POLARISATION OF LIGHT. 



31 



resultant force of .7500 ; but the angle * 

 or C EG = 40 41', so that the resultant 

 lies in the plane BEG; and hence if we 

 combine with this resultant, or +.7500, 

 the force -.7500 produced by the axis 

 B, the result will be *. 



The same method is applicable to the 

 combination of axes of double refraction ; 

 the numbers corresponding to a, b, c be- 

 insr' in this case the difference between 

 the squares of the velocities of the ordi- 

 nary and extraordinary rays, as produced 

 by each axis separately. 



Intensity of the polarising force in 

 different crystals. As the force of double 

 refraction, which depends on the angular 

 separation of the ordinary and extraordi- 

 nary images, is proportional to the in- 

 tensity of the polarising force, it would 

 be extremely interesting to possess a 

 complete list" of doubly refracting crys- 

 tals with numerical measures of the two 

 forces. M. Biot determined these inten- 

 sities for a few crystals ; but the fol- 



lowing list, which is much more com- 

 plete than his, has been given by Mr. 

 Herschel. 



As these numbers form the most valu- 

 able mineralogical characters*, it would 

 not be difficult for a mineralogist to ac- 

 quire the art of making such minerals. 

 To do this he has only to obtain the 

 maximum or equatorial tint of crystals 

 with one axis, or the tint perpendicular to 

 the two resultant axes in crystals with 

 two axes, and reduce the measures to a 

 given thickness of the mineral. Now 

 the equatorial tint T, in the first case, 

 may be found by the rule given in p. 22, 



t 

 col. 2, or by the formula T=-^ , where 



sm. 2 



t is the tint expressed numerically at any 

 angle <p with the axis ; and in the second 



case, by the formula T = - : 



sin.? x sin.p 



where <t> and <p' are the angles which the 

 refracted ray forms with the resultant 

 axes of the crystal. 



* The preceding very general explanation of the 

 combination of three axes has been rendered necessary 

 by the following remark in Mr Herschel's able Trea- 

 tise on Light recently published : 



" !t appears to as that the rule for the parallelo- 

 grams of tints, as laid down by Dr. Brewster, becomes 

 inapplicable when a third axis is introduced: for this 

 obvious reason, that when we would combine the 

 compound tints arising from two of the axes (A,B), 

 with that arising from the action of the third (C), al- 

 though the sides of the new parallelogram, which must 

 be constructed, are given (viz the compound tint T, 

 and the simple tint t"}, yet the wording of the rule 

 leavs us completely at a loss whatto consider 

 angle inasmuch as it assigns no single line which 

 can be combined with the axis C in the manner there 

 required, or which, quoad hoc, is to be taken as a re- 

 sultant of the axis A, B." We humbly conceive that 

 the distinguished author of this passage has commit- 

 ted an oversight iu supposing that Dr. Brewster has 



given any rule for the combination of three axes. 

 This rule or law, which is distinguished by italic 

 printing, as in page 27, col. 2, of this treatise, relates 

 solely to the combination of the two axes. In the pa- 

 ragraph following the rule given in the Philosophical 

 Transactions, 1818, Dr. Brew>ter remarks that " if 

 the crystal has three or more axes, the resulting tint 



Koduced from any two of them may, in like manner, 

 combined with the third. and this resulting tii.twith 

 the fourth, till the general resultnnt of all the forces is 

 obtained." Here he obviously states no rule, but 

 merely that the third axis may be combined in like 

 manner with the resultant of the other two. This 

 manner he did not think it necessary then to point 

 out, as he conceived it would occur to any person who 

 studied the subject. We have, therefore, felt it ne- 

 cessary to show that the rule or law is perfectly ap- 

 plicable in all cases. 

 * Edin. Phil. Journ. vol. vii. p. 13. 



