ON USEFUL SUBSTANCES IN CACTUS 



exceedingly long one, covering many thousands of 

 cactus generations, during which the plants were 

 becoming better and better protected; and each 

 stage of such development may be thought of as 

 having its hereditary factors in the germ plasm, 

 capable of acting independently. 



Thus it is that in the same fraternity some 

 seedlings are exceedingly spiny, while others have 

 a comparatively small number of spines, and a 

 few may be absolutely spineless. Thus, also, is 

 explained the fact, to which attention has been 

 called, that the plants that are altogether spineless 

 may still be provided with minute spicules. Such 

 minute spicules were, perhaps, the first defensive 

 mechanism to be developed in the evolution of the 

 cactus tribe, and they have back of them such 

 numberless generations of heredity that they hold 

 their own with exceptional persistency. 



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 earlier studies 

 have taught us that where several or many heredi- 

 tary 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 



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