E. W. Brown — Magnetic and other Forces. 529 



Art. XLY. — On the Effects of Certain Magnetic and Gravi- 

 tational Forces on the Motion of the Moon • by Ernest 

 W. Brown. 



1. There exists a difference between the observed and com- 

 puted places of the moon which has hitherto defied explanation. 

 Its magnitude is so great in comparison with the accuracy 

 obtainable both in theory and observation that it seems highly 

 improbable that it should be due to error of any kind. From 

 the observational side it has been known for over thirty years 

 and during that time many efforts have been made, without 

 success, to find its cause in the ordinary gravitational theory. 

 It therefore seems pertinent to inquire whether some force 

 or forces whose existence is only suspected may not be the 

 cause of the discrepancy. 



In setting forth the hypotheses mentioned below, my object 

 is not at the outset to present a solution of the difficulty, and 

 indeed no solution which can be accepted at the present time 

 is offered. The reasons for the publication of the results of the 

 investigation are of a different nature. The first is the consid- 

 eration of certain forces whose constants are unknown but 

 whose magnitudes can certainly be limited. It becomes possi- 

 ble in this way to exclude hypotheses which before actual 

 computation do not appear to be highly improbable. The 

 second object is to point out forces which are able to produce 

 the inequality but which require to be confirmed by observa- 

 tions of a kind different from those obtained by the old 

 methods of positional astronomy. And a third is for the pur- 

 pose of indicating certain directions in which observations 

 may be useful for the purpose of testing these hypotheses. 



A possible magnetic attraction between the earth and the 

 moon has occasionally been suggested, though its detailed 

 consequences do not appear to have been worked out. The 

 results below show that, although the magnitude of this attrac- 

 tion need not be very great, if it be a constant force its direction 

 is unusual ; or, if the magnitude of the force itself varies, the 

 difficulty is only removed a step further back in that we know 

 of no cause for such variation. The result arising from the 

 figure of the sun demands conditions which may possibly be 

 fulfilled but for which we must await further evidence. The 

 supposed long-period term in the libration of the moon may in 

 time be tested. For this purpose a long series of accurate 

 observations would be necessary. In any case, such a series is 

 needed in order to furnish more exact information than we at 

 present possess of the motion of the moon about its center of 

 mass, and this quite independently of any theory, gravitational 

 or otherwise. 



Am. Jour. Sci.— Fourth Series, Vol. XXIX, No. 174.— June, 1910. 

 35 



