120 A. A. Michelson — Measurement by Light-waves. 



It is evident therefore that one- thirtieth of a wave is much 

 too large an estimate of the average error in a setting, and that 

 it is in fact Less than a hundredth of a wave, corresponding to 

 an error in distance of one two- hundredth of a wave, or about 

 one ten-millionth of an inch.* 



Angular Measurements. 



In the measurement of angles the microscope is replaced by 

 the telescope. From considerations quite analogous to those 

 employed in the former case, it can be shown that the limit of 

 accuracy attainable in the estimation of angles involves an 

 error of about one tenth of a second for a ten-inch glass. Let 

 this be compared with the performance of the refractometer, 

 5, Group III, the distance mm being also ten inches. If the 

 line joining mm be rotated in the plane of the figure, there 

 will be a corresponding difference in path. Taking one hun- 

 dredth of a fringe as the smallest perceptible displacement, this 

 would correspond to a distance of one two-hundredth of a wave, 

 or in ten inches, to an angle of one five-hundredth of a second. 



In the use of the revolving mirror — as in galvanometers, 

 gravity and torsion balances, etc. — the accuracy can be increased 

 only by making the surface, and therefore also the moment of 

 inertia, of the mirror larger ; but here we may make the mirrors 

 insignificantly small and yet — with the same distance between 

 the outer edges — increase the accuracy at least twenty-fold. It 

 is important to note that any motion of the line joining the 

 two mirrors as a whole, or even a tilting of the mirrors in a 

 plane at right angles to this line, has absolutely no effect on the 

 central part of the fringes. Fig. 3, plate III, shows the appli- 

 cation of this method of angular measurement to the testing of 

 the ways of a dividing engine, comparator, etc. 



Spectrometer Measurements. 



It is not at first evident that there is any resemblance be- 

 tween the spectroscope and the refractometer. A considera- 

 tion of the figures under Group V will show that there is a 

 close analogy. Exactly as in the case of mirrors and lenses, 

 we may here too sacrifice resolution and definition by using 

 only the extreme portions of the surface, with an actual- gain in 

 accuracy. To compare numbers, it appears that the probable 

 error in the measurement of a wave by a grating with an ex- 



* It may be possible with the aid of photography to increase this degree of 

 accuracy many times. Thus, the curve representing the brightness of the fringes 

 is a simple sine function, fig. 1, plate III. Now if the intensity at the minima 

 is reallv zero, and a photographic plate be very much over-exposed to the image 

 of such interference fringes, the resulting curve would be represented by fig. 2, 

 plaie III, and it is evident that the error in setting on the darkest points (the 

 brightest on the negative) must be far less than by direct observation. 



