is a spheroid flatted towards the poles." See page 163 of the work. For the longer a degree is, the greater must be the circle of which it is a part; and the greater the circle is, the less is its curvature. The first person who measured the length of a degree with any appearance of accuracy, was Mr. Richard Norwood; by measuring the distance between London and York, he found the length of a degree to be 367196 English feet, or 691 English miles; hence, supposing the earth to be a sphere, its circumference will be 25020 miles, and its diameter 7964* miles; but if the length of a degree, at a medium, be 57069 toises, the circumference of the earth will be 24873 English miles, its diameter 7917 miles, and the length of a degree 69 miles.† CONCLUSION. Notwithstanding all the admeasurements that have hitherto been made, it has never been demonstrated, in a satisfactory manner, that the earth is strictly a spheroid; indeed, from observations made in different parts of the earth, it appears that its figure is by no means that of a regular spheroid, nor that of any other known regular mathematical figure; and the only certain conclusion, that can be drawn from the works of the several gentlemen employed to measure the earth, is, that the earth is something more flat at the poles than at the equator.-The course of a ship, considering the * 5280 feet make a mile, therefore, 367196 divided by 5280 give 69 miles nearly, which multiplied by 360 produces 25020 miles, the circumference of the earth, but the circumference of a circle is to its diameter as 22 to 7, or more nearly as 355 to 113; hence, 355 113 :: 25020 miles: 7964 miles, the diameter of the earth. Again, 6 French feet make 1 toise, therefore, 57069 toises are equal to 342414 French feet; but 107 French feet are equal to 114 English feet; hence, 107 F. f. 114 E. f. 3424 F. f.: 364814 English feet, which, divided by 5280, the feet in a mile, gives 69.09 miles, the length of a degree by the French admeasurement. Or, 342414, multiplied by 360, produces 123269040 French feet the circumference of the earth, and 107: 114 :: 123269040: 131353369 English feet, equal to 24873.74 miles, the circumference of the earth, and 355 : 113 :: 24873.74 : 7917 miles, the diameter of the earth. - 69.12 The length of a degree in lat. 51° 9′ N. is 364950 feet English miles. Trigonometrical Survey of England and Wales, vol. II. part II. page 113. Mr Swanberg, a Swedish mathematician, found the length of a degree to be 57196.159 toises 365627.782 En: glish feet = 69.247 miles. earth a spheroid, is so near to what it would be on a sphere, that the mariner may safely trust to the rules. of globular sailing, even though his course and distance were much more certain than it is possible for them to be. For which, and similar reasons, mathematicians content themselves with considering the earth as a sphere in all practical sciences, and hence the artifi cial globes are made perfectly spherical, as the best representation of the figure of the earth. CHAP. IV. Of the Diurnal and Annual Motion of the Earth, THE motion of the earth was denied in the early ages of the world, yet as soon as astronomical knowl edge began to be more attended to, its motion received the assent of the learned, and of such as dared to think differently from the multitude, or were not apprehensive of ecclesiastical censure. The astronomers of the last and present age have produced such a variety of strong and forcible arguments in favour of the motion of the earth, as must effectually gain the assent of every impartial inquirer.-Among the many reasons for the motion of the earth, it will be sufficient to point out the following: 1. Of the Diurnal Motion of the Earth. The earth is a globe of 7964 miles in diameter (as has been shown in Chap. III.) and by revolving on its axis every 24 hours from west to east, it causes an apparent diurnal motion of all the heavenly bodies from east to west.—We need only look at the sun, or stars, to be * Robertson's Navigation. Book VIII Art. 145. That is, the time from the sun's being on the meridian of any place, to the time of its returning to the same meridian the next day; but the earth forms a complete revolution on its axis in 23 hours 56 minutes 4 seconds; see definition 61, page 13. convinced, that either the earth, which is no more than a point* when compared with the heavens, revolves on its axis in a certain time, or else the sun, stars, &c. revolve round the earth in nearly the same time. Let us suppose, for instance, that the sun revolves round the earth in 24 hours, and that the earth has no diurnal motion. Now, it is a known principle in the laws of motion, that if any body revolve round another as its centre, it is necessary that the central body be always in the plane in which the revolving body moves, whatever curve it describes ;† therefore, if the sun move round the earth in a day, its diurnal path must always describe a circle which will divide the earth into two equal hemispheres. But this never happens except on two days in the year, viz. at the time of the equinoxes, when the sun rises exactly in the east, and sets exactly in the west; for, in our summer, the sun rises to the north of the east, and sets to the north of the west; and, therefore, its diurnal path divides the globe into two unequal parts; consequently, the sun does not move round the earth. To render this more intelligible to a young student, let a pin, of some inches in length, be fixed perpendicular upon an horizontal plane, and