MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES

Volume X!

WASHINGTON
1911

2 7 f 1

CONTENTS.

MEMOIRS.

Page.

1. The absolute value of the acceleration of gravity determined by the ring-pendulum method, by Charles E.

Mendenhali 1

2. Clayton hi Gronov. A morphological and anatomical study, by Theodore Holm 25

3. A research upon the action of alcohol upon the circulation, by Horatio C. Wood and Daniel M. Hoyt 39

4. Phoronis architecta: Its life history, anatomy, and breeding habits, by William Keith Brooks and Rheix-

art Parker Cowles 71

5. The affinities of the pelagic tunicates, No. 1: On a new Pyrosoma, by William Keith Brooks 149

6. Commelinacese. Morphological and anatomical studies of the vegetative organs of some North and Central

American species, by Theodore Holm 157

7. Tables of minor planets discovered by James C. Watson, Part 1: Tables of (93) Mini rva, (101) Helena, (103

Bern, (105) Artemis, (115) Thyra, (119) Althaea, (128) Nemesis, (133) Cyrene, (139) J a, (161) Atlior,

(174) Phaedra, and (179) Klytaemnestra, by Armix O. Leuschnek 193

in

ILLUSTRATIONS

Plate 1. Finished steel ring for use in ring pendulum 24

2. Milling machine arranged for grinding the steel ring shown in plate 1 24

3. Comparator used in ring-pendulum experiments 24

1. Fig. 1. CI a allium parvifolia __ 38

2—4. ( 'laytonia megarrhiza 38

5-6. Clayton in sarmentosa 38

7. Clayton in chamissonis 38

8. Clayton ia. diffusa 38

2. Fig. 9. Claytonia megarrhiza 38

10-18. Claytonia virginica 38

19. Mont in rivularis 38

1. Result of experiment upon a dog, using Ludwig's stromuhr 70

2. Result (if experiment upon a dug, using Ludwig's stromuhr 70

3. Result of experiment upon a frog's heart, using Williams's apparatus 70

1-5. Phoronis arch itecta 116-124

6-10. Actinotrocha 126-134

11. Actmotroclin and Phoronis architecta 136

12-17. Phoronis architecta 138-148

1. Dipleurosoma elliptica Brooks 156

1. Commelina nudiflora L 192

2. Commelina virginica L. and Tradescantia rosea Vent 192

3-4. Commelina nudiflora L 192

5. Commelina nudiflora L. and Commelina hiriella Yah] 192

6. Commelina nudiflora L., Commelina hirtella Vahl., and Commelina virginica L 192

7. Commelina hirtella Vahl., Commelina virginica L., Tradescantia rosea Vent., and Tradescantia

virgin ica L 192

8. Tinantia anomala (Torr.) Clarke, Tradescantia war, eidcziana Kunth and Brouche, and Weldenia

Candida Sehult. fll 192

Figure 1. Diagram illustrating calculation of the vibration of a perfect ring 4

2. Diagram illustrating calculation of radius of equivalent "simple ring" pendulum 5

3. Diagram illustrating calculation of effect of flaws in ring pendulum 6

4. Diagram illustrating calculation of effect of flaws in ring pendulum 7

5. Diagram illustrating calculation for errors of figure in ring pendulum '■<

6. Diagram illustrating calculation for errors of figure in ring pendulum 10

7. Diagram illustrating calculation for errors of figure in ring pendulum 11

8. Diagram illustrating calculation for azimuth error in ring pendulum 12

9. Diagram illustrating determination of temperature coefficient of ring in ring pendulum 16

10. Diagram illustrating variation in diameter of ring in ring pendulum 16

11. Plan of piers, pendulum case, and scheme of illumination in ring-pendulum experiments 18

12. Diagram illustrating method of making azimuth adjustment in ring pendulum 19

1. Kroneker's apparatus for measuring action of alcohol upon the isolated reptile heart 56

2. Williams's apparatus for measuring action of alcohol upon the isolated reptile heart 57

3. Wood and Hoyt's apparatus for measuring action of alcohol upon the isolated reptile heart 60

v

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

Volume X.

