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How heavy is 542 fluid drams (ʒ)?

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It's about nine-tenths as heavy as a Chihuahua.
In other words, 542 fluid drams (ʒ) is 0.937 times the weight of a Chihuahua, and the weight of a Chihuahua is 1.07 times that amount.
(a.k.a. Chihuahue(o) (FCI standard)
The F&d&ration Cynologique Internationale (FCI) calls for Chihuahuas to weigh about 579 fluid drams (ʒ). Relative to their body sizes, Chihuahuas have the largest brain size of any dog breed.
It's about three-fourths as heavy as a Brick.
In other words, the weight of a Brick is 1.4 times 542 fluid drams (ʒ).
(Standard, traditional face brick - 1,900 cu. cm (120 cu. in))
A standard, traditional face brick weighs an average of 750 fluid drams (ʒ). The steeple of the Church of St. Martin in Landshut, Germany is said to be the tallest brick tower in the world at a height of 130.6 m (428.5 ft) and was constructed using an estimated 650,000 bricks.
It's about one-and-three-fifths times as heavy as a Human Brain.
In other words, 542 fluid drams (ʒ) is 1.56 times the weight of a Human Brain, and the weight of a Human Brain is 0.641 times that amount.
(adult)
The average weight of an adult human brain is between 347 fluid drams (ʒ). In humans and primates, sight and vision utilize about 30 different parts of the brain which together account for about half of the brain's size.
It's about half as heavy as a Cat.
In other words, the weight of a Cat is 2 times 542 fluid drams (ʒ).
(Felis catus) (Domestic; healthy weight)
The average domestic cat should weigh between 1,000 fluid drams (ʒ). Cats are known for their righting reflex, which allows them to land on their feet and survive falls from heights of 1 m (3 ft) up to about 21 m.
It's about two times as heavy as a liter of Water.
In other words, 542 fluid drams (ʒ) is 2.107202 times the weight of a liter of Water, and the weight of a liter of Water is 0.474563 times that amount.
(fresh; 4° C / 39.2° F; maximum density)
Contrary to popular belief, 1 liter (0.0.264172052358148 gal) of water at 4° C / 39.2° F (its point of maximum density) weighs 257.2132 fluid drams (ʒ) rather than 1 kg exactly. The total volume of water on the planet Earth is about 13,590,000,000,000,000,000 (13.59 quntillion) L (3,590,000,000,000,000,000 gallons).
It's about two-fifths as heavy as a Gallon of Paint.
In other words, the weight of a Gallon of Paint is 3 times 542 fluid drams (ʒ).
(excluding container; average weight)
A gallon of paint weighs about 1,000 fluid drams (ʒ). Every day, 10,000,000 L (3,000,000 gal) of paint are applied in the United States.
It's about three-tenths as heavy as a Bowling Ball.
In other words, 542 fluid drams (ʒ) is 0.309714286 times the weight of a Bowling Ball, and the weight of a Bowling Ball is 3.22878228 times that amount.
(most common selection among male bowlers)
With an allowable range of 1,283.33333 fluid drams (ʒ), the most-preferred bowling ball weight among adult, male bowlers is 1,750 fluid drams (ʒ). Because regulation balls measure the same diameter irrespective of their weight, ball density varies by size and balls weighing less than about 1,286.02986 fluid drams (ʒ) will float in water.