266 



NATURE 



{July 4, 1878 



was assumed in a former paper.^ The case is next considered 

 where the disturbing force is regularly periodic in time ; this is 

 the assumption appropriate for the tidal problem. The forces 

 which act on the spheroid in this case do not form a rigorously 

 equilibrating system ; but there is a small couple called into 

 existence, the consideration of which is deferred to a future 

 paper. 



It appears that the bodily tide lags, and is less in height than 

 it would be if the spheroid were perfectly fluid ; also the ocean 

 tides on such a spheroid are accelerated, and are less in height 

 than they would be on a rigid nucleus. * 



This theory is then applied to the lunar semi-diurnal and fort- 

 nightly tides, and numerical tables of results are given. 



A comparison of the numbers given with the viscosity of 

 pitch at near the freezing temperature (as roughly determined 

 by the author) shows how enormously stiff the earth must be to 

 resist the tidally distorting influence of the moon. It may be 

 remarked that pitch at this temperature is hard, apparently 

 solid and brittle ; and if the earth was not very far stiffer than 

 pitch, it would comport itself sensibly like a perfect fluid, and 

 there would be no ocean tides at all. It follows, therefore, that 

 no very considerable portion of the interior of the earth can 

 even distantly approach the fluid condition. 



This does not, however, seem conclusive against the existence 

 of bodily tides in the earth of the kind here considered ; for, 

 under the enormous pressures which must exist in the interior of 

 the earth, even the solidest substances might be induced to flow 

 to some extent like a fluid of great viscosity. 



The theory of the bodily tides of an " elastico-viscous " 

 spheroid is next developed. The kind of imperfection of elas- 

 ticity considered is where the forces requisite to maintain the 

 body in any strained configuration diminish in geometrical pro- 

 gression, as the time increases in arithmetical progression. 

 There are two constants which define the mechanical nature of 

 this sort of solid : first, the coefiicient of rigidity, at the instant 

 immediately after the body has been strained ; and second, " the 

 modulus of the time of relaxation of rigidity," which is the time 

 in which the force requisite to maintain the body in its strained 

 position has diminished to '368 of its initial value. The author 

 is not aware that there is any experimental justification for the 

 assumption of such a law ; but after considering the various 

 physical objections which may be raised to it, he concluded that 

 the investigation was still of some value. 



■ The laws of flow of such an ideal solid have been given (with 

 some assistance from Prof. Maxwell) by Mr. Butcher,^ and they 

 are such that the solutions already found might easily be adapted 

 to the new hypothesis. The results of the application to the 

 tidal problem are not quite so simple as in the case of pure vis- 

 cosity. By a proper choice of the two constants, the solution 

 becomes either that for a purely viscous spheroid or for a purely 

 elastic one. This hypothesis is therefore intermediate between 

 those of pure viscosity and piu-e elasticity. 



Sir William Thomson worked out numerically the bodily 

 tides of elastic spheres with the rigidities of glass and of iron ; 

 and tables of results are given for those rigidities, with various 

 times of relaxation of rigidity, for the semi-diurnal and fort- 

 nightly tides. 



It appears that if the time of relaxation of rigidity is about 

 one-quarter of the tidal period, then the reduction of ocean-tide 

 does not differ much from what it would be if the spheroid were 

 perfectly elastic. The acceleration of high tide still, however, 

 remains considerable ; and a like observation may be made in 

 the case of pure viscosity approaching rigidity. This leads the 

 author to think that perhaps one of the most promising ways of 

 detecting such tides in the earth, would be by the determination 

 of the periods of maximum and minimum in a tide of long period 

 in a high latitude. 



The second part of the paper contains a dynamical investiga- 



' On the Influence of Geological Changes on the Earth's Axis of Rotation. 

 Phil. Trans., vol. clxvii. Pt. I. 



