S62 



NATURE 



[August 7, 19 13 



V: 



If we take the time-integral of both sides of the 

 energy equation once round the path we get the 

 theorem of elliptic motion stated above. 



It may be remarked that 2mw^/ia is the action 

 for one revolution of the particle in its orbit, and thus 

 we have the curious result (already known) that the 

 action (and therefore the mean kinetic energy) for one 

 complete revolution in an elliptic orbit is independent 

 of the eccentricity. If the centre of force be shifted 

 along the major axis, so that for different orbits 

 about the centre of force the length of the major 

 axis remains unaltered, the period and the action 

 remain also unchanged. 



It may be noticed that the process used above shows 

 very clearly that the area traced out by the radius 

 vector from the "empty focus" is proportional to the 

 action, for the time given by the corresponding area 

 traced out by the radius vector from the centre of 

 force. I observed this fact some years ago, but found 

 that it had previously been put on record by Tait. 



For a hyperbolic path round the centre of attraction 

 the energy equation is 



W = ,„„(l + ±), 



where ia is the distance between the vertices 



of the two branches of the hyperbola; and 

 we see that in this case the kinetic energy at 

 distance r exceeds the potential energy exhausted in 

 the transference from infinity to that distance bv the 

 mean kinetic energy of the motion in an ellipse of 

 semi-major axis a. Thus if a planet formed in the 

 course of the condensation of a nebula is to have a 

 hyperbolic orbit, it must, by an explosion of chemical 

 energy, or by some other convulsion or process, have 

 a quantity of kinetic energy given to it, in excess of 

 that produced by the transference of the matter from 

 infinite dispersion in space. In the evolution of 

 planets according to the nebular hypothesis hyperbolic 

 orbits would thus be exceptional cases. 



It may be noted that in a certain sense mp/2a is 

 also the mean kinetic energy in the hyperbolic orbit. 

 For, when r has become considerable, hnv 2 is sensibly 

 equal to mnlia, and the time for this sensibly constant 

 value is infinite. A. Gray. 



Boat of Garten, July 23. 



"Phosphorescence" of Pennatulida. 



Prof. Newstead and I have had two of the few 

 British Pennatulida — Pennatitla phosphorca and 

 Funiculina quadrangularis — " phosphorescing " to-day 

 before our eyes, so it may be worth recording the 

 impressions while they are fresh. Pennatitla phos- 

 phorca, as its name indicates, has long been known 

 to emit light, and, writing from memory, I think 

 Sir Wyville Thomson, in his "Depths of the Sea," 

 refers to the "lilac phosphorescence of Pavonaria " 

 ( = Funiculina). Prof. Newstead and I have just seen 

 the colour and distribution of the light very clearly 

 in a makeshift dark-room (the lazarette of the yacht), 

 and also on the deck at midnight. In Funiculina the 

 distribution of the luminosity is very curious and 

 quite different from that of Pennatula. There are 

 many distinct sparkles over the polype-bearing part 

 of the colony (corresponding, no doubt, to the indi- 

 vidual polypes), but the long, bare lower part of the 

 stem, q in. to a foot in length, when gently stroked 

 in the dark glows with a continuous sheet of light of 

 (it seems to me) a pale-green colour which flickers 

 NO. 2284, VOL. 91] 



or pulsates like a lambent flame. The light on this 

 bare part of the colony is certainly more intense than 

 that of the polypes, and is the most brilliant "phos- 

 phorescence" 1 have seen in any marine animal. I 

 have not seen Pyrosoma alive, but 1 imagine from 

 the descriptions it may be even more brilliant than 

 Funiculina. 



In Pennatula, on the other hand, the light appears 

 to be restricted to the polypes. I have not been able 

 to excite any luminosity in the stem portion of the 

 colony, but the illumination of the polypes is very 

 general and beautiful — more general and more lasting 

 than the sparkles that the polypes give in Funiculina. 



Prof. Hickson, in a letter just received, asks me, if 

 possible, to observe the phosphorescence of the other 

 British Pennatulid, Virgularia mirabilis. I have not 

 yet succeeded in dredging Virgularia here, but it 

 ought to be found in these waters, and probably when 

 examined alive in the dark will show some degree 

 of phosphorescence like its two relations referred to 

 above. 



We have been able to get detailed colour notes of 

 the living Funiculina, and some photographs of 

 polypes extended to nearly an inch in length, which 

 we hope may be useful. W. A. Herdman. 



S.Y. Runa. Loch Sunart, N.B., July 26. 



A Red-water Phenomenon due to Euglena. 



A \ ekv remarkable red-water phenomenon is at 

 present observable in a small pond in Broad Oak 

 Park, Worsley, near Manchester, just in front of the 

 seventh tee on the golf course. The surface of the 

 pond — at any rale at times — is covered in places with 

 an almost blood-red scum, which seems to float on 

 the surface film like fine dust. The scum sometimes 

 assumes a greenish hue. Microscopical examination 

 shows that it is due to the presence of immense num- 

 bers of a large species of Euglena, the green chloro- 

 phyll of which, as in the case of Haematococcus, is 

 more or less replaced by red haematochrome. 



On keeping some of the water and scum under 

 observation in a soup-plate, it is seen that the organ- 

 ism occurs chiefly in two conditions — crawling on the 

 bottom in an elongated form, and resting on the 

 surface in a spherical form. It does not seem 

 to swim freely about in the intermediate zone of 

 water, so that the red colour is confined to the bottom 

 and the surface, and not, as in the case of the active 

 form of Haematococcus, dispersed through the water 

 itself. Crawling seems to be effected by typical 

 "Euglenoid" contractions, but a very long flagellum 

 is sometimes visible at the anterior end, while the 

 posterior extremity is formed by a sharp projection 

 free from pigment. 



Since writing the above 1 have been able to observe 

 how the Euglena? reach the surface of the water. They 

 evidently secrete some sort of slime in which they 

 become entangled. Bubbles of oxygen gas, given off 

 bv the Euglena' in presence of sunlight, are also 

 caught in this slime, and when these reach a certain 

 size they rise to the surface, trailing strings of slime, 

 with numerous entangled Euglena?, after them. 



Arthur Dendy. 



University of London, King's College, July 30. 



The Terrestrial Distribution of the Radio-elements. 



I\ my litter of June 19 I briefly outlined three 

 arguments which consistently point to a concentration 

 of the radio-active elements in the earth's crust, such 

 concentration having been accomplished at the expense 

 of the material of the interior. The first of thesi 



