TBANSACTIONS OF SECTION A. 519 



2. An apparent maximum and minimum of spotted area approximately corre- 

 sponding in time to the conjunction and opposition of Mercury and Jupiter. 



3. An apparent maximum and minimum of spotted area approximately corre- 

 sponding in time to tlie conjunction and opposition of Venus and Jupiter. 



4. An apparent maximum and minimum of spotted area approximately corre- 

 sponding in time to the conjunction and opposition of Venus and Mercury. 



Whatever truth there may be in these conclusions, it appears to be quite certain 

 that pei'iodical relations between the various knotun planets will not account for all 

 the sun-spot inequalities with which we are acquainted. They may account for 

 some, but certainly not for all. For there are solar inequalities of short duration, 

 which, presuming them to be real, can only be accounted for on the planetary 

 hypothesis by supposing the existence of several unknown intra-mercui-ial planets. 



In conjiuiction with Mr. William Dodgson I have devised a method for detecting 

 imknown niequalities, which, when applied to the sun, reveals a period in sun-spots 

 of 24'011 days. Is this the period of an intra-mercurial planet ? 



It is quite easy to put this hypothesis to a test, taking for our guidance the 

 results obtained by the Kew observers. For what do these results exhibit ? In the 

 first place, they exhibit the probability of a sun-spot inequality corresponding to 

 the period of Merciu-y round the sun ; and in the next, they exhibit the probability 

 of similar inequalities corresponding to the synodic period of Mercury and Venus, 

 and to that of Mercuiy and Jupiter. Now, if there be an intramercuiial planet of 

 period 24011 days, it will have the following synodic periods : — 

 With Mercuiy .... 33-025 days. 

 With Venus .... 26-884 „ 



With Jupiter .... 24-145 „ 



In conjunction with Mr. Dodgson I have applied the above method of analysis 

 ■with the view of ascertaining whether there be well-marked sun-spot inequali- 

 ties nearly corresponding to these periods, and we have obtained the following 

 results : — 



A very prominent inequality of period 32-955 days. 

 A very prominent inequality of period 26-871 „ 

 A less prominent inequality of period 24-142 „ 

 It will thus be noticed that there are prominent sun-spot inequalities, the 

 periods of which agi-ee very well with the synodic periods of the supposed planet 

 with Merciu-y, Venus, and Jupiter, more especially if we bear in mind that this is 

 only a first approximation. 



The test, however, is not yet complete. Referring once more to the results of 

 the Kew observers, it will be noticed that we have approximately maxima of sun- 

 spot areas when Mercury and Venus, or when Mercury and Jupiter are in conjunc- 

 tion. Now, if we assume that there is an intra-mercurial planet of period 

 24-011 days, we areas yet unable to assign its exact position inecliptical longitude 

 at any moment. We know its period, and we may presume that it has consider- 

 able excentricity, but we know nothing else. We may, however, assume as most 

 probable that the maximiun point of the inequality of period 32-955 days 

 corresponds to the conjunction of the planet with Mercury, and so on for the other 

 inequalities. On this assumption, and knowing the average rate of motion of the 

 planet in its orbit, we may decide approximately its position at a given epoch in- 

 dependently from each of the three synodic periods, above mentioned, and these 

 positions ought to agi-ee together, if our hypothesis be correct. 



I have done this approximately, but am not able to bring exact figures be- 

 fore this meeting. The agreement is'^as gi-eat as can be expected, bearing'm mind that 

 we know only the average rate of motion of the planet, and not the variations 

 of its rate, inasmuch as we are ignorant of its excentricity. I think I may state 

 that three independent values of its position, corresponding to January 1, 1832, will 

 be obtained, and that the mean difierence of a single value from the mean of the 

 whole will probably not be more than twenty degi-ees. It would thus appear from this 

 investigation that the evidence is in favour of the sun-spot inequality of 24011 days 

 being due to an intra-mercurial planet. 



