5 GO Mr. H. S. Allen on the Effect of Errors in Ruling 



the ruling is changing. This new method resembles in 

 principle, and was indeed suggested by, Toepler's Method of 

 iStriae {Schlieren Methode), which I have had occasion to employ 

 in another connexion *. 



In the diagram (fig. 1, PI. XXIV.) ABC represents a section 

 at right angles to the ruling of a plane grating, the ruling in 

 the portion AB being wider than that in the portion BC. The 

 grating is supposed to be illuminated by a parallel beam of 

 light from the left-hand side of the diagram. The light 

 from the broader ruling which goes to form a single line of 

 the spectrum is brought to a focus at Fj by the objective of 

 the observing-telescope, the light from the narrower ruling 

 is brought to a focus at Fg. At A'WQ/ an image of the 

 grating would be formed by the objective. In the focus of 

 this lens is placed a slit S1S2 with its aperture parallel to the 

 coUimating-slit and to the lines of the grating. The slit is 

 capable of adjustment in a direction at right angles to its own 

 length and to the axis of the telescope. It is evident that a 

 displacement of the slit towards Sj will have the effect of 

 obstructing the light connng to a focus at F2 ; so that the 

 light coming from the narrower ruling will be cut off and 

 B^C^ will not be illuminated. On the other hand, a dis- 

 placement of the slit in the opposite direction allows the light 

 from the narrower rulings to pass, but cuts off that from the 

 wider rulings. By placing a photographic plate at A'B^C^ it 

 is possible to obtain a photograph of the grating, showing the 

 narrower rulings either as dark or as light bands. This 

 method of determining the errors in a grating is more difficult 

 in practice than the former one, as the adjustments have to 

 be made with much greater care, and a longer exposure is 

 required ; but it has an advantage in that the negative is 

 placed at the optical image A^B^C instead of in a position 

 such as A^^^B^^^C^^^ 



In using the photographs obtained by these methods to 

 determine the position of the periodic error existing in the 

 dividing-engine the negatives were measured under the 

 Blythswood micrometer (Hilger) with a low-power micro- 

 scope. The position of each band was thus given by its 

 distance from the commencement of the ruling. Knowing 

 the number of lines cut on the strip examined and the 

 number (720) corresponding to one revolution of the ratchet- 

 wheel, it was easy to determine the breadth representing a 

 single " period." The figures giving the positions of the 

 bands were divided into sets, each set corresponding to one 

 period, and the number fixing the position of any particular 

 *^^'ature, vul. Lw. p. 57o (1002). 



