HEAT 565 Y ntific The graduation is clearer and more easily read in this kind of thermometer than in any other. The complete protection of the paper scale against damp and damage afforded by its hermetically sealed glass envelope gives a perennially enduring quality to this form of thermometer, 1 such as is passessed by no others except those graduated on the glass ; and the lightness of the paper renders its proper attachment to the inner stem, by gum or otherwise, thoroughly trustworthy, when once well done by the maker of the instrument. For scientific purposes the paper scale was too cheap, and common, and good, to rmo- sa ^ s ^y the ideas of those instrument makers who in
- er of Germany and France substituted the heavy gradu-
cury ated slab of opal glass for the paper, while still
- lass. adhering to the bath thermometer pattern in her
metically enclosing this scale in an outer containing glass tube, very unnecessarily, as the glass scale, unlike the paper scale, does not require any such protection. This is now, however, a thing of the past. At the present time all high-class scientific thermometers are graduated on the glass of the stem without any attached scale of other material. Except in respect to ease of reading the indications this simplest form is, both for popular and for scientific purposes, superior even to the German bath thermometer with hermetically sealed paper scale; arid this will be the form intended when we speak of a mercury thermometer, or a spirit thermometer, or a liquid thermometer, without any special qualification. 29. Properties of Matter concerned in Liquid Thermometers. The indications of the liquid ther mometer depend not only upon the expansion of tho liquid with heat ; they are seriously modified by the expansion experienced also by the containing solid. The instrument in fact consists of a glass measure measuring the bulk of a liquid. If the bulk of the hollow space in the glass and the bulk of the liquid expand by the same amount, the apparent bulk of the liquid as thus measured will remain unchanged. Now, supposing the glass to be perfectly homogene ous and isotropic (see art. ELASTICITY, 38, 39, and chap. i. of Mathematical Theory), and the bulb to be free from internal strain, the glass will, when warmed uniformly, expand equally in all directions, and the volume of the hollow space will be altered in the same ratio as the volume of the glass itself. Hence the indications of the thermometer depend on a difference between the expansion of the glass anl the expansion of tlue liquid. 30. To define exactly the indications of a ther mometer founded on the expansion of a fiuid, let the volume of the bore of the stem between two consecu tive divisions be called for brevity a degree measure. The degree measure is habitually made as nearly Fig< 5- as possible equal throughout the scale in the best mercury- in-glass thermometers ; and, as we shall see ( 62), it ought to be so in an air thermometer to give indications agreeing with the absolute thermodynamic scale nearly enough for the most accurate practical thermometry. But in practical spirit-thermometers the divisions are made to correspond as nearly as may be to degrees of a standard mercury or air 1 Provided it is never exposed to "browning" temperatures (or temperatures high enough to produce partially destructive distillation of the paper). Instrument makers ignoring this caution have actually made it with graduation extending to such temperatures for kitchen use. The result is that it gets injured to the extent of partially bro-wning the hermetically sealed paper, and befogging the inner surface of the glass envelope, by applying it to test the temperature of melted fat in cooking. For this purpose the simple scientific ther mometer with graduation on the glass stem is proper. thermometer, and the degree measures are therefore (Table II. below) larger and larger from the lower to the upper end of the scale. For the purpose, however, of comparing the thermometric performances of different liquids, we shall suppose the degree measure to be of equal volume through out the scale in each case. Let 1ST be the number of degree measures contained in the volume of the bulb and stem up to the point marked zero on the scale ; and let D* denote the volume, at any temperature t, of the degree measure reckoned in absolute units of volume. The volume of the bulb and stem up to zero will be ND ( . On the sup position of perfect isotropy and freedom from strain in the glass, N will be independent of the temperature and D</D will be the ratio of the volume of any portion of the glass at temperature t to its volume at the temperature called zero, if D denote the volume of the degree measure when the glass is at this zero temperature. Let now Lj and L denote the volumes of the whole liquid in a thermo meter at the two temperatures t and ; we have L<, = ND . And if s be the number of scale divisions marking the place of the liquid surface in the thermometer tube, we have Lt=(N-f-s)D t . Hence = (l+s/N)D,/D . Hence s = NU^,- - 1 . Hence, if E| denote augmentation of bulk of the liquid, and E ( augmentation of bulk of each degree-division of the stem, when temperature is raised from to t, each reckoned in terms of the bulk at zero tem- pcTature, we have This is the formula for the ordinary liquid thermometer. It is also applicable to the constant pressure air ther mometer, in which, with proper instrumental means to keep the pressure constant, air is allowed to expand or contract with elevation or depression of temperature, and its volume is measured in a properly shaped glass measuring vessel. We may arbitrarily determine to take s as the numeric for the temperature which is indicated by any one particular thermometer of this kind, for instance, a methyl butyrate thermometer, or an alcohol thermo meter, or a mercury or an air thermometer. But if s = t for any one individual thermometer, it cannot be exactly so for any other. In the first advances towards accurate thermometry it was taken so for the mercury-in- glass thermometer, and by general consent it was con tinued so until it was found ( 25) that different mercury- in-glass thermometers, each made with absolute accuracy, differ largely in their reckonings of temperature. 31. Numerical Thermometry. In 12 above, a perfectly Thermo definite and very simple basis for numerical thermometry meter was described, not as having been adopted in practice, but dcfine 1 as an illustration of a very general principle upon which c nstan reckoning of temperature may be done in numbers. The the spe- principle is this. Two definite temperatures depending on cific properties of some particular substance or substances are ]ieat of first fixed upon and marked by two arbitrary numbers, er< as, for instance, the temperature of melting ice marked zero, and the temperature of steam issuing from boiling water under atmospheric pressure of exactly one atmo, marked 100. Then any intermediate temperature i! is obtained by taking t parts of water at 100 and (100 - t) parts at and mixing them together. As said in 12 this method is limited to temperatures at which liquid water can be obtained, and therefore practically it is only applicable between the melting point of ice and the boiling point of watef, under ordinary atmospheric pressure. 32. Any other liquid of permanent chemical constitu- Thermo- tion might be used instead of water as the thermometric metry substance in thermometry founded on mixtures ; so even 1>y mix " might a powdered solid. Oil if used instead of water would have the advantage of being available for higher temperatures ; but want of perfect definiteness and con stancy of chemical constitution is a fatal disqualification for it as the fundamental thermometric substance for ther-
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