246 
CORRESPONDENCE. 
have arrived. Meantime, as a preparation for what we may expect, a 
comparison of his published figures supplies sufficient material for 
estimating his accuracy as an observer. 
In the first place it will be remembered that, having expressly 
tested a glass of his own, he wrote to say he had found its angle to be 
100°. But on the following day his secretary writes to say that 
having looked again he found it was a mistake ; the angle was really 
110 3 . 
Again looking at last table we find him claiming for one of his 
glasses an aperture of 178°. (By-and-bye, for it is in the nature of 
Art to progress, we may expect to hear one announced having 179°, 
to be followed, doubtless, in due time, by another of 180°.) 
Again, in the same list (p. 106) we find the figures contradicting 
themselves. We have, e.g., two glasses with apertures of 175°, having 
different angles in water, the first giving 117°, against the smaller 
angle of 113° for the second ; but going on to the column for balsam, 
the reduction is inverted, the second, which was lower in water, being 
now the higher in balsam, — 95° against 93°. Both results cannot be 
true. For the loss for different media is connected by a fixed relation 
(though not of simple proportion) ; a diminution for one answering 
necessarily to a corresponding diminution for the other. All four 
measurements therefore cannot be right. (As a matter of fact, all four 
are wrong. The true aperture for both sets is in water 97^°, in balsam 
a few minutes over 80° ; on the supposition, that is, that the angle in 
air has been correctly taken.) 
Further, I have only to observe, that Mr. Tolies in this paper re- 
peats mistakes formerly pointed out, and repeats them without apology 
or explanation, as if they had never been corrected. Under these cir- 
cumstances it may perhaps be allowed that as much attention has now 
been given to these “ demonstrations ” as can in courtesy be required, 
and that further notice of them will not be necessary. 
It is perhaps not fortunate for the “ general reader ” that so much 
of this subject has been elucidated controversially ; for the style natu- 
rally used in proving a disputed truth is not generally the best that 
might be chosen for making clear what it is. I think it not unlikely, 
therefore, that one result of these discussions may be the appearance of 
some obscurity as to the application of the principle, on account of the 
variety of combinations which occur. The object, e. g., may have a 
cover, or it may be without one ; it may be in air, or it may be im- 
mersed in water, or immersed in some denser medium ; and the object- 
glass may be dry or it may be immersed. These combined in different 
ways give an appearance of complexity, which however is apparent 
only, and not real. I therefore take the opportunity of this letter to 
re-state the principle in its application, which may be done simply 
enough ; for whatever the number of cases, the same invariable prin- 
ciple governs them all. 
Every case that can arise comes under one or other of two classes ; 
the object itself is either dry or immersed. 
Suppose, firstly, that it is dry. It may be either with or without a 
cover ; this will not affect the aperture. The glass itself may be either 
