H. A, Newton—Origin of Comets. : 169 
sphere into 18 zones by parallels of latitude at even decades 
of degrees from +80° to —80°, then the orbits whose positive 
poles lie in the northernmost segment will have inclinations less 
than 10°.* The orbits whose positive poles lie in the next 
zone will have inclinations between 10° and 20°, and so on up 
to 180°. Hence the numbers of the orbits whose inclinations 
to the ecliptic are included in the successive decades of degrees 
will be as the areas of the zones. But these zones are as the 
sines of 5°, 15°, 25°, ete. Therefore we conclude that if the 
comets come from the stellar spaces their original orbits should 
have been so distributed that the numbers of orbits whose 
inclinations to the ecliptic fall in the successive degrees from 
0° to 180°, should have been proportional to the sines of incli- 
nations. ‘I'he distribution of the aphelia would have been uni- 
form over the heavens. Hence their relative frequency at dif- 
ferent latitudes would have been as the cosines of the latitudes. 
e may represent the distribution of the inclinations by 
adiagram, Let the axis of abscissas (fig. 1) extend from 0° to 
180°, and upon this describe the first half cycle of the curve of 
Sines, y=a sinz. Draw also the straight line, AB, parallel to 
the axis of abscissas, y=%. The ordinates of the two lines 
represent the original distributions of the inclinations from 0° 
to 180° of a given number of orbits according to the two theo- 
ries. The aphelia, according to one theory, are distributed iu 
latitude as the cosines of the latitudes, in the other they are all 
in the ecliptic, 
18. If the comets came from the stellar spaces their original 
orbits were hyperbolas. If they originated from our system 
they were ellipses. In either case if their origin was very dis- 
tant the orbits would have differed so little from bolas that 
the deviations in portions visible to the earth would, in general, 
be covered up by the ordinary errors of our observations. If 
the orbits tas remained unchanged by perturbations the ques- 
on of origin would be simply cones by determining whether 
the orbits are now elliptic or hyperbolic. But the hyperbolic 
orbits might be changed by a resisting medium (if there is one) 
into ellipses, and perturbations by a large planet may change 
ellipses into hyperbolas, or hyperbolas into ellipses. If there 
18 any known orbit of a comet that is beyond question hyper- 
bolic, and its path was such that in approaching the sun at its 
present appearance it did not so pass near to a large planet as 
to have its velocity thereby increased, then that comet at least 
must be rded as coming to us from the stellar spaces, — ee 
ety orbits have been assigned to certain comets, but is th 
Yperbolic character of any of them not open to reasonable 
* By positive pole is meant that pole from which the comet's motion appears to 
be oppoted to the motion of the hana of a watch. . 
