OK, I see that there is in fact a measurable difference in the two weights.
Getting back to Chronos’ statement that the centrifugal force affects the water in the water level as well as the river, while this may well be the case, I would contend that the use of the water level is still the only way to determine “level” , centrifugal force or no centrifugal force, and the only way to determine “uphill” or “downhill”.
Without the water level, there is no possible way to establish a datum against which to measure declivity, and the terms “uphill” and downhill" become meaningless.
I suppose, yes, that is in fact what I am saying … unless there is some other point of reference to establish “level” “uphill” and “downhill”.
If the earth were a perfectly machined metal sphere with perfectly machined channels along which the rivers flow, and perfectly machined depressions to hold the oceans, then things might be different, and “uphill” river flow might well be measurable, but as things stand, there is no reference point against which to measure “uphill” or “downhill” other than against a water level.
I have this mental picture of millions of tall poles along the banks of the Mississippi, each pole engraved with an accurate level mark, as determined by the meniscus in a water level. All these marks, by definition, are on the same “level”. They are not, of course in a straight line (or rather in a flat plane) due to Earth curvature, but they are all on the same level, whether or not the centrifugal force affects the readings.
I am surmising that any measurements taken at any point of the distance between the engraved mark and the surface of the river will show either the same measurement or a gradual increase the further towards the mouth of the river.
No, they wouldn’t be different. A water level, sea level, the direction of river flow (barring weather and tides) would still be a function of gravity and rotation.
I think you are possibly misunderstanding what previous replies in this thread are trying to say. No one is seriously arguing for a new definition of “uphill” or “downhill”.