1883.] of Dqrk Rings in Quartz. 55 



After some preliminary trials the first careful set of observa- 

 tions were taken by turning the quartz till the thin line of light 

 between the ring and the cross wire almost disappeared first on 

 one side, then on the other, and taking the mean of the two 

 readings. I took two series of these, and the two means agreed 

 with one another usually within one minute, though in one case 

 they differed by about six minutes. To get the radii I found the 

 centre of each ring, and then measured the radius of each ring to 

 right and to left from the mean centre. The general result was 

 that the observed radius of the second ring was 5' greater than the 

 calculated ; of the third ring 3'. greater ; while the other rings 

 agreed within 2'. 



I then took a similar double set of observations of the second 

 and third rings, and measured the first ring by placing the cross 

 wire over the blackest part. These observations agreed pretty 

 well with one another and with the previous ones, the extreme 

 differences amounting to 3'. The observed radius of the first ring 

 was 10' greater than the calculated. 



Next I took a double set of observations of the first nine rings ; 

 this time placing the cross wire as nearly as possible in the centre 

 of each black band. These observations were not quite so good, 

 the extreme differences amounting to 4', and in the case of the 

 first ring to 7'. Still the mean results agreed with the previous 

 ones within 3'. 



The two methods of reading just described have a tendency to 

 give rather too small values of the radii of the rings. This is due 

 to the fact that the rings shade off more rapidly on the outside 

 than the inside. What we actually measure is the middle of the 

 dark band ; while the darkest part of the band, which is what we 

 want to measure, lies on the outside of the middle. This error 

 may be estimated in the above observations to amount to about 5' 

 in the second ring and 2' in the third ring. So if we take this into 

 account we double the discrepancy between the observed and the 

 calculated values. 



I thought it possible however that there might be some error, 

 due to the difficulty of measuring a curved band with a straight 

 cross wire ; so I took out the cross wires and substituted for them 

 two needle points opposite one another and nearly in contact. I 

 put the right hand needle point in contact with the right side of 

 the band, and then the left needle point in contact with the other 

 side, and took the mean of the two readings for the middle of the 

 band. These observations, though not quite so accurate as the 

 previous ones, confirm their results and shew that no serious error 

 was due to the curvature of the bands. 



Besides these I took some observations with the needle points 

 more widely separated, so that I could place the band exactly 



