94 Mr. J. F. W. Herschel on the action of 
l, l', &c. in the apophyllite approximate pretty closely to 
this limit, we should expect to see a much greater number of 
rings, and this I find to be really the case. By enclosing 
a thick plate in balsam of copaiba in a proper apparatus to 
increase the range of incidence, I have counted as far as the 
35th order, when I desisted ; not from any want of alternate 
colours, but owing to their extreme closeness, which rendered 
it impossible to number them distinctly. Indeed I have no 
doubt, that could a very thick and limpid specimen be pro- 
cured, hundreds might be seen without artificial aid. 
In two instances then, at least, and probably in many more, 
or perhaps to a certain small degree in all cases, the minimum 
lengths of the periods deviate in their respective propor- 
tions from those of the fits of easy transmission and reflec- 
tion ; a circumstance which of itself is sufficient to prove 
the independence of the causes of these laws of periodicity. 
If we take Rr = RA, Fig. 5, PI. V. and construct a curve 
whose abscissas A P are the values of c, c 1 , &c. and ordinates 
those of /, l 1 , 8cc. the straight line royghi v inclined at 45 0 to 
A R will represent the locus for crystals, such as carbonate 
of lime, in which the periods follow the Newtonian law, 
r 1 o' y g' b' i' v' will represent the same locus for tartrate of soda 
and potash, while r ,, o , 'y"g"b ,, i"v n is the curve similarly traced 
for apophyllite.* 
• Having communicated to Dr. Brewster my observations on the deviation of 
tints, and the conclusion I had thence deduced as to the separation of the axes of the 
differently coloured rays, I received in answer a letter, from which, in justice to that 
indefatigable observer, I subjoin the following extracts. 
** Mv BearSir, Esk Hill , by Roslin Laswade, Sept. 18, 1819. 
“ In consequence of having been some time from home, I have only now received 
your letter, and hasten to reply to that part of it in which you request me to state 
