456 
MINUTES OF PROCEEDINGS OF 
line, and perpendicular to the spirit level. It will be this so called vertical 
which will determine the position of the fictitious point in space on which the 
axis of the piece is directed, and the propelling force will also be exerted in 
this vertical plane.* But immediately the projectile leaves the earth it 
becomes its satellite, and tends to revolve round its centre of attraction, 
instead of holding its constrained orbit round the polar axis, so that centri¬ 
fugal force being no longer exerted in the same direction as heretofore, the 
shot falls direct to the centre of the earth. The deviation under these 
circumstances in this hemisphere is always northerly, and if the gun be 
fired east or west in latitude 45°, at a range of 2700 yards, and at an 
elevation of 45°, the resulting error does not exceed 14 ft. The projectile 
is projected with a velocity compounded of that received from the earth, and 
that imparted by the powder. 
Now there will be a correction to apply to these results, more curious than 
practical, which will in all cases tend to infinitesimally diminish the deviation. 
As the shot travels south the air will impinge against it with gradually 
increasing velocity, and by the impulses it will give to the projectile will tend 
to diminish the distance PM. In whatever latitude also, the shot is fired, 
the higher strata of the atmosphere will be moving with greater velocity from 
west to east than the shot, and consequently this action will also tend to 
diminish the deviation when the shot is fired south, but increase it when it 
is fired north in our hemisphere, and have the effect of increasing the range 
when the shot is fired east, and diminishing it, when it is fired west. 
Shape of the Earth considered . 
The shape of the earth is the next of the cosmical causes to consider, and 
the range appears to be increased in proportion to the curvature as on an 
oblique descending plane. But this inaccuracy is of itself very trifling, and 
is nearly compensated for by the retarding effect of gravity due to the central 
action of this force (Fig. 11). Thus in vacuo, the increased range is to 
the calculated range only as the arc to the chord, a difference inappreciable 
[chdY 
for arcs of 5000 yards, being nearly v ' 
24r 3 
If 
we 
take into account the 
resistance of the air, this difference will be even less, as gravity will act longest 
on the shotf when it has the greatest retarding effect. 
Spheroidal form of the Earth . 
The spheroidal form of the earth is another moot point, as gravity and its 
corresponding effect on the shot will diminish by -^ir from the poles to the 
equator. This would give for ranges calculated in vacuo an increase of 10 
yards in 2310 from the poles to the equator. With regard to ranges 
in a resisting medium, owing to the nature of the equations there is great 
* It is always tacitly assumed in tlieory that either a plumb line or a spirit level has been used to 
direct the piece, as without these there is no perfect adjustment of aim. 
f Owing to the resistance of the air the time of descent for all projectiles is greater than their 
time of ascent. 
