July 7, 1892] 



NATURE 



m 



the coin, whilst a second coin is placed above the first. The 

 coins are put in connection with the poles of an electrical 

 machine, giving one-inch sparks for two minutes. When the 

 coins are removed and the glass breathed on, clear frosted pic- 

 tures of the coins are seen on the glass. The microscope shows 

 that moisture is deposited on the whole surface, the size of the 

 minute water granulation increasing as the part of the picture is 

 darker in shade. The thickness of the glass seemed to make no 

 difference to the result, and several plates and coins might be 

 piled up alternately. If carefully protected, time appears to have 

 little effect on the figures, but they can be removed by rubbing 

 whilst the glass is moist. Failures and their causes were dis- 

 cussed, and the more complex phenomena produced by strong 

 discharges described. It was also pointed out that breath figures 

 could be produced by laying a coin on a freshly split surface of 

 mica, and that a coin laid on glass for some time leaves its 

 traces. Perfect reproductions of printed matter have been 

 obtained by placing a paper printed on one side only between 

 two sheets of glass for ten hours. Some substances, such as silk 

 in contact with glass, give white figures ; whilst wool, cotton, 

 &c., give black ones. Various analogous effects are noticed in 

 the paper, and the several views put forward in explanation of 

 the phenomena examined. — A communication on the same sub- 

 ject, from the Rev. F. J. Smith, was read by Prof. Perry, 

 He had investigated .some of the eflPects, and succeeded in 

 photographing the impressions, prints from which were shown. 

 He had also examined the influence of various gases on the 

 results, and found that oxygen gave the best figures. In a 

 vacuum no figures could be obtained. The effect of temperature 

 had also been tested. Prof. S. P. Thompson said details of 

 early researches were given in Poggendjrff's Annalen for 1842. 

 It was there pointed out that better results were obtained tiy 

 putting a spark gap between the coin and the machine. Since 

 the effects did not depend on the way in which the sparks 

 passed, he thought it was probable that electrical oscillations 

 were involved. He himself had worked at the subject in 1881, 

 and recently repeated some of the experiments. Figures could 

 be produced on almost any polished surface ; he got the best 

 results by using a small induction coil giving 3 mm. spirk, for 

 about five seconds. In 188 1 he accidentally noticed that photo- 

 graphs could be got on ebonite. Hot coins put on uncleaned 

 glass gave good breath figures. A member said that instead of 

 breathing on the plates, he and Mr. Garrett had sifted finely 

 powdered red lead on them, to get the figures. They had also 

 fixed the figures by etching with hydrofluoric acid. Mr. Croft 

 exhibited some figures he obtained two years ago, which were 

 still quite distinct. — On the measurement of the internal resist- 

 ance of cells, by Mr. E. Wythe Smith. After referring to the 

 methods hitherto used, the author describe! a modification of 

 Mance's test which he had recently devised. One pole of the 

 battery to be tested is connected to the similar poles of two 

 other batteries ; each battery has a separate circuit, through 

 which currents are allowed to pass. Selecting a point A at the 

 opposite pole of the battery to be tested, points B and C in the 

 circuits of the auxiliary batteries are found, whose potentials are 

 equal to that of A. The resistances between each pair of points 

 AB, AC, BC, are then measured by a Wheatstone's bridge. 

 Calling these resistances R^, Rj, and R3 respectively, it is shown 

 that the internal resistance required is given by the formula 



/^ = x-H-'-f--^+ &c., where x = ^i + R2-Ra ^ and r is the 

 r r^ 2 



external resistance of the circuit containing the battery tested. 

 For an accumulator discharging, d = x to within about 2 per cent. 

 Prof. Perry inquired how far the results obtained agreed with 

 those got by the older methods, and whether they depended on 

 the time the keys were kept down. In the old methods it was 

 assumed that an instantaneous rise in P.D. occurred on break- 

 ing the circuit. This might or might not be true. He was 

 inclined to regard the P.D. and current as functions, both 

 of resistance and time. The behaviour of cells seemed to in- 

 dicate the existence of something like capacity, or rather, 

 capaci:ies and resistances in series. Prof. Ayrton said the 

 paper was of great interest, for it made possible what could not 

 be done before, viz. to find the resistance of a cell without 

 appreciably altering the current through it. Although the new 

 method required more cells, this was not prohibitive, for the 

 result sought was of considerable scientific importance. The 

 s-ime method was applicable for finding the resistance of 



NO. I 184, VOL. 46] 