2 The law is as follows : — If — be the frequency of the tide, fx the coeffi- 

 27r 

 cient of viscosity, g., gravity, a, earth's radius, w, earth's density, and if 



tan 6 = J'y''^ the tide of the viscous spheroid is equal in height to theequi- 



librium tide of a perfectly fluid spheroid multiplied by cos e, and the tide is 



retarded by L. Also the equilibrium tide of a shallow ocean overlying the 



V 



nucleu? is equal to the like tide on a rigid nucleus multiplied by sin t, and 

 there is an acceleration of the time of high water equal to— — —, 



■2V . V 



3 Proc. Lond. Math, Soc, December 14, 1S76, pp. 107-9. 



tion of the ocean tides in an equatorial canal running round a 

 yielding nucleus, and the results are confirmatory of the previous 

 ones. 



The author states as the chief practical result of this paper 

 that it is strongly confirmatory of the view that the earth has a 

 very great effective rigidity ; but that its chief value is, that it 

 forms a necessary first chapter to the investigation of the pre^ 

 cession of viscous and imperfectly elastic spheroids— an investsi- 

 gation which he hopes to complete very shortly. 



PHYSICAL GEOLOGY^ 



A Geological Proof that the Changes of Climate in past titnes were 

 not due to changes in the position of the Pole ; with an attempt 

 to assign a minor limit to the duration of Geological Time. 



T F we examine the localities of the fossil remains of the Arctic 

 ■*■ regions, and consider carefully their relations to the position 

 of the present North Pole, we find that we can demonstrate that 

 the Pole has not sensibly changed its place during geological 

 periods, and that the hypothesis of a shifting pole (even if per- 

 mitted by mechanical considerations) is inadmissible to account 

 for changes in geological climates. 



We are thus driven to the conclusion that geological climates 

 are due to the combined cooling of the earth and sun ; and on 

 comparing the rates of cooling of such a body as the earth with 

 the maximum measured thicknesses of the several strata, we 

 find a remarkable proportion between them, which leads towards 

 the conclusion thac the maximum thicknesses of the strata are 

 proportional to the times of their formation ; and so I deduce a 

 minor limit of geological time. 



Climate of the Parry Islands in the furassic Period, — Capt. 

 M'Clintock found in the 'Parry Islands, on the north coast 

 of America, at Point Wilkie, in Prince Patrick's Island, lat, 

 76° 20', tropical shells, and drew the attention of geologists to 

 the difficult task of providing a tropical climate inside the 

 Arctic Circle, to accommodate the habits of the animals that 

 lived there in Jurassic times. The tropical fossils found in the 

 Parry Islands were : — 



Ammonites M'Cliniocki (M'Clintock). 



Monotis septentrionalis ,, 



Pleurotomaria spr ,, 



Nucula sp. ,, 



Ichthyosaurus j/..(v«rtebr2e) (Sir Edward Belcher).* 



Teleosaurus sp. (vertebrae) (Capt. Sherard Osborne).^ 



The Teleosaurus was a reptile closely resembling the gavial of 

 India, which is found nowhere outside the Tropics, and requires 

 warmer water than the alligator of America. The alligator 

 flourishes in the neighbourhood of New Orleans, whose climate 

 is represented by the following figures : — 



Mean Monthly Tempei-ature of New Orleans. 



S* Reptiles requiring a climate such as is indicated by the pre- 

 ceding table, lived in the Jurassic period within 900 miles of the 

 North Pole, where the present climate is represented by the 

 following figures : — 



Mean Monthly Temperature of Melville Island. 



January ... 

 February ... 

 March 

 April 



May 



June 



Yearly mean .. 



31-3 F. 

 32*4 ,. 

 i8-2„ 

 8-2 „ 

 i6-8„ 

 36'2 „ 



July 



August 



September ... 

 October 

 November ... 

 December 

 -f 1-2 F 



42-4 F. 

 32'6 ,, 



22-5 „ 

 2-8 „ 



2I"I ,, 

 21*6 ,, 



' " Notes on Physical Geology." Paper read at the Royal Society, 

 April 4, by the Rev. Samuel Haughtcn, M.D. Dublm, D.C.L. Oxon, 

 F.R.S., Professor of Geology in the University of Dublm. No. IV. 



2 Exmouth Island, lat. 77'' 12' N. (only 900 miles from the Pole). 



3 Rendezvous Hill, at north-west extremity of Bathurst Island, lat. 77' JM- 



