REMARKS.

1st. The most material consequence to be derived from the above table is the great diminution of the effective force of the wind, as the velocity of the sail increases; which shews, that the sail-cloth should be placed as near the centre as possible, only observing that the wind must have a free escapement; for a square foot of sail, moving with half the velocity of the wind, appears to have three times the effective power as when moving with double the wind's velocity; for the power of the lever when time is considered must be out of the calculation; this also agrees with Mr. Smeaton's experiments, who found, that by enlarging the breadth of his sails, he gained more than by increasing the radius. Probably the extremity of the sail should not exceed the velocity of the wind; and as this will increase the angle of weather, the wind will have a more free escapement, and its reflections be less liable to impede the following sail: the angle of reflection is easily seen from the relative angle of incidence, DSR.

2dly. That Mr. Hall Gower's hypothesis is highly disadvantageous; for by approximating to 90° at the centre it has the least power, where it should have the most.

3dly. It appears evident from theory, and all Mr. Smeaton's experiments, that the greater the angle of weather the slower will be the motion; therefore if by any simple contrivance the angles of weather could be occasionally altered, it would be the best mode of making the revolutions more uniform, and even of stopping them altogether: I am now making an experiment at large on this method.

4thly. Although the forces appear greatest in the first column, from taking RF3×RG÷SN3 as the measure, yet if the measure had been taken

RF2XRG

SN XSR

according to Maclaurin,

then the second column had shewn the greatest forces, and the third column, if Bb was the true measure-but on no hypothesis could Gower have any competition.

N. B. RF1× RG is a maximum when WCxcC is a maximum, and RF RG is a maximum, when cWXcC is a maxium— the first when Wc is of Wv, the last when Wc is of Wv; the greatest right-angled triangle in the segment VBW.

G g

No. LVIII.

Extract from a paper on the Meteoric Stones, written by F. R. Hassler Esq. Mathematical Professor in the Military School at West Point.

Read June 17th, 1808.

THE first thing to be considered on the supposition that these bodies are projected from the moon, is, whether the power exerted by any lunar volcano can be sufficient to throw a heavy body beyond the sphere of its predominant attraction, and of course enter that of the earth. This may be made a subject of calculation on the following principles.

Heavenly bodies exercise an attractive power in the direct ratio of their masses, and inverse ratio of the squares of their distances. Let A, M, and D, represent the attraction, mass, and distance of the earth; a, m, d, those of the moon; then the M m

whole force exerted by the two bodies will be A : a ::——.

D2 d2

A body placed in circumstances most favourable to the hypothesis would of course be between the two bodies, and in a right line with the centers of both; and in order to be merely suspended in equilibrio between them, the two first terms of this proportion must be equal to each other, and the two last

must also be equal, that is,

M m

D2 d2

Now, taking M to be, in round numbers, equal to 70m, and D+d equal to the distance of the moon from the earth=D, the

found=

-; but D=60× the radius of the earth, which is,

1+√70

in round numbers, equal to the mean distance of the moon;

earth; and multiplying by 3.67, the ratio of the radius of the earth to that of the moon, d=23.5×radius of the moon, which diminished by one radius of the moon, leaves 22 times the radius of the moon, or 24310.4 miles for the distance to which a heavy body must be thrown by some internal power of the moon, in order to remain suspended between the moon and earth.

According to the ratio of the quantity of matter in the moon and earth, and the observed rate of falling of a heavy body at the surface of the earth in the first second of time, the rate of falling at the surface of the moon is equal to 3.018 feet. Now, let g=this rate=3.018, s=the distance to which the body must be thrown=24310.4 miles; V-the initial velocity, or the velocity which the body must have at leaving the surface of the moon, then V=2Vgs=39364.3 feet, or about 7 miles per second, or more than ten times the velocity of the moon in its orbit. Can we believe that there exists in the moon any internal power, capable of producing this effect? When we consider how small the attraction of gravitation is at the moon, would not the existence of such a projectile force prove in the lapse of ages, destructive to that body? And when centuries, and even thousands of years have passed away without any diminution of its magnitude, are we not irresistibly led to deny that there is in the moon any power of projecting a part of itself beyond the sphere of its own attraction?

No. LIX.

Extract of a letter from a member of the Society, relative to the great cold in January, 1807, at the town of Hallowell, in the district of Maine, Massachusetts, Head of tide-water on Kennebeck River. Communicated by John Vaughan.

Hallowell, January 29, 1807,

THE cold here on the night of the 22d-23d, brought the

1

thermometer, for a short time, to 33° (Fahrenheit) below the zero; and again, on the 26th-27th, for a much longer time. But the sky, on the last occasion, became cloudy at 3 A. M. and stopped short our career, or I should have frozen quicksilver by a natural process, for the first time in the United States, and for the first time any where in so low a latitude as 44° 16′ by the side of tide waters; that is, at the level of the sea. Quicksilver, by Mr. Hutchins' experiments at Hudson's Bay, as explained by Mr. Cavendish, and confirmed by various others, freezes at-383°; and I had the thermometer at-36° or—37° on the surface of the snow; consequently, had darkness continued without clouds, by day break I should have had my requisite temperature at the surface of the snow, though I did not expect more than-36° in the air. I had prepared diminutive cups of fine writing paper, of a size to hold each a globule of quicksilver; and tools were ready cooled to strike, in order to obtain a proof of malleability.—In all this cold weather our female invalids were riding about the country, and our stages and town patroles (of which in my turn I am one) by night. On the two coldest nights, I sat up with my son, and wore neither hat, nor gloves, nor great coat, nor boots. I observed with three thermometers made by Blunt, the king's instrument-maker in London, a fourth by Jones, and a fifth by an Englishman (who supplies some Italians at Boston) and which proved my third best instrument. At mid-day on the 26th we had a violent wind, with the thermometer 7° below the zero; against which our ladies rode, without inconvenience, in a sleigh; other thermometers in the neighbourhood, including one by Adams, corroborated the above. This winter, till lately, has not differed from any common cold winter in Europe.