December 15, 1892] 



NATURE 



151 



length of the day. Except at the time of the equinox, the gradual 

 lengthening or shortening of the day, as the solstice is 

 approached, mo^^t materially affects, especially in the higher 

 latitudes, the total amount of sunshine received in twenty-four 

 hours. 



But are there any convenient and readily accessible tables — as 

 there easily might be— which would at a glance show numerically 

 the comparative amounts of sunshine at certain selected times 

 ind places ? I would wish to see such tables, say, for every 

 tenth day, for the three months from an equinox to a solstice, for 

 about every third degree of latitude in each hemisphere. I see 

 not how, without this, either the causes or the effects of meteoro- 

 logical changes in different regions at different seasons can be 

 justly estimated. I would propose to express the amount of 

 sunshine during twelve hours at the equator at the equinox by, 

 say, icx>; the figures rising above this, or falling below it. 

 Thus there would be more than lOO given for the latitude of the 

 Tropic of Cancer at the summer solstice, with a vertical sun and 

 more than twenty-four hours' sunshine ; with lOO for a latitude 

 still further north. Reginald Courtenay. 



The Imperial Hotel, Sliema, Malta, November 14. 



Quaternions. 



By the kindness of the author I have just received a copy of 

 Mr. Heaviside's paper " On the Forces, Stresses, and Fluxes of 

 Energy in the Electromagnetic Field" {Phil. Trans., 1892, 

 P- 423)) in which he reopens a question debated in your columns 

 some time ago — -the question of Quaternions versus other methods 

 of vector analysis for the use of physicists. 



At present the matter stands thus :— There are two 

 widely-known systems of vector analysis before the public 

 — Quaternions and the Ausdehnungslehre — and quite a 

 multitude of less known ones, of which Prof. Gibbs's seems 

 to be one of the least open to objection, and of which, 

 in my opinion, Mr. Heaviside's is by no means so. It would 

 take too long, however, to justify this opinion, but I 

 wish to make an appeal to Mr. Heaviside and Prof. Gibbs 

 on grounds independent of the merits or demerits of their par- 

 ticular systems. 



Of the Ausdehnungslehre I do not feel competent to speak. 

 As to (Quaternions, there are undoubtedly some inconveniences 

 in physical applications, and I am quite willing to concede that 

 a grave one is the very frequent use of the letters S and V (Mr. 

 Heaviside uses the latter). I do not regard the sign of the 

 scalar product Which vexes the soul of Mr. Heaviside as of any 

 consequence. But while thus admitting that a better system 

 than Quaternions is conceivable, I think I can show that the 

 position of the dissenters is little short of suicidal. 



The band of physicists who use and urge the use on others of 

 vector analysis is woefully small. Let me put a question to two 

 of the justly best known of that band. Prof. Gibbs and Mr. 

 Heaviside. What is the first duty of the physical vector analyst 

 qua physical vector analyst ? I think I may anticipate that 

 the answer will be— to convince the world of mathematical 

 physicists that vector analysis must beunshelved and set to work. 

 The next question that arises is one of tactics. What should 

 be the plan of campaign to bring this desirable result about ? 

 Here I am afraid we cannot hope for unanimity even among 

 the members of the small band, and this is to be most grievously 

 deplored. But surely every sane man will agree that what most 

 certainly the analysts should not do is to present their arguments 

 to those they would convince in a dozen different mathematical 

 languages, each of which is puzzling enough to those learned in 

 allied languages. Grant this, and it follows that Quaternions 

 and the Ausdehnungslehre should be left in sole possession of 

 the field. The day for Prof. Gibbs's improvements is not yet. 

 i'rof. Gibbs and Mr. Heaviside have not yet convinced the rest 

 f the small band — not to say each other — of the merits of their 

 ilgorithms. Let me implore them to sink the individual in the 

 <;ommon cause, and content themselves with the faith that 

 posterity will do them justice. 



Apart from the question of notation there seem to be two 

 schools of opinion as to the proper conduct of the campaign. 

