3 8 THE POPULAR SCIENCE MONTHLY. 



purpose of pointing out that the application of the wax in the most 

 economical manner, making it go as far as possible, subject to the con- 

 dition of forming prismatic cells, is a geometrical result from adopting 

 the simplest plane and solid figures, namely, the circle and the sphere. 

 Let me illustrate this by a single example. Suppose I gave a copper- 

 smith a lump of copper, and said, " Make this into a bowl of given 

 thickness, having a maximum of capacity " ; my coppersmith would 

 undoubtedly be posed. But suppose I said, "Make this into as 

 simple a bowl as you can, and let the material be of such a thickness": 

 he would almost certainly make it hemispherical, or nearly so, because 

 that is the simplest form ; but his hemispherical bowl would, as a 

 matter of fact, possess the property of maximum content which I 

 wished it to have. 



It seems to me, therefore, that there may be not a few cases in 

 which arrangements, that appear at first sight to be the result of a 

 choice among many that might be possible, are in fact arrangements 

 which are necessitated by geometrical conditions, or what may be 

 equivalent to them. This consideration should make us cautious in 

 attributing to an arbitrary will facts which might seem at first sight 

 to warrant this conclusion. Then, again, there are phenomena in the 

 ordinary functions of nature, having the appearance of chance, which 

 yet are not chance in the true sense of the word, but which have 

 strongly the appearance of it, and for which it is difficult to give any 

 account. The manner in which plants turn toward the light is to 

 me a profound mystery ; there must be a force to produce the motion, 

 but I do not perceive whence it can arise. And the instinct of seek- 

 ing the light sometimes assumes the most wonderful form. I think I 

 have read of a potato in a dark cellar throwing out a long sprout 

 which extended itself till it emerged at a hole at a distance through 

 which light entered. The power which living matter has to adapt 

 itself to unforeseen circumstances, of which this potato may be taken 

 as a humble instance, has very much of the appearance of choice. A 

 limb is broken, or a skull is trepanned, and the limb becomes as strong 

 as ever, and the skull retains whatever brain it may have had within 

 it, in virtue of new efforts of nature exactly adapted to the wants ; 

 but these wants are such as could not have been foreseen, and could 

 scarcely have been included in the original idea, so to speak, of the 

 man to whom the accident has happened. 



Therefore I feel that we are on very difficult and mysterious ground 

 when discussing the place which should be assigned in nature to choice. 

 I think that we ought to recognize the fact that many things in the 

 edifice of nature, which might strike us at first sight as the arbitrary 

 touches of the great Architect, may in reality be the results of geo- 

 metrical or other necessity inherent in the conditions of space, or time, 

 or matter. Nevertheless, it is difficult to believe that a creation such 

 as we see round about us, and of which we form a part, could have 



