324 Sir William Thomson on the Ultramundane 



the mutual distance of parallel bars of one of the cages, that the 

 weights of the celestial bodies do not differ sensibly from being 

 in proportion to their masses. 



2nd. They are isolated; so that their progressive movements 

 are necessarily linear. 



3rd. They are so sparsely distributed (that is to say, their 

 diameters are so small relatively to their mean mutual distances) 

 that not more than one out of every hundred of them meets 

 another corpuscule during several thousands of years ; so that the 

 uniformity of their movements is scarcely ever troubled sensibly. 



4th. They move along several hundred thousand millions of 

 different directions, in counting for one same direction all those 

 which are [within a definite very small angle of being] parallel 

 to one straight line. The distribution of these straight lines is 

 to be conceived by imagining as many points as one wishes to 

 consider of different directions, scattered over a globe as uniformly 

 as possible, and therefore separated from one another by at least 

 a second of angle, and then imagining a radius of the globe 

 drawn to each of those points. 



5th. Parallel, then, to each of those directions, let a current 

 or torrent of corpuscules move ; but, not to give the stream a 

 greater breadth than is necessary, consider the transverse section 

 of this current to have the same boundary as the orthogonal 

 projection of the visible world on the plane of the section. 



6th. The different parts of one such current are sensibly equi- 

 dense, whether we compare, among one another, collateral 

 portions of sensible transverse dimensions, or successive portions 

 of such lengths that their times of passage across a given surface 

 are sensible. And the same is to be said of the different currents 

 compared with one another. 



7th. The mean velocities, defined in the same manner as I 

 have just defined the densities, are also sensibly equal. 



8th. The ratios of these velocities to those of the planets are 

 several million times greater than the ratios of the gravities of 

 the planets towards the sun to the greatest resistance which 

 secular observations allow us to suppose they experience. For 

 example, [these velocities must be] some hundredfold a greater 

 number of times the velocity of the earth, than the ratio of 

 190,000 * times the gravity of the earth towards the sun to the 

 greatest resistance which secular observations of the length of 

 the year permit us to suppose that the earth experiences from 

 the celestial masses. 



* To render the sentence more easily read, I have substituded this 

 number in place of the following words : — " le nombre de fois que le 

 firmament contient le disque apparent du soleil." 



