When to reject suspected observations

If x = rt, where rt represents the number of errors less than x which may be expected to occur in an extended series of observations when the total number of observations is taken as unity, r represents the probable error of a single observation. Any measurement containing an error greater than x is to be rejected. If n denotes the number of observations and also the number of errors, then nP indicates the number of errors less than rt, and n(l — P) the number of errors greater than the limit rt. If this number is less than any error rt will have a greater probability against than for it, and, therefore, may be rejected. 

By a successive application of these formulae, two or more doubtful results may be tested. The value of t, or, what is the same thing, of P, and hence also of n, can be read off from the table of integrals, page 622 (Table XI.). Table XII. contains the numerical value of x/r corresponding to different values of n. 

Examples.—(1) The result of 13 determinations of the atomio weight of oxygen made by the same observer is shown in the first column of the subjoined table. Should 19 81 be rejected Calculate the other two columns of the table in the usual way. 

The deviation of the suspected observation from the mean, is 8 59. By Chauvenet s criterion, probable error = r = 0-7281, n = 18. From Table XII., x/r = 8-07,x = 3 07 x 0-7281 = 22-7. Since the observation 19-81 deviates from the mean more than the limit 22-7 allowed by Chauvenet s criterion, that observation must be rejected. 

Nearly two hundred years ago Maupertius tried to show that the principle of least action was one which best exhibited the wisdom of the Creator, and ever since that time the fact that a great many natural processes exhibit maximum or minimum qualities has attracted the attention of natural philosophers. In dealing with the available energy of chemical and physical phenomena, for example, the chemist seeks to find those conditions which make the entropy a maximum, or the free energy a minimum, while if the problems are treated by the methods of energetics, Hamilton s principle  

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