34 Proceedings of the Royal Irish A cailenvj. 



end, or from both ends of the locomotive, and taking off corresponding 

 segments from the original span. In some cases observe that the 11-ton 

 driving-wheel becomes the rv.ling-whccl. 



To find the rivaximum of maxima hending-momenis loherc there is a given uniform 

 load and the locomotive. 



Eetuming to fig. 5, suppose that on the 42 -foot span AB there is 16 tx)ns 

 uniformly spread, which would give a parabolic locus the same as that for 

 8 tons rolling on one wheel, the height of the locus being \ v. 8 tons x 42 feet 

 or 84-foot tons. To allow for this it is only necessary to adopt a finer scale 

 so that the height of the parabolic segment in fig. 5 shall measure 441 + 84 

 foot-tons instead of 441. Adopting this finer scale for verticals, it becomes 

 necessary to lower the chord EF down to the position shown hatched, that is, 

 lower in the ratio of 42 to 50, just as we already noted when we passed from 

 the 42-foot span to a 50-foot span. So that bisecting mn at the black spot, 

 measuring the vertical height to the parabola on the original vertical scale, 

 we get 288'6, but multiplying by the ratio 50 to 42 it becomes 343'56 foot- 

 tons. But in this case the original horizontal scale still obtains, so that the 

 horizontal distance of the black spot from the middle point of AB is only 

 2'52 feet In the former case, where mn was the oblique base for a 50-foot 

 span bearing the locomotive only, this 2*52 had to be multiplied by the ratio 

 50 to 42, which made a product 3 feet, as it must, for on any span that bears 

 the locomotive only, 3 feet to the right of the middle is the most critical point, 

 for then the ruling-wheel, 12 tons, and the centre of gravity of the locomotive 

 are equidistant from the two abutments, or are each 3 feet from the middle 

 of the span. But in the case we are now considering, the niling-wheel, 

 12 tons, must stand 2"52 feet to the right of the centre ; and it will be foimd 

 that the centre of gravity, not of the locomotive but of the load made up 

 of the 16 tons spread uniformly, together with that of the locomotive, is 

 2'52 feet to the left of the middle of the span. 



The KcsEMATicAi Model axd A>r Ideal LocoMoxmE which d-xludes the 



Spread Load. 



By J. T. .Jackson', jla.!.. Assistant to the Professor of Civil Engineering 



in the University of Dublin. 



The sunilarity between the above construction and that described on p. 25 

 at once suggests that it must be possible to devise an ideal locomotive which 

 shall produce the same maximum bending-moments at every point of the span 

 as are actually due to the combined effects of the real locomotive and the 



