REPORT ON MINERALOGY. 
351 
distinction to the eye of the common observer, would coincide 
exactly in their angles when tried by the severe test of the gonio¬ 
meter. Whether they do so or not, may be considered as a ques¬ 
tion still under decision. We know that we have, in some in¬ 
stances, groups in which the angle varies slightly in correspond¬ 
ence with certain variations of the physical properties and in¬ 
gredients. And the question is, whether this is a variation per 
saltum ,—so that the carbonate of lime has one invariable angle, 
that of iron and lime another, that of iron a third, and so on ;— 
or whether it is a variation by insensible degrees, the angle 
passing from one magnitude to another by gradations corre¬ 
sponding to the minutest gradations in the proportions of the 
ingredients. Of these opposite opinions Mr. Brooke maintains 
the former, M. Beudant the latter. The most exact and mul¬ 
tiplied observation alone can decide the point. 
It may be observed that the groups of which we have already 
spoken as isomorphous groups, are not, in all cases, such ac¬ 
cording to the etymological sense of the term; for the forms 
and angles of the members of these groups are near to each 
other, but not equal. They have hence been termed plesio- 
morphous groups by Professor Miller, who has examined some 
of them; and as the majority of the so-called isomorphous 
groups are certainly of this character, it may perhaps be ques¬ 
tioned when there are any groups strictly isomorphous (those 
belonging to the tessular system being of course excepted in 
all such assertions). Thus Rose has shown that several 
varieties of minerals, crystallizing like pyroxene, agree in com¬ 
position by the vicarious substitution of one mineral for another; 
and Bonsdorff has shown the same thing for amphibole. But 
I am not aware that in these instances the exact identity of the 
angles of the crystals compared was ascertained by means of 
the goniometer, so that slight differences in the angles of the 
different kinds of pyroxene or of amphibole which were com¬ 
pared, may still have existed, as we know that such differences 
do exist in felspar. 
M. Breithaupt has carried still further this scepticism con¬ 
cerning the constancy of crystalline angles. He finds by 
measurement that crystals of calc spar, apparently equally pure, 
from different localities, vary in their angles to the amount of 
half a degree. What is a still more unexpected blow to the fix¬ 
ity of these angles, he finds (1829), that corresponding, or, as a 
geometer might call them, homologous angles of the same crystal, 
which ought to be precisely equal by the law of symmetry, are 
perceptibly different under the goniometer. Thus two pairs of 
opposite planes of the square pyramid of anatase were found 
