140 
THE REV. W. WHEWELL ON THE SOLAR INEQUALITY 
A 0' = 
dt . , 
* . -n A h 
1 + t 2 ‘ dh 
h' sin 2 (<p — a) . , 
= — h 2 + hi* + 2 h JO cos 2 (<p - «) * A 
Hence for a given value of A h, that is, for a given month, A O' goes through a cycle 
which has a minimum and a maximum, when cos 2 (<£>— a) = — + ^, 2 . If = 3, 
which lias been found to be nearly the value by other phenomena, the two values of 
2 (<p — a) are 144° and 216°, or 10 h and 17 h nearly; and if in this case, a be — l 11 30 m , 
the maxima and minima will agree with <p = 3 h 30 m , p = 7 m 0 m , which appears best 
to represent the phenomena. 
20. After drawing the lines described in Art. 18, I drew interpolated curves for the 
hours l h 30 in , 2 h 30 m , 3 h 30 m , and 5 h 30 m , 6 h 30 ni , 7 h 30 m ; the general agreement of the 
course of the interpolated and the original curves appeared to me to be such as to show 
that the errors arose from a solar inequality, following in its general changes the law 
given by the equilibrium-theory. I have given the corrections upon this supposition in 
Table (C. T.). The displacement of the zero points and maxima, and the want of 
proportionality in the maximum values, which appear in some of the lines, I have ad- 
mitted, because such modifications may arise from my not having got rid of the whole 
of the non-periodical effect. Such irregularities may also arise from there being still 
some vestige of the lunar declination correction not got rid of by the processes which 
I have employed : but this, if it exists, must be very small, and I do not think there 
can be any doubt as to the general form of the solar correction of the time. I have, 
however, abstained from filling up the Table, as not thinking my present materials 
sufficient to enable me to do so with any confidence. 
