Mr. Greville on the 
426 
beginning, the differences of Bourguet and Capeller were not 
more pointed than those of Rome'de L'IsLEand the Abb^HAUY 
but the progress of observation and calculation having demon- 
strated their mutual utility, the observer and measurer of crys- 
tals will now rest satisfied only when calculation confirms ac- 
tual measurement. To the Abbd Hauy is also due a late scheme 
to simplify calculation, by expressing, according to algebraical 
formulae, the different laws which determine the modifications 
of crystals. So far as they are the result of calculation and mea- 
surement, we may admit the laws of crystallization ; for, when- 
ever the superposition, or subtraction, of simple or compound 
molecules on a nucleus, shall, by calculation, give a series of 
planes and angles, which corresponds exactly to the angles and 
planes measured on natural crystals, it will amount to no more 
nor less than a demonstration of the rule or arrangement of 
elective attraction by figures. 
These laws may be reduced to simple practice; for instance, 
the Abb£ Hauy, by measuring the rhombic plane of Corundum, 
found its two diagonals to be as two to three ; which gives to 
its acute angle 8i° 4/ 10", and to its obtuse angle 98° 12' 50"; 
the same as martial vitriol. * 
The forms of fragments in Corundum are all acute rhom- 
boids. The cosine of the little angle in Corundum is ~ of the 
radius ; but, in calcareous spar, the cosine is -i of the radius ; 
in shorl, -J of the radius ; in the garnet, ; and, in rock crys- 
tal, yV* 
Thus, the application of general laws, to ascertain constant 
* This result is extracted from the Journal de Physique ; but it appears, from the 
Journal des Mines, No. 28, that the Abbe Hauy has since rectified this measure, 
and given 86° 26' for the acute angle, and 93 0 34' for the obtuse angle. 
V • 
