404 



NATURE 



{Feb. 2 1, 1889 



This value satisfies the equation— 



A2 



so soon as we settle that, 



and - will be the velocity of light. And, indeed, the introduced 



equation is satisfied everywhere, except at the origin. 1 



In order to find out what electrical processes are set up by the 



distribution of forces specified by n, we investigate its immediate 



surroundings. 



We put p vanishing in comparison with A, and neglect mp in 



comparison with nt. 

 Then— 



n 



Since, now- 



we have — 



E— sin nt. 

 P 



\dx' dy- )p dz- \p J 



", Y 



dxdz 



/2n 2 = - '^ 



dydz' dzdz' 



So the electric forces appear as the derivative of a potential — 



^ dn ^, . , dfi\ 

 <p = — = E/ sin ni . — ( - ) ; 

 dz dz\p J 



and this expresses an electrical \_Doppelpunkt, by which I suppose 

 is meant either an involution or a spherical harmonic] whose axis 

 coincides with the z axis, and whose moment oscillates between 

 the extreme values E/ and - E/ with the period T. 



Our force distribution, therefore, represents the action of a 

 rectilinear oscillator which has the very small length /, and on 

 whose poles at the maximum the quantities of electricity ± E 

 are free. 



The magnetic force perpendicular to the direction of the 

 oscillator is, in the immediate neighbourhood, 



P = - AE/« cos nt ^— . 

 P 

 According lo the Biot-Savart law, this is the force of a 

 current element in the direction of the axis of z, of length /, 

 whose intensity, magnetically measured, oscillates between the 



extreme values ± '^ _ . In fact the motion of the electricity 



E corresponds to a current of that magnitude. 

 From n we get — 



I cos {mp- nt) - ^^°i^P--:ii^l 

 I mp ) 



and from this the forces Z, R, P follow by differentiation. 



The formulae are too complicated for it to be possible to obtain 

 immediately from them in their general form a representation of 

 the distribution of the forces. For some special cases the results 

 are meanwhile proportionately simple. We get these at once— 



(1) The immediate neighbourhood of the oscillator we hive 

 already treated. 



(2) In the z axis, i.e. in the direction of swing, we have 

 dr — pdd, dz = dp, = o; so then — 



R = o, P = o, 



Z = 2-^ jcos (mp-nt) - smi^-«^) 

 p I mp 



Elm 



svcC- 6, 



}■ 



The electric force acts always in the direction of the oscilla 

 tor ; it diminishes for small distances a-; the inverse cube, for 

 greater distances as the inverse square, of the distance. 



(3) In the xy plane, or z = o, we have dz = - pd6, dp = dr, 

 6 = 90, and so — 



P = 



AE/mn 



sin {mr 



R = o, 



sin (mr - nt) - 



«^) + ^os {mr-_nt)\ 

 mr J 



cos (mr 



mr m'r- J 



The electric force in the equatorial plane through the oscillator 

 is parallel to the oscillation, its amplitude being — 



E/ 



-J Vl - 'w'^^ + m*r\ 



The force decreases with distance, at first quickly as the 

 inverse cube, later only slowly, and inversely as the distance 

 itself. At great distances the action of the oscillator can only 

 be noticed in the equatorial plane, not in the axis itself 



(4) At very great distances we can neglect higher powers of l/p, 

 compared with lower ones. So we get at such distances — 



whence- 



Thence follows- 



Q = E/m cos [mp - nt) sin- Q, 



P = A ^^"^^ sin {mp - nt) sin B, 

 P 



ry Elm''' ■ , ., • .1 /. 



Z = - sm (;«p - nt) sm-' d, 



P 



Elm"' 



sin {mp - nt) sin Q cos 0. 



Z cos e + R sin 6 



The direction of the force is therefore at great distances every- 

 where normal to the radius vector from the origin of force ; the 

 spreading out occurs in pure transverse waves. The magni- 



tude of the force is equal to 



Elm^ 



sin {mp - nt) sin 9, and de- 



creases at a constant distance from the origin towards either axis, 

 being proportional to the distance from this latter. 



{To be continued.) 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Cambridge. — A Report on the new Chemical Laboratory 

 states that it has cost in all ;^33,697, an excess of ^^3000 above 

 the estimate in 1885. The fittings and machinery have cost 

 ;^i90O more than was estimated, and the foundations had to be 

 made stronger at a cost of £^'^0. The Financial Board state 

 that they have every reason to believe that the University has 

 full value for the outlay. The building and fittings are sub- 

 stantial and well adapted to their purpose. Prof Liveing 

 reports that the lecture-rooms are such that the audience can 

 both see and hear, can sit comfortably and write with ease, and 

 that the laboratoriis will bear comparison with the best of those 

 to be found elsewhere. 



^200 is asked for the purchase of additional apparatus for the 

 Pathological Laboratory (the old Chemical Laboratory). 



At Cavendish College eight scholarships of ^^jo per annum 

 will be offered on July 23 next to students who will be under 

 eighteen years old on October i next. One or more may be 

 given for natural science (chemistry, physics, botany, geology, 

 in all of which there will be a practical examination). Further 

 particulars may be obtained from the Master of Cavendish 

 College. 



SCIENTIFIC SERIALS. 



Bulletins de la Societe d\4nthropologie de Paris, tome II, 

 fasc. 3, 1888. — Continuations of M. G. Herve's observations on 

 the cerebral convolution known as " Broca's." Great import- 

 ance attaches to the discovery by the late eminent M. Broca of 

 this anatomical characteristic in man, which he found to be 

 absent in all animals below the Anthropomorpha, and while it 

 appears in the latter only in a simple and rudimentary form, it 

 is fully developed in the human brain. This fact in itself gives 

 support to the hypothesis that intermediate types, now lost, 

 must have been interposed between man and the still existing 

 forms of the Anthropomorpha, and yet more important are the 

 results yielded by recent physical researches, which clearly show 

 that the normal human brain possesses a quadruple system of the 

 frontal convolutions due to the doubling of the binary frontal 

 lobes, while in Broca's convolution we must, moreover, recc^- 

 nize the origin and function of speech and memory. In the 

 microcephali, in idiots, deaf-mutes, and in all persons of inferior 

 intelligence, this convolution is more or less atrophied, espe- 

 cially within the insula or centre, where it unites with the other 

 frontal convolutions near the extremity of the olfactory channel. 

 — Close of the statistical inquiry regarding the colours of the 

 eyes and hair in France, by M. Topinard. After having col- 

 lected the results of 180,000 observations, M. Topinard an- 



I 



