Sept. 19, 1878] 



NATURE 



541 



a " cubo," as this wasp is called in Ecuador, had my whole hand 

 and forearm considerably swollen for a couple of days. 



A common spot chosen by the cubo for his nest is high up on 

 a palm stem at the river-side, and natives are well aware of the 

 danger of uttering any loud cry when in its proximity. I have 

 frequently experimented by giving a shrill whistle — his particular 

 abhorrence — from a safe distance, with the invariable result of 

 all the wasps flying in confusion from the nest in manifest 

 anger. 



It is said that there is a wasp in New Granada in whose prox- 

 imity one dare not speak, but for this I cannot vouch, and very 

 possibly this may be an exaggerated account of the cubo. It 

 would certainly be a dangerous experiment to speak loud when 

 very close to a cubo's nest, even on the Guayas, and a shrill 

 voice would be sure to irritate the wasp. Alfred Simsox 



4, Fairlie Place, Calcutta, August 20 



'\ Circulating Decimals 



In Nature, vol. xviii, p. 291, is an extract from a letter by 

 Mr. R. Chartres, in which is given a remarkable property of 

 certain circulating decimals. Air. Chartres only refers to frac- 

 tions of the form — (where r — 10) ; but I have since 



nr — \ 



found that a somewhat similar property belongs to other frac- 

 tions when expressed as circulating decimals. 



For instance, \ = 142857 ; here we observe that the last 

 figure of the circulator is the same as the denominator of the 

 vulgar fraction ; moreover, by multiplying the 7 by 5, we get 

 the next figure, and this by 5, taking in the remainder, gives the 

 third from the end, and so on till we get the whole recurring 

 decimal. 



So far this is somewhat similar to Mr. Chartres' discovery, but 

 now observe the curious property in the following fractions : — 



f = -142857 

 iV = -6588235294117647 



?V = '037 



s\ = -027 

 In each case the last figiu-e of the circulator is the same as the 

 unit figure of the denominator of the vulgar fraction. Now the 

 multipliers which give the remaining figures are, for the first 

 fraction, 5 ; for the second, (5 + 7) ; for the third, (5 + 14) ; 

 for the fourth, (5 + 21) ; and generally to convert a vulgar 



fraction of the form 



{r = 10) to a circulator, we put 



n y + y 

 down the last figure 7 and multiply successively by 7 « -f 5. 



For fractions of the form — the multiplier is 3 w -f i. 



and the last figure 3. 



For fractions of the form 



»>" + 3 



the last figure in the circu- 



nr + I 

 lator is 9, and the multiplier is 9 « + i . 



Of course the last figiure must be that one which, multiplied 

 into the unit of the denominator, and the unit of the result 

 being subtracted from 10, leaves a remainder of i. 



These rules added to that of Mr. Chartres include every case 

 of fractions which, when reduced to decimals, circulate. 



Littlehampton, Sussex Edmund P. Toy 



Autophyllogeny 



With reference to the note in Nature on autophyllogeny 

 in a leaf of Papaya vulgaris, I wish to place on record another 

 freak which I have more than once noticed in the Papeea 

 or Papeeta, as we call Carka papaya out here. The plant is 

 dioecious, the female being stumpy and her flowers and fruit 

 sessile ; the male plant, on the other hand, is tall and grace- 

 ful, and the flowers depend from long stalks. The freak I have 

 above alluded to consists in the presence of distinct and well- 

 formed fruit on the male plant, and I regret I was unable, on 

 both occasions, to secure the anomalous production for examina- 

 tion. R. F. Hutchinson, M.D., 



Mussooree, August 19 Surgeon-Major, Bengal Army 



The Sea- Serpent Explained 



The letters of Dr. Drew and others i-emindme of what I wit- 

 nessed at Sandgate twenty-four years ago. I was stayirg at a 



cottage on an elevation which commanded an extensive sea-view. 

 One morning my attention was called to a large, dark, undulat- 

 ing body, which moved rapidly through the sea. As it was 

 some way out from shore, I naturally concluded it to be of 

 enormous length. I lost no time in making inquiries as to the 

 nature of this phenomenon, and was so fortunate as to discover 

 a fisherman who had witnessed it. He told me it was a flight of 

 petrels. But for this I should certainly have believed that I had 

 seen the Great Unknown. I have often seen a Eimilar pheno« 

 menon, but nothing nearly so striking as this. 



Valentines, Ilford, September 16 C. M. Ingleby 



RECENT PROGRESS OF SELENOGRAPHY 



THE most active period in the study of selenography 

 during late years is comprised between two epochs, 

 that of the announcement of a change in the crater 

 Liruik in the year 1866 by Dr. Schmidt, Director of 

 the Observatory at Athens, and that of the announce- 

 ment of a new crater north-west of Hyginus, by Dr. 

 Klein, of Cologne, in the year 1877. The years elapsed 

 between the two events above-mentioned have been 

 characterised more or less by the manifestation of con- 

 siderable interest in lunar studies, of which the projectionr 

 of a map of the moon 200 inches in diameter, to have been 

 constructed under the auspices of the British Association 

 for the Advancement of Science was the first indication. 

 Of this map, four sections embracing an area of 100 

 square degrees of lunar latitude and longitude have been 

 published, containing all the formations known in 1866- 

 1868 to exist on this area, each of which is separately 

 catalogued. Three of these sections, with catalogues, 

 were published in the Reports of the British Association. 

 for 1866 and 1868 ; the fourth was published by the aid 

 of a private subscription, in 1870. We are not aware that 

 much use has been made of these areas and catalogues 

 in endeavouring to ascertain if the 433 objects chronicled 

 in them retain the" characteristics they possessed in the 

 above-mentioned years. It was a part of the duty of the 

 Committee appointed by the Association to receive the 

 reports of volunteer observers who undertook to examine 

 the objects in certain subzones at stated intervals, which 

 resulted in the addition of several new objects to those 

 originally published, but nothing has been effected in this 

 direction since the Committee was not reappointed in 

 1868. 



In February,~i869, a map of the Grey Plain, the Mare 

 Serenitatis, was published in the Astroiiomical Register 

 for that month, by Messrs. Joynson and Williams. It 

 contained several new objects not on former maps, and. 

 was followed in the course of a few months by a map and 

 monogram of the same region. The map was divided into 

 the British Association areas, and it contained 277 objects, 

 each being distinguished by a British Association symbol; 

 they were briefly described in a table of the areas in which 

 any part of the Mare was found. 



The four areas of the British Association map on a 

 scale of 200 inches to the moon's diameter accompanied 

 by a monogram of the formation Hipparchus on a scale 

 of 100 inches, with that of the 2dare Serenitatis form a 

 collection of maps, which, with the descriptions of 71a 

 separate objects embody the conditions of those portions 

 of the moon's surface which were telescopically or photo- 

 graphically examined between 1S66 and 1870. As 

 placing in the hands of the student a body of facts espe- 

 cially suitable for future reference, these maps and mono- 

 grams will furnish most important information on the 

 condition of objects recorded on or in them during the 

 four years above mentioned. It is in the future the real 

 progress of the past is more truly measured. 



In the years 1871 and 1872, Reports of a Committee 

 appointed for discussing observations of lunar objects 

 suspected of change, was read before the British Asso- 

 ciation for the Advancement of Science, the principal 

 results being the discovery of about thirty-six spots and 



