May 9, 1889] 



NATURE 



39 



the higher branches of mathematic " is not a vain hope. 

 He could not, in our opinion, have made a better 

 beginning. If our critical responsibility compels us to 

 point out some defects in the execution of the work, we 

 trust that this will be understood as indicating our desire 

 to see the book made perfect ; and not construed into 

 depreciation of a valuable service to the cause of pure 

 mathematics. 



We strongly advise the author to have the translation 

 read by some one who is familiar with both English and 

 German idioms, and who possesses also some familiarity 

 with the departments of mathematics concerned. In 

 proof of the necessity for such a revision, we draw the 

 author's attention to the following points, which are 

 merely a few of tho?e that have attracted our attention. 

 When Klein says (Pt. I. chap, iii., § 7), " Die Lineare 

 Differentialgleichung zweiter Ordnung, verlangt also, 

 . . ,, zu ihrer Losung nur noch eine einzige Quadratur ; " 

 he does 7iot mean, "The linear differential equation of 

 the second order, therefore, requires, . . . , only a single 

 square root besides in order to solve it." Quadratur 

 means simply quadrature {i.e., direct integration), it 

 never means square root. Here a knowledge of the 

 properties of the Schwarzian derivative might have helped 

 the translator to divine the meaning of the German 

 technical term. On p. 96, " But for this the determina- 

 tion of the R's themselves is more easy to carry out," is 

 not a good, but in fact a misleading translation of the 

 German " Dafiir aber ist die Bestimmung . . ." Dafiir 

 here means " in compensation for this." At the foot of 

 the same page occurs a very common confusion between 

 wenn eben and wenn gleich, which has the effect of 

 ■exactly reversing the meaning of the note. " Hierdurch 

 kann/(jr)= o (wenn eben y, in den x geschrieben, nicht 

 transitive ist) moglicherweise reducibel geworden sein," 

 means, " Hereby /(.v) = o may possibly have become 

 reducible (namely if (or precisely if) y, when expressed in 

 terms of the jr's, is intransitive) " for, of course, an 

 equation is reducible if, and not unless, its group be 

 intransitive. A still more important error occurs on the 

 following page, where, in the definition of the Galois 

 resolvent, " ihre einzelne Wurzel bei jeder in G enthal- 

 tenen Vertauschung der x umgeiindert wird" is trans- 

 lated " its individual roots are unaltered, &c." First of 

 all, this makes nonsense of the definition, as definite 

 knowledge of the subject would have shown ; and farther, 

 supposing the translator to have read un- by mistake for 

 um-, a knowledge of German idiom would have shown 

 him that " ungeandert wird" makes nonsense of the 

 German. The error is deliberately repeated on the fol- 

 lowing page, where " in umgeanderter Reihenfolge " is 

 translated in " unaltered sequence," instead of " in 

 altered sequence." These are vital errors, which should 

 at once be corrected by means of an " errata-slip " ; for 

 they would be a serious rock of offence for a tyro in 

 reading the passages where they occur. There are many 

 other cases, however, where loose translation somewhat 

 obscures the crisp and lucid exposition of Klein, which is 

 a pity, for this quality is not all too common among 

 Klein's countrymen. There are a considerable number 

 of misprints, many of them copied from the original. 

 An amusing instance of this occurs in the first footnote 

 on p. 73, where the title of Schwarz's well-known 

 memoir begins " Ueber dienigen Falle, &c." ; this is in 

 the original, but the transcriber should have known that 

 dienigen is impossible German. Nevertheless, we declare, 

 with all the sanction of our critical stool of infallibility, 

 that Mr. Morris's translation is a notable piece of good 

 work ; and he did well to publish it without waiting to 

 perfect his knowledge of German idiom or of Galois's 

 theory. The blemishes alluded to can be easily amended 

 when another edition is called for, which will be speedily, 

 if our good wishes avail. 



G. Ch. 



THE NORTHFLEET SERIES ELECTRIC 



TRAMWAY. 



C\^ Monday, April 29, there was opened for regular 

 ^^ passenger traffic an electric tramway at North- 

 fleet, near Gravesend, which marks an era in the 

 history of electric traction. This line has been run 

 experimentally for the last month, but the seven years 

 Board of Trade certificate having been received, this 

 line now enters on the commercial stage of its exist- 

 ence. Four tramways on which electricity is the motive 

 power have been in regular use for the last few years in 

 Great Britain : it is not, therefore, because the North- 

 fleet line is the first electric tramway in this country 

 that it has attracted considerable attention ; nor is it 

 because it is the longest electric tramway, for two of the 

 other four are of much greater length ; but it is because 

 this Northfleet line has been constructed on a totally 

 different principle from that hitherto adopted on this side 

 of the Atlantic that it is worthy of special consideration. 



When a number of electric lamps or motors have to be 

 supplied with power from a common centre, there are 

 two well-known methods by which this can be done. 

 They can either be joined " in parallel," as it is technic- 

 ally called, or they can be coupled up " in series." In 

 the parallel system, the one generally adopted with 

 electric lighting, and hitherto the only method that has 

 been employed with the electric tramways in Europe, the 

 electric current that passes through any lamp or motor 

 does not pass through any other, and the dynamo pro- 

 duces a large current equal to the sum of all the currents 

 passing through all the lamps or motors. In proceeding, 

 therefore, from the dynamo end of the circuit to the 

 distant end, there is a steady falling off in the current, but 

 the electric pressure remains, or may remain, nearly 

 constant. In the series system, on the other hand, the 

 whole current produced by the dynamo passes through 

 all the lamps or motors in succession, and therefore this 

 current can be small. The initial electric pressure, on 

 the other hand, must be large, since the energy imparted 

 by the current to each lamp or motor is represented by a 

 drop in the electric pressure. Since the energy furnished 

 by the dynamo depends on the product of the current 

 into the electric pressure it produces, while the waste of 

 power in heating the conductor depends on the square of 

 the current flowing through the conductor, it is clear that 

 while any amount of energy can be supplied by either 

 system, the use of high pressure and small current is by 

 far the more economical as regards the power wasted in 

 heating the conductor, this economy being the greater 

 the greater the number of lamps or motors on the circuit. 



Until a few years ago, however, it was not clear how it 

 was possible to run motors electrically in series when 

 the motors were themselves in bodily motion, as they 

 must be when employed to propel tramcars. In 1881, 

 Profs. Ayrton and Perry, for the purpose of diminishing 

 the loss of power through the leakage of the current that 

 occurs from the insulated rail of an electric railway to 

 the earth, and which becomes serious when the line is 

 long, proposed a plan of electrically subdividing the 

 railway track into sections so arranged that the electric 

 current was only supplied to that section of the track on 

 which a train happened to be at any moment. This 

 system was described and shown in action at a lecture 

 given by one of the inventors at the Royal Institution in 1882, 

 and the late Prof. Fleeming Jenkin, on reading the account 

 of this lecture, saw that the device of employing an elec- 

 trically subdivided conductor supplied the means of 

 running electrical trains in series. A combination was, 

 therefore, brought about between these three Professors 

 to develop electric traction. This combination resulted 

 in the formation of the Telpherage Syndicate, and lastly 

 in the Series Electrical Traction Syndicate, to whom is 

 due the construction of the first series line in Europe, the 



