February i8, 1892 



NATURE 



371 



This may be written 



Now, if there be no inductive action — that is, if the 

 field be wholly electrostatic — 



dYlcil, dGjcit, dUlcit = o, 

 and hence, for two electric shells — 



""/^M^T-- 



On the other hand, if the action be wholly inductive- 

 that is, if we have no so-called electrostatic action — 



d<l>/dx, d(pldy, dtpjdz = o, 

 and for two varying solenoids we have — 



--/^vM'^; 



If, then, there be the same mutual action between the 

 two varying solenoids as between their equivalent electric 

 shells, we must have U = U'. But because of the equi- 

 valence the value oi dYldt, &c., produced at any point by 

 either solenoid, must be the same as those of d(f)/(/x, &c., 

 produced at the same point when the solenoid is re- 

 placed by its equivalent electric shell. Thus we get 

 U/U' = K/(K - X), and therefore X = o. Thus, if the 

 principle of the unity of electric force is true, X = o, and 

 we have Maxwell's theory. 



Dr. Oliver Lodge has, as is well known, endeavoured 

 to detect the existence of an electrostatic field produced 

 by varying magnetic action (Nature, May 23, 18S9, and 

 Electrician, May 17, 1889), and has reason to believe 

 that he has been successful. It is also possible, as Poin- 

 car^ suggests, that this kind of electrostatic action may 

 be developed when iron rings, &c., are placed in the field 

 of an alternating electromagnet, as in the experiments of 

 Elihu Thomson. 



In a note, which forms a supplement to the comparison 

 of the theories of Helmholtz and Maxwell, M. Poincard 

 points out that when the mutual action of a varying 

 solenoid and an electric shell is considered, contradictory 

 results are obtained accordmg as the solenoid is regarded 

 as fixed and the shell movable, or the shell fixed and the 

 solenoid movable. Thus the theory of Helmholtz in this 

 application does not give fulfilment of the third law of 

 motion. 



Possibly, some such theory as this may throw some 

 light on the electric phenomena of voltaic cells, with their 

 finite steps of potential across the surfaces of separation 

 of dissimilar substances, and help to refer the production 

 of all currents to the single cause — electromagnetic 

 action. 



We come now to the discussion which the book con- 

 tains of the experiments of Hertz. This fills considerably 

 more than one-half of the work, and we cannot, in the space 

 left at our disposal, give an adequate account of it. Of 

 the experiments themselves it is not necessary to say 

 anything, as they have been fully and ably discussed in 

 Nature by Mr. Trouton (February 21, 1889). Hertz's 

 own theory of the radiation of electric and magnetic 

 energy has also been given in these pages by Dr. Lodge 

 (February 21, 1889, et seq.). Poincare's presentment of the 

 theory is, however, marked by many points of originality, 

 and abounds in acute and interesting remarks. 



The theory of the dumb-bell exciter used by Hertz is 

 first considered, then the field produced is discussed, and, 

 last of all, the action of the resonator or receiver is dealt 

 with. Taking the exciter as a couple of spheres, 15 cms. 

 in radius, placed with their centres 150 cms. apart, and 

 joined by a wire \ cm. in diameter, Poincard calculates 

 (i) the capacity, (2) the self-induction of the arrangement. 

 The value of the capacity of the arrangement of two 



NO. I 164, VOL. 45] 



spheres used by Hertz in the calculation of the period of 

 the exciter was that of each of the spheres by itself, viz. 

 15 cms. Now, if one of the spheres were alone in its own 

 field with a charge q and at a potential V, we should have 

 ^/V = 15. But at any instant when the charge of one 

 sphere is q, that of the other sphere \% — q \ and since 

 the spheres may be taken as nearly without mutual influ- 

 ence, the difference of potential between them is 2V. 

 The capacity is, then, ^/2V, or 7-5 cms. — half the value 

 used by Hertz. That this is the proper value to use for 

 the capacity is easily verified by a reference to the mode 

 of establishing the equation of oscillation, when it is seen 

 that the capacity is really defined by that equation as the 

 charge on one of the sjrfieres divided by their difference 

 of potential. 



The calculation of the self-induction given by Poincard 

 is interesting. Regarding, as an approximation, the 

 currents in the spheres, and the influence of the spark- 

 interval, as negligible, and taking the wire as of length / 

 (equal to the distance between the centres of the bulbs), 

 and of diameter d, and assuming that the current is wholly 

 on the surface of the wire (which it is approximately, when 

 in rapid alternation) he finds — 



L = 2/jlogi^- 



- I \ 



-2 i 



where k is the quantity which appears in Helmholtz's 

 theory. 



This differs from the value given by Hertz in having 



- I for the middle term within the brackets instead of 



- 75, and {k - i)/2 instead of (i - k)li for the third 

 term. The first discrepancy arises through the currents 

 having been taken by Hertz as uniform over the cross- 

 section of the wire, and the second probably through an 

 error in sign. The self-induction, L, is 1902 cms. if the 

 term involving k is not taken into account, and (1902 + 

 150) cms. if k be put equal to zero. 



Calculating the period T (= 27r\/LC, where C is the 

 capacity in electromagnetic units), we find it to be 

 2-51 X 10-^ seconds, and multiplying by the ratio of the 

 electromagnetic unit of quantity to the electrostatic unit, 

 or V, we get for the wave-length 7 '53 metres. Hertz gives 

 177 for the calculated half period, and 531 for the corre- 

 sponding half wave-length. On account of the error in the 

 estimation of the capacity, it is clear that this value of the 

 half period and half wave-length must be divided by x''2, 

 and this brings them into agreement with the values first 

 stated. There is, however, a serious discrepancy between 

 the results of theory and experiment, which we shall 

 notice presently. 



The calculation of period, &c., of course proceeds on 

 the assumption that the resistance is negligible, and this 

 is no doubt the case to a sufficient degree of approxima- 

 tion. In the theory itself, also, no account is taken of 

 the induction coil or of the displacement currents in the 

 dielectric ; further, the energy is dissipated, not merely 

 by the production of heat, but by radiation into the di- 

 electric. That the influence of the induction coil is 

 indeed negligible Poincard gives reasons for supposing ; 

 in fact, on account of the enormous self-induction of the 

 induction bobbin, and the small mutual induction of the 

 exciter and the bobbin, the corrected differential equation 

 is the one formerly found for the oscillation, with the 

 addition of an exceedingly small term, so that the solu- 

 tion is practically the same as before. (Here, p. 162, the 

 expression ''a dtant trts grand" should be "a dtant 

 tr^s petit"). As Poincard states, the vibration of the 

 exciter is like that of a very small pendulum attached to 

 a massive pendulum of long period ; the period of the 

 former is very little affected by its mode of support. For 

 a similar reason the period is very little affected by the 

 very considerable capacity of the bobbin. 



Experimenting on the velocity of propagation of electro- 



