500 Mr. J. Preseott on the 



earth. Dr. Hecker has analysed the motion of his pendulums 

 and has separated the effects of the sun and moon. But the 

 variation of the temperature of the earth's surface in a solar 

 day produces a distortion of the surface which gives rise to 

 an apparent motion of the plumb-bob, the magnitude of which 

 motion is several times as great as the motion due to the 

 attractions of the sun and moon. This motion dne to 

 temperature is mixed up with that due to the sun's attrac- 

 tion since they have the same period and further very careful 

 analysis is necessary to separate them. But the average 

 temperature effect on a large number of lunar days is insig- 

 nificant on account of the difference in period. For in a 

 large number of lunar days the temperature effect will be 

 positive and negative in nearly equal proportions so that it 

 will disappear from the average. For this reason the lunar 

 deviation is much more reliable than the solar deviation in 

 calculating the rigidity of the earth. 



It is shown in the article on " Tides " in the ninth edition 

 of the Encyclopcedia Britannica that the motion due to one 

 tide-producing body, say the moon, may be analysed into 

 two elliptic-harmonic motions whose periods are respectively 

 a lunar day and half a lunar day. These ellipses vary with 

 the declination of the moon. The linear dimensions of the 

 diurnal ellipse are proportional to sin 28, and those of the 

 semi-diurnal ellipse to cos 2 S, where 8 denotes the declina- 

 tion of the moon. It follows then that the diurnal ellipse 

 vanishes when the moon is in the equator, whereas the semi- 

 diurnal ellipse has then its greatest dimensions. 



Let u and f3 denote the mean lengths of the axes of the 

 lunar semi-diurnal ellipse calculated on the assumption of 

 perfect rigidity. These would correspond to a relative 



ellipticity of the equipotential surface of magnitude — . If 



the actual relative ellipticity were /~- the axes should be 



foe and f/3. Now the mean lunar semi-diurnal curve obtained 

 from Dr. Hecker's observations, extending from December 

 1902 to May 1905, is an oval curve, approximately elliptical, 

 with axes 0*786 a and 0*357/3. The inequality of the co- 

 efficients has not yet been satisfactorily accounted for. The 

 mean of the two coefficients 0*786 and 0*357 is 0*571, and 

 this may be taken as / to calculate the mean rigidity. In 

 another series of observations extending from August 1905 

 to July 1907 the axes were 0*586 a and 0*400 /3. The mean 

 of the coefficients in this case is 0*493. Thus the earlier 



