84 EXAMPLES. 



being 9 Ibs., compare the specific gravities of the solid and 

 of water. Ans. 5 : 7. 



29. A piece of wood which weighs 57 Ibs. in vacuo, is at- 

 tached to a bar of silver weighing 42 Ibs., and the two 

 together weigh 38 Ibs. in water. Find the specific gravity 

 of the wood, that of water being 1, and that of silver 10.5. 



Ans. 1. 



30. Equal weights of two fluids, whose specific gravities 

 are s and 2s, are mixed together, and one-third of the whole 

 volume is lost. Find the specific gravity of the resulting 

 fluid. Ans. 2s. 



31. Two fluids of equal volume, and of specific gravities 

 s and 2s, lose of their whole volume when mixed together. 

 Find the specific gravity of the mixture. Ans. 2s. 



32. A cylinder floats vertically in a fluid with 8 ft. of its 

 length above the fluid ; find the whole length of the cylin- 

 der, the specific gravity of the fluid being three times that 

 of the cylinder. Ans. 12 ft. 



33. A body floats in one fluid with f of its volume im- 

 mersed, and in another with f immersed. Compare the 

 specific gravities of the two fluids. Ans. 15 : 16. 



34. A block of wood, the volume of which is 4 cubic feet, 

 floats half immersed in water. Find the volume of a piece 

 of metal, the specific gravity of which is 7 times that of the 

 wood, which, when attached to the lower portion of the 

 wood, will just cause it to sink. Ans. f of a cubic foot. 



35. A cone, whose specific gravity is , floats on the water 

 with its axis vertical, (1) with its vertex downwards and (2) 

 with its vertex upwards. What part of the axis is immersed 

 in each case? Ans. (I) \ ; (2) 0.0436. 



36. A cone, whose specific gravity is , floats with its 

 axis vertical. Compare the portions of the axis immersed, 

 (1) when the vertex is upwards, (2) when it is downwards. 



Ans. ^2-1:1. 



