484 



NA TURE 



[September 14, 1905 



LETTERS TO THE EDITOR. 

 \The Editor does not hold himself responsible for opinions 

 expressed 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.] 



Observations of the Total Solar Eclipse in Tiipoli, 



Barbary, 

 Our eclipse took place in the midst of the fierce heat 

 of the Gibleh, or Sahara sirocco ; but an hour or two 

 before totality the wind very fortunately changed, and 

 brought skies of the highest possible optical transparency. 

 There was no wind, and the conditions, except for the 

 intense heat, which we momentarily feared would snap 

 our great cameras, were the most nearly perfect imagin- 

 able at a sea-level station. 



Unfortunately, on account of leaving home at very short 

 notice, we brought no spectroscopic outfit, and our efforts 

 were directed solely toward coronal photography with 

 automatic and semi-automatic coronagraphs, and to ex- 

 posure of plates for the slightly suspected intra-Mercurial 

 planet. Other branches of our work related to coronal 

 sketches, both with and without occulting discs, and to 

 shadow band observations, both optically and photo- 

 graphically. 



By the kindness of His Majesty's Government, repre- 

 sented by Mr. Alfred Dickson, Vice-Consul, the American 

 expedition from Amherst College was permitted to establish 

 its instruments on the terrace of the consulate, in the 

 midst of the white city — in precisely the same spot occupied 

 for the similar eclipse of 1900. 



Many citizens of Tripoli took immediate and constant 

 interest in our operations, and contributed very greatly to 

 our success by their liber- 

 ality in granting that 

 service which only the 

 chief of an expedition re- 

 mote from home can fully 

 appreciate. I am glad to 

 mention especially Mr. 

 W. F. Riley, Mr. W. H. 

 \'enables, Maris de Nunes 

 \'ais, the excellent photo- 

 grapher of the expedition, 

 and Etim Bey, a Turkish 

 gentleman resident in Tri- 

 poli, whose unique collec- 

 tion of photographic and 

 mechanical appliances was 

 frequently and helpfully 

 drawn upon. 



The observations of shadow bands were conducted by 

 parties organised by Mrs. Todd and Miss Todd, and will 

 be reported to my friend Mr. Lawrence Rotch, of Blue 

 Hill, at whose request they were made. These bands 

 were seen as early as ten minutes before totality, and had 

 many remarkable and pronounced peculiarities. They were 

 wavering and narrow, moving swifter than one could 

 walk, at right angles to the wind, their length with 

 it, and waxing and waning five times during the eight 

 minutes preceding totality. 



The coronal sketches revealed nothing out of the 

 ordinary. Extended rays beyond the occulting discs were 

 looked for eagerly, but the disc (8 inches diameter at 

 35 feet distance) covered everything. The sky and general 

 illumination were exceptionally bright. Totality as pre- 

 dicted was 3m. 9s. in duration ; as observed 3m. 6s. 



Our chief and largest instrument was a photographically 

 corrected lens by Clacey, of 12 inches full aperture. To 

 this was attached an orthochromatic screen for photograph- 

 ing Baily's beads, and a Burckhalter occulter as de- 

 scribed by the writer four years ago in the Monthly 

 Notices. Of the results obtained with this instrument I 

 shall write elsewhere ; about twenty exposures were made 

 with it, and the beads are excellently shown in the 

 accompanying photograph. The occulter was only in part 

 successful. 



Alongside it were the large Clark cameras, containing 

 a pair of 3-inch lenses of 11 feet 4 inches focus, which 

 took plates on which are a great number of stars, not 



NO. 1872, VOL. 72] 



Eclipse of 

 Photographed at 



vet fully examined. Owing to the unexpected brilliancy 

 of the sky, the plates were exposed longer than would 

 seem to have been wise. Everything to the eighth magni- 

 tude seems to have been caught, however. 



