OcL lo, 1878] 



NATURE 



617 



1869 1870 1871 1872 1873 1874 



"(BritSes)'"' 1 '■-* S'o "7 679 57. 658 



Cyclones (W. Indies) 07301? 



The period covered by the table is too short to afford any ground 

 for a definite induction ; but, as far as they go, these figures 

 ^SoxA primd fade evidence in favour of the theory. 



I may add that the probability of this relation between the 

 gales of the temperate zones and the cyclones of the tropics has 

 been pointed out on purely speculative grounds by Mr. E. D. 

 Archibald, in a pamphlet on the rainfall of the world, recently 

 published by him in India. S. A. Hill 



Allahabad, September il 



Magnetic Storm, May 14, 1878 



In the Bulletin Mensuel of the observatory of Zi-kawei, near 

 ■Ghang-hai, China, the following interesting remark occurs in the 

 number for May, 1878 : — 



" Durant le mois de Mai, une seule perturbation a ete enre- 

 gistree par le magnetophotographe ; elle commen9a le 14, a 

 2h. 20m. de I'apres-midi, et se termina 24 hemes apres ; ce 

 jour-la la declinaison, par extraordinaire, ne presenta pas d' oscil- 

 lation diurne normale, mais de tres-nombreuses petites oscilla- 

 tions comme le bifilaire." 



On examining the photographic trace of the Stonyhurst 

 magnetograph I find that the only magnetic storm in May last 

 commenced on the 14th at 6h. 4m,, and lasted rather more 

 than twenty-four hours. The longitude of Zi-ka-wei being 

 Sh. 15m. 38s. E. of Stonyhurst, the storm began at the same 

 time at both stations. Tlie character of the movement was also 

 identical, for the only disturbance at Stonyhurst from 6 A.M. 

 until 4 P.M. was a tremulous motion of the declination and 

 horizontal force magnets. 



The storm was at its height at midnight, when all the magnets 

 were much disturbed, and the vertical force magnet was thrown 

 completely off its balance. 



It is impossible to obtain more than the roughest outline of a 

 magnetic storm from hourly readings, but even this slight datum 

 from China shows a general agreement in the declination curves 

 during the storm at these two distant stations. 



The Monthly Record of the Melbourne Observatory also men- 

 tions the same magnetic disturbance, which commenced there at 

 4 P.M. on the 14th, and lasted until 8 A.M. on the 17th. Mel- 

 bourne lies 9h. 39m. 54'8s. E. of Greenwich, and therefore 

 ih. 34m. 103. E, of Zi-ka-wei. We thus see that the Zi-ka-wei 

 storm commenced at 3h. 54m. Melbourne time : it was therefore 

 simultaneous at the three observatories. 



Stonyhurst Observatory, September 27 S. J. Perry 



Winds and Currents in the -Pacific 



The occasional prevalence of westerly winds and of currents 

 setting east in the intertropical portion of the Pacific, has such 

 an important bearing on the possible eastward migrations of 

 the Polynesians that I think the following, which I take from 

 the Samoa Times for April 20, is worth recording in Nature. 



The brigantine Ryno is reported as having arrived at Apia, 

 Samoa, on April 16, from the Tokelau, or Union Group. She 

 was among those islands from March i to April 11, and, while 

 thfere, she "experienced a succession of strong westerly and 

 north-west winds, with high sea and firequent squalls and much 

 Tain, which made sad havoc amongst the vessel's canva-. Capt. 

 Bower states that, when off Tokelau, he found a strong current 

 setting to the eastward at the rate of two miles per hour. The 

 Ryno left Tokelau on April ii, had fine E.S.E. weather, and 

 otio current whatever." S. J. Whitmee 



Blackheath, September 27 



Blackburn's Double Pendulum 



I TRUST I may be pardoned for observing, in reference to 

 Prof. A. M. Mayer's description of the curves produced by 

 Blackburn's Double Pendulum (Nature, vol. xviii. p. 594), 

 that a typical series of those curves was placed before the 

 readers of Nature in the year 1871 (vol. iv. pp. 310, 370), in 

 illustration of a paper of mine on "Pendulum Autographs." 



