62 FRESNEL OX THE COLOUllS PRODUCED IN 



vve perceive that it is always possible, by the value which is 

 given to r, to introduce the fraction that is requisite into the 

 parenthesis 2 r — 2 tt (e — o), and to cause this last discordance 

 to disappear. It is this last fraction that determines the azimuth 

 into which the plane of double reflexion must be turned to obtain 

 the complete disappearance of one of the images. 



From some experiments of this nature, which I have not been 

 able at present to conduct with all the precision of which they 

 are capable, it appeared to me that the condition which I have 

 just announced was visibly fulfilled in the oil of turpentine, for 

 I observed the complete disappearance of one of the images, at 

 least as far as I could judge. 



The first experiment which I made is that which 1 have 

 already mentioned at the beginning of this memoir. Having 

 filled a tube 0'"*50 in length with oil of turpentine, I fixed at its 

 posterior extremity a glass parallelopipcd in which the emerging 

 rays suflfcrcd double total reflexion in a plane parallel to that of 

 primitive polarization; then, by placing between this parallelo- 

 pipcd and the rhomboid of calcareous spar a lamina of sulphate 

 of lime, about 0™™"12 in thickness, and inclining its axis to 

 the right at an angle of 45° to the plane of double reflexion, I 

 caused the extraordinary image, which was violet-red or purple 

 of the third order, to disappear. A lamina of sulphate of lime, 

 ()ram.i2 in thickness, does not quite correspond to this tint in 

 the table of Newton ; but, as it was necessary to incline this 

 lamina a little perpendicularly to its axis to obtain complete dis- 

 appearance, I estimated that the tube O^'SO in length ought 

 to be compensated by a lamina of sulphate of lime, correspond- 

 ing to the number 21 in the first column of Newton's table. If 

 the rotation of the plane of polarization of the mean red rays, 

 produced by a similar lamina comprised between two parallelo- 

 pipeds placed at right angles to each other, is calculated, we find, 

 by means of the formula — 



? = — TT (e — o), 

 for the entire arc, 309°'6. But, from the succession of colours 

 which oil of turpentine presents from zero to a length of 0'°-50, 

 we have seen that there ought to be for this fluid one undula- 

 tion less in the interval between the two systems of waves. Now, 

 one undulation corresponds here to 180°; deducting 180° from 

 309°-C, there remain 129°-6, which, divided by 50, give 2°'59 

 for the rotation of the red rays corresponding to 1 centimetre. 



