414 PRINCIPLES OF NATURE AND GRACE 



smaller spermatic animals, in comparison with which 

 they in turn may be counted large, for everything in 

 nature proceeds ad infiniium 72 . Thus not only souls but 

 also animals are ingenerable and imperishable : they are 

 only developed, enveloped, clothed, unclothed 33 , trans- 

 formed. Souls never put off the whole of their body, 

 and do not pass from one body into another body which 

 is entirely new to them. Accordingly there is no metem- 

 psychosis, but there is metamorphosis. Animals change, 

 take on and put off, parts only 3 *. In nutrition this 

 takes place gradually and by little imperceptible [insensible] 

 portions, but continually ; and on the other hand, in con- 

 ception or in death, when much ; 5 is gained or lost all at 

 once, it takes place suddenly and in a way that can be 

 noticed [notablement],- but rarely. 



7. Thus far we have spoken merely as pure physicists : 

 now we must rise to metaphysics, making use of the 

 great principle, usually little employed, which affirms that 

 nothing takes place urithout sufficient reason, that is to 

 say, that nothing happens without its being possible for 



3a ' So, naturalists observe, a flea 



Has smaller fleas that on him prey ; 

 And these have smaller still to bite 'em, 

 And so proceed ad infinitum.' Swift, On Poetry. 

 The idea of ' infinities of infinity ' is a favourite one with Leibniz, 

 and it is closely connected with the notions underlying his diffe- 

 rential calculus. ' For instance, we must conceive (i) the diameter 

 of a small element in a grain of sand, (2) the diameter of the grain 

 of sand itself, (3) that of the globe of the earth, (4) the distance of 

 a fixed star from us, (5) the magnitude of the whole system of fixed 

 stars, as (i) a differential of the second degree, (2) a differential of the 

 first degree, (3) an ordinary assignable line, (4) an infinite line, (5) 

 an infinitely infinite line.' Lettre a M. d'Angicourt (1716), Dutens, iii. 

 500. Cf. Monadology, 65-70. 



33 Cf. 2 Corinthians, v. 4. 



34 Cf. Monadology, 71, 72, 77. Aristotle condemns the theory of 

 transmigration of souls in his De Anima, i. 3, 407 b 13. 



35 E. omits beaucoup ['much'] and reads, ' all is gained or lost at 

 once.' 



36 i. e. students of nature. 



