VOL. LXXI.] PHILOSOPHICAL TEANSACTIONS. 95 



and melted lead being poured into this mould, the cavity that surrounded the 

 small plaister bullet was entirely filled up, and a bullet was produced, which to 

 the eye had every appearance of solidity, but was as much lighter than a solid 

 leaden bullet of the same diameter, as the plaister bullet was lighter than a leaden 

 bullet of the same size. In the experiments N° 88 and N° 89, solid leaden 

 bullets were used. In the experiment N° 90, 2 bullets were discharged at once; 

 in the experiment N° 91, 3; and in the experiment N° 92, 4 were used. In 

 each of these experiments a fresh sheet of paper was used as a screen to the pen- 

 dulum, that the velocities of the bullets might be measured more accurately; 

 and also, that the quantity of unfired powder might be estimated with greater 

 precision. 



In the experiments N° 93 to 99 the piece was fired with powder only. 



In the experiments N° IOO and N° 101, the bullets were not put down into 

 the bore, but were supported by 3 wires, which being fastened to the end of the 

 barrel projected beyond it, and confined the bullet in such a situation that its 

 centre was in a line with the axis of the bore, and its hinder part was -fa of an 

 inch without or beyond the mouth of the piece. In experiment N° 102, the 

 bullet was just stuck, into the barrel in such a manner that near 4- of it was with- 

 out the bore. All that part of the bullet which lay towards the bore of the piece 

 appeared to be quite flat from the loss of substance it had sustained ; and its sur- 

 face was full of small indents, which probably were occasioned by the unfired 

 grains of powder that struck, against it. 



The experiments N° 103 to 123 were made with the pendulum N° 4. The 

 rest of the apparatus as before. 



Of the method used in computing the velocities of the bullets. — As the method 

 of computing the velocity of a bullet from the arc of the vibration of a pendu- 

 lum into which it is fired is so well known, Mr. T. does not enlarge on it, but 

 just gives the theorems that have been proposed by different authors, and refers 

 those who wish to see more on the subject to Mr. Robins's New Principles of 

 Gunnery; to Mr. Euler's Observations on Mr. Robins's book; and lastly to Dr. 

 Hutton's paper on the initial Velocities of Cannon Balls, published in the Philos. 

 Trans, for the year 1778. 



If a denote the length of the axis of the pendulum to the ribbon which mea- 

 sures the chord of the arc of its vibration ; 



g, the distance of the centre of gravity below the axis; 



/, the distance of the centre of oscillation ; 



h, the distance of the point struck by the bullet; 



c, the chord of the ascending arc of the pendulum ; 

 p, the weight of the pendulum ; 

 b, the weight of the bullet, and 



