March i6, 1893] 



NATURE 



46: 



nelids in 1884, gives us some results of his personal experience, 

 which I believe have never been placed before the English 

 reader. He says that he had the good fortune once at least to 

 ob-erve an interesting case of phosphoresence in connection 

 with the brandling. It was one warm July night in the year 

 1 88 1, when he was exploring a dung-heap. Naturalists do not 

 usually work with kid gloves and diamond rings. Presently a 

 spot of soft, bluish-white light appeared, which, however, was 

 changeful and unsteady. Now it would disappear, then return 

 anew and shine forth over a larger space, though never with a 

 brilliant hue. He thereupon removed a portion of the manure 

 from the spot where he had observed the luminosity, and found 

 that the light appeared brighter, and shone for a longer time 

 without disappearing, or before it migrated to another spot. By 

 means of a lantern Vejdovsky was able to secure a large number of 

 specimens of the brandling from the dung-heap, which he placed 

 in a vessel for the purpose of subjecting them to careful obser- 

 vation. To his great surprise he found that his finger soon 

 glowed in the darkness with the phosphorescence, which ex- 

 tended generally over the hand where it came into contact with 

 the worms. It was therefore apparent that the luminosity was 

 the product of a fluid secreted by the cutaneous glands, which 

 had attached itself to the hand of the investigator, and now 

 manifested itself in this curious way. 



We have an interesting observation on the same subject by 

 Prof, von Stein, which was published at Leipzig in 1883. One 

 evening in the middle of September the Professor was spending 

 some time with a circle of friends at a parsonage not far from 

 Potsdam, when the conversation turned upon phosphorescence 

 and the phenomena of light. Hereupon one of the younger 

 members of the family — who are usually the keenest and most 

 shrewd observers of Nature, and the best friends of the naturalist 

 — observed that there were fountains in the adjoining gardens, 

 the water from which was frequently observed to be full of 

 light-"bearing creatures when it was violently agitated. He re- 

 garded the affair at first simply as a hoax, or an attempt to make 

 a fool of him — as people are ever ready to do with a hobby-rider 

 — but ascertained eventually that the luminosity was due to the 

 presence of a species of worm which possessed the property of 

 shining when disturbed. As with Vejdovsky, so with Prof, 

 von Stein, the finger which had come into contact with the 

 worm continued to glow for some time after. What species of 

 worm was under observation is not recorded. 



It now becomes a question, What end could be served 

 thereby ? The philosopher no sooner learns a new fact than he 

 begins to pry into the secret which lies beneath, and stands to 

 it as cause to effect. We have analogy to guide us. The water 

 worms may be compared with the marine animals which pro- 

 duce phosphorescence, while the brandling may be studied in 

 the light of the glow-worm. It may be objected that as worms 

 have no eyes there can be no advantage in their luminosity. 

 But such an argument would be based on the erroneous assump- 

 tion that a creature without eyes is incapable of receiving 

 impressions from light. That worms are influenced by light is 

 proved both by their habit of avoiding light, and by the experi- 

 ments which have been carried out by various students. Darwin 

 remarks that as worms are destitute of eyes he at first thought 

 they were quite insensible to light. Hefound, however, that "light 

 affects worms by its intensity and by its duration." Hoffmeister 

 slates that with the exception of a few individuals worms are 

 extremely sensitive fo light, and from my own observations I 

 have been able to demonstrate that there are marked differences 

 in the susceptibility of the different species — some being very 

 much more susceptible than others. 



Now it follows that if a number of species of worms lived 

 together in one place, as they usually do in a manure heap, it 

 would be a great advantage for a given species to possess a dis- 

 tinguishing feature, such as that of luminosity, to enable two 

 individuals to discover each other's whereabouts, just as the 

 male glow-worm detects the female by the light emitted from 

 her upturned abdomen. We have, moreover, the fact that 

 certain species of earthworm are characterised by a peculiar 

 odour, which must be of great service in preventing promiscuous 

 copulation and hybridity. Though earthworms are destitute of 

 nasal organs they can detect odours, and though sightless they 

 are affected by light. 



Viewed in this light a new field of research is opened up 

 which hitherto has been totally unworked, but which may be 

 hoped to yield, remarkable results if diligently, patiently, and in- 

 telligently tilled. 



