230 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 30 



be equivalent to stating a fundamental law of nature; for example, 

 to say that the question, " What is the true velocity of the north star 

 through space? " has no meaning is a fairly good statement of at 

 least a part of the relativity theory. 



In some cases it may have no meaning to ask whether or not 

 there is a magnetic field in a certain portion of space. For example, 

 suppose an observer, stationary on the earth, studies an electron in 

 motion. The motion of an electron constitutes an electric current 

 and experimentally he will observe the characteristic magnetic field 

 surrounding this electron corresponding to this current. If another 

 observer moves along with the electron, it will appear to him to be 

 at rest, and, of course, he can observe no magnetic field. Otherwise, 

 the presence or absence of a magnetic field around an electron or 

 group of electrons could be used to determine absolute motion 

 through space, which would be contrary to the relativity theory. 

 The relativity theory thus requires that a magnetic field can have no 

 real existence in any absolute sense. 



We have seen that there are fundamentally as many different con- 

 cepts of length as there are different ways in which length may be 

 measured; nevertheless, we find approximate agreement between 

 different ways of measuring the diameter of molecules and therefore 

 are justified in assigning some reality to the concept diameter of a 

 molecule. When, however, we ask what is the diameter of an elec- 

 tron, we find that the question is practically without meaning. It is 

 true that we can calculate a diameter by assuming that the electron 

 behaves like a charged sphere and that the classical laws of electro- 

 dynamics can be applied in this case. However, since we have no 

 independent way of measuring this diameter, the process is one 

 which involves reasoning in a circle. 



There are many meaningless questions which afflict the chemist. 

 It clearly has no meaning to ask what is the molecular weight of 

 sodium chloride in a crystal. It is very doubtful whether it has any 

 meaning to ask what is the molecular weight of water in liquid 

 water. There are many cases where the concept of temperature has 

 no definite meaning. Strictly speaking, temperature acquires mean- 

 ing in terms of operations only in so far as an approach is made to 

 equilibrium conditions. When the motions of molecules or atoms 

 follow Maxwell's distribution law, that is, a random or probability 

 distribution of velocity among the molecules, the concept of tempera- 

 ture becomes very definite. If, however, we deal with mercury 

 vapor streaming into a high vacuum, or the conditions near a hot 

 tungsten filament in a gas of low pressure, temperature has very 

 little meaning. The same is true of the conditions frequently exist- 

 ing in an electric discharge tube such as a mercury arc, where the 



