Weight Variation by Latitude

Weight Variation by Latitude refers to the claims that scales have measured masses to weigh up to 0.5% less near the equator compared to the polar areas. It is asserted that this is due to a combination of the centrifugal effect from the rotation of the earth and the increased mass at the equator.

Upon assessment of the experiments supporting this, it is found that these experiments are conducted with the scale and test body exposed to the surrounding atmosphere. A scale is calibrated for one area and then taken to another area, uncalibrated. Measures are not taken to isolate the test body and the measuring device from the influences of the environmental atmosphere. Weight is affected by factors other than 'gravity'. Pressure, humidity, and other properties affect scales. It is known that that pressure is greater at the poles and lesser at the equator.^[1] It is further known that pressure is greater at lower altitudes near sea level and lesser at higher altitudes. Humidity likewise has a relationship with the latitudes^[2] and altitudes, as well as other interrelated properties such as air viscosity.

Andrew Huszczuk, Ph.D., writes (Archive):

“ Would you take a medication knowing that a pharmacy used an uncalibrated scale to weigh its ingredients? Would you board a plane knowing that the fuel or altitude gauges are not calibrated at frequent intervals?

In these and thousands of other applications scientific bases and rules of metrology must be obeyed to assure chaos-free operation of modern societies. To scrutinize performance of measuring devices a process of calibration must be carried out by means of applying a known standard and getting back a correct reading. ”

Scales Affected by Atmosphere

Precision Scales

From Drift in Measurements with Analytical Balances (Archive) we read:

“ Pharmaceutical laboratories and bioscience research institutes make extensive use of analytical balances that are highly sensitive. These analytical balances are greatly affected by their environment and also by the way they are installed and handled. ”

One precision scale manufacture lists many factors (Archive) which can affect a scale:

Factors That Can Affect Your Scale’s Accuracy

“ Differences in air pressure – Scales can provide inaccurate measurements if the air pressure from the calibration environment is different than the operating environment. ”

If the air pressure from the calibration environment is different than the operating environment, it will affect the scale. Also listed on the page are temperature and humidity which can affect the operation of a precision scale.

Standardscale

Standardscale.com says (Archive):

How does the environment affect weighing on a lab balance?

“ The environment surrounding a balance is vital if you are to maintain the manufacturer's stated performance ratings. Really, the manufacturer doesn’t matter in this regard, as a bad environment will adversely affect any balance. There are many influences to consider and to remove, as far as is possible, from the area surrounding the balance. ”

Industrial Scale Comany

The Industrial Scale Company tells us (Archive):

Sources of Error in Weighing Instruments

“ Environmental Factors – A scale’s accuracy and precision are highly dependent on the environment in which it is installed. ”

Bathroom Scales

Inconsistent scale readings are also readily seen at home in bathroom scales. If left uncalibrated, the reading can vary.

Can I Trust My Bathroom Scale? (Archive)

“ A dietician who weighed herself 15 times over the course of a day found that she’d “gained” seven pounds. ”

Uncalibrated Scale Drift

On the topic of uncalibrated scale drift precisionscale.com portrays a 0.5% variance as small, and gives it as an example of why calibration is necessary.

https://precisionscale.com/scale-calibration/ (Archive)

Understanding the Importance of Scale Calibration

“ In more complex terms, scale calibration involves the process of comparing a known standard, such as a calibration service’s certified weights, to the results given by the unit that is being tested (your company’s scales). Such a procedure ensures the accuracy of the unit being tested. When your business relies on accuracy of weights to run and operate smoothly and protect profits, calibration of your scales is not negotiable. It is an absolute must and will also ensure that your business is adhering to industry standards and Canadian laws and regulations if you use the weights and measurements to calculate truck loads.

Why Is Calibrating Your Business’s Scales So Important?

While you may not realize it, your business’s scales and the accuracy they produce have a direct impact on your company’s bottom line. If your scales are off, your profits can be off as well. For example, let’s say that your business deals in a very expensive powdered cleaning product. If the product cost is $10 per pound and on average you weigh 1,000 pounds of product per day, the total value of product weighed each day is $10,000.

