Struts and Tie-Rods with Lateral Loads. 269 



where D = 1, 



~ \n i2n+l\v) * ^ |p| p-l {| 2n + l-i> } 2 \v/ < 



In the particular case of the screens supplied from the 

 Royal Observatory, Greenwich, 



2 2 



^=7 : 



and hence, 



when /3R 4 = j, I = 7r 2 R 4 x 0*0256 x 0*9811 ; 



„ /3R 4 =|, I = tt 2 R 4 x 0-0256x0-9262; 



the corresponding values of the intensity in the case of 

 the full aperture being tt 2 R 4 x 0*9464 and tt 2 R 4 x 0-8003 

 respectively. 



XXVII. Struts and Tie-Rods with Lateral Loads. 

 By Professor John Perry, D.Sc, F.R.S.* 



I THINK that this subject has not yet been taken up 

 scientifically; yet it is very important. The practical 

 treatment of the whole subject of struts is in a very unsatis- 

 factory condition ; and it is mainly due to this that, of two 

 bridges designed for the same spans and loads, by two 

 engineers, one has sometimes more than twice the weight of 

 the other ; and in all probability the one of least weight is in 

 some parts very much too strong, and in other parts has very 

 little strength in excess of what is absolutely necessary. 



It will be in the recollection of some of the members pre- 

 sent that Professor Ayrton and I, in 1886, showed why 

 experiment always gave a breaking-load for a strut which was 

 less than that which results from Euler^s theory. 



A strut is a prismatic body of homogeneous material sub- 

 jected to equal and opposite crushing forces at its ends. 

 Taking its length, 21 ; the least moment of inertia of its cross 

 section about a straight line through its centre of area, I ; 

 Young's modulus of elasticity, E ; f c the compressive stress 

 which the material will stand : then for a strut hinged at its; 

 ends (that is, if the resultant force at each end acts at the 



* Communicated by the Physical Society: read December 4, 1891, 

 Phil. Mag. S. 5. Vol. 33. No. 202. March 1892. U 



