132 



ESSAY ON PROBABILITIES. 



between A K and A L. Let K B and B L be equal, 

 and suppose positive and negative errors equally likely. 



The probability of any one measurement giving 

 exactly any predicted result, say A N, must be in- 

 appreciably small ; since A N is only one out of an 

 infinite number of possible cases. But take any point 

 V, however near to N, and the chance that the result 



ETV I. 



of an observation shall lie between AN and AV is 

 capable of being imagined to be finite, though small. 

 'Whatever the law of errors may be, let a curve KCL 

 be so drawn that the chance of something between 

 AN and AV shall be the proportion which the area 

 NPQV is of the whole area KCL. Or if we call the 

 whole area 1, the area RPNW, for example, is that 

 fraction which expresses the chance of a result lying 

 between AW and AV. The symmetry of the curve 

 on the two sides of CB is an expression of the hypo- 

 thesis of positive and negative errors being equally 

 likely : and the approach of C K and C L towards the 

 axis is equally an expression of the supposition that 

 large errors are not so likely as small ones. If we wish 



