350 G. F. Becker — Proof of the Earth? s Rigidity. 



water and low water, the long period tides wonld coincide with 

 those of equilibrium and then observation would give a rea- 

 sonably accurate value of the rigidity of the earth. Laplace 

 supposed that the fortnightly tides did sensibly coincide with 

 the equilibrium heights. On this hypothesis Darwin discussed 

 the observations and found that the amplitude of the lunar 

 fortnightly and monthly tides is about 2/3 of the equilibrium 

 height. This would correspond to the rigidity of steel. Later 

 however he came to the conclusion that these periods are too 

 short to bring the waters to rest and that the result is thus 

 vitiated. 



It is certain, however, as Mr. Darwin wrote me in Novem- 

 ber, 1889, " that these tides will not be large on a rigid earth 

 and hence the investigation remains as a general confirmation 

 of the rigidity of the earth, without giving any quantitative 

 evaluation of its amount."* 



If the earth had the rigidity of brass the semidiurnal rise 

 and fall of the land would be half the amplitude of the real 

 tides and would equal the apparent tides. Were the continents 

 uniform in lithological composition and elevation the tidal wave 

 might pass under our feet unnoticed, as it does under a ship at 

 sea. But it seems to me that at points near abrupt changes of 

 density, as along the foot of a great mountain range or near the 

 edge Of a great oceanic abyss such as lies close to the Pacific 

 Coast, a semidiurnal rise and fall of two or three feet would 

 surely manifest itself in differential displacements. 



Solidity of the earth. — The earth is thus a very rigid body. 

 It does not follow as a matter of logical necessity that it is 

 solid, because under certain circumstances a fluid in motion 

 may act like a rigid mass toward certain external forces. On 

 this subject it can only be said that, though the matter has 

 been considered, physicists have thus far been unable to devise 

 any system which will account for the effective rigidity of the 

 earth as displayed in the tidal phenomena in this manner. 

 No such explanation would be satisfactory unless the fluid 

 were treated as viscous. 



* Mr. Osmond Fisher quotes Mr. Love in the Proc. London Math. Soc, vol. xix, 

 1888, p. 206, as reaching the result that only the fortnightly tides can settle the 

 question. If there is such a tide "we shall be entitled to say that the tidal 

 effective rigidity of the earth is too great to allow us to suppose it to consist of a 

 liquid mass covered with a thin solid crust." But, he says, "the Tidal Committee 

 of the British Association appears to be still doubtful whether there really is an 

 appreciable fortnightly tide.'' Mr. Darwin is or has been a member of the Brit. 

 Assoc, committees on tides (excepting one to promote tidal observations in Can- 

 ada) and has usually written the reports of these committees. I can find no 

 evidence in these reports of any such doubt as is mentioned. Darwin speaks of 

 these tides as "distinctly sensible" in Proc. R. S., Nov. 25, 1886, and as being 

 2/3 of the equilibrium height in Encyc. Brit., Art. Tides, 1S88. That he is still 

 confident of their existence is clear from the extract from his letter given in the 

 text. 



