of an electric fluid 403 



Case 5. Suppose now that a canal opens into the plane Hh as in Case 2, 

 then will matter run into the space EH, and the density will be everywhere 

 the same as without, except in the space EF, where the particles will be pressed 

 close together, the quantity of matter therein exceeding the natural quantity 

 by as much as is naturally contained in the space EC. 



Case 6. Suppose now that a canal opens into the plane Aa, the fluid will 

 have no tendency to run out thereat. 



Case 7. Let us now consider what will be the result if the repulsion of the 

 particles is inversely as some other power of the distance between that of the 

 square and the cube; and first let us suppose matters as in the first case. There 

 will be a certain space, as EF, which will be a vacuum, and a certain space, 

 as FG, in which the particles will be pressed close together; for if the matter 

 is uniform in EH, all the particles will be repelled towards H if there is not a 

 vacuum at E, nor the particles pressed close together at G, but only the density 

 less at E than at H, then the repulsion of space EH at E will be less on [a] 

 particle at E and greater on a particle at H than if the density was uniform 

 therein, consequently on that account as well, as on account of the repulsion 

 of AC a particle at E or H will be repelled towards H, but if the space EF 

 is a vacuum and the particles in GH pressed close together, then if the spaces 

 EF and GH are of a proper size, a particle at F or G may be in equilibrio. 



Case 8. If you now suppose a canal to open into the plane Hh as in the 

 3rd case, some of the matter will run out thereat, so that the whole quantity 

 of matter in the space EH will be less than natural. For if not, it has already 

 been shown that a particle at H will be repelled from A, but the quantity of 

 matter which runs out will not be so much as the redundant matter in AC, 

 for if there was, the want of repulsion of the space EH on a particle at h would 

 be greater than the excess of repulsion of the space AC. 



Case 9. Suppose now that a canal opens into the plane A a as in Case 3; 

 a particle at will be repelled from Dd, but not with so much force as if there 

 had been the natural quantity of fluid in the space EH, so that some of the 

 fluid will run out at the canal, but not with so much force, nor will so much 

 of the fluid run out as if there had been the natural quantity of fluid in EH. 



Case 10. If you suppose matters to be as in the 4th case, then there must 

 be a certain space adjacent to Ee, in which the particles will be pressed close 

 together, and a certain space adjacent to Hh in which there must be a vacuum. 



Case ii. If you suppose a canal to open into the plane Hh, some matter 

 will run into the space EH thereby, so that the whole quantity of matter therein 

 will be greater than natural. 



The proof of these two cases is exactly similar to that of the two former. 



Case 12. If you now suppose a canal to open into Aa, some fluid will run 

 into it, but not with so much force nor in so great quantity as if the natural 

 quantity of fluid had been contained in the space Hh. 



26 2 



