On the Difference between Active and Ordinary Oxygen. 261 

 terminate, or impossible except in particular cases, is 



e = 3s-5. 



This condition is sufficient to determine the possibility of finding 

 a system of forces along the edges which will keep the summits 

 in equilibrium ; but it is manifest that the mechanical problem 

 may be solved, though the reciprocal figure cannot be constructed 

 owing to the condition of all the sides of a face lying in a plane 

 not being fulfilled, or owing to a face belonging to more than 

 two cells. Hence the mechanical interest of reciprocal figures 

 in space rapidly diminishes with their complexity. 



Diagrams of forces in which the forces are represented by 

 lines may be always constructed in space as well as in a plane, 

 but in general some of the lines must be repeated. 



Thus in the figure of five points, each point is the meeting 

 place of four lines. The forces in these lines may be represented 

 by five gauche quadrilaterals (that is, quadrilaterals not in one 

 plane) ; and one of these being chosen, the other four may be 

 applied to its sides and to each other so as to form five sides of a 

 gauche hexahedron. The sixth side, that opposite the original 

 quadrilateral, will be a parallelogram, the opposite sides of which 

 are repetitions of the same line. 



We have thus a complete but redundant diagram of forces 

 consisting of eight points joined by twelve lines, two pairs of the 

 lines being repetitions. This is a more convenient though less 

 elegant construction of a diagram of forces, and it never becomes 

 geometrically impossible as long as the problem is mechanically 

 possible, however complicated the original figure may be. 



XL VI. On the Difference between Active and Ordinary Oxygen. 

 By R,. Clausius*. 



IN a paper communicated in March 1858, " On the Nature of 

 Ozone^fj I g ave an explanation of this modification of oxygen, 

 which stood in connexion with the views I had shortly before 

 published as to the internal condition of bodies, especially of 

 gases. Our knowledge of ozone was at that time much less than 

 now. The antithesis between ozone and antozone had not been 

 discovered. It was merely known that oxygen by various pro- 

 cesses could be brought into an excited condition, in which its 

 oxidizing action is more energetic than that of ordinary oxygen ; 



* Translated from vol. viii. of the Vierteljahrschrift der nalurforschen- 

 den Gesellschaft hi Zurich. Read October 18, 1863. 

 t Phil. Mag. S. 4. vol. xvi. p. 45. 



