32 Professor J. D, Everett's Description of a Method 
through all values from 0 to 22, so that sin (@ + e,) goes 
through all values which a sine can possibly have. 
Our unit of length must be taken, such that the straight 
line KM = 22, where = is 3:14159, &e. 
Then if O be the origin of co-ordinates, ON is a, and KN 
is e,. The maximum ordinate QT is a,, and corresponds to 
that value of # which makes # + e, = 3 
When the annual curve of temperature is compared with a 
simple harmonic curve, 27 must be taken to represent the 
length of the year, and the portion KQLSM of the curve 
will represent one year’s temperature, the point K corre- 
sponding to the vernal mean, @ to the summer maximum, L 
to the autumnal mean, S to the winter minimum, and M to 
the vernal mean again. (By vernal and autumnal mean are 
here meant the days whose mean temperature is the same as 
that of the year.) 
Definition 2—By a harmonic series is meant a series of 
the form a, + a, sin (w + e€,) + a, sin (2a + e,) + a, (sin 
3x + e,) + &e. The quantity 27 + e, goes through all 
values between O and 22, while w goes through all values 
from 0 to +; and since z represents half a year, the term a, 
sin (22 + ¢,) will go through its cycle of values in that period. 
It is therefore called the half-yearly term. 
The term a, sin (3a + e,) is the third-yearly term, and 
goes through its cycle of values in one-third of a year; and so 
on for the other terms. 
The constants a, a, a3, &c., are called the amplitudes of the 
respective terms, and the constants e,, ¢€,, €,, &c., the epochs. 
A little reflection will show that if the epoch of a term receive 
a small increase, the term will take its maximum just so much 
earlier. 
Theorem I.—If a simple harmonic curve be represented by 
the equation y = a sin a, the area intercepted between two 
ordinates, whose mutual distance is given, varies directly as 
the length of the ordinate drawn midway between them. (In 
the annexed figure, the area PQRS varies directly as TN. 
Areas below the axis of a must be considered negative). 
Proof—Let the abscissa of N be a, and let the given dis- 
