ASTRONOMICAL LECTURES.
BY PROF. ORSON PRATT.
LECTURE SECOND.
In our last lecture, it was demonstrated that the earth is of a globular form, and of a determinate magnitude; that it exists without any external supports or foundations, surrounded on all sides by space; and that bodies can exist on all sides of its surface without any danger of falling away from it. We now proceed to investigate the grand and important question, whether the earth be at rest or in motion.
It is evident that we can never make any considerable advance in astronomy until this question is determined. We perceive nothing in the constitution of the earth which disqualifies it for motion. Its shape and magnitude can be no obstacle; the qualities and proportions of its various elements and compounds do not render it immovable; the atmosphere by which it is enveloped, and the internal forces within, do not effect its mobility in the least. If the spaces surrounding the earth on all sides be empty and void of substance, there can be no external resistance offered to its motions. Under such circumstances the earth must be free to yield to the slightest presure or impulse from without; and the result of such pressure or impulse would necessarily be motion, however feeble and imperceptible to us.
It is impossible for us to judge whether the earth be at rest or in motion by our feelings. When a ship is becalmed on a smooth sea, it will frequently swing round so as to head in different directions; no one would be sensible of this rotation without reference to some external object; no one has felt any rotary motion. If the ship were wafted along by unknown currents at the rate of 5 miles per hour, no one would perceive the motion, but might fancy themselves at rest, until by an observation on the heavenly bodies, they detected such motion. A person in a balloon, if wafted by a heavy, yet steady gale, at the rate of 60 miles an hour, would feel no motion of the wind, and might suppose himself at perfect rest in a calm, until by a reference to the surface of the earth, he perceives his great velocity. The earth, with all it contains, might fly in empty space with any conceivable velocity, however great, and no one upon the earth would know whether he were at rest or in motion, unless by a reference to external objects. The earth might have a rotary movement upon an axis unperceived by us, and which could only be detected by the most careful observations and experiments.
As a man passing down a river, carried by a swift smooth current, would be obliged to refer to the shore to determine whether he were in motion, so a man who would satisfy himself whether the earth be in motion, must refer to objects in the heavens, unconnected with the earth; if the heavenly bodies constantly shift their position in regard to the earth, he is forced to conclude that either the heavenly bodies themselves are in real motion, or else, if they are stationary, that the earth must be in motion; or if both be in motion, that the phenomenon is the result of their relative motions; hence, it is not easy to conclude from such observations alone, whether it be the earth or the heavens that are really in motion.
By referring to the starry heavens above us, we see them all apparently in motion from east to west. Let any one who wishes to view this magnificent scenery and become acquainted with the apparent motions of the stars, station himself on some clear evening in a convenient position facing the south; let him fix his attention upon those stars which are near the southern horizon, and he will perceive that they will not remain long above the horizon; they arise just east of the point where the meridian cuts the southern horizon, ascend gradually to the meridian where they attain their greatest altitude, and then gradually descend, and finally set at a small angular distance west of the meridian. During the short time of their visibility, they appear to describe only the small upper segment of their diurnal circle.
Let him next turn his attention to that quarter of the horizon between the south and east, and he will behold a succession of stars and clusters of stars, rising one after another, as if they came out of the earth at different points along the horizon; the farther their rising point is from the south, the larger will be the segments of their circles which they will describe above the horizon, and the greater will be the length of time that they will remain in sight. Each star will attain its greatest altitude on the meridian, and will set precisely as many degrees to the westward of south as they rose to the eastward. Those stars that rise exactly in the east, will set exactly in the west, and will describe a semicircle nearly in 12 hours.
