934 



SCIENCE 



[N. S. Vol. XXV. No. 650 



large. The trustees of the Carnegie Institu- 

 tion early recognized the fact that similar 

 opportunities were needed in the United States 

 for puhlieations which the scientific societies 

 are too poor to undertake, and which, for a 

 business firm, would simply mean a gift to 

 education. The subject of this article is one 

 of the earliest projects of the institution; its 

 successful completion gives reason to hope 

 that it may be the forerunner of others on the 

 same lines. 



The memoirs of Dr. G. W. Hill occupy over 

 seventeen hundred pages arranged in four 

 quarto volumes. Of these just one third (Vol. 

 III.) are taken up by his well-known theory 

 of Jupiter and Saturn. In his preface to this 

 work Dr. Hill says: "It was desired to 

 abandon the use of the antiquated tables of 

 Bouvard, and it appeared uncertain when 

 Leverrier would publish his. The plan, there- 

 fore, was to form theories of Jupiter and 

 Saturn which would be practically serviceable 

 for a space of three hundred years on each 

 side of a central epoch taken near the center 

 of gravity of all the times of observation; 

 theories whose errors in this interval would 

 simply result, not from neglected terms in the 

 developments, but from the unavoidable im- 

 perfections in the values of the arbitrary con- 

 stants and masses adopted from the indica- 

 tions of observation." How well he succeeded 

 is now beginning to be seen. The observa- 

 tions which were used in forming the tables 

 ended with the year 1888. In memoir 76, a 

 comparison between the results of theory and 

 observation is given from 1889 to 1900 which 

 shows that the mean error for each year in 

 right ascension and declination scarcely ex- 

 ceeds one second of arc. And further, unliko 

 the comparisons from the majority of astro- 

 nomical tables, the errors show no tendency to 

 increase steadily as time goes on. 



But the subject which is more closely as- 

 sociated with Dr. Hill's name is the theory of 

 the moon's motion. It is difficult to overesti- 

 mate the services which he rendered by the 

 publication in 1878 of the one memoir, 'Re- 

 searches in the Lunar Theory.' Before this 

 time there had been a growing feeling amongst 

 mathematicians that the motions of the moon 



and planets, as subjects for investigation on 

 theoretical lines, had been worked out and 

 that there was little to attract a student unless 

 he wished to take up the practical side by more 

 accurate computations of existing develop- 

 ments. This false view of the situation was 

 corrected in a single step, although it was 

 reserved for Poincare to show the full im- 

 portance of the advance which had been mads 

 by his development of Hill's idea of the 

 periodic solution. But the advance from the 

 point of view of computation was not far 

 behind, since this paper also laid a basis for 

 the accurate calculation of the moon's motion 

 without the excessive labor which the earlier 

 theories would have demanded. The newly 

 awakened interest in celestial mechanics is 

 made sufficiently evident by the fact that over 

 twenty treatises and text-books have appeared 

 during the last thirty years and these quite 

 apart from scores of original memoirs. 



Connected with this paper was the memoir 

 on the motion of the perigee of the moon, in 

 which the idea of a determinant with an in- 

 finite number of elements to solve an infinite 

 system of linear equations was introduced and 

 used as a powerful instrument for accurate 

 computation. In the introduction written by 

 Poincare and printed in the first of the four 

 volumes the latter says : " Avait-on le droit 

 d'egaler a zero le determinant de ces equa- 

 tions ? M. Hill I'a ose et c'etait la une grande 

 hardiesse; on n'avait jamais jusque-la con- 

 sidere des equations lineaires en nombre 

 infini; on n'avait jamais etudie les deter- 

 minants d'ordre infini ; on ne savait meme pas 

 les definir et on n'etait pas certain qu'il fut 

 possible de donner a cette notion un sens 

 precis." * * * "Hais il ne suffit pas d'etre 

 hardi, il faut que la hardiesse soit justifiee par 

 le succes. M. Hill evita heureusement tous 

 les pieges dont il etait environne, et qu'on ne 

 dise pas qu'en operant de la sorte il s'exposait 

 aux erreurs les plus grossieres; non, ei la 

 methode n'avait pas ete legitime, il en aurait 

 ete tout de suite averti, car il serait arrive h 

 un resultat numerique absoliunent different 

 de ce que donnent les observations." But is 

 there not something more than the mere 

 numerical agreement? Does not intuition. 



