DESCENSION

, in Astronomy, is either right, or oblique.

Right Descension is a point, or arch, of the equator, which descends with a star, or sign, below the horizon, in a right sphere, and

Oblique Descension is a point, or arch, of the equator, which descends at the same time with a star, or sign, below the horizon, in an oblique sphere.

Descensions, both right and oblique, are counted from the first point of Aries, or the vernal intersection, according to the order of the signs, i. e. from west to east. And, as they are unequal, when it happens that they answer to equal arcs of the ecliptic, as for example to the 12 signs of the zodiac, it follows, that sometimes a greater part of the equator rises or descends with a sign, in which case the sign is said to ascend or descend rightly: and sometimes again, a less part of the equator rises or sets with the same sign, in which case it is said to ascend or descend obliquely. See ASCENSION.

Refraction of the Descension. See Refraction.

Descensional Difference, is the difference between the right and oblique descension of the same star, or point of the heavens.

, or Fall, in mechanics, &c, is the motion, or tendency, of a body towards the centre of the earth, either directly or obliquely.

The descent of bodies may be considered either as freely, like as in a vacuum, or as clogged or resisted by some external force, as an opposing body, or a fluid medium, &c.

1st, If the body b descend freely, and perpendicularly, by the force of gravity; then the motive force urging it downwards, is equal to its whole weight b; and the quantity of matter being b also, the accelerative force will be b/b or 1.

2dly, If the body b descending, be opposed by some mechanical power, suppose a wedge or inclined plane, that is, instead of pursuing the perpendicular line of gravity, it is made to descend in a sloping direction down the inclined plane: then if the sine of the angle the plane makes with the horizon be s, to the radius 1, the motive force urging the body down the plane will be bs; and therefore the accelerative force is bs/b or s; which is less than in the former case in the proportion of s to 1.

3dly, In a medium, a body suspended loses as much of its weight, as is the weight of a like bulk of the medium; and when descending, it loses the same, beside the obstruction arifing from the cohesion of the parts of the medium, and the opposing force of the particles struck, which last produces a greater or less resistance, according to the velocity of the motion. But, the weight of the body being b, and that of a like bulk of the fluid medium m, the motive force urging the body to descend, is only b-m; that is, the body only falls by the excess of its weight above that of an equal bulk of the medium.

Hence, the power that sustains a body in a medium, | is equal to the excess of the absolute weight of the body above an equal bulk of the medium. Thus, a piece of copper weighing (47 1/3)lb, loses (5 1/3)lb of its weight in water: and therefore a power of 42lb will sustain it in the water.

4thly, If two bodies have the same specisic gravity, the less the bulk of the descending body is, the more of its gravity does it lose, and the slower does it descend, in the same medium. For, though the proportion of the specisic gravity of the body to that of the fluid be still the same, whether the bulk be greater or less, yet the smaller the body, the more the surface is, in proportion to the mass; and the more the surface, the more the resistance of the parts of the fluid, in proportion.

5thly, If the specific gravities of two bodies be different; that which has the greatest specific gravity will descend with greater velocity in the air, or resisting medium, than the other body. Thus, a ball of lead descends swifter than wood or cork, because it loses less of its weight, though in a vacuum they both fall equally swift.

The cause of this descent, or tendency downwards, has been greatly controverted. Two opposite hypotheses have been advanced; the one, that it proceeds from an internal principle, and the other from an external one: the first is maintained by the Peripatetics, Epicureans, and the Newtonians; and the latter by the Cartesians and Gassendists. See also Acceleration.

1st, Heavy bodies, in an unresisting medium, fall with an uniformly accelerated motion. For, it is the nature of all constant and uniform forces, such as that of gravity at the same distance from the centre of the earth, to generate or produce equal additions of velocity in equal times. So that, if in one second of time there be produced 1 degree of velocity, in 2 seconds there will be 2 degrees of velocity, in 3 seconds 3 degrees, and so on, the degree or quantity of velocity being always proportional to the length of the time.

2nd, The space descended by an uniform gravity, in any time, is just the half of the space that might be uniformly described in the same time by the last velocity acquired at the end of that time, if uniformly continued. For, as the velocity increases uniformly in an arithmetic progression, the whole space descended by the variable velocity, will be equal to the space that would be described with the middle velocity uniformly continued for the same time; and this again will be only half the space that would be described with the last velocity, also uniformly continued for the same time, because the last velocity is double of the middle velocity, being produced in a double time.

