THE COAST ARTILLERY JOURNAL - Air Defense Artillery

U x= Rotation about the X-axis
U y= Rotation about the Y-axis
U z= Rotation about the Z-axis
PROFESSIONAL NOTES 269
Tbe term in acceleration, U'b, is included in the value of g used, thus -in meters
g = 9.8060-0.0260 cos 2L (Helmert)
The rotation of the earth on its axis is a simple physical fact and the mathematical
formulae for its effect on the flight of a projectile may be developed as follows:
Let u, v, lV, be the component velocities in space of a particle whose rectangular co-
ordinates are x, y, z with origin at the gun. The resolved velocities relatively to the moving
axes are x', y', z'. To find the motion in space we must add to these the resolved velocities
due to the motion of the axes. If we suppose the particle to be rigidly connected with the
axes, its velocities would be express~ by -z U y + y U z , -x U z + z U x ' - y U x + x U y • By
adding the parts together the actual resolved velocities of the particle will be
(2) u = x' - Z U y + y U z ' v =y' - x U z + z U x • lC =z' - y U x + x Uy
Since acceleration is the rate of increase of velocity just as velocity is the rate of
increase of space, it is clear that the relations which hold between accelerations and ve-
locities must be the same as those which hold between velocities and spaces. Thus the rela-
tions between the accelerations, X, Y, Z, and ll, v, U', follow at once from those between
ll, v, u;, and x, y, z, hence:
(3) X = u' - u; Dy + v Dz' Y =v' - u Uz + u; Qx' Z = w' - v Qx + u Qy
From (2) by differentiation we obtain,
(4) u' = x" - z' Qy + y' Qz. v' =y" - x' Qz + z' Qx' Ie' =z" - y' 12x + x' Qy
whence (3) becomes
X = x" - 2z' 12y + 2 y' Dz + terms containing D'
(5) Y = y" - 2x' Qz + 2 z' Qx + terms containing D'
Z = z" - 2y' 12x+2 x' Qy + terms containing Q'
Without rotating II = x', V = y', u; = z'
(6) and X =u' = x", Y = v' = y", Z = u;' = z"
From (5) and (6) and substituting the values of Qx. On Qz. from (1), given above,
the effect of rotation of the earth may be written:
ox" = - 2 y' Q cos L sin A + term in z'
oy" = + 2 x' Q cos L sin A - term in z'
oz" = + 2 y' 0 cos L cos A - 2x' U sin L.
The Irish Free State Army
It is announced that the Government of the Irish Free State, intent on economy.
proposes to make a big reduction in the strength of the Free State Army. The last Army
Estimates amounted to £1,800,000. This year there is to be a cut of £300,000. The Army
has an active strength at the present time of 736 officers and 7,919 other ranks. During the
present year it is to be reduced to a total strength of 5,000_ There will be a Class "A"
Reserve for those who have served in the Regular Army, and a Class "B" Reserve for those
who have had no military service. In addition, there will be a "\olunteer Force on the
lines of the British Territorial Army. Those enrolled in this force ",ill drill weekly in their
own areas, and will be called out for annual training. Among the additions to the equip-
ment of the Army is a tank of Japanese design-which is odd. Special inducements are