ABSTRACTS OF FOUR LECTURES TO STUDENTS. 



513 



The reader will here observe that 1, 6, 9, 14, 17, 22 fall over each 

 other, corresponding to the cycles 1 to 5, 1 to 8, 1 to 13, 1 to 16 ( = 2 x 8) 

 1 to 21, and represented by the fractions J, f, |, 2 8 T . -J is not re- 

 presented. 



Besides changes from opposite pairs of leaves into the above alternate 

 arrangements, others sometimes appear arising from whorls of threes on 

 stems of the Jerusalem Artichoke. These give rise to alternate leaves re- 

 presentable by ^, J, f , i T , &c. 



Enough has now been said to show how leaf-arrangements occur in 

 nature. There remains one more application, and that is to flowers ; for 

 all the parts of flowers are really foliar organs. 



It has long been noticed that fives are peculiarly common in the 

 w T horls of flowers of Dicotyledons and threes in those of Monocotyledons. 

 They are really cycles of the § and ^ arrangements respectively, the 

 former deducible from opposite cotyledons and the latter from a single 

 •one. 



Where petals, stamens, or carpels are very numerous, as are also the 

 florets of a head of any composite, there it has been found, on counting 

 the numbers of hundreds, sometimes thousands of examples, that certain 

 numbers form maxima. Then these correspond with cycles. Thus the 

 Corn Marigolds had 13, 21, and 34 as the prevailing numbers of ray- 

 florets. In Primroses 8 and 13 prevailed, as well as the normal number 5. 



Why Nature should prefer, so to say, "cyeular numbers " for whorls, 

 as "dominant," over other, when the whole series of petals &c. forms a 

 continuous spiral, is not at all obvious, but so it seems to be. 



It has been found, too, that 13 is a maximum of the stigmatic rays of 

 Poppies, and such are more fertile, a curious but inexplicable coincidence. 



Stipules. — These consist of a pair of appendages arising from the 

 stem, one on either side of the base of a leaf, or they may be adherent to 

 the petiole itself, as on a Eose-leaf. 



They assume various forms and have various functions, or they may 

 be rudimentary and functionless, or even absent, their former presence 

 being only detected by the internal anatomy. 



A common use is to protect the bud in the axil of a leaf, as in the 

 Garden Pea, and Lathyrus Aphaca, &c, in which plants they are large and 

 green or foliaceous, and so form additional assimilative uses to that of the 

 blades. They thus compensate for the loss of leaflets which are now re- 

 presented as tendrils. 



In Galium and Woodruff the stipules are exactly like the leaves, and 

 are sometimes increased in number beyond the usual four, at the node, 

 i.e. two for each of the pair of opposite leaves. 



The members of the tribe Stellatce of the order Bubiacece (to which 

 Galiums, Madder, Woodruff, &c, belong ; the tribe being so called 

 because the leaves and stipules are whorled or "star-like") supply a 

 convenient way of examining the true connection between leaves and 

 stipules. 



If a thin section be made by cutting a stem across just above and 

 just below the whorl, thin enough to be translucent, the circle of woody 

 fibres with cellular tissue or pith in the middle will be readily seen. Two 

 fibres or cords pass out on opposite sides, or ends of a diameter, one 



