288 OF THE EQUILIBRIUM OF FLOATATION. 



w' 



V I varies as . 

 r* 



In the above investigation, we have supposed the specific gravity of 

 the fluid to remain constant ; but admitting it to vary, so that s may 

 become equal to s' ; then, in order that the upright stem may rest at 

 the same depth of immersion, w must become equal to (w -f- w') ; if, 

 therefore, we substitute s and (w -)- w'), for s and w in equation (223), 

 we shall obtain 



_ w -\-w' cs' 



I , , 



TrrV 



an equation from which we find the value of s' to be 

 w w' 



and by a similar reduction, equation (223) gives 



w 



consequently, by analogy, and suppressing the common denominator, 

 we get 



s' : s : : w -}- w' : w. 



From this analogy, the difference between the specific gravities in 

 the two cases can very easily be ascertained, for by the division of 

 ratios, we have 



s' s : s : : w -\- w' w : w, 



which, by reduction, becomes 

 __ w' s 

 ~ 17* (224), 



367. This is a very simple equation for expressing the difference 

 of the specific gravities ; it may be reduced by the following practical 

 rule. 



RULE. Multiply the added weight by the lesser specific 

 gravity ; then, divide the product by the lesser weighty and 

 the quotient will be the difference between the specific gravities 

 sought, 



368. EXAMPLE. An aerometer, whose absolute weight is equal to 

 23 ounces, is quiescent in a fluid whose specific gravity is 0.5738 

 ounces, as referred to a cubic inch ; but on being put into a denser 

 fluid, it requires the addition of 0.7536 of an ounce, to cause the 

 instrument to sink to the same depth ; what is the specific gravity 

 of the denser fluid? 



