in Prof. Rowland's Concave Gratings. 191 



with greater precision in the special determinations with the 

 intention to obtain by the exactness of the adjustment the 

 same scale through the whole spectrum. 



However, when all adjustments were completed, no distinct 

 image could be obtained in any part of the spectrum. In 

 the visible spectrum of the first order the image was not very 

 much out of focus, but the deviation increased gradually, so 

 that it became necessary to displace the eyepiece several 

 centimetres to obtain well-defined images of the spectra of 

 higher orders. All details being executed with the same 

 accuracy, there was nothing that could indicate the cause of 

 the discrepancy, so that nothing remained but to make all 

 the adjustments OA^er again, determining at the same time 

 the extreme limits of the errors. For this purpose I have 

 made use of new methods of adjustment, and I have ascer- 

 tained by these researches : — 



1. That the courses which the apex of the grating and the 

 cross hairs of the eyepiece follow in their movement on the 

 rails do not deviate in any point from straight lines by more 

 than 0*2 millim. 



2. That the angle formed by the average directions of 

 the rails did not differ from a right angle by more than 

 15" (corresponding to an arc of 0*5 millim. at one of the ends 

 of one of the rails), the difference probably not amounting to 

 more than a third of this value. 



3. That the middle of the slit could not be more than 0*2 

 millim. from the crossing-point of the lines that are described 

 by the apex of the grating and the cross hairs of the eye- 

 piece. 



4. That the apex of the grating and the cross hairs of the 

 eyepiece were not more than O'l millim. distant from the 

 axes of the carriages. 



5. That the distance between the centre of curvature of 

 the grating and the axis of the carriage on which the eye- 

 piece was placed, did not amount to 0*5 millim. during the 

 whole movement. 



6. That the lines of the grating and the direction of the 

 slit were parallel and at right angles with the plane of the 

 rails. 



7. That the grating was entirely free from all constraint 

 and of spherical form, the images in the centre of curvature 

 being of excellent definition. 



8. That the optical state of the slit was perfectly normal. 

 With these results it was only in the grating itself that 



the cause of the displacement of the spectra could be looked 

 for, either in some imperfection of the theory or in some 