Next, let him carefully observe those stars which rise between the east and north-east points of the horizon, and he will find that they remain above the horizon more than 12 hours; that the various segments which they describe are greater than semicircles, and that they descend behind the western horizon as far to the north of west as they rose north of east. Those stars which come to the meridian directly over our heads, and whose zenith distance does not exceed nine degrees north, will remain above the horizon nearly 24 hours, and their visible diurnal arcs will be nearly the whole circumferences of circles; they will sink below the edge of the horizon a little to the west of north, behind which they will remain only for a few minutes and then they will rise again as far on the east of north as they set on the west; while all the balance of the stars in the northern regions will appear to describe entire circles around one point in the heavens, called the Pole. This polar point is on our northern meridian, and is elevated above the north point of our horizon about 40 3-4 degrees, being the same as the latitude of our city. All the heavenly bodies within 40 3-4 degrees of this polar point, never rise or set to us. In describing their diurnal circles, they come to the meridian twice as equal distances from the Pole, at which time they are due north of us. They approach the upper meridian from the east and then gradually descend in semicircles and apparently approach the lower meridian from the west, at which point they begin again to ascend in the semi-diurnal arcs which lay east of the meridian, until they again attain their greatest altitude on the upper meridian. The polar point seems to be the only one in our northern sky but what is in apparent motion. This point is not marked by any star, but is purely an imaginary, immovable centre. A bright star, called the Pole Star, is situated about one and a half degrees from this centre, and describes a very small circle around it, in the same time and in the same manner as the rest. The diurnal circles of the stars seem to grow smaller in proportion to their distance either north or south of the equinoctial line. From these appearances we may reasonably expect that there is another pole of the heavens in the south, situated directly opposite the north pole, being as much depressed below the southern horizon as our pole is elevated above the northern.
Let any one who wishes to satisfy himself upon this subject by observation, travel to the south; and as he proceeds towards the equator, he will behold the stars which are just above the northern horizon begin to sink below it; and consequently when describing the lower segments of their circles, they will be invisible; while new stars, which perform their diurnal circles below the southern horizon, will be brought into view. When he has arrived at the equator, he will perceive all the stars of the firmament, both in the north and in the south, describing semicircles and remaining nearly 12 hours above the horizon. When he arrives at the same distance south of the equator that we are north, he will observe a point in the heavens, elevated 40 3-4 deg above the southern horizon, around which all the heavenly bodies in the southern regions, circulate from east to west, exhibiting all the phenomena manifested by our northern regions in this latitude. This point is called the South Pole of the heavens. If he turns his eyes to the north, he will find that our north pole, and all the circumpolar stars have sunk beneath the horizon, and will no more in that latitude, render themselves visible.
The stars that now pass over our heads, will rise and remain a few minutes above his northern horizon, and then set below it. All the heavenly bodies north of the equatorial circle will present the same phenomena to him, that those south of that circle do to us; and all the stars in the southern hemisphere will exhibit to him the same appearances that those in the northern hemisphere do to us.
All the heavenly bodies which we see set behind the western horizon, will pass under the earth and rise again in the east. If any one will have patience to watch the stars, during a long winter’s night, he will in the morning behold the same stars rising in the east which he saw, early in the evening, setting in the west; and thus the upper and lower hemispheres of the heavens will be gradually and successively brought to his view. The precise time in which every star performs its apparent diurnal revolution around the earth is 23 hours, 56 minutes and 4 seconds. This is called a sidereal day, and is 3 min and 56 sec. shorter than a mean solar day.
Our earth seems to be at rest, while the starry sphere appears to move around us from east to west; but if we suppose the stars to be at rest, and the earth to rotate upon an axis from west to east, all the phenomena above described will take place in the same order and in the same time. These phenomena, therefore, when considered alone, do not determine, whether it is our globe or the starry sphere that is in rotation. One or the other it must be.
