186 PHENOMENA DEPENDENT ON MOLECULAR PATHS 77 



transpiration experiments of Graham on the one hand, and 

 of Springmiihl and myself l (which were made later) on the 

 other ; such proof being founded on the law discovered by 

 Graham, that the times in which two different gases flow 

 through a tube under the same circumstances have always 

 the same ratio. 



After all these researches it still remains undecided 

 whether Maxwell's law of the constancy of the coefficient 

 of friction still holds at very small pressures of the gas, or 

 to what extent of rarefaction the law may be considered 

 valid. That it cannot hold right down to the limit zero has 

 already ( 76) been pointed out. We may therefore expect 

 that deviations from it will be exhibited when the pressure 

 is only a few millimetres of mercury, or when it is lowered 

 so exceedingly far as in the Geissler's tubes used for electro- 

 optical experiments by Pliicker, Hittorf, and Crookes. 



A first attempt to decide this question was made by 

 Kundt and Warburg, 2 who repeated Maxwell's ex- 

 periments and pursued the phenomenon down to extremely 

 low values of the pressure. Their experiments confirmed 

 Maxwell's result that the law is valid till the pressure 

 falls to g 3 ^ atmosphere ; but from that point onward they 

 noted a marked diminution in the value of the logarithmic 

 decrement. But they explained this diminution not as a 

 consequence of the coefficient of friction being smaller at 

 such low pressures, but by a considerably increasing effect at 

 low pressures of the slipping of the gas on the discs of the 

 apparatus. We shall return to this point later ( 83). 



That this explanation is correct, and that the coefficient 

 of viscosity really remains constant, as Kundt and War- 

 burg assume, down to extremely small values of the 

 pressure, was proved by Crookes 3 by observations in 

 which he employed a vertically suspended leaf of mica 

 instead of a horizontally oscillating disc. From the oscilla- 

 tions of this leaf he was able, by help of a theory developed 

 by Stokes, 4 to arrive at conclusions with respect to the 



1 Pogg. Ann. 1873, cxlviii. pp. 1, 526. 



2 Monatsber. d. Berl. Akad. 1875, p. 160 ; Pogg. Ann. 1875, civ. pp. 337, 525. 



3 Phil. Trans. 1881, clxxii. p. 387. 4 Ibid. 1881, clxxii. p. 435. 



