36
The problem is indeed rendered difficult by theoreticaland practical considerations of much complexity. Butpresenting the problem roughly, we may say that,after careful attention to the observations, we obtainL-f S and L—S, where L is the lunar action and Sthe sun’s ; the first at spring tides, the second atneap tides. Now, the sum of these compound actionsis 2L, and the difference 2S; so that we can infer Lthe lunar action, and S the solar action. These enableus to infer the relation between the moon’s mass andthe sun’s. Newton was led by comparing the resultsof his theory with the observed height of the tides, tothe conclusion that the moon’s mass is 3 -Lgj, the earth’s ,being represented by unity. Laplace was led by theobservation of the tides at Brest to the theory thatthe moon’s mass is A of the earth’s. He considered,however, that this result, although less than Newton’s, >might still be considerably too large, since he judged jthat the height of the tides at Brest might be in- 1fluenced by several local circumstances. It seemsobvious that this method cannot be susceptible ofvery great accuracy, since the figures of the oceanmasses, as well with respect to their horizontal as totheir vertical proportions, render the direct applica-tion of the theory of the tides impracticable.
Another method depends on the circumstance thatthe earth circuits once in each lunation around thecentre of gravity of the earth and moon. Owing tothis circumstance, the earth is sometimes slightlyin advance of, and sometimes slightly behind, her