410 
other cases than that of the funicular polygon were given by 
Rankine in his Applied Mechanics (1857). 
The method was independently applied to a large number of 
cases by Mr W. P. Taylor, a practical draughtsman in the office 
of the well-known contractor Mr J. B. Cochrane. I pointed out 
the reciprocal properties of the diagram in 1864, and in 1870 
showed the relations of this method to Airy’s function of stress 
and other mathematical methods. 
Prof. Fleeming Jenkin has given a number of applications 
of the method to practice, Trans. R. &. E, Vol. xxv. 
Cremona’ has deduced the construction of the reciprocal 
figures from the theory of the two linear components of a wrench. 
Culmann in his Graphische Statuk makes great use of 
diagrams of forces, some of which, however, are not reciprocal. 
M. Maurice Levy in his Statique Graphique (Paris, 1874) 
has treated the whole subject in an elementary and complete 
manner. 
Mr R. H. Bow, C.E., F.R.S.E., in a recent work On the 
Economics of Construction in relation to Framed Structures 
(Spon, 1873), has materially simplified the process of drawing a 
diagram of stress reciprocal to a given frame acted on by any 
system of equilibrating external forces. 
Instead of lettering the joints of the frame as 1s generally 
done, or the pieces of the frame as was my own custom, he 
places a letter in each of the polygonal areas enclosed by the 
pieces of the frame, and also in each of the divisions of the 
surrounding space as separated by the lines of action of the 
external forces. 
When one piece of the frame crosses another, the point of 
intersection is treated as if it were a real joint, and the stresses 
of each of the intersecting are represented twice in the diagram 
of stress, as the opposite sides of the parallelogram which repre- 
1 Te figure reciproche nella statica grafica (Milano, 1872). 
