318 Hydrostatics. 



it does when empty. This divided by 300, or f |'o 4 , gives for the 

 absolute weight of a cubic inch of air 0,308 parts of a grain. 

 By dividing this by 252,525, the weight in grains of a cubic inch 

 of water, gives 0,00122 or T | 7 nearly for the specific gravity of 

 common air, at the surface of the earth in its mean state of den- 

 sity and moisture, the temperature being that to which specific 

 gravities are generally referred by English philosophers, name- 

 ly, 60 of Fahrenheit. Hence bodies weighed in air lose at a 

 mean T 7 part of the weight lost on being weighed in water. 

 Accordingly, if we weigh a body in air and increase this weight 

 by 8"|o f tne difference between the air and water weight, we 

 shall have the absolute weight very nearly ; that is, if w be the 

 absolute weight, a/ the air weight, and w" the water weight, we 

 shall have w = w f + j^ (w' w") very nearly.! 



If it were proposed to find how much a solid ball must weigh 

 in the air in order that its absolute weight may be 1000 grains, 

 from the equation 



1000 = uf -f T io (w' w"), 

 we should have 



or, 



/ = 1000 ^ (w' "), 

 w " being 328, for example, w' = 1000 0,4 = 999,6. 



t To be strictly correct, the formula should be 



' + T*T (> *>"), 



but the object of this formula is to find tw, and when we have ol> 

 tained it nearly, we may substitute this value, and thus approximate 

 the true value of w to any degree of exactness. But generally 

 speaking, the correction derived from the second approximation is 

 very small, Thus, in the example that follows above, | (w 1 w") 

 is 0,4 grains, and the second approximation would give only T ^ of 0,4 

 grains or 0,0005 of a grain. Where the results are intended to be ve- 

 ry accurate, the coefficient F should be corrected for the particu- 

 lar state of the atmosphere at the time of the experiment, the meth- 

 od of doing- which depends upon instruments to be described here- 

 after. 



