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belongs by +, the other by — . The following list then indicates on 

 which side of each of the six spheres the successive tetrahedra I, 

 II, etc. are situated and by which they are limited. For the non- 

 limiting spheres the sign has been placed in brackets. 



It is clear that the tetrahedra I and VII are opposite to each 

 other, likewise II and VIII, III and IX, etc., whilst the tetrahedron 

 I again follows tetrahedron XII. 



Thus the whole range consists of 12 tetrahedra which are two by 

 two opposite to each other, in contrast to what we found in the three- 

 dimensional space, where two ranges of spherical triangles are formed 

 of which one contains the triangles opposite to those of the other. 



7. Between the volumes of each pair of tetrahedra belonging to 

 the range exists a simple relation. 



If we call Vi the volume of the first tetrahedron then the relation: 



dVj = £ a,, da i4 -f- h a l4 da it + £ a 84 da lt 



holds for each variation of the tetrahedron remaining doublerectan- 

 gular (thus a iv « 14 and « 14 not changing). 

 Likewise 



dV n = i (i*r — a l4 ) da it -f £ ftjj — a l4 ) da lt — £ (£rr — « 84 ) da xt . 



