PHYSICAL ASTRONOMY. 



respect of the forces which these two exert on one 

 another. 



The force of this third body is called a disturbing 

 force, and its effects in changing the places of the 

 other two bodies are called the disturbances of the 

 system. 



Though the small disturbing forces may be more 

 than one, or though there be a great number of 

 remote disturbing bodies, the computation of their 

 combined effect arises readily from knowing the 

 effect of one ; and therefore the problem of Three 

 bodies, under the conditions just stated, may be 

 extended to any number. 



Two very different methods have been applied to the 

 solution of this problem. The most perfect is that 

 which embraces all the effects of the disturbances 

 at once, and by reducing the momentary changes 

 into fluxionary or differential equations, proceeds, 

 by the integration of these, to determine the 

 whole change produced in any finite time, whe- 

 ther on the angular or rectilineal distance of the 

 bodies. This method gives all the inequalities at 

 once, ancl as they mutually affect one another. 



The other method of solution is easier, and more 

 elementary, but much less accurate. It supposes 

 the orbit disturbed to be nearly known, and pro- 

 ceeds to calculate each inequality by itself, inde- 

 pendently of the rest. It cannot, therefore, be 



exact,, 



