of a Liquid Substratum beneath the Earttis Crust. 

 putting, as before, 2( -J_ ^ =c, 



221 



= c{ cos 2«- 1 1? cos (2a> + 2S) }• 



To find its maximum height put — =0; 



.-. = c|-sin2ft)+|^cos(2w + 2S)|. 

 Squaring, and adding, and calling the high tide H, we have 



I 5 afi \ 5 a.fi / ) 



from which the diminution of the ocean high tide by the earth- 

 tide, or c — H, can be found. 



(8) The canal theory of the tides is doubtless less applicable 

 to the fortnightly than to the semidiurnal tide. Nevertheless 

 a certain fortnightly tide would be raised in an equatorial 

 canal ; and since we are seeking the pro rata diminution only, 

 and not the absolute height of the tide, we may assume that 

 this result will be applicable to the fortnightly tide if we assign 

 corresponding values to the symbols. It is evident that the 

 earth-tide must be of the same period as the ocean-tide which 

 is affected by it : so that H, c, and E will belong to tides of 

 the same period. 



The foregoing equation is suitable to find the diminution of 

 the ocean- tide by the earth-tide, whether we consider the tidal 

 deformation of the ocean-bottom to arise from a bodily tide in 

 a non-rigid, but solid, earth, or from a tide in a liquid layer 

 beneath the crust, and of a depth which is small compared with 

 the radius. The latter is the theory of the constitution of the 

 earth which I have maintained in my ' Physics of the Earth's 

 Crust,' and against which the tidal argument has been held to 

 present a formidable objection. It is therefore with this sup- 

 position that I am concerned. The canal theory of the tides, 

 dealing with a layer of liquid, seems to be the suitable one 

 upon which to estimate the deformation of the crust through the 

 tide in the liquid substratum — that is, to give the value which 

 we ought to assign to E. Let, then, i) be the tide which would 

 be formed in such a substratum were it of uniform depth, 

 perfectly liquid, and frictionless. Then, from what has been 

 already proved, 



E=??cos2S. 



