494 



SCIENCE. 



of inequalities will be easily understood by an illustration. 

 Suppose we had in our possession extensive records of the 

 temperature of the earth's atmosphere at some one place 

 in middle latitudes, and that, independently of astronom- 

 ical knowledge, we were to make use of these for the 

 purpose of investigating the natural inequalities of terres- 

 trial temperature. We should begin by grouping the 

 observations according to various periods taken, say, at 

 small but definite time-intervals from each other. Now 

 if our series of observations were sufficiently extensive, 

 and if some of our various groupings together of this 

 series should correspond to a real inequality, we should 

 expect it to exhibit a well-defined and prominent fluctua- 

 tion, whose departures above and below the mean should 

 be of considerable amount. 



Suppose, for instance, that we have twenty-four points 

 in our series, and that we group a long series of 

 temperature observations in rows of twenty-four each, 

 the time distance between two contiguous members 

 of one row being one hour. The series would thus rep- 

 resent the mean solar day, and we should, without doubt, 

 obtain from a final summation of our rows a result ex- 

 hibiting a prominent temperature fluctuation of a well- 

 defined character, which we might measure (as long as 

 we keep to twenty-four points) by simply adding together 

 all the departures of its various points from the mean, 

 whether these points lie above or below ; in fine, by ob- 

 taining the area of the curve, which. is the graphical rep- 

 resentation of the inequality above and below the line of 

 abscissae taken to represent the mean of all the poiuts. 

 Suppose next that, still keeping to rows of twenty-four, 

 we should make the time interval between two contigu- 

 ous members of a row somewhat different from one 

 hour, whether greater or less, we should now in either 

 case obtain a result exhibiting, when measured as above, 

 a much smaller inequality than that given when the inter- 

 val was exactly one hour ; and it is even possible that, if 

 our series of observations were sufficiently extensive, we 

 should obtain hardly any traces of an inequality what- 

 ever. 



In fine, when each row accurately represented a solar 

 day, the result would be an inequality of large amount; 

 but when each row represented a period either slightly 

 less or greater than a day, the result would be an in- 

 equality of small amount. This process, as far as I have 

 described it, is not new, inasmuch as something of this 

 kind must be pursued in all attempts to detect inequal- 

 ities. In the present instance we should by its means, 

 after bestowing enormous labor in variously grouping, 

 in accordance with a great number of periods taken at 

 small intervals from each other, obtain definite results. 

 These might be graphically represented in the following 

 manner : — 



The line of abscissas might be taken to denote the 

 exact values of the various periods, forming a time-scale, 

 in fact, while the ordinates might represent the areas or 

 summations obtained as above by employing these 

 various periods. There would thus be in the case 

 now used for illustration a very prominent peak, corre- 

 sponding to twenty-four hours, which would fall off vety 

 rapidly on either side. • 



By means of the process now described we should at 

 length, after enormous labor, obtain a graphical result, 

 showing the exact position in the time-scale of the ob- 

 served maximum inequality. In conjunction with Mr. 

 William Dodgson, I have devised a method by which 

 this labor is very grea'ly reduced, and the process so 

 modified has been applied by us in order to determine 

 whether there be inequalities of short period in the ob- 

 served areas of the sun-spots occurring on the visible hem- 

 isphere of the sun. We have detected an inequality of this 

 nature corresponding in period to 24.01 1 days, which, 

 when subjected to a certain purifying treatment, appears 

 to us to exhibit the marks of a true periodicity. But it 

 has been suggested by I'rof. Stokes that a method of this 



nature for detecting inequalities might with greater pro- 

 priety be employed as a crucible for testing the value of 

 some hypothesis introduced into it from without. 



Acting upon this suggestion I have ventured to intro- 

 duce the planetary hypothesis, and to ask whether the 

 above sun-spot inequality of short period may not in 

 reality be caused by an intra-Mercurial planet. It is 

 quite easy to put this hypothesis to a test, taking for our 

 guidance the results obtained bv the Kew observers. 

 For what do these results exhibit ? In the first place they 

 exhibit the probability of a sun-spot inequality corre- 

 sponding to the period of Mercury round the sun ; and 

 in the next they exhibit the probability of similar inequal- 

 ities corresponding to the synodic period of Mercury and 

 Venus, and to the synodic period of Mercury and Jupiter. 



Now if there be an intra-Mercurial planet of period 

 24.0 [I days, it will have the following synodic periods : — 



With Mercury. . . 33-°25 days. 



With Venus 26 884 days. 



With Jupiter 24. 145. days. 



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 inequalities nearly 



corresponding to these periods, and we have ob'ained 

 the following results : — 



A very prominent inequality of period 3 2 -95 5 days. 



A very prominent inequality of period 26.871 days. 



A less prominent inequality of period 24.142 days. 



It will thus be noticed that there are prominent sun- 

 spot inequalities, the periods of which agree very well 

 with the synodic periods of the supposed planet with 

 Mercury, 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 conjunction. Now if we assume that there 

 is an intra-Mercurial planet of period 24.011 days, we 

 are as yet unable to assign its exact position in ecliptical 

 longitude at any moment. We know its period, and we 

 may presume that it has considerable eccentricity, but 

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

 probable that the maximum point of the inequality of 

 period 32.955 days corresponds to the conjunction of 

 the planet with Mercury, the maximum point of the in- 

 equality of period 26.871 days to its conjunction with 

 Venus, and the maximum point of the inequality of 

 period 24.142 days to its conjunction with Jupiter. On 

 this assumption, and knowiDg the average rate of motion 

 of the planet in its orbit, we may deduce approximately 

 its position at a given epoch independently from each of 

 the three synodic periods above mentioned, and these 

 positions ought to agree together, if our hypothesis be 

 correct. 



I have done this approximately, but am not able to 

 bring exact figures before this meeting. The agreement 

 is as great as can be expected, bearing in 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 eccentricity. I think I may state that 

 three independent values of its position corresponding to 

 January 1, 1832, will be obtained, and that the mean 

 difference of a single value from the mean of the whole 

 will probably not be more than twenty degrees. It 

 would thus appear from this investigation that the evi- 

 dence is in favor of the sun-spot inequality of 24.01 1 

 days being due to an intra-Mercurial planet. Of course 

 a single research of this nature is insufficient to establish 

 a theory of this importance, but as there are several 

 short-period solar inequalities, the same method may be 

 pursued for each, an operation which demands nothing 

 but time and labor. It appears to me of great importance 

 that these short-period solar inequalities should be sys- 

 tematically examined after this method. 



