A like peculiarity in the motions of Jupiter's fourth satellite was similarly detected by Maraldi in 1713. Remarkable conjunctions of the planets may sometimes allow us to compare their periods of revolution, through long intervals of time, with great accuracy. Laplace in explaining the long inequality in the motions of Jupiter and Saturn, was much assisted by a conjunction of these planets, observed by Ibyn Jounis at Cairo, towards the close of the eleventh century. Laplace calculated that such a conjunction must have happened on the 31st of October, A. D. 1087; and the discordance between the distances of the planets as recorded, and as assigned by theory, was less than one-fifth of the apparent diameter of the sun. This difference being less than the probable error of the early record, his theory was confirmed as far as facts were available b. The ancient astronomers often shewed the highest ingenuity in turning any opportunities of measurement which occurred to good account. Eratosthenes, as early as 250 B. C., happening to hear that the sun at Syene, in Upper Egypt, was visible at the summer solstice at the bottom of a well, proving that it was in the zenith, proposed to determine the dimensions of the earth, by measuring the length of the shadow of a rod at Alexandria on the same day of the year. He thus learnt in a rude manner the difference of latitude between Alexandria and Syene, and finding it to be about one fiftieth part of the whole circumference, he ascertained the dimensions of the earth within about one sixth part of the truth. The use of wells in astronomical observation appears to have been occasionally practised in comparatively recent times, as by Flamsteed in 1679°. Hipparchus employed the moon instrument of measurement in several sagacious Grant's, 'History of Physical Astronomy,' p. 129. modes. When the moon is exactly half full, the moon, sun, and earth, are at the angles of a right-angled triangle. He proposed therefore at such a time to measure the moon's elongation from the sun, which would give him the two other angles of the triangle, and enable him to judge of the comparative distances of the moon and sun from the earth. His result, though very rude, was far more accurate than any notions previously entertained, and enabled him to form some estimate of the comparative magnitudes of the bodies. Eclipses of the moon were also very useful in ascertaining the longitudes of the stars, which were invisible when the sun was above the horizon. For the moon when eclipsed must be 180° distant from the sun; hence it was only requisite to measure the distance of a fixed star in longitude from the eclipsed moon to obtain with ease its angular distance from the sun. In later times the eclipses of Jupiter have usefully served to give a measure of an angle; for at the middle. moment of the eclipse the satellite must be exactly in the same straight line with the planet and sun, so that we can learn from the known laws of movement of the satellite the longitude of Jupiter as seen from the sun. If at the same time we measure the elongation or apparent angular distance of Jupiter from the sun, as seen from the earth, we have all the angles of the triangle between Jupiter, the sun, and the earth, and can calculate the comparative magnitudes of the sides of the triangle by simple trigonometry. The transits of Venus over the sun's face are other natural events which seem to give most accurate measurements of the sun's parallax, or apparent difference of position as seen from distant points of the earth's surface. The sun forms a kind of background on which the place of the planet is marked, and serves as a measuring instru ment free from all the errors of construction, which affect human instruments. The rotation of the earth, too, by variously affecting the apparent velocity of ingress or egress of Venus, as seen from different places, discloses the amount of the parallax. It has been sufficiently shown that by rightly choosing the moments of observation, the planetary bodies may often be made to reveal their relative distance, to measure their own position, to record their own movements with a high degree of accuracy. With the improvement of astronomical instruments, such conjunctions become less necessary to the progress of the science, but it will always remain advantageous to choose those moments for observation when instrumental errors enter with the least effect. In other sciences, exact quantitative laws can occasionally be obtained without instrumental measurement, as when we learn the exactly equal velocity of sounds of different pitch, by observing that a peal of bells or a musical performance is heard harmoniously at any distance to which the sound penetrates; this could not be the case, as Newton remarked, if one sound overtook the other. One of the most important principles of the cone theory, was proved by implication, before the use the balance was introduced into chemistry. Wenzel Cerved, before 1777, that when two neutral substances www.po oach other, the resulting salts are also neutral. V sodium sulphate and barium nitrate, we Nodibly barium sulphate and neutral sodium Pus result could not follow unless the nitric e tu saturate one atom of sodium, were so that required by one atom of barium, ege could take place without leaving Ang principle of mechanics may also be established by a simple acoustical observation. When a rod or tongue of metal fixed at one end is set in vibration, the pitch of the sound may be observed to be exactly the same, whether the vibrations be small or great; hence the oscillations are isochronous, or equally rapid, independently of their magnitude. On the ground of theory, it can be shown that such a result only happens when the flexure is proportional to the deflecting force. Thus the simple observation that the pitch of the sound of a harmonium, for instance, does not change with its loudness, establishes an exact law of nature e. A closely similar instance is found in the proof that the intensity of light or heat rays varies inversely as the square of the distance increases. For the apparent magnitude certainly varies according to this law; hence, if the intensity of light varied according to any other law, the brightness of an object would be different at different distances, which is not observed to be the case. Melloni applied the same kind of reasoning, in a somewhat different form, to the radiation of heat-rays f. Modes of Indirect Measurement. Some of the most conspicuously beautiful experiments in the whole range of science, have been devised for the purpose of indirectly measuring quantities, which in their extreme greatness or smallness surpass the powers of sense. All that we need to do, is to discover some other conveniently measurable phenomenon, which is related in a known ratio or according to a known law, however complicated, with that to be measured. Having e Jamin, 'Cours de Physique,' vol. i. p. 152. f Balfour Stewart's, 'Elementary Treatise on Heat,' 1st edit. pp. 164, 165. once obtained experimental data, there is no further difficulty beyond that of arithmetic or algebraic calculation. Gold is reduced by the gold-beater to leaves so thin, that the most powerful microscope would not detect any measurable thickness. If we laid several hundred leaves upon each other to multiply the thickness, we should still have no more thanth of an inch at the most to measure, and the errors arising in the superposition and measurement would be considerable. But we can readily obtain an exact result through the connected amount of weight. Faraday weighed 2000 leaves of gold, each 3 inch square, and found them equal to 384 grains. From the known specific gravity of gold, it was easy to calculate that the average thickness of the leaves was 22.000 of an inch g We must ascribe to Newton the honour of leading the way in methods of minute measurement. He did not call waves of light by their right name, and did not understand their nature; yet he measured their length, though it did not exceed the 2,000,000th part of a metre or the one fifty thousandth part of an inch. He pressed together two lenses of very large but known radii. It was not difficult to calculate the interval between the lenses at any point, by measuring the distance from the central point of contact. Now, with homogeneous rays the successive rings of light and darkness mark the points at which the interval between the lenses is equal to one half, or any multiple of half a vibration of the light, so that the length of the vibration became known. In a similar manner many phenomena of interference of rays of light admit of the measurement of the wave lengths. The fringes of interference arise from rays of light which cross each other at a small angle, and an excessively Faraday, Chemical Researches,' p. 393. |