while in the second almost all the corrections which are usually to be applied in resistance measurement are here insignificant, even when temperature increments of .01° C. are in question. For neither w, nor we nor their differences need be known in absolute value. The position of the sliding bridge contact, c, alone requires careful attention. This, together with the resistance standards Z in branch 2 of the bridge, including the necessary terminal and connecting wires, must be the same and similarly circumstanced during temperature measurements, as during the actual measurements relative to changes of gas pressure.

Our resistance standards were made of manganine wire. Thick copper terminals and yokes, dipping into large mercury troughs, enabled us to connect the individual units of Z at pleasure. All the connection pieces were stout and of copper wire. Hence changes of temperature in the laboratory were quite without influence on the resistance measurement.

III. SYSTEMATIC ERRORS.

Before proceeding to a report of the experimental data, we will endeavor to form some estimate as to the effect of systematic errors on the results. The chief assumption in the present and all preceding and similar methods is fundamental: Even supposing the intrinsic equation for the perfect gas to be fully applicable to the actual phenomena, what assurance have we that the expansion obtained is truly adiabatic? Rigorously considered, none; for heat will certainly gain access into the interior of the gas. This heat enters partly by conduction or convection, partly by radiation, and its influence on the results will be such as to make the values found for smaller than the true values. The influx of heat due to conduction comes partly from the walls of the receiver, partly by direct metallic conduction from the terminals and flaps of the bolometer strip. The former source of discrepancy occurs uniformly in all experiments in which measurements are made relative to an expanding gas. It is just in this respect that the present procedure for measurement has distinct advantages over all earlier methods; for these determined T indirectly, by the aid of a special pressure measurement; and therefore the total heat conducted inwards from the walls of the receiver must

have entered the results as an error. In our experiments, however, the bolometer strip is suspended in the centre of a large sphere and that part only of this heat can be effective which moves as far as the bolometer through the concentric layers of gas. In virtue of the low order of heat conduction in gases, the time in which heat can reach the centre is so long an interval, in spite of convection, that appreciable rise of temperature at the bolometer cannot occur until the expansion is complete and T2 fully measured. The superiority of the present method of attack

is evidenced, for instance, by results which show all resistance changes in the bolometer to be independent of the time of efflux, within time limits as broad as 2 to 8 seconds, in the case of air. True, in the best of the earlier experiments, the heat influx from conduction from the walls of the vessel is of serious moment only for the better conducting gases, since the receivers used were all of large capacity. Röntgen, however, openly acknowledges that the value of x for hydrogen found in his experiments must be considerably below its real value. We therefore refer to it as conclusive evidence in favor of our method, that, at variance with the results of all earlier investigators, our method actually gives us a larger -value for hydrogen than for air.

Neither can the heat which enters by metallic conduction along the electrical terminals of the bolometer adjustment have produced any serious rise of temperature-certainly not in that part of the gas immediately around the strip. The thin film of pure platinum by which the measurements are virtually made, is free from silver and quite distant from the walls of the receiver. It is, moreover, placed below the levels of the terminals, so that true conduction heat only and not convection heat can reach it. For this reason the bolometer temperature remains constant even for several seconds after the completed expansion of air.

Regarding the heat imparted by the bolometer to the gas, the following inferences may be drawn. We have intimated that the measuring current was always reduced to so small a value as not appreciably to change the temperature of the bolometer strip. Hence we may abstract from the Joule heat set free within the film altogether. Similarly the heat which the bolometer strip gives up to the expanding gas is negligibly small; the thermal capacity of the strip, in view of the dimensions stated, is only about .000 007 gram calories. This is about equivalent to the thermal capacity of 4 cm3 of air. Similarly the heat removed from the silver-covered parts of the bolometer is without moment, for these cool very rapidly.

40

Thus it happens that at least those regions of the gas which immediately surround the etched part of the platinum strip may be regarded as screened from all heat conduction. They therefore expand quite adiabatically.

We have now to consider the question in what degree the temperature 7 of the gas after expansion, coincides with the actually measured minimum temperature of the bolometer strip. Since the temperature of the bolometer is constant for several seconds during the observation of T, it follows that the bolometer temperature can only differ from that of the gas if there is a permanent flow of heat into the strip. In such a case a stationary distribution of temperature is conceivable, in which the bolometer would impart heat to the gas at the same rate in which it receives it. We can but acknowledge that there must be accession of heat in the

bolometer from the following three sources: (1) as the result of electric current in the strip (this, as we have already seen, being negligible); (2) as due to conduction through the terminals; (3) as due to direct radiation impinging upon the strip from the walls of the receiver.

