Rodolfo Amedeo Lanciani.

The American journal of science and arts online

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-200


347 5 50-4


-47-8


60


233 94 2-7


+ 2-6


-12-3


233 63 52-9


52 58-3 + 30-0


-17-2


223 53 111


-31-8


60


120 41 201


+ 1-6


-12-3


120 41 9-4


40 20-3 + 261


-131


120 40 33-3


—36-8


70


7 28 37-4


+ 0-9


-10-8


7 28 27-5


27 42-2


+ 22-5


- 81


7 27 66-6


-30-9


80


254 15 64-8


+ 0-4


- 8-0


264 15 47*2


15 4-2


+ 19-2


- 2-3


264 15 21 1


-261


90


141 3 121


+ 01


- 4-2


141 3 7-8


2 261


+ 16-1


+ 3-9


141 2 461 -21*7


1700


27 50 29-5


+ 0-0


+ 0-2


27 50 29-7


49 48-1


+ 13-3


+ 100


27 50 11-4 -18-3


10


274 37 46-8


+ 0-1


+ 4-4 274 37 51-3


37 100


+ 10-8


+ 15-6


274 37 36-4 —14-9


20


161 25 4-2


+ 0-4


+ 8-3!l61 26 12-9


24 820


+ 8-5


+ 20-6


161 26 1-0


-11-9


80


48 12 21-5


+ 0-9


+ 11-0 48 12 33-4


11 59-9


+ 6-5


+ 24-2


48 12 24-7


- 8-7


40


294 59 38-9


+ 1-6


+ 12-4


294 59 52-9


59 15-9


+ 4-8


+ 26-4


294 59 47 1


- 5-8


60


181 47 66-2


+ 2-5


+ 12-2


181 47 10-0


46 37-9


+ 3-3


+ 26-9


181 47 81


- 2-9


60


68 34 13-6


+ 3-6


+ 10-6


68 34 27-8


33 59-8


+ 21


+ 26-7


68 64 27-6


- 0-2


70


315 21 30*9


+ 4-9


+ 7-8


316 21 43-7


21 21-8


+ 1-2


+ 22-9


316 21 45-9


+ 2-2


80


202 8 48-3


+ 6-4


+ 3-9


202 8 58-6


8 43-7


+ 0-6


+ 18-5


202 9 2-7


+ 4-1


90


88 56 6-6


+ 8-1


- 0-4


88 56 13*4


56 5-7


+ 01


+ 12-8


88 66 18-6


+ 5-2


1800


335 43 23*0


+ 10-0


- 4-7


335 43 28-4


43 27-7


00


+ 61


336 43 33-8


+ 6-4


10


222 30 40-4


+ 12-1


- 8-3


222 30 44-2


30 49-6


+ 01


- 1-1


222 30 48-6


+ 4-4


20


109 17 57-8


+ 14-4


-110


109 18 1*2


18 11-6


+ 0-6


- 8-4


109 18 3-7


+ 2-6


30


366 6 16-2


+ 16-9


-^2-4


356 6 19-7


6 33-5


+ 1-2


-15-4


356 5 19-3


- 0-4


40


242 52 32-5


+ 19-6


-12-2


242 52 39-9


52 66-6


+ 21


-21-6


242 62 36-0


- 3-9


60


129 39 49-9


+ 22-6


-10-6


129 4« 1-8


40 17-6


+ 3-3


-26-5


129 39 64-3


- 7-5


60


16 27 7-2


+ 25-6


- 76


16 27 25-2


27 394


+ 4-8


-29-8


16 27 14-4


-10-8


70


263 14 24-6


+ 28-9


- 3-8


263 14 49-7


15 1-4


+ 6-5


-31-3


263 14 86*6


-131



Burckhardt's tables have been selected for this comparison
because they have been extensively compared with observations
made before 1700. The additions to the Gonnaissance des Temps
for 1824 contain a paper by Burckhardt himself giving a com-
parison of his tables with observations of occultations made by
Flamstead, Hevelius and others, between 1687 and 1700. The
general result of this comparison is that the mean longitude of
bis tables could hardly have been more than a very few seconds
in error in the year 1670. But, the preceding table shows that
for this epoch Hansen's mean longitude is 80 less than Burck-
hardt's. Therefore, unless we suppc«e Burckhardt's investi-
gation to be affected with some egregious systematic error we
must admit that the mean longitude of Hansen's tables for the
epoch 1670 is about 30'' too small

