1883.] of Dark Rings in Quartz. 57 



tion, I have not thought it advisable to apply it or to introduce the 

 observations without it. 



The results of my observations are stated in the table opposite. 

 The first column gives the number of determinations of which the 

 given figures are the mean. I have then taken the mean of the 

 observed values giving equal weight to all fourteen observations. 

 I have added the probable corrections already mentioned, and then 

 taken the difference between these corrected observed values and 

 the calculated values. 



These probable corrections are obtained in the following man- 

 ner. In the observations with the needle points the difference 

 between the readings for the two sides of a band varies from about 

 27' for the second ring to about 17' for the seventh ring, while 

 in the observations with the cross wire the difference falls from 36' 

 to 27'. 



It is clear that in one case the distance between the needle 

 points has to be added in order to obtain the apparent breadth of 

 a band, and in the other case the thickness of the cross wire has to 

 be subtracted. The thickness of the cross wire was very consider- 

 ably greater than the distance between the needle points ; so we 

 shall not be far wrong in putting the apparent breadth of the 

 second band at 29'. Dividing this in the ratio of the calculated 

 distances of the two adjacent bands we get an approximate value 

 of the position of the darkest part of the band. Of course the 

 apparent breadth of a band varies to some extent with the bright- 

 ness of the light, but by taking the mean breadth we get the 

 proper correction to apply to the mean observed value. The 

 apparent breadth of the third band was similarly found to be about 

 24' and so on to about 20' for the seventh band. The first band 

 was so much fainter and more ill-defined that the above remarks 

 do not apply and the proper correction is probably small. 



With regard to the calculation. MacCullach {Trans. Roy. Ir. 

 Acad. 1837, p. 463) assumes the equations 



df dz 2 + dz 3 



df ~ dz 2 dz 3 . 



Thus £ and rj are the displacements parallel to x and y at any 

 time t. The axis of z is the wave normal. 



where a and b are the principal wave velocities and </> is the angle 

 between the wave normal and the optic axis. 



.(1), 



