26 Messrs. A. C. and A. E. Jessup on the 
eight members. Consequently, if our idea of evolution is to 
hold good, one at least of these protons must have given rise 
to more than one direct product of evolution. 
If it be admitted that some double growth has occurred, 
the next step is to find the place of its occurrence. Examining 
the atomic volume curve, we find that sodium and potassium, 
magnesium and calcium occupy similar positions on the curve, 
and also that the same relations hold good between phosphorus 
and arsenic, sulphur and selenium, chlorine and bromine : and, 
consequently, these pairs must be directly connected together 
in the process of evolution. Now sodium and potassium, 
magnesium and calcium, are corresponding members of 
consecutive horizontal series of MendeleefFs table ; but the 
three next pairs, phosphorus and arsenic, sulphur and selenium, 
chlorine and bromine, do not belong to two consecutive hori- 
zontal series, for the elements vanadium, chromium, and 
manganese, respectively, lie between the members of these 
pairs. We may conclude, therefore, that the evolution must 
have sub-divided at some position between magnesium and 
phosphorus ; in other words, that either aluminium or silicon, 
or both, must have given rise to more than one series of 
evolution products. 
Now potassium and sodium, calcium and magnesium, 
arsenic and phosphorus, selenium and sulphur, bromine and 
chlorine must be consecutive products of evolution in their 
respective families, and we are driven to the conclusion that 
vanadium cannot be derived from phosphorus at all. Similar 
arguments apply to chromium, manganese, &c. We are 
therefore justified in concluding that vanadium, chromium, 
manganese, &c, must be derived by indirect evolution from 
aluminium or silicon. 
If we compare the chemical characteristic properties of 
boron, aluminium, and scandium, with those of lithium, 
sodium, and potassium, and of beryllium, magnesium, and 
calcium, the analogy between the three groups is sufficiently 
strong to justify our considering scandium as the direct 
derivative of aluminium, and, for the same reasons, we must 
consider titanium to be the direct derivative of silicon. Now, 
silicon and phosphorus undoubtedly follow one another in 
order of atomic weight, i. e., there are no elements of atomic 
weight lying between 28'4z and 31*0 ; and inasmuch as 
titanium and arsenic have been shown to be direct evolution 
products of silicon and phosphorus, it is quite evident that 
all the elements possessing atomic weights lying between that 
of titanium (18*1) and arsenic (75) must be derived from 
silicon by indirect processes of evolution. 
