706 THE PRINCIPLES OF SCIENCE. [CHAP. 



coloured corollas. Naturalists believe with the utmost con- 

 fidence that "Ruminants" and "Ptuminants with cleft feet " 

 are identical terms, because no ruminant has yet been dis- 

 covered without cleft feet. But we can see no impossibility 

 in the conjunction of rumination with uncleft feet, and it 

 would be too great an assumption to say that we are 

 certain that an example of it will never be met with. 

 Instances can be quoted, without end, of objects being 

 ultimately discovered combining properties which had never 

 before been seen together. In the animal kingdom the 

 Black Swan, the Ornithorhynchus Paradoxus, and more 

 recently the singular fish called Ceratodus Forsteri, all 

 discovered in Australia, have united characters never 

 previously known to coexist. At the present time deep- 

 sea dredging is bringing to light many animals of an un- 

 precedented nature. Singular exceptional discoveries may 

 certainly occur in other branches of science. When Davy 

 first discovered metallic potassium, it was a well established 

 empirical law that all metallic substances possessed a high 

 specific gravity, the least dense of the metals then known 

 being zinc, of which the specific gravity is 7*1. Yet to 

 the surprise of chemists, potassium was found to be an 

 undoubted metal of less density than water, its specific 

 gravity being O'865. 



It is hardly requisite to prove by further examples that 

 our knowledge of nature is incomplete, so that we cannot 

 safely assume the non-existence of new combinations. 

 Logically speaking, we ought to leave a place open for 

 animals which ruminate but are without cleft feet, and 

 for every possible intermediate form of animal, plant, or 

 mineral. A purely logical classification must take account 

 not only of what certainly does exist, but of what may in 

 after ages be found to exist. 



I will go a step further, and say that we must have 

 places in our scientific classifications for purely imaginary 

 existences. A large proportion of the mathematical func- 

 tions which are conceivable have no application to the cir- 

 cumstances of this world. Physicists certainly do investi- 

 gate the nature and consequences of forces which nowhere 

 exist. Newton's Principia is full of such investigations. 

 In one chapter of his Mdcanique Celeste Laplace indulges 

 in a remarkable speculation as to what the laws of motion 



