



5 





PQ 



31° 



19' 



45" 



■68 



PR 



31 



19 



58 



•34 



72 C. 8. Hastings — Double Refraction in Iceland Spar. 



It remains to calculate the values of fi' e from Huyghens's 

 theory from the known values of <p' or <p' and the assumed 

 direction of the crystalline axis denned by z above, since y 

 is so small that it can be regarded as zero. The measured 

 value of £ is V 4" with a considerable uncertainty, but I find 

 that a value of V 6" will make the differences between obser- 

 vation and theory symmetrical. "With this value we have 



/i' e [calc] 



l*606109=bl*8 



l-606099rbl"8 



where the probable errors are calculated without disregarding 

 the fact that we have imposed the arbitrary condition that the 

 differences shall be symmetrical. 



The difference between a measured index of refraction in 

 Iceland spar at an angle of 30° with the crystalline axis, and 

 the index calculated from Huyghens's law and the measured 

 principal indices of refraction, thus appears to be 4*5 units in 

 the sixth place decimals, while, assuming the truth of the law 

 we ought to expect, from the probable errors of the quantities 

 involved, a difference of ±2*4, only about half as great. There 

 is, however, one source of constant error in the observations 

 which has not been alluded to, namely, the fact that the 

 temperatures of the prism were measured by a different 

 thermometer in the case of the angles of the prism and 

 the angles of deviation. In the former a rather insensi- 

 tive thermometer divided to single degrees and estimated 

 to tenths was used, and in the latter a very sensitive 

 thermometer divided to half-degrees. By reference to my 

 notes I find that the two systems of temperatures are 

 connected only by an eye comparison on a single day, so, 

 although I believe that the error of comparison cannot be 

 much over one tenth of a degree, it is by no means certain, or 

 even improbable, that an error of this magnitude may enter. 

 It was not thought in that stage of the investigation that such 

 an error was of any significance. Unfortunately one of the 

 thermometers has since been broken so that a direct comparison 

 is out of the question. The observations of the ordinary 

 indices contain implicitly, however, the desired correction as 

 appears from the following reasoning : — 



Let dt be the excess of the reading of the first thermometer, 

 used in the prism-angle measures, over that of the second ; 

 then its most probable value is that which renders the probable 

 error of the mean value of p. a minimum, when the three 

 observed values are regarded as independently determined 

 magnitudes. 



