342 Dynamical Theory of the Tides of Long Period, [Nov. 25, 



-^ r ==-2363-l-0016/t 2 + -5910 / a' i --1627/. 6 + -0258^ -_-0026/t 1 H '0002^2 



Jh 



At the pole h=—Ux "3137= -f^x '471, 



at the equator h=+Ex '2363= + 709. 



With a deeper ocean we should soon arrive at the equilibrium value 

 for the tide, for JV 2 , JV 3 , &c., become very small, and becomes 

 equal to §. 



These two cases, /3=40, /3=10, are two of those for which Laplace 

 has given solutions in the case of the semi-diurnal and diurnal tides. 

 We notice that, with such oceans as we have to deal with, the tide of 

 long period is certainly less than half its equilibrium amount. 



In Thomson and Tait's 'Natural Philosophy' (edition of 1883) I 

 have made a comparison of the observed tides of long period with the 

 equilibrium theory. The probable errors of the results are large, 

 but not such as to render them worthless, and in view of the present 

 investigation it is surprising to find that on the average the tides of 

 long period amount to as much as two-thirds of their equilibrium 

 value. 



The investigation in the ' Natural Philosophy ' was undertaken in 

 the belief of the correctness of Laplace's view as to the tides of long 

 period, and was intended to evaluate the effective rigidity of the 

 earth's mass. 



The present result shows us that it is not possible to attain any 

 estimate of the earth's rigidity in this way, but as the tides of long 

 period are distinctly sensible, we may accept the investigation in the 

 ' Natural Philosophy ' as generally confirmatory of Thomson's view 

 as to the great effective rigidity of the whole earth's mass. 



There is one tide, however, of long period of which Laplace's argu- 

 ment from friction must hold true. In consequence of the regression 

 of the nodes of the moon's orbit there is a minute tide with a period 

 of nearly nineteen years, and in this case friction must be far more 

 important than inertia. Unfortunately this tide is very minute, and 

 as I have shown in a Report for 1886 to the British Association on 

 the tides, it is entirely masked by oscillations of sea level produced 

 by meteorological or other causes. 



Thus it does not seem likely that it will ever be possible to evaluate 

 the effective rigidity of the earth's mass by means of tidal observa- 

 tions. 



