Application of the probability calculus to natural philosophy

Abstract

Natural phenomena are most often surrounded by so many foreign circumstances, and so many perturbing causes confound their influence, that it is very difficult ^α to recognize them [1]. In such a case they can be discovered only by increasing the number of observations ^aor experiences {or experiments}^a, so that as the foreign effects finally cancel each other out, these phenomena ^band their various components^b are clearly revealed by the mean results.^{β c}The more observations there are, and the less they differ from one another, the more their results approach the truth. This latter condition can be realized by the choice of the methods of observation, by the precision of the instruments, and by taking care to make accurate observations. Then the optimal {or most advantageous} mean results, or those that give the smallest error, are determined by probability theory. But this is not enough: it is moreover necessary to estimate the probability that the errors in these results lie within given limits, for without this one would have only an imperfect knowledge of the degree of accuracy obtained. Formulae appropriate to the achieving of these ends are thus a true improvement of the scientific method, and it is very important that they be subjoined to that method.