REED — RELATION BETWEEN VALENCE & ATOMIC WEIGHT. 667 



On the next pair of lines we find again the same vibratory 

 -movement. See Fig. 4. 



The peculiar position occupied by Sz', P, S, and C/, at the 

 posititive end of the first pair of lines and the negative end of the 

 second, shows that i/ie second pair is only a continuation of the 

 Jirst through a vertical displacement of eight units of valence^ 

 corresponding to an increase of sixteen units of atomic weight. 



This points to the conclusion that saturation-valence is an 

 equicrescent rotary function of atomic weight. 



To represent this idea graphically we must locate the points 

 on the surface of a cylinder instead of a plane. 



Let 0,0.', Fig. 5, be any cylinder referred to the rectangular 

 axes, XX', Y Y', and Z Z' (its own axis), and having the origin 

 at O. 



Let R be the radius of the cylinder, and MN any line drawn 

 around the cylinder so that the angle MF2'i = a, a constant ; z^z\ 

 being the element of the cylinder which passes through any point, 

 P, of the line MN. Then will the line MN be a helix, and 



~ tan « — R(^4-^) - . . . (3). 



its general equation when referred to any element, ^-j^^'i, of the 

 cylinder and the circumference ( R = ^/ a -'-|-J/':, z = 6) of the cylin- 

 der lying in the plane, X X', Y Y' ; the intersection, Oj, being the 

 origin ; 6 the angular departure of any point, P', of the line MN 

 measured upward from the element, ZxZ{., as origin of the arc ; and 

 <5, the angular departure of the point of intersection, <5i, of the 

 line MN with the plane XX', YY'. 



Let z be the atomic weight of any chemical element ; R^ its 

 saturation-valence X K'- Assume R = 4r- and tan a = 5. Then 

 \{ b = b^ = — — "- , we have from (2) 



^tan« = R^— JI? - - - (a). 



This is the equation of the artiads. 

 If ^ ^ ^. = — ^^- , we have 



' 8 



z tan « = R^ — tan^tt - - - (b). 



This is the equation of the perissads. See PI. IL 