Now, let’s say that your scale is out of balance by just 0.5 percent. That discrepancy will cost you approximately $50 per day, or $1,000 a month. Unless your company is in the position to literally throw away $1,000 a month ($12,000 a year), then it becomes very apparent why scale calibration is a necessity. In fact, keeping these numbers in mind, one can actually say that such a service is actually an insurance policy protecting your business’s bottom line, rather than just another routine business expense. ”

Legitimate Measuring Device

In fact, in the EU if a scale is not calibrated before use after repositioning then it is not considered to be a legitimate measurement device. From a precision scale manual we see:

https://www.soehnle-professional.com/documents/all/406/Manual_9437_EN.pdf (Archive)

Kern Gnome Experiment

The precision scale manufacturer Kern conducted a public test of the variation of weight by latitude, showing that weight changed when a resin composite gnome and one of its precision scales were sent to members of the public at different latitudes:

Website: http://gnome-experiment.com/ (Archive)

Scale Not Calibrated

The scale was calibrated in Germany and then sent to different areas:

https://www.chemistryworld.com/news/gnomadic-experiment/4924.article (Archive)

“ Kern the gnome and a Kern and Sohn balance, calibrated at the firm’s laboratory in Balingen, Germany, are travelling around the world to anyone who requests a visit in a specially designed flight case. Gloves and cleaning implements also come along for the ride, so the mass of the gnome isn’t altered by dirt or over enthusiastic cleaning.

Several factors affect the gravitational field at different locations on the Earth, for example the closer Kern gets to the equator, the less he should weigh because the velocity of the Earth’s spin at the equator (1670km/hr) counteracts the force of gravity by up to 0.3%. This weight loss will also be increased by the equatorial bulge that means Kern would be further from the centre of our planet and gravity is proportional to the inverse square of the distance between two objects. ”

Long weigh from gnome: The bizarre experiment where a garden ornament travels the world to measure gravity (Archive)

“ Kern travels in a reinforced case containing himself and a Kern EWB 2.4 Scale calibrated according to local gravity in Balingen, Germany, to ensure any weight change he encounters on his travels shows up. ”

Procedure

Members of the public were instructed to place the gnome onto the scale and to record their results:

Spring Scale Experiment

The Spring Scale Experiment shows a similar methodology of calibrating in one area and taking to another:

http://physicstasks.eu/930/spring-scale-on-the-pole-and-on-the-equator (Archive)

“ We calibrated a spring scale on the North Pole and then we moved the scale to the Equator.

Does the spring scale give the same readings as on the pole? Give reasons. ”

The book Practical calculations for engineers (Archive) describes the same method:

“ Suppose such a spring balance be made and calibrated in London by suspended weights which are mutiples or sub-multiples of the point weight. Then if the balance and the standard pound weights were taken to different latitudes, it would be found that the balance would show increasing readings for the same weight in passing from the equator to the poles. ”

Worldwide Air Pressure Gradient

The following sources explain that air pressure has a relationship with latitude, being lower near the equator and greater near the poles:

https://www.pmfias.com/pressure-belts-pressure-systems-equatorial-low-sub-tropical-high-sub-polar-low-polar-high/ (Archive)

World Distribution of Sea Level Pressure

“ The atmosphere exerts a pressure of 1034 gm per square cm at sea level. This amount of pressure is exerted by the atmosphere at sea level on all animals, plants, rocks, etc.

Near the equator the sea level pressure is low and the area is known as equatorial low. Along 30° N and 30° S are found the high-pressure areas known as the subtropical highs. Further pole wards along 60° N and 60° S, the low-pressure belts are termed as the sub polar lows. Near the poles the pressure is high and it is known as the polar high. ”

and further down:

“ Polar High Pressure Belt

- The polar highs are small in area and extend around the poles. - They lie around poles between 80 – 90° N and S latitudes.

Formation

- The air from sub-polar low pressure belts after saturation becomes dry. This dry air becomes cold while moving towards poles through upper troposphere. - The cold air (heavy) on reaching poles subsides creating a high pressure belt at the surface of earth. ”

https://en.wikipedia.org/wiki/Polar_High

“ Polar High

The polar highs are areas of high atmospheric pressure around the north and south poles; the north polar high being the stronger one because land gains and loses heat more effectively than sea. The cold temperatures in the polar regions cause air to descend to create the high pressure (a process called subsidence), just as the warm temperatures around the equator cause air to rise to create the low pressure intertropical convergence zone. ”

Worldwide Humidity Gradient

Humidity, like temperature and pressure, has a relationship with the equator as well:

https://en.wikipedia.org/wiki/Humidity#Climate

“ The most humid cities on earth are generally located closer to the equator, near coastal regions. Cities in South and Southeast Asia are among the most humid. Kuala Lumpur, Manila, Jakarta, and Singapore have very high humidity all year round because of their proximity to water bodies and the equator and often overcast weather. ”

Addendum

When one examines the properties of the air they will find that other elements too are related to pressure, temperature, and humidity; such as air viscosity and thermal diffusivity -- all of which may affect the operation of scales complex ways. If a scale is affected by any of that then those factors should be excluded, ideally in a vacuum chamber experiment which demonstrates the matter empirically, independent of any assumption about the atmosphere. Merely claiming or asserting that there are no factors that affect the device is insufficient. Yet, a search for examples of this experiment conducted in a vaccum chamber finds none.

