August 17, 1893J 



NA rURE 



367 



burden after burden, in the form of new notation, is added 

 apparently for the sole purpose of exercising the faculty of 

 memory." He would vastly prefer, it would appear, to write 

 with Hamilton »/(f ' - ', "when m represents what the unit 

 volume becomes under the influence of the linear operator." 

 But this notation is only apparently compact, since the m re- 

 quires explanation. Moreover, if a strain were given in what 

 Hamilton calls the standard trinomial form, to write out the 

 formula for the operator on surf.ices in that standard form by 

 the use of the expression mr/,' -^ would require, it seems to me, 

 ten (if not fift)) times the effort of memory and of ingenuity, 

 which would be required for the same purpose with the use of 



I may here remark that Prof. Tait's letter of endorsement of 

 I'rof. Knott's paper affords a striking illustration of the con- 

 venience and flexibility of a notation entirely analogous to <I'^*, 

 viz. * : *. He gives the form SvVj So-tr, to illu?trate the 

 advantage of quaternionic notations in point of brevity. If I 

 understand his notation, this is what I should write v<r : Vtr. (I 

 take for granted that the suffixes indicate tha' v applies as dif- 

 ferential operator to a-, and Vj to (t„ cr and o-j being really iden- 

 tical in meaning, as also v and v,.) It will be observed that in 

 my notation one dot unites in multiplication the two v's, and 

 the other the two <r's, and that I am able to leave each v where 

 it naturally belongs as difTerential operator. The quaternionist 

 cannot do this, because the v and cr cannot be left together 

 without uniting to form a quaternion, which is not at all 

 wanted. Moreover, I can write * for vc, and * : * for Vir : v<r. 

 The quaternioni-t also uses a (p, whith is practically identiial 

 with my * (viz. the operator which expresses the relation be- 

 tween cfcr and i^p), but I do not see how Prof. Knott, who I 

 suppose dislikes * ; * as much as * x *. would express 

 SvVi Sffir, in terms of this <p. 



It IS characteristic of Piof. Knott's view of the subject, that 

 in translating into quaternionic from a dyadic, or operator, as 

 he calls it, he adds in each case an operand. In many cases it 

 would be difficult to make the translation without thi,. But it 

 is often a distinct advantage to be able to give the operator 

 without the operand. For example, in tran lating into quater- 

 nionic my dyadic or operator *xp, he adds an operand, and 

 exclaims, " The old thing!" Certainly, when this expre.-sion 

 is applied to an operand, there is no advantage (and no dis- 

 advantage) in my notation as compared with the quaternionic. 

 But if the quaternionist wished to express what I would write 

 in the fjrm {* x p)-\ or |*xpl, or (* i< p\, or (*xp)x, he 

 would, I think, find the operand very much in the way. 



J. VVlLLARD GlBBS. 



On Secular Variations of our Rainfall. 



In studying the rainfall of this country, it is instructive, I 

 think, to compare a number of curves for different places, and 

 a long series of years, all smoothed by means of five year 

 averages. In the case of places not too far apart, one may then 

 recognise a common type amid some diversity of detail. But 

 It IS not easy to trace such "family likeness" between ; " 

 curves for the west of .Scotland and the east of England. ^'' 



The east of England curves seem to conform to the general 

 law affirmed by Biiickner for the greater pait of the globe, viz. 

 cold and wet periods alternating with warm and dry ones at in- 

 tervals of about 35 years ; so that, taking recent year.s, there 

 was, in most places, a rainy period between 1841 and 1855 and 

 again between 1871 and 1885, while a dry period occurred be- 

 tween 1856 and 1870. I 



In the accompanying diagram are shown two east of England 

 curves, one for East Anglia, giving mainly the rainfall for | 

 Dickleburgh, in Norfolk, continued forabout 17 years by that of ' 



Twich (according to />'/7V(i/4 Rainfall), the other for Boston 



im the same woik). These curves, it will be noted, dip down 

 irum a relative maximum in the early year^, 1843 and 1847 and 

 rise again to maxima in 1877 and 1881. 



