Application of the Inverse-Square Law to Oil-Immersed Tubes

During the past several years, doubt has been expressed regarding the validity of applying the inverse-square law to the small oil-immersed x-ray tubes (140 kv. p. and less) which are used for both diagnostic and therapeutic purposes. This doubt has been particularly emphasized in respect to the short target-skin distances which are possible with the modern shock-proof oil-immersed tube. According to the inverse-square law, the radiation intensity at a given site varies inversely as the square of the distance from the source. It implicitly includes two factors which are often overlooked. One is that the radiation be emitted from a point source; the other that there be no absorbing or scattering media between the source and the site in question. While radiation from an x-ray tube is, of course, never actually emitted from a point source, the focal spots of these small tubes are generally so small that they can be considered practically point sources, even at short distances. The insertion of a layer of oil in the x-ray beam may, however, be an important factor in causing a deviation from the law. It was for the purpose of determining whether or not the inverse-square law could be applied under this condition that the following experimental work was done. A wooden “jig” was constructed, into which the chamber tube of a Victoreen r-meter could be inserted at various levels. The several levels of the “jig” were so spaced that if the ionization chamber were placed in the lowest level, and then placed 20 inches from the tube target, the other levels would give distances, respectively, of 14 inches, 10.06 inches, 7 inches, and 5 inches. By the use of this “jig” it was possible to keep all operating factors constant with the exception of target-ionization chamber distance, which could be varied with extreme accuracy. Before each set of measurements, the x-ray tube was leveled with a spirit level, and the ionization chamber centered by means of a plumb-bob and divider system. If a good synchronous type timer was connected to the x-ray machine, the timing was accomplished by it; otherwise a stop watch was used. Eleven different tubes were tested. These included Machlett Type CYS, Machlett Thermax, Machlett Aeromax, General Electric Type S.P. 140, Eureka Therograph, and Picker Airflow. Kilovoltages of approximately 80 were used. At least three determinations were made at each distance, and the arithmetic average was recorded. If one assumes a radiation intensity of 10 units at a 20-inch distance, the intensities at the other distances would be as follows, if calculated by the inverse-square law: The observed intensities at the various distances were reduced to a base value of 10 units at a 20-inch distance, and these reduced values were compared with the values calculated according to the inverse-square law. The percentage of deviation of the observed from the calculated values is shown in Table I.