March 9, 1900.] 



SCIENCE, 



371 



To appreciate the full force of the above 

 statements one must have a realizing sense 

 of the great length of the above arcs. The 

 combined length of all the arcs used by 

 Colonel Clarke in 1880 to deduce the figure 

 of the earth was equivalent to 89 degrees 

 of a great circle. The arc of the thirty- 

 ninth parallel is equivalent in length to 37 

 degrees of a great circle ; the Atlantic ob- 

 lique arc is 22 degrees long, and the Cali- 

 fornia oblique arc 8 degrees ; and the com- 

 bined length of these three arcs is 67 

 degrees, or more than two-thirds the total 

 length used by Clarke. 



The most interesting recent development 

 in geodesy has been the investigations of 

 variations of latitude. It may be asked, 

 " Why is this investigation classed as geo- 

 detic rather than astronomic?" The answer 

 is: It belongs in both classifications. Ob- 

 viously it is an astronomical investigation, 

 but it concerns the geodesist also ; it con- 

 cerns him directly, because the astronomical 

 latitudes with which he must deal are now 

 known to be a function of the time of obser- 

 vation. It is interesting to note also that 

 many of the observations upon which our 

 knowledge of the latitude variation depends 

 were made with the zenith telescope, an 

 instrument which the geodesist claims 

 rather than the astronomer. 



For ten years past there has been marked 

 activity in investigating this question along 

 two lines. One class of investigators worked 

 by the inductive method, and slowly built 

 up empirical mathematical expressions for 

 the observed facts as to the variations, in- 

 dependently of any theory as to their causes. 

 For this purpose they used many series of 

 old observations, made at various fixed 

 observatories, but not primarily for this 

 purpose. In addition they have used many 

 modern series of observations, made with 

 zenith telescopes, for this special purpose. 

 It has been shown that the motion of the 

 pole in the past may be represented with 



considerable accuracy as a combination of 

 two motions, each circular, one with a mean 

 period of about 428 days and the other 

 with a period of one year. A still closer 

 approximation is obtained by assuming that 

 the amplitude and epoch of each these mo- 

 tions is subject to a periodic variation. A 

 somewhat closer agi-eement between the 

 mathematical curves and the observations 

 is secured when elliptical paths are substi- 

 tuted for the circular paths above referred 

 to. The net result of the investigations 

 by the inductive method has been certain 

 mathematical expressions which closely 

 represent the known facts of the past, but 

 there is great uncertainty as to how far into 

 the future these mathematical expressions 

 may be extended, because their basis is 

 wholly empirical. 



The progress made along this empirical 

 line of investigation has been due to Pro- 

 fessor S. C. Chandler, of Harvard, more 

 than to any other one man or, possibly, any 

 group of men. His results have been pub- 

 lished as the investigations proceeded in 

 the Astronoyiiical Journal, and form an ex- 

 ceedingly interesting series, not only on ac- 

 count of the remarkable success attained, 

 but because of the ingenuity and skill 

 shown in devising methods of investigation 

 which are independent of any theoretical 

 basis. 



Another class of investigators has worked 

 from the standpoint of pure theory. Their 

 endeavor has been to furnish an adequate 

 explanation for the observed facts. Up to 

 the time when the latitude was shown, by 

 direct observation, to be subject to periodic 

 variations, one of the fundamental assump- 

 tions upon which astronomical computa- 

 tions were based was that the latitude of a 

 given point on the earth's surface is invari- 

 able. Pure theory, indeed, indicated that 

 the latitude of a point should be subject to 

 a periodic variation of small amplitude with 

 a period of about 305 days. Special inves- 



