i2o The Rev. Thos. P. Kirkman 



on 



A 2 /-zoned prime can take only one posture when using 

 a zoned polar base-tie ; upon a zonal or epizonal base-tie it 

 can take two postures. 



Every prime can, face-up and face-down, take two 

 postures upon a zoneless polar base-tie, and four postures 

 upon an asymmetric base-tie. 



In order to use correctly the following rules for the 

 posture-number of any prime, it is only necessary to know 

 whether the prime be /-zoned, /-pie, or asymmetrical. 



I. An /-zoned prime, z">l, having, out of a belt, m mar- 

 ginal triangles, can take in a belt, by using all its base-ties, 

 m(in— i)i~ l postures, and no more. 



2. An /-pie prime, />2, having, out of a belt, m marginal 

 triangles, can take in a belt, by using all its base-ties, 

 2in{i7i— i)/ -1 postures, and no more. 



3. An asymmetric prime that has, out of a belt, m mar- 

 ginal triangles, can take in a belt, face-up and face-down, 

 2ui{in—\) postures, and no more. 



This gives us, if ir be the posture-number of a prime, 

 and m the number of its marginal triangles, 



For the 3-zoned A, ;;/ = 3, n = 2 ; 

 „ 3-zoned B, m — 3, 7r = 2 ; 

 ,, 2-zoned Ci, m = 6, tt= 15 ; 

 ,, 3-zoned Di, in — 6, tt= 10 ; 

 ,, i-zoned C 2 , 111 = 6, ^ = 30; 

 „ i-zoned C 3 , m = 6, n = 30 ; 

 ,, i-zoned D 3 , m = 6, it = 30 ; 

 ,, asymmetric D 2 , m — 6, nr = 60. 



The table following gives the posture-factor of every 

 belt, as the product of five posture-numbers : — 



