Proceedings of the American Academy of Arts and Sciences.

VOL. XLII. No. 6. — JULY, 1906.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE.

FRICTION AND FORCE DUE TO TRANSPIRATION AS DEPENDENT ON PRESSURE IN GASES.

BY J. L. HOGG.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY

OF HARVARD COLLEGE.

FRICTION AND FORCE DUE TO TRANSPIRATION AS DEPENDENT ON PRESSURE IN GASES.

BY J. L. HOGG.

Presented by J. Trowbridge, November 8, 1905. Received April 6, 1906.

PROBLEM IN GENERAL AND RESULTS IN GENERAL.

THIS is a preliminary paper on an investigation whose object is threefold.

It is known that at pressures lower than about 1 cm. of mercury the resistance which a solid body meets in passing through a gas is noticeably smaller than it is when the pressure is that of an atmosphere. This is because the phenomenon of slip presents itself at the low pressures. The first object of the investigation is to study fully the relation between the friction of a gas on a solid body and the pressure in the gas at those pressures where slip is appreciable.

Again, it is known that, if a given volume of gas is divided into two portions by means of a partition one side of which is kept hotter than the other, and if a small opening of any form be made in the partition, the gas will flow from the cold side to the hot side of the partition until there is an excess of pressure in the chamber contiguous to the latter. This excess of pressure depends on the difference of temperature of the two sides of the partition and on the mean pressure.

The second object is to examine in a particular simple case the relation between the force on the partition (called the transpiration force), resulting from this flow of gas towards the hot side of the partition, and the mean pressure in the gas.

The third object of the investigation is to examine the feasibility of measuring the pressure in a gas when either of these relations is known without having recourse to the McLeod gauge. That this third object is by no means the least significant will appear when the evidence as to whether the McLeod gauge is reliable for the measurement of small pressures is adduced.

The progress made in the solution of these problems up to the present may be summed up as follows:

(1) The great difficulty in devising and carrying out methods of constructing the pieces of apparatus required has been overcome. This, which was by no means the least difficulty encountered, can be appreciated only when one knows the form of the apparatus required, and the treatment which the apparatus must receive in order that all traces of moisture may be removed from all the solid surfaces exposed to the interior of the containing vessel.

(2) The friction has been measured at pressures ranging from that of an atmosphere to 0.00024 mm. of mercury, the small pressures being measured by the McLeod gauge. Figure 6, in which ordinates are proportional to friction and abscissas proportional to pressure, shows how the friction diminishes as the pressure diminishes. The curve, whose error is certainly less than one per cent (if the McLeod gauge can be considered trustworthy over the range of pressures indicated), is very regular; and a discussion of the numerical results in that part of the curve which corresponds to pressures above 0.1 mm. of mercury shows that the law

first deduced by Kundt and Warburg for pressures down to 0.6 mm., holds very well down to about 0.1 mm. Beyond this point, however, the theoretical curve, i. e., the curve obtained by calculating p from the above relation after the constants have been determined from observations at comparatively large pressures, does not coincide with the actual curve.

(3) The force due to transpiration has been measured over a range of pressure varying from 1.42 mm. to 0.0093 mm.

(4) Figure 7 (the error in the curve may very well be five per cent), in which the ordinates are proportional to the transpiration force and abscissas to pressure, shows that, for pressures below that for which the force is a maximum, the relation between the force and the pressure rapidly approaches a relation of mere proportionality, or at worst a proportionality disturbed by a constant term. In other words, the curve becomes a straight line passing very nearly through the origin.

PROBLEM IN DETAIL.

Introduction.

Aside from the interest which attaches itself to an investigation of the law relating viscosity to pressure at low pressures, the advantage of being able to measure gas pressure by measuring the friction of the gas on a pendulum is apparent. By this method the state of the gas remains unchanged during the time the measurement is in progress, while by the method of the McLeod gauge the gas must be compressed in order that the pressure may be measured. It is, however, beyond doubt very important that in establishing a method of gas pressure measurement by friction, or otherwise, a second method should if possible be obtained to serve as a check upon the one which we may consider most convenient and therefore the most desirable. Though the investigation of the law relating pressure in a gas to transpiration force when the transpiration space is of special form is interesting and important for its own sake, yet additional interest and importance is imparted to it when the possibility of making its results serve as the desired check upon the proposed friction method of measuring gas pressure is considered.

Thus, in so far as the object of the present investigation is to test or replace the McLeod gauge, the function of what has been called the transpiration apparatus is to serve as a check upon the results of pressure measurement obtained by the viscosity apparatus. As will appear in the sequel, the problem to be solved with the transpiration apparatus is that of investigating the law of gas action on a radiometer vane of special form surrounded by a containing vessel whose parts are symmetrically placed with respect to the vane.

That at least another attempt should be made to decide the question as to how much reliance can be placed on the McLeod gauge for measurement of pressures below 0.1 cm. is very forcibly brought home to one who examines the conflicting evidence of high authority.

The attempts to investigate the behavior of the gauge when the vacua are high, have as a rule been made, not with the avowed intention of testing the gauge, but with the object of testing the validity of Boyle's law at various pressures, any departure from which for any gas would at once limit the use of the gauge for that particular substance. The method used was to enclose a certain quantity of gas, measure accurately its volume and its pressure, calculate pv; change this volume, and therefore pressure; measure again, and so on. The various values of pv thus obtained should be the same, that Boyle's law may be obeyed, and hence that the principle of the gauge may be sound.