70 W. A. Norton on the Dimensions of Donati’s Comet. 
cave side cannot be represented without supposing the effective 
attraction of the sun to be greater than 0°455. But if this 
attraction be only increased to 0°500, we get p’= —2°1.A, and the 
particles therefore could not leave the nucleus. We e may con- 
clude therefore that the mean density of the nucleus is in all prob- 
ability less than 1°75; the mean density of the earth being taken 
equal to unity. 
If we attribute to the density of the nucleus ies values, 
less than unity, we obtain larger and larger positive values for 
p'; which however cannot possibly exceed 88.4. Upon every 
such supposition, therefore, there would be an effective repul- 
sive force to expel the particles in question from the nucleus. 
But the idea here naturally PERO: itself that the limit to the 
solar attraction, for the concave side of the tail, may have been pre- 
cisely that value which did not aoe of any increase without con- 
verting the effective action of the nucleus into an attractive force. If 
this plausible idea be admitted, we have for the limit in question 
the value aber to a lateral velocity equal to zero, which, as 
we oe seen, 
m this meant we deduce for the probable density of the 
‘aloe, 1-25. If the ‘density be supposed greater than this, P 
becomes an attractive force, and if it be taken materially less, p' 
is no longer the feeble reptsive foree which the hypothesis of a 
limit resulting simply from the pposesality of the particles 
— repelled from the nucleus — 
m the calculations which hay oe been made we may 
os pn insight into the probable nature of the forces of repul- 
sion exerted by the sun and nucleus upon cometary ae 
We find that the ratio of the actual repulsive forces exerted 
two bodies is not the same as that of their actual attractive fortes 
Thus upon the supposition that the density of the nucleus is 
equal to that of the earth, thé ratio of the attractive forces at the 
surface of the nucleus, is ‘OT: 37, while the ratio of the repulsive 
forces is equal to ae or 82°4. We obtain similar results, 
if we attribute other values to the density, as will be seen from 
the comparison made in the following table. 
Density. $ Ratio of Attr. | Ratio ofRep. | Density. { Ratio of Attr. | Ratio of Rep. | 
82 3 
I a) 79 
I = 4 92 0-50 4 
2 ee 0°25 73 
a‘ O10 ss 7 ee 
* In effecting this determination o eo density it is tacitly supposed that the Leomep 
= i Seorts of the nucleus becom into ak pig for the partic 
would be ejected in the difect. line toward ees If, as we shall aa 
oa ‘oan is reason to believe, this change should occur ner for the particles emitted 
gers e the radius-vector, and because of a diminution in the actual repul- 
eus and sun as ue Aon becomes greater, the above determination 
: ve Rect eh yo must be discard 
