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SCIENCE 



[N. S. Vol. XXXIII. No. 845 



than our individual capacities for encom- 

 passing them. Historically, astronomy 

 and mathematics have been most inti- 

 mately related. In antiquity the roll of 

 the celebrated mastei-s in one of these sci- 

 ences would almost exactly coincide with 

 that in the other; and in more modern 

 times the names of Newton, Euler, La- 

 grange, Laplace, Gauss, Cauehy, Poincare 

 and many others, which are equally hon- 

 ored by both astronomers and mathema- 

 ticians, show how much they still have in 

 common. It is for this reason that in ac- 

 cepting our secretary's invitation to pre- 

 sent a paper before you I have chosen to 

 lay emphasis on these close relations ; and 

 in doing so I apologize only because I am 

 so poorly prepared adequately to treat so 

 worthy a theme. If you will permit the 

 interjection of a purely personal remark, 

 I should like to state that it is not solely 

 because of the close relations of astronomy 

 and mathematics that I have chosen my 

 topic, but because a most fortunate experi- 

 ence has taught me that the lack of sym- 

 pathy, if not of respect, for the efforts in 

 one domain by workers in another is due 

 almost wholly to a lack of acquaintance 

 with them. I refer to the fact that for 

 fifteen years I have been intimately 

 associated with one of the former presi- 

 dents of the American Association, with 

 the present president, and with the vice- 

 president of Section A. The first has 

 taught me how the mind of the nat- 

 uralist works, how vivid and constructive 

 is his imagination, how fertile he is in in- 

 venting hypotheses, how exhaustively he 

 gathers his data, and how impartially he 

 weighs evidence where prejudices easily 

 might have influence ; the second has shown 

 me how keen are the intuitions of the phys- 

 icist, how his quantitative estimates almost 

 rival in accuracy mathematical calcula- 

 tions, and how his marvelous instruments 



increase the delicacy of our senses a mil- 

 lion fold at a single leap, making it un- 

 necessary for us to wait inconceivable ages 

 for their evolution to that degree of per- 

 fection; the third has revealed to me how 

 beautiful are the logical structures which 

 can be built on independent and consistent 

 hypotheses, how keen are the pleasures in 

 establishing all the harmonious relations 

 involved in a mathematical theory, and how 

 great is the satisfaction in the discovery of 

 that which is common and fundamental to 

 many apparently distinct theories. Here 

 I confess my profound and equal respect 

 for all these phases of scientific activity, 

 and my belief that they are all of funda- 

 mental importance. If in my attempts to 

 accomplish something I follow more nearly 

 along the line of one than another, it is be- 

 cause I believe that on account of personal 

 tastes and training I am less likely to fail 

 there than in the others. 



There does not seem to be a disposition 

 on the part of any one to limit the field of 

 activity of the astronomer. He is sup- 

 posed not only to know how to measure the 

 distances, to calculate the motions, and to 

 determine the composition of the heavenly 

 bodies, but also to understand fully those 

 complex factors which produce the weather 

 changes, to be familiar with certain mys- 

 terious forces which bring good or bad 

 luck to an individual, to have reliable data 

 respecting the location of heaven and its 

 antithesis, and to be an expert on the ques- 

 tions of the freedom of the will, the exist- 

 ence of an infinite being, and the immor- 

 tality of the soul. But the matter is quite 

 different in the case of the mathematician. 

 Often he is criticized for busying himself 

 with pure fictions of the mind rather than 

 with the so-called actualities of physical 

 problems. It is no mere passive antagon- 

 ism, for there are many places in these 

 halls to-day where a storm can be raised 



