i^^
a^
^■??fe,
IMAGE EVALUATION
TEST TARGET (MT-3)
■/
-'%
X
?l^./4!;fiM
■|S,fi,
1.0
1125 i 1.4
■ 2.0
Mil
■ 1.6
6"
^Sciences
Corporadon
23 WIST MAM STMIT
WnSTlLN.Y. M5M
(71«)t7a-4S03
r<\^
\
^v
V>
^
v\
CrHM/ICMH
Microfiche
Series.
CiHIVI/ICIVIH
Collection de
microfiches.
CaiMdIan Imtltuw for HInorlul Mleroraprixluetlora / ImUtut cnwdim d* nUcrorapRMluotloiM MMoriqiiM
a&s«s«iiSsi<»««fc.-9 < A#!««i«^'. ^-<-"- -**#^^. 0-.W..—
*■
Technical and Bibliographic Notes/Notes techniques et bibiiographiques
The institute has attempted to obtain the best
original copy available for filming. Features of this
copy which may be bibliographlcally unique,
which may alter any of the images in the
reproduction, or which may significantly change
the usual method of filming, are checiced below.
D
D
D
D
Coloured covers/
Couverture de couieur
I I Covers damaged/
Couverture endommagie
Covers restored and/or laminated/
Couverture restaurAe et/ou pelliculAe
Cover title missing/
Le titre de couverture manque
□ Coloured maps/
Cartes g^ographiques en couieur
□ Coloured ink (i.e. other than blue or blacit)/
Encre de couieur (i.e. autre que bleue ou noire)
I I Coloured plates and/or illustrations/
D
Planches et/ou illustrations en couieur
Bound with other material/
RellA avec d'autres documents
Tight binding may cause shadows or distortion
along interior margin/
La reliure serr^e peut causer de I'ombre ou de la
distortion le long de la marge intirieure
Blank leaves added during restoration may
appear within the text. Whenever possible, these
have been omitted from filming/
II se peut que certaines pages blanches ajoutAes
lors d'une restauration apparaissent dans le texte,
mais, iorsque cela Atait possible, ces pages n'ont
pas AtA filmAes.
Additional comments:/
Commentaires supplAmentaires:
L'Institut a microf llmA le meilleur exemplaire
qu'il lul M AtA possible de se procurer. Les details
de cet exemplaire qui sont peut-Atre uniques du
point de vue bibliographique, qui peuvent modifier
une image reproduite, ou qui peuvent exiger une
modification dans la mAthode normale de filmage
sont Indiqute ci-dessous.
□ Coloured pages/
Pages de couieur
□ Pages damaged/
Pages endommagtes
□ Pages restored and/or laminated/
Pages restaurtes et/ou pe.'MculAes
I — I Pages discoloured, stained or foxed/
D
Pages dAcolortes, tachetAes ou piqutes
Pages detached/
Pages d6tach6es
Showthroughy
Transparence
Quality of prir
Quality inigale de I'impressior
Includes supplementary materii
Comprend du materiel suppKmentaire
Only edition available/
Seuie Edition disponible
r~~1 Pages detached/
Jr~l Showthrough/
I I Quality of print varies/
I I Includes supplementary material/
r~~| Only edition available/
Pages wholly or partially obscured by errata
slips, tissues, 9tc., have been refiimed to
ensure the best possible Image/
Les pages totalement ou partiellement
obscurcies par un feuillet d'errata, une pelure,
etc., ont 6t6 fllmtes A nouveau de fapon A
obtenir la meilleure image possible.
This item is filmed at the reduction ratio checked tMlow/
Ce document est fiim6 au taux de reduction indiquA ci-dessous.
10X 14X 18X 22X
26X
X
12X
16X
20X
24X
Itol
'e
6tails
m du
raodifiar
tr una
llmaga
B8
arrata
I to
i
I palura,
on A
n
32X
Tha copy fiimad hara has baan raproducad thanks
to tha ganarosity of:
_,. Library of Congrass
Photoduplication Sarvica
Tha imagas appaaring hara 9f tha bast quality
possibia considaring tha condition and iagibility
of tha original copy and in kaaping with the
filming contract spacification^.
Original copias in printad papar covars ara fiimad
baginning with tha front covar and anding on
tha last paga with a printad or illustratad impras*
sion, or tha back covar whan appropriata. All
othar original copias ara fiimad baginning on tha
first paga with a printad or illustratad impras-
sion, and anding on tha last paga with a printad
or illustratad imprassion.
Tha last racordad frama on aach microficha
shall contain tha symbol — »> (moaning "CON-
TINUED"), or tha symbol V (moaning "END"),
whichavar applias.
Maps, platas, charts, ate. may ba fiimad at
diffarant raduction ratios. Thosa too larga to ba
antiraly includad in ona axposura ara fiimad
baginning in tha uppar laft hand cornar. laft to
right and top to bottom, as many framaa as
raquirad. Tha following diagrams lllustrata tha
mathod:
t
(
a
3
L'axamplaira fllmA f ut raproduit grica A la
gAnArositA da:
Library of Congrass
Ph^tpduplication Sarvica
•*»*<?•/_
-;i#
Las imagas suivantas ont *t4 raproduitas avac la
plus grand soin, compta tanu da la condition at
da la nattat* da l'axamplaira filmA, at an
conformity avac las conditions du contrat da
fiimaga.
Laa axamplalras originaux dont la couvartura an
papiar ast ImprimAa sont filmte 9n commandant
par la pramiar plat at an tarminant soit par la
darnlAra paga qui comporta una amprainta
d'imprassion ou d'illustration. soit par la sacond
plat, salon la cas. Tous las autras axamplalras
originaux sont filmte an commanqant par la
pramiAra paga qui compoiita una amprainta
d'imprassion ou d'illustra*ion at an tarminant par
la darnlAra paga qui comporta una talia
amprainta.
Un das symbolas suhrants apparattra sur la
darnlAra Imaga da chaqua microficha, salon la
cas: la symbols — »> signifia "A 8UIVRE", la
symbols V signifia "FIN".
Las cartas, planchaa, tablaaux, ate, pauvant Atra
fllmte A das taux da rAductlon diff Arants.
Lorsqua la documant ast trop grand pour Atra
raproduit mn un saul cllchA, 11 ast filmA A partir
da I'angla supArlaur gaucha, da gaucha A drolta.
at da haut an bas. an pranant la nombra
d'imagas nAcassalra. Las diagrammas suivants
lllustrant la mAthoda.
t
2
3
4
5
6
— -«fr'"
^^w
t ?■
i I
•^ i
iJ
^
■■ I III III
*i^
mpa
A.PPE3Sri>IX I.
■ «0l^'
DESCRIPTION
or THR
TRANSIT CIRCLE
or THB
UNITED STATES' NAVAL OBSERVATORY,
■w
i
WITH AM
/
INVESTIGATION OF ITS CONSTANTS,
PBnpARn> BT emtmB, or
Rear Admiral CHARLES HENRY DAVIS, U. 8. N.
■ VPRItlHTBiriDXVT,
BY SIMON>^NKWOOMB.
noriMOBiwiun^uiiet, «. «. h.
/'WASHINGTON:
OOVEBNMENT PRINTING OFFICE.
1867.
^1
■I
'
■^ t
mmiimmmi''^mmmmmmmmm'''mmmmmm^ii''
^'^mmm
•%
TABLE OF CONTENTS.
^••«^»«hm of lfc« iaitrauMBt and Ht a^aaste
OtMty ncOod of iannal%irtl«g Ot «nran or » 1V«Mtt Canh .... ..
&m"%MiM «r tiM eoiMlMti of tin IVHub <%«d« ud ita t^fridiHy
IWtiftrMhwpNrfUawran ,
PeifonauMorthtiaitranaat
A^MbitiMltedM. ...,. '
1
9
ai
41
•46
40
H
, 'f
ii
""ww i i i lii n iiiii i i iiii i iiti M
-mm iwWiafiiiii^iiia-ii, ..:^,^.
'""T*?"ffTi1 i rT i iiHfrVY''- i '^ f-f' "■ i r'- nrnt i ftf- r U i b fa
■Plp^nnRiH
INTBODDCTORY NOTE.
The imtrament denribed in the following pages wm proonred for the ObMrvatory by the
late Oaptaio CKUIm. On hie aeoewon to the Saperintendency, the want of a snttable Meridian
Circle was atrongly felt. The military operations of the government temporarily delayed the
supply of this want In October, 1868, however, the necessary authority was grant#.d by the
Hon. Secretary of the Navy, and the instrament was ordered from Messrs. Pistor and Martins,
of Berlin. Correspondence respecting the sine and pbu of the instrument occupied the remain'
der of the yew, and terminated by concluding on an object glass of at least eight Paris inches
dear aperture, and by leaving the plan of the instrument and its mountings altogether in the
bands of the artiste.
The pa^s of the instrument arrived in October, 1866. The work of mounting was com-
menced on the 16th of that month, and on the 28th the instrument was in position. The next
two months were occupied in determining the errors of flexure and division, and in making the
necessary preparations for active work. Begnfor astronomical observations were commenced
on January 8, 1866.
1
m
\
,.:i
%
i
1 I
■\
ii
■ \
iMaMiMMIIMNiiliMI
APPENDIX I.
DESCRIPTION
or TBI
TRANSIT CIRCLE
OrTBC
UNITED STATES NAVAL OBSERVATORY.
1
i
PAST I.
DB80BIPTI0N OP THE INSTRUMENT AND ITS ADJUNCTS.
OENBBAL DESCBIPTION. (PLATE m.)
(1) The instrnmeDt is moanted in the west wing of the Observatory, the room formerly
occapied by the Transit Instrument The interior dimensions of the room are 24.3 feet from
east to west, and 18.4 feet from north to south. On the north and south sides of the room are
built two recesses, each six feet in length, and six in depth, to make room for the collimators.
The slits in the wall and roof for observing are thii'ty inches in breadth, and closed by four
shutters on the roof, and a door on each side.
(2) The piers are solid monoliths of marble. The forur of each pier is that of a frustrnm of
a pyramid, surmounted by a prism. The base at the floor me.>'iures 44 inches from north to south,
and 38 inches from east to west. The top of the pyramidal portion is 80 inches above the floor,
and measures 18.6 inches from north to south, by 24.6 from east to west. The dimensions of the
■lal iiBg horizontal sections of the prism are the same, while the heighv of the prisms is 28 inches;
the whole height of the piers 9 feet above the floor. The inside faces of the piers form a ver*
tical continuous plane 19 inches in breadth, and 9 feet in height. On each side of this plane
the stone is cut away in the form of a section of a hollow cylinder. The distance of the inside
faces is 64 inches. A cylindrical hole 6 inches in diameter is cut from east to west through
each prism for the illumination.
Into these openings the inside ends of hollow brass cylinders are flrmly set with plaster to
the depth of 6 inches. The outside end of each cylinder expands into a disk 8| inches in diam*
eter and 0.7 of an inch from the face of the pier. The arms which cai:ry the four reading micro*
scopes of each circle are attached to these disks, radiating from the central axis at an angle of 46°
from the horizontal and vertical directions. Within each disk, near its centre, is a system of
prismatic reflectors for illuminating the divisions of the circle. The illuminating lamps are
each at the large end of a conical tube, the small end of which extends through the opening of
the pier and fits into the interior of the cylinder carrying the microscope disks. The large end,
carrying the lamp, extends three feet from the outer face of the pier. One lamp illuminates
the field of the telescope, the other the wires.
The Ys are fastened into semi-^cyliwlrioai pieces of brara which extend inward from the
head of the disk carrying the microscope arms, the axis of the cylinder being a continuation
of that of the openings in the pier, as shown in Plate lY.
2 DUBORTPnON OF THK TBAi.lIT OIBOUB OP TBI
(3) The telescope is of 12 feet focal length, and 8.6 inches dear apertare. The eye-piece
is furnished with a system of twenty*three fixed vertical wires, (eight of which it is intended to
remove,) and two borizonta' ones, distant 8". There is also a horizontal and a vertical microm*
eter screw, the former carrying one vertical, and the latter four horisontal wires — a central
pair, distant ^".f>, and two single ones, 2^' each side of this pair.
(4) The circles are each 42 inches in diameter, and divided on silvc to every S'. The
cylinder on the clamp-end of tne axis also has a coarser division to every 10' for setting. The
general character of the arrangement of circles, clamp, counterpoises, Ac, may be seen by ref*
erence to Plate IV.
Notwithstanding its dimensions, the instrument is reversible, and the operation of revers'
ing can be performed by a single person with great facility. The entire weight of the mov* •
able part of the instrument is only about 900 pounds.
(5) The sides of the central tube of the telescope are pierced by openings 2) inches in
diameter, through which the collimators may be set on each other when the instrument is ver-
tical. These are not shown in Plate III.
(6) The instrument is completely spanned from north to south by an arched flight of steps
for reflection observations of stars. They are so flgured that when the telescope is at any point-
ing between 120° and 240^ of zenith distance, the eye-piece will be in a convenient position to
look into. Above the fifth step the arch is bifurcated, so as not to interfere with the line of
sight. The highest step is a platform three feet in length, suspended from the roof by iron
bars and braces. Hand-rails, net shown in the plate, extend from the bars nearly to the floor.
(7) In the spring of 1867 another mechanical improvement, for convenience and certainty
in observing the nadir point, was introduced. On each side of the platform, over the axis of
the instrument, a seat is erected. The observer can sit astride of either seat and look into the
eye-piece when the telescope points to the nadir. On the inside of each seat, between the
observer and the telescope, a board, eight to nine inches wide, rises from the platform nearly to
the eye-piece. Bach of these boards is furnished with a pair of shutters of the same size, which
the observer can turn so that the tube of the telescope shall be completely enclosed in a wooden
hexagonal prism, or, more exactly, a frustmm of a pyramid, and thus protected from the heat
of the observer's body.
(8) The steps for reading the microscopes need no explanation except that a hand-rail
runs along the platform, by which the observer passes from one side of the pier to the other,
without descending to the floor.
DETAILED DESCRIFTIOM, WITH EXPLANATIONS OF THE PLATES.
(9) Plate I is a plan of the observing-room.
Plate II is a section of the walls and masonry below the floor in the plane of the meridian
of the instrument, with a view of the room as seen from the west
B is the entrance from the main building. It is dosed by two doors. The floor of the
room being thirty inches lower than that of the main building, a platform and flight of steps is
erected inside the door for convenience in entering the room.
(10) Below the floor all the masonry is of rough stone set in lime and sand mortar. The
base of the masonry rests upon the ground about six feet below the flooring joists.
L L are the collimator piers, the bases being of masonry, three feet square, and the upper
parts octagonal monoliths of marble.
S S are piers which support the turn-table, T, and the floor of the room under the in-
strument. ' '
B, plate n, shows the masonry which supports the circle itself. B is a prism of the ma-
sonry already described, eleven feet from east to west, four and a half from north to south, and
' 4MIHik4w«MMA<>*Wita
^m
milTID ITATia HAYAL OBSUTATOtT.
1
five io height. lU boricontal diroensioos are therefore only tuffioient to support the great piers
of the inatrnment. It is covered by a solid oap Q, Plate II, of hard bluok stone, of the same
horiaontal dimensioos, and about one foot m tbiokness.
On this cap rest the marble piers P, P'. Their bases are Ijollowed oat ho that they each
reet on three points, and thus remain secure without cement or other fastening. Their great
mass insures perfect steadiness without such aids. 0, 0, show how the inside corners of the
piers are cut away. The concaye faces 0, 0, 0,'0, are parts of the surfaces of four vertical cyl<
inders, the axes of which are in the plane of the inside face? of the piers, 23^ inches north and
south of the middle, and therefore 47 inches apart.
The perforation through each pier, at the end of the axis of the instrument, is shown at
0, Plate II.
(11) B, B, R, B, B, R, show the railroad on which the reversing carriage runs. Under
the instrument the rails rest upon two strong joists, supported by the piers S S. The turn-
table T revolves on six cannon balls. By it the reversing carriage, with the circle on it, may
be run into either the northeast or the northwest corner of the room. The turn •table is not
necessary in reversing, as the T's uf the reversing carriage themselves revolve on a pivot.
The whole floor is on the same levbl, except around the collimator piers, on three sides of which
a platform is built.
(12) Plate IV exhibits » i nd dlevation of the instrument from the south, with the hanging
level and so much of the reve-tiing carriage as is not concealed by the telescope. The ladders
are omitted.
Plate y is an isoa. ;'ic side elev> ion from the eaitt; the east pier with its appurtenances,
the step-ladders, and the hanf o^ level, all being removed.
(13) a is a movable rt' ji, 'or supporting a lump in observing the nadir poiut. b, b are the
counterpoises which lighten the weight of the instrument upon the pivots. The levers o, o
which support them have a siigbt movement around the pivots &, d. The hooks ,/*, / nave
friction rollers at the bottom for supportiut^ most of the weight of the instrument. At the top
they expand into a strong rectangular frame, throiu^h which the ond of the lever c paitsen, as
shown at o, Plate Y. Through the top of th«i frame passes the screw d^ the lower end of
which being rounded off, rests in a socket in the top of the lever, and thus supports the weight.
Small pieces of rubber have beeu placed in these sockets and under the supporting screws,
for reasons to be explained hereafter. When the instrument is raised from its pivots the
counterpoises are supported by the screws e, e, which are adjusted so as to allow a small play
to the levers.
(14) Jfoitn/tngr <tf the Microtoopea. — Enlarged views of the hollow cylinder D with its attach-
ments are shown in Plate YI. The portion P iaset into the pier with plaster; grooves are cat
through the flanges p, p, p to, let the plaster run through. I is the disk to whi<^h the microscope
arms are fastened. It expands in thickness toward its circumference. The portions J and k
of the microscope arms hold the disk firmly between them, being held together by means of
clamping screws, the heads of which are shown in Fig. 1. These screws pass through^' to k, just
outside the edge of the disk. To keep j in position when these screws are loosened, it is fitted
with pins which fit corresponding holes in k. By loosening the screws the microscope arms
can be moved independently around the disk, but will not come nearer to each other than
about 48°.
Outside of k, the microscope arms are loosely encased in mahogany shields I, to protect
them against rapid changes of temperature.
The outer ends of the arms are hollow, holeb about f-inch in diameter running into them,
to receive the holders which carry the microscope. They are encircled by the circular clamps
t, which are tightened by means of the screws h, partially shown in Fig. 2, but hidden by the
i
1
Kk Ji
^^m
DESCRIPTION OF THE TRANSIT CIRCLE OF THE
Tjr
t4M(
clatnpH in Fig, 1. When /♦ is tightened, the microscope is firmly held by the arm. By loosen-
ing it the microscope may be drawn out, and three views, as thus removed, are given in Plate
VII, Figs. 1, 2, 3, each of which is from a position at right angles to the other two.
(15) a (Plate VII) in the solid metallic support which passes into and is held by the micro*
scope arm, as already described. The holders b and the circular clamps c, enveloping the body
of the microscope, form a single piece with a. When the screws d are loosened, the microscope
can be moved longitudinally, and the end e carrying the object glass can be slid into or out of
the other portion, for adjusting the focus, and the angular value of a revolution of the microme-
ter. For the accurate adjustment, the independent clamp y is used. Loosening d and tighten-
ing y by means of the screw d, a fine motion is given the microscope by turning the screw c.
The head of this screw ic kept pressed against b by the spiral spring ^ pressing y and b apart.
(16) is a perforated reflector for throwing light on the divisions. Its reflecting surface
is not polished, but is of a bright white. It can be turned in any direction by the milled head/,
and can be moved longitudinally by loosening the clamp g.
k \b & cylinder of white felt, extending very nearly to the face of the circle, at the same
time keeping out stray light and assisting the illumination from o.
