Hydrostatics.

305

Since Bodies of different specific Gra-vities, equiponderating each other in Air,

upon

Weight of the Body B, and A -f- B V c — Weight of

the Compound. But A«-fBi = A-(-BXr=:As-f- B c ; whence A a — Ac — Bc — b B ; consequentlyA : B :: r— b\a — c, which is the Rule above laiddown where A is the Quantity of Gold, and B that ofSilver, and A + B the Composition of Hiiro’s Crown.

3. When King Hiiro (suspecting the Workmen hadallayed the Gold with more Silver than was necessary)sent to Archimedes to examine into, and detect the Fraud,if there were any ; this great Mathematician was longat a loss to think of any Method of doing it; till oneDay getting into a Tub full of cold Water to bathehimself, he observed, that as he entered the Tub theWater ran out, and he immediately saw it must follow,that if the Tub were full, the Water which ran outupon his Immersion, must be equal in Bulk to hisBody.

4. Hence the Philosopher began thus to reason : IfI immerse the Crown in a Vessel full os Water, it willprotrude as much as is equal to its Bulk. If after thisI immerse the fame Weight of pure Gold, and pureSilver, I shall get Bulks of Water equal to each ; con-sequently having the Bulks of Gold, Silver, and Crownof equal Weight, I have the specific Gravities, whichmust be as the Bulks inversely. Then i proceed to findthe Ratio, or Proportion of Gold to the Silver in theCrown as follows.

5. Suppose A M L B be a Vessel filled with Waterto the Height D C, and that the Mass of Gold equalin Weight to the Crown, being immersed into theWater, raises the Surface thereof to E ; and after that,the Mass of Silver of the fame Weight immersed raisesthe Surface to G ; then if the Height of the Vesselabove C be divided into equal Parts, and DF — 11,and D G — iq; it is plain the Bulks of the Gold and"Silver will be as D F to D G, and the specific Gravi-tes as D G to D F. Lastly, if the Crown be immersed,

Vol. I. X it

PI. XVI.Fig. 5.