90 



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



diffraction images the greater the attainable accuracy, because 

 a given percentage error of subdivision A may be attained 



Fia-. 3. 



with a smaller absolute value of 8. Hence in this case the 

 conditions assumed by Boys, i. e. dark images on a bright 

 field, are more favourable to accuracy of reading (because 

 the images appear narrower) than the reverse arrangements 

 Under the most favourable circumstances (see experimental 

 results quoted on p. 85) the smallest observable movement of 

 one image with respect to the other seems to be between ^ and 

 I the limit of resolving power. This corresponds to a linear 

 movement of about ^ A, in the case of the microscope, and to 



\ , IX. 

 5 b 



an angular movement of from jq t to T 7 " in the case of the 

 mirror. 



III. Suppose the cross-wire and the image unlike in 

 character — one light, the other dark. In this case the 

 accuracy in setting will increase with the width of the image 

 with respect to the reference-wire (Michelson) provided the 

 former is bright enough to be distinctly seen. Jf the width 

 is great enough the position of the image with respect to the 

 wire can be determined to within one per cent., i. e. the 

 accuracy may be 50 times the resolution of the instrument. 

 But from what has already been said (p. 87) it is evident that 

 the only method of broadening the image of a narrow line, 

 as seen through a telescope or microscope, with reference to 

 the image of the cross-wire as seen through the eyepiece 

 alone, is to make the effective angular aperture of the tele- 

 scope or microscope objective much smaller than that of the 

 eyepiece. This entails a loss not only in contrast between 

 the two images, but also (if carried too far) a decrease in the 

 resolving power of the instrument; for, as Bayleigh has 

 pointed out, " the Ihrit of the resolving power of telescopes 

 is attained, with a Mjvy moderate magnification, probably 



