Arithmetical Relations between the Atomic Weights. 277 
ART. XXX VL—On the Arithmetical Relations between the Atomic 
Weights ; by M. D. C. Hopess. 
THE group of elements, fluorine, chlorine, bromine and 
iodine, have, as their atomic weights, 19, 35, 5, 80 and 127 
respectively. "These numbers form a series, in which the dif- 
ference between the succeeding terms is at first 16° 5, then 44°, 
and finally 47. The following groups of elements give similar 
series, 
Li=7 
=—12 O—16 —14 Na=23 Mg=24 
Si=28 S—32 P=31 K=39 Ca=40 
Se—79°4 As=—75 Ru=—85°5) Ss Sr —=87°5 
Te=128 Sb==122 Cs=2133 Ba=137 
The grouping of some of the above elements may be objected 
to, but there isno great change from that generally accepted. 
Tha group of such elements as copper, silver, cadmium, mer- 
cury, lead and bismuth is taken, the series of atomic weights 
gives a similar, but somewhat different result; in this case 
each term of the series is composed of several members. 
Cu=63°4 (Zn==65'2) The new difference, 96+, for the 
Ag=108 Cd=112 higher terms occurs. 
Hg=200 Pb=207 Bi=210 
Zine may be added to the first term, and corresponds to the 
second member of the second term. The lower terms are here 
wanting. Similar to these are the following: 
Ru=104°4 Rh=104*4 Pd=107 
Au=196°7 Pt=—197°4 N=197°4 Os=199°4 
Many = the remaining elements may be placed in the follow- 
ing seri 
eeeaie Ti —50 In=75'8 Y=68 WV =61'3 
Al=27°4 Nb=94 U=120 E112 Mo=96 
Th=231 Ta—182 =204 W184 
hromium, 
Rete, cerium, Heese aid ium, hadi n and boron. 
The position of these may be better seen in the pasexed table, 
in which all the elements, with ae exception of hydrogen, are 
arranged on lines, the succeeding elements in the same line dif- 
fering in their atomic weights by a few units or parts of uni 
and those in different lines from the corresponding elements i 
the preceding or following line by one of the differences 
mentioned. 
