October 20, 1911] 



SCIENCE 



535 



To secure comparable images, the exposures to 

 the moon must be less than a thousandth of those 

 on the neighboring stars; and, except during this 

 short exposure the objective must be completely 

 shielded from the moon's rays to avoid fogging 

 by diffusely reflected light. This was accom- 

 plished by placing a disk, some distance in front 

 of the telescope, which shades the objective from 

 the moon, but is not so large as to cut off much 

 of the light from the surrounding stars. This disk 

 may be turned edgewise for a short exposure on 

 the moon, the exact time of which is recorded 

 chronographically. 



The instrument employed was the Metcalf tele- 

 scope of sixteen inches aperture and eighty-seven 

 inches focal length, stopped down to 3i inches 

 aperture, with a disk five inches in diameter car- 

 ried on a pole nine feet long attached to the 

 telescope tube. Exposures of ten minutes on the 

 stars and of 0.2 to 0.4 second on the moon, gave 

 very satisfactory plates. 



A standard reseau was photographed on each 

 plate. The rectangular coordinates of the stars 

 chosen for reference points were measured with 

 respect to this system, and also those of ten or 

 more points on the moon's illuminated limb (most 

 of these being the intersections of the limb and 

 reseau lines). After allowing for the slight dis- 

 tortion of the moon's apparent disk by refraction, 

 the circle which passed as close as possible to the 

 measured points on the limb was determined by 

 least-squares, and its center assumed to coincide 

 with that of the moon. The determination of the 

 right ascension and declination corresponding to 

 this point on the plate and the comparison with 

 the tabular places of the American Ephemeris, 

 were made in the usual way. 



The probable error with which the coordinates 

 of a star relative to its neighbors are determined 

 from a single plate is ± 0".25. The absolute posi- 

 tions of the same stars, given in the catalogues 

 consulted, appear to have probable errors of about 

 ± 0".4 in each coordinate. The measures of the 

 moon's limb are almost as accurate as those of 

 the star-images; but the actual irregularities of 

 the surface raise the probable error of position 

 of one measured point (determined by means of 

 its departure from the mean circle of the limb) 

 to ± 0".47. 



More dangerous than any of these errors is that 

 arising from imperfect guiding. If the telescope 

 is not directed towards exactly the same point in 

 the heavens during the short exposure on the moon 



as, on the average, it is during the long exposure 

 on the stars, errors will result which with a poor 

 mounting might be very serious. 



To investigate such errors, special plates were 

 taken, on which bright stars were photographed in 

 exactly the same way as the moon. These showed 

 that the combined effects of errors of guiding and 

 measurement is equivalent to a probable error of 

 ± 0«.031 in E.A. and ± 0".29 in declination. 



Combining all these results it appears that the 

 known errors of observation will account for prob- 

 able errors in the deduced places of the moon of 

 ± 0».044 in E.A. and ± 0".40 in declination. 



Eleven plates have so far been discussed. The 

 agreement of pairs taken on the same night is 

 satisfactory. Comparison of the results of obser- 

 vations on different nights is complicated by the 

 fact that the errors of the moon's tabular place 

 are now large and variable. Through the courtesy 

 of the Astronomer Eoyal, Professor Dyson, the 

 results of the Greenwich meridian observations of 

 the moon are available for comparison. The 

 Greenwich and Harvard results agree excellently 

 inter se, showing that in December, 1910 (during 

 which month most of the plates now discussed 

 were taken), the moon was ahead of her tabular 

 position by an amount varying from 10".7 on 

 December 9 to 4".8 on December 22, and at the 

 same time 0".6, on the average, south of the 

 tabular place. Eepresenting this by an empirical 

 curve, it is found that the outstanding probable 

 errors of one observation at Greenwich are 

 ± 0''.048 E.A. and ± 0".57 in declination, while 

 those of the result of one plate are ± 0'.043 and 

 ± 0".55. 



The photographic method, therefore, appears to 

 give results, on its first trial, somewhat superior in 

 accuracy to those of meridian observations of the 

 first class. It also appears, upon comparison of 

 the observed and predicted probable errors of 

 observation, that the greater part of the error of 

 the photographic results arises from definitely 

 known sources of error. There is little doubt that 

 these can be considerably diminished by appro- 

 priate methods. 



The photographic method has also the two great 

 advantages that its errors are for the most part 

 different in origin from those of meridian observa- 

 tions, and hence independent of them, and that it 

 is available over a wide range of hour angles. It 

 seems, therefore, likely to prove of great value in 

 the attempt to improve our knowledge of the 

 moon's motion. 



Many more plates have already been taken at 



