446

of r to be 1, and A to be the corresponding value of v : then th eA

area = I X": and from Kepler’s Law of the equal descripti° Dof areas

r* v A

▼ <n

whence

and consequently, in order to compute r, we must be able Wdetermine A and v.

A is the angle corresponding to the mean distance 1, an ^’therefore, in an ellipse of very small eccentricity (and such a"ellipse is the solar orbit) is nearly, the mean ol the greatest an^least angular velocities, or has for its measure half the sumthe angles respectively described, in twenty-four hours, at theperigean and apogean distances : which angles, as it has bee"already explained, aie the daily increases of the Sun’s longitude*'Now, by examining the longitudes, it will be found that the#greatest daily difference takes place at the end of Decemb er 'their least at the beginning of July : the value of the former is

1° l' 9"94

of the latter.57 11.48

so that their mean is 59 10/7

-y/C-

and, if we take this latter angle to represent the value ofwe have

'59' 10".7^

In order to determine v for any particular day, we must fi ,s |take the difference of the Sun’s longitudes on the noon of 11day, and on that of the day succeeding, and if (which will aln>°ever be the case) the interval between the two noons be greaterless than twenty-four mean solar hours, we must, in comp llt, | , f’V, allow for such excess: for instance, let d represent theference of two longitudes of the Sun on two successive nooB 9,and let 24 + x represent the time elapsed, then, very nearly,