# A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well as Private Tuition, Volume 2

Samuel Campbell, Evert Duyckinck, T. & J. Swords, Peter A. Mesier, R. M'Dermut, Thomas A. Ronalds, John Tiebout, and George Long, 1818 - Mathematics

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### Contents

 Practical Gunnery 141 The Mechanical Powers 154 cae 157 Centre of Gravity 169 Strength and stress of beams c 176 Centre of Percussion 193 Centre of Gyration 199 Of Hydraulics 212 Of the Syphon 227 Thermometer 233 Practical Exercises concerning Specific Gravity 239 of the Piling of Balls and Shells 247
 To find Logarithms 364 of Involute and Evolute Curves 370 Practical Questions 376 Practical 384 On the JMotion of Bodies in Fluids 402 luids 410 On the JMotion of JMachines and their JMazimum effects 416 nd their JMazimum effects 432 Theory and Practice of Gunnery 444 rercises in Mechanics Statics Dynam 480 Additions 555

### Popular passages

Page 11 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 200 - Then say, As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
Page 397 - Or, by art. 31* of the same, the pressure is equal to the weight of a column of the fluid, whose base is equal to the surface pressed, and its altitude equal to the depth of the centre of gravity below...
Page 167 - Hence the magnitude of the whole body, is to the magnitude of the part immersed, as the specific gravity of the fluid, is to that of the body.
Page 411 - From the same table it also appears, that the time of the ball's flight is nearly as the range ; the gun and elevation being the same.
Page 411 - ... increasing the charge, the velocity gradually diminishes, till the bore is quite full of powder. 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 bore in the long guns, than it does in the shorter ones ; the part which is filled being indeed nearly in the inverse ratio of the square root of the empty part.
Page 169 - As the weight lost in water is to the whole, or absolute weight ; so is the specific gravity of water ' " to "the specific gravity 'of the body . 2.
Page 407 - Finally, as these experiments prove the regulations with respect to the weight of powder and shot, when discharged from the same piece of ordnance ; so, by making similar experiments with a gun varied in its length by cutting off from it a certain part, before each set of trials, the effects and general rules for the different lengths of guns, may be with certainty determined by them.
Page 101 - ... powder, and that but a small one too ; so that all those nearly agree with the parabolic theory. Other experiments have also been carried on with the ballistic pendulum, at different times ; from which have been obtained some of the, laws for the quantity of powder, the weight and velocity of the ball, the length of the gun, &c. Namely, that the velocity of the ball varies as the square root of the charge directly, and as the square root of the weight of ball reciprocally ; and 'that, some rounds...