Desiring an independent test of this conclusion T have select-
ed certain observations which, with the data available, seemed



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of long period in the mean motion of the Moon,



189



well fitted to answer this purpose and compared them directly
with Hansen's Tablea
They are

1. Occultation of AldeBaran, 1680, Sept 13, observed at
Greenwich by Flamstead.

2. Occultation of the same star 1680, Nov. 7, observed at
Greenwich by Flamstead, and at London by Halley.

8. Total eclipse of the sun 1715, May 8, observed at Lon-
don, Greenwich and Wanstead by Halley, Flamstead and
Pound.

To compute the occultations of Aldebaran the mean position
for 1680*0 was derived from Le Verrier's Tables (Annales de
rObservatoire, Tome II) correcting the right ascension by
+0*'01, and was as follows :

a(1680) = 4»» 17" 37»-01

d +15^49' ll"-8

The corrections for reduction to apparent place are'
for Sept. 13, Aa =+2«-90 ; Ad=:+l"'l

Nov. 7, Aa z=4-4*18 A^=+2-4

The following geocentric positions of the moon were derived
from Hansen's Tables.



Date (jTUlan Cal.)


Sept. 18.


Nov. 7.


Gr. Mean Time,

D *8 Longitude,

" Latitude,

" Parallai,


b m 8
15 63
640 54/ 24"-3
-4 46 29-8

59 300


h m ■
16 12 63
65° 37' 20"-4
-4 48 10-6

59 28-8


h m 8

7 50 39
64^ 33' ll"-6
-4 39 26-9

1 1 18-5


h m 8
8 48 15
65° 9'49"-6
-4 40 480
1 1 17-8



From these data we derive the following times for the im-
mersion and emersion of Aldebaran for the dates in question.
The observed times have been concluded from the observed
altitudes and clock times given by Flamstead in the Historia
Cfefesfti, kindly ftirnished me by rrot Winlock. They differ
but little from the results of Flamstead himself, when the latter
are corrected for the equation of time.





Computed.


Obsenred.


0-0.


h m 8






B


Sept 13, Immersion,


16 2 49


15


53


+ 116


Emersion,


16 10 5


16 9


12


+ 53


Nov. 7. Immersion,


7 51 47


7 60


48


+ 64


Emersion,


8 48 16


8 47


12


+ 64



The great difference between the results of the two phases of
the first occultation gives rise to a suspicion of error in the ob-
servations or the data of reduction. The second observation is
confirmed by that of Halley in London, he having observed
the immersion at 1^ 50™ 9«, and noticed that the star was " new-
ly emerged " at 8** 47™ 1'. His place of observation was prob-
ably twenty-five or thirty seconos west of Greenwich, and tncre-



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190



S. Newcomb on the apparent ineqpmlities



fore his observation agrees well with that of Flamstead. The
discordance between the observed and computed times, of this
second occultation indicates a correction of, about +82" to
Hansen's mean longitude at the ep<5ch 1680, and the first may
be considered as confirming this correction in direction, if not
in amount
For the eclipse of May 8, 1716 we have the following com-

Euted and observed times. I have assumed Halley's station to
e in latitude 51^ 31' and longitude 25' west. Pound's is taken
in accordance with his own statement to be in latitude 51*^ 34',
and longitude 8" west These agree pretty well with Flam-
stead's statements that Wanstead is seven or eight miles N. by
E. from Greenwich,* and that Crane Court is half a minute of
time West of Greenwich.