FIRST MEMOIR.

WASHINGTON':
GOVERNMENT PRINTING OFFICE.

1905.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

FIRST MEMOIR.

THE ABSOLUTE VALUE OF THE ACCELERATION OF GRAVITY
DETERMINED BY THE RING-PENDULUM METHOD.

BY

CHARLES E. MENDENHALL,

PROFESSOR OF PHYSICS IN THE UNIVERSITY OF WISCONSIN.

PRESENTED TO THE ACADEMY BY ROBERT S. WOODWARD.

89369°— vol 10—11 1

THE ABSOLUTE VALUE OF THE ACCELERATION OF GRAVITY
DETERMINED BY THE RING PENDULUM METHOD.

The use of a ring- pendulum for the determination of the absolute value of the acceleration
of gravity was first proposed by Dr. T. C. Mendenhall, who in 1S98 presented to the National
Academy of Sciences a brief report of some preliminary experiments made by Prof. A. S. Kim-
ball at the Worcester Polytechnic Institute. The use of the method as an ordinary laboratory
exercise in the physics department of the institute (in charge of Professor Kimball) had shown'
that even with rather roughly constructed apparatus results were obtained agreeing well with
each other and with the approximately known value of the constant at that point. It seemed
desirable, therefore, that a careful examination and test of the method should be made, since the
importance of a knowledge of the value of this constant is so great and the known methods of
determining it are so few that any process which may serve as a check upon these methods can
not fail to be of value. Accordingly a grant from the Bache fund of the Academy was made to
Dr. Mendenhall by the trustees of this fund to enable him to procure the apparatus necessary
for a more exacting test of the method. During the two succeeding years some preliminary
work was done under his direction by Dr. Edward Rhoads at the Worcester Polytechnic
Institute, consisting mostly of a study of some points relating to the theory of the method and
the design of a part of the apparatus. Dr. Mendenhall being at that time unable to give
further attention to the investigation, it was placed in my hands; the material turned over to me
consisting of the unfinished pendulum case, and some notes by Dr. Rhoads, to which I am glad
to acknowledge indebtedness. It is only, however, at intervals during the past two years that
the work has been under way, the greater part of this time having been devoted to the comple-
tion of the pendulum case and other accessory measuring apparatus, and more especially to the
completion of the rings.

Geometrically, the ring pendulum is a figure bounded by two plane parallel surfaces and two
concentric cylindric surfaces whose axis is perpendicular to the plane faces, and it is to be vibrated
on a knife edge resting on an element of the inner cylindric surface. The relation between the
dimensions of the ring, the period, and " g" is quite simple, the most interesting point being the
existence of a particular ratio of the inner and outer radii which makes the period depend only
on the value of the outer radius; that is, the period is very insensitive to changes in the inner

radius. This ratio, =^3" is one which gives a very deep, and hence a very rigid, ring. For a

convenient coincidence interval of about 6 minutes (with a one-second clock beat) — that is, a
period of about Is. 003 — the external diameter should be about 28. *5 cm. and the inner 16.65 cm.
The ring can be swung from any internal element and by so doing irregularities of density or
figure, not otherwise easily discovered, can be detected and their effects to an extent eliminated.
This matter will be discussed more in detail later, but the above considerations are enough to
suggest the three points on which the desirability of the ring pendulum method will certainly
depend, namely:

I. A definite and easily observable length to measure — the external diameter of the ring.
II. The great rigidity of the pendulum, hence but slight departure from its measured figure when suspended.
III. Detection of, and partial correction for, nonhomogeneity of pendulum.

3

4 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

It is evident, however, that any nonhomogeneity or figure error which is symmetrical with
respect to the center of the ring can not be detected by observations on the period; hence the
necessity of comparing results with a number of rings. With this in mind, five forgings for
rings were obtained, of which one was broken during construction; but on account of the great
labor involved in making a finished ring, only two have been completed and used.

