A Course of Mathematics: For the Use of Academies, as Well as Private Tuition, Volume 2

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S. Cambell, 1818 - 558 pages
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Page 13 - 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 196 - 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 385 - 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 169 - 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 399 - 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 399 - ... 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 171 - 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 395 - 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 103 - ... 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...

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