Halley at London.





Computed.


Obeerred.


c-o ,


h m


8


h


m


8


s


First contact,


20 2


35


20


2


37


— 2


Beginning of Totality,


21 6


52


21


5


39


+ 13


End of


21 9


3


21


9


2


4- 1


End of Eclipse,


22 16


55


22


16


37


+ 18



Pouna at Wanstead.








Eclipse first peroeived,
The total immersion,
The emersion,
The just end of the eclipse.


Gompated.


Observed.


0-0


h m B

20 3 18

21 6 38

21 9 48

22 17 42


h
20
21
21
22


m
3
6
9
17


8

15

6

26

10


B

+ 3
+ 32
+ 22
+ 32



The only information I have respecting Flamstead's observa-
tions is contained in a letter of his found in Baily s * Life and
Correspondence of Flamstead, p. 315, from which it appears that
his times differ only a few seconds from Halley's, instead of
differing by the half minute required by the difference of meri-
dians. An obvious slip of the pen, {later being written instead
of earlier) makes it douotful in which way the " few seconds "
are to be counted. It can, however, be fairly inferred from his
statement that his observations diverge fix)m the tabular times
as much or more than Pound's.

The discordance of the results of first and last contact may
be attributed to this cause : that with their imperfect telescopes
the observers did not begin to see the moon until several seconds
after the actual commencement of the eclipse, and lost sight of
it a few seconds before the actual end. Tne discordance m the
duration of totality indicates with a high probability that the
computed shadow path falls a few miles too far nortn. In tiiis
case the mean of the results for beginning and end of totality

* BaU/s Flamstead, p. 316, p. 328.



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of long period in the mean motion of the Moon,



191



will be about right, and we have for the excess of computed
times

Halley*8 observations, + 7*

Pound's, + 27

Flamstead's, + 80 zh

I infer from these results that the correction to Hansen's mean
loDffitude at the epoch 1716 is about +11'^

Comparing the corrections thus found for the epochs 1680 and
1 715, we find they are substantially those required to reduce
Hansen's mean longitude to Burckhardt'a 1 conclude, there-
fore, that no egregious systematic error has crept into the re-
searches by which Burckhardt sought to show that the epoch of
his tables was substantially correct during the latter half of the
seventeenth century, and that the difference between the mean
longitude of Hansen and Burckhardt during that period repre-
sents approximately, at least, errors of Hansen's mean longitude.

The observations of the moon made at the observatories of
Greenwich and Washington during the last ten years, indicate
a tabular deviation of a remarkable character. JFrom 1860 to
1862 we find the moon slowly running ahead of the tables,
until the latter required a correction of plus two seconds in lon-
gitude to make them agree with observation. But this correc-
tion, instead of continuing to increase as all analogy would
have led us to anticipate, suddenly began to diminisn, so that
since 1862 the moon seems to have Been falling behind the
tables at the rate of a second a year. This is shown by the fol-
lowing exhibit of the corrections to Hansen's mean longitude,
or right-ascension, deduced from the meridian observations of
the two observatories.





Correction given by






Tear.


Greenwich.


WMhington.


Mean.


Corr. mean.




//


//


ti


//


1860


+ 0-3


-1-3


00


+ 1-0


51


+ 1-6


+ 0-6


+ 1-3


+ 2-7


52


+ 0-9





+ 0-9


+ 2-4


56


+ 1-0





+ 1-0


+ 1-4


57


+ 1-5


- . -


+ 1-6


+ 1*4


68


i-20


+ 1-5


+ 1-8


+ 13


62


+ 2-4


+ 2-4


+ 2-4


+ 0-9


63


+ 2-2


+ 1-2


+ 1-7


+ 0-6


64


+ 01


-10


-0-4


-1-2


66


-11


-2-4


-1-7


-21


66


-2-2


-2-6


-2-4


-2-4


67


—3-9


-41


-4


-3-6


68


-4-4


-4-5


-4-5


-36


69





-66


-5-5


-4-3



The corrections here given as those of Greenwich are, previ-
ous to 1859, derived from the comparison found in the ween-



