July 7, 192 1] 



NATURE 



5«5 



is purely electrolytic, we should expect the alkalinity 

 to be neutralised by the acid radicle ions driven into 

 solution from the glass. The initial current was 

 8-5 micro-amperes, rising at the end of fifteen minutes 

 to 13 micro-amperes. By this time the solution in 

 contact with the thinner parts of the bulb was a deep 

 pink. The current was then reversed, the initial 

 value being now i6 micro-amperes. After six minutes 

 the solution in contact with the glass was very nearly, 

 if not quite, colourless. If the current in the glass 

 were electrolytic, there can be little doubt that sodium 

 ions would have been driven into solution, thus main- 

 taining the pink colour. The large changes in the 

 conduction current with time and reversal of direc- 

 tion are probably attributable to alteration and 

 polarisation effects in the glass. The thin parts 

 of the bulb carrying most of the current probably 

 represented an area of only 2 or 3 sq. cm., so that 

 the current density was comparatively large, and the 

 potential gradient probably between i and 2 mega- 

 volts per cm. The evidence of the colour changes, 

 which were repeated several times, is strongly in 

 favour of the view that under such gradients and at 

 air temperature the conduction current is largely, if 

 not entirely, of a ncm-electrolytic nature. 



Horace H. Poole. 

 Roval Dublin Societv, June 20. 



The Displacement of Spectral Lines by a Gravita- 

 tional Field. 



According to the theory of relativity the paths of 

 moving: particles or light pulses are geodesies in a 

 four-dimensional Riemann space defined by the metric 



The resulting abstract kinematics is brought into re- 

 lationship with the facts of experience by the identifi- 

 cation of the Gaussian co-ordinates x with the ob- 

 server's space-time co-ordinates in a Newtonian- 

 Euclidean system. Since the spaces are Euclidean, 

 and since the velocity of light is the same for each 

 observer, it follows that the systems .of two different 

 observers are similar, but not necessarily on the same 

 scale. 



Consider the field of a single gravitating centre. 

 The metric is given by 



■ ih* = - y- Wr2 - r*[d6-^ + sin2 ddcf)'-] + yd/*. 



Taking the unit of ds as the fundamental unit, and 

 measuring radial and transverse lengths and times at 

 two different points of the Riemann space, we see that 

 throughout the space the local scale is constant for 

 transverse lengths, varies as yJ for radial lengths 

 and as y-i for times. Since the separated space-time 

 systems of different observers are to be similar, it is 

 clear that their scales cannot be obtained by carrying 

 over the scales of the Riemann space at the observers' 

 world-points. Assume that the observer's time-scale 

 bears to the time-scale at his world-point in the 

 Riemann space the ratio i : f(r). The scales of the 

 liuclidean systems of two different observers then 

 vary inverselv as y^f(r). 

 i This variation of scale has no effect on the mercury 

 problem or on the deflection of a beam, but it is of 

 fundamental importance in the third crucial pheno- 

 menon, the displacement of the spectral lines. 

 The usual argument shows that 

 yhdt<. = yK.dfi:, 

 where dt^, dU. are measured in the units of the 

 Riemann space. If we transfer to the Euclidean 

 spaces of local observers, the equation becomes 



■y^s fsd/^^yKfrdf^E.' 

 NO. 2697, VOL. 107] 



Eddington's argument on p. 129 of "Space, Time, 

 and Gravitation " shows that the time-period as 

 measured in the units of any one observer is trans- 

 mitted by the radiation. Hence dts can be compared 

 with df E by observation. The measurement of the 

 displacement of the spectral lines determines- thei 

 function f. * 



No displacement is to be expected if fz^y-i. In .^. 

 this case, if dt is a time-interval in the Riemann 

 space, yldt is the corresponding observer's interval, 

 and yidt or ds is propagated by the radiation as sug- 

 gested in my letter of March 10. H. J. Priestuiy. 



University,' of Queensland, Brisbane, May 11. 



The Measurement of Single and Successive Short 

 Time-Intervals. 



The following modification of the well-known 

 method of determining small time-intervals by the dis- 

 charge of an electrical condenser does not appear to 

 be generally used, judging from some inquiries I have 

 had. Though the modification possibly has been pub- 

 lished somewhere — the man who can claim originality 

 in these days is fortunate — this letter may be a help to 

 some other workers. 



The well-known method to which I refer consists in 

 so arranging the circuit with a condenser and baFistic 

 galvanometer that the former is charged or discharged 

 during the interval. The potential of the condenser 

 is measured before and as soon after the interval as 

 possible by the galvanometer, and the duration of the 

 interval is proportional to the difference of the 

 logarithms of these quantities. 



The modification I first used during 1915 in connec- 

 tion with the measurement of the velocity of detona- 

 tion of explosives consists in connecting one side of 

 the condenser to the string of a Laby string electro- 

 meter. The displacement of the string is proportional 

 to the potential of the condenser, so that during an 

 experiment the string falls from one position to 

 another, and the Ic^arithm of the ratio of these dis- 

 placements from the zero position is proportional to 

 the time. The accuracy of the method can be in- 

 creased by using a moving plate and photographing the 

 string's position ; it can be increased up to the limit 

 imposed by the accuracy within which the condenser 

 capacity and discharging resistance are known bv 

 measuring the displacements on the plate 'with a 

 microscope. 



The advantages of this method as compared with 

 the ballistic method are : (a) the procedure and cir- 

 cuit are much simplified, (b) small leakage is of no 

 importance or embarrassment, (c) the whole process 

 being self-recording, the result is available for 

 measurement at any time, and, further, the inertia 

 of the string or its natural period of vibration does not 

 affect the result. 



Its disadvantage in common with the ballistic 

 method is the disturbing influence of the inductance 

 of the circuit upon the rate of flow. It may be possible 

 in some applications to calculate this, or to allow for it 

 by calibration. 



If a bicvcle ball suspended by a long thin wire be 

 allowed to impinge against, and rebound from, the 

 vertical face of an anvil until it comes to rest, the 

 resulting record with its gradually diminishing steps, 

 corresponding to the several durations of contact, 

 affords a pretty example of the application of this 

 method to the measurement of rapidly successive 

 short time-intervals. Alan Pollard. 



The Imperial College of Science and 



Technology, South Kensington, 



S.W.7, June 14. 



