ZERO, is mothematics, the absence of magnitude; the remainder that is obtained when any quantity is subtracted from itself ; nothing, considered as a quantity; that which separates real positive quantities from real negative quan tities. Zero is denoted by the symbol 0 'cipher'), and this symbol itself is often called zero.' In the theory of functions, any value of a variable which reduces a given function of that variable to zero is called a •zeros of the given function. In infinitesimal analysis. infinitesimal quantities are sometimes called zeros. This usage is incorrect, and it leads to confusion of thought. An 'infinitesimal' has an actual magnitude, and although that magni tude is smaller than any quantity that can be definitely stated or assigned, the fact that it exists distinguishes the infinitesimal from zero, properly so-called.
In physical measurement, the 'zero' of any scale is the starting point from which measure ments on that scale are reckoned. In ther mometry (q.v.) it is customary to distinguish three different kinds of zeros. These are, re spectively, (1) the arbitrary zero, (2) the raP zero and (3) the 'absolute' zero. The arbitrary zero on such a scale is a zero that is selected arbitrarily, u a convenient point of reference; the selection being governed by prac tical considerations of convenience, or by the facility with which the point can be experunen tally determined. (See TmamomEruit). The 'natural' zero is employed chiefly in connection with the gas thermometer. In a gas thermom eter in which the temperature is indicated by the expansion of a given volume of gas at con stant pressure, the 'natural' zero is the tem perature at which the volume of the gas would just vanish, if the contraction of the gas were to follow, at very low temperatures, the law of variation with temperature that prevails be tween the freezing and boiling points of seater. Similarly, in a gas thermometer in which tem perature is measured by the change in pressure of a mass of gas that is confined at constant volume, the 'natural' zero is the temperature at which the pressure of the gas would just vanish, if the law of variation of pressure were the same, at very low temperatures. as it is
between the freezing and boiling points of water The 'natural* zeros of the various gas ther mometers that are in actual use are not iden tical, but their positions differ only by • few degrees, at the most.
The 'absolute' zero of temperature is the temperature that a body would have. if it were absolutely deprived of heat; and this 'absolute' zero is identically the same for all snhstancet It happens that the 'absolute' zero has nearly the same position on the thermometer soak as the 'natural' zeros of the various gas ther mometers that are in use, and this fact has led to a great deal of confusion in popular and it-un scientific writings upon the subject of tempera ture, the 'natural' and 'absolute' zeros beige very commonly confounded with one another. The 'absolute zero is slightly lower than the "natural* zero of any gas thermometer that we know of, with the possible exception of the 'natural' zero of the hydrogen thermometer. There is some reason for believing that the 'natural' zero of the normal hydrogen ther mometer (whether at constant volume or at constant pressure) is a few hundredths of a centigrade degree lower than the true 'abso lute' zero. If further research bears out this opinion, then it is plain that the •natural* zero of the hydrogen thermometer can never be at tained; for the 'absolute' zero, being the tem perature corresponding to absolute cold, is the Ion est temperature that can possibly have a real existence. On the absolute centigrade scale, the temperature of the 'absolutes zero is ap proximately 273.10' below the freezing point of water. This estimate is probably in error by a few hundredths of a degree. There is no the°. retical reason why the position of the °abso lute" zero cannot he determined to the thou sandth of a degree; hut the experimental data required for such a determination are not yet available. See THatMODYNAMIc3.