If we measure over and over again the same angular magnitude by the same divided circle, maintained in exactly the same position, it is evident that the same mark in the circle will be the criterion in each case, and any error in the position of that mark will equally affect all our results. But if in each measurement we use a different part of the circle, a new mark will come into use, and as the error of each mark can hardly be in the same direction, the average result will be nearly free from errors of division. It will be still better to use more than one divided circle.

Even when we have no clear perception of the points of our apparatus at which fixed error is likely to enter, we may with advantage vary the construction of our apparatus with the hope that we shall accidentally detect some latent imperfection. Baily's purpose in repeating the experiments of Michell and Cavendish on the density of the earth, was not merely to follow the same course and verify the previous numbers, but to try whether variations in the size and substance of the attracting balls, the mode of suspension, the temperature of the surrounding air, &c., would yield different results. He performed no less than 62 distinct series, comprising 2153 experiments, and he carefully classified and discussed the results so as to disclose the utmost differences. Again, in experimenting upon the resistance of the air to the motion of a pendulum, Baily employed no less than 80 pendulums of various forms and materials, in order to ascertain exactly upon what conditions the resistance depends. Regnault, in his exact researches upon the dilatation of gases made arbitrary changes in the magnitude of parts of his apparatus. He thinks that if, in spite of such modification the results are unchanged, the errors are probably of inconsiderable amount"; but in reality it is Jamin, 'Cours de Physique,' vol. ii. p. 60.

u

always possible, and usually likely, that we overlook sources of error which a future generation will detect. Thus the pendulum experiments of Baily and Sabine were directed to ascertain the nature and amount of a correction for air resistance, which had been entirely misunderstood in the experiments upon which was founded the definition of the standard yard, by means of the seconds pendulum in the Act of 5th George IV. c. 74. It has already been mentioned that a considerable error was discovered in the determination of the standard metre as the ten-millionth part of the distance from the pole to the equator (p. 368).

We shall return in the second volume to the further consideration of the methods by which we may as far as possible secure ourselves against permanent and undetected sources of error. In the meantime, having completed the consideration of the special methods requisite for treating quantitative phenomena, we must return to our principal subject, and endeavour to trace out the course by which the physicist, from observation and experiment, collects the materials of natural knowledge, and then proceeds by hypothesis and inverse calculation to educe from them the laws of nature.

END OF THE FIRST VOLUME.

BOOK IV.

INDUCTIVE INVESTIGATION.

CHAPTER XVIII.

OBSERVATION.

ALL knowledge proceeds originally from experience. Using the name in a wide sense we may say that experience comprehends all that we feel, externally or internally the aggregate of the impressions which we receive through the various apertures of perception-the aggregate consequently of what is in the mind, except so far as some portions of knowledge may be the reasoned equivalents of other portions. As the word experience impliesa, we go through much in life, and the impressions gathered intentionally or unintentionally afford the materials from which the active powers of the mind evolve science.

No small part of the experience actually employed in science is acquired without any distinct purpose. We cannot use the eyes without gathering some facts which may prove useful. Every great branch of science has generally taken its first rise from an accidental observation. Erasmus Bartholinus thus first discovered double refraction in Iceland spar; Galvani noticed the twitching of a frog's leg; Oken was struck by the form of a a Max Müller's 'Lectures on Language,' vol. ii. p. 73.

vertebra; Malus unintentionally examined with a double refracting substance light reflected from distant windows; and Sir John Herschel's attention was drawn to the peculiar appearance of a solution of quinine sulphate. In earlier times there must have been some one who first noticed the strange behaviour of a loadstone, or the unaccountable motions produced by amber. As a general rule we shall not know in what direction to look for a great body of phenomena widely different from those familiar to us. Chance then must give us the starting point; but one accidental observation well used may lead us to make thousands of observations in an intentional and organized manner, and thus a science may be gradually worked out from the smallest opening.

Distinction of Observation and Experiment.

It is usual to say that the two modes of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. Sir John Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.

It may readily be seen that we pass upwards by insensible gradations from pure observation to determinate b Preliminary Discourse on the Study of Natural Philosophy,' p. 77