HYIHIOSTATICS. 329 



1. '>.">. An isosceles triangle is immersed with its axis vertical 

 and its base in the surface of a uniform heavy fluid ; prove that 

 thr resultant pressure on the area intercepted between any two 

 horizontal planes acts through the centre of gravity of that portion 

 of the volume of a sphere, described on the axis as diameter, which 

 is intercepted between the planes. 



1 ">"''. A conical shell is placed with its vertex upwards on a 

 horizontal table and fluid is poured in through a small hole in the 

 vertex ; the cone bigins to rise when the weight of the fluid 

 poured in is equal to its own weight : prove that this weight is to 

 the weight of fluid which would till the cone as 9 - 3 ^3 : 4. 



1557. A parabolic lamina bounded by a double ordinate per- 

 pendicular to the axis floats in a heavy uniform fluid with its focus 

 in the surface of the fluid and its axis inclined at an single 

 tan" 1 2 to the vertical ; prove that the density of the fluid is to 

 that of the lamina as 8 : 1 ; and that the length of the axis 

 is to the latus rectum as 15 : !. 



1558. A lamina in the form of an isosceles triangle float 

 a heavy uniform fluid with its plane v.rii.-al and (1) its ba-< 



of the fluid, (2) its base totally immersed in the fluid, its axis in 

 these positions making angles 6, < with the vertical ; prove that 



-, 



sin' a cos* a ' 



positions will not be possible unless 2a the vertical 

 angle < cos' 1 (J'2-\). 



1559. A right circular cone with its axis vertical and vertex 

 downwards is filled with two fluids which do not mix, and th-ir 

 common surface cute off one -f. MM th <>t th. ; ,\is tV.-m the vertex; 

 prove the whole pressures of tho fluids on th. 



face be equal, their densities are as 45 . 1 . 



1560. A barometer stands at 29-88 inches and mo- 

 meter is at the dew-point; a barometer and a cup of wat. 



