io6 



Appendix to Preliminary Proposition. 1 : 



such that the repulsion of the coatings AB and DF thereon shall be not sensibly 

 less than if it was infinite, and that the thickness of the glass Gg is very small 

 in respect of the distance of R from it, and that the repulsion of R does not 

 sensibly alter the disposition of the fluid in Tt and Ss, and also that the re- 



pulsion of R on GC and EM together is not much less than if GM was infinite, 

 and also not much greater than the repulsion of the glass NnvV on CG. 



For let the quantity of fluid in Tt and Ss be so much altered that the united 

 repulsion of R and tihpse two coatings on the two canals GC and EM together, 

 and also their repulsion" *pn gP, shall be the same as that of the two coatings 

 alone before the approach oi 'i& 



By Prop. II, Cor. i the quantity '.of fluid in Tt will be very little altered 

 thereby, for the repulsion of R on the c^anal gP is very nearly the same as its 

 repulsion on gC and EM together. 



As the repulsion of Tt, Ss and R together von the two canals GC and EM 

 together is the same as before the approach of R, it follows that if their re- 

 pulsion on gC is less than before, their repulsion onh\M will be as much increased. 



Let now the quantity of fluid in AB and DF be s-o much altered that their 

 repulsion on gC shall be as much diminished as that i of Kkil and R on the 

 same column is diminished, and that their repulsion on > EM shall be as much 

 diminished as that of Kkil and R on the same is increased- 1 , it is plain that the 

 fluid in ah 1 three canals will be exactly in equilibrio, and' by the preceding 

 corollary the quantity of fluid in AB will be very little altered, and therefore 

 the proportion of the redundant fluid in AB and Tt to each ot her will be very 

 little altered*. V 



186] COR. VII. By Prop. [XXIV, Art. 86] all which is saicfc in this pro- 

 position and corollaries holds good equally whether the canals Q7C, EM and 

 GP are straight or crooked. 



LEMMA. 

 * [Note 16, p. 392.] 



