150 Mr. J. Rose-lnnes on the Physical 



equations * 



£= h . cosh at + k . sinh at + H . cos ftt + K . sin /3£, 



2 2 /Q2 _i 2 



t; = a 9 ~ 7 (7i . sinh at + /j . cosh at) ir ~- (H. sin (3t—K. cos £*), 



where a, /3, y are numerical constants, h, k, H, K, depend 

 on the initial conditions, and L is the origin of co-ordinates. 



9. In the case o£ disturbed motion we may assume these 

 same equations where h, k, H, K vary as well as the origin 

 L'. The motion will therefore be represented by a variable 

 elliptic superposed on a variable hyperbolic motion. If the 

 former predominates the particle may remain near L for 

 some considerable time ; if the latter, it will rapidly depart 

 from L. Moreover, it may happen that the disturbing force 

 is such that 7i 2 — k 2 passes through the value zero and changes 

 sign. The orbit will then cross the asymptote and a particle 

 which was approaching 1/ will begin to recede from it along 

 the other branch of the hyperbola. 



If therefore the initial value of Ji^h 2 is small, a small 

 disturbing force may be sufficient to completely change the 

 form of the orbit, even to transforming a direct into a 

 retrograde orbit through the limiting cusped form which 

 separates the direct from the retrograde members of a 

 family. 



XV. On the Physical Interpretation of the Michel son-Morley 

 Experiment. By J. Hose-Innes, M.A., B.Sc.t 



nnHE theoretical aspects of Michelson and Morley's well- 

 X known experiment have given rise to considerable 

 discussion. The explanation put forward by FitzGerald 

 was eagerly acclaimed and is still widely accepted in 

 substance : viz., that an elongation of the apparatus across 

 the line of motion occurred, together with a contraction 

 along the line of motion, of just sufficient magnitude to 

 neutralize the difference in the times of passage of a light- 

 wave due to a drift of the apparatus with respect to the 

 sether. (See Lodge's Presidential Address to the British 

 Association, 1913.) There is, however, no independent 

 experimental evidence for this change of dimensions, Lord 

 Kayleigh's attempt to detect it by means of a possible 



* " On certain discontinuities connected with Periodic Orbits," 

 S. S. Hough. Acta Mathematica, vol. xxiv 1901, pp. 257 to 288. 

 ■f Communicated by the Author. 