The grand object which the Almighty had in view in producing these diurnal movements, was the alternate succession of day and night. This important end could be obtained by a simple rotation of the earth upon its axis, instead of causing the sun and innumerable other worlds to revolve around it. The planet Jupiter, though fourteen hundred times larger than the earth, moves round its own axis in a little less than ten hours. Saturn is nearly a thousand times larger than the earth, yet it turns on its own axis once in ten hours and a half. The inhabitants upon the surfaces of these planets will see the starry heavens apparently revolving around them in a different position and with more than twice the velocity that they appear to have round the surface of our earth. If not informed to the contrary, they might suppose that the motion of the sun and stars around their axes was real; whereas we know from observation that the succession of day and night upon those planets is produced by their own rotations. If, then, day and night upon other planets is caused by their own rotation, why may not our day and night be occasioned in the same manner? Is it reasonable to suppose that our globe is an exception to the general law of rotation which we know obtains in many of the other planets? If the magnitude of our globe be an objection to its rotation, then the magnitudes of Jupiter and Saturn, which are a thousand times larger, would be a far greater objection to their motions. If any one suppose that the earth must not move because of its magnitude, let him turn his attention to the sun, which is more than 1,300,000 times larger than the earth, and yet it turns round upon its own axis in about 26 of our days.
Moreover if the earth has no diurnal motion, that vast luminary must fly around us every 24 hours, performing a revolution of 500,000,000 of miles every day and all this merely to accommodate the inhabitants of our little globe with the blessings of day and night. No wisdom would be displayed in such an arrangement of things. When we stand before a fire and wish to warm different sides of ourselves, how shall we accomplish it? It can be done in two ways: by attaching a piece of machinery to the chimney and moving the fireplace, fire and all, around us, we may be equally and alternately warmed on different sides; but how much more simple would it be to merely turn round ourselves and let the chimney and fire-place remain stationary? The rotation of the earth, therefore, in order to experience the benefits of the heat and light of the sun on its different sides, is infinitely more simple, and displays infinitely more wisdom than to suppose revolution of the vast body around it.
Another presumptive argument against the apparent diurnal movements of the heavens being real, is that the sun, moon and stars have nearly the same period of revolution, though they are bodies of different magnitudes, and are placed at different distances. The sun is 400 times further from us than the moon. Saturn is about 9 times the sun’s distance from us. The planet Herschel [Uranus] is double the distance of Saturn. The planet Neptune is more than a thousand million of miles beyond Herschel. The nearest fixed stars are 10,000 times further off than Neptune. And many of the telescopic stars must be at least 1000 times more distant than those seen with the naked eye. The most of these bodies, and probably all, differ not only in their distances, but in their magnitudes. Now how is it possible for us to conceive all these bodies to revolve around our globe in the short period of 24 hours? Why should they all have about the same period when they differ so immensely in their distances? Why should the sun travel 400 times faster than the moon? Why should the planet Neptune travel 30 times faster than the sun? Or why should the nearest fixed star fly 10,000 times swifter than Neptune? Can we for a moment believe that there are bodies in the universe that fly 800,000,000,000 times swifter than light? All these inconceivable velocities must exist, if we admit the apparent diurnal motions of the stars to be real.- These arguments, if not demonstrative, carry with them an irresistible conviction that the diurnal motion must be referred to the earth and not to the heavens.
