IO2 Appendix to Preliminary Propositions 



APPENDIX: FROM MS. NO. 5. 



175] As the following propositions are not so necessary towards under- 

 standing the experiment as the former, I chose to place them here by way of 

 appendix. 



PROP. I. Let everything be as in Prop. XXXIV, except that the bodies 

 H and L are not required to be at an infinite distance from the plates of glass; 

 let now an overcharged body N be placed near the glass in such manner that 

 the force with which it repels the column CG towards G shall be to that with 

 which it repels the column EM towards M as the force with which the deficient 

 fluid in DF attracts the column CG is to that with which it attracts EM: it 

 will make no alteration in the quantity of redundant fluid in AB, provided thu 

 repulsion of N makes no alteration in the manner in which the fluid is disposed 

 in each plate. 



For increase the deficience of fluid in DF so much as that that coating and N 

 together shall exert the same attraction on EM as DF alone did before, they 

 will also exert the same attraction on CG as DF alone did before, and conse- 

 quently the fluid in the two canals will be in equilibrio. 



176] COR. In like manner, if the forces with which the body N repels the 

 columns CG and EM bear the same proportion to each other as those with 

 which the plate AB repels those columns, and therefore bear very nearly the 

 same proportion to each other as those with which EM repels those columns, 

 the quantity of deficient fluid in DF will be just the same as before N was 

 brought near, and the redundant fluid in AB will be diminished by a quantity 

 whose repulsion on CG is the same as that of N thereon. 



Therefore, if the repulsion of N on CG is not greater than that of H thereon, 

 the diminution of the quantity of redundant fluid in AB will bear but a very 

 small proportion to the whole. For the quantity of redundant fluid in AB is 

 many times greater than that which would be contained in it if DF was away, 

 id est, than that whose repulsion on CG is equal to the repulsion of H thereon 

 in the contrary direction. 



177] PROP. II. From the preceding proposition and corollary we may con- 

 clude that if the force with which N repels the columns CG and EM bears very 

 nearly the same proportion to each other as the force with which DF attracts 

 those columns, the quantity of redundant fluid in AB will be altered by a 

 quantity which will bear but a very small proportion to the whole, unless the 

 repulsion of N on CG is much greater than that of H thereon. 



If the reader wishes to see a stricter demonstration of this proposition, as 

 well as to see it applied to the case in which the fluid is supposed moveable in 

 the intermediate spaces, as in Prop. XXXV, he may read the following: 



178] PART i. Take Ee = thickness of those spaces in which the fluid is 

 moveable, draw def equal and similar to DEF, and let the deficient fluid therein 

 be equal to that in DF: the repulsion of the intermediate spaces on EM is to the 



