March 



;i] 



NA TURE 



421 



ON THE VISCOSITY OF GASES AT HIGH 

 EXHAUSTIONS^ 



BY the viscosity or internal friction of a gas is meant the 

 resistance it oiTers to the gliding of one portion over another. 

 In a paper read before the British Association in 1859 Maxwell - 

 presented the remarkable result that on theoretical grounds the 

 coefficient of friction, or the viscosity, should be independent 

 of the density of the gas, although at the same time he stated 

 that the only experiments he had met with on the subject did not 

 seem to confirm his views. 



An elaborate series of experiments were undertaken by Max- 

 well to test so remarkable a consequence of a mathematical 

 theory ; and in 1S66, in the Bakerian lecture for that year,^ he 

 pabU-^hed the resuUs under the title of " The Viscosity or In- 

 ternal Friction of Air and other Gases." He found the coefficient 

 of friction in air to be practically constant for pressures between 

 30 inches and 05 inch ; in fact numbers calculated on the hypo- 

 thesis that the viscosity was independent of the density agreed 

 very well with the observed values. 



The apparatus used by Maxwell was not of a character to 

 admit of experiments with much lower pressures than o'5 inch. 



Maxwell's theory that the viscosity of a gas is independent of 

 the density presupposes that the mean length of path of the mole- 

 cules between their collisions is very small compared with the 

 dimensions of the apparatus ; bat inasmuch as the mean length 

 of path increases directly with the expansion, whilst the distance 

 between the molecules only increases with the cube root of the 

 expansion, it is not difficult with the Sprengel pump to produce 

 an exhaustion in which the mean free path is measured by inches, 

 and even feet,^ and at exhaustions of this degree it is probable 

 that Maxwell's law would not hold. 



The exiieriaients recorded in this paper were commenced early 

 in 1876, and have been continued to the present time. In 

 November, 1S76, the author gave a note to the Royal Society on 

 some preliminary results. Several different firms of apparatus 

 have since been used one after the other, with improvements and 

 comjjlexities suggested by experience or rendered possible by the 

 extra skill acquired in manipulation. The earlier observations 

 are noA- of little value, but the time spent in their pro.-.ecution 

 was not thrown away, as out of those experiments has grown the 

 very complicated apparatus now finally adopted. 



The' Viscosity Torsion Apparatus, with which all the expc-i- 

 ments here given ha\e been performed, is a very complicated 

 instrument. It consists essentially of a glass bulb, blown with 

 a point at the lower end, and sealed on to a long narrow 

 glass tube. In the bulb is suspended a plate of mica, by means 

 of a fine fibre of glass 26 inches long, which is sealed to the top 

 of the glass tube, and hangs vertically along its axis. The plate 

 of mica is ignited and lamp-blacked over one-half. The tube is 

 pointed at the upper end, the upper and lower points are 46 

 inches apart, and are accurately in the prolongation of the axis 

 of the tube. Sockets are firmly fixed to a solid .support, so that 

 when the tube and bulb are clamped between them they are only 

 able to move around the vertical axis. Tlie glass fibre being 

 only connected with the tube at the top, rotating the tube on its 

 axis communicates torsion to the fibre, and sets the mica plate 

 swinging on the same axis without giving it any pendulous move- 

 ment. The diameter of the fibre is about 0"ooi inch. The 

 viscosity apparatus is connected to the pump by a flexible glass 

 spiral, so as to allow the apparatus to rotate on the pivots and at 

 the same time to be connected to the pump altogether with sealed 

 glass joints. An arm working between metal stops limits the 

 rotation to the small angle only which is necessary. 



The torsional movement given to the mica plate by the light 



* Abstract of a paper read before the Royal Society, February 17, 1881, 

 b^ W.lhamCrookes, F.R.S. 



^ Phil. Mag., 4th ser. vol xix. p. 31. 



3 Phil. Trafis. 1S66, part i, p. 249. 



■* Thus, supposing tlie mean free path of the molecules of air at the ordi- 

 nary pressure is the r-io,oooth of a millimetre, at an exhaustion of the ten- 

 thousandth of an atmosphere, the mean free path will be i millim. At one- 

 millionth of an atmosphere the mean free path will be locentiinetres, and at an 

 exhaustion of one hundred miiliontli — by no means a difficult point to attain with 

 present appliances — the mean free patn will be over 30 feet. This rarefaction 

 corresponds to tliat of the atnosphere at a height above the earth of a little 

 more than ninety miles, assuming that its density decreases in geometr.cal pro- 

 gression as its height increases in arithmetical progression, and neglecting 

 the small corrections for diminished gravity and temperature. As the height 

 above the earth increases, the length of the mean free path of the molecules 

 of air rapidly approaches to planetary distances ; at ab^ut 200 miles height 

 the mean free path is to million miles, whilst between eighty and ninety miles 

 higher the rarity is such that the mean free path would e.\tend from here to 

 Sirlus. 



of the candle shining on it or by the rotation of the bulb and 

 tube on its axis by the movement of the arm between the stops, 

 is measured by a beam of light from a lamp, reflected from a 

 mirror to a graduated scale. 



