46] ROYAL ASTRONOMICAL SOCIETY TO M. LE VERRIER. 371 



I learn directly from M. Le Verrier that this second investigation entirely 

 confirms the accuracy of the first as regards the periodic inequalities, but 

 that the secular variations of the eccentricity and longitude of the perihelion 

 are slightly changed. 



The effect of these changes is to bring the theory into very satisfactory 

 accordance with the observations of Bradley, but the discrepancies above 

 mentioned in the time of Maskelyne and in the modern observations still 

 remain unaffected. 



The character of the discrepancies shewn by the modern observations 

 makes it very improbable that they can be due to any errors in the theory. 



In fact, the error appears to change almost suddenly from a positive one 

 of 4"'4 in 1839 to a negative one of 5"'0 in 1844, a variation of nearly 9" - 5 

 in five years. Now no terms or group of terms due to the action of the 

 planets could thus suddenly disturb the motion in five years, at a given 

 epoch, and then leave the motion unaffected during the following twenty-five 

 years. 



M. Le Verrier is therefore inclined to think that the discrepancies arise 

 from errors in the observations, notwithstanding that the Greenwich and 

 Paris observations are mutually confirmatory of each other. 



He suggests that it is possible that the varying aspects presented at 

 different times by the ring may affect the accuracy of the observations of 

 the planet, and may cause changes in the personal equations of the observers, 

 which, from being rather large in the case of the ancient observations, have 

 gone on diminishing as the system of observation has become more perfect. 



One unlooked-for result follows from M. Le Verrier's comparison of his 

 theory of Saturn with the observations. Considering that the influence of 

 Jupiter on the longitude of Saturn may amount to 3800", it might have 

 been expected that from observations of the planet extending over 120 years 

 the mass of Jupiter could have been determined with great precision. M. 

 Le Verrier has found, however, that this is not the case. 



The equations of condition furnished by the comparison of the heliocentric 

 longitudes of Saturn as deduced from theory and observation contain five 

 unknown quantities, viz. the corrections of the assumed values of four 

 elements and the correction of the assumed mass of Jupiter. 



472 



