344 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739, 



change their contact from one of those points to another; because in the roll- 

 ing of these little spheres, they do not come into more or less contact, in one 

 situation than another. But if we suppose the point n in each spherule to be a 

 pole, with a force to repel all the other points n in any other spherule, and 

 likewise s another pole, repelling the other points s ; the spherules will cohere 

 best, and be at rest in that position, where the points c, c, are in contact, and n 

 and s at equal distances on either side. For if the spherules be turned a little, 

 so as to bring the points d, d, into contact, as in fig. li, the poles, n, n, being 

 brought nearer, act against each other with more force than the points s, s, 

 which are now farther off, and consequently drive back the spherules to the 

 contact at c c, beyond which continuing their motion, they will go to SS, 

 fig. 12, and so backwards and forwards, till at last they rest at cc, which we 

 may call the point of equilibrium for rest in a spring. Now there are, besides 

 this, two other points of equilibrium, beyond which the spring may break, 

 which are the points e, e, towards n, and f, f, towards s; see fig. 13, that is, 

 when the spherules have their poles n, n, brought very near together, the mu- 

 tual repulsion increases so, that the attraction at the contact is not able to hold 

 them, and then they must fly asunder, the spring breaking. We suppose the 

 points e, e, to be the points of contact, beyond which this must happen ; but 

 that if the contact be ever so little short of it, as between e and d, the spherules 

 will return to their contact at c, after some vibrations beyond it, as has been 

 already said. This is the reason why he calls e, in one of the spherules, and 

 its correspondent point £, on the other side c, the points of equilibrium ; for if 

 the spring be bent towards a, fig. Q, so that the spherules, like a and b, fig. 13, 

 touch beyond e, the spring will break. Likewise if the spring be bent the 

 other way, till the spherules touch beyond e, then it will break the other way. 

 Now when the spherules touch at e,e, or at f, s, the spring is as likely to return 

 to its first position as to break ; for which reason he has called the points e and 

 I, points of equilibrium, as also, having known by experience, that a spring 

 left bent to a certain degree, has, after some time, broke of itself. 



From all this it appears, that spherical particles will never make a tough 

 spring ; therefore the figure of the particles must be altered, in order to render 

 it useful ; and this is what is done in bringing down the temper of the hard 

 steel, and letting down a spring, as it is called. What change ought to be 

 made in the particles, we shall first show ; and then consider how far that is 

 done by those who make springs. 



If the parts supposed globules, as in fig. Q, are now flattened at c, where the 

 contact is, so as to put on the shape n e dc Jt s, as in fig. 14, the contact will 

 be much increased, and reach from d to S, so that in bending the spring there 