(17) The micrometer screws of the microscopes revolve with the head. Instead of being
attached to the moving frame of the diaphragm, they screw into the latter, and thus give it a
slow motion to or from the bead. Each revolution of the microscope micrometers is 30" in
angular measure on the circle, and about one hundredth of an inch in linear measure on the
screw ; 30" on the circle measuring about -jaT ''^^^i ^^^ image of the divisions is magnified
about 3.3 times in the focus of the microscopes. The face of the circle is about 1.9 inches
from the object glass and the micrometer wires about 8.3 inches.
Each microscope micrometer is set upon the image of the division by a pair of parallel
spider lines, distant from 10" to 11". Microscope YII is also supplied with two extra pair of
wires, about 2' on each side of the original pair, for the convenient measurement of consecutive
divisions.
The micrometer head is divided into thirty second -spaces, each of which is again sub-
divided by a shorter line to half seconds. The entire revolutions are read from the interior by
a serrated scale. The divided drum may be turned on the axis of the screw by simple pressure,
without turning either the screw or its bearing.
(18) Supports of the Pivots. — Referring again to Plate VI, the cylinder D is hollow to the
depth of about an inch, the external part in fact consisting of a rim about an inch thick. The
cylindrical space forming the interior of this rim contains the metallic plate e, Fig. 1, into which
screw the antagonistic screws 8, a, the beads of which press against the inside of the rim. The
top and bottom of this plate are bevelled toward the pivot, and the bevelled edges are held by
the plates b, b'. When the screws c, c are loosened the plate e can be moved from right to left
by the screws s, «, but when they («re tightened, e is firmly held between the plates 6, b'.
The view actually given is that of the west plate, by which the axis is adjusted in azimuth.
The east one is similar, except that the plates and screws are turned 90° for adjusting the level.
n is a thin perforated plate of metal which presses against the end of the pivot, to prevent
longitudinal motion of the axis. As now arranged for observation, the eastern one is firmly
screwed against the V plate, while the western one is pressed against the pivot b}' a spring
behind it.
The V's are carried in the rounded plate y, which forms one piece with the plate c. They
consist simply of small pieces of soft metal v v, (Fig. 4,) slightly convex on their upper surfaces,
so that only a single point of each pivot at first rests upon them. But a slight hollow is soon
worn into each of them by the pivot.
"h"^^
UNTTKO STATES RATAL OBSBBYATOBT.
J
(19) The Tdeacope and ita External Appendage*. — Betnrning to Plates lY and Y, and para*
ing from the Y'b, we first have the pivots, which are 2.1 inches in diameter, and 1.8 inch in
length, and are apparently of the same diameter throughout their length.
(20) Next to the pivots the axis expands into the frustrum of a coue, the diameters of the bases
of which are somewhere about three and a half and four and a half inches, respectively, and the
height about three inches. Back of this frustrum the axis again expands perpendicularly to ita
length. Over these frustrums the circles C, fit with great nicety; the central perforations in
the latter being tightly filled by the former when the circles are pressed against the expansion
at their bases. The thickness of the circle is slightly greater than the depth of the frustum,
so that the latter does not pass quite through the perforation. The circle is held in its place
by the friction of the plates p, p which are pressed against it by the screws a, a, a, a, «, (Plate Y)
passing through them and into the top of the frustrum, without touching the circle. When these
screws are loos^ened, the circle can be turned round so as to take any desired position relatively
to the telescope.
(21) The circles each appear to be cast in a single piece. The manner in which they are
stiffened can be seen by a comparison of Plates lY and Y. The middle of the plane face of
each circumference is inlaid with a band of silver on which the divisions are cut to every two
minutes. The breadth of each division as seen under the microscope seems to be between two
and three seconds, corresponding to a thickness of about 7^ of an inch.
The circle next to the clamp has also a coarse division to every ten minutes, for setting
the telescope.
(22) Next to the circles come, on one end of the axis, the clamp n, and on the other end
a ring to counterbalance it, into which screw four handles A, h for turning the telescope on its
axis. The clamp is tightened by means of the screw q, q, (Plate Y,) and a slow motion may
then be given the telescope by another screw, not shown in the figure.
(23) The friction rollers are received by grooves cut around the axis.
On the clamp end of the axis four curved handles A', V (Plate lY) are screwed into the cone
for turning the telescope.
Near the base of the cone flat bands are seen, by which the instrument is supported when
on the reversing carriage.
(24) The central cube is 16 inches square, and forms a single piece with the axis. Its sides
are perforated in a direction perpendicular to the telest-ope and the axis, by openings 2^ inches
in diameter, through which light can pass from one collimator to the other. They are closed
by covers which screw into them.
The tubes of the telesi ope are each fastened to the cube by sixteen screws, as shown in
Plate lY.
(25) The Eye-piece. — Three views of the eye-piece and its appendages are given in Plate
YIII. From Figures 2 and 3 it will be seen that there are six 8<)ries or strata of plates in the
eye-piece. The first or outside stratum, of which a face view can be seen in Fig. I, carries
the ocular a and the slide for giving it a horizontal movement by means of the rack work and
milled head b.
The second stratum consists of the slide and fixed guides for giving a vertical aiiovement
to the whole of the first plate, with its guides and slide, by the milled head c.
(26) The third stratnpa consists of the declination micrometer plate with its guides. A
portion of its outside surface is seen at of, d, d, d, Fig. 1 . e is a fixed index for reading the
approximate position of the plate in micrometer revolutions. / is an opening in the plate to
admit of the free passage of e. An opening about two inches square is cut in the middle of
■«
f^m
e
DB80BIPTI0N OF THE TBAN8IT OIBOLB OT THK
61
m
the plate, and across this opening on the posterior sarfaoe of the plate are stretched the hori*
zontal spider Hues for zenith distance observations with the micrometer. From Fig. 3 it will
be seen that the micrometer plate d carries the falcram of the milled head o by which the
ocular is moved vertically. Consequently, when the micrometer is moved, the ocalar is carried
with it, and the movable spider lines are thus kept in the middle of the field without touching c.
(27) The fourth plate is moved in right adcension by the micrometer head B. It has a
rectangular opening like Plate III, and across this opening, on the anterior surface of the plate,
is stretched a single vertical spider line.
(28) The fifth plate carries the fixed spider lines. These are stretched across the anterior
surface of a thin annnlns about 1^ inch in diameter, which projects from the surface of the fifth
plate by an amount equi ! to the thickness of the fourth plate, passing through the rectangular
perforation in the latter. Thus, the three sets of spider lines are sensibly in the same plane.
The entire plate can be moved horizontally by the three antagonistic screws g hg, to adjust
the line of collimation. The plate is fastened to the piece through which the screws pass by
the projection t.
The sixth plate forms the basis for all the rest, and is pierced for the holes in which the
micrometer screws turn. It is fastened to the eye-tube E by a cylinder which slides tightly
into E, and is fastened by the six screws k.
,. (29) The Uterometer Movements. — In all the micrometers of this instrument the screws
revolve with the heads. In the microscope micrometers the bearings of the heads are fixed,
and the screws passing into the movable plates draw them toward the micrometer heads as the
screws turn forward. But in the eye-piece the female screws are bored into the sixth plate, and
the bearings of the heads move with the micrometer plate. The projection d of the senith dis-
tance micrometer plate is attached to a cross n, n, n,(Fig. 3) through a circularr^be opening in the
centre of which the micrometer screw passes freely, and on which it presses. Thus, as the screw
turns forward, the screw, the micrometer head, n, and d are all slowly moved downward. Tho
middle n is the index from which the fractions of a revolution are read, but they can equally
be read from the front index, a is one of two spiral springs by which the cross is kept pressed
against the micrometer head, and made to follow it as it is withdrawn.
(30) Rogers^ Sdf-regiMlering Micrometer Head. — ^The zenith distance micrometer head is
famished with the self-register invented by Mr. Joseph A. Bogers, and described in the Astro-
nomische Nachrichten, No. 1493. The four arms o, o', o", o"' (Fig. 1) are movable around the
same centre with the micrometer, which passes through openings in the middle of them. They
are held to the micrometer by the friction of elastic bent plates which surround the centre.
Tims, when free, they move with the micrometer head; but when held, the head moves past
them. One end of each terminates exactly with the radius of the micrometer head, and serves
R8 an index, as may be seen in Fig. 3. The other end projects a little beyond the cylindrical
surface of the head, and may be held by notches in the levers 1 1, (Fig. 2.) When thus held,
the index ends are in the same vertical line with the principal fixed index, as shown in Fig. 3.
The mode of operation is as follows : The micrometer being in any position which it is
desired to register, one of the levers (Figs. 1 and 2) is moved back with the finger to the
position l\ and the movable index is thus set free. It now moves round with the micrometer,
and thus points continually at the reading indicated when it was set free. Four successive
readings may thus be registered in succession without taking the eye from the telescope.
The object of the two extra divided cylinders on the micrometer head is simply to facilitate
the reading of the four movable indexes.
UinrBO STATES HATAL 0B8BBVAT0BT.
(31) The Oculara. — The instnimeDt n ftimished with five oonlan, of which the in«gnifyiDg
powers are, approximately —
No. 1.
ISO;
8,
160;
3.
180;
4.
260;
6,
360.
No. 3 18 that hitherto most used in aslronomioal observations.
(32) The Retiotde. — ^The fixed vertical spider lines are twenty-three in number, arranged
as in Fig. 4. Seven of these are at eqnal intervals of 12^ seconds of time, and are designated
by the Roman nnmerals I-VII. For convenience, a second notation is adopted, as shown at
the bottom of the figare, the wires being divided into five groups A to E, and the wires of
each group designated by subscript Arabic numerals. Thus the wires II, III, IV, T, and YI
are designated indiflferently by these numbers or by the symbols A„ B|, G,, D„ Ep The wires
of set G are 24. apart ; those of B and D It, 5 and 2«.6 respectively. Sets A and E are rarely
used. Stars are usually observed in right ascension ^ver B D and the three middle wires of 0.
In observations of planets one limb is observed ove. B and D, the other over C.
The middle of the field is shown by a single pair of fixed horizontal wires about 8" apart.
A single vertical wire is moved by the horizontal micrometer.
(33) The horizontal movable wires consist of a single pair 4".6 apart, between which objects
are usually observed, and a couple of single wires at a distance of ten micrometer revolutions
on each side of the central pair. The former were inserted by the machinist of the observatory
after the mounting of the instrument, in lien of a single wire inserted by the makers.
(34) The IttumincUion. — The flames of the two lamps L, L, Plate lY, are nearly surrounded,
by parabolic reflectors. The light passes through the supporting tube and the pier into the cyl-
inder D; here it meets a combination of lenses and prisms, shown in Plate YII, Figs. 4 and 6.
Fig. 4 gives an end view of the combination, as seen from the lamp. Fig. 5 gives a side view.
The nearly cylindrical frustum of a cone G is pierced in the direction of its axis by five holes,
a, b, b, b, b. The light which enters a passes through two lenses, and through the perforations
in the pivots of the instrument to the centre of the axis. That which passes through the b'a
meets four prisms, p, p, from the interior surfaces of which it is refiected at an angle of about
42^°, BO as to be deflected in all about 85°. G and D fit snugly in a perforation in the centre
of the cylinder D, Plate lY; a hole receives the pin e, and thus fixes the position of the appa*.
ratus. The latter can be removed by unscrewing the lamp-tubes T, and reaching the arm
through the pier. When in place, its position is such that the light reflected from the prisms p
passes down the pipes k, (Plate lY,) and into the reflectors of the microscopes, by which it is
thrown upon the divided limb.
(35) The central ray, passing {ihrough a, if it enters the clamp end of the axis, is conducted
to four prisms in the central tube of the axis, from which it is reflected down the side of the
tube to four more prisms in the eye-piece, and thence to the wires, in the usual way. Thus
the wires may be iUuminate<lf. or darkened by turning a milled head on the clamp side of the
eye- piece.
(36) The light which enters the other end of the axis is reflected from a prism about 4^
inches from the centre of the axis, directly to the eye-piece. It shows the dark wires on the
bright field. It may be changed in color from yellow to blue, or cut off entirely by turning a
milled head on the side of the tye-piece opposite the clamp.
(37) The CoRimaiora. — Fig. 6, Plate YII, gives a general view of each collimator. The
object glasses have each 2| inches clear aperture, and 35 inches focal length. The eye-piece
8
DBSORIPnON OF THB TBAN8XT OIBOLB OF THX D. 8. NAVAL 0B8BBVAT0BT.
of one, which is designated collimator A, is fornished with a pur of parallel wires, ditit»nt
about 9", with a single wire crossing them at right angles. The wires of the other, called col-
limator 3, form a simple cross. When it is required to .set the collimators opposite each other,
the coincidence is that of a single wire of B with the mean of the parallel wires of A.
The steel plate which carries the wires is held between four antagonistic screws, but has
no binding screws.
The supporting collars of the collimators are only 23 inches apart, so that each end of the
collimators projects about six inches from its support.
Each collimator is furnished with a delicate spirit level, which sets on the supporting collars.
(38) The Ts of the collimators, with the way in which they are fastened to the piers, is
shown in Figs. 7 und 8. The hemispherical bottoms of the screws a, a, a, rest in three cavities
in a Y-shaped block of metal, which is set into the pier with plaster. The outline of the block
is shown by the dotted lines. The three screws 6, b, b, pass centrally through a, a, and thus
bind the Y-plate firmly to the block. The level of either pivot is adjusted by loosening 6, and
turning a to the required extent. The azimuth is adjusted by the antagonistic screws c, e.
When the V is in position it is bound by the screws d, d, e, e.
m
PAKT II.
GENERAL METHOD OP INVESTIQATINQ THE ERRORS OP A TRANSIT CIRCLE.
(89) The most important and •'iffioult part of this investigation is the determination of the
effect of gravity in changing the relative positions of the various parts of the instrnment, and
the correction of observations for this effect. It is therefore proposed to develop a general
method of determining, either rigorously, or with a near approach to rigor, the effect of gravity
in changing results of the various observations by which the position of a star is determined.
The necessity for a flexure correction may be regarded as an imperfection in an instru-
ment, since, if it were well balanced, and equally elastic in all its parts, no such correction
would ever be necessary. Artists generally attempt to avoid this imperfection by distributing
the weight of the instrument so that it shall be perfectly symmetrical with respect to the centre.
Thus, in the Washington Transit Circle, the two circles are of equal weight; the clamp is coun-
terpoised by a cylinder at an equal distance on the other end of the axis; and the tubes of the
telescope had their outer and inner surfaces turned simultaneously, in order to secure perfect
equality of thickness in every rectangular section of the tube. Yet, the effect of irregular
flexure cannot, by any means, he neglected, and that of the two circles exhibits a very sensible
difference. A similar remark will probably apply to every large instrument ever made. It
will not, therefore, do to assume that such an instrument is equally elastic in any of its corre-
sponding parte, however unexceptionable may be its construction.
(40) The only arbitrary hypothesis we shall assume respecting any law of elatitioity in the
instrument is, that the relative flexure of the various parts is the same as if the instrument,
during a revolution on its axis, were always supported by the same particles of its mass.
The nature and the results of this hypothesis will be rendered more clear if we suppose the
instrument to remain at rest, and gravity, with the forces which oppose it, to act in various
directions. The parts of the instrument which sustain these opposing forces are mainly those
which press on the friction rollers of the counterpoises. Reflecting, now, that the direction of
these forces always passes within two or three inches of the centre of the axis, and that our
hypothesis can be incorrect only by a combination of the two following circumstances, viz:
l' An unequal elasticity in the parts of the conical axis on which the friction rollers succes-
sively press; 2. Such a relation of elasticities in other parts of the instrument that the unequal
elasticity of this narro<v band on the conical axis causes the instrument to change its form ac-
cording to a different law from that which would hold true if the elasticity of the band were
uniform — ^it would seam that the hypothesis must be a safe one.
Experiment shows that the effect on elastic bodies of forces which are very small in pro-
portion to the rupturing force is strictly subject to the law of superposition of small motions;
that is, that the combined effect of several such forces is the sum of the effects that each would
produce acting separately.
^■-mmmmmmm
10
DESOHIPnON OF THE TBTMSIT OIBOLB OF THK
(41) Still snpposing the inatrament fixed, and the direction of gravity variable, let b rep-
resent the amonnt by which a point of the inBtrument is moved from its normal position in the
direction of an arbitrary fixed axis when gravity acts in the direction of that axis, and let a rep-
resent the displacement in the same direction when gravity acts at an angle of 90° with the
axis. If gravity acts at an angle W with the axis, it may be resolved into the forces g cos W
and g sin W, acting along and perpendicularly to the axis. The first component will, by the law
just referred to, produce the displacement 6 cos W, and the second the displacement a sin W,
and the whole effect of gravity will be a sin W-|-6 cos W.
Suppose, then, any system of rectangular co-ordinates fixed in the instrument, and revolv-
ing with it; then, as the instrument revolves, the law of displacement of any point in the di-
rection of the movable co-ordinates will be given by the equations
dx=a sinW+b cosW,
iy=a' Bin W-\-f/ cob W,
*««sa" Bin W+i" COB W.
W being the angle of position of the instrument, and a, a', a", b, 6,' 6," constants, to be
determined by observation.
(4*2) The method of determining such of these constants as are necessary in the correction
of afltronomical observations will next be shown. To admit of the application of this method it
is necessary that the instrument ahculd be supplied with a pair of collimators, each of which
admits of being accurately levelled, in order that it may be used to determine the horizontal
point, and an artificial horizon for observing the nadir point by reflection from mercury. A
vertical collimator, to be fixed over the centre of the instrument, and set vertical ither by re-
flection of its wires from the mercury bath, or by levelling its axis, would also be valuable as
an independent check on some of thd results.
(43) Let us now consider the causes which will affect the reading of any microscope. If
the divisions are truly cut in direction — that is, if each stroke is sensibly in the same plane with
the axis of the circle, the error of each point in any one division may be regarded as the same.
We shall therefore regard the diviftions as a series of points. When a microscope is read, the
position of the point under the microscope is determined by bringing a micrometer wire into
coincidence with the image of the point in. the microscope. This micrometer wire in the Ger-
man instruments is an imaginary one bisecting the space between two real ones. The division
point is then in the plane which passes through this micrometer wire and the optical centre of
the object glass of the microscope. Let us consider, as the zero of the micrometer its position
when the plane passing through the object glass and the micrometer wire is at right angles to
the face of the circle. The micrometer reading of the division will then be proportional to the
ttingent of the angle which the plane containing the division makes with this last plane. No
appreciable error will result from supposing this adjustment to be perfect.
The subsequent investigation will be precisely the same if we suppose the divisions to
radiate from the centre of the circle, and the micrometer wires in the microscope to be a point,
which is brought into coincidence with the image of the division. The micrometer reading
will then represent the tangent of the angle which the plane, passing through the centre of the
object glass and the division, makes with that passing through the centre of the object glass
and the axis of the circle.
If the eight microscopes were correctly adjusted in position, and the circles perfect in form
and position, and not acted on by gravity, the instrument might be so set that all the micro-
scopes should read zero at the same time. The following include all possible deviations of the
circles and the microscopes from this state.
URITET) K'AnS NATAL OBURTATORT.
11
a. Errora in the Angtihr PoMiont of tht MRoro9Cope$. — When all the microscope micrometers
are set at zero, the planes passing through the micrometer wires and the centre of the object
glasses onght to cut the line of divisions at points making angles with the centre of the axis
equal to the nominal distance of the microscopes.
p. Error$ m the Oeneral PoaUixmt^ the Cirtlte.—The»9 will be six in number: small motions
of translation in the direotion of three co-ordinate axes, and small motions of rotation around
those axes. *
f. Enron in the Position </ the Divieion on the Oirde. — ^These may be three in number. I.
Errors in the angular position of the division. 2. Deviation of the surface on which the divis*
ions are cut from a plane cutting the axis of revolution of the instrument at ri|{ht angles. 3.
