28 POSNJAK AND MERWIN: BUCHER CYANIDE PROCESS 



be considered a direction in the space corresponding to + 1 , 

 and a direction in one of the planes in which rotation occurs. If 

 the plane is not perpendicular to the direction, there is one line 

 in the plane which is, and only one. The rotation will turn this 

 line into another direction in that plane, and, consequently, will 

 change a right angle into some other angle; hence, the plane 

 must be perpendicular to the direction. 



In a similar way, consider two planes in which there is rota- 

 tion. Unless the planes are perpendicular, there is just one line 

 in one of the planes which is perpendicular to the other plane. 

 The operation of the rotation in the two planes will throw this 

 line into some other, and again angles will be changed, which is 

 impossible in a rotation; and the planes must, therefore, be per- 

 pendicular. It therefore follows that the fixed space and space 

 in which directions are reversed and the various planes in which 

 there are rotations are all mutually perpendicular in the sense 

 of complete perpendicularity.^ 



This brings the discussion to an end by the determination of 

 the fundamental existence-theorem for rotations in generalized 

 space. It is the theorem which Moore establishes prior to subse- 

 quent work. The method of treating rotations in ordinary space 

 which was given by Gibbs in his lectures, and may be found in 

 the Vector Ajtalysis,^ is dependent upon the knowledge that 

 in three dimensions a rotation has a fixed axis. Much of the 

 subsequent work, however, could, I beheve, be carried over to 

 higher dimensions in much the same way as the simpler case was 

 treated by Gibbs. 



CHEMISTRY. — Note on the Bucher cyanide process for the 

 fixation of nitrogen. EuGEN Posnjak and H. E. Merwin, 

 Geophysical Laboratory, Carnegie Institution of Washington. 



In the course of an investigation of the Bucher cyanide 

 process^ undertaken by this Laboratory at the request of the 



5 The treatment may, of course, be carried through analytically by taking a 

 general vector p and its transform <t>p calculated from the canonical form, and by 

 expressing the conditions on the coefficients of 5 which require constancy of length 

 and invariance of angle. 



* Wilson, Edwin B. Vector Analysis (Gibbs). New York, Charles Scribner's 

 Sons, 1901. See pp. 334-347- 



1 Journ. Ind. Eng. Chem. 9: 233. 19 17. 



