THE CACTUS 165 



explained the fact, to which attention has been 

 called, that the plants that are altogether spine- 

 less may still be provided with minute spicules. 

 Such minute spicules were, perhaps, the first 

 defensive mechanism to be developed in the evo- 

 lution of the cactus tribe, and they have back of 

 them such numberless generations of heredity 

 that they hold their own with exceptional per- 

 sistency. 



In dealing with the spines and spicules of 

 the cactus, then, we must consider that we have 

 to do not with a single hereditary factor or two, 

 but with a multitude of factors. Now our ear- 

 lier studies have taught us that where several 

 or many hereditary factors are in question, the 

 probability that they will all be combined in any 

 given way in a single individual decreases at a 

 geometrical ratio. We found, for example, 

 that where ten hereditary factors were under 

 consideration, the probability of their combina- 

 tion in a predicted manner was only one in 

 something over a million. In the case of the 

 cactus the factors for spininess doubtless number 

 far more than ten; from which it follows that 

 the probability that any given seedling will have 

 germ plasm absolutely free from any of the fac- 

 tors for spininess is much less than one in a 

 million. 