The pump employe 1 has already been described. The mea- 

 suring apparatus is similar to that described by Prof. McLeod^ 

 before the Physical Society, June 13, 1S74. As it contains 

 several improvements shown by experience to be necessary when 

 working at very high vacua, a detailed description is given in the 

 paper. 



When taking an observation the arm is moved over to the 

 stop, and in a few seconds allow'ed to return to its original 

 position by the action of a spring. This movement rotates the 

 viscosity apparatus thi'ough a small angle, and sets the mica 

 plate vibrating, the reflected line of light traversing from one 

 side of the scale to the other in arcs of diminishing amplitude till 

 it finally settles down once more at zei-o. 



The observer watching the moving index of light records the 

 scale number reached at the extremity of each arc. The numbers 

 being alternately on one and the other side of zero are added 

 two h\ two together, to get the value of each oscillation. The 

 logarithms of these values are then found, and their differences 

 taken ; the mean of these differences is the logarithmic decrement 

 per swing of the arc of oscillation. For the state of brevity this 

 is called the log dec. 



A very large number of experiments have been made on the 

 viscosity of air and other gases. Observations have been taken 

 at as high an exhaustion as 0'02 M, but at these high points they 

 are not sufficiently concordant to be trustworthy. The pump 

 will exhaust to this point without difficulty if a few precautions 

 are taken, but at this low pressure the means of measuring fail 

 in accuracy. 



The precautions which experience shows to be necessary when 

 exhausting to the highest points are fully described in the paper. 



Viscosity of Air, — The mean of a very large number of closely 

 concordant results gives as Ihe log decrement for air for the 

 special apparatus employed, at a presure of 760 raillims. of 

 mercury and a temperature of 15° C, the number 0'II24. 

 According to Maxwell the viscosity should remain constant until 

 the rarefaction becomes so great that we are no longer at 

 liberty to consider the mean free path of the molecules as 

 practically insignificant in comparison with the dimensions of 

 the vessels. 



The author's observations show that this theoretical result of 

 Maxwell's is at least approximately and may be accurately true 

 in air up to comparatively high exhaustions ; and that at higher 

 exhaustions the viscosity falls off, as it might be expected to do 

 according to theory. 



The le-ults are embodied in a table and diagrams. 



The first half of the ta'ile gives the viscosity of air, in so far 

 as it is represented by the log dec, at pressures intermediate 

 between 760 millims. and 076 millim. (1000 millionlhs of an 

 atmosphere). In order to avoid the inconvenience of firequent 

 reference to small fractions of a millimetre, the millionth of an 

 atmosphere" (= M) is now taken as the unit instead of the 

 milimetre. The second half of the table is therefore given in 

 millionths, going up to an exhaustion of o"02 millionth of an 

 atmosphere.* 



Starting from the log dec. o'il24 at 760 millims., the vis- 

 cosity diminishes very regularly, but at a somewhat decreasing 

 rate. Between 50 millim-. and 3 millims. the direction is almost 

 vertical, and a great change in the uniformity of the viscosity 

 curve commences at a pressure of about 3 millims. At this point 

 the previous approximation to, or coincidence with, Maxwell's 

 law begins to fail, and further pumping considerably reduces 

 the log decrement. 



From 1000 M the diminution of viscosity is very slight until 

 the exhau.tion reaches about 250 M ; after that it gets less with 

 increasing rapidity, and falls away quickly after 35 M is 

 reached. 



The curves of increasing mean free path and diminishing vis- 

 cosity closely agree. This agreement is more than a mere coin- 

 cidence, and is likely to throw much light on the cause of 

 viscosity of gases, 



' Philosophicnl Magazine, vol. xlviii. p. no. August, 1874. 



» M = 0OD076 mdhm. ; 1315-789 M = i millim. 



3 To give some idea of the high exhaustions at which its measurements 

 can be taken it may be mentioned that the highest exhaustion on the table — 

 0^02 M — bears about the same proportion to the ordinary atmospheric pressure 

 that I millimetre does to thirty miles, or, 'converting it into time, that one 

 second bears to twenty months. 



