280 
CHEMISTRY: HARKINS AND WILSON 
elements, but in addition, after this has been appHed it is seen that 
there is a great regularity in the number of hydrogen atoms, H3, which 
must be included to give the atomic weights of the elements of odd 
atomic number. 
The table gives an explanation of the fact that the atomic weight of 
argon is higher than that of potassium while its atomic number is lower. 
This is seen to be due to the general tendency for the increment between 
the third and fourth series to take the value 5He, and in this sense it 
is the potassium and calcium which are irregular in behavior, and not 
the argon. In this part of the table there is seen to be a tendency to 
add 2He instead of IHe for one step between elements of even atomic 
number. 
Symbolic Representation of the Atomic Weights According to the Helium System Derived from 
THE Behavior of the Radioactive Elements in their Alpha Disintegrations 
H DETD.= 1.0078 
group 
0 
1 
2 
3 
4 
5 
6 
7 
8 
Series 2 
He 
Li 
Be 
B 
C 
N 
0 
F 
He 
He+Hs 
2He+H 
2 He+Ha 
3 He 
3 He+2 H 
4 He 
4 He+Hs 
Calc. 
7. 
9. 
11. 
12. 
14. 
16. 
19. 
Detd. 
4. 
6.94 
9.1 
11. 
12. 
14.01 
16. 
19. 
Series 3 
Ne 
Na 
Mg 
Al 
Si 
P 
S 
CI 
5 He 
5 He+H3 
6 He 
6 He+Hs 
7 He 
7 He+Hs 
8 He 
8 He+Hs 
Calc. 
20. 
23. 
24. 
27. 
28. 
31. 
32. 
35. 
Detd. 
20. 
23. 
24.3 
27.1 
28.3 
31.02 
32.07 
35.46 
Series 4, 
A 
K 
Ca 
Sc 
Ti 
V 
Cr 
Mn 
Fe 
Co 
10 He 
9 He+Hs 
10 He 
11 He 
12 He 
12 He+Hs 
13 He 
13 He+Ha 
14 He 
14 He+Hs 
Calc. 
40. 
39. 
40. 
44. 
48. 
51. 
52. 
55. 
56. 
59. 
Detd. 
39.88 
39.1 
40.07 
44.1 
48.1 
51. 
52. 
54.93 
55.84 
58.97 
Increment from series 2 to series 3 = 4 He. 
Increment from series 3 to series 4 = 5 He. (For K and Ca = 4 He.) 
Increment from series 4 to series 5 = 6 He. 
If a weight of 4 is added for each increase of 2 in the atomic num- 
ber, then the average increase of the atomic weight per atomic number 
should be 2, and that this is in accord with the facts is shown by the 
atomic weights of neon and calcium. These elements have the atomic 
numbers 10 and 20, and the atomic weights, 10 X 2 = 20, and 20 X 
2 = 40. The equation^ which gives the atomic weights of the lighter 
elements is W = 2/^ + J + 2 ("~ l)"~S where n is the atomic number. 
In order to include the heavier elements it is necessary to insert an- 
other term, the meaning of which will be considered in a later paper, to ac- 
count for the tendency of the increment of weight to become greater as the 
atomic weight increases, as follows: W = 2(w + w0+i + i(~ 1)''"^ 
That no system can explain the atomic weights of the heavier ele- 
ments, unless account is taken of the fact that different series of ele- 
