MECHANICAL PHILOSOPHY. 431 



sion of the apogee would necessarily arise from that part of the 

 sun's disturbing force which acts in the direction of the radius- 

 rector of the moon's orbit ; but on calculating the amount of the 

 progression due to this cause, it was found to be only the one-half 

 of that observed. Clairaut, Euler, and D'Alembert, attacked the 

 problem with all the resources of analysis, and their first investi- 

 gations led to a similar conclusion. This remarkable discrepancy 

 between observation and theory was so startling, as to induce 

 Clairaut for a time to doubt the accuracy of the Newtonian law 

 of gravity, and to propose a new and more complex one in its 

 stead ; but he soon after abandoned this idea, and found that the 

 apparent deviation arose from the incompleteness of his approxi- 

 mations. There are few things which tend so strongly to confirm 

 our belief in a law, as when a fact, which at first appears at 

 variance with it, turns out on fuller examination to be one of its 

 necessary consequences ; and accordingly we find that the explana- 

 tion of the progression of the lunar apogee, on the law of Newton, 

 dissipated all remaining doubts as to its truth. 



The complete solution of the problem of the figure of the earth 

 was also reserved for Clairaut. In Newton's determination of this 

 question, the mass was assumed to be homogeneous ; and his method, 

 limited by this hypothesis, was followed up and perfected by 

 Maclaurin. But Clairaut considered the problem generally, and 

 upon any supposed law of change of density ; and the result at 

 which he arrived and which has been distinguished by the name 

 of Clairaut's theorem is as beautiful as it is comprehensive. 



The general methods adopted by Clairaut (and after him by 

 other writers) in the lunar theory were soon found to be appli- 

 cable, with proper modifications, to the determination of the 

 planetary inequalities also. Since all the bodies of the system 

 attract one another, these attractions must cause each to deviate 

 from the elliptical path, in which it would move under the 

 influence of the sun alone ; and the determination of these devia- 

 tions was obviously of the utmost importance in the completion 

 of the theory of the system. The planetary theory, in this 

 enlarged sense, was the next great addition made to physical 

 astronomy, and is due to the united labours of Clairaut, D'Alem- 

 bert, and Euler. 



Bnt among the perturbations of the bodies composing the 

 solar system, there was one wliich, on account of its magnitude, 



