666 TRANS. ST. LOUIS ACAD. SCIENCE. 



PAnT III. 



The Graphical Representation of the Relation between 

 Atomic Weight and Valence. 



Let Z Z' and Y Y', Plate I., be any two rectanf^ular axes with 

 the origin at O. Let z represent the atomic weight and y the 

 valence XlO of any element. Locate a point in the plane for the 

 maximum, minimum, and characteristic valence of each element. 



Nearly all of these points are found to lie on a double series of 

 parallel lines, the successive pairs of which are separated by equal 

 distances ; and the general equation for any of the lines is 



y^S^-\-b, (i). 



The values of b .for the successive lines are almost exactly as 



follows : 



Ditr. 



First line 3, r= -}- 55 



Second " = — 20 75 



Third " = — 25 5 



Fourth '• z=. — 100 75 



Fifth " = — 105 5 



Sixth " = — 180 75 



Seventh " z=z — 185 5 



If we accept Prout's hypothesis, these values are exact ; and 

 the actual deviation does not exceed, in the mean, .035 of the unit 

 in the first seventeen elements, if we exclude C/, whose deviation 

 will be accounted for later. If we include C/, the mean deviation 

 is .056. The algebraic sum of the deviations of these elements 

 divided by the number of elements (17) is, including C/, .021 ; 

 excluding C/, .0051. 



These deviations are so small that they cannot, except in C/ and 

 Sz*, be represented graphically without using a much larger scale. 



At Sc, however, we find an abrupt termination of what ap- 

 pears to be a rigid law for the first seventeen elements. 



If we construct a complete series of lines according to the law 

 indicated on the diagram by assigning to b in equation (i) succes- 

 sively, values which diminish by 75 and 5 alternately, we shall 

 find that most of the elements fall on or very near one of these 

 lines. 



What is the meaning of these singular coincidences, and par- 

 ticularly the regular oscillation from one line to the opposite as 

 we pass from O to QP. This oscillation is shown in Fig. 3. 



