to the wrong position of the zero be reversed. As the axis of the Aactly horizontal, it is now reversed r as the transit instrument, the end of erly pointed east being made to point se of readings is taken.

may arise from the axis not passing gh the centre of gravity of the bar, and nly be detected and eliminated on reagnetic poles of the bar by the application agnet. The error is thus made to act in To ensure all possible accuracy each to be combined with each other reversal, needle will be observed in eight different

teen different readings, the mean of the wca will give the required inclination free ...able errors k.

certain cases of experiment in which a so can with much ease be made to act in ons, in alternate observations, so that the results will be free from disturbance. Thus

ments upon the velocity of sound in the air between stations two or three wind is a cause of error. It will be well, t to choose a time for the experiment very nearly at rest, and the disturbance

same moment signal sounds be made served at the other, two sounds will e directions through the same body will accelerate one sound almost sit retards the other!. Again, in es the apparent height of a point se du Globe,' p. 174. Jamin, 'Cours de

...dia Metropolitana,' p. 748.

will be affected by atmospheric refraction and the curvature of the earth. But if in the case of two points the apparent elevation of each as seen from the other be observed, the corrections will be the same in amount, but reversed in direction, and the mean between the two apparent differences of altitude will give the true difference of level m.

In the next two chapters we really pursue the Method of Reversal into more complicated applications.

m Hutton, 'Philosophical Transactions,' abridgment, vol. xiv. p. 422.

CHAPTER XVI.

THE METHOD OF MEANS.

ALL results of the measurement of continuous quantity can only be approximately true. Were this assertion doubted, it could readily be proved by direct experience. For if any person, using an instrument of the greatest precision, makes and registers successive observations in an unbiassed manner, it will almost invariably be found that the results differ from each other. When we operate with sufficient care we cannot perform so simple an experiment as weighing an object in a good balance without getting discrepant numbers. Only the rough and careless experimenter will think that his observations agree, but in reality he will be found to overlook the differences. The most elaborate researches, such as those undertaken in connexion with standard weights and measures, always render it apparent that complete coincidence is out of the question, and that the more accurate our modes of observation are rendered, the more numerous are the sources of minute error which become apparent. We may look upon the existence of error in all measurements as the normal state of things. It is absolutely impossible to eliminate separately the multitude of small disturbing influences, except by balancing them off against each other. And even in drawing a mean it is to be expected that we shall come near the truth rather than exactly to it. In the measurement of continuous quantity,

absolute coincidence, if it even occurs or seems to occur, must be purely casual, and is no indication of precision. It is one of the most embarrassing things we can meet when experimental results agree too closely. Such coincidences should raise our suspicion that the apparatus in use is in some way restricted in its operation, so as not really to give the true result at all, or that the actual results have not been faithfully recorded by the assistant in charge of the apparatus.

If then we cannot get twice over exactly the same result, the question arises, How can we ever attain the truth or select the result which may be supposed to approach most nearly to it? The quantity of a certain phenomenon is expressed in several numbers which differ from each other; no more than one of them at the most can be true, and it is more probable that they are all false. It It may be suggested, perhaps, that the observer should select the one observation which he judged to be the best made, and there will often doubtless be a feeling that one or more results were satisfactory, and the others less trustworthy. This seems to have been the course adopted by some of the early astronomers. Flamsteed when he had made several observations of a star probably chose in an arbitrary manner that which seemed to him nearest to the truth".

When Horrocks selects for his estimate of the sun's semidiameter a mean between the results of Kepler and Tycho he professes not to do it from any regard to the idle adage, Medio tutissimus ibis,' but because he thought it from his own observations to be correct. But this method will not apply at all when the observer has

a Thomson and Tait, Treatise on Natural Philosophy,' vol. i. p. 309. b Baily's Account of Flamsteed,' p. 376.

6

P. 146.

The Transit of Venus across the Sun,' by Horrocks, London, 1859,