Change in the position of the division produced by the effect of gravity on the circle.
The position of a division may be in error by any of the nine causes, ]9 and y. To deter-
mine their effect, let us refer the position of the division to three co-ordinate axes, those of X
and T being in the plane of the circle, and that of Z being the axis of revolution. Let A be
the angle which the plane of the micrometer wire and object glass makes with the axis of the
circle, B the angle of position of the microscope, counted from the axis of X.
B, the radius of the circle.
c, the distance of the centre of the object glass from the plane of the circle.
r, the reading of a microscope from its own zero.
p, the mean reading of a pair of opposite microscopes.
m, the error of position of a microscope.
M, the mean error of a pair of opposite microscopes.
e, the error of division.
t, the mean error of a pair of opposite divisions, or an error in iue position of a diameter.
a, b, the flexure coefficients of any point of the circle.
a, /9, half the difference of a or b for two opposite points of the circle.
£, 17, the possible motions of translation of the centre of the circle relatively to X and Y.
at, the error of pointing of the telescope.
The differential coefficient of tan A, (which is proportional to r) with respect to the co-
ordinates of the division, will then be:
<2.tanA B.ir
dm °*c<te
SinB
<2.UnA Bir
cosB
c '
<itanA Edr
dz cdy
tanA
e
The effect of small changes dx iy and dz on the reading of a microscope will therefore be
dr=:--8inB^-fco«B^+tanA^. (1)
Changes in the co-ordinate z can arise only from a motion of translation of the instrument
in the direction of its axis; from motions of rotation around the axis of X or of Y, in consequence
of irregularity of pivots; from deviation of the circle from a plane cutting the axis at right
angles ; or from lateral flexure of the circle. If the effect of any of these causes is appreciable,
9z must be determined by direct measurement, independently of the readings of the micro-
mmsmsssmsmsm
12
DEBORIPnOM or THB TBAMBIT OIBOLI OF THB
%
«;
Bcopes, and the latter mast be oorreotfid accordingly. To jadge when d» can be senBible, we
remark that in general
tanAi
Bf->-+eonitaiiti
the constant being the valne of tan A when the micrometer reads aero, and therefore depend-
ing on the parallelism of the microscope to the axis of the circle. If the changes in r do not
R
exceed 10" and - does not exceed 12, A will not differ more than 1' from ito mean valne in a
aeries of readings. Since, by proper adjustment, this mean valne may be made ver> small,
there is no necessity that A should ever exceed 1' in a aeries of measures. In this case, s will
have to change by -y^ the radius of the circle to produce a change of 0". 1 in r. This change
being ten times as great as any that a well made instrument need be liable to, the last term in
ir may be regarded as insensible, if the microscopes are carefully adjusted. This will dispose
of four of the nine causes which may affect the relative position of the divifipp , and object
glass. The remaining five will be included in the equations of condition. >
Every micrometer reading will then, by equation (1), give an equation of the form
r«M-g tin B+l COS B+a cos B+ft sin B+e+i*.
(«)
(44) The problem now is to make such mechanical arrangements and such readings, that
from a series of equations of this form we may be able to determine the values of the coefficients
in thejiecond member, so far as it may be necessary for the correction of observed senith dis-
tances. To obtain a complete correction for the readings of a single microscope world require
the solution of equations of extreme complexity ; we shall, therefore, hereafter consider the
corrections of a pair of oppos te microscopes. If, now, another microscope be placed at the
angle 180°-|-B, and its reading, taken simultaneously with (2,) be indicated by an accent, we
shall have
r'«m'+- sin B-l ooB B-a' eos B-»' sin B-(-e'+».
r It
Adding this equation to (2), and observing that by the rotation already given
r -I- r'as8/»,
a — a'aeSa,
6 - VnmSfi,
e + tfasit,
we shall have, by taking the mean reading of a pair of microscopes,
/>=M+aeo8B-|-j^sinB-|-c-f«. (3)
an equation more simple than (2) and equally complete.
(45) The mechanical arrangements necessary for the proposed method are these : The
instrument must be furnished with two finely divided circles, each read by four microscopes.
At least one circle must be capable of being turned on the axis of the telescopp, aqd set in
any required position relatively to the telescope. In what follows, we shall sUppese both
circles thus movable. The microscopes must also be capable of being set at different angular
positions. The details of the arrangement, and the mode of numbering the mioroaoopes and
■- '¥^f-mm^'f-'jfim.fS^r^: 3?^CTa3Rtsa«»KW»««~^- w»M?»»!t!<www^5""<
UNITID flTATIS KATAL OMIBTATOBT.
li
S$ulh
counting the degrMs, will be rappoied to correspond to thoee of the Wwhington transit
circle. The Accompanying diagram shows the arrangements referred to, as seen from the
west. The oater circle represents the westernmost
one, and shows the positions of microscopes I to
lY, which are on the west pier. The inner circle
represents the eastern one, and shows the positions
of the four microscopes V to VIII, which are on the
east pier. The arrows point in the direction in
which the degrees, as nnmbered on each circle,
increase. It will be seen that the two circles are ^orth
divided in opposite directions, so that when the
instmment is reversed the circle now east will read
in the same direction as the former one, and so for
the west. Also, as the instmment is turned in any
direction, the snm of the readings of any microscope
on the west pier and any microscope on the east pier ^
will be a constant depending on the relative posi* sj
tions of the circles.
We shall suppose the axis of X to pass in the direction of microscopes I-ni, and that of
Y in the direction of II-IV. Thns, we have for microscopes
I and VIII. B=180O}
II sad VII, B« 90O;
III sod VI, B= OO;
IV and V, B«270O.
(46) The flexnre effect which it is required to determine is the change in the relative di«
rection of two lines, namely, the line joining the object glass and eye-piece micrometer of the
telescope, and that joining any pair of opposite divisions which chance to be under a pair of
microscopes. This will be determined by finding the change of direction of each line relatively
to that part of the central axis to which the circle is fastened. The total flexure will therefore
be divided into two parts: 1. The flexure of the central axis relatively to the ends of the tele-
scope. 2. The flexnre of the diameters of the circle relatively to the centre. The coefficients
of the first flexure we shall represent by / and g for the east circle, and by / and g* for the
west one. Suppose, then, that the line joining the object glass and eye-piece revolves uni-
formly; that part of the axis which passes through the circle and holds it by pressure may
be affected with an inequality of the form
/rinZ+^eosZ.
Again, supposing this part of the axis to revolve uniformly, it is possible that a diameter
of the circle may be affected with an inequality of the form
a8tnC4>i9eos(,
a and ^ being coefficients to be determined separately for each pair of divisions, and ( being
the angle <^ position of the diameter counted from an arbitrary axis. On the east circle we shall
for convenience, count C from microscope VI through V, VIII, and VII, and on the west circle
from microscope II through I, IV, and IIL Then, when any division D comes under microscope
V, the mean reading of V and VII will, by the effect of gravity, be increased by the quantity
«J>.
When the same division comes under VI, the mean reading of microscopes VI and VIII will
be increased by the quantity
uiuHii i Mmiiii i iiiiiiiw
u
DKSCBIPTIOR or THB TBAMSIT OIBOUi OF THE
,.T>.
Tba Mme stotement will apply to the we«t drole by dimioishing the nnmber of the mioro-
•cope by lY, to that ti.H and ^.D will be the flexare when the diviiion D comes under mioro-
icopea I and II.
Since changing ^ by 180° la the same as changing the algebraic sign of a and ^, we have
a.(D-fl80O)»-a.D,
;9.(D+l80O)«.-/J.D.
In equation (3) we hereafter substitute for a cos B-f-^ sin B the two floxnrea
/■in Z-\-g OM O+a sin C+Z* eos C
Let us now take four divisions on each circle, such that they may all be under the micro-
scopes at once. Represent them by a, ft, o, d on the east circle, and a', V, cf, d' on the west
circle, the lettering being in the same direction with the numbering of the degrees, and of the
microscopes. We then have
cascca error of position of line joining a—e,
a.a^ error of flexure of a—c when under mierosoc^ V.
p.a= error of flexure of a— e when nnder mieroseope VI.
Suppose, also, that when a is under niicroscope V, of is under microscope I. Also put
/sin Z+j- eos Z=/ *.— /. («+180O),
-/ sin Z+^ eos Zax/je.—/. («+ ISQO),
and let
Zo. ^+900, Z«4-180O, Z,+270O
be the four zenith distances of the telescope toward the south when the divisions are brought
successively under the four microeoopes. Bepresent by fin.» the mean readings of a pair of
opposite microscopes. Then we have the following equations of the form (3):
First position of telescope Z^
^5.0=:M|+(.a+/jr»-|-a.a+«»,n. />1.0aiMi+('ui-4- /'jst+a'ui— •.0,
Second position, 2^+90*.
/>fi.90=M,-|-c.i+/.(ire+90O)+a.6+«.90, />1.90»M,-f<'.<{+/'.(«k+90O)+a'.<I— «.90.
/>6.90=M«+<.e +/(«^+90O)+i'-e+»-90, />8.90asMt+«'.a4-/'.(««+00O)+/»'.a-«.90.
Third position, Z.+ISO^'. .
/.6.180s=M,+«.c +/(«,+ 180O)+a.c-|-«».180, /jl.lSO-Mj+t'x +/'.(««+ 180O)+a'.c --.ISO,
/>6.180sM,-f(.<2+/(««+i80O)+/}.i{+«.180, /»8.180xsM«+t'.<{4-/'.(«k+^80O)+^.<2-<».180.
Fourth position, S^+270°.
/.6J870«M,+«.<l+/(«o+2700)4.a^+»^70. ^lJ70=|li+«'.*+/'.(»o+8700)+«'A-»^70,
/.6JB70asM,+t.c+/.(««+870O)+/9.a+*.270, />2.870»M,+«'x +/'.(«»+870O)+/!'jj -i»J870.
(47) For perspicuity, let na reoapitalate the adopted notation, by ezphiinii^ the meaning
of the i^ve equations.
If l^ere were no errors of division or adjostoMnt, and no elasUdty of the parte of the in<
stmment, the readings of all the microscopes wonid be sero. The readings not being aero, and
/>6.0 being the mean reading of microscopes Y and YII ^hen the telescope poiattf approzi*
mately at zenith distance Z^ the first equation indicatri that this value of />6.0 is due to the
five following causes:
1. Error of position of the microscopes Y and YII, (M,.)
ihmm
nvimmmm
tmrrwD arAnt mawml oBsnTAioiT. U
5. Brrora of the divitioos a and o which we ooder thete miorotoopee, (t.o.)
8. RoUtion of the sxis of the telesoope reletively to iU Hne of sight, in consequence of
the irregolar effect of gravity, (Av)
4. Angular change of Hne joining divuiona a and o relatively to axis of rotation from the
same cause, (a.a.)
6. Incorrect setting of the telescope, («.0.)
In any one of the above fonr positions take the snm of />, or p„ and /i^or />,. Take alito the
corre»|K)nding sum in a position of the circle 180** .different, then subtrHCt the two sums, remern*
bering that
/»— /(«+180O),
•41 or/94iM— a.(a-f 180O) or /».(a+180O),
'. f.a«Bt.(«+180O),
and call the difference K, using the notation
K.ie.i— A>i.»-|-/»i.i— />i («+180O) — /»,.(i4- 180°).
Put also g.K=/.n-^/.% and we have the e^ations
K.15.0mi2aM+W a+2g z, K lS.90xs 9a.b'-'2a'.b+^.{z+9(P),
K.16.0»2/9.*+2o'.a+2^«, K 10.90— 2a./9-2«'.A+2f («+90O),
K.26.0»B2a.o+2/9'.4+%.«, K.26.90- 2a 5+2/J'.a+2f .(«+90«>),
K.26.0a,2liA+ail'*b+agje, ** K.2e.90aB-2i9.a+2/9'4>-|-2^.(«+g0O).
Of these eight equations it will be seen that only six are independent, any one of each four
being identically derivable from the other three.
Now, let the poeition of the east circle on the axis of the telescope be changed by 180",
and let the same divisions be again read. Treating the equations derived from the readings in
the same manner, and distinguishing the new K's by an accent, we shall have
KM6.0aB-8a.a+2o'4i+^.«, KM6.90ss-2a.A-2«'.i+;^.(*+90O),
K'M.0ss—2fii+2a'.a-^2g.», K' 16.90= 2fi.a-2a'.b+2g.{z+9(i°),
K'.25.0ss:-2« 0+2/9'.*+^^. K'J85.90»-2a.*+2/S'a+^.(«+90O),
K'M.0=—2fiA+2^i+2gjK, K'.S6.90s 2fiM+2fi'.a+2g.{z+9<P).
Now, turn the west circle 180° on its centre and again repeat, distinguishing the K's by
two accents, and we have
K".16.0s»-2«.a— 2«'.a+ai^.«» K'Mfi.90=r-2o.i-|-2a'.A+S!^.(«-|.90<'), •
K".16.0rB—2fi.b—2a'M-{-2gje, K".16.90s: 2fi.a+2a'.b+2g.{zf9(P),
K"MJ0sB^2a.a'-2fi'A+2g.z, K".26.90sai—2a.b-'2^M+2g.{z+90O),
K"J»6.0sB—2fib-2fi'.b+2g.z, K".26.90=s 2/J.a-2/J'.a-»-^.(*-f-90«>).
These equations suffice to give two values of each of the required quantities. But, to
have as many independent determinations as possible, a fourth series of readings are taken
with the east circle restored to its original position. We then have
K"'.li.0a»2mM'-2afM+2ga, K"M5.S!0» 2a.b+2afJb+2g.{+z9V>),
K"'M.0ma»fiA^2»fM+2g.z, K'".l6.90sM^2fiM+2afA+2g^z+0<P),
K"'26 0^2aM-'2fi'b+2ga, K'".86.90as 2*^—2^M+2g.{z+9(P).
K"'MJ0ss2(t.b-2fi'.b+2g.z, K'"M.90sm^2fi.a'-2/i'M+2g{z+W>).
Adding together the corresponding equations of the first and third series, and also those
of the second and fourth, we shall have
^«sK. 10.O+KM5.OaBK. 16.U+K'M6.0»K. 2A.0+K".2fii0»K. 86.0+ K". 26.0
!=KM«.0+K''M5.0»K.'16.0+K"'.l6.0=sK'.26.0+K."25.0s=K'.26.0+K'".86.0.
i^ms^tmrxm^'sm
If
DMOUPTKM or TBI nUMUT OnOLB OF TBI
*.»
Of these eight raliiec only nx un really independent, being rabjeet to the condition thnt
the Bam of the extreme ynlaee ie eqaal to the ram of the meuit, which fhmiihea » check on
the aconrecjr of the compatntion.
Again, by eimple lobtraction of the correeponding eqaatione in iracceaaive aeries, we find
the following four distinct valnea of each of the eight qoantitiea o^, /9.a, tuh, fiJb, af.a, fi^jo^
af.b, fif.b, which gire the circle flexure.
K .lfi.O-K' .15.0.
K JB0.O>K' SA-O,
K'".lfi.O-K" .16.0,
K'".««.0-K" .85.0.
K .Ifi.O-K'" Ifi.O,
K .16.0-K"'.16.0,
K' .16.0-K'M6.0,
K' .16.0-K" .16.0.
KM6.90-K .16.90.
K' 26.90-K .S6.90.
K'M6.90-K"M6.90,
K".S6.90-K'".86.90.
4/9'.«»
K J0 9O-K"'JA.9O.
K J6.90-K"'.86.90,
K' .86.90-K" J8S.90,
K' .86.90 -K''J6.90.
K .16.90— KM6.90.
K .86.90-K' .86.90,
K'" 1A.90-K".16.90,
K'".8«.90-K".86.90.
K"M6.90-K .lAJO,
K'" 16.90-K .16.90,
K" .16.90-K' .16.90,
K" .16.90-K' .16.90.
K .16.0-K' .160,
K JM.O-K' M.0,
K'".16.0-K" .16.0.
K"'.86.0-K» .86.0.
K J6.0-K"'.S6.0,
K .86.0-K'".86.0,
K'.86.0-K"J6.0.
K' .86.0-K" .86.0.
(48) Thus, the flexure of the circles, in so far as it affiects the mean reading of any pair of
opposite microscopes, and the relative flexure of the two ends of the axis, are completely wnd
rigorously determined. It remains to determine the flexore of the line joining the eye and
object end of the telescope relatively to the axis itself. We have supposed, for brevity,
and have shown how to find g.u, and therefore /— ^, and g-{-f^. The coefficients / g, f g', may
DOW be found separately and independently by observations of the nadir point and collimators.
An observation of a levelled collimator, corrected for inequality of collimator pivots, diffisreuce
of latitude of circle and collimator, aerial refraction, and oollimation error of the collimator,
shows the circle reading when the line of sight of the telescope is truly horiiontal. The coin*
cidence of the direct and refiected images of the zenith-distance wires shows the circle reading
when the telescope is truly verticaL When these readings are corrected for circle flexure, the
horizontal and vertical circle readings will be as follows:
Ewtdrala. Wostdnl*.
Bonth horiiontal reading, 0«4-/ O't—f
North horisontsl resdiog, 0«— / O't+f
Nadir reading, 0«-jr C'^—g'.
Cg being the true reading, independent of flexure. From these equations the values of 0^ /,
and g, tf^f, and g', may all be determined.
The values of/ and f may also be determined independently by viewing the wires of one
collimator through the other, and making the horiiontal wires of the latter coincide with the
images of those of the formeir. If, then, the micrometer wires of the telescope be set sucoes*
sively upon the images of the two collimator wires, the line joining its object glass and microm-
eter wires will have moved accurately through the space of 180°, while the circle will indicate
a motion of I80°d=2/. The agreement of the two values of/ will afford a check upon the ao-
curacy of the collimator determinations.
(49) One precaution is, however, indispensable to an accurate result The different strata
of air in the room must be as nearly as possible of the same temperature. For, if there be any
admixture of warm and cool air, the former will ascend, and we shall thus have a temperature
increasing with the height If, now, this increase amount to one degree Fahrenheit in nine feet,
the curvature of the ray will be equal to that of the water level, so that it would never leave
the earth.
"■"•'*''***■*""■""■'■'' "" ' — -I TT- K ii .jj i mf in«iuii . i i i i.i]iiininn-|inr—
UJfinO ITATM HATAL OBaBBYATOBY.
It
The oonrae of the rey being carved, the yalae of/ obtaiDed from the opposing oollioDitori
will be vitiated. On the other hand, if we adopt the other method, there is always a possibility
of error arising from irregalarities or nnoertaiu differences of diameter of the collimator pivots,
or poaeible flexure of some part of the collimator itself. However / is determined, the obser-
vations shoold be made with the shntters open, and under atmospheric conditions, as necrly as
praotioable, like those nnder which the astronomical observations are made. Considering the
difficulty of rigorously fulfilling this condition, it would, perhaps, be better to determine / by
reflection observations of stars, g also admits of being determined by a comparison of North
Polar Distances of stars near the zenith in reversed positions of the instrument.
EBR0B8 OF DiyiSION.
(60) The method of determining the errors of division is, in principle, that usually adopted,
the operation being so conducted as to eliminate all irregular flexure of the circles.
liOt us suppose the two pairs of opposite microscopes set at the distance B, the angle posi-
tion of the flrst pair being 0°, and that of the second pair, B. Take a series of pairs of divis-
ions at the distance B, and let these divisions be successively brought under two pairs of
microscopes. Then, using the same notation as in § (43),
Mio. I. ri»wi+^-J-ai-»-«i-f-«»i,
II. niaiMt-|--^cosB stoB+OteosB-faiflinB-fck-t-wi.
ni. fi>-M— 3^--as4-«»-f Ml,
rV. r4BM4— 4eosB-h-gsiaB— OtCOBB— i4B{nB-^«4-fi»i.
