124 
MINUTES OF PROCEEDINGS OF 
17. The experiments numbered XXXII. to XXXVI. inclusive were 
undertaken with this view, but in laying down in the form of a diagram 
the results thus obtained, marked differences were found to exist, which 
will best be understood by comparing the two curves delineated in 
fig. 1, in the accompanying diagram. The black line in this diagram 
shows the relation of the initial velocity to the charge as derived from 
this series, by actual observation, while the red line denotes the hypo¬ 
thetic relation as determined from the equation— 
where ^ and m denote the weight of the charge and shot in lbs., the 
value of the constant in this equation being determined from the 
Velocity when the service charge of 1 lb. 8 oz. was employed. 
It will be observed that while the hypothetic curve is always 
concave to the line of abscissas, in the curve derived from actual 
observation there are two points of inflexion, it being in one portion of 
its trace convex instead of concave to the axis of x. 
18. To check the results obtained in this series, a second series with 
another gun was subsequently made, the details of which are given in 
XXXVII. to XLIII. Their graphical representation is delineated 
in fig. 2 ., in which as before the black line denotes the observed 
curve, the red, the computed one, the value of v being given by the 
equation— 
the coefficient in this case, as in the former, having been determined 
from the data furnished in the case where the service charge was 
used. 
19. Although in this second case, the initial velocities are, owing to 
powder of a different strength having been used, very considerably 
under the velocities in the former case, it will be noticed that the same 
peculiarities are observable, there being a portion of the curve with its 
convexity turned towards the axis of abscissae. 
20 . The cause of the wide departure from the normal law exhibited 
in these diagrams is easily explained. It will be remembered that in 
the Armstrong gun, the shot always occupies a definite position in the 
bore, the service charge nearly filling the powder chamber. Hence it 
follows, that if reduced charges be used, additional air space is left in 
the chamber, so that in addition to the decrement of velocity due to 
the reduction in the charge, there is to be added the decrement due 
to the increased air space, and it is easy to see how the combination of 
these conditions may produce the abnormal results alluded to. 
21 . The annexed Table gives an abstract of the results of these ex¬ 
periments, and I also attach a table giving for powder of average 
strength, the initial velocities for various charges. 
