## Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous Important Articles, the Theory of Bridges, with Several Plans of Recent Improvement; Also the Results of Numerous Experiments on the Force of Gunpowder, with Applications to the Modern Practice of Artillery ... |

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2gfs altitude angle ascending avoirdupois axis ball ballistic pendulum Barometer body bore centre of gravity charge of powder chords computed correct fluent corresponding curve cylinder degree denote density descending determine diam Diffs discharged Dist distance Ditto elevation eprouvette equal experiments feet feet feet per second feet velocity fired flight fluxion force formula give greatest velocity gun n gun pend struck hemisphere hence horizontal inches feet inches oz increase lb inches length less linches locity long gun medium motion nearly numbers ounces of powder oz dr sec oz lb oz of powder oz oz dr parabola pendulum penetration plane prob PROBLEM proportion quantity radius range ratio recoil resistance round Scholium shot side space specific gravity square surface terminal velocity theorem theref Thermometer tion Values of Veloc vibration wads weight whole windage

### Popular passages

Page 165 - GH revolve in the same time, as when p was fixed to it ; this smaller weight being taken from M, the remainder is obviously equal in effort to the resistance of the revolving body p; and this remainder being reduced in the ratio of the length of the arm to the semi-diameter of the barrel, will then become equal to the absolute quantity of the resistance. And as the time of one revolution is, known, and consequently the velocity of the revolving body ; there is thereby discovered, the absolute quantity...

Page 79 - ... the increase in length ; the velocities being in a ratio somewhat less than that of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the two.

Page 215 - ... by further increasing the charge, the velocity gradually diminishes, till the bore is quite full of powder. That this charge for th,e greatest velocity is greater as the gun is longer, but yet not greater in so high a proportion as the length of the gun is ; so that the...

Page 380 - Accordingly, the next morning, with a joyful countenance, he brought me the construction neatly drawn out on a large sheet of pasteboard, saying he esteemed it a treasure, having found it quite right, as every point and line agreed to a hair'sbreadth by measurement on the scale.

Page 215 - It appears, from the table of ranges, that the range increases in a much lower ratio than the velocity, the gun and elevation being the same. And when this is compared with the proportion of the velocity and length of gun in the last paragraph, it is evident that we gain extremely little in the range by a great increase in the length of the gun, with the same charge of powder. In fact the range is nearly as the 5th root of the length of the bore ; which is so small an increase, as to amount only...

Page 80 - It has been found, by these experiments, that no difference is caused in the velocity, or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ramming, nor by firing the charge of powder in different parts of it.

Page 328 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.

Page 216 - ... nearly as the logarithms of the charges, instead of being as the charges themselves, or, which is the same thing, as the square of the velocity.

Page 78 - That this charge for the greatest velocity is greater as the gun is longer, but yet not greater in so high a proportion as the length of the gun is ; so that the part of the bore filled with powder, bears a less proportion to the whole...

Page 216 - ... degrees of ramming, nor by firing the charge of powder in different parts of it. But that a very great difference in the velocity arises from a small degree in the windage : indeed with the usual established windage only, viz, about ^ of the calibre, no less than between -j- and £ of the powder escapes and is lost : and as the balls are often smaller than the regulated size, it frequently happens that half the powder is lost by unnecessary windage.