98 BIOLOGICAL EFFECTS OF RADIATION 



as the source of radiation, one is dealing generally with distributed sources 

 of considerable dimensions compared with the distance at which the 

 material is placed. The inverse square law is not applicable to such a 

 source. For practical purposes one may subdivide it into very small 

 areas, each of which can then be considered to be a point source, and the 

 simple mathematical relation may be applied to each without introducing 

 a large error. The resultant intensity at the point is then the sum of the 

 intensities due to the assumed point sources. It should be noted in 

 this connection that the intensity of radiation from each point source 

 represents the flow of energy through a surface of unit area perpendicular 

 to the direction of travel of the photons, at the point in question. Since 

 photons will reach this point from different directions, the surfaces 

 through which the flow of energy is reckoned have different orientations. 

 The summation of the individual intensities is justified in the case under 

 consideration, because we are really interested in the number of photons 

 (and their respective energies) reaching a very small volume surrounding 

 the point. While the intensity of radiation is expressed in the c.g.s. 

 system of units in terms of the energy flow per square centimeter, it does 

 not follow that the area of the surface must be 1 cm.-. In fact, it should 

 always be at least small enough to insure a practically uniform distribu- 

 tion of radiation throughout the area. 



The inverse square law holds strictly in a vacuum. If matter is in 

 the neighborhood of the point at which the intensity of radiation is 

 desired, or near the source, certain complications arise which will be 

 discussed presently. At this time, it is important to note that with a 

 given constant source of radiation the same amount of energy in the 

 form of photons is distributed over a larger and larger area as the radius 

 of the sphere (distance from the source) increases. Therefore, the energy 

 flow per unit area {i.e., the intensity) must decrease correspondingly. 

 The influence of matter on the intensity of radiation at any point is 

 superimposed on this geometrical effect. On the basis of the inverse 

 square law alone, therefore, the intensity of radiation is different at points 

 in a biological object which are located at different distances from the 

 source. The variation of intensity with distance is particularly impor- 

 tant in the practical use of radium on account of the short distances 

 commonly employed. This will be readily appreciated from the follow- 

 ing numerical examples: Suppose that the object to be irradiated is 

 1 cm. thick. If a radium container of very small dimensions (approxi- 

 mately a point source) is placed at a distance of 1 cm. from the object, 

 the intensity on the far side will be only one quarter of that on the near 

 side of the object, on the basis of the inverse square law alone. If the 

 radium is placed at 0.5 cm. distance, the intensity on the far side is only 

 3-^ of that on the near side. On the other hand, in the case of X-rays, 



