L66 TENDKIL-BEAKEKS. Chap. IV 



in opposite directions, with straight pieces between 

 them; and M. Leon has seen seven or eight such 

 alternations. Whether the spires turn once or more 

 than once in opposite directions, there are as many 

 turns in the one direction as in the other. For 

 instance, I gathered ten attached tendrils of the 

 Bryony, the longest with 33, and the shortest with 

 only 8 spiral turns ; and the number of turns in the 

 one direction was in every case the same (within one) 

 as in the opposite direction. 



The explanation of this curious little fact is not 

 difficult. I will not attempt any geometrical reasoning, 

 but will give only a practical illustration. In doing 

 this, I shall first have to allude to a point which was 

 almost passed over when treating of Twining-plants. 

 If we hold in our left hand a bundle of parallel strings, 

 we can with our right hand turn these round and 

 round, thus imitating the revolving movement of a 

 twining plant, and the strings do not become twisted. 

 But if we hold at the same time a stick in our 

 left hand, in such a position that the strings become 

 spirally turned round it, they will inevitably become 

 twisted. Hence a straight coloured line, painted along 

 the internodes of a twining plant before it has wound 

 round a support, becomes twisted or spiral after it has 

 wound round. I painted a red line on the straight 

 internodes of a Humulus, Mikania, Ceropegia, Con- 

 volvulus, and Phaseolus, and saw it become twisted as 

 the plant wound round a stick. It is possible that 

 the stems of some plants by spontaneously turning on 



