( 696 ) 



(2A:+1) (I) f\j (1) ri) (l) 



/, ={k^4),I, +(^f?'.)./2 +{A-f2),i3 +(^+l)./-'i+(^)./-iv.(3) 

 which two relations in connection with the ratios of volunie lead 

 back to the identities 



^^ = (A: + 3), + 11 {k f 2), + 11 (^ + 1), -f {k), j 



(2^+ir = (^ + 4), + 76a:+3), f 230(^ + 2), + 76(^ + 1), + (A), (' 



From (1), (2), (3) we can now easily deduce all results. To prove 



this we mention for the two cases, in which the block consists of 



an even or of an odd number of measure-polytO|)es, the composition 



of the central section in the form 



(2k) 5 I (2) (2) 



/3 =— F (23P-ll)2'i -^(23F-^1)T2 + 



(2) (2) ) 



+ (23A;' — 1) 3'_2 + (23F -f 11) T_i , 



(2it+l) 5 1 / (1) (i)\ 



Is =— )t(^'+l) (23F + 23^— 10)ij, +/_ij + 



12 



+ (iSF + 23/: -f 8) ( / 2^^ + I-l) \ 



^ (115F + 230P + 185F 4- 70Z; + 12) /g^. 



1 u 



5. We shall now consider in the space Spn the net of measure- 



(2) 



poljiopes Mn and shall discuss the transition sections and the inter- 

 mediary forms situated in the middle between two adjacent transition 

 sections furnished by spaces Spn—\ perpendicular to a diagonal. We 

 then tind 



2w 



Mn 



0, 



— Mn = 



In 



2n-2. 

 1 3 



= /«= s 



(0 



(1) 1 (3) 



2n-2 2?i-2y 3 



5 (2) 

 2w " V 2n-2 ' 2n-2 



for n even 



(1) 3 (5) 



5 



w-1 (2.) /n-3 n-\\ (I) w-3 («-,) 

 Zn \ln-L Zn-ó J n-\ 



for n odd 



1 (2) 



n-2 n 

 2n-2 ' 2^ 



= 7 



(1) M-2 (n) 



1 (2) 



n 



0, 



1 



w-1 

 1 2 



(2) 



(2) 



2 (1) 



/* Vn-l n-\ 



2 ' 



M Vw-i w-1/ Ö 



i("+i; 



= 5 



for 71 even 



1 ^^(2) /n-2 n 



-Mn H > 



2 V'^^«-2 2w-2 

 for n odd 



M-1 (2) / n-3 n-\ 



Mn = , 



2n V 2n-2 2n-2 



(2) n-2 » 

 n 



(2) n-3 (n-i: 

 n-l 



