288 THE ROYAL SOCIETY OF CANADA 



the set of readings belonging to Plate 4. The first decimal place in 

 the wave-length values might quite properly have been calculated 

 and shown, but it did not seem requisite for the purpose of the present 

 paper. 



Fig, 3 illustrates the relation between n and X by curves, one 

 for each plate, and shows the range of values for n corresponding to 

 the selected values of D, as well as for the different wave-lengths of 

 the spectrum. On account of the great range of values of n each 

 curve is drawn with a separate calibration on the n axis, the values 

 being marked for each beneath the corresponding peak. It will be 

 seen that there is a very large number of observations available for 

 plotting each of these curves. (See also Section 5.) 



4. Solving (1) gives ix = l+D/T—n \/T, from which values of 

 H may be calculated with a high degree of precision since the major 

 part 1 -\-D/ T is independent of the variable. For Plate 4, for example, 

 the numerical formula is ^u = 1 . 648919 — . 5351 n X. 



The relation between the indices at the various parts of the 

 spectrum may also be expressed in somewhat different form. Un' 

 is the order of the interference fringe at the wave-length X' and m' 

 the index, then 



fx' = l-i-D/T-n' \'/T. 



Hence ju' = /x+(w \ — n' \')/T, by which the index at wave-length 

 X' may be calculated from the index at wave-length X. n' is determined 

 by adding to n the number of fringes by which X is more remote than 

 X'j^from the central point of the system. 



If the fringes at X and X' are of the same order n, being on opposite 

 sides of the centre, then 



m' = m+(X-X') n/T. 



5. In (1) w may be a maximum corresponding to the wave-length 

 in the spectrum for which the fringes are most widely separated. 

 The condition for this gives 



i.e., a formula for the dispersive power at the wave-length X of the 

 central point of the fringe system. Both factors, n^ax and T, may be 

 determined to a high degree of precision, the relative accuracy in- 

 creasing with the thickness of the specimen. It is true that Umax 

 must be determined by interpolation, but it lies within . 25 of a direct 

 reading in a number which is upwards of one thousand so that even 

 without closer estimation the»error cannot be greater than one part 

 in four thousand. The value of X corresponding to the maximum 



