PROFESSOR FORBES ON THE CLIMATE OF EDINBURGH. 347 
56. The greatest value of this correction of the numbers in the preceding 
table, in order to obtain the curve of daily mean temperature, is about 0°15. 
As it will only be sensible in the second term of the equation of the annual curve, 
and as it tends to increase its co-efficient, this latter, instead of 10°-83, becomes 
10°98; and if we farther modify the angular constants of Art. 52, so as to 
adapt them to the beginning of the year as an origin, instead of the middle of 
January, the formula becomes (# being the distance of any day of the year from 
the beginning, in angular measure)— 
y=46°88—10°-98 sin (w + 68° 28’) + 0°96 sin (Qu + 22°). 
57. If we consider the two first terms only of this formula, the hottest day 
will be the 23d July; if all three terms, it will be the 27th July. The coldest 
day in the former case would be the 22d January, or in the latter, the 17th 
January. The effect of the third term is therefore to shorten the period of 
declining temperature by about six days, and to increase the period of rise by the 
same quantity. The days corresponding to the mean temperature of the year 
shown by the geometric curve are the 28th April and the 18th October. The 
temperature is therefore above the mean for 173 days, and below it for 182 days. 
58. We next proceed to compare this equation with the annual curve in 
detail, as derived from Mr Apte’s forty years’ observations. 
which the monthly mean is to be increased, in order to make it coincide with the temperature of the 
middle day of the month. § is the centre of gravity of the daily temperatures lying in the arc 
BC. Considering these daily temperatures as equally heavy points distributed uniformly with respect 
to a double ordinate BC parallel to the tangent at 6, we have by the properties of the centre of gravity 

2 
So ea 
. oa. : 
oe. : where the equation to the parabola is y2=2aa, and where the weight of an indi- 
p.dy 
2 
_ vidual observation is p. Hence we have po=-— ==, where zis the abscissa 6 b’ intercepted by 
the chord or double ordinate BC. In like manner wa=1aa’ and ye=4icc’. But a, c, the points 
representing the middle of the preceding and following months, are 60 days apart, while B and C 
are only 30 days apart. Therefore 1D=4bb’ and b= ,bD, which is equal (neglecting small 
quantities) to very nearly 6D’. So that the required correction is found by increasing the 
co-ordinate of temperature expressed by the periodic part of the equation in the text (+ or — as 
the case may be) at the middle day of each month by 51, of the difference between the mean tempera- 
ture of the month and the average of the temperatures of the preceding and following months. 
VOL. XXII. PART II. 4U 
