240 OF THE PARTS OF [SECT. vn. 



stroke be 5 feet ; then 4x3:5:: pressure on the piston : stress on the teeth of 

 the wheel, equal five-twelfths of the pressure on the piston. The stress thus found 

 is to be considered as a weight applied at the point to which the motion belongs. 



In like manner, the period of the motion of the working point of any machine 

 may be considered unity ; and by comparing the chords of the arcs described in 

 the same time, and the revolutions in the same period, the stress may be found in 

 terms of the force required to overcome the resistance at the working point. 



501. The method to be followed in determining the strength, is, when there is 

 only one working point to proceed from the engine, taking its power as the measure 

 of the stress at every point, and to make the part so that it shall be sufficiently 

 strong to bear a reversion of the motion ; but if the power of the engine be divided 

 among various trains of machinery, then its power should be the measure of 

 strength only to the point where the trains branch, and for each separate train the 

 greatest possible stress at the working point should be made the measure of the 

 strength of its parts. 



502. The advantage of reasoning by general formulae is so great, that it will 

 be adopted, and the rules as they arise given in words at length with examples. 



Let, 



D = the diameter of the piston in inches, 



L = the length of its stroke in feet, 



P = the double of the whole elastic force of the steam in the boiler, in 



Ibs. per circular inch. 



/ = the length from the centre of motion to the centre of stress in feet, 

 a = the depth or diameter, 

 b = the breadth in inches ; 



f = the cohesive force of a square inch at the point of alteration, and 

 R = the radius of any wheel. 

 Then the force on the piston is D 2 P in Ibs. 



503. STRENGTH OF RODS WHERE THE STRAIN is WHOLLY TENSILE. There is in 

 every case of this kind a possibility of the strain deviating one-sixth of the diameter 

 of the rod from the axis, and when it does so the resistance is, 



= : 



consequently, D* P = ^-, or a = D 

 For malleable iron /= 17800, consequently, 



VT: 



This rule applies to rods subject to a tensile strain only : such are piston rods 

 of single acting engines ; pump rods. 