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192 S, Newcomh on the apparent inequalities

wich observations for 1859. From 1863 forward they are deriv-
ed from a paper by Mr. Dunkin in the Monthly Notices of the
Royal Astronomical Society for April, 1869. The work of
only the four principal observers is therefore included in the
comparison. The object of this comparison being not so much
to determine the absolute correction to the epoch of the tables
as to show the changes of this correction, it is better to reject
the results of the observers whose labors were discontinuous.
In the case of the Washington observations, such a selection
could not be made : the results given are therefore an indis-
criminate mean of alL The systematic personal differences are
however found to be very smalL

That these corrections are real will not, I conceive, be dispu-
ted. To suppose them due to errors of observation, would be
to suppose that six or eight long practiced observers divided
between the two hemispheres, all progressively changed their
habits of observing in the same way, and to nearly the same
amount, through a period of seven or eight years.

A portion oi the observed discordance may arise from a small
error in Hansen's value of the coefficient depending on the
ellipticity of the earth, which is more than a second greater
than the values derived by previous investigators, either from
theory or observation- T^he last column of the preceding table
shows what the correction would be if Hansen's coefficient were
l''*5 smaller than it is.

From all these comparisons it would appear that the problem
of the inequalities of long period in the moon's mean motion is
really no nearer such a solution as will agree with observation,
than when it was left by La Place. By a partially empirical
correction, Hansen has succeeded in securing a very good agree-
ment during the period 1760-1860, but, if the results of the
preceding examination are correct, this has been gained only by
sacrificing the agreement for the century previous to 1760, and
for the years following 1860. This failure to reconcile theory
with ol«ervation must arise from one of two sources. Either :

(1) The concluded theory does not correctiy represent the
mean motion of the moon. Or : —

(2) The rotation of the earth on its axis is subject to inequal-
ities of irregular chanocter and long period.

The first hypothesis admits of two explanationa We may
suppose either that the mean motion of the moon is subject to
change from some other cause than the gravitation of the
known bodies of the solar system, or that the effect of this grav-
itation is incorrectlj calculated, and that theory and observa-
tion will be reconciled by a correct calculation.

There are difficulties in the way of accepting either of these
explanations. In reference to the first it may be remarked that



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ofltmgpericd in the mean motion of the Moon. 198

anomalies of mean motion cannot be accounted for by a devia-
tion from the received law of gravitation inversely as the
square of the distance, because the anomalies produced by such
deviation would be regularly progressive, and' would be most
sensible in the secular motion of the moon^s perigee. The com-
parison of the theoretical and observed values oi this motion is,
perhaps, the severest test to which the Newtonian law has yet
been subjected. That the anomalies proceed from the attrac-
tion of unknown bodies passing througn the system seems ex-
tremely improbable, since, if they were distant, they would
affect the earth and planets more than the moon, while the clo-
ser passage of bodies coiild scarcely escape detection. Still,
this explanation does not admit of being mathematically dis-
proved. If we attribute the deviation to the impact of mete-
oric matter, we must suppose the moon to have encountered
such matter in quantities nearly incredible.

These three causes exhaust those on which we can base the
first explanation, unless we invalidate the third law of motion.
For, by that law, matter moves only by the influence of other
matter. Other matter can affect the motion of the moon only
by impact and gravitation. The gravitation of known bodies,
the gravitation of unknown bodies, and the impact of matter is
therefore an exhaustive enumeration.

