THE RIGIDITY OF THE EARTH 599 



well as for the thirteen months. A calculation for 306 periods was 

 also made, omitting this month from both the observed and cal- 

 culated data. This value is given opposite F12. 



In the case of the N-S diurnal tide it will be noted that the 

 amplitude is very small, about 0.5 fringe, as it should be since this 

 tide has the coefficient cos 2I, where / is the latitude. For Yerkes 

 Observatory cos 2/ = 0.0848. This tide is too small to admit of 

 much accuracy in the determination, but the results are included, 

 as they are not without interest. Mean values are added for the 

 whole year, and the means omitting the fourth month, and also 

 omitting both the third and the fourth. The calculations are also 

 added for the year as a whole, 326 periods; omitting the fourth 

 month, 306 periods; and omitting both the third and fourth 

 months, 282 periods. The omission of these months is perhaps 

 justified, since both R and A<^ are decidedly abnormal. The mean 

 of the six values gives R = o. 584 and A0 = 7°46'. Probably the only 

 conclusion which is justified for the N-S diurnal tide is that R is 

 about 0.6='= . 2 and that the difference of phase is small. 



An effort was made to deduce the fortnightly lunar tide of 

 period 13.66 days. Here the E-W tide should be zero, and the 

 residual sine curves were less than 0.05 fringe from both the 

 calculated and observed curves. The N-S tide, however, had an 

 amplitude of about i . 8 fringes and gave i? = o. 628 and A<^ = — 8^24', 

 quantities which agree as well as could be expected with the shorter 

 periods. The negative sign of A0 merely indicates that the uncer- 

 tainty is considerable. 



The results are collected in Table VII. The value given in each 

 case is the average of the mean value for the thirteen lunar months 

 and the value deduced by treating all the observations in a single 

 set, except in the case of the N-S diurnal tide, where the values 

 given are the mean of the six determinations mentioned above, and 

 in the case of the E-W diurnal tide, which is the mean of four 

 similar determinations. 



The amphtudes are those for the observed curves averaged as 

 indicated above. The errors indicated for the different tides are 

 the average differences from the means of the thirteen months, 

 except in the case of the N-S diurnal tide, where it is simply an 



