262 Mr. C. Spurge. On the Effect of Polish on the 



The observations in Table XII made with the elliptic analyser are 

 divided into sets of 12, for our object is not only to determine what is 

 the change produced by repolishing, but also to discover the error of 

 a mean of 12 sets of observations with a view to fixing the accuracy 

 of working with the elliptic analyser, and also the errors of the 

 means of the sets of observations recorded in Tables I — IV. For 

 convenience of comparison the means are exhibited together in 

 Table XIII. 



Table XIII. — The Means of Observations with a Repolished Face 

 (Elliptic Analyser). 





r'—r. 



R'-R, 



sin (r'—r). 



sin (R'-R). 



COS 2ar. 



■sr. 



tan or. 



No. 1. . 

 No. 2. . 

 No. 3. . 



93 -448 

 93 -476 

 93 -418 



91-550 

 91 -429 

 91 -422 



-998190 

 -998160 

 -998221 



0-999634 

 0-999689 

 0-999692 



-998555 

 -998471 

 0-998529 



1 32 -41 

 1 35-07 

 1 33-25 



0-02689 

 0-02766 

 -02713 



Mean. . 



93 -447 



91 -467 



-998190 



0-999672 



-998518 



1 33-57 



-02723 



We now proceed to consider the accuracy of the sets of obser- 

 vations with the elliptic analyser. Table XIII shows that the 

 greatest deviation of a single set of 12 observations from the mean 

 is less than 1*6 per cent, for the ratio of the axes. The best set 

 differs from the mean by under | per cent. Again, Table XII shows 

 that the greatest deviation from the mean for I is 0046° or under 3', 

 whereas the least deviation from the mean is under 1'. We take, 

 then, the upper limits as the errors of observations. Let us now 

 consider the effect produced by repolishing. Before repolishing, the 

 calculation following Table IX shows that — 



tan w = 0-02655. 



After repolishing, Table XIII shows that — 



tan w = 0-02723. 



The difference between the two values of tan vr is 2 \ per cent., 

 which may be covered by the limits of errors of observation. 

 Again, before repolishing — 



I = 87-654° 



After repolishing, Table XII shows that — 



I = 87-712°. 



There is thus a difference of 0*058° or 3*48', which is covered by the 

 limits of errors of observation. 



