114 MECHANICS. 



scale, and the working of tlie full-sized macMne. It is a 

 common and mistaken opinion that a well-constructed 

 model presents a perfect representation of the strength 

 and mode of operation of the machine itself. 



When we enlarge the size of any thing, the strength of 

 each part is increased according to the square of the 

 diameter of that part ; that is, if the diameter is twice as 

 great, then the strength will be four times as great ; if the 

 diameter is increased three times, then the strength will 

 be nine times, and so on. But the v^eight increases at a 

 still greater rate than the strength, or according to the 

 cube of the diameter. Thus, if the diameter be doubled 

 (the shape being similar), the weight will be eight times 

 greater ; if it be tripled, the weight will be twenty-seven 

 times greater. Hence, the larger any part or machine is 

 made, the less able it becomes to support the still greater 

 increasing weight. If a model is made one-tenth the real 

 size intended, then its different parts, when enlarged to 

 full size, become one hundred times stronger, but they are 

 a thousand times heavier, and so are all the weights or 

 parts it has to sustain. All its parts would move ten 

 times faster, which, added to their tliousand-fold weight, 

 would increase their inertia and momentum ten thousand 

 times. For this reason, a model will often work perfectly 

 when made on a small scale ; but when enlarged, the parts 

 become so much heavier, and their momentum so vastly 

 greater, from the longer sweep of motion, as to fail entirely 

 of success, or to become soon racked to pieces. 



This same principle is illustrated in every part of the 

 works of creation. The large species of spiders spin 

 thicker webs, in comparison with their own diameter, 

 than those spun by the smaller ones. Enlarge a gnat 

 until its whole weight be equal to that of the eagle, and, 

 great as that enlargement would be, its wing will scarcely 

 liave attained the thickness of writing-paper, and, instead 

 of suj^porting the weight of the animal, would bend down 