NO. 1220, VOL. 47] 



It would be an easy thing for any one living in the country, 

 with access to an old manure heap, where the brandling {Allolo- 

 hophora fcetida, Sav.) usually abounds, to ascertain whether such 

 luminosity is of common occurrence, and it would be excep- 

 tionally valuable to record the period of the year, the state of 

 the atmosphere, the age of the moon, and other data which 

 would enable the specialist to arrive at a satisfactory conclusion. 

 I shall be glad to receive communications, addressed "The 

 Grove, Idle, Bradford," from observers who may find pleasure 

 in such pursuits. Hilderic Friend. 



Quaternions and the Algebra of Vectors. 



In a recent number of this Journal (p. 151) Mr. 

 McAulay puts certain questions to Mr. Heaviside and to me, 

 relating to a subject of such importance as to justify an answer 

 somewhat at length. I cannot of course speak for Mr. Heavi- 

 side, although I suppose that his views are not very different 

 from mine on the most essential points, but even if he shall have 

 already replied before this letter can appear, I shall be glad to 

 add whatever of force may belong to independent testimony, 



Mr. McAulay asks : " What is \.\^g first duty of the physical 

 vector analyst qua physical vector analyst ? " The answer is 

 not doubtful. It is to present the subject in such a form as to 

 be most easily acquired, and most useful when acquired. 



In regard to the slow progress of such methods toward recog- 

 nition and use by physicists and others, which Mr. McAulay 

 deplores, it does not seem possible to impute it to any want of 

 uniformity of notation. I doubt whether there is any modern 

 branch of mathematics which has been presented for so long a 

 time with a greater uniformity of notation than quaternions. 



What, then, is the cause of the fact which Mr. McAulay and 

 all of us deplore ? It is not far to seek. We need only a glance 

 at the volumes in which Hamilton set forth his method. No 

 wonder that physicists and others failed to perceive the 

 possibilities of simplicity, perspicuity, and brevity which 

 were contained in a system presented to them in pon- 

 derous volumes of 800 pages. Perhaps Hamilton may 

 have intended these volumes as a sort of thesaurus, and we 

 should look to his shorter papers for a compact account 

 of his method. But if we turn to his earlier papers on Quat- 

 ernions in the Philosophical Magazine, in which principally he 

 introduced the subject to the notice of his contemporaries, we 

 find them entitled "On Quaternions; or on a New System of 

 Imaginaries in Algebra," and in them we find a great deal 

 about imaginaries, and very little of a vector analysis. To show 

 how slowly the system of vector analysis developed itself in the 

 quaternionic nidus, we need only say that the symbols S, V, and 

 V do not appear until two or three years after the discovery of 

 quaternions. In short, it seems to have been only a secondary 

 object with Hamilton to express the geometrical relations of 

 vectors, — secondary in time, and also secondary :in this, that it 

 was never allowed to give shape to his work. 



But this relates to the past. In regard to the present status, 

 I beg leave to quote what Mr. McAulay has said on another 

 occasion {see Phil. Mag. June, 1892): — "Quaternions differ 

 in an important respect from other branches of mathematics 

 that are studied by mathematicians after they have in the course 

 of years of hard labour laid the foundation of all their future 

 work. In nearly all cases these branches are very properly so 

 called. They each grow out of a definite spot of the main tree 

 of mathematics, and derive their sustenance from the sap of 

 the trunk as a whole. But not so with quaternions. To let these 

 grow in the brain of a mathematician, he must start from the 

 seed as with the rest of his mathematics regarded as a whole. 

 He cannot graft them on his already flourishing tree, for they 

 will die there. They are independent plants that require sep- 

 arate sowing and the consequent careful tending." 



Can we wonder that mathematicians, physicists, astronomers, 

 and geometers feel some doubt as to the value or necessity of 

 something so separate from all other branches of learning ? Can 

 that be a natural treatment of the subject which has no relations 

 to any other method, and, as one might suppose from reading 

 some treatises, has only occurred to a single man ? Or, at best, 

 is it not discouraging to be told that in order to use the quater- 

 nionic method, one must give up the progress which he has 

 already made in the pursuit of his favourite science, and go back 

 to the beginning and start anew on a parallel course? 



I believe, however, that if what I have quoted is true of vector 

 methods, it is because there is something fundamentally wrong 



