Feiiruary 24, inOS.] 



SCIENCE. 



305 



ineclianics appear to be open to criticism on 

 the ground of false or defective logic. 



Consider, for example, Stephan's treatment 

 of the law of composition of forces, which is 

 substantially identical with that found in 

 many text-books. In Art. 69 is the statement : 

 ' If several forces act simultaneously upon a 

 particle, the acceleration which each force im- 

 parts to the particle is independent of the 

 existing velocity and of the action of the other 

 forces.' For the explanation of simultaneous 

 accelerations and of the method of combining 

 them reference is made to Art. 66. But this 

 explanation relates to a particle having a cer- 

 tain motion with respect to one base of refer- 

 ence, while this base is itself in motion with 

 respect to a second base, so that the two 

 ' simultaneous accelerations ' refer to different 

 bases or axes of reference. This throws no 

 light on what is meant by simultaneous ac- 

 celerations of a particle when only a single 

 base of reference is in question. In the com- 

 position of forces we are not concerned with 

 moving axes,* and in the analysis of motion 

 with respect to any single base it is only by an 

 arbitrary use of language that a particle can 

 be said to have at the same time two different 

 accelerations. Its actual acceleration may, of 

 course, be expressed as the vector sum of com- 

 ponents, but this may be done arbitrarily and 

 in any number of ways ; in choosing a partic- 

 ular set of components and associating each 

 with a force we are merely assuming the 

 parallelogram of forces. 



From a logical standpoint the treatment of 

 the theory of energy is an unsatisfactory fea- 

 ture of many text-books. Commonly energy 

 is defined as the ' cajiacity of a body to do 

 work,' or as the ' quantity of work a body can 

 do,' while the meaning of work as done by a 

 body is nowhere ex]i]ainod, work being de- 



* It is worth while to piiipliasize thp ar«niiieiit 

 by remarking that the acpolerations nf a particle 

 with respect to two difTerent sets nf axes are not 

 related by a simple parallelngraiii law unless the 

 relative motion of the two bases is a translation. 



A full logical analysis of the laws of motion, in- 

 cluding the parallelogram law, must include a 

 consideration of the meaning of absolute and rela- 

 tive motion — a question which may well be 

 omitted from an elementary book and which will 

 not be entered into here. 



fined only as done by a force. Another logical 

 defect is to make ^mv' the definition of kinetic 

 energy instead of proving from a general 

 definition of energy that a particle possesses 

 by virtue of its motion the quantity of energy 

 ^mv^. Of the three books under review, that 

 of Professor Maurer is the only one that in- 

 cludes a logical and systematic presentation 

 of the theory of energy. 



Although the discussion of questions of 

 terminology often seems fruitless, it may be 

 worth while to refer to certain of these because 

 of their importance as affecting the acquire- 

 ment of sound notions by the beginner. That 

 there has been little progress toward general 

 agreement in the use of such terms as stress, 

 centrifugal force, inertia force, is unfortu- 

 nately due in part at least to the fact that 

 discussions over them have involved more 

 than mere questions of terminology. 



The word stress is too often used vaguely, 

 without attempt at exact definition. Among 

 writers whose iisage is clear, two definitions 

 are current, which were formulated by 

 I'ankine and by Maxwell respectively. Ran- 

 kine defined as stresses the forces which the 

 particles of a body exert upon one another to 

 resist strain (i. e., departure from the ' nat- 

 ural ' configuration). By Maxwell the action 

 and reaction between any two portions of 

 matter was called stress.* The usage of engi- 

 neers, so far as it is definite, usually conforms 

 more or less closely to the former definition, 

 while the latter has been adopted in a number 

 of works on both theoretical and applied me- 

 chanics. There are reasons in favor of each 

 of these definitions, but it is to be regretted 

 that the writer of a text-book should depart 

 from both. Professor Ziwet apparently uses 

 stress to designate any pair of equal and op- 

 posite forces in the same line, whether consti- 

 tuting an action and reaction or not. This 

 sacrifices the chief value of Maxwell's defini- 

 tion, which is that it keeps clearly before the 

 mind the fact that every force has its reaction 

 and that action and reaction act upon different 



* See Eankine's ' ISIiscellaneous Scientific 

 Papers.' p. 120; Maxwell's 'Matter and Motion,' 

 Chapter III. It shoiild be said that neither author 

 used the word in a uniform sense throughout his 

 writings. 



