198 Mr. C. Davison on the Periodic 



It remains to show that the cause invoked is sufficient, and 

 yet not too great, to produce the effects observed. Let t° F. 

 be the average rise of temperature over the distance P C (fig. 

 3), due to a given rise of external temperature; lete = 7 x 10"^; 

 and let tan a = |^, where a is the inclination of the ground 

 outside. Then the value of t necessary to produce a change 

 of inclination of 1'' is given by the equation 



t X -000007 X iPQ = ^ ^^n^,!f .n 

 * / X 180 X bOx60 



or t = 2°'8 nearly. 



The nearly uniform temperature of the cellar * will tend to 

 increase this estimate ; but, on the other hand, the linear 

 coefficient of dilatation only has been used, whereas the ex- 

 pansion will take place chiefly upwards. Hence, as the levels 

 are close to the surface of the ground, and as the annual and 

 daily ranges of temperature at Geneva are considerable, we 

 may, I think, conclude that changes of external temperatrire 

 are an eAHrenielz/ probable cause of the pritwipal periodic move- 

 merits of the ground observed by M. PLintamonr. 



There are other movements, however, whose causes are not 

 so clear. If the surface of the ground were perfectly plane, 

 and the movements were due solely to changes of temperature, 

 then we should expect the curves in fig. 1 to be simply straight 

 lines parallel to the slope of the ground. Possibly the move- 

 ments at right angles to this direction may be due to inequa- 

 lities in the ground or to differences in its covering, causing 

 the normal to the horizontal section of the isothermal surface 

 at any point to vary. It is evident that the direction of QP 

 (fig. 3), for which the product of the length PC into its change 

 of avemge temperature is greatest, may viiry, and the direction 

 of the resultant motion be consequently changed. 



Influence of the Formation and Melting of Polar Ice. — It 

 may be thought that the alternate formation and melting of 

 ice and snow on the two polar ice-caps might produce a small 

 periodic movement in the direction of the meridian. It must, 

 however, be inappreciable. For the centre of gravity of the 

 earth must be displaced by 147 feet along its axis to produce 

 a change of 1" in the direction of the vertical at Geneva. 

 Let us suppose a layer of ice (of density '92) of uniform 

 thickness to be melted off the whole south polar zone, and the 



* It should be noted that Colonel Orff, who has made observations on 

 levels in the cellar of the Observatory of Bogeuhausen, near Munich, 

 placed therniometers en the opposite sides of the pillars supporting- the 

 levels, the bulLs touching the pavement and being covered with sand. In 

 one case the average difference of temperatures during the year amounted 

 to C°a8 C. {Arch, des Sc. S^e p6r. vol. vi. p. 618.) 



