ROTATION OF PROJECTILES. 
109 
Again, Ci — M (l + ^ «) > aQ d c% — m(\ + ^ y); 
fi + £--4^4--■) 
1 17 C-. 
* c. = Jftj 2 
c* — a' 
Hence » 2 = 
c 3 + a 2 
(l + £ a) X »3 4 
(0+ ZA)j’ 
and = Mk£, 
4+ £y) X jKV(! + '«) x M^(a-y) 
where a' = 
^ 3 V 
C-A 
C-A+ %r-^XC+ZJ) 
C* + or 
1 + p - a 
icfik-f - (a — y) (l + ^ y) (l + ^ a) 
■*V 
4«v - (® - y) 1 + A? +-»(-) + c(-) + &<!• 
where A, B, C are some coefficients. 
ttVc^ 
4 
„-„j£ + ^(|)- + J (£) + ^ 
But as, for metal projectiles, ^ is obviously a very small quantity 
(being in the case of a cast-iron common shell less than ’00025), the 
square and higher powers of ^ may be neglected. 
Hence the formula becomes 
4fl 2 & 1 2 - (a — y) 
Let us, however, work out the value of n for (say) the Martinb 
Henry bullet from the exact formula 
2 - ^Ve 2 
4«V 4 ( c i — c s) 
* It is hardly necessary to remind the reader that the moment of inertia (usually denoted by 
Mk 2 ) of a rigid body about a given axis is the sum Of the products of the mass of each particle of 
the body and the square of the distance of that particle from the axis. The radius of gyration (&) 
of a body about a given axis is the distance of a point from the axis at which, if the whole mass 
were collected, the moment of inertia would be the same as before. 
