The "Eureka" story about Archimedes and the bath tub was as well known in Galileo's day as it is in ours. Galileo, who was a great admirer of Archimedes and adopted many of his methods, probably read it in one of the editions of Vitruvius's The Ten Books on Architecture,[1] which was very popular in Renaissance Europe. Supposedly, it was in the bath tub that Archimedes figured out the solution to the problem posed to him by the king of Syracuse: was a crown (or wreath) supposedly made of pure gold in fact entirely gold? He measured the amount of water displaced by the crown and by an equal weight of gold, and found that the crown displaced more water. Its specific gravity was thus less than that of gold, and therefore it had been adulterated with another metal.
Weighing precious metals in air and then in water was presumably a practice that was common among jewelers in Europe. Galileo had some ideas for refining the practice and, at the age of 22, he wrote a little tract about it, which he entitled La Bilancetta, or "The Little Balance." What Galileo described was an accurate balance for weighing things in air and water, in which the part of the arm on which the counter weight was hung was wrapped with metal wire. The amount by which the counterweight had to be moved when weighing in water could then be determined very accurately by counting the number of turns of the wire, and the proportion of, say, gold to silver in the object could be read off directly.
This little tract illustrates the mixture of the theoretical and practical that marks Galileo's science in contrast to that of most of his contemporaries.
Notes: [1] There are many editions of The Ten Books on Architecture. The story of Archimedes is related in the introduction to Book IX.
Sources: The tract is available in English translation in Laura Fermi and Gilberta Bernardini, Galileo and the Scientific Revolution (New York: Basic Books, 1961), pp. 133-14
A common equipment used to measure the density of a material based on Archimedes' principle is a density balance or a hydrostatic balance. This equipment calculates the density by comparing the mass of the object in air to its apparent mass when submerged in a fluid. By measuring the buoyant force acting on the object, the density can be accurately determined.
The balance scale was invented by the ancient Egyptians around 3000 BC. This simple device consists of a beam pivoted at its center with pans on both ends to hold the objects being weighed. It is still widely used today for measuring the weight of objects.
The hydrostatic paradox refers to the principle that the pressure at a given depth in a liquid is determined solely by the weight of the fluid above that point, regardless of the shape or volume of the container holding the liquid. This means that the pressure at a specific depth in a liquid is constant, and does not depend on the shape of the container.
Yes, Tesla coils are still used today primarily for educational and entertainment purposes, such as in science demonstrations, music performances, and hobbyist projects. They are also occasionally utilized in niche applications like in medical devices and research instruments.
Yes, Albert Einstein's work is still very influential and widely used today in theoretical physics, particularly in the areas of general relativity and quantum mechanics. His contributions have had a lasting impact on our understanding of the universe.
Galileo's hydrostatic balance is a device used to compare the densities of liquids or solids by measuring the buoyancy force exerted on a submerged object. By balancing the weight of the object in water with the weight in air, the density of the object can be determined. This device was crucial in Galileo's study of buoyancy and density.
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