106 
ROTATION OP PROJECTILES. 
To determine a, the medium is supposed to flow with a velocity u in 
a negative direction perpendicular to the longer axis of the spheroid. 
To determine y, the medium is supposed to flow with velocity w in 
the direction of the longer axis. 
The “ stream lines ” have been more than once referred to. The 
accompanying sketch may serve to show, to some extent, what is 
meant by them. 
The various lines of the flowing medium are parallel at an infinite 
distance to the right and left of the fixed spheroid. On approaching 
that obstacle they are deflected. No line can pass through it, and 
consequently they must all pass round it. The lines which would 
strike the centre of the spheroid are most deflected; those above and 
below them to a less extent. After rounding the obstacle, they tend 
again to resume their parallel courses. 
The amount of deflection of these “ stream lines 99 being known, it 
is then possible to calculate the velocity at any point of the medium. 
In the above we suppose the medium to be flowing with velocity u. 
Now suppose the medium to be originally at rest, and the spheroid to 
move with velocity u. Thus we obtain the resulting motion in the 
medium by superposing * a positive velocity u at any point of the 
previous state of motion, when the body was supposed to be fixed and 
the medium to move. 
The velocity at any point of the medium is now known, the body 
moving with velocity u 9 and hence the whole kinetic energy in the 
medium can be calculated. The quantity a is the ratio of the kinetic 
energy of the external medium to the kinetic energy of a body pro¬ 
ducing the motion of the medium; this body being supposed to have 
the same density as the medium, and the same external shape and 
motion as the actual body. A similar remark applies to y. 
The mathematical work of determining a } and similarly of deter¬ 
mining y, is omitted, as too intricate and laborious.'* 4 ' The results only 
are given. 
Page 578. It may be remarked that in establishing the formulas for the values 
Formulae J ° 
for C and A. _____ 
* The subject may be found treated at length in “ Green’s Mathematical Papers,” edited by 
the Rev. N. M. Ferrers. 
