Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/523

   [ 59 ] and in the cae of the planets, always near the double of that equation. THE angle RFA at the upper focus F being known, the angle RSA at the Sun in the other focus, is found by the common rule of Bihop Ward ; viz. the tangent of half the angle RSA, is to be to the tangent of half the angle RFA, always in the given proportion of the perihelion ditance SP to the aphelion di- tance SA. How thee equations are in the everal eccentricities of the Moon's orbit, will appear by the following Table. Eccentr,  E.   S. 0.040     1.23  09 0.045    1.45  13 0.050     2.09  17 0.055     2.36  23 0.060     3.06  30 0.065     3.38  38 0.070     4.14  47

To add one example; uppoe the ec- centricity 0.060, the mean anomaly 30°. The ine of the double of the mean ano- maly, that is, the ine of 60 is to the ra- dius, nearly as 87 to 100; whence, if the equation E = 3'.06", be divided in that                                     propor-