September 29. 1898] 



NATURE 



535 



find this instrument a help in explaining to beginners the pro- 

 perties of roulette curves in general. While most teachers will 

 probably reply that machines of this kind are more trouble than 

 they are worth in teaching, no one will question their interest to 

 the full-grown mathematicians themselves. 



A second paper by the same author dealt with his experi- 

 ments on the motion of a viscous fluid between two parallel 

 plates. A remarkable theorem, due to Sir George Stokes, 

 which was communicated together with the experimental paper, 

 renders this work of great importance. In Prof. Hele-Shaw's 

 arrangement, liquid is forced between close parallel plates, past 

 an obstacle of any form ; and the conditions chosen are such 

 that, whether from closeness of the walls, or slowness of the 

 motion, or high viscosity of the liquid, or from a combination of 

 these circumstances, the flow is regular. This is best attained 

 by using glycerine as the fluid ; then by colouring the jets which 

 enter between the plates at certain points, the lines of flow in 

 the liquid are made visible, and can be thrown on a lantern- 

 screen or copied. Now Sir George Stokes's discovery is this, 

 that the stream-lines thus experimentally obtained are the same 

 as the stream-lines in the steady motion of z. perfect (i.e. abso- 

 lutely inviscid) liquid flowing past an infinitely thin long rod, a 

 section of which is represented by the obstacle between the 

 parallel walls which confine the viscous liquid. A complete 

 graphical solution is thus experimentally obtained of a problem 

 which, from its complexity, baffles the mathematician except in 

 a few simple cases. 



Owing to the similarity, so far as mathematics are concerned, 

 between problems relating to the motion of a perfect fluid and 

 the problems of electricity and magnetism, this gives also a 

 method of investigating electrical and magnetic problems, in 

 which the effiect of placing a body of any required form and 

 resistance {i.e. with any value of fi) in a uniform field can be 

 obtained. 



The beauty of the experiments greatly interested the audience, 

 many of whom were probably unable to follow easily Sir George 

 Stokes's mathematics ; it is to be hoped that some of the results 

 will figure before long as diagrams in hydrodynamical text- 

 books. 



Of the next paper, "Graphic representation of the two 

 simplest cases of a single wave," by Lord Kelvin, an account 

 will subsequently appear in these columns. 



At meetings of the mathematical session in future years it is 

 proposed to have a number of reviews of recent progress in 

 various branches of pure mathematics, similar to those frequently 

 prepared by German and American mathematicians. Several 

 such reports are being arranged for next year, and this year a 

 paper on "The recent history of the theory of the functions 

 used in analysis " was given by Mr. E. T. Whittaker. The 

 paper traced some of the more notable developments in the 

 theories of special classes of functions, notably the auto- 

 morphic functions and the functions of harmonic analysis. 

 Then, speaking of the way in which most of the knowledge 

 reviewed has been gained, " Isolated functions are invented, as 

 Legendre'sand Bessel's functions were invented, for the solution 

 of physical problems. The work of the pure mathematician is 

 to find the connection between them, to assign them places in 

 an ordered series, and to develop their common theory. The 

 arrangement once made, the gaps in the series are manifest. 

 Every gap points to a function hitherto unknown, which is dis- 

 covered and returned to the physicist, as the interest on his 

 original deposit." 



Two papers by Dr. Johnstone ,Stoney followed. The first, 

 " The dynamical explanation of certain observed phenomena 

 of meteor streams," attempts to account for the facts observed 

 in meteoric showers on the earth, by considerations as to the 

 streams of meteors which cause them. A shower may be very 

 short, or it may last several days ; its radiant — the point in the 

 sky from which the stars appear to shoot — may remain fixed, or 

 it may move ; the disposition of the shower about its maximum 

 may be symmetrical, or it may not; and in all these respects, the 

 showers due to the same stream of meteors may behave 

 differently in different years. 



At each encounter of the meteors with the earth a number are 

 caught and blaze themselves out in the atmosphere ; a still larger 

 number narrowly escape, and are deflected from their course by 

 the earth's attraction. Dr. Stoney showed how the subsequent 

 history of these " clino-meteors " will account for the facts 

 noticed. This is especially interesting in view of our approaching 

 encounter with the Leonid meteors. 



NO. 1509, VOL. 58] 



In a second paper, " A survey of that part of the scale upon 

 which nature works, about which man has some information," 

 Dr. Stoney reviewed the range of our knowledge of magnitudes, 

 and discussed what might be if the scale of our conceptions 

 were of another order. 



The last paper on the day's list was by Prof. G. J. Stokes, of 

 Cork, on "The imaginary of logic." The search for a philo. 

 sophical theory of >/ - i has occupied men's minds ever since it 

 was found that "impossible" quantities were useful. After 

 classifying various views on the matter, the author said that the 

 generally adopted position, that y/ - i is uninterpretable in single 

 or pure algebra, is paradoxical ; for how can what is essentially 

 meaningless possess an important meaning in its extraneous use? 

 Then explaining the logical theory of the imaginary, he applied 

 it to De Moivre's Theorem. The paper concluded with a com- 

 parison of the Calculus of Boole's Laws of Thought with that 

 of Grassmann's Ausdehnungslehre, and some remarks on the 

 relation of non-commutative algebras to ordinary mathematics. 



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