Any singular assessment appears insufficient. It is due to the complex nature of the air that scale manufacturers and metrologists recommend calibrating often, whether a scale is indoors or outdoors. A company's failure to calibrate its scales in certain fields can result in fines and even legal action. Adopting this basic and reasonable level of scrutiny, an experiment which is based on bringing uncalibrated scales to different environments and then looking for differences of a fraction of one percent of a body's weight must only be questioned for validity.

Historical Fudging

Of interest, upon reviewing the history of weight changes by latitude we find that the nature of the Earth was modified because the theory did not meet the data. This is the origin of the flattening of the poles.

From Voltaire we see (Archive):

“ The celebrated Huygens, by calculating centrifugal forces, had proved that the consequent diminution of weight on the surface of a sphere was not great enough to explain the phenomenon, and that therefore the earth must be a spheroid flattened at the poles. ”

Hence, the theory was changed to fit the result, giving us a round world with flattened poles. However logical a bulging equator is in concept, the ability to change a theory to meet a desired result exists as a fudge factor. Had the results been any more or less different, the theory or associated theories would have been changed to fit those results, either by bulging out the equator more or less to fit the data or by looking for other elements to modify.

Time Dilation by Latitude

In contradiction to an uncontrolled three hundred year old practice of bringing weighing devices to different environments and adapting the theory to fit the results, other situations involving devices which are not affected by atmosphere do not show changes by latitude. See: Time Dilation by Latitude

Gravity Variation by Altitude

It is seen that the historical weight variation by altitude experiments are also guilty of being conducted in uncontrolled conditions. The following researcher says that, although he believes that gravity decreases with altitude, that the experiments in the literature do not take factors related to the atmosphere into account. The author calls for better experiments.

Unchecked Aspects of Variation of Acceleration due to Gravity with Altitude
Ajay Sharma

https://www.gsjournal.net/Science-Journals/Research%20Papers-Astrophysics/Download/3606 (Archive)

“ It is correctly established that g decreases with altitude, but the variation of g with atmospheric of g with atmospheric pressure (decreases with altitude) is not considered in precise experiments in the existing literature. Torricelli determined in pioneering experiments that height of mercury column in barometer as 0.76m due to atmospheric pressure in 1644. Newton formulated g in 1685, and then Pascal’s Law was treated in presence of gravity for imaginary cylinder of liquid. Thus equation P=DgH is obtained which relates acceleration due to gravity, g with atmospheric pressure, P. The expression for variation in g with altitude as gh = g/(1+h/R)2, by both methods will be compared. At sea level the heights of liquid columns (for water 10.33m , for glycerine 8.202m , ethyl alcohol 13.16m ) are independent of other factors such as diameters of tubes, viscosity, surface tension of liquid, angle of contact and capillarity etc. At height of 2 km above the surface of the earth the heights of liquid columns are reduced e.g. for mercury 0.5967m, for water 8.1158m and for glycerine 6.4411 m. Now measuring P, H and g can be calculated. The value of g can be determined by both methods at various heights and should be same. Theoretically when atmospheric pressure becomes zero then value of gH (P/DH) must tend to zero; according to gh = g/(1+h/R)2, gh becomes zero at infinite large distances. But no such attempts have been reported in literature, hence it is open problem especially when tubes of various diameters are considered and characteristics of liquids are different. Due to diverse experimental conditions of liquids and equipments, mercury may be regarded as ideal liquid for such measurements of pressure. The value of g due to altitude decreases steadily, whereas due to atmospheric pressure g decreases abruptly. So sensitive experiments are absolutely necessary to draw concrete conclusions. ”

“ There is no factor which takes in account the diameter of the tube in which height of liquid column is measured. Theoretically, the height of liquid column must be same for capillary tube (closed upper end ) and tube of diameter two feet. However the phenomena of rise or fall of liquids is observed in capillary, whereas upper end is open. This aspect is not taken in account ”

“ At height of 50km the total air is only 1% implying considerable decrease in pressure as atmospheric pressure decreases. At height of 50 km, atmospheric pressure is 75.944 Pa and the same at height of 25 km is 2511.02 Pa. Thus accordingly g will decrease ”

Under the section Table II: Heights of liquid columns of different liquids in tubes of different diameters at different heights the paper goes on to show the historical results of the diminution of g up to an altitude of 50 meters.

There are other factors of the atmosphere to consider other than air pressure, of course, and which may escape consideration. It is far more appropriate to conduct such an experiment in a controlled setting, such as a vaccum chamber, where external influence of the atmosphere is eliminated and only the location changes.