300 Mr. F. Y. Edge worth on the Law of Error. 
will lead to a possible error of „,„„. = 1031"7 seconds in the 
determination of the isotropic plane a. 
The last two numerical results serve to illustrate the diffi- 
culty which would be experienced in attempting to determine 
by direct measurement whether two planes are absolutely or 
only approximately coincident with isotropic planes; in other 
words, whether or not two planes are permanently isotropic. 
The expansion £ 2 perpendicular to the plane of symmetry 
found (Prop. XV.). 
Since aTis 35° 46' 32' / *58, the expansion A in the direction 
Oa will be given by 
A-S=(8 1 -S) sin 2 35° 46' 32"'58 [Prop. XIV.], 
where S 1 — B = '0029001; 
thus A-S=+ -000991177. 
Also (Prop. XIII.) 
^ . 2(bm / — bm) 
B 2 -A= v . J . 
sin zbm 
From page 294, bm!—bm=h' 25", 
whence 8 2 - A = + -0033839, 
and 8 2 -8 =0-0043757. 
Neumann's result is 0*004371. 
With the exception of Propositions IV. and XV., which re- 
quire the zone-plane to be a plane of symmetry, all the above 
propositions are applicable not only to planes perpendicular to 
a plane of symmetry, but to any zone of a crystal whatever the 
system to which the crystal belongs; but it is clear that the 
directions of the maximum and minimum expansions of the 
crystal for lines lying in a given zone-plane are only those of 
the principal expansions of the whole crystal when the zone- 
plane is a plane of symmetry. 
[To be continued.] 
XLII. The Lav: of Error. By F. Y. Edgewokth*. 
THE Law of Error is deducible from several hypotheses, 
of which the most important is that every measurable 
(physical observation, statistical number, c\:c.) may be regarded 
* Communicated by tbe Autbor. 
