1903.] STONEY—UNIVERSE OF REAL EXJSTENCES. 109 
investigations: the data of nature are loaded with minute detail 
and are far too much involved ; they have to be simplified to bring 
the task within the range of man’s power over mathematical 
analysis. 
But for our present purpose a specially instructive instance is 
found in Geometrical Optics. The correct objective theory of light 
appears to be that light consists objectively of waves of alternating 
electro-magnetic stresses advancing through the ether. Now the 
whole of Geometrical Optics—which is one of our most useful 
sciences—is built upon:the supposition that light consists of rays— 
a supposition which must not be mistaken for a ¢heory of light: on 
the contrary, this supposition is to be employed as a useful and 
therefore legitimate hypothesis. In Geometrical Optics what we 
investigate is the succession of events, not in nature, but in a model 
of nature. We have substituted a model which contains far more 
easily handled machinery than that which operates in nature, every 
step in the progress of which can be foretold by the application of 
singularly easy mathematical analysis, can be represented in easily 
understood diagrams, and can be imagined and followed without 
difficulty by students who possess but little skill. What a loss we 
should sustain if that most useful hypothesis were not available ! the 
justification of which is that it is so easily dealt with, and that it 
furnishes results that are true within known limits. For example, 
the new machinery furnishes the correct positions of optical images, 
although the image itself, the geometrical image as it is called, 
differs in material respects from any real image. Thus, it pre- 
sents us with an unlimited amount of detail, much of which must 
be regarded as false, because it is detail which does not exist in the 
images produced by nature. The hypothesis is useful wz¢hzx cer- 
tain limits, but will mislead if misapplied. 
of equal volumes of hydrogen and chlorine, only occurs about once in 1000 
million encounters in sunshine, and less frequently in feebler light, down to about 
once in 100 millions of millions of encounters, so far as the observations have 
been recorded. An infrequency of this kind would have but little effect at the 
bottom of our atmosphere, but would make the distribution of molecular speeds 
differ altogether from that which has been computed in that penultimate stratum 
of the earth’s atmosphere from which the escape takes place. 
