'Electric fluid communicating by canals 401 



repulsion a particle placed at B might be in equilibrium, but one placed at /3 

 could by no means be so. 



So that there is no way by which the particles can be in equilibrium, unless 

 there is a vacuum all round the globe to a certain distance. How the density 

 of the fluid will be affected beyond this vacuum I cannot exactly tell, except 

 in the following case: 



If the repulsion of the particles is inversely as the square of the distance, 

 there will be a perfect vacuum between BDE and /?8e, and beyond that the 

 density will be perfectly uniform, jSSe being a sphere concentric to BDE, and of 

 such a size, that if the matter in BDE was spread uniformly all over the sphere 

 /?e, its density would be the same as beyond it. 



For any quantity of matter spread uniformly over the globe /JSe or BDE 

 affects a particle of matter placed without that sphere just in the same manner 

 as if the whole fluid was collected in the center of the sphere, so that any 

 particle of matter placed without the sphere /J8e will be in perfect equilibrio. 



In like manner if the fluid within BDE is rarer than without, there will be 

 a certain space surrounding the globe, as that between BDE and /JSe, in which 

 the density will be infinite, or in which the particles will be pressed close 

 together, and if the repulsion of the particles is inversely as the square of the 

 distance, the density of the fluid beyond that will be uniform: the diameter 

 of jSSe being such that if all the matter within it was spread uniformly, its density 

 would be the same as without. 



Let a fluid of the above-mentioned kind be spread uniformly through 

 infinite space except in the canal acdef of any shape whatsoever, except that 

 the ends aghb and mden are straight canals of an equal diameter, and of such 

 a length that a particle placed at or d shall not be sensibly affected by the 

 repulsion of the matter in the part gcmnfh, and let there be a greater quantity 

 of the fluid in this canal than in an equal space without. 



Then the density of the fluid in different parts of the canal will be very 

 different, but I imagine the density will be just the same at a as at d. For 

 suppose ab and de to be joined, as in the figure, by a canal of an uniform 

 diameter and regular shape, nowhere approaching near enough to gcmnfh to 

 be affected by the repulsion of the particles within it. If the matter was not 

 of the same density [at a and .d] the matter therein could not be at rest, but there 

 would be a continual current through the canal, which seems highly improbable. 



c. p. i. 26 



