852 Dr. C. V. Burton : An Experiment indicating 



a few days the earth's orbital velocity may also, with suf- 

 ficient approximation, be treated as constant in direction and 

 magnitude. Thus at any well-defined time of year the terms 

 in cos 2c/>, sin 2(/> which occur in (6a) represent a semi-diurnal 

 constituent of UV, and the terms in cos </>, sin </> a^ diurnal 

 constituent; the amplitude of the semi-diurnal term is 

 i(A 2 + B 2 )(l + cos 2 0), 



and that of the diurnal term is 



-i^(A 2 + B 2 )Csin 2 2<9. 



21. The corresponding amplitudes of the semi-diurnal and 

 diurnal turning-moments about a vertical axis are 



£(A 2 + B 2 )(l + cos 2 0)F 2 />M<rH, ... (7) 



and ^(A 2 + B 2 )Csin 2 2^VMo-H ? ... (8) 



respectively ; and limits can be named which these certainly 

 did not exceed with the apparatus u^ed. In seeking to assign 

 an extreme upper limit to the value of F 2 p, we must assume 

 for A B, C the values least favourable to the production of 

 measurable amplitudes. If a large number of observations 

 were available, well distributed over a year, the most un- 

 favourable assumption would be that the sun was at rest 

 (or nearly so) with respect to the sether. For a single set 

 of observations taken at one time of the year, this assumption 

 would no longer be the most unfavourable; for it might be 

 thought possible that the sun's velocity was equal and opposite 

 to the earth's orbital velocity at the time in question, the 

 earth's centre being then at rest with respect to the aether. 

 All the same, we should be justified in saying that F 2 p was 

 probably below a certain value, calculated on the supposition 

 that the sun was without motion through the eether. 



22. Of the observations taken there are two sets suitable 

 for reduction ; one made in 1910 October 29-31, the other 

 (with considerably greater refinement) in 1913 Feb. 4-10. 

 In the earlier set, the plate shown in fig. 1 was used, and it 

 appeared from a plot of the micrometer readings that the 

 azimuth of the mirror showed no semi-diurnal variation with 

 an amplitude as great as 1*5 seconds. The moment of inertia of 

 the plate being '00076 (C.G.s.) and the period 8"50 seconds, 

 this implies that there is no semi-diurnal couple acting on 

 the plate with an amplitude as great as 3*15 x 10" 9 dyne-cm.; 

 that is, in virtue of (7), 



i(A 2 + B 2 )(l + cos 2 6)F 2 P . Mo-H<3-15 x 10" 9 . 



