ANNUAL ADDRESS OF THE PRESIDENT. XXXVII 
and explaining transformations by the arrangement and position 
of atoms.” * . 
But it is in the physical philosophy of Epicurus, as that philo- 
sophy has been expounded and expanded by Lucretius, that we can 
discover the fullest and clearest exposition of the doctrine of atoms, 
considered as a key to the structure of the Universe. We here have 
the doctrine formulated into a theodicy of naturism, a theory of 
psychology, a cosmogony, and an anthropology. According to 
Epicurus, in his Lucretian rendering, atoms are minute material 
particles, indivisible, not by reason of their smallness, but of their 
solidity which makes them indestructible and unchangeable in their 
constitution ; they have size, weight, and shape, yet are forever in- 
visible to the eye; in shape, some of the atoms are different from 
the others, but, while the number of the different shapes is finite, 
the number of atoms of each shape is infinite; every atom must 
have at least three cacumina (yovias), that is, infinitesimally small 
bounding points which are incapable of existing apart from the 
atom, but must be conceived to coexist with it in order to give 
definition to it and to enclose its “solid singleness;” some of the 
atoms are hook-shaped, some only slightly jagged, some smooth, 
&c.; atoms are in incessant motion, racing through space in all 
directions under the stress of their weight, according to the fa- 
voring conditions of a vacuum more or less complete, yet so that 
the sum of their motions results in the supreme repose of gross 
matter, except when a thing exhibits the motion of translation in 
space—a form of motion which is molar and not atomic; atoms 
move besides at an enormous uniform speed, in parallel lines, up 
and down, so far as there can be any up and down in a universe 
equally boundless in all directions, and except so far as some of the 
atoms have originally a shape which makes them capable of slight 
deflections from parallel straight lines—that elinamen principiorum 
which was invented by Epicurus to explain the phenomena of so- 
* Arist.: De Generat. et Corrup., I, ii, 4 (Didot’s ed., vol. 2, p. 484.) 
t Epicurus derived the motion of atoms from their weight, which gives 
movement i7 vacuo. Democritus derived the motion of atoms from an im- 
pulse given to them in the beginning. So says Cicero (De Fato, 20, 46), 
but for the contrary opinion, ¢f. Zeller: Philos. der Griechen, Erster Theil, 
702, 714. 
