OF NATURE. 567 



defined through the labours of Galileo and Newton did 

 the mechanical sciences start upon that assured way of 

 progress which they are now following. The very fact 

 that, in spite of much mathematical and mechanical 

 knowledge in former ages, it took such a long time before 

 the now current definitions were reached, is an indi- 

 cation how little the popular notions connected with 

 the word force are immediately applicable and useful 

 in scientific inquiry. The sensations which have led to 

 the popular definition of the word, force are connected 

 with subjective experiences, such as effort, pressure, 

 resistance, and many others which are not externally 

 visible, which every person, in fact, only experiences for 

 himself. This subjective origin and signification of the 

 term force has led to two difficulties. First, in order to 

 make the term useful for describing external phenomena, 

 the conception must be cleared of those purely psychical 

 or subjective attributes, and only such data must be 

 retained as can be shown to exist for the external 

 senses that is to say, the conception must be defined 

 by the measurable quantities of time, space, and mass. 

 This was accomplished by measuring a force by the 

 velocity which it imparts to a definite quantity of 

 matter. In this way no knowledge of force as the 

 cause of motion was required ; it was simply measured 

 and defined by its effect; in mathematical language it 

 was equated, or made proportional, to its effect. In the 

 second place, however, the word force, in spite of the 

 clearance through mathematical definition, retained in 

 the popular understanding, as well as in the purely 

 descriptive natural sciences, that subjective meaning 



