FOR HIGH LEVELS IN THE EARTH's ATMOSPHERE. 33 



II. The Level Surfaces of Gravity. 



We first consider the level surfaces of gravity because, by reason of their abso- 

 lutely fixed positions with relation to the earth, they are specially adapted to serve as 

 coordinate planes in the atmosphere. Let it be remarked in passing, that all the 

 burdensome corrections in meteorological work arising from the variations of gravity 

 with elevation and geographical latitude disappear * if once for all we introduce level 

 surfaces of gravity as the coordinate planes in place of surfaces of equal elevation 

 above scale vel. 



The level surfaces of gravity are surfaces whicli are at every point perpendicular 

 to the direction of the gravitational force.f A fundamental property of the level 

 surfaces of gravity results directly from this definition, viz.: no work is necessary to 

 shift a mass from any point in a level surface to any other point in the same surface. 

 Further it also follows that the same amount of work must be performed to transfer a 

 mass from any given level surface to any other given level surface, quite independently 

 of the path along which the transfer takes place. We shall make use of this property 

 in the construction of our system of level surfaces in the atmosphere by choosing the 

 surface of sealevel [i. e., the geodesist's spheroid] , as our zero-surface and distributing 

 the other surfaces in such a way that it will always require just one unit of work to 

 raise the unit of mass from one level surface to the surface next above it. As unit 



of mass we choose 1 pound (English) and as unit of work one r — -2 • 



To raise one pound through the vertical distance of one mile requires a number g 

 of units of work, if by g we indicate the acceleration of gravity in mile/ hour-. If 



*Thi9 does not refer to the reduction of the mercurial barometer to normal gravity, because this is to be considered 

 as an instrumental correction. 



t Note by the Editor : This is the so-called "apparent gravity " or the attraction of the earth as diminished 

 by the distance from the earth's center and also by the centrifugal force due to the diurnal rotation of the globe. 



Let the term geoid apply to the natural irregular surface of the earth and the term spheroid to the ideal regular sur- 

 face of the geodesist which coincides nearly with sealevel and is necessarily a level surface. The observed values of 

 acceleration of apparent gravity made at points on the surface of the geoid are usually reduced vertically downward to a 

 point on the ideal spheroid by some one of several formnlEe, and the collation of all snoh reduced values shows that for 



this spheroid in general 



J = 32. 172 6 ( 1 — 0.002 59 COS 2A). 



For a point on the geoid surface, li in feet, or H in meters, above this spheroid apparent gravity diminishes by 



distance but increases by the attraction of the intervening earth, as represented altogether by the factor (l — 7 • -\,i.e., 



( 1—0.0000000597/1) or (1 — 0.000 000 196fl'). 



For a point in the atmosphere, z in feet or Z in meters, above the geoid surface apparent gravity diminishes by 

 increase of distance only, or by the factor (1— 2«/JJ), 1. e., (1—0.000 000 095 72) or (1 — 0.000 000 3142). Hence 



starting from the geoid surface we may say that apparent gravity increases with descent by the factor ( 1 + , • „ )• ^^^ 

 decreases with ascent by the factor (1 — 2z IR). 