What has been said as to the simplicity of the theory is also true of the measurements
involved; the difficulty of the problem lies in the construction of the ring. But before taking
up this, it will be well for the sake of reference to consider the following:

1. The vibration of a perfect ring, that is, one having no irregularities of figure or density.

•2. The effect of "flaws" in general.

3. Special cases of nonhomogeneity, and error in figure:
(a) Nonparallelism of faces.

(f>) A particular case of irregular density.

(c) One face conical.

(d) Inner edge conical.

4. Effect of error in adjusting the plane of the ring at right angles to the knife edge.

1. PERFECT RING.

[After Kimball. 1

Let:

Then:

Fig. 1.

R=external radius.
r= internal radius.
M = mass of ring.
T= period of vibration around P.
p, f, =density and thickness of ring, which may lie assumed unity.

I0= ^(R*— >•*) = moment of inertia around O.

Ip = I0+7t(R2 — r)r2 = nioment of inertia around P.
= |(R2-r) (R2 + 3r2)

= 1JVI (R2+.V).

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL.

Differentiating with respect to r:

But if

the period will be independent of /'.
which gives the condition —

2TfT= 4«f» *1
dr \_2g &gr _\

dT

dr'

W

=0

or

2g 2;//

R2 = 3r2

[By noting the effect of putting r=0 this condition is seen to be that tor a minimum value of T].
Introducing this relation above we find —

Ip=MRs=3Mr»

T=2^

Rx/3

RV3 is evidently the length of the equivalent simple pendulum.

It is also useful to know the radius of the equivalent "simple ring" pendulum— i. e., a
linear ring concentric with the real ring, and vibrating (by means of a massless support) around
the same point of suspension (P) with the same period.

In this case:

and:

By hypothesis:

or

4 R

Fi

g- 2.

IP = 27rr

,3 + 2;

T' = 2tt ,

2+_Rl
3

/

V

i;

T' = T.

= R8

'=&■

6

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

Such a ring could be added to or taken from the perfect ring without altering the period;
hence any symmetrical system of tine lines or graduations could be made on the ring at the
distance /•' from the center without sensibly altering its period.

The degree to which the period of a perfect ring is independent of /■ when the relation
R = v/jjy is nearly satisfied is shown by the following computed values of T for a constant R and
varying r.

R= U.413 cm.

ff=980.

r= , 8cm.31
T= Is. 00567

Is. 005669+

8cm.33

Is. 005671-

It is evident from this that it is a very easy matter to satisfy the relation R=v/3> with suf-
ficient accuracy.

2. THE EFFECT OF FLAWS, OR SMALL IRREGULARITIES IN DENSITY, ON" THE PERIOD OF THE RING.

[Rhoads.]

Suppose a Haw of magnitude J/// located at the point /•,, 9 (fig. 3), and let this Haw produce
a change AT in the period T of the otherwise perfect ring.

Then:

(1)

Fig. 3.

T-f-JT = 2^

'An<r~ + Jinr'i

\ g(mr-\-rt cos 6 Am)

(2)

Aw

3rH — -n
m

i Am, ...

'/{'■+ /\ cos H)

(3)

= 2w/

gr(l+ 5 — cos 9)

(4)

-T 'uJ'i Am\~Ti n~\

-TM1+J-m7lfr-cos0J

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL.

(5)

(")

(7)

1 r\ -li"\~i\_

2 r in |_3/'

cos 6

AT_1 r, Amfr,
T

This may be written:

1 r, AmTr, 1

■9 r ^rLsr" COS "J

*t= fs cos 0 ±A/:

t^ cos^-24^ j;;J

which is the equation of a family of circles (or circular cylinders), the variable parameter being
-fwc a—; that is, a given flaw m will produce the same change in period T if located anywhere on
one of these circles. The distance of the center of these circles from P is evidently:

D=j£rlii_0+rli,_irJ=jj»'

JT

The condition that -?p- = 0 gives rt — 3r cos 0 as the equation of the locus of a flaw which will

have no effect on the period. This is evidently a circle tangent to the inner cir lumference at P;
if Am is positive and located insidt of this circle it will decrease T; if outside, it will increase it.
A question more to the point is that of the resultant effect of a number of flaws for different
positions of the knife-edge.

