BIOGRAPHICAL NOTICE. 



analytical development in powers of m. He mentions also that, many years before, he 

 had obtained the values of the inequalities independent of the eccentricities and inclination 

 to a great degree of approximation, the coefficients of the longitude and those of the 

 reciprocal of the radius vector, or of the logarithm of the radius vector, being found 

 to ten or eleven places of decimals. Adams always preferred to treat the lunar theory 

 as far as possible by means of its special problems; and this was also the method 

 which he followed in his Cambridge lectures. 



In 1878 he published a short paper on a property of the analytical expression for 

 the constant term in the reciprocal of the Moon's radius vector. Plana had found that 

 the coefficients of e 2 and 7" in this term vanished when account was taken of terms in- 

 volving m? and in 3 , and Pontecoulant, who carried the development further, had found 

 that this destruction of the terms in the coefficients still continued when the terms 

 involving m* and m 5 were included. Thinking it probable that these cases in which 

 the coefficient had been observed to vanish were merely particular cases of some more 

 general property, Adams was led to consider the subject from a new point of view, 

 and, so far back as 1859, he succeeded in proving that not only did these coefficients 

 necessarily vanish identically, but that the same held good also for coefficients which 

 were much more general, so that the coefficients of e'e", e'-e'*, &c. j-e'-, y'*e' 4 , &c. were also 

 identically equal to zero. Further reflection on the subject led him in 1868 to obtain 

 a simpler and more elegant proof of the property in question. He also obtained subse- 

 quently, in 1877, some very simple relations connecting the coefficients of e 4 , e 2 7 2 , and </. 

 Of this theorem he says himself that it "is remarkable for a degree of simplicity and 

 generality of which the lunar theory affords very few examples." We thus see that a 

 striking result and one moreover which admitted of being isolated from the rest of 

 the lunar theory was obtained in 1859, but was not published till nearly twenty years 

 afterwards, although in the meantime he had obtained another and more satisfactory 

 proof. This illustrates the disinclination that Adams seems always to have felt to prepare 

 his work for publication ; a disinclination which was mainly due to his desire to obtain 

 a still higher degree of simplification or perfection. The discovery of the additional 

 relations in 1877 shows that his attention was at that time still occupied with the 

 theorem of 1859. 



It may be remarked that Adams's shorter papers deserve more attention than their 

 mere length might seem to entitle them to, not only because they frequently consist 

 wholly of results derived from laborious researches, but also because they afford glimpses 

 of the nature and extent of the work with which he was occupied. For forty-five 

 years his mind was constantly directed to mathematical research relating principally to 

 astronomy; and it is evident that what he had accomplished is very inadequately 

 represented by what has been published. It is also noticeable that so few of his 

 papers should have appeared quite spontaneously: it frequently happened that he was 

 incited to give an account of something which he had done himself probably years 

 before by the publication of a paper in which the same ground was partially covered by 

 another investigator, and in several cases he was called upon to correct misapprehensions 

 which were leading others astray. 



As already stated, there can be no doubt that he constantly allowed himself to 

 postpone the immediate publication of his researches, with the intention of effecting 



