438 THE PRINCIPLES OF SCIENCE. 



ance of the excepted case, immediately prior to its occur- 

 rence V 



As Babbage further showed f , a calculating engine, 

 after proceeding through any required number of motions 

 according to a first law, may be made suddenly to suffer 

 a change, so that it shall then commence to calculate 

 according to a wholly new law. After giving the natural 

 numbers for any finite time, it might suddenly begin to 

 give triangular, or square, or cube numbers, and these 

 changes might theoretically be conceived as occurring 

 time after time. Now if such occurrences can be designed 

 and foreseen by a human artist, (it is surely within the 

 capacity of the Divine Artist to provide for similar 

 changes of law in the mechanism of the atom, or the 

 construction of the heavens. ) 



Physical science, so far as its highest speculations can 

 be trusted, gives some indication of a change of law in 

 the past history of the Universe. According to Sir W. 

 Thomson's deductions from Fourier's Theory of Heat, 

 we can trace down the dissipation of heat by conduction 

 and radiation to an infinitely distant time when all things 

 will be uniformly cold. But we cannot similarly trace 

 the heat-history of the Universe to an infinite distance in 

 the past. For a certain negative value of the time the 

 formulae give impossible values, indicating that there was 

 some initial distribution of heat which could not have re- 

 sulted, according to known laws of nature, from any pre- 

 vious distribution . There are other cases in which a 

 consideration of the dissipation of energy leads to the 

 conception of a limit to the antiquity of the present order 

 of things 11 . Human science, of course, is fallible, and 



f ' Ninth Bridgwater Treatise,' pp. 34-43. 



g Tait's c Thermodynamics,' p. 38. ' Cambridge Mathematical Jour- 

 nal,' vol. iii. p. 174. 



h Clerk Maxwell's ' Theory of Heat,' p. 245. 



