198 Dr. J. R. Rydberg on a certain Asymmetry 



grating. It seems more likely that it touches it, but at 

 another point, which, as can be seen by construction and 

 calculation, would be situated at a distance of 46*4 millim. 

 from the apex C. In reality, the conclusions that could be 

 drawn from the measurements would remain almost the same, 

 if we had replaced in fig 1 the circle CL^OMj by a circle 

 passing through but not through C or O t and touching 

 the grating at CV This circle would have a radius equal to p. 

 that is to say 0*17 millim. less than that of the former. As 



to the variation AS of the ansde S, we find sin AS=-r : , 



° 2 cos /a 



a quantity varying with /n, but which falls within the limits of 

 errors of observation in all parts of the spectra, that we can 

 use. The arc CCj differs from the arc OO x (16 '4 millim.) 

 only by some tenth of a millimetre. Under this new sup- 

 position an exact adjustment according to Prof. Rowland's 

 theory is obtained by displacing the grating 46*4 millim. 

 along its own surface, until the point of contact of the focal 

 circle falls in with the axis of the carriage, where the apex of 

 the grating was situated before. The considerable obliquity 

 that the position of the grating would show in that case is 

 the only difficulty with this arrangement. Hence I have 

 preferred the first method of adjustment, after having con- 

 vinced myself that the difference is of no importance from a 

 practical point of view. 



VI. On the other hand, the last manner of considering the 

 matter seems to possess a considerable advantage, because it 

 will allow us to account in a simple way for the relations 

 between the true focal circle and the grating. In reality, 

 the accordance with Prof. Rowland's theory is perfect and 

 the obliquity is only due to the point of symmetry of the 

 grating not coinciding with the apex of the concave mirror. 



Let ACxCBO (fig. 2) be a section through the centre of 

 curvature, perpendicular to the surface A C B and to the 

 lines of the grating. Let AB be the chord of the section, 

 which is perpendicular to the radius CO that passes through 

 the apex of the spherical cap. The lines of the grating 

 being drawn perpendicular to the axis of the dividing- 

 machine (and perpendicular according to our supposition to 

 the plane of the paper) it will always be possible to draw in the 

 plane of the paper a straight line EF parallel to the axis in 

 question. On a tangent plane TT X to the spherical surface, 

 parallel to EF and perpendicular to the plane of the paper, 

 the dividing-machine would draw equidistant lines. On both 

 sides of the point of contact Cx of this plane the distances of 

 the corresponding lines are also equal, C x is the point of 

 symmetry and the point of contact of the focal circle. Then 



