24 Prof. Challis on Newton's 



differential equation involving an unknown expression or 

 function of a variable quantity. This was Newton's most 

 important discovery, which his contemporaries, although, as 

 he says, they were acquainted with the law of the inverse 

 square, in vain attempted to make. Part (HI.) is composed 

 of determinations of unknown expressions by virtual solutions 

 of differential equations, together with physical inferences 

 drawn from the solutions, and comparisons of these results 

 with facts of observation. In short, in analytical language 

 Newton effected the solution of a differential equation of the 

 second order between two variables, whereby he not only ac- 

 counted for Kepler's laws, but also demonstrated, a posteriori, 

 by the comparison of calculation with observation, the hypo- 

 thesis of the inverse square and that of Galileo's Theorem. 



The course of inquiry by which the science of physical as- 

 tronomy has been established forms a paradigm to be followed 

 in the more advanced department of physical research embra- 

 cing the theories of light, heat, force of gravity, electricity, 

 galvanism, and magnetism. Here also Newton has pointed 

 out the way of proceeding, having stated in his Third Rule 

 of philosophizing, and at the end of the Third Book, the 

 primary hypotheses on which such research must be founded. 

 These constitute Part (I.) of this new stage of physical philo- 

 sophy. They consist of two kinds, namely, hypotheses abso- 

 lutely true, and hypotheses which admit of being proved to be 

 true by comparison of mathematical results derived from them 

 with facts of observation. To both kinds Newton's dictum, 

 " hypotheses non Jingo " (I do not arbitrarily make hypotheses), 

 applies. The several hypotheses may be stated as follows. 

 The " least parts " (atoms) of bodies have only sensible -qua- 

 lities, as form, magnitude, mobility, and intrinsic inertia. 

 These are absolute and necessary qualities, inasmuch as their 

 existence is immediately conveyed to us by our senses, and 

 apart from them we cannot conceive of matter. Newton adds 

 the quality of " impenetrability " relative to the least parts, 

 which signifies that they admit of no change of form or mag- 

 nitude. In fact, they would otherwise not be conformable to 

 that part of the enunciation of the Third Rule, which states 

 that the ultimate qualities of bodies cannot be increased and 

 diminished (intendi et remitti nequeuni). Moreover he does 

 not allow the possibility (or conceivableness) of one body 

 / ( acting upon another without intervening substance ; and in 

 the scholium at the end of the Principia he adverts to the 

 agency of a certain " very subtle " medium (the asther), per- 

 vading the grosser bodies. On adopting these Newtonian 

 "principles for the purpose of extending the boundaries of phy- 



