89-93] WEIGHT. 95 



At any place on the Earth's surface the mass of a body is 

 proportional to its weight. 



92. Determination of the mass of a body. To determine 

 the masses of bodies near the Earth's surface, small enough to be 

 handled, it is only necessary to weigh the bodies in a common 

 balance. Bodies which equilibrate when weighed are of equal 

 mass. 



Any particular body is chosen, and its mass is taken to be 

 unity. Other bodies are weighed against it and their sizes 

 adjusted until they separately balance with it. When a body 

 balances with n of these unit bodies its mass is n. In the same 

 same way taking a smaller mass than the unit, and adjusting it so 

 that precisely n masses equal to the smaller mass balance the unit, 

 we have n bodies each of which has mass 1/n. In this way we can 

 see how it is possible to determine the mass of a body with a 

 degree of accuracy depending only on the sensitiveness of the 

 balance employed. The mass of a body is a positive number, 

 in the general sense, which expresses the mass ratio of the body 

 and a body of unit mass. 



93. Objective Validity of the conception of mass. The 



ratio of the masses of any two small bodies can be determined 

 with great accuracy by weighing them. 



Now it is part of the conception of mass that when two bodies 

 act on each other so as to produce changes of motion, the changes 

 of velocity produced in any time by their mutual actions are 

 inversely as their masses. 



The objective validity of the conception is confirmed if the 

 ratio of the masses deduced by direct observation of the velocities 

 produced by their mutual action coincides with the ratio of the 

 masses determined by weighing the bodies. 



Direct experiments of this nature can be devised of which the 

 principle is as follows : 



Two spherical bodies are suspended by strings from points in 

 the same horizontal line, the strings being of such lengths, and the 

 points at such distances, that, when the strings are vertical, the 

 bodies are in contact and the line of centres is horizontal. 



