &es 
Now, for small differences of temperature, the series on the 
right-hand side may be considered as equal to unit, and then 
we get 95 b p = 1, 
which is no other than Professor Leslie’s formula. The accuracy 
of the Professor’s theory is therefore confirmed for moderate ele- 
vations ; but then it is proved to be equivalent in such cases to 
the more simple law of a uniform decrease of heat, the only dif- 
ference being, that the barometrical pressures are used instead of 
the altitudes to which they belong. In the case of great altitudes, 
and considerable differences of temperature, the series will be no 
longer equal to unit, and the formula will diverge from the theory 
of barometrical measurements. Thus in Gay-Lussac’s ascent, é 
being about 40°, the difference of the two methods will be about 
4° or 5°, or a tenth of the whole, the Professor’s formula being 
farther from the truth. In reality the difference will be greater, 
because it is augmented by the correction for temperature in the 
barometrical formula, which has been neglected in the foregoing 
investigation. It would be easy to supply this defect, but it ap- 
pears hardly necessary. It has been sufficiently proved, that for 
moderate elevations Professor Leslie’s formula is equivalent to the 
law of a uniform decrease of heat, and that in great altitudes 
it 
