234 NEWTON S PRINCIPIA. 



have W. According to Newton the density of water 

 is 860 times that of air ; hence 



A -- B = 860 (A - W) 

 W-B 



and 



The value of a can be found from those of A and B, 

 for the weight of a globe of water one inch in diameter is 

 132.645 grains in air, and therefore 132.8 grains in vacuo. 

 And since the weights of globes vary as the cubes of 

 their diameters, hence 



where A B is measured in grains, and a in inches. 



We are now therefore able to calculate the value of x 

 when t is given. If t be not very small, the last term 

 may be neglected. For since when a is small 



log. (1 + a) = a nearly, 

 the value of that term is very nearly 



M 2 -U t 



. g 



9 



and the exponent being large, this term will be insensible. 

 We may therefore take 



u 2 

 x = u t -- - f log. 2. 



The space deduced from this formula requires a correction 

 depending on the narrowness of the wooden vessel in which 

 the experiments were made. Now if a globe descend in a 

 cylinder, the area of whose section is L, the resistance will 

 be increased in the ratio 



