# Full text of "Scientific Papers - Vi"

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```1919]
ATMOSPHERIC  REFRACTION
601
Accordingly
Now for air at 0° C. and 760 mm. pressure p = 1 '000292, so that
, = '000292 (p-p0)/Po = - '000146 (g2-Z72)/F2..........(14)
000146U* /« d fq2\  , * =-------FT-"]. ayU/i)^'  ..................<15>
and the integral is the quantity already calculated under (9). It will be-observed that the effect is independent of the absolute size of the obstacle, and is proportional to the square of the fluid velocity U. As regards the sign of the effect, we see that, so long as (9) is positive, the retardation diminishes as y increases, and thus a ray originally parallel to x is bent inwards. This action in a range-finder leads to an over-estimate of the distance.
We may now consider the actual magnitude of %.   If we take the highest value of (9), viz. T36, we have
X = - '000199 U*/V2............................(16)
To take a numerical example, let us suppose that
17-as 5532-112022:,
hours            sec.
and
F(0° C., 760 mm.) = 33100  *. v                      '               sec.
The angle is then                 ~X= 2'28* x 10~7-
This is in circular measure, and it corresponds to '0470* second.   An error of a twentieth part of a second may be considered negligible.
The corresponding problem with a sphere in place of the cylinder could be treated, but it is rather more complicated. It does not appear necessary to enter upon it here.
The objection may present itself that the motion in two dimensions round a cylinder does not well represent the case of a ship. This must be admitted; but it seems clear that a range-finder, carried well above the deck of a ship, would be much less liable to be disturbed in the manner discussed.