86 Prof. F. L. 0. Wadsworth on the Optical Efficiency 



to the narrowness of the diffraction images of the lines of his 

 scale*; a condition exactly the reverse of that assumed by 

 Michelson as necessary for accuracy of measurement. To 

 explain this apparent contradiction we must consider a little 

 more closely just how angular measurements of position are 

 usually made. As a rule the angular motion is determined 

 by observing the motion of the image of a point either actually 

 moving with the system (microscope and pointer), or appa- 

 rently moving with it. f (mirror and scale), with reference to 

 some fixed point. The image and fixed point are examined 

 either with the eye directly or with the aid of an eyepiece. 

 In the first case the reference-point is a line or series of lines 

 engraved on a screen upon which the moving image is pro- 

 jected ; in the second case it is generally a cross-wire placed 

 in the focus of the observing eyepiece. In either case the 

 object examined is, when the highest degree of accuracy is 

 aimed at, a narrow line whose image is represented at the 

 focal plane of the mirror or objective (rectangular aperture) 

 by the diffraction pattern of fig. 1. 



The problem is to determine the position of the centre of 



Fi<?. 1. 



this pattern with reference to a fixed line (or wire) parallel 

 to the axis of symmetry ao. When the relative position is 

 judged by means of the eye it makes no difference whether 

 the image is thrown on a ruled screen or seen through an 

 ej'epiece. In either case the image of the diffraction pattern, 

 as formed on the retina, is another diffraction pattern similar 



* The scale having black lines on a very brightly illuminated field, the 

 effect of diffraction would be to make the images of the lines appear 

 narrower than their geometrical images. 



t It does not matter which, for it is the motion of the image only with 

 which we are concerned. 



