168 PROCEEDINGS OF THE AMERICAN ACADEMY 



be shown mathematically, if we regard the meteoric particles as solids, 

 reflecting light iri*egularly, that an apfjearance like the zodiacal cone, 

 with an indefinite vertex, would result. On this subject, the work of 

 Geelmuyden may be consulted (G. 95, 106). 



APPENDIX. 



In passing from one system of spherical co-ordinates to another, an 

 approximate result is sometimes all that is required. This is usually 

 the case when the zodiacal light is the subject under consideration, and 

 occasionally happens in the course of other inquiries ; for example, 

 durinw the computation of differential refraction, or when it is desirable 

 to know that no gross error has occurred in the computation of an 

 exact position. For all such purposes, the projection of a hemisphere 

 with the poles upon the circumference is a convenient resource. A 

 stereographic projection, like that given in the annexed figure, has 

 the advantage of being very easily constructed, at least when the scale 

 is small, but any circular and symmetrical chart of a hemisphere will 

 sufTicc. It is needless to state the principles of this method of chan- 

 ging co-ordinates, but a few illustrations of its use may be serviceable. 

 In the following directions, a piece of tracing paper is su|)posed to be 

 at hand, but it may obviously be replaced by measurements from the 

 centre and from the proper points on the circumference of the chart. 

 Althou'-^h the figure here given is a somewhat distorted copy of the 

 drawing which it represents, it will probably be found sufficiently 

 accurate to be of some use. 



In discussing observations of the zodiacal light, we may require the 

 zenith distances, and perhaps the azimuths of a number of points 

 the latitudes and longitudes of which are known, while we also have 

 the latitude and longitude of the zenith, and the azimuth of one pole 

 of the ecliptic. In this case, consider the circumference of the projec- 

 tion as representing the circle of latitude passing thronsrh the zenith. 

 Begin by regarding the chart as one exhibiting latitudes and longi- 

 tudes. Mark the centre of the projection upon the tracing paper, and 

 lay down the place of the zenith, by means of its latitude, upon eitiier 

 side of the circumference, as may be preferred. Knowing the longi- 

 tude of the zenith, we can also lay down the place of the Sun and those 

 of the required points, or we can make a sketch of the zodiacal light 

 as defined by elongation and latitude. Then turn the paper so that 



