RELATION OF ORGANIC FORMS. 467 



member of it, even the humblest plant, is perfect in itself. From a com- 

 mon origin, a simple cell, all have arisen : there is no perceptible micro- 

 scopic difference between the primordial vesicle which is to produce the 

 lowest plant, and that which is to produce the highest ; but the one, un- 

 der the favoring circumstances to which it has been exposed, has contin- 

 ued in the march of development, the career of the other has been stop- 

 ped at an earlier point. The organic aspect at last assumed The forms of 

 is the strict representation of the physical agencies which have organization 



, i TT j .0. * j i depend on 



been at work. Had these for any reason varied, that varia- physical 

 tion would at once have been expressed in the resulting form, a s ents - 

 which is, therefore, actually a geometrical embodiment of the antecedent 

 physical conditions. For what reason is an offspring like its parent, 

 except that it has been exposed, during development, to the same condi- 

 tions as was its parent ? Comparative physiology is not a fortuitous col- 

 lection of experiments. Our -noblest conception of it is the conception 

 we have of analytical geometry, and, speaking in mathematical language, 

 each member of the organic series is an embodied result of a discussion 

 of the equation of life for one special case. Nay, I would present the 

 whole system of Nature as included in the same idea. The inorganic 

 and lifeless combinations which are all around us are,, to my mind, in 

 truth, in that equation of life, the analogues of the imaginary solutions of 

 the calculus. 



It was a felicitous thought of Descartes that we may represent a geo- 

 metrical form in an algebraical equation, and, by the proper Illustration of 

 consideration and discussion of such an expression, determ- the relation of 

 ine and delineate all the peculiarities of such a form ; that here Jf? 8 

 it should become concave and there convex, here it should analytical ge- 

 run out to infinity, there have a cusp. The equation determ- 

 ines all the peculiarities of the form, and enables us to construct it. But 

 if the original conditions are inconsistent with one another, the construc- 

 tion can not be fulfilled, it having become impossible. In the same man- 

 ner are all living and lifeless forms related : an increase in the value of 

 one condition carries development forward in one direction, and increase 

 in the value of another condition determines development in another way, 

 and these variations give rise in their succession to the whole organic 

 series. But in these, as in the other case, if inconsistent conditions have 

 existed, their presence is indicated in the resulting solution, which can 

 not be constructed as an organic form, but is represented as a lifeless 

 mass. 



"God ever geometrizes," ajid, it might be added, ever materializes. 

 Every organism is the result of the development of a vesicle under given 

 conditions, carried out into material execution. It is the incarnation, the 

 embodiment, the lasting register of physical influences ; for, if such Ian- 



