148 
NATURE 
[ Dec. 14, 1882 
Should any one be interested in the subject, I would refet 
them to the experiments of Mr. J. T. Bottomley (Proc. R. Soc., 
No. 197, 1879), of Prof. Ewing (Proc. #. Soc., 1880, June 10), 
and of myself (‘‘ Influence of Stress and Strain on the Action of 
Physical Forces, Phil. Trans., 1882, second volume). 
HERBERT TOMLINSON 
King’s College, Strand, December 4. 
Intra-Mercurial Planets—Prof. Stewart's 24o11d, Period, 
Leverrier’s and Gaillot’s 24°25d., and Leverrier’s 330225d, 
Sidereal Periods Considered 
As your regular monthly numbers did not reach our Free 
Library from September, 1881, until comparatively recently, and 
I was absent from home when they did arrive, it was only quite 
lately that I had an ofportunity of seeing Prof. Balfour Stewart's 
very interesting paper ‘‘On the Possibility of Intra-Mercurial 
Planets,” read at last year’s meeting of the British Association, 
and published at length in your issue of September 15, 1881. 
<The possibility ” has been almost an admitted fact for over a 
century, but Prof. Stewart’s valuable paper discusses the relation 
of certain sun-spot periods to a probable sidereal period, ap- 
proximately at least, of an intra-Mercurial planet of 24011 
days. 
On looking through your subsequent numbers, I was rather 
surprised that so suggestive a paper had not elicited quite a dis- 
cussion, although it is true that Prof. Stewart remarked that ‘‘ the 
test was not yet complete,” and many may have waited to see 
the final results, which have not yet appeared, but perhaps will 
be forthcoming at the next meeting of the British Association. 
But the first pomt that struck me, although not referred to by 
Prof. Stewart, was the near approximation periods of 24011 
days affords to Leverrier’s and Gaillo~’s period of 24°25 days 
noticed in your columns of August 22, 1878, which M. Gaillot 
endeavoured to fit to Prof, Watson’s observation, in Wyoming 
State, of a supposed intra-Mercurial planet at 2° 9/ from the 
Sun, during the total eclipse, July 29, 1878. M. Gaillot’s difficulty 
seemed to be to reconcile Leverrier’s fora:ula with Prof. Wat- 
son’s reasonable belief that he saw the planet in the superior part 
of the orbit, while Gaillot made the formula and interval require 
it to be in the inferior part of the orbit July 29, 1878. The only 
interval that Gaillot referred to was from 1750 (January 1, I 
presume) ; it might have been obvious, therefore, that quite a 
small fractional difference in eaca of so many revolutions would 
suffice to make the period accord with either condition 
that Prof. Watson’s observation required; namely, ¢hat she 
planet was seen at 2° 9! from superior conjunction, or 2°°9! 
past infirior conjunction, For instance, I have obtained these 
two result for the synodical periods. The same interval for both 
about 469624 days, requiring 18083} revolutions of 25°96825104d., 
each 41 being equal to 11’90211506d.; that accords very 
closely with Prof. Watson’s belief, while 1808.4, revolutions of 
25 9742355d. each, and 1°08226d. remainder, meet the condi- 
tion of its being 2° 9’ past the inferior conjunction. Of course, 
as a matter of opinion, I presume it would be impossible to see 
the planet so near its inferior conjunction during any total eclipse 
of the Sun, the planet’s crescent being altogether too fine. These 
results are simply what the conditions require in relation to 
approximate 26-day apparent-periods, but we must avoid exactly 
26 days, or the interval would put the planet at 7zts elongation, 
perhaps apparently 10° from the Sun, and if we tried the Les- 
carbault interval, from March 26, 1859, 70654 days, singularly 
enough it would put the planet zn the other elongation. Fractional 
differences are of course very important therefore. And I do 
not find either that M. Gaillot’s figures 24°25d. for the sidereal 
time, and 14°°8462 for the diurnal motion exactly accord, and 
neither fills the conditions required by Prof. Watson’s observation, 
if I am approximately correct, which I think I am. For 
instance, 14°°8462 diurnal motion, gives us 24°24862928d. for 
the sidereal periods, not 24°25d., and the synodical period would 
be 25°9729903466d., and the planet’s position would be about 
46° 12' inits orbit past inferior conjunction, or apparently about 
$° 24 from the Sun, and 46° 12’ would be about 34 days. 
The sidereal period of 24°25 days, makes the diurnal motion 
14°'8453608247, and puts the planet at about 6°°8 past inferior 
conjunction, or apparently less than 1°, The synodical revolu- 
ions would be 25°974562624d. and fractional remainder ‘0188945, 
or 1th, 46m. 43s., which of course would be too close to the 
sun, But the sidereal period and the diurnal motion should 
both agree, instead of producing such a difference as I have here 
indicated, of nearly 49° in the revolutions. But although I 
| believe we cannot accept the exact published figures, 24°25d., or 
14°'8462, still I have shown how near we may make the final 
results conform to them, 
Adopting the s1me number of synodical revolutions, and prac- 
tically making the best use of the formula, obtaining 18084 
revolutions, and 1808. The revolution being 25°96825104d., 
or 25°9742355d., and the remainders 11°90211506d., or 1'08226. 
