122 Mr, Ivory on a new Method of deducing 
indebted for the first accurate knowledge of the laws of the 
planetary motions. This step in our knowledge of the uni- 
verse was reserved for Sir Isaac Newton, The principal and 
leading discovery of that great philosopher consisted in gene- 
ralizing the laws of Kepler ; in proving that they are neces- 
sary consequences of a more general fact, namely, that all the 
planets are continually deflected from a rectilineal motion to- 
wards the sun in the inverse proportion of the squares of their 
distances from that body. He demonstrated that the motions of 
such a system of bodies must be performed in the conic sections, 
having the sun in the focus, the species of the curve depend- 
ing upon the proportion of the rectilineal velocity to the quan- 
tity of the deflection towards the common centre. This theory 
comprehends an infinite variety of motions, all flowing from 
one common principle; and the ellipse alone, by the changes 
of form which it undergoes according to the degrees of its 
eccentricity, seems, at one extreme, when it is greatly elon- 
gated, as well adapted to account for the phenomena of the 
comets, as it is, at the other extreme, when it differs little from 
a circle, to represent the motions of the planets. 
To try if this theory will account for the actual appearances, 
it is necessary to determine, by means of terrestrial observa- 
tions, the magnitude and position of the curve in which a comet 
moves round the sun. Having selected as many observed 
places of a comet as are necessary for this purpose, the re- 
maining observations will serve as so many tests of the accuracy 
of the theory. When a comet appears for the first time, it is, 
indeed, hardly possible to determine its orbit with exactness. 
The very eccentric ellipses in which those bodies move, allow 
them |o be seen only when they are near the sun ; and in this 
