COLOURS OF THICK PLATES. [167] 



system of rings with both eyes at once, if the eyes be situated symmetrically with respect 

 to the flame and its image. The rings so seen appear to be situated between the flame 

 and its image. Let E be the right and E' the left eye, and suppose the head so placed 

 that the line LL 3 bisects EE' at right angles. On account of the similarity of position of 

 the two eyes, the system of rings seen with one eye must be exactly like the system seen 

 with the other, and therefore, in order that a single system may be seen with both eyes at 

 once, it is necessary and sufficient that the axes of the eyes be directed to the centres of the 

 respective systems. It has been shewn already that the projected place on the mirror of the 

 centre of the system seen with either eye, suppose the right eye, bisects the line joining the 

 projected places of the flame and its image. On account of the supposed smallness of the 

 obliquities, this is the same thing as saying that the centre of the system seen by the right eye 

 appears in the direction of a line bisecting the angle LEL 3 . Similarly, the centre of the system 

 seen by the left eye appears in the direction of a line bisecting the angle LE'L 3 . In order 

 therefore that a single system only may be seen, the axes of the eyes must be made to converge 

 to the point in which the bisecting lines intersect LL S , and therefore the system of rings will 

 appear to be situated between the flame and its image. 



Since the angles LEL 3 , LE'L 3 , are bisected by the axes of the eyes when the system 

 of rings is seen single, it follows that the flame and its inverted image are each seen double in 

 such a manner that the erect flame seen by either eye is superposed on the inverted flame seen 

 by the other. This agrees with observation : in fact, I was led by experiment to the above 

 rule for determining the apparent position of the rings before I had deduced it from theory. 

 The observation was made when the flame was in front of its image, in which case the position 

 of the rings in space appears more definite than when the image is in front of the flame. 



Section IV. 



Straight bands formed by a plane mirror at a considerable angle of incidence, and viewed 

 by the eye, either directly, or through a telescope. 



23. As the angle of incidence increases, the bands become finer and finer, and after they 

 have become too fine to be distinguished by the naked eye they may still be seen through a 

 telescope, provided the source of light be sufficiently small. When the source of light was 

 the image of the sun in a lens of short focus, I saw traces of the bands when the angle of 

 incidence was about 24° 50', but they were not at all well formed beyond an angle of about 

 10° 40', after which they began to be confounded with rays which shot in all directions from 

 the image of the luminous point. With a mirror made of thinner glass they would probably 

 have been visible at a still larger angle of incidence. The theory of Section II. sufficiently 

 explains their origin and general character ; but inasmuch as the obliquity was supposed small 

 in investigating the formulas of that section, it may be desirable to obtain an expression for 

 their breadth, in which no approximation shall be made depending on the smallness of the 

 obliquity, in order to meet the case of any future measures which may be taken at a large 

 angle of incidence. 