It is a principle of mechanics, founded on the laws of motion, that the more distant a body is from a central gravitating force around which it revolves, the less will be its velocity, and the greater will be its period of revolution. Under the present laws of gravitation, all bodies which do really revolve around the earth must have velocities which vary according to the inverse square roots of their distances; that is, bodies situated from us 4 times the distance of the moon, will have only one half the velocity that the moon has; because 1-2 is the inverse square root of 4; those which are 9 times further from us than the moon, will have only 1-3 of her velocity; 16 times the distance will give 1-4 the velocity; 100 times the distance will give an orbitual velocity of 1-10. The distance of the sun being 400 times greater than the moon would require only a velocity of 1-20 of that of the moon’s, in order to balance the centripetal force of the earth’s gravitation; consequently, if the sun and moon’s apparent diurnal motions be admitted as real, he would have a velocity 8000 times too great for the earth’s gravitation in order to get round the earth as soon as the moon. Hence the sun’s diurnal period, compared with that of the moon’s, would be 8000 times shorter than it should be according to the known mathematical principles of mechanics. But even the moon’s diurnal period, if performed in one day, is about 27 1-3 times too quick to balance the centripetal force of the earth’s gravitation, and therefore, the sun’s true period, compared with the moon’s true period, would be 27 1-3 times 8000, or more exactly 218,572 days, which reduced to years, would be 598 years and 302 days. The intensity of gravitation at the earth’s surface has been determined by experiment, and knowing the earth’s radius, it is a simple problem in mechanics to calculate the period which a body must have in order to revolve around the earth near its surface, without falling; this would be 1h 23m 22s. Now if gravity is a force which varies inversely as the square of the distance, (as it may easily be proved to be) then it may easily be calculated how far all bodies must be placed from the centre of the earth in order to have their periods equal to the diurnal period of the stars; this distance would be 26,680 miles: and none of the heavenly bodies must be placed any nearer or farther off than this; if so, their periods would be less or greater than one day; and as it is known that none of them are placed at that distance, we know that their apparent diurnal periods are not real. This, then, is a demonstration of the diurnal rotation of the earth to all persons who are capable of solving these mechanical problems.
Another demonstrative evidence that the earth has a diurnal motion, may be obtained from experiment. Let a ball be dropped from the top of a high tower or precipice; if the earth has no rotation it will fall perpendicularly to the surface of the earth; but if it has a rotation from west to east, it will fall a short distance to the east of the perpendicular line at the foot of the tower. This is occasioned by the unequal velocities of the bottom and top of the tower, resulting from the earth’s rotation: for instance, the bottom of a tower or perpendicular precipice one half of a mile high, situated on the equator, and being nearer the center of motion, would move slower than the top, which is half a mile further from that centre. The time of falling would be about 13 seconds, during which time the top of the tower or precipice would describe an arc about 2 1-2 inches longer than the arc described by the bottom, and the ball, partaking of this velocity when it first leaves the top, will fall about 2 1-2 inches east of the foot of the perpendicular line. The greater the height from which it falls, the greater will be its deviation from the perpendicular. Experiments of this nature have been performed with the greatest accuracy, and the results have proved beyond all controversy, that the earth really has a diurnal rotation from west to east.
The diurnal rotation of the earth may be proved to exist from a careful consideration of its true figure. When we loosely speak of its figure, we represent it to be a sphere—a globe, because it so nearly approximates such a figure; and it is only by the most careful observations and measurements that we find any deviation from a sphere. Indeed, before the days of Newton, the earth was generally supposed to be a perfect sphere. But that great philosopher demonstrated that a globe composed in part of fluid materials, could not have a rotation upon an axis without changing its figure, by having its polar diameter shortened and its equatorial diameter increased. His calculations showed that the earth, if it rotate, must be flattened in its polar regions in the shape of a turnip, or an orange.—Subsequent observations have verified his calculations and theory to be true; and the earth is no longer, in strictness, considered a globe, but an oblate ellipsoid or spheroid, having the diameter which coincides with the axis 1-300 shorter than the equatorial diameter.
It will be seen that the oblateness is so small that it does not differ much from a sphere. If we held in our hand a wooden model of our globe whose diameter at the equator was 15 inches, the polar diameter would lack only 1-20 of an inch of being the same length—a quantity so small that it could not possibly be detected by the eye, but would require very nice, delicate measurements to show its deviation from a globe.
For the purpose of determining the ellipticity of the earth, commissioners of various nations have been appointed by their respective governments, and furnished with the best of instruments to measure arcs of the meridian in different intitudes in various parts of the earth. By a comparison of all these measurements, it is found that the length of a degree increases with the latitude, being the least at the equator and greatest at the poles; therefore, the curvature of the earth’s surface must be greatest at the equator, and must decrease with the latitude, and be least at the poles. These meridianal sections which pass through the poles, cutting the equator at right angles, are ellipses; and the geometrical properties of an ellipse are such that we are enabled to assign the proportion between the lengths of its major and minor axes, corresponding to any proposed rate of variation in its curvature; and having determined the proportion of the two axes or diameters, we can still further determine their absolute lengths by knowing the length of a degree in any given latitude. Mr. Airy, by a combination of 13 different arcs, measured in different parts of the earth, has determined its ellipticity and given the diameters as follows:
Miles
Equatorial diameter . . . . 7915.648
Polar diameter. . . . 7809.170
Polar compression . . . . 26.478
Proportion of diameters as 299.33 to 298.33.
