372 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [46 



On solving the equations with respect to the first four unknown quan- 

 tities, the corrections to be applied to the elements are found to be greatly 

 influenced by the indeterminate correction of the mass of Jupiter, and after 

 they have been substituted in the equations of condition, the coefficients of 

 the correction of the mass of Jupiter in great part destroy each other, 

 nowhere amounting in the resulting equations to one-tenth part of their 

 values in the primitive equations. Hence these equations are insufficient to 

 determine the mass of Jupiter with any precision. 



Consequently, in the formation of the Tables of Saturn, M. Le Verrier 

 has employed the value of the mass of Jupiter determined by the Astronomer 

 Royal from his observations of the 4th satellite. 



The result which has just been noticed will appear to be less paradoxical 

 if we consider that by far the larger part of the disturbances which Jupiter 

 produces in the motion of Saturn is represented by the inequalities of long 

 period which affect the mean longitude and the elements of the orbit. Now 

 in the course of 120 years these inequalities have run through only a small 

 part of their whole period, and therefore, during this interval, the greater- 

 part of their effects may be represented by applying changes to the several 

 mean elements equal to the mean value of the corresponding long inequalities 

 during the interval. It is only from the residual disturbances, which are 

 comparatively small in amount, that any data can be obtained for the cor- 

 rection of the mass of Jupiter. 



In the course of a few centuries, when these long inequalities, as .well 

 as the secular variations of the elements of Saturn, shall have had time to 

 develop themselves, it will be possible to determine the mass of Jupiter from 

 them with all desirable precision. 



I trust that the review which I have just given, however hasty and 

 imperfect, of the work of our distinguished Associate has been sufficient to 

 convince you that your Council have done well in according him your Medal. 



In conclusion, I may be allowed to express the great satisfaction I have 

 felt in becoming the mouthpiece of the Council on this occasion, and in thus 

 joining in doing honour to the eminent Astronomer whose untiring labours 

 have added so greatly to our knowledge of the motions of the principal 

 members of our Solar System. 



