644 



NATURE 



[Oct. 31, 1889 



might be expected, as Nos. 2 and 3 are obviously descended 

 from the hermaphrodite No. I, I have never, however, found 

 a single individual in any sense intermediate between Nos. 2 and 

 3, which appear to be two distinct female forms developed from 

 No. I along different lines. 



These two forms, it will be observed, differ remarkably from 

 each other in the following points, viz. size of capitulum, size 

 of florets and arrangement on the receptacle, colour of corolla, 

 stoutness, colour and general form of style, and in the absence 

 or presence of stellate hairs. 



The stellate hairs are utilized to catch stray pollen-grains 

 detached from the bodies of insect-visitors coming from neigh- 

 bouring hermaphrodites, most of which would otherwise be 

 wasted. As it is, they are retained by the hairs until the 

 arrival of other insects, which in depressing the already bent and 

 twisted styles bring their viscid stigmas into contact with the 

 pollen-grains collected by the hairs of adjacent florets — a result 

 facilitated by the manner in which the stigma is set on the style. 

 By this arrangement the chances of fertilization are much 

 increased, as each stigma generally receives a full share of 

 pollen. 



With regard to the relative size of the three forms it is 

 remarkable that while one of the female forms is so much 

 smaller than the hermaphrodite (as is the case, according to 

 Darwin, in all gynodioecious species known to him), the other 

 even exceeds it in size. It is also noteworthy that the capitulum 

 of the second female form, although larger than that of the 

 hermaphrodite, contains a much smaller number of floi'ets, and 

 these are very large. 



I can discover no rule as to the distribution of the different 

 forms. In one station near here (a large common) all the plants 

 are hermaphrodites. In a certain wood where the species 

 abounds, the "bent-styled" females appear to be nearly as 

 common as the hermaphrodites, while no "straight-styled" 

 females can be found. In another wood, not half a mile distant 

 from the first, the "bent-styled" form is almost entirely sup- 

 planted by the "straight-styled," which is plentiful. Lastly, in 

 a fourth station (a barren strip of ground by the roadside), all 

 three forms are found growing together. Arthur Turner. 



Box Hill, September. 



On the Aquatic Habits of Certain Land Tortoises. 



It has always proved of more or less interest to me to 

 observe the method of aquatic locomotion adopted on the 

 part of any of our strictly terrestrial vertebrates, and never 

 is this more keen than when the opportunity has been afforded 

 to study the swimming propensities of certain of our Reptilia. 

 Most snakes swim well, but who of us has not been sur- 

 prised upon first observing the violent wriggling, froward- 

 propelling motions of some of the smaller lizards when they are 

 thrown out into the water some little distance from the shore ? 

 The American chameleon {Anolis principalis) well illustrates this 

 last ; and this lizard, in common with others, seems to possess 

 an actual dread of getting into deep water. For a long time 

 it has been known that most species of the so-considered 

 stricter types of land tortoises soon drown when placed in water 

 of any considerable depth, and it would be but natural to 

 suppose that such species would avoid that element as far as 

 possible, but I have found this by no means always to be 

 the case. Take the ordinary land turtle of the United States 

 {Cistudo Carolina) for example : it will voluntarily enter the 

 water under certain circumstances. Not long ago the writer 

 noticed one of these hunting for food in three or four inches 

 of water along the edge of a pond that had rising banks ; and 

 the first time I discovered the nest of this variety the eggs 

 were deposited in the water in a depression at the miry margin 

 of a marsh. But this is not all, for if we place one of these 

 reptiles upon a little island of land, well removed froin the 

 shore, and surrounded by water several feet in depth, and 

 withdraw to watch its movements, we note that as soon as it 

 satisfies itself as to its position, it will, without further ado, 

 take at once to the water and swim to the nearest shore. It does 

 not, however, sink beneath the surface, but, holding its head 

 high out of that element, and filling its lungs with air, strikes 

 out vigorously, with alternate pairs of feet, until it accomplishes 

 its purpose, and regains the mainland. How far one could 

 swim in this manner I am unable to state, but that it would 

 not exceed a few yards I am quite certain. Nevertheless, 

 even the power to accomplish the feat to the extent indicated 



might, under a variety of circumstances, have its influence upon' 

 the distribution of the'species, or of any species of typical land- 

 tortoise, and it would be interesting to know how far this power 

 may be enjoyed by this class of reptiles generally. 



