35 2 Dr. Herschel’s observations of the satellites 
the fifth, contains the natural sine of the inclination given in 
the fourth column multiplied by 6. 
Such a Table has also been calculated for every degree, 
from three signs qo° to seven signs 12 0 , which takes in the 
whole compass of the observations that have been given. I 
insert the three first lines of the Table as a sample of its con- 
struction. 
Geor. longi- 
tude of tne 
planet. 
Position of 360 
or zero. 
Distance of zero 
from ditto. 
Inclin. of the plane 
of the orbits to the 
plane of projection. 
Natural sine 
of the 
Inclin. x 6. 
3 s 20° 
79° 2 7' n P 
105 ° 
34' 
36 ° 
T 
4.85 
21 
80 17 
105 
1 
36 
57 
4.79 
22 
81 5 
104 
3° 
37 
54 
4>73 
In order now to use these preparatory calculations, I made 
an apparatus consisting of a square piece of pasteboard, upon 
which a circle was drawn and graduated as in figure 1 . To 
the centre of this, I joined a moveable circle also drawn upon 
pasteboard, and graduated as in the figure. The radius of 
the inner circle was exactly $ix inches, and its circumference 
was nearly in contact with the inside of the outer circle. From 
what has already been said of the construction of this figure, 
its use in the identification of the satellites, will easily be 
understood by a few examples of it. 
With the geocentric longitude of the planet taken from the 
Nautical Almanack, I take out the required quantities from the 
different columns of the Table. In this operation it might 
be sufficient to take only the nearest degree for entering the 
