a : October + 1916] 
a ” ~ 
reproduction, “the apical or head region develops 
independently of other parts, but controls or domi- 
nates their development, and in general any level 
of the body dominates more posterior or lower 
levels and is dominated by more anterior or apical 
levels.” The dominance depends primarily upon 
the rate of metabolism, and seems to operate by 
impulses, excitations, or changes transmitted in 
various ways from the dominant region to other 
parts of the body. 
What Prof. Child seeks is a dynamic conception 
of the organism, and he maintains that “the indi- 
vidual is primarily a metabolic gradient in a speci- 
fic protoplasm; the only primary difference be- 
tween the dominant and other levels of the 
gradient is a difference of metabolic rate. At this 
time the products of metabolism at different levels 
of the gradient are not specifically different, but 
differ in quantity.” But the differences in rate at 
different levels bring about, sooner or later, differ- 
ences in constitution and character of the proto- 
plasmic substratum. Here one stable substance 
and there another remains as a constituent of the 
colloid substratum. Thus “each level of the 
gradient develops a characteristic protoplasm, and 
the character of the protoplasm in turn modifies 
and alters the character of the reactions, and so 
specific, or what we call qualitative, differences 
arise, and different specific substances may be 
produced at different levels of the gradient.” Then 
for the first time chemical or transportative corre- 
lation in the commonly accepted sense becomes 
possible. The individual is there before the 
orderly specificities of chemical correlation are 
present or possible. ‘“‘The starting point in dif- 
ferentiation is in differences in metabolic rate.” 
The organism is a dynamic reaction system—‘“a 
protoplasm of specific constitution with a cor- 
responding metabolic specificity.” Individuation 
is a relation of dominance and subordination of 
parts. Development is a realisation of the capa- 
cities or possibilities which are given in the 
physico-chemical constitution of the fundamental 
reaction system. We have said enough to indi- 
cate the trend of the author’s exceedingly interest- 
ing theory, which is doubtless a good one to work 
with, though it seems to our prejudiced vision to 
leave half of the Prince of Denmark out of the 
play. For, colloid substratum and metabolic 
gradient notwithstanding, we must regard even 
Prof. Child’s Planarians as_ psycho-physical 
beings, mind-bodies or body-minds as you will, 
but organisms as well as mechanisms through and 
through. 
HYDRAULIC FORMULA RECON- 
me" SERUCRION. 
Hyvdraulic Flow Reviewed. By A. A. Barnes. 
Pp. xi+1s58. (London: E. and F. N. Spon, 
Ltd., 1916.) Price 12s. 6d. net. 
7) Hieoot is in two parts, the first of which 
deals with the flow of water in pipes and 
channels. The author had occasion to investigate 
certain conditions of flow in the Thirlmere aque- 
duct, which supplies water to Manchester, and, 
NO. 2449, VOL. 98]. 
‘ 
NATURE 
87 
finding the variation in the coefficients of accepted 
formule unsatisfactory, he was led to review the 
whole subject of the laws of flow, with the result 
that he has devised a series of formule in which 
the coefficient is independent of variations in the 
size or gradient of the conduit. Taking the equa- 
tions of five well-known experimentalists, which 
he styles ‘the more salient formule” on the 
subject, he shows that they are of the form 
=Km's'. He then points out that the square 
root indices of m (the hydraulic mean depth) and 
of i (sine of slope) are incompatible with a con- 
stant value for the coefficient k, for a particular 
class of pipe or channel. In accordance with the 
precedent set by Hagen and followed by Thrupp 
and others, he recommends the adoption of the 
more general expression v=Kym,'*°, and from the 
analysis of a considerable number of published 
data he is enabled to assign a series of values to 
K, a, and B which give consistent and satis- 
factory results when applied to a wide range of 
cases. The formule thus obtained are sixteen in 
number, of which we only quote the first as typical 
of the rest. For new asphalted cast-iron pipes 
the value is v=174"1m 7529, The results are 
plotted in diagrammatic form for reference, and 
the advantages of using a system of logarithmic 
co-ordinates (which give straight-line diagrams) 
for this purpose are pointed out. 
In the second part of the book, dealing with 
the measurement of water by means of triangular 
notches, rectangular weirs, and circular orifices, 
the author discards the basic expression in com- 
mon use, and advocates the application of the 
general formula adovted in nart i., which he casts 
in the form v=Km*H’. For a right-angled V 
notch this becomes :— 
v= 2°462m —*00703 F] 48703 
whence Q=2°48H?'*. 
It is interesting to note that this latter expres- 
sion corresponds very closely with the results ob- 
tained quite recently by Messrs. Gourley and 
Crimp in researches made on the river Alwen. 
Their formula reads :— 
Q=2°48nH?47 
(n is the tangent of half the included angle of the 
notch, and, therefore, is unity for a notch of go°). 
For weirs with end contractions Mr. Barnes 
has determined :— 
v=3°324m HS, 
and for weirs without end contractions :— 
V=3°324m- "2H ob 
while for circular orifices :— 
v=4:652m-015F{ 5. 
There are a large number of authenticated 
results incorporated in the volume, tabulated in 
support of these equations, as well as plates 
giving the results graphically. The author 
claims that his formule are proved correct by 
experiment for quantities as small as 0'0034 cubic 
foot per second, by means of orifices, and as large 
as 320 cubic feet per second, by means of weirs. 
