352 KELATIVE MOTION AND UNIVERSAL GRAVITATION. [CH. XIII. 



expressed by that law if the frame of reference is fixed relatively 

 to the stars. If then we wish to describe the motion of a body by 

 applying the Law of Gravitation we must refer to axes which are 

 not fixed in the Earth, but which, relatively to the Earth, rotate 

 with the stars. 



277. Gravity. We have given a provisional account of the 

 acceleration due to gravity, and of the weight of a body. We said 

 that relatively to axes fixed in the Earth a falling body near the 

 Earth's surface moves very nearly in a vertical direction, and with 

 an acceleration which is very nearly equal to yE/R 1 *, where 7 is 

 the constant of gravitation, E the Earth's mass, and R the Earth's 

 radius. In this statement the vertical at a place was understood 

 to mean the line of a flexible cord freely supporting a body so 

 that it remains at rest relative to the Earth, and this line makes 

 with a line drawn to the Earth's centre of inertia an angle which 

 is very nearly zero. Treating these approximate statements as 

 exact, we said that the weight of a body is the force with which 

 the Earth attracts it, that its direction at any place is the vertical 

 at the place, and that its magnitude is the product of the mass of 

 the body and the acceleration due to gravity ; further with the 

 same degree of inexactness the weight of a body is equal to the 

 force exerted by a cord or by a spring supporting the body so that 

 it remains at rest relatively to the Earth. Also we said that the 

 most exact process for experimentally determining the acceleration 

 due to gravity is provided by pendulum experiments. 



We wish as far as possible to replace these provisional state- 

 ments by exact ones, and to exhibit the relations between the 

 quantities involved. We accordingly give the following defi- 

 nitions : 



(i) The vertical at a place is the direction of the plumb-line 

 there, i.e. the direction of a flexible cord which supports a body so 

 that it remains at rest relatively to the Earth. 



(ii) The weight of a body at a place is a force equal and 

 opposite to the force which must be applied to support the body 

 in equilibrium relatively to the Earth. Its direction is that of the 

 vertical at the place. 



(iii) The acceleration due to gravity at a place is the initial 

 value of the acceleration (relative to axes fixed in the Earth) of a 



