RECENT STUDIES TN GRAVTTATION.'' 



By Prof. John H. Poyxtixg. D. Sc. F. R. S. 



The studios in oravitatioii which I am to describe to you this evening- 

 will j)erhaj)s fall into l)etter order if I rapidh' run over the well-beaten 

 track which leads to those studies, the track tirst laid down by 

 Newton based on astronomical observations, and only luade tirmei- and 

 broader by every later observation, 



I may remind you. then, that the motion of the planets round the 

 sun in ellipses, each marking- out the area of its orbit at a constant rate, 

 and each having a year proportional to the square root of the cube of 

 its mean distance from the sun. implies that there is a force on each 

 planet exactly proportioned to its mass, directed toward, and inversely 

 as the square of its distance from the sun. The lines of force radiate 

 out from the sun on all sides equalh', and always grasp any matter 

 with a force proportional to its mass, whatever planet that matter 

 belongs to. 



If we assume that action and reaction are equal and opposite, then 

 each planet acts on the sun with a force proportional to its own mass; 

 and if, further, we suppose that these forces are merelv the sum totals 

 of the forces due to every particle of matter in the bodies acting, we 

 are led straight to the law of g-ravitation, that the force between two 

 masses Mj Mg is alwa3\s proportional to the product of the masses 

 divided by the square of the distance r between them, or is equal to 



G X Mt X Ma 



and the constant multiplier G is the constant of gravitation. 



Since the force is always proportional to the mass acted on, and 

 l)i-oduces the same change of velocity whatever that mass may be. the 

 • hange of velocity tells us nothing about the mass in which it takes 

 place, but only about the mass which is pulling. If, howevei-. we 

 compare the accelerations due to different pulling bodies, as for 

 instance that of the sun pulling the earth with that of the earth pull- 

 ing the moon, or if we compare changes in motion due to the different 



"From Proceedings of the Royal Institution of Great Britain, Vol. XVI, part 2, 

 November, 1901. Read at weekly evening meeting, Friday, February 2.3, 1900, His 

 Grace the Duke of Northumberland, K. G., F. S. A., president, in tiie chair. 



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