dynamo-armatures when working, a quantity which had hitherto 

 been unattainable by direct measurement. Mr. Lane Fox said 

 the perplexing changes in the P.D. of secondary cells were to 

 be accounted for by changes in the electrolyte, which occurred 

 in the pores of the plates. He could detect no flaw in the 

 reasoning given in the paper. Dr. Sumpner remarked that the 

 method was a valuable one, for it depended on bridge tests 

 which could be made with considerable accuracy. On the other 

 hand, it was a false zero method, and therefore liable to errors 

 arising from changes of this zero. Prof. Ayrton pointed out 

 that these errors could bi eliminated by reversing the bridge 

 battery. Mr. Rimingtoa siid a though the testing currents 

 were small they might affect the E.M.F., and thus introduce an 

 error in d. This might be tested by using alternate currents and 

 a telephone. In reply to Prof. Perry, Mr. Smith said the re- 

 sults agreed with those obtained by the older methods to within 

 the limits of accuracy obtainable by the latter methods ; this 

 might amount to something like 15 per cent. — On the relation 

 of the dimensions of physical quantities to directions in space, 

 by Mr. W. Williams. In February 1889, Prof. Riicker recalled 

 attention to the fact that, in the ordinary dimensional formulae 

 for electrical quantities, the dimensions of fx (permeability) and 

 A (specific inductive capacity) are suppressed. In the discussion 

 on that paper Prof. S. P. Thompson pointed out that lengths 

 should be considered as having direction as well as magnitude, 

 for, if so regarded, difficulties arising from different units, such 

 as cou/i/e and 2vor/:, having the same dimensions, would be 

 avoided. Developing this idea, the author takes three mutually 

 perpendicular lines, along which lengths are measured. Calling 

 unit lengths along these lines X, Y, and Z respectively, the 

 various dynauical units, such as velocity, acceleration, force, 

 work, &c., are expressed in terms of M, T, X, Y, and Z. The 

 formulae then denote the directional as well as the numerical 

 relations between the units, and the dimensional formulae are 

 therefore regarded as the symbolical expressions of the physical 

 nature of the quantities, so far as they depend on lengths, mass, 

 and time. In this system areas and volumes are represented by 

 products of different vector lengths instead of by powers of a 

 single length, and angles and angular displacements by quotients 

 of rectangular vectors, instead of being pure numbers. For 

 physical purposes pure numbers may be defined as ratios of 

 concretes of the same kind similarly directed (if directed at all). 

 A plane angle has dimensions X-^Y, X being in the direction 

 of the radius, and Y that of the arc, whilst solid angles have 

 dimensions YZX"^, and radii of curvature Y-'X"^. It is also 

 shown that tt is a concrete quantity of the dimensions either of 

 plane or of solid angle. This is of c:)nsiderable importance in 

 connection with the radial and circuital fluxes in the electro- 

 magnetic field. In deducing the dimensional formulae for 

 electrical and magnetic units, the rational and simplified rela- 

 tions given by Mr. Oliver Heaviside in the Electrician of 

 October 16 and 30, 1891, are used. Instantaneous axes are 

 taken at any point of an isatropic medium (the ether) 

 such that X coincides with the electrical displacements, Y 

 with that of the magnetic displacement, and Z with the 

 intersection of the two equipotential surfaces at that point. 

 Starting with the relation fx\\ — energy per unit volume, the 

 formulae for the various quantities in terms of ^u are obtained. 

 These simplify down to those of the ordinary electro-magnetic 

 system by putting m =1 and suppressing the distinction between 

 X, Y, and Z. Similarly, commencing with k^" = energy per 

 unit volume, formulae in terms of k are obtained, which, when 

 simplified as above, give those of the ordinary electrostatic 

 system. Examples of the consistent way in which the results 

 work out are given in the paper, and the whole subject is dis- 

 cussed in detail, both by Cartesian and vectorial methods. The 

 formulae in terms of fx and k are used to trace out and examine 

 the various analogies between electro-magnetism and dynamics, 

 thereby obtaining a connected dynamical theory of electro- 

 magnetism. Inquiry is then made as to what dimensions of ^t 

 and k in terms of M, T, X, Y, Z, render the interpretation of 

 electrical and magnetic units simple, natural, and intelligible as 

 a whole. The conditions imposed (for reasons stated in the paper) 

 are, first, that the dimensions of ix and k satisfy the relation 

 [fxk] = Z-T"2 ; second, that the powers of the fundamental units 

 in the dimensional formulae shall not be higher or lower than 

 those found in the formulae of the ordinary dynamical quantities ; 

 and, third, that quantities which are scalar or directed must also 

 be scalar or directed when their dimensions are expressed abso- 



