Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/578

2. For the probable value of the result from several series of experiments

M=A/a²+B/b²+C/c²&c./1/a²+1/b²+1/c²&c..

• M = general mean.
• A, B, C, &c., being the mean results as above.
• a, b, c, &c., being the probable error of each.

3. For the probable error of this general mean = m

m=1/√(1/a²+1/b²+1/c²&c.).

These mean values are for

 
Series I. Number
of experiments in
each sub-series. Impurity equally
in both gases. Number
of experiments. Impurity all in
hydrogen.   Ib. (2) 1.997600±.00100 (2) 1.997500±.00100 Ic. (2) 1.999050±.00010 (2) 1.998800±.00006 Id. (4) 1.998500±.00070 (4) 1.998200±.00070 Ie. (6) 2.000110±.00040 (6) 2.000550±.00050 If. (5) 2.001400±.00005 (5) 2.001040±.00018   General mean for Series I.   (19) 2.000903±.00004 (19) 1.99925±.00005    
Series II. Number
of experiments in
each sub-series. Impurity equally
in both gases. Number
of experiments. Impurity all in
hydrogen.   IIa. (19) 2.002000±.00024 (19) 2.001900±.00024 IIb. (7) 2.003800±.00620 (7) 2.003700±.00600 IIc. (10) 2.001500±.00036 (10) 2.001600±.00036 IId. (5) 2.003000±.00022 (5) 2.003000±.00022 IIe. (12) 2.002450±.00007 (12) 2.002450±.00007   General mean for Series I.   (53) 2.002435±.00006 (52) 2.002431±.00006