PRESIDENTIAL ADDRESS SECTIOX A. 37 



or by an alteration of the physical properties of space. The law 

 of Newton explains it by a direct action. 



This law is a consequence of the principles of mechanics of 

 ■Galileo and Newton himself. The principle of inertia introduces 

 the notion of force in all movements that are not uniform and 

 Tectilinear. So it is necessary to assume the existence of a force 

 directing celestial bodies. 



By Ptolemy the movements of the celestial bodies were 

 explained by a network of circular orbits, because circumference 

 was regarded as the noblest and 7nost perfect of lines and was, 

 therefore, the way in which a free body moved. 



It may be said that Ptolemy also created a principle of 

 inertia which differs from the principle of Galileo as being circular 

 instead of rectilinear. 



In the law of Newton, force appears as explaining curvature. 

 If mechanics -yvere based on the principle of Ptolemy instead of 

 the principle of Galileo, force would appear as explaining the 

 changes of curvature. 



We would have then a law of the planetary movements 

 .different from Newton's law, but it is easy to see that such a 

 law would be more complicated. 



As to that law we might say, as we say about Newton's law, 

 that it is not possible to deny the influence of a body on the 

 movement of another ; but how is that influence exerted ? 

 Apparently, as the law states; really, we do not know. 



Indeed, we never measure forces; what we observe are their 

 consequences, i.e., acceleration or equiLbrium, in all cases, 

 movement. The principles of mechanics give us the standard for 

 this measurement. We measure movements by comparison with 

 a standard inovement we name rectilinear and uniform, as a 

 merchant measures the length of a piece of cloth by comparing 

 it with the length of a bar he names metre or yard. 



The study of mechanics might be made without the intro- 

 duction of the notion of force. This notion is, however, useful 

 because it facilitates that study and is necessary when Me deal 

 with changes of energy, that is, when we have to relate heat, 

 electricity, etc., to movement. 



When apparatus and methods of observation were improved, 

 it was recognised that the law of Newton did not altogether 

 explain the observed motions. It was the planet Uranus which 

 presented the greatest irregularities. Nobody, however, doubted 

 the accuracy of the law, and these irregularities were ascribed to 

 some unknown body. Acti)ig on this assumption, Adams and 

 LeveiTier discovered, by calculation, the planet Neptune. 



But other bodies still present irregularities. Outstanding 

 examples are the Moon and Mercury. In explanation of these 

 irregularities, it was necessary to put aside the accuracy of the 

 law, and explanations are many and varied. One of them 's to 

 -alter the exponent —2 of the fundamentrd law, which changes 



