412 
NAT ORE 
(Sept. 3, 1885 
§ 335. Simplification by multiplication, addition, and 
subtraction. 
An impatient Briton might be tempted to call this 
‘simplification to the death,” but after calmly perusing 
the whole he might be induced to confess that he had 
said so in his haste. The last three chapters deal with 
applications of determinants: one is arithmetical, and is 
mainly concerned with continuants and magic squares— 
a rather invidious juxtaposition ; one is algebraical, and 
gives the determinantal solution of a set of simultaneous 
linear equations; and the last is geometrical. A very 
valuable feature of the book is a 7éswsné in 4o pp. of all 
the definitions and theorems given in the preceding 
410 pp. No one but a most enthusiastic and painstaking 
teacher would have thought of adding such an admirable 
abstract. 
The next book on our list might have been more accu- 
rately described as a very elementary treatise : it must 
have been intended for pupils with exceedingly little 
algebraical training. The first 18 pp. are occupied with 
determinants of the second order, and they are followed 
by 33 pp. treating of those of the third order. It may be 
safely affirmed that the pupil who requires 18 octavo pages 
to teach him the theory of such abstruse functions as 
determinants of the second order would do well to re- 
direct the expenditure of his mental energy. The book 
is carefully and accurately written, and there is a wealth 
of simple exercises in it, worked and unworked. 
Dr. Kaiser’s pamphlet is of the same ultra-elementary 
character—considerately restricted, however, to 23 pp. On 
a former occasion (NATURE, vol. xxix. pp. 378, 379) we 
drew attention to the fact that a new Introduction of this 
kind appears every year in Germany, and that of late 
they. have not been improving. We merely notify, there- 
fore, that this is the production for 1884. 
The preparation of a new edition of Salmon’s “ Modern 
Higher Algebra” has been entrusted to Mr. Cathcart. It 
contains about 40 pp. of new matter, the chief increase 
arising from the expansion of the chapter on “ Applica- 
tions to Binary Quantics” into ¢wo chapters, the first 
with the old title, and the second headed “ Applications 
to Higher Binary Quantics.” The changes made on the 
portion which deals with determinants are slight, and 
consist chiefly in the insertion here and there of well- 
chosen examples. 
OUR BOOK SHELF 
The Three First Years of Childhood. By Bernard 
Perez. Edited and translated by Alice M. Christie. 
With an introduction by James Sully, M.A. (London: 
W.S. Sonnenschein and Co., 1885.) 
THE earliest years of infancy are of importance to two 
classes of inquirers—to the educator who knows how 
much evil results trom the wrong treatment of young 
children, and to the evolutionist who, rejecting the Zadu/a 
vasa of Locke, looks to infancy as the time freest from 
any effect of artificial training. In the study of other 
men’s minds the observer is as likely as not to be pur- 
posely deceived by them, whereas deceit is an accom- 
plishment which few infants have attained to. 
Mr. Bernard Ferez seems well to combine these 
characters. He is an educator who has published 
various works on school matters, and he describes man 
as an animal which ought to be reasonable, while he is 
not necessarily so, as criminal scandals and the success 
of bad novels prove. He notes that the preponderating 
elements in a child’s will are impulsiveness and stubborn- 
ness, incapability of fixed attention, qualities most 
opposed to the temperament of philosophy and discipline. 
Much of his book is advice to practical educators, whom 
he urges to study the manifestations of infancy and to 
endeavour to lead their youngest pupils by example and 
not check their behaviour by authority ; their intellect 
should be helped, not controlled. He specially points 
out the danger of deceit before even the youngest of 
children. 
But, on the other hand, there is little of the tone of the 
pedagogue in his book. Far more is it a book of sugges- 
tion than one teaching with authority, and it will en- 
courage the spirits of fruitful doubt and inquiry in the 
mind of every reader. He enters heartily into the teach- 
ing of modern science, even to using the argument that 
infants have not certain sensations decause they would be 
of no use to them at that age; and, thinking it necessary 
to caution his readers against leaving everything to 
hereditary dispositions and powers. He urges the im- 
portance of comparing early human life with animal life, 
thus making cats, dogs, birds, and babies more interest- 
ing than before. We may engey his book without accept- 
ing the teaching that human language has grown out ot 
such involuntary signs as laughter, sobs, and screams, 
afterwards performed voluntarily. No doubt these in- 
voluntary sounds are of more use to an infant than more 
sober utterances, and have therefore become innate and 
involuntary, while language is an artificial acquirement. 
We think that few who have watched their vigorous 
antics will feel sure that a state of equilibrium, a passive 
state of health, or even that of moderate and appropriate 
exercise in moving their Jimbs, is the most enjoyable 
sensation fo infants, though this latter pleasure is sufficient 
to explain many actions of infants for which our author 
seeks a deeper reason. On the other hand, we think that 
the moral sense has become more deeply impressed than 
he suggests, and is far from entirely the result of approba- 
tion and disapprobation. 
Attention and vivid perception seem strangely shaken 
up in his remarks ; the latter faculty explains the dislike 
which children have to hearing a tale repeated with 
variations, They have indeed got it all “by heart.” 
Mr. Sully, in his very suggestive introduction, raises 
the question, Who is best qualified to follow up this 
delicate business of observing and rightly explaining all 
the movements and utterances of such young objects? 
Neither father, mother, nurse, nor doctor is completely 
qualified for the study. Mr. Sully concludes that the 
father and mother must conjointly undertake the work, 
the cooler intellect of the one checking and steadying the 
close and loving knowledge of the other, Let us suggest 
that an elder sister is most likely to succeed, and thus 
indicate a path to intellectual usefulness and even emin- 
ence well fitted for a lady’s sphere. It will elevate every 
little labour from drudgery into a scientific study of varia- 
tions and resemblances of the greatest importance, and 
add immensely to the interest of nursery life in a large 
family. On such observations may be based, by herself 
or by more ambitious philosophers, theories of racial 
varieties, of biology, and of education. Sir W. Hamilton 
points out that the study of the human mind requires no 
scholarship or costly apparatus, and the principal acquire- 
ment necessary for success in the study we suggest is a 
little close knowledge of one’s own thoughts and feelings. 
In recording observations Darwin’s golden rule must 
always be strictly adhered to: Theorise freely—every 
other observer will help to demolish anything that will 
not hold water, and whether true or not it may be a sug- 
gestive hypothesis. Be most scrupulous as to recording 
as a fact anything not strictly correct ; no one can dis- 
prove it, and it may throw back the reception of a useful 
truth for a generation. W. ODELL 
