those at the distance of two feet eleven inches; and the result is 
that by careful and constant experimental observation of comparative 
dimness and constant experimental observation of comparative dimness 
and clearness, we are enabled to infer with great exactness the 
configuration of the object observed. 

    An instace will do more than a volume of generalities to make my 
meaning clear. 

    Suppose I see two individuals approaching whose rank I wish to 
ascertain.  They are, we will suppose, a Merchant and a Physician, or 
in other words, an Equilaterial Triangle and a Pentagon; how am I to 
distinuish them? 

    It will be obvious, to every child in Spaceland who has touched 
the threshold of Geometrical Studies, that, if I can bring my eye so 
that its glance may bisect an angle (A) of the approaching stranger, 
my view will lie as it were evenly between the two sides that are next 
to me (viz. CA and AB), so that I shall contemplate the two 
impartially, and both will appear of the same size. 

    Now inthe case of (1) the Merchant, what shall I see?  I shall see 
a straight line DAE, in which the middle point (A) will be very bright 
because it is nearest to me; but on either side the line will shade 
away _rapidly to dimness,_ because the sides AC and AB _recede rapidly 
into the fog_ and what appear to me as the Merchant's extremities, 
viz. D and E, will be _very dim indeed._ 

    On the other hand in the case of (2) the Physician, though I shall 
here also see a line (D'A'E') with a bright centre (A'), yet it will 
shade away _less rapidly_ to dimness, because the sides (A'C', A'B') 
_recede less rapidly into the fog:_  and what appear to me the 
Physician's extremities, viz. D' and E', will not be _not so dim_ as 
the extremities of the Merchant. 

    The Reader will probably understand from these two instances how -
- after a very long training supplemented by constant experience -- it 
is possible for the well-educated classes among us to discriminate 
with fair accuracy between the middle and lowest orders, by the sense 
of sight.  If my Spaceland Patrons have grasped this general 
conception, so far as to conceive the possibility of it and not to 
reject my account as altogether incredible -- I shall have attained 
all I can reasonably expect.  Were I to attempt further details I 
should only perplex.  Yet for the sake of the young and inexperienced, 
who may perchance infer -- from the two simple instances I have given 
above, of the manner in which I should recognize my Father and my Sons 
-- that Recognition by sight is an easy affair, it may be needful to 
point out that in actual life most of the problems of Sight 
Recognition are far more subtle and complex. 

    If for example, when my Father, the Triangle, approaches me, he 
happens to present his side to me instead of his angle, then, until I 
have asked him to rotate, or until I have edged my eye around him, I 
am for the moment doubtful whether he may not be a Straight Line, or, 
in other words, a Woman.  Again, when I am in the company of one of my 
two hexagonal Grandsons, contemplating one of his sides (AB) full 
front, it will be evident from the accompanying diagram that I shall 
see one whole line (AB) in comparative brightness (shading off hardly 
at all at the ends) and two smaller lines (CA and BD) dim throughout 
and shading away into greater dimness towards the extremities C and D. 

    But I must not give way to the temptating of enlarging on these 
topics.  The meanest mathematician in Spaceland will readily believe 
me when I assert that the problems of life, which present themselves 
to the well-educated -- when they are themselves in motion, rotating, 
advancing or retreating, and at the same time attempting to 
discriminate by the sense of sight between a number of Polygons of 
high rank moving in different directions, as for example in a ball-
room or conversazione -- must be of a nature to task the angularity of 
the most intellectual, and amply justify the rich endowments of the 
Learned Professors of Geometry, both Static and Kinetic, in the 
illustrious University of Wentbridge, where the Science and Art of 
Sight Recognition are regularly taught to large classes of the _elite_ 
of the States. 

    It is only a few of the scions of our noblest and wealthies 
houses, who are able to give the time and money necessary for the 
thorough prosecution of this noble and valuable Art.  Even to me, a 
Mathematician of no mean standing, and the Granddfather of two most 
hopeful and perfectly regular Hexagons, to find myself in the midst of 
a crowd of rotating Polygons of the higher classes, is occasionally 
very perplexing.  And of course to a common Tradesman, or Serf, such a 
sight is almost as unintelligible as it would be to you, my Reader, 
were you suddenly transported to my country. 

    In such a crowd you could see on all sides of you nothing but a 
Line, apparently straight, but of which the parts would vary 
irregularly and perpetually in brightness or dimness.  Even if you had 
completed your third year in the Pentagonal and Hexagonal classes in 
the University, and were perfect in the theory of the subject, you 
would still find there was need of many years of experience, before 
you could move in a fashionable crowd without jostling against your 
betters, whom it is against etiquette to ask to "feel," and who, by 
their superior culture and breeding, know all about your movements, 
while you know very little or nothing about theirs.  in a word, to 
comport oneself with perfect propriety in Polygonal society, one ought 
to be a Polygon oneself.  Such at least is the painful teaching of my 
experience. 

    It is astonishing how much the Art -- or I may almost call it