Mr. Bessel has more recently calculated the same from a combination often of the measured arcs, and his results do not differ from the diameters as given by Mr. Airy the 1-16 part of a mile.
From a comparison of the above diameters, it will be seen that the equatorial regions of our earth are about 13 miles higher or more distant from its center than the polar. This ascent from the two poles towards the equator is not sudden, but gradual, the elevation increasing at an average rate of about one mile in every 6 deg. 48 min. of difference of latitude, or 1 mile in 470 in traveling from the equator to the poles, there would be a rapid descent of 11 feet per mile. The gulf of Mexico, at the mouth of the Mississippi river, is 4840 feet higher than the Salt Lake City; and the Atlantic and Pacific oceans at the equator are elevated more than 3 miles above our city, and more than 3 3-4 miles above the highest peaks of the mountains which bound our valley on the east. The mouth of the Mississippi river is more than 1 mile higher than the city of St. Louis, which is situated upon its banks some seven hundred miles to the north. Its mouth is also several miles higher than the tops of the highest mountains from which it takes its rise. The equatorial ocean is 13 miles higher than the Arctic and Antarctic oceans. All these phenomena arising from the spheroidal form of the globe.
When we speak of different mountains and planes being elevated above the sea level, we have no reference to their relative elevations above the center of the earth, unless when compared with that portion of the sea which has the same latitude as the places themselves. When we say that our city is elevated 4300 feet above the sea level, we do not mean that it is so much higher above the centre of the earth than the equatorial or polar seas, but we mean that it is so much higher, or more distant from the centre of the earth than that portion of the sea which is in 40 deg. 45 min. of N. latitude. That protuberant mass of land and water which envelopes our spheroid at the equator is more than 2 1-2 times higher above the poles than the highest mountains upon the earth are above the sea level.
Perhaps some of this audience may be startled at these declarations and ready to call them in question as being contrary to their experience. How, it may be enquired, can water run up hill? Or how can the great ocean be prevented from rushing down from the equator to the poles? If there is an average of 11 feet fall per mile, how can water be kept from descending such a declivity? We answer, that it is the diurnal rotation of the earth upon its axis that preserves the earth in its present form, and that maintains the waters in their present state of equilibrium, and that causes the waters of the Mississippi to run up an acclivity on its ascending journey towards the equator. Were it not for the rotation of the earth, the great protuberant mass of the waters would rush down from the torrid zone with awful and tremendous force, inundating the highest mountains in the temperate and frigid zones; the foundations of the great deep for hundreds of miles each side of the equator, would be laid bare, and a zone of dry land would appear encircling the whole earth from east to west, connecting the equatorial portions of the eastern and western continents—while their northern and southern portions would be overwhelmed in the midst of two great polar seas. The surfaces of these polar seas would no longer maintain their elliptical form, but would take the form of a sphere; every part being equally distant from the center of the earth.
The equatorial continent thus formed, would in the lapse of ages be worn down by the constant action of the seas, rains, &c; and the worn off fragments and particles would eventually be scattered over the bed of the oceans in the form of pebbles, sand and mud, which would, like the fluid portions of the earth, seek their own level in the deepest portions of the polar seas; and in this manner the flattened portions of the solid spheroid would become rounded, and the whole earth, both solids and fluids would assume the spherical form; and thus, in the course of millions of ages, under the present laws, if no rotation existed, the solid portions of our spheroid would become covered with a spherical ocean of uniform depth. Geological facts seem to afford abundance of evidence that the existing continents and islands have all undergone changes as great as the one which we have just described; they appear to have been, more than once, torn into fragments, reduced to powder, submerged in the great deep, and then by some process reconstructed and made new.
