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 Instantiæ 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.”
In the absence indeed of advanced theory and analytical 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 scrupulously accurate observations of Flamsteed were the proper complement to the intense mathematical 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 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. 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 as 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 as that 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 Rœmer and Flamsteed to reduce this error to seconds. Bradley, the modern Hipparchus, carried on the improvement, his errors in right ascension, according to Bessel, being under one second of time, and those of declination under four seconds of arc. 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.1
It would be a matter of great interest to trace out the dependence of this progress upon the introduction of new instruments. The astrolabe of Ptolemy, the telescope of Galileo, the pendulum of Galileo and Huyghens, the micrometer of Horrocks, and the telescopic sights and micrometer of Gascoygne and Picard,