Density of the Mther. 50i> 



stream lines relative to the cylinder are, as is well known, steady 

 and beautifully simple ; but the actual path of the particles of this 

 fluid as they are put into motion by the neighbourhood of the 

 cylinder and finally left at rest in a displaced position after the 

 cylinder has passed on, is a very different affair, as may be seen 

 from the traces given in Maxwell's paper. 



" As your proof-sheets and queries have forced me back on this 

 subject, I hope to arrange for obtaining some early investigation of 

 the corresponding magnetic problem, viz. the displacement and strain 

 in a rotational aether due to an electron rushing through it, on the 

 usual kind of working hypothesis that the electron is representable 

 as if it were a small charged body," 



P.S. " On second thoughts the total displacement of position of 

 an element of aether at P due to an electron e passing near it at 

 distance h with uniform velocity v, is readily worked out. For it 



takes place around the axis of motion of the electron ; and, if 

 velocity of aether = 7c x magnetic force, we have 



arc of displacement = h I — -j— dt, where udt = dx 



e 



->■ 



, sin . dd 

 h 



= —j- , independent of u ; 



2ke 

 and the angle turned through in traversing this arc = -pr- 



"This rotational total displacemement of the element of aether, 

 arising from a motion differentially irrotational, is greatest when h 

 is smallest. When h is but little greater than the effective radius 

 a of the electron, the analysis is not adequate, for the electron cannot 

 then be treated as a point. 



"It will, however, still give the order of magnitude of the rotation; 

 so putting e=10 -21 , 7i = a = lQ- u cm. it gives 2.10 7 k radians *. If 

 this is to be small, 7c must be at least of the order 10 ~ 9 : so that 

 unit cg.s. magnetic field would be represented by an aether-velocity 

 of not more than 10 ~ 9 cm. per sec. This would require the density 

 of aether to exceed say 10 16 . But observe that the total arcual dis- 

 placement, being proportional to h— 1 , can mend itself (as is of course 



* The numerical index of each of these estimates would by me be 

 reduced by unity ; but it does not matter for the main lines of the 

 argument. — 0. L. 



