410 H. S. Uhler — Deviation Produced by Prisms. 



bounding cylinders, that is, beyond the convex sides of these 

 cylinders. However, in figures 2 to 5 the loci of constant 

 deviation have not been plotted beyond the boundary loci. 

 The relative index of refraction has been given the value 1*5 

 throughout. Each figure corresponds to a different value of 

 the prism angle, (/3), so that the group of figures taken collec- 

 tively shows how the dimensions of the ^/D surface depend 

 upon the angle of the prism. To facilitate comparison, figures 

 2 to 5 are drawn to the same scale. The values of /3 pertain- 

 ing to figures 2, 3, 4, and 5 are, respectively, 20°, 43° 37' 58", 

 60° 47' 39", and 75°. The angles 20° and 75° were chosen 

 arbitrarily as being relatively small and large. On the other 

 hand, with n = 1-5, /3 = 43 b 37' 58" illustrates the case of 

 equality between the deviation at grazing incidence in a prin- 

 cipal plane and the deviation at simultaneous grazing incidence 

 and emergence. This value of /3 was derived from the cubic 

 equation (51). Figure 4 illustrates the special case in which 

 the two minima of deviation at grazing incidence coalesce with 

 the maximum of deviation at grazing incidence in a principal 

 plane. The angle of the prism was calculated from condition 

 (48), namely, tan /3 = 2 tan <?. The acute angles which the 

 boundary loci make with the rj/D coordinate planes equal 

 78° 27' 34", 61° 40' 18", 44° 47' 29", and 25° 24/ 55" for 

 figures 2, 3, 4, and 5, respectively. The successive increments 

 of deviation from one locus of constant deviation to the next 

 are kept constant for each diagram, but the value of this con- 

 stant difference is not the same for all four figures. More pre- 

 cisely, for each of the figures, 2, 4, and 5, the value of e was 

 subtracted from the value of the greatest possible deviation, 

 (P 1 or X> 2 ), and this difference was divided by 6. This 

 accounts for the presence of minutes and seconds of arc in the 

 deviations in these families. In figure 3 the five increments 

 of deviation are practically constant. They have the values 

 4° 52' 25", 5° 0' 0", 5° 0' 6", 5° / 0",and5 6 6' 6". Hence, for 

 each family of curves, the relatively great distance of the 

 innermost locus of constant deviation from the origin and the 

 crowding together of the constant deviation loci near the 

 boundary curve show how the steepness of the X?;/Z> surface 

 increases as the deviation exceeds the value of the absolute 

 minimum by ever increasing amounts. The values of the most 

 important quantities pertaining to the four families of constant 

 deviation loci are collected in Table 1. 



A few additional points deserve notice. For ft = 20° the 

 minimum of all deviations along the boundary locus has the 

 value 22° 2' 42", and the coordinates X == 0° 18' 51" and 77/ = 

 40° 44' 50". Hence, only within the small interval (22° 23' 22") 

 -(22° 2' 42") = 0° 20'' 40" is it possible for the curves of con- 



