if2 



NATURE 



[October 13, 192 1 



pp. 251 ff., May, 192 1) and, with theory and methods 

 used, in the Philippine Journal of Science (vol. 17, 

 pp. 607-14, 1920). 



The time observations, made with field-glass or 

 telescope, stop-watch, and ordinary watch, show that 

 with type A there is, on the whole, a slight excess of 

 observed duration over computed, amounting for 

 forty-four cases to 055 per cent. ; a few cases give 

 small deficiencies. This may be, perhaps, explained 

 by atmospheric dispersion. Type B, however, always 

 gives excess, sometimes remarkably large, even 

 2 min., or 68 per cent., with an average excess for 

 twenty-two cases of 123 per cent., which is difficult to 

 explain. 



Records of duration of sunrise and sunset are almost 

 non-existent ; a careful search, with inquiries of 

 several prominent astronomers, has failed to produce 

 more than about half a dozen, mostly made by Le 

 Gentil at Pondichery in 1769 while on his transit of 

 Venus expedition. While he made no such use of 

 them, on computing they give results in agreement 

 with the above. It would seem, perhaps, worth while 

 for others to take the matter up and record and pub- 

 lish at least date and hour, geographical position, 

 nature of horizon, duration, and type or form of disc. 

 The horizon should be quite level or distant if at all 

 irregular. Naturally, the best horizon is that of the 

 sea or a large lake ; but I have reason to believe that 

 the results of observing with a distant level land 

 horizon might be sometimes quite extraordinary. 



While the sun is the source of light in such observa- 

 tions, and the Nautical Almanac and four-place 

 logarithms have to be used in the computing, the 

 subject is not astronomical, but meteorological, and, 

 I believe, has to do with temperature distribution in 

 the atmosphere. We have here one of those residual 

 phenomena the study of which may lead to the dis- 

 covery of interesting facts and which can be for- 

 warded by amateur obsen-ers, the more and the more 

 widely scaFtered the better. 



WiLLARD J. Fisher. 



Cambridge, Mass., September 14. 



Is Bisexuality in Animals a Function of Motion? 



In Nature of September 29, p. 145, Dr. Orton 

 makes the interesting suggestion that bisexuality in 

 animals may be causally connected with the develop- 

 ment of a freely moving, as opposed to the sessile or 

 sluggish, habit. Reviewing the incidence of herma- 

 phroditism and bisexuality in the animal kingdom, he 

 reasserts the proposition put forward by Claus that 

 hermaphroditism is found most frequently in fixed, 

 parasitic, and sluggish animals. The two modes of 

 reproduction may therefore be functions of the degree 

 of motor activity manifested by animals. 



I do not wish to contradict Dr. Orton 's general 

 proposition, especially as he has framed it tentatively 

 and without dogma. But I would like to point out 

 that in the Mollusca we have an excellent opportunitv 

 of testing the truth of the suggestion in a single 

 group. The streptoneurous Gastropoda are, with 

 some exceptions, bisexual ; the Euthyneura are ex- 

 clusively hermaphrodite. I do not think, however, 

 that we can select the Euthyneura as exclusively 

 "sluggish" animals and the Streptoneura as ex- 

 clusively "active-," The Pulmonata (Euthyneura), 

 with their lengthy aestivation or hibernation period, 

 might be regarded as more sluggish than the average 

 Prosobranch. But other Euthyneura which apparently 

 do not aestivate or hibernate for a long period cannot 

 be regarded as more sluggish than the Streptoneura, 



NO. 271 1, VOL. 108] 



viz. the Tectibranchs and Nudibranchs. Having kept 

 many of these animals in captivity myself, I can 

 testify that they are no less active than Streptoneura 

 observed under similar conditions. An Aplysia is not 

 more sluggish than a Buccinum or a Paludestrina. I 

 admit that an intimate study of the habits of all Gastro- 

 poda is not available, but the known facts go to show 

 that many of the hermaphrodite forms are as active 

 as the bisexual ones. Dr. Orton may reply that many 

 of the apparently bisexual forms may be liable to 

 intermittent hermaphroditism. I have no doubt that 

 permanent and intermittent hermaphroditism may be 

 commoner in the Streptoneura than we imagine, but 

 all the evidence accumulated over many years goes to 

 show that bisexuality is regular and very widely 

 developed among this group. During the last two 

 years, for example, I have examined more than a 

 hundred examples of various species of Paludestrina 

 and kindred genera, and not found a single hermaphro- 

 dite form. In Pelseneers's "Variations et leur 

 Heredite chez les Mollusques " (1920) there are only 

 five genera cited in which occasional hermaphroditism 

 is recorded, though doubtless Dr. Orton could add a 

 few more to the list. . 



The suggestion that hermaphroditism is either the 

 direct result of the sedentary habit or that it is in 

 some way facultative for animals leading such a mode 

 of life is indeed interesting. But in that case it is 

 difficult to see why it is not found as the exclusive 

 mode of reproduction among the Scaphopoda, the 

 Lamellibranchia, and the Polyplacophora (Chitons), 

 which are all, on the whole, more sluggish than the 

 Streptoneura. Dr. Orton 's proposition may well be 

 true of sessile or parasitic forms, but it scarcely seems 

 to be true of animals which are merely sluggish. It 

 should be pointed out that great diversity of habit 

 occurs in the various groups of Gastropoda which 

 might on a superficial view, perhaps, be categorised 

 as "active" or "sluggish." Along with really 

 sluggish forms are associated species which are active 

 swimmers, burrowers, and climbers. Finally, it might 

 be asked whether The locomotor test is an entirely safe 

 criterion of phvsiological "sluggishness" or "ac- 

 tivity." G. C. ROBSON. 



Zoological Department, British Museum 

 (Natural History), October 3. 



An Algebraical Identity. 



In Nature of Julv 21 (vol. 107, p. 652) appears a 

 letter from Mr. W. E. H. Berwick, inquiring whether 

 the values of y, z satisfying the equation z--py^=-4, 

 which are derivable from Gauss's cyclotomic formulae, 

 constitute generally the primitive solution of this equa- 

 tion. In replv I liave to point out that a comparison 

 of Gauss's formulae (Mathews, "Theory of Numbers," 

 p. 215) with Kronecker's formula 



{i(T-HbVD)}'' = n(i -co'^"^')/n(l 



") 



(Mathews, p. 253), where T'-DU' = 4 is the primitive 

 solution of this equation, T and U being positive, 

 shows that s, y are connected with the primitive solu- 

 tion a, h by the relation 



^\ + s/p \y\ J a+ypb y^ 



where h is the number of properly primitive classes 

 of determinant p. Incidentally, ic appears that z is 

 always positive and y negative. 



R. F. Whitehe-AD. 

 September 20. 



