100 
NAT OTE 
[JUNE 1, 1899 
blood to the cells which is required.” In many places 
the sense is seriously interfered with by faulty punctu- 
ation, and we note a rather plentiful crop of misprints, 
especially towards the end of the book. Such are 
“centre nervous system,” “tircuspid,” “vertebre,” (for 
““vertebrata ”), “‘cauda equine,” “ straining ” (for ‘‘stain- 
ing”), ‘“‘Weber-Feehner law,” ‘fenestra rotundis,” 
(several times repeated), “scala tampani,” “selerotic,” 
““viteous humour.” Nor do we care for the form “ oculi- 
motor.” It is to be hoped that a future edition will be 
more carefully revised. The author has been fortunate 
in securing the use of the well-known and admirable 
figures from Quain’s “‘ Anatomy ” and Schafer’s “ Essen- 
tials of Histology.” They add materially to the value 
of the work. 
The Dawn of Reason. By James Weir, jun., M.D. Pp. 
xiii + 234. (New York: The Macmillan Company, 
London: Macmillan and Co., Ltd., 1899.) 
THIS book on the mental processes of animals is the 
fruit of much original observation, and in many cases this 
observation has been supplemented by experiment ; but, 
unfortunately, all the author’s results are vitiated by his 
uncritical and biased attitude in favour of an extreme 
view of the mental life of animals, and there are few of 
his facts which the comparative psychologist would be 
justified in using without ample corroboration by other 
observers. Instinct is regarded as the great bane of 
psychology, and it almost seems as if the author believed 
it to be a special invention of those whom he calls 
“creationists.” He poses as an ardent evolutionist, but 
is so blind to the most elementary principles of the 
evolution of mind that when a water-louse frightens some 
rhizopods, he can only conclude either that the latter have 
eyes and ears so small that lenses of the highest power 
cannot make them visible, or that these creatures are the 
possessors of senses utterly unknown to and incapable of 
being appreciated by man. He makes observations on 
spiders which show that they are differently affected by 
loud and soft vibrations of an organ—observations which 
do not even demonstrate the existence of hearing—and 
concludes that these animals have attained a very high 
degree of esthetic musical discrimination. He has also 
seen a spider “intentionally beautifying” its web with flakes 
of logwood, and he has watched rhizopods employing their 
time in “ simple amusement” resembling a game of tag. 
Nevertheless, among these extravagances, one meets 
with observations which would be of distinct value and 
interest if one had confidence in the observer. 
The Arithmetic of Chemistry. By John Waddell, B.Sc. 
D.Sc. Pp. vii + 133. (New York: The Macmillan 
Company. London: Macmillan and Co., Ltd., 1899.) 
THE volume does not differ essentially from other books 
on chemical arithmetic. Every teacher has his own 
method of presenting an arithmetical problem, which he 
often feels impelled to share with others. The author’s 
methods seem thoroughly sound and logical, and no ex- 
ception can be taken to them. There is a good deal to 
be said, too, for the plan oftreating the calculations on a 
purely experimental basis independently of theories ; but 
it is not always advisable to hold to it too rigidly. A 
good illustration is offered by the following example. 
The author begins by showing that the combining 
weight of oxygen “taken as 8 is thoroughly satisfactory, 
not only in its relation to hydrogen (1) in water, but to 
carbon (6) in its two oxides. It then becomes necessary 
to explain that this number for oxygen does not fulfil the 
expectations which it first raised, and that the formula 
for water HO(g) must be discarded in fav our of H,O(18). 
“Tt is found that while by electrolysis of water all of the 
hydrogen that is in the water is set free as a gas, and } 
of the water decomposed is hydrogen; on the einer 
hand, when sodium acts on water, only one-half as much 
hydrogen is set free, that is 7 of the weight of water | 
NO. 1544, VOL. 60] 
acted upon.” It is questionable whether this explanation 
would carry conviction to the beginner. A plain dogmatic 
statement would surely serve the purpose better, until the 
student had advanced to a stage when he could grasp the 
whole question involved. The author has collected to- 
gether an excellent set of examples from a variety of 
sources, which should be useful to teachers in Suen ay 
classes. Vx 18%; 
The Flora of Cheshire. By the late Lord de A 
(Hon. J. Byrne Leicester Warren), edited by Spencer 
Moore ; with a Biographical Notice of the Author by 
Sir Mountstuart Grant Duff. Pp. cxiv + 399, with a 
portrait of the author and a map of the county. 
(London; Longmans, Green, and Co., 1899.) 
THE manuscript of this “Flora,” we are told, was com- 
pleted a quarter of a century ago. Those who knew the 
sensitive, retiring disposition of the late Lord de Tabley 
will not be surprised that he laid it aside as not ready for 
press ; nor will they be surprised at the excellence of 
what was done. There is little beyond an enumeration 
of.the plants of the county, but made with extreme care 
and with conscientious acknowledgment of doubts and 
difficulties in dealing with critical plants. 
Two classes of vegetation seem particularly to have 
attracted the author’s notice, and both in a decidedly 
historical aspect. The one class is that of the alien 
plants, whose spread from ballast-heaps, &c., is traced ; 
the other is the shore vegetation of a coast which has 
been much changed both by man and by tidal denuda- 
tion. There probably exists no “Flora” of any county 
in Britain which approaches it in interest in either respect, 
unless it be that of Middlesex by Trimen and Thisel- 
ton-Dyer, published in 1869 at the time when Lord de 
Tabley was at work on what has just been printed. 
To the matter which was put into his hands, the editor 
has wisely added enough to bring the work into line with 
our present knowledge of Cheshire botany. The bio- 
graphical notice in its want of facts is a little disappoint- 
ing; and the attempt to give each plant a binomial 
English name leads one to a curious and not altogether 
happy result. These, however, are small matters. 
J Vials 18} 
"LETTERS TO THE EDITOR. 
[Zhe Editor does not hold himself responsible for opinions ex- 
pressed by his correspondents. Neither can he undertake 
to return, or to correspond with the writers of, rejected 
manuscripts intended for thts or any other part of NATURE. 
No notice 2s taken of anonymous communzcations. | 
Fourier’s Series. 
THE statement of Fourier’s theorem for the special case 
which has intermittently for some months past been a subject 
of discussion in NATURE, is as follows:—The function whose 
value is 4(7 —.v), when x lies between 0 and zm, and — }(7+.), 
when .v lies between 0 and —z, can be expressed by the series 
> 
k= 
sin 4x 
for values of x which lie between a and —7. 
The proof of the theorem, whether in this special case or in 
more general cases, consists in summing the series; and the 
result obtained in this special case is that the sum of the series is 
3(a—«), when x lies between 0 and 7, 
—4(r+.~), when x lies between 0 and —7z, 
oO , when «=o. 
Prof. Michelson has found a difficulty in this result in that, 
whereas the sum of any number of terms of the series is a con- 
tinuous function of x, the sum of the series is a discontinuous 
function of x. If I have not misunderstood him, he contends 
that for extremely small positive values of « the sum of the series 
should be regarded as indeterminate and as having any value 
between o and 47, and I understand him to support this con- 
tention by the consideration that when z terms of the series are 
taken, so that w being extremely small x is finite, such an 
indeterminateness is found. 
Such a position involves a misconception of the meaning of 
