188 OF THE PRESSURE OF UNMIXABLE FLUIDS OF DIFFERENT DENSITIES 



RULE. Multiply the difference of the yiven specific gravities, 

 by the natural cosine of the circular space in contact with one 

 of the fluids ; to the product, add the natural cosine of the 

 whole circular space drawn into the less specific gravity , and 

 from the sum subtract the greater specific gravity for a 

 dividend. 



Again. Multiply the difference between the specific gravi- 

 ties, by the natural sine of the circular space in contact^with 

 one of the fluids, and to the product, add the natural sine of 

 the whole circular space drawn into the less specific gravity, 

 and the sum ivill be the divisor. 



Lastly. Divide the dividend by the divisor, and the quotient 

 will give the natural tangent of a circular arc, which being 

 found in the tables, enables us to assign the actual position of 

 the fluids when in a state of equilibrium. 



201. EXAMPLE. On the inner surface of a circular tube containing 

 mercury and rectified alcohol, it is observed, that when the tube is 

 held in a vertical plane, and the fluids in a state of equilibrium, a 

 space of 75 degrees of the circumference, is occupied by, or in contact 

 with each fluid ; it is required to determine the position of the fluids 

 at the instant of observation, their specific gravities being 14000 and 

 829 respectively ? 



In this example there are given /= 14000; s 829; ^ 7 7 

 its natural sine and cosine equal to .96593 and .25882; 2^>rr: 150, 

 its natural sine being .50000, and its cosine .86603 ; consequently, 

 by proceeding according to the directions contained in the foregoing 

 rule, we shall obtain 



For the dividend scos.2^ -f (s' s)cos.< s'= 829 X .86603 -|- 



(14000 829) x .25882 14000 = 11 309 .02065 ; 



For the divisor s sin .2< (V s) sm.^> 829 X .50000 (14000 



829) X .96593 = 1 3136.76403 ; 



consequently, by division, we obtain 



ta "-* = = - 86086 = at - tan - 40- 43' 25'. 



202. The positions of the fluids in this example, are manifestly 

 very different from what they are in the preceding, the point F in the 

 vertical diameter falling on the other side of the centre; but in this 

 case, we shall leave the construction for the reader's amusement, and 

 proceed to inquire what changes the general formula will undergo, in 



