142 



NATURE 



{Dec. 21, 1871 



arc Bl, which is in the same plane with it, will be at right angles 

 to the arc 12. The third arc 2B' will therefore be the hypo- 

 thenuse of a right-angled spherical triangle, of which Bi, 12, are 

 the two sides. Calling tliese arcs or the angles of the faces re- 

 sented by them, a,b,c, and the angles opposite to them in the 

 spherical triangle, A,B,C, the proof of Napier's Rules, with this 

 solid figure, proceeds by the same direct steps as those already 

 described, with a special example of the figure in my former 

 letter. As the construction there described is confined to the 

 representation of a particular kind of right-angled spherical 

 triangle, and is therefore inapplicable to illustrate the proof of 



Napier's Rules experimentally in every given case, the geneial 

 construction supplied by ''J. J. W.," which is limited by nosucli 

 restrictions, and which is at least equally convenient, will evi- 

 dently serve more effectively the same practically useful and in- 

 structive purpose. 



Instead of " accessible," as applied to the difficulties of the 

 geometrical proofs produced by IMr. Cooley in his letter on 

 "Elementary Geometry" (in Nature, No. 103), which are 

 indeed there obviously overcome, I would have used the word 

 " surmountable" as more descriptive of geometrical difficulties, 

 properly treated and discussed, had the word immediately pre 

 sented itself to me ; but having often found an easily executec 

 model extremely useful and convenient in practical applicatit)n; 

 of Napier's Rules, with whose design, as a general resource tt 

 facilitate their study. I was not, however, so fully satisfied, 

 applied, perhaps unconsciously, to Mr. Cooley's demonstrations 

 a terra expressing strictly only the diffidence with which I ven 

 tured to present to readers of Nature my own very imperfect 

 geometrical contrivance. In thus making my difficulties acces 

 sible to " J.J.W.," I very gratefully acknowledge the assistance 

 which I have derived from his remarks on ray letter in Nature, 

 No. iii., and I cheerfully admit the merit and superiority of tire 

 general rule for constructing a proper model in cardboard, to 

 illustrate the proofs of Napier's Rules, and to facilitate their 

 study, v.'hich he has kindly consented to describe. 



Newc.istle-on-Tyne, Dec. 16 A. S. Herschet, 



Alternation of Generations in Fungi 

 I am sure that the Rev. M.J. Berkeley will exonerate me from 

 any deliberate intention to misrepresent him ; nor do I think 

 that there is, after all, much difference of opinion between us 

 regarding the present subject, unless, perhaps, iliat I am more 

 sceptical. I alluded to the paper cited by hinr from the "Journal 

 of the Horticultural Society," on propagation of bunt spores, and 

 not to his communications on the hop or vine mildew. I was 

 under the impression that he regarded the " four consecutive 

 forms of reproductive cells in the bunt" as an instance of 

 alternation of generations. On reference to the original paper, 

 I find that he did not go so far then as to indicate four consecu- 

 tive forms of reproductive cells ; but that Tulasne followed on 

 his track in 1854, and in 1857 Mr. Berkeley seemed to have 

 accepted the results of Tulasne's observations, since, in his " In- 

 troduction," he gives figures at page 318, in the description of 

 which the following phrases occur: — "spores of the second 

 order," " spores of the third order," "spores of the fourth order." 

 Here are the "four consecutive forms of reproductive cells" to 

 which I alluded. At page 321 he writes concerning the bunt : 



