By combining the two proportions already given, we have by logarithms:
| M. R. V. minor | = | 3256 Log. | 3.512683 |
| M. S. D. of moon | = | 940″" | 2.973128 |
| P. S. D. of earth | = | 3950 A. C. | 6.403403 |
| Radius | 10.000000 | ||
| T. S. D. of moon | 885″.5 A. C. | 7.052811 | |
| Log. Cosine arc AR | = | 28° 57′ 3″ | 9.942025 |
As the only variable quantity in the above formula is the “True” semi-diameter of the moon at the time, we may add the Constant logarithm 2.889214 to the arithmetical complement of the logarithm of the true semi-diameter, and we have in two lines the log. cosine of the arc AR.
We must now find the arc RK equal at a maximum to 2° 45′. The true longitude of the moon’s node being 79° 32′, and the moon’s longitude, per Nautical Almanac, being 58° 30′, the distance from the node is 21° 2′, therefore, the correction is
To find the correction for displacement.
| True longitude | of sun at date | 100° | 30′ |
| " | of moon" | 58° | 30′ |
| Moon’s distance from quadrature | 48° | 0′ | |