J. D. Everett on Reducing Observations of Temperature. 27 
The last edition of the Encyclopaedia Britannica has an article 
on “ Meteorology” by Sir John Herschel, in which the attention 
of meteorologists is called to the great practical utility of the 
ode of reduction above described, which has been for some 
time known but has been little used. The formule which Sir 
John Herschel there gives for deriving the values of the con- 
stants from monthly means, are in reality identical with those 
above given, though the identity is not at first sight obvious. 
He asserts that the values thus obtained are the most probable 
values, as derived from the application of the method of least. 
Squares. Also that “it is a peculiarly valuable property of these 
expressions, that if the approximation be stopped at an 
m,.... then should it be considered afterwards desirable to 
carry it a term further, .... it is not necessary to recompute the 
former coefficients, their values remaining unaltered.”? 
Instead of using the temperatures of 12 equidistant days, as 
the basis of calculation, there are obvious advantages in employ- 
ing the mean temperatures of the 12 months which compose the 
year; but it will be necessary to apply a correction to the results 
thus obtained ; for it is not true, even on the average of a long 
Series of years, that the mean temperature of a month is the 
Same as that of its middle day. We shall proceed to investigate 
© hature and amount of the correction which must be applied, 
deducing by the way some interesting relations between the mean 
and instantaneous values of variable elements. 
Y 
Let OACX be the curve which represents the variations of 
temperature through the year. Let the ordinates AB and CD 
represent the temperatures at the beginning and end of an inter- 
val of time represented by BD. It is obvious that the mean 
temperature of this interval will be obtained by dividing the 
area ABCD by the distance BD. 
mperature of : ponth 
been applied (unknown to me) by Professor (now dese J. D, Forbes, in a paper 
read March 25th, 1860, (Trans. R. S. E, vol. xxii, Part I!) 
remark that the correction has not usually been made. But the method there em- 
roximate ar different principles from that 
Ployed w; 
d gg only approxima: was based on 
