of Edinburgh, Session 1877—78.. 
647 
dulum, and determine both the initial velocity and the resistance by 
accurate observations of the angle, the range, and the time of flight. 
For the purpose of facilitating the solutions of the various problems 
which may arise in practice, auxiliary tables may be derived from 
the fundamental ones. 
When a shot is fired in a steady breeze, the direction in which 
the ball meets the air is not the apparent direction of the gun, it is 
that of the resultant of the two motions, and the computations have 
to be made as for that resultant. 
Thus if AZ (fig. 5) represent the horizontal direction of the 
gun, and AB the initial velocity of the ball projected on the hori- 
zontal plane, while £>B represents the velocity of the wind, A b will 
be the horizontal direction in which the ball meets the air. Since 
the vertical motion is not affected, the tangent of the elevation of 
the gun must be changed in the ratio of A b to AB in order to get 
the tangent of the true angle of elevation in relation to the air, and 
A b multiplied by the secant of that elevation is the true initial 
velocity. 
If we now, using these corrected arguments, compu te the hori 
zontal distances corresponding to equal intervals of time, measure 
those along the prolongation of Ah and from the successive points 
draw parallels cC, dl . ), &c., multiples of 6B, we shall have the 
