3°6

Hydrostatics.

upon being immersed into Water, willhave the Equilibrium immediately destroyed

by

it will raise the Surface to E, so that D E r: io.Whence the Proportion of the Bulks of the Gold andSilver in the Crown may be determined.

6. For since the Difference of specific Gravities ofthe Gold and Silver is D G — D F = F G = 8 j if theBulk of the Crown be divided into 8 equal Parts, it isevident, that since the specific Gravities of the debasedand pure Gold Crowns will be as the Bulk inversely ;that is, as DE to D E, we can easily find the Point H,which will express the specific Gravity of the former ;for D E : D F :: D G : 1 ) H, Now the Point H al-ways divides the Difference F G into two Parts G H,H F, which have the fame Proportion as the Parts ofSilver in the Crown have to the Parts of Gold ; foras the Point E ascends, the Point H descends, and whenE coincides with G, H falls upon E, and the Crownbecomes all Silver; as on the contrary, when E de-scends to F, and H ascends to G, the Crown becomesall Gold ; therefore every where F H will be to H G asthe Parts of Gold to the Parts of Silver in the Crown.

7. Therefore, in the present Cafe, because the Crown,when immersed, raises the Water to the Height D E,and PI is 3 Divisions below G, it shews that 3 of the8 Parts of the Crown are Silver, and consequently theother 5 Parts are Gold, as H is 5 of the Divisions aboveF. Hence the Bulk of Gold in the Crown is to thatof the Silver as 5 to 3, as before determined. ThatArchimedes took some Method like this is certain ; andit is said, he offered to Jupiter a Hecatomb of Oxenfor inspiring him with the Thought.

8. To the Problems in the Lecture, I shall add thefollowing. Let there be two Bodies A and B, oneheavier, the other lighter than Water; let their spe-cific Gravities be a and b, and let the Weight of A begiven, and denoted by W ; and let it be required tofind what Weight (w) of the lighter Body B must beconnected with the heavier, that so the Compound shallhave the fame specific Gravity with Water. Now be-cause.