Some rainfall statistics for Oviedo were recently given in the 

 Mtteorohgische Zeilschrijl (Eel,., 1892, p. 71). This is, it may 

 be well to state, a university town in the north of Spain, cai>ital 

 of the province of Asturias, and about 20 miles from the coast 

 of the Bay of Biscay. Now, the smoothed curve of this place 

 from 1853, has a form distinctly opposite to tho;e just considered 

 (is the diagram shows'). It rises to a maximum in 1864, goes 

 ' The vertical scales, right and left, are not to be taken as equivalent. 



NO. 1242, VOL. 4.S] 



djwn to a minimum it. 1877, ^f'er which it rises again, reaching, 

 peihaps, another maximum in 1887. 



This opposiieness in the variation of rainfall appears to merit 

 attention. How is it to be explained ? 



One of the most interesting meteorological fads brought to 

 light in recent years is, that the depressions which come over 

 from the west do not take, as it were, a random course, but lend 

 to follow, with more or less frequency, certain well-defined 

 patlft. The course of several of these paths has been indicated 

 by Van Bebber, who has made a special study of the subjed. 

 Some of the paths are known to shift in ihe course of the year, 

 having a different direction in midsummer from what ihey have 

 in midwinter. And there can be little doubt, though the matter 

 is still obscure, that the paths shift in successive years. The 

 paths numbered IV and V by Van Bebber, are said to have 

 shifted in the years 1879 to 1884-5 ffO"! a more maritime to a 

 more Continental position, and Lang connects with this an ob- 

 served variation in the rate of ti avel o( thunderstorms in -South Ger- 

 many (^eeMel.Zei'ls., Nov., 1891, p. [68], ol LiUraturher ). Such 

 shifiing is very probably accouipanied with variations of rainfall. 

 Hellmann supposes this to be the reason why in Sjiain a year 

 ihat is wet in the north-west is generally dry in the south-east, 

 and vice versa. We might, peih.ips, roughly compare such 

 variations to ihe case of a man watering a lawn with a garden 

 hose, .and directing the jet of spray now on one side, now on 

 the other. 



I do not know whether any suggestion of this nature is applic- 

 able to the case before us, or whether some other and belter 

 explanation may be forthcoming. 



Oviedo is not, apparently, included in BiiicVner's data for 

 estimating Spanish rainfall ; and it is to be noted that he 



Ovittls 



ISuc 



Oo\tm. 



S 9' 



regards the north of Spain as conforming to his thirty-five years 

 law, while southern Spain is reckoned exceptional. 



Biiickner has two classes of exceptions : the "permaneni," 

 in which the curves are opposite to the noimal (Ireland and the 

 Atlantic islands being examples), and the "temporary," in 

 which there is conformity to the rule, for a time ; then, during 

 some lustra, ihere come irregular variations. To this latter class 

 are relegated south and middle Spain, Mediterranean Fiance, 

 West England, and Scotland. If Biiickner's view regarding the 

 north of Spain is correct, how comes it that the Oviedo curve 

 has the character indicated, which is apparently that of the 

 permanent exceptions ? 



In discussions on the subject of sunspot influence on weather 

 one sometimes hears the opposite character of weather in 

 different regions urged as a difhculty in the way of accepting such 

 influence. Thus, in connection with a paper read by Mr. Scott 

 to the Royal United Service Institution last year (/^wvm/, M.iy 

 p. 510) 1 find him remarking: "It is not possible 'to say 

 whether or not the mere fact of our having very wet or dry 

 weather is due to the sunspots, when our neighbouLs not very 

 far off are having exactly the contrary. . . . Last summer 

 everybody was abusing the weather because of its wetness. I 

 myself was then living in the Black F^lresl, and we had four 

 days' rain in eight weeks. Which of these conditions depended 

 on the sunspots ? Was it my fine weather or was it the rain 

 here ? " 



With all deference to an excellent authority, ard without 

 offering an opinion upon the particular cases cited, it seems to 

 me not impossible that the influence of ihe solar cycle might 

 be manifested in an opposite succession of effects in diOerent 



