Ai.EXANUEii AND Jackson — Polygons to Generate Diagrams^ ^-c. 11 



on the span shall read sq. root of -^ x 42 x 56, and on it the height at 1\ feet 

 scales 20-14, and squaring we get 405| foot-tons, the sixper-max. stress for 

 the combined loads. 



But, by compelling the load to be numerically equal to the span, we may 

 scale the height at 2| directly as 17'44 on the feet scale; this squared gives 

 the super-max. = 304-15 foot - 1^ tons = 405| foot-tons. 



The product 56 x 42 suggests a third way of scaling the diagram. 

 Using a finer scale for feet, the 56 becomes the span of a longer girder, the 

 ideal loco, regains its original length, and to make the uniform load numeri- 

 cally double the new span, the unit of load must now be three-quarters of 

 a ton, and this again makes the wheels of the loco, return to their original 

 weight, so that the 16-ton wheel returns to 12 tons, the 2| feet returns 

 to 3 feet, and we have the scaled height there on the finer scale to be 23-26, 

 and this squared gives 540-9 foot - f tons = 405f foot-tons. 



The fig. 9 is a diagram of the sq. roots of bending moments due to the 

 42-ton loco, alone, on a 56-foot girder, or of 28 tons of dead load, together 

 with the loco, on a 42-foot girder, according as we use a scale that makes 

 the span 56 feet or 42 feet; in each case the unit of force must be changed 

 so as to make the weight of the loco, numerically equal to the span. 



The 42-foot span is chosen as the shortest non-overhanging girder that 

 will accommodate all the wheels when the 12-ton wheel stands 3 feet to the 

 right of the centre, its most trying position. With any given loco, this 

 shortest span is chosen as a beginning, and the unit of load taken so as to 

 make the load numerically equal to that span. A template can then be 

 prepared for rolling out the stress diagram on a bold scale. Then by shifting 

 the tracing point it will roll the stress diagrams for increasing spans with or 

 without an included dead load. 



Lesser spans formed the subject-matter of our former paper, already 

 referred to ; they can only accommodate a few wheels of the locomotive. 



The tem])late for practically generating the stress diagram clue to a locomotive 

 with or ivithout a dead load. 



We now give, on fig. 10, the template for generating the diagram of 

 square roots of maxima bending moments on a 42-foot girder, due to the 

 transit of a 42-ton loco, with five wheels, among which the load is dis- 

 tributed, and the wheels themselves spaced thus — 



Loads 5 5 11 12 9 = 42 tons. 

 Feet 5 8 10 7 =30 feet. 



The polygon Ahcdef is to be pricked through on cardboard, drawn. 



