July II, 1878] 



NATURE 



291 



The new historical museum of Frankfort-on-the-Main was 

 Oldened on June 14. The new museum now contains all the 

 objects of antiquity and art which were hitherto distributed in 

 various public buildings of the old city. Several local scientific 

 societies have presented the whole of their collections to the 

 new establishment. 



The foundation stone of the Chadwick Natural History 

 Museum was laid last week. The building is to be in the public 

 park, Bolton. At present the town, although the third in 

 importance in Lancashire, does not possess a museum. 



A LETTER from the Prefet de la Seine has been sent to M. 

 Mascart, the Director of the French Central Meteorological 

 Bureau requesting that arrangements be made to post the 

 \\eather warnings at the Bourse, Pont St. Eustache, and Halles 

 Centrales, three places where monumental barometers have been 

 placed at the expense of the municipal exchequer. It is airious 

 that Paris does not yet receive a single warning although warn- 

 ings are sent daily to 1,500 parishes, most of them of the 

 smallest description. . • 



The first number of V Electriciti, a French semi-monthly 

 periodical, has been issued, 



A GENERAL meeting of the Mineralogical Society of Great 

 Britain and Ireland was held at 1 16, Victoria Street, S.W., on 

 Thursday, July 5, R. H. Scott, F.R.S., in the chair. Prof. 

 Harkness read a paper on " Cotterite," a new variety of quartz 

 from Ireland. A paper by Prof, Heddle, of St. Andrews, on 

 •* A New Manganesian Garnet from several Localities in Scot- 

 land," was read by the Secretary. The Secretary also read 

 papers on " Youngite," and on "The Artificial Production of 

 Psilomelane," communicated by Mr. J. B, Hannay, of Owens 

 College, Manchester; and on " Penwithite, a New Cornish 

 Hydrous Manganesic Silicate from Cornwall," analysed and 

 described by himself. The annual meeting was fixed for 

 Wednesday, August 14, at 2,30 P,M., to beheld at Dublin, 



Besides those whose names we gave last week, Mr, A, 

 Cowper Ranyard, Mr, F. C. Penrose, and Mr. Giles Loderhave 

 also sailed for America, to observe the eclipse of the sun on the 

 29th inst. 



We have received the July number of the Pantiles Papers, a 

 monthly literary magazine and review published at Tunbridge 

 Wells. We are glad to see that the journal pays some attention 

 to science. 



Two aeronautical ascents have been made from the Paris Cour 

 des Tuileries in balloons of 450 cubic metres filled with hydrogen 

 gas ; the first took place on June 30 by MM. Gaston Tissandicr 

 and Jules Godard, and the second on July 7 by MM, de Fon- 

 vielle and Albert Tissandier, Both balloons were guided by a 

 N,W, wind. On July 7 the balloon travelled at a regular rate 

 of nine metres per second. Some interesting observations were 

 made. It was noticed that cumuli have a height sometimes 

 twice as great as their horizontal dimensions. The summit 

 was observed to reach an altitude of 3,500 metres when the 

 base was floating at an altitude of 800 metres. These clouds 

 play the part of humid conductors connecting inferior with 

 superior strata, and their dissolution in the form of rain is con- 

 nected with electric phenomena, 



Mr, Bryce M, Wright has reprinted in a separate form 

 from the Journal de Conchyliologie his "Description of the New 

 Genus Delphinnlopsis, and of the New Species Delphinulopsis\ 

 lesourdi" 



The Paris Jardin d'Acclimatation has just made a most exten- 

 sive and valuable acquisition of animals from Nubia, It includes 

 fourteen giraffes, seven elephants, ten lions, two young hippo- 

 potami, seventy dog-faced baboons, and a number of antelopes, 



panthers, birds, &c, Herr Reiche, of Hanover, who captured 

 these animals on the banks of the White Nile, receives for them 

 the sum of 10,000/. 



The ancient records of the monastery of Fulda, and other 

 German cloisters, which have been recently published among 

 the Monumenta Germanice, give detailed accounts of a visitation 

 of grasshoppers in the year 873, surpassing in point of destruc- 

 tiveness even those prevalent of late years in America, The 

 grasshoppers appear to have come from the East, and, after 

 having devastated nearly the whole of France, perished in the 

 Atlantic, They are described as having hidden the sim, and 

 having been able to eat everything gi-een on a hundred acres in 

 the course of an hour. Spanish monastic archives relate like- 

 wise the appearance of grasshoppers in 873, which appears to 

 be the first record of an invasion by these insects in Europe. 



We are asked to state, on behalf of the Sunday Society, that, 

 through the praiseworthy liberality of Sir Coutts Lindsay, the 

 proprietor and director of the Grosvenor Gallery, New Bond 

 Street, the Summer Exhibition at this institution will be open 

 on the three following Sunday afternoons, between the hours of 

 two and six : — On Sunday, July 14, the gallery will be opened 

 free to the subscribers and members of the Sunday Society, and 

 on July 21 and August 3 to the public, by tickets, which will be 

 issued by the Sunday Society. These will be forwarded by 

 post on receipt of stamped envelope. All applications to be by 

 letter to the Honorary Secretary, 19, Charing Cross. 



We give the following extract from a letter sent us by Mr, R» 

 Chartres on recurring decimals of the form — 



•abc . .ka-^b^c-^.. k-^, where a-t-ai = 9 = ^ + 3i = &c, 

 ^ = -05263 I 57894736842 i. 

 Here we obser\'e a remarkable connection between the figures. 

 Beginning w ith the last figure i we notice that each figure is 

 double of the one to the right of it, one being carried when the 

 double is over ten. Thus the eighteen recurring figures can be 

 written down in a moment. Similarly the twenty-eight recurring 

 figures of ^V can be written down at once by multiplying by 3, 

 thus :— 



-^ = •0344827586206896551724137931. 



I 



Generally, 



= - I -f 



«r — I . 

 nr 



(where r = 10) 



- I + 



I 



n r 



■=■ Sum of the terms after the first of a geometric series ad 

 infinitum whose first term is unity and common ratio 

 I 

 « r 

 Now, to divide a decimal by n r is simply to divide by n, and 

 remove the figures one place to the right ; and since the last 

 recurring figure will be unity, we can get the whole period by 

 beginning with I, multiplying by «, and placing it to the left. 



M, Borel, the French Minister of War, has prepared a 

 decree, which has been signed by the President of the Republic, 

 for establishing in the army a high school of war. Besides 

 tactics and special lectures on military topics, pupils will be 

 taught geodesy, topography, geography, and telegraphy. They 

 will be taken from among officers who have been commissioned 

 fc^r some length of time. 



J Article No. V. of the third volume of "Hermathena" is 

 an exceediiagly able and interesting sketch of " Greek Geometry 

 from Thales to Euclid," by Dr. G. J. Allman. At the outset 

 it is stated that the present century is "characterised by the 

 importance which is attached to historical researches, and by a 

 widely-diffused taste for the philosophy of history," In mathe- 