Whence, adding the odd and even equations
/>^2^sMt4-at COS B-H/S* sin B-f-«i-f- wf
Turning the circles through the distance B, we shall have
(1)
^<y»Mi.J-a,+.,+«,,
Turning again
,<»>.
'<?■
:M|-(-a3 cos B-f-^3 sin B-f ts+coi.
(«)
Mi-J-a3-|-«j-f-«3.
p^^sMr^a^ tM B+fit sin B-(-C4+«»4.
Let 2» be the number of motions necessary to bring the circle back to its first position.
Then, the (t+l)th reading will have brought it round 180°, so that the same divisions as at
first will be under the microscopes. The readings after the tth will then give
/.<j+^)=:Mt-ai+.i+«(i+l).
/.<*+^)asM,-.a,cosB-A"inB+«,+«'(«+l).
^<j+*)=Mi-«,4..,+«(i+8), ^^5
/•+2)^M,-«, eoB B-A •»» B+t,+«(H 8).
10 ■
ice.,
ace.
i ;i *ii:jii«i«» i iiiiiiiiiiift i iii! 8
18
UE8CBIPTI0N OF TQE TRANSIT CIRCLE OF THE
'M
Taking the suma of readings in opposite positions of the circle, we have
Using the notation
we have
Mt— Mi + Ci— Ci=rI.1.2,
Ma— Mi+ca— ct=I*2.3,
Mj— Mi+e4--(3=I.3.4,
&c.« &c.t tee.
(4)
(fi)
Taking the sum of the entire series of values of I, and dividing by their number, the
c's will destroy each other, and we shall have
Putting
we shall have
Mj^Mi:=-r-.
J.1.2=:I.1.2-(tf,— Ml),
(7)
«4-C3=^.3.4, (8)
&»., Ice.
Thus, where one e is known, all the others may be found by successive addition of the
differences A. If, however, the number t is considerable, the accidental errors of the various
As may in the additions become considerable; it is therefore necessary that at least every fifth
c in each series be corrected by the results of another series in which the value of t shall be
less than in the series in question. The correction will be really applied to M',— M„ which
will thus be determined independently for each sub-series. Suppose, for example, that in a
first series the microscopes are at the distance 45°, so that t==4. The preceding formulte will
then give
t.ifi —e.O =4 .0.45,
C.90 — C.46 ssJ.45.90, (9)
c.l35->c.90 r=:J.90.135,
c.O — c.lSffssJ.lSff.O.
In a second series, let the microscopes be placed at the distance 16°.
then give
e.l5— c.O ssJ.O.ld, C.60— c.45s=J.45.60, &c.;
e.30— c.l5=J.15.30, (.75— c.60=J.60.75, &;c.;
t.45— c.30=J.30.45, c.90— (.75=^.75.90, &;e.
Adding each of (10) and comparing with (9), we have
■A ,0.15+J.16.30+J.30.45=J .0.45,
J.46.60+J.60.76+J.75.90=J.46.90,
&c., &c., &c.
The formulae will
(10)
».*lip>.vn'-;9t^-'.-WS«;i'«,»riMP^>aiSr«'KS*^^
the
UNITED STATES NAVAL OBSBBVATOBT.
19
If tbe readings were perfect, these equations ought to be exactly satisBed. Not being satis-
fied, the difference is due to tbe accidental errors of the readings. Let i be the probable error
of each of the left-hand ^^s, « that of the right-hand ones, and e the amount of the discrepancy.
The most probable distribution of the discrepancy will then be,
to each left-hand A, . ^
and to each right hand A,
The corrected values of A being substituted in (10), we shall have a series from which the
most probable values of f„ fu. &c,, may be found by successive addition from any arbitrarily
assumed value of «,.
DETEBMINATION OP THE EBEOES OF SPECIAL DIVI8IONS.-PBOBABLE ACCIDENTAL EBBOB OP
ISOLATED DIVISIONS.
(51) The determination of the error of each separate division being impracticable, this
question arises: What is the probable error of any isolated division relatively to any consider-
able number of the divisions near it? Measuring a series of contiguous spaces on any part of
the circle we have the data for answering this question. These measures can also be made
aviilable for the termination of the special divisions used in observing the nadir and horizontal
points, or any special star the position of which is required with a high degree of accuracy.
The method of treating these measures is as follows: - . •
The space between two adjacent divisions being very nearly four revolutions of the microm-
eter, let the measure of the first, second, third, Ac, spaces be
4 rev. 4-di, 4 rev. +«i», • 4 rev. -i-«is. &«•
Represent also by x the error of runs of the microscope in four revolutions, and by e,, e,, Ac,
the errors of division. Then the measures give the series of equations
(1)
Here we have n equations for the determination of n-|-2 unknown quantities. The remain-
ing two equations are given by the condition that the sum of the squares of the errors of divi-
sion must be a minimum. We thus have
A* . <fcl , - <*«•• A
(8)
(3)
e in the last equation representing any error of division taken at pleasure. Regarding x and e
as independent variables, any change in e (« being given) will cause an equal change in all the
other errors of division. We have, therefore.
and therefore.
^ <**» *.«
deM ,
de
«^-f ei-|- Ac. • . . -f-ejiasO.
(*)
wmmtm
so
DE8CKIPTI0N OF TBI TRANSIT OIBCLB, ETC.
ml
This eqnation, united with the equations (1,) will enable us to express each error of division
in terms of x. Multiplying the first of equations (1) by », the second by n— 1, the third by n— 2,
Ac, and adding, remembering that
JSemiO,
we have an equation which gives e^ in terms of x. By using the proper coefficients of elimi-
nation, we have each of the other errors in terms of x. These coefficients are indicated in the
following table, in which each column is to be read downward, in connection with the words
Mi the left,
To express e^ «i c^ en—1 m
the eoeffieient of ai is « —1 —1 . . . —1 ->1
* " " at is »— 1 »— I — 2 . . . —8 —2
« •• « oa is «— 2 »— 2 «— 2 ... —8 —8
m
tip
M
U
a.(>i-l)is 2 2 2 . . . -(w-l)
« " " aji is 1 1 1 . . . 1
The equations thus obtained are as follows:
-(•-1)
— «
•jn+l)
2
x+Hai+(n~-l)at+ .... +a4i+(fi+l)A,a=:0,
{n-2){n+iy
2
«— ai+(fi— 1>8,+ .... +a.»+(ii+l)«is=0,
%S;^J («-4)(ll+l)
2
X— ai— 2a,+()i— 2)a3+ . . . +an+{n+l)e,ssO,
(6)
2
X— fli— 2<i|— Sas— .... — iiaji+(fi+l)ejiassO.
We have now only to suppose the last members of these equations to be accidental errors,
and solve by least squares. This solution gives for the eqnation in 0,
»{n+l)(n+ 2)
6
x+nai+2{n—l)at+2(n'-2)a3+ .... +na.nssO.
Having thus obtained the value of a;, the quantities e^—% ^t'^* ^^'•i ^^^ immediately formed
from equations (1.) Thus, when we have e^ the other e's are formed in succession by the adding
on of successive differences. The value of e^ may be obtained from the equation
formed by multiplying the first member of (1) li>y n, the second by n — 1, Ac, and adding with
reference to (4.) But the most ready way of obtaining all the e's is perhaps by forming them
from e;,:=0, and then subtracting from each ci them the mean value of the e's thus obtained.
If one of the e's is known by the methods already explained, the values of the differences
eg— e,, Ac, will not be changed, and the vulues of aU the other errors may be found by addition
of the differences to this known value.
m
«««
MMMW
^■1
PART III.
DETERMINATION OP THE CONSTANTS OP THE TRANSIT CIRCLE AND ITS
SUBSIDIARY APPARATUS.
«
(62) Valve <f me divitum <^ ike Spirit Lends. — It will be remembered that there are three
levels — one striding level for each coUimatov, and a hanging level for the axis of the in trament.
The former are distingmshed by the letters A and B.
1865, October 18. The old moral circle was turned until the telescope was horizontal,
and the collimator levels were set astride of the telescope. Microscopes A and B of the circle,
and the two ends of the babble of the level, were then read in different positions of the tele*
scope, as follows:
IficA.
lO&B.
LOTdA.
L«r«lB.
S.«d.
N.end.
S.eiid.
N.end.
1 1$
It
i.
i.
d.
4.
w«r.»
70.8
1&4
«i.3
18.6
38.3
64.8
66.4
1.1
85.8
1.6
81.5
7S.8
77.9
87. 6
51.3
97.6
47.3
M.4
87.1
8.3
86.8
3.0
98.8
75.1
77.6
86.6
50.5
96.4
46.8
6K.S
67.8
15.0
38.1
16.4
36.8
t r^^'i
66.8
44.6
96.5
41.0
81.8
(
flO.9
63.4
36.5
18.6
34.1
14.8
•
49.7
68.8
60.0
86.1
46.0
86.8
\.
71.0
7a8
83.8
— 0.6
81.4
1.6
a
50.9
68.8
49.6
96.5
46.8
86.0
1
68.8
71.8
86.7
8.6
84.3
4.6
5
L59.9
68.7
37.8
13.4
34.0
14.8
Temperatnre 57°.
Prom tiie observations is concluded —
One division of levd Ab0".826.
One division of levd B8sO".860.
The level error of the collimators being kept quite small, rarely no great as 3", the valae of one
division,
0".84,
has been adopted for both levels.
*lWil|l!M'>IW>im'*l*WU#!gi
w
2S
DESCRIPTION OF THE TRANSIT OIROLB OF THE
1866, November 21. The hanging level was nnspended from the telescope of the Moral
Circle, and the following readings taken:
Mie.A.
IficB.
Level.
N.end.
a end.
//
//
d.
d.
16.8
81.1
JSt.l
84.5
86.9
31.8
80.6
78.3
40.3
46.1
6.8
67.8
14.9
19.4
34.4
86.3
41.5
46.1
4.0
66.9
35.7
40.6
10.8
61.1 68.1(7)
90.8
36.8
16.4
68.3
84.8
89.0
S8.8
74.9
18.6
83.8
89.8
81.8
13.8
17.8
36.8
88.8
48.9
47.7
8.0
64.1
Temperature 53*^. From which is concluded
One divi8ion=0".872a0«.068. *
The three readings preceding the last seem to indicate a diminution of the value as we
r^pproach the end of the scale, but the diminution is no greater than what may be due to errors
of the microscopes.
(53) Difference of ccUara of ooRimaiora, — It is requisite that we know the difference be<
tween the true level of the axis of the collimator and the readings of the spirit level set upon
the collars on which the collimators turn. This is effected by reading the level when the col-
limator is in its regular position, and when reversed, end for end, around a vertical axis, the
operation being repeated a number of times in succession to eliminate the possible changes of
level during the operation.
The following are the level indications of the two collimators in different angles of position.
The angle of position of the collimator indicates its position as it is turned upon its Ts, with-
out being raised from them. They are used only in those four positions in which one of the
wires is horizontal; and, in practice, the positions are almost entirely confined to two, which
are designated as 0° and 180°. The angle is measured by the position of the clamp which
binds the eye-piece, being called 0° when this clamp points horizontally to the right of an ob-
server looking into the eye end of the collimator, and 90° when it points upward.
The collimator is said to be direct when the collimator points toward the Transit Circle;
reverse when it points from it. The level readings are positive when the pivot farthest from
the Transit Circle is too high.
COLLIMATOR A.
Ftr«< acrtM.— Position changed from 0° to 180°, and the collimator reversed alternately
one pair level readings between each change.
PoeiUon 0°.
FMltton 180°.
Direct.
Reverae.
Diraet
Reverse.
Level A . .
Level B . .
d.
f 3.84)
+ 8.91 J
— 0.46
-1- 0.08
d.
+ 1.35
— 0.78
— 0.96
d.
+ ^fiX
-- 8.60$
■ - l.OS
-• 0.56
d.
+ 1.86
— 0.90
— 1.08
Meen. D-R.
+ 1.32
d.
+ 1.80.
tk
UNITBD STATES NAVAL OBSERVATOBT.
Second »erie». — PoBition 0°.
Third amw.— Position 180°.
Diraet.
d.
+0.81
+0.32
~0J84
0.00
Mean. D~B.
d.
-0.18
+0.36
-0.39
BareiM.
d.
-1.S4
-0.94
-1.42
d.
+1.42.
d.
-0.96
-1.65
-0.89
d.
+ 1.09
'-m '•'
Mean, D— K.
The ooncloded correction for diflFerence of collars, when in the position 0° or 180®, is one-
fonrth D— E. or 0".29, the eye-pivot being too large.
Two similar, but more accordant, series gave for the correction to position 90°— 270°
0".09, so that the collars are not perfectly cylindrical.
OOLLIHATOB B.
The results are
The determinations have been made only for the positions 0° and 180°.
d.
D-B for 0°, +1.06 i ;r^ .
for ISOO, +0.66 ; .
Concluded correction, 0". 17, the eye collar being too large, as in the other collimator.
The collars are decidedly conical, diminishing toward the ends of the telescope, so that
entire dependance cannot be placed on the absolute horizontal point obtained from a single
collimator. But, by interchanging the collimators, this error is completely eliminated from the
zenith point.
(54) Periodic InequaliHeso^ i^he Micrometer Screws.— In the case of the eight microscope
micrometers the inequalitie" *« --6 determined by measuring the intervals between the parallel
wires of each pair with different portions of the screw. The circle being clamped and properly
set, one of the micrometer wires was brought to a distance from the edge of a division approx-
imately equal to the thickness of the wire. The observer retained a quite accurate idea of the
intervening space, though the idea could not be defined in language. The micrometer was
then read. The other wire was then brought into the same position, and the micrometer was
again read. The operation was twice repeated, making three measures in all. The circle was
then moved forward 6" by the tangent screw, and a similar series of measures again taken.
The operation was continued through the two revolutions of the screw most used.
Repeated trials showed that the wires could be set more accurately in position by this
method than by making them coincide with the circle division, the probable error of a single
setting being about 0".10, scarcely greater than that in putting the division midway between
the wires.
The results of a determination made in November, 1865, were:
For microacopes I, II, III, inequality InsenBible ;
IV. Ineq. = — 0".63 cos ti+0".67 sin t»+0".13 cos 2i»— 0".l 1 ain 2« ;
V. —0 -0900811+0 .028ini(;
VI. +0 .24co8«+0 .aSsiDw;
VII. — .06cos«+0 .06Bini»;
VIII. +0 .06coa«+0 JilBinu;
u being the angle of the reading of the head.
n
w^<i.„V>aw*|-jM— MWiWWWilll
"mm
w
i;
24
OESOSIPTION OF THE TRANSIT OUtOLH OF THE
WW
;,i
Microscopes V-YIII being alone employed in astronomical operations, their inequalities
were redetermined in March, 1866, with the following result:
V. — 0".05 COB «+0".05 sin « ;
VI. +0 •84COBU+0 -Sfisinit;
VII. —0 .07cos«+0 .OSsiiiK;
yill. +0 .llcos«(+0 JS6tin«.
The mean of the two results is adopted as the correction for the year 1866.
(55) A rough check upon the general accuracy of the screws is given by the mean dis*
tance of the wires as measured in different revolutions of the screw. The following are the
distances given by the same measures which determine the inequalities :
' 1866.
1666.
Difference.
29 nv.
30 rev.
29 rev.
30 rev.
1866.
1866.
Mic. V .
Mic. VI .
Mio. VII .
Mic. VIII .
10.98
10.88
10.63
10.88
//
11.06
10.82
10.47
10.87
II
10.80
10.80
11.86
10.74
//
10.91
10.95
11.76
10.92
+ 0.07
— 0.06
— 0.06
— 0.01
II
+ 0.11
+ 0.16
- 0.10
+ 0.18
The method of observing is such that the microscope micrometers are seldom moved through
more than a fraction of a revolution . No very accurate investigations have therefore been
made to find whether the value of the revolution of any one of them changes progressively; but
the measures occasionally made for runs show that the change, if it exists, is entirely inappre-
ciable.
There are, however, outstanding discrepancies, amounting sometimes to three or four
tenths of n second, which I have not been able to refer to any law.
(56) The Dedination Micrometer of Telescope. — Neither the collimators nor the telescope
micrometer were originally furnished with double wires; the usual method could not, therefore,
be used to determine the inequality of the lalter. The plan was, therefore, adopted of meas-
uring successive half revolutions of the telescope micrometer with the microscope micrometers,
by setting the wire of the former upon the collimator. The following are the value of eight
successive half revolutions, as given by two microscopes of each circle, in one series, and the
four microscopes V-VIII in the other :
Fint Mriei.
Mid.
Mio. III.
Mic VI.
MicVm.
Meui.
r. r.
//
//
//
//
//
24.0-24.6
7.70
7.61
7.91
8.39
7.90
24.5-85.0
7.77
7.76
7.86
7.49
7.78
85.0-85.6
7.66
7.37
7.66
7.66
7.66
85.5-86,0
7.81
7.41
7.46
7.41
7.68
86.0-86.5
7.75
7.86
8.00
&86
7.96
86.5 — 87.0
7.86
7.61
7.63
7.38
7.60
87.0 — 87.6
7.65
7.65
8.03
7.86
7.77
87.5 — 88.0
7.83
7.63
7.61
7.76
7,71
The mean of the odd measures is 7 ".80, and of the even ones, 7". 64.
•3 ■•V«r»WW««rfj*tTjn'^f«.:-*,'s^5»:tBBi
UNITED STATES NAVAL OBSEBVATOBY.
Second lerioi.
MicL
Mio. III.
Mlc. VI.
Mi«.VIII.
Mean.
r, r.
II
//
H
//
//
31.25 — 31.75
7.64
7.fl9
7.51
7.36
7.58
31.75-38.85
7.54
7.9fi
7.73
8.02
7.82
38.25 — 32.75
7.75
7.66
7.S6
7.86
7.78
32.75-33.25
7.51
7.49
7.24
7.22
7.36
33. 2C- 33. 75
7.37
7.50
7.64
7.71
7.56
33.75 — 34.25
7.57
7.76
7.6«
7.61
7.66
34.25 — 34.75
7.94
7.64
7.75
7.85
7.79
34.75 — 35.25
7.49
7.57
7.62
7.60
7.57
J}
\% iM'-'%h' '-
The meau of the odd lueasare is 7". 66, and of the even ones, 7". 60.
From the differences 0".16 and 0".06 of the half revolutions the screw would seem to be
affected with the error .
0".04co8«+0".02 8in«;
an error so Hmall that it has been neglected, especially as the screw is used about equally
through several revolutions for every class of observations, by which the periodic errors will
disappear from the final result of the observations. After double wires were placed in the
collimators, measurements of successive half revolutions of the micrometer were made, which
gave for the periodic correction, . ,
0".07 COB «— 0".05 sin «.
(57) Value of. a Revolution of the Micrometer /Screws.— 1866, June 12. — The telescope was
set on collimator B. The record does not state whether it was north or south. The microscopes,
however, indicate that it was south.
The following readings of the microscopes and zenith distance micrometer were taken
successively in different positions of the telescope. Each micrometer reading is the mean of
nine; three for coincidence of collimator image with each wire, and three for a position midway
between wires:
I
•■
'
JS
.a
1
1^
Readings of microecopes—
Corr. for—
"^*
•s-^
Mean.
!^
*\
1^
^i
1
1
V.
VI.
vn.
vra.
lueq.
Div.
c
5
(
r. "
//
//
41
II
/ It
r.
56
9 19.5
SO. 3
21.2
23.7
21.18
- .16
- .04
56 50.99
28.408
.54
16.5
18.0
19.2
21.8
18.89
- .14
— .12
53 48.63
20.392
58
21.4
22.8
23.2
26.0
23.35
~ .12
+ .16
57 53.39
.%.377
64
15.8
17.9
18.9
21.2
18.45
- .14
— .12
53 48. 19
20.373
58
21.6
22.8
23.4
25.9
23.43
- .12
+ .16
57 53.47
36.393
66
19.0
20.6
21.4
23.7
21.18
- .15
-.04
65 60.99
28.395
These readings give from 20 r. to 28 r., 1 rev. =15".286,
28 r. to 36 r., 1 rev. =15 .337.
