Ii6 



NA TURE 



[December i, 1892 



the whole of the great marsh to the south is flooded up to 

 Chitambo. The level at that time was made out to be 3750 

 feet, about 250 feet lower than Livingstone's estimate. Altera 

 rest for recovering health the expedition followed the Luapula 

 eastward through fertile country, and leaving it where the curve 

 from the north occurs, struck across for the Kafue, but small-pox 

 reappeared, the land was ravaged by half-caste Portuguese 

 slave-raiders, Mr. Thomson himself fell ill, and the course had 

 to be changed to the south with the hope of turning west again. 

 But matters got worse instead of better, and after touching the 

 borders of Manica, a return had to be made to Lake Nyassa, 

 along the southern margin of the plateau, through deep valleys, 

 and climbing the steep slopes of the Muchinga Mountains, here 

 separated by the great parallel valley of the Lukosashe from the 

 plateau. All the way the land was seen to be of immense 

 possibilities for cultivation, but neglected, and inhabited by a 

 wretched people governed by Mpeseni, himself the vilest of them 

 al). Kotakota on the- lake was reached again on January 

 4th, 1891, after a total journey of 1200 miles, which resulted 

 in many important rectifications of position and much infor- 

 mation as to the future possibilities of the plateaux. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Cambridge. — Dr. Hobson, late deputy Lowndean Professor, 

 has been elected a representative of the Mathematical Board on 

 the General Board of Studies. 



Plans for a handsome building to serve as the Sedgwick 

 Memorial Museum of Geology have been submitted to the 

 Senate, the estimated cost being ;^26,ooo. Four members of 

 the Syndicate appointed to prepare the plans dissent from the 

 report of the majority, chiefly on the ground that the internal 

 arrangements are unsatisfactory, and that the cost, initial and 

 annual, of the proposed building will be excessive. The diver- 

 gent views held on the subject will be discussed by the Senate 

 on Saturday, December 3. 



The Senate have agreed to confer on Sir R. S. Ball, the new 

 Lowndean Professor, the complete degree of M.A., honoris 



SOCIETIES AND ACADEMIES. 

 London. 

 Physical Society, November ii. — Mr. Walter Baily, M.A., 

 Vice-President, in the chair. — The discussion on Mr. Williams's 

 paper, the dimensions of physical quantities, was resumed by 

 Dr. Burton. He remarked that the idea that so-called *' specific 

 quantities," such as specific gravity, are pure numbers was an 

 erroneous one, and liable to lead to difficulties. The specific 

 gravity of a substance was of the nature of density, and was 

 only a simple number on the convention that the density of 

 water was taken as unity. If dimensions be given to specific 

 quantities their interpretation would, he thought, be easy when 

 the rational dimensional formulae were found. Referring to 

 Prof. Fitzgerald's comments, he said, although the contention 

 that all energy is ultimately kinetic could not be gainsaid, the 

 distinction commonly drawn between kinetic and potential 

 energy involved nothing contrary to this view, and was useful 

 and convenient in many cases. As to the dimensions of jx and k 

 he was inclined to favour Mr. Williams's views, for several con- 

 siderations suggest that the two capacities of the medium are 

 essentially different. Arguments to show that fx. was probably 

 absolutely constant in the ether, whilst k might be variable, 

 were brought forward. Of the two systems of dimensions for 

 /i and k suggested by Mr. Williams, that which made ^u a 

 density seemed preferable, — Prof A. Lodge said he was greatly 

 interested in propagating the idea that physical quantities are 

 concrete, and therefore welcomed Mr. Williams's paper. He 

 thought it desirable to keep some names for abstract numbers, 

 and "specific gravity" should be one. If another name 

 involving dimensions was required "specific weight," or 

 "weight per unit volume," might be used. Speaking of the 

 dimensions of the various terms of an equation he did not think 

 it was usually recognized that in ordinary algebra or Cartesian 

 geometry the principle of directed terms was rigidly ad- 

 hered to, for if directed at all every term of such an equation 

 was directed along the same line. In this respect ordinary 

 algebra was more rigid than vector algebra. Even if circular 



functions were involved, as in polar co-ordinates, they had the 

 effect of making the directions of the terms the same. Other 

 instances of problems bringing out the same fact were men- 

 tioned. Mr. Boys thought Mr. Madden had been arguing in a 

 circle when he spoke of the astronomical unit of mass, and 

 deduced the dimensions of mass as L^T^ from the equation 

 MLT~2 = M7L'', for it was quite impossible that this equation 

 could be true unless 7, the gravitation constant, was intro- 

 duced on the right-hand side. Mr. Williams's method 

 was quite the reverse, for he maintained that unless k and 11 

 were introduced in the dimensions of electric and magnetic 

 quantities, their dimensional formulae could not indicate the true 

 nature of those quantities, and hence were open to objection. 

