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16.

mercury to wires on the plank. A record of the displacements was made by a stilus consisting of a steel rod, S, pointed and hardened at the lower end. This rod slid freely in a vertical brass sleeve, attached to the under side of the plank, and made a mark upon a smoked glass strip, G. In this way the first backward and forward displacements of the pendulum were recorded, and the elimination of friction was thereby made possible.

The data and results of these experiments are given in Table II, in which [[underlined]] d [[/underlined]] is the displacement corrected for friction.

The velocities and efficiencies were obtained from the usual expression for the velocity in which a ballistic pendulum, with the bob constantly horizontal, is used, namely,

^[[v = M/m √2gl (1-cos𝛉),]]

where [[underlined]] M [[/underlined]] = the total weight of the bob,

m = the mass ejected; powder plus wadding,

l = the length of the pendulum,

𝛉 = the [[strikethrough]] nozzle [[/strikethrough]] ^[[angle]] through which the pendulum swings,

g = the acceleration of gravity.

The cosine of 𝛉 was corrected for friction by observing the two first displacements ^[[ d[[subscript]] 1 [[/subscript]] ]] and ^[[ d[[subscript]] 2 [[/subscript]] ]] and obtaining therefrom

^[[d = d [[subscript]] 1 [[/subscript]] √ d [[subscript]] 1 [[/subscript]]/ d [[subscript]] 2 [[/subscript]]

It will be noticed that the highest velocity was obtained with "Infallible" powder, and was over 7,000 ft/sec. The corresponding efficiency was close to 50 per cent. In view of the fact that this velocity, corresponding to [[underlined]] c [[/underlined]] in the exponents of equations (6) and (7), is seven fold greater than for an ordinary rocket, it is easily seen that the employment of a chamber and nozzle such as has just been 

Transcription Notes:
Not sure how to indicate subscript numerals 1 and 2 towards the end, twice each, when both are in part of hand-written notes, so I just typed the numbers.