ps — vr + 
i s \ 
2 ( m—t ) ps ~ ) , Z ’ t ^ ie va ^ ue f ract i° n > if w e neglect the subsequent terms, becoming 
3.41 ; and this expression is sufficiently accurate for calculating the whole refraction, except for altitudes of 
a few degrees. Now the fluxion of p — v — 4. 
1 ss \ rr 
2 (w — t)p 2 } ss 
rr l dm — d^ d p\ 
which we may call p — v — + 
/ 1 ss\rr I v ft ss\ 2 r\ rr I dm — d^ d/>\ _ . .... 
1 ~ — ’ !s dp — — — dr — 1 H — — , the coefficient of dr being 
\ w 2 I ss r \ s T \ to 2 I ss I ssw \ in — tp\ 6 
rr t dp 
rr 
SSIU 
dm — d t 
in — t 
being 3.41, and m — t, on 
this supposition, 519. The proportional variation of p, or — , will be for every degree that the ther* 
P 
766 
= .003. 
mometer varies from co°; and — 1 being also -ri K , — ’ n ■■ 
3 m 6 5 m—t 
will be 
The variation of t 
519 x 500 
can only be determined from conjecture; but supposing the alteration of temperature to cease at the height 
of about 4 miles, it must increase, with every degree that the thermometer rises at the earth’s surface, about 
==.004. The alterations of the barometer will affect^* 
d t 
dt 
247 
■3-L5, and — being ^3, — — will be 
t s 120 ’ m — t 519 x 120 
only, being -Ay for every inch above or below 30. It is evident, since m ~ , 395 % X $280 x 12 ^ beine: 
13.57 b d ’ 6 
the height of the barometer, and d the bulk of air compared to that of water, that m must diminish, as well 
as p, when the temperature increases ; and the correction for t being subtractive, the three variations will co- 
operate in their effects ; but the proportion will be somewhat different from that of the simple densities. If 
we preferred the expression derived from Professor Leslie’s hypothesis, we should merely have to substitute 
— n for — ~~i > anc ^ the variation depending on the law of temperature would become about as great. 
It must however be limited to such changes as affect the lower regions of the atmosphere only, its “ argu- 
ment” being the deviation from the mean temperature of the latitude ; but even in this form it cannot be sa- 
tisfactorily applied to the observations at present existing ; although it appears to be amply sufficient to ex- 
plain the irregularities of terrestrial refraction, as well as the uncommon increase of horizontal refraction 
in very cold countries : and we may even derive from all these considerations a correction of at least half a 
second, or perhaps of a whole second, for the sun’s altitude at the winter solstice, tending to remove 
the discordance, which has so often been found, in the results of some of the most accurate observations 
of the obliquity of the ecliptic. 
T. Y. 
