202 Mr. D. D. Heath on Secular Local 



1 Reader' so long ago as October 7), that the principle on which 

 Mr. Croll attempts to solve the problem he has proposed is 

 altogether erroneous. 



His proposition is (Reader, September 2), " the surface of the 

 ocean always adjusts itself in relation to the earth's centre of 

 gravity, no matter what the form of the solid mass of the earth 

 may happen to be -," the fallacy of which may be illustrated to 

 the non -mathematical geologist by observing that the common 

 explanation of the phenomena of the tides, by reference to the 

 tendency of the ocean, under the influence of the moon or sun, 

 to assume an elliptical shape, with the long axis pointing towards 

 the luminary and the solid nucleus of the earth at the centre, 

 would not be in anywise affected by supposing either luminary 

 to be attached to the " solid mass of the earth " by a rod of in- 

 sensible weight; whereas Mr. Croll's axiom would lead, in the 

 first case, to the gathering up of the waters, not into two oppo- 

 site semidiurnal tides respectively under and antipodal to the 

 moon, but into one globular mass under it, leaving the opposite 

 hemisphere absolutely bare once a day ; and in the other case, to 

 the abstraction of all the water of our globe to gather round that 

 point within the sun's mass, which is the common centre of gra- 

 vity of the two bodies. The truth is, the water will gather, but 

 unsymmetrieally, round the centre of gravity of the more pow- 

 erful mass — as will be seen. 



In the following investigation, which closely follows Laplace 

 (Mec. Cel. liv. 3. ch. 4), I have simplified the problem by 

 starting with the ideal case of a solid spherical nucleus, either 

 homogeneous or with its matter disposed in concentric homo- 

 geneous layers, everywhere covered by the sea. I then suppose 

 the equilibrium disturbed by a capping of ice at the north pole, 

 of uniform thickness, and with a circular boundary to the south, 

 and that the action of each vertical elementary prism on the 

 waters may be conceived to be concentrated in one point of its 

 length, and that all these points lie at equal distances from the 

 centre of the " earth " — by which word I everywhere mean the 

 terraqueous globe exclusive of this superficial capping. With 

 these assumptions, we may omit any reference to the effect of 

 the rotation of the earth (with which indeed the conditions would 

 be incompatible, unless with much deeper seas than the existing 

 ones); for the difference of surface between the primitive and the 

 disturbed state, which is all we are inquiring about, would be the 

 same in either case. It is further necessary to assume the dis- 

 turbance of the surface to be nowhere great enough to make the 

 curvature differ much from that of a sphere passing through the 

 point under consideration, and having its centre in the centre of 

 figure of the earth. 



