542 



NATURE 



[October 6, 1692 



infinitesimal distance perpendicularly across it to the 

 next equipotential on either side of it ; and through the 

 divisional points draw curves, cutting the iequipotentials 

 at right angles. These curves are the stream lines. They 

 and the («+i) closed equipotentials (including the in- 

 finitely conductive borders) divide the whole surface into 

 n m infinitesimal squares, if ;« be the number of divisions 

 which we found in the equipotential. The arrows on 

 the diagram show the general direction of the electric 

 current in dififerent parts of the complex circuit ; each 

 arrow representing it for the thin metal shell on 

 either far or near side of the ideal section by the paper. 



Considering carefully the stream-lines in the neigh- 

 bourhoods of the four open lips marked in order of the 

 stream i, 2, 3, 4, we see that for each of these lips there 

 is one stream-line which strikes it perpendicularly on one 

 side and leaves it perpendicularly on the other, and which 

 I call the flux-shed-line (or, for brevity, the flux-shed) 

 for the lip to which it belongs. The stream-lines infi-- 

 nitely near to the flux-shed, on its two sides, pass 

 infinitely close round the two sides of the lip, and come 

 in infinitely near to the continuation of the flux-shed on 

 its two sides. Let Fj, F^, F., F4 (not shown on the 

 diagram) be the points on the + terminal lip from which 

 the flux-sheds of the lips i, 2, 3, 4 proceed ; and let G^, 

 G2, G3, G4, be the points at which they fall on the — lip. 

 Let Sj, Tj, S2, T2, &c., denote the points on the four lips 

 at which they are struck and left by their flux-shed-lines. 



Let ;)i, /i, A') 4' A' ''s' A' ^4' Pb t>6 ^he differences of 

 potential from the -t- lip to Sj, from S^, to Tj, Tj to S2, 

 .... S4 to T4, and T4 to the -lip. Measure these nine 

 differences of potential. We are now ready to make the 

 Mercator chart. We might indeed have done so without 

 these elaborate considerations and measurements, simply 

 by following the rule of my previous article ; but the 

 chart so obtained would have infinite contraction at eight 

 points, the points corresponding to Sj, Tj, . . . . S4, T^. 

 This fault is avoided, and a finite chart showing the 

 whole surface on a finite scale in every part is obtained 

 by the following process. 



Take a long cylindric tube of thin sheet metal, of the 

 same thickness and conductivity as that of our original 

 surface ; and on any circle H round it, mark four points, 

 Ai, 7^2) ^hi ^\i ^t consecutive distances along its circum- 

 ference proportional respectively to the numbers of the 

 7)1 stream-lines which we find between F^ and F2, F2 and 

 F3, Fg and F4, F4 and F^ on the + lip of our origmal sur- 

 face. Through Aj, //g, ^3, h;^ draw lines parallel to the 

 axis of the cylinder. 



Let now an electric current equal to the total current 

 which we had from the + lip to the -lip through the 

 original surface be maintained through our present 

 cylinder by a voltaic battery with electrodes applied to 

 places on the cylinder very far distant on the two sides of 

 the circle H. Mark on the cylinder eight circles, K^, K2... 

 Kg, at distances consecutively proportional to /i,/2> 4» A> 

 /31 fi^-, ^i, and absolutely such that /j, A» &c., are equal to 

 the differences of their potentials from one another in 

 order. 



Bore four small holes in the metal between the circles 

 Kj and K2, K3 and K4, Kg and Kg, Kj- and Kg on the 

 parallel straight lines through A^, ho. ^3, /tt, respectively. 

