Influence of the Tidal Wave on the Motion of the Moon. 107 



capillary pipette. A portion of the dried particles of gold are 

 fused on a charcoal splinter with soda, and yield bright golden- 

 yellow particles in the mortar ; a second portion is shown to be 

 insoluble in hydrochloric acid, but soluble in aqua regia, and the 

 solution after evaporation is tested with stannous chloride, and 

 the purple of Cassius obtained. One centigramme of the sub- 

 stance, containing only a few tenths of a milligramme of gold, 

 amply suffices for all these reactions. 



XIII. On the Influence of the Tidal Wave on the Motion of the 

 Moon. By James Croll*. 



NEARLY twenty years ago M. Mayer showed that, as the 

 tidal wave is always a little to the east of the moon's me- 

 ridian, the attraction of the moon tends to pull back the wave 

 against the earth's rotation. The wave thus acting as a brake 

 or drag must diminish the motion of rotation. 



The researches of Mr. Adams and M. Delaunay show that the 

 change in the excentricity of the earth's orbit accounts for only 

 about one-half of the secular acceleration of the moon's motion 

 as determined by observation, namely about 6" in a century. 

 Professor Hansen suggested that the other 6" would be accounted 

 for by simply assuming that the length of the sidereal day has 

 increased by merely '01197 of a second in the course of 2000 

 years. 



About six months ago M. Delaunay showed that the retarding 

 effect of the tidal wave, pointed out by M. Mayer, was perfectly 

 sufficient to account for the increase required in the length of 

 the day. Professor W. Thomson, who has lately investigated 

 the subject, arrives at the conclusion that in a century the earth 

 is rotating so much slower that, regarded as a time-keeper, it is 

 losing about four seconds in a yearf. 



The conclusion to which M. Delaunay has arrived is that the 

 6" of acceleration resulting from the change in the excentricity 

 of the earth's orbit is real, but that the other 6" is only appa- 

 rent %. That is, in making our calculations regarding the actual 

 amount of the acceleration from the date of ancient eclipses, we 

 make it 6" more than it really is, owing to our taking as a stand- 

 ard of measurement the present length of the sidereal day, which, 

 on account of the influence of the tides on the earth's rotation, 

 is now too long by a small fraction of a second. 



* Communicated by the Author. 



t Phil. Mag. for June 1866 (Supplement). 



X M. Delaunay, in his reply to M. Bertrand, has since admitted that the 

 tides produce a real acceleration of the moon's motion. (Comptes Rendus, 

 January 29, 1866.) 