— " The spores, however, are not immediate means of propaga- 

 tion ; they are, in fact, only a sort of prothallus, from which the 

 mycelium grows, producing at the tips, or on lateral branchlets, 

 bodies of various forms, which are themselves capable of germi- 

 nation, and immediately reproduce the spacies." The real 

 issue between us seems to lie in the phrase, " alternation ol 

 generations." If tlie bunt spores, on germination, produce 

 fusiform bodies, which, after conjugation, produce short 

 cylindrical spores, and thus intermediate reproductive cells 

 unlike the parent cell come between that and the ultimate repro- 

 duction of the species, I am induced to call it an "alternation 

 of generations." It would be waste of time to discuss phrases, 

 or I might take exception to the application of this phrase to the 

 Erysiphc'i. The conidia and pycnidia of the hop mildew may be 

 developed without sporangial conceptacles, and the parasite 

 reproduced without sporangial fruit, but I cannot recognise alter- 

 nation of generations in the reproduction of a species by means 

 of conidia, stylospores, or sporidia, or by one of these alone. If 

 such may be construed into an alternation of generations, it must 

 be by permitting greater elasticity to the phrase. Conidia ger- 

 minating and producing pycnidia, the stylospores of the pycnidia 

 germinating and producing sporangial conceptacles, containing 

 the sporidia which, upon germination, will produce the mycelium 

 and conidia again, returning to the original form after two or 

 three consecutive departures from it, appears to me a perfect type 

 of alternation of generations. I fully admit that " if it is once 

 established that a Puccinia produces an /Ecidium, or an^-Ecidium 

 a Puccinia, we sli'juld have a clear case, especially when the 

 third form reverts to the first again." Without the slightest 

 desire to " depreciate the labours of Oersted and De Bary," I 

 cannot admit that they have established facts until their obser- 

 vations are confirme I, especially when there is an evident possi- 

 bility of their having been deceived. I shall have no hesitation 

 in accepting the facts when they are confirmed by independent 

 and equally trustworthy observers, although I may be unable to 

 account for some of the phenomena. At present I must confess 

 that I am not so sanguine as Mr. Berkeley appears to be. 



The correspondent signing himself "Mycelium" wishes to 

 know if " the liability to produce parasitic fungi is communicated 

 from the seed to the mature plant." In some instances we know 

 such to be the case, in others perhaps only suspect it. The 

 " bunt " is an instance, or why thesteeping of seed corn ? or how 

 did the Rev. M. J. Berkeley succeed in producing Ininted wheat 

 plants from seed corn inoculated with bunt spores? Two or three 

 years since I published particulars of a similar instance of celery 

 seed and Puccinia Apii. It would be as rash to affirm that this 

 is always tire case as to deny its occurring at all. 



M. C. CooiCE 



In Re Fungi 

 The letters in your last two numbers have reminded me how 

 ill this subject is studied by some botanists in this country. I 

 will give two recent instances : I. In the last number of the 

 jfounial of Botany, p. 3S3, it is positively stated that Agariciis 

 carti/a^iucits {a rare and very critical species by the way) was de- 

 termined by a growth which is there described a mere mass of 

 inycclinni. He must have been a bold man «'ho ventured to 

 name an agaric (above all things) from a mass of mycelium. 

 2. In tlie first number, October 1871, of the luio edition of 

 "Paxton's Botanical Dictionary" — "enlarged and revised" — 

 under the article Ai^aricus there is to be found such a collec- 

 tion of obsolete names and absurd errors as to make the article 

 simply ridiculous. W. G. S. 



Mr. Lowne and Darwinian Difficulties 

 Mr, Lowne (Nature, December 7) sees no difficulty what- 

 ever in explaining by what natural process an insect with a suc- 

 torial moulh is developed from one having the mandibular type 

 of mouth, but still he does not explain. He affirms there is no 

 doubt that "the pupa state is a modification (!) of the ordinary 

 process of skin shedding," and that this is " proved " by so many 

 facts that he cannot understand how it could be "denied," &c., 

 but he does not prove it. 



For aught I can tell, every internal tissue and every external 

 scale of the butterfly may be represented in the larva ; but I do 

 nor know and cannot prove that this is so, nor do I believe any 

 one can prove it. That the changes which take place during the 

 pupa state are very different from those that occur during any 

 portion of the larva period, will be admitted by every one who 



