Mr. W. J. M. Rankino on Barycentric Perspective. 387 



from other important consequences, it would certainly be an 

 interesting and beautiful result if, from a thing apparently so 

 remote as the velocity of sound, we could deduce a priori the fact 

 which has been now illustrated by nearly five years' experiments — - 

 that the elementary gases have no sensible radiative power, while 

 the compound gases are endowed with this power in very differ- 

 ent degrees. 



Royal Institution, 

 October 24, 1863. 



LVI. On the Application of Barycentric Perspective to the Trans- 

 formation of Structures. By W. J. Macqtjorn Rankine, 

 C.E., LL.D., F.B.SS.L. §■ £.* 



1. riiHIS paper contains the substance of some remarks which 

 J- I made at the recent Meeting of the British Association, 

 on the elegant investigation by Professor Sylvester of the princi- 

 ples of Barycentric Perspective and Homalographic Projection. 



2. In the r Proceedings of the Royal Society ' for the 6th of 

 March 1856, I published a theorem called that of " the Trans- 

 formation of Structures/' which may be briefly expressed as 

 follows : — 



If a structure of a given figure he balanced and stable under 

 forces represented by given lines, then will any structure whose 

 figure is a parallel projection of the original figure be balanced and 

 stable under forces represented by the corresponding projections of 

 the lines representing the original forces. 



3. By a parallel projection of a figure is meant a figure derived 

 from the original figure by altering the coordinates in uniform 

 proportions, or by substituting oblique for rectangular coordi- 

 nates ; and it is called parallel because to every pair of equal 

 and parallel lines in the original figure there correspond a pair of 

 equal and parallel lines in the transformed figure. For example, 

 every orthographic projection of a plane figure is a parallel pro- 

 jection ; all ellipsoids are parallel projections of each other and 

 of a sphere, &c. 



4. That theorem was applied in ' A Manual of Applied Me- 

 chanics ' to the deduction of the figures of a skew arch and of a 

 ramping arch from that of a common arch, of an equilibrated rib 

 from a common catenary, of arches for supporting earth from 

 arches for supporting the pressure of a liquid, &c. 



5. Its applications, however, were limited by the condition of 

 parallel projection ; and there were consequently many conceiv- 

 able transformations of structures to which it could not be 

 applied. 



* Communicated by the Author. 



