this axis ; consequently in the line of the proper inter- 
_ mediate angle there is no dilatation or contraction what- 
~ ever from heat. Endeavours will therefore be made thus 
to obtain an invariable standard measure of length, by 
- comparison with which the rate of dilatation of measures 
variable with heat may be determined. 
There are other subjects of the investigations of the 
committee which might be noticed, but we have probably 
stated enough to enable some idea to be formed of the 
magnitude of the work undertaken by the International 
_ Metric Commission, and of the value and importance of 
the anticipated results of their labours ; as well as the ad- 
vantages expected to be obtained from the proposed 
establishment of the permanent International Metric 
Institution. H. W. CHISHOLM 
DE MORGAN'S BUDGET OF PARADOXES 
A Budget of Paradoxes. By A. De Morgan. (Longmans, 
1872.) 
4 hag work is absolutely unique. Nothing in the 
slightest degree approaching it in its wonderful 
combinations has ever, to our knowledge, been produced. 
True and false science, theological, logical, metaphysical, 
physical, mathematical, &c., are interwoven in its pages 
in the most fantastic manner: and the author himself 
; mingles with his puppets, showing off their peculiarities, 
posing them, helping them when diffident, restraining 
them when noisy, and even occasionally presenting him- 
self as one of their number. All is done in the most 
perfect good-humour, so that the only incongruities we 
are sensible of are the sometimes savage remarks which 
several of his pet bears make about their dancing- 
master. : 
‘De Morgan was a man of extraordinary information, 
We use the word advisedly as including all that is meant 
by the several terms knowledge, science, erudition, &c. 
Everywhere he was thoroughly at home. An old edition 
and its value-giving peculiarities or defects, a complex 
mathematical formula with its proof and its congeners, a 
debated point in theology or logic, a quotation from some 
almost-unheard-of author, all came naturally to him, and 
from him. With a lively and ready wit, a singularly 
happy style, and admirable temper, he was exactly fitted 
to write a work like this, And every page of it shows 
that he thoroughly enjoyed his task. Witness, for in- 
_ stance, the following extract :— 
*T will not, from henceforward, talk to any squarer of 
the circle, trisector of the angle, duplicator of the cube, 
constructor of perpetual motion, subverter of gravitation, 
stagnator of the earth, builder of the universe, &c, I will 
receive any writings or books which require no answer, 
and read them when I please: I will certainly preserve 
them—this list may be enlarged at some future time. 
There are three subjects which I have hardly anything 
upon: astrology, mechanism, and the infallible way of 
winning at play. I have never cared to preserve astrology, 
The mechanists make models, and not books, The infal- 
lible winners—though I have seen a few—think their 
secret too valuable, and prefer #utare guadrata rotundis— 
to turn dice into coin—at the gaining-house : verily they 
have their reward.” 
He was not, let it be at once said, a great original 
- mathematician—not, that is, of the order of men like 
NATURE 
pee He) 4 Phe ee a i aes 
ji ae hee Sie ee 1p jieh os re vg ; f 
239 
Boole or Rowan Hamilton—but extraordinarily great 
mathematicians like these are very rare, and there were 
not in Britain a dozen who were his superiors. We are 
told in the Preface to this work that it was his intention 
to have composed a companion volume on “the contra- 
dictions and inconsistencies of orthodox learning.” What 
a loss we have here sustained—how narrow an escape 
several of our most popularly idolised men of science, &c., 
have made—must be known to many, perhaps even dimly 
suspected (at least we hope so) by those who would 
assuredly have been the earliest and most , prominent 
sufferers. 
A great part of the volume consists of reprints from a 
series of almost weekly papers in the Atheneum ; but 
much new matter has been added, and several modifica- 
tions and corrections have been made. The task of 
editing has been undertaken by the author’s widow, and 
appears to have been exceedingly well done throughout. 
The volume is not one which can be read through at a 
sitting—nor even at three or four: the multiplicity of 
subjects renders it bewildering if more than a dozen or 
two of pages be read at a time—but we do not envy the 
man who cannot, at a spare moment, find both pleasure 
and profit in the perusal of a moderate portion of it, taken 
ad aperturam. 
De Morgan was a very dangerous antagonist. Ever 
ready, almost always thoroughly well informed, gifted 
with admirable powers of sarcasm which varied their 
method according to the temperament of his adversary, 
he was ready for all comers, gaily tilted against many so- 
called celebrities; and—upset them. It is unfortunate 
that the issue of his grand contest with Sir William 
Hamilton (the great Scottish Oxford Philosopher) is but 
in part indicated in this volume—it is softened down, in 
fact, till one can hardly recognise the features of the extra- 
ordinary A¢hene@um correspondence of 1847. There the 
ungovernable rage of the philosopher contrasts most 
strongly with the calm sarcasm of the mathematician, 
who was at every point his master, and who “ p ayed” 
him with the dexterity and the tenderness of old Isaak 
himself! But it is characteristic of De Morgan that, 
though he was grievously insulted throughout the greater 
part of this discussion, no trace of annoyance seems to 
have remained with him after the death of his antagonist ; 
for none would gather from the “ Budget” more than the 
faintest inkling of the amount of provocation he received. 
Yet De Morgan had his weak points, and in an un- 
guarded moment he made a first, and last, attack—one of 
the few assaults in which he was unsuccessful—on Faraday. 
At least he gets the credit of having reviewed a lecture of 
Faraday’s in the Atheneum of 1857, and of having 
for once wholly missed the main point at issue. 
To return to the “ Budget.” The tenderness displayed for 
trisectors, duplicators of the cube, circle squarers, per- 
petual motionists, e¢ hoc genus omne—from J. Reddie 
through J. Symons, to J. Smith—is most touching. The 
real human interest evidently taken in the careers of those 
hopelessly ignorant writers, does credit to De Morgan’s 
heart. He does not hang up his Paradoxer on high as a 
warning, nor does he dissect him for purposes of psycho- 
logical study; he carefully spreads him out, under suffi- 
cient but not extravagant pressure, on the white page of 
his herbarium, and fondly preserves him as a specimen 