It will simplify matters to transfer tne origin to the center of the. ring, using the variables /'
and <f>, which are determined by:

/', cos d— r-\-r' cos (j>

/\ = \/r''2+r'i+2?'' cos
Making this substitution, equation (6) becomes:

z/T_l A

m [-2+[0+? COS<* "

8 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. N, NO. 1.

Now let there be a number of flaws Jnix. Jm.,. dm3, .... whose position is determined by
the radii /, p" and the angles t,. ea, which these radii make with a diam-
eter fixed in the ring, which, in turn, makes an angle a with the vertical line through the knife-
edge. We should then have, if

t=24T

is the resultant change in period produced by all the flaws:

- _/,//,/(•<>* (r,— «) + J,//(/'cos ((',, — a) + . . .)

or. if-

A=2Jl/nr'cos e,
B=2-J1////,'sin el

-T^tan'1 x

We have-

4 = A \24mr'2-2 2Am- l n/A2+Bscos(«- r)~]

The effect of the flaws is then in general to produce a certain change in T which is independent
of the position of vibration (i. e., of the angle «) and in addition a change dependent on this
position. As is otherwise evident, for any S3'mmetrical distribution of flaws, A = B = 0 and the
change in T will be independent of a. If at the same time —

\2Jmrri = 22Jw
r

the constant part of the change, t, will also be O; and this determines the radius of the equivalent
"simple ring" previously deduced from other considerations.

3. SPECIAL CASKS OF NONHOMOGENEITY AND ERRORS OF FIGURE.

In order to the better interpret the behavior of the actual rings, it will he well to consider
a few special cases of departure from a perfect ring which, on account of the method of making
the ring, are especially to be guarded against. The first of these is the matter of nonparallelism
of the side faces, which is equivalent to the addition of a wedge-shaped ring to a perfect ring.
Exactly the same effect would be produced by a special case of nonuniform density — i. e.,that in
which the density varied as the distance from a plane tangent to the outer circumference of the
ring. The method of procedure has been to determine the period of the " ring and wedge," for
three positions, thick edge up, thick edge down, and one of the symmetrical positions with thick
edge to right or left. By comparing these periods with that of the perfect ring, the effect of a
given wedge as to both the " constant " and " variable" changes in the period can be determined.

VALUE OF ACCELERATION OF GRAVITY— MEXDEXHALL.

9

Let-

t — thickness of ring.
At = maximum thickness of added wedge.
Jin — mass of added wedge.
A\v = moment of inertia of added wedge about P.

Then-

Similarly-
Also —

Am _ 1 At

m ~ -2 t

JI,= JI0+J„/[(| + /f-(-|)2

At

= 0.692 MR2 -j putting R = V3 r
JIP. = 0.307MR2-^

•In 1

I+^Iy

l\l (Mr+Amk)g
(Where h=r distance from P to center of gravity of wedge)

J/

= 2711

= T,

Rx/3 (1+0.692 -t

~~A~t
27(1+0.788 -j)

Similarly

1 + 0.692 -j
1+0.788 -j

At
1+0.307 -j

~~A~t
1+0.230 —

10

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. XT NO. 1.

At . .

If we assume as a special case , =0.001, that is, for the actual ring At=\bn, approxi

mately. the above expressions become —

TV- = 0.999952 T

TV= 1.000039 T

From which

TV -TV = 0.0000S6 T

^(T'p + P'p) = D.999995 T.

Also for either symmetrical position in which the thick edge is to right or left, we have,
neglecting terms of second and higher orders in

MR (1+ap

^1>

=T.

