August 2, 1888] 



NA JURE 



335 



That is, 



'II 

 dt 



dx 



, &c, on S'. 



Therefore the creation of the given system of currents on S 

 acts as an electromotive force tending to produce the currents 

 //, r, 7v with reversed signs on S'. And since this system of 

 currents in S' is self-inductive, it will be actually generated by 

 induction. As an example, if 



f 



S = - 



b' c- 



</S di> 



ay dz 





+ JL * O. 



dt 



dy' 

 &> — 



de 



and <p = Kz, 



dS dd> 



u = ~ 



dz dy 



and therefore v"« = o. 



It follows that the creation in an ellipsoidal shell of thickness 

 proportional to the perpendicular from the centre on the tangent 

 plane of a system of currents of the type (f> = Az generates by 

 induction the corresponding system of currents with reversed sign 

 in an inner concentric similar and similarly situated ellipsoidal 

 shell. 



(17) Case of an Infinite Plane: Aragds Disk. — In this case, 

 if the shell be of uniform thickness, a system of currents in it will 

 not be generally self-inductive, but admits, nevertheless, of 

 mathematical treatment. Suppose the plane to be fixed, and 

 the field to revolve round an axis perpendicular to it, taken for 

 that of z, with uniform angular velocity, w. 



Let j' be the normal force due to the field, y' that due to the 

 induced currents. Then we have, as the effect of induction, — 



dy 



dt 



As the effect of resistance— 



dy' _ a dy\ 



dt 2ir dz 



and, therefore, for the whole variation of y' — 



dy dy' a dy' 



dt dt ■ 27r dz ' 



When the motion is steady — ■ 



dy dv dy' 



— = « — , i- 

 dt 11B dt 



6 being the angle through which the field has turned. Hence— 



~'tfy d/\ a_ d/ 



\dd + dd J 2ir dz' 



a result which agrees with Maxwell's (23) of Art. 699. 



June 21. — " Effects of Different Positive Metals, &c, upon the 

 Changesof Potential of Voltaic Couples." ByDr.G. Gore, F.R.S. 



In this research numerous measurements were made, and are 

 given in a series of tables, of the effects upon the minimum- 

 point of change of potential of a voltaic couple in distilled water 

 (Roy. Soc. Proa, June 14, 1888), and upon the changes of 

 electro-motive force attending variation of strength of its 

 exciting liquid {ibid.), obtained by varying the kind of positive 

 and of negative metal of the couple, and by employing different 

 galvanometers. The measurements were made by the method 

 of balance through a galvanometer, with the aid of a suitable 

 thermo-electric pile (Birm. Phil. Soc. Proa, vol. iv. p. 130; 

 The Electrician, 1884, vol. xi. p. 414). The kinds of galvano- 

 meter employed were, an ordinary astatic one of 100 ohms 

 resistance, and a Thomson's reflecting one of 3040 ohms 

 resistance. 



The following were the proportions of hydrochloric acid 

 (HC1), required to change the potential of different voltaic 

 couples in water : — 



Table I. — Hydrochloric Acid. 

 Astatic Galvanometer. 



Zn + Pt between 1 in 9,300,000 and 9,388,185 



Cd + Pt „ 1 ,, 574»°oo ,, 637,000 



Mg + Pt ,, 1,, 516,666 ,, 574,000 



Al + Pt ,, 1 ,, 12,109 ,, 15,000 



Reflecting Galvanometer. 

 Zn + Pt between 1 in 15,000,000 and 23,250,000 

 Cd + Pt .,, 1,, 1,162,500 ,, 1,550,000 

 Mg + Pt ,, 1 ,, 775,ooo ,, 930,000 

 Al -J- Pt ,, I „ 42,568 „ 46,500 



With iodine and the astatic galvanometer the following 

 proportions were required : — 



Table II.— Iodine. 

 Zn + Pt between 1 in 3,100,000 and 3,521,970 

 Mg + Pt „ i ,, 577,711 ,, 643,153 

 Cd + Pt ,, 1 ,, 2-0,431 ,, 224,637 



With bromine and the astatic galvanometer : — 

 Table III. — Bromine. 

