Note 148 — Chapter XI · GRAVITATIONAL ASTRONOMY IN THE 18TH CENTURY.
Reading edition
If n, n′ are the mean motions of the two planets, the expression for the disturbing force contains terms of the type
= sin (np ± n′p′) t,
cos
where p, p′ are integers, and the coefficient is of the order p⁓p′ in the eccentricities and inclinations. If now p and p′ are such that np⁓n′p′ is small, the corresponding inequality has a period 2π∕(np⁓n′p′), and though its coefficient is of order p⁓p′, it has the small factor np⁓np′ (or its square) in the denominator and may therefore be considerable. In the case of Jupiter and Saturn, for example, n = 109,257 in seconds of arc per annum, n′ = 43,996; 5n′ - 2n = 1,466; there is therefore an inequality of the third order, with a period (in years) = 360°∕1,466″ = 900.