[HorstFue]

Another nice chapter from Earth not a Globe
Deflection of Falling Bodies.

"The falling of bodies from high places is a further proof of the daily rotation of the earth. By this motion everything upon the earth describes a circle, which is larger in proportion as the object is raised above the surface; and as everything moves round in the same time, the greater the elevation of the object, the faster it will travel; so that the top of a house or hill moves faster than its base. It is found then that when a body descends from a high place, say a few hundred feet, it does not fall exactly beneath the spot it left, but a little to the east .of it. This could not happen unless the earth had a motion from west to east. Were the earth stationary the body would fall immediately under the place it left."

This is more or less a description of the Coriolis effect in vertical direction.

But that's not the issue. What the experimenters neglected is: Inertia!

But lets first have a look at the results. All experiments have in common, that a deviation to the south was noticed.

...The experiments of Guglielmani gave indeed such a deviation; but, at the same time, they gave a deviation to the south...
... Dr. Benzenberg undertook new experiments at Hamburgh, from a height of about 240 feet, which gave a deviation of 3·99 French lines; but they gave a still greater deviation to the south ...
... Professor Reich, in a pit of 540 feet, at Freiberg. Here the easterly deviation was also found in good agreement with the calculated result; but a considerable southern deviation was observed...
... The whole of the bullets and plummets dropped south of this datum line, and so much to the south that only four (An.: of 48 in total) of the bullets fell upon the platform placed to receive them... (An.: this datum line was placed exactly beyond the "release point" and oriented in East/west direction)

What would a real scientist do with this result? Dismiss it? Or search for an explanation?

Analogy: The  classic centrifugal experiment: You tie an object to a thin rope or similar and then swing this object in a circle around you. Now release or cut the rope, what's happening? The object will - due to inertia or conservation of momentum - fly away in a straight line, tangential to the circle it was forced to follow before.

The same is happening with these experiments. All objects on earth - as long as these are "connected" to the ground - follow a circular path around Earth's axis, the latitude circle.
Now release the object. Ok, it will most notably fall down, but this is only the vertical component.
The horizontal component: The object will no more follow the latitude circle, it will follow a straight line, tangential to the latitude circle!
Another ok: This effect is small - as the experiments above show, but perceivable.
And: The object will deviate away from the latitude circle, away form the North pole, so in southern direction.

A coarse estimation:
Given a drop height of h = 100m;  Fall time (release to impact) will be t = sqrt(2/g*h) = sqrt(2/9.81*100) = 4.5 s
Earth's Radius for latitude 45°, R = 6371000m * cos(45°) = 4504989m
speed at circumference at latitude 45°= 2*pi*r/T = 2*3.1415*4504989m/24/3600/s= 328 m/s   (734 miles/hour)
So: the horizontal distance the object will fly in 4.5s "s" is 4.5*328 = 1476m

The object will "fly" very close to the latitude circle. It will not fly somewhere into the distance, as all other objects nearby are "running" at the same speed, with nearly identical heading.
This deviation is quite similar to the "earth's curvature calculator". You can also approximate it by this rectangle scheme.
Deviation d = sqrt(R²+s²)-R = sqrt(4504989*4504989+1476*1476 )-4504989 = 0.24 m

So the deviation is as shown about 1 feet to the south. Which is - on a coarse estimation - consistent with the experiments shown.


Great R. closed the chapter with the charming words:

What value can such uncertain and conflicting evidence possess in the minds of reasoning men? They are shameless logicians, indeed, who contend that, from such results, the earth is proved to have a diurnal rotation!

[Humble B]

Great R. closed the chapter with the charming words:

What value can such uncertain and conflicting evidence possess in the minds of reasoning men? They are shameless logicians, indeed, who contend that, from such results, the earth is proved to have a diurnal rotation!

Great R was clearly not the sharpest knife in the drawer of math and physics, especially shameless behind on the topic of centrifugal forces.

[Tom Bishop]

What a terrible thread.

Read the deflection of falling body articles. You are the one who believes yourself to be smarter than the entire scientific community of the 1800's. It was the scientists and mathematicians of the 1800's who said that there would be negligible southern deflection. Rowbotham is simply relaying those sentiments.

[Humble B]

It was the scientists and mathematicians of the 1800's who said that there would be negligible southern deflection. Rowbotham is simply relaying those sentiments.