We pass now to the second explanation of the first hypothe-
sis, namely, errors or omissions in the theoretical computation
of the effect of gravitation. The wide difference between the
conclusions of Hansen and Delaunay suggests the possibility
that there may be inequalities stUl overlooked. We nave how-
ever the assurance of Hansen that there are none, and we shall
find it extremely difficult to introduce any periodic terms what-
ever which will represent the observed deviation of the moon
from the tables during the past ten years, without discordance
during the century previous, when the agreement of Hansen's
tables with theory is believed to be quite close. It is however
hardly worth while to dwell upon this explanation until we
have a more rigorous theory of the inequalities of long period
produced by gravitation.

Considering that the reconciliation of theory and observa-
tion is not very probable, the second hypothesis may become
worthy of serious consideration. If we accept it we must ad-
mit that between the years I860 and 1862 the rotation of the
earth was so accelerated that our reckoning of time is already
eight or ten seconds ahead of what it would have been had the
day remained invariable. Such an acceleration could proceed
only from a change in the arrangement of the matter of the
earth. The possioility of this effect being produced by changes
in the quantity of ice accumulated around the poles nas, I be-



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194 S, Kewcomb on the apparent inequalities^ etc

lieve, been pointed out by geologista But the eflfect of this
cause could scarcely be sensible But, if we admit that the
interior of the earth is a fluid, and also admit that general
changes in the arrangement of this fluid are possible, we have
all that is necessary to account for considerable changes in the
rotation of the outer crust That this fluid, admitting its ex*
istence^ is not in a state of entire quiescence is rendered proba-
ble by the phenomena of volcanoes and earthquakes. If we
suppose a large mass of it to move from the equatorial r^ons
to a position nearer the axis, a mass from the latter position
taking its place, the following effects will follow : —

1. A diminution in the angular velocity of the sxu&ce of
the fluid, accompanied by a corresponding increase in the velo-
city of the axial portion. The velocity of the outer crust will
then be gradually retarded by friction.

2. The gradual transmission of the increased rotation of the
central mass to the surfiswje by friction and viscosity. The
motion of the crust will then be gradually accelerated. The
velocity of rotation finally attained will be greater or less than
the original velocity, according as the radius of gyration of the
fluid mass is diminished or mcreased by the change in the
arrangement of the fluid.

I conclude, from this discussion, that we have reason to sus-
pect that the motion of rotation of the crust of the earth is
subject to inequalities of an irregular character, which, in the
present state of science, can be detected only by observations of
the moon. This suspicion can be neither contoned nor remov-
ed until we have more positive knowledge than we now have of
the possible inequalities which may be produced in the mean
motion of the moon bv the action of ^vitation.

The operation of calculating these meaualities, though com-
plicated and difficult, is certainly within tne powers of analysis,
when it is completely and thoroughly done, we may ascertain
whether the result can be made to represent observationa If
so, well ; the length of the day is not variable, and the future
positions of the moon can be safely predicted. If not, it wiU
follow either that the motion of the moon is affected by other
causes than the gravitation of the known bodies of the solar
system, or the day is irregularly variable.

By the end of the present century, if not sooner, we shall
have an independent test of the latter hypothesis, in the agree-
ment of the observed and theoretical times of the transits of
Mercury and Venus. K the hypoth^is is a true one, the irreg-
ularities may ran^e over half a minute of time in the course of
a century, and this quantity m^ht be detected even by merid-
ian observations of the planets in question.



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A. J£ Mayer — Besearches in Mectro-Magn^iam. 195



Art. XX. — Besearches in Electro-Magnetism; by Alfbed M.
Mayer, PLD.

The refined experiments of Weber, Tjudall and Knoblauch
having ftiUy established the fact of the reversed polarity of a
bar of bismuth, when subjected to the magnetizing influence
of a helix, the attention of natural philosophers is naturally
directed to the necessity of subjecting Ampere's theory of mag-
netism to as severe deauctive tests as can be applied. Thus,
from new experiments and lines of research suggested by theo-
retic deduction, we may hope for such addition to our know-
ledge as will evolve a theory which wiQ embrace both magnetic
and diamagnetic phenomena, as completely as Amp^'s oeau-
tiful gCDcralization contains the explanation of the magnetiza-
tion of iron.

Among^ other experiments, thus suggested, was the follow-
ing : Ascertain the relative forces of two electro-magnetic cores ;
one composed of insulated wires, the other of the same number
of similar wires uninsulatod.

Theory indicates that the insulated bundle will be found the
weaker ; for, in this case, we have not only the reaction of the
molecular currents, but also, the reaction of the infinitelv larger
currents flowing around each insulated wire. Also, admitting
the truth of the moleciilar hypothesis, we have in the uninsu-
lated wire-core the interaction of exceedingly small currents
separated by distances, great when compared to their size ; while
in the insulated wire-core we have, in addition, very large cur-
rents reacting at distances very small when compared to their
diameters.

It was the attempt to solve this problem which led to the
invention of the experimental method described in this paper ;
for, it will appear nirther on, that it could not have been at-
tacked by methods heretofore used. The satisfactory solution
of this question and the ascertained delicacy and precision of
the apparatus encouraged me to make other determinations,
which 1 here present ; not as a finished and neatly rounded piece
of work, but as showing what may be expected from a more
complete discussion of the method used, and from that perfect
experimental control of the apparatus which a more extended
experience will give.

In my first experiments I adopted the plan of Miiller (Pog-
gendorff *s Annaien, Bd. LXXix and Lxxxii) and tried the forces
of the different cores, magnetized in one and the same helix,
by their action on a distant magnetic needle ; keeping the cur-
rent, as far as possible, of the same intensity during the two
comparison& This method I found could not serve the purpose
of measuring forces differing but slightly in intensity ; and the



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196 A. M, Mayer — Researches in Mectro-Magnetism,

impossibility of obtaining a current so constant as not to pro-
duce continual motion and vibration of the needle caused me to
devise the following method, which I have found from expe-
rience to be both sensitive and precise.

Apparatus for the comparative measures of electro-magnetic forces.
— On a table 10 ft. long was drawn a center line and divided into
fractions of an inch. This line was then accurately placed at
right angles to the magnetic meridian. Two helices, which I
designate as E and W, were placed 8 ft. apart with their axes in
the same vertical plane as the above lina A surveyor's com-
pass, with a sensitive needle 6*85 in. long was so arranged that
the point of suspension of the needle could be moved between
the helices in the line of their axes. The same battery current
passed through both helices, and in such direction that the N.
pole of each was facing the needle ; by reversing the current,
the S. poles could be opposed to each other.

Both helices were composed of 10 layers of 1 inch " extra cov-
ered" copper wire, wrapped on copper spools of 8f inches long,
1*82 inches diam., and having flanges at the ends 1*25 inches
high. These spools, with their flanges, were split in the direc-
tion of their length by an opening of j\ incL Each layer of
coils was saturated with a thick solution of shellac in alcohol and
covered with thick paper, coated with shellac, before the suc-
ceeding layer was wrapped.

Helix !K contains 557 '5 feet of wire in 696 turns, and on ac-
count of its better insiilation and neater number of turns is
superior in strength to helix W. Helix W contains 551 feet
of wire in 688 turns.

1.




.a:^




The accompanying diagram shows the arrangement of the
apparatus. Helix E to the east ol the compass ; helix W to the



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A. M, Mayer — Besearchea in MecirchMagnetism, 197

west ; at C the compass ; and at G the tangent galvanometer
sufficiently removed irom E and W, not to be afiected by the
magnetized cores. The Bunsen battery is shown at B.

Each end of the compass needle is thus subjected to the
powerful action of two opposing forces and a magnetic couple is
thus formed whose equilibrium, shown by the needle, is readily
disturbed by a change in the relative forces of the cores or by
a change in the distance of the needle relatively to the two
helicea

It was found that when the needle was placed at such a posi-



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