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Remarks on the Central Forces of Bodies 



Art. IV. — Remarks on the Central Forces of bodies revolving 

 about fixed axes ; by Joseph Martin, M. D. 



The theory of curvilinear motion may justly be considered 

 one of the most important and interesting subjects connected 

 with the physical sciences. It explains the motions of the heav- 

 enly bodies, and, by unfolding some of the grand phenomena of 

 nature, makes them applicable to the most important and useful 

 purposes of life. It has accordingly engaged the attention of the 

 greatest philosophers for centuries, who have, by means of the 

 most searching analyses, not only pointed out the slightest irreg- 

 ularities of those bodies which compose the great planetary sys- 

 tem, but have discovered the causes of the seeming aberrations, and 

 given satisfactory explanations of them. And yet it would seem 

 that the most simple case of "central forces," the rotation of a 

 heavy body about a fixed axis, has been in some measure neg- 

 lected, or at least, treated as a subject of too little importance, 

 either in a theoretical or practical point of view, to deserve more 

 than a passing notice. 



To explain the motions of the heavenly bodies it has been 

 found necessary, by means of mathematical reasoning, to deter- 

 mine the ratio of attraction and original impulse, or projectile 

 force, and to show the effects of their separate and combined 

 operation. In this way the part that each of the three forces, 

 the projectile and the central, perform in producing and pre- 

 serving the motion of a planet in its orbit, is clearly defined ; 

 as well as the results that would follow if either of the last 

 should cease to act. But the ratio of the forces which act upon 

 a body made to revolve about a fixed axis, and the nature 

 and extent of their separate or combined action, have not been 

 distinctly shown. In other words, it is believed that the relative 



