DEDUCTIONS FROM THE TIDES. 45 



intended to include a liberal allowance for the slope-tracts of the oceanic 

 islands, which, however, are not subtracted from area c. 



(c) The abysmal section is given a depth of only 9,000 feet and an 

 area 20 per cent greater than that of the deep ocean, this reduction of 

 depth and increase of area being intended to offset the frictional effects 

 of the inequalities of the actual bottom. 



The mean height of the tide in the substitute ocean is taken as 4,09 

 feet, which is equivalent to 4.9 feet for the actual ocean. The mean range 

 of the tide for the 280 available stations given in Harris's table of tides 

 harmonically analyzed is 4.548 feet.^ As these stations are chiefly in harbors 

 where local concentration is felt, 4.548 feet is probably rather high for the 

 average range of the tide, even on the coasts, and it is certainly much too 

 high for the mean range over the whole ocean. In using the equivalent of 

 4.9 feet for the substitute tide in addition to the large allowances made 

 above, it would appear that the computation is amply guarded against 

 underestimation. 



In using the foregoing guards against underestimation, which seem to 

 me excessive, I have been somewhat influenced by the thought that there 

 are derivatives from the observed tides which are not recognized and 

 measured as such, but whose dissipation of energy should be covered by 

 the computation. But, however well guarded, it is not presumed that 

 any results now attainable will have much value beyond indicating the 

 order of magnitude of the total friction. With the foregoing precautions 

 the results should not be seriously less than the actual fact. But, if they 

 are thought to be so by any one, the results can easily be multiplied accord- 

 ingly. 



With these data, a computation was made by Dr. W. D. MacMillan 

 in the manner set forth by him in a following paper of this series, p. 71. 

 This computation, it will be observed, was made for continuous motion; 

 but in estimating the rate, 12.5 minutes between each lunar tide were 

 allowed for the turn of the tide. He finds the yearly loss of energy to be 

 38,918 X 10^* foot-pounds. The rotational energy of the earth, reckoned 

 on the assumption that the Laplacian law of density obtains, is 157 X 10" 

 foot-pounds. At the computed rate of loss, this amount of energy would 

 last 40,440,000,000 years. The length of the day would be increased one 

 second in about 460,000 years. In 100,000,000 years the total lengthening 

 of the day would be about 3.6 minutes. 



If this result does not wholly misrepresent the order of value of the 

 friction of the water-tides, it follows that, even if the allowances for the 

 irregularities of the tidal water-bodies be greatly increased, and if the 

 formulae of the engineers for the effects of friction be multiplied several 

 times, and other allowances be made in the most generous manner, the 

 effects of the water-tides on the rate of rotation of the earth during the 

 known geological period are neghgible. If the friction of the body-tides 

 and the air-tides is also very small, there is no reason to expect to find in 

 the geological evidences any appreciable deformations of the earth's body 

 bearing the distinctive characteristics of tidal effects. On the other hand, 



' Rept. Coast and Geodetic Surv., 1900, pp. 664-677. 



