270 SEE— SECULAR EFEECTS OF THE [April 21, 



character.'- The modern discussions based on the analytical methods 

 of Gylden are, however, much more satisfactory than those of the 

 age of Laplace; and I propose to give a brief account of them, 

 chiefly with a view of summarizing the state of our knowledge, and 

 of removing some inconsistencies which may mislead those who are 

 unfamiliar with the literature of the subject. 



For example, in the late Professor Benjamin Peirce's " Ideality 

 in the Physical Sciences," Boston, 1881, p. 131, the following 

 curious statement occurs : 



The constant increase of the solar mass would have an influence on the 

 planetary orbits. It would diminish their eccentricities, according to a law 

 of easy computation. Hence it is possible that the orbits of the planets may 

 have been originally very eccentric, almost like those of the comets ; and 

 their present freedom from eccentricity may have resulted from the growing 

 mass of the sun. What modification of the nebular theory may be involved 

 in this supposition cannot easily be imagined, without the guidance of some 

 indication from nature. 



This statement is misleading and erroneous, and the only way I 

 can explain its appearance in the writings of Peirce is by the fact 

 that his last lectures were prepared when he was at an advanced age 

 and in ill health ; and thus it is probable that some confusion 

 occurred. Quite recently an analogous confusion has appeared in 

 the Asirononiischc Nachrichioi, Xo. 4454, in a short article by Dr. 

 R. Bryant, on the secular acceleration of the moon's mean motion. 



In order to place before the reader a summary of the chief 

 investigations bearing on the problems now under discussion we cite 

 the following papers : 



1. " The Problem of the Newtonian Attraction of two Bodies 

 with masses \'arying with the Time," H. Gylden (A. N., 2593). 



2. ■' Ein Specialfall des Gylden'schen Problems," J. Mestschersky 

 (A. X., 3153 and 3807). 



3. " I'eber Central Bewegungen," R. Lehmann-Filhes {A. N., 

 3479-80). 



4. " Note on Gylden's Equations of the Problem of Two Bodies 

 with Masses \"arying with the Time." E. O. Lovett {A. N., 3790). 



5. " l/eber die Bedeutung Kleiner Massenanderungen ftir die 

 Xewtonsche Central Bewegung," Dr. E. Strtimgren (A. .V., 3897). 



■ Mecanique Celeste, Liv. X., § 20. 



