tJic late Balfour Stewart. 261 



that during conjunction of Mercury and Venus both sun spots 

 and declination range showed an increased range, but the 

 smallest range coincided with a difference of 90^ between 

 the positions of the two planets. The relative position of 

 Mercury and Jupiter gave a maximum of declination range 

 shortly after conjunction, and a minimum shortly after 

 opposition. As regards the position of Mercury, a maximum 

 and minimum declination range nearly coincided with peri- 

 helion and aphelion. In two further papers (Proc. Roy. Soc, 

 XXVII., p. 81 and 389, 1878) the same results are deduced 

 from the declination ranges of Trevandrum and Prague. 



Balfour Stewart has, in connexion with others, spent 

 much labour on the discovery of certain short-period 

 inequalities in terrestial and solar phenomena. Fourrier has 

 taught us how a series of observations, however irregular^ 

 may, by a purely analytical process, be represented by 

 a series of harmonic oscillations ; there are an infinite 

 number of ways in which this can be done by varying the 

 length of time within which we wish to represent the series. 

 But the amplitudes and phases of the oscillations thus de- 

 duced have no prophetic virtue, that is to say, from the 

 observations taken within certain limits we can tell nothing 

 as to what will happen outside those limits. If on the other 

 hand we have reason to believe that our series of observa- 

 tions is actually formed by the superposition of certain 

 definite oscillations, which are due to real but unknown 

 causes, we may have to deduce the periodicities of these 

 causes, and this is a different and much more difficult pro- 

 cess. Balfour Stewart has described a method {Proc. Roy. 

 Soc, Vol. XXIX., p. I, 1879) by means of which this can be 

 done, and has applied the method of a number of problems. 

 It is an inherent difficulty of this, as of any other method, 

 that results deduced from a single series do not give us any 

 certain results. Accidental regularities, such as we must 

 expect, can only be eliminated by a repetition of the work, 



