< 
ro 
‘Oct. 16, 1873} 
- quickly follow, and we may thus hope to acquire, before 
long, a complete knowledge of one of the most won- 
_ derful floras and faunas of the world’s surface. 
Beka S. 
THE MOTION OF PROFECTILES 
_ A Mathematical Treatise on the Motion of Projectiles , 
founded chiefly on the results of Experiments made 
with the author’s Chronograph. By Francis Bashforth, 
B.D., Professor of applied Mathematics to the advanced 
class of Royal Artillery Officers, Woolwich, and late 
Fellow of St. John’s College, Cambridge. (London: 
Asher and Co., 1873.) 
E are told in the Preface to this work that “the 
2 " consideration of the motion of a projectile naturally 
divides itself into three parts—first, its motion in the 
bore of the gun ; second, its motion through the air ; and 
third, its motion during its penetration into a solid sub- 
stance.” The author directs his attention chiefly to the 
second of these parts. Galileo was the first person who 
determined with anything like accuracy the motion of a 
solid body moving through space under the action of 
gravity. Treating the vertical and horizontal motions as 
perfectly independent (which of course is in accordance 
with Newton’s laws of motion), he showed that a particle 
moved in a parabola. In this theoretical investiga- 
tion gravity is supposed to be constant, and to act in 
parallel directions, while the effect of the resistance of 
the air is totally disregarded. The parabolic motion is 
approximately true for bodies whose velocities are small, 
but the greater the velocity of a projectile, the more does 
its path deviate from a parabola, and, in the present days 
of large guns and heavy charges, we can at once see the 
importance of solving with the greatest possible accuracy 
the problem of the motion of a projectile through the air, 
considering the air as a resisting medium materially 
affecting the motion of the shot. Newton solved the 
problem of the motion of a body through a medium 
whose resistance varies as the first power of the velocity, 
and John Bernoulli extended it to the case of resistance 
varying as any power of the velocity. 
Experiments, however, show that the resistance cannot 
be regarded as varying as any single power of the velocity, 
though, within certain limits, the third power gives pretty 
accurate results. 
Mr. Bashforth has applied himself to the task of 
throwing Bernoulli’s solution into a practical shape, so 
that by means of copious tables, of which his book con- 
tains more than 100 pages, such problems as the following 
may be solved :—“ The 16-pounder muzzle-loading gun 
fires an ogival-headed shot 16 lb. in weight, and 3°54 
inches in diameter. If the angle of projection be 2°, and 
the initial velocity 1,358 feet per second, find the trajec- 
tory and time of flight.” “A Rodman shot weighing 
452 lb. is fired with an initial velocity of 1,400 feet per 
second, at a target 500 yards off, find the striking 
velocity.” 
_ Experiments were made by Robins and Rumford last 
century to ascertain the pressure of fired gunpowder 
and several persons have attacked the problem during 
the present ‘century. General Mayevski attempted to 
NATURE 
solve the problem by firing shot, into the back of which a 
rod was screwed, the rod running through an aperture 
in the breech of the gun, and carrying a knife edge 
which cut two thin wires at a given distance, the interval 
of time between the two breakages being measured as 
accurately as possible. Captain Rodman made use of 
the following arrangement :—A gun was mounted in a 
gun-pendulum, and a revolving cylinder was placed with 
its axis parallel to that of the gun. When the gun was 
fired, a tracing point on the gun drew a curve on the re- 
volving cylinder, the shape of which curve determined 
the whole motion of the gun’s recoil. Mr. Bashforth 
suggested that much greater exactness would be procured 
if the tracing-point were connected with the projectile, 
He managed to do this to some extent by firing a shot 
through a number of equi-distant vertical screens, made 
of very thin metal wires. By an ingenious arrangement, 
the time of the shot breaking a wire in each screen was 
registered by means of an electric current on a revolving 
cylinder, special care being taken that all the registra- 
tions should be made under the same circumstances, so 
as to eliminate what we might call the personal error on 
the different registrations. This gave the times of transit 
of the shot over the successive intervals between the 
screens : from them, the velocities at the different screens 
can be calculated with great exactness, and also the 
resistance of the air on the shot. Mr. Bashforth has 
made great numbers of experiments with shots of different 
shapes and sizes, fired with different charges of powder, 
and from them has with great labour calculated the tables 
above referred to, which are sufficient for the solution of 
the problems we have given above as examples of what 
Mr. Bashforth has been able to accomplish. 
The work is one which is too mathematical to do full 
justice to in our columns, but we have no hesitation in 
recommending it to such artillerists as are not unac- 
quainted with mathematical analysis. 
OUR BOOK 
Half-hours with the Microscope. 
(Hardwicke.) 
THIs excellent and well-known little work would scarcely 
require to have special attention now drawn to it, if it 
were not that the present edition contains an additional] 
chapter, which adds much to its value as a text-book fo, 
amateurs. Until now the subject of polarised light ha, 
been omitted, and as the many beautiful and striking re_ 
sults which can be obtained by its employment are among 
the most important and attractive in the whole field of 
microscopy, any work on the subject in which it is omitted 
must be necessarily incomplete. The author, evidently 
feeling this, has added a “Half-hour with Polarised 
Light,” which he has entrusted to the hand of Mr. F. 
Kitton, who, in the short space allowed him, has explained 
the theory of this rather intricate subject in a clear and 
popular manner, and has described some of the most 
striking of the phenomena exemplified by it, such as the 
appearance of the slides of iodo-sulphate of quinine, as- 
paragine and sulphate of copper in gelatin, together with 
the methods for arriving atthem. The addition of this 
chapter has made this work as complete as it is useful to 
the commencing microscopist. 
Proceedings of the Belfast Natural Ristory and Philoso- 
phical Society. (Belfast, 1873.) 
WE welcome with pleasure the first number of the Belfast 
Society’s Proceedings, which includes a number of papers 
SHELF 
By E. Lankester, M.D. 
