358 ON A NEW SPECIES OF AGELACRINITES. 
viz., in an equation where only the ratios of a, 6, and ec, occur; the 
ratios being numbers. Thus, if 6= 8a, and cya, we might have 
numerical value of C=/ (f, y). 
But this is altogether a different thing from saying that C ifself, 
the angle properly so called, the inclination of a and 6 to one another, 
can be expressed in terms of a, 6, andc. Now, if C itself (not its 
numerical value, but the absolute angle) is determined by a, 6, and c; 
and if, nevertheless, it cannot in the nature of things be expressed in 
terms of a, 6, and c; Legendre’s demonstration, the very foundation 
of which is that a quantity which is determined by certain others, can 
be expressed in terms of them, falls to the ground. 
Should it be maintained that C (the angle itself) may be expressed 
in terms of the numbers 6 and y, a right angle being understood to be 
the unit of measure ; or more fully thus: 
C = right angle x f (8, y); 
I reply that in the same manner the line ¢, in Legendre’s reasoning, 
may be expressed in terms of A, B, C, some line L being understood 
to be the unit of linear measure ; thus: 
c=Lx f(A, T, C). 
ON A NEW SPECIES OF AGELACRINITES, AND ON THE 
STRUCTURAL RELATIONS OF THAT GENUS. 
BY KE. J. CHAPMAN, 
PROFESSOR OF MINERALOGY AND GEOLOGY IN UNIVERSITY COLLEGE, TORONTO. 
Read before the Canadian Institute, 17th March, 1860. 
Introductory Notice.--The accompanying figure represents, on a 
somewhat enlarged scale, the upper side ot the undescribed species of 
Vanuxem’s rare and interesting genus Agelacrinites, referred to in a 
late number of the Canadian Journal. As there stated, the species 
in question was discovered amongst some Lower Silurian fossils, from 
the Trenton Limestone of Peterborough, Canada West, collected by 
Mr. W. M. Roger, of the University of Toronto. It is dedicated to 
the able paleontologist of the Geological Survey of Canada, whose 
