O16 PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 
The following method of determining the absolute maxima and minima of 
the temperature curves and the epochs seems to be simpler in its application than 
those hitherto in use. 
Although the temperature-curves cannot be represented, either altogether or 
in great part, by parabolas, the summits may always be represented sufficiently 
accurately by osculating parabolas, which may, of course, be determined from three 
points of the curve, and that with the less error as these three points approach 
more nearly to the point of maximum or minimum sought. In the preceding 
cases, the ordinates of the curve are already calculated for abscissee corresponding 
to every 30°. It is easy to find, by simple inspection of the Tables, between which 
two ordinates the summit of the curve lies. It will necessarily be between those 
having the greatest values (+ or —); or, if there be two ordinates with the same 
value, it must be precisely half way between (supposing the portion of the curve 
to be parabolic). 
Let 7, y”, be the two greatest ordinates (calcu- 
lated by the formula), and let y” be an ordinate half 
way between them (calculated from the Equations, 
Table XVI.) Then the difference of abscisse MN, 
N O, is in this case 15°. Let it be more generally m, 
a number always positive. Let VP be the axis of | 
the parabola whose position is sought; and let its Mi NP 0 
distance from the ordinate y’, or NP be 2 (+ if to the right hand, — if to the 
left). Then, supposing the parabola found, and the tangent to the vertex drawn, 
by the property of the curve, 

a. Mm=MV 
a.Nn=NV 
a.00=O0V- 
where a is the parameter. Or, 
a(V P—y') =(m+2) : : Z (1) 
a(V Pay") =F : 4 : , (2) 
a(V P—y”)=(m— 2)? ; : : (3) 
Subtracting (2) from (1), 
a(y’—y)=m?+2Qm2 ; ; (4) 
Subtracting (2) from (38), 
a(y”—y")=m*—-2mx : : ; (5) 
Making y’—y'=A and y’—y'”=B, and adding together the last two equations, 
a(A+B)=2 m? 
2 m? 
A+B 

a= 
