108 



KANSAS ACADEMY OF SCIENCE. 



Besides the sums in the margin, obtained by addition of the lines, col- 

 umns, and diagonals, we obtain the following sums from this square: The 

 four corners, K, Mn, Cu and Br equal 237.7; the central square, Cr, Ti, Ge and 

 Zn equal 237.7; parallelograms, Se, Fe, Co and Ca equal 234.3; Ga, As, Sc 

 and V equal 239.4; diagonal quadrats, Ga, Fe, V and Co equal 235.8; As, Se, 

 Sc and Ca equal 238; rhombs, K, Ge, Ti and Br equal 239.4; Mn, Zn, Cr and 

 Cu equal 236; rhomboids, K, Sc, As and Br equal 238.1, etc., etc. In all of 

 these sums the greatest is 239.7, and the least is 233.6, a difference of 6.1, 

 equal to 2i/^ per cent., or 1^/4 per cent, on each side of a fixed mean. 



By rejecting fractions and bringing Ca within the limit of variation and 

 changing slightly the elements in the third column, we obtain the following: 



237 



237 



237 



237 



237 



237 



237 



237 



237 



237 



Here it may be seen that, though the atomic weights are not an arith- 

 metical series, all sums, taken as before, are equal, showing that the series is 

 harmonic. 



A similar result is obtainable from a similar placing of the atomic weights 

 of the Rubidium hecdecade, thus: 



Rubidium Hecdecade. 



Rb 



85.5 



Te VI 



125 



Rh IV 



103 



Ag I 



107.9 



421.4 



In IlllSb 

 113.7 



V 



120 



Mo VI 



96.1 



Sn IV 



117.8 



Yt III 

 89.1 



416.7 



Zr IV 



90.6 



Cd II 



112 



Cb V 



94 



416.6 



Ru VII 



101.6 



Pel IV 



106.6 



Sr II 



87.6 



I VII 



126.9 



417.9 



420.8 



418.3 



420.4 



417.9 



422.7 420.5 



