AucusT 10, 1899] 
NATURE oe 
o 
Again, complete correlation does not subsist only when 
““every single deviation of the one characteristic cor- 
responds to a precisely equal deviation of the other” 
(p. 43), but whenever the deviations are in any constant 
proportion. This definition, moreover, ought only to be 
held to apply to the case where the means of arrays lie 
‘on straight lines. 
We do not like the definition of correlation as a 
“Beziehung ... welche bewirkt....” This is not a 
statistical definition, and confusion arises if the word be 
used carelessly, sometimes in one sense and sometimes in 
another. The definition of the correlation coefficient on 
p. 54 is much better ; but why does the author call it a 
““morphological definition”? It is purely statistical. 
The statement that it is mainly correlation which main- 
tains the type (“die Korrelation ist es hauptsachlich, 
welche den Typus einer Formengemeinschaft aufrecht 
erhalt”) is a very pretty error; possibly due to the fact 
that biologists use correlation in a more “intensive” 
sense than statisticians do. Statistical correlation has 
absolutely nothing whatever to do with the maintenance 
of type. The type is described by the coordinates of 
the mode. If X,) be the modal size of any organ in a 
parent, Y, the modal size of the same organ in the off- 
spring, the “type is maintained,” or constant, whenever 
X) = Yo; 
and this relation is quite independent of the correlation. 
The correlation between parent and offspring might be 
absolutely zero, z.2. every single parent’s offspring might 
be a fair sample of the whole population, and yet the 
type might remain absolutely fixed; or, on the other 
hand, parent and offspring might be perfectly correlated, 
and yet the type change entirely. This is at least 
formally possible. Thus, in the extreme case of alter- 
nating generations A B A B..., there might in the 
Statisticians sense be perfect correlation—perfect in- 
heritance—between A and B, although A and B differ 
absolutely. 
Of course in a work of the present kind, written chiefly 
for drawing attention to the work of others, one does 
not look for much that is original. There is a curious 
approximate relation given by the author between geo- 
metric mean, arithmetic mean, and standard deviation 
(p. 38), a relation discovered empirically and given 
without proof. If 
G = geometric mean, 
M = arithmetic mean, 
o = standard deviation, 
then approximately in many cases 
o? = M?-G?°. 
The relation depends solely on all deviations being small 
compared with the mean, and admits of a simple 
algebraical proof. 
Amongst small points we have marked, we would like 
the term “individual” variation suppressed, as it is fre- 
quently misleading, and surely not equivalent to “ spon- 
taneous” ; the word “variant” seems to us unnecessary 
and misleading in the case of continuous variation where 
arbitrary groupings are used ; the distinction between 
““Rasse” and “Formeneinheit” (p. 17) (“... erstere 
nothwendig in mehreren Merkmalen, letztere in einem 
einzigen differiren”) is surely inadequate ; a preliminary 
NO. 1554, VOL 60] 
calculation of the mean before calculating the moments of 
a frequency distribution (p. 18) is quite unnecessary, as 
the mean is given by the first moment ; and the author is 
unfortunately in error in ascribing to the present writer 
(p. 52) the extension of the formule of correlation to 
several variables. 
We regret that this notice has had to be for the most 
part fault-finding, as the author has undertaken a 
useful and somewhat thankless task, and we believe that, 
notwithstanding our criticisms, the pamphlet will be 
useful in extending a knowledge of the statistical method 
in Germany. There is a bibliography of 111 items at 
the end of the pamphlet, a feature which will render it 
useful to English readers as well as German. We are, 
of course, in sympathy with the author’s aim, and hope 
he may have the opportunity of revising some of the 
points we have noted in a second issue. GenUsye 
TEXT-BOOKS OF PHYSICS. 
Physics, Experimental and Theoretical. By R.H. Jude 
and H.Gossin. Pp.xiii + 926. (London : Chapman 
and Hall, Ltd., 1899.) 
HE increasing study of science in schools has been 
the cause of a considerable crop of text-books of 
elementary physics, but there is still the want of a more 
advanced book on the subject. This want Mr. R. H. 
Jude has endeavoured to supply, and as far as can be 
judged by a glance through his book, supplemented by 
a more careful examination of a few chapters, he has 
succeeded in giving us what promises to be a very useful 
work both to teachers and students. Experience only can 
show whether he has hit on the right standard of diffi- 
culty, and whether the learner will find the explanations 
sufficiently clear and complete; but there seems no 
reason to doubt it, considering that the work is an 
English adaptation of a book by Prof. Gossin, which is 
apparently much used in France. 
Originally intended to be a translation, the volume 
before us contains many new articles and chapters, and 
the translated portions have been amplified. The first 
volume treats of mechanics, heat and sound. The 
following remarks are not intended to be special criti- 
cisms of this particular book, but rather are suggested 
by it and put down as matters for consideration, being 
of general interest to teachers of science. 
It seems a little doubtful to me how far a book which 
contains a somewhat advanced treatment of experi- 
mental physics should enter into questions of ele- ; 
mentary mechanics. It is impossible to believe that a 
student who can follow the method of treatment given 
in the chapters on heat in this volume should not be 
familiar with the parallelogram of forces, and the con- 
struction of the common pump. Some portions of 
dynamics, such as moments of inertia, must, of course, 
be included, and it may be argued that it is better to 
present a complete than a partial statement of mechanical 
principles. This is true, and of course a good deal 
might be said about the parallelogram of forces and 
velocity that is worth reading at any stage in a 
student’s career, but what strikes me in this volume is 
that the standard of treatment does not quite correspond, 
