In some rudimentary experiments we may wish merely to establish the existence of a quantitative effect without precisely measuring its amount; if there exist causes of error of which we can neither render the amount known or inappreciable, the best way will be to make them all negative so that the quantitative effects will be less than the truth rather than greater. Mr. Grove, for instance, in proving that the magnetization or demagnetization of a piece of iron raises its temperature, took care to maintain the electro-magnet by which the iron was acted upon at a lower temperature, so that it would cool rather than warm the iron by radiation or conduction 1.

Rumford's celebrated experiment to prove that heat was generated out of mechanical force in the boring of a cannon was subject to the difficulty that heat might be brought to the cannon by conduction from neighbouring bodies. It was an ingenious device of Davy to produce friction by a piece of clock-work resting upon a block of ice in an exhausted receiver; as the machine rose in temperature above 32°, it was certain that no heat was received by conduction from the support m. In many other experiments ice may be employed to prevent the access of heat by conduction, and this device, first put in practice by Murray ", is beautifully employed in Bunsen's

calorimeter.

To obtain the true temperature of the air, though apparently so easy, is really a very difficult matter, because the thermometer employed is sure to be affected either by the sun's rays, the radiation from neighbouring objects, or the escape of heat into space. These sources

1 The Correlation of Physical Forces,' 3rd ed. p. 159.

m Collected works of Sir H. Davy,' vol. ii. pp. 12-14. 'Elements of Chemical Philosophy,' p. 94.

n 'Nicholson's Journal,' vol. i. p. 241; quoted in Treatise on Heat,' Useful Knowledge Society, p. 24.

ir are too fluctuating to allow of correction, so that rv accurate mode of procedure is that devised by Zee of surrounding the thermometer with a copper der ingeniously adjusted to the temperature of the as described by him, so that the effect of radiation Se mullified o. De

When the avoidance of error cannot be carried into Now, it will yet be desirable to reduce the absolute out of the interfering error as much as possible before ploying the succeeding methods to correct the result. Aapneral rule we can determine a quantity with less maccuracy as it is smaller, so that if the error itself be and the ortor in determining that error will be of a still lower order of magnitude. But in some cases the absolute Pont of an error is of no consequence, as in the index enor of a divided circle, or the difference between a chronometer and astronomical time. Even the rate at which a clock gains or loses is a matter of little importance provided it remains constant, so that a sure calculation of its amount can be made.

2. Differential Method.

When wo cannot avoid the entrance of error, we can te resort with great success to the second mode of ang phenomena under such circumstances that the

Mall remain nearly or quite the same in all the van, and neutralize itself as regards the purposes This modo is available whenever we want a between quantities and not the absolute other. The determination of the parallax aar is exceedingly difficult, because the tax is far less than most of the corrections Theory of Heat,' p. 228. 'Proceedings of the ciety, Nov. 26, 1867, vol. vii. p. 35.

for atmospheric refraction, nutation, aberration, precession, instrumental irregularities, &c., and can with difficulty be detected among these phenomena of various magnitude. But, as Galileo long ago suggested, all such difficulties would be avoided by the differential observation of stars, which though apparently close together are really far separated on the line of sight. Two such stars in close apparent proximity will be subject to almost exactly equal errors, so that all we need do is to observe the apparent change of place of the nearer star as referred to the more distant one. A good telescope furnished with an accurate micrometer is alone needed for the application of the method. Huyghens appears to have been the first observer who actually tried to employ the method practically P, but it was not until 1835 that the improvement of telescopes and micrometers enabled Struve to detect in this way the parallax of the star a Lyræ.

It is one of the many advantages of the observation of transits of Venus for the determination of the solar parallax that the refraction of the atmosphere affects in an exactly equal degree the planet and the portion of the sun's face over which it is passing. Thus the observations are strictly of a differential nature.

By the process of substitutive weighing it is possible to ascertain the equality or inequality of two weights with almost perfect freedom from error. If two weights A and B be placed in the scales of the best balance we cannot be sure that the equilibrium of the beam indicates exact equality, because the arms of the beam may be unequal or unbalanced. But if we take B out and put another weight C in, and equilibrium still exists, it is apparent that the same causes of erroneous

History of Physical Astronomy,' p. 549. Herschel's 'Outlines of Astronomy,' 4th ed. p. 550.

weighing exist in both cases, supposing that the balance has not been disarranged, and that B must be exactly equal to C, since it has exactly the same effect under the same circumstances. In like manner it is a general rule that, if by any uniform mechanical process we get a copy of an object, it is unlikely that this copy will be precisely the same in magnitude and form as the original, but two copies will equally diverge from the original, and will therefore almost exactly resemble each other.

Leslie's Differential Thermometer was well adapted to the experiments for which it was invented. Having two equal bulbs any alteration in the temperature of the air will act equally by conduction on each and produce no change in the indications of the instrument. Only that radiant heat which is purposely thrown upon one of the bulbs will produce any effect. This thermometer in short carries out the principle of the differential method in a mechanical manner.

3. Method of Correction.

Whenever the result of an experiment is affected by an interfering cause to an amount either invariable or exactly calculable, it is sufficient simply to add or subtract this calculated amount. We are said to correct observations when we thus eliminate what is due to extraneous causes, although of course we are only separating the correct effects of several agents. Thus the variation in the height of the barometrical column is partly due to the change of temperature, and since the coefficient of absolute dilatation of mercury has been exactly determined, as already described (p. 395), we have only to make cal

a Leslie's 'Inquiry into the Nature of Heat,' p. 10.

culations of a simple character, or, what is better still, tabulate a series of such calculations for general use, and the correction for temperature can be made with all desired accuracy. The height of the mercury in the barometer is also affected by capillary attraction, which depresses it by a constant amount depending on the diameter of the tube. The requisite corrections can be estimated with accuracy sufficient for most purposes, more especially as we can check the correctness of the reading of a barometer by comparison with a perfect standard barometer, and introduce if need be an index error including both the error in the affixing of the scale and the effect due to capillarity. But in constructing the standard barometer itself we must take greater precautions; the capillary depression depends somewhat upon the quality of the glass, the absence of air, and the perfect cleanliness of the mercury, so that we cannot with confidence assign the exact amount of the effect. Hence a standard barometer is constructed with a wide tube, sometimes even an inch in diameter, so that the capillary effect may be rendered of little account г. Gay Lussac made barometers in the form of a siphon so that the capillary forces acting equally at the upper and lower surfaces should balance and destroy each other, but the method fails in practice because the lower surface, being open to the air, becomes sullied and subject to a different force of capillarity.

In a great many mechanical experiments friction is an interfering condition, and drains away a portion of the energy intended to be operated upon in a definite manner. We should of course reduce the friction in the first place to the lowest possible amount, but as it cannot be altogether prevented, and is not calculable with certainty from any general laws, we must determine it r Watts' Dictionary of Chemistry,' vol. i. pp. 513-15.

D d