RECORDS. 157 



2. That the photographic copy of the rcscaii, as it appears on 

 the star-plate, really reproduces exactly the division errors of 

 the original. 



3. That the bisection of photographed reseau lines on a star- 

 plate can be made with a microscope as accurately as the lines 

 of a scale can be bisected. 



It is of course possible to discuss each of these assumptions 

 separately ; but in the present note I shall consider one simple 

 experiment only. This consisted in measuring a couple of 

 Pleiades photographs twice, once by the rcscau method, and 

 once with a metallic scale. A simple comparison ought then 

 to show how far the two methods of measurement differ in 

 their results. Seventy-five stars were observed in each case, 

 and the same stars were used. The first plate was made at Paris, 

 1 90 1, January 14, and the "probable discordance" between 

 the two methods of measurement was dz o" . 1 1 . No corrections 

 were applied for possible division errors of the Paris reseau, as 

 none have been published, though the MM. Henry have satis- 

 fied themselves that the Paris reseau errors are inappreciable. 

 The second plate was made at Helsingfors, 1900, Dec. 12, 

 and gave a probable discordance of ±o".2 2. In this case the 

 reseau measures were corrected with Donner's division errors ; 

 but these are not large enough to affect the result appreciably. 

 In both cases, measures made with the metallic scale were 

 corrected for the division errors determined at Columbia Uni- 

 versity. The larger discordance in the case of the Helsingfors 

 plate is probably due to the less well defined character of the 

 photographed reseau lines. In many cases it is impossible to 

 bisect these lines under the microscope anywhere except at 

 the corners of the squares, where two lines cross and form a 

 point. 



But when we consider that the above discordances involve 

 the errors of both measurements, they do not appear unduly 

 large. Divided by -^ 2, they give for the probable error of 

 a measurement by one method only ± o".o8 for Paris, and 

 d= o" . 16 for Helsingfors ; and there is no evidence of a systematic 

 arrangement of signs in the differences between the two methods. 

 Annals N. Y. Acad. Sci., XV, April, 1904 — 12. 