To treat the second case first: the heat received by the strip from the thick terminals may be approximately computed, at least with reference to the error resulting. We will assume for this purpose that the terminals retain their initial temperature during the whole interval of expansion. Let the bolometer strip be a thin straight conductor, one end of which is kept permanently at the temperature 9, of the terminals, while the surrounding air is at the temperature 9,. Let a be the distance of any point of the strip from the terminal end at temperature 90, and let 9 be the temperature at this point at the time t. Hence by Fourier's equation of the temperature distribution in an infinitely long rod subject to radiation

But the thickness, d, of the strip is negligibly small as compared with its breadth: therefore

At the close of the expansion the thermal distribution is stationary along the wire as observation has shown. Hence 99

=0, and equation (3) becomes

If for x =

=

0, the temperature of the strip, we put 99%, and for x = ∞, we put 99,, the integral of equation (4) is

The following values may be assumed for the middle or etched part of the

platinum strip:

all quantities being here given in terms of milligrammes, millimetres, and seconds. Thus f/a is very nearly 1 and we obtain

Hence when the gas cools down as far as 90-91 = 15° C., we find for

If, therefore, the very thin silver-free platinum film were soldered directly to the stout copper terminals, a fall of temperature would be manifest at the ends of the plat inum strip, the influence of which would be far from negligible in its bearing on T2.

In view of the interposition of the gradually narrowing or arrow-shaped flap of platinum and silver between the terminals and the effective bolometer strip, the distribution of temperature is materially changed. For the flap in question the constants may be estimated as follows:

k = 109,

h = .003,

c = .06,

μ = 10.5,
d = .0066,

all taken, as before, with reference to milligrammes, millimetres, and seconds, while h is entered unfavorably with a value decidedly large. In this case the quotient f/a is found by computation to be .09, and the temperature distribution for 90-91 = 15° is now such that at a distance of 3 cm., the increment is but 1° C. The effect of using the end flaps of silver is thus a reduction of temperature from the terminals to the strip, fast enough to quite wipe out any serious discrepancy due to unequal temperature in the strips.

In view of the good conduction of electricity by the silver flaps, furthermore, the change of resistance due to change of temperature is equally inappreciable. any marked discrepancy due to conduction of heat along the terminals to the

Thus

'This number has been obtained for thick rods of iron and German silver. We were obliged to enter it, not having found any special value for platinum. Clearly the quantity cannot in any real case be a constant. It must increase very rapidly with the decreasing diameter of a given rod. Thus the value above assumed is considerably too small. For very thin rods Cardani finds h = .06 (Nuov. Cim., [3], vol. 30, pp. 33-60, 1891). If a larger value for than the above is put into the equations, the results obtained would be more favorable to our argument than those given in the text. Thus if h .06, and x = 0.1 cm., = .14°.

=

bolometer strip seems to have been effectually excluded in the form of experiment stated.1

We may also use the Fourier equation to find in what degree the platinum strip coincides with or follows the temperature of the gas. For simplicity we will assume that the gas temperature sinks from its original value (96), at a constant rate in the lapse of time. In other words, put

If now we neglect the heat flux from the ends of the bolometer strip toward the middle,

and 99 for t=0. The integral of the general equation (3) thus becomes

The difference (99) between the temperature (9) of the bolometer strip and the temperature (9,) of the air has therefore a maximum value of b/f. For the platinum measuring strip (silver removed), the above constants show ƒ = 15. Hence the bolometer will coincide in temperature with the air after about 1/15th second. However, since h has been taken very decidedly too small, the real case is correspondingly more favorable. With this deduction our observations agree; for the bolometer reached the stationary state immediately after the noise due to outrush of gas on expansion had subsided.

The last of our sources of error, viz., internal radiation, remains to be discussed. By this agency the bolometer permanently receives heat from the environment, since the walls of the receiver B retain their initial temperature T1. But this heat, which is proportional to T1- 12, may be computed only if the values of the emission and absorption coefficients of the reciprocating bodies were known. In the absence of satisfactory data for these quantities we made an endeavor to determine the effect of radiation experimentally.

With this end in view, we covered the silver-free part of the bolometer strip, galvanically, with platinum black, and then repeated the expansion experiments

If with the same constants and in the same manner the fall of temperature be computed for our original device of a bolometric spiral of silver wire, .004 cm. in diameter, the results are such as fully to account for the difference between our earlier values and the present.

2 According to the recipe given by Lummer and Kurlbaum, cf. Verh. der Physik. Gesell., Berlin, June 14, 1895.