MODELS OF MACHINES. 173 



a drawing-knife, and but little strength in turning a 

 Lrace-bit or working a dasher-churn. Hence, too, the 

 reason that, in turning a grindstone, the pulling and 

 thrusting part of the motion is more powerful than 

 that through the other parts of the revolution. This 

 also explains why two men, working at right angles to 

 each other on a windlass, can raise seventy pounds 

 more easily than one man can raise thirty pounds 

 alone. Tliis principle should be well miderstood in the 

 construction or selection of all kinds of machines for 

 hand labor. 



SECTION VI. 

 MODELS OF MACHINES. 



Serious errors might often be avoided, and some- 

 times gross impositions prevented, by understanding 

 the difference between the working of a mere model, 

 on a miniature scale, and the working of the full-sized 

 machine. It is a common and mistaken opinion that 

 a well-constructed model presents a perfect representa- 

 tion of the strength and mode of operation of the ma- 

 chine itself. 



AVlien 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 thi*ee times, then the 

 strength will be nine times, and so on. But the weight 

 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 



