W. A. Norton on the Dimensions of Donati’s Comet. 57 
form and dimensions of the train of the comet, as well as of the 
head, and derive the phenomena of the rise and gradual recess 
from the nucleus of successive envelopes, we have in a supposed 
rotation of the nucleus the probable cause of certain special phe- 
nomena observed, as the spiral form of the outline of each incip- 
lent envelope, the inclination of the first direction of the axis of 
the tail to the radius-vector produced, &c. 
Dimensions and Form of the Train of Donati’s Comet,—theoreti- 
cally investigated, and compared with the results of observa- 
tion. j 
& 
We will first observe that if we adopt, for the moment, the 
prevailing notion that the matter of which the train is made up 
is directly expelled by the sun froma nebulous envelope sur- 
Tounding the nucleus, the divergence of the lines of the sun’s 
action tangent to this envelope on opposite sides must have been 
exceedingly small; since the greatest breadth of the observed 
envelope was only 40,000 miles, while its distance from the sun 
was 55,000,000 miles, or more. The breadth of the train, result- 
ing from this divergence at the distance of 55,000,000 miles from 
the nucleus could not have exceeded 80,000 miles; whereas the 
actual breadth, at less distances than that, was several millions 
of miles. If we discard the idea of an envelope in a condi 
tion of permanent equilibrium about the nucleus, and take ac- 
Count, in accordance with the Dynamical Theory now under 
discussion, of the divergent velocities of the jets streaming up 
from the nucleus, on one side and the other of the radius-vectot 
of the comet, we are still unprovided with a cause adequate to 
develop a train of the enormous breadth just stated. According 
to calculations that will be presented in another connection, the 
velocity in a direction perpendicular to the radius-vector, of any 
caus 
thetical basis numerous calculations have been made, with the 
formule already given (pp. 54 and 58), and tested by comparison 
With the results of observation. These calculations consist in 
Am. Jour. Sct.—Szconp SzriEs, Vou. XXXII, No. 94—Jutr,186L 
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