T in all these expressions being the period of a perfect ring having the same outer and inner
radii as the imperfect ring under discussion. The above conclusions will be of interest in
connection with the experimental results later discussed. They will, of course, apply equally
well to the special case of nonuniform density before mentioned, where the increment of
density at a point ■/■', 0, is given by

Ap'=^(R-7-' cos 9)

Ap being the maximum increment in density (at the bottom of the ring in this case); in the final

Ap Af

result — would appear in the place of - above.

Another error of figure which must be especially guarded against is that shown in figure 6,
one face being symmetrically conical; here, if Am is the increment of mass
and Al the increase in moment of inertia about Pdue to the added conical ring,
we find

4

and

Am .At
=0.54—

in t

f=o.*f

1+0.6

At

from which

If

T'=T'

l-|-0.54-

At

At

Fig. 6.

= 0.0001

(At=1.5M)

T = 1. 000006 T.

Even a systematic error in thickness as small as this could be detected and corrected in the
course of construction.

VALUE OF ACCELERATION OF GRAVITY— MENDEXHALL. 11

Irregularities in the outer radius must be determined in each case and their effect computed.
Irregularities in the inner radius are of no importance (except as they affect the amount of con-
tact on the knife edge) unless they result in making the inner surface conical, and hence forcing
the rine to swing out of its own plane. In this case if we consider a thin lamina of the ring, it

will evidently he equivalent to its elliptical projection upon the vertical plane; and for small
values of a (tig. 7), since the external diameter is supposed uniform, all lamina^ will be equally
affected and it will suffice to consider a plane ring whose —

external major axis (horizontal) =2R.

external minor axis (vertical)=2R cos a.

internal major axis (horizontal) = 2—-=.

v 3

internal minor axis (ve rtical) = 2— - cos a.

v3

If
I'=the moment of inertia of this equivalent elliptical ring:

I =the moment of inertia of a corresponding circular ring about a normal axis through P
we find

r n , a ., \

y = COS K ( o + o COS (( J

and

— vs-Vi%l^

M75'

V

1,2 ,
o+o cos" a

If. as a special case, t=15 mm.

// ,.=0.001 mm.
Then cos (7 = 0.9999998

12

MEMOIKS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

and the resulting error in T would be much less than

1

Even an error in /• two and

1,000,000
one-half times as great, which could be easily detected, would produce a negligible error in T.

Other special cases, such as abnormal density throughout a certain segment of the ring,
have been computed, but the results are of no particular assistance in discussing the experimental
data, and therefore need not be given here.

4. THE AZIMUTH ERROR.

Thei-e remains to consider onl}' the azimuth error — that is, an error in adjusting the plane of
the ring at right angles to the knife edge. (Rhoads.)

Fig. 8.

Consider a ring lamina of thickness dt (normal to its plane), and radii R and /'. To determine
its period of vibration around an inner circumferential axis making an angle n with its plane.
The moment of inertia of the lamina around a central axis will be:

*V/7(R4-/-4) (l+eos2«) = Ji„

The complete ring will be made up of a number of such laminae, which will not. however, be
symmetrically situated with respect to the axis of rotation.

The moment of inertia of the complete ring about the central axis will be:

Io = ^r(l+cos2«) (R*-y*) J2 dt+'lrrp {W-r) sin 2a j ' t'dt
= ^-fc(Ra-^)r(2-Sins«)(R2+^)+|sin^].

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL.

13

About ii parallel axis through the inner circumference, we have:

Ip = I„+ //(/•'■

anl

unci, if we put /';-KK'-

:f|RS+3^+|(|-RE-

, /R2 + 3r2+^-R2-r2Ysin

t«=«wv w —

/r2 , f-iR1 . t
T«=T ^/l3

[Since R2 = 3r2J

4 • ,
- sin" «

12

*~± sin2 « +
24

:T(l

)

Iii the actual rings K=0.0113 [about J so that:

T« = T (1-0.166 hr + a )

From which expression the following table of changes in the period (4T) produced by various
errors in azimuth has been calculated:

a

3'. 5

8'. 4

17'

34'

1° 7'

JT

0s. 00000016

0s. 0000010

0s. 0000041

0s. 000016

0s. 000066

Evidently if « can be made less than 8' in practice, the azimuth correction will be quite
negligible.

