346 PROFESSOR FORBES ON THE CLIMATE OF EDINBURGH. 
SECTION 6. On the Form of the Annual Curve of Temperature at Edinburgh, and on its 
Accidental Fluctuations. 
52. The method usually employed to represent the annual curve of tempera- 
ture, is to take the mean temperature of the twelve separate months (each month 
being represented in extent by 30° or one-twelfth of an entire circumference), 
and to express them by a series of the form— 
Yn =A+B sin (80° xn+u,),+C sin (80° x 2n+u,) + D (380° x 3n+ uz), + &e. 
Where y, is the temperature of any month whose number is » (reckoning Janu- 
ary=0, February=1, &c.) Eliminating the constants (by the method given, for 
example, in Dove’s Repertorium, vol. ii. p. 275, or “ Encyclopzedia Britannica” (8th 
Edition), Art. Meteorology, p. 665, we obtain the following numerical formula :— 
Yn =46°-88— 10°83 sin (80n + 83° 28’) + 0°-963 (60n + 52° 8’), + &e. 
(the fourth term is negligible, its greatest value being only 0°-104). 
53. A comparison of this calculation with the observations collected in Table I. 
gives the following results :— 

















TABLE XI. 
Temperature. Beets af 5 Temperature. nga 
Month. Observed. | Calculated. | Calculation. plone Observed. | Calculated. | Calculation. 
January,.....| 8664 | 36-88 | 40:24 | July,......... 5829 | 5840 | +011 
February,....| 87°92 37°84 — 0:08 August,......| 57°49 57°70 + 0°21 
Marchi, 4.33 40°58 40°53 —0:05 September,..) 53°72 53:46 — 0:26 
April ndesucd, S404 44-89 + 0:05 October,......| 47°49 47°35 —014 
Eh ole a ee 50°26 50°30 + 0:04 November,...| 41°17 41°68 +051 
JUNG, soos ix. al (0O'OO 60°45 — 0:20 December,...| 38°57 38°05 — 0°52 



54. Consequently, the mean temperatures of the months are satisfactorily 
represented by the formula. It is evident, however, that the annual curve drawn 
through the mean temperatures of the months will lie somewhat too low during 
the hotter part of the year, and too high in winter; in other words, the inflection 
of the curve will be too small. This arises from the fact that the mean elevation 
of a given number of points, which all coincide with the arc of a curve, will neces- 
sarily fall within the concavity of the curve, and the true curve will be external 
to the curve of the means, especially if the period embraced in the means be so 
considerable as thirty days. 
55. The correction for this (which, I think, has not usually been made) is 
easily found, with sufficient approximation, as shown in the subjoined note.* 
* Let A B CD be four points in the ¢rue annual curve which is sought, and which is assumed 
to be symmetrical on either side. It will be sufficient for a first approximation to assume that these 
points, so far as they are considered at one time, are situated in a parabolic arc, formed by daily 
temperatures horizontally equidistant from one another. The mean temperature of the month BC 
(for example) will lie at 8, and not at 6 in the parabolic arc. In like manner @ and ¥ are the 
tabular averages for the preceding and following months. We want to find the quantity 6b, by 

eee sees SS: Ce SO ee Se eee 
— 
