43° THE POPULAR SCIENCE MONTHLY 



by the circle. The station where these vertical distances are the small- 

 est will, in general, have obtained the most accurate results. An in- 

 spection of the figure shows that the best agreement was obtained at 

 Mizusawa. It is rather significant that at Carleforte, where more than 

 twice as many observations are obtained than at some of the other sta- 

 tions, and the meteorological conditions are exceptionally fine, yet the 

 agreement between the observed and the computed curves is not so close 

 as at some other stations. This is a good illustration of the precept 

 that, in general, little or nothing is to be gained by increasing beyond 

 a certain moderate amount the number of observations made with the 

 same instrument under similar circumstances. In fact it is quite pos- 

 sible that just as good results could be obtained by limiting the number 

 of observations taken at each station to a monthly average of a hundred 

 or thereabouts. 



As Tschardjui and Ukiah are separated by nearly 180° of longitude, 

 the curve of the one is almost the counterpart of the other. It may 

 be seen from Fig. 5 that the maximum change in the latitude, during 

 the time represented, is less than 0".5, which corresponds to about fifty 

 feet on the surface of the earth. The observatory then apparently 

 swings back and forth in the meridian to a distance of twenty-five feet 

 on either side of the mean position. 



Having now the actual observed variations in the latitude at six 

 different stations, separated widely in longitude, it is a comparatively 

 simple problem in mathematical analysis to compute what the actual 

 motion of the pole, with respect to its mean position, must be in order 

 to produce the observed changes in the latitudes. If the difference 

 between an instantaneous value of the latitude and the mean value be 

 represented by A<£; the rectangular coordinates of the instantaneous 

 pole, with respect to the mean position of the pole, by x and y ; and the 

 longitude of the observing station by A; then the following equation, 

 the derivation of which is given in the review mentioned above, may be 

 written, 



A<p = x cos X + y sin X. 



Early investigations showed that the observations were not repre- 

 sented to the highest degree of accuracy by this equation and Dr. 

 Kimura, the Japanese astronomer, suggested the addition to the equa- 

 tion of a third term, z, independent of the longitude. The observa- 

 tions are satisfied much better by an equation of this form, and z turns 

 out to be a small variable quantity of an annual period. No satis- 

 factory physical explanation of this term has as yet been given. 

 Several have been suggested, one of which is that perhaps there is a 

 small annual shift in the position of the center of gravity of the earth. 



In order to solve the problem connected with this term, two addi- 

 tional latitude stations were established in the southern hemisphere in 