3d, The spaces descended by an uniform gravity, in different times, are proportional to the squares of the times, or to the squares of the velocities. For the whole space descended in any number of particles of time, consists of the sums of all the particular spaces, or velocities, which are in arithmetical progression; but the sum of such an arithmetical progression, beginning at 0, and having the last term and the number of terms the same quantity, is equal to half the square of the last term, or of the number of terms; therefore the whole sums are as the squares of the times, or of the velocities.

This theory of the descents by gravity was first discovered and taught by Galileo, who afterwards confirmed the same by experiments; which have often been repeated in various ways by many other persons since his time, as Grimaldi, Riccioli, Huygens, Newton, and many others, all consirming the same laws.

The experiments of Grimaldi and Riccioli were made by dropping a number of balls, of half a pound weight, from the tops of several towers, and measuring the times of falling by a pendulum. Ricciol. Almag. Nov. tom. 1 lib. 2, cap. 21, prop. 4. An abstract of their experiments is exhibited here below:

The space descended by a heavy body in any given time, being determined by experiment, is sufficient, in connection with the preceding theorems, for determining every inquiry concerning the times, velocities, and spaces descended, depending on an uniform force of gravity. From many accurate experiments made in England, it has been found that a heavy body descends freely through 16 feet 1 inch, or 16 1/12 feet, in the first second of time; and consequently, by theorem 2, the velocity gained at the end of 1 second, is 32 1/6 feet per second. Hence, by the same, and theorem 3, the velocity gained in any other time t is (32 1/6)t, and the space descended is (16 1/12)t². So that, if v denote the velocity, and s the space due to the time t, and there be put g = 16 1/12; then is .

The experiments with pendulums give also the same space for the descent of a heavy body in a second of time. Thus, in the latitude of London, it is found by experiment, that the length of a pendulum vibrating seconds is just 39 1/8 inches; and it being known that the circumference of a circle is to its diameter, as the time of one vibration of any pendulum, is to the time in which a heavy body will fall through half the length of the pendulum; therefore as 3.1416 : 1 :: 1 : 1/3.1416 which is the time of descending through 19 9/16 inches, or | half the length of the pendulum; then, spaces being as the squares of the times, as 1/(3.1416²) : 1² :: 19 9/16 : 193 inches, or 16 feet 1 inch, which therefore is the space a heavy body will descend through in one second; the very same as before.

4th, For any other constant force, instead of the perpendicular free descent by gravity, find by experiment, or otherwise, the space descended in one second by that force, and substitute that instead of 16 1/12 for the value of g in these formulæ: or, if the proportion of the force to the force of gravity be known, let the value of g be altered in the same proportion, and the same formulæ will still hold good. So, if the descent be on an inclined plane, making, for instance, an angle of 30° with the horizon; then, the force of descent upon the plane being always as the sine of the angle it makes with the horizon, in the present case it will be as the sine of 30°, that is, as 1/2 the radius; therefore in this case the value of g will be but half the former, 8 1/24, in all the foregoing formulæ.

Or, if one body descending perpendicularly draw another after it, by means of a cord sliding over a pulley; then it will be, as the sum of the two bodies is to the descending body, so is 16 1/12 to the value of g in this case; which value of it being ufed in the said formulæ, they will still hold good. And in like manner for any other constant forces whatever.

5th, The time of the oblique descent down any chord of a circle, drawn either from the uppermost point or lowermost point of the circle, is equal to the perpendicular descent through the diameter of the circle.

6th. The descent, or vibration, through all arcs of the same cycloid are equal, whether great or small.

7th. But the descent, or vibration, through unequal arcs of a circle, are unequal; the times being greater in the greater arcs, and less in the less.

8th, For Descents by Forces that are variable, see Forces, &c. See also Inclined Plane, Cycloid, Pendulum, &c.

Line of Swiftest Descent, is that which a body, falling by the action of gravity, describes in the shortest time possible, from one given point to another. And this line, it is proved by philosophers, is the arc of a cycloid, when the one point is not perpendicularly over the other. See Cycloid.