6 J. LeConte on the Silver-Spring in Florida. 
with recognized optical principles. But a little reflection will 
show that when the eye is placed near the surface of the pool, 
and when we are looking down in a direction approaching the 
vertical, the only method of estimating its depth is by means of 
the apparent intervals between intervening objects, as for exam- 
le, the intervals between the branches of a sunken tree and the 
as the rays of light proceeding from the fathom mark which is 
nearer the surface make a greater angle of incidence than those 
coming from the mark next below, they must undergo a greater 
degree of refraction, hence the apparent angle subtended at the 
eye by the interval in question (one fathom,) is greater than if it 
had been viewed in the air, and therefore the length seems to be 
exaggerated. 
Moreover, as the apparent length of a fathom depends on the 
angle subtended at the eye, while the degree of refraction is 
proportional to the sine of the angle of incidence ; it follows 
that when the incidence is large, the augmentation of the angle 
by refraction will be relatively greater than when it is small. 
_ Hence the uppermost fathom should appear to be longer than 
those below it; this is precisely in conformity with observa- 
tion. Our estimate of the decrease of these apparent lengths 
with increasing depth, is doubtless vastly exaggerated by the 
greater fore-shortening of the lower fathoms. But asall of them 
seem to be more or less elongated, and as the whole depth is thus 
—as it were—measured by exaggerated linear units, it must ap- 
ear to be greater than the reality. : 
The general result to which these optical laws lead is, that to 
an observer sitting ina boat in the’middle of the pool, the bottom 
near the margin (if visible at all, for if the angle of incidence is 
too large, the light from subaqueous objects will be totally re- 
flected, and will not emerge from the water,) will seem to be ele- 
vated and the water appear to be shallower than it really is; 
while the bottom near the centre will seem to be depressed, and 
the apparent depth exaggerated. In other words, near the 
‘margin, the depth is measured by the angle made at the eye by 
the rays proceeding from submerged objects with those coming 
from the shore-line; this angle being diminished by the refrac- 
tion of the former, the depth is apparently diminished. On the 
aes 
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