DISCUSSION. 145 



tension, but its efficiency as ties is greatly discounted by the 

 difficulty and cost of making joints and connections to take up 

 tensile strength, a proportion of the value of wrought iron is lost 

 in this way but a much greater loss is made on wood. An 

 example is given in the paper of the most common form of small 

 span railway viaducts used in New South Wales, where the span 

 is ten feet between the piers, crossed by two beams each, for single 

 line, 12" x 12" on which are laid ties or sleepers 8" x 8", the dis- 

 tance between the beams is 7 ft. and between the centre of rails 

 5 feet ; thus the weight is not brought directly over the beams 

 but on a point 1 foot inside thereof. This induces a bending 

 moment of 60 inch-tons, but the resistance of the tie is shown to 

 be 533 inch-tons, therefore there is a factor of safety of 8'8. In 

 Victoria the beams are placed directly under the rail, therefore 

 no bending moment at all is produced on the cross ties, and an 

 ordinary 9" x 4" sleeper spaced 3 feet apart answers the purpose. 

 This was the first type of light lines made in 1872-3-4, at about 

 .£2,000 per mile ; a case of derailment with such a type would be 

 fatal, therefore later on the ties were planked with 4" hardwood 

 decking and ballasted, still the rails were placed over the beams, 

 without cause for complaint that I have heard of ; such a plan 

 makes for economy in the cross timbers, though probably the New 

 South Wales method gives a more elastic road. The paper gives 

 formulae for transverse resistance of beams as well as for deter- 

 mining deflection in their simplest forms and of great value to 



students, the former viz : — -g- = — — - is recognizable as identical 

 withProf. Rankine'si¥° = ^= N f b h* where N = J and /the 

 co-efficient representing the strength of any given timber. As 

 there are round beams in some of the structures illustrated by the 

 plates it may be desirable to supplement the above formula, which 

 is for rectangular beams with the following modification to adapt 



it for round beams, as given by Hankine —~- — -~~ for a distributed 



load, or -^- = -^J- for a central load. The paper not only furnishes 



the formulae but gives practical examples worked out so as to 

 render the information accessible to aspirants for knowledge on 

 timber bridge building. Indeed this paper with copious examples 

 of cases and illustrated by the drawings so liberally allowed to be 

 published by the Commissioner for E-oads and Bridges and the 

 Engineer for Bridges, places before young engineers (and old 

 engineers for that matter) a means of fitting themselves as muni- 

 cipal engineers, such as would have been most acceptable to me 

 and my contemporaries when studying for the profession, and 

 Professor Warren is entitled to the hearty thanks of this Society 

 and the community generally for placing within reach of students 

 the means of learning to design public structures, as well also as 



J— September 3, 1890. 



