Water and Mercury at nearly Perpendicular Incidence. 319 



surface thus obtained would not be free from a greasy layer, 

 but it is not probable that this would sensibly influence the 

 reflexion. 



Appendix. 



The calculation of the reflexion depends upon the assump- 

 tion that the reflecting surface is plane ; and a very moderate 

 concavity would suftice to explain the small excess in the 

 observed number for water over that calculated from Fresnel's 

 formula. It is thus of importance to assure ourselves that 

 the concavity due to capillarity is really small enough to be 

 neglected. For this purpose an estimate founded upon the 

 capillary surface applicable in two dimensions will suffice. 



If 6 be the inclination to the horizon at any point, x the 

 horizontal and y the vertical coordinate, the equations to the 

 surface are : — 



x= 2a cos \6 + a log cot J0, y = 2a sin J#, 

 where 



At a great distance from the edge, 



0=0, y=0, a' = qo . 

 At the vertical edge of a wetted vessel, 



The origin of x corresponds to 



0=7r, y = 2a. 



In the case of water T = 74, p=l, and # = 981 C.G.S. ; so 

 that 



a =*274 centim. 



In the experiments upon reflexion the part of the surface in 

 action was about 11 centim. away from the boundary, so 

 that A'/a = 40, and 6 is very small. 

 For the curvature 



l/p —yjo? — 2 sin \Q . /a ; 



or for our present purpose 



l/p=0/a. 



To find 6 we have approximately, 



cot^ = ^ 38 , or0=4e- 38 . 



