May II, 1893] 



NA TURE 



-45 



may be extended to the measurement of convex and concave 

 reflecting surfaces within the limits of this instrument, i.e. from 

 6 to lomms. of radius. 



The theory of itsconstruction is based on a particular application 

 of the following well-known optical law : — that when two centred 

 optical systems are so combined that their principal foci coincide, 

 the ratio of the size of the object to the size of the image formed 

 by the combined systems is equal to the ratio of the principal 

 foci of the two optical systems adjacent respectively to object 

 and image. The two optical systems in this case are a convex 

 lens and the cornea as a reflecting surface, the object being in 

 the principal focus of the convex lens. 



The instrument is composed of the following parts : an aplanatic 

 lens of 26 mms. focus, a rectangular prism neutralised in the 

 visual axis by a smaller prism, one side of the rectangular prism 

 being adjacent to the lens and an iris diaphragm being opposite 

 to the other side in the principal focus of the lens. Behind the 

 prism is a telescope with a double image prism iixed in front of 

 the object glass of the telescope, which has precisely the same 

 focus as that of the aplanatic lens. Cross wires at its principal 

 focus are viewed by a Ramsden eye-piece. 



Before using the instrument it is essential that the cross wires 

 should be distinctly seen at the punctum remotum of the observer. 

 The adjusted instrument is held in the observer's left hand, which 

 rests on the forehead of the patient, the diaphragm being directed 

 to a luminous source to the right of the observer. When the 

 observed eye is directed to the central or fixation point of the 

 instrument, the image of the diaphragm in the cornea can only 

 be distinctly seen, when the principal focus of the lens coincides 

 with the principal focus of the cornea, the point of coincidence 

 of the principal foci being found by moving the instrument to 

 and fro. The image of the diaphragm by means of the double 

 im^e prism appears as two images in the centre of the field, 

 when the visual line of the observer's eye is perpendicular to the 

 surface of the cornea, through which it passes. If these images 

 are not seen in the centre, their position indicates the direction 

 of the angle a. The size of the corneal image being constant 

 (2 mms.) the images are brought into exact contact by suitable 

 variations of the iris diaphragm. By using a circular object, the 

 circular, elliptical or irregular form of the image reveals at once 

 the condition of the surface. When the images are elliptical, 

 the minor axes of the two images are to be brought into the same 

 straight line by a rotation of the telescope, and similarly with 

 the major axes. 



Equal differences in the size of the diaphragm correspond to 

 equal differences in dioptric power, each millimetre of difference 

 in diameter corresponding to three dioptres. The amount of 

 astigmatism in dioptres can thus be read off on a graduated scale 

 fixed to the instrument. 



This instrument reads certainly to within half a dioptre, which 

 between 7 and 8 mms. of radius of curvature is equivalent to 'oSS 

 rams, of difference of radius. 



April 20. — " The Potential of an Anchor Ring," by F. W. 

 Dyson, Fellow of Trinity College, Cambridge, Isaac Newton 

 student in the University of Cambridge. Communicated by 

 Prof. J. J. Thomson, F.R.S. 



This paper is a continuation of some researches on rings pub- 

 lished in the Phil. Trans. 1893. Asystemof solutions of Laplace's 

 equation applicable to space inside an anchor ring is found. By 

 means of these and the value of the potential at external points 

 found in the previous paper, the potential of a ring at internal points 

 is found. The stability of the annular form of rotating gravitating 

 fluid is discussed ; the ring form is shown to be stable for fluted 

 and twisted disturbances, but unstable for long beaded ones. 

 The potential of a ring of gravitating matter whose cross section 

 is elliptic is obtained. Applying the result to Saturn's system, 

 it is shown that for his ring to be continuous fluid its density 

 would have to be too times that of the planet. The steady 

 motion of a single vortex-ring of finite cross section in an in- 

 finite fluid is discussed, and also the motion of a number of 

 vortex rings on the same axis. Numerical calculations are 

 entered into for the particular cases of a vortex ring followed by 

 another of equal strength, a vortex ring approaching an infinite 

 plane, and one passing directly over a spherical obstacle. 



Physical Society, April 28.— Prof. W. E. Ayrton, F.R.S., 

 Fast-President, in the chair. — Adjourned discussion on the 

 viscosity of liquids, by Prof. J. Perry, J. Graham, and L. W. 

