40 



Proceedings of the Royal Irish Academy. 



Appendix. 



On fig. 11 is shown the manne;r of constructing a right parabolic segment. It 

 shows the half -base OB divided into sis equal parts and the upright BH, which 

 is equal to the height of the segment, also divided into sis equal parts. The 

 vectors from the vertex A to the subdividing points on BH cut off the heights 

 P,, Pi, etc., on the uprights from the corresponding subdividing points on the 

 half -base. The manner of drawing a tangent is also shown ; and the tangent 

 PiE is seen to bisect AB in F, so that the vertical height of E above P^ is twice 



Fig. 11. 



the height of A. As the curvature is sharp near the vertex, the divisions near 

 the centre on the half-base should be further subdivided to give intermediate 

 points on the curve near the vertex. 



An analytical investigation and rules for the maximum bending-moments 

 on a girder, due to the transit of a locomotive, were given by the author for the 

 first time in E-ngineenng of -January 10th and -July 25th, 1879, in response to 

 queries asking for such rules ia Du Bois' treatise on Graphic Statics, prior 

 to 1877. In Du Bois' later treatise, Straiti-s in Framed Girders, 188-3, he 

 quoted them at great length, so that the author has reason to believe that his 

 was the first exact solution of this problem. 



