66 



SCIENCE. 



lection, he can communicate his thoughts to h s fellow- 

 men in either of two ways ; first, scientifically by the 

 medium of conventional symbols or language ; and sec- 

 ond, artistically, by a model or a drawing. This second 

 method reaches a larger audience. What I write con- 

 cerning a sphere, for example, can be understood onl/ 

 by those who have learned the language in which I write. 

 But if I illustrate my propositions by good drawings or 

 good models, the thought will be grasped by persons 

 unlearned in mathematics — and persons of all nations, 

 whether they understand English or not. 



A form or model is therefore the clearest and most 

 complete statement of a mathematical truth. Nor can a 

 person give a more convincing proof of his understand- 

 ing a truth than his ready and accurate drawing of an 

 original diagram illustrating it. When we see material 

 particles, the fine particles ot crayon, for example, on the 

 blackboard, obeying geometrical law, we recognize at 

 once the expression of geometric thought. Law is a 

 mental reduction of particulars to mental order. A 

 geometric locus is a space in which each point is men- 

 tally referable to a single proposition ; that is, a space in 

 which the position of every point can be mentally 

 grasped and defined by giving properly the posiiion of 

 one of them. When therefore we see numerous parti- 

 cles of matter conforming to a geometric locus, we are 

 forced to believe that that mass of matter was moulded, 

 directly or indirectly, by a mind which comprehended the 

 law of the locus ; and in the moulding of it, enounced 

 the condition which defines the position of its points. 

 The enunciation of a thought can come only from a 

 mind comprehending that thought ; and the formation 

 of a geometric figure is the clearest enunciation of a 

 geometric thought. 



In the physical forces, therefore, which govern inor- 

 ganic matter, is revealed the existence of a guiding in- 

 tellect, since the forces are constantly producing perfect 

 geometrical forms or leading to harmonious arithmetical 

 relations. If we are forced to believe that gravity a ;d 

 chemical differences and chemical affinities inhere in 

 matter, we must still, from the geometrical and algebrai- 

 cal powers exhibited by these forces, believe that they 

 were bestowed upon matter by an intelligent power, who 

 oresawaid comprehended their effects. The study of 

 the natural sciences might otherwise well be given over 

 to the reproach of Dr. Johnson in the Rambler, and 

 Swift in the voyage to Laputa. Without a faith that law 

 lies hidden in the material world, all the efforts of scien- 

 tific explorers would be paralyzed ; and without faith 

 that that law is the choice of infinite wisdom, and 

 adapted perfectly to fulfil the purposes of infinite love, 

 the success of the scientific explorer in discovering it 

 would be robbed of its highest and peculiar value. 



In fact, the physical forces governing inorganic matter, 

 acting under definite laws, and tending towards a state 

 of stable equilibrium, nevertheless show in the intellec- 

 tual, the geometrical and algebraical nature of thjse 

 laws, a spiritual origin ; they show that, however inde- 

 pendent of will we may now conceive them to be, they 

 nevertheless are the embodiment of thought ; and we 

 know of no way of embodying thought without a 

 volition. 



But if the Creator has thus stored in crystallizable 

 matter, in a manner transcending all our thoughts, forces 

 which carry out His geometrical and algebraical concep- 

 tions, much more marvellous and beautiful are the modes 

 in which he has imparted to the souls of plants and ani- 

 mals (if I may thus extend the use of the word soul) the 

 power of carrying into execution more complxated geo- 

 metrical and algebraic plans. 



For in every organized being, plant or animal, there is 

 a guiding principle which we may call, if we please, a 

 soul, which causes the forces of matter no longer to act 

 under laws tending towards stable equilibrium, but under 



a variety of laws, d.fferent in each species, tending not 

 towards stable but towards unstable equilibrium. This 

 guiding principle has in itself no forces. The most 

 careful investigators ot the phenomena of organic growth 

 fail to find any evidence of vital force, although there is 

 abundant evidence which must convince the most care- 

 less observer that there is in organized growth a vital 

 guidance of force peculiar to each species of plant or 

 animal, which I cannot conceive as inherent like the phy- 

 sical forces in matter and which 1 therefore, must attrib- 

 ute either directly t o the Deity, or to an animal or vege- 

 table psyche, empowered by him to cany out these 

 higher geometric forms, just as in each species of matter 

 he has implanted the ability to carry out the simpler 

 geometrical forms of crystals. 



There are those whose philosophy differs from mine, 

 and who hold to the opinion that the vital guiding prin- 

 ciple in organic growth, and even the rational soul of 

 men and animals are inherent in matter, in the same 

 manner as the forces w.iich they guide are inherent in 

 matter. According to this philosophy ;he vital principle 

 and the rational principle, inherent in matter, are usually 

 latent and are brought into operation only under pecu- 

 liar combinations of circumstances. 



Now even should we grant the soundness of this vie v, 

 I should still find it necessary, for the explanation of the 

 logical series of vegetable and animal forms, to suppose 

 that this universally diffused vital principle originally 

 spratig from an intelligent self-conscious being who com- 

 prehends the laws of geometry perfectly ; and who has 

 expressed certain of his geometric thoughts through the 

 psyche or soul of plants and animals, whether we sup- 

 pose that psyche diffused but latent through all matter, 

 or confined to the organisms in which it is patent. 



The nature of this psyche, of course, transcends our 

 knowledge. We recognize it only through its operations ; 

 and consciousness aids us in our attenpts to understand 

 it only so far as to show that its effects are intellectually 

 identical in geometric form with the product of our geo- 

 metric imagination. But we cannot suppose the psyche 

 of the plant or animal conscious of all the thoughts which 

 it develops, since we, whose psychical development is 

 evidently vastly higher than that of any other terrestrial 

 beings, are not conscious of the geometric law of our 

 own bodies, which our souls unconsciously fulfill ; not 

 only during the period of our growth, but daily as we 

 supply by nutrition the daily waste of the frame. 



The fact that the plant or animal may, without the ex- 

 ertion of any mechanical force, guide the forces of elec- 

 tricity, and light and heat and chemical affinity, to the 

 building of peculiar forms imprinted on its own soul, 

 may receive a coarse illustration from the operations of 

 the steam-engine in which, by delicacy and accuracy of 

 workmanship, the direction given to the power can be 

 changed by a force infinitesimal in comparison to the 

 force exerted by the engine. The chemical forces which 

 govern the organogens in their compoun Is are always 

 the same, but the results vary for each individual plant 

 or animal, and the law which those results indicate is 

 different for each species. The forces, building out of 

 these few simple elements so great a variety of forms, are 

 tremendous in their energies, and their existence is forced 

 upon the attention of the naturalist ; but the vital force, 

 if such a thing exist, which guides these tremendous 

 powers and determines what result they shall bring to 

 pass, has eluded the sight of the most careful and accur- 

 ate observers. The nicer the investigation into the phe- 

 nomena of organic form, the more wonderful do the re- 

 sults appear. The persistence of type, for example, 

 through successive generations for many thousands of 

 years, and the very evident transmission of all physical 

 and psychical characteristics from the male parent to the 

 offspring, how utterly inexplicable upon any gross mate- 

 rial theory, when we reflect that from the male pareit no 



