46] ROYAL ASTRONOMICAL SOCIETY TO M. LE VERRIER. 357 



On the 20th of May, 1872, M. Le Verrier presented to the Academy an 

 elaborate memoir, containing the first part of his researches on the theories 

 of the four superior planets, Jupiter, Saturn, Uranus, and Neptune. This 

 memoir contains an investigation of the disturbances which each of these 

 planets suffers from the action of the remaining three. Throughout this 

 investigation the development of the disturbing function, as well as that of 

 the inequalities of the elements is given in an algebraical form, in which 

 everything which varies with the time is represented by a general symbol, 

 so that the expressions obtained hold good for any time whatever. Thus 

 the eccentricities and inclinations, the longitudes of the perihelia and of the 

 nodes are all left in the condition of variables. The mean parts of the 

 major axes, which suffer no secular variations, are alone treated as given 

 numbers. 



At the end of the resume of the contents of this memoir, given in the 

 Comptes Rendus, M. Le Verrier lays down the following almost appalling 

 programme of the work still remaining to be done. 



It would be necessary, he says, 



1. To calculate the formulae, and to reduce them into provisional tables. 



2. To collect all the exact observations of the four planets, and to 



discuss them afresh, in order to refer their positions to one and 

 the same system of coordinates. 



3. By means of the provisional tables, to calculate the apparent positions 



of the planets for the epochs of the observations. 



4. To compare the observed with the calculated positions, to deduce 



the corrections of the elliptic elements of the four planets, and to 

 examine whether the agreement is then perfect. 



5. In the contrary case, to find the causes of the discrepancy between 



theory and observation. 



Extensive as is this programme, it has already been completely carried out 

 as regards the planets Jupiter and Saturn, and partly so as regards Uranus 

 and Neptune. 



Having received from the Academy the most effectual encouragement to 

 pursue his researches, M. Le Verrier lost no time in bringing them gradually 

 to completion, so that they might become available for practical use. 



