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Physics. — Stokes's TJieonj of Aberration in the Supposition of 

 a Variable Dcnsilij of the Aether. By Prof. H. A.. Lorkntz. 



In the theory of aberration that has been proposed by Prof. Stokes 

 it must be assumed tliat the aether has an irrotalional motion and 

 that, all over the earth's surface, its velocity is equal to that of the 

 planet itself, in its yearly motion. These two conditions are easily 

 shown to contradict each other, it the aether is understood to have 

 everywhere the same invariable density. 



Prof. Planck of Berlin had the kindness to call my attention to 

 the fact that both conditions might be satisfied at the same time, 

 if the aether were compressible and subject to gravity, so that it 

 could be condensed around the earth like a gas. It is true, a certain 

 amount of sliding is not to be avoided, but the relative velocity of 

 tlu! aetlier with legard to the earth may be made as small as we 

 like by supposing the condensation sufficiently large. 



At my request Prof. Planck permitted me to communicate his 

 treatment of the case ; it is as follows. 



Instead of considering the earth moving through the aether w e 

 shall suppose the planet to be at rest and the aether to flow along 

 it; this comes to the same thing. Let this motion be steady and 

 irrotational and let the velocity at infinite distance be <■, constant 

 in direction and magnitude. Let the aether obey Boyle's law and 

 be attracted by the earth according to the law of Ne"V\'TON. 



^Ye shall place the origin of coordinates in the centre of the planet 

 and give to the axis of z the direction of the velocity c Finally we 

 shall call the distance to the centre ?•, the radius of the earth ro, 

 the velocity-potential »/', the pressure p, tiie density /(•, and the poten- 

 tial of gravity per unit mass V. We shall denote by u the constant 



h 

 ratio — , and by (j the value 

 P 



T" l*" = ''o) 



of the acceleration at the surface of the earth. 

 The motion will be determined by the equations 



è('f^)+r,(40+è('-s)=»-- •■'" 



and 



0+'-+l|(55) + (|) + (IOl=- ■ -f^) 