 Mr, W, Baily, whilst agreeing with Mr. Williams on most essen- 

 tial points, thought the total omission of L from dimensional 

 formulae made the expressions more complicated and less sym- 

 metrical. For example, such expressions as XY/Z, X^ and 

 XYZ, which respectively represent undirected length, area, and 

 volume, might with advantage be written L, \?, and L* respec- 

 tively. The restriction of the dimensions of fx. and k to those 

 which give interpretable dimensional formulas for electrical and 

 magnetic quantities seemed scarcely justified. Both the systems 

 proposed could not be right, and he thought it would be more 

 in accordance with our present want of knowledge, if a quantity 

 U of unknown dimensions were introduced such that jii or ^= U". 

 density and /^~i or /i"^ = U-. rigidity. This would keep in view the 

 fact that the absolute dimensions of quantities involving U were 

 unknown. A list of the dimensions of the various quantities 

 based on this arrangement was given. Mr. Swinburne, referring 

 to the conventional nature of many units, said great differences 

 exist between the ideas held by different persons about such 

 units. Starting with the convention that unlike quantities 

 could be multiplied together, he might have six amperes flow- 

 ing in an electric circuit under a pressure of ten volts, and he 

 might say he had sixty volt-amperes. The term "volt-ampere" 

 could be regarded as indicating that the sixty was the numerical 

 result of multiplying a number of volts by a number of amperes, 

 or on the other hand it might be understood as a new unit, a 

 watt, compounded of -a volt and an ampere. Before Prof. 

 Riicker's paper on suppressed dimensions was published, an 

 electrician might have suggested measuring the length of a 

 bench by sending an alternating current through it and deter- 

 mining its self-induction, which he regarded as a length. 

 Prof. Riicker, however, would say that this could not give the 

 right result, for fx must be taken into account. He was inclined 

 to think that dimensions were liable to mislead. Referring to 

 scientific writers as authorities, he said Maxwell had been 

 careless in some cases, for he had sometimes given dimensional 

 formulae as zero, which really ought to have been L° M° T°, or 

 unity. In French text-books the errors had been corrected. 

 Mr. Williams, in reply to Mr. Madden's remarks about self- 

 induction being a length, pointed out that the subject might be 

 looked at in two different ways, depending on whether one 

 thinks of the j/««a^ar(f of self-induction as the practical standard 

 of measurement, or the unit of self-induction as a physical 

 quantity. In the former case the standard yf&s a length, but in 

 the latter the tmit was a quantity of the same species as self-induc- 

 tion, the nature of which was as yet unknown. If its dyna- 

 mical nature was known, then the absolute dimensions of all 

 other magnetic and electric quantities would also be determined. 

 In answer to Prof. Fitzgerald's remarks he said it was hardly 

 likely that he should be unacquainted whh the common view 

 that kinetic and potential energies were ultimately quantuies of 

 the same kind, for it was a view with which he was quite 

 familiar. The fact that they have the same dimensions was 

 sufficient to show their identity, and the idea that all energy is 

 ultimately kinetic was fundamental to his paper. This, how- 

 ever, did not imply that electrification and magnetization are 

 of necessity the same, and the suggestion that they may be the 

 same was only one of several "probable suggestions," all of 

 which were entitled to consideration. His chief reason for 

 regarding Prof. Fitzgerald's suggestion as probably incorrect 

 was that it led to a system of dimensional formulae incapable of 

 rational mechanical interpretation, and containing fractional 

 powers of the fundamental units. Prof. Fitzgerald's system 

 would make resistance an abstract number, and yu and k directed 

 quantuies, whereas the former was a concrete quantity and the 

 two latter must be scalar in isotropic media. If he (Mr. 

 Williams) had erred in treating electrification and magnetiza- 

 tion as different phenomena he could only plead that he had 



NO. 



1205, VOL. 47] 