Newton described the role of centrifugal force upon the height of the oceans near the equator already in his "Philosophiæ Naturalis Principia Mathematica" published in 1687 and English translation published in 1728.
This shows that the centrifugal force of a spinning globe was already known and acknowledge by scientists and mathematicians for two centuries before Rowbotham started to ignore that the science of his time already had proven a spinning globe in many different and irrefutable ways.

[Tom Bishop]

Read moar. It is the scientists and mathematicians of the 1800's who predicted that there would be negligible southern deflection.

[Tom Bishop]

Thought experiment: We have a spinning record on a record player. If hold out a small BB over its 'equator' and drop it, will the BB hit the record south of the record's equator?

[Humble B]

Thought experiment: We have a spinning record on a record player. If hold out a small BB over its 'equator' and drop it, will the BB hit the record south of the record's equator?

Depends on the motion of the BB. When it is spinning with the record before it is dropped, it will hit the record outside (south) of the equator, just like this ball will always drop outside its own orbit when released:

[Tom Bishop]

Sure, but as I said, that force was predicted to be minimal.

A professor explains here:

if there is eastern deviation, there must also be southern deviation, the eastern will be much the greater

However, many experiments were giving contradictory results. The experiments were even contradictory to themselves.

The claims of observing "easterly deflection" is only gauged by statistics, which as we know, is easily manipulated.

Even when one cherry-picks the experiments showing the mean statistical easterly deflection, as with the Benzenberg experiment which supposedly shows the eastern deflection and is used as a "proof of the earth's rotation," we find a greater southern deflection. See here:

the result is that the experiments of Benzenberg should give a deviation of 3-95 French lines. The mean of his experiments gave 3-99; but they still gave a greater deviation south

This is the basis of the controversy. They cherrypicked easterly deflected experiments to show the supposed proof of the earth's rotation, but those cherries were not playing nicely with the supposed southern deflection that was expected.

The actual data for these cherrypicked experiments is ridiculous, in that a mean deviation of one tenth of an inch to the east supposedly shows the rotation of the earth whereas a southern deviation, measured in inches or feet, means nothing and is due to experimental error. Other experiments which do not show an easterly deflection are thrown away as being false and obviously in error.

[HorstFue]

A coarse estimation:
Given a drop height of h = 100m;  Fall time (release to impact) will be t = sqrt(2/g*h) = sqrt(2/9.81*100) = 4.5 s
Earth's Radius for latitude 45°, R = 6371000m * cos(45°) = 4504989m
speed at circumference at latitude 45°= 2*pi*r/T = 2*3.1415*4504989m/24/3600/s= 328 m/s   (734 miles/hour)
So: the horizontal distance the object will fly in 4.5s "s" is 4.5*328 = 1476m

Deviation to the south was d = sqrt(R2+s2)-R = sqrt(4504989*4504989+1476*1476 )-4504989 = 0.24 m

I owe you still the coarse estimation of the deviation in eastern direction:
The dropped object has an initial horizontal speed that is compared to the bottom (R+h)/R, or 1 + h/R.
The distance the object has gone in eastern direction compared to the ground will follow the same ratio:
so it's   s * (1 + h/R) or the delta is  s * h/R that's  1476m * 100m/4504989m   =  0.03m

[Tom Bishop]

The 1800's scientific community knew more about the RET than that.

0.03m is 1.18 inches, and they were measuring statistical easterly deflections of about 1/10th of an inch.

It may be that they themselves were rigging the math to undervalue the situation and salvage their model because such a magnitude of easterly deflection was not being seen, but nonetheless, a minimal southerly deflection is what was predicted.

[HorstFue]

Another excerpt from
Mechanics Magazine, Museum, Register Journal and Gazette, December 25th –June 24th, 1848, Vol. XLVIII

reads quite different on page 486 to what great R. and Tom "cherry picked" from the text.

The whole of the bullets and plummets
dropped south of this datum line, and so
much to the south that only four of the
bullets fell upon the platform placed to
receive them, the others, with the plummets,
falling on the steps of the man-machine, on
the south side of the shaft, in situations
which precluded exact measurements of the
distances being taken. The bullets which
fell on the platform were from 10 to 20 ins.
south of the plumb line.
The deflection being much greater than I
had anticipated could arise from any cause
which appeared likely to produce a devia-
tion, I feared the whole experiment was a
failure, but more recent considerations have
induced me to again test the method em-
ployed, I feel confident that the deflection
is not due to errors arising from the method
of dropping the bullets, and that it is not
at all likely that draughts of air in the shaft
had any important influence on the result,
but that there is a real deflection to the
south of the plumb line, and that in a fall of
one quarter of a mile it is of no small
amount.

