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How heavy is 359 fluid drams (ʒ)?

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It's about one-and-one-tenth times as heavy as a Human Brain.
In other words, 359 fluid drams (ʒ) is 1.03 times the weight of a Human Brain, and the weight of a Human Brain is 0.9710 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 one-and-two-fifths times as heavy as a liter of Water.
In other words, 359 fluid drams (ʒ) is 1.3957290 times the weight of a liter of Water, and the weight of a liter of Water is 0.71647150 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 257.21320 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 three-fifths as heavy as a Chihuahua.
In other words, 359 fluid drams (ʒ) is 0.620 times the weight of a Chihuahua, and the weight of a Chihuahua is 1.610 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 half as heavy as a Brick.
In other words, 359 fluid drams (ʒ) is 0.480 times the weight of a Brick, and the weight of a Brick is 2.10 times that amount.
(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 two times as heavy as a Basketball.
In other words, 359 fluid drams (ʒ) is 2.23792207790 times the weight of a Basketball, and the weight of a Basketball is 0.446843082640 times that amount.
(NBA official ball standards, Size 7)
A regulation NBA basketball, manufactured by Spalding, is known as a Size 7 ball and weighs 160.416666670 fluid drams (ʒ). These balls have 4,118 pebbles each with a diameter of 2.5 mm
It's about three times as heavy as a Football (Soccer).
In other words, 359 fluid drams (ʒ) is 3.20 times the weight of a Football (Soccer), and the weight of a Football (Soccer) is 0.310 times that amount.
(a.k.a. Soccer, a.k.a. Association Football) (FIFA Law 2 specification)
According to FIFA's Law of the Game number 2, a football must weigh between 110 fluid drams (ʒ) and 120 fluid drams (ʒ). An artifact on display at the Smith Art Gallery in Museum in Stirling, Scotland is said to be the world's oldest football and is about one-third to one-half the size of a modern football.
It's about three-tenths as heavy as a Gallon of Paint.
In other words, the weight of a Gallon of Paint is 3 times 359 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.