An increase in the value of a revolution as the turns increase seems to be indicated.
In the great majority of observations the micrometer is used between 26 and 34 revo-
lution?; a determination of the value between those limits was therefore made which gave
I5".296. The value actually adopted was the mean of the two determinations, or 15".303.
A third determination, made on September 3, 1866, gave
From 26 r. to 34 r., 1 rev. =il5".311 ;
34 r. to 4fi r., 1 rev. sl5 .375 ;
which seems to confirm the suspicion of an increase in the value of a revolution as the screw
is advanced.
4
'^^*h~^--m&^St
M Pt WM
mmKmieMms &satmmmm s i/^mwtmim ^xm^
hi
li
26
DESCBirnOH OP THS TRAKSrr OIBOLS OP THE
^:
(58) Irregularity of the Screw. — It is desirable to know whether this change in the valae
of revolution is regularly progressive, or whether it is subject tr sudden changes. To learn
this, advantage was taken of the fact that the distance of the pair of wires in collimator A,
and of the close pair of wires moved by the micrometer, are together nearly equal to a revo-
lution of the latter. Consequently, turning the telescope on that collimator when its double
wires are horizontal, we have a measure of a constant space by setting first the upper microme-
ter wire on the lower image of the collimator wire, and then the lower micrometer wire on the
upper image. The measures were commenced, as nearly as practicable, at an even revolution,
and therefore ended nearly at the beginning of the next revolution. The measures were made
on three different dates, and three measures of each revolution made on each date. But the
measures were not always continued through the entire range of the screw. About 30 revolu-
tions they were prevented by the interference of the fixed horizontal wires of the reticule.
a 1
I
IfeaniN.
1
i
^
h
1
Her.
Arc.
Cor. arc
1
r.
r.
r.
//
II
//
17.7
18.7
0.964
15.06
14.97
+ 0.13
-- 0.18
1
18.7
19.7
.964
15.06
14.97
1
19.6
20.6
.978
14.88
14.80
— 0.05
1
30.0
21.0
.986
15.09
15.03
-f 0.17
+ 0.08
3
80.5
21.5
.980
15.00
14.93
4
81.
88.0
.971
14.86
14.79
— 0.06
4
28.0
83.0
.976
14.94
14.88
-1- 0.03
4
33.0
84.0
.978
14.88
14.63
— 0.02
3
84.0
85.0
.973
14.89
14.85
0.00
3
85.0
86.0
.966
14.77
14.73
— 0.13
3
86.0
27.0
.973
14.88
14.85
0.00
3
27.0
88.0
.965
14.77
14.75
— 0.10
3
88.0
80.0
.964
14.76
14.75
— 0.10
3
31.0
33.0
.970
14.85
14.86
-1- 0.01
3
38.0
33.0
.968
14.88
14.83
— 0.08
3
33.0
34.0
.976
14.93
14.94
-)- 0.09
1
34.0
35.0
.961
14.71
14.74
- 0.11
1
35.0
36.0
.965
14 77
14.81
— 0.04
I
36.0
37.0
.966
14.79
14.83
- 0.08
1
Of the three columns headed "Measure," the first gives the measures in revolutions of a
micrometer; in the second these revolutions are turned into arc, using 1 rev.ssl6".303 ; in
the third they are corrected for progressive change in the value of the revolution. The resid-
uals show the excesses of the individual corrected measures over the mean value 14". 85. I
conceive that they proceed mainly from the accidental errors of reading and temporary derange-
ments of the motion of the screw by dust, displacement of the oil, and other causes, and that
the screw itself may be regarded as sensibly regular.
' (59) J7. A. Micrometer. — ^The value of a revolution of this micrometer seems to be exactly
the same as that of the other. Wide measures give 15". 300. Owing to its limited use, no
special investigation of its movement has been entered upon.
(60) Flexure of the Cirdes.—The work of determining separately the flexure of the different
parts of each circle was commenced in 1866, January 19. But after taking one series of read-
ings, it was found that the axes of several of the microscopes deviated quite sensibly from the
perpendicular to the face of the circle; some deviating as much as 40'. To adjust them with
entire accuracy appeared to be a difficult and troublesome operation ; but a kind of ^ T-square
was made by which they could be set without an error exceeding 5', and they w^re adjusted
by it on April 7. The set of readings previously made were not used.
The following are the details of the operations by which the definitive values of the flexure
coefficients were obtained:
UNITBD STATU VAVAL OBSKBYATOSY.
%1
In the first series of readings the position of the circles wm snch that when the telescope
pointed to the senith, the divisions of circle A, which were nnder microscopes V-VIII, were:
MIc. V, ISfiO; VI, 2SfiO; VII, 31 5° j VIII, IfiO
The divisions of circle B, under microscopes I-IV, were:
Mie.1, 3160. II, 4AO; III, ISfiO. IV, SSfiO.
When the telescope pointed at senith distance s, the above readings of microscopes V-VIII
wonld be increased, and those of I-IV diminished by i.
The operation was began on divisions 0°, 90<^, 180°, 270°. The division 0° of circle B was
brought under microscope I, and the eight microscopes were read , one observer reading each
circle. The telescope was then turned 90°, and the microscopes were again read. The tele-
scope was again turned 90°, and the operation of turning and reading continued until the
microscopes had been read three times in each 6( the four positions of the telescope. The
mean of the three readings was taken as that corresponding to each position.
The telescope was then set 15° backward from its first position, and the same operation
was performed on divisions 75°, 165°, Ac, of circle A, and 15°, 105°, Ac, of circle B. The
operation was repeated through every 15° of the quadrant. The first series was now complete.
In the second series circle A was loosened and turned 180° on its axis, so that when the
telescope pointed to the senith, the division 315° was under microscope V. A series of read-
ings exactly like the first was then made on the two circles.
Circle B was then turned on its axis 180°, and a third series of readings were made.
Finally, circle A was returned to its original position, and a fourtb series of readings were
made.
The mean of the three readings for each position of the instrument is given in the foUoW'
ing table:
8EBIES I.
I
I
I
46
las
986
315
30
190
310
300
15
106
196
986
90
160
£70
346
75
165
966
330
60
160
940
9.0
180
00
986
106
106
16
300
910
190
30
316
996
136
45
330
940
160
60
345
965
165
78
180
970
00
166
966
346
76
160
940
330
60
136
996
315
45
190
910
300
30
106
105
985
15
Beading* of micnwcopM.
97.00
97.40
93.43
94.37
96.57
96.43
93.47
99.97
96.87
97.3:1
94.03
93.17
96.57
97.73
96.47
93.30
96.03
97.13
96.37
99.86
94.77
97.43
96.30
99.70
n.
95.63
95.60
93.70
91.00
33.67
95.10
93.70
90.13
84.77
95.03
93.63
91.50
93.00
96.00
94.60
99.35
99.43
96.07
94.17
99.60
91.97
96.87
95.57
99.37
m.
4.97
4.77
3.73
3.07
3.40
3.83
4.40
1.80
4.67
4.77
3.30
9.47
4.53
5.33
4.70
9.60
3.30
4.70
4.03
9.60
3.10
4.60
4.93
3.13
lY.
0.67
99.13
97.83
98.50
98.03
98.87
97.00
87.17
99.70
90.40
97.07
97.03
90.97
0.40
97.77
97.75
98.13
0.93
87.47
97.36
98.57
0.03
88.67
97.57
V.
4.07
5.33
5.43
4.50
6.93
6.30
5.80
6.10
4.83
5.97
6.00
6.17
4.67
4.67
4.93
5.00
5.83
6.17
5.33
5.45
5.80
5.97
5.40
6.33
VI.
7.07
6.87
4.63
6.73
8.60
8.00
4.47
8.60
6.83
7.43
5.60
6.77
7.30
6.67
6.07
6.90
8.13
7.00
6.43
5.35
7.70
7.77
6.30
6.77
YU.
8.87
0.67
8.17
4.57
4.77
1.83
1.63
5.57
3.67
1.67
1.43
4.63
a03
1.50
0.63
6.80
4.17
8.87
1.03
8.96
5.03
3.30
0.93
9.83
Yni.
3.43
a 10
3.80
5.63
4.13
9.37
3.97
5.16
6.60
9.93
3.73
4.80
■MwiwilMlM
m u mm
M
'#'
315
45
136
886
300
30
190
SIO
985
15
106
196
870
90
180
856
346
75
166
840
330
<M)
150
DESCRIPTIOir or THE TKANSIT OIBOLK OW THK
8EKIEB II.
o
870
IHO
90
16
886
196
106
30
300
310
180
45
315
885
136
60
330
840
150
75
345
856
165
195
885
15
105
Raitdingf of microMsopM.
89.00
1.70
86.90
85.36
86.70
0.80
87.40
84.73
84.80
98.97
96.70
89.80
83.67
87.77
86.47
83.30
89.73
86.90
87.03
83.80
89.50
86.80
87.47
84.87
II.
88.30
0.90
96.65
96.35
96.00
99.93
97.63
96.57
94.93
87.90
96.17
83.37
83.77
85.90
96.73
83.33
83.60
95.13
97.10
99.97
83.10
96.37
97.13
94.10
III.
6.70
7.30
9.96
3.45
4.60
6.87
3.00
a90
9.33
4.67
8.17
0.67
0.66
.^57
9.07
0.63
0.83
3.13
9.97
0.10
0.80
3.99
3.47
0.77
IV.
0.45
1.50
96.56
96.86
98.73
0.80
86.30
84.77
86.63
88.53
95.63
89.83
84.57
87.03
86.97
88.73
83.83
96.77
87.30
89.40
83.93
87.80
97.33
93.93
4.70
5.10
6.06
6.80
6.67
5.73
6.37
6.40
6.17
6.33
6.57
6.57
7.17
7.33
7.90
7.13
7.00
7.10
6.87
7.00
7. S3
7.07
6.97
7.97
VI.
VII.
8.40
5.80
8.36
9.66
9.90
6.80
7.60
9.97
11.10
7.63
7.00
9.77
11.93
9.33
8.97
10.53
10.80
10.47
7.90
10.93
11.70
10.43
7.87
9.83
0.40
98.76
3.80
4.60
1.83
99.67
9.77
4.53
a60
0.10
9.60
6.67
4.70
1.47
9.77
6.80
5.60
1.83
1.60
6.37
6.03
9.37
1.33
5.90
SERIES m.
VIU.
90.70
30.30
4.66
9.56
1.50
0.87
4.93
9.37
9.13
0.77
4.43
4.90
9.67
9.07
4.07
6.07
3.00
9.03
9.90
6.70
3.98
1.93
3.07
5.83
135
90
96.30
94.80
6.40
97.97
6.57
9.40
4.47
4.93
885
870
180
89.57
97.80
6.77
98.93
8.77
10.37
6.17
3.50
315
180
870
88,77
98.63
6.87
96.50
6.90
10.87
3.37
9.90
45
90
86.17
97.80
7.17
96.63
7.80
ao3
1.97
a90
ISO
15
76
83.70
93.17
4.97
96.40
7.37
0.07
4.87
6.77
810
985
166
98.40
85.87
4.30
97.70
7.17
10.60
6.73
3.93
300
196
956
98.07
93.03
4.40
96.90
7.10
11.47
3.70
9.97
30
106
345
96.53
97.87
6.97
94.93
7.00
7.47
1.93
9.33
106
30
60
94.93
84.40
6.47
96.10
6.70
8.37
3.10
4.63
196
300
150
87.60
94.97
4.47
97.97
6.83
0.97
6.67
4.97
986
910
940
98.40
97.30
4.40
96.70
e.'v
11.67
4.17
9.87
16
180
330
96.17
97.03
6.17
94.80
6.93
8.97
OOS
1.60
90
46
45
93.63
84.80
6.97
96.00
7.63
8.07
8.93
4.60
180
315
135
96.67
83.07
4.63
96.47
7.37
10.87
6.77
6.13
970
886
985
87.63
96.70
3.60
96.87
7.67
19.40
6.90
3.47
136
315
96.80
96.87
6.00
94.17
7.70
9.00
1.80
9.63
78
60
30
93.90
86.83
6.00
95.80
7.37
7.40
1.90
8.43
166
330
180
96.80
93.97
6.77
96.93
7.80
10.40
6.30
6.70
966
940
810
87.87
96.97
3.00
96.97
7.30
11.30
5.60
a30
345
160
300
96.77
96.M
6.70
84.90
7.93
10.07
9.10
9.40
60
76
15
94.37
96.70
6.90
96.00
7.93
7.n
1.47
3.«7
160
346
105
96.77
93.80
6.63
97.30
7.98
9.67
5.13
6.87
840
966
195
98.17
96.60
4.63
97.30
7.13
11.40
6.77
4.03
330
166
886
97.50
98.00
6.90
86.97
7.93
10.63
9.63
9.13
BM
uirmD iTATn watal OBtnnrAToxr.
8EHIE8 IT.
1.'
li
if
Baadiofft of tlM
niiofOfloopM.
I.
II.
m.
IV.
V.
VI.
VII.
vm.
o
o
//
II
II
II
//
II
//
«»
316
46
870
ISO
00
870
00
180
88.87
96.33
93.90
19.40
90.97
93.63
99.33
91.67
3.60
8.47
90.87
1.73
95.60
96.17
90.77
90.17
5.90
5.87
5.67
6.37
8.80
6.43
7.97
8.80
1.10
99.93
3.33
3.63
0.33
1.87
4.73
a 17
190
no
300
30
16
966
106
106
956
346
75
166
91.07
97.10
83.80
90.33
90.90
93.53
93.13
98.37
3.47
3.17
0.17
1.93
96.03
96.77
91.93
19.70
6.13
5.13
6.07
5.90
8.80
5.33
7.00
8.00
1.90
90.90
9.17
3.10
1.70
0.73
a 03
8.07
106
106
9H6
16
30
30O
910
190
940
330
60
150
90.70
96.80
94.47
90.47
80.33
83.10
88.93
88.10
9.40
9.83
0.93
1.30
93.07
96.80
91.93
19.93
6.13
6.17
5.90
5.93
0.37
6.13
6.70
7.37
9.93
90.33
1.13
a 10
•8.00
0.80
a 80
8.80
00
180
870
46
316
985
136
986
315
45
136
90.43
86.40
84.70
90.63
81.47
88.50
83.33
81.80
1.97
3.60
0.60
0,37
99.83
96.80
93.93
18.60
6.17
6.30
6.07
5.33
8.83
6.57
6.60
8.90
9.17
99.47
0.83
a33
1.53
0.67
9.57
a 43
76
166
986
346
60
330
940
160
910
300
30
190
19.07
93.97
95.13
91.47
81.30
81.00
8a 63
81.37
1.70
9.80
1.40
0.10
91.63
94.97
94.73
18.47
5.90
5.30
6.97
5.13
8.93
8.03
5. .17
7.83
9.73
0.07
89.90
8.63
1.80
1.03
1.47
a 90
60
150
940
330
76
346
956
166
195
386
16
106
10.30
83.60
85.77
89.90
81.10
81.43
83.63
88.17
1.07
9.03
1.67
0.17
90.00
96.60
94.03
19.77
6.63
6.70
5.60
5.47
9.17
8.53
6.83
7.80
a 67
0.83
0.10
a 87
9.73
0.97
9.07
4.90
One of the most obvioua couclasioiis, from the above table, is that the two ciroleo do not
give the same result for the distance the telescope has moved. If they did, the sum of the
eight microscope readings would be constant for each series and each set of circle divisions.
In the first set of the first series, for instance, there is a difierence of 1".45 after the circle has
been turned 180°. One or both circles are therefore affected with a quite sensible flexure.
The above readings were corrected for inequality of screw, and the flexare coefiicients
were then computed from the formula) already given. We give an example of the form of
computation adopted, by presenting in full so much of the computation as relates to the four
cardinal divisions.
8EBIES I.
■»
Zo=3160; a=90o o'=0°
z
9K.15
9K.I6
9K.96
8K96
8a.«
8/?.«
e^.zo
ap.i
^9
9p.b
9pA
Ml+S)
s^d-HJ)
»>>.(9+5)
S^-(9+«)
o
II
II
II
II
II
II
//
II
II
II
II
II
II
//
//
316
98.0
19.9
9.1
19.7
7.1
10.7
99.0
9.6
-1.0
—1.7
-1.9
-1.0
-8.7
^8.3
+ 0.8
46
39.9
96.0
7.8
10.5
10.7
ia4
33.8
6.5
+5.9
+5.0
+5.9
+5.9
—8.3
—1.7
- 0.5
136
39.9
94.3
5.9
10.9
8.1
13.4
30.3
4.5
^ ^
.
.
^ ^
-1.9
—1.4
+ 0.4
895
87.9
90.3
7.6
10.3
4.8
7.5
97.9
0.6
• •
• •
• •
—9.1
-1.9
- 0.3
SERIES n.
o
9K'.16,«te.
%a.h
-S-5
//
315
36.3
98.4
5.0
8.4
11.3
14.7
a4
6.8
ti;;
+1.5
+a7
+1.1
KS
--1.3
0.0
46
39.0
39.1
4.8
6.0
ia8
16.0
6.9
8.1
+6.1
-^.8
—8.8
-- 0.9
135
99.8
88.5
9.8
ia4
9.6
ta8
9.3
6.9
.
, ^
-1.7
-0.8
.. 0.6
+ 1.5
986
98.8
91.4
10.4
18.5
9.9
11.3
1.8
a9
- •
• •
- •
- -
+8.9
—1.0
'-.%^-
:.y^gifM^ppm-pt-,-!S-a6=;»,-;it-«Jf-n ■ . WMi«W!«.u»ilWMi««I»l«»iB*
ti
SO
DiaOBIPTIOIf OP THK TRAMfllT OBOLK OF THE
SERIEfl ni.
z
Z,r=316°; «»:90O M'saOO
9K".16.«to.
Sa'ui
8^.«
vg\gtvrw)\
%>.!
8^.8
8p.5
%>.6
a>,.(l+6)a>..(l+6)9^.(8+6)|9^.(8+6)
o
II
//
//
t/
//
II
//
II
II
II
II
II
II
II
//
315
4.6
84.5
10.3
14.0
14.9
18.6
4.8
8.5
+1.8
+1.8
+1.6
+1.6
-0.3
+10.8
+10.1
0.0
45
8.3
99.7
9.1
11.7
11.4
14.0
1.6
4.4
-6.9
—5.6
—6.6
-6.1
—8.1
+
0.4
135
8.7
98.9
11.0
14.7
13.7
17.4
3.8
6.9
• •
^ ,
^ ,
+0.5
+0.3
+11.6
+10.3
0.6
896
6.3
96.3
19.0
14.9
17.3
19.6
6.3
10.5
• •
• •
• •
• •
—
0.8
HERIE8 IV.
8a'.»
9fif.h
315
83.1
19.6
0.0
13.8
38.1
6.3
81.6
96.8
-0.7
+0.4
—0.6
+0.6
-10.1
-0.7
—
0.6
45
9t.l
11. a
* 9.9
18.4
30.3
3.5
80.5
83.7
-4.8
-4.1
—4.3
-4.8
—10.0
-9.6
—
1.4
135
86.5
15.8
6.3
0.4
39.8
6.9
89.1
85.8
• •
• •
^ ^
^ _
—10.5
—0.5
+
0.8
885
88.8
19.1
6.7
6.8
34.5
7.6
94.8
87.9
• •
• •
• •
• •
— 9.8-0.7
0.0
The oompntation for the other divisions was performed iu the same way. The complete
results for every 15° are given in the following table, which is so arranged that the two coeffi*
cients which correspond to the same pqsition of the circle are under each other. For this
purpose some of the angles are changed by 180°, and the signs of the coefficients are changed
to correspond.
