438 Miscellaneous Bibliography. 
able addition to Mathematical science was published in a thick octavo 
volume entitled Lectures on Quaternions (Dublin 1853). The later years 
of the author’s life have been spent upon the present volume, which cov- 
ers the same ground as the dectures and yet can hardly be regarded as a 
second edition of them. 
be overestimated, and that it is destined to change the 
atics. 
A student should read this volume rather than any presentation of the 
n by another mind. It requires a previous 
u 
Integral Calculus, and the applications of the caleulus to geometry. Some 
portions of the volume, especially the later pages, imp!y also a knowledge 
of Analytical and Celestial Mechanics, 
ass of cos age which are severally measured by the ratio of one 
er, that is, by a zero number of factors. Such are the cireu- 
t functions, and angles. To this class belongs the Quaternion. Like 
the sine and the tangent it is the quotient of one line divided by another. 
ut the lines are considered, in this instance, to have not only length but 
also direction in space. There enters into the conception of the quater- 
nion, 1st, a relative length of the two lines; 2d, the angle which they 
two of these are each determined by a single condition, the third by two 
its use of the imaginary expressions to denote directions B 
4. A Prelimin of t. Geological Su 
with A observations and an outline of the Mineral Deposits of 
assistant to Dr. oie ake had the charge of the geo ’ 
