494 
adopting the results of so-called experiments. It must be 
evident that the efforts of the Krupp party are directed to 
spread an impression that his system of constructing guns 
and projectiles has some mysterious property of reducing 
the resistance of the air. Now it is perhaps fortunate 
that the English experiments were made when the Service 
guns did not shoot quite so steadily as they do now, 
because all the observations were made near the gun 
when the motion of the shot was most nearly in the 
direction of motion. Although one gun was an extremely 
good one—-we will suppose that the average of the four 
guns gave coefficients slightly above those due to per- 
fectly steady motion in direction of the axis of the shot. 
Let us consider now what actually takes place on a long 
range. The elevation we will suppose 10°, and also that 
the shot leaves the muzzle with perfect steadiness. The 
tendency of the shot is to preserve the parallelism of its 
axis, but the curvature of the trajectory soon causes the 
axis of the shot to be inclined to the direction of motion. 
The resistance of the air then acts od/¢guely on the shot, 
and so tends to place the axis in the direction of motion. 
If it succeeded in accomplishing this feat at any instant, 
all would be out of order the next moment. In this way 
the axis is kept zearvZy in the direction of motion. Our 
shot would perhaps fall at an angle of 12°, making 22° as 
the angle through which the axis of the shot had been 
turned during its flight, by the od//gue action of the resist- 
ance of the air. This oblique action of the air causes 
other disturbances, as “ drift,” &c. Thus if in the English 
experiments the shot moved with their axes at times 
slightly inclined to the direction of their motion they 
would give coefficients more nearly corresponding to the 
conditions of their motion on long ranges than if they 
had been obtained from shot moving with the axis exactly 
in the direction of their motion. 
Afterwards Capt. Ingalls treats of the general properties 
of trajectories, the rectilineal motion of shot, and the cal- 
culation of tables. He explains the methods of calculating 
trajectories adopted by Euler, Bashforth, Niven, and 
Siacci. Numerous examples are given to illustrate and 
explain these methods, and examples taken from Bash- 
forth’s treatise are worked out by approximate and other 
methods. 
The work concludes with three ballistic tables adapted 
for the calculation of trajectories by Siacci’s approximate 
method. Table I., for spherical shot, is based upon 
Mayevski’s coefficients (1872); Table II., for elongated 
projectiles, is based on Bashforth’s coefficients ; and Table 
III. is said to be copied from Didion, who copied from 
Euler. This table is given by Otto for every minute up 
to 87° o', which is its most complete form. 
OUR BOOK SHELF 
Illustrations of the Indigenous Fodder Grasses of the Plains 
of North-Western India. (Roorkee: Nature-printed 
at the Thomason Civil Engineering College Press, 
18386.) 
THIS is an atlas of forty plates, the representations in 
which are most natural and life-like, the characteristic 
habit of each species being effectively shown. About half 
the plates are accompanied by diagrams of the spikelets ; 
or florets. 
NATURE 
Andropogon, 7 to Panicum, 3 to Eleusine, 3 to Eragrostis, 
and 2 each to Aristida, Cenchrus, and Paspalum. The 
I4 remaining genera, represented each by 1 species, 
include, amongst others, Saccharum, Setaria, Sorghum, 
and Sporobolus. All the species shown are extra-British, 
excepting Cynodon Dactylon, Pers. [and Panicum Crus- 
Galli, L.]. Of these grasses none perhaps is of greater 
current interest than Sorghum halefense, Pers., known 
amongst English-speaking peoples as ‘‘ Johnson grass,” 
respecting the drought-withstanding capacity of which - 
very favourable reports continue to be received from 
Australia and from the Western United States. Mr. J. F. 
Duthie, under whose careful supervision the work has 
been published, states in a short introduction that “the 
increasing demand for reliable information concerning 
the various grasses used in this country, either as fodder 
or forage, has induced me to collect materials for the 
preparation of a work embodying all the available infor- 
mation on this very important subject.” This admirable 
atlas is a contribution in the direction indicated, and the 
descriptive letterpress, which Mr. Duthie promises to 
have ready by next cold season, will be welcomed by 
those—and their number is rapidly increasing—who are 
interested in the economic study of the Graminea. 
W. FREAM 
Exerctses on Mensuration. By T. W. K. Start. 
(Lon- 
don: Sampson Low and Co., 1886.) 
A WRITER who invariably mis-spells “ hypotenuse ” speaks 
of squaring two numbers and “‘ subtracting the results,” 
and treats of the area of a triangle before the area of a 
rectangle, does not deserve success. Yet so unsuited for 
non-technical schools is the scope of most of the existing 
books on mensuration, that a little manual like this of 32 pp. 
hasan excellent chance in the struggle for existence. We 
hope the present edition may be rapidly sold, and fol- 
lowed by a second edition thoroughly revised. TT. M. 
Lectures in the Training Schools for Kindergartners. By 
Elizabeth P. Peabody. (Boston: D. C. Heath and 
Co., 1886.) 
IN these eight lectures, which have been addressed during 
the past nine or ten successive years to training classes 
for Kindergarten teachers in Boston and elsewhere, Miss 
Peabody explains the system of Froebel, and the prin- 
ciples on which it rests. The very first sentence of the 
first lecture shows the serious view entertained by Miss 
Peabody of the duties of such teachers: “* Whoever pro- 
poses to become a Kindergartner according to the idea 
of Froebel, must at once dismiss from her mind the 
notion that it requires less ability and culture to educate 
children of three, than those of ten or fifteen years of 
age. It demands more.” 
Le Mouvement scientifique et industriel en 1885. 
Causeries scientifiques. Par Henry Vivarez. (Paris: 
Librairie Centrale des Sciences, 1886.) 
THIS volume is a republication of a number of sketches 
on scientific subjects contributed weekly to the journal 
La Gironde, with a view to keeping the readers of that 
periodical aw courant with the progress of science in its 
various branches. They are therefore popular, and are 
made as entertaining as possible. The writer has the 
gift, so common amongst his countrymen, of rendering 
the most technical and abstruse subject clear and interest- 
ing. The “ Causerie” is peculiarly a French device in 
journalism: hitherto it has been mainly devoted to liter- 
ature and the drama. M. Vivarez has applied it with 
much success to science. It would be absurd to speak 
of this as a work of science, but it certainly is a work in 
which the latest results of science are explained and 
Of the 4o selected species, 7 belong to | illustrated for the million. 
[ Sept. 23, 1886 
