369 
of Edinburgh, Session 1867-68. 
by u the equivocal process of means ” (p. 259), and insinuates 
against one particular final quantity— which is the mean of the 
largely varying results of four different observers, — that it is “ an 
11 exact measure which certainly none of its many measurers ever 
“ yet found it (the thing itself measured) to be ” (p. 256), — -I can 
only hold up my hands in astonishment. 
For here is a person criminating utterly the simple arithmetic pro- 
cess of taking arithmetical means in physical science ; and bringing 
up the special accusation, equally applicable, if at all, in pure, as 
well as applied, arithmetic, — that the mean does not come out 
exactly the same as one of its component numbers. 
This is surely something worse than advocating perpetual motion, 
spirit-rapping, or any other absurdity which would not be permit- 
ted to enter the books of the Eoyal Society of London : and indi- 
cates that the Proceedings' author is running a-muk, in the manner 
of certain of the Javanese, against the method of averaging em- 
ployed in every scientific, commercial, and insurance establishment 
in every country throughout the civilized world. And if the Eoyal 
Society of Edinburgh has permitted such sentiments to be uttered 
at their meeting and printed in their Proceedings , — I would beg 
them to explain, through their Council or otherwise,' — if they be 
lieve the sentiments, — how they maintain them ; and if they do not 
believe them,— why they give them honourable publicity, and 
against the Pyramid subject alone? 
(In the meanwhile* that there may be no doubt of the fact as 
held hy the Proceedings' author, I subjoin, in a note,f an extract 
from one of the daily papers of April 21, — expressing the gentle- 
man’s sentiments as delivered to the Eoyal Society of Edinburgh, 
on April 20, more fully ; and I hope completely relieving me of 
any necessity for answering him on the point.) 
MINUTENESS OF MODEEN PEACTICAL STANDAEDS 
OE GAUGES. 
Under the above heading the Proceedings' author has tabled some 
* This paragraph in parenthesis, was added after the reading of the paper. 
t “ It was an erroneous method of procedure to take the mean of different 
“ measurements. Such a method of procedure Sir J. Y. Simpson alleged 
“ was childish : it was a species of mathematical aberration, and it ran 
“ through the whole of Professor Smyth’s book.” — Scotsman of April 21. 
