Feb. 23, 1871] 
AC=DF,andBC=EF. Then angle A =D; for 
if they were unequal, sides B Cand E F would be un- 
equal. Therefore A = D.” In violation of the most obvious 
of all logical rules, Mr. Morell here professes to prove a 
theorem by the simple assertion of it in its contra-positive 
form! To assert that B C and E F would be unequal if 
A and D were unequal is logically equivalent to saying 
that A and D would be equal if B C and E F were equal, 
which is precisely the proposition to be proved. The 
truth of either of these stateinents involves that of the 
other by the necessary laws of thought, and neither can 
be said to require geometrical demonstration more than 
the other. It is true that Euclid himself (véde Props. 
7 and 9g, Book iii.) overlooked this necessary relation 
between contra-positive theorems. But Euclid’s error 
was very trivial in comparison with Mr. Morell’s. Euclid 
proved doth theorems geometrically when a proof of one 
would have sufficed, but Mr. Morell unwarrantably asserts 
the truth of one, and imagines he has thereby proved 
the other. 
Notwithstanding the fact that Mr. Morell devotes a 
considerable part of his book to the approximate calcula- 
tion of the ratio of the circumference of a circle to its 
diameter, we fear that he must henceforth be classed 
amongst the “circle squarers of the period.” For, as is 
well known, the solution of this vexed problem is at once 
reducib!e to that of the rectification of the circumference ; 
and on page 62 we find it stated that “the graphic con- 
struction which gzves us the length of the circumference 
in a straight line is the following.” For obvious reasons 
we forbear to reproduce it. 
The “ technical classes ” to whom Mr. Morell professes 
to have “adapted” his text-book, will, we fear, derive as 
little profit from its pages as the “students preparing for 
examination.” How can.it profit them, for instance, 
to be told that “many public buildings have as 
fagade a front elevation like A F B?” Yet it is 
Wee er 
with this 7zso/ated technical observation that Mr. 
Morell terminates the forty-first page of his book. 
Again, what earthly, not to say technical use can 
they make of the three very bad pictures of a surveying 
rod, a Gunter’s chain, and a measuring tape, with which 
they are favoured on page 36? On page 37, Mr. Morell 
starts with his technical class to determine a straight line 
through “a winding narrow street ;” but he fails utterly 
to bring them round the very first corner. On page 38 
he proposes to show them how “to draw a perpendicular 
bisector of a given straight line in nature,” but we will 
not disfigure this page of NATURE with a reproduction of 
his unintelligible method. Although readers might be 
amused by it, we are not ina humcur to extract amuse- 
ment from a work which was certainly not written for the 
purpose of providing it, but with the serious intention of 
teaching Geometry in an improved manner. 
We have by no means exhausted the incongruities of the 
book ; but we have, we think, sufficiently shown that the 
teaching of Geometry cannot but be vitiated by its use ; 
that, in fact, this text-book of Her Majesty’s ex-Inspector 
of Schools will itself bear no inspection whatever. 
NATURE 

325 

RODWELL’S DICTIONARY OF SCIENCE 
A Dictionary of Science: comprising Astronomy, Chc- 
mistry, Dynamics, Electricity, Heat, Hydrodynamics, 
Hydrostatics, Light, Magnetism, Mechanics, Metec- 
rology, Pneumatics, Sound, and Statics. Edited by 
G. F. Rodwell, F.R.A.S., F.C.S. (London: E. Moxon 
and Co., 1871.) 
HERE are Dictionaries and Dictionaries. We have 
had occasion to expose the shortcomings of some 
books that are called by this name ; it is a far pleasanter 
task to direct attention to the merits of a work like the 
one before us, which really deserves its title. Mr. Rod- 
well’s “ Dictionary of Science” is a repertory of fac’s 
connected with physical science, which will be invaluable 
to the student. From Chemistry to Chladni’s Figures ; 
from Thermo-dynamics to Turacine, scarcely aterm will be 
met with in scientific works, of which the learner will not 
here find an explanation. The articles have the great 
advantage of being short, and presenting the salient points 
of each subject at a glance before the reader’s eye ; and 
that their scientific accuracy may be relied on, is guaran- 
teed by such names (amongst others) as those of Mr. 
Crookes, Prof. Guthrie, and Mr. Wormell in the list of 
contributors. To illustrate the style of the book, we 
cannot do better than select two of the shorter articles, 
The first is on a subject which has recently been discussed 
in these columns :— 
“ Mass.—Mass is a term for the quantity of matter in a 
body. In order to measure mass, we assume that the 
attraction of the earth on all particles of matter is the 
same, and is not dependent on the nature of the matter 
attracted. This assumption seems to be justified by the 
fact that bodies of all kinds fall with equal velocity in the 
exhausted receiver of an air-pump. Hence we measure 
the mass of a body by its weight, and can only define 
the mass asa quantity proportional to the weight. If, 
then, at the same spot of the earth’s surface, one body is 
twice as heavy as another, the mass of the first is twice 
that of the second. Suppose, however, that the body be 
weighed by a spring-balance at a certain place, and 
weighed again by the same instrument at another place 
nearer the equator, it will be found that the body is lighter 
at the latter place. It is found also that the acceleration 
due to the attraction of the earth is also less at the second 
place than at the first, in the same proportion. This 
illustrates the fact that when the mass remains the same, 
the weight varies as the acceleration of gravity. Hence 
the weight varies as the product of the mass and the 
acceleration of gravity, and, consequently, when suitable 
units are chosen, the mass of a body is equal to its weight 
divided by the acceleration due to gravity.” 
Our next extract is chemical :— 
“ Alcohol.By this name, when standing by itself, is 
usually understood the second term of the series of ordi- 
nary alcohols, or vinic alcohol. It is a transparent, 
colourless, mobile liquid, of a specific gravity 0°7939 at 
60° F.; it boils at 74°4°C. (173"t F.) ; its vapour density 
is 1613; its tormuia is C,H,O; it is the spirituous 
principle of wine, beer, and spirits, and is produced by 
the fermentation of sugar, which is split up into alcohol 
and carbonic acid. In the diluted state alcohol is some- 
times called spirits of wine. It is difficult to render 
anhydrous ; distillation alone will not produce an alcohol 
containing less than 9 per cent. of water, and this remain- 
ing quantity must be removed by adding something which 
unites with the water chemically, as quick-lime. By 
oxidtion it is converted into aldeliyde, and then in-o 