Let us next consider the case of a perfect globe of the magnitude of our earth, covered with an ocean of water of uniform depth, composed of materials of uniform density, or, at least, of a density increasing at a uniform rate from the surface to the centre.—All the particles of such a globe, if at rest, would be in a state of equilibrium. Now let such a globe begin by degrees to rotate upon an axis; let the rotation be accelerated until it shall perform one revolution in 23h 56m 4s; it will then have a velocity equal to the earth. When this rotation commences, each particle, situated without the axis, will have a centrifugal force, or a tendency to recede from the axis, varying in proportion to its distance from it.
Near the poles, where the centrifugal force at the surface of the globe is the weakest, it acts nearly at right angles to the force of gravity; the watery fluid under the influences of those two forces would be urged towards the equator; as the water proceeded upon its journey, its distance from the axis of motion would be increased and its centrifugal force would consequently be more powerful, though it would act at a disadvantage in consequence of its being more in opposition to the central force, that is, forming a greater angle with it than when near the poles; but still the direction of the resultant motion would be towards the equator. The obtuseness of the angle under which these two forces operate would continue to increase from the pole to the equator, at which place the centrifugal force would act in direct opposition to that of gravity, and consequently the particles would have no more tendency to proceed either to the north or south; but the whole effect of the centrifugal force now would be to render all bodies specifically lighter by their upward tendency from the centre.
Under these circumstances, it is easy to perceive, that the globular form of the ocean would not any longer be the form of equilibrium, and that the ocean, surrounding the two poles must, in obedience to the laws of motion, proceed towards the equator and there form a protuberance of a sufficient elevation to counteract any further motion of the fluid particles, arising from the centrifugal force of rotation. The form thus assumed by the fluid ocean would be an oblate spheroid, which would be a permanent form of equilibrium as long as the rotation continued uniform. And it is also easy to conceive that the solid nucleus of the earth for thousands of miles around each pole would be laid bare, forming two great polar continents, while the ocean would encircle the whole earth, forming a belt or zone several thousand miles in breadth, of which the equator would be in the midst.
These polar continents, as we observed concerning the equatorial continent, would in the lapse of many ages become worn down and reduced to pebbles, sand, mud, &c., and be submerged beneath the ocean, where, under the same laws of force and motion which govern the fluid elements, it would be carried towards the equator and arrange itself in a spheroidal form similar to that of the ocean with which it would be enveloped. Thus the whole earth would be covered with an ocean of nearly uniform depth, and both the solid and fluid portions would be in equilibrium, having a degree of oblateness sufficient to balance the combined effects of the centripetal and centrifugal forces. If by any means the rotation should be increased, the oblateness would be increased, the fluids upon the surface would first yield to the impulse, and afterwards the solids would, by a slower process, arrange themselves in the form of equilibrium, accommodated to the increased degree of rotation. Should the rotation be decreased down to its former velocity, an equatorial ridge of mountains would be formed. Should an increase or decrease of rotation take place before the solids had time fully to arrange themselves in the form of equilibrium, the consequences would be, that ridges or continents would be formed in different latitudes which in places that were of a softer texture might be worn down and submerged beneath the sea; while those of a harder and more unyielding nature might still be standing above the surface of the water in the form of continents and islands. We do not pretend to state that this is the way that the continents and islands of our earth have received their present form and position; but we merely state, that such would be the natural tendency, were the earth to receive an addition or diminution to its velocity of rotation before the solid nucleus had time to fully accommodate itself to the different forms of equilibrium, corresponding to its different states of velocity. Whether the velocity of rotation has ever been greater or less than at the present time, we have not as yet discovered any means of ascertaining.
