AucusT 24, 1899] 
NATURE B87 
no other living scholar had done more than he for 
the study of the “Book of the Dead,” both by the 
publication of new material and by the interpretation 
and translation of the entire work. The present volume 
is unique in its own sphere, and no private individual or 
firm of publishers could have undertaken the respons- 
ibility of such a production. The Trustees have earned 
the gratitude of scholars by making so much new material 
available for general study, and they are to be congratu- 
lated on the production of a monumental work which 
worthily carries on the scholarly traditions attaching to 
the Museum at Bloomsbury. 
HAMILTON'S QUATERNIONS. 
Elements of Quaternions. By the late Sir W. R. 
Hamilton. Second edition. Vol. I. Edited by C. J. 
Joly. Pp.xxxiii + 583. (London: Longmans, Green, 
and Co., 1899.) 
OR many years Hamilton’s “ Lectures” and “ Ele- 
ments” have been out of print, and the ardent student 
of quaternions was oftentimes unable to secure a copy of 
either of these great classics. Prof. Tait’s treatise on qua- 
ternions is probably a better introduction for the beginner, 
who is more quickly brought into touch with the essential 
spirit of the method than he would be in Hamilton’s 
pages. But he must, some time or other—unless he be 
a second Hamilton—bathe his mathematical being in the 
inexhaustible streams of quaternion analysis and sym- 
bolism that flow from the great master’s mind. A second 
edition of Hamilton’s immortal work is therefore to be 
warmly welcomed. English-speaking students will now 
be able to study Hamilton freely without having recourse 
to French or German translations ; and it is our hope 
that the issue of this second edition will lead to a wider 
appreciation of the value of quaternions as a mathematical 
method peculiarly adapted to the geometry of space and 
general problems in dynamics. 
The new edition is printed by direction of the Board 
of Trinity College, Dublin, and is edited by Prof. Joly. 
In the larger size of page and larger and wider type 
there is a great improvement on the original form, 
although it has necessitated dividing the book into two 
volumes. The small print has been done away with 
altogether. This, in itself, no doubt is better for the 
reader ; but the advantage is lost that he can no longer 
discern at a glance what is illustration and particular 
from what is general and fundamental. For example, in 
the very important sections on the linear and vector 
function, one of the most beautiful of Hamilton’s cre- 
ations, the reader cannot pick out so readily as in the 
original edition the broad line along which the funda- 
mental properties of this function are developed. Many 
of the illustrations are really of the character of examples, 
such as Prof. Tait puts at the end of his different chapters. 
Printing these in the same style as the more important 
parts tends to give them a fictitious value, and to blurr 
the whole perspective of the book. 
The editor has added occasional notes to elucidate 
points which might appear obscure to the student. In 
some of these a different line of proof may be suggested, 
or they may simply amount to a reference to another 
0. 1556, VOL. 60] 
section, Prof. Joly has exercised this editorial function: 
with judgment. One of the longest of these notes is. 
appended to the chapter on the well-known 2, 7, & rela- 
tions, and brings out clearly the necessity for the neg- 
ative sign of the square of a vector, ¢/f the associative law 
in products ts to hold. The system which is built on the 
assumption that z2=7?=?= +1 is ascribed to Mr. Oliver 
Heaviside. It ought, strictly speaking, to be ascribed 
to O’Brien, a contemporary of Hamilton’s. 
We are not called upon at this date to consider the 
merits of Hamilton’s great calculus. The objections 
taken to it by mathematicians great and small have been, 
so curious and, in some cases, so puerile that we doubt if 
these critics have ever seriously set themselves to study 
its true character. One really eminent mathematician 
who had been fortunate enough to pick up a copy of 
Hamilton’s “ Lectures” for a trifling sum, gladly trans- 
ferred his prize next day to a friend, remarking that the 
man must have been mad who invented quaternions, for 
he made two sides of a triangle equal to the third side ! 
Maxwell adopted the compact suggestive notation in his 
“Electricity and Magnetism” ; and many of the trans- 
formations which are so necessary now-a-days in con- 
nection with electromagnetic waves, and take a page or 
two to effect in ordinary notation, are done almost by 
inspection by quaternion methods. Maxwell did not use 
the quaternion method, not because he regarded it as 
inferior to the notation, as one writer has with curious 
logic argued, but simply because the world was not ready 
for it. Let us hope that with this handsome re-issue of 
one of the most characteristic works of our century a 
renewed interest will be taken in the study of quaternions, 
so that in the near future operations and notations alike 
may be freely used in works on mathematical physics. 
Prof. Joly deserves the gratitude of all for his labour of 
love. When we remember the peculiar characteristics of 
Hamilton’s style, with its redundant italics and capitals, 
we realise the hardness of the task the editor has set 
himself in reproducing to the letter (barring misprints) 
this great monumental work. 
One word in conclusion. Is no new edition of the 
“Tectures” to be brought out—or at any rate of 
Lecture vii., which is nearly as long as the other six put 
together? A re-issue of Lecture vii., with perhaps an 
introductory chapter giving the fundamental principles 
of the calculus, would confer a boon on many students. 
In this so-called “Lecture,” the great mathematician 
moves with a giant stride over the greater part of the 
whole field of geometry and dynamics. From it alone 
Tait drew his inspiration. C> Gake 
OUR BOOK SHELF. 
A Short History of the Progress of Scientific Chemistry 
in ourown Times. By Prof. W. A. Tilden. Pp. x +276. 
(London: Longmans, Green, and Co., 1899.) 
IN size and scope Prof. Tilden’s short history recalls 
Wurtz’ brilliant little “History of Chemical Theory,” 
published thirty years ago. But whereas the key-note 
of Wurtz’ book was the ‘immortal memory” of La- 
voisier, and its main theme the vindication of French 
chemists contra mundum, the spirit of Dr. Tilden’s bool. 
ies in its impartiality and sound judgment. In mode of 
