January 1, 1890.] 



KNOWLEDGE 



45 



lowest of these, remaining at the bottom of the cavity of 

 the archegonium, becomes the oospheie or egg-cell. 

 And from tliis oospbere, when fertilized by an antherozoid, 

 !i yomig plant is de\eloped, which is what we ordinarily 

 know as the fern. Thus, ferns are subject to what 

 is called alternation of generations. The alternating 

 generations may be distinguished by different names ; 

 thus our fern is termed the xji(iro)ih<tre or spore-bearing 

 generation, and from the perfectly asexual spores it pro- 

 duces is developed the prothallium, the oojiharc or egg- 

 hearing generation, which produces, from the fertili- 

 zation of the archegonium by the antherozoids of its 

 antheridia, the large and complicated organism commonly 

 known as the fern. The law of alternation of generations 

 seems to be this : that a se.iual generation, i.e. producing 

 sexual organs, alternates with an a,<si:niiil generation which 

 jjroduces only spores. This alternation of generations 

 holds in nearly all the flowering plants. We get the following 

 parts answering in a tolerably exact fashion to the two kinds 

 of spores. The pollen-grain represents the microspore, 

 which pollen-grain gives rise to the pollen-tube corre- 

 sponding to the antheridium of the microspore's prothallium, 

 •n'hile the division of protoplasm of the pollen-tube gives us 

 an indication of the formation of antherozoids. Also, in 

 the pollen-grain of flowering plants, and notalily so in that 



Fig. 0. — Egg df Astkiuas 

 Glacialis. a, Polar Bodies ; 

 j8, Female Pronucleus. 



Fig. 7. — Feutiliz.\th)N of a 

 Flowering - plant, a, Pollen 

 tube ; B, Synergadac ; c. Egg- 

 cell ; D, Emhryo-sac. 



of Gymnosperms, there are two cells, one larger than the 

 other, and usually it is this larger one which pushes itself 

 out as the pollen-tube. Hence, the small cell, the 

 vegetative part of the grain, taking no part in 

 the formation of the pollen-tube, is equivalent to that 

 portion of the prothallium of a microspore which does 

 not produce antheridia ; consequently tlie larger cell of the 

 pollen gi'ain corresponds to the part of the prothallium 

 which does produce antheridia. Agivin, the embryo-sac of 

 flowering plants, producing as it does by gernnnation the 

 egg-cell, presents a very striking similarity to the niacrospore 

 of a rhizocarp, which gives rise to the oospbere in the 

 archegonium of its prothallium ; while the merely vegetative 

 portion of the products of the embryo-sac and of the 

 macrospore is in both cases called the eudosporm. 



Thus from the .s'/zocK/i/Kirc generation in the rliizocarps we 

 have two kinds of sporesgiving rise to protballia — theodjilum 

 generation — furnished with either antheridia or arehegonia, 

 and from the development of the fertilized oospbere in the 

 latter we get the xjKiroiihtnc, the rliizocarp, again. 

 Similarly, in flowering plants, the K/Kiniiilmre generation is 

 what we know as the plant, producing macrospores, i.e. 

 embryo-sacs, and microspores, i.r. polkn-giains ; these give 

 ri.se to the oophore generation, the protballia in the one 

 case forming oospheres (the last remnant of arehegonia 



being found in the corpuscula of the Gymno-sperms). and 

 in the other, antheridia — the pollen-tube. By the fertiliza- 

 tion of the egg by the pollen-tube. 1\n- s/Kinijiliurr generation 

 is commenced again in the embryo plant, and tiietwogtne- 

 rations. sexual and asexual, continue to repeat themselves in 

 this order over and over again. What are ordinarily called 

 the sexual organs of a flower do not deserve that title, for 

 the stamen is simply a leaf modified to bear microsporangia, 

 — the anthers — whence eventually the male organs will 

 come, while the carpel is only a leaf modified to bear 

 macrosporangia in a somewhat similar way. 



We left the oospbere mattire and ready for fertilisation 

 by the antherozoids. They enter the canal of the arche- 

 gonium, and as soon as the oospbere has been fertilised by 

 them it begins to di^•ide into four cells ; of these the two 

 lowest sub-divide into a plug-Uke, cellular mass, which 

 imbeds itself firmly in the substance of the prothallium. 

 Probably this, called the foot, takes up nourishment for the 

 embryo from the prothallium. It also serves to distin- 

 guish cryptogams of the most difl'erentiated kind fi-om 

 flowering plants generally, for in all the latter the sw<- 

 jicnsar is the organ corresponding to this foot. In some 

 orchids this suspensor curiously enough actually grows out 

 of the mieropyle into the placenta, to absorl) nutriment 

 for the embryo. In several of the flowering plants the 

 use of the suspensor seems to finish after a certain period, 

 and its place is taken by what Dr. Charles Darwin termed 

 " the peg," between the plumule and the radicle. The 

 presence of this peg has rather complicated the subject, 

 but Dr. Vines has been able to show, by comparative 

 studies, that the suspensor of selaginella and of the flower- 

 ing plants is homologous with the foot of the vascular 

 cryptogams, seemg that it is derived fi-om the same cell of 

 the embryo. Of the remaining two upper cells, which 

 also sub-divide, one gives rise to the rhizome — the stem of 

 the young fern — w'hile the other becomes its first rootlet. 

 As the rhizome grows and develops its fronds, it rapidly 

 attains a size vastly superior to that of the prothallium, 

 which ceases to have any work to do, and disappears. 



SOME PROPERTIES OF NUMBERS. 



By Rout. W. 1). C'hkistie, Head Masti-r, Wavirtree Park 

 College, Liverpool (Member of the Lond. Math. 

 Soc, &c.). 



Jtoiitx ami I'liufis iif Xuiiihtlx. 



IS the square root of 1234507 an integer '? No ; be- 

 cause the square of no integer can possibly end in 

 the digits 2, 3, 7 or 8. This is easily shown as 

 follows: — Square the ten digits 1, 2, 3, iS.c. succes- 

 sively, and we get nimibers ending in all the digits 

 except those given above, viz. the digits 0, 1, 4, 9, 6, 5. 



The cube of an integer may end in any of the ten 

 digits. It is curious, however, to note that the cube of 

 any integer ending in the same six digits, viz. 0, 1,4, 9, 6, 

 5, ends in the same digit as the number itself does ; and 

 moreover the cube of any integer ending in the four digits 

 mentioned above, viz. 2, 3. 7, 8, ends in the same figures 

 but in the reverse order 8, 7, 3. 2. 



Me can thus very easily determine by inspection the 

 cube root of any perfect cube less than a million, l-'.r. i/r.. 

 Find the cube root of 912673 by inspection. 



Pointing ofl' as usual, we see at once that there must he 

 two figures u» the root, and that one of them is 7 (since 

 the culie of 7 ends in 3), and tlie nearest cube root of 912 

 is 9 ; thus we easily get 97 as the required root 



The fourth power of an integer may end in the four 



