VOIy. 6, 1920 
PHYSICS: A. G. WEBSTER 
659 
In order to show the functional relation (19) between the five quantities 
p, X, Uy z, G, an ''ahaque a glissemenf was constructed, so that by placing 
a transparent index on four of the variables the fifth could be found. 
This will be described elsewhere, but inasmuch as it was found to take 
longer to set the index than to set up the numbers on the arithmometer, 
of which we have several models, it was not used. After z was calculated, 
curves were drawn : 6{p,x), the indicator diagram (p. 652) for the gun; 7(z,t), 
8{dz/dt,t), 9{x,z), I0{dx/dz,z), 11(1— 2)" for various values oin; 12{p,z), 
13{dp/dz,z) (with a different zero of ordinates); 14(m,^); I5{du/dz,z)\ 
lQ{dz/dt,z). 
For graphical differentiation, a simple contrivance was used consisting 
of two metal rulers jointed together at one end. Near the other end 
of one was placed a plane mirror normal to the edge of the rule. By 
looking at the curve in this, and making its reflection join it without a 
corner, the direction of tangency could be found more accurately than 
by making the ruler tangent. The other ruler is then set parallel to the 
horizontal lines of the paper, and for a horizontal distance of ten or twenty 
centimeters the vertical distance between the rules read off, giving the 
trigonometrical tangent. Thus in a few minutes we may lay down the 
derivative curve with nearly three figure accuracy. 
I have the following criticisms to make on the curves. After they had 
been given to the photographer it was discovered that the left-hand 
portions of (9) and (10) are incorrect, since dx/dz must vanish when x 
and u are zero. This is probably due to an error in choosing this point, 
which should be at the inflexion of the p curve, which should have been 
determined with the mirror directly on the film, instead of on the enlarge- 
ment. When this is done, the pressure to start the shot is found to be the 
same as on curve 2, which (like 1) is so good that films of two different shots 
may be laid one over the other without being distinguishable. Making 
this correction will slightly displace curves (3) and (4). I realize that I 
have given hardly enough here to verify the theory, but as this paper is 
too long already, and as I am very shorthanded for assistance, I consider 
it best to publish it for the method, and to leave the verification, which 
should be by the construction of the observed curves from calculation, 
for another paper. By the courtesy of Rear-Admiral Ralph Earle, we 
have a Naval one-pounder gun, to which we hope to apply the methods, 
on which we hope to improve by experience. For a larger gun, where 
the wires might be blown out of the gun by the blast, we have another 
method of finding the velocity in the bore. 
It should have been stated in our former paper, and is now stated 
here, that these experiments have been made possible by means of a 
generous grant from the Rumford Fund of the American Academy of 
Arts and Sciences, and to my colleagues on the Rumford Committee 
I hereby express my hearty thanks. 
