122 PROCEEDINGS OF SECTION C. 



To obtain the error in « due to errors in t and d equation 

 (I) is differentiated as foll( ws : — 



'■>'--= ji-^i^ + fAik,)''-'' 



The vahies of t>i and 6d are, from the nature of the measurements, 

 equally Hkely to be positive or negative, and hence the negative 

 sign attaching to the coefhrient of ^t has no practical significance* 



From (I) / — d^t/ii 

 and (i=(/<— !)//(. 



Hence by ehminating d from (1) and (2) 



ffi = y — -r^ + y<^« {•>) 



As the real test of accuracy is the ratio of the error to the 

 amount measured, it is better to write equation (3) in the form 



r«//< = —"-^.r/ + ~fd (3)a 



/* / 



From this equation the following facts are clear : — 



( 1 ) For a given thickness of material more accurate results are 



obtained with minerals of low refractive index than with 

 those of high refractive index. 



(2) In determining the refractive index of any mineral more 



accurate results are obtained from thick than from thin 

 sections. 



Since the great majority of minerals have refractive indices 

 between I '4 and 2 it will be sufficiently practical to consider the 

 variations between these limits. 



The values of -^^d are of a definite order of magnitude, which, 

 according to my own observations, approximates to .01 m.m. 



Mr. Sorby.i who has made a series of experiments with this 

 method, states that "an accuracy of .001 inches can easily be 

 obtained." 



The value of / may be ascertained to any required degree of 

 accuracy, but in practice it is usually determined by the same 

 method which is used in obtaining the value of d. Thus, the value 

 of H=?.d=.Ol m.m. 



If the thickness of the plate used be such that the co-eificient 

 of cd in (3) A be not greater than unity, then /( can be calculated 

 with considerable accuracy, 



The maximum errors which can occur in determining refractive 

 indices of the values 1 '4 and 2 are shown to be respectively as follow: 



1 H. C. Sorby : " On a Simple Method of Determining the Index of Refraction of Small Portions of 

 Transparent Substances," Min. Mag., 1877, Vol. I., pp. 97 98. 



