I 



I 



Aberration of the Concave Gratincf. 155 



An oxaniination of the two tables of \vav(^-lenoth deter- 

 minations made by Mitchell with his instrument shows that 

 the mean error of measurement was very much greater than 

 this. In the case of the wave-lenoth of the series of liydro- 

 oen-lines in the spectrum of Rigel, the mean error of three 

 detei-minations on each of the twenty- two lines (H^ to head 

 of series) as compared with the theoretical wave-lengths 

 calculated from Balmer's law is about 0"120 tenth-metre. 

 No data are given from which the individual errors of setting 

 on each line can be determined, but they must necessarily 

 have been cjr eater than this. In the case of the wave-length 

 measurements of the lines in the nebula of Orion the mean 

 error as determined by a comparison of the two series of 

 measurements is about 0'480 tenth-metre. Here also each 

 determination tabulated is presumably (although it is not so 

 stated) the mean of several settings, and if so, the mean 

 error of individual settinos would aoain be much greater than 

 that given. Ea^cu without any allowance for such an in- 

 crease, the errors of setting as they appear are respectively 

 about thirty times and one hundred and twenty times what 

 they would be if the full optical power of the grating were 

 being realized. 



In the case of Table II. of Mitchell's paper, there is further 

 evidence that the grating was not gi^^ing the results which 

 one of this aperture should attain under proper optical 

 conditions. There is a group of three well-sej^arated lines in 

 the nebula of Orion which, according to AVright, have wave- 

 lengths X = 3970*24 ; 3967'69 ; and 3965*1 ; and intensities 

 of 5, 3, and 1 respectively. These lines were clearly resolved 

 and accurately measured to about 001 tenth-metre by 

 Wright with the Mills spectrograph, which has a theoretical 

 resolving-power in this region of the spectrum practically 

 equal to that of MitchelFs instrument. On MitchelPs list 

 only one of these lines — the brighter one — appears at all, 

 and the error of measurement on this amounts to between 0*6 

 and 0*7 tenth-metre. 



These comparisons of Mr. Mitchell's work are instituted, 

 not because of any wish to criticize the work itself, per se^ but 

 only to show that the general conclusions reached in this 

 paper by the mathematical analysis are not incompatible with 

 his experimental results. There now seems to be no question 

 but that both Dr. Poor and Mr. Mitchell, in common with 

 Mohler and Daniel and Jewell, have considerably overrated 

 the advantages of the direct concave-grating spectroscope, 

 or, as the writer prefers to call it, the concave objective- 

 grating spectroscope. I am not myself in a position to 



