300 ANNALS NEW YORK ACADEMY OF SCIENCES 



terns. If the species are absolutely unknown outside of their respective 

 systems, the evidence is so much the stronger, but the difference is one 

 of degree only, and no assumption is made that a species at present known 

 in the Carboniferous may not subsequently be found in the Devonian or 

 vice versa. That a species has not yet been found in the other system, 

 however, rightly gives it exceptional weight especially in regions where 

 the available data on range are considerable. 



This principle is of course unsatisfactory. It is impossible to estimate 

 or to state the results mathematically. Different species have different 

 values, and the same species may have different values in different re- 

 gions. While these values are not expressible in numerical terms and 

 indeed must vary somewhat with each observer according to the character 

 and extent of his experience, nevertheless, in practice, the evidence is 

 seldom so nicely balanced or the antecedent experience of those who judge 

 it so diverse that reasonably satisfactory and unanimous conclusions are 

 impossible. 



In determining the relationship of geologic formations, which includes 

 also the determination of their geologic age, some species have, as already 

 pointed out, greater importance than others. This is partly because we 

 know more about some than others. The determination of such rela- 

 tionships as I have mentioned rests very largely on our knowledge of the 

 range in geologic time of different types of fossils and involves one of the 

 most fallible of all processes of inductive reasoning. Because a fossil 

 has not yet been found above or below a certain horizon it does not follow 

 that it never will be so found, yet that is virtually the inference on which 

 all correlations and age determinations are based. At best, this fur- 

 nishes conclusions which are fairly safe, and at worst it furnishes con- 

 clusions which are highly unsafe. At its best, the conclusion depends 

 upon the concurrence of a large number of species and upon species 

 whose range has been ascertained by a large number of observations. 

 For the same reason, it is clear that common species are more significant 

 than rarer ones, because our knowledge about their range is more trust- 

 worthy, and, in some cases, fairly sound inferences can be drawn from a 

 single species. 



It is, however, not only the trustworthiness of our knowledge which 

 lends greater significance to some forms than to others, but also the 

 length of range in geologic time, which differs with almost every form; 

 for, obviously the presence of a form which had an established range of 

 100 feet would be much more significant in correlation than that of one 

 whose range was 1000 feet. Here enters also the consideration of groups 

 larger and smaller than species, the range of which is, generally speak- 



