displaced; the third method in fact is adopted. To make all the calculations in the frequent weighings requisite in chemical analysis would be exceedingly laborious, hence the correction is usually neglected. But when the chemist wishes to weigh a quantity of gas contained in a glass globe for the purpose of determining its specific gravity, the correction becomes of much importance. Hence chemists avoid at once the error, and the labour of correcting it, by attaching to the opposite scale of the balance a sealed glass globe of exactly equal capacity to that containing the gas to be weighed, noting only the dif ference of weight when the globe is full and empty. The correction, being exactly the same for both globes, may be entirely neglected ©.

A device of nearly the same kind is employed in the construction of galvanometers which measure the force of an electric current by the deflection of a suspended magnetic needle. The resistance of the needle is partly due to the directive influence of the earth's magnetism, and partly to the torsion of the thread. But the former force may often be inconveniently great as well as troublesome to determine for different inclinations. Hence it is customary to connect together two exactly equal needles, with their poles pointing in opposite directions, one needle being within and another without the coil of wire. As regards the earth's magnetism, the needles are now astatic or indifferent, the tendency of one needle being exactly balanced by that of the other.

An elegant instance of the elimination of a disturbing force by compensation is found in Faraday's researches upon the magnetism of gases. To observe the magnetic attraction or repulsion of a gas seems impossible unless we enclose the gas in an envelope, probably best made of

Regnault's Cours Elémentaire de Chimie,' 1851, vol. 1. p. 141

glass. But any such envelope is sure to be more or less affected by the magnet, so that it becomes difficult to distinguish between three forces which enter the problem ; namely, the magnetism of the gas in question, that of the envelope, and that of the surrounding atmospheric air. Faraday avoided all difficulties by employing two exactly equal and similar glass tubes connected together, and so suspended from the arm of a torsion balance that the tubes were in similar parts of the magnetic field. One tube being filled with nitrogen and the other with oxygen, it was found that the oxygen seemed to be attracted and the nitrogen repelled. The suspending thread of the balance was then turned until the force of torsion restored the tubes to their original places, where the magnetism of the tubes as well as that of the surrounding air, being exactly the same and in the opposite direction upon the two tubes, could not produce any interference. The force thus required to restore the tubes was measured by the amount of torsion of the thread, and it indicated correctly the comparative attractive powers of oxygen and nitrogen. The oxygen was then withdrawn from one of the tubes, and a second experiment made, so as to compare a vacuum with nitrogen. No force was now required to maintain

tubes in their places, so that nitrogen was found to approximately speaking, indifferent to the magnet, tis, neither magnetic nor diamagnetic, while oxygen was proved to be positively magnetic f. It required the ghest experimental skill on the part of Faraday and Fyndall, to distinguish between what is apparent and real magnetic attraction and repulsion.

As a

Experience alone can absolutely decide when a compensating arrangement is conducive to accuracy. eneral rule mechanical compensation is the last resource,

and in the more accurate observations it is likely to introduce more uncertainty than it removes. A multitude of instruments involving mechanical compensation have been devised, but they are usually of an unscientific character, because the errors compensated can be more accurately determined and allowed for. But there are exceptions to this rule, and it seems to be proved that in the delicate and tiresome operation of measuring a base line, invariable bars, compensated for expansion by heat, give a very accurate result, the observation of their varying temperature and the calculation of the corrections being an uncertain and tedious work h.

We thus see that the choice of one or other mode of eliminating a simple error depends entirely upon circumstances and the object in view; but we may safely lay down the following conclusions. First of all, seek to avoid the source of error altogether if it can be conveniently done; if not, make the experiment so that the error may be as small, but more especially as constant, as possible. If the means are at hand for determining its amount. by calculation from other experiments and principles of science, allow the error to exist and make a correction in the result. If this cannot be accurately done or involves too much labour for the purposes in view, then throw in a counteracting error which shall as nearly as possible be of equal amount in all circumstances with that to be eliminated. There yet remains, however, one important method, that of Reversal, which will form an appropriate transition to the succeeding chapters on the Method of Mean Results and the Law of Error.

g See, for instance, the Compensated Sympicsometer, Philosophical Magazine,' 4th Series, vol. xxxix. p. 371.

h Grant, History of Physical Astronomy,' pp. 146, 147.

5. Method of Reversal.

ethod of eliminating error is most potent ory whenever it can be applied, but it re, we shall be able to reverse the apparatus and ocedure, so as to make the interfering cause etely in opposite directions. If we can get two Pental results, one of which is as much too great as too small, the error is equal to half the dif ad the true result is the mean of the two results It is an unavoidable defect of the balance, for instance, that the points of susthe pans cannot be fixed at exactly equal proga the centre of suspension of the beam. weights which seem to balance each other

quito equal in reality. The difference is seversing the weights, and it may be estimy wong suflicient small weights to the deficient ere equilibrium, and then taking as the true wolle geometric mean of the two apparent weights If the difference is small the arith

A

Die half the sum, may be substituted for on, from which it will not appreciably

1

'teversal is most extensively employed The apparent elevation of a vrved by a telescope moving upon am which the inclination of the Now this reading will be erroneous de telescope have not accurately the we read off at the same time both cina vys the one reading will be about as all acre other is too great, and the mean In practice the observa

4

tion is differently conducted, but the principle is the same; the telescope is fixed to the circle, which moves with it, and the angle through which it moves is read off at three, six, or more points, disposed of at equal intervals round the circle. The older astronomers, down even to the time of Flamsteed, were accustomed to use portions only of a divided circle, generally quadrants, and Römer made a vast improvement when he introduced the complete circle.

The transit circle, employed to determine the meridian passage of heavenly bodies, is so constructed that the telescope and the axis bearing it, in fact the whole moving part of the instrument, can be taken out of the bearing sockets and turned over, so that what was formerly the western pivot becomes the eastern one, and vice versa. It is impossible that the instrument could have been so perfectly constructed, mounted, and adjusted that the telescope should point exactly to the meridian, but the . effect of the reversal is that it will point as much to the west in one position as it does to the east in the other, and the mean result of observations in the two positions must be free from such cause of error.

The accuracy with which the inclination of the compass needle can be determined depends almost entirely on the method of reversal. The dip needle consists of a bar of magnetized steel, suspended like the beam of a delicate balance on a slender axis passing through the centre of gravity of the bar, so that it is at liberty to rest in that exact degree of inclination in the magnetic meridian which the magnetism of the earth induces. The inclination is read off upon a vertical divided circle, but to avoid any error in the centring of the needle and circle, both ends are read, and the mean of the results is taken. The whole instrument is now turned carefully round through 180°, which gives two new readings, in