6oo 



A. A. MICHELSON AND HENRY G. GALE 



estimate. In combining the different tides to get a mean in each 

 direction, the ratios and phase differences were weighted in pro- 

 portion to the amphtudes of the tides except that the N-S diurnal 

 tide was omitted. The final means of R and A(^ are the mean 

 values obtained by weighting the five determinations in this way. 



TABLE VII 



This seems to be the most logical procedure and is perhaps justified 

 by the fact that the average difference from the mean for the dif- 

 ferent tides in each direction is roughly inversely proportional to 

 the amplitude. The probable error, computed in the usual way, is 

 given with the final value of R. 



The final result indicates that the rigidity of the earth in the 

 N-S and E-W directions is the same' and the ratio Riso. 690 with 

 a probable error of ± o . 004. That the viscous yielding of the earth 

 is small is indicated by the small difference in phase between the 

 observed and computed tides. It will be noted that the two 

 solar tides appear to agree excellently in phase displacement with 

 the E-W semi-diurnal tide and that for the N-S semi-diurnal, 

 and probably also the E-W diurnal lunar tides the phase displace- 

 ment is definitely smaller. 



However, for lack of a better method of finding the means of 

 the N-S and E-W phase displacement, each was averaged as the 

 ratios were, that is, simply by weighting them in proportion to the 

 amplitudes of the tides. This gives a displacement in phase of 



^ The preliminary experiment, through an error in computation, indicated a 

 difference in the rigidities in the two directions. The ratio should have been 0.710 

 for both the N-S and E-W. See Science, October 3, 1919, p. 327. 



