Pfof. Stokes on the Polarization of Diffracted Light. 159 



all the positions of the other sides till it returns into itself, the 

 external angles of every right-lined figure must always be equal 

 to four right angles, and therefore the interior angles of a tri- 

 angle to two. My argument then would assume this form : that 

 if there be any result which the pure conception of space leaves 

 unexplained, we have not seized that conception aright, or 

 there is no basis for a complete science. If we have, no arbi- 

 trary result can be admitted which is not explicable, or we have 

 the principle of the sufficient reason to go upon. If a change of 

 position in space can alter the truth of a proposition i-especting the 

 relation of lines and angles, or the parts of a specific form, or I 

 might rather say, the evidence for the truth of such a propo- 

 sition, then is there no complete universal conception of space. 

 I defend Euclid^s twelfth axiom, therefore, as the best, most 

 simple and natural mode of presenting the case in an element- 

 ary and practical treatment of it, that is, if we are to omit the 

 deduction from the vdtimate conception of straight line and 

 angle. In other words, Mobile I would contend for a strictly 

 philosophical analysis of the question, which I believe to be pos- 

 sible, I do not think that any construction of the' proof by means 

 of lines or schemes, or any mental intuition of this sort, will 

 make the axiom more self-evident. This is all that can be meant 

 when we deny that a geometrical proof has been given ; but the 

 necessary truth of the axiom can be shown from our conception 

 of space by reasoning in which lines and schemes give no assist- 

 ance, call the proof metaphysical, or what you will. All we require 

 is, to agree upon the best way of presenting the subject in a form 

 which shall not be discreditable to the present advanced state of 

 philosophy. 



Clifton, January 1857. 



XXV. On the Polarization of Diffracted Light. 

 By Professor G. G. Stokes, M.A., Sec. R.S. ^j-c* 



ON considering the recent interesting experimental researches 

 of jM. Holtzmann on this subject, I am induced to make 

 the following remarks. 



In the more common phsenomena of diffraction, in which the 

 angle of diffraction is but small, we know that the character of 

 the diffracting edge, and the nature of the body by which the 

 light is obstructed, are matters of indifference. This was made 

 the object of special experimental investigation by Fresnel ; and 

 it.s truth is further confirmed by the wonderful accordance which 

 he found between the results of the most cai'efui measurements 



♦ Communicated by the Author. 