 Heath. Prof. Perry read a communication he had received from 



NO. 1228, VOL. 48] 



Prof. Maurice Fitzgerald on the subject, in which the latter dis- 

 cusses the corrections necessary for reducing the results obtained 

 by circular motion to the corresponding motion in plane layers. 

 He shows that in addition to the circular motion, the effect is 

 complicated by radial flow due to "centrifugal head," which 

 causes the liquid to pass outwards near the bottom of the trough 

 and inwards across the edge of the suspended cylinder, with 

 continuations along the sides of the trough and cylinder. Taking 



'+- B . 

 this motion into account the formula v = Ar c -f- — is de- 



r 



duced, where v is the velocity, /i the viscosity, A and B 



arbitrary constants, and c a constant depending on the radial 



flow. When c = o the formula reduces to equation (5) of the 



C 

 paper, whilst if f = — 2/i it becomes v = — . The subject of 



critical velocities in non-turbulent motion is referred to, and 

 some probable effects of the anomalous variations of density and 

 viscosity of sperm oil noticed by the authors of the paper are 

 pointed out. Prof. Perry, in further reply to Prof. Osborne 

 Reynolds' comments, said he understood Prof. Reynolds to have 

 proved that friction was proportional to velocity when the motion 

 was steady. Experiments he (Prof. Perry) had made with discs 

 of iron and glass in revolving mercury seemed to show that this 

 was not the case. On replacing the mercury by sperm oil he 

 found that up to a certain speed friction was strictly proportional 

 to velocity, whilst above that speed friction varied as v^"-^. 

 Coloured streaks in the liquid remained unbroken even at the 

 highest speeds. He therefore concluded that continuity of 

 the streaks was not necessarily accompanied by a linear law of 

 friction. — Mr. E. C. Rimington read a paper on luminous dis- 

 charges in electrodeless vacuum tubes. The laminous rings 

 produced in exhausted bulbs and tubes by discharging Leyden 

 jars through coils surrounding them, had, he said, been attributed 

 by Mr. Tesla {E/ec. Eng. ^ New York, July I, 189:) to the 

 electrostatic action of the surrounding wire rather than to the 

 rapidly varying magnetic induction through the rarefied gas. 

 The present paper describes several experiments bearing on this 

 point which lead the author to conclude that varying magnetic 

 induction is the chief cause of the luminous rings. They also 

 show that a superposed electrostatic field greatly assists the pro- 

 duction of the luminosity. Most of the experiments described 

 were performed before the meeting, some of the effects being 

 particularly brilliant. In one experiment an exhausted bulb was 

 placed within a coil connecting the outside coatings of two 

 Leyden jars and placed between two metal plates, which could 

 be connected at will with the outside of either jar. The spark 

 gap between the inner coatings was then arranged so that no 

 luminosity was seen in the bulb. On connecting one or both 

 the metal plates with the jars in such a way as to increase the 

 electrostatic field through the bulb, bright rings immediately 

 appeared. An electrostatic field produced by a small induction 

 coil connected to a piece of tin-foil on the bulb caused the rings 

 to form at irregular intervals when the discharge of the jars and 

 coil happened to be properly timed. In another experiment two 

 loops of wire in series were used, and when put on the bulb in 

 such a way as to produce a large magnetic effect but small 

 electrostatic field, bright rings appeared, but if the magnetic 

 effects of the coils opposed each other, whilst the electrostatic 

 field was increased, no rings were seen. The subject is treated 

 mathematically at some length in the paper, the times at which 

 the maximum values of the current, the potential difference 

 between the outside of the jars and the rate of change of current 

 occur, as well as the values of their successive maxima being 

 determined. The influence of size of jars is next considered, 

 and the time-integral of rate of change of current on which the 

 effect on the eye depends, expressed as a geometrical series. 

 Taking an approximation the author shows that the time-integral 

 is roughly proportional to the fourth root of the capacity. Large 

 jars are therefore theoretically only slightly better than small 

 ones, and this agrees with observation. On the subject of 

 apparently unclosed discharges, such as are seen when dis- 

 charges pass through a coarse spiral wound on an exhausted tube, 

 the author said he had observed that the discharges were really 

 closed, but the return part much diffused and of feeble intensity. 

 Experiments were exhibited showing that under some circum- 

 .stances an exhausted bulb act%d like a closed metallic circuit, 

 whilst under 01 her conditions dissimilar effects were produced. 

 Another experiment was shown in which a faint luminous ring, 

 produced by a single turn of insulated wire round a bulb, was 



