May 1, 1903.] 



SCIENCE. 



689 



the inquiries hitherto made into ontology 

 have been pursued on a wholly different 

 plane, and do not seem to have solved any 

 of the real enigmas which the study of na- 

 ture presents. It appears, therefore, in an 

 eminent degree desirable that an attempt 

 shall be made to bring ontological studies 

 into line with physical by ascertaining in 

 what way the scientific study of nature 

 (with which experience shows that the hu- 

 man mind is fitted to cope) stands related 

 to the real events and real existences of 

 which the universe actually consists (but 

 which our human minds find it more diffi- 

 cult to probe). 



The aim of the present paper is, there- 

 fore, to bring ontological and physical in- 

 vestigations into accord by substituting a 

 Copernican for the Ptolemaic point of view 

 of the metaphysician, and by throughoiit 

 foUo'wing up the ontological investigation 

 from the standpoint of the student of na- 

 ture. 



FRIDAY, APRIL 3. 



Morning Session, 10 o'clock. 

 Vice-President Langley in the chair. 

 The DouUe Star System I" 518: Mr. Eric 

 DoOLiTTLE, of Philadelphia. (Intro- 

 duced by Professor M. B. Snyder.) 

 The Constant of Aberration: Professor 

 Charles L. Doolittle, of Philadelphia. 

 The Degree of Accuracy of the Newtonian 

 Law of Gravitation: Professor Ernest 

 W. Brown, F.R.S., of Haver ford, Pa. 

 Two bodies attract one another inversely 

 as the square of the distance, that is, if 

 the distance be halved the force is increased 

 four times; if the distance is divided by 

 ten the force is increased one hundred 

 times. This is the Newtonian law of 

 gravitation. The moon, earth, sun and 

 planets all should obey this law, which was 

 discovered by- Isaac Newton in the seven- 

 teenth century. 



How far do the bodies obey it? The 



most sensitive is the moon. We are able 

 to observe its motions so accurately and 

 predict its places with such unfailing cer- 

 tainty by means of this law that we can 

 scarcely have much"doubt that it is correct. 

 But, nevertheless, there are some small 

 deviations, and the question is whether 

 these deviations are due to errors in the 

 calculations of astronomers or to some- 

 thing wrong in the law itself. 



Hansen's theory of the moon's motion 

 has been accepted up to the present, but 

 there are still some small differences be- 

 tween his theory and observation. Two 

 at least of these have been unexplained in 

 the periods of revolution of the perigee 

 and node. My calculations have shown 

 that the differences are due to errors in 

 Hansen's theory and that on a correct 

 theory they do not exist. Thus it appears 

 that Newton's law is accurate to one mil- 

 lionth per cent. ! It is by far the most 

 accurate physical law known and perhaps 

 the most striking evidence of the fact that 

 our existence and surroundings are not the 

 result of chance. 



New Applications of Maclaurin's Series 

 in the Solution of Equations and in the 

 Expansion of Functions: Professor P. 

 A. Lambert, of Bethlehem. (Introduced 

 by Professor C. L. Doolittle.) 

 In an equation of any degree, numerical 

 or literal, f{y) ^0, introduce a factor x 

 into several terms. There results an equa- 

 tion f{x, y)=0 which defines y as an 

 implicit function of x. The successive de- 

 rivatives of y with respect to x are now 

 formed, and the values of y and the de- 

 rivatives found when x = 0. An applica- 

 tion of Maclaurin's series gives the value 

 of t/ in a series in powers of x multiplied 

 by factors which depend on the coefficients 

 oi f{x, y) =0. By properly selecting the 

 terms of f{y)^0 into which the factor 

 X is introduced and placing a; == 1 in the 



