I have found it convenient to proceed in the observations rather differently from the manner indicated by Guillaume. The tube T is placed in a calorimeter containing about a litre and a half of water, and that again is surrounded in an outer jacket. The latter is filled with water about 2° above that in the calorimeter, so that the thermometer is kept slowly rising. The air-space in T being exhausted, a few observations are taken at measured intervals of time, air is suddenly admitted, and a further series of readings are taken, as in the following example : Taking the arithmetical mean between the first seven observations, it is found that the average temperature corresponding to the time 17m was 159.139, and by combining the observations in pairs in the usual fashion we deduce the average rate of rise per interval as 108. Hence 159.139 +4 × 10·8=159.571 gives the calculated reading at 2h 19m, but after the seventh reading the air was admitted, so that the last seven observations were taken at full atmospheric pressure. The reduction being made in exactly the same fashion, another reading is deduced for the time 2h 19m, viz., 163-583. The difference betwen the two gave 4012 divisions of the thermometer as the effect of a change of pressure of 72.6 centim. A number of observations of a similar character were taken and are collected in Table IV. They were always so combined that the observation at atmospheric pressure followed that at reduced pressure. Otherwise a fall of the thermometer would have taken place, and owing to the sticking of the thread the first few observations would have been uncertain. Mean excluding last number. 0563 The observation which is quoted in full above is the one which shows greater irregularities in the rise than the others, and it gave the result (0548) which differs most from the Part of the discrepancies between the different observations is no doubt due to the irregularities in the graduation of this thermometer, but the result is sufficiently accurate for the purpose for which it is intended. mean. Reduced to degrees, the final results are as follows: Knowing the distance of any scale-division from the centre of the reservoir, we may calculate the corresponding pressure correction. A table was calculated once for all, giving in this way the differences between the readings of the thermometer in the horizontal and vertical positions for every 50 divisions. The numbers are given in the last column of Table I. It will be noticed that an error of 1 per cent. in the pressure correction would cause a difference of less than 0°.002 on a range of over 30°, which difference of course would be quite inappreciable. Some experiments were made to find how much the thermometer A lagged behind when placed in water the temperature of which was uniformly rising. They were carried out according to the manner described by Thiesen*, and gave sufficiently consistent results showing the time constant to be 12. *Guillaume, Thermomètrie, p. 187. The Apparatus used in the Comparison of Thermometers. The comparison of the thermometers was carried out in a bath made of sheet-iron having a length of 114 centim. and width and depth of 20 centim. This bath was placed for protection inside a wooden box, on the bottom of which it rested upon two ribs covered with guttapercha, so that the inner vessel was practically insulated thermally. The wooden box K is shown in Pl. VI. fig. 4, placed on two stools and in front of a table T. A frame FF fitted into the bottom of the bath and carried 38 turns of No. 21 nickel wire, the ends of the wire being brought to binding-screws placed at two of the corners of the outer box. With a suitable electric current passing through the wire, the temperature of the water in the bath could either be kept constant or increasing at a desired rate within a range from 1° to 15° above the temperature of the room. The whole of the interior of the bath, also the frame, and wire were coated with white paint. A tank of water of this kind containing over 40 litres cannot with any reasonable amount of stirring be kept at a sufficiently uniform temperature. The bulbs of the thermometers were therefore placed into a small copper box B, within which the stirring was much more efficient. The box was 15 centim. in breadth and 10 centim. deep, and was rigidly suspended from a wooden cross-bar resting on the side of the case. Vertically down the centre of the box passed a spindle carrying a double 3-bladed screw-paddle; one of these paddles was fixed just below the bottom of the box, and the other just inside the box, as shown in the figure. There was a further paddle at the other end of the bath, the power being supplied by two Cuttriss motors. The stirring was sufficient to secure a very approximately uniform temperature all over the bath. The box B sheltered the thermometers from outside radiation, and protected them against jets of hot water coming from the heated water, the paddle below the box being specially intended to prevent irregular heating of the box. The water inside B was thoroughly stirred, a mere rotation of the water being prevented by oblique diaphragms fixed to the sides. One further precaution was found advisable. Owing to evaporation and radiation the water lost heat at its upper surface, and the thermometers had to be protected against an inflow of cold water through the opening through which the spindle passed. This was done by a horizontal disk H fixed to the spindle, and by covering the whole box as far as possible with asbestos. The thermometer bulbs passed through a window W 3.3 centim. wide, cut into one side of B, and a sliding shutter of thin brass served to close the window partially so that there was only very little, if any, circulation of water between the inside and the outside of the box. The thermometers were read by a small microscope M which could be moved parallel to itself along the upper edges of the outer vessel. The microscope was mounted so that it also had a free motion at right angles to the length of the box. This double motion allowed it to be moved quickly above the ends of the threads of any two thermometers to be compared. Latterly two microscopes were used, one for each of the thermometers. The water was covered by a sheet of glass, which kept the surface calm in spite of the disturbance set up by the stirring. The thermometers were supported in triangular grooves cut into two adjustable brass uprights P, P. Care was always taken to set them horizontally by first placing a straight edge across the uprights and levelling. This horizontal position is not necessary when the thermometers are transparent, so that their divisions can be read either from the front or from the back, as errors of parallax are thus eliminated. But when this cannot be done the reading microscope must be placed at right angles to the thermometer, and then it is most convenient to have one vertical and the other horizontal. The optic axis of M was put into the vertical position by keeping at a proper distance in the bath a horizontal glass-scale silvered at the back. When the adjustment is correct the two images of the division which is in the centre of the field of view should cover each other, otherwise there is parallax. As the object of the adjustment is to avoid parallax in the reading of the thermometers, this method answers very well if the glass-scale is about 2 millim thick. It is instructive to notice how great the danger of error due to parallax is when sufficient care is not taken to read only in the centre of the field of view. The Method of Comparison and Reduction. Two observers were found necessary to carry out a satisfactory comparison, one calling out the time at regular intervals and taking the notes, the other reading the thermometer. An example will show the method adopted. On June 20, 1893, a comparison was made between Joule A and a Tonnelot Standard No. 4929. Both thermometers were kept in the bath at a temperature of 18° for several hours, then their freezing-point was determined and found as follows: Tonnelot, No. 4929: 00082 (mean of 4 observations). : 23.23 (1 6 Joule A ). The air of the room was above that of the bath, the temperature of which was slowly rising without the use of an electric current. The thermometers being replaced in the bath, readings were taken alternately every quarter minute, first with the divisions in front of the thread, and finally with the divisions behind. The numbers obtained were as follows: The zeros were now again determined and found :— Tonnelot 0.0075 (mean of 4 observations). Joule A 23.192 ( A small correction is applied to the Joule thermometer for the lagging behind, and we thus got for corresponding temperatures: Tonnelot 18.538 Zero . . ⚫008 Joule 458.99 23.21 In the first series of comparisons the Joule A was compared in this way with the Tonnelot thermometer. The latter had been calibrated and investigated at the Bureau International des Poids et Mesures, so that its indications could at once be reduced to the normal scale. The results of the comparison are given in Table V. The first column gives |