234 ANNUAL KEPOKT. SMITHSONIAN INSTITUTION, 1908. 



value of hj^pothesis ? " appear to them as irrelevant as the questions 

 " What is the vahie of poetry ? " " Wliat is the vahie of music ? " 

 " What is the vahie of philosoph}^ ? " 



Recent investigations on electricity have done a good deal to unite 

 various branches of physics, and I wish this evening to call your 

 attention to some of the consequences of applying the principle of 

 the equality of action and reaction — Newton's third law of motion — 

 to some of these researches. According to this law the total amount 

 of momentum in any self-contained system, that is, any system un- 

 influenced by other systems, is constant, so that if any part of such a 

 system gains momentum another part of the system must simulta- 

 neously lose an equal amount of momentum. This law, besides being 

 the foundation of our ordinary system of dynamics, is closely con- 

 nected with our interpretation of the great principle of the conserva- 

 tion of energy, and its failure would deprive that princiiile of much 

 of its meaning. According to that principle the sum of the kinetic 

 and potential energies of a system is constant ; let us consider a 

 moment how we are to estimate the kinetic energy. To us the objects 

 in this room appear at rest, and we should say that their kinetic 

 energy was zero, but to an observer, say on Mars, these objects would 

 not appear to be at rest but moving with a considerable velocity, for 

 they would have the velocity due to the rotation of the earth round 

 its axis and also that due to the revolution of the earth round the 

 sun; thus the estimate of the kinetic energy made by a Martian 

 observer would be very different from our estimate. Now the ques- 

 tion arises. Does the principle of the conservation of energy hold with 

 both these estimates of the kinetic energy, or does it depend upon the 

 particular system of axes we use to measure the velocity of the 

 bodies? Well, we can easily show that if the principle of the equality 

 of action and reaction is true, the conservation of energy holds what- 

 ever axes we use to measure our velocities, but that if action and 

 reaction are not equal and opposite this principle will only hold when 

 the velocities are measured Avitli reference to a particular set of axes. 



The principle of action and reaction is thus one of the founda- 

 tions of mechanics, and a system in which this principle did not hold 

 would be one whose behavior could not be imitated by any mechanical 

 model. The study of electricity, however, makes us acquainted with 

 cases where the action is apparently not equal to the reaction. Take 

 for example the case of two electrified bodies, A and B, in rapid 

 motion. We can, from the laws of electricity, calculate the forces 

 which they exert on each other, and we find that, except in the case 

 when they are moving with the same speed and in the same direction, 

 the force which A exerts on B is not equal and opposite to that which 

 B exerts on A, so that* the momentum of the system formed by B 

 and A does not remain constant. Are we to conclude from this result 



