No. 1071, Vol. 42] 



NATURE 



31 



other words, the reef will advance nineteen times as slowly as it 

 does 560 metres from the shore, whilst the surface which is ex- 

 posed to the dissolving effect of the sea-water has also increased 

 nineteen-fold. Where an ocean-current strikes such an incline, 

 no G'iobigerina ooze can be deposited on it, and here the dis- 

 solving action of sea-water will balance the accumulation of 

 coral dibris long before such a height — of looo metres— is 

 attained. It is clear that as soon as such equilibrium is reached 

 there is a limit to the further extension of the reef in that direc- 

 tion. On the opposite side, however, where ooze will accumulate 

 and protect the advancing reef from solution, such advance would 

 be possible, but on that side the growth of coral is notoriously 

 slow. Certainly, when the foot of the reef has advanced to 

 depths below the zone of protecting Globigerina ooze no further 

 lateral growth in any direction will be possible, and on the 

 whole I should not think that lateral growth can play any con- 

 siderable part in the formation of great reef-;. Only positive coast- 

 line shifting has such a result. In places where there is no such 

 coast-line shifting (Gulf of Suez) the reefs are exceedingly small 

 and insignificant. 



Although therefore lateral growth no doubt does take place, 

 it is not the actual cause of the formation of the great coral 

 reefs. 



We must, I think, revert to Darwin's subsidence theory, which 

 is equally proved by the untenability of the hypothesis suggested 

 for the purpose of superseding it, and by the direct evidence of 

 the structure of the Triassic reefs in the Eastern Alps, which have 

 actually attained their immense thickness during a period of 

 positive shifting of the coast line. R. voN Lendenfeld, 



Innsbruck. 



Slugs and Thorns. 



In Nature, vol. xli. p. 393, I pointed out that thorns 

 might not always be a protection from snails and slugs, since 

 they were found in the stomach of a European slug, Par- 

 tnaccUa. In further confirmation of this view, I have to-day 

 dissected a number of sharp, straight, reddish-brown thorns, over 

 a millimetre long, from the intestinal tract of Arioliniax niger, 

 var. nov. maciilatus, a slug of rather doubtful affinities (possibly 

 referable to A. andersoni), received from Dr. J. G. Cooper, who 

 found it under drift-wood at Haywards, California. It is curious 

 that the thorns do not pierce the intestine, but they appear to 

 cause no inconvenience. T. D. A. Cockerell. 



West Cliff, Colorado, April 21. 



COMETS OF SHORT PERIOD. 

 T T is now generally accepted that the periodic comets 

 -^ of our system did not originate in it, but are bodies 

 captured from outer space by one of the planets, the 

 parabolic orbits in which they approached the system 

 being transformed into elliptical ones. On account of the 

 perturbing action of Jupiter, however, the orbits of short- 

 period comets are liabla to considerable modifications, 

 and it is practically impossible to identify two apparitions 

 of the same comet without laborious computations of the 

 perturbations which it must have been subjected to be- 

 tween the two epochs. But even such computations may 

 lead to a negative result, for frequently comets quite dis- 

 tinct have elements very much alike, probably because 

 they are parts of an old comet travelling along the same 

 orbit at greater or less intervals. 



In some recent investigations on the capture theory of 

 comets {Bulletin Astrotiomique, June and July 1889), M. 

 Tisserand developed a relation that might be employed 

 to determine the possibility of identity of comets whose 

 elliptical elements are known. This criterion depends 

 upon the fact that the velocity of a body revolving round 

 a central one is the same for equal radius-vectors. In 

 the case of a comet having a parabolic orbit coming 

 under the influence of a planet, the latter plays the part 

 of the central body, and the relative velocity of the comet 

 with reference to it will be the same at the point of entry 

 into the sphere of attraction as at the point of departure 

 from it, the one point being in the old orbit, the other in 

 the new one. If two comets are identical, their velocities 



with reference to the perturbing planet vyill be the same 

 at these points.^ 



M. L. Schulhof has discussed the possibility of identity 

 of several comets by means of M.Tisserand's formula (5«//. 

 Astr., November and December 1889, and Astr. Nach., 

 2964), and the following tables contain the values of n 

 found for those having periods from 33 to 88 years. 

 In the first table, the comets whose periods are well 

 known are given ; in the second, those having uncertain 

 periods. Comets which have undergone strong perturba- 

 tions since discovery, and those for which perturbations 

 prior to the first known apparition have been calculated, 

 are given more than once, and the year indicated for 

 which the elements are found. The symbols used have 

 their usual signification, and / is the longitude of the 

 comet at the point of nearest approach to Jupiter. 



Comets of Known Period. 



The value of n therefore found by the formula given is 

 almost constant for the 21 known short-period comets, 

 being contained within the limits 0-41 for Denning's 

 comet, and 0-59 for Encke's and Tempel's comets. 



It will also be seen that only five comets have their 

 minimum distance to Jupiter's orbit between / = 284" 

 and /= 112°, while twelve have the point of nearest 

 approach between / = 153' and /= 233'. This unequal 

 distribution along the ecliptic cannot be accidental, and 



' yi. Tisserand expressed the criterion very approximately by the 

 fjrmula— 



_L - ' = zv/A 



(cos iWP-X - cos h\^/i). 



where dj, «.2> /li/2> 'li '2. ^""^ '^' semi-major axes, parameters, and inclina- 

 tions of the old and new orbits ; A and R the planet's semi-major axis and 

 radius-vector at the point of nearest approach. This relation may be 

 divided up into two parts, having the form — 



2\/A 



R 



cos /\//. 