Reduced to clock time they stand as follows: 1808}; being 
equal to 25d. 23h. 14m. 16°9s. each, and 11d. 23h. 39m. 2°7s. 
remainder, and 1808, being equal to 25d. 23h. 22m. 54s. each, 
and 1d. th. 58m. 274s. remainder. Zhe latter ts almost abso- 
lutely identical with the periods that would fit the Fritsch and 
Stark interval from October 10, 1802, to October 9, 1819, 6208 
days, or 239 periods of 25d. 23h. 23m. 51s. And from Stark 
to Lescarbault makes 14,413 days, which would require 555 
periods of 25d. 23h. 15m. 534s., which affords almost exact 
rdentity with the general mean, placing Prof. Watson’s observa- 
tion in the superior part of the orbit. Thus, then, we have 
almost positive assurance that Fritsch, Stark, Lescarbault, and 
Prof. Watson’s planet were identical, and that Prof. Watson was 
correct about it being 2° 9’ from superior conjunction : these in- 
teresting facts, giving a record to Lescarbault’s planet of 80 
years from Fritsch’s observance October 10, 1802, to October 
next. What other ‘‘myths” will stand such satisfactory 
results? I am afraid that Prof. Proctor and some other astro- 
nomers have not given the attention to this question that it 
deserves. But there are a few exceptions deserving credit: M. 
de la Baume, in Paris, was engaged last year in a classification 
of reported observed transits, although he did not then draw 
any inferences respecting apparent revolutions. He regarded 
Fritsch, De Cuppe, Lescarbault, and Lummis’ transits as the 
same planets, agreeing relatively with the nodes. While 
Lichtenburg, November 19, 1762, Hoffman, about May Io, 1764, 
Scott, June 28, 1847, Ritter and Schmidt, June 11, 1855, and 
W. G. Wright, of San Bernardino, California, October 24, 
1876, whose transit was illustrated in the Scéertific American of 
November 18, 1876, he regarded as another larger planet than 
Lescarbault’s. 
Adopting the same principle with Prof. Stewart's hypothetical 
sidereal periods of 24'o11d., I first find what results that gives, 
as applied to the same interval from January 1, 1750, and then 
take the nearest modification I can to the conditions of Prof. 
Watson’s observation. 360 divided by 24*o1Id. gives us 
14°°99312818 for the planet’s diurnal motion, which, multiplied 
by 46,9624 days, gives us 704114°°78215325, from which, sub- 
tracting the earth’s motion, 46288°-463941, leaves a residue ot 
657826°°318213, which, divided by 360° gives us 1827°29533 
synodical revolutions ; using that to divide the 469623 days, we 
obtain the synodical periods of 25°700553d. ‘The fractional 
revolution *29533 is equal to 106° 19’ 17”, or 7d. 14h, Lom. 
Now while that would put the planet in the superior part of the 
orbit, it would still be nearly 60° from where Prof. Watson 
observed it. I ought to have explained before that 2° 9, or 
2° 10' apparently, is about equivalent to 15° from swfertor con- 
junction, or, 15° past 7fertor conjunction in the planet's orbit ; 
15° from 180°, therefore, leaves 165° as the required position, 
instead of 106° 19’ 17”. Perhaps I am only approximately 
correct, but sufficient for illustration. It is very evident, how- 
ever, that a very slight modification of Prof. Stewart's infer- 
ential sidereal periods, 24’011d., would give us the 60° more 
required, or exact accord with Prof. Watson’s observation, and 
the evidence would te rather in favour of 18274} revolutions, 
obtained from such a solar analogy, and may still have an inci- 
dental bearing or relation to the Leverrier-Gaillot formula I 
have construed to require 18083} or 1808; revolutions. 182754 
revolutions would give us 25°698260334253d. for the synodical 
periods, and a remainder of 11°77836931986d. Reduced to 
clock time, that would give us 25d. 16h. 45m. 29°7s. for each 
apparent revolution, and 11d. 18h, gom. 5111s. for the re- 
mainder. It must be understood that these definitions, 180834 
and 182744, with their results, are intended only to express 
possible general mean periods of apparent revolutions, and may 
not exactly apply to any of the intervals between the long list of 
recorded observations of supposed transits. When Leverrier, 
October 1876, had strong faith in sidereal periods of 33°0225d., 
it was probably a general mean from January I, 1759, to Lesear- 
bault, March 26, 1859, and only approximately fitted Lummis, 
De Cuppis, Stark, Fritsch, and others, but still in a general 
sense applied to some of them, while Leverrier was led to predi- 
‘s'e= 7 BF, ati <i =—- ae 
