326 Sir William Thomson on the Ultramundane 



vast number of specifications which instructed or indulgent 

 readers do no not require of them. One understands " a demi- 

 mot" and " sano sensu" only familiar propositions towards which 

 one is already favourably inclined. 



Some of the details referred to in this concluding sentence of 

 the appendix to his Lucrece Newtonien, Le Sage discusses fully 

 in his Traite de Physique Mecanique, edited by Pierre Prevost, 

 and published in 1818 (Geneva and Paris). 



This treatise is divided into four books. 



I. " Exposition sommaire du systeme des corpuscules ultra- 

 mondains." 



II. " Discussion des objections qui peuvent s'elever contre le 

 systeme des corpuscules ultramondains." 



III. " Des fluids elastiques ou expansifs." 



IV. " Application des theories precedentes a certaines affi- 

 nites/' 



It is in the first two books that gravity is explained by the 

 impulse of ultramundane corpuscules, and I have no remarks at 

 present to make on the third and fourth books. 



From Le Sage's fundamental assumptions, given above as 

 nearly as may be in his own words, it is, as he says himself, easy 

 to deduce the law of the inverse square of the distance, and the 

 law of proportionality of gravity to mass. The object of the 

 present note is not to give an exposition of Le Sage's theory, 

 which is sufficiently set forth in the preceding extracts, and dis- 

 cussed in detail in the first two books of his posthumous treatise. 

 I may merely say that inasmuch as the law of the inverse square 

 of the distance, for every distance, however great, would be a 

 perfectly obvious consequence of the assumptions, were the 

 gravific corpuscules infinitely small, and therefore incapable of 

 coming into collision with one another, it may be extended to 

 as great distances as we please, by giving small enough dimen- 

 sions to the corpuscules relatively to the mean distance of each 

 from its nearest neighbour. The law of masses may be extended 

 to as great masses as those for which observation proves it (for 

 example, the mass of Jupiter), by making the diameters of the 

 bars of the supposed cage-atoms constituting heavy bodies, small 

 enough. Thus, for example, there is nothing to prevent us from 

 supposing that not more than one straight line of a million 

 drawn at random towards Jupiter and continued through it, 

 should touch one of the bars. Lastly, as Le Sage proves, the 

 resistance of his gravific fluid to the motion of one of the planets 

 through it, is proportional to the product of the velocity of the 

 planet into the average velocity of the gravific corpuscules ; and 

 hence, by making the velocities of the corpuscules great enough, 



