51G 



Prof. J. D. Everett. 



[Jan. 22, 



both these terms are included, the largest departures from agreement 

 with the twelve data amount to about ^wo °f tne e ^ e ^ amplitude for 

 /'. and Jq- for m and a . The harmonic expressions to which these 

 remarks apply are 



V= -0-0624 sin + 0*0032 sin 20, 

 m = 0-7103-0-0628 cos + 0*0033 cos 20, 

 n = 0-6997 + 0-0645 cos - 0047 cos 20, 

 from which are deduced 



m = 0-0075 - 0-0900 cos + 0-0057 cos 20, 

 n = 0-9970 + 0-0013 cos 0-0-0010 cos 20. 



The maximum error for m is about ^ of the amplitude. 



As regards n, the largest departure from agreement is about 20 x 0o 

 of the large constant term 0-9970, and therefore does not materially 

 affect the values of x and y calculated from 



x = sin + 1 (f - Col v = m + " l (f - Co), 



n n 



in accordance with equations (5). 



21. By plotting the values of / and m as co-ordinates, we obtain the 

 direction-curve — the large outer curve which stands first in Plate 10. It 

 is a section of the direction-cone } that is of a cone having its vertex at 

 the origin and its generators parallel to the emergent rays. The large 

 dot in the centre of the inner curve is the point in which the section is 

 cut by the axis of f, and indicates the direction of no deviation. The 

 plane of deviation for any ray passes through this point ; and the radius 

 vector drawn from this point is proportional to the tangent of the total 

 deviation. The direction-curve m&y be otherwise called the section at 

 infinite distance, being the form to which the section tends as the distance 

 is increased. 



The small inner curve represents the annulus as projected on the 

 plane of the section, the scale being half that of Plate 9. The seven 

 selected points in the positive half of the annulus are marked with 

 their values of ; and a comparison of these with the markings of 

 on the outer curve shows the inversion which each ray undergoes, both 

 up-and-down and left-and-right. 



Crossing of Bays in the Secondary Focal Lin'-. 



22. The rays from two symmetrically placed points ± meet in the 

 plane of symmetry ; and the locus of these meetings is the seeortda.i t/ 

 focal line of the hollow pencil. Five of them can be found by putting 



