How fast the winged moments fly.”

In like manner may be formed a calendar of Flora: thus, if we consider the time of putting forth leaves, the honeysuckle protrudes them in the month of January; the gooseberry, currant and elder, in the end of February, or beginning of April; the oak and ash in the beginning, or towards the middle of May, &c.

Note 2, p. [32].--Gravity and centrifugal force.

It may, perhaps, be asked how this decrease of weight could have been ascertained; since, if the body under examination decreased in weight, the weight which was opposed to it in the opposite scale must also have diminished in the same proportion; for instance, that if the lump of lead lost two pounds, the body which served to balance it must also have lost the same weight, and therefore that the different force of gravity could not be detected by such means. It is undoubtedly true that the experiment in question could not have been performed with an ordinary pair of scales, but by using a spiral spring it was easy to compare the force of the lead’s gravity at the surface of the earth, and at four miles high, by the relative degree of compression which it sustained in those different situations. We may take this opportunity of observing, that as the force of gravity varies directly as the mass, or quantity of matter, a body weighing a pound on our earth would, if transferred to the sun, weigh 27-3/4 pounds; if to Jupiter, 3-1/10 pounds; if to Saturn, 1-1/9; but, if to the moon, more than three ounces.

With respect to the effect of the centrifugal force as alluded to in the text, it may be here observed, that it has been found by calculation that, at the equator, the diminution of gravity occasioned by the centrifugal force arising from the rotation of the earth, amounts to about the 289th part. But since this number is the square of 17, it follows, that, if our globe turned more than 17 times faster about her axis, or performed the diurnal revolution within the space of 84 minutes, the centrifugal force would predominate over the powers of gravitation, and all the fluid and loose matters would, near the equinoctial boundary, have been projected from the surface. On such a supposition the waters of the ocean must have been drained off, and an impassable zone of sterility interposed between the opposite hemispheres. By a similar calculation, combined with that decreasing force of gravity at great distances from the centre, it may be inferred, that the altitude of our atmosphere could never exceed 26,000 miles. Beyond this limit, the equatorial portion of air would have been shot into indefinite space. If it were possible to fire off a cannon ball with a velocity of five miles in a second, and the resistance of the air could be taken away, it would for ever wheel round the earth, instead of falling upon it; and supposing the velocity to reach the rate of seven miles in a second, the ball would fly off from the earth, and be never heard of more.

Note 3, p. [35].--Velocity of light.

It is scarcely possible so to strain the imagination as to conceive the velocity with which light travels. “What mere assertion will make any man believe,” asks Sir W. Herschel, “that in one second of time, in one beat of the pendulum of a clock, a ray of light travels over 192,000 miles, and would therefore perform the tour of the world in about the same time that it requires to wink with our eyelids, and in much less than a swift runner occupies in taking a single stride?” Were a cannon ball shot directly towards the sun, and it were to maintain its full speed, it would be twenty years in reaching it, and yet light travels through this space in seven or eight minutes.

Note 4, p. [36].--Velocity of falling bodies.

In order to perform this experiment with the highest degree of accuracy, a body of considerable specific gravity should be selected, such as lead or iron; for a common stone experiences a considerable retardation in falling, from the action of the air. Where the arrival of the body at the bottom of the cavern to be measured cannot be seen, we must make allowance in our calculation for the known velocity of sound; thus, suppose a body were ascertained to fall in five seconds. As a heavy body near the earth’s surface falls about 16-1/12 feet in one second of time, or for this purpose 16 feet will be sufficiently exact; and as sound travels at the rate of 1142 feet per second, multiply together 1142, 16, and 5, which will give 91360, and to four times this product, or 365440, add the square of 1142, which is 1304164, and the sum will be 1669604; then if from the square root of the last number = 1292 the number 1142 be subtracted, the remainder 150 divided by 32 will give 4.69 for the number of seconds which elapsed during the fall of the body; if this remainder be subtracted from 5, the number of seconds during which the body was falling and the sound returning, we shall have 0.31 for the time which the sound alone employed before it reached the ear; and this number multiplied by 1142, will give for product 354 feet equal the depth of the well. This rule, which, it must be allowed, is rather complex, is founded on the property of falling bodies, which are accelerated in the ratio of the times, so that the spaces passed over increase in the square of the times.

The following is a more simple but less accurate rule. Multiply 1142 by 5, which gives 5710; then multiply also 16 by 5, which gives 80, to which add 1142, this gives 1222, by which sum divide the first product 5710, and the quotient 4.68 will be the time of descent, nearly the same as before. This taken from 5, leaves 0.32 for the time of the ascent; which, multiplied by 1142, gives 365 for the depth, differing but little from the former more exact number.