Theory of conducting strata in glass plate 99 



Let the canals GC and EM be perpendicular to the plate of glass and opposite 

 to each other, so as to form one right line, and let them meet AB and DF in 

 the middle of their shortest diameters. The coating AB will be very much 

 overcharged, and DF almost as much undercharged, in consequence of which 

 some fluid will be driven from the surface Pp to Rr and from 5s to Tt. Moreover 

 the quantity of fluid driven from any portion of the surface Pp near the line 

 CE will be very nearly equal to the quantity of redundant fluid lodged in the 

 corresponding part of AB, or more properly will be very nearly equal to a mean 

 between that and the quantity of deficient fluid in the corresponding part of DF. 



For a particle of fluid placed anywhere in the space PprR near the line CE 

 is impelled from Pp to Rr by the repulsion of AB and the attraction of DF, 

 and it is not sensibly impelled either way by the spaces SstT, &c., as the attraction 

 of the redundant matter in Ss is very nearly equal to the repulsion of the re- 

 dundant fluid in Tt; and moreover the repulsion of AB on the particle and the 

 attraction of DT are very nearly as great as if their distance from it was no 

 greater than that of Pp and Rr, and therefore the particle could not be in 

 equilibrio unless the quantity of fluid driven from Pp to Rr was such as we have 

 assigned. 



As to the quantity of fluid driven from Pp to Rr at a great distance from 

 CE, it is hardly worth considering. It is plain, too, that the quantity of fluid 

 driven from Ss to Tt will be very nearly the same as that driven from Pp to Rr. 



Let now G, g, M, m and W signify the same things as in the preceding 

 proposition, and let the quantity of redundant fluid in AB be called A as 

 before, and let NP + RS + TV + &c., id est, the sum of the thicknesses of 

 those spaces in which the fluid is immoveable, be to NV, or the whole thickness 

 of the glass, as S to i, and let PR + ST + &c., or the sum of the thicknesses 

 of those spaces in which the fluid is moveable, be to NV as D to one. 



Take 11 equal to PR, the repulsion of the space PprR on the infinite 

 column EM is equal to the repulsion of the redundant fluid in Rr on EH, and 

 therefore is to the repulsion of AB on CE very nearly as 11 or PR to CE. 

 Therefore the repulsion of all the spaces PprR, SstT, &c. on EM is to the 

 repulsion of A B on CE very nearly as D to one, or is equal to mD, and therefore 

 the sum of the repulsions of AB and those spaces together on EM is very nearly 

 equal to M m + mD or to M mS. 



But the attraction of DF on EM must be equal to the above-mentioned sum 

 of the repulsions, and therefore the deficient fluid in DF must be very nearly 



, . A(M-mS) 

 equal to ^ - . 



By the same way of reasoning it appears that the force with which CG is 

 repelled by AB, DF, and the spaces PprR and SstT, &c. together is very nearly 



equal to 



(M - mS) (G -g) Mg P mgS 



M - -! - gD, or to 6 + mS -- - - gD, 



which, as M differs very little from G, and - is very small in respect of 



72 



