NOTICES OF MEETINGS, 285 

at the last meeting was little more than a running comment upon Professor 
Abbe’s paper, but as the subject was this evening to come up for what you may 
call a detailed discussion, I thought it better that I should commit my thoughts 
to paper ; firstly, because it would, perhaps, prevent me repeating myself; and, 
secondly, because it would prevent me, perhaps, overlooking some little points 
to which I wish to call your attention. 
I think I have the sympathy of those gentlemen who are of my way of think- 
ing, and I hope I shall have the indulgence of those who differ with me. At 
all events, if I stumble in my endeavours to-night to do the subject justice, I 
am sure you will bear with me. I will just say to commence with, that this 
aperture question is, in my opinion, a very simple one, but, unfortunately, there 
is a variety of relative matters bearing upon it which are introduced and sur- 
round it, and make it appear to be more complicated than it should be. As 
you are aware, I was going to refer to one other subject, because I wish to-night 
to attempt what I have never seen done, because I thought it would perhaps be 
information for some of our younger members. That is, I wish to explain what 
is meant by ‘‘aperture.” It is a very simple thing, in my opinion ; I don’t 
think I can make any mistake over it. There are gentlemen who are more 
fully able to explain the question than I am, but I will attempt to demonstrate 
to you what aperture is. I do so, because this is a simple question, something 
like another question that crops up annually, and that is kitchen boiler explo- 
sions. There is not a more simple thing, perhaps, that you could study than 
that, and yet there is not one plumber out of twenty, nor one educated man 
out of a hundred who talk about it, that knows the cause of them. Perhaps I 
had better commence straight off by trying to explain what is meant by aperture. 
You all know that in geometry, for the purpose of measuring angles and seg- 
ments of circles, a circle is divided into 360 degrees. I putacircle here. If 
we draw a straight line right through the circle, we cut it in two, and we have 
180 degrees left. I want to point out one thing to you to start with. Of course, 
many people, speaking of an angular aperture, are not aware when a possible 
aperture ceases. An angular aperture, or a possible aperture, ceases somewhere 
a little over 170 degrees. I am sorry Mr. Davis is not here, because he speaks 
of an aperture of 178 degrees, and I wish to ask him a question, whether he 
had ever seen or verified a glass of 178 degrees. As I was saying, this semi-circle 
cut in two represents half” of 360 degrees, which is 180 degrees. The right 
angle is an angle of 90 degrees, and if we make another bisection we have an 
angle of 45 degrees. And so we go on until we arrive down here, somewhere 
about 170 degrees. Perhaps that will do to start with. I think this is per- 
fectly clear. F shall have to refer to it again to show you what I mean by this 
question, but I think that, as far as it goes, it will answer the purpose for the 
resent. I hope every one can see it. When we speak of the aperture of a 
ens, I take it to refer to the visual angle at which, by its aid, we see an object. 
Now, as our President pointed out to you in May last, amplification, or the 
apparent magnitude of an object, depends upon the distance from which it is 
viewed ; consequently the visual angle under which we see an object is always 
in just proportion to its amplification. My contention to-night is, for the pur- 
pose of argument, That in the computation or formulating of objectives, a just 
roportion of power and aperture should always be maintained. Some con- 
fasion is likely to arise at this point; I therefore desire that this proposition of 
mine should not be misunderstood. It really involves what Professor Abbé 
calls ‘‘ progressive increase of aperture in the higher powers.” Now, as the 
highest attainable aperture is soon reached, it remains only a question as to 
what rate of progression should take place conjointly with increased amplifica- 
tion. If we seek for the highest attainable aperture in a 1-roth inch objective, 
(and I see lenses of 1-8th inch wide aperture 170° advertised), objectives 
giving a greater amplification will be, correspondingly, glasses of a low angle. 
deas upon aperture are sometimes rather vague, and this is occasionally be- 










































