214 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 
The dates in the preceding Table are the mean of the corresponding days of 
observation during the five years. More correctly they ought to be about half 
a-day earlier; thus, the temperature of February 4 belongs to February 3°5, or 
to midnight of the 3d, instead of the 4th at noon, and so of the others. 
The practice of denoting periodic variations of temperature by a series of the 
form 
Yo= A+B sin (n+ 6) + C sin (Q2n+c) + &e. 
(where y, is the temperature corresponding to the fraction of the year denoted 
by x, and A, B, C, 6, c, are constant quantities), has prevailed in Germany at 
least since the time of Lamprert.* I have thought it worth while to compute 
the equations for each of the 12 curves, so as to facilitate comparison with the 
results of QUETELET} and others. But my method of proceeding has been some- - 
what different from his. I sketched very carefully interpolating curves through 
the curves of Plate VIII., so as to diminish their remaining irregularities, and 
having divided the horizontal space corresponding to a year into 12 equal parts 
(each of which may be represented by the space of 30°, the whole period of varia- 
tion being 360°), I measured and inserted in a table the ordinates of the inter- 
polated curve corresponding to these points; and with the aid of these ordinates, 
the equation to the curve was calculated by the aid of the tables given at the end 
of the second volume of Dove’s Repertorium. The results were as follows :—The 
first term is of course the mean temperature of the year, which has been taken 
from Table V. 
TABLE XVI. CONTAINING THE EQUATIONS TO THE ANNUAL CURVES. 
3 FEET. 
Observatory, y,=45°49 — 7°39 sin (n . 30°+ 43°) + 0°362 sin (n . 60° + 29°) 
Ex. Garden, y,=46-13—9-00 sin (n . 30°+49°) + 0°737 sin (n . 60°+ 63°) 
Craigleith, y,=45:88— 8°16 sin (n . 30°+47°) +0°284 sin (n . 60° + 34°) 
6 FRET. 
Observatory, y, =45°86 — 5:06 sin (n . 30°+ 28°) +0.433 sin (n. 60°+ 7°) 
Ex. Garden, y, =46'42—6°66 sin (n. 30°+ 29°) +0°501 sin (n.60°+ 5°) 
Craigleith, y,,=45-92—6-16 sin (nm . 30°+36°) +0.368 sin (n . 60° + 340°) 
12 FEET, 
Observatory, y, =46°36 — 2-44 sin (n . 80°+ 344°) +0:075 sin (nm . 60° + 330°) 
Ex. Garden, y, =46-76— 3°38 sin (n . 80°+ 348°) + 0-280 sin (n . 60°+ 319°) 
Craigleith, y,=45°92—4-22 sin (n. 30°+4 13°) 
24 FEET. 
Observatory, y,=46°87 — 0°655 sin (n . 30°4+ 85°) 
Ex. Garden, y, = 47°09 —0°920 sin (n . 30° + 275°) 
Craigleith, y,=46-07—1-940 sin (n . 30 + 327°) 

The following table contains the experimental ordinates, and those obtained 
from the preceding equations. The coincidence would have been somewhat 
closer had the mean of the 12 equidistant ordinates been taken for the mean tem- 
perature (A), instead of the mean of the entire observations. 
* Pyrometrie, § 675. t+ Ann. de l’Observatoire de Bruxelles, iv. 169. 