A third instrument was a 35-inch Goerz doublet of 

 about 18 inches focus, from which I removed the back lens, 

 increasing the focal length to 335 inches. This was 

 attached to one of the automatic movements used in my 

 previous expeditions of 1896, 1900, and 1901. It was 

 geared up to a rate of 265 photographs during the 189 

 seconds of totality, the exposure being about J second 

 for each. Most of these pictures are very good, and I 

 enclose a print from one of them (Fig. i), which does not, 

 however, do the original negative justice. The corona was 

 much less impressive, it strikes me, than other coronas 

 I have seen — 1878 and 1900 in clear skies, and 1887, 

 1889 (ft), 1896, and 1901 in clouds; in fact, the shadow 

 bands and Baily's beads seem to have been rather more 

 interesting to the general observer than the corona itself. 



David Todd. 



British Consulate, Tripoli, Barbarv, August 31. 



On the Class of Cubic Surfaces. 



In Salmon's " tieometry of Three Dimensions," the 

 classes of the twenty-three different species of cubic 

 surfaces are stated ; but the process by which these results 

 are obtained is not obvious. I therefore propose to indicate 

 an easy method. 



The class of a plane curve is equal to the number of 

 tangents which can be drawn froin a point not on the 

 curve ; hence the class of a curve is equal to the degree 

 of its reciprocal polar. And since the line joining two 

 points on a surface corresponds to the line of intersection 

 of two tangent planes to the reciprocal surface, it is 

 necessary, in order to make the theories of curves and 

 surfaces correspond, to define the class m of a surface 

 to be equal to the number of tangent planes which can 

 be drawn through a given straight line. Let (a, 0, y, 5) 

 be quadriplanar coordinates referred to a tetrahedron of 

 reference .ABCD ; then the equation of the tangent plane 

 at any point (/, g, h, k) is 



d? ,iF dF dF 



''d/ + ^a. + yd/, + ^ui=° ('.' 



and if this plane passes through the line CD, we must have 

 dF/dh=o, dF/dk = o. Hence the points of contact of the 

 tangent planes which pass through CD are the points 

 of intersection of the three surfaces 



F = o, <:'F/,/7 = o, dF/dS = o (2) 



and their number is equal to n{n — i)-, which is the value 

 of m for an anautofomic surface. The elimination of 

 (o, ;8) between (2) will furnish a binary quantic in 

 (7, S) the degree of which is equal to the class of the 

 surface. 



It is obvious from geometrical considerations that a 

 conic node must diminish the class by 2. The equation 

 of a cubic having a binode B, is o^S-i-m, = 0, where u^ is 

 a ternary cubic in (/3, 7, S). Differentiating with respect 

 to 7 and 5, and then putting 5 = A7, we obtain 

 \ay- + ii\ = o 1 



\ay + du\ldy = o [ (3) 



07 + dti'JdS = o ) 

 where the accents denote what the quantities become when 

 5 is put equal to \y after differentiation. Equations (3) 

 are those of the sections of the cubic and the polar quadrics 

 of C and D by niiy plane through AB ; and since they 

 intersect in three coincident points at A, )n = i2— 3=9. 



The equation of a cubic having a binode B, at A is 



ayS + B-v^ + /Sfj + 2/3 = (4) 



where j/nisaAwarj' quantic in (7,8). Let v' „ = dv,Jdy,v"„ — dv„hii. 

 Differentiating {4) with respect to 7 and 5, and eliminating 

 a, we obtain 



^- (?', - 7i''i) + fl (v„ - yv\) + .'a - 77/3 =0 ( 

 ;8" (z-i - l-j\) -I- B[v„- S-y'2) + fj - iv".i = Q I 



The eliminant of (5) is a binary octavic in (7, 5) ; 

 whence B, reduces the class by 4. 



The classes of all the remaining species may be found 

 by means of the eliminant of (5), or directly from their 

 equations. A. B. Basset. 



September 6. 



(5) 



