2 
of General Mayevski, we obtain, with the metre and kilogramme as units :— 
From v= 1000 m/s to v= 800 m/s, resistance p= 0°7130 7 R2 yp 1:55 
cn) 
800 » 550 ' = 02616 r Re y 1-70 
cL) 
550 x Lae) - = 00394 7 R27 y 2 
a) 
419 aa 0 STS ¥ 55 =0°04940 7 R27 y 8 
ca) 
375 295 B 5 =0'09670 r Rey 5 
To) 
295 -- + - 940 -, 5, =0°04583 7 R27 y 8 
a5) 
240 downwards % 5 = 0°0140 r R22 y 2 
™) 
where & is the radius of the cylindrical portion of projectile in metres, 
a =the density of the air during experiment, 
7) = 1206 kilogrammes per cubic metre. 
From the above formulee it is seen that with low velocities, the resistances are 
proportional to the square of the velocities ; with velocities near to that of sound 
they increase according to a higher power ; and with velocities above 550 metres 
per second, the increase is ascording to a lower power than the square. 
If we regard the air as consisting of particles: colliding with one another and 
possessing velocities various according to their magnitude and direction, then on 
the basis of the mechanical theory of gases the mean velocity of the progressive 
motion of the particles at a temperature of melting ice is equal to 485 metres 
per second and at 15° C. about 500 metres per second. 
Thus the law of the increase of the resistance of air changes at the velocities 
which are connected with certain properties of the air, 7.¢. at the velocity of sound 
and at the mean velocity of the air molecules. 
2. Proposing in an edition of Internal Ballistics (which I have undertaken) 
to print detailed tables for the solution of problems of fire for velocities up to 
1100 metres per second, calculated from the above formule, I shall in this note 
attach an abbreviated table of the values of the functions 
D (u), A (uw), L (u), T (u), B (w) and M (u) 
corresponding to the values w from 600 metres per second to 1000 metres per 
second. 
In calculating the values of these functions the air resistances is expressed by 
the formula 
p=0'5091 + R27 y 16, 
™ 
the resistances determined by this formula (for velocities. between 600 and 1000 
metres per second) being nearly those of Krupp’s 1890 tables. 
This table, together with the ballistic tables of Lieut.-Colonel Langensheld, can 
be employed in the solution of problems of direct fire for velocities up to 1000 
metres per second, but the signs of the functions must be paid attention to. 
For values of w near to 700 m/s the functions, with the exception of I (w), pass 
through zero; the functions D (w), 4 (w) and MW (w) change sign and become 
negative; the function B (w) has a double root, as it preserves its positive sign 
on passing through zero. 
The values of w where the functions pass through zero are shown in the note 
to the attached table. 
_ 8. We shall now apply this table and the tables of Lieut.-Colonel Langensheld 
to the solution of two problems. 