 Enlarge these holes and alter their positions, so that the 

 altered stream-lines through //j, /i^, ^3, ^4 (these points 

 supposed fixed and very distant) shall still be their flux- 

 sheds. While always maintaining this condition, enlarge 

 the holes and alter their positions until the extreme 

 differences of potential in their lips become /j, A, 4, /4, 

 and the differences of potential between the lips in suc- 

 cession become A< A» A- I" thus continuously changing 

 the holes we might change their shapes arbitrarily ; but 

 to fix our ideas, we may suppose them to be always made 

 circular. This makes the problem determinate, except 

 the distance from the circle H of the hole nearest to it, 



NO. I 197, VOL. 46] 



which may be anything we pleased, provided it is very 

 large in proportion to the diameter of the cylinder. 



The determinate problem thus proposed is clearly 

 possible, and the solution is clearly unique. It is of a 

 highly transcendental character, viewed as a problem for 

 mathemetical analysis ; but an obvious method of" trial 

 and error" gives its solution by electric measurement, 

 with quite a moderate amount of labour if moderate 

 accuracy suffices. 



When the holes have been finally adjusted to fulfil our 

 conditions, draw by aid of the voltmeter and movable 

 electrodes, the equipotentials, for A above the greatest 

 potential of lip i, and for A below the least potential of 

 lip 4 ; and between these equipotentials, which we shall 

 call/and ^, draw n-i equidifferent equipotentials. Draw 

 the stream-lines, making infinitesimal squares with these 

 according to ,the rule given above in the present article. 

 It will be found that the number of the stream-lines is /«, 

 the same as on our original surface, and the whole num- 

 ber ofinfinitesimal squares on the cylinder between /'and 

 g\sm n. Cut the cylinder through at/and^y cut it 

 open by any stream-line from / to g^ and open it out 

 flat. We thus have a Mercator chart bounded by four 

 curves cutting one another at right angles, and divided 

 into in n infinitesimal squares, corresponding; individually 

 to the m n squares into which we divided the original 

 surface by our first electric process. In this chart there 

 are four circular blanks corresponding to the lips i, 2, 3, 4 

 of our diagram ; and there is e.xact correspondence of their 

 flux-sheds and neighbouring stream-lines, and of the 

 disturbances, which they produce in the equipotentials, 

 with the analogous features at the lips of the original sur- 

 face as cut for our process. The solution of this geome- 

 trical problem was a necessity for the dynamical problem 

 with which I have been occupied, and this is my excuse 

 for working it out ; though it might be considered as 

 devoid of interest in itself. Kelvin. 



THE RECENT ERUPTION OF ETNA} 



^pHE southern flank of Etna has been the site of three 

 *■ consecutive eruptions, remarkable for the diversity 

 of the phenomena they presented. 



On March 22, 18S3, after several violent shocks of 

 earthquake, the ground was rent open in a N.E. and 

 S.W. direction, almost on the continuation of the big rift 

 formed in the eruption of 1879, and near Monte Concilio 

 a most interesting eruptive apparatus was formed. Very 

 quickly, however, the eruption was arrested, but the 

 eruptive energy had not had sufficient vent, as evidence 

 of which were the frequent shocks which followed it and 

 persisted, until on March 18, 1886, the ground was again 

 split open .as a prolongation of the rift of 1883, giving 

 rise to an imposing eruption, during which an enormous 

 quantity of lava was poured forth. This eruption from 

 the very beginning manifested a great explosive force. 

 The fragmentary materials were projected to an extra- 

 ordinary height from several craterets formed along the 

 rift, most of which, however, soon became quiet and 

 were buried by the ejectamenta of the others, remaining 

 alone the one twin crater now called Monte Gemmellaro. 

 After this eruption the geodynamic phenomena and the 

 volcanic activity at the central crater remained exceed- 

 ingly feeble up to the last few days, so that this actual 

 eruption did not present any grand display of premonitory 

 phenomena. 



On the evening of July 8, at about 10.30, the central 

 crater of Etna began to send up a dense column of 

 vapour, charged with dust, lapilli, and large rock frag- 

 ments, which rose as an imposing mass with the 



I This paper was written in Italian, and sent as a letter to Dr. H. J. 

 Johnston-Lavis, who has kindly translated it for Nature, as requested 

 by the author. 