Smithsonian Institution, R. W. Shufeldt. 



Washington, D.C., September 13. 



Delambre's Analogies. 



Four of the most important formula2 in spherical trigono- 

 metry were given by Gauss, without proof, in his " Theoria 

 Motus Corporum Coelestium " (1809), and were therefore called 

 Gauss's theorems or analogies. 



They were, however, given by Mollweide in Zach's Monat- 

 liche Correspondenz for November i8o8, and before that by 

 Delambre in the Connaissance des Temps, issued in April 1807, 

 so that they are now justly ascribed to the latter. 



They may be deduced in the most simple manner fron:> 

 Napier's analogies, and thus easily remembered. 



Napier's analogies are — 



tan i(A -f B) = ^°^ ^}^^JZ_3 

 cos \{a + b) 



sin \{a ~ b) 



tan ^(A - B) = 

 tan \[a + b) = 

 tan \{a - b) 



sin \{a + b) 

 _ cos ^(A - B) 

 cos ^(A + h) 



_ sinJ(A -B) 



cot iC 



cot ^C 



, tan \c 



tan \c 



(«) 

 (-8) 

 (7) 



(S) 



(I) 

 (2) 



(3) 

 (4) 



sin i(A + B) 

 Let m . sin ^{i^ + B) = cos \{a - b) cos ^C 

 . •. /« . cos ^(A -f B) = cos h[a + b) sin JC 

 These are numerator and denominator of (a). 



Let « . sin ^(A - B) = sin ^{a - b) cos \C 

 n . cos ^(A - B) = sin \{a + b) sin ^C 

 Numerator and denominator of (/9).. 

 Square, and add — 



. •. m- + n^ = I. 



Divide (4) by (2), and it follows by (7) that — 



n . 1 

 — = tanic; 

 m 



m — cos \c, n — sin \c. 



Substitute these values, and (i), (2), (3), (4), are Delambre's 

 analogies. 



R. Chartres. 



Classified Cataloguing. 



The principle suggested by Mr. Petrie, on "Classified Cata- 

 loguing" (Nature, August 22, p. 392), is already successfully 

 used in many of the chief libraries of the United States, having 

 been originated by Mr. Melville Dewey, while Librarian at 

 Amherst College. It is equally applicable to collections of all 

 kinds, and the classification has already been extended to a 

 considerable extent in certain departments, particularly in 

 botany, and is capable of unlimited extension. It possesses all 

 the advantages mentioned by Mr. Petrie, but is broader, 

 inasmuch as it includes all subjects. 



In the "Decimal Classification" of Mr. Dewey (Boston, 

 1885, second edition), we find, for illustration, under 500, 

 General Science; 580, Botany; 583, Dicotyledonas ; 583 '9, 

 Apetalse ; 583 '95, Unisexuales, 583-951, Euphorbiaceae ; 590, 

 Zoology; 598, Reptiles; 598'i3, Chelonia, &c. 



If an extension of this system, which would, I have the 

 means of knowing, be most acceptable to Mr. Dewey, were 

 to be adopted for general museum use, the advantages would 

 be incalculable. JAS. Lewis Howe. 



Polytechnic Society, Louisville, Kentucky. 



Valuable Specimens of Vertebrates for Biological 

 Laboratories. 



What specimens of Vertebrates are the best to be used by 

 the student in the biological laboratory ? This is certainly a 

 very important question. In Europe, the following animals are 

 generally dissected : some fish, the common frog, the pigeon. 



