232 
RADELFINGER. 
papers will be found in the foot-notes of Mittag-Leffier’s last 
two notes. 
One of the most extensive and important of these papers 
is due to Borel.* I refrain from going into details concern¬ 
ing this paper since the results thereof, as well as those of 
Mittag-Leffler’s first note, are now very accessible in Borel’s 
book.f 
Conclusion .—An attempt has been made by Dr. Moulton, of 
Chicago, to apply Mittag-Leffler’s results to the lunar theory. 
In a synopsis of Moulton’s paper,! which was read before the 
American Association and to my knowledge has not as yet 
been published, it is stated that expansions representing the 
moon’s coordinates were constructed which converge for a 
predetermined length of time; but the labor of constructing 
such series is very great and the constants therein cannot be 
readily determined from observations of the moon. How¬ 
ever, this need not discourage us in expecting practical re¬ 
sults, since Mittag-Leffler’s papers show that convergent series 
of polynomials can be constructed in many ways which 
permit a large range of choice for the arbitrary constants, so 
useful developments may yet be determined by direct meth¬ 
ods which will play as important a part in the mathematics 
of the future as the well-known expansions in terms of 
spherical harmonics have in the past. 
*Sur les Series de Polynomes et Fractions Rationnelles, Acta Mathe- 
matica, tome 24, page 307. 
fLecons sur Series Divergent (Ganthier-Villars, 1901). 
X Bulletin of the American Mathematical Society, vol. IX, pages 98-99. 
