COMETARY ORBITS DETERMINED. 



object may be established, even were there no other means of 

 determining it. 



Unlike planets, comets do not present to us those individual 

 characters above mentioned, by which their identity may be 

 determined. None of them have been satisfactorily ascertained 

 to be spherical bodies, nor indeed to have any definite shape. 

 It is certain that many of them possess no solid matter, but are 

 masses consisting of some nearly transparent substances ; others 

 are so surrounded with this apparently vaporous matter, that it 

 is impossible, by any means of observation which we possess, to 

 discover whether this vapour enshrouds within it any solid mass. 

 The same vapour which thus envelopes the body (if such there 

 be within it) also conceals from us its features and individual 

 character. Even the limits of the vapour itself, if vapour it be, 

 are subject to great change in each individual comet. Within a 

 few days they are sometimes observed to increase or diminish 

 some hundred- fold. A comet appearing at distant intervals 

 presents, therefore, no very obvious means of recognition. A 

 like extent of surrounding vapour would evidently be a fallible 

 test of identity ; and not less inconclusive would it be to infer 

 diversity from a different extent of nebulosity. 



If a comet, like a planet, revolved round the sun in an orbit 

 nearly circular, it might be seen in every part of its path, and 

 its identity might thus be established independently of any 

 peculiar characters in its appearance. But such is not the course 

 which comets are observed to take. 



In general a comet is visible only throughout an arc of its 

 orbit, which extends to a certain limited distance on each side 

 of its perihelion. It first becomes apparent at some point of its 

 path, such as g, g' or g", fig. 1 ; it approaches the sun and dis- 

 appears after it passes a corresponding point //, g' or g" in departing 

 from the sun. The arc of its orbit in which alone it is visible 

 would therefore be g a g, g' a g', or g" a g". 



If this arc, extending on either side of perihelion, could always 

 be observed with the same precision as are the planetary orbits, 

 it would be possible, by the properties of the conic sections, to 

 determine not only the general character of the orbit, whether it 

 be an ellipse, or parabola, or an hyperbola, but even to ascertain 

 the individual curve of the one kind or the other in which the 

 comet moves, so that the course it followed before it became visible, 

 as well as that which it pursues after it ceases to be visible, would 

 be as certainly and precisely known as if it could be traced by 

 direct observation throughout its entire orbit. 



12. If it be ascertained that the arc in which the comet moves 

 while it is visible is part of an hyperbola, such as g a g, it will be 



153 