CONSTRUCTION OF THE RINGS.

The first question in the matter of construction is that of choice of material. Obviously the
material should be of a hardness comparable with that of agate, of which the knife-edge is best
made: homogeneous, free from slow changes in shape, having a definite temperature coefficient,

i i ..• Young's Modulus

and a large ratio: - — gen3ity

Probably the ideal material would be fused quartz, and next, properly annealed glass; but
the difficulty and expense of construction with either of these would be much greater than with
the tool steel actually used. Troubles with permanent magnetization which might perhaps be
anticipated with a hardened steel ring have not been found, and of course the finished ring can
I >e demagnetized if necessary. Uncertainties as to the degree of homogeneity and permanence
of form which could be obtained with this material could only be settled by trial.

Owing to the mechanical difficulties of the work and the necessarily exacting conditions, no
manufacturing mechanician could be found who was willing to undertake the making of these
rings, and it was therefore taken up and completed at the -University of Wisconsin. On this
account it will, perhaps, be desirable to devote somewhat more space to the matter of construction
than would otherwise be done. The finishing of the glass-hard ring must, of course, be clone by
grinding, and during this process the ring must be so held as not to distort its figure and, at the
same time, in such a way that the inner and outer cylindrical surfaces and one face can be

14 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

finished without in any way disturbing the adjustment of the ring on its .support; otherwise
errors of eccentricity, etc., would be likely to occur.

Two forgings of '"Crescent special" tool steel were obtained from the Crucible Steel Company
of America and two of a special self-hardening steel from the Westmoreland Steel Company of
Pittsburg. A fifth forging of phosphor bronze (the hardest available nonmagnetic metal, unless,
possibly, some nickel steel) was also obtained, it being intended to vibrate this with a small agate
plate interposed between the ring and the knife-edge; but only the first rough work has been
done on this. With a view to getting greater homogeneity all of these blanks were made so
that more than one-half inch of material had to be cut away at the center and rim, and one-fourth
inch from the faces, this, of course, being done with the annealed ring before hardening.

The hardening of such a large piece of metal is not a simple matter, and, indeed, one of
the "Westmoreland" rings cracked quite in pieces shortly after hardening; however, the other
Westmoreland and one "■Crescent" ring were successfully hardened. After a little preliminary
grinding to remove the "skin." the rings were artificially aged by several days' "tumbling" in
an ordinary foundry rattler, and being heated and cooled through about 100° C. A little further
grinding proved the mechanical arrangements then available to be inadequate and the rings were
laid aside for nearly a year while the grinding facilities were being improved: this gave them
time to assume a more permanent condition.

The funds at command did not permit the construction of a special grinding machine — so a
small milling machine was rigged up for the purpose. The general result may be seen in plate 1.
Profiting by the first experience, a solid spindle head was built, having a heavy vertical axis run-
ning in conical bearings and carrying a large horizontal face plate, (^reat care was taken as
to the accuracy of the bearings, the proper support of end thrust and the relief from belt strain.
This self-contained spindle head was mounted on the milling machine carriage, and could be given
at will a vertical, in and out. or transverse horizontal motion with respect to the grinding wheel
which was rigidly fastened to the top of the milling machine. Projecting from the top of the
face plate were three hardened steel lugs (on which the ring rested), the tops of which were first
ground until coplanar. Around these lugs, between the ring and the face plate, was a flat zig-
zag of insulated wire, waxed to the plate below, and having on its upper surface small lumps of
wax which projected above the plane of the steel lugs. After the ring had been put roughly into
position the wire would be heated electrically, and the whole mass of the ring slowly warmed
until the lumps of wax softened and stuck to the steel; the ring would then be centered, tempo-
rarily held in position by clamps bearing immediately over the lugs, and left to cool. Mounted
in this way the ring was held very solidly and at the same time three surfaces were exposed for