Oct. 30, 1884] 



NA TURE 



631 



adapted. Prof. Thompson has chosen to classify dynamos 

 according to the nature of the field of force and the 

 manner in which the armature moves in the field of force. 

 It is doubtless difficult to find any very satisfactory mode 

 of classification of these machines : but the reason for the 

 particular classification adopted here is certainly not 

 apparent in the descriptive chapters, in which the nature 

 and effect of the field in the various machines is perhaps 

 the point on which a great deal more information would 

 be desirable. The diagrams and figures in these chapters 

 are all that could be wished for. They are admirably 

 chosen and are well executed. 



The mathematical theory of the dynamo machine has 

 of late received considerable accessions ; though much 

 yet remains to be done in working out a satisfactory 

 theory by mathematics and experiment combined. The 

 fundamental principles are well known. The experiments 

 of Faraday and Joule, and the mathematical investigations 

 of Helmholtz, Sir William Thomson, and Clerk-Maxwell 

 have formed a good foundation ; and considerable ad- 

 vances have recently been made by the labours of Joubert, 

 Mascart, Hopkinson, and Marcel Deprez. The invention 

 by Hopkinson of the "characteristic curve" is a most 

 important step ; and the study of these curves is at the 

 present time doing for the dynamo machine the same 

 thing that the study of Watt's indicator diagram does 

 for the steam-engine. 



Prof. Thompson devotes a considerable number of 

 chapters to the mathematical theory of the dynamo, and 

 his treatment of the subject is on the whole satisfactory. 

 There are, however, a few points on which in our opinion 

 it requires revision. One of these is the notation ; and it 

 would be a great satisfaction if mathematicians and elec- 

 tricians could by some means — for instance, by appointing 

 a committee for the purpose — agree upon some standard 

 notation which would be convenient, and which would har- 

 monise with notations commonly employed in dynamics 

 and in general physics. In several points we could wish 

 to see Prof. Thompson's notation different. It seems, to 

 say the least, a very great pity to use the letter H in 

 mathematical writing connected with magnetism for any 

 purpose besides Earth's Horizontal Force, while the use 

 of the letter i for strength of the current is only a per- 

 petuation of French want of logic. 



Prof. Thompson's formulas on the subject of efficiency 

 of a motor are not satisfactory ; and it is most unfor- 

 tunate that he has allowed himself to be misled by his 

 friend, Mr. W. M. Moorsom, into fancying an error in 

 the fundamental equation of Joubert for an alternate- 

 current dynamo. The investigation of Appendix IV. 

 and the physical assumption that the coefficient of 

 self-induction for the armature and the coefficient 

 of mutual induction for the armature and electro- 

 magnets are approximately equal in all dynamos will not 

 bear examination. It is more than doubtful whether 

 there is any dynamo in which this is approximately true. 

 Certainly it would not be true for the Siemens alternate- 

 current machine, with which M. Joubert concerned him- 

 self. M. Joubert did not leave the matter as a question 

 of supposition ; but showed by experiment that the term 

 which is concerned with mutual induction is unimportant, 

 and that on this account the differential equation in 

 question becomes manageable. 



One other blemish we cannot pass over. It is the 

 introduction of two or three new words which have been 

 adopted without due weighing of the consequences. That 

 mathematicians have been too slow to form words for 

 new ideas we quite admit ; and of the advantage of good 

 words to express clear ideas there can be no question. 

 Witness the comfort of having such words as " radian " 

 for the unit angle, of " volt," " ampere," " watt." But 

 word-making may be carried too far unless caution and 

 judgment be used ; and that words so grotesque as 

 " torque " and as " gausses " should be adopted into the 

 English language would be, to say the least, a very great 

 misfortune. 



The faults which we have found are, however, few, and 

 not of vital importance, and in conclusion we must once 

 more express our gratitude to Prof. Thompson for a very 

 valuable work. We feel confident that it will find a very 

 wide circle of usefulness and of appreciation. 



OUR BOOK SHELF 



An Elementary Treatise on Conic Sections and Algebraic 

 Geometry, with Numerous Examples and Hints for 

 their Solution, especially designed for the Use of 

 Beginners. By G. Hale Puckle, 'M. A. (London: 

 Macmillan& Co., 1884.) 

 We are not often called upon to notice the fifth edition of 

 a school text-book, but now that we have examined this 

 one and compared it with our familiar third edition copy 

 (issued in 1868) we are glad to be able to say that, though 

 new editions have not appeared with the sensational 

 rapidity of some similar works of late, yet with the steady 

 advance in public favour there has been an evident desire 

 on Mr. Puckle's part to bring up his work to the level of 

 other treatises on the subject. Contrasting the two edi- 

 tions, we find there has been an increase from 343 to 379 

 pages, and not only has there been careful revision, but 

 also an addition of very many articles of interest. It is 

 to be borne in mind that no attempt is made to bring out 

 a work which shall satisfy the requirements of a Univer- 

 sity man who is "reading high," but the writer's aim has 

 throughout been to write a purely elementary treatise on 

 the lines of Dr. Salmon's "Conies." Mr. Puckle rightly 

 acknowledges his great indebtedness to this now classic 

 work, and on the other hand it should be borne in mind 

 that the first edition came out at a time when Salmon was 

 not openly used as a College text-book at Cambridge. We 

 are very glad to notice that Mr. Puckle has, in this last 

 edition, adopted the notation of the general equation of 

 the second order, according to Salmon. It is quite time 

 that this notation should be adopted in all our text-books, 

 for it is a needless burden upon the memory to get up 

 the several conic formula? under different forms. A use- 

 ful addition has been made to the number of worked-out 

 exercises. A result of the book's having reached a fifth 

 edition is that we have not noted any errata in the text. 



LETTERS TO THE EDITOR 



[ The Editor does not hold himself responsible for opinions expressed 

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 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications. 



[The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 op communications containing interesting and novel facts.] 



The Cretaceous Flora of North America 



In the abstract of a paper on the above subject by Mr. J. 



Starkie Gardner in Nature of September 25 (p. 528), it is 



stated that " the lowest beds (of the American Cretaceous) are 