Prof. Mayer adheres to the funnel and sand as the mode of 

 laying the curve on paper. The ' sand-trail thus left is neces- 

 sarily rather coarse, and cannot be conveniently preserved. A 

 more delicate and more enduring trace, in ink, can be obtained 



by the use of a tubular glass pen, as described by me in the 

 paper above-mentioned. Only the increased friction makes it 

 necessary to use a heavier bob. HUBERT AlRY' 



Circulating Decimal Fractions 



As a supplement to the interesting properties of circulating 

 decimal fractions which have been published in two recent num-. 

 bers of Nature, I give you the following, which I think is 

 sufficiently curious to merit attention : — 



If the decimal fraction equal to i -i- n recur in a cycU of n -1 

 digits, the average value of the digits is constant, viz. , i^for all 

 values of n ; hz other words, the sum of the digits of the cycle is 



4l(«-l)- . ■ 



For example, — 



T= '142857, 



and (I-f4-f2-f8-i-S-l-7)-^6 = 27-^6 = 4i..r.tTTT 



Again, ^ » 



tV = -65882352941 1 7647^ -^. 

 and (o -f- 5 -f 8 4- 8 -f- &c.) -^ 16 = 72 -m6 = 4^ 



The theorem is easily established from the two facts (i) that 

 I -7- «, 2 .-^ «, 3 -^ «, . . . . have the same digits in their cycles, 

 and (2) that the sum of i, 2, 3, ....,?«- r is \n{n - i). 



The properties of circulating decimal fractions have beea 

 often studied from the time of Wallis downwards, and very 

 probably those lately and now brought forward have been noted 

 before, but have niain entombed in some out-of-the-way comer 

 since. However, until a full index to mathematical literature is 

 prepared, or exhaustive monographs on special departments like 

 this are written, such resurrections are very desirable. 



If either of your two previous correspondents on the subject 

 would care to undertake a full examination of it I should be glad 

 to furnish him with my quota of references to the extent of ten 

 or a dozen, and, I have little doubt, other readers of Nature 

 would give like help. Thomas Muir 



High School of Glasgow, September 23 



[Mr. Muir's theorem is practically contained in the result that 

 the two halves of the period are complementary, whence the 

 sum of the figures is equal to half as many nines as there are 

 figures in the period. — Ed.] 



An Old Map of Africa. «m'-> 



Early in the year 1870 I visited the vineyard of Mr;"^'. EJ- 

 Cloete at Constantia, near Cape Town. 



Among other things of interest Mr. Cloete showed me an 

 old map of Africa done, I think, in Amsterdam. This map 

 had been in the possession of his family from time immemorial. 

 My acquaintance with the geography of Africa was too slight 

 to enable me to pronounce upon its accuracy, but I was greatly 

 surprised to see marked upon it several large lakes and many 

 rivers in the region now so well known to us through recent 

 explorations. 



In the critical study of this subject I have thought that a 

 knowledge of the existence of this map, if it be as I remember 

 it, might prove of value. C. F. Goodrich, 



Torpedo Station, Lieut. -Commander, U.S. Navy 



Newport, Rhode Island 



[We would refer Commander Goodrich to our article on Old 

 Maps of Africa, in Nature, vol. xviii. p. 149. — EDil ' ' 



Earth Pillars 



A letter in your issue for September 26 (p. 569) refers to 

 miniature earth pillars seen in the Tyrol. But there is no need to 

 travel out of the country to obtain these mimic representations, 

 at any rate on a moderate scale. Twice I have found them, 

 formed by the drops from railway bridges, upon bare clays ; 

 and once in a half-finished building, in a sand-heap containing 

 numerous pebbles. Evidently the heavy drops and the protec- 

 tion from driving rain favoured the result. One of the bridges, 

 between Shepton Mallett and Wells, Som., covered Lias clays, 

 protected by cinders, &c. The other instance, the bridge on the 

 new North Approach just outside York Station, is the more 

 interesting in its mimicry of the original Botzen earth pillars, 

 since small boulders and pebbles in the glacial clays form the 

 caps and shoulders in the Lilliputian columns. 



September 28 J- Edmund Clark 



