THE ROYAL ARTILLERY INSTITUTION. 
457 
difficulty in finding the corresponding increment. I imagine however the 
increase of range will be very nearly as in vacuo. 
An unexpected increase or decrease of range is of course a great source of 
radial deviation, as the angles of descent of projectiles at long ranges are 
very considerable. Were the angle of descent of the projectile 19°, an object 
six feet high, and eight yards in front of the target would be practically safe. 
Yet this occurs actually in practice with the Prussian cylindro-conical bullet 
at a range of 1000 yards.* 
The great law of universal gravitation is of course applicable just as much 
in the consideration of the motion of projectiles, as in those of larger heavenly 
bodies. Thus the sun and the moon which are both in the ecliptic cause a 
southerly deviation of the projectile, but to counterbalance this they also 
cause a southerly deviation of the plummet, and a northerly deviation of the 
line of aim, if the plummet be used for this purpose. Happily, however, 
the resulting action is too imperceptible to justify attention. The lunar 
excess of attraction (the difference of attraction which it exercises on a body 
situated on the surface of the earth and a like body placed at the centre) is 
however nearly three times that of the sun. The corresponding deflections 
of the plummet in terms of the zenith distance will be sin 2a (sun), 
jy/ loO 
and —r sin 2a (moon ); and if we wish to find the effect on the projectile we 
oU ^3 23 
find in pounds [-qJqqqqqo sin 2a (sun), and 168Q00Q q q sin 2a (moon), 
will represent the amounts of attraction, results only mathematically 
interesting. 
Physical Causes . The Resistance of the Air . 
We will now pass on to a subject already most fully considered, namely the 
resistance of the air, which stands first of the physical causes. The effect 
of this force is to render the time of descent for all projectiles greater than 
the time of ascent, at the same time greatly retarding their flight. For 
particular elongated projectiles it acts too no doubt by forming a line of 
descent of least resistance; perhaps only in a less degree to the well known 
case of the Australian boomerang. But one result I wish particularly to lay 
stress upon here is its action in as it were clogging the ball with a layer of 
air, which may increase the surface exposed to the action of the wind. 
That some such action as this takes place is manifest, for as the ball 
passes through the air it must drive before it a considerable quantity, and 
this layer will be increased in proportion to the velocity of the shot, and the 
friction between its head and sides and the condensed air. A side wind will 
then act upon it to a greater extent, in proportion as this layer increases the 
section exposed to its action. I would point out also a curious effect of this 
mass of air, for when the wind acts on an elongated projectile, which has a 
head of smaller section than the hinder part, this would tend to steady the 
projectile, when otherwise it would have a tendency to turn up head to 
wind. The envelope of condensed air is also partly due to the attraction 
* Sir Howard Douglas on “ Small Arms.” 
