640 VERHOEFF AND BELL. 



Verification of Law of Inverse Squares. 



The outcome of this series of experiments was that radiation from 

 the mercury vapor lamp to the amount of 4 X 10 ® erg-seconds per 

 square cm. is required to set up the first definite symptoms of photoph- 

 thalmia. This assumes that the effect is proportional to time, in 

 other words, that the pathological results are determined by the total 

 amount of energy, and the next series of experiments was directed 

 to the establishment of the truth or falsity of this assumption. For 

 this purpose, having ascertained the liminal exposure for a single 

 distance, ..5 meter, exposures were made at various distances for times 

 computed for equal total radiation, assuming the law of inverse 

 squares to hold for the relative intensities. For example, at 1 meter 

 the time required to produce the determining symptoms, assuming 

 the law of inverse squares, sliould be four times that required for .5 

 meter, which was found to be closely the case. By repeated experi- 

 ments at distances varying from about 20 cm. to 2.5 meters, the inverse 

 square law was verified over a range of radiation intensities in the 

 ultra violet varying from 72,000 ergs per square cm. per second down 

 to 455 ergs per second per square cm., at a range in other words of 

 156 to 1. For any source yielding rays capable of producing patho- 

 logical effects on the cornea therefore, the exposure time required to 

 produce symptoms of photophthalmia is inversely proportional to 

 the intensity of the radiation of such rays, and can be definitely deter- 

 mined when the intensity of the damaging radiation is known, subject 

 to the condition that if the computed time reaches many hours it 

 may be even further lengthened by the intervention of physiological 

 repair. This conclusion is of fundamental importance, since it shows 

 that the symptoms are due to or are proportional to, the direct and 

 primary effect of the energy. Since, as we shall show later, the rays 

 which are able to injure cells by chemical action are only those of 

 wave lengths below 305 ix/jl, these present experiments of ours show 

 that the critical amount of such radiation required to set up well 

 marked photophthalmia is approximately 2 X 10 ® erg-seconds per 

 square cm. In other words only half of the total ultra violet already 

 specified is effective in producing such symptoms. 



A close general relation l)etween the amount of incident energy and 

 its effects on the cornea was beautifully shown by the results obtained 

 after relatively severe exposures. In such cases after the symptoms 

 had developed there was a distinct haziness confined chiefly to the 



