182 SCHLESINGER— RADIAL VELOCITIES. [April 20, 



more serious than any that we have mentioned. This is the distor- 

 tion of the field due to the presence of the prism. Let us suppose 

 that there were in the sky a row of stars in the same right ascension 

 and equally spaced in declination. Let us photograph the spectra 

 of these stars with the help of an objective prism whose refracting 

 edge is parallel to the equator. Then, quite apart from the effect 

 of radial velocity, the spectra would by no means be equally spaced 

 upon the plate, the intervals on one side of the center being all too 

 small, and those on the other side all too great. When the prism 

 is reversed, those spaces that were too large are now too small and 

 tAcc versa; so that the distance between the two spectra of the same 

 star depends upon its declination. I have computed this double dis- 

 tortion for a spectrograph whose dimensions are such as one would 

 choose for this work, and have found it to amount to two millime- 

 ters at a point only two degrees of arc from the center. This quan- 

 tity is about one thousand times as great as the accuracy that an 

 observer would hope to attain in his measurements, so that it is 

 readily seen how intimately he would have to become acquainted 

 with his prism in order that he might apply this very large correc- 

 tion within the limit of accuracy that the case demands. Further- 

 more, there is an additional distortion of nearly the same size in the 

 other direction. That is, if we could photograph a row of stars on 

 the equator, their spectra on the plate would not appear in a straight 

 line, but would lie in a curve that is approximately a para'bola with 

 its convex side toward the refracting edge of the prism. ^ If, there- 

 fore, the prism is reversed the curvature of this line is also reversed, 

 and when the two plates are compared we again have a double dis- 

 tortion, depending now (in the position of the prism that we have 

 imagined) upon the star's right ascension. It is worthy of remark 

 that these distortions are smaller in the design proposed by Com- 

 stock than in any of the others. Furthermore, if we confine our 

 attention to a single pair of spectra in the axis, as in Stewart's sug- 

 gestion, these distortions do not enter at all. 



We see, then, that the obstacles in the way of the practical appli- 



® It is this same distortion that causes the curvature of the lines upon a 

 sht spectrogram, the formula for which is given by Ditscheiner in the 

 Sitau)igsberichte der Math. Klasse der k. Akademie cu Wein, 51, part 2, 

 1865. 



