( 448 ) 



We sliall apply these equations to a steady motion with velocity- 

 potential <p, without supposing that Bio \> vanishes. We shall how- 

 ever neglect quantities of tlie order O". 



Now if, instead of t, we introduce as a new independent variable 



<' = « + — , 



and instead of b and Sp the vectors 5' and ^', defined by 



g'., z=4:7i V^ t», + {iu .f-)^ — v^ /p,), etc., 

 and 



.p'^. = .pj. — 4-1 ('0, by — Vy &,), etc., 



the equations become 



Biv d' — , 



Div Sp' =0 , 



9y 3^ " 3<' ' ^ ''' 



These formulae have the same form as those that would hold for 

 an aether without motion, and this is sufficient to obtain in a moment 

 the well known theorems concerning the rotation of the wave-fronts 

 and the rectilinearity of (he rays of light. At the same time we 

 sec that at the boundary of the different layers of the aether, which 

 slide one over the other, there is never a reflection of light. 



It is curious that in the two rival theories somewhat the same 

 mathematical artifices may be used. 



3. There seems to be nothing against the assumption that, while 

 the aether may be condensed by gravitation, molecular forces are 

 incapable of producing this effect. In this way it might be explained 

 that small masses, e. g. the flowing water in Fizeau's experiments, 

 cannot drag the aether along with it. In these cases the coefficient 

 of Fresnel would I'omain of use. 



4. A decision between the two theories would be soon obtained, 

 if the phenomena of the daily aberration were sufficiently known. 

 Unfortunately, this is by no means the case; even, as Prof, van de 

 Sandr Bakhuyzen assures me, one has never purposely examined 

 what the existing observations teach us concerning this aberration. 



Mathematics. — "0» reducible hypereUiptk Integra^.'' By Prof. 

 J. C. Kluyvek. 



(Will be published in the Proceedings of the next meeting.) 

 (April 33tli 1899.) 



