98 Preliminary Propositions 



the coating AB, the redundant fluid in AB will be to that in H very nearly as 

 CW to 



For the quantity of redundant fluid in H will be 28. 



167] COR. VII. On the same supposition the redundant fluid in AB will 

 be very nearly the same whether the glass is flat or otherwise, or whatever 

 shape the coatings are of. 



168] COR. VIII. On the same supposition, if the size and shape of the 

 coatings and also the thickness of the glass is varied, the size and quantity of 

 redundant fluid in H remaining the same, the quantity of redundant fluid in 

 AB will be very nearly directly as its surface, and inversely as the thickness of 

 the glass. 



169] PROP. XXXV (Fig. 9). Let Pp, Rr, Ss, Tt represent any number of 

 surfaces whose distance from Nn, and consequently from each other, is the 

 same in all parts, and let everything be as in the preceding proposition, except 

 that the fluid in the spaces PprR, SstT, &c., that is, in the spaces comprehended 

 between the surfaces Pp and Rr, and between 5s and Tt, &c. is moveable*, in 

 such manner, however, that though the fluid in any of these spaces as PprR 

 is able to move freely from Pp to Rr or from Rr to Pp, in a direction perpen- 

 dicular to the surface Pp or Rr, yet it is not able to move sideways, or in a 



Fig. 9. 



direction parallel to those surf aces f, and let the fluid in the remaining spaces 

 NnpP, RrsS, TtvV, &c. be immoveable: the quantity of redundant fluid in AB 

 and the deficient fluid in DF will be very nearly the same that they would be 

 if the whole fluid within the glass was immoveable, and its thickness was only 

 equal to NP + RS + TV, &c., that is, to the sum of the thicknesses of those 

 spaces in which the fluid is immoveable, provided that NV, the thickness of 

 the glass, is very small in respect of the smallest diameter of AB, and also in 

 respect of the radius of curvature of the surface of the glass. 



* To avoid confusion I have drawn in the figure only two spaces in which the 

 fluid is supposed to be moveable, but the case would be just the same if there were 

 ever so many. 



t [Note 15.] 



