1 26 Statics. 



ratio between this power and the force which it is capable of 

 exerting in the direction of the axis. 



214. We shall have a pretty just idea of the screw, by rep- 

 resenting the thread as formed by wrapping round the cylinder 



'the hypothenuses CAT of as many right-angled triangles CIK, as 

 there are revolutions of the thread, each triangle having for its 

 height, the distance CI between two adjacent threads, and for its 

 base IK, the circumference of the cylinder corresponding to the 

 point /; so that, according as the thread becomes thicker, IK is 

 increased in length, the height CI remaining the same. 



In figure 118, where the threads are edge-shaped, according 

 as the protuberant part becomes thicker, or departs farther from 

 Fig.119. the axis, we must suppose that the base /AT increases, and that 

 the height CI diminishes. 



215. The screw AB being fixed, and having a vertical posi- 

 tion, no allowance being made for friction, or for the nut hav- 



118. 'ing its natural gravity, it is evident that the nut in turning would 

 pass over the several threads of the screw by sliding upon each 

 as upon an inclined surface. It is also evident that this tenden- 

 cy may be overcome by applying to the nut XZ, a certain pow- 

 er, which admits of being directed in several different ways. 

 But as the nut has manifestly no motion, if it be prevented from 

 turning, we shall confine ourselves to inquiring what must be the 

 ratio between the weight of the nut, or in general between the 

 force which urges it in a direction parallel to the axis of the 

 screw, and the force capable of preventing its turning. Of the 

 several points of the nut, we shall first consider only that which 

 rests upon one point of the thread of the screw. 



The force which acts immediately on this point to prevent 

 the turning, and that which tends to make it descend parallel to 

 the axis, must be regarded as being in equilibrium upon an in- 

 clined plane whose height is the perpendicular distance between 

 two adjacent threads, and whose base is the circumference of the 

 circle which would be described by the point in question. This fol- 

 lows from what we have said of the nature of the screw. Now of 

 these two forces, the first is parallel to the base of the inclined 

 pane, and the second is perpendicular to it ; hence, by article 208, 



