Page:The American Cyclopædia (1879) Volume XIV.djvu/120

 112 PYROMETER ry, and that their true difference of levels has been correctly determined. To graduate the apparatus, the globe is surrounded with melt- ing ice and the mercury is brought to the level R in the tube E ; then the height of the ba- rometer, &, and the height, A , of the mercu- ry in C above the level R in E, are observed. We will call 5 + ^o=Ho. The heights bo and ho must be reduced to what they would be if the mercury in the apparatus were at 0. To measure any temperature,, we expose the globe to this temperature for a length of time sufficient to heat uniformly the contained air, which is .known to be the case when the mer- cury is stationary in B and in 0. When this condition has been reached we obtain the height A, which is the difference of the read- ings of the levels of mercury at R and in reduced to 0., and then read the height I of the barometer reduced to 0. Calling h + b=ll, we have for the sought tempera- ture * = .oo366 H 5 r-ri^TT in which formula 8c is the cubical expansion of the porcelain or other material forming the globe. In this formula the volume of air contained in the ca- pillary tube E, up to the mark R, is neglect- ed ; but when the most accurate determina- tions are desired, it must be remembered that this portion of air in the pyrometer remains at or about the temperature of the air sur- rounding the part of the apparatus outside of the furnace. This temperature, which we will call t', can be determined by means of a thermometer placed close to the tube E. Now to obtain the exact value of the tempera- ture to which the globe has been exposed, we must add to the value of t as given above the following correction : t. ' V' H 1 + -00360W" in which expression represents the volume of the globe, t' the volume of the capillary tube from its junction with the globe up to the mark R, and v the reading of the thermometer con- tiguous to the tube E. The ratio is found o by determining the weight of the globeful of mercury up to the junction with it of the capil- lary tube, and the weight of the mercury in the capillary tube from its junction with the globe to the point R. If p be the weight of the mercury in the globe alone, and P the weight when both globe and capillary tube are filled up to the mark R,'then -=-~^. The v p determinations thus made with the air pyrome- ter are universally accepted as standards with which to test all other methods of pyrometry, and the confidence placed in any pyrometer increases with the constancy and closeness of its agreement with the determinations made with the air pyrometer. 4. The range and ac- curacy of pyrometers using the melting points of solids are limited to the number of metals and definite alloys whose melting points have been determined with precision. The method evidently gives only successive steps in eleva- tion of temperature. Some of these steps ac- cording to the determinations of fusibility by Pouillet, who used an air pyrometer in his ex- periments, are given in the article FUSIBILITY. 5. The method of pyrometry by the chemical decomposition of solids is described in the article DISSOCIATION, and more detailed infor- mation may be found in Lamy's papers pub- lished in the Compte* rendus of the institute of France, vol. Ixix., p. 347, and vol. Ixx., p. 393. 6. In measuring high temperatures by the heat- ing of water with heated platinum or other metal, according to Pouillet's method, we heat to the temperature to be measured a mass of the metal and then suddenly immerse it in a mass of water. Knowing the weight of the metal and its specific heat, and the weight of the water and its temperature before and after the immersion of the metal, we can compute the temperature of the latter before its immer- sion as follows : Let m be the weight of the metal, c its specific heat, and t its high tem- perature before immersion in the water. Let m' be the weight of the water, and t' its tem- perature before the introduction of the hot metal. The specific heat of water is unity. The thin metallic vessel containing the water has a weight, and its specific heat is ft. The thermometer which shows the amount of elevation of temperature of the water by the heated metal has a portion of its length heated ; let us call the weight of this part of the thermometer, and its specific heat d. Finally let 6 be the temperature of water, met- al, vessel, and thermometer after the immer- sion of the heated metal, and at the moiiient they have all reached the same temperature. The metal in falling in temperature from t to has lost t 6 degrees, and a quantity of heat equal to mc(t6). The water in being heated from t' to 6 has gained in temperature 8 t' degrees, and a quantity of heat equal to m 1 (Qf). For a similar reason the vessel and the thermometer which partake of the heating of the water gain respectively ab(6 t 1 } and ed(0t'). Hence the whole quantity of heat gained is (m' + ab + ed)(6 $'), or m,(0t') if we make m i = m' + ab + ed ; m t is then called the equivalent mass of water. In forming an equation between the quantity of heat re- ceived and the quantity of 'heat lost we have mc(t-e) = mtft 1 ) whence, the tem- perature of the heated metal, is expressed by t = - + 6- In using this method Pouil- let heated a ball of platinum in a crucible of the same metal, and the vessel containing tho water had a wire cup in its centre into which the heated platinum mass was thrown. One of the elements of accuracy in this method is the precise knowledge of the specific heat of platinum at high temperatures. Pouillet made this a special study, and determined it up to 1,200 C., using an air thermometer in obtain- ing the successive temperatures. To obtain