The following formulae will serve to convert any given number o degrees on Fahrenheit's scale into the corresponding number of degree on Ite.aumur's and the Centigrade scales, and vice versa.
Let F, a, and c express any corresponding numbers of degrees of the three scales respectively : then N.B. When F is between zero and 32°, the values of a and c are negative, and express the required number of degrees below zero on R6aurnur's and the Centigrade scales. Also, when F, c expresses my given number of degrees below zero on its proper scale, it must be considered as negative.
The scale invented by De l'Isle of St. Petersburg, in 1733, being still occasionally in use, it may be necessary to mention that it is formed by making the space included in each degree equal to one hundred-thousandth part of the whole volume of the mercury ; the zero of the scale is at the point of boiling-water, and between this point and that of freezing-water the space is divided into 150 parts.
It may be observed that the situation of the freezing-point on the scale of a thermometer can be determined with great accuracy if the ball and part of the tube be immersed in pounded ice; for itsis known that water containing ice and snow remains of the same temperature till the ice is entirely dissolved, every accession of heat to the water being employed in promoting the dissolution. But the point of boiling water is far from being so precisely known, since it varies with the density of the atmosphere at the time of making the deter mination. Distilled water in an open vessel, and under a given pressure of the atmosphere, boils at an invariable temperature, except as far as the nature of the vessel may make some difference; for if the heat communicated to the water be increased, the only effect produced is that of driving off a greater quantity of steam in a given time : in a vessel exhausted of the air the water will boil at a temperature expressed by about 70° of Fahrenheit's scale, while in a vessel con structed so as to prevent the steam from escaping it will remain in a liquid state at a temperature of and upwards. In order therefore that the temperatures indicated by different instruments may agree together, it is recommended that this point should be found from water boiling in the open air at a time, if possible, when the height of the mercurial column in the barometer is 30 inches, and when the temperature of the air is indicated by 55' of Fahrenheit's scale.
This effect of the pressure of the atmosphere on the boiling of water was noticed by Fahrenheit in 1724, and M. Deltic, in his Recherches stir les .]edification de l'Atmosphere,' has investigated a formula for determining the height of the boiling-point above the freezing-point of the scale in terms of the height of the mercury in the barometer ; but the English artist, Bird, was the first who applied a correction on account of the state of the barometer, for the purpose of fixing the point of boiling water on the scales of thermometers.
The Royal Society having, in 1776, appointed a committee to con sider the best means of adjusting the fixed points of thermometers, the formula of Deluc was verified and reduced to English measures for the benefit of artists, in the event of their being obliged to make the instruments under different states of the atmosphere with respect to density and temperature; and the following are some of the cor rections which are given by Sir George Shuckburgh for determining the true place of the boiling-point of water. The first column contains the height of the barometer in inches ; and the second, the correction which is to be applied with its proper sign to the number 212 ou Fahrenheit's scale, in order to give the correct number of degrees at which the water will boil under the pressure expressed by the height of the mercurial column. The committee observe that in trying the heat of liquors, the quicksilver in the tube of the thermometer should be heated to the same degree as that in the ball ; or if this cannot be done, a correction should bo applied on that account. (' Phil. Trans.,' vol. lxvii.) Thermometer-tubes should have their bores very slender, and, if possible, perfectly equable in the whole of their length. When there is any inequality in the transverse sections, the best artists make the graduations of the scale vary so that they may correspond to the equal divisions of a cylindrical tube ; and in order to ascertain the relative dimensions of the sections, they cause a small quantity of mercury, about an inch in length, to slide along the interior of the tube, measuring its length in different places ; then, since the lengths are inversely proportional to the areas of the sections, the variations of the former will immediately show the corresponding variations of the latter. The method of calibration, as it is called, recommended by the Kew committee, will be noticed presently. It is usual to give to the bore an oval form, with the broader side towards the front, in order that the mercury or spirit may be easily distinguished at a certain distauce, as by approaching very near the instrument, the heat of the observer's person may affect the length of the column. Mr. Sheepshanks found that tubes with round bores were far more nearly true than those with flat ones. He also approves of bulbs three or four-tenths of an inch in diameter. They should not be too small, or the graduations of the scale will be close together, nor too large, or the instrument will not be sensitive on account of the large body of mercury required to be heated. The bulb should not bo blown by the breath, lest moisture be introduced, but by an India rubber bag.