170 PROCEEDINGS OF THE AMERICAN ACADE3IY 



III general, a chart of this form may he used for the solution of any 

 spherical triangle, two sides of which, with the included angle, are 

 given. The drawing might be constructed on a scale large enough 

 to read tenths of a degree with considerable accuracy, and a sheet of 

 slightly ground glass or of transparent parchment might be permanently 

 centred over it to make its use more expeditious and precise. It may 

 sometimes be worth while to take the mean of results obtained in dif- 

 ferent quadrants. With the help of two traced parallels, indicating 

 respectively the declinations of the pole of the ecliptic and of the 

 zenith, the chart may be applied to the solution of various problems 

 in which the three sides of a triangle are known. 



The time of an observation of the zodiacal light is seldom recorded, 

 with precision. Even if it were possible to fix the time of such an 

 observation accurately, there is as yet no ap[)arent advantage in at- 

 tempting to do so, except when rapid changes seem to be occurring in 

 the brightness and extent of the light. It is consequently superliuous 

 to make any exact determination of the position of the ecliptic in the 

 visible hemisphere at the time of each observation. In such compu- 

 tations of the kind as are required, we may disregard tiie changes in 

 the relation between mean and sidereal time, at given dates and 

 places, due to the occurrence of leap year, to the gain of the sidereal 

 clock during a single day, and to the longitude of the observer. 

 Tables III. to IX. inclusive (pp. 179-184) give the approximate 

 position of the ecliptic for any date and any mean time. They have 

 been employed in the formation of the subsequent tables, but are given 

 here in a modified form for the sake of convenience in printing, which 

 may occasionally make a slight change in single results derived from 

 them. Table III. gives the approximate longitude of the Sun for the 

 first day of each month, and the hour angle of the north pole of the 

 ecliptic for each hour of mean time on the same days. This hour 

 angle is counted towards the west, from 0° to 3G0°. Interpolation in 

 this table is effected without trouble by allowing one degree a day for 

 a change in date, and fifteen degrees an hour for a change in time. 

 With the hour angle thus obtained for one argument, and the latitude 

 of the observer's station for another, Tables IV. to IX. inclusive give 

 the zenith distance of the north pole of the ecliptic, the azimuth of the 

 same pole, counted from north to west and fi-om 0° to 3G()^, and the 

 longitude of the zenith. Each of these tables is divided into two parts 

 by a heavy rule between the latitudes G0° and 70°, to show that inter- 

 polation is subject to some inconvenience at these places, on account 

 of the passage of the pole of the ecliptic. This part of the tables, 



