136 



Sir J. HerschelV s address 



its major and minor axis ought to hold with respect to the points, 

 a, b, certain calculable positioDs and no other. Hence it follows 

 that the distances a c and b c will each of them be subject to annual 

 increase and diminution ; and that, 1st, in a given and calculable 

 ratio the one to the other ; and, 2ndly, so that the maxima and mini- 

 ma of the one distance (a c) shall be nearly contemporaneous with 

 the mean values of the other distance b c, and vice versd. 



Thus we have, in the first place, several particulars independent of 

 mere numerical magnitudes ; and, in the second place, several dis- 

 tinct relations ct priori determined, to which those numerical values 

 must conform, if it be true that any observed fluctuations in these 

 distances (a b) (a c) be really parallactic. So that if they be found 

 in such conformity, and the above-mentioned maxima and minima do 

 observe that interchangeable law above stated : and if, moreover, all 

 due care be proved to have been taken to eliminate every instrument- 

 al source of annual fluctuation ; there becomes accumulated a body 

 of probability in four of the resulting parallax, which cannot but 

 impress every reasonable mind with a strong degree of belief and 

 conviction. 



Now, all these circumstances have been found by M. Bessel, in his 

 discussion of the measures taken by him (which have been very 

 carefully and rigorously examined by Mr. Main in the paper alluded 

 to, as have also M. Bessel's formulae and calculations, for in such 

 matters nothing must remain unverified), to prevail in a very signal 

 and satisfactory manner. Not one case of discordance, in so many 

 independent particulars, have been found to subsist ; and this, of it- 

 self, is high ground of probability. But we may go much farther. 

 Mr. Main has projected graphically the deviations of the distances 

 (a c) and (b c) from their mean quantities (after clearing them of the 

 effects of proper motion and of the minute differences of aberration, 

 &c). Taking the time for an abscissa, and laying down the devia- 

 tions in the distances so cleared as ordinates, two curves are obtain- 

 ed, the one for the star (a), the other for the star (b). Each of 

 these curves ought alternately to lie for half a year above, and for half 

 a year below, it axis. — It does so. Each of them ought to intersect its 

 axis at those dates when the maximum and minimum of the other above 

 and below the axis occurs. With only a slight degree of hesitation at 



