94 MASS AND FORCE. [CHAP. V. 



must be assumed in order that the observed accelerations may be 

 the resultants ; all we can generally observe is the resultant 

 acceleration of a body or of a part of a body. Thus, having fixed 

 upon our frame of reference, and attributed a mass to a body, we 

 can find by observation the resultant force acting on the body. 

 This resultant is in fact a vector localised at the position of the 

 centre of inertia of the body, having the direction and sense of the 

 acceleration with which the centre of inertia moves, and equal to 

 the product of the mass and the acceleration. In most cases the 

 acceleration has a value depending, in a simple way, on the 

 relative positions of the body, neighbouring bodies, and the frame 

 of reference. When this is the case we call the region where such 

 acceleration can be observed a field of force, and define the intensity 

 of the field at the point to be a vector localised at the point, and 

 having the magnitude, direction, and sense of the acceleration. 

 We may also say that every particle gives rise to a field of force, 

 and regard any field as a region where such forces combine at any 

 point to produce a resultant. 



90. Gravity. We have stated already in Article 44, that in 

 the neighbourhood of the Earth any body, small enough for us to 

 handle or to move by machinery, falls towards the Earth with an 

 acceleration approximately constant, and in a vertical direction. 

 We attribute this acceleration to the action of the particles of 

 which the Earth is conceived to be made up on the particles of 

 which the body is conceived to be made up. The neighbourhood 

 of the Earth is a field of force, and the acceleration at any point in 

 the field, i.e. the intensity of the field, is, at any place, directed 

 vertically downwards and is equal to g, where g is the acceleration 

 described in Article 44, and there called the acceleration due to 

 gravity. 



91. Weight. In the neighbourhood of the Earth the result- 

 ant force on a free falling body is numerically equal to the product 

 of the mass of the body and the acceleration due to gravity. This 

 force is called the weight of the body. 



We conceive that this force is always acting on the body whether it is 

 falling freely or not. If the body is supported, or is moving with an acceleration 

 unequal to g or not in the vertical direction, we conceive it to be acted upon 

 by other forces as well. 



