282 Dr. Marshall Watts on the 
the difference is a linear function of the logarithm of the 
atomic weight, and their formula 
atomic weight =log—!(0°2005 + 0°5997 log x), 
where « denotes the differenee between the lines of the 
doublet, are equivalent to the assertion that in the group 
magnesium, calcium, strontium, and barium, the difference 
is pr oportional to the atomic weight raised to the power 5/3. 
Any two elements are sufficient for the calculation of such 
Taking the differences as given by Runge and 
viz. 91-7 for Mg, 223-for Ca, "801 for Sr, 1691 for 
Ba, and 4858 for Ra, we find the following formulee :— 
a formula. 
Precht, 
From Mg and Ca at. wt.=log—1(0-28002+0°56088 log 2’) whence Ra=222°7 
Me ,, Sr ,,. =log~'(0-22788+-0:59051llogz) ,,  Ra=2539 
gh ns Dis yet. ina Ue =log~ *(0-221924+0-59355 log wy 15, Ra=297'1 
» Ca , Sr ,, =log~4(0-16809+0°61110log2) . ,,  Ra=2636 
ae Oe Ba ,, =log—1(017563+0-60789 log.) ,, © Ra=261°0 
» Sr ,, Ba, =log '(0-19338+0°60239 log 7) ,, Ra=2595 
It we take the differences between the first and second 
lines of the triplets in zinc, cadmium, and mercury, viz. 
386°39, 1159°39, and 4633°27, we obtain from the numbers 
for Zn and Cd the formula 
atomic weight =log—!(0°5405 + 0°49285 log x), 
which gives for mercury 222748, .a result considerably too 
high. 
I conclude, therefore, that this method of calculation has a 
tendency to give the number too high for bac: higher atomic 
weights. 
If radium has the atomic w eight 225, it no doubt occupies 
the i below mercury in the vertical column containing 
Mg, Ca, Sr, Cd, Ba, Hg, in the arrangement of the periodic 
law : if it were 258 it must find a place either in a different 
vertical column altogether, or in the same column lower 
down, for which the atomic weight should not exceed 250, 
and in this case it should be more closely analogous to 
mereury and cadmium than to barium and strontium. 
If the true weight is 258, and if the chemical determination 
gives 225 because of contamination of the material with 
barium, then it must have contained more than 25 per cent. 
of impurity, and this seems an impossible supposition. 
Assuming the truth of Runge and Precht’s law we may 
indulge in some speculations as to the classification of the 
elements. 
In the group B, Al, Ga, In, Tl, taking the differences as 