CIBCLE A.
«=s
OO
16°
30°
45°
600
76°
90O
106O
190"
1360
160°
1660
VkluMofSa^i
II
—1.3
-0.8
—1.7
-41.8
-0.19
II
—4.0
—3.9
—3.1
-A8
—0.41
-3.8
—3.3
-8.4
-8.6
-0.38
-0.9
—0.8
-9.9
—3.1
-0.84
//
-9.4
—8.5
—3.8
—3.3
—0.38
II
-9.7
-«.8
-9.6
-9.7
—0.34
II
—9.7
-8.3
—1.9
-8.1
— o.8e
II
—0.7
—9.1
—1.6
—9.1
—0.90
II
-1.8
0.0
—0.6
—1.4
-0.10
1/
-1.9
—0.9
-0.01
II
+0.9
+0.6
+1.3
+0.8
+0.11
II
+1.6
+0.8
-.0.9
+1.7
+0.16
—
90O
106O
180°
136°
160O
1660
180O
1950
910O
9800
940O
966°
f
YalnnofS^.*
//
-9.9
—1.9
—0.89
II
-3.1
^2.3
—3.0
—9.7
-0.35
II
-3.1
—8.6
—8.9
-3.1
-0.37
//
-8.6
—8.6
-8.8
-8.9
— 0.3«
II
-3.3
—8.4
— 4. i
—8.6
— 0.«li
//
».'3.0
— ».e
™3.f'
— •./.38
It
-3.9
-9.8
-0.8
—1.0
-0.84
II
—0.8
—1.9
—1.1
—1.7
—0.16
—0.7
+0.5
0.0
-0.9
-0.03
II II
+0.8 +0.6
+1.8 +0.9
-0.6 +1-3
—0.3 -^.8
+0.03 +0.09
II
+9.0
+1.3
+0.6
+1.4
+0.17
CIBCLE B.
•^
0°
le''
30°
4^
60O
760
90°
106O
190"
1360
160O
1860
II
II
II
//
II
II
II
II
II
II
II
II
Valne«of8«'.« J
-0.3
—8.1
+0.6
+0.3
-9.8
-9.8
—9.1
—9.1
-4.1
-4.8
—5.8
-6.6
—4.7
-6.7
-6.7
-0.9
—8.4
-8.0
—7.0
—7.8
-0.1
-8.8
-8.9
-8.7
-10.1
—10.0
-10.5
— 9.9
—9.7
-0.9
-9.1
—8.6
—8.9
—7.9
-8.6
-8.6
-8.9
—7.7
-6.8
-6.3
-4.8
-.4.8
-f6.&
-6.5
-8.6
—1.8
—1.7
-1.9
a'.«=r
—0.06
—0.97
-^.63
-0.77
-0 98
-1.09
-1.84
—1.16
—1.04
-0.89
-0.64
-0.99
UmraD ITATBS MATAL 0B8BBTAT0BT.
n
OIBOLE B.— OonMniMd.
■ SB
90°
106O
180°
135°
1600
166°
160O
I960
810°
886°
840»
885'>
ViivmolS^.*
II II
-0.7 -1.9
-8.6 -1.9
-0.6 —1.8
—0.7 —1.8
-0.14 ~«.83
./ II
-4.8 -4.1
—4.9 -6.1
-6.0 -6.4
-&.1 -6.6
-0.60 -0.79
II
-8.8
—8.4
-ai
-8.9
—1.07
//
-9.3
-9.0
-S.9
-9.4
—1.14
II II
-10.9 - 9.6
-10.1 - 9.7
—11.6 —10.4
-10.3 — 9.8
- 1.38— 1.83
II
-8.4
-8.1
-8.7
-«.7
—1.06
II II
-«.0 —5.1
—7.5 -5.1
-6.0 —3.8
-6.0 —3.7
—0.86 —0.66
-8.7
-8.0
-8.7
-9.8
-0.30
(61) It will be remembered that a represents the excess of reading of microsoopea Y-YII,
when a division of circle A is brought under microscope Y, and ^ the excess of YI-YIII, when
a division is brought under microscope YI. Also, when the division a is under mioroncope Y,
the division a-f90° is under microscope YI. The same remarks hold true for circle B, by
diminishing the number of the microscope hy lY. Now, comparing the values of a with those
of p immediately under them, it will be seen that there is generally a quite dose agreement,
the difference amounting to one*tenth of a second in only one case out of the tw«nty-four, and
the mean difference being less than 0".05. If we suppose, as seems probable, that these differ*
ences are no greater than the unavoidable errors of the determinations, we arrive at tbe con-
clusion :
Hie geometriced form of the oirde rdalive to any ayatem of Jhced aae» rem^ii'\n invariable a»
U revolve$.
The large values of a and fi show that if the central part of the cirde revoi untforndy, the
drcutnftrmoe don not revolve tm^ormly, ha is qfected with a periodic inequality
I am disposed to attribute this singular phenomena to a slight deviation of the centre of
gravity of the circle from its centre of figure. The circles weigh about 80 pounds each, and
a weight of a few ounces on their circumference is sufficient to produce a flexure of 1". But
to whatever cause we attribute it, the circumstance of invariability of form of the circle involves
the law that the flexure shall be of the form of a sin x+b cos s. If, then, we suppose
a a A sin (D +460)+B cos (D + 4fiO).
/9 sA sin (D -460)+B COS (D -450),'
o'sbA' sin (D'-f 460)+B' cos (D'+460),
/ysA' sin (iy-460)+B' cos (D'-4fiO).
D being the circle division, we flnd by equating the preceding values of a and ^, and solving
by least squares,
A=-0".37; B«i+0".01}
A'—0".84; B'=!+0".86.
(62) The outstanding apparent errors are seen in the following table, which includes the
combined errors of the two hypothesis; first, that the geometrical form of the circle remains
invariable, in other words, that
«ua=/J.(a+90O).
Second, that a and are each of the form,
AsinD+BeosD.
The first column of the table gives the reading of the finding microscope, which, for circle
A, is midway between Y and YI, and for circle B, midway between I and II.
The second gives the flexure for that position of the circle as computed by the formnle,
which is assumed to be the same for each pair of microscopes.
^jiEjsS«i»saM».;i5s%5!S:
I
h
t fl-
am- DESCBIPTION OF THE TRANSIT CIBCLE OF THE
The third gives the observed flexnre of the mean of microscopes VI- VII, or I-III, for that
position of the circle, in other words, the value of a.(R— 45°.)
The fourth gives the observed flexure of the mean of microscopes VI-VIII, or II-IV, for
the same position of the circle, or the value of ^.(R+45°.)
The lifth and sixth give the outstanding errors.
R
Flexure
formula.
ObBorved flexure.
Errors,
R'
Flexure
by
formula.
Obserred flexure.
£rron.
V-VII.
VI-VIII.
V-VII,
VI-VIII.
i-m.
II-IV,
i-in.
II-IV.
o
46
60
75
90
105
120
135
150
165
180
195
210
225
//
—0.25
—0.31
-0.36
-0.37
— o.:}6
—0,32
-0,27
—0,19
-0,11
—0.01
4-0. 09
+0,18
+0.25
//
—0.19
—0.41
—0,38
—0,24
— o.:«
—0,34
—0.28
—0.20
—0.10
—0,01
+0.11
+0. 15
+0.16
//
—0.22
—0.35
—0.37
—0.34
—0.45
—0.38
—0.24
—0.16
—0.03
+0.03
+0.1J9
+C. 17
+0,19
//
+0,06
—0,10
—0,02
+0. 13
—0,02
-0,02
—0,01
—0.01
+0.01
0.00
+0.02
—0.03
—0.09
//
+0.03
—0.04
—0,01
+0,03
—0,09
—0.06
+0,03
+0.03
+0.08
+0.04
0.00
—0,01
—0.06
o
45
60
75
90
1(»
120
135
150
165
180
195
210
225
II
+0,02
—0,30
—0.69
—0.84
-1.03
—1.16
—1.20
—1.16
—1.05
—0.86
-0.61
-0,32
—0.02
—0.05
—0.27
—0.63
—0,77
-0.98
—1.09
—1,24
—1.16
—1.04
-0,89
—0,64
-0,22
—0,01
—0.14
—0,23
—0.60
—0.72
-0.07
—1.14
—1.32
—1.23
—1.06
-0,86
—0.55
—0.30
+0.14
//
—0.07
+0.03
—0.04
+0.07
+0.05
+0.07
—0.04
0.00
+0.01
—0,03
—0.03
+0.10
+0.01
-0,16
+0.07
—0,01
+0.12
+0.04
+0.02
—0.12
—0.07
—0,01
0.00
+0,06
+0,02
+0.15
The lower line of the table is, it will be seen, only a repetition of the upper with the
sign changed. We always have
V w . , . /R+/(R+180O)=0
by the fundamental hypothesis of the investigation.
(63) Values of g z. — Taking the differences of the K's, we have eight distinct values of
8 g.z, the sum of which gives the value of 64 gji, derived from the observation. The mean is
as follows:
+.01
16
+0.14
30
+0.07
46
-0,02
60
+0.08
75
+0.10
90
+0.C8
105
+0,06
120
+0.02
136
-0,04
150
+ 0.02
165
—0.02
Though these values are quite well marked, indicating a twisting flexure coefficient of
0".06, I am not at all satisfied of their reality, and have therefore preferred to dispense with
their use, and derive the telescope flexure for each end of the axis directly from the observations.
(64) Flexure of the Telescope. — The preceding investigation gives the flexure of the circle
divisions relatively to the central nucleus of the circle. We next wish to know the flexure of
the line joining the micrometer wire, and the optical centre of the object glass relatively to
the same nucleus. During the early part of the year 1866, I was greatly trooble4 by finding
a constant difference of a large fraction of a second between the horizontal flexnre determined
from the opposing and that from the levelled collimators. It seemed to follow from this, that
if the axes of the collimators were so*^^ optically in the same line, tbe difference of their level
H
mm
UNITEU STATES NAVAL OB8EBVATORY.
88
9 mean is
errors would not be equal to their d fference nf latitude, m it should be. On April 17, 1860.
this was tested directly, in the following way: The error both of level and coUitnation of each
collimator was reduced as much as possible. The telescope was set vertically, the cube opened,
and collimator A turned till its double wires were horizontal. The shutters were closed, as
usual, in observing the collimators. Three observers were employed; one to read the level
of each collimator, and one to make the images of the horizontal wires coincide. The latter
looking into collimator B, set the wires opposite in each of the four combinations of position of
the collimators, A 90°, B 180°; A 90°, B 0°; A 270°, B 0°; B 180° and in each combinatitm a
set of level readings of each collimator was taken. To eliminate any possible personal error
in setting, the observer then went to collimator A, and the operation was repeated. The result
was as follows:
Mean level of A, (North,) p".87, (8. end high.) .
" " B, (SoQth.) .29, " " •
Dififorence - - •
Oorr. for diff. of collars,
Gorr. for diff. of latitude,
+0" 58 8.
+0 .26
+0 .25
Sum 1".09 ,..,:>..-.„■:.,-' ^ _;■
This sum ought to be zero, so that there is a seeming discrepancy of 1".09. That this is
due to refraction, I entertain no doubt, for the following reasons: (I.) A p-iori; an increase
of temperature amounting to 1** Fahrenheit in two feet, will entirely account for it; and the
actual increase frona the floor to the roof is found to exceed this on a sunny day. (2.) A
few days afterward the observations were partly repeated with the shutters open, and a cold
wind blowing through the room. The discrepancy was 0".61 in the opposite direction. The
images were quite unsteady, and the wind troublesome.
(66) The flexure by the opposing collimators was determined by setting the telescope on
one collimator, and reading the telescope and microscope micrometers. The telescope was then
pointed upward, and the horizontal wires of the other collimator set on those of the first. The
circle reading was then determined for the other collimator, and the telescope again pointed to
the zenith. The first collimator was then set independently on the second, and the two colli,
mators were thus alternately set and read as often as was deemed advisable. The following
are the separate results obtained on different dates:
1865. Dec. 16, /=4-0".15;
1866. Mar. 29,
Apiil 16,
26,
May 31,
Jane 9,
+0 .83,
+ 1
+0
-♦-0
+0
.42,
/'=0".77;
1 .30;
.71, wt. =1 ;
.89. wt. =2;
.49, wt. =:1.
After the first determination the screws of the object end of the telescope tube were tight-
ened. The two next v,ere made without suspecting that the results might be vitiated by re-
fraction, and therefore without attention to the equality of temperature in the different strata
of air. They are therafore rejected. The last three were made with the shutters open, at
times when the int'jraal and external temperatures were nearly equal. That of May 31 was
particularly satisfactory, and depends on four readings of one collimator, and three oi the other,
the separate readings being
N.
48".39
47 .81
48 .12
47 .87
B.
50".77
50 .87
60 .09
mmnm i m mm
fcVti*a!»^,Uiit'WPrt^'ailK«»«S- It'^'V^'ftW
'M DESCBIPTION OF THE TRANSI1' CIRCLE OK THE
The valae of /, concluded from obsttrvHtions of the opposing collimatora. is
0".76.
In the beginning of 1867 the object glass was taken out and cleaned. Gonceiviug a
change in the elasticity of its bearings possible, a careful determination of/' was made on
September 9, 1867. The circumstance taken advantage of to secure equality of temperature
was a cold ruin. Two thermometers were fastened to the stairway below the line from the
object glass of the telescope to each collimator, and two more were suspended just under the
roof. The upper pair indicated a higher temperature of 1°.2 before tho observations, and 2°.2
afterward. The separate readings uncorrected for circle flexure were:
SonthcoU. North coll.
fi'=90O B'b270O
• 14".69 lfi".13
15. 10 15. 18
14. 97 16. 26
16, 43 16. 67
.,^^ 16.61
The readings were commenced on the south collimator. On looking into it to set it on the
north one, preparatory to its second reading, the mean of wires were seen to differ quite sensibly
from coincidence with th«i wire of the other collimator. The first reading is therefore regarded
as doubtful. The result of these readings is
/'=+0".78.
During the autumn of 1866 the levelled collimators were regularly observed at night with
the shutters open, so that the mean result ought to be free from refraction. The result, from
observations made by Messrs. Hall and Rogers and myself, was:
Mean excess of reading for S. collimator, 1".86 ;
, > t Uncorrected flexure coefficient - -
, u^ - Correction for difference of latitude
1, *i «rv difference of pivots -
circle of flexure • -
Resulting coefficient . . - . .
o there is a discrepancy of more than half a second between the flexure coefficients found by
the two methods. The error is probably in that determined from the levelled collimators, the
conical character of their shoulders rendering their results uncertain.
The discrepancy is so great that I think it best to try alio the method of comparison of
direct and reflection observations.
(66) Fertiocd Flexure. — Thus fiir, the coefficient of cos Z has been found only by the method
already set forth, namely, by comparison of the nadir reading obtained from observations of the
collimators, and that obtained directly by coinoidenoe of the wires with their images reflected
from mercury . The observations were so conducted as to completely eliminate every constant
error of the collimator itself, the following b^ing the usual order:
(1) Nadir;
(2) OoUimator B (north);
(3) OoltimatorA(sooth); ' ' '
(4) OoUimator B (soadi);
(6) OoUimator A (north);
(6) Nadir.
.93;
-0
.12;
—
.23;
-0
.37;
- +C ,21.
•Jl
UNITED STATES MAVAL OBSSRVATORT. 99
If. now. eitlier collimatoi' be nifected with any conntHnt cnnse of error wlion on one »ido of
tlie inatrament, lliat canoe will act in the opposite direction on the circle reading when t' o col-
limator is carried to the other side. By interchanging the collimators we therefore eliminate
all constant errors pecniiar to them.
The following are the separate results obttined in this way:
Co
C-g
t
Wt.
Co
C\-f
m.
1865.
II
II
II
t/
tl
Dee. 39
13. S9
13.76
—a 54
8
16.35
15.96
+0.39
3
30
88.34
88.44
-0.10
a
33.61
33.61
0.00
3
1886.
Jan. 30
88.34
88.48
—0.14
3
68.88
68.78
--0.04
3
Apr. 7
84.87
84.96
—0.09
3
18! 43
14.88
•■0.04
- .0. 11
3
16
19.80
80.00
—0.80
3
18.38
.3
17
17. «
17.40
+0.88
3
16.50
16.66
—0.16
3
. J8
1
11.68
11.88
-0.88
3
16.44
16.17
+0.87
3
From which results
g =:-0".U,
^=+0".09.
There must always be a possibility of the nadir determinations being affected with undis-
coverable sources of error, depending either upon the habits of the observer, or the disturbing
conditions to which the instrument may be subjected, as, for example, the heat of the observer's
body. I think it best, therefore, to depend for the final value of gr upon the comparison of ob-
servations made in reversed positions of the instrument, the effect of the cosine flexure being
reversed with the instrument. For the present, therefore, the quantity — 0".14 is regarded
simply as the reduction of an observed nadir reading of circle A to the mean of the horizontal
readings.
' (67) In the flexure of the telescope is included the effect of gravity in changing the posi-
tion of the declination micrometer slide relatively to the fixed plates of the eye-piece. As the
telescope turns, the reading of the- micrometer for coincidence of the fixed and movable wires
is affected with the inequality
— 0r.0876 sfa Z— 0r.0197 cos Z,
Z being the zenith distance of the telescope counted in such a direction that sin Z is positive
when the micrometer head is above the screw, and negative when below it.
The flexures alretidy found being corrected for this inequality, the value of the sine coef-
ficient would be quite small, while that of the cosine coefficient would be increased to 0".44.
(68) In observing tSe sun, the aperture of the telescope is diminished to about three
inches by means of a cap weighing 5.3 ounces. It is found, by experiment, that this weight
causes a flexure of — O'MO fet'n Z. A further flexure correction of
+0M08inZ
is therefore required in reducing observations of the sun.
»»»<««f'ffi-?'*!W,'«B!(S*SW*-M«'^«fl'^»«**w^»'»"
■<^^U<-v4 JJiil! ■ immisiihW'"
S6
L*R8CRIPriON OF THi'. TBAN8IT CIRCLE OF THE
, ERRORS OF DIVISION.
(G9) The readings Cor errors of diviaion of every 5° were made during November and
December, 18()5, before the cummenceraent of astronomical observations with the instrument.
The observers, beside mys«!lf, were Professors Hall and Eastman, and aides Rogers and Thirion.
Each observer rend two microscopes. Any personal error in reading will appear only in the
distance of the microsfopes.
A few readings were tirst taken on the 0° and 90° divisions, with the microscopes 90°
apart, to determine their angle. This, however, is of little importance, since any error, in its
value, is eliminated in the mean of four microscopes, the number always read in astronomical
observation.
To determine the error of every 45°, the microscopes were set 45° apart, and both circles
were read thirteen times in each of the eight positions. Assuming the error of 0° to he zero,
the following are the resulting values of 4e, or the negative of four times the correction for
error of division for every 45°:
* , V''; Circle A. Circle B.
0.00
II
... 0.00
46
-1 19
—2 87
90
-1.12
—0.80
130
-0.67
-0.69
To find the errors of every 15°, two determinations were made: the first being made with
the microscopes 60° apart, the second with the microscopes 75° apart. The circle was read
five times in each position in each series. For circle A another and more exact series was
made with microscopes 75° apart.
The tirst series could not give an independent determination of the 45° spaces, but the
latter did, and small corrections were applied to them accordingly; not, however, with exact
reference to the forniulsB for weights already given. The following are the results:
Circle ▲.
Circle B.
Mic.60.
76° (l«t.)
75° (8d.)
Concluded.
60°.
75°.
