ORIGINATING THE CONSTRUCTION OF A HYDROSTATIC QUADRANT 185 



For the divisor, 



sin.20 (w l)sin.20= .98481 13 X.76604z= 10.94333; 

 consequently, by division, we obtain 



= - 53159 = nat.tan. 27 59' 41". 



195. Having discovered the value of x by the preceding operation, 

 the actual position of the fluids, with respect to the vertical diameter 

 of the tube, may from thence be very easily exhibited. 



Let AC BE represent a circular tube of glass, or some other trans- 

 parent matter, partly filled with mercury and 

 water, in such quantities, that when the tube 

 is retained in a vertical plane, and the fluids 

 in equilibrio, a space equivalent to fifty de^ 

 grees of the inner surface comes in contact 

 with each ; it is therefore required to assign 

 the actual~position of the fluids. 



Draw the vertical diameter AB, and from the point B where it meets 

 the inner circumference of the tube, set offsc from a scale of chords, 

 equal to 27 59' 41" ; then, take 50 in the compasses, and setting one 

 foot on c extend the other to G, thereby marking off the space occu- 

 pied by the mercury, including the lowest portion of the tube ; then, 

 with the same extent of the compasses, set off G E the space occupied 

 by the water, and the position of the fluids is from thence determined. 



Through the points c, G and E draw the straight lines CD, GII and 

 EF respectively parallel to the horizon, and meeting AB the vertical 

 diameter perpendicularly in the points D, H and F ; then are DH and 

 FH the perpendicular altitudes of the mercury and the water, as 

 referred to the plane passing through their common surface at G ; and 

 BD, BF are the respective altitudes, as referred to the vertical dia- 

 meter AB. 



Now, according to the question, the specific gravity of the mercury, 

 is fourteen times greater than that of the water ; and by the third 

 proposition preceding, the perpendicular altitudes are inversely as the 

 specific gravities; consequently, FH must be fourteen times greater 

 than DH; when the positions of the fluids are properly determined ; 

 let us therefore inquire if this be the case. 



It has been found above, that BC is equal to 27 59' 41", and by 

 construction CG and GE are each equal to 50 degrees; consequently, 

 BG 50 27 59' 41" 22 0' 19", and B E = 50 + 22 0' 19" 

 72 0' 19" ; hence we have 



