# On the Conformity-to-a-Law of the Distribution of Errors in a Series of Observations

Chapter

## Abstract

In order to specify completely the assumptions underlying the discussion to follow, we will suppose that we are dealing with some process in which the value of a measurable characteristic arise entirely from random errors of observation?

*B*varies with another,*A*(as, for example, the pressure of a body of steam varies with temperature, or the like). Then, on the one hand, for a series of values*a*_{1},*a*_{2}…*a*_{n}of the determining variable*A*, let the corresponding values*b*_{1},*b*_{2}…*b*_{ n }of*B*be obtained by direct measurement; on the other hand, suppose that some theoretical formula, expressing the dependence as*B = F(A)*, gives calculated values*β*_{1},*β*_{2},*β*_{n}corresponding to*a*_{1},…*a*_{ n }.^{1}The question is now: what is the probability that the*n*differences$$
\beta _1 - b_1 = x_1 ...\beta _n - b_n = x_n
$$

## Keywords

Prob Ability Functional Determinant Observational Process Successive Error Probability Apriori
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## References

- 1.Situations occurring in practice can in most cases be reduced to this simple scheme, even when more than two variables are involved.Google Scholar
- 1.There is evidently no loss of generality in immediately taking zero as one of the limits.Google Scholar
- 1.The use of an integral similar to the above as discontinuity factor is familiar to me through the lectures of Professor Riemann in Göttingen.Google Scholar
- 1.s. Baltzer.
*Theorie der Determ. ( Theory of Determinants*presented with reference to the original sources) (1857). Leipzig: S. Hirzel.Google Scholar - 1.; A proof of this theorem can be found in
*Zeitschr. f. Math. u. Phys.*Vol. VII, 1862, p. 440. [G. Zehfuss: Applications of a special determinant, idem, pp. 439— 445.]Google Scholar - 1.M.A. Stern, Lehrb. d. algebr. Analysis [Leipzig, C.F. Winter, 1860] p. 385.Google Scholar

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