xxxvi BIOGRAPHICAL NOTICE. 



very remote ages. The next investigation relating to the subject is by Laplace, who showed 

 that the acceleration could be accounted for by supposing that the transmission of the 

 force of gravitation was not instantaneous, but that the rate of propagation was about 

 eight million times that of light. Some years later, however, Laplace unexpectedly dis- 

 covered the true gravitational cause of the acceleration. While working at the theory 

 of Jupiter's satellites, he remarked that the secular variation of the eccentricity of Jupiter's 

 orbit produced secular terms in their mean motions. Applying this result to the Moon, 

 he found that the secular variation of the eccentricity of the Earth's orbit produced on 

 the Moon's motion a secular term which agreed very well with the value assigned to it 

 by observation; he found also that the same cause produced secular terms in the motion 

 of the Moon's node and perigee. This result was communicated to the French Academy 

 in November, 1787, and the memoir containing the details of the calculation was published 

 in the following year. The Stockholm Academy of Sciences had already proposed in 

 1787 the secular variations of the Moon, Jupiter and Saturn as the prize subject for 1791, 

 but no essays being sent in, the prize was adjudged to Laplace for his memoir published 

 in 1788. 



Laplace's discovery was received with general satisfaction, and the complete ex- 

 planation of so intractable a variation by means of the Newtonian principles, after so 

 many years of fruitless attempt, was an important event in the history of astronomy. 

 The honour of the discovery might very easily have belonged to Lagrange, for the formulae 

 given by him in a memoir published in 1783 would at once, if applied to the Moon, have 

 produced Laplace's result. But Lagrange had found that, in the case of Jupiter and Saturn, 

 these formulae gave nearly insensible values, so that he did not extend the investigation 

 to the other planets, or to the Moon, although the latter application would only have 

 involved easy numerical substitutions, much simpler than those required for the principal 

 planets. 



In 1820, at the instigation of Laplace, the lunar theory was taken in hand afresh 

 by Plana and Damoiseau, the approximations being carried to an immense extent, especially 

 by the former. Damoiseau calculated the acceleration numerically, and found it to be 

 10"'72. Plana's process was algebraical, and he carried the series, of which Laplace had 

 only calculated the first term, as far as to quantities of the seventh order. By reducing to 

 numbers the twenty-eight terms of this series he found 10'' - 58 as the complete value of 

 the acceleration, the first term, which alone had been included by Laplace, giving 

 10"'18. Subsequently Hansen gave the values 11"'93 (1842), 11"'47 (1847); and in his 

 tables published in 1857 he used the value 12"18. It does not seem clear, however, 

 to what extent these values are to be regarded as theoretical determinations. 



Thus when Adams published his memoir in the Philosophical Transactions for 1853 

 no suspicion had arisen that Laplace's discovery was not absolutely complete, and that 

 the question of the acceleration had not been finally set at rest. In this short paper of 

 only ten pages Adams showed that the condition of variability of the solar eccentricity 

 introduces into the solution of the differential equations a system of additional terms 

 which affect the value of the acceleration. He found that the second term of the series 

 on which the acceleration depends was really equal to ^ff^m 4 , instead of z^-m', as found 

 by Plana. The former is more than three times as great as the latter, and the amount 

 of the acceleration is greatly decreased by the correction of this error. For some time 



