ROTATION OF PROJECTILES. 
105 
allowing it to wabble is analogous to the angular velocity required to 
keep the projectile in stable equilibrium, point foremost; and this is 
the point elucidated in Prof. Greenhilks paper. 
The amount of spin is calculated in the customary notation of one 
turn in n calibres, and it will be shown that this is the correct way of 
reckoning it. 
It will now be well to make a few remarks on various points con¬ 
tained in Prof. GreenhilPs paper. (The marginal references refer to 
that paper.) 
The symbols c Uj c 33 , c 44 , c 66 may be replaced by c h c 3 , c 4 , c 6 ; the 
double suffix being only required when an unsymmetrical body is dealt 
with, which is not the case in the present paper. 
The state of motion set up in the surrounding medium is considered 
by means of the component linear velocities u, v, w of the body, taken 
separately, and also by means of the component angular velocities 
q, r of the body, taken separately. (Note that the angular velocity 
r round the longer axis of the body does not impart motion to the 
surrounding medium, as the latter is assumed to be frictionless.) 
When the body has the velocity u its energy is \Mu 3 (if being 
weight of body in lbs,), and the energy of the medium will be pro¬ 
portional to u 2 , to p (the density of the medium), and to the volume of 
the body; i.e., the energy of the medium will be proportional to u 2 
and to M' (the weight of medium displaced). Hence 
= + laM'u 2 (where a is some constant) 
= * Jft *( 1 + F a ) 
= P& 2 (l + ■;«). 
On the assumptions made above, of the medium being frictionless 
and incompressible, a will be a function of the external shape of the 
n .. . .. 0 M' weight of displaced air 
body only, and £ = ^ = veight of body .- 
The great mathematical difficulty of the investigation consists in the 
determination of a. Hitherto, as stated above, it has only been deter¬ 
mined for an ellipsoid, which includes the spheroid. 
Precisely similar reasoning and remarks apply to y. 
To determine a and y, it is necessary to find the “ stream lines ” of 
the medium. The latter is first supposed to flow past the spheroid 
fixed. 
Page 577. 
2nd line of 
3rd para, 
Page 577. 
4th. para. 
Page 588. 
1st para, 
