249 
of Edinburgh^ Session 1863 - 64 . 
17. By making small alterations in the angular elements of Grlase- 
rite, Brookite, Epsomite, Groslarite, Cordierite, the calculated may be 
made to agree with the observed angle within the limits of errors of 
observation. 
18. Hence if — — ? = the expressions (1), (2), (3), for the incli 
nation of the optic axes to the crystallographic axes c, a, 6, when 
they lie in the planes ca, ah, he, respectively, agree with observa- 
tion, in some cases, without making any, or only slight changes, 
in the angular elements *, but in other cases it is necessary to make 
considerable changes. It is therefore important to consider whether 
the changes required are greater than the possible errors in the 
angular elements. 
19. Now, the measurements of the angles between the faces of 
different specimens of the same mineral, by the same or by dif- 
ferent observers, often vary very considerably, sometimes as much as 
1° or 2°. In Karstenite, for instance, the angle between the faces 
of the form 110, which are truncated by the face 010, is variously 
stated as 96° 36' or 98° 54', which differ by 2° 18'. This difference 
is too great to be ascribed to errors of observation. It only appears 
possible to account for these differences in the measurements of 
the same or of equally accurate observers, by supposing that the 
angular elements of a given mineral are liable to vary slightly in 
different specimens. The question is, to what causes is this varia- 
tion due? Now, in isomorphous substances, the angular elements 
often differ by a degree or more. For instance, the angular ele- 
ments of the minerals isomorphous with Aragonite are, — 
100, 100 
010, on 
Aragonite, . . 
. . 58° 5' 
40° 50' 
Cerussite, . . 
. . 58°36'-5 
40° 9'-5 
Strontianite, . 
. . 58° 39' 
ib 
o 
o 
Witherite, . . 
. . 59° 15' 
CO 
CO 
o 
Alstonite, . . 
. . 59° 25'-5 
38° 39' 
It will be observed that the angular elements of Alstonite differ 
respectively by 1° 20' *5 and 2° 11' from those of Aragonite, those of 
the other minerals differing by less. Now Alstonite may be con- 
sidered as Aragonite, in which half the carbonate of lime is replaced 
by carbonate of baryta. Hence we may say, that when half the 
