1881.] Bimodular Method of Computing Logarithms. 381 



III. " On a Method of Destroying the Effects of slight Errors of 

 Adjustment in Experiments of Changes of Refrangibility 

 due to Relative Motions in the Line of Sight." By E. J. 

 Stone, F.R.S., Director of the Radcliffe Observatory, 

 Oxford. Received January 17, 1881. 



Let arrangements be made for the reversion of the prisms without 

 any disturbance of the other optical arrangements, including, of 

 course, the position of the cylindrical lens, if one be used. Any slight 

 errors of adjustment which prevent the light from the star and the 

 comparison light from falling upon the train of prisms under the same 

 optical circumstances, so far as mere direction is concerned, will have 

 opposite effects in the reversed positions of the prisms ; but the 

 separation of the emergent lights due to relative motion will remain 

 unchanged by the reversal of the positions of the prisms. 



If, therefore, the apparent change of refrangibility due to relative 

 motion remains unchanged by the reversion of the prisms, all doubts 

 about the effects of errors of adjustment will be removed. But if the 

 results in the reversed positions of the prisms sensibly differ, then the 

 existing errors of adjustment must be removed, or their effects 

 allowed for by taking a mean of the results in reversed positions, 

 before any reliance can be fairly placed upon the determination of 

 relative motions in the line of sight. 



A reversible spectroscope was arranged by me, and made by 

 Mr. Simms, some years ago, but I have never since had an equatoreal, 

 with a good driving clock, under my control with which the experi- 

 ment indicated could be properly tried. 



With the direct prisms now in use, the required reversion can be 

 easily arranged. I am not likely, for some time, to have the use of 

 a good equatoreal, and I, therefore, publish the plan with the hope 

 that some one more fortunately situated may give it a fair trial. 



The experiment is a crucial one, and, in my opinion, should be 

 tried. 



IV. " On an Improved Bimodular Method of computing Natural 

 and Tabular Logarithms and Anti-Logarithms to Twelve 

 or Sixteen Places, with very brief Tables." By Alexander 

 J. Ellis, B.A., F.R.S., F.S.A. Received January 17, 1881. 



Section I. — Nature of the Bimodular Method and its 

 Improvement. 



The Bimodulus is a constant, which is exactly double of the modulus 

 of any system of logarithms. The Bimodular Method is derived from 



