January 2, 1903.] 



SCIENCE. 



I 



partial solutions may illustrate, but will 

 not overcome, the fundamental difficulty. 



The arrangement of our solar system is 

 such that the distances of the planets from 

 one another are very great with respect to 

 their dimensions, and this facilitates very 

 much the determination of their motions. 

 Should two bodies approach very near each 

 other the disturbing force might become 

 great, even in the case of small masses. 

 In the case of comets this condition hap- 

 pens in nature, and the comet may become 

 a satellite of a planet, and the sun a dis- 

 turbing body. In this way it is probable 

 that comets and meteoric streams have 

 been introduced into our solar system. We 

 have here an interesting set of problems. 

 This question is sometimes treated as one 

 of statics, but since the bodies are in mo- 

 tion it belongs to dynamics. Further 

 study may throw light on some relations 

 between the asteroids and the periodical 

 comets. 



The great question of astronomy is the 

 complete and rigorous test of the New- 

 tonian law of gravitation. This law has 

 represented observations so well dm-ing a 

 century and a half that it is a general be- 

 lief that the law will prove true for aU 

 time, and that it will be found to govern 

 the motions of the stars as well as those of 

 our solar system. The proof is cumulative 

 and strong for this generality. It will be 

 a wonderful result if this law is found 

 rigorously true for all time and throughout 

 the universe. Time is sure to bring severe 

 tests to all theories. We know that the 

 law of gravitation is modified in the mo- 

 tions of the matter that forms the tails of 

 comets. There is an anomaly in the theory 

 of Mercury which the law does not ex- 

 plain, and the motion of our moon is not 

 yet represented by theory. The lunar 

 theory is very complicated and difficult, 

 but it does not seem probable that the de- 



fect in Hansen's theory will be found by 

 recomputing the periodical coefficients, 

 that have been already computed by many 

 mathematicians and astronomers, and with 

 good agreement by Hansen and Delaunay, 

 by very different methods. Hansen was 

 a computer of great skill, but he may have 

 forced an agz'eement with observations, 

 from 1750 to 1850, by using a coefficient of 

 long period with an erroneous value. No 

 doubt the error of this theory will be dis- 

 covered. Back of all theories, however, 

 remains the difficulty of solving the equa- 

 tions of motion so that the result can be 

 applied with certainty over long periods 

 of time. Until this is done we shall not 

 be able to subject our law to a crucial test. 

 The constants that enter the theories of 

 the planets and moon must be found from 

 observations. In order to compare obser- 

 vations made at distant epochs, the motions 

 of the planes of reference must be known 

 with accuracy, and also the motion of our 

 solar system in space. As the stars are 

 our points of reference their positions and 

 their proper motions must be studied with 

 great care. This department of astron- 

 omy was brought to a high degree of order 

 by the genius of Bessel, whose work forms 

 an epoch in modern astronomy. The re- 

 cent progress made in determining the 

 positions of the stars in aU parts of the 

 heavens will be a great help to the investi- 

 gations of the future. We must have ob- 

 servatories where accurate and continuous 

 observations are made. Our country is 

 well situated to supplement the work of 

 Europe, and we hope it will never fail 

 to add its contribution to the annals of 

 astronomy. American astronomers should 

 keep pace in the improvements for increas- 

 ing the ease and accuracy of making ob- 

 servations. The spectroscope has given a 

 new element in the motions of the stars, 

 not to speak of the interesting physical re- 



