I’m not sure what you got taught in school, but it’s a basic undergraduate physics experiment. All you need is a balance and a way to capture water overflow.
1. Use the balance to collect known pure gold equal in weight to the crown.
2. Fill a bowl with water, capture the runoff from immersing the crown.
3. Fill a bowl with water, capture the runoff from immersing the pure gold.
4. Test the balance of the two runoffs. If the crown is pure gold, then they balance. If the crown is adulterated, and thus less dense than pure gold, the crown’s runoff will be greater.
No need for precise measurements of volume or mass or density, just simple comparisons on a balance.
Reading the link, it looks Galileo is solving the more difficult question of the exact ratio of gold and silver used to make the crown. I think that can be solved by using pure gold and pure silver in differing amounts.
This page, on the same site as the one Pardel-Lux linked to, explains the problems with that approach. The three reasons mentioned are, first, that it’s not very ingenious, second, that it doesn’t use Archimedes Law at all, and third, that it couldn’t be done with sufficient accuracy using the tools available. The first two arguments can be dismissed (a technique that works doesn’t need to be ingenious), but for the third point, they make this argument. The largest known gold wreath from that time weighs 714 grams and has a maximum diameter of 18.5 cm. They round up to 1000 grams and assume that a 20 cm diameter vessel is used to contain it. 1000 grams of gold has a volume of 51.8 cm3, while if 30% were replaced with silver, it would have a volume of 64.8 cm3. The difference in the rise of the level of water would then be only 0.41 mm. They say
This is much too small a difference to accurately observe directly or measure the overflow from considering the possible sources of error due to surface tension, water clinging to the gold upon removal, air bubbles being trapped in the lacy wreath, and so forth.
You talked to him live, over the phone? I remember calling the number to submit a song for the Funny Five. It was a recording, and I had to leave a message.
I’ve wondered how Richard Nixon’s political career might have been different if in the late 1940s he had invested in a nose job and electrolysis on his facial hair.
The oldest confirmed shark attack is about 3,000 years old. A hunter gatherer in Japan was buried; he was missing a hand, a leg, and the other leg was present but detached, upside down, and missing a foot. At first researchers thought it was some kind of war injury, but they were able to match the lacerations on his bones with a tiger or great white shark.
After watching one of the better Hawaii Five-O episodes The Finishing Touch, I learned that guest star George Voskovec (remembered as juror #11 in 12 Angry Men) has a minor planet co-named after him and Jan Werich for their contributions to the Czech theatre.
At a glance, Czech arts and letters are well-represented: with planetary bodies named after Karel Čapek, Josef Škvorecký, Karel Jaromír Erben, Ondřej Sekora, Božena Němcová, Milan Kundera, Jaroslav Seifert, Jaroslav Hašek, Alphonse Mucha, and of course Kafka.
By comparison, the Irish didn’t do as well. Joyce got a planet, Yeats a crater on Mercury, Wilde an asteroid. But nothing for Lady Gregory, John Millington Synge, George Bernard Shaw(!), Micheál Mac Liammóir or Hilton Edwards.
How could I never have heard until today that in mammals the males have two different sex chromosomes (X and Y) but in birds it’s the females who have two (Y and W).
Researchers now think that’s the reason why male mammals, on average, have shorter lives than females, but male birds, on average, have longer lives than females.
