j6 Dr. Young's remarks on the reduction 
We must not, however, lose sight, in this calculation, of 
the original condition of liability to a certain constant error in 
each trial. For example, we may infer from it, that if we 
made 100 observations of the place of a luminary, each dif- 
fering 1' from the truth, but indifferently on either side of it, 
the error of the mean result would probably not exceed 
~ . i'= 3.6"; and that in 1000 observations it would probably 
be reduced to about a second. Now although, in the methods 
of observing which we employ, the error is liable to consi- 
derable variations, yet it may be represented with sufficient 
accuracy, by the combination of two or more experiments in 
which the simpler law prevails. For example, the combina- 
tion of two counters, such as have been considered, is equiva- 
lent to the effect of a die with four faces, or a tetraedron, 
marked o, 2, 2, and 4, or with errors expressed by 1, o, o, 
and — 1 ; the combination of three counters is represented by 
a die having eight faces, or an octaedron, with the errors 1, 
i> i ’ i ~ t ’ — I — — 1 > anc * the combination of four, by 
a solid of 16 sides, with the errors 1, 4 x •§•, 6 x o, 4 x — — 1. 
These distributions evidently resemble those which are gene- 
rally found to take place in the results of our experiments ; 
and it is of the less consequence to represent them with greater 
accuracy, since the minute steps, by which the scale of error 
varies, have no sensible effect on the result, especially when 
the number of observations is considerable. If, for example, 
instead of two trials with the tetraedron, having the errors 
1, o, o, — 1, we made two trials with a solid of 21 faces, 
having the errors distributed equally from 1, .g, .8 . . to — 1, 
the mean error of all the possible combinations would only 
