10 



Proceedings of the Royal Irish Academy. 



closer together in the ratio 3:4. A vertical sealed from the diagram with the 

 scale of feet, when squared, is the bending moment in ft.-l^-tons, and 

 becomes ft.-tons when multiplied by the ratio 4: 3. 



Another way of considering the diagram, fig. S, is to consider the loco, to 

 have been closed up to 42 tons roUing on one wlieel, and the 28 tons of 

 spread load closed up to be 14 tons on one wheel. Those then become 

 56 tons, which is extended into the ideal hea\aer, shorter loco. 



A SHORTER, HEAVIER IDEAL LOCOMOTIVE, EQUIVALENT TO 



A REAL LOC0iV:0TIVE 



Fig. 9. 



A heavy uniform moving load shorter than the span was used to test 

 some long bridges in America. It is the limit of a loco, with equal loads on 

 a great number of wheels, and can in a Like manner absorb a uniform dead 

 load, becoming itself heavier and shorter. 



On fig. 9 a special obHque scale is used to read directly the verticals. 

 It is a standard scale sloped till the height (21) of the semicircle standing 