[stack]

It may be that they themselves were rigging the math to undervalue the situation and salvage their model because such a magnitude of easterly deflection was not being seen, but nonetheless, a minimal southerly deflection is what was predicted.

"It may be"? Perhaps, perhaps not. How is that evidence of anything? What exactly is your point founded on? Seriously?

[Tom Bishop]

Another excerpt from
Mechanics Magazine, Museum, Register Journal and Gazette, December 25th –June 24th, 1848, Vol. XLVIII

reads quite different on page 486 to what great R. and Tom "cherry picked" from the text.

The whole of the bullets and plummets
dropped south of this datum line, and so
much to the south that only four of the
bullets fell upon the platform placed to
receive them, the others, with the plummets,
falling on the steps of the man-machine, on
the south side of the shaft, in situations
which precluded exact measurements of the
distances being taken. The bullets which
fell on the platform were from 10 to 20 ins.
south of the plumb line.
The deflection being much greater than I
had anticipated could arise from any cause
which appeared likely to produce a devia-
tion, I feared the whole experiment was a
failure, but more recent considerations have
induced me to again test the method em-
ployed, I feel confident that the deflection
is not due to errors arising from the method
of dropping the bullets, and that it is not
at all likely that draughts of air in the shaft
had any important influence on the result,
but that there is a real deflection to the
south of the plumb line, and that in a fall of
one quarter of a mile it is of no small
amount.

Yes, some experimenters reported significant southerly deflection. If you read through the full text of that particular experiment, the experimenter reports no easterly deflection.

Take a look at this author, who rejects many experiments and comes up with two that he likes:

http://adsabs.harvard.edu/full/1913PA.....21..208R

He obtained a mean easterly deviation of 28.4 mm, an excellent result. His mean southerly deviation of 1.5 mm is sufficiently small in view of his experimental errors not to weaken in any way the theory of Gauss and Laplace, according to whom meridational deviation is sensibly zero.

http://adsabs.harvard.edu/full/1913PA.....21..208R

Laplace and Gauss declared it (the southern deviation) to be practically insensible, and Bertram says that in latitude 45 degrees with a ten second fall it would not be more than the one-hundredth of a millimeter”

Names such as Gauss, Laplace, and Bertram were all predicting negligible southerly deflection. Significant southerly deflection goes against the Round Earth Model.

[Mysfit]

I agree with Tom.
Picking and choosing experiments to fit a hypothesis is silly.
I would like exactitude, but that would require infinite experiments.
For now, I will stick with wobbly knowns instead of certain unknowns.
Why is there a deflection to the south?

[HorstFue]

Puhhh difficult. Looks like I was wrong.
I could now ask, where's the error in my - and also W. RUNDELL's - conclusions?
Anyone? Couldn't find it in the thread so far.

I found it myself: What's the plumb line on a rotating earth? Does this line go through earth center?
No, due to the centrifugal forces, it deviates to the south (at medium latitudes).
The deviation of the plumb line compensates most if not all of the effect, described by me and W. Rundells paper. (explanation looks quite the same as my humble try)

Meanwhile I found another book, exactly giving this explanation.
MECHANICS MAGAZINE, MUSEUM, Register, Journal, GAZETTE, JULY 1 ST – DECEMBER 30TH, 1848. VOL. XLIX.
Page 13 - ON THE DEVIATION OF FALLING Bodies FROM THE PERPENDICULAR. - W. SLOGGETT

If the earth were at rest, a plumb line would tend direct to its centre, and thus indicate the true perpendicular; but the
centrifugal force arising from its rotation must evidently thow the plummet off, and thus cause a deviation in this likewise.

To illustrate these formulae by an example:it will be found that in lat. 53°1/4 nearly
(i.e. the lat. whose sine is ,6) a body dropped (in vacuo) without the earth's surface
through a height of 1254 feet falls 2.087716 feet from the perpendicular, while a plumb
line of the same length deviates 2.087340 feet. Hence the body falls ,000376 feet
south of the plumb line.