i82 



NA TV RE 



[Al'RlL 20, 189^ 



bute to the small spheres, so that all three spheres may touch 

 one another. They touch when c - i + 2;- ; whence we get 



9;-* + 2£,r^ -f- 22r- 



24;- 



15 = o, 



the solution of which is *85078. 



Hence if the smaller spheres have their radii "85078 of the 

 large one, they are all three in contact, and there is no pressure 

 between ihe small ones, when they revolve with proper orbital 

 angular velocity. Now the analogue of this solution in Roche's 

 problem is very interesting. The problem is to find the relative 

 sizes of planet and satellite, so that where the satellite is in 

 limiting equilibrium the two bodies shall just touch. The solu- 

 tion will give a fair approximation to that hour-glass figure of 

 -equilibrium of rotating fluid, which I have treated otherwise in 

 a paper in the Philosophical Transactions (vol. clxxviii. A., 

 P- 379)- The solution would be improved, although compli- 

 cated, by allowing the larger body to be also deformed. 



Unfortunately the solution requires the tabulation of several 

 functions depending on elliptic integrals. Roche made, but did 

 not publish, tables of certain integrals, which he used for obtain- 

 ing his results. It appears that the problem to which I refer did 

 not occur to him. 



Some years ago I began the computations necessary for this 

 solution, but as it appeared to be a much more laborious task 

 than I had anticipated, I have put the work aside until I should 

 find leisure to attack the problem again. G. H. Darwin. 



April 10. 



The Afterglows and Bishop's Ring. 



1 AGREE with your correspondents (pp, loi and 127) that there 

 has been a marked increase in the amount of dust in the u{5per 

 regions of the atmosphere within the last few months, as evidenced 

 by sky phenomena. 



I did not notice the sunset of November 27, and it was not 

 till the next morning I observed any increase in the dust pheno- 

 mena here. About sunrise on the 28th "Bishop's Ring" was 

 very conspicuous for the first time for a considerable period, as 

 also were the v\hitish wisps in and near it, very similar to those 

 forming such a noticeable feature of the Krakatab sunsets ; but 

 I have never again seen them so small and definite as when those 

 sunsets first took place. The sunset of that day (November 28) 

 was a magnificent and striking one, with a very deep pink glow. 

 0.1 the 3o:h there was a somewhat definite bright segment below 

 the rosy glow, at first a dull buflf, and then orange. This seg- 

 ment was a very striking feature of the earlier Krakatab sunsets, 

 but I have rarely seen it since till that day. I noticed it again 

 on December 4. The wisps continued to be very conspicuous 

 up to December 13, after which date they gradually grew less 

 so, and have now disappeared altogether. 



After the middle of December 1 was travelling in Portugal, 

 the Canaries, and Spain. The segment was invisible — or at 

 any rate not a noticeable feature — after December 19 to January 

 30 ; but most of the time I was not favourably situated for seeing 

 it on account of hills. From the last-mentioned date to Feb- 

 ruary II (during which time I was in the neighbourhood of the 

 Straits of Gibraltar) the sunsets — generally on a cloudless sky — 

 were very striking, and almost nightly the orange segment was 

 very bright and definite, though I think not quite so definite in 

 outline as in the Krakaiab sunsets, but it reminded me much of 

 them. As 1 had not been in that locality before, I do not 

 know whether such sunsets are common there, or whether the 

 phenomena were due entirely to a general accession of dust. 



Since returning to England on February 14, the segment has 

 sometimes been visible, though much less striking than in Spain. 



"Bishop's Ring" still continues very conspicuous about 

 sunset. I have not seen it of late years when the sun has had 

 any considerable altitude, except on the i8th ult., from 1.30 to 

 3.30 p.m.; I was then in Teesdale at from 1300 to 1700 feet 

 above sea-level ; it was quite plain when the sun was behind a 

 cloud, and visible even with the sun free from clouds. It has 

 never ceased to be visible at about sunrise and sunset since 

 November, 1883, although at times very faint. Has it always 

 occurred when the sun is near the horizon, and is it only because 

 attention was called to it by its remarkable vividness at the time 

 of the Krakatab sunsets that one has been able to see it ever 

 since, though never before ? Unlike Mr. S. E, Bishop I 

 always see a certain amount of red in the outer margin ; though 

 in the late accession to its conspicuousnessthe red has been very 



NO. 1225, VOL. 47] 



dull, rather to be called dull brown than red. This has also been 

 the case at times before. 



