408 Mr. Sylvester on the Motions produced by the [June, 



Article IV. 



On the Motions produced by the Difference in the Specific Gravity 

 of Bodies. By Mr. Charles Sylvester. 



(To the Editor of the Annals of Philosophy.) 



DEAR SIR, Grmt RusseUstreet, Jpril 22, 182?. 



All the writers on dynamics have treated largely on the 

 effects of fluids in motion, as regards their resistance and their 

 direct impulse on surfaces, without entering scarcely at all into 

 the causes of their motion, and particularly those motions 

 resulting from, or affected by, a difference of specific gravity. 

 Prof. Robinson, and several other authors, have given us the 

 principles and excellent formula for calculating the different 

 results of air rushing into a vacuum and into any other rarified 

 medium approaching a vacuum ; but these do not at all apply to 

 the subject I here wish to treat. The ordinary formula and 

 calculations for falling bodies are all made on the supposition 

 that the efffects take place in vacuo. They, of course, will not 

 apply when the body falls in a medium of the least possible den- 

 sity. The data relative to falling bodies are : 



h = the hei<rht the body falls from. 



/ = the time of falling. 



-> = the velocity acquired by the fall. 



fir = the space a body falls through in one second = 16-;^. 



Then since a body in falling through any space acquires a 

 velocity which would take it through twice that space in the 

 same time ; the velocity of g will be equal to 2 g. 



The body would, therefore, pass through 2 g in the next 

 second, if gravity were to cease, but it causes the body to pass 

 through another g in the second second, making the whole i3 g; 

 this with the one g in the first second makes 4 g. It will be 

 found by similar reasoning that it will have passed over 9 g at 

 the end of the third second, and so on as the square of the time* 

 The velocity acquired in each successive second will be 2 g for 

 the first second, 4 g for the second, 6 g for the third, and so on. 

 Hence it will appear that the whole space passed over in any 

 time IS as the square of that time, and as the square of the 

 velocity ; and that the velocity is, therefore, as the time. It 

 may appear unnecessary to a mathematician to give these parti- 

 culars, presuming that those likely to read this article will be 

 acquainted with such elementary knowledge. But I do it with 

 the hope that some may read it, who would have stopped short 

 of what I have in future to communicate from the want of such 

 elementary knowledge. 



From the above reasoning, we shall have as the square of one 



