THE VARIATION OF ANGLES OBSERVED IN CRVSTALS. 
471 
In the afternoon 
96° 44', 
96° 42' 
= 70° 30', 
26° 17' 
03^3 = 70° 25', 
26° 14'. 
On the following day 
96° 48' two overlapping images, 
03 96° 46' = 70° 38', 
03 96° 38' 03 W 3 = 70° 16', 
"2 26° 22 ' „ 
26° 10 ', 
and so on. 
This example will serve to illustrate the difficulty of adjusting and measuring one 
of these crystals, for images which lie on the horizontal wire at one time are 
subsequently replaced by images slightly out of the zone. This difficulty necessitated 
the introduction of the micrometer eye-piece described above, hut the observations 
were enough to show that each octahedron face of potash-alum is replaced by twm, 
three, or more vicinal faces which continually change during growth. 
I may now pass over a number of intermediate experiments, which ultimately 
suggested the correct interpretation of these multiple images, in order to state at 
once the explanation to which I was led, and will give one or two sets of experiments 
by which it is illustrated. 
When an eye-piece of sufficient strengtli is employed, it is seen that many 
apparently simj^le images are in reality overlapping images lying very close together. 
These are usually three in number; one may be brighter than the others, and one or 
two of them may he so faint as to be almost invisible. Similarly, whien the surface 
of the growing crystal is minutely examined,'^ and with a sufficient 
magnification, it is seen that corresjDonding to these three images 
are tliree reflecting surfaces; when the images are equally bright 
the octahedron face is seen to be replaced by three equal-sized 
facets of a very flat triakis-octahedron, as in fig. 3 ; when two are 
bright and the third is almost invisible, two of the faces are large 
and the third small (fig. 4); when the octahedron face apj^arently 
yields a single image, one facet is much larger than the other two, 
and gives an image in the zone if the arrangement is as in fig. 5, but an image 
situated below the zone if the arrangement is as in fig. 6 . 
* This may very conveniently be done by a lens held in front of the eye-piece. 