The fact that dry land and mountains do exist near the equator, elevated several thousand feet above the sea, would seem to indicate that the velocity of rotation has, at some former period, been greater than at present; otherwise there must have been some sudden convulsion sufficiently great to upheave from the bosom of the great deep the solid portions of the earth to their present elevation in those regions. Observation shows that there has been no perceptible change in the period of the earth’s rotation during the last 2000 years. If our earth were a globe when the rotation was first impressed upon it, its period must have been shorter, or its velocity greater than it would be after having assumed the spheroidal form; for the ocean, receding from the poles where the centrifugal force is the least, and proceeding to the equator, where that force is the greatest, would, during its progress, be constantly accelerated in an eastern direction by virtue of its increased distance from the axis of rotation; the acceleration at first would not be sufficiently great to keep up with the velocity of the spherical mass over which it was passing; consequently it would lag behind, producing a rapid current towards the west, which combined with the current proceeding towards the equator, would in the northern hemisphere inclined it to the south-west, and in the southern hemisphere towards the north-west. These currents acting upon the spherical form of the earth over which they passed in a direction from east to west contrary to that of rotation, would have a tendency to retard that rotation. The momentum gained by the protuberant mass brought from the poles, would be exactly equal to the momentum lost by the whole sphere. Mathematicians, by knowing the proportions of the masses and velocities, could easily calculate the original velocity and period of the earth’s rotation as a globe, from its present velocity and period as a spheroid.
Among the numerous phenomena resulting from the rotation of the earth may be mentioned the diminution of the weight of all bodies in proportion to the amount and direction of the centrifugal force with which they are affected. At the equator, the decrease of weight is the greatest amounting to 1-289 of its whole gravity.
The exact amount of the centrifugal force can be calculated if we know the dimensions of the earth and the time of its rotation. For instance, at the equator all bodies on the surface of the earth describe an arc of about 1528 feet in one second of time; this arc deviates from a straight line or from the tangent about 2-3 of an inch; and a body will fall during one second about 193 inches. During the time that a body would fall, by its weight, 193 inches, it would have an upward tendency of 2-3 of an inch is nearly 1-289 of the whole distance through which a body would fall in one second if the earth were at rest. Hence a body would fall in one second 193 inches if there were no rotation and 192 1-3 inches with its present rotation; the downward tendency being diminished 2-3 of an inch by the tendency to recede from the centre in the direction of the tangent. Hence, also, bodies that weigh 288 lbs at the equator, would weigh, at the same place, 280 lbs if the rotation did not exist, and the earth were maintained in its present shape. As you recede from the equator towards the poles, the centrifugal force diminishes and the weight of bodies increases. The rate of increase being as the square of the sign of the latitude; for instance, if we were to purchase at the equator 455 lbs weight of gold dust or any other substance, and bring it to the latitude of our city, it would weigh 456 lbs, increasing one pound by the increase of gravity: 194 lbs at the equator, if transported to the poles, would weigh 195 lbs. Thus it will be seen that the fraction 1-194 expresses the excess of polar gravity over the equatorial.
There are two causes for the increase of gravity in going from the equator to the poles; one is the diminution of the centrifugal force, and the other is the elliptical form of the earth. This form alone independent of the centrifugal force, would, at the poles, increase the weight of bodies 1-590 part; this added to 1-289, the fraction expressing the increase of weight when the centrifugal force is reduced to nothing, becomes equal to 1-194; that is, 194 lbs at the equator, if transported to the poles, would, in consequence of its removal from the influence of the centrifugal force, receive an addition to its weight amounting to a trifle over 2-3 of a pound; it would also receive another addition to its weight, arising from the elliptical figure of the earth, amounting to a trifle less than 1-3 of a pound; from both of these causes it would weigh just 1 lb more than at the equator.