One other feature of the Krakatao sunsets has occasionally 

 been visible of late in this country, namely, the second pink 

 glow in the western sky. This was much more striking in 

 Teneriffe, though still much fainter than in the Krakatab sunsets. 



It would appear that if this dust is the same as that seen at 

 Honolulu, it took six weeks to get from there to Dublin and 

 Sunderland, while the Krakatab dust took two months in reach- 

 ing the south of England from Honolulu. 



Sunderland, April 10. T. W. Backhouse. 



Thunderstorms and Auroral Phenomena. 



I AM residing in tropical Queensland, lat. 21° S., and con- 

 sequently am not likely to see any auroral phenomena, particu- 

 larly in the middle of our hot and rainy season ; but last night 

 between 8 and 9 p.m there occurred the following remarkable 

 appearances, which were seen by me and several others. 



There was a sharp thunderstorm with incessant lightning 

 visible on the southern horizon, occupying a width of 10° and an 

 altitude of from 5° to 10° above the horizon, probably from 80 

 to 100 miles off. 



But for the distant thunderclouds the sky was clear and star- 

 light, with a few light cirrhus clouds drifting before the north 

 wind. 



I was sitting on the lawn watching the distant flashes, when 

 suddenly a patch or cloud of rosy light — 5° to 6° in diameter — 

 rose up from above the thimderstorm and mounted upwards, 

 disappearing at an elevation of from 40° -45°. There were 

 about twenty to twenty-five of these patches in the course of 

 half an hour, sometimes three or four in quick succession ; they 

 took from one to two seconds to mount, and were not associated 

 with any particular flash ; the rosy colour contrasted strangely 

 with the silvery light of Nubecula Major just above. There 

 were also occasional streamers, sometimes bifurcated, of 2° in 

 breadth, which shot up in the same way as the auroral streamers, 

 which 1 have seen both in the arctic and antarctic zones. 



Auroral phenomena are known to be electrical manifestations-, 

 but here were the same phenomena exhibited in connection 

 with a thunderstorm in the tropics. Thinking this phase of 

 electrical action worthy of note, I send you this account and 

 enclose my card. J. EwEN DAVIDSON, 



Branscombe, Mackay, Queensland, 

 February 5th. 



P.S. — The thunderstorm, patches of light, and streamers 

 were distinctly connected; it was not a case of an ordinary aurora, 

 with a thunderstorm interposed. 



Fossil Floras and Climate, 



Sir William Dawson demonstrates that the plants of the 

 cretaceous and tertiary series of Canada prove that the tem- 

 perature of Greenland during the tertiary period was mild but 

 not subtropical. That is sufficiently extraordinary, but geologists 

 prefer, with strange inconsistency, the more astonishing con- 

 trast between Heer's arctic niioccne palms and the glacial period. 

 The fact is that these floras, comprismg a few large-leaved ever 

 greens and relatively lender ferns and coniferse, are not normal 

 in such high latitudes, but confined to localities which might 

 have been stations on the north coast of a warm Atlantic Ocean. 

 Therefore they perhaps require nothing more prodigious than 

 the circulation of a gulf stream in an Atlantic isolated from the 

 Arctic Ocean, a probable state of things at that time. At all* 

 events tertiary plants collected from near the Equator negative 

 any generally enhanced temperature. 



This applies solely to the tertiary period, when many actually 

 living species of plants were in existence. As we recede in 

 time species become more strange and extinct, and likely to 

 mislead. No wise person would define, for instance, from sur- 

 viving cycads the climatic conditions they may have endured 

 when as common and widely diffused as blackberries are to-day. 

 Even estimates based on such a group as Gleichenia may be 

 quite inapplicable when they sustained the role now usurped l)y 

 the bracken. 



Sir William Dawson is aware that with even the best preserved 

 fossil leaves, and with access to the most complete herbaria in 

 the world, half-a-dozen difi'erent conclusions may be come to in 



