GAMBLING SUPERSTITIONS. 361 



matical reasoning, that, if a straight rod be so tossed 

 at random into the air as to fall on a grating of equi- 

 distant parallel bars, the chance of the rod falling 

 through depends on the length and thickness of the 

 rod, the distance between the parallel bars, and the 

 proportion in which the circumference of a circle ex- 

 ceeds the diameter. So that when the rod and grating 

 have been carefully measured, it is only necessary to 

 know the proportion just mentioned in order to cal- 

 culate the chance of the rod falling through. But also, 

 if we can learn in some other way the chance of the rod 

 falling through, we can infer the proportion referred to. 

 Now the law we are considering teaches us that if we only 

 toss the rod of ten enough, the chance of its falling through 

 will be indicated by the number of times it actually does 

 fall through, compared with the total number of trials. 

 Hence we can estimate the proportion in which the 

 circumference of a circle exceeds the diameter by merely 

 tossing a rod over a grating several thousand times, 

 and counting how often it falls through. The experi- 

 ment has been tried, and Professor De Morgan tells us 

 that a very excellent evaluation of the celebrated pro- 

 portion (the determination of which is equivalent in 

 reality to squaring the circle) was the result. 



And let it be. noticed, in passing, that this inexorable 

 law for in its effects it is the most inflexible of all the 

 laws of probability shows how fatal it must be to 

 contend long at any game of pure chance, where the 

 odds are in favour of our opponent. For instance, let 

 us assume for a moment that the assertion of the foreign 



