...common way is to add together the errors of observation, and to take the arithmetical mean: the tablesto which the least mean error belongs, are accounted...the terms be the same, the mere comparison of the sums of the squares decides on which side the preference lies. This instance of the utility of the...

...wager that the error was less than this quantity. It will no doubt appear singular, that a quantity M/T having apparently no connection with the matters in...the terms be the same, the mere comparison of the 12 sums of the squares decides on which side the preference lies. This instance of the utility of the...

...brought into expressions, where it was not expected. Bernoulli was the first who found the quantity T enter into the expressions of probability ; and he...the terms be the same, the mere comparison of the sums of the squares decides on which side the preference lies. This instance of the utility of the...

...are represented by the coefficients of the terms of an algebraic formula. As an instance:—Suppose it were required having two sorts of lunar tables...the terms be the same, the mere comparison of the 18 sums of the squares decides on which side the preference lies. This instance of the utility of the...

...spite of 1-758 volumes obtained at 0°, proceed in the following manner : The number 0-00723, the sum of the squares of the differences between the observed and the calculated results, is a minimum. Any alteration in the value of either a or b will cause this term to increase....

...24 hours, p=rock pressure in pounds, p<.=14.6 pounds. The numbers in parentheses at the riptht are the sums of the squares of the differences between the observed and computed values of v. On applying the usual least-square criterion that this sum must be a minimum,...

...therefore expect the probable error to depend on the size of the area included in the survey. We denote the sums of the squares of the differences between the observed and calculated values of N by v2 (N). If r be the probable error of a single observation, the probable...

...proceeds from the assumption that the most probable values of the constants are those for which the sum of the squares of the differences between the observed and the calculated results are minimized, provided the errors are random. y = a -I- bx (61) and which would correspond...

...therefore expect the probable error to depend on the size of the area included in the survey. We denote the sums of the squares of the differences between the observed and calculated values of N by u2 (N). If r be the probable error of a single observation, the probable...

...energy levels, the corrected values of the parameters including their statistical deviations and the sum of the squares of the differences between the observed and the calculated levels, were obtained. The rms error is then defined as A = where the A, are the differences between...