426 Mr. Tovey's lu'searc/ics in the 



and that the velocity is not affected by any change in the di- 

 rection of the vibrations: consequently the sums s^, 5,^, Scd 

 musty lor this medium, be the same whatever be the directions 

 of the coordinates. But it is found, by experiment, that if 

 glass be expanded or contracted in one chrection only, it ex- 

 hibits the same optical })ha5nomena as im uniaxal crystal ; the 

 optical axis lying in the direction of the expansion or contrac- 

 tion. (Airy's Tracts, p. 403, art. 178.) Now, it is manifest 

 that since the sums s- , s^ , &c. are originally the same for all 

 directions of the coordinates, these sums must, in the altered 

 state of the glass, be still such that their values will not be 

 affected by turning the coordinates upon an axis taken in the 

 direction of the expansion or contraction; and consequently 

 this experiment affords a verification of our formulae. 



(15.) Whatever be the arrangement of the molecules, v/e 

 have, by the equations (3.) and the assuuiption of article (9.)^ 



r,; = -|- S.vI/(;-)A^'"-A;:^ 

 provided (art. 3.) the directions of j/ and ~ are so taken that 



2. tI/(?-) A.r^Aj/A;: = 0. 



Let xj^yl^zl be rectangular coordinates having fixed 

 directions, and the same origin as x,y , z ; let the axis of x 

 coincide with that of a:' ; and let 9/ be the angle between y' 

 and y : then 



A .r = A x/ , 



A 7/ = At// cos S/ — A ;:/ sin 9/ , 



Az = Ay sin 9/ + A zf cos $/. 



By substituting these values and, for the sake of abridge- 

 ment, putting 



2.v^(r) Aa-7A3/7 = cr , 

 ^ . ^ {}•) Ax'''Az';' = a', 

 ^.i>{7-)Ax'} Ay',A.,\ = a", 



we have 



7H Vt 



v^ — -— a cos- 9/+ -^ <t' sin- 5/— m a-" sin 9/ cos d], 



v^i' = — 0- sin" 9/ + -^ 0"' cos^ dj + m a" sin &-J cos 9/ , 

 :i:.^{r)Ax' AyAz = {<T- a') sin 9/ cos 9/ + cr" (cos^ 9/ - sin' $,'. 



