1898 - 99 .] 
Note on Dew Bows. 
351 
angle is about 42°. Hence, all possible bow-producing drops must 
lie on or near the surface described by the revolution about this 
line of the circle which circumscribes any one of these triangles. 
The plane sections of this toroidal surface give the various 
forms of dew bow that may be seen on level ground. Many of 
these have a heart shape ; and if the eye of the spectator were on 
the level of the ground the two halves of the curve, which is 
symmetrical with regard to the vertical plane containing the 
source and the eye, would form a cusp-like point as they met at 
the eye. 
The equation of the dew bow referred to the stance of the 
observer as origin is easily shown to be 
( r 2 - ar cos 9 + 7iH) 2 = cos 2 a(r 2 + h 2 )(r 2 - 2 ar cos 6 + a 2 + H 2 ) 
where r, 6 are the usual polar co-ordinates, H the 'height of the 
source of light, li the height of the observer’s eye, a the horizontal 
distance between the eye and the source of light, and a the angle 
of maximum deviation of any particular ray which has suffered 
two refractions and one reflection in the drop. By choosing 
different values for r, and solving for 0 , we can very rapidly 
trace any particular case by points. The particular form of the 
curve will of course depend upon the relative values of 7^, H, 
and a. 
A set of curves for different values of these constants may be 
traced out with great ease by means of a triangular frame with 
two grooves cut on it so as to meet at the proper angle of 42°, the 
grooves being made to slide simultaneously on the tops of two 
pillars, of which the one represents the lamp post and the other 
the observer. The point where the grooves meet will trace out 
the required curve on any chosen plane surface, and indeed on 
any surface whatsoever. 
Clerk Maxwell, in his note on the bow observed on ice, says : — 
“ How a drop of water can lie upon ice without wetting it and 
losing its shape altogether, I do not profess to explain.” 
In the phenomenon described in this paper a similar difficulty 
meets us. We have all seen dew drops of different sizes more or 
less distorted from the spherical form ; but not usually on the 
damp surface of the ground. What we have to postulate for the 
