184 " SEE— FURTHER RESEARCHES ON - 



[April 24, 



examination of the method for calculating the fortnightly tide led 

 to the conviction that Laplace's argument is regard to the effects of 

 friction was unsatisfactory. That friction would greatly effect the 

 motion of the water in slow ocean currents within a few days was 

 seen to be untenable. In consequence of this defect it turned out 

 that long period tides as short as a fortnight would not enable the 

 physicist to evaluate the rigidity of the earth, though the 18.6 yearly 

 tide, depending on the revolution of the Moon's nodes, if it can be 

 determined by observation, will eventually give the desired result. 

 The height of this 18.6 yearly tide, however, is only one third of an 

 inch at the equator, and great accuracy will be required for its 

 detection. 



Acting on the old belief Darwin compared the lunar fortnightly 

 and monthly tides observed for 33 years at various Indian and 

 European ports, with the equilibrium theory, and found that the 

 tide-heights were about two thirds of the theoretical height. Ac- 

 cordingly he remarks : " On the whole we may fairly conclude that, 

 whilst there is some evidence of a tidal yielding of the earth's mass, 

 that yielding is certainly small, and the effective rigidity is at least 

 as great as that of steel." (Thomson and Tait's " Nat. Phil.," Vol. 

 I, Part II, §848.) 



This was written prior to the discovery of the theoretical defect 

 in the method of calculating the height of tides with periods not 

 exceeding a fortnight in duration ; yet even after the discovery of 

 this defect it was still possible to infer that tides of long period in 

 oceans such as ours must conform much more nearly to the equi- 

 librium laws than do the tides of short period. " Whilst, then, this 

 precise comparison with the rigidity of steel falls to the ground, 

 the investigation remains as an important confirmation of Thomson's 

 conclusion as to the great effective rigidity of the earth. ... It ap- 

 pears by numerical calculation on viscous and elastico-viscous tides 

 that in order that the oceanic semi-diurnal tide may have a value 

 equal to two thirds of the full amount on a rigid globe, the stiffness 

 of the globe must be about twenty thousand times as great as that 

 of pitch at freezing temperature, when it is hard and brittle." (Sir 

 G. H. Darwin, article " Tides," Ency. Brit., §§ 44-45.) 



§ 16. On, the Rigidity of the Earth as found by Comparing the 



