of Methods for Observing Small Rotations. 85 



power) ; and a is a constant whose value varies with different 

 instruments, but is, according to Michelson, principally 

 dependent upon the magnification of the object whose position 

 is to be determined in comparison to the reference object*. 



If the magnification is so high that the diffraction-fringes 

 about the measured object are much broader than the reference 

 object (usually a cross-wire in the eyepiece of the observing 

 instrument), the value of a may be as large as 100. Under 

 practical conditions, however, no such degree of magnification 

 can be attained, for reasons which will be presently considered, 

 and the value of a will be correspondingly lower. For the 

 microscope Michelson fixes the limiting value of a at 5 (from 

 experiments of Rogers and Morley), corresponding to an error 

 of about ^ x^ anc l a t 4 in the case of the telescope, or 8 in 

 the case of the revolving mirror, corresponding to an error in 

 angle of O'^OS for a mirror of 25 centim. aperture. In a later 

 paper t the same author assumes a slightly higher value as the 

 limiting value of a (i. e., 10) in the case of the mirror, 



In a former paper describing some results of some work on 

 the testing of straight edges J, I have pointed out that with a 

 mirror of 4 centim. aperture an angular movement of 0"*15 

 could be detected, and one of not more than 0"'2 to //# 3 

 measured with certainty. From (1) we find for a r for a 

 4 centim. aperture 



\— about 0-00055 ,„ K 



80 



The two corresponding values of a in this case are there- 

 fore 20 and 10. More recently Boys, in his great memoir on 

 the Newtonian Constant, has also pointed out that with his 

 apparatus (which had a mirror of about 2 - 3 centim. aperture) 

 the accuracy of measurement was at least seven times the 

 resolution, or nearly four times the theoretical measuring- 

 power § as given by Rayleigh. Boys, however, ascribes this 



* " Measurement of Light Waves," A. Michelson, Amer. Journ. 

 Science, vol. xxxix. p. 115. 



t " Light Waves and their Application to Metrology," ' Nature,' 

 vol. xlix. p. 56, Nov. 16, 1893. 



% "The Manufacture of Very Accurate Straight Edges," Journal 

 Franklin Inst., vol. cxxxviii. p. 1, July 1894 ; 'American Machinist,' 

 Aug. 23rd, 1894. 



§ " On the Newtonian Constant of Gravitation," Phil. Trans, 

 vol. clxxxvi. A, pp. 1-72 (1895). See particularly p. 33, and also review 

 of this memoir by the writer, in the ' Astrophysical Journal ' for April 

 1896, vol. iii. p. 303. Prof. Boys states that this degree of accuracy could 

 easilv have been exceeded if the divisions on his scale had been finer. 



