838 



TITANOTHERES OF ANCIENT WYOMING, DAKOTA, AND NEBRASKA 



represent the average condition of the same bio- 

 character in a species or mutation descendant from T. 

 Then Tn — T is the measure of the evolution of the 

 biocharacter, and 100 (Tn — T) T is its percentage in- 

 crement. Hence 



^"=t+(4)t 



where Ynr, represents the total percentagii increment. 



Suppose that this total percentage of increment in 

 the biocharacter were made up of the following con- 

 tributory increments: 



H (heredity), that part of the total percentage 

 increment which may be ascribed hypothetically to 

 an orthogenetic or germinal tendency to accelerate, 

 balance, or retard the typical condition of T. 



(ontogeny), that part of the total percentage incre- 

 ment wliich may be ascribed hypothetically to modi- 

 fications arising in the soma, evoked either by use and 

 disuse or by physico-chemical correlation (interaction) 

 during individual development. 



E (environment), that part of the total percentage 

 increment which may be ascribed hypothetically to the 

 reaction to the geographic and physical environment. 



L.E (life environment), that part of the total per- 

 centage increment which may be ascribed hypo- 

 thetically to the action of surrounding titanotheres 

 and other organisms. 



S (selection), that part of the total percentage 

 increment which may be ascribed to the cumulative 

 effect of natural selection upon germinal variations, 

 fluctuations, etc. 



Substituting the above symbols in the formula 



we obtain the formula 



/ H + + E + L.E + S \ 



^° ^"^V 100 J 



whence 



'Tn-T' 



Tn = T- 



H + O + E + L.E = 100 + S 



{^) 



In paleontologic research on certain proportion 



biocharacters in continuous phyla one may be able 



T 

 to determine the numerical value of Tn — m, and 



hence to obtain an exact measm-e of the total per- 

 centage of increment due to the combined action of 

 H + O + E + L.E + S taken together, but not to measure 

 any one of these factors separately. 



In the application of the tetrakinetic theory it is 

 the causes of the invisible, germinal increment which 

 we have to explain — the increment, for example, 

 which separates the germ of Brontotherium from that 

 of Eotitanops. 



It is not claimed that the theory of tetrakinesis, in 

 which the incessant action of natural selection plays 

 a large part, will explain the origin of a single bio- 



character, rectigradation, or allometron. It is still 

 in the stage of a working hypothesis, to be tested by 

 observation and experiment, in the way, for example, 

 that the original Lamarckian and Darwinian theories 

 have been and are being tested. The only insight 

 we now have into the possible worldng of this theory 

 is afforded by the phenomena of organic selection and 

 of interaction in the changes in the velocity of certain 

 biocharacters which are known to be due in the soma 

 to the circulation in the system of "physico-chemical 

 messengers" of the kind designated among physiolo- 

 gists as enzymes and internal secretions, including 

 the hormones (accelerators) and chalones (retarders) 

 of the individual growth of certain biocharacters. So 

 far as known at present these are purely somatic phe- 

 nomena. Experiment may prove that similar inter- 

 Tetrajola sy 

 Centrifu.aal stream of ener(^y 



envtro^^ 



Figure 751. — Diagram illustrating the 

 principle of tetraplasy 



Represencing the conception of a centrifugal stream of 

 potential heritages and predispositions passing from 

 the heredity germ into the life of the organism (ontog- 

 eny), both into the new reproductive organs and into 

 every cell of the body (protoplasm and cell chromatin), 

 as acting, reacting, and interacting with all the other 

 functions and structures within the body as well as 

 with the stream of energy interchanged between the 

 body and the physical environment and the life en- 

 •vironment, showing that every visible biocharacter 

 represents the action, reaction, and interaction of 

 these four complexes of energy. 



actions originally arising through adaptive modifica- 

 tions of the body (soma) may affect the correspond- 

 ing predispositions and potentialities of the germ. ' 



ANALYSIS OF THE MODES OF VARIATION; THEORETIC 

 IMPORTANCE OF INITIATION 



We have set forth above an analysis of the modes 

 of variation; let us apply this analysis to proportions. 



Until the causes, as yet unknown, of predisposition, 

 of increment, of acceleration, of retardation, of recti- 

 gradation, of allometry in the germ itself are discovered 

 experimentally we must confine our observations to 

 what we see going on in the body and must seek to 

 answer the all-important question whether the initia- 



