SEPTEMBER 4, 1902] 
NATURE 
aie) 
read “ place them so that any two corresponding sides are 
parallel.” In p. 63, ex. 19, for “ prove also that OT, ON 
equal OP,” read “ prove alsothat OT.ON equals OP?.” 
Diagrams of Mean Velocity of Uniform Motion of Water 
in open Channels, based on the Formula of Ganguillet 
and Kutter. By Prof. Irving P. Church. 11 Diagrams 
+1 page Text. (New York: Wiley and Sons ; 
London: Chapman and Hall, Ltd., 1902.) 
THIS little work, in spite of its ponderous and somewhat 
ambiguous title, is a useful and workmanlike collection 
of curves from which may be obtained the value of the 
mean velocity v in the empirical formula v = cNn’rs, 
so much used in computing the flow of water in channels. 
To the ordinary reader the term “mean velocity of 
uniform motion” is puzzling; but anyone versed in 
hydraulics will understand that the author wishes, very 
properly, to restrict the application of his curves to cases 
where the rate of flow is constant, z.e. where the same 
number of cubic feet or gallons pass a given section of a 
channel of uniform cross-section every second. 
In the formula the trouble is with the coefficient c, 
which is not independent of 7 and s—the hydraulic mean 
depth or “hydraulic radius” and the slope. The co- 
efficient may be computed, for channels of different 
materials, from well-planed timber to earth and stones, 
by the formidable law of Ganguillet and Kutter, 
I = + 4165 4 "00281 
) 
where 7 is the arbitrary constant which ranges in value 
from 0°009 to 0'035 in the two extreme cases cited. 
Very few people, we imagine, actually calculate c in 
this way, as tables by Trautwine and othérs give its 
value for all likely values of 7, x ands. Prof. Church has, 
however, gone a step further, and his diagrams give 
values, of of c, but of v, thus avoiding the further calcu- 
lation usual after c is found from tables. 
There are eleven diagrams, each corresponding to a 
particular value of 7, the vertical lines in each diagram 
showing “slopes,” inclined lines “hydraulic radii,” and 
horizontal lines ‘mean velocity” v. The intersection of 
any three of these lines satisfies the relations referred to, 
and shows for the selected values of 7, x» and s the 
required mean velocity in feet per second, which, multi- 
plied by the cross-sectional area of the channel in square 
feet, gives the flow in cubic feet per second. 
A test or two, worked out from the formulz, shows the 
curves to be accurate enough for practical purposes. 
Thus, selecting 7 = ‘ol, 7 = 10, s = 20 + 1000, the 
calculation gives 
a— Ss eo 
n 700281 
1+ 7=(41 65 + 
Nir 
1811 Pe 00281 
+ 4I 65 mae 
ee — 224°155 ! 
c = a = SS See 
my 41°65 + coast) 1136 197°3 
Tat 37162 ( 2 
and : 
v = 197°3NI0 x ‘002 
= 27°89 feet per second. 
The diagram gives v about 28. 
In another test where 7 = ‘03,7 = Io, s = 2'0 = 1000, 
the diagram gives v about 10°5; calculation makes it 
10°38. 
There is no doubt, therefore, that Prof. Church has 
compiled a real “labour-saver” for those who have to 
make numerous calculations of the kind referred to. 
Near the end of the author's explanation he mentions 
the application of the diagrams to cylindrical pipes and 
sewers “running full or half-full” ‘We would point 
out that the rule v = cV7s is not applicable with success 
to pipes running full, though various American writers 
NO. 1714, VOL. 66] 
attempt to use the law in this sort of universal sense. 
Much more authentic formule are available for calculating 
the flow in pipes, and the curves given in this little work 
should not be applied to that purpose. R. G. B. 
A First Course of Chemistry (Heuristic). By J. H. 
Leonard, B.Sc. Pp. vi + 134. (London: John 
Murray, 1902). Price ts. 6d. 
THIs little work provides a course of elementary chemistry 
resembling the well-known course which was drawn up 
some years ago by Prof. Armstrong and endorsed by a 
British Association committee. Great pains are taken 
to make the teaching undogmatic and to imbue the 
pupil with the zeal of a scientific inquirer. The topics 
include a study of chalk, lime and carbonic acid, air, 
water, combustion, acids and salts. Though the work 
cannot be pronounced superior to some that have already 
been written with the same object, it gives a good 
representation of what many people now think the right 
way of approaching elementary chemistry. On any 
system the teaching of elementary chemistry will for 
long remain full of difficulties and inconveniences. We 
notice that on p. 43 there is an instruction to collect 
oxygen by displacing air in an inverted cylinder, and on 
the next page an experiment, correctly enough described, 
perhaps, leading to the conclusion that oxygen is lighter 
than air. 
An Elementary Book on Electricity and Magnetism and 
their Applications. By Profs. D. C. Jackson, C.E, 
and J. P. Jackson, M.E. Pp. xi+482. (New York: 
the Macmillan Company; London: Macmillan and 
Co., Ltd., 1902.) _ Price 75. 6d. 
THE object of the authors has been to write a book 
which will serve both as an elementary text-book and as 
an interesting account of the subject for the general 
reader who has a taste for the science. With this in 
view they have naturally taken industrial development as 
a guide, and wherever possible have shown the connec- 
tion between the simple principles of the science and 
their technical applications. As the general reader is 
usually ill-equipped with mathematics, we find that little 
more than the simplest equation is used in the book. 
Each chapter is followed by questions. Here are 
some of the questions which come at the end of the first 
chapter :— 
“How much is known about the real constitution of 
electricity ?” 
“What is 
scientists ?” 
‘What kind of electricity will a positively charged ball 
induce?” 
The book contains twenty-three chapters, and from 
chapter xv. to the end the subject-matter is principally 
technical applications. Thus polyphase motors, electric 
welding, cooking and Rontgen rays, and other new uses 
are each described in their appropriate chapters. 
electricity supposed to be by some 
The Face of Nature. By the Rev. C. T. Ovenden, D.D. 
Pp. ix + 188. (London: John Murray.) Price 2s. 
IN this little volume we have the material for several 
“popular readings in elementary science,” the subjects of 
the four chapters being weather forecasting, vegetable 
life, the record of the rocks, and stones from boulder 
clay. The village clergyman or teacher who desires to 
show that there are “sermons in stones” and other natural 
objects and phenomena will find Canon Ovenden’s short 
addresses of service. 
A few points will, we think, lead to misconception if 
accepted as they now stand. For instance, a barometer is 
said to weigh the air, whereas it really measures pressure. 
Again, it is only true in the northern hemisphere that 
a ‘‘cyclone spins always against the hands of a clock, 
and the anticyclone rotates with the hands of the clock.” 