Concluded.
o
II
It
tl
//
//
II
II
0.00
0.00
0.00
0.00
0.00
0.00
0.00
15
— 0.02
- 0.81
— 0.18
0.18
- 1.73
— 8.58
— 8.13
30
+ 0.14
+ 0.38
+ 0.36
+
0.31
— 1.07
— 1.48
— 1.86
46
— 1.19
— 1.37
— 1.11
1.19
— 8.93
L- 8.93
— 8.93
60
— 8.89
— 8.81
— 8.88
8.86
- 3.91
— 3.88
— 3.90
76
— 1.86
— 1.79
— 8.05
1.79
- 1.51
— 0.99
- 1.86
90
— 1.18
— 1.13
- 1.18
.^
1.18
— 0.80
— 0.80
— 0.80
106
— 0.68
+ 0.03
— 0.08
_
0.13
- 1.11
— 1.07
— 1.09
180
— 1.14
r- 8.19
— 1.11
1.39
- 1.75
h- 8.3S
— 8.03
136
— 0.67
— 0.76
— 0.68
_
0.07
- 0.43
— 0.43
— 0.43
180
- 0.60
- 1.43
— 8.88
,m^
1.68
— 0.94
— 1.43
— 1.18
166
+ 1.16
+ 1.16
^ 0.90
+
1.08
— 0.13
— 0.86
— 0.19
For the errors of every 5° two series of readings were made; one with a distance of 50°,
the other with one of 55°. Three readings wore made in each po.»ition of the circle in each
series, except the second series of circle B, when only two readings were made. The following
are the separate results. The lust column in each table gives one-fourth the negative of the
mean by weights of the two preceding columns, and is the correction to be applied to the mean
of opposite microscopes on account of errors of division:
UNITED STATES NAVAL 0B8BRVAT0BT.
m
1
Circle A.
Circle B
60°.
66°.
Concluded
— e.
60".
65°.
Conclnded
o
//
//
•/
//
//
ti
0.00
0.00
0.00
0.00
0.00
0.00
5
+
1.44
+
0.89
— 0.88
—
0.86
— 1.06
+
0.34
10
+
1.55
+
1.39
+ 0.37
—
0.99
— 0.76
+
0.88
15
0.17
0.18
+ 0.04
+ 0.86
_
3.08
— 8.13
0.58
80
—
0.93
— .
1.10
—
1.96
— 1.91
0.48
86
—
1.56
—
8.05
+ 0.45
—
1.88
— 8.03
+
0.48
»0
+
0.34
+
0.3i
- 0.08
1.88
— 1.33
+
0.33
35
0.64
0.96
+ 0.80
—
3.77
— 3.07
+
0.78
40
—
1.41
_
0.83
+ 0.88
—
3.19
- 8.63
0.74
45
_
1.19
-
1.19
+ 0.30
—
3.93
— 8.93
0.73
50
1.09
0.08
+ 0.14
,_
3.80
— 3.33
■1-
0.90
55
— .
1.08
—
8.89
4- 0.43
—
3.35
— 3.44
-\.
0.85
60
_.
8.88
—
8.18
+ 0.55
3.98
— 3.84
+
0.97
66
_
8.80
_
8.38
+ 0.56
—
3.47
— 4.06
+
0.9H
70
—
0.88
0.36
+ 0.16
—
3.83
— 3.93
t
0.88
78
_
1.79
1.70
+ 0.44
1.87
— 1.31
0.38
80
+
1.79
+
8.85
— 0.51
_.
O.I"8
— 0.96
+
0.13
85
0.66
0.38
■+■ 0.13
■f 0.88
+
0.84
— 0.91
+
0.06
90
—
1.18
_
1.18
0.80
— 0.80
+
0.30
95
8.05
1.78
+ 0.48
—
1.34
— 1.46
+
0.35
100
—
8.84
—
1.36
+ 0.45
—
1.81
— 0.88
+
0.36
105
—
0.88
— .
0.13
+ 0.04
—
1.06
— 1.04
+
0.86
no
+
0.71
+
0.09
— 0.10
+
0.88
— 0.89
0.01
115
1.09
1.04
+ 0.87
1.33
-1.30
0.3:1
180
—
1.51
—
1.43
+ 0.36
' —
8.07
— 1.96
0.51
185
_
8.86
—
0.90
4- 0.40
-j- 0.48
1.10
— 1.81
0.34
130
—
1.79
_
8.07
—
0.84
— 0.78
A.
0.80
135
—
0.63
—
0.67
+ 0.16
—
0.43
— 0.43
+
0.11
140
+
1.48
+
1.51
— 0.37
+
0.56
— 0.03
0.08
145
0.87
0.08
+ 0.04
0.16
+ 0.10
M
0.08
150
—
1.50
— .
1.53
+ 0.38
—
1.30
- 1.81
^
0.38
155
0.40
0.44
+ 0.10
__
1.19
— 1.41
+
0.33
(60
+
1.61
u.
0.97
— 0.38
0.83
— 0.44
+
0.08
165
0.97
1.09
— 0.86
0.18
— 0.80
+
0.06
170
0.89
0.66
— 0.19
—
0.38
— 0.11
0.07
175
T"
0.87
T"
0.51
— 0.17
"■•
0.88
— 0.78
"T"
0.18
We have here two entirel)- independent determinations of each division error, except
those which are multiples of 16°. The mean difference between the two values of 4« is 0". 52 for
circle A, and 0".4I for circle B. The difference of accuracy between tlie circles arines from
differences in the eye^sight of the observers. It appears then that the probable value of a
concluded e is about 0".065 for circle A, and 0".05l for circle B. The probable error of the mean
reading of four microscopes, when these divisions are under them, will therefore be about
0".046 for circle A, and 0".036 for circle B, a quantity smaller than the probable accidental
error of the isolated divisions. Little advantage would therefore be gained by making the,
determination more exact.
(70) When the mean of divisions, 90° apart, is taken, the progression of the errors in the case
of circle B are so regular that a determination of the intermediate divisions was supposed to be
hardly necessary. But, as circle A was used for all the observations in 1866, it was thought
desirable to determine at least some intermediate points on that circle. Accordingly, the micro-
scopes of that circle were placed at the distance 43°20', and one complete series of readings were
made, which gave the error of every 10°40'. The result ghoived that the errors of the intermediate
divisions were systematicaUy greater than those of the 5° divisions, the mean difference being -f-0". 39.
This was supposed to indicate a cyclical inequality in the error, the period of which was
5°. In order to determine it accurately, it was necessary to determine the error of every de-
gree of both circles. This was done on September 17-19, 1866. The microscopes of each
circle were placed at the distance 48°, and the circles were both read once in each position
Again the result was anomalous, and the cyclic hypothesis bad to be modi6ed or abandoned.
The systematic mean difference between the 5° divisions and the intermediate even degrees
was only 0".14 for circle A, and 0".08 for circle B.
w
f^^
38
DBHCItlPTION OK THE TRANSIT CIRCLK OP THE
mJi
A larit Htteiiipt lo discover the f^enernl liiw of the inequality without the laborioiii) operation
of deterniiiiiiifj; the error of every 10' wus made in January, 1867. The 6° interval wa» di
v'uUn\ into six parts by setting the microscopes of circle 8 44" 10' apart, and this circlw was read
on<!o in each position. The cycle now seemed to be reduced to 30'.
To show the nature of the law the correction for the mean of four microscopes, as it re-
sulted from the above determination, is shown for each circle in the following tt»ble:
_ CIRCLE A.
Correction for
error of diviBion of—
A
A+
A+
A+
A+
A+
A+
A
o
O ; :
o
o
(
o
1
1 40
8
3
3 20
4
II
//
//
//
//
ft
//
--0. 14
+0.08
—0.34 —0.10
-0.05
-0.84
+0.07
5
- -0. 13
+0.10
—0.20 —0.33
—0.40
—0.18
-0.88
10
--0.04
-0.24
—0.56 +0.25
—0.22
—0.23
-0.41
15
--0.04
+0.15
-1-0.02 +0.06
-0.18
—0.18
+0.24
W
--0.08
—0.05
—0.33 +0.14
+0.17
+0.15
-■0.15
•25
+0.35
- -0. 14
-0.17
-0.64 -
-0.08
-0.16
-0.18
■-0.08
:w)
+0.18
—0.14 -
h0.07
—0.25
-0.08
+0.10
- -0. 10
35
■■0,30
- -0. 18
--0.26
-0.14 --0.24
+0.18
-f.0.35
—0.08
40
--0.38
-0.08 --O.IB
+0.02
+0.22
45
--0.23 i-»0,06
-0.44 ;-
-0.10
-0.04
-0.24
-0.25
50
-fl. 12 i 0. 13
-0.45 --0.02
+0.08
—0.30
+0.18
56
-i . 23 04
-0.34 -
-0.15
+0.18
-}-0.20
—0.18
-H).30
GO
-.•0.4S r'..58
-O.07 -
-0.18
--0.10
■■0.04
-H).08
65
U0.33
+0.15
—0.12 -
-0.26
0.00
-0.05
70
-0.08
-0.08
—0.76 ;— 0.18
-0.16
—0.78
-0.16
75
i-'.Of
-0.2('
_-fl.48 —0.29
-0.44
-0.46
—0.18
80
-fl.3i ''.S*
•..E5 —0.40
-0.43
—0.48
—0.29
85
—0.02
--0. !2
-0.39 —0.88
-0.07
-0.85
-H).35
Mean . .
+0.13
+0.02
—0.33 ;
0.00
-0.08
—0.19
+0.08
M.— <)."13
0.00
—0.16
-0.46 —0.13
-0.81
—0.32
-O.U
CIRCLE B.
A
. —
Correction for error of division of—
A+
A+
A+
A+
A+
A+
A+
A+
A+
A
O /
o
/
O /
o
O 1
o
/
50
I ♦
1 40
8
8 30
3
3 20
4
4 10
II
It
//
//
//
It
//
II
//
II
-fO.lO
-0.39
0.10
—0.05
0.18
-0.09
0.11
—0.06
0.06
-0.88
5
.30
.04
— .01
.31
— .06
.08
.85
— .06
.18
- .01
10
.89
- .09
.14
.00
.16
.86
.37
.24
.04
- .05
15
.39
— .01
.32
.34
.31
.40
.10
.14
.39
.14
20
.24
.88
.88
.10
.30
.31
.38
.34
— .09
.01
25
.40
.80
.84
.06
.88
.86
.58
.34
.16
.04
30
.42
.16
.59
.36
.33
.41
.36
.54
.58
.31
35
.53
.24
.37
.46
.46
.31
.38
.39
.04
.16
40
.47
.20
.47
.30
.40
.61
.45
.58
.43
.11
45
.42
.08
.88
.01
.03
.19
.10
.80
.10
.30
50
.41
.30
.85
.16
.88
.85
.81
.19
.88
.16
55
.44
.16
.39
— .04
.35
.84
.15
.18
.46
.89
60
.64
.66
.82
.51
.56
.64
.48
.54
.30
.86
65
.ei
.40
.44
.48
.48
.60
.58
.61
.64
.89
70
.48
.85
.53
.36
.88
.39
.68
.86
.37
.44
75
.18
.80
.48
.06
.88
.00
.86
.11
.86
-.04
80
.10
— .01
— .04
— .06
.40
.80
.15
.88
.88
— .04
85
0.09
—0.48
0.08
-0.88
-0.08
-0.89
-O.06
0.01
-0.16
-0.88
//
tl
//
II
//
//
//
//
If
'ii
MOMI . .
0.36
0.13
0.31
0.16
0.86
0.87
0.38
0.86
0.23
0.09
M.-0'.'36
0.00
—0.83
—0.05
-0.80
~C 10
-0.00
—0.08
—0.10
—0.13
-0.8T
UNITED STATES NAVAL OB8BBTATORY. >< flf
The 8yAtematic irregnlarity is well marked in this table, and HeiMnx to follow the Rnme law
in the two circles, except that it is nearly twice hh great for A a» for B. Two important quoH>
tions now present themselves respecting the nature of the law.
1. Do the intermediate errors really depend upon those of the 5° spaces on each side of
them more than on any other part of the circle? If not, the attempt to determine the errors
with precision might as well be abandoned. Innpection of the above tab^es, however, shows
that for circle B, at least, the question is to be answered in the affirmative; the corrections of
the intermediate divisions increase and diminish with those of the 5<^ ones, and to about the
same extent with the latter.
2. Do the systematic errors of the 5° spaces peculiar to them affect them alone, or is the
law of error continuous? For example, are the systematic errors of the divisions 4° 68' and
5° 2' the same as those of 6°, or are they the same as those of 4° 10' and 5° 60'? If the former, '
the spaces on each side of the 6° divisions will be equal; if the latter, they will differ by half a
second. Twenty pain, of i itervals of circle B — those adjacent to every 16° from 0° to 136°,
and from 180° to 316° — were measured and compared, and the mean difference found to ' e
0".07. The law of periodic error, whatever it maybe, is therefore continuous. It seems
result, in great part at least, from two cycles in the errors of division; the one having a peric?
of 6°, the other a period of 30'.
(71) The course which it seems best to adopt is this: instead of attempting to determine
the errors of division with the last degree of precision, we shall seek to eliminate them by
changing the position of the circles from year to year, so that the poxition of any one star will
depend on different divisions in different years. If the periodic errors be entirely ne;;lected,
the effect of their probable amount, at least in the case of circle B, will be lass than C". I. and
the total probable effect of the difference between the actual and the adopted error uf any iso-
lated error of division will not much exceed that amount. The uncertainty of the moan of
four divisions will, therefore, scarcely exceed the probable error of the declinations of funda-
mental stars derived from all the observations hitherto made.
(72) To obtain a general table of the corrections of the divisions, we have first corrected
the determinations given in the preceding tables for periodic error, so as to take the mean of
the entire degree divisions, those which are a multiple of 6 excepted, as the standard. This
has been effected by applying the following correction;) to the different vertical columns:
Colomn. Circle A. Circle B.
o t It It
A —0.14 —0.19
A+0 60 + .14
A4-1 .00 .00
A+1 40 + .32 -f- .11
A+2 .00 .00
3 +2 30 .00
A+3 .00 .00
A.+3 20 + .16 .00
A+4 .00 . .00
A+4 10 + .18
The corrections are thus reduced to what they would have been had there been no peri-
odic error, and arranged consecutively in a table. The mean difference between consecutive
numbers was now found to be 0".160 for circle A, and 0".136 for circle B, indicating a prob-
able error of each individual determination, combined with the accidental error of division, of
leas than 0".l.
;
;
I
1
40
Tahit ^ rerreetumt to
OESCRIFTIOM OP THE TEAMSIT OIROLK OP THE
(ffjimr mieroieope* fur errort vf divuiom.
microwope.
ArgumefU, mdimg ^ hori*<nUal
Arg.
Circle A.
Circle B.
Aiv.
Circle A.
Circle B.
o
II
(/
o
//
//
+0.18
+0.30
45
+0.08
-0.01
1
+ .06
.83
46
.00
.00
s
.00
.18
47
— .08
.00
3
— .06
.18
46
— .04
.00
4
— .11
.88
49
— .04
+ .06
6
— .17
.87
50
— .04
.18
6
- .10
.87
51
— .08
.18
7
— .08
.86
68
— .88
.18
8
.00
.86
53
— .80
.13
9
+ .04
.87
54
— .16
.14
10
.07
.89
55
— .18
.15
11
.08
.89
56
— .12
.16
IS
.10
.89
67
— .18
.17
13
.13
.36
68
— .18
.19
14
.80
•<<
59
— .18
.80
15
.88
.68
60
— .05
.88
16
.87
.66
61
+ .05
.86
17
.84
.57
68
.06
.86
18
.83
.57
63
.05
.87
10
.80
.58
64
.08
.85
80
.16
.48
65
.00
.88
ai
.17
.49
66
.08
.28
82
.16
.68
67
.09
.88
8:»
+ .10
.53
68
.15
.82
84
-.08
.50
69
.14
.83
85
— .14
.46
70
+ .08
.84
86
— .18
.44
71
-.03
.85
87
— .88
.48
78
— .18
.87
88
— .84
.40
73
- .18
.88
89
— .80
.34
74
— .06
.31
30
— .16
.87
75
+ .04
.35
31
— .83
.84
76
.04
.40
38
— .89
.88
77
.02
.45
33
— .38
.19
78
.00
.46
34
— .36
.15
79
.01
.45
35
— .37
.11
80
.18
.44
36
— .36
.18
81
.16
.41
37
— .36
.15
88
.17
.38
38
— .36
.14
83
.18
.36
39
— .89
.08
84
.19
.36
40
— .88
+ ,08
e&
.20
.36
41
— .17
-.07
86
.23
.40
48
— .18
— .12
87
.25
.44
43
— .06
- .13
68
.25
.44
44
- .08
— .07
89
.19
.37
45
+0.03
-0.01
90
+0.18
+0.30
The correctioua thuB obtained wore now made continaous, and the above table was formed
in the following way. Represent the correction for y° by (Y). Then, for circle A was taken
[1^1- >^ (i)+(l|)+(2) J..
[3H=i<{ (3)+(3t)+(4) ^
&e.t Ace.
[Oj=i'{ [88i]+(0)+[l|] J.,
l«]=H [3i]+(«)+[6|U.
[2J]«H (2)+(3) ^
&.
dee.
&c fcc.
■''^^^^S^SS^f^-y?
UMITBD STATn HAYAL OBSBBYATOBT. m.
The concluded corrections were then interpolated between [0], [[2^]], [6], [[7|]], Ao.
For circle B was taken
[i*]«H (t)+(i)+(ii)+(8) y,
[Sil-H (3)+(34)+(4)+(4j) },
• tcct cbc.
(0]-t^[8^)+(0)+fli]}..
[7i]^u*m]Hn)+m]>.
oCC.t «cc>
The condaded corrections were then interpolated between [0], [2)], [5], [11^], Ac.
In the table the argument is changed 45°, so as to correspond to the reading of the finding
microscope.
ERRORS OF CERTAIN ISOLATED DIVISIONS.
(73) During the year 1866 the circle was so set that when the telescope pointed toward
the nadir, the reading of the finding microscope was 359° 56' . It therefore becomes necessary
to determine the error of the particular divisions then under the microscopes, relatively to
the others. For this purpose microscope YII was furnished by the machinist of the Observ*
atory with two extra pair of spider lines at a distance of, as nearly as possible, 2^ on each side of
the central pair. Each division, from 44° 42' to 45° 8', was then brought in succession under
the middle pair of wires, and at each setting the three pairs were placed in succession over
their corresponding divisions. Thus, two measures of each space were obtained. These
measures, being treated in the way already set forth, gave the following corrections for each
division relatively to the mean of the fourteen divisions from 44° 42' to 45° 8', 134° 42' to
136° 8', Ac:
DlY.
Cor.
Div.
Cor.
DIv.
Cor.
Dlv.
Cor.
Mora.
O '
(/
/
//
o /
II
O '
it
II
44 48
+0.86
134 48
+0.87
384 48
-0.01
314 48
+0.18
+0.16
44
+ .19
44
+ .07
44
— .09
44
— .09
+('.08
46
-.09
46
-.31
46
— .83
46
— .11
—0.18
48
— .06
48
- .01
48
+ .03
48
+ .01
0.00
60
— .06
60
+ .03
60
— .07
60
-.83
-0.08
68
+ -*ih
68
— .04
68
+ .10
68
+ .«
+0.08
64
— .18
64
— .09
54
.00
64
-.86
—0.18
66
- .06
66
— .13
— .81
+ .81
56
-- .09
56
— .08
—0.04
68
+ .36
68
68
-- .40
68
+ .09
+0.16
46
— .03
136
885
-• .04
315
+ .10
+U.08
8
— .08
»
+ .43
8
— .01
8
-.08
--O.08
4
— .86
4
— .03
4
— .11
4
— .14
—0.13
6
— .14
6
— .19
6
+ .04
6
+ .a
—0.08
8
+ .19
8
— .01
a
— .80
H
+0.16
+0.04
TESTS FOR OTHER POSSIBLE ERRORS.
