32 A: C. D. CROMMELIN, ESQ., D.SC., F.R.A.S., ON 
very near the horizon, and the sky having begun to brighten. 
We have thus every reason to look for a fairly good display as 
an evening star during the last ten days of May, thouzh ae is 
right to warn those who saw the great comet of 1882, 
Donati’s comet in 1858, that there will be nothing to commen 
with these from a spectacular point of view. It may not even 
equal the bright object which formed a nine days’ wonder last 
January. It is just because the old records speak of it as one 
of the brightest comets of its time, that I think it must have 
greatly declined since then. 
A few words on the subject of computing the perturbations 
may be of interest. The planets are pulling the comet all the 
time, altering its speed and direction of motion and thus chang- 
ing the ellipse in which it is moving round the sun. Whatever 
inethod we employ, we have to calculate the distance and 
direction of the comet from each of the larger planets at short 
intervals of time during the whole revolution. The old method 
assumed the comet to move for some time exactly in some 
definite ellipse, and the disturbances were calculated and 
added up; their combined effect applied to the ellipse gave a 
new ellipse, and the comet was then assumed to follow this for 
another space of time, and so on. This method was both cum- 
brous and inexact; Mr. Cowell devised the better plan of not 
making the assumption of elliptical motion at all, but 
determining the curvature at each point of the path, from the 
whole of the forces acting (solar and planetary) and then 
building up the path, are by are, from these curvatures. It is 
necessary when the comet is near the sun, and the curvature 
great, to compute it with extreme accuracy; the unit of length 
at this part of the orbit was taken as the eleventh decimal of 
the distance from the earth to the sun, or about 5 feet. Need- 
less to say, we do not know the actual place of the comet to — 
anything like this degree of accuracy, in fact, not within some 
20 miles. But unless the curvature were investigated with a 
much higher degree of accuracy than the actual place is known, 
errors would arise in the deduced path, which would be very 
serious at the end of a revolution. Far the largest perturbations 
are those that arise when the comet is passing near Jupiter, and 
it is interesting to note that the perturbations arising at one of 
these approaches do not make a very appreciable alteration in 
the comet’s place for the next year or two, but show their full 
effect when it comes back seventy-five years later. For the 
perturbations are really small changes in the amount and 
direction of the motion, and it takes time for these to develop 
into appreciable alterations in the comet's place. 
