246 THE PRINCIPLES OF SCIENCE. [chap. 



slight alteration from the atmospheres of some of tlie 

 planets. A fresh confirmation of the truth of the Coper- 

 nican theory is thus furnished. 



Herscliel proved in this way the connection between the 

 direction of the oblique faces of quartz crystals, and 

 the direction in which the same crystals rotate the 

 plane of polarisation of light. For if it is found in a 

 second crystal tliat the relation is the same as in tlie first, 

 the probability of this happening by chance is ^ ; the 

 probability that in another crystal also the direction 

 will be the same is |, and so on. The probability that 

 in n + 1 crystals there would be casual agreement of direc- 

 tion is the nth power of |. Thus, if in examining fourteen 

 crystals the same relation of the two phenomena is dis- 

 covered in each, the odds that it proceeds from uniform 

 conditions are more than 8000 to i.^ Since the first 

 observations on this subject were made in 1820, no excep- 

 tions have been observed, so that the probability of in- 

 variable connection is incalculably great. 



It is exceedingly probable that the ancient Egyptians 

 had exactly recorded the eclipses occurring during long 

 periods of time, for Diogenes Laertius mentions that 373 

 solar and 832 lunar eclipses had been observed, and the 

 ratio between these numbers exactly expresses that which 

 would hold true of the eclipses of any long period, of 

 say 1200 or I3(X) years, as estimated on astronomical 

 grounds. It is evident that an agreement between small 

 numbers, or customary numbers, such as seven, one 

 hundred, a myriad, &c., is much more likely to happen from 

 chance, and therefore gives much less presumption of de- 

 pendence. If two ancient writers spoke of the sacrifice of 

 oxen, they would in all probability describe it as a heca- 

 toml), and there would be nothing remarkable in the coin- 

 cidence. But it is impossible to point out any special 

 reason wliy an old writer should select such numbers as 

 373 and 832, unless they had been the results of observa- 

 tion. 



On similar grounds, we must inevitably believe in the 



' Edinburgh Review, No. 185, vol. xcii. July 1850, p. 32 ; Herschel's 

 Esxitys, p. 421 ; Transactions of the Cambridge Philosophical Society, 

 vul. 1. p. 43. 



