﻿396 Dr. C. V. Barton on 



to adjust the position of the carriage on which both W and S 

 are mounted. 



24. Finally, it may be pointed out that, although the slit 

 is illuminated as intensely as possible, its length need not 

 be more than 3 or 4 mm., while its width has to be made 

 exceedingly small ; so that the heating and other disturb- 

 ances due to radiation falling on the mirror are reduced to 

 a minimum. This may become a matter of some importance 

 when sensitivities are being pushed to extremes. In regard 

 to the mirror, it may be well once again to emphasise the 

 importance of a good optical surface of uniform reflecting 

 power, and to repeat that the boundary of that surface must 

 be a rectangle whose sides are respectively vertical and 

 horizontal. Notwithstanding the name suggested for the 

 apparatus described, its applicability is clearly not limited to 

 the detection and measurement of azimuthal deflexions. 



Appendix. 



Approximate Theory of the Instrument. 



25. In the case where the slit is illuminated by homo- 

 geneous light, it is not difficult to develop an approximate 

 theory of the instrument ; from this some qualitative con- 

 clusions may be drawn as to the performance to be expected 

 when white light is substituted. The slit, on which the image 

 of a luminous body is focussed, may be regarded as made up of 

 innumerable independent point-sources. Corresponding to 

 any one such point-source, a diffraction nattern is formed 

 about the position of the '• geometrical '' image, the bright- 

 ness B of which at any point, in terms of the central 

 brightness B , is given by 



B = B _^- sin* ?** AVI sin2 ^ m 



Here x and y are respectively horizontal and vertical co- 

 ordinates in the focal plane, the origin being the point 

 representing the geometrical image ; \ is the wave-length of 

 the light employed, and /the focal length of the lens, while 

 a is the breadth and h the height of the effective reflecting 

 surface. The pattern thus represented is traversed by lines 

 of absolute blackness, parallel to the axes of coordinates. 



26. If, instead of a single point source of light, we have 

 an infinitely narrow uniformly illuminated slit, whose length 

 < /) is vertical and is considerable in comparison with \f/a, 



