I'm afraid to say that there is a glaringly logical flaw in at least one of
Samuel Birley Rowbotham experiments (namely: expt
, and I wouldn't
be surprised if was this same misunderstanding of his that lead to all of
his flawed results.
For those who would like to refer to his experiments:
http://www.sacred-texts.com/earth/za/za13.htmI'll start off by refering to these images:
Notice how he assumes that the horizon would appear curved on a
spherical earth. This would not at all be the case when viewing a sphere
from a distance l << R (The radius of the sphere)
To demonstrate my point, lets pretend for a while that the world was a
giant but finite cylinder. Standing on a beach and looking out over flat
water, one would in fact notice a distinctly curved horizon. (ignoring
atmospheric effects and so assuming one could see out indefinitely)
If we measured altitude in the sense of "distance from the plane
perpendicular to the observer through which the axis runs" C would be on
the same altitude as the observer, but the points A and B would be a
distance R (radius of the cylinder) below that.
The red dotted lines simply show the field of vision.
In this case, the horizon would indeed be curved since each end of the
horizon is lower than its center. The image might look something like this.
If we were to now extend this analogy to standing on a sphere...
The visible horizon will now be a circle on the face of the sphere, centered
on the point where we stand, the radius of that circle, entirely dependent
upon our height above the surface of the sphere, as well as the radius of
the sphere on which we stand.
In this case now, points A, B and C lie on the same circle centered at O.
This means they all lie on a plane perpendicular to the earths radius.
So when samuel assumes there would be a "fall" from A to B or from A to
C he is in fact wrong, they should all lie on the same level.
What you will see in this case would be the expected:
Obviously this is not a mathematical argument, its only meant to provide
an intuitive understanding in the flaw of his reasoning.
I've thought of a way you should all be able to experiment on this
yourselves, using the model of a sphere that many of us have on our own
computers. The following snapshots were taken from google earth to
demonstrate what a large sphere actually looks like from relatively close
to its surface.
Note: These shots were all taken looking along a vector tangential to the
earths surface (In much the same way that we would see our horizon)
I advise you also to take careful note of the altitude each time.
At about 5000 km
At about 1500 km
At about 100km
At about 11km
(Note: this is about flying altitude - for those of you who think you should be able to see the earths curvature from a plane)
At about eye level
The horizon looks pretty level here wouldn't you say?
Nothing like our dear friend Samuel might describe it.
I encourage someone else who might be more adept at it to do the
maths, otherwise I might take a shot at it later.... I just don't really have
the time.
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