466 BEPORT — 1882. 



always in electrical contact with the latter, the circuit is only completed when it is 

 brought into contact with the former. Accounts of experiments showing the satis- 

 factory action with this apparatus were then given. Finally, the most recent form of 

 apparatus which is portable was illustrated and described. 



6. On a Machine for ruling large Diffraction Gratings. 



By A. IklALLOCK. 



Considerable interest attaches to the rulir.g of diffraction gratings, both on 

 account of the mechanical difficulties involved in then- production, as well as the 

 admirable results which are obtained by their means when used for the purpose of 

 analysing light. - j.^- 



The author did not intend to enter into the general theory of diffraction grat- 

 ings, further than was necessary to point out the kind of accuracy which must be 

 attained in ruling them if they are to give anything approaching the best results ; 

 but merely to give a short description of a machine made by him for the production 

 of large gratings, and to mention some of the results obtained by it. 



In all optical apparatus, whether lenses, prisms, mirrors, or diffraction gratings, 

 the unit of length in which errors or deviation from the form or position of lines 

 must be reckoned, is the wave-length of the light dealt with, and it has been shown 

 by Lord Rayleigh, and is indeed tolerably obvious when once pointed out, that if, 

 as is generally the case, the object of an optical siu'faceis to cause the whole of a 

 wave-front of finite area to reach a certain point in the same phase, a result not 

 differing much from the best possible will be obtained, if the errors of the surface are 

 such as not to cause an average disagreement of phase of more than one-fourth of a 

 wave-length at the focal point. 



The actual value of the permissible error indicated by the above condition is, 

 for nearly perpendicular refraction and reilection, in glass about half a wave- 

 length, and in mirrors about one-eighth of a wave-lengtb. For further informa- 

 tion on these points, the reader is referred to papers by Lord Rayleigh in the ' Phi- 

 losophical Magazine' (October and December 1879, and January 1880). The 

 surfaces on which diffraction gratings are ruled should have an accuracy of this 

 kind, and the accuracy with wliich the lines of the grating are placed should be such 

 that the projection of their errors of position on the path of the diffracted ray shoidd 

 not be greater than one-fourth of a wave-length for the first spectrum, or 1 for the 

 «th spectrum, if the performance of the grating in that order of spectrum is to 

 approach perfection. 



These remarks apply when the angle between the incident and diffracted ray is not 

 very large, i.e. when the distance between the lines is a considerable multiple of the 

 wave-length. In the limiting case in which a diffi-action spectrum can be formed, 

 which is when the lines are only separated by one-half a wave-length, the permis- 

 sible error in their position becomes, as in case of mirrors, one-eighth of a wave-length. 



The definition of a grating depends, ceeteris paribus, on its width, in the same 

 way that that of a telescope depends on the diameter of the object-glass. It Ls 

 very doubtful if any optical work hitherto produced approaches the extreme exact- 

 ness which one-eighth wave-length error indicates, but the above remarks show 

 at any rate that a very high order of accuracy is required in order to produce 

 effective diffraction gratings. The author proceeded to describe the principles 

 adopted in his machine by which this accuracy is intended to be secured. 



Most of the sketches for the machine were made during the yeai-s 1876-78. At 

 the close of 1878 the author made an application to the Government Grant Com- 

 mittee of the Royal Society for aid in the construction of the machine, and tliis 

 being fovourably received, "the working drawings were put in the hands of Mr 

 W. R. Munro, of King's Cross Road, in 1879. 



The machine was completed at the close of last year, and some good results have 

 been obtained by it. The chief difficulty experienced, and one which continues 

 to give trouble, "is of a very commonplace kind, viz., that of getting a suitable 

 motor, which will go for several weeks without verj- constant attention, and above 



