3 ° 4

Hydrostatics.

Having given the specific Gravity ofGold to Silver as ly to u, and supposeany Compound thereof, as King Hiero T sCrown, whose specific Gravity is 16 ; todetermine the Proportion and Weight of theGold and Silver employed in making it, lay,yls the Difference of the specific Gravities of theCompound and the lighter Ingredients viz. 5,is to the Difference of the specific Gravities ofthe heavier Ingredient and the Compound , viz.

3, Jo is the Bulk of Gold to that of Silver madeuse of. That is, if the whole Crown weredivided in 8 Parts, the Gold would consist of5, and the Silver of 3 : Then the Magni-tudes 5 and 3, multiplied by the specificGravities 19 and 11 severally, will give theNumbers 95 and 33, which express the Pro-portion off' the Weight of the Gold to that ofthe Silver (LXV).

Since

(LXV) 1. The Rules here given for solving thethree first Problems are only those Theorems expressedin Words which you find in Annot. LVI1. Art. 9, 10,11. But that which concerns the fourth, relating toKing Hi era's Crown, I shall here demonstrate as fol-lows :

2. Let A and B be any two Sorts of Matter, and aand b denote their specific Gravities ; the Compoundmade of those two Bodies will be A 4- B ; and let cbe the faecific Gravity thereof. Then since the abso-lute Weight of a Body is equal to its Bulk. multipliedby its specific Gravity (See Annot. LVII. Ait. 10.)we shall have Au = Weight of the Body A, and B b— '

Weight