352 
POPULAR SCIENCE REVIEW. 
for this its main purpose, hut that it would he doing it some injustice to call 
it a mere cram-hook. The author’s notion was to supplement the use of the 
ordinary text-hooks, with the view of assisting the student in the task of 
revision of hook- work, and, in the author’s own words , 1 To this end I have, 
in many cases, merely indicated the salient points of a demonstration, or 
merely referred to the theorems hy which the proposition is proved. I am 
convinced that it is more beneficial to the student to recall demonstrations 
with such aids, than to read and re-read them. Let them he read once, and 
recalled often.’ This is a sound view of mathematical teaching, whether the 
object of that teaching he a mere cram for a tripos, or the preliminary grind 
which is necessary to all high reading. 
Besides this, the author has endeavoured to make the hook a general 
aide-memoire. In this we think he has not been quite so successful, the 
scholastic requirements of arrangements interfering not only with the facility 
of reference, hut also governing the subject-matter, especially in respect of 
that concreteness which is so necessary for practical uses, and so much out 
of the direct line of usual instruction. As a work of reference’it is not so 
well planned as another Synopsis hy another Mr. Carr, of which a second 
edition was published hy Weale in 1843.* 
With a view of making the hook one of reference, there has been prefixed 
to it a chapter containing an account of the centimetre-gramme-second sys- 
tem of units, and some mathematical tables, chiefly in very short abstract, 
hut with two tables fully given — a factor table from 1 to 99,000, reprinted 
from Burckhardt, and a table of the Gamma function, reprinted from Legen- 
dre. This set of tables does not appear to us to he very well selected or 
arranged, nor to he of much utility. Moreover, as the first volume is con- 
cerned exclusively with pure mathematics, the physical units are rather out 
of place in .it, and might advantageously have been reserved as an introduc- 
tion to the applied mathematics which are to he included in the second 
volume. 
The part before us includes algebra, the theory of equations, and deter- 
minants, plane and spherical trigonometry, elementary plane geometry, and 
geometrical conics. Of these it seems to he a well-selected synopsis, well 
arranged too for its chief purpose as a hook of repetition, and containing a 
good number of useful theorems, especially in the algebra, which are not 
usually to he found in the hooks of elementary reading. Among them we note 
Gauss’s resolution of a hypergeometrical series into a continued fraction, and 
various theorems upon equations and determinants. 
The type, and paper, and the general 1 get-up ’of the hook, are not at all to 
our taste. It is, however, clearly printed, and there is a good table of con- 
tents. On the whole, if the work, when complete, is supplemented hy a 
good index, it will occupy a place not filled up at present. 
* There is a curious story about this hook. It was printed in Durham 
some years before the above-mentioned date, and soon became out of print 
and scarce, although it was known that 5000 copies had been struck off. In 
1842 the stock of a London publisher came to the hammer, and among the 
remainders were found, in sheets, 3500 copies of the work. The re-issue of 
these formed Weale’s second edition. 
