396 



SCIENCE 



[N". S. Vol. XL. No. 1029 



the principle mentioned. The analogy to 

 the figure of the earth with its marked land 

 and sea hemispheres is perhaps worth 

 pointing out, but the higher ground in the 

 moon is mainly on the south of its equator, 

 while that on the earth is north. Unfor- 

 tunately we know nothing about the other 

 face of the moon. Nevertheless it seems 

 worth while to direct the attention of geol- 

 ogists to facts which may ultimately have 

 some cosmogonic applications. The astron- 

 omical difficulties are immediate: different 

 corrections for meridian observations in 

 latitude, in longitude, on Mosting A, for 

 occultations and for the photographic 

 method, will be required. 



I next turn to a question, the chief inter- 

 est of which is geodetic rather than astron- 

 omical. I have mentioned that a certain 

 value of the earth's elliptieity will make the 

 observed motions of the perigee and node 

 agree with their theoretical values. This 

 value is 1/293.7 ± .3. Now Helmert's 

 value obtained from gravity determinations 

 is 1/298.3. The conference of "Nautical 

 Almanac ' ' Directors in 1911 adopted 1/297. 

 There is thus a considerable discrepancy. 

 Other evidence, however, can be brought 

 forward. Not long ago a series of simul- 

 taneous observations at the Cape and Green- 

 wich Observatories was made in order to 

 obtain a new value of the moon 's parallax. 

 After five years' work a hundred simulta- 

 neous pairs were obtained, the discussion of 

 which give evidence of their excellence. 

 Mr. Crommelin, of the Greenwich Observ- 

 atory, who undertook this discussion, deter- 

 mined the elliptieity of the earth by a 

 comparison between the theoretical and ob- 

 served values of the parallax. He found 

 an elliptieity 1/294.4 ± 1.5 closely agree- 

 ing with that which I have obtained. 

 Finally, Col. Clarke's value obtained from 

 geodetic measures was 1/298.5. We have 

 thus three quite different determinations 



ranging round 1/294 to set against a fourth 

 determination of 1/298. The term in the 

 latitude of the moon which has often been 

 used for this purpose is of little value on 

 account of the coefficient being also depend- 

 ent on the value of the obliquity of the 

 ecliptic; such evidence as it presents is 

 rather in favor of the larger value. I omit 

 Hill's value, obtained from gravity deter- 

 minations, because it is obviously too large. 



Here, then, is a definite issue. To satisfy 

 the observations of the moon in at least 

 three different parts, a value near 1/294 

 must be used; while the value most care- 

 fully found from gravity determinations 

 is 1/298. As far as astronomy is concerned, 

 the moon is the only body for which a cor- 

 rect value of this constant is important, and 

 it would seem inadvisable to use a value 

 which will cause a disagreement between 

 theory and observation in at least three 

 different ways. It is a question whether 

 the conference value should not be changed 

 with the advent of the new lunar tables. 



In looking forward to future determina- 

 tions of this constant, it seems to be quite 

 possible that direct observations of the 

 moon's parallax are likely to furnish at 

 least as accurate a value of the earth's 

 shape as any other method. This can be 

 done, I believe, much better by the Har- 

 vard photographic method than by merid- 

 ian observations. Two identical instru- 

 ments are advisable for the best results, one 

 placed in the northern and the other in the 

 southern hemisphere from 60° to 90° apart 

 in latitude and as nearly as possible on the 

 same meridian. On nights which are fine 

 at both stations, from fifteen to twenty 

 pairs of plates could be obtained. In a few 

 months it is probable that some 400 pairs 

 might be obtained. These should furnish 

 a value for the parallax with a probable 

 error of about 0".02 and a value for the 

 elliptieity within half a unit of the denom- 



