576 HEAT perfectly trustworthy intrinsic thermoscope ( 15 and 16 above), by means of thermal appliances not represented iu the drawing but easily imagined. This condition being fulfilled, the one desired pressure of the thermometric gas is attained with exceedingly minute accuracy by working the micrometer screw up or down until the oil is brought precisely to a mark upon the manometric capillary. In fact, if the glass and mercury and oil are all kept rigorously at one constant temperature, the only access for error is through irregular variations in the capillary depres sions in the borders of the mercury surfaces. With so large a diameter as the 2 centimetres chosen in the figured dimensions of the drawing, the error from this cause can hardly amount to T ^j- per cent, of the whole pressure, supposing this to be one atmo or thereabouts. For ordinary uses of our constant-pressure gas ther mometer, where the most minute accuracy is not needed, the rule will still be to bring the oil to a fixed mark on the manometric capillary ; and no precaution in respect to temperature will be necessary except to secure that it is approximately uniform throughout the mercury and con taining glass, from lower to higher level of the mercury. The quantity of oil is so small that, whatever its tempera ture may be, the bringing of its free surface to a fixed mark on the capillary secures that the mercury surface below the oil in the lower reservoir is very nearly at one constant point relatively to the glass, much more nearly so than it could be made by direct observation of the mercury surface, at all events without optical magnifying power. Now if the mercury surface be at a constant point of the glass, it is easily proved that the difference of pressures between the two mercury surfaces will be constant, notwithstanding considerable variations of the common temperature of the mercury and glass, provided a certain easy condition is fulfilled, through which the effect of the expansion of the glass is compensated by the expansion of the mercury. This condition is that the whole volume of the mercury shall bear to the volume in the cylindric vertical tube from tha upper surface to the level of the lower surface the ratio (A. - 3-o-)/(A - o-), where A denotes the cubic expansion of the mercury, and o- the cubic expansion of the solid for the same elevation of temperature, it being supposed for simpli city of statement that the tube is truly cylindric from the upp3r surface to the level of the lower surface, and that the sectional area of the tube is the same at the two mercury surfaces. The cubic expansion of mercury is approximately seven times the cubic expansion of glass. Hence (x-J^Ax-fl-)- (7-^/6-1-111^ Hence the whole volume of the mercury is to be about I lll times the volume from its upper surface to the level of the lower surface ; that is to say, the volume from the lower surface in the bend to the same level in the vertical branch is to be |- of the volume in the vertical tube above this surface. A special experiment on each tube is easily made to find the quantity of mercury that must be put in to cause the pressure to be absolutely constant when the surface in the lower reservoir is kept at a fixed point rela tively to the glass, and when the temperature is varied through such moderate differences of temperature as are to be found in the use of the instrument at different times and seasons. A sheet-iron can containing water or oil or fusible metal, with external thermal appliances of gas or charcoal furnace, or low-pressure or high-pressure steam heater, and with proper internal stirrer or stirrers, is fitted round the bulb and manometric tube to produce uniformly throughout the mass of the thermometric gas the temperature to be measured. This part of the apparatus, which will be called for brevity the heater, must not extend so far down the manometric tube that when raised to its highest tempera ture it can warm the caulking mercury to as high a temperature as 40 C., because at somewhat higher tem peratures than this the pressure of vapour of mercury begins to be perceptible (see Table V. below), and would vitiate the thermometric use of the pure hydrogen or nitrogen of our thermometer. To secure sufficient coolness of the mercury it will probably be advisable to have an open glass jacket of cold water (not shown in the drawing) round the volumetric tube, 2 or 3 centimetres below the bottom of the heater, and reaching to about half a centi metre above the highest position of the bottom of the piston. 67. It seems probable that the constant-pressure hydrogen or nitrogen gas thermometer which we have now described may give even more accurate thermometry than Regnault s constant-volume air thermometers ( 2*4 above), and it seems certain that it will be much more easily used in practice. We have only to remark here further that, if Boyle s law were rigorously fulfilled, thermometry by the two methods would be identical, provided the scale in each case be graduated or calculated so as to make the numerical reckoning of the temperature agree at two points, for example, C. and 100 C. The very close agreement which Ilegnault found among his different gas thermometers and his air thermometers with air of different densities ( 25 above), and the close approach to rigorous fulfilment of Boyle s law which he and other experimenters have ascer tained to be presented by air and other gases used in his thermometers, through the ranges of density, pressure, and temperature at which they were used in these thermo meters, renders it certain that in reality the difference between Ilegnault s normal air thermometry and thermo metry by our hydrogen gas constant-pressure thermometer must be exceedingly small. It is therefore satisfactory to know that for all practical purposes absolute tempera ture is to be obtained with very great accuracy from Regnault s thermometric system by simply adding 273 to liis numbers for temperature on the centigrade scale. It is probable that at the temperatures of 250 or 300 C. (or 523 or 573 absolute) the greatest deviation of tem perature thus reckoned from correct absolute temperature is not more than half a degree. 68. The thermometric scale being now thoroughly estab lished in theory and practice ( 33-69 and 18-30), we are prepared to define, without any ambiguity, the expressions thermal capacity and specific heat with reference to matter at any temperature and in any physical condition. Definition 1. The thermal capacity of a body (whether it be a portion of matter homogeneous throughout or of homogeneous substance in two different conditions as liquid and steam, or solid and vapour of solid, or a piece of apparatus consisting of different parts as glass and metals, and containing as the case may be liquids or gases, subject only to the condition that the whole matter considered is at one temperature) is the quantity of heat required to raise its temperature by one degree on the absolute thermo- dynamic scale. Definition 2. The specific heat of a substance is the thermal capacity of a stated quantity of it. This stated quantity is generally understood to be the unit of mass, unless some other definite quantity is explicitly designated, as for instance the quantity of the substance which occu pies unit of volume at some definite pressure and tem perature, for instance, one atmo and temperature 273 absolute. It is of no consequence what unit of mass is , chosen provided it be the same as that which is used in defining the thermal unit ; but, unless the contrary be explicitly stated, we always understand one gramme as the unit of mass and the thermal unit as the quantity of heat Cone! sion < ther- mom< "Tin oapa ties "spe
heat.