92 Prof. F. L. 0. Wads worth on the Optical Efficiency 



must now add a third, the interferometer method, first sug- 

 gested* by Michelson. I think that the only applications of 

 this method to the measurements of the deflexions of a sus- 

 pended system that have yet been made, are those recently 

 described by Barusf and by myself J, but these are sufficient 

 to prove its practicability and determine its accuracy as com- 

 pared with those just discussed. Professor Michelson has 

 shown that theoretically this method of angular measurement 

 may be made from 20 to 50 times as accurate as either of 

 the preceding. Practically, however, the accuracy in the 

 case of a freely suspended system is considerably less, because 

 the unsteadiness of the fringes, due to irregular motions of 

 the system, prevents the estimation of as small a fraction of 

 a fringe as is possible with the more stable forms of the 

 instrument. From the experiments just referred to the 

 writer has concluded that the smallest movement that can be 

 measured with certainty by this means is that corresponding 

 to a shift of 2 T o °f a fringe § . This means, in the form of 

 instrument used in these experiments, an angular movement 

 of 



V being the distance between the centres of the two mirrors 

 B and D (see fig. 4) on the suspended system. 



The smallest movement observable with the mirror is, as 

 just stated, about yV the limit of resolution, or 



1 X 2 



Hence, when h — V the interferometer method is at most 

 about three times as accurate as the mirror method ||. It has 



* See papers : " Measurement by Light Waves," Am. Jour. Science, 

 vol. xxxix. p. 115 ; " Application of Interference Methods to Astrono- 

 mical Measurements," Phil. Mag. vol. xxx. p. 1 ; " Application of Light 

 Waves to Metrology," ' Nature,' Nov. 16, 1893. 



t " On a Possible Development of the Ideostatic Electrometer," ' The 

 Physical Peview,' vol. iv. p. 400, March-April 1897. 



t " On the Application of the Interferometer to the Measurement of 

 Small Angular Deflections of a Suspended System," ibid. vol. iv. p. 480, 

 May-June 1897. 



§ Dr. Barus assumes the limit to be J_ f a fringe. 



|| If we could get rid entirely of the effects of vibration the advantage 

 of the interferometer over the simple mirror would be much greater. 

 For such purposes as measuring the twist or the bending of bars, or the 

 errors of straight edges, &c, the mountings of the mirrors may be made 

 so stable that irregular motions are almost entirely eliminated, and it 



