minute difference in the lengths of the waves makes a very perceptible difference in the position of the point at which two rays will interfere and produce darkness. M. Fizeau has recently employed Newton's rings in an inverse manner, to measure small amounts of motion. By merely counting the number of rings of sodium monochromatic light passing a certain point where two glass plates are in close proximity, he is able to ascertain with the greatest accuracy and ease the change of distance between these glasses, produced, for instance, by the expansion of a metallic bar, connected with one of the glass platesh. Nothing excites more admiration than the mode in which scientific observers can occasionally measure quantities, which seem beyond the bounds of human observation. We know the average depth of the Pacific Ocean to be 14,190 feet, not by actual sounding, which would be impracticable in sufficient detail, but by noticing the rate of transmission of earthquake waves from the South American to the opposite coasts, the rate of movement being connected by theory with the depth of the water i. In the same way the average depth of the Atlantic Ocean is inferred to be no less than 22,157 feet, from the velocity of the ordinary tidal waves. A tidal wave again gives beautiful evidence of an effect of the law of gravity, which we could never in any other way detect. Newton estimated that the moon's force in moving the ocean is only part of the whole force of gravity, which even the pendulum, used with the utmost skill, would fail to render apparent. Yet the immense extent of the ocean allows the accumulation of the effect into a very palpable amount; and from the comparative I 2,871,400 h 'Proceedings of the Royal Society,' 30th November, 1866. heights of the lunar and solar tides, Newton roughly estimated the comparative forces of the moon's and sun's gravity at the earthk. A few years ago it might have seemed impossible that we should ever measure the velocity with which a star approaches or recedes from the earth, since the apparent position of the star is thereby unaltered. But the spectroscope now enables us to detect and even measure such motion with considerable accuracy, by the alteration which it causes in the apparent rapidity of vibration, and consequently in the refrangibility of rays of light of definite colour. And while our estimates of the lateral movements of stars depend upon our very uncertain knowledge of their distance, the spectroscope gives the motion in another direction in absolute quantity, irrespective of all other quantities known or unknown, excepting the motion of the earth itself1. The rapidity of vibration for each musical tone, having been accurately determined by comparison with the Syren (p. 12), we can use sounds as indirect indications of rapid vibrations. It is now known that the contraction of a muscle arises from the periodical contractions of each separate fibre, and from a faint sound or susurrus which accompanies the action of a muscle, it is inferred that each contraction lasts for about of a second. Minute I 300 quantities of radiant heat are now always measured indirectly by the electricity which they produce when falling upon a thermopile. The extreme delicacy of the method seems to be due to the power of multiplication at several points in the apparatus. The number of elements or junctions of different metals in the thermopile can be increased k 'Principia,' bk. iii. Prop. 37, 'Corollaries,' 2 and 3. Motte's translation, vol. ii. p. 310. 1 Roscoe's, Spectrum, Analysis,' 1st ed. p. 296. so that the tension of the electric current derived from the same intensity of radiation is multiplied; the effect of the current upon the magnetic needle can be multiplied within certain bounds, by passing the current many times round it in a coil; the excursions of the needle can be increased by rendering it astatic and increasing the delicacy of its suspension; lastly, the angular divergence can be observed, with any required accuracy, by the use of an attached mirror and distant scale viewed through a telescope (p. 234). Such is the delicacy of this method of measuring heat, that Dr. Joule succeeded in making a thermopile which would indicate a difference of part of a degree centigrade m. I 72,000 I 8800 A striking case of indirect measurement is furnished by the revolving mirror of Wheatstone and Foucault, whereby a minute interval of time is estimated in the form of an angular deviation. Wheatstone viewed an electric spark in a mirror rotating so rapidly, that if the duration of the spark had been more than of a second, the point of light would have appeared elongated to an angular extent of one-half degree. In the spark, as drawn directly from a Leyden jar, no elongation was apparent, so that the duration of the spark was immeasurably small; but when the discharge took place through a bad conductor, the elongation of the spark denoted a sensible duration". In the hands of Foucault the rotating mirror gave a measure of the time occupied by light in passing through a few metres of space. Comparative Use of Measuring Instruments. In almost every case a measuring instrument serves, m Philosophical Transactions' (1859), vol. cxlix. p. 94. and should serve only as a means of comparison between two or more magnitudes. As a general rule, we should not even attempt to make the divisions of the measuring scale exact multiples or submultiples of the unit, but, regarding them as arbitrary marks, should determine their values by comparison with the standard itself. Thus the perpendicular wires in the field of a transit telescope, are fixed at nearly equal but arbitrary distances, and those distances are afterwards determined, as first suggested by Malvasia, by watching the passage of star after star across them, and noting the intervals of time by the clock. Owing to the perfectly regular motion of the earth, these time intervals give an exact determination of the angular intervals. In the same way, the angular value of each turn of the screw micrometer attached to a telescope, can be easily and accurately ascertained. When a thermopile is used to observe radiant heat, it would be almost impossible to calculate on à priori grounds what is the value of each division of the galvanometer circle, and still more difficult to construct a galvanometer, so that each division should have a given value. But this is quite unnecessary, because by placing the thermopile before a body of known dimensions, at a known distance, with a known temperature, and radiating power, we measure a known amount of radiant heat, and inversely measure the value of the indications of the thermopile. In a similar way Mr. Joule ascertained the actual temperature produced by the compression of bars of metal. For having inserted a simple thermopile composed of a single junction of copper and iron wire, and noted the deflections of the galvanometer, he had only to dip the bars into water of different temperatures, until he produced a like deflection, in order to ascertain the temperature developed by pressureo. 0 'Philosophical Transactions' (1859), vol. cxlix. p. 119, &c. In many instances we are indeed obliged to accept a very carefully constructed instrument as a standard, as in the case of a standard barometer. But it is then best to treat all inferior instruments comparatively only, and determine the values of their scales by comparison with the assumed standard. Systematic Performance of Measurements. When a large number of accurate measurements have to be effected, it is usually desirable to make a certain number of determinations with scrupulous care, and afterwards use them as points of reference for the remaining determinations. In the trigonometrical survey of a country, the principal triangulation fixes the relative positions and distances of a few points with rigid accuracy. A minor triangulation refers every prominent hill or village to one of the principal points, and then the details are filled in by reference to the secondary points. The survey of the heavens is effected in a like manner. The ancient astronomers compared the right ascensions of a few principal stars with the moon, and thus ascertained their positions with regard to the sun; the minor stars were afterwards referred to the principal stars. Tycho followed the same method, except that he used the more slowly moving planet Venus instead of the moon. Flamsteed was in the habit of using about seven stars, favourably situated at points all round the heavens. The distances of the other stars from these standard points, were determined in his early observations by the use of the quadrant P. Even since the introduction of the transit telescope and mural circle, tables of standard stars are formed at Greenwich, the positions being determined with every Þ Baily's 'Account of Flamsteed,' pp. 378-380. |