11. 



ON THE APPLICATION OF GRAPHICAL METHODS TO THE SOLUTION 

 OF CERTAIN ASTRONOMICAL PROBLEMS, AND IN PARTICULAR TO 

 THE DETERMINATION OF THE PERTURBATIONS OF PLANETS AND 

 COMETS. 



[From the Report of the British Association (1849).] 



AFTER briefly pointing out the advantages of graphical methods, the 

 author proceeded to give some instances of their practical application. It 

 was shewn that the solutions of the transcendental equation which expresses 

 the relation between the mean and eccentric anomalies in an elliptic orbit 

 is obtained in the most simple manner by the intersection of a straight 

 line with the curve of sines. Attention was directed to Mr Waterston's 

 graphical method of finding the distance of a comet from the Earth, and 

 an analogous method was given for determining the distance of a planet, 

 on the supposition that the orbit is a circle in the plane of the ecliptic. 



The author then passed on to the more immediate object of his com- 

 munication, the graphical treatment of the problem of perturbations of 

 planets and comets. He first shewed how to obtain geometrical represen- 

 tations of the disturbing forces, and then gave simple constructions for 

 determining the changes produced by these forces in each of the elements 

 of the orbit, in a given small interval of time. Having obtained the total 

 changes of the elements in any number of such intervals, it was shewn 

 in the last place how to find their effect on the longitude, radius vector 

 and latitude of the disturbed body, and thus to effect the complete solution 

 of the problem of perturbations without calculation. 



