172 Hi, A. Newton— Origin of Comets. 
such parameter as was judged suitable. In the present discus- 
sion in the equation of the curve y=ce—"’2’, I assumed h=0°2. 
This makes the average removal of the area from the central 
ordinate less than 3°. e area for one orbit at an inclination 
of 90° is represented in fig. I. at the bottom of the figure. A 
similar area is assigned to each one of the 247 orbits and is 
supposed to be placed centrally on the ordinate correspondin 
to its inclination. The total ordinate for any abscissa is the 
sum of the corresponding ordinates of these several small 
areas. Th t is exhibited in the figure by the upper 
irregular curved line. The line cannot be carried within two 
or three degrees of the extreme ordinates without some assump- 
tion of numbers beyond 0° and 180° in the original table, and 
such assumption is, of course, not allowable. 
Fig. 1: showing the theoretical and the social distributions of the inclinations of the 
e cometic orbits of the ecliptic. 
» chen 
la Ab IY VIN | 
ace te Nurs 
) 30 60 90 120 150 180 
24. The periodic comets form so peculiar a group that it was 
well to separate them from the rest. There are thirteen such 
comets, if we add to the ten certainly seen at different returns 
the comet of the November meteors (1866 I, seen undoubtedly 
in 1366), Lexell’s comet, (1770 II), and Di Vico’s, (1841 I). 
The shaded area is the part contributed by these thirteen 
comets, and the lower curved line represents the distribution 
for the remaining comets. _ 
We have then in the line AB, fig. 1, the expression of the 
law of original distribution of the inclinations required by the 
hypothesis of Kant; in the smooth curve, or curve of sines, that 
