In this equation P varies directly with V^ sin <\ the deviating

P (Cs
component of V^ Now n/r^^^rfi expresses the relation between

the variable force Pand the acceleration impressed upon the mass
M, From this we see that the acceleration for the same mass will
vary directly with the value of P. Therefore, as /^varies the ac-
celeration of the projectile sidewise varies directly with it. Accel-
eration being the velocity impressed in a unit of time, it follows
that the spaces described must vary directly with acceleration and
the accelerating force.
Thus, it follows that for all cases to which /'= ->,. — t> V^ sin ^

C g



54 THE QUARTERLY,

applies, the pressure and deviations will vary directly with V^.
Therefore, if V^ increases to twice its original value, the deviation
will be doubled. From this we obtain the rule that in moder-
ate values for V^, deviation varies directly with the velocity of the
wind.
Now, passing on to higher winds, since, as just shown, the devi-
ating force for head winds increases more rapidly than the velocity,
deviation must follow the same laws, and for all winds with accel-
erating components the converse is true.
These deductions are independent of any increase or decrease
in the time of flight.
The law that deviations are proportional to the wind's velocity,
though not theoretically true in any case, will apply practically
whenever tan <p may be substituted for sin <p without appreciable
error. It is highly probable that all deviations follow this law so
closely that no variation from it will be sensible in practice.
