June 23, 1892] 



NA TURE 



187 



(Jesus), G. Ingham (Merton), A. L. Ormerod (New). Second 

 Class: D. Berridge (Wadhara), P. Henderson (Queen's), A. E, 

 Richardson (Wadham), F. R. L. Wilson (Keble). Third Class : 

 C. J. M. Parkinson (Jesus), H. Wynne-Finch (New). Fourth 

 Class : S. Wellby (Trinity). 



Physiology.— First Class : P. S. Hichens (Magdalen), H, H. 

 G. Knapp (nonCoU.), A. C. Latham (Balliol), E. Mallam 

 (Magdalen), W. Ramsden (Keble). Second Class : G. J. Con- 

 ford (Christ Church), E. Stainer (Magdalen). Third Class : 

 S. B. Billups (non-Coil.). Fourth Class: J. S. Clouston 

 (Magdalen). 



Physics.— First Class : S. A. F. White (Wadham). Second 

 Class : G. M. Grace (Jesus). Third Class : none. Fourth 

 Class : F. W. Bown (University), J. C. W. Herschel (Christ 

 Church). 



Morphology.— First Class: R. W. T. Giinther (Magdalen). 

 Botany.- Second Class : O. V. Darbishire (Balliol). 

 Women :— Louisa Woodcock is placed in the Second Class, 

 Morphology. 



University Extension. — In a Convocation held on Tuesday 

 the following persons were declared on a scrutiny to be duly 

 elected as delegates, under the provisions of the statute Of the 

 delegates for the extension of teaching beyond the limits of the 

 University : — H. J. Mackinder, M.A., Student of Christ 

 Church; W. W. Fisher, M.A., Corpus Cliristi College, Al- 

 drichian Demonstrator of Chemistry; J. F. Bright, D.D,, 

 Master of University College ; A. Sidgwick, M.A., Fellow of 

 Corpus Christi College ; J. Wells, M.A., Fellow of Wadham 

 College; and the Rev. W. Lock, M.A., Fellow of Magdalen 

 College. 



The Encivnia. — In a Convocation holden in the Sheldonian 

 Theatre on Wednesday, June 22, the degree of D.C.L. {honoris 

 causd) was conferred upon the following persons : — 



His Excellency, William Henry Waddington, Ambassador 

 Extraordinary and Minister Plenipotentiary from the French 

 Republic at the Court of St. James, Honorary Fellow of Trinity 

 College, Cambridge, Hon. LL. D. 

 His Highness the Thakore of Gondal. 



The Very Rev. Henry George Liddell, D. D. , late Dean of 

 Christ Church. 



Edward Caird, M.A., Professor of Moral Philosophy in the 

 University of Glasgow, formerly Fellow of Merton. 

 W. M. Flinders Petrie. 



The Rev. John Gwynn, D.D., Regius Professor of Divinity 

 in the University of Dublin. 



Daniel John Cunningham, M.D., Professor of Anatomy and 

 Chirurgery in the University of Dublin. 



Edward Dowden, LL.D., Erasmus Smith's Professor of 

 Oratory in the University of Dublin. 



The Rev, John P. Mahaffy, D.D., Professor of Ancient 

 History in the University of Dublin. 



Benjamin Williamson, M.A., Sc.D.,Fellow of Trinity College, 

 Dublin. 



SOCIETIES AND ACADEMIES. 



London. 



Royal Society, June 2. — "On Current Curves." By 



Major R. L. Hippisley, R.E. Communicated by Major 



MacMahon, F. R.S. 



(l) Starling with the equations 



(I 



and 



^ sin(//- e), 



which represent the curves of currents in circuits without iron 

 cores, according as the impressed E.M.F. is constant or varying 

 as sin //, we can determine the curves according to which the 

 current rises and falls in circuits with iron cores, both for a 

 constant impressed E.M.F. and for a sinusoidal E.M.F. 



(2) In the first case, with constant applied E.M.F., we can 

 determine by Lagrange's formula of interpolation the equation 

 to the (B, H) curve of the particular core under consideration. 

 This will be of the form 



B = ao -(- a^W -f ^.^H^ + 



+ fl„H' 



where « is one less than the number of observed simultaneous 

 NO. II 82, VOL. 46] 



values of B and H from which the equation is calculated 

 Substituting in the equation 



E - '^» = R/, 



dt ' 



we get, after integration, 

 ■p 

 t = <5olog ^— ^^^ - byi - b.f' - &c., to « -f I terms, 



<^o. ^1. ^2. &Cm being numerical. The paper gives b^, b,, b^, &c., 

 in terms of the constants of the circuit, &c. 



The corresponding equation when the E.M.F. is removed 

 and the current is dying away is 



E 

 ^ = '"o 'og rr ~ <"i' ~ ^2*' - &c. -fa constant. 

 l\i 



From these two equations the curves can be plotted. 



(3) This method is not applicable to the case in which the 

 impressed E.M.F. is sinusoidal, on account of difficulties of 

 integration. But both cases can be treated in another way :— 

 Take a series of points on the (B, H) curve of the iron core, 

 such that the chords joining them practically coincide with the 

 curve itself. Let B„ H„ and B^^.,-!, H, + i, be the co-ordinates 

 of two consecutive points. The equation to the curve between 

 these points is approximately 



B = OT, + jH -{-constant, 

 where 



Substituting in the equation 



E-^ 

 iit 

 we get, after integration, 



/«, + 1 L 



hV 



Ri, 



= /« + 



R '°Se- 



R/. 



Ri,. 



which is true to a very close approximation for any simultaneous 

 values of /and i between the above limits. From this equa- 

 tion, by determining the various values of m, and remember- 

 ing that t„ and /q are both zero, we can determine in succes- 

 sion the times at which the current has the known values o, 



—1, -j-^, . . . &c. , and the current curve can be plotted. 



On making E = o in the original differential equation, and 

 observing the proper limits, we get 



t„ + , = t,. ' '«''+^L.„ H. 



R ^H„+, 



as the equation to the curve representing the dying away of the 

 current when the E.M.F. is wiihdrawo ; /«„, m„.^.^ bei«g deter- 

 mined from the descending (B, H) curve. 



(4) When the impressed E.M.F. is sinusoidal, we substitute 

 for dhjdt in the equation 



E sin// - 'i^ = Ri, 

 dt 



having determined the various values of d^jdl, as in the fore- 

 going. 



As by the present method the value of m changes abruptly 

 from m, to »»<-{- 1, we must employ the general solution of the 

 above, which for the interval /,, /<+i, is 

 E 



~ sin(// - e«. 



1) 



in order that the current at the commencement of the interval 

 4, /» + !, may have the same value which it had at the end of the 

 interval t^.^t,. The complementary function 



enables us to insure this condition ; for, by taking the constant 

 A«+i of such a value that the above equation is satisfied when 

 i = », and / = /„ there is no abrupt change in the current. The 

 complementary function, in fact, represents the gradual dying 

 away of whatever excess or defect of current there would be in 

 the circuit when m changes. 



This equation is true ior all values of i between A and /, + , ; 

 and, therefore, enables us to find the time, /. + ], at which ihe 

 current attains the known value H, + i/L. 



By changing k into k -(- i, we o\)tain similarly the time /,+.;, at 

 which the current has the value H,^-J/L, and so on. 



Thus the determination of /.-t-j is made to depend upon /„ and 



