January 5, 1893] 



NA rURE 



225 



pound." But in past centuries castoreum was considered 

 a sovereign remedy for every kind of disease. Many 

 amusing details on this part of the subject are given by 

 Mr. Martin, mostly extracted from the " Castorologia " 

 of Johannes Francus, published in 1685. The wisdom of 

 Solomon himself is attributed by this learned author to 

 the virtues of the beaver. To acquire it, it is only neces- 

 sary " to wear a hat of beaver's skin, to rub the head and 

 spine with that animal's oil, and to take twice a year the 

 weight of a «old crown piece of castoreum." 



At the end of his volume Mr. Martin places a short 

 account by Mr. C. V. Riley, the well-known American 

 entomologist, of Platypsillus castoris, a parasite on the 

 beaver, and one of the most remarkable among the many 

 extraordinary forms of parasitic insects. Mr. Riley cor- 

 rectly refers this creature to the coleoptera, although other 

 naturalists, and, amongst others, its discoverer, Ritsema, 

 have expressed different views on this point He omits, 

 however, to refer to the excellent account of Platypsillus 

 castoris, written by the late John Leconte, and published 

 in the Proceedings of the Zoological Society of London 

 for 1872. Dr. Leconte has here shown that it is necessary 

 to make a special family (Platypsillidae) for the reception 

 of this curious parasite, but that it must be unquestion- 

 ably referred to the coleoptera. 



On account of these and other peculiarities the beaver 

 is unquestionably an animal of great general interest, and 

 Mr. Martin has done well to devote a volume to what is 

 evidently his favourite theme. There is, we must allow, 

 little, if anything, original in it, and the statements on 

 scientific points cannot always be implicitly depended 

 upon. But the author has brought together a large amount 

 of information on the subject, and his book is " popularly 

 written " and " fully illustrated," though we cannot quite 

 agree to his claims to have produced an " exhaustive 

 monograph." 



An Atlas of Astronomy. By Sir Robert Stawell Ball, 

 LL.U., F.R.S. (London: George Philip and Son, 

 1892.) 

 A NEW book by Sir Robert Ball is always a matter of 

 interest, but the present one naturally larks the usual 

 characteristics. It is described as " a series of 72 plates 

 with introduction and index." In addition to monthly 

 and general maps of the stars, the atlas reproduces 

 pictures of the sun, moon, planets, and comets, and 

 contains diagrams illustrating their motions and dimen- 

 sions. As the book is chiefly meant to be a companion 

 to more general works, the introductory matter is pur- 

 posely brief, but still it has several features of interest. 

 Special attention may be drawn to the excellent de- 

 scription of a simple graphical method of determining the 

 orbit of a binary star. 



To the serious student who may possess a small tele- 

 scope the new atlas will be very useful. Here he may 

 learn how to determine the positions of sun spots, how 

 to find the places occupied by the various planets, and 

 what objects are most likely to be within reach of his 

 instrument. Those interested in selenography will derive 

 much assistance from the twelve plates showing the moon 

 at different phases, which have been specially drawn by 

 Mr. E ger, each being accompanied by an index map. 

 One can only wonder, however, that some of the recent 

 excellent photographs of the moon have not been pressed 

 into the service. 



The star maps, on the whole, are excellent, and our 

 only complaint is of the excessive density of the Milky 

 Way, which, in some parts of the maps, is almost sufficient 

 to obliterate the names and numbers of the stars. The 

 monthly maps will be particularly useful to those who 

 are just learning the constellations, a new feature being 

 a belt indicating the track of the planets. 



Spectroscopic astronomy is entirely omitted, the author 

 being of opinion that this great branch of work can only 



NO. 1210, VOL. 47] 



receive justice in a separate atlas. In this we heartily 

 agree, and trust that such an atlas will soon be forth- 

 coming. 



The author's large following of readers will no doubt 

 weldome the new comer, but we must express regret that 

 astronomical photographs are not more fully represented. 

 It would be interesting, for example, to reproduce a series- 

 of photographs of typical nebulae, all of which, we believe, 

 are now available. A plate showing the advantages of 

 photography in the delineation of stars would also add. 

 to the interest of the atlas. 



LETTERS TO THE EDITOR. 



{The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymotts communications. ] 



Vector Analysis. 

 I FANCIED that, in reply to the voluminous letters of Pr )f. 

 Willard Gihbs (Nature, xliii. 511 ; xUv. 79), I had said in a 

 few words all that is requisite (if, indeed anything be requisite)- 

 to show the necessary impotence, as well as the inevitable un- 

 wieldiness, of every system of (so-called) Vector Analysis vi\\\z\k 

 does not recognize as its most important feature the product (or 

 the quotient) of two vectors : — i.e. a Quaternion. 



A recent perusal of the first four pages of a memoir by Mr. 

 O. Heaviside {Phil. Trans. 1892) :— for so far only could I 

 go:— has dispelled the illusion. For he calls the correspond- 

 ence just spoken of a " rather one-sided discussion" :— a truly 

 Delphic delivery : — cleared up, however, by what follows it. I 

 particularly desired to read the memoir (which the Author had' 

 kindly sent me) as I hoped to learn from it something new in 

 Electrodynamics. But, on the fifth page, I met the check-taker 

 as it were : — and found that I must pay before I could go 

 further. I found that I should not only have to unlearn Qua- 

 ternions (in whose disfavour much is said) but also to learn a 

 new and most uncouth parody of notations long familiar to me ; 

 so I had to relinquish the attempt. In the last of the four pages^ 

 of my progress, I had found that Mr. Heaviside (though, as 

 above stated, he has a system of his own) is an admirer of Prof. 

 Gibbs' system, to such an extent at least that he thinks " his 

 treatment of the linear vector operator specially deserving of 

 notice." There I was content to leave the matter. 



But Mr. Heaviside has just published {Electrician, 9ll2i<)2)- 

 an elaborate attack on Quaternions, of a kind which is calcu- 

 lated to do real injury to beginners. In answer to his remarks, 

 in which he continues to point to me as the persistent advocate 

 of a system which all right-minded physicists should avoid, I 

 would simply refer him (and his readers, if there be such) to a 

 brief Address which I gave a short time ago to the Pnysical 

 Society of Edinburgh University {Phil. Mag. Jan. 1890). 

 One or two sentences, alone, I will quote here : — 



"if we can find a language which secures, to an unparalleled 

 extent, compactness and elegance, and at the same time is 

 transcendently expressive— bearing its full meaning on its face- 

 it IS surely foolish, at least, not to make habitual use of it." 



" For (Hamilton) the most complex trains of formulae, of the 

 most artificial kind, had no secrets :— he was one of the very few 

 who could afford to dispense withsimplificadons : yet, when he 

 had tried quaternions, he threw over all other methods in their 

 favour, devoting almost exclusively to their development the last 

 twenty years of an exceedingly active life." 



The main object, however, of my present letter, is to call 

 attention to a paper by Dr. Knott, recently read before the 

 Royal Society of Edinburgh. Dr. Knott has actually had the 

 courage to read the pamphlets of Gibbs and Heaviside ; and, 

 after an arduous journey through these trackless jungles, has 

 emerged a more resolute supporter of Quaternions than when 

 he entered. He has revealed the (from me at least) hitherto 

 hidden mysteries of the Dyadic, and of Prof. Gibbs strange 

 symbols Pot. Lap, Max, New, &c. The first turns out to be only 

 the linear and vector function ; and the others are merely more 

 or less distressing symptoms characteristic of imperfect digestion 

 or assimilation of V. And when, at my request, Dr. Knott 



