24 J. D. Everett on Reducing Observations of Temperature. — 
In the application of meteorology to agriculture, date of phase 
cannot, without serious error, be overlooked. e earliness of 
crops at one place as compared with another, must necessarily 
depend upon this element as well as upon mean temperature and: 
range, and it will be interesting to ascertain how much of the 
effect is due to each of these causes. 
Thus far we have endeavored to describe in general terms the 
objects and principles of the st method of reduction. 
The remainder of this paper will be devoted to the mathematical 
investigation on which the method rests. 
taking observations of temperature at any place for a suf- 
ficiently long series of years, it would be possible to ascertain 
the average temperature of each day in the year, and if the 
mean daily temperatures thus found were projected into a curve, 
its‘course would be free from those sudden and irregular devia- 
tions which characterize the curve of temperature for any par- 
ticular year. 
Such a curve would admit of being expressed, to any required 
degree of accuracy, by an equation of the form 
y= A,+A, sin (e-LE,)-FA, sin (22--E,)+A, sin (3¢--E,) + dee. 
x and y being the codrdinates of any one point in the curve, and 
» A, E,, &ec. being constants. The coefficients A, A, Aj, 
&c., are the amplitudes of the terms in which they occur, and 
, H, E,, &c. are epochs. The term which involves A, and H, 
attains one maximum and one minimum in the space of a year, 
it is therefore called the annual term. The term involving A, 
and EH, attains one maximum and one minimum in half a year, 
it is therefore called the half yearly term; and in general the 
term A, sin (nz+E,) goes through its entire cycle of values in 
the “th part of a year. We assume of course that a year is rep- 
resented in arc by 27, or the entire circumference. 
For places in the temperate zones the amplitudes of succes- 
sive terms in the above series diminish so rapidly, that for or- 
dinary purposes all terms involving A, and higher coefficients — 
may be neglected. © 
The mean daily temperatures for any single year or for the 
average of a few years are too irregular to admit of being ex- 
pressed with accuracy by any simple formula, but it is possible 
to represent by a few terms of the above series the probable 
curve of annual temperature as deduced from the actual daily 
temperatures even of a single year. It is one object of the Pee 
ent communication to show how this may conveniently be done. 
We shall now proceed to the solution of the following problem. — 
Given the temperatures at twelve equidistant points in the 
year, it is required to deduce the values of the constants in an 
expression of the above form which shall be applicable to them. — 
