28 Remarks on the 
minute of a degree. In order to reconcile the theory with astro- 
nomical observations, the elevation for one degree of depression 
of the thermometer must be diminished by a fifth part, or rather 
more. If, instead of a uniform decrease of temperature, we sup-~ 
pose that the increments of altitude for one degree of difference 
of temperature form an increasing progression, the error of the 
horizontal refraction will be greater than before ; and, in order to 
correct it, the initial rate of the decrease of heat must be made 
still more rapid than in the former supposition. On the other 
hand, if we adopt the opposite law, and suppose that the incre- 
ments of altitude for one degree of the thermometer, form a series 
of decreasing quantities, the horizontal refraction will be less than 
it would be if the initial rate of the decrease of heat continued 
progressively uniform. Thus, while the two first laws are con- 
trary to experience, it may be possible, by making the variation 
of temperature according to the last supposition sufficiently rapid, 
so to correct the excess of refraction arising from the actual de- 
crease of heat at the eartin’s surface, as entirely to reconcile the 
theory with observation. We are indeed in possession of no so- 
lution of the problem of the atmospherical refractions that pro- 
ceeds upon the supposition mentioned 3, but, in the present state 
of our knowledge, the argument is not less conclusive in favour 
of the law, that the heat of the atmosphere decreases in a greater 
ratio than the height increases. 
Professor Leslie, of Edinburgh, has given a precise and mathe- 
matical theory of the variation of heat in the atmosphere. If 6 
denote the height of the mercury in a barometer at the lower of 
two stations, and § the like height at the upper one; then, ¢ be- 
ing the difference of temperature in centesimal degrees, we have 
this relation between the quantities, viz. 
a5 (4). 
This formula was first published in 1811, in ‘the notes to the 
second edition of the author’s Geometry, p. 495. In the article 
Cximare in the Supplement to the Encyclopedia Britannica, 
it appears in a form somewhat different, the ratio of the densities 
at the extremities of the elevation, being substituted for that of 
the barometrical pressures. Strictly speaking, the two ratios are 
not equivalent ; because at the top of the column the tempera- 
ture is always less than it is at the bottom, and the density of a 
mass of air depends both on the pressure and the temperature ; 
but, as in all the examples adduced in the article CLiMaTE, the 
density is estimated by the pressure alone, it seems to have been 
the author’s intention to make no distinction between the two 
formule, 
However 
