_ dawn of civilisation until now. 
Sept. 30, 1886] 
ratios, conducting easily to results otherwise unattainable 
even by his transcendent genius. The secrecy observed 
regarding it may have been due, in part to the difficulty 
of setting it forth in the absence of a suitable algorithm, 
in part to the conventional prevalence of the synthetic 
mode of exposition. The art was doubtless held in 
common with Apollonius, and other geometers of the 
time ; but was treated as a mere rude tool, not worth the 
labour of bringing to a higher perfection. Had this early 
analysis been independently cultivated, and set free from 
its servitude to geometry, the “method of exhaustions” 
must, by its aid, in our author's opinion, have given birth 
to the Calculus eighteen hundred years before Cavalieri 
thought of his “ infinitesimals.” 
The work before us aims, above all, at developing, asa 
coherent whole, the logical sequence of ideas. It would 
be unfair to say that this aim has been missed ; yet we 
cannot help thinking that it might have been more per- 
fectly attained. A vivid light, it is true, is frequently 
thrown upon obscure passages of research, and the filia- 
tion and significance of discoveries are, here and there, 
brought out with uncommon sagacity. Nevertheless, 
there is something wanting which M. Marie could easily 
have supplied. 
A somewhat fragmentary plan has governed the com- 
position of the book. The twenty-four centuries embraced 
by it are divided into sixteen periods of very unequal 
length, treated each in a section apart, consisting of a 
prefatory sketch of the progress accomplished during its 
course, followed by a series of biographies of those who 
contributed towards it, arranged in strict chronological 
order. Chemists and mathematicians, astronomers and 
botanists, mechanicians and physiologists, are thus placed 
side by side, with no closer tie of connection than the suc- 
cessive occurrence of the years of their birth. We have 
no sooner done with Lagrange’s Calculus of Functions 
than we are confronted with Watt’s transformation of 
Newcomen’s steam-engine ; the convulsions of Galvani’s 
memorable frog succeed; and we pass thence to Par- 
mentier’s triumphant growth of potatoes on the plain of 
the Sablons,—all subjects of great interest, and treated 
with singular charm. Yet their variety, if it form, in a 
certain sense, an attraction, demands a stronger bond of 
unity than is here afforded. The true historical element, 
in short, is deficient. Nor is the want satisfactorily sup- 
plied by M. Marie’s sixteen prefaces. We should be 
sorry to lose them; but they do not suffice. The absence 
of a connected narrative is still sensibly felt. Even if its 
design had otherwise remained unchanged, the book 
might at least have been provided with a general intro- 
duction, delineating and characterising the course of 
events to be detailed, pointing out the confluence, at 
epochs of discovery, of various and distant streams of 
thought, and presenting, in one luminous view, the pro- 
gress in exact knowledge made by our race from the first 
Perhaps it may not even 
yet be too late to add to a most valuable work a supple- 
mentary volume which would go far towards rendering it 
complete. 
In another direction, M. Marie has perhaps unduly 
extended the scope of his enterprise. To have treated 
adequately the history of 2// the sciences, natural as well 
as mathematical, would have demanded, not a dozen, but 
NABECRE 
519 
fifty volumes. Yet all are nominally included in his 
scheme, while, in point of fact, those branches of know- 
ledge remote from his principal theme receive only the 
casual attention of some stray jottings, with biographical 
notices of their leading promoters. 
His choice of representative names, too, is open to 
criticism. Among omissions, that of Adelard of Bath, 
the first translator of the “ Elements of Euclid” from the 
Arabic, is very remarkable. He was one of the most 
effective popularisers of Arab science in the thirteenth 
century, and played no unimportant part in the revival of 
mathematical learning. Yet he is not only ignored by 
M. Marie, but his version of Euclid is handed over to 
Campanus of Novara, with whose commentary it was 
published at Venice in 1482, and who has in conse- 
quence frequently gained the credit of its execution. 
Nor should the unfortunate Cecco d’Ascoli have been 
altogether forgotten. His “ Acerba,” if not all that it has 
been claimed to be, contains many striking intuitions of 
natural truths. M. Marie, however, takes little interest 
in the premonitory symptoms of discovery ; and the rage 
for unearthing its obscure anticipations has possibly been 
carried a little too far. We miss, further, the name of 
Giambattista della Porta, the effective inventor of the 
camera obscura, whose “Magia Naturalis” was of 
European fame and influence. And William Cullen, the 
founder of rational chemistry in Great Britain, was at 
least as well worthy of notice as Kunckel, known in con- 
nection with the manufactures of ruby glass and of phos- 
phorus, to whom just three times the space is allotted as 
to Black, the discoverer of “fixed air,” and of “latent 
heat.” 
A crowd of superfluous names, on the other hand, 
might be cited. It seems ungracious to object to the 
presence of a sketch so interesting in itself as that of the 
career of Ambroise Paré ; yet it is not easy to see what 
the treatment of gunshot wounds has to do with the 
history of mathematical or physical science. Equally 
outside the proper scope of its cognisance are Henkel’s 
improvement of Dresden china, Bose d’Antic’s contribu- 
tions to the art of glass-making, Perronnet’s bridges, 
Trudaine’s “superb” highways, and Vaucanson’s auto- 
mata. If these give a valid title to admittance, why 
exclude Hargraves, Arkwright, Smeaton, MacAdam, and 
a host besides? Why should the spinning-jenny be 
passed over in silence, when Loriot’s ribbon-loom comes 
in for honourable mention? In truth, however, industrial 
and mechanical inventions belong elsewhere. 
It remains that we should justify our hint that M. 
Marie’s facts and dates occasionally stand in need of 
revision. A perusal of Prowe’s “Life of Copernicus ” 
would have obviated several inaccuracies in his brief 
account of the reformer of astronomy. ‘The intention of 
Copernicus to embrace the ecclesiastical state was not 
superseded, even momentarily, by his journey to Italy ; 
on the contrary, he received his appointment as Canon 
of Frauenburg in 1497, shortly after he had entered the 
University—not of Padua, as stated by M. Marie, but of 
Bologna. Nor was he ordained a priest at Cracow in 
1501. Hetook minor orders on entering the Chapter, 
but 2ever became a priest ; and his sojourn in Italy was 
unbroken between 1501 and 1505. Moreover, his 
doctoral degree (not in medicine, but in canon law) 
