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XXIX.— AN EXPEEIMENTAL METHOD OF DETEBMINING 

 MOMENTS OF INEETIA. By GEKALD STONEY, B.A. 



[Read, December 15, 1886.] 



Of the integrals which are found to be useful to engineers, pro- 

 bably that which is most frequently required is the moment of 

 inertia of a plane round an axis in the plane — 



where y is the distance of an element of area da from the axis 

 round which the moment of inertia is to be taken. On the value 

 of this moment of inertia depends, among other things, the calcu- 

 lation of the transverse strength and deflection of beams ; of the 

 strength of long pillars ; of the distribution of the pressure on the 

 foundations of retaining walls and abutments, &c. In all such 

 problems it is necessary to determine the moment of inertia of the 

 cross-section ; and where this is of complicated form the calculation 

 is often difficult, so that it would be a boon to engineers to have 

 some simple experimental method of arriving at the result. Even 

 where the moment of inertia is determined by calculation, it is 

 often useful to have an experimental method of checking the cor- 

 rectness of the work. 



The following method of determining the moment of inertia 

 occurred to the author when engaged in employing the graphical 

 method of investigating the distribution of pressure along the over- 

 hung bearing of a shaft. In this method ordinates being erected 

 proportional to the pressures at various points along the bearing, the 

 centre of gravity of the figure so formed is a point on the line 

 of pressure. In the analytical method the same result would be 

 reached by the help of a moment of inertia, and the comparison of 

 these two methods suggested the following experimental way of 

 determining moments of inertia : — 



Cut from the pillar, of the section of which we want to find 

 the moment of inertia, or from a model of it, a parallel slice S, 

 between two cross-sections, and a wedge W between a cross-section 



