389 



a plan similar to that which I have adopted, and which, in a 

 general way, I had previously sketched in the Proceedings 

 of the Academy (vol. i. p. 159). There was this difference, 

 however, that he used a plate of mica instead of Fresnel's 

 rhomb. Now as he worked with common white light, the 

 use of the mica plate must have rendered, two kinds of errors 

 unavoidable. In the first place, it would be impossible 

 always to take the observations for the same ray of the 

 spectrum ; and next, as a consequence of this, the thick- 

 ness of the plate would be genei'ally inexact for the particu- 

 lar ray to which the observations happened to correspond. 

 If the thickness of the plate were exact for a certain ray, it 

 would, be very sensibly inexact even for the neighbouring 

 parts of the spectrum ; and as the part of the spectrum to 

 which the observations belonged was continually changing, 

 the results obtained for different incidences and azimuths 

 would not be comparable with each other, even though, in 

 each separate case, the error of the plate were allowed for 

 and eliminated. The values of 9, however, as determined 

 by M. de Senarmont, would be correct, so far as this error is 

 concerned ; those of /3 alone would be erroneous. For the 

 values of 9 were determined in two ways : by measuring the 

 angles 9', 9", and taking their sum for 20 ; also by measur- 

 ing the angles 7', 7", and taking their sum for the same quan- 

 tity. Now each of these methods gives a true value of 6, 

 because by the preceding formulae we have 29 = 9' -{- 9" zz 

 7' + 7" ; and this accounts for the agreement, shown by the 

 tables of M. de Senarmont, between the values* of 20 ob- 

 tained by these different methods. But the values of 8 were 

 deduced from the angles y', y", by simply making their dif- 



* Or rather the values of 180" + 29; because the angle to, the double of which 

 appears in the tables of M. de Senarmont, is equal to 90" + 0. The angles which 

 he calls yi and y^ are equal to 90° + y" and 90" + y' respectively. It therefore 

 comes to the same thing, whether the one set of angles or the other is supposed 

 to be measured. The letter /3 has the same signification in both notations. 



