144 ARITHMETIC. 



3. How much corn at 23. 6d. 3s. 8tl. 4s. ana 43. 8d. pet* 

 bushel, must be mixed. together, tliat the compound may- 

 be worth 3s. lod. per bushel ? 



Ans. 12 at 2S. 6d. 12 at 3s. 8d. 18 at 4s. and 18 at 4s. 8d- 



4. A goldsmith has gold of 17, 18, 22 and 24 carats 

 fine : how much must he take af each to make It 21 carats 

 fine ? Ans. 3 of 17, i of 18, 3 of 22 and 4 of 24. 



i;. It is reqiiired to mix brandy at 8s. wine at 7s. eider 

 at IS. and water at o per gallon together, so that the mixt- 

 ure may be worth 5s. per gallon ? 



Ans. 9 of brandy, 9 of wincj 5 of cider, and 5 of water. 



RU.LE 2.* 



JVhen the whole composition is limited to a certain quantity^ 

 find an answer as before by linking 5 then say, as the sum 



of 



* A great number of questions might be here given relating to 

 the specific gravity of metals, &c. but one of the most curious^ 

 with the operation at large, may serve as a sufQcient specimen. 



HiERO, king of Syracuse, gave orders for a crown to be madtf 

 entirely of pure gold ; but suspecting the workmen had debased it 

 by mixing it with silver or copper, he recommended the discove- 

 ry of the fraud to the famous Archimedes ; and desired to knoW 

 the exact quantity of alloy in the crown. 



Archimedes, in order to detect the imposition, procured two 

 other masses, one of pure gold, the other of silver or copper, 

 and each of the same weight with the former ; and each being put 

 separately into a vessel full of water, the quantity of water expell- 

 ed by them determined their specific bulks : from which and their 

 given weights, the exact quantities of gold and alloy in t\\c crown 

 may be determined. 



Suppose tlfe weight of each crown to be lOib. and that the wi-* 

 ter expelled by the copper or silver v/as •921b. by the gold '^ilh. 

 and by the compound crown •641b. what v;iil be the quintlties of 



gold and alloy in t*he crown ? 



The 



