=;& 



NATURE 



[May 1 8, 1905 



coloration. They existed in tlie rocli before cleavage was 

 induced. Many of them are broken up lilce broken egg- 

 shells. Those which are complete lie with their longest 

 axes in the plane of cleavage, and would well agree with 

 the theory that they were deformed along with the envelop- 

 ing rock 'by a shearing process, and that the plane of the 

 greatest distortion was the plane of cleavage. 



In my paper on cleavage and distortion in the Geo- 

 logical Magazine I pointed out that it is to Sir John 

 Herschel that we are indebted for the theory of the 

 " molecular movement," which, I remarked, was in fact 

 a " shear " — a term which has now been universally 

 accepted for this kind of action in rocks ; and in my 

 " Physics of the Earth's Crust " I have explained how the 

 crumpling in the harder and cleavage in softer layers of 

 a rock would simultaneously arise from such a shearing 

 movement. O. Fisher. 



Harlton, Cambridge, May 8. 



A Relation between Spring and Summer. 



A FAIR idea of the larger fluctuations of a given meteor- 

 ological element may be had by means of a two-fold 

 smoothing process, e.g. adding the series of values in 

 groups of five (i to 5, 2 to 6, 3 to 7, &c.), and then doing 

 the same with those sums. In each case the sum is put 

 opposite the middle member of the group. 



When this is done with (a) the amounts of rainfall in 

 spring (March to May) at Greenwich since 1841, and (b) 

 the numbers of warm months in summer (same place and 

 period), we have the two curves in the diagram. The 



/Sj.^- t? fo 



lower one (that for summer) is inverted, so that its crests 

 represent few warm months, or coolness. 



One must be struck, I think, with the similarity of the 

 curves ; four long waves (roughly) in each, those of the 

 lower curve lagging in phase somewhat (one to three years) 

 on those of the upper curve. The four centres of wetness, 

 as we may call them, of the spring series are followed at 

 a brief interval by four centres of cold in the summer 

 series, and the four centres of dryness in the former, at 

 much the same interval, by four centres of warmth in the 

 latter. 



Let us look briefly at the nature of those centres, and 

 we may do so by indicating, first, the character of the 

 group of five springs about each of the dates 1849, 1862, 

 1878, and 1888 (wave-crests of upper curve), and the corre- 

 sponding summer groups (wave-crests of lower curve). We 

 find in each group of five springs an excess in the total 

 rainfall, and at least three of the five wet ; further, in each 

 summer group a small number of warm months. 



Making a similar comparison of the centres of dryness in 

 spring with the centres of warmth in summer, we have : 



be 



159 



1897 



Here the relations are all of an opposite character. 



To what are those long waves of variation 

 attributed? And can any physical explanation be given 

 of the sequence which has been indicated ? Perhaps some 

 of your readers may be able to throw light on these points. 

 I will only remark that there is no obvious connection 

 with the sun-spot cycle. Thus the first two crests in the 

 upper curve come close after maxima (1848 and i860), 

 while the two latter are near minima (1878 and 1889). 



With regard to the point now reached by this curve (a), 

 the rainfall of the present spring (already in excess, 

 .May 10) should extend it upwards, but it must apparently 

 be near another crest. Some help in forecasting our 

 summers might perhaps be derived from a consideration of 

 the facts above given. Alex. B. MacDow.all. 



Fictitious Problems in Mathematics. 



In Nature of April 27 (vol. Ixxi. p. 603) your reviewer 

 finds fault with Cambridge examiners for endowing bodies 

 with the most inconsistent properties in the matter of 

 perfect roughness and perfect smoothness — " A perfectly 

 rough body placed on a perfectly smooth surface." Your 

 reviewer adds, the average college don forgets that rough- 

 ness or sinoothness are matters which concern two surfaces. 

 not one body. 



Will your reviewer give a reference to some page of 

 Whittaker's book (that under review), or to some page of 

 any other text-book used in the last half-century at Cam- 

 bridge, in support of his charge against Cambridge ex- 

 aminers? Fifty years ago, William Hopkins was still 

 directing the mathematical teaching of Cambridge, and 

 enforcing the conservation of energy where friction is taken 

 into consideration. A perfectly rough sphere moving on a 

 rough surface is intended to mean that, during the motion 

 considered, the sphere rolls without any slip. " A perfectly 

 rough sphere moving on a smooth surface " would no 

 doubt be equivalent to "A sphere moving on a smooth 

 surface ": but where does the phrase occur? 



An Old .Average College Don. 



The alleged inaccuracies of language in stating the 

 assumed conditions of smoothness or roughness prevailing 

 lietween two bodies in contact are unfortunately so common 

 that it is the exception rather than the rule to find any 

 problem in which these conditions are correctly worded. 

 In working through a chapter of Besant's " Dynamics " 

 with a class the other day, I came across no less than two 

 problems in which a " perfectly rough " body was sup- 

 posed to be in contact with a second body which in turn 

 rested against a third " perfectly smooth " body. In these 

 cases the framer of the question carefully avoided giving 

 any information as to the roughness or smoothness of the 

 middle body, so that the inaccuracy of language might 

 easily be overlooked. But this does not apply to the 

 following example : — 



" A person is placed at one end of a perfectly rough 

 board which rests on a smooth table. Supposing he walks 

 to the other end of the board, determine how much the 

 board has moved. If he stepped off the board, show how 

 to determine its subsequent inotion " (Routh, " Elementary 

 Rigid Dynamics," 1882 edition, p. 69, example 4). 



At the time of writing the review I was quite unaware 

 that such an example had found its way into a text-book 

 written by so careful a teacher of applied mathematics as 

 Dr. Routh, and it says much for the prevalence at Cam- 

 bridge of these erroneous forms of statement that this 

 wording failed to attract the author's attention. Since 

 writing my review, it has been brought to my notice that 

 similar inaccuracies widely prevail in the statement of 

 problems involving so-called " perfectly elastic " or " in- 

 elastic bodies." The Reviewer. 



NO. 1855, VOL. 72] 



