December 2, 192 2 J 



NA TURE 



733 



in a similar manner. In the process of this in- 

 vestigation, some results were found which I now 

 describe. 



Water vapour in contact with films renders them 

 insensitive to the extreme ultra - violet, and on the 

 other hand, new films may be made sensitive for 

 immediate use if they are thoroughly dried. 



Water vapour gives a spectrum in the ultra-violet 

 extending to about X900. It consists of oxygen lines, 

 hydrogen series lines, the secondary spectrum of 

 hydrogen, and some bands probably not due to 

 hydrogen. The A.C. or D.C. current used was found 

 to dissociate water into its elements almost completely. 

 A condensed discharge, however, formed compounds 

 in the receiver of the vacuum grating spectrograph 

 which fogged the films in the path of the light. It 

 is, therefore, not surprising that a spectrum of water 

 vapour should be found in this region of short wave- 

 lengths, for hydrogen is known to be transparent 

 here, and the author has shown (Physical Review, 

 in press) that oxygen likewise is remarkably trans- 

 parent in a portion of this region. 



With condensed discharge and low pressure in 

 receiver and discharge tube, a spectrum was obtained 

 for air to ^350. In this experiment no attempt was 

 made to eliminate mercury vapour. Many of the 

 lines in the neighbourhood of X6oo, recently found 

 by Lyman to constitute a helium series, were also 

 found on these films. 



Ordinary commercial films were found sensitive at 

 X12157, so that a very clear line was produced on 

 the fiim after only five minutes' exposure, with 

 hydrogen at a pressure of 0-3 mm. 



Using wet hydrogen and a long discharge tube 

 three new members of the Lyman series of hydrogen 

 were found. Thus there are now six lines of that 

 series known. Appearing on the same spectrogram 

 with these was a line X243-2 io-2. This was observed 

 on many films, and on some of them it occurred in 

 the first, second, and third orders. Its wave-length 

 agrees within limits of experimental error with the 

 equivalent wave - length (^248) for the L critical 

 potential of oxygen, observed by Kurth, using photo- 

 electric methods. The observation of this line in 

 hydrogen at a pressure of 0-3 mm., after the light 

 had traversed a distance of one metre, shows the 

 transparency of hydrogen in this region. This fact 

 may be useful to those working in soft X-rays or in 

 the region of these short ultra-violet radiations. 

 Furthermore, the presence of this line indicates that 

 the great absorption band of hydrogen which begins 

 at about A850 terminates on the long wave-length 

 side of ^243. J. J. Hopfield. 



Department of Physics, University of California, 

 Berkeley, October 30. 



Molecular Viscosity. 



The following remarks are offered rather in the 

 nature of a foreword, suggesting a particular line of 

 research, than as an article of belief. Although the 

 conclusions arrived at are purely theoretical, and 

 have at present no experimental confirmation, the 

 practical test outlined at the end of the paper should 

 supply a definite answer as to whether there is any 

 foundation for the theory advanced. 



Our conception of the physical forces which are 

 called into play when a liquid is caused to flow with 

 linear or stream-line motion is gradually undergoing 

 a change. The old definition of viscosity as internal 

 friction needs revising. Already Dunstan and Thole 

 (Journ. Inst. Petr. Tech., vol. iv. p. 197) have 

 come to regard viscosity in the nature of a dual 

 phenomenon, which they attribute partly to internal 



NO. 2770, VOL. I io] 



friction and partly to deformation of molecular 

 grouping (although these may conceivably be one 

 and the same thing). There is one aspect of the 

 subject which does not seem to have received its 

 fair share of notice. Allusion is made to the gyro- 

 scopic resistance offered bv any orbits, the motion of 

 which has components at right angles to the line of flow. 



When a vapour condenses into a liquid, the mole- 

 cules still retain the major portion of their high 

 velocity ; and since it is only their mutual attraction 

 that prevents them from escaping again into space, 

 it follows that their paths must be very curved, and 

 that in all probability there will be at any instant 

 of time a certain number of them revolving round 

 one another in orbits,' after the fashion of the twin 

 stars. These systems would doubtless have only a 

 short life, being destroyed by collision with neighbour- 

 ing molecules, but for the instant of time during 

 w Inch conditions were favourable similar orbits would 

 be formed to take their place. 



For want of a better name this particular form of 

 viscous resistance will be referred to as gyro-viscosity. 

 We may then consider the property, common to all 

 liquids, of resistance to flow as made up of at least 

 two parts, namely : 



(a) gyro-viscosity. 



(b) molecular friction or deformation. 

 Whereas (a) lends itself readily to mathematical 

 treatment, (b) is still so largely a matter of conjecture, 

 that while our ideas are in their present state of 

 flux, we cannot be sufficiently definite about anything 

 in this connexion to attempt any sort of analysis. 

 We can, however, be moderately confident that in 

 some degree (a) must obtain, and it is hoped to show 

 a means whereby it may be measured. When a 

 liquid is subjected to a shearing stress, in other words 

 when flow starts, there will be at once the gyroscopic 

 resistance of those components of the orbits at right 

 angles to the line of flow ; and when these have 

 been turned through a right angle and flow continues 

 there will remain the constant resistance of those 

 orbits which are produced during flow. Viewed in 

 this way the initial momentary resistance should be 

 greater than the subsequent constant resistance ; and 

 since the former is independent of the rate at which 

 the orbits are being formed, it would afford a means 

 of estimating the relative molecular gyro-viscosity, 

 if only it could be measured with sufficient accuracy. 

 A method of doing this which suggests itself is based 

 upon the correct resolution of the forces which go 

 to produce the so-called Couette correction for flow 

 through capillary tubes. 



Couette found that when the length / of the tube 

 was doubled the corresponding time t was not quite 

 doubled, and that in order to satisfy his equation 

 it was necessary to replace I by I + kd, where d is the 

 diameter of the capillary and k a constant having 

 an approximate value of 0-25. Since this correction 

 is, in a sense, a measure of the total work W done 

 outside the tube, it must contain also the preliminary 

 work W ra required to turn all the orbits in existence 

 at any instant of time in the whole volume run. 

 The difference W, - W m represents the work done 

 outside the tube in overcoming viscous resistance of 

 the liquid already in motion (the kinetic energy 

 correction was, of course, allowed for, and therefore 

 does not enter into these quantities). 



The Couette value affords a direct means of deter- 

 mining W„ but the calculation of W„ - W m presents 

 considerable difficulties. We are faced with the 

 problem of finding (1) an expression for the distribu- 

 tion of the velocities in the trumpet-shaped lines 

 of flow of the liquid before it enters the tube ; (2) the 

 varying acceleration of any one of these lines before 

 it attains its final constant velocity on entering the 



