200 HISTORY OF SCIENCE. 



the sun, whereas the several planets must also by gravitation act upon 

 each other. Hence the orbits cannot be absolutely but only approxi- 

 matively elliptical, and the other Keplerian laws must be also only 

 very nearly true. Now, observation showed that these divergences 

 really existed, and while the greater phenomena furnished a general 

 proof of Newton's theory, these less phenomena of" perturbations," as 

 they are called, contributed confirmatory and more convincing proofs 

 of its absolute correctness. It is true that the accurate investigation 

 of the mutual actions of bodies, such as those of the solar system, is 

 an intricate and difficult one, and the beautiful apparent simplicity of 

 absolute elliptic orbits must be given up for more perplexed paths, to 

 be traced out in detail only by laborious calculations ; yet these per- 

 turbations and intricacies are essential to the truth of the principle of 

 universal gravity, so grand in its own simplicity. The most prominent 

 instance of perturbations presents itself in the movements of our satel- 

 lite, whose elliptical orbit about the earth is disturbed by the action 

 of the sun. The inequalities produced by this course are of sufficient 

 amount to have been noticed even by the ancient astronomers. Newton 

 investigated many of the effects of the mutual actions of the three 

 bodies, the sun, earth, and moon, and although the imperfect data and 

 means within his reach left much for his successors to do in order to 

 reduce the moon's motions to the exact and complete forms which 

 constitute the "lunar theory" of the present time, his results must be 

 regarded as evidence of the unrivalled skill which enabled him to arrive 

 at conclusions very near the truth. 



There is a very common misconception arising from the manner 

 in which the mechanism of the solar system is popularly described. 

 There is doubtless a certain convenience in saying that the moon 

 revolves about the earth in an elliptical orbit, and the earth itself re- 

 volves about the sun in another ellipse, of which the sun occupies one 

 focus. As a matter of fact, however, this is by no means the case, as 

 this mode of presenting the case leaves out of account the reaction 

 referred to in Newton's third law. If the earth attracts the moon, the 

 moon in an equal degree attracts the earth ; and, indeed, the explana- 

 tion of the tides presently to be given turns upon this reciprocal action. 

 The earth is not stationary as regards the moon, but it and our satellite 

 revolve together about their common centre of gravity. This is a point 

 situated in the straight line joining the centres of the two bodies, and 

 at a distance from each centre inversely proportional to the mass of 

 the body. As the earth has about forty times the mass of the moon, 



v the point in question is about six thousand miles from the earth's 

 centre, or two thousand miles above the part of its surface nearest to 



, the moon. Again, it is not the earth which revolves in the approxi- 



\ mately elliptical orbit about the sun, but this common centre of gravity. 



) The centre of the earth is thus obviously six thousand miles within 

 the orbital ellipse at each full moon, and six thousand miles beyond 



