176 
MINUTES OF PROCEEDINGS OF 
then be assumed that the cylinder will lose its angular velocity according 
to some law, which law can be determined from the intervals between five or 
six successive records of the beats of the clock. The weight of the mark¬ 
ing apparatus and electro magnets does, in some measure, act as a driver of 
the fly-wheel and cylinder, and so tends to keep up the velocity; but it was 
not introduced for that purpose, and its effect is slight. The gradual loss of 
angular velocity of the cylinder gives a little trouble in the calculation when 
extreme accuracy is desired, but creates not the slightest difficulty to the 
mathematician. The subject now must be divided into two parts; (1) where 
a thoroughly trustworthy velocity of a projectile is required, and (2) where 
the utmost attainable precision is desired, with a view to determine the 
exact amount and law of the resistance of the air to projectiles of various 
forms and sizes. 
In the first case, the intervals between at least three successive beats of the 
clock should be measured, so as to extend beyond the screen marks on both 
sides. Three screens are the least that can be used with safety, which may 
be placed 60 or 70 feet apart, or at greater equal distances, if possible. By 
taking three records from the clock, and three from the shot, we have a com¬ 
plete check. If the records be found to be consistent, and if A , B , C t 
represent the beats of the clock, and a the position of the three screen 
marks, then the length AB must be taken to represent a second, and the 
ABC 
distance from the first to the third mark at a would represent, very nearly on 
the same scale, the time occupied by the shot in passing from the first to the 
third screen—the use of the middle screen being merely to test the reliability 
of the screen records. The only calculation is comprised in the proportion— 
velocity in f: s : distance between first and third screen :: AB : distance 
between first and third record at a. If the three screen records fall at b near 
B, then \ (AC) must be taken as the representative of a second; or if they 
fall at Cj then length of BC must be used to represent a second. The 
velocity so determined would be thoroughly trustworthy, and sufficiently 
accurate for all practical purposes. 
In the second case, where the utmost attainable accuracy is desired, it 
becomes necessary to have more numerous equidistant screens spread over a 
greater distance. The screens are placed at equal distances because that 
facilitates calculation, and enables us to judge whether the records are con¬ 
sistent. This principle should be carefully observed in all experiments. 
Thus, if it be required to find how far the initial velocity depends upon the 
charge of powder, vary the charge by equal quantities. If several rounds 
are to be fired with each particular charge, begin with the highest or lowest, 
and fire one round of each charge up to the lowest or highest, and so on over 
again till the experiment be completed. If it be desired to find range tables 
corresponding to various elevations of the gun, fire one shot at 0°, one at 1°, 
one at £°, and so on up to the greatest elevation, and repeat till the experiment 
is completed. If now the mean range for each degree of elevation be taken, 
these ranges will follow some kind of law, and after small adjustments have 
