554 SCIENCE PROGRESS 



The normal date No. 16 is the mean of all the observed dates 

 from Nos. 3 to 29 inclusive. The other normal dates are found 

 by the successive application of the average period, 7677 years. 

 The column "First — second " shows the discordance of the actual 

 aphelion passage from the normal date. These are plotted in a 

 diagram, and it is readily seen that more than one wave is 

 indicated. There is one pretty regular wave (discovered by 

 Angstrom) with a period of io| revolutions of the comet, and 

 an amplitude of about 2*07 years. This is tabulated above, and 

 also the residual after the Angstrom term has been removed. 

 Angstrom considered that the residuals formed another regular 

 wave with period 2,650 years. This is not borne out by the 

 longer and more exact series of returns of the comet that 

 is now available. Some part of it may form a wave, but it 

 seems not unlikely that part of it is a parabolic curve, which 

 would indicate an acceleration of the comet's motion, such as 

 has already been detected in the case of Encke's comet. 



This may arise from a resisting medium. The effect of such 

 a medium is not to lengthen the period, as might be thought ; 

 for it causes the comet to approach the sun, and the effect of 

 this more than counterbalances the diminished rate of motion. 

 Another cause that may affect the period is the alteration of 

 mass produced by the matter driven off in the tail when the 

 comet is near the sun. It should be borne in mind that the 

 effect of all non-gravitational causes on the period cannot 

 amount to more than a day or two in each revolution. Thus it 

 is difficult or impossible to make calculations sufficiently exact 

 to detect their effect in modern times ; but, since the effect of an 

 acceleration increases as the square of the time, even a small 

 acceleration produces sensible effects in the course of 

 29 revolutions. We have an exactly similar case in the ac- 

 celeration of the moon's motion ; this cannot be found even 

 from all the exact observations made in modern times, and yet 

 the rough observations of ancient eclipses are of use in its 

 determination. 



We now propose to trace the movements of the comet 

 since its last visit. One year after perihelion it crossed the 

 orbit of Jupiter, and five months later made its nearest ap- 

 proach to that planet, the distance being 27 astronomical units. 

 It had made a still nearer approach to the giant planet (1*3 units) 

 nine-and-a-half months before perihelion. It was these com- 



