XVI 



OF RECIPROCAL DIAGRAMS 



997 



diagram in the other*. Now all this is but the modern rendering 

 of one of Galileo's most famous propositions. In the Dialogue which 

 we have already quoted more tlfan oncef, Sagredo says "It would 

 be a fine thing if one could discover the proper shape to give a solid 

 in order to make it equally resistant at every point, in which case 

 a load placed at the middle would not produce fracture more easily 



I 



Fig. 475. 



than if placed at any other point J." And Gahleo (in the person 

 of Salviati) first puts the problem into its more gen'eral form; and 

 then shews us how, by giving a parabolic outline to our beam, we 

 have its simple and comprehensive solution. It was such teaching 

 as this that led R. A. Millikan to say that "we owe our present-day 

 civilisation to Galileo." 



* The method of constructying reciprocal diagrams, of which one should represent 

 the outlines of a frame and the other the system of forces necessary to keep it 

 in equilibrium, was first indicated in Culmann's Graphische Statik; it was greatly 

 developed soon afterwards by Macquorn Rankine (Phil. Mag. Feb, 1864, and 

 Applied Mechanics, passim), to whom the application of the principle to engineering 

 practice is mainly due. See also Fleeming Jenkin, On the practical application 

 of reciprocal figures to the calculation of strains in framework, Trans. R.S.E. 

 XXV, pp. 441^48, 1869; and Clerk Maxwell, ibid, xxvi, p. 9, 1870, and Phil. Mag. 

 April 1864. 



t Dialogues concerning Two New Sciences (1638); Crew and Salvio's translation 

 p. 140 seq. 



X As in the great case of the Eiffel Tower, supra, p. 29. 



