140 



BECREATIVE SCIENCE. 



fore an uncertainty of about two years in tlie 

 comet's next appearance, according as to 

 which set of elements is adopted. One and 

 a quarter of two years having passed away 

 without anything having been heard of the 

 comet, we may reasonably expect it in the 

 course of the next few months. 



It is worthy of note that brilliant comets 

 appeared in the years 975, 683, and 104, aU 



of which present some indications of identity 

 with the one we have now been considering ; 

 " but the accounts we possess are too vague 

 to admit of anything more than conjecture." 

 M. Hock, of Leyden, has made some inves- 

 tigation relative to the first of the above 

 three, but his results throw much doubt on 

 the identity of that with the one of 1556. 



Geo. W. F. Chambees. 

 JEasthourne. 



LEA.F GEOMETRY. 



A HI3T0ET of discoveries would, at any rate, 

 prove one very remarkable fact, viz., that 

 occurrences the most familiar to us, and 

 things apparently worthless, are pregnant, 

 nevertheless, with truths which acute ob- 

 servers discover as it were by accident, and, 

 thenceforth, the meanest understanding can 

 acquire a knowledge of phenomena which 

 had been for ages staring clever men in the 

 face, and had yet remained undiscovered, 

 though all-important to the general welfare 

 of mankind. 



I wish, in this paper, to point out some 

 very simple and interesting, if not useful, 

 phenomena in that very common thing — a 

 leaf. Look at that oak-tree. The branches, 

 as they move gently in the wind, seem to 

 break out from the trunk without any regu- 

 larity ; and the leaves, it would be impossible 

 indeed, at first sight, to see any order or 

 arrangement in their position on the branch. 

 But go up closer, and break off" a little sprig, 

 like that in Fig. A. Fix on one leaf, cut half of 

 it off, and then trace up the stem with your 

 finger till you come to the next leaf imme- 

 diately above it. Now tie a thread to the 

 upper one on the stalk as close as possible 

 to the stem, and draw it down, twisting it 

 round the stalk of each leaf, till you come 

 to the leaf which you had already marked. 

 You will find that you have to pass four 

 leaves before you come to the marked one, 



and that you have drawn the thread twice 

 round the stem, thus completing the cycle. 

 Now, if you go on downwards on the branch, 

 you will find precisely the same thing ; at tlie 

 fifth leaf below, you wUl be again exactly 

 under the cut one. So you see that the ap- 

 parent confusion of the leaves upon yon 

 waving oak is in reality an exact order, 

 which would be at all times perfect, but for 

 the various accidents to which the tree is 

 liable from its exposure to weather and de- 

 structive insects. 



It has been discovered that the leaves o 

 all plants and trees are arranged in regular 

 order upon their branches, and botanists 

 mark this arrangement, or " phyUotaxis," as 

 they call it, by a fraction, the numerator of 

 which consists of the number of turns round 

 the stem, and the denominator the number 

 of leaves in the cycle. This oak, therefore, is 

 marked by the fraction |. But there is a 

 great variety of different arrangements of 

 leaves in the common trees and plants which 

 surround us, and it is interesting to find them 

 out. Thus the hoUy will be found to be f, 

 the yucca of our gardens i\, and the lime- 

 tree, the yew, and the bean \. This fraction 

 shows also the distance between the leaves, 

 expressed in parts of the circumference of the 

 circle. This may be seen at once by referring 

 to Figs. B and C, which represent stems with 

 numbers where the leaves are supposed to 



