Alexander — Maximum Bending -moments on Short Girders. 17 



In calculating the bending-moments for each span of one series, Farr used 

 Culman's original method of drawing a link-polygon for the locomotive 

 standing still, then moving the span about within the polygon, and when in a 

 promising position projecting its ends up to the polygon, which is then closed 

 by an oblique chord, having the span for its horizontal projection. The highest 

 ordinate of this closed polygon is scaled off, and gives a maximum' bending- 

 moment for that particular position of the span placed under the locomotive 



or under some portion of it. Taking a number of those positions, by a sort of 

 trial and error, an approximate value of the maximum of maxima is obtained. 

 As this method is laborious and not quite certain, Farr thought of trying the 

 author's method, which required the use of a parabolic set-square, but found a 

 difficulty in adapting 'it to the continual change of span. 



In the correspondence on Farr's paper tlie author of this paper proposed 

 his method of using circular arcs, and received inquiries as to that method from 

 engineers both at home and in the colonies. 



For the purposes of this paper an ideal locomotive weighing 42 tons is 

 adopted, having its weight divided among live wheels as shown on the under 

 line, while the spacing of the wheels is shown on the upper line, thus — 



5 8 10 7 = 30 feet. 



5 5 11 12 9 = 42 tons. 



In the first instance a span of 42 feet is chosen, as it greatly simplifies the 

 description of the graphical constructions to have the span and total load given 

 by a common number. The centre of gravity of the locomotive falls in the 



[3*] 



