THE PRINCIPLE OF GENERAL RELATIVITY 



AND 



EINSTEIN'S THEORY OF GRAVITATION 



Einstein's theory of gravitation has presented difficulties to 

 many readers on account of the compHcated analysis involved. 

 The object of this paper is to present the mathematical part of the 

 theory in as simple a form as possible, and at the same time to 

 translate Einstein's tensor analysis into a notation more closely 

 resembling' the vector analysis of Gibbs, in the hope of making 

 this very remarkable theory more readily intelligible to the 

 average physicist. 



(a) THE PRINCIPLE OF GENERAL RELATIVITY. 



A moving element is defined as a point — whether in a material 

 body or at the head of a light signal — which can be continuously 

 identified. Every physical measurement, when analyzed, is found 

 to consist of observations of coincidences of two or more moving 

 elements. Thus the measurement of temperature by means of 

 the mercury thermometer consists in noting a coincidence between 

 the top of the mercury column and a certain division on the 

 scale beside it, or, more strictly, a coincidence between the light 

 rays coming to the observer's eye from these two points. A 

 physical phenomenon, then, may be defined as a coincidence in 

 time and space of two or more moving elements. In order to 

 specify the place and time of a physical phenomenon, it is neces- 

 sary to have a set of reference elements each of which locates 

 a point in space, and with each of which is associated a device 

 for assigning numerical values to the times of occurrence of 

 successive events at that point. A reference system is an as- 

 semblage of such reference points filling all space for all time. 

 A physical phenomenon is specified relative to a given reference 

 system by the identification of the reference point at which it 

 happened, and the time at that point of the occurrence. 



The determination of a physical law involves the measurement 

 of space and time intervals between a number of phenomena. 

 Consequently a device is needed for measuring the distance be- 



