Motion of the Earth and the zElher. 811 



to the square of their distance apart. It follows from this 

 that a source put in a stream of aether will be acted on by a 

 force proportional to the velocity of the stream. This analogy 

 between electrostatics and hydrodynamics is well known, so 

 that it is unnecessary to discuss it further. A force is required 

 to keep a source moving through the aether, so that the anulogv 

 only holds up to a certain point. 



Thus matter containing hydrodynamical doublets is ana- 

 logous in hydrodynamics to matter containing electrical 

 doublets in electrostatics, or to matter like iron containing 

 molecular magnets in magnetism*. 



If then we suppose matter to contain hydrodynamical 

 aether doublets and that these doublets are arranged in an 

 irregular manner, like the atoms in an unmagnetized piece 

 of iron, then if a stream of aether is made to flow through the 

 matter each doublet will tend to set itself so that its axis 

 coincides with the direction of the stream : taking the direction 

 of the axis to be from the sink to the source. We may suppose 

 that the doublets are acted on by restoring couples so that the 

 angles through which they turn depend on the velocity of 

 the stream. Consider a plate of matter with parallel sides 

 perpendicular to the stream of aether. Let f denote the 

 average displacement of the sources relative to the sinks in 

 the direction of the stream, and S be the volume of aether 

 emitted by all the sources per second in unit volume of the 

 matter. If the velocity of the aether outside the plate is V 

 and that inside V', we have V=Sf -t- V. Let £ = AV, so that 

 V = V'(1 + AS). We may call 1 + AS = P the aetherial per- 

 meability of the matter. V can be defined as the velocity of 

 the aether in a long narrow hole bored in the matter parallel 

 to the stream of aether. If the doublets are supposed free to 

 turn round without any appreciable restoring couples, then 

 P. becomes infinite provided Sf is greater than V, where \ 

 denotes the maximum value of f. 



It follows that if a piece of matter is put in a stream of 

 aether the stream-lines outside the matter will be the same as 

 the lines of force outside a similar piece of insulator of specific 

 inductive capacity equal to P put in a corresponding electric 

 field. 



Consequently if we suppose that the matter composing 

 the earth has a high aetherial permeability, then it follows 

 that the distribution of aetherial velocity outside the earth 

 will be that which has been deduced above from the facts of 



* An analogy between hydrodynamics and magnetism was fully dis- 

 cussed by Lord Kelvin, who introduced the term permeability. In 

 Kelvin's analogy greater permeability was due to greater porosity.' 