J -
(74) The errors of an instrument may be divided into two clatwes; those which we expect
to find, determine, and allow for in the reduction of observations, and those we expect the
6
42
DBSosipnoif or ths tbariit oisolb op ths
1(*
,. i
111
I* §
artist to avoid entirely, or at least render insenaible. The olaaaifioation is somewhat arbitrary,
depending, as it does, upon the degree of precision sought by the astronomer, and the degree
of excellence attained by the artist ; yet the custom of astronomers has rendered it quite
definite. The errors we have investigated are generally recognised as of the first class; we
shall now consider those of the second.
(76) IrregularUy of Pivot*. — No apparatus fur determining directly the influence of possible
irregularity of pivots upon the axis of rotation was furnished with the instrument, but the
artists did furnish an extremely delicate instrument for determining any difference nf diameters
of the same pivot. It consists of a pair of calipers, which are screwed upon one of the Y
bearers, and grasp the horissontal diameter of the pivot. The telescope being turned, any
change in the distance of the calipers amounting to the two hundred thousandth of an inch
will be rendered sensible by a pair of multiplying levers, the end of the last of which moves
over a divided scale. The telescope being turned through an entire revolution with the cali>
pers on one pivot, no difference of diameters so great as this was detected. Only one pivot
was thus tested.
As an additional test, the hanging level was placed upon the pivots, and read at every 20°
of zenith distance of telescope, from 20° to 160°; the telescope being moved by one of the
west handles. It was then returned by the same handle, and the readings repeated. The effect
of the pressure of the handle in changing the level of the pivot was quite sensible, amounting
to 0". 25 ; but this effect was reversed by the backward motion, and the extreme range of the
mean level reading for different positions of the telescope was 0".05. It was conc'uded that
the form of the pivots might be regarded as perfect.
(76) Another possible source of irregularities in the motion of the optical axis of the tele-
scope at first caused me considerable solicitude. It has been seen in the description that the
fulcrum of the levers of the great counterpoises are not, as I conceive they should be in so large
an instrument, knife edges, but pivots. Owing to the unavoidable friction of these pivots, and
also to the friction of the end springs, the instrument, when balanced by the counterpoises,
will allow changes of weight of perhaps eight or ten pounds without causing motion of the
lever. Consequently, the division of the weight between the friction rollers and the pivots
will be uncertain to this amount. If, now, there bo uny irregularity in the grooves of the axis
by which the friction rollers act on the instrument, this division may vary in different positions
of the instrument, the friction roller acting more powerfully on points more distant from the
centre of rotation. And such a change of pressure will produce a vertical flexure of the axis,
which will change the direction of the optical axis of the telescope. To avoid any possible
error from this source, small pieces of rubber cloth were inserted in the sustaining sockets on
the levers, the elasticity of which would take up any minute irregularities of the kind referred
to, and make the pressure nearly constant.
To test the effectiveness of this contrivance, a piece of thin paper, probably 7^ of an
inch thick, was drawn under the friction rollers, and the effect upon the level of the axis and
the verticality of the teloscope was noted. The former waa not changed at all. The latter,
which was determined by comparing the position of the vertical middle wire, and its image
reflected from mercury, did not admit of exact measurement, as the image was nearly hidden
by the wire. Certainly, however, there was no change as great as 0".S. The paper being
many times as thick as any probable irregularity in turning the axis, there is little danger of
error from the source in question.
(77) Part of the same general investigation was the determination of the effect en'the level
of the axis when the action of the counterpoise was changed from its maximum to its minimum
amount. One pivot being raised from its Y, by pressing on the counterpoise, was gently let
down ngain, and the level carefully noted. It was then pressed downward by pressing the
UMITKD 8TATM NATAL OBSmVATOST
48
oonnlerpoiM upward, and the level again noted. The changes of reading varied from 0".3 to
1".0. They are, I conceive, almnat entirely due to flexure of the Y'a under the weightH of the
"ivots.
(78) Ooincidenre of the Divided Facet <^ the Cirdet with Ptama perpendtcvlar to the Axis of
Botation — There is no error in tbia respect which affects the definition of the divisionH in the
Belds of the microscope, and I have made such measures as to satisfy myself that no appreciable
error arises from the product tan A it, p. 11-12.
(79) Oenercd Bemark. — Beside the above systematic examinations, the instrument is from
time to time in an irregular way examined for every cause which I can think of, as liable to
vitiate the results of observations. Nothing serious has yet been detected.
#.1
*«*
PART IV.
REMARKS ON THB PBRFORMAi^CB AND USB OF THE TRANSIT OIROI.E.
(80) The general design of the inttrament ia entirely that of the makem. Specific direc-
tions were sent them only on a few minor points, saoh as the arrangement of the micrometers,
the self- registering micrometer head, and the wires of the retioale. It was the opinion of
Captain Oilliss, that, considering the repataion and expent.aoe of the artists, he would be
more likely to secure a good instrument by allowing tiiem U carry out their own vIbwh, and
holding them responsible for the performance of the instrument &han by designing it himself.
As a general remark, it may be said that the mechanical execution of every part of the
instrument is of the first order of excellence. I cannot speak with certainty of the object glass,
as it has not been severely tested. Oertainly, however, it has no defect which interferes with
the performance of the instrument. After being transported by land and water a fourth of the
way round the globe, all tli delicate and complicated parts of the instrument were put together
without impediment or dumy, and immediately went into successful operation.
As a knowledge of the defects in design and performance, which we have thus far suc-
ceeded in discovering, may be valuable to astronomers, I shall set them forth.
The only defects of design which can yet be pronounced upon with certainty have already
been alluded It). They are :
1. Making the zenith distance micrometer carry the slides of the ocular, thus causing the
screw to carry too much weight when the head points downwards.
2. The form of the supporting fulcmms of the counterpoise levers.
3. The instability of the collimators and their levels, owing to the small distance (22 inches)
between the supporting shoulders. The only inconvenience which results from this construc-
tion is the increased labor of levelling the collimator.
(81) StabUUy qfthe Instrument. — ^Invariableness of instrumental constants is generally con.
sidered one of the most desirable qualities in a meridian instrument. A deficiency in this
respect, however, need not vitiate the results of observations, if only the astronomer can deter*
mine and apply the constants with a frequency proportioned to the instability of his instrument.
The most precise way to measure and indicate the variableness or uncertainty of the instru-
mental constants is to take the mean difference between consecutive determinations of the con-
stants. This I have done for the latter part of the year 1866, and the results are given in the
following table. During the summer of 1867 the stability of the zenith point has decidedly
improved, the mean difference being reduced to 0".60.
Collimation, October, 1866, to July, 1867 - - • -interval 1 week ■ • - - (K'.23
Level, Jnly to November, 1866 interval 1 to 4 days- -
Level on consecative days interval 1 day • • •
Mean difference of consecative transit of Polaris - - • interval 1 day • - -
Resoltiog mean change of axfmath interval 1 day • - •
Zenith point interval 3 to 12 hours -
Inclination of £. pier ........... interval 1 day . . -
0"51
0".89
3t. 2
1". 6
0". 1
0".65
i
|B |Hi lS 'M'^W l ii i W ' ''M WBtt>^^
46
DK8CR1PTION OP THE TRANSIT CIRCLE OP THE
* .>
If e be tlio meun error of the detormination itself, we raay expect a mean difference of
■\/2e owing (o tiiat error alone, supposing the instrument to remain invariable. The stability
of the line of collimiition may therefore be regarded as perfect, and that of the level error
practically so, if determined for each day of observation.
It is far otherwise with the zenith point and the azimuth. Not only are they variable to
an annoying degree, but the causes of the variations are not definitely determined. Home light
may, however, be thrown upon them.
(82) Zenith Point. — Previous to any trial of the instrument, its most objectionablo feature
seemed to bo the mode of mounting the microscopes, and many astronomers would have pre-
dicted instability from this cause. But the relative positions of the microscopes have proved
unexpectedly steady. The following table shows the amount by which the line through the
zero of V and VII was in excess of 90° from that through VI and VIII, at various dates between
June 29 and September 17, 1866, the longest interval as yet in which the microscopes have
been subjected to no disturbance. They are formed by subtracting the mean reading of V and
VII for the two collimators, from that of VI and VIII, and are therefore the difference between
the nadir points of the circle as given by the two pairs. The dates are taken at random, except
with reference to the observer:
Date.
A.
1866.
•M'^
y&'ik'^'ii--
;'.&}^y:.
June 29,
//
+ 0.05;
29 9.
+ 0.02;
July 2,
-0.12 ;
—0.08 ;
9,
-0.05 :
12.
-0.32 ;
26,
-0.10;
30.
+ 0.30;
Aug. 6,
+ 0.32;
15,
—0.20 ;
20,
—0 28;
29,
+ 0.15;
Sept. 3.
-0.16;
10,
+0.12;
14.
-0.16.
I am persuaded that this degree of steadiness has never been exceeded, so that if the cen-
tral core has been sot in the pier in such a way as m secure immobility, the positions of the
microscopes relative to the pier will be as invariable in this mounting as in any other.
Passing from the microscopes to the circle — the nicety of fit and firmness of connection of
every part, from the divisions of the circle to the ends of the tube of the telescope, is beyond
reasonable doubt.
The constancy of position of the optical axis of the tube is rendered highly probable by the
steadiness of the error of coiiimation. Moreover, the object end of the telescope: has been sub-
jected to shocks several times greater than it ever receives in ordinary use, without any effect
upon the nadir point.
The constancy of the reading of the zenith-distance micrometer head for a given position
of the wires is all that could be desired.
(83) Supposing, from these considerations, that the changes observed must be due to move-
ments of the pier itself, a horisontal cylinder was fastened to it in July, admitting of being
levelled by one of the collimator levels and the changes in the inclination of the pier thus
determined. But the changes of nadir point were still only partially accounted for, and the
correct nadir reading sometimes exhibits a progressive change, continuing through a period of
several days.
T7NITBD STATES NAVAL OBSERVATORy.
47
(84) Apparently, the only untested link in the chain ia the stability of the setting of the
microscope holder (D, plate lY, D-P, plate YI, Fig. 2) into the pier. To insure the solidity
of this setting, a hole was cut from the top of the pier to the perforation which received the
core of the holder, and the plaster poured in until the hol«) was full, when it oozed out on all
aides of the core. The setting is, therefore, as solid as it can be with plaster. It will, indeed,
yield, and allow the microscopes to turn by a strong pressure of the hand ; but under pressures
several times as great as they are ever subject to in observing, the microscopes are not dis-
turbed at all. Still, consi'jering the known hygrometric qualities of plaster; considering, also,
that the relative readings of the microscopes on the two piers are subject to changes of the
same general character and magnitude with the zenith point, I decidedly think that ''^e greater
part of the instability of the zenith point is due to the want of firmness of the plaster setting.
(85) The Azimuthal Error. — 0^ the cause of the variation of azimuth I. entertain little
doubt. The extreme breadth of the masonry on which the piers are supported is only four
and a half feet from north to south. With so narrow a base injurious changes of inclination of
the piers, from motion of the ground and consequent tipping of the masonry, seem to me un-
avoidable. And that such clfanges do take place is shown conclusively by the levelling appa*
ratus attached to the piers. If every part of the masonry tipped equally, the nadir point
alone, and not the azimuth, would be affected. But since the masonry is not perfectly rigid,
this condition would be fulfilled only by the ground giving way equally at each end of the
pier, which we have no reason to suppose the case. The piers tipping unequally, we may look
for changes of azimuth us well as of nadir point. The height of the axis above the centre oK
the pier being three times the distance of pivots, the change of azimuth from the cause in
question will be three times the change of relative inclination of the piers.
(86) In the spring of 1867 a levelling cylinder was attached to the west pier also, and the
difference of tipping of the piers compared with the changes of azimuth. The latter were not
accounted fur, a fact which may be attributable to the imperfections of the apparatus itself.
(87) Dependence of the CoUimation Error on Temperature. — Toward the end of the year 1866
the amount of this error was found to be dependent on the temperature, varying 0".05 for ewery
degree of Fahrenheit. The cause was discovered when the object glass was taken out at the
end of the year. It was then found that the glass was held in its cell by the pressure of three
chucks, 120° apart, two of them being fixed, Aud the third pressed in by a strong spring. The
direction of action of the spring was horizontal. Hence, owing to the different expansibilities
of the brass and glass, the centre of the latter would take different positions relative to the
centre of the former at different temperatures. The calculated change of collimation on the
hypothesis of perfect rigidity of both object glass and cell, is 0".07. The difference between
this and the observed change is probably due to the fact that the spring is not perfectly flex-
ible, nor the glass and brass perfectly rigid.
(88) It is probable that such changes will ultimately be made in the mounting of the object
glass, the microscope holders, and the great piers as may seem sufficient and necessary to
secure greater in>:iiobility of the collimation, azimuth, and zeiiitii point, the instability of the
two latter arising, as has been seen from defects of mounting rather than of construction.
■i,
:::i
-J
i
1
'*■;
wrr
t
■ f
Wi.-
" , *
.£;;
«».ai* ) » « tl - i ) i4i— ^Wii r ut w
■"'■■*•""■■■■
^HSUBtitasuimmtiii-miiiiimlmtii
ALPHABETICAL INDEX.
(THE NU1IBEB8 HEFEB TO TH|^ PABAGBAPH&)
Azb, dataila of
twkt of, daring roTolaUon
teste of ite motion
lorel of, afftcted hj oonntorpoiM. . .
end tprinff of 5.
AiimnUi, amonnt of ite ehuigM..
33
«3
75,76
77
18
80
85
4.21
SI
Cireles, diMnetor anddivisfcwia
owHagof
Law faatenedtoub ao
perpendienlvitjr of, to azie • 78
lawf of floxnre of. 61
table of flasnin.. .4 02
Cirale dirifiona. (flte DiTiakna.)
Clamp, deaoriptionof 89
CSolUmation error, ohanfesof. 81
depead on tamporatare , • 87
OolUmatoia, deseriptionof 37
Y'« of. 38
maj be aet on each otber ^ 5,!i4
difforenoea and form of eoUara of 63
diacrepaneiea o^ due to refica^ion 64
reoaaaaafor pladng 1
Connterpdaea, action of. „ 13
aflact level 77
posaible bad ellitet of, bowteatad 76
Cube, oantial, of axia S4
Deaignof tba inatmmant, Uatory and defcota of „ 80
Diviaiona of eireia, number and thtckneas 91
formula for wrofa '60,51
errora of; iaoiated 51-73
table for evei7 6C< 69
10 78
cjoUeal, inequality of. 70
bowteatad 71
Bnma, general pncaotion againat 79
inatnuHintal, table of inrtabUity of 81
Eya-fieoe, dewsription «rf 86-88
Flwnre . 39
f hnd a mant al hypotberia in Inireatigattng 40
geaatal tbaomnof 4i
requititH for determining 48-45
of drda, apedal invaatigation of 60
e b awrved lawaof 61
tabloof 68
of t a l ae e ope, general metbod ^ 48
preeautiona in daterminiog 40,64
produoad b7 ann oqt 08
vertteal, or ooaine 48,66
"M
3
i
■W^
50
ALPHABETICAL INDEX.
^f 3
Flazureof dedinAtion micrometer snppoiti., 07
twisting, of (uii * 63
Floor, level of , 9,11
IlluminatioD, lamps for 34
of the field 38
ofthewirea on dark field 36
of mieroeoopes » • 10,34
Lerela, tpirit, valne of divisioiu ..i 6S
Level error, cbuigei of 81
Micrometer, general deacription of ■erawi 39
declination, how moved 89
Bogeri'B Mlf-registering head df*
periodic ineqoalitiee of..... « 66
- value of ravoiation of 67
irregularity of motion of 66
right aacension, deacription of 96
revolution, &o., of 69
wireaof. (SMWirea.)
of nticroacopea. (8m MicroscqMa.)
Mioroacopea, at^a for obaerving ....« <...... 8
mounting of » • 14
a^jnatment of focua * ••• 16
illnmiMtiou of 16,34
dimenalona and power 17
relative ateadineas of , ... 88
probable uuateadineaa of holder 84
micrometera of • 64
deacription of Uwir pwiodic iaeqoalitiea 66
of their irregnlaritiea 17
Nadir point, platform and aeata for obaarving ..«. 6,7
Object glaaa, aperture of •. 3
mode of mounting 87
Piera, form, material, and dimenaioua. ^ 8
aupporting maaonry of. 10
changea of their inclination 81,83,86
Pivota, teat of their form • 78
dimenaiona of. --.. 19
Powera, magnifying, of oculars 31
B^lroad, for reversing carriage 11
Ejection observations, faoilitiea fi>r making 6
Befraotion, atmospheric, inimical to flexure inveatigatiou 49,64
Room, dimensions of. •- J
details of - »
Stability of instmment, tables of. , 81
Telescope, dimenaiona of ^ - 3
Wirer, of declination micrometer • 80,33
of right asceaaion micrometer 87,38
of microscope micrometers >•. '• 17
fixed, of diaphragm, how carried • 88
ufiangemant uid notation • 38
how used in observation 39
Zenith point, changes of 81,88,84
••>« ^ ' ''iti'trm^nn u timim iimMMmiUlimm
•••MWMMMMMiMtMil
Hi.^g i l i
-.■» .-'iv
er
63
9,11
M
M
»
16,34
68
81
»
»
66
67
68
96
60
L-- *
8
14
16
16,34
17
8i
84
54
66
17
6,7
3
87
S
10
»,83,86
75
1»
it
11
6
49,64
)
9
81
3
«U,33
87, 3S
17
88
88
39
U,88,84
iif'.' " -'^«^*"3i; ,,
' rJ.
'-'*^f.-;-\'/, '■
■■■ .-■^-
•^.
*mt<utiMtitiA>
U.4^4.
W. Baumann deJ.
■ .^-
^1
^Ip^^^^f^p^
3r
M^^^^^^M
£
PLATE I
vy,- / -. -
m^
iiiui^iMiiiiui^UJdm^
■A
T
"1 ; i. Jtiii
=*==»=
■^ ! -
4*=
^
m.
^
Scale of fi>el .
■»<-f -:''^M« » '• S; ■ -t-rj*-;..
•v-r'-;-
Si-
<^6Kondrui) £<tt|^.
i»^
fr^wW'' ♦**%«'•«•» -i.i'-iCf-f
\V RrturnanTi del.
Scale of Vert.
HATK II
■-■^»T4f ilhUuBPi I I ilMMw.nniii,|^
i-^^^-Jw., .
|3
-:1' ■
J.CJCbndntp Biigr*
'■■rtV^''^*S^-. ■^■^^
^i^
WBaumaim del
IM.ATK 111
J.C.Kaiidrup Eng^
"WBRumaiui del.
m¥
f ' fMll in i.i Bumiw Mi W B nj M L i i i
IM^ATK IV:
J.C.Kondriip Engl"
> ^ 'Ww »WB i jlnil l MiWli n i0. t lM
^
WiSnunuum del.
i - i
J
J.r Kdiidi'i-t) Kiigf'
yf-^i^ mnaimmmim iwiiiWiiiimiwiiaimi[iif(iiiiiniiji.B)i ^i.m
■•■kw,-»„L'i-i*>-:5a,,^,j.y.L3i*>>;,^iiii. K^-.i~--
«•«!••*■*«•■ !ir
S
Bamsi*r°tiO> Philaila
/__»[) ^__..^j1J\ 1
^
W baumjim <i»-l
.IV Kniidriij' K1151''
:' . ,^\
-Stew
'.V ,\«iimmn\ ili'l.
1 IV
iL,;;-^{{» »
f«iito* • •■*>'««»»•
:i-ism,^>'----"'-»--~'~^''''--^''-'-f^'itMX.A.^-,.--A^»t,m.fm^ i.,-4i--™.:'- '