senting the earth itself. The bee constructs this solid; and ancient 

 geometers such as Pappus were so struck with the beauty of these cells 

 that they considered the bee to be a mathematician and geometer ; 

 they reckoned the bee amongst themselves as worthy of being called 

 mathematicians, and they accepted the bee-cells as a challenge. Pappus 

 says angrily in one of his works : "I cannot admit that the bee is so 

 expert a geometer as we are, for we can perform a problem greater 

 than the bee, describing polygons with the least perimeter." He pro- 

 ceeds to show how he could make cells more perfect than those of the 

 bee. There is in this an unconscious supposition of the same kind as 

 in the case of Kepler, that the bee makes the cell by some knowledge 

 or intelligence of its own. Now, the cell of the bee possesses remark- 

 able properties : it possesses the property of making the largest quantity 

 of cell-space with the minimum quantity of wax ; or, in other words, it 

 performs the problem of doing a given work with the least amount of 

 trouble to the bee. It costs the bee trouble to make wax, and, there- 

 fore, if he acted consciously or unconsciously on the principle of least 

 action, he will make his cells in such a form as to produce a given space 

 for the accommodation of the honey with the minimum or smallest 

 quantity of trouble to himself and of wax as material. In all these 

 cases, in the motion of the planet, in the motion of light, or in the case 

 of living beings like the bee or the unconscious oyster- woman, we have 

 the same principle at work. Nature aims at producing a given quantity 

 of work with the least quantity of material, and this is the precise form 

 which the principle of least action takes in muscular mechanics. 

 Nature has to produce a certain quantity of muscle to do a certain 

 quantity of work. The production of that quantity of muscle costs an 

 effort which is exhausting to the animal ; the muscles so produced from 

 day to day, from hour to hour, from minute to minute must be fed by 

 blood-vessels, must be nourished and sustained, and this causes a daily 

 waste of labour. It is, therefore, obviously the interest of nature, 

 whatever be the intelligence that guides her movements, it is the interest 

 of the creatures that she makes, that they should do the work which 

 they have to do with the minimum amount of muscle. The principle 

 of least action is that the arrangement and mutual position of all mus- 

 cular fibres, bones, and joints must be such as to produce the required 

 effect with the minimum amount of muscular tissue. I hope to show 

 you in my lecture on this day week by two very remarkable examples 

 from the limbs of the tiger and the wings of the albatross a complete 

 and perfect demonstration of the truth of this principle ; and in my 

 closing lecture I shall ask your attention to the most interesting and 

 attractive of all the applications to which animal mechanics can be ap- 

 plied, namely, to the heart and other involuntary muscles of great 

 importance. 



