Cleveland. Since the bars, taken with the correction certified by the Société Génevoise, give the same value for the metre within the limits of the precision of the observations, the length of my bar is perhaps well enough known. At 20.9°, by observations with two thermometers on each bar, in a room whose temperature varied half a degree during the six hours of the observations, my bar was found to be 1.000114 metres in length. If we assume for my bar the coefficient of expansion of glass used in computing the table for reducing the height of the barometer given in the compilation of Landolt and Boernstein, and with this compute the length at 0°, the value obtained will be uncertain to some extent, but it will reproduce the true value at 20.9°, and will enable us to use these tables for the necessary reductions. We then have

Length of my bar at 20.9°.

Expansion for 20.9°, 20.9 X .0000085
Length of bar at o°

1.000114

.000178

.999936

The errors of the graduation were found to be insignificant for our purpose. The observations were therefore reduced by multiplying the observed pressure by the factor

.999936.*

17.-THE BALANCE USED IN THE FIRST SERIES OF EXPERIMENTS.

The balance used in the present series of experiments was made by Becker of Rotterdam, and will carry 1200 grammes in each pan. It was procured for this investigation, and has been used for nothing else. During these experiments, it was mounted on a case of non-conducting materials, thirteen centimetres thick, with doors of the same thickness. It was placed in a small room containing no source of heat, but surrounded on all sides with rooms kept as nearly at constant temperature as is usual in large buildings.

Much difficulty was experienced at first in determining the difference of weight between the globe and its counterpoise with sufficient accuracy and within a reasonable time. This difficulty is mostly due to currents of air affecting unequally the two globes, or, possibly, the two pans of the balance. The balance itself was enclosed in a case which had doors for manipulating the weights, and had also two openings in front, each some three centimetres in diameter. The lower of these contained a lens by which light could be condensed on the scale over which * Since this paper was written, Professor Dayton C. Miller has had these two metres compared by the United States Coast and Geodetic Survey with the national prototype metre, which is in its custody; with the result that they are a thirty-thousandth part too short. It is too late to correct the reduction of each observation on density which is mentioned in this paper, but the means of each series, and the final values, have been corrected by increasing each by a thirtythousandth part,

the pointer of the balance moves. Through the other, the observer could watch the vibrations of the balance with very little possibility of disturbance of its indications by his presence. The arrangement is shown in Figure 9, which is in part a section from the front to the rear of the balance through its centre. With this arrangement, it became certain that most disturbances were due to causes affecting the globes.

The inside of the case, seen in Fig. 10, was, therefore, lined with sheet metal, so as to lessen the entrance of air currents through the joints of the woodwork. But the opening for an instant of the room in which the balance stood, so as to admit warmer or colder air, would in a few minutes disturb the indications of the balance, not of course by changing the temperature within the case, but by producing currents of air in the room which penetrated the case and affected the globes unequally. Then the remaining joints in the woodwork around the doors were closed during a weighing by pasting paper over them; this lessened the disturb ances, but not sufficiently. A metal box was then made, seen in Fig. 10, which had a cover with two openings for the suspension of the globes, but had no opening except at the top. The globes being put in this box, it was covered, and placed in the non-conducting case mentioned before, and the globes were hung on the balance. Since the only openings of this box were at the same level, and were small and symmetrically placed, it was hoped that the entrance into it of the air currents due to the motion of the air in the room would be mostly prevented, so that there would remain only the disturbing influence of the convection currents produced within the box itself by differences of temperature. This hope seemed to be justified, for weighings of the globes placed within the box had a mean error not larger than in the case of objects of the same mass, but far less bulk. The box contained calcium chloride for drying somewhat the air which surrounded the globes. It was not till the art of quickly weighing a globe had been learned by some months of trial that experiments on oxygen or hydrogen were made.

FIG. 9.-Balance surrounded with nonconducting case: illumination of scale and pointer.

The globe containing the gas to be weighed was always suspended, in this series of experiments, from the left pan of the balance, and the weights required to produce equilibrium were also placed on the same pan. After an hour, three suc cessive excursions were noted, the balance was arrested, and the observation

repeated a few times. Riders were not used. The globe remained on the balance at least twenty-four hours, and the observations were repeated at intervals. The position of equilibrium of the unloaded balance and the value of a scale division were observed sufficiently often.

FIG. 10.-Balance, case, and metal box: for accurate weighing of globe.

The exhaustion of the globes for the purpose of determining the tare, hardly needs mention. The weight of the gas remaining in the globe was always computed from the indications of the McLeod gauge. All weights were corrected for the weight of the air displaced by them.

18.-VERIFICATION OF THE WEIGHTS EMPLOYED.

The weights employed were, first, a brass kilogramme and its subdivisions to one milligramme, and, secondly, a platinum gramme and its subdivisions to one tenth of a milligramme. The relation of these to each other has been determined on three occasions. The chief object of determining the relation between the small

weights and the kilogramme is of course to make the unit of weight and the unit of volume concordant. The true value of the weights is a matter of indifference.

The values of all the weights of the two sets, assuming the kilogramme as the standard of reference, are given below. The table shows the values of the brass weights at the two dates at which they were compared, as it may be of interest to know the amount of the change to which lacquered brass weights are liable, even when used but little and with extreme care.

VALUES OF THE FRACTIONS OF THE GRAMME IN SETS MARKED K AND B.

The following table gives the results obtained by this method, together with the values of the density of oxygen computed by the formula

*

If we increase the mean by one thirty-thousandth, we get

20. SECOND METHOD OF DETERMINING DENSITY.

In the second series of determinations of the weight of one litre of oxygen, the barometer and thermometer were not used to measure the temperature and pressure of the gas at each observation. A globe like those used for the weighings was connected to a delicate differential manometer and filled with pure dry hydrogen. It was surrounded with melting ice, the open branch of the differential manometer was connected to the syphon barometer mentioned before, and the pressure required to bring the differential manometer to equilibrium was elaborately determined.

When afterwards a globe was filled with oxygen, it was connected with the open branch of the differential manometer, the temperature of the two globes was made the same, and the pressure of the oxygen was made such as to produce equilibrium in the manometer. It is obvious, assuming for a moment that oxygen and hydrogen have the same coefficient of expansion, that if the gases in the two globes had the same pressure at some unknown but uniform temperature, they would also have the same pressure at the temperature of melting ice, which pressure has been determined for the hydrogen. For the actual difference in the coefficients of expansion we can make a numerical correction.

One advantage of the method is that we may observe the equilibrium of pressure and temperature as long as we please, whereas, when we measure pressure and temperature, we are limited to the reading at the instant of closing the globe. This advantage can also be obtained by surrounding the globe with melting ice. A second advantage is that the globe in which the gas was weighed by this method was kept untouched, contained in a desiccator and surrounded by dry air, during the two determinations of the weight of the globe empty and of the globe filled with oxygen.

*

See note, page 28.