10 A NEW METHOD OF DETERMINING 
dQ : es : 
ments, we would at once have a a by differentiation. And since 
G2 dQ 
i ahi? 
dw 
only two multiplications would be needed in finding the value of aan 
, whose expres- 
sion has been given above. 
In the present paper we have dealt only with the perturbations of the first order 
with respect to the mass. The method has been employed in determining those of the 
second order also for two of the minor planets ; but as those of Althsea, the planet em- 
ployed in our example, have not yet been found, it was thought best not to give any- 
thing on the subject of the perturbations of the second order, until the perturbations of 
this order, in case of this body, are known. 
The writer desires here to record his obligations to Prof. Edgar Frisby, of the 
U.S. Naval Observatory, Washington, D. C., and to Prof. George C. Comstock, 
Director of the Washburne Observatory, Madison, Wis., for kindly furnishing him 
with observations of planets that had not recently been observed; to Mr. Cleveland 
Keith, Assistant in the office of the American Ephemeris, for most valuable assistance 
in securing copies of observed places. And to Prof. Monroe B. Snyder, Director of 
the Central High School Observatory, Philadelphia, he is under special obligations for 
the interest manifested in the publication of this work, and for continued aid and most 
valuable suggestions in getting the work through the press. 
