88 REPORT— 1876. 



Oil the Eai'tliquaTce Districts of Scotland. By James Brtce, LL.D. 



On the Tidnl-Betardation Argument for the Age of the Earth. 

 By James Ckoll, LL.D., F.R.S., of the Geological Survey of Scotland. 



Many years ago Sir William Thomson demonstrated from physical considerations 

 that the views which then prevailed in regard to geological time and the age of our 

 globe were perfectly erroneous. His two main arguments, as are well known, 

 were, first, that based on the limit to the sun's possible age, and, secondly, 

 that based on the secular cooling of the earth. More recently he has advanced a 

 third argument*, based on tidal retardation. It is well known that, owing to tidal 

 retardation, the rate of the earth's rotation is slowly diminishing, and it is therefore 

 evident that if we go back for many millions of years we reach a period when the 

 earth must have been rotating much faster than now. Sir William's argument is, 

 that had the earth solidified several hundred millions of years ago, the flattening 

 at the poles and the bulging at the eC[uator would have been much greater than 

 we find them to be. Therefore, because the earth is so little flattened, it must have 

 been rotating when it became solid at very nearly the same rate as at present. 

 And as the rate of rotation is becoming slower and slower, it cannot have been so 

 many millions of years back since solidification took place. 



A few years ago I ventured to point outf what appeared to be a very obvious 

 objection to the argument, viz. that the influence of subaerial denudation in alter- 

 ing the form of the earth had been entirely overlooked ; and as the validity of the 

 objection, as far as I am aware, has never been questioned, I had been induced to 

 believe that the argument referred to had been abandoned. But I find tliat Pro- 

 fessor Tait, in his work on ' Recent Advances in Physical Science,' restates the 

 argument as perfectly conclusive, and makes no reference whatever to my objection. 

 As the subject is one of veiy considerable importance, I may be permitted again to 

 direct attention to the objection in question, which briefly is as follows : — 



It has been proved by a method pointed out a few years ago|, and which is now 

 generally admitted to be reliable, that the rocky surface of our globe is being lowered 

 on an average, by subaerial denudation, at the rate of about 1 foot in 6000 years. 

 It follows as a consequence from the loss of centrifugal force resulting from the 

 retardation of the earth's rotation, occasioned by the friction of the tidal wave, 

 that the sea-level must be slowly sinking at the equator and rising at the poles. 

 This of course tends to protect the polar regions and expose equatorial regions to 

 subaei-ial denudation. Now it is perfectly obvious that unless the sea-level at Ihe 

 equator has, in consequence of tidal retardation, been sinking during past ages at a 

 greater rate than 1 foot in GOOO years, it is physically impossible that the form of 

 our globe could have been very much different from what it is at present, whatever 

 may have been its form when it consolidated, because subaerial denudation would 

 have lowered the equator as rapidly as the sea sank. But in equatorial regions the 

 rate of denudation is no doubt much greater than 1 foot in 6000 j-ears, because the 

 rainfall is greater there than in the temperate regions. It has been shown in the 

 papers above referred to that the rate at which a country is being lowered by 

 subaerial denudation is mainly determined, not so much by the character of its 

 rocks as by the sedimentary carrying-power of its river-systems. Consequently, 

 other things being equal, the gi-eater the rainfall the greater will be the rate of 

 denudation. 



We know that the basin of the Ganges, for example, is being lowered by denu- 

 dation at the rate of about 1 foot in 2-300 years, and this is probably not very far 

 from the average rate at which the equatorial regions are being denuded. It is 

 therefore evident that subaerial denudation is lowering the equator as rapidly as the 

 sea-level is sinking from loss of rotation, and that, consequently, we cannot infer 



* Trans. Glasgow Geol. Soc. vol. iii. p. 1. 

 + 'Nature,' August 21, 1871 ; 'Climate and Tirae,' p. 335. 



t 'Philosophical Magazine,' May 1868, pp. 378-.384, February 1867, p. 130; 'Climate 

 and Time,' chap. xx. ; Trans. Glasgow Qeol. Soc. vol. iii. p. 153. 



