G. Hinrichs on Spectral Lines. _ 365 
If the atom has a quadratic base, a=b, we have 
Aes at ce. 
If provided with one or several pyramidal additions, we hav: 
= @.0 : 
_ Elements will of course show similar properties when of sim- 
ilar form (a theorem which I have demonstrated in my notes 
many years ago—and which is closely allied to the well known 
properties of isomorphous bodies). hus prismatic atoms will, 
when they have the same base a.b and only differ in length c=n, 
form a natural group 
Aas x ab, 
or when quadratic eh CE, 
or when with pyramidal additions, 
=k-+n.ab, 
or A=k-+n.a?, ete. 
We shall here refer only to those natural groups of elements 
that have been treated of in the preceding, viz: the chlorine 
group, the oxygen group, the group of the alkaline earths and 
the group of the alkalies 
Oxygen group ; quadratic. Formula A =n.4?. 
7% 
A Cale. Obs. Error, 
Oxygen, 1 144— 16 16 0-0 
Sulphur, 2 24% == 82 32 0-0 
Selenium, 5 § 44 =- 80 80 0-0 
Tellurium, 8 8:42 — 128 128 0-0 
Chlorine group; quadratic. Formula A =7.3?+1. 
n A Calc. Obs. Error. 
Fluorine, 2 232-+1=— 19 19 0-0 
Chlorine, 4 4:32 —1= 35 855 =f 5 
Bromine, 9 9°37 —1= 80 80 0:0 
odine, 14 14324+1=127— 127 0-0 
Alkaline group ; quadratic with pyramid. A=7+7n.4?. 
n Ae Obs. Error, 
Lithium, 0 7 7 0-0 
ium, 1 7+ 1.47% = 238 23 0-0 
Potassium, 2 7+2.47= 39 39 0-0 
Rubidium, 5 7+5.427= 87 854 —16 
zesium, 8 748.42=135 1330 —2-0 
Alkaline-earths group ; quadratic. A=n.2?. 
n As Cole Obs. Error. 
Magnesitim, 3 322 = 12 12 0-0 
Calcium, 5 5°22 = 20 20 0-0 
Strontium, 11 11:22 = 44 43-8 —2 
Barium, 17 17:22 = 68 68°5 +5. 
