430 PROFESSOR EVERETT ON A METHOD OF REDUCING 
v=A,+P, sin (27+E,) +P, sin (4-5,+E:) +&0. 
the general term being P, sin (2nsy, +E,) 
Where v is the temperature at the line ¢ from the epoch of reckoning, T is the 
periodic time (a year), 7 is the ratio of the circumference of a circle to the dia- 
meter, and A», P,, P,, E,, E,; &c. are constants, whose value must be found from 
the temperatures observed. 
It is evident from the form of the expression that A, is the mean temperature 
of the whole year, and that the maximum and minimum values of any subsequent 
: t ‘ 
term P, sin ( 2naq,+E,) are +P, and —P, respectively. As the range of value 
through which any term passes depends only on the coefficient P,, this coefficient 
is styled the amplitude of the term, being in fact equal to half the range. 
The epochs of maxima and minima will be very different for different terms. 
The term involving P, has one maximum and one minimum in the year. The 
term involving P, has two maxima and two minima, and generally the term in 
P, has 2 maxima and ” minima in the year, its values going through their entire 
cycle in the “th part of a year. The term in P, is therefore called the annual 
term, and the term in P, the half-yearly term. 
The maximum and minimum values of a term will occur earlier or later in 
the year, according to the value of the constant E,, any diminution in the value 
of E, being the same thing as a retardation of the maxima and minima. Suc 1 
retardation is called retardation of phase. Tt is the diminution of amplitude and 
retardation of phase between the terms for thermometers at different depths, that 
afford the means of deducing the conducting power of the soil. 
In order to find from the observed temperatures the values of the constants 
in expression (1), we must make use of the equivalent expression— 
v=A,+ (A cos Qan+B, sin 2m.) + (4, cos qn% +B, sin 4, r) +8. 
T yh 
the general term being (4, cos Qn +B, sin ns) . . Ga 
and then by applying the equations of transformation 
2. BR? An 
J A? +B, =P,,7;7-t0E 9. = 
we shall obtain the values of the constants in expression (1). . 
In the calculations performed for Professor Tuomson, the expressions wer¢ 
carried as far as the terms depending on A, and B,. I have carried them only ai 

