286 OF THE EQUILIBRIUM OF FLOATATION. 



d ,__1728?<; cs 

 c 



from the first of which the standard specific gravity is obtained, and 

 in the second, the specific gravity as calculated from the first must be 

 employed. 



By comparing the quantities in equation (222) with each other, it 

 will readily be perceived, that a very small variation in w the weight 

 of the instrument, or in s the specific gravity of the fluid, will produce 

 a very considerable variation in Z, the immersed portion of the stem 

 or wire ; for it is manifest, that the numerator of the fraction w cs, 

 expresses the weight of the fluid displaced by the wire or upright 

 stem of the instrument, and consequently, since r the radius of the 

 stem is a very small quantity, it follows, that the weight of the fluid 

 which it displaces must also be very small. 



PROBLEM LIV. 



363. Suppose that a small variation takes place in the density 

 of the fluid in which the instrument is immersed : 



It is required to determine the corresponding variation that 

 takes place in the depth to which it sinks before the equili- 

 brium is restored. 



Let the notation for the first position of equilibrium remain as in 

 Problem LII., and let I' denote the immersed length of the stem or 

 wire, corresponding to the specific gravity s' ; then, by equation (222), 



we have 



_ w cs' 



7T?'V ' 



consequently, by subtraction, the variation in length becomes 

 w cs w cs' 



and this, by a little farther reduction, gives 



(223). 



364. The practical rule for reducing this equation, may be expressed 

 in words as follows. 



RULE. Multiply the whole weight of the aerometer by the 

 variation in the specific gravity ; then, divide the product by 

 the area of the transverse section of the upright stem or wire, 