The variation of that force called weight or gravity, in different latitudes, may be very accurately determined by ascertaining the velocity with which a body falls in a given time, as one second. One of the best methods of ascertaining the velocity furnished us by the principles of mechanics. It has been mathematically proved from mathematical principles, that if one and the same pendulum be made to oscillate in different parts of the earth that the squares of the number of oscillations in equal times at different stations will be to each other as the intensities of the force of gravity at these stations. For instance, if at the equator, a pendulum of a certain form and length, make 86,400 oscillations in 24 mean so’op hours, and when transported to the Great Salt Lake City, it is found that the same pendulum makes 86,495 oscillations in the same time; then we know that the intensity of gravity at the equator is to the intensity of gravity at this city as the square of 86,460 is to the square of 86,495; or as 1 to 1.0022; or in other words, a mass of matter weighing 10,000 lbs at the equator will weigh at this place 10,022 lbs.
Great numbers of experiments of this kind have been made with the greatest possible accuracy in all accessible latitudes; and by these means the law of the variation of gravity in different latitudes has been developed, by which we are enabled to calculate, without any further observation, the difference of the weight of bodies in different latitudes; and by knowing the difference of the intensities of this force at different latitudes; we can calculate the true figure of the earth and the degree of its oblateness without measuring an arc of the meridian. Who could have supposed that by the simple oscillations of a clock pendulum, mathematicians could sit in their chairs, and determine the proportions between the equatorial and polar diameters of our earth. But this is only one among ten thousand wonders opened to us by the skillful application of that grand key called mathematics. It is highly satisfactory to know that the shape of our earth as ascertained by pendulum experiments, agrees with the shape deduced from the measurements of arcs of the meridian. And thus from two entirely different processes we arrive at the same great conclusion; and having thus demonstrated that the earth is an oblate spheroid, we know that it must have a rotation upon its axis in order to preserve the spheroidal form, so far, at least, as the fluid portions of its surface are concerned.
This may be illustrated by a very simple experiment within the reach of any one to perform. If a pail partially filled with water, be suspended by a long string, and made to revolve swiftly around, the water within will be seen to arise around the sides of the pail, while the centre will be proportionally depressed; the greater the revolution the greater will be the depression of the centre, and the higher the water will the water arise around the interior sides of the pail; here then, in this simple illustration, we can see how water may be made to run up hill from the centre of the pail; and when it has once ascended, how its surface may be maintained in the form of a steep declivity by the continued rotation. As the water around the sides of the pail are maintained at a greater elevation than at the centre or axis of the rotation, so is the water at the equator maintained at an elevation of 13 miles above the water at the poles, merely by the earth’s rotation. As the rotation of the pail gradually diminishes, the water gradually descends from the sides of the pail towards the centre, which may be termed the pole of the axis around which the pail revolves. So, in like manner, if the rotation of the earth should be gradually diminished, the waters of the ocean would gradually descend from the equator and raise up the depression around the poles until the highest mountains in the northern and southern regions were completely inundated. On the other hand, if the rotation of the earth should be gradually increased, the water at the poles would become more depressed, while the protuberance at the equator would be proportionally increased. If the rotation should become a little over 17 times faster than at present, the water and all bodies at the equator would entirely lose their weight, the centrifugal force or tendency to recede from the centre of motion being equal to the centripetal force of gravity; while the polar gravity would be greatly increased by the increased eccentricity of the ellipsoidal form of the earth.
Under such a condition of things, a mass of lead which now weighs 1,000,000 of tons, could with the greatest of ease, be picked up and carried upon our heads, indeed if our earth revolved upon its axis once in 83m and 22s, a mountain of lead or any other substance placed 10 feet in the air above our heads at the equator, would have no tendency to fall or recede from the earth, but would keep its position, standing, as it were upon nothing. If the rotation were still increased, all the waters of the ocean, together with the mountains, rocks, and all other substances, composing the upper stratum, in the earth’s surface near the equator, would recede from the earth upwards, or rather in the direction of the tangent.
[Transcribed by Tiffany Woods Whiting and Heather Hoyt, Sept. 2012]
Orson Pratt, Astronomical Lectures: Lecture Second, Unknown newspaper, January 10, 1852.