448 



NA TURE 



[April 6, 1876 



Lisbon Magnetic Observations 



Mr. de Brito Capello, Director of the Lisbon Magnetic 

 Observatory, having addressed to me several interesting results 

 having reference to the notice of his observations which appeared 

 in Nature, vol. xiii, p. 301, I am anxious to communicate 

 them to your readers. 



With reference to the movement of the declination magnet 

 from 8 A.M. to 2 p.m. Mr. Capello gives me the following mean 

 values for each year from 1858 to 1875 : — 



1S5S 



1859 

 i860 

 1861 

 1862 

 1863 

 1864 

 1865 

 1866 



874 

 10-54 



lOII 



9 00 

 7 '84 

 765 

 694 

 661 

 6"i9 



1867 

 1 858 

 1S69 

 1870 

 1871 

 1872 



1873 

 1874 

 1875 



615 



7-17 



8-42 



10-83 



10 -60 



9-45 



8-22 



7 '23 

 6-09 



These quantities, Mr. Capello remarks, show the maxima 1859-8 

 and 1870-9, and the minimum 1867-1, agreeing very nearly with 

 the epochs of maximum and minimum sun-spots. 



It also appears as if the minimum had been reached again last 

 year, the mean oscillation (6' -09) being less than in 1867. This 

 agrees with the conclusion derived by me from the Trevandrum 

 observations, and communicated to the French Academy of 

 Sciences last year. Dr. R. Wolf had previously (as I now 

 find ^) concluded from his sun-spot observations that the mini- 

 mum would probably appear in 1875-6 ; and he considers we 

 have now one of the short periods, which his tables of sun-spots 

 show may be expected every 80-90 years. My own conclusion 

 to the same effect (that we have now a short period) was founded 

 on a consideration of the magnetic observations. The last short 

 period was that from the maximum 1829-7 (shown by Arago's 

 observations) to that of 1837-5 (shown by Gauss's observations), 

 an interval of rather less than eight years. If we may take 

 1 875 -5 as the epoch of the present minimum, then the interval 

 from the last is nearly nine years. As the interval from the 

 minimum of Arago (1824-2) to the next was nearly 9*2 years, we 

 find a space of nearly forty-two years from the last short period 

 to this one. Should this hold for the next maximum it will 

 occur about 1879-0. 



Mr. Capello has obtained the interesting result that the curve 

 showing the mean diurnal disturbance of the vertical magnetic 

 force is the exact inverse of that for the mean diurnal disturbance 

 of declination at Lisbon ; a movement of the north pole of the 

 declination magnet towards the west corresponding to one 

 downwards of the south pole of the balance needle. It ap- 

 pears also that the difference of sign in the temperature co- 

 efficient for the balance magnet due to changes of the compen- 

 sation bar from brass to zinc and zinc to brass, on which a remark 

 was made in Nature, vol. xiii. p, 302, does not affect the re- 

 sults lor the diui'nal variation, each year giving the same mean 

 law of a minimum vertical force between 11 A.M. and noon, and 

 a maximum near 5 p.m. whatever the sign of the temperature 

 coefficient. It appeal's also that the results at Lisbon are con- 

 firmed by those obtained at Coimbra, ninety miles to the north. 



John Allan Broun 



The Early History of Continued Fractions 



The reviewer in Nature, (vol. xiii., p. 304), very properly 

 points out that the first mathematician who used continued frac- 

 tions was Catald), and not Lord Brounker, as is still often 

 stated. 



To this fact I drew attention in a pamphlet, published in 

 1874, not then knowing that De Morgan had done the same 

 many years ago. There is, however, in connection with the 

 fame subject, another historical fact almost equally interesting, 

 which few in this country seem to be aware of, and which there- 

 fore it may be desirable to bring before your readers. 



Daniel Schwenter, a professor at Altdorf, in the first quarter 

 of the seventeenth century, made use of the present well-known 

 process for expressing the ratio of two integers as a continued 

 fraction, and calculated the convergent, exactly in the mode at 

 present followed. He does not indeed seem to have written 

 as we now do the actual continued fraction obtained in any case, 



I " Astronomische Mittheilungen," 38, p, 378, July 1875. 



but the process of repeated division, .ind the mode of finding the 

 convergents were most fully described and exemplified by him. ^ 



The following, therefore, seems td be, in few words, the early 

 history of continued fractions : — 



I. Cataldi published, in 16 13, his discovery that the square 

 root of an integer can be expressed as an interminate continued 

 fraction, e.^., 



sjl% 



+ 2 



+ 2 



2. Schwenter, almost certainly without knowledge of what 

 Cataldi had done, published in 1636 the mode of changing an 

 ordinary fraction into a continued fraction with unit-numerators, 

 and of calculating therefrom convergents to the given fraction, 



117 _ I 



+ I 

 3 + I 



6 + 1 



4 + J, 

 2 



3. Brounker, very probably in ignorance of what had been 

 done by Cataldi and Schwenter, made the discovery that 



I + I 



2+4 



2 + 9 



2 + . . . 



which was published by Wallis in 1655 (" Arithmctica Infmi- 

 torum "p. 181), along with a tolerably complete theory of con- 

 tinued fractions in general. 



The necessary details bearing on these three main facts will be 

 found in a painstaking work by Prof. Favaro, *' Notizie Storiche 

 suUe Frazioni Continue," Roma, 1875, or in shorter form, in a 

 school "programme" by Dr. Glinther, "Beitrage zur Erfind- 

 ungsgeschichte der Kettenbriicke, " 1872. 



That Cataldi, Schwenter, and Brounker, starting from totally 

 different points should all light on the continued fraction form, 

 and that it should be twice (perhaps nearly thrice) lost, are cer- 

 tainly strange facts, forming a curious chapter in the history of 

 scientific discovery. Thomas Muir 



High School of Glasgow 



The Dry River-beds of the Riviera 



Mr. R. E, Bartlett (Nature, vol. xiii. p. 406) asks fur 

 some theory to account for the existence of the broad stony river- 

 beds of Piedmont. He instances the Paglione at Nice, which 

 is indeed the merest rudiment of a river for the greater part of 

 the year. But if Mr. Bartlett will wait, not so much for the 

 snows on the Maritime Alps to be melted, as for the rainy weeks 

 of autumn to come again, 



Quum fera diluvies quietos 

 Irritat amnes, 



he will see that that now despicable river annually flows with a 

 vehemence and a volume worthy of its size. Many a dry and 

 insignificant torrent-bed in the neighbour-hood of Nice swells 

 during the rainy season to a torrent indeed ; the thoroughness 

 with which they then drain the adjacent slopes is amply sufficient 

 to explain their existence and their appearance when their 

 "occupation's gone." Henry T. Wharton 



London, April 2 



The Flame of Common Salt 



Having been much interested in the progress of the investi- 

 gations concerning the blue flame of common salt when thrown 

 into a coal fire, I made the following experiments, by which I 

 came to the conclusion that the origin of the blue flame is due to 

 the presence of copper, which occurs in nearly every coal as an 

 ingredient of the pyrites. 



According to " Bercelius," by agency of the blow-pipe, small 



' See " Daniel Schwenter, Delicia; physico-niathematicae," Niirnberg, 

 1636, p. III. " ^L Daniel Schwenter's Geometriae practice novs et auctae, 

 Libri IV." durch Georgium Andrem Bocklern, Niirnberg, 1657, p. 431. 



