420 BEPORT— 1892. 



the receut large span-roofs of large stations and exhibitions, the gigantic 

 floating machines of our navy, the St. Gothard, Mont Cenis, and other 

 tunnels, no one will be found to dispute the fact that the unknown in 

 practical science is greater than the known. Thus we have Poncelet 

 saying, in words which are quoted by Culmann in the first edition of bis 

 work, ' Die Grapbische Statik,' ' What are we to do with all those 

 theories which have arisen in the various branches of engineering that 

 are capable of scientific treatment ; which theories, though enabling us 

 to solve some certain problems, at a great expenditure of time and 

 trouble, are far too tedious to be applied to any and every case occurring 

 in practice, and, for the same reason, are not even suitable as a basis on 

 which to work out ready-calculated tables ? ' and proceeds further to 

 remark : ' This question, no doubt, was in Poncelet's mind when he 

 endeavoured to invent geometrical solutions for the various problems 

 presented in engineering. 



' And, in fact, the constructing engineer will give preference to geo- 

 metrical solutions wherever an accuracy of results up to three decimals 

 (one-thousandth), which can be perfectly well obtained, is sufficient ; for 

 his drawing-instruments are always at hand. Drawing is his habitual 

 expression of thought — " his language," and, thanks to his topographical 

 and geodetical training, he is more accustomed to judge as to the exact- 

 ness of sections, and to define lines and points with great precision, than 

 the architect or mechanician.' 



' Poncelet's solutions were, invariably, mere conversions of previously 

 evolved analytical terms. No doubt Poncelet himself felt that this was 

 a roundabout way, and that a geometrical construction will much less 

 readily impress itself on the mind if, in applying the same, it is necessary 

 to bear in mind an analytically developed formula, the derivation of 

 which, probably, has meanwhile slipped our memory, than if the configu- 

 ration of lines presented by the problem does in itself form the basis 

 from which tbe solution may be evolved on purely geometrical principles. 

 It was for this reason, probably, that he devoted himself industriously to 

 the study of geometry — as if filled with a presentiment of the great use 

 which the study might afford him. But it was in exceptional instances 

 only that he applied geometry for the solution of statical problems in the 

 architectural branch, while otherwise he invariably preferred analytical 

 solutions, which he subsequently " converted." ' 



These remarks of Culmann have been quoted at length because of 

 the prominent position which he occupies as an exponent and advocate 

 of the purely geometrical method of treating graphical problems, and are 

 well worthy of careful consideration. 



They incidentally contrast the two lines of operation, viz. : — 

 a. The analytical method ; 

 h. The geometrical method ; 

 upon one or other, or a combination of which, workers in diflPerent coun- 

 tries, approaching from whatever point of view, have attempted the solu- 

 tion of such problems. 



It may at once be remarked that the allusions to the geometrical 

 treatment of problems refer entirely to the representation of forces by 

 lines, and to one branch of such work, viz., statical problems in structures. 

 Hereafter other problems, such as those of dynamics and the representa- 

 tion of velocity, will be dealt with, but for the present the argument 

 refers solely to that branch of the subject known as graphic statics. 



