488 HENRY A. ROWLAND 



immediately designed the remainder of the machine, and have now had 

 the pleasure since Christmas of trying it. The screw is practically per- 

 fect, not by accident, but because of the new process for making it, and 

 I have not yet been able to detect an error so great as one one-hundred- 

 thousandth part of an inch at any part. Neither has it any appreciable 

 periodic error. By means of this machine I have been able to make 

 gratings with 43,000 lines to the inch, and have made a ruled surface 

 with 160,000 lines on it, having about 29,000 lines to the inch. The 

 capacity of the machine is to rule a surface 6^ x 4| inches with any 

 required number of lines to the inch, the number only being limited by 

 the wear of the diamond. The machine can be set to almost any num- 

 ber of lines to the inch, but I have not hitherto attempted more than 

 43,000 lines to the inch. It ruled so perfectly at this figure that I see 

 no reason to doubt that at least two or three times that number might 

 be ruled in one inch, though it would be useless for making gratings. 



*A11 gratings hitherto made have been ruled on flat surfaces. Such 

 gratings require a pair of telescopes for viewing the spectrum; these 

 telescopes interfere with many experiments, absorbing the extremities 

 of the spectrum strongly; besides, two telescopes of sufficient size to 

 use with six inch gratings would be very expensive and clumsy affairs. 

 In thinking over what would happen were the grating ruled on a sur- 

 face not flat, I thought of a new method of attacking the problem, and 

 soon found that if the lines were ruled on a spherical surface the 

 spectrum would be brought to a focus without any telescope. This 

 discovery of concave gratings is important for many physical investiga- 

 tions, such as the photographing of the spectrum both in the ultra- 

 violet and the ultra-red, the determination of the heating effect of the 

 different rays, and the determination of the relative wave lengths of 

 the lines of the spectrum. Furthermore it reduces the spectroscope to 

 its simplest proportions, so that spectroscopes of the highest power may 

 be made at a cost which can place them in the hands of all observers. 

 With one of my new concave gratings I have been able to detect double 

 lines in the spectrum which were never before seen. 



The laws of the concave grating are very beautiful on account of their 

 simplicity, especially in the case where it will be used most. Draw the 

 radius of curvature of the mirror to the centre of the mirror, and from 

 its central point with a radius equal to half the radius of curvature 

 draw a circle; this circle thus passes through the centre of curvature 

 of the mirror and touches the mirror at its centre. Now if the source 

 of light is anywhere in this circle, the image of this source and the 