 Mg + Pt between I in 310,000,000 and 344,444,444 

 Zn + Pt ,, 1 ,, 77,500,000 ,, 84,545,000 

 Cd + Pt ,, 1 ,, 3,470,112 ,, 3,875,000 

 The magnitudes of the minimum proportions of bromine 

 required to change the potentials of the three couples in water 

 varied directly as the atomic weights of the three positive metals. 

 With chlorine the following were the minimum proportions- 

 required : — 



Table IV. — Chlorine. 



With the Reflecting Galvanometer. 



Mg -i- Pt between 1 in 27,062,000,000 and 32,291,000,000 



With ths Astatic Galvanometer. 



Mg + Pt between 1 in 17,000,000,000 and 17,612,000,000 



Zn + Pt ,, 1 ,, 1,264,000,000 ,, 1,300,000,000 



Zn + Au ,, 1 ,, 518,587,360 ,, 550,513,022 



Cd + Pt „ 1 „ 8,733,5*5 „ 9,270,833 



Zn + Cd ,, 1 ,, 55,436 „ 76,467 



In the case of chlorine, as well as that of bromine, the 



magnitudes of the minimum proportions of substance required to 



change the potential of magnesium-platinum, zinc-platinum, and 



cadmium-platinum, varied directly as the atomic weights of the 



positive metals. 



The examples contained in the paper show that the proportion 

 of the same exciting liquid necessary to disturb the potential of 

 a voltaic couple in water varied with each different positive or 

 negative metal, and that the more positive or more easily 

 corroded the positive metal, or the more negative and less 

 easily corroded the negative one, the smaller usually was the 

 minimum proportion of dissolved substance necessary to change 

 the potential. 



By plotting the results in all cases, it was found that the order 

 of change of potential, caused by uniform change of strength of 

 liquid, varied with each positive metal. 



The results also show that the degree of sensitiveness of the 

 arrangement for detecting the minimum-point of change of 

 potential depends largely upon the kind of galvanometer 

 employed. 



As a more sensitive galvanometer enables us to detect a 

 change of potential caused by a much smaller proportion of 

 material, and as the proportion of substance capable of detection 

 is smaller the greater the free chemical energy of each of the 

 uniting bodies (Roy. Soc. Proa, June 14, 1888) it is probable 

 that the electromotive force really begins to change with the 

 very smallest addition of the substance, and might be detected if 

 our means of detection were sufficiently sensitive, or the free 

 chemical energy of the uniting bodies was sufficiently strong. 



"The Voltaic Balance." By Dr. G. Gore, F.R.S. 



A New and Simple Lecture Experiment. — Take two small clean 

 glass cups containing distilled water ; simultaneously immerse in 

 each a small voltaic couple, composed of either unamalgamated 

 magnesium or zinc with platinum, taking care that the two 

 pieces of each metal are cut from the same piece and are per- 

 fectly clean and alike. Oppose the currents of the two couples 

 to each other through a sufficiently sensitive galvanometer, so 

 that they balance each other and the needle does not move. 

 Now dip the end of a slender glass rod into a very weak aqueous 

 solution of chlorine, bromine, iodine, or hydrochloric acid, and 

 then into the water of one of the cups. The voltaic balance is 

 at once upset, as indicated by the measurement of the needle,, 

 and may be shown to a large audience by means of the usual 

 contrivances. 



The chief circumstance to be noticed is the extremely great 

 degree of sensitiveness of the arrangement in certain cases. This 

 is shown by the following instances of the minimum proportions 

 of substance required to upset the balance with an ordinary 

 astatic galvanometer, and with a Thomson's reflecting one cf 

 3040 ohms resistance. 



1. Zinc and Platinum with Iodine. — With the astatic 

 galvanometer, between 1 part of iodine in 3,100,000 and 

 3>5 2I ,97° parts of water. 



