# The Encyclopedia Americana (1920)/Zero

**ZERO**, *in mathematics*, 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
quantities. 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 “zero” of
the given function. In infinitesimal analysis,
infinitesimal quantities arc sometimes called
zeros. This usage is incorrect, and it leads to
confusion of thought. An “infinitesimal” has
an actual magnitude, and although that magnitude
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 measurements on that scale are reckoned. In thermometry (q.v.) it is customary to distinguish three different kinds of zeros. These are, respectively, (1) the arbitrary zero, (2) the “natural” zero and (3) the “absolute” zero. The arbitrary zero on such a scale is a zero that is selected arbitrarily, as a convenient point of reference; the selection being governed by practical considerations of convenience, or by the facility with which the point can be experimentally determined. (See Thermometer). The “natural” zero is employed chiefly in connection with the gas thermometer. In a gas thermometer in which the temperature is indicated by the expansion of a given volume of gas at constant pressure, the “natural” zero is the temperature 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 between the freezing and boiling points of water. Similarly, in a gas thermometer in which temperature 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 thermometers that are in actual use are not identical, but their positions differ only by a 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 substances. It happens that the “absolute” zero has nearly the same position on the thermometer scale as the “natural” zeros of the various gas thermometers that are in use, and this fact has led to a great deal of confusion in popular and semi-scientific writings upon the subject of temperature, the “natural” and “absolute” zeros being 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 thermometer (whether at constant volume or at constant pressure) is a few hundredths of a centigrade degree lower than the true “absolute” zero. If further research bears out this opinion, then it is plain that the “natural” zero of the hydrogen thermometer can never be attained; for the “absolute” zero, being the temperature corresponding to absolute cold, is the lowest temperature that can possibly have a real existence. On the absolute centigrade scale, the temperature of the “absolute” zero is approximately 273.10° below the freezing point of water. This estimate is probably in error by a few hundredths of a degree. There is no theoretical reason why the position of the “absolute” zero cannot be determined to the thousandth of a degree; but the experimental data required for such a determination are not yet available. See Thermodynamics.