CELESTIAL MECHANICS: LEUSCHNER 25 



the British Nautical Almanac, and his own computations. The fol- 

 lowing comparisons are illustrations of the results: 



1890 1892 1894 1896 1898 



Nautical Almanac Aa +l s .18 +1 8 .00 +1 8 .73 +l s .71 +2 8 91 



AS +0".9 5".8 +8".9 2".0 + 16".3 



Leveau ' Aa +0 3 .03 +0 S .01 +0 S .25 +0 S .06 +0 3 .19 

 A8+0".4 +0".5 +2".0 



Further results of Leveau's theory are published in Comptes Rendus, 

 T. 145, p. 903-906, "Determination des Elements Solaires et des 

 Masses de Mars et de Jupiter par les Observations Meridiennes de 

 Vesta." Extending the comparison with the meridian observations 

 from 1807 to 1904 and taking into consideration the masses of Jupiter 

 and Mars and also the solar elements, Leveau determines a new set 

 of smaller corrections to the elements of Vesta and for Jupiter's mass, 

 1/1046, and mass of Mars 1/3601280. The tables of residuals shows 

 the poor quality of the meridian observations before 1826. A period 

 of 36 years, (three revolutions of Jupiter, or ten of Vesta) , points to 

 the effect of the critical terms in the residuals ; the amplitude is about 

 1". The effect of the earlier observations on the value for the mean 

 motion is also illustrated by the last residuals. 



In Annales de 1'Observatoire Astronomique de Toulouse, T. I., B. 1 

 to B. 90, M. J. Perrotin published his extensive investigation on the 

 "Theorie de Vesta," applying the method of Le Verrier (Annales de 

 1'Obs. de Paris, T. X.). The method consists first of deriving mean 

 elements from previous osculating elements by computing provisional 

 periodic perturbations and applying these to the osculating elements 

 for a first approximation. In order to avoid considerable labor, Per- 

 rotin starts with a certain fixed major axis and develops corrective 

 terms for the variation in the assumed value. The final mean motion 

 is determined from two extreme groups of observations in 1807 and 

 1876 when the planet was near the same place in its orbit. The per- 

 turbative function is developed by Le Verrier to the seventh degree in 

 the inclination and eccentricity ; thus Perrotin includes terms of 10n' 

 3n. Venus, Earth, Mars, Jupiter, and Saturn are taken into account. 

 Derived from the secular terms e is always smaller than 0.15, the 

 mean motion of the perihelion is +38", that of the node 38", and 

 the inclination remains less than 9. The terms of the second order 

 are then considered. Those due to the square of Jupiter's mass of the 

 second degree are small. Those depending on the product of the 

 masses are more important, especially those depending upon 5n" 2n', 



