July 17, 1885.] 



SCIENCE. 



49 



accuracy by a circle with a radius of two 

 incties ; and on the circumference we mark the 

 yernal equinox ( T , fig. 3) , — a zero point from 

 which longitudes are to be measured. We 

 count in the direction opposite to the hands of 

 a watch, which is also the direction in which 

 the earth moves. We mark also the ' line of 

 nodes' (fig. 3), — the line in which the two 

 planes intersect, making the angle Q, with the 

 line of the equinoxes. 



is ' retrograde,' they will be moving in opposite 

 quadrants. The centre of our circle, and the 

 focus of our ellipse, are, of course, made to 

 coincide. 



For a parabolic orbit, the construction of a 

 model is not materially altered, though there 

 is this important difference between a parabola 

 and an ellipse. The parabola is an ' open ' 

 curve, and, the farther we recede from the sun 

 at the focus, the farther apart do the branches 



TXTiT TSTT :xxr !5r sk ^^^vttt "xyn' 



:xxni ^"c^TT 5X1 XE tit xvm 'wir 35t 



Fig. 5. — Apparent paths of comets 1884 ii and iir. 



The next thing we want to know is how the 

 major axis of the comet's orbit is pointing. 

 This is determined by supposing that P and 

 Q, (fig. 2) at first coincide, and then that P 

 is moved till PQ, = oj (in fig. 3 this angle is 

 300° 46', so that the acute angle QqP is 59° 

 14') . The planes are inclined at the angle i 

 (not shown in fig. 3, but given in fig. 2) ; and 

 it only remains to fasten the two pieces of 

 cardboard in this position, cutting a slit in 

 either one, so that they will fit together. If 

 the comet's motion is ' direct,' the comet and 

 earth will be moving in the same quadrant, as 

 they move away from the node. If its motion 



become ; and consequently a comet moving in 

 such an orbit, will, if undisturbed, ' double ' 

 the sun, and then go off forever on its journey 

 through space. 



For the parabola, the elements are given 

 in a little different form. The eccentricity is 

 equal to 1. The major axis stretches out to 

 infinity, and we give in its place the perihe- 

 lion distance g, and the distance from the 

 focus to the vertex of the curve PF (fig. 1 ) . 

 But five elements are then necessary to repre- 

 sent the parabola. 



Collecting these symbols for reference, they 

 are as follows : — 



