SPRINGS OF MINIMUM INERTIA. 



H. C. Lord. 



In certain forms of apparatus where springs are employed to 

 indicate the instantaneous value of a varying force it is of the 

 utmost importance that they should be as light as possible in 

 order that the inertia should be reduced to a minimum. In 

 designing such a piece of apparatus the writer found it necessary 

 to investigate mathematically the conditions which must be 

 fulfilled in order that the spring might be of minimum weight. 

 In the course of this investigation certain unexpected and very 

 interesting results were reached which not only are of general 

 application, but also lead to simple formulae of design. Such 

 springs may be grouped into two classes, namely, those whose 

 action depends upon bending and those whose action depends 

 upon torsion. Evidently, in either kind, the maximum allow- 

 able fiber stress and the maximum deflection to which the 

 beam will ever be subjected must be reached simultaneously 

 with the maximium load for, were it otherwise, the spring could 

 have some metal removed and still be strong enough to resist 

 the stress. We will take, therefore, as the quantities entering 

 into this investigation the following: 



f = the maximum allowable fiber stress. 



P = the maximum load. 



A = the maximum deflection. 



Z = the modulus of the section. 



I = the moment of the inertia. 



E = Young's Modulus. 



w = the weight per cubic inch. 

 W = the total weight. 

 bt = the breadth. 



d = the depth. 



L = the length. 



tin beams of constant strength, and depth constant, b is breadth of base. 



320 