observe the shadow that the top of it describes on any day of the year; this shadow will always be a curve, except at the time of the equinoxes; hence, the earth is never in the sun's apparent diurnal orbit but then; for if the top of the pin kept all the time in the plane of the sun's apparent diurnal orbit, the shadow described would be a straight line, because it would fall in the in. tersection of two planes; therefore, the sun has no diurnal motion round the earth; consequently, the earth has a diurnal motion on its axis. It is no argument against the earth's diurnal motion that we do not feel it; a person in the cabin of a ship, on smooth water, cannot perceive the ship's motion when it turns gently and uniformly round; neither does the * Dr. Keill, Lect. 26. + Emerson's Astronomy, page 11. Emerson's Dialling, Prop II. p. 9th. It is demonstrated in Euclid, Prop. III. Book XI that if two planes intersect each other, their common section is a straight line. Ferguson's Astronomy, Art. 119. motion of the earth cause bodies to fall from its surface; for all bodies, of whatever matter they are composed, are drawn to the earth by the power of its central attraction ;* which, laying hold of them according to their densities, or quantities of matter, without regard to their magnitudes, constitutes what we call weight. The phenomena of the apparent diurnal motion of the sun may be explained by the motion of the earth; thus, let IFGH (plate I. figure v.) represent the earth, S the sun, and the circle DSBC the apparent concavity of the heavens. Let the earth revolve on its axis from I towards G (viz. from west to east.) Suppose a spectator to be at I, the sun, which is at an immense distance, and enlightens half the globe at once, will appear to be rising. As the earth moves round, the spectator is carried towards F, and the sun seems to increase in height : when he has arrived at F, the sun is at the highest. As the earth continues to turn round, the spectator is carried from F towards G, and the altitude of the sun keeps continually diminishing; when he has arrived at G, the sun is setting. During the time the spectator has been carried from I to G, the sun has appeared to move the contrary way. Hence, it is evident, that while the spectator is carried through the illuminated half of the earth, it is day-light; at the middle point F, it is noon; also, while he is carried through the dark hemisphere, it is night; and at H it is midnight. Thus, the vicissitude of day and night evidently appears by the rotation of the earth about its axis: what has been said of the sun is equally applicable to the moon, or any star placed at S; therefore, all the celestial bodies seem to rise and set by turns, according to their various situations. The spectator at I, F, G. H, will always have his feet towards the centre of the earth, and the sky above his head, whatever position the earth may have: agreeably to the laws of gravitation or attraction. Thus an inhabitant at a will be the most powerfully attracted towards his antipodes b, because there is the greatest mass of earth under his feet in that direction; for the same reason b will be the most attracted towards a, m towards n, * Newton's Principia, Book III. Prop. vii. and n towards m, &c. hence, it appears that every body on the surface of the earth is attracted towards its centre, or rather, towards the antipodes of that body, for the whole earth is the attracting mass, and not some unknown substance placed in the centre of the earth. There is no such thing as an upper and under side of the earth suppose a to be an inhabitant of Nankin in China, b will be an inhabitant of South America, near Buenos Ayres, each having the earth under his feet and the sky above his head; also, if n be an inhabitant a little east of Quito in South America, on the equator, m will be an inhabitant upon the equator in the Island of Sumatra, and in the course of 12 hours n will have the same position as m, by the revolution of the earth. 2. Of the Annual Motion of the Earth. The diurnal revolution of the earth on its axis being proved, the annual motion round the sun will be readily admitted; for, either the earth moves round the sun in a year, or else the sun moves round the earth: now, by the laws of centripetal force, if two bodies revolve a bout each other, they revolve round their common centre of gravity ;* and it is evident that if the two bodies be of equal magnitude and density, the centre of gravity will be equidistant from each body; but, if they be of different magnitudes, the centre of gravity will be nearest to the larger body; if the earth, therefore, remain in the same situation while the sun revolves round it, its magnitude must be vastly greater than that of the sun; for it is contrary to the laws of nature for a heavy body to revolve round a light one as its centre of motion: but from observations on the dimensions† and distances of the sun and planets, it appears that the sun so * The centre of gravity of two bodies is a point, on which, if they were both supported by a line joining their centres, they would rest in equilibrium. + The apparent diameters of the planets are found by a micrometer, placed in the focus of a telescope, or, the apparent diameter of the sun may be measured by means of the projection of his image into a dark room, through a circular aperture. From these apparent diameters, and the respective distances from the earth, the real diameters of the sun and planets may be determined. |