276 MR E. SANG ON THE CURVES PRODUCED BY REFLECTION , ETC. 
V =40°, 30°, 20°, and 10°, which should form, as it were; equal steps between 
- the two extremes. The asymptote approaches to O, and the upper part of the 
curve passes across that asymptote, wherefore, after having reached a maxi- 
mum distance beyond, it must again bend inwards, and so must have a point 
of reflexure; as is seen in the figure for V =10°. 
The difference in character between the figures for 10° and for 0 being very 
marked, another set was interpolated, namely, the forms for 5°, 4°, 3°, 2°, and 1 
centesimal degree. In the last of these we see well the progress of the upper 
part of the loop towards infinite curvature, as also that of the curve at the point 
of reflexure ; and in order that this may be still better seen, the form for V= 
one-half of a centesimal degree has been interjected. | | 
This sudden change in the character of the curve is an interesting case of 
a general class of such transformations. 

