March 25, 1904.] 



SCIENCE. 



511 



current of thought, simplifying and clarifying 

 in this sense, that runs through Professor 

 Ostwald's ' Naturphilosophie ' is undeniable, 

 whatever particular attitude between full ac- 

 ceptance and opposition we may take toward 

 the author's expressed or implied philosophy. 

 But in summing up the gain due to such move- 

 ments, that lesson from history must not be 

 lost sight of which teaches that a new inter- 

 pretation of phenomena rarely supersedes the 

 previous views ; it most often supplements and 

 modifies them. So here, while we may accept 

 the suggestion from energetics, and cry good 

 riddance to a cumbrous apparatus of molecular 

 forces, premature, at least, for our present 

 state of experimental knowledge and, perhaps, 

 finally illusory, it is not required by con- 

 sistency to follow the extremists in their 

 tendency to banish the conception of force 

 completely, nor need we even derive those 

 parts of mechanical doctrine which are stated 

 through equations of motion from an ex- 

 clusive source in energy relations. 



It is something, of course, that we have a 

 direct and roughly quantitative appreciation 

 of force through muscular sensation ; but fur- 

 ther, attacking the matter more broadly, sev- 

 eral points may be urged in restraint of rele- 

 gating force to the scientific lumber-room. 

 First, let us grant fully one great advantage 

 of an energy equation : that it renders possible 

 a true statement of relation between conditions 

 at the boundaries of an interval, while we are 

 ignorant of the internal mechanism, i. e. the 

 details within the interval. But let us notice, 

 also, that this is coupled with a corresponding 

 disadvantage. The energy equation is not 

 inunediately capable of recording internal de- 

 tails, even where the process has been traced 

 continuously or minutely; and to this extent 

 it fails to represent completely our acquaint- 

 ance with those cases. In parallel with the 

 energy equation (the integrated form), there- 

 fore, the force equation or its equivalent (the 

 differential form) is then justified and 

 reqiTisite. That is, though it is well to 

 acknowledge ignorance and bridge the gap 

 with the energy equation, yet it would be 

 pedantic to use equations of that type ex- 

 clusi-s'ely, and thus ignore knowledge that we 



really possess. Secondly, it is part of the 

 general intellectual position which has led to 

 the development of energetics, that the intro- 

 duction and use of physical quantities are to 

 be determined according to their convenience 

 and sufficiency. Now it is true and interest- 

 ing that the condition of equilibrium (zero 

 value of accelerations) can be described as a 

 compensation of one form of energy by an- 

 other (Ostwald, passim) ; but that does not 

 settle any question of practical convenience in 

 the definite calculation of conditions for equi- 

 librium. And it is precisely when those con- 

 ditions obtain, that one factor of energy be- 

 comes indeterminate or unimportant, leaving 

 attention to be concentrated upon the remain- 

 ing factor. Hence the universal procedure 

 in measuring the forces, pressures, etc., that 

 are practically essential elements in a state 

 of balance, through the whole range from con- 

 structing the piers of a bridge to applying 

 D'Alembert's principle. Por the purpose of 

 physics it is not always enough to laiow that 

 an algebraic sum is zero ; the magnitude of the 

 self -neutralizing terms is of imjportance. To 

 be sure, this particular aspect of the situation 

 may be met by using freely coordinate deriva- 

 tives of energy, and thus narrowing the ques- 

 tion to the choice between the directer and 

 the more artificial introduction of the neces- 

 sary forces. But even this resource would 

 not occupy the vacant field entirely; a third 

 point remains to be considered. What ac- 

 count does the view peculiar to energetics give 

 of normal forces, those actions which guide 

 moving bodies without directly affecting their 

 energy of motion ? The scalar kinetic energy 

 is unaffected by mere cliange of direction; 

 there is no measurable exchange of energy 

 (apart from friction) between a body moving 

 with constant speed in a curved path and the 

 guiding mechanism. Yet these are not in- 

 stances of equilibrium, either, describable in 

 terms of compensating fonns of energy; none 

 of the extensions of energy equations to cover 

 tangential forces by means of coordinate de- 

 rivatives apply here. This seems to be the 

 weakest spot in the scheme of energetics, at 

 which it stands most in need of supplement by 

 direct use of equations of motion. Everywhere 



