Great Aurora of 1859. 
tion in hand, we are led to take a point of view somewhat dif — 
ferent from that’ occupied by either of these eminent astrono 
mers. It is now proposed to determine both the true andap 
parent positions of the receding particle, after the lapse of any — 
interval of time, directly from the initial velocity and direction 
of motion; in order to take account of the various circumstances 
of the original motion of the different particles supposed to pro- 
ceed from the nucleus. The following formulas will serve for 
this purpose. Equs. (12) to (15) have been deduced from the gen- 
eral equations of motion of a body around a centre of attraction, 
by changing the sign of the force, and adapting them to com — 
venient computation. Equ.(17) for calculating the true anomaly 
of the particle in its hyperbolic orbit, from the time, was inde 
pendently investigated. It is sufficiently accurate for our pur 
pose, and the calculation can be more readily effected with it — 
than by the intervention of the eccentric anomaly. Lhe com 
stants which enter into the equation can be determined ni Mit: 
of any one comet. They depend upon the initial circumstances 
of motion of the particle emitted from the nucleus. Equ. (16) 
17) 
or this case. There will be occasion to make use 0 ge 
_ when we shall undertake to determine all possible particles of 
at any assumed date may go to make up the concave ou ne 
New Haven, March 28th, 1860. 
(To be continued.) . 
Eee ee q 
Art. XXXV.—The Great Auroral Exhibition of Aug- 26% » q 
Sept. 4th, 1859.—47TH ARTICLE, a 
In the three preceding numbers of this Journal we aide oe 
observations of the Aurora of Aug. 28th to Sept. ee 4 
Asia, and accounts of a simultaneous auroral exhibition 
Southern hemisphere, 
a 
servations of the same aurora in Europe, with some a ie a 
