474 KEPORT — 1882. 



The X and y of the two classes of tide were in the first instance regarded as 

 distinct, but the manner in which they arise shows that it is legitimate to regard 

 them as identical, and thus we have sixty-six equations for x and sixty-six for y. 



The equations were then reduced by the method of least squares, with the 

 following results : — 



For the fortnightly tide — • 

 And for the monthly tide — 



.V- 



•675 + -056,2/ = -020 + -055. 

 •680 ±-258, 2/ = -090 + -218. 



The numbers given with alternative signs are the probable errors. _ 



The very close agreement between the x and y for the two tides is probably 

 somewhat due to chance. 



The smallness of the two p's is satisfactory; for, as above stated, it the 

 equilibrium theory were true, they should vanish. Moreover, the signs are m 

 agreement with what they should be, if friction is a sensible cause of tidal 

 retardation. But considering the magnitude of the probable errors, it is of course 

 more likely that the non-evanescence of the y's is due to errors of observation 

 or to the method of reduction. 



The author had already submitted to the British Association at this meetmg a 

 paper on a misprint, discovered by Professor Adams, in the Tidal Report for 1872. 

 This report forms the basis of the method of harmonic analysis which has been 

 employed in the reduction of the tidal observations, and it appears that the 

 erroneous formula has been systematically used. The large probable error in the 

 value of the monthly tide may most probably be reduced by a correct treatment 

 of the original tidal records. 



It has been already remarked that it is legitimate to combine all the observa- 

 tions together, for both sorts of tide, and thus to obtain a single x and y from 

 sixty-six years of observation. Carrying out this idea he found : — 



X = -676 + -076, y = -029 + -065. 



These results really seem to present evidence of a tidal yielding of the earth's 

 mass, and the value of the x is such as to show that the effective rigidity of the 

 whole earth is about equal to that of steel. 



But this residt is open to some doubt for the following reason : — ■ 



Taking only the Indian results (forty-eight years in all), which are much more 

 consistent than the English ones, he fomid 



X = -9.31 + -056, y = -loo + -068. 



We thus see that the more consistent observations seem to bring out the tides 

 more nearly to their theoretical equilibrium values with no elastic yielding of the 

 solid. . . 



It is to be observed however that the Indian results being confined ^ylthln a 

 narrow range of latitude give (especially when we consider the absence of minute 

 accuracy in his evaluation of the definite integral) a less searching test lor the 

 elastic yielding than a combination of results from all latitudes. 



On the whole we may faii-ly conclude that, whilst there is some evidence of a 

 tidal yielding of the earth's mass, that yielding is certainly smaU, and that the 

 effective rigidity is at least as great as that of steel. 



8. On the Transmission of Force through an Elastic Solid. By Professor 

 Sir WiLLUM Thomson, F.E.S. 



9. On a Method of investigating Magnetic 8usce;ptihility . By Professor 

 Sir William Thomsois', F.B.S. 



