;86 



NATURE 



[October i i, 1906 



are unknown to the quaternionist. It is a suggestive fact 

 tliat both Gibbs and Jahncke, in order to develop their re- 

 spective systems, found it necessary to introduce quite other 

 kinds of products of vectors — products which are as different 

 from one another as each is from the quaternion product, 

 and yet have not the geometrical significance of Hamilton's 

 creation. 



There is an idea in some minds that there is a rivalry 

 between vector analysis and quaternions. There is nothing 

 of the kind. There is a quaternion vector analysis and a 

 crowd of other vector analyses known best by the names of 

 their authors, such as Grassmann, O'Brien, Gibbs, Heavi- 

 side, Bucherer, Jahncke, Henrici, Peano, Macfarlane, &c., 

 no two of whom, curiously enough, agree with one another. 

 Of all these, Hamilton's is the only vector analysis 

 associative in its vector products. The importance of this 

 associative law does not, of course, appear so long as we 

 restrict ourselves to products of two vectors only, and, as 

 a matter of fact, many vector analysts never really get to 

 higher products. When, however, three or more vectors 

 are to be combined, the associative law must be fulfilled 

 if simplicity and flexibility of operation are to be retained. 

 The vector analysis which admits the associative law in 

 product combinations is the quaternion vector analysis, 

 however it may be disguised by arbitrary symbolism and 

 notation. C. G. Knott. 



Edinburgh University, September 21. 



I ALSO deplore the use of the current but misleading 

 phraseology which Prof. Knott points out. Quite certainly 

 Prof Knott's more detailed statement should be substituted 

 in the interests of "terminological exactitude." 



The Writer of the Report. 



Remarkable Rainbow Phenomena. 



When I read Mr. Spence's interesting letter (p. 516), it 

 occurred to me that the appearance of the second primary 

 rainbow was due to the reflection of the sun from the sea. 

 The apex of this second bow would be above that of the 

 first bow, the angular distance between the apices being 

 about equal to double the sun's altitude at the time of the 

 observation. 



Taking approximate figures, 1 make Deerness to be in 

 longitude eleven minutes of time west of Greenwich, and 

 in latitude 50° north. Assuming Mr. Spence's times to be 

 Greenwich times, the sun's altitude at 6h. 30m. p.m. was 

 about 4°, so that the angular distance between the apices 

 of the bows would be about 8°, a result differing but 

 little from Mr. Spence's estimate of 5° or 6°. As the sun 

 sank this distance would diminish. 



I should be glad to know if Mr. Spence observed any 

 difi'erence in the intensity of the light. One would expect 

 the higher bow to be the fainter of the two, as it was due 

 to a reflected sun, though the loss of light by reflection 

 would be diminished by the very low altitude of the sun. 

 By Fresnel's formula, the reflected sunlight would be to 

 the direct sunlight in the ratio of 13 to 20. If we neglect 

 the slight polarisation of this reflected light, these numbers 

 will also express the relative brightness of the higher and 

 lower bows, other conditions being alike. 



Probably the most remarkable case on record is that of 

 the octuple rainbow, seen in 1841, by the late Mr. Percival 

 FrosI, from the top of Dunstaffnage Castle, near Oban. 

 The sea, both behind and before the observer, was perfectly 

 smooth. Four bows were seen in the sky, viz. ordinary 

 primary and secondary bows due to direct sunlight, and, 

 above these, primary and secondary bows due to sunlight 

 reflected from the water behind the observer. 



Seen in the water in front were also four bows, inverted 

 by reflection. These bows were not images of the first 

 four, but images of four bows that could have been seen 

 in the sky had the water been removed and the observer 

 brought down vertically to a position as far below the 

 sea-level as the actual observer was above it. The eight 

 bows formed four intersecting circles. For further details 

 and an illustration reference should be made . to Nature, 

 vol. xli. (p. 316). C. T. Whitmeix. 



Invermay, Hyde Park, Leeds, September 29. 



NO. 1928, VOL. 74] 



Suspended Germination of Seeds. 



The letter of " H. B. P." in N.vruRE of September 27 

 (p. 540), while giving an interesting instance of the sudden 

 appearance of the foxglove on a bare hill in the north 

 country, does not appear to be conclusive as to the seed- 

 lings having developed from long-buried seeds. They 

 might have originated equally well, it appears to me, from 

 wind-blown seeds being conveyed to a recently disturbed 

 soil, where they had an opportunity of germinating, and 

 where they were not subject to the competition of other 

 and stronger species. On the e.xtensive shingle deposit 

 near Dungeness, in Kent, one of the earliest species to 

 appear on the newly deposited shingle is the foxglove. 

 The first is usually the oat-grass Arrhenathtirum 

 avenaceiim, and the third is often the wood-sage 

 Teucrium Scorodonia ; the seeds of all these must have 

 come from some considerable distance, and it is not sug- 

 gested that the plants arose from long-buried seeds. 



I am by no means asserting that seeds may not under 

 suitable conditions remain dormant for considerable 

 periods, but we want instances to prove this in which 

 other factors have been carefully and completely eliminated. 

 This does not appear to be the case in the above instance, 

 where it is also possible that the seeds produced in the 

 summer may have been blown into the interstices of the 

 wall, the disturbance of which led to their dispersal over 

 the site, and this might account for the absence of the 

 seedlings from the neighbouring turf-surface which had 

 also been disturbed, and which should have yielded them 

 had tTie seeds been blown from the dry capsules of the 

 plant after the destruction of the wall in the spring. 



Yardley Lodge, Oxford. G. Claridge Druce. 



The Rusting of Iron. 



Has anyone inquired whether the rusting of iron mav 

 not be associated with some micro-organisms? The facts 

 that oxygen, water, and carbon dioxide are necessary ; 

 that iron does not rust when immersed in boiling water 

 and then sealed up ; that certain solutions are said to 

 inhibit rusting (e.^. potassium ferrocyanide, a poison), and 

 that certain other solutions encourage rusting (c.^. 

 ammonium chloride and perhaps sea-water, compare the 

 composition of plant-culture solutions) ; that iron is a 

 constituent of chlorophyll, and that rusty nails sometimes 

 cause blood-poisoning, all these facts suggest a case for 

 inquiry. There is, I think, an iron bacterium noted In 

 some of the bacteriological books. The precipitation of 

 iron carbonate might conceivably hold a place in the life 

 of some organism corresponding to the precipitation of 

 calcium carbonate by foraminifera. 



Hugh Richardson. 



12 St. Mary's, York, October i. 



Colour Illusions. 



With reference to Mr. T. Terada's letter in your issue 

 of September 27 (p. 540), I noticed some similar effects 

 while making experiments with a form of colour top last 

 year. .\u old gramophone motor forms a very convenient 

 way to observe this, and by using various discs painted in 

 different rings and segments many curious optical effects 

 may be seen. 



I was, in fact, trying to see whether the effect of the 

 persistence of vision could not be used to indicate the 

 speed, and, to a certain extent, it can no doubt, but the 

 effect is not sufficiently definite, and there is too much of 

 the personal equation present to make it of practical use. 

 If a disc is painted in two or more rings, and each ring 

 is divided into a different number of segments, in colours 

 or black and white, it is well known that each ring will 

 become a uniform colour above a certain speed, according 

 to the number of segments ; the effect takes place at about 

 forty alternations per second. Very interesting strobo- 

 scopic and complementary colour effects may be obtained 

 in this way, some of which I have not seen mentioned 

 vet ; the complementary colours only appear at a certain 

 speed, and show best in sunlight; the effect is peculiar— 

 almost iridescent sometimes. B. J. P. R- 



October 3. 



