The principles of science

by William Stanley Jevons

In other cases a quantitative effect will be the difference of two causes acting in opposite directions. Sir John Herschel invented an instrument like a large thermometer, which he called the Actinometer,‍[234] and Pouillet constructed a somewhat similar instrument called the Pyrheliometer, for ascertaining the heating power of the sun’s rays. In both instruments the heat of the sun was absorbed by a reservoir containing water, and the rise of temperature of the water was exactly observed, either by its own expansion, or by the readings of a delicate thermometer immersed in it. But in exposing the actinometer to the sun, we do not obtain the full effect of the heat absorbed, because the receiving surface is at the same time radiating heat into empty space. The observed increment of temperature is in short the difference between what is received from the sun and lost by radiation. The latter quantity is capable of ready determination; we have only to shade the instrument from the direct rays of the sun, leaving it exposed to the sky, and we can observe how much it cools in a certain time. The total effect of the sun’s rays will obviously be the apparent effect plus the cooling effect in an equal time. By alternate exposure in sun and shade during equal intervals the desired result may be obtained with considerable accuracy.‍[235]

Two quantitative effects were beautifully distinguished in an experiment of John Canton, devised in 1761 for the purpose of demonstrating the compressibility of water. He constructed a thermometer with a large bulb full of water and a short capillary tube, the part of which above the water was freed from air. Under these circumstances the water was relieved from the pressure of the atmosphere, but the glass bulb in bearing that pressure was somewhat contracted. He next placed the instrument under the receiver of an air-pump, and on exhausting the air, the water sank in the tube. Having thus obtained a measure of the effect of atmospheric pressure on the bulb, he opened the top of the thermometer tube and admitted the air. The level of the water now sank still more, partly from the pressure on the bulb being now compensated, and partly from the compression of the water by the atmospheric pressure. It is obvious that the amount of the latter effect was approximately the difference of the two observed depressions.

Not uncommonly the actual phenomenon which we wish to measure is considerably less than various disturbing effects which enter into the question. Thus the compressibility of mercury is considerably less than the expansion of the vessels in which it is measured under pressure, so that the attention of the experimentalist has chiefly to be concentrated on the change of magnitude of the vessels. Many astronomical phenomena, such as the parallax or the proper motions of the fixed stars, are far less than the errors caused by instrumental imperfections, or motions arising from precession, nutation, and aberration. We need not be surprised that astronomers have from time to time mistaken one phenomenon for another, as when Flamsteed imagined that he had discovered the parallax of the Pole star.‍[236]

Methods of Eliminating Error.

In any particular experiment it is the object of the experimentalist to measure a single effect only, and he endeavours to obtain that effect free from interfering effects. If this cannot be, as it seldom or never can really be, he makes the effect as considerable as possible compared with the other effects, which he reduces to a minimum, and treats as noxious errors. Those quantities, which are called errors in one case, may really be most important and interesting phenomena in another investigation. When we speak of eliminating error we really mean disentangling the complicated phenomena of nature. The physicist rightly wishes to treat one thing at a time, but as this object can seldom be rigorously carried into practice, he has to seek some mode of counteracting the irrelevant and interfering causes.

The general principle is that a single observation can render known only a single quantity. Hence, if several different quantitative effects are known to enter into any investigation, we must have at least as many distinct observations as there are quantities to be determined. Every complete experiment will therefore consist in general of several operations. Guided if possible by previous knowledge of the causes in action, we must arrange the determinations, so that by a simple mathematical process we may distinguish the separate quantities. There appear to be five principal methods by which we may accomplish this object; these methods are specified below and illustrated in the succeeding sections.

(1) The Method of Avoidance. The physicist may seek for some special mode of experiment or opportunity of observation, in which the error is non-existent or inappreciable.

(2) The Differential Method. He may find opportunities of observation when all interfering phenomena remain constant, and only the subject of observation is at one time present and another time absent; the difference between two observations then gives its amount.

(3) The Method of Correction. He may endeavour to estimate the amount of the interfering effect by the best available mode, and then make a corresponding correction in the results of observation.

(4) The Method of Compensation. He may invent some mode of neutralising the interfering cause by balancing against it an exactly equal and opposite cause of unknown amount.