November 17, 1892] 



NATURE 



69 



This was ea'^ily reduced by a Bunsen flame, so as to represent 

 a metallic prism with an aa^Ie of some 20 seconds. Only oae 

 in twenty of the prisms could be used, and only one in 200 silver 

 or gold prism-!. The source of li^ht was a zironiu a burner 

 with a red shade transmitting light of the mean wave-lenijth 

 64 X 10- cm. The index of refraction was found to vary with 

 the incidence. For perpendicular incidence the following 

 values were found : Au 0*26, Ag 0'35, Cu 0"48, Pt i 'gg, Ni 

 2"oi, Iron 302, Co 3 16. For silver the index was 0*39 at an 

 incidence of lo*, o"6oat 30°, o"8o at 50°, I'oi at 80°, and 1*03 

 at 90°. The following refractive indices for various wave- 

 lengths illustrate the dispersion : 



Li, a D F G 



Au ... 029 ... 066 ... 0-82 ... 0-93 

 Ag ... o 25 ... 0-27 ... 0-20 ... 0-27 

 Cu ... 0-35 ... o-6o ... I-I2 ... 1-13 

 Pt ... 202 ... 176 ... 163 .. 1-41 

 —On a law of refraction for the entrance of light into absorptive 

 media, by H. E. J. G. du Bois and H. Rubens.— On the infra- 

 red emission spectra of the alkalies, by Benjamin W. Snow.— 

 Absolute change of phase in light by reflection, by Paul Glan. 

 — Inducti e r.-presentation of the theory of double refraction, by 

 Franz Kolacek. — Studies in the electric theory of light, by D. 

 A. Goldhammer. — On the passage of feeble currents through 

 electrolyte cells, by Rud. Lohnstein. — On the m >tion of the 

 lines of force in the electro-magnetic field, by Willy Wien. — On 

 the electric theory of magneto-optic phenomena, by D. A. 

 Goldhammer. — An automatic interruptor for accumulators, by 

 H. Ebert. This is to prevent the current from the accumulator 

 exceeding the supply for which it is constructed. Tato mercury 

 cups are inserted in the circuit, connected by a piece of ^tout cop- 

 per wire. The current next passes through an electro-ma.jntft. As 

 soon as the current reaches a certain strength the electro mignet 

 overpowers an adjustable spring, and lifts the copper connecting- 

 piece out of the cups.^ — Contribution to the history of the 

 spheroidal phenomena, by G. Berthold. 



SOCIETIES AND ACADEMIES. 

 London. 

 Physical Society, October 28.— Dr. J. H. Gladstone, 

 F. R.S., past president, in the chair. — The discussion on Mr. 

 Williams's paper, "On the relation of the Dimensions of Physical 

 Quantities to Directions in Space," was opened by Pr )f. Perry 

 reading a communication from Prof. Fitzgerald, president. 

 The writer said Mr. Williams disagreed with the suggestion that 

 electric and magnetic inductive capacity are quantities of the 

 same kind principally because he had not got over the curious 

 prejudice that potential and kinetic energy are different. No 

 theory of the ether could be complete unless it reduced its energy 

 to the kinetic form. Electric and magnetic inductive capacity 

 would pro'iably be found to be similar in the ether, and ulti- 

 mately have the same dimensions. The analogies were not yet 

 complete, but only in respect of matter was it probable that any 

 difference existed between them. Diamagnetism corresponded to 

 electrostatic induction, but paramagnetism had no definite 

 electrical analogue. He was inclined to regard the phenomena 

 of paramagnetism as connected with the arrangement of the 

 material molecules, whilst diamagnetism depended on the 

 electric charges on those molecules. So far no matter had been 

 found which conducts magnetism, and such may not exist in our 

 universe, but it may be gravitationally repelled by matter as we 

 know it. — Mr. Madan remarked that in the first part of his 

 paper Mr. Williams recognized that dimensional formulae were 

 originally change-ratios, but puts this aside for the higher con- 

 ception which regards the e formulse as expressing the nature of 

 the quantity. Fourier showed how to find the dimensions of 

 units by making the size of the fundamental units vary. But 

 k (specific ind ictive capacity) did not vary with the fundamental 

 units, for it was merely the ratio of the capacities of two con- 

 densers, and therefore, by Mr. Williams's definition, a pure 

 number. It was difficult, he said, to see how k could have 

 dimensions, but Mr. Williams regarded it as a physical quantity, 

 and therefore possessing di nensions. The object in giving 

 dimensions to k and /x seemed to be to get over the double 

 system of units. Mr. Madan did not think that dimensions 

 could express the nature of physical quantities, and said differ- 

 ences of opini )n existed amongst authorities on this point. For 

 example, Dr. J. Elopkinson, at the last B. A. meeting, said that 

 because a co-efficient of self-induction had the dimensions of 



NO. 1203, VOL. 47] 



length it must be a length, whilst other learned professors 

 oDjected to this view. Even if one admitted that dimensions 

 are a test of the nature of physical quantities it was not necessary 

 that the two systems of units should be identical. The connect- 

 ing link between the two systems was Q = C /, and the validity 

 of this equation had beenqaeslioied. If this objection be con- 

 firmed, then there would be no current in electrostatics and no 

 Q in the electromagnetic system, and the units would not clash. 

