254 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1909. 
omy did not come until 1704, when he was appointed professor of 
geometry at Oxford. He immediately began the study of comets, 
basing his studies upon Newton’s law. He became the first great 
calculator of comet orbits. Ina little more than a year he had twenty- 
four to his credit; orbits of all the comets, in fact, for which he could 
find accurate observations. This meant prodigious labor, in those 
days, for the good observations and the highly developed methods 
of our time were unknown. He found that three comets out of the 
twenty-four had traveled from distant space, around the sun, and out 
into distant space, along the same path, whereas the other twenty-one 
had each a different path. Were these three comets one and the same 
body? If so, their common orbit must be an ellipse. . The crude ob- 
servations of the sixteenth and seventeenth centuries did not permit 
him to decide whether the orbit was a long ellipse or a parabola (a 
curve extending out to an infinitely great distance). If the latter, the 
three comets would have traveled away from our solar system never 
-to return. If they were the same body, they should have returned at 
about equal intervals of time; and this is what did occur, for the dates 
when the three comets had been nearest to the sun were August 24, 
1531; October 16, 1607 (interval, 76.2 years) ; September 4, 1682 (in- 
terval, 74.9 years). 
The small inequality of intervals he correctly attributed to the 
disturbing attractions of the planets Jupiter and Saturn. He pre- 
dicted that the great comet would complete another revolution in 
its orbit in seventy-five or seventy-six years and reappear about 
1758. He said that he could not predict the time more accurately, 
for the effects of Jupiter’s and Saturn’s disturbing attractions were 
not yet computed. Halley (born 1656, died 1742) knew that he 
would not live to witness the return, but he confidently and patri- 
otically called upon posterity to remember that this prediction had 
been made by an Englishman—* ab homine Anglo.” 
The comet did return in March, 1759. It was a little later than 
expected because of the disturbing attractions of the planets Uranus 
and Neptune, which had not yet been discovered, and whose influence 
upon the comet’s orbit, therefore, could not be taken into aécount. 
This was indeed a great triumph in exact science, made possible by 
Newton’s overwhelming genius and Halley’s vigor. It is easy to 
predict the returns of comets in the twentieth century, but this is so 
because Newton and Halley lived and labored as pioneers. 
ITalley’s comet reappeared in 1835, within a few days of the pre- 
dicted time. It is due to be again “in perihelion,” i. e., nearest to 
the sun, in the first half of April, 1910. The comet, though invisible, 
is at present (April, 1909) much closer to us than Jupiter is, and 
slowly drawing nearer to the sun. When we may expect to see it 
