We could evidently divide the space between the boiling point and the freezing point into as many equal "degrees" as we chose; for there is no reason, in the nature of things, why a °de gree could not have any one size, just as well as any other size. It is desirable, however, to have some uniform practice in this respect, and hence the manufacturers of thermometers in variably conform to one or the other* of three standard systems. In France, and also for scientific work in nearly every country, it is customary to follow the plan introduced by Professor Celsius of Upsala, which consists in dividing the fundamental interval between the two fixed points into 100 equal parts, the freez ing point being called "zero,* or 0°, and the boiling point 100°. This method of graduation is lcnown as the "Centigrade* (or "hundred degree") system. For general purposes in the United States and in England, it is far com moner to graduate thermometers according to the system introduced by Fahrenheit of Dantzig, about 1714. In this system the interval between the freezing and boiling points is divided into 180 equal spaces, or gdegrees"; but the freezing point is here called 32° and the boiling point 212° (32° + 180° ==212°). There has been much discussion as to the reason that Fahren heit had for dividing the fundamental interval into 180 equal parts; but there can be no doubt but that his zero point was intended to repre sent the greatest cold that was known in his day, this being obtained by mixing salt and snow. By adopting this lowest temperature as his zero, he probably sought to avoid the use of negative temperatures; but in these days when temperatures several hundred degrees lower than his zero can be produced, the significance of the 32 is iost, and we now adhere to it sim ply from custom. The third thermometric sys tem that has been used to a considerable extent is that due to Reaumur. In this system the fundamental interval is divided into 80 equal degrees, and the freezing and boiling points are marked 0° and 80°, respectively. This method of graduation is extensively used in Germany upon thermometers intended for household purposes; but for most other pur poses in that country it has given way to the Centigrade system.
After a thermometer that is to be used for precise measurement has been made and grad uated, it is subjected to certain experimental in vestigations, for the purpose of ascertaining the errors to which it may be liable. One of the most important of these investigations relates to the "calibration error," which is due to such irregularities of calibre as the bore of the stem may possess. In order to determine the calibra tion errors, a thread of mercury of suitable length is detached temporarily from the column in the stem, by shaking the instrument. An expert in this kind of work can usually detach a thread of almost any length that he pleases, whether it be long or short. The instrument is then inclined so that the detached thread may be brought into various positions in the stern; and in certain of these positions its length is observed with great care. The volume of the thread being constant, it is plain that its length will be greater where the calibre of the tube is small than it will be where the calibre is rela tively large. The details of the operation of determining the calibration errors of a ther mometer are very involved; but the general plan consists in observing the lengths of de tached threads of mercury at different points of the stem and then computing from these ob served lengths, the relative areas of cross-sec tion of the stem-calibre at various points. It is then possible to calculate a table of calibration corrections, by the aid of which it will be easy to correct any given reading of the instrument, so as to'find what reading would have been ob tained if the item had been of absolutely uni form calibre throughout.
Prominent among the other sources of er ror, there are four that merit special attention. (1) In the measurement of a temperature, the bulb of the thermometer is supposed to be fully exposed to that temperature; but since the mercury in the stem must be seen in order to be read, it often happens that the stem of an instru ment is necessarily exposed to conditions of temperature that are materially different from those to which the bulb is subjected. Hence there is often a °stem error" to a thermometer, due to the fact that the mercury thread in the stem is colder (or hotter) than that in the bulb, and, therefore, 'shorter (or longer) than it really ought to be. The magnitude of this stem error will obviously vary with the conditions under which the thermometer is used. It is always uncertain in amount and hence it is customary, in well-executed scientific work, to design the apparatus that is to be used (including the thermometer itself), with special reference to the desirability of keeping the stem error. as
small as possible. (2) When the barometric pressure upon the bulb of the thermometer varies, the bulb yields elastically to these vari ations and often to an extent quite sufficient to influence the reading of the Instrument by an amount that cannot be neglected. The error due to this cause can be determined and elimi nated by means of the *external pressure co efficient," which is obtained by subjecting the thermometer, at some fixed temperature, to a known change of external pressure and noting the alteration of the reading that this variation of pressure produces. (3) The pressure of the mercury upon the inner surface of the bulb may from several causes, one of which is the position of the thermometer itself. If the stem is in a vertical position, the bulb will be sub jected to a pressure due to the height of the column of mercury in the stem; and when the thermometer is horizontal, this static pressure will be absent. In small thermometers the error due to this cause is unimportant ; but in instru ments of high preci4ion, in which the stem may be several feet in length, it must receive due consideration. The constant which is used for correcting for this source of error and which is to be determined by experimenting with the thermometer in different positions but at the same constant temperature is called the "in ternal pressure coefficient." (4) It is found that the glass of which a thermometer is composed exhibits certain anomalies in its expansion and contraction, when its temperature is altered. These result in an apparent variation in the po sition of the "zero point" of the thermometer, which is very troublesome when measurements of the highest precision are to be made. It is on account of this anomalous variation in the position of the zero point that the three kinds of glass mentioned in the earlier part of this article are recommended for the manufacture of the bulb; the variation of the zero having been studied in the case of these species of glass with great care. The phenomena as ob served in the case of *verre dui." are thus described by Guillaume: "When a verre dur thermometer is quickly exposed to a tempera ture of C., after having reposed for a con siderable time at the ordinary temperature of the laboratory, its zero point falls with such rapidity that after an exposure of one minute at 100° C. the displacement is practically com plete. If the thermometer is then placed in ice-water, its zero ascends, for the first few moments, at the rate of about 0.001° C. per minute; but this rate diminishes rapidly. When a thermometer is maintained at a constant temperature, its zero point rises little by little and the change can be traced plainly for sev eral years. For thermometers of verre dur, the gradual rise at constant temperature amounts to about C. per month when the ther mometer is two years old; and at the end of four or five years the motion is found to have diminished to about C. per annum." The ideal way of measuring a temperature, with a thermometer made of one of the three glasses mentioned above, is as follows: The thermometer is exposed to the temperature that is to be measured, and its zero point falls to a certain (presumably unknown) position. Af ter the instrument has been read, it is intro duced, as quickly as is consistent with its safety, into a mixture of water and pulverized ice. The mercury sinks at once and soon at tains a stable position, which, on account of the slowness of .the change of zero with falling temperature, is taken to be the zero corresponding to the higher temperature to which the instrument has been previously ex posed. In accordance with this plan, the temperature to be measured is found by sub tracting the subsequent reading in ice-water from the reading obtained at the temperature to be determined. The method here outlined, for eliminating the effect of variations in the zero point of a thermometer, is known as the °method of movable zeros," and is now adopted at practically all of the centres of ac curate thermometry except Kew, for tempera tures between the freezing and boiling points. It is not yet possible, by any method of pro cedure, to, determine temperatures more than a few degrees below the freezing point, or more than a hundred degrees (Centigrade) above the boiling point, by the aid of a mercury-in-glass thermometer, with a precision comparable with that which is attainable within the fundamental interval that lies between C. and 100° C.