1882.] -^'l [Chase. 



flinm, in adjusting their relative positions to tlie ever- varying requirements 

 of equilibrium, and causing harmonic oscillations which are easily trace- 

 able by means of systematic barometric observations. There can be no 

 friction, provided the adjustments are made by the simple approach or 

 separation of particles, and such appears to be the case. In the most 

 thorough series of observations that has been published for any station 

 near the equator, the harmonic oscillations are of the simplest character 

 conceivable, representing the quarter-daily sums of the instantaneous ten- 

 dencies and the changes in atmospheric weight so accurately as to give an 

 estimate of Sun's distance, which differs by less than one-half of one per 

 cent, from the latest astronomical estimates {Proc. Am. Ph. Soc, ix, 287; 

 X, 375-6, foot note.) 



217. Ratio of Tidal Adjustments. 



Sir William Thomson has found a partial solution of the theoretical re- 

 quirements of terrestrial rigidity, in his theory of vortex atoms. Perhaps 

 the solution may be completed by supposing an intermolecular elasticity 

 which is greater than that of glass, instead of a rigidity which fe greater 

 than that of glass. The influence of atmospheric pressure on the height of 

 ocean tides, which has been noticed by many observers, suggests the 

 likelihood that the whole mass of the earth may contribute to the adjust- 

 ments of equilibrium which satisfy tidal tendencies. If that is the case, 

 the entire change which would be required in the distance between any 

 two molecular centres is less than ^o^ooo of their mean distance, even at 

 the spring tides, Avhen the sun and moon combine their disturbing ener- 

 gies. The whole adjustment might be accomplished, through fethereal 

 elasticity, in less than ^V of a second, but it only needs to be accomplished 

 four times in about 25 hours. 



218. Summation of Tendencies. 



The triumphs of calculus spring from the fact that its differentials repre- 

 sent only tendencies and its integrals are summations of tendencies. No 

 integration or series of integrations can be rightly looked upon as con- 

 clusive, unless it has been extended to all the tendencies which can have 

 any bearing upon the problem which we are examining. Nothing is more 

 certain than mathematics, except our knowledge of our own spiritual 

 existence and faculties. Neither in mathematics nor in psychology, how- 

 ever, is it safe to assign any value to our results beyond their necessary re- 

 lations to the data from which they were obtained. Delaunay's hypothe- 

 sis of tidal friction undoubtedly follows from his postulates, and if we ac- 

 cept it, we may be satisfied with the explanation which it gives of appar- 

 ent lunar retardation, but his postulates are not all axiomatic ; they do 

 not cover the whole ground ; and the errors in the lunar tables may spring 

 from some portion of a cycle of mutually compensating perturbations. 

 The tidal tendencies are towards accelerated rotation in two of the quad- 