 Referring to dynamical units, Mr. .Madan pointed out that two 

 units of mass were used in astronomy, but asir )nomers got over 

 the difficulty by using a co-efficient. Dimensional formulse, he 

 sai I, zxi the result of a convention that certain definitions should 

 hold true generally, b it they contain no further information 

 respecting the nature of the quantities beyond that involved in 

 those definitions. As an example of the inability of such 

 formulae to expre-s the nature of quantities, he p minted out that 

 whilst physical differences were known to exist between + and 

 - electricity the dimensional formulse showed so signs of such 

 differences. — Prof. Riicker said every correct physical equation 

 consisted of a numerical relation between physical quantities of 

 the same kind, and might be written either as a mere 

 numerical equation or as a relation between the physical 

 quantities themselves. . The equation 2-1-1=3 ™ay 

 correspond to 2 feet + I foot = 3 feet, and the 

 latter may be written 2, L] -(- i[L] = 3[L]. where [L] repre- 

 sents the unit of length. So far as he was a^'are, noOody but 

 a rec.-nt writer in the Electrician had denied that in such an 

 equation [L] represented a concrete quantity. Maxwell ex- 

 plicitly stated that it does in his article on "Dimensions" 

 (" Encyl. B itt.") and elsewhere, and Prof. J. Thomson, in his 

 paper on the same subject, makes no statement contrary to this. 

 The ab)ve equation might also be written 2[feet] -f- i[foot] 

 = l[yardj. Another equation involving time is 6o[sec.] = 

 I [minute], and ilividing one by the other one gets 



A difficulty was felt here in understanding what dividing a foot 

 by a second meant ; tmt this difficulty Prof. Riicker considered 

 was not greater than that involved in dividng an impossible by 

 a real quantity, a very famibar ana'ytical device. Reasons for 



regarding the symbols I - — I as legitimate were then given. 



L=»cc J 

 Prof. Henrici said the communication under discussion was one 

 ofthev..ost important contributions to physical science which 

 he had come across for a long time. Such difficulties as pre- 

 sented themselves in the paper arose from its fundamental 

 character. The author had attempted to express all physical 

 quantities in terms of three, but quantities may exist which 

 cannot be completely represented in terms of L, M and T. 

 The tendency of modern mathematics was to express everything 

 dynamically. Mathematicians had lo g been in the habit of 

 using q lantities which were neither numbers nor concretes in 

 the ordinary sense, and different kinds of algebra wiih units not 

 understandable had been developed. If a quantity, a times a 

 unit M, be multiplied by b times another unit v, the result is 

 expressed by cib uv, where al> is a num')er and uv a new unit 

 which may or may not be physically interpretable. The inter- 

 pretation of a product depended on the meaning attached to 

 "multiplication," and if this be restricte.l to "repeated ad- 

 dition " the range is very limited. The narrow conceptions 

 concerning multiplication acquired at school could only be re- 

 moved by a careful study of vectors. .Mr. Williams had treated 

 his subject by vector methods, but a few traces if quaternions 

 remained which might be omitted. To truly understand the 

 subject, vectors must be treated vectorially. Dimensions might 

 then show the nature of the quantities involved. The system 

 adopted in Mr. Williams's paper was probably the best attain- . 

 able at present, hut he (Prof. Henrici) looked forvtard to the 

 use of a more fundamental quantity than the vector— viz. " the 

 point " — as the ultimate basis. Grassmann had worked out a 

 "point calculus" in 1844, which was republished in 1880, 

 Quantities more complex than vectors, viz. rotors, screws, mot >rs, 

 &c., had been used with advantage by Clifford, Ball, and others. 

 Dr. Sumpner thought the first ideas of students on the subject of 

 dimensions were that they represented the nature of the 

 quantities, but could not see why every quantity should be ex- 

 pressed in terms of L, M and T. Prof. Kiicker's paper on 

 "Suppressed Dimensi >ns " had cleared up several important 

 points, and he (Dr. Sumpner) now considered that every quantity 



