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that events will long continue to happen as they have previously happened.

We have now pursued the theory of inductive inference, as far as can be done with regard to simple logical or numerical relations. The laws of nature deal with time and space, which are indefinitely, or rather infinitely, divisible. As we passed from pure logic to numerical logic, so we must now pass from questions of discontinuous, to questions of continuous quantity, encountering fresh considerations of much difficulty. Before, therefore, we consider how the great inductions and generalizations of physical science illustrate the views of inductive reasoning just explained, we must break off for a time, and review the means which we possess of measuring and comparing magnitudes of time, space, mass, force, momentum, energy, and the various manifestations of energy in motion, heat, electricity, chemical change, and the other phenomena of nature.

BOOK III.

METHODS OF MEASUREMENT.

CHAPTER XIII.

THE EXACT MEASUREMENT OF PHENOMENA.

As physical science advances, it becomes more and more accurately quantitative. Questions of simple logical fact after a time resolve themselves into questions of degree, time, distance, or weight. Forces hardly suspected to exist by one generation, are clearly recognised by the next, and precisely measured by the third generation. But one condition of this rapid advance is the invention of suitable instruments of measurement. We need what Francis Bacon called Instantiæ citantes, or evocantes, methods of rendering minute phenomena perceptible to the senses; and we also require Instantia radii or curriculi, that is measuring instruments. Accordingly, the introduction of a new instrument often forms an epoch in the history of science. As Davy said, 'Nothing tends so much to the advancement of knowledge as the application of a new instrument. The native intellectual powers of men in different times, are not so much the causes of the different success of their labours, as the peculiar nature of the means and artificial resources in their possession b'. In the absence indeed of advanced theory and analyti

a Novum Organum,' bk. ii. Aphorisms 40, 45 and 46.

b Chemical Philosophy,' Works, vol. iv. p. 39. Quoted by Young, Works, vol. i. p. 576.

cal power, a very precise instrument would be useless. Measuring apparatus and mathematical theory should advance pari passu, and with just such precision as the theorist can anticipate results, the experimentalist should be able to compare them with experience. The laborious and scrupulously accurate observations of Flamsteed, were the proper complement to the intense mathemetical powers of Newton.

Every branch of knowledge commences with quantitative notions of a very rude character. After we have far progressed, it is often amusing to look back into the infancy of the science, and contrast present with past methods. At Greenwich Observatory in the present day, the hundredth part of a second is not thought an inconsiderable portion of time. The ancient Chaldæans recorded an eclipse to the nearest hour, and even the early Alexandrian astronomers thought it superfluous to distinguish between the edge and centre of the sun. By the introduction of the astrolabe, Ptolemy and the later Alexandrian astronomers could determine the places of the heavenly bodies within about ten minutes of arc. But little progress then ensued for thirteen centuries, until Tycho Brahe made the first great step towards accuracy, not only by employing better instruments, but even more by ceasing to regard an instrument

correct. Tycho, in fact, determined the errors of his instruments, and corrected his observations. He also took notice of the effects of atmospheric refraction, and succeeded in attaining an accuracy often sixty times as great

thest of Ptolemy. Yet Tycho and Hevelius often erred several minutes in the determination of a star's place, and it was a great achievement of Roemer and Flamsteed to rocco this ottor to seconds. Bradley, the modern Hipparchus carried on the improvement, his errors in right Konton bong under one second of time, and those of de, under four seconds of arc according to Bessel.

In the present day the average error of a single observation is probably reduced to the half or quarter of what it was in Bradley's time; and further extreme accuracy is attained by the multiplication of observations, and their skilful combination according to the theory of error.

Some of the more important constants, for instance that of nutation, have been determined within the tenth part of a second of space.

It would be a matter of great interest to trace out the dependence of this vast progress upon the introduction of new instruments. The astrolabe of Plotemy, the telescope of Galileo, the pendulum of Galileo and Huygens, the micrometer of Horrocks, and the telescopic sights and micrometer of Gascoygne and Picard, Romer's transit instrument, Newton's and Hadley's quadrant, Dollond's achromatic lenses, Harrison's chronometer, and Ramsden's dividing engine such were some of the principal additions to astronomical apparatus. The result is, that we now take note of quantities, 300,000 or 400,000 times as small as in the time of the Chaldæans.

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It would be interesting again to compare the scrupulous accuracy of a modern trigonometrical survey with Erato'sthenes' rude but ingenious guess at the difference of latitude between Alexandria and Syene-or with Norwood's measurement of a degree of latitude in 1635. Sometimes I measured, sometimes I paced,' said Norwood; and I believe I am within a scantling of the truth.' Such was the germ of those elaborate geodesical measurements which have made the dimensions of the globe known to us within a few hundred yards.

In other branches of science, the invention of an instrument has usually marked, if it has not made, an epoch. The science of heat might be said to commence with the

C

Baily, 'British Association Catalogue of Stars,' pp. 7, 23.

construction of the thermometer, and it has recently been advanced by the introduction of the thermo-electric pile. Chemistry has been created chiefly by the careful use of the balance, which forms a unique instance of an instrument remaining substantially in the form in which it was first applied to scientific purposes by Archimedes. The balance never has been and probably never can be improved, except in details of construction. On the other hand, the torsion balance, introduced by Coulomb towards the end of last century, has rapidly become essential in many branches of investigation. In the hands of Cavendish and Baily, it gave a determination of the earth's density; applied in the galvanometer, it gave a delicate measure of electrical forces, and was essential to the introduction of the thermo-electric pile. This balance is made by simply suspending any light rod or thread attached to the middle point. it almost all the more delicate investigations in the theories of heat, electricity, and magnetism.

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Though we can now take note of the millionth of an inch in space, and the millionth of a second in time, we must not overlook the fact that in other operations of science we are yet in the position of the Chaldæans. Not many years have elapsed since the magnitudes of the stars, meaning the amount of light they send to the observer's eye, were guessed at in the rudest manner, and the astronomer adjudged a star to this or that order of magnitude by a rough comparison with other stars of the same order. To the late Sir John Herschel we owe an attempt to introduce an uniform method of measurement and expression, bearing some relation to the real photometric magnitudes of the stars. Previous to the re

Outlines of Astronomy,' 4th ed. sect. 781, p. 522. 'Results of Obvations at the Cape of Good Hope,' &c., p. 371.

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