544 



NA TURE 



[October 6, 1898 



LETTERS ^ TO THE EDITOR 

 [The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications. "l 



■ Undercurrents in the Strait of Bab-el-Mandeb. 



An interesting observation has recently been made by one of 

 H.M. surveying vessels, and I forward the Preface to the ac- 

 count of the details published by the Hydrographic Department, 

 •which contains the principal facts, and also the Analy.sis of the 

 observations, both of which may be of interest to some of your 

 readers. W. J. L. Wharton. 



Hydrographic Department, Admiralty, Whitehall, 

 .London, S.W., September 27. 



Undercurrents in the Strait of Bab-el-Mandeb. 



It has long been known that in the Bosporus and Dardanelles 

 when the surface water sets strongly from the Black Sea to the 

 Mediterranean, the lower strata of the water for a certain height 

 from the bottom sets strongly in the opposite direction. 



While in this instance it is probable that the many large 

 rivers which discharge their waters into the Black Sea have a 



originally devised by Lieutenant Pilsbury, U.S.N. , and con- 

 siderably altered after a series of experiments by Captain 

 Usborne Moore in the English and Faeroe Channels, seemed to 

 offer a chance of more success. 



Lieutenant and Commander Gedge, commanding H.M. sur- 

 veying ship Sto7-k, was therefore directed to endeavour to get 

 further observations in Bab-el-Mandeb by means of this instru- 

 ment, and has admirably and most successfully carried them out. 



On January 19, 1898, the Stork was anchored in 118 

 fathoms about seven miles S.W. by W. from Perim Island, and 

 remained constantly observing, during daylight, for four days, 

 when the parting of the cable brought the series to a close. 

 Had not the wind been unusually light, varying from force 3 to^ 

 6, it is probable that the observations could not have been con- 

 tinued so long. 



The observations are appended (in publication quoted), but 

 the broad result may be briefly stated. 



There was a permanent current on the surface setting into the 

 Red Sea of about \\ knots per hour. 



There was at 105 fathoms depth a permanent current setting 

 outwards of probably the same velocity. 



The tidal stream was about i\ knots at its maximum, and 

 flowed for about twelve hours each way, as might be expected 

 from the fact that in this locality there is practically only one 

 tide in the day. 



share in producing the surface current, the observations by which 

 the undercurrent was revealed appeared to plainly indicate that 

 the surface drift, caused by the generally prevailing N.E. wind 

 heaping the water up in the south-western part of the Black Sea, 

 was the main factor. 



The somewhat similar conditions which occur in the strait 

 of Bab-el-Mandeb off'ered another opportunity of observation on 

 this interesting form of oceanic circulation, and for many years 

 such observations have been a desideratum. 



In this strait for nearly half the year a more or less strong 

 easterly wind prevails, driving much water before it into the 

 Red Sea, and, great as is the evaporation from the surface 

 of that sea, which must be made up wholly by an inflow of 

 water through the strait of Bab-el-Mandeb, it appeared on the 

 whole probable that during this season the phenomenon of the 

 Dardanelles would be repeated. 



The observation is, however, difficult. The water is deep, 

 over 100 fathoms ; the sea generally heavy ; there is a tidal 

 current to complicate matters ; and it seemed doubtful whether 

 the somewhat crude apparatus which served to unravel the 

 movement of the lower strata in the shallower and smoother 

 Dardanelles would give good results in this locality. 



Nevertheless, Captain W. Usborne Moore was directed to 

 attempt it in H.M.S. Penguin in 1890, but the results, while 

 showing that the under strata were not running with the surface, 

 were two ambiguous to afford much definite information. 



The possession, however, of a deep-sea current meter, 



NO. I 5 10, VOL. 58] 



This tidal stream prevails to the bottom, with variations of 

 strength. 



Somewhere about 75 fathoms is the dividing line between the 

 two permanent currents, but it would require a longer series of 

 observations to determine this point with any precision. 



Fourier's Series. 



In all expositions of Fourier's series«which have come to my 

 notice, it is expressly stated that the series can represent a 

 discontinuous function. 



The idea that a real discontinuity can replace a sum^ of con- 

 tinuous curves is so utterly at variance with the physicists' notions 

 of quantity, that it seems to me to be worth while giving a very 

 elementary statement of the problem in such simple form that 

 the mathematicians can at once point to the inconsistency if 

 any there be. 



Consider the series 



y = 7. [sin X - \ %va. 2. X -k- \ %\v\. Zx — . • • ] 



In the language of the text-books (Byerly's " Fourier's Serie> 

 and Spherical Harmonics " ) this series ' ' coincides with j' = x fron : 

 x = -'jrtox = ir. . . Moreover the series in addition to the 

 continuous portions of the locus . . . gives the isolated point -^ 

 ( - •;r, O) (ir, o) (3», o), &C." 



