288 SCIENCE PROGRESS 



so do the apes antedate by a great length of time many groups 

 of our familiar ungulates. Apes, as apes, have witnessed the 

 entire drama of elephantine and equine evolution. 



This difference between the times at which different groups 

 have reached, or virtually reached, the termination of their 

 evolution may, I think, be brought out clearly in a diagram. 

 The diagram is constructed upon a principle which is a variant 

 of what I have seen used elsewhere in geology, and which is, 

 moreover, almost identical with that applied by mathematicians 

 in plotting a curve on squared paper. The vertical lines mark 

 off the geological periods from one another, and the rising lines 

 represent the progress of the several groups towards the termi- 

 nation of their evolution, which they virtually reach when they 

 pass the second horizontal line of the diagram. I say " virtually " 

 reach, because the evolution of characters of specific and generic 

 value never ceases of course. There can of course be no pre- 

 tence of mathematical accuracy. The method merely consists 

 in attempting to visualise the evolution of each group as revealed 

 by paleontology and then expressing the conception in a curved 

 line. The extreme cases of the whales and horses illustrate the 

 principle best, and it would be still more forcibly brought out 

 by another diagram of the entire geological record showing the 

 brachiopods and birds diverging from their common ancestor ot 

 Algonkian times, the brachiopods reaching their climax in the 

 Cambrian and the birds continuing to evolve until the Cainozoic. 

 The diagram has of course certain imperfections; it expresses 

 only part of the truth. Thus, any kind of evolution, whether 

 progressive or degenerative, is represented by ascension, and 

 the height of the lines fails altogether to convey an impression 

 of the relative distances which the various groups have travelled 

 from their common ancestor. It should be noted, however, that 

 these relative distances, if they could be shown, would have no 

 connection with the points at which the climaxes are reached, 

 since no mammals are so divergent as the whales. The varying 

 widths of the five columns are intended to express the relative 

 duration of the periods. This, it must be admitted, is scarcely 

 better than guesswork, but I have followed Penck's estimates 

 for the later periods. The ape-line does not pass above the 

 climax-line because it is intended to represent the Primates minus 

 the Hominidae. In spite of its imperfections, I think a diagram 

 constructed on this principle can express aspects of the truth 



