THE PROBLEM OF A FLYING-MACHINE. 71 



all dimensions, therefore, the weight will quickly overtake the 

 strength. There is a limit, therefore, beyond which it is impossible 

 to make an arch or suspension-bridge support itself. This fact is 

 so well recognized that it is unnecessary to dwell upon it. I have 

 brought it forward at all only because I wish to apply the prin- 

 ciple to other cases where it is not so well recognized. 



2. Application to Walking. — Now, this principle applies not 

 only to bridges and arches, but to all kinds of structures, and 

 therefore, also, to locomotive-machines, whether natural or arti- 

 ficial. For example, there is a limit of size beyond which it is 

 impossible to make a successful walking - machine, and beyond 

 which, therefore, a walking animal can not exist. Beyond that 

 limit the supporting bones would crush beneath the weight of 

 the animal. It is in vain to say that we will make the bones and 

 muscles thick and strong in proportion to the increasing size of 

 the animal ; for, as the animal increases in size, its weigJit increases 

 as its volume or as the cube, while the strength of bones and mus- 

 cles increases only as the cross-section or as the square of the diam- 

 eter. Therefore, as the animal increases in size, a larger and 

 longer portion of the whole strength is consumed in the support, 

 and less and less is left over for motion, until, finally, the weight 

 overtakes the utmost strength of bones to supx)ort or muscles to 

 move. It is probable that the limit of an efficient walking-ma- 

 chine has actually been reached in the largest animals which 

 have walked the earth ; such, for example, as the huge dinosaurs 

 of the Jurassic period, recently brought to light by the researches 

 of Marsh and Cope. The whale has probably passed the limit, 

 and therefore was compelled to change its form and take to the 

 water, and become a swimming-machine. Or, to speak more defi- 

 nitely and also more truly, the whale family in times long ago, 

 perhaps in earliest Tertiary times, before it became a true whale 

 family, found it profitable, either for food or for safety, to take to 

 the water ; and this not only determined a change of form, but 

 also allowed it to attain a greater size than was compatible with 

 walking. 



This principle explains many other things in nature which 

 would otherwise be inexplicable. The marvelous vivacity and 

 energy of insect-motion — the arrowy swiftness of flight of many 

 kinds of flies, the prodigious leaps of fleas, the immense weights 

 dragged by ants — are familiar to all. In text-books on natural 

 history these are given as examples of the almost inconceivable 

 nervous and muscular energy of insects, as compared with verte- 

 brates. It is often said that if our nerve- and muscle-energy were 

 as great as that of a flea, we might easily leap a quarter of a mile. 

 In that case we would have little use for railroads or for seven- 

 league boots, or indeed for flying-machines. Now, this is an entire 