 To vary the metaphor, Maxwell, Clifford, Gibbs, Fitzgerald, 

 Heaviside prescribe a course of spoon-feeding the physical 

 public. Hamilton and Tait recommend and provide strong 

 meat. I do not think that harm, but rather good, will come 

 from this double treatment, as one course will suit some patients 

 and the other others. Bui let the spoon-feeders provide spoon- 

 NO. 1207, VOL. 47I 



meat of the same kind as the other physiciat:s. Is not Maxwell, 

 Clifford, and Fitzgerald's food as digestible as Prof. Gibbs's and 

 Mr. Heaviside's? Alex. McAulav. 



Ormond College, Melbourne, October 31. 



Animals' Rights. 



Mr. Salt disputes the justice of the statement that he has 

 given two contradictory definitions of animals' rights, inasmuch 

 as, according to him, that which he has set forth on p. 28 is 

 but a repetition and amplification of the one to be found on p, 9. 



By the definition on p. 9 animals' rights are said to consist 

 in a " due measure " of the restricted freedom which constitutes 

 the right of man, i.e. (as Mr. Salt notes) the freedom "to do 

 that which he wills, provided he infringe not the equal liberty 

 of any other man " — "a restricted freedom " which guarantees 

 to the harmless individual the security of his life and liberty. 



But on p. 28 the rights of animals (which were said before 

 to consist in a " due measure " of that just quoted) being here 

 stated to be " subject to the limitations imposed by the perma- 

 nent needs and interests of the community," are found to be 

 burdened with so serious a qualification that security for the life 

 and liberty of the harmless itidividual is by it completely 

 destroyed. 



A European might settle with confidence in an unknown 

 island, on the assurance that he would be allowed a measure 

 of the general right of the natives to the freedom to do that 

 which they would, provided they infringed not the equal rights 

 of any other, but were he afterwards to discover that the 

 " measure " of this right which was considered to be the "due " 

 of a foreigner was in reality limited "by the needs and 

 interests of the community," and that, a community where 

 the custom of enslaving and eating strangers had existed from 

 time immemorial, we venture to assert that his departure from 

 the island would be effected with as little delay as possible. 

 We should much regret misrepresenting Mr. Salt's statements, 

 but the assertion that the second definition of rights is but 

 a repetition and amplification of the first is manifestly untenable, 

 and if, by '^' due measure" for animals of the rights of man, 

 Mr. Salt would have us understand that he meant — only such 

 a measure as is consistent with the nullification of the most 

 fundamental privileges secured by them, he must have been 

 discussing the subject in a vein of sarcasm which we are 

 bound to confess we had quite failed to appreciate. 



The Revie\ver. 



The Height and Spectrum of Auroras. 



There was a magnificent aurora on the evening of the 4th, 

 part of which, from loh. 46im. to 48m. or 49m., was an intense 

 red. I noted the positions of some of the features at the exact 

 half-hours and also at some other times, for comparison- with 

 any observations that may have been made in other places, for 

 ascertaining the height of the phenomenon ; and I hope some 

 such observations have been made of the recent display, and 

 will be made of further ones in the future, for Dr. Veeder, of 

 Lyons (New York), has kindly consented to calculate the 

 heights from the observations. 



1 am surprised that none of our persevering photographers 

 have as yet obtained a good photograph of the auroral spectrum. 

 I do not think it would be more difficult than the stellar photo- 

 graphs that have been taken, seeing that the exposure might go 

 on for hours. It would be desirable to have it done with a 

 camera that could be pointed in any direction at will, so that 

 wherever the observer saw a bright portion of the aurora he 

 could direct the instrument, to it. T. W. BACKHOUSE. 



Sunderland, December 6. 



The Teaching of Botany. 



There appeared in Nature (vol. xxxi. p. 229) a paper 

 entitled "Experiments suitable for illustrating Elementary 

 Instruction in Chemistry," by Sir H. E. Roscoe and W. J. 

 Russell. I have long felt the want of a similar series of experi- 

 ments in physiological botany. There is not much difficulty in 

 teaching the morphological side of the subject, but it is not easy 

 for the ordinary high-school teacher to devise and carry out a 

 suitable series of experiments for demonstrating the more im- 

 portant aspects of physiological botany. If some master in the 



