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AMERICAN JOURNAL OFSCIENCE 



[FIFTH SERIES.] 



Aet. X. — Some Mechanical Curiosities connected tvith 

 the Earth's Field of Force;^ by Walter D. Lam- 

 bert, U. S. Coast and Geodetic Survey. 



By the earth's field of force is meant the field due to the 

 attraction of the earth according to the law of inverse 

 squares combined with the apparent forces due to the 

 movement of our frame of reference resulting from 

 the rotation of the earth. In general we shall consider the 

 field of force for statical purposes only and then the 

 apparent forces due to the motion of our frame of refer- 

 ence reduce to the ordinary centrifugal force; we thus 

 avoid the complications arising from the presence of the 

 compound centrifugal acceleration or accleration of 

 Coriolis,^ which enters into problems of motion relative 

 to the earth. 



It is convenient to distinguish between gravity and 

 gravitation. By gravitation is meant the force of mass- 

 attraction only according to the law of inverse squares ; 

 by gravity is meant the force of mass-attraction combined 

 with the centrifugal force of rotation. This paper deals 

 exclusively with gravity. 



As a first approximation, corresponding to the assump- 

 tion that within the region considered the surface of the 

 earth may be treated as a plane, we may consider gravity 

 as constant in amount and as acting in parallel lines. 

 The equipotential or level surfaces will be parallel planes 



^ Eead at the meeting of the Maryland-Virginia-District of Columbia Sec- 

 tion of the Mathematical Association of America held at Annapolis, Mary- 

 land, December 11, 1920. 



^ The compound centrifugal acceleration of a particle referred to a set oi 

 rotating axes is equal to twice the vector product of the angular velocity 

 of rotation of the axes themselves by the linear velocity of the particle 

 relative to the axes. The compound centrifugal acceleration governs the 

 easterly deflection of a falling body, the rotation, of the plane of oscillation 

 of the Foueault pendulum, the direction of the trade winds, etc. 



Am. Jour. Sci.— Fifth Series, Vol. II, No. 9.— September, 1931. 

 9 



