NEWTON S PRINCIPIA. 235 



Hence & 2 will be decreased in the same ratio, and .*. 

 u decreased in the ratio of ft : 1. In all the following ex 

 periments the area of the greatest circle of the sphere is 

 small compared with the section of the cylinder ; the value 

 of [i* is therefore nearly unity. In the expression for x, 

 the first term is usually a hundred times the second ; hence 

 it will be sufficiently accurate to reduce the space x by 

 simply multiplying it by ft. This will be evident on an 

 inspection of the numbers in the following experiments. 



Experiment 1. A globe whose weight was 156^ grains 

 in air, and 77 grains in water, described the whole height 

 of 112 inches in 4 seconds. On repeating the experiment, 

 the globe again spent the very same time of 4 seconds 

 in falling. 



Here A= 156^f grains, 2 a = .84224 inches, 



.. u = 29.03 11 inches per second. 

 The principal term in x is 1 16.1245, 

 The second is 3.0676, 



.-. x= 113.0569, 

 and ft= .9914. 



Hence the space which the globe falling in water de 

 scribes in four seconds is, by 



theory - 112.08, 

 experiment - - 112. 



Experiment 2. Three equal globes, whose weights were 

 severally 76 J grains in air, and 5^ grains in water, were 

 let fall successively. Every one fell through the water in 

 15 seconds of time, describing in its fall 112 inches. 



Here A = 76 T 5 2 grains, 2 a = .81296 inches, 



.. ?&amp;lt; = 7.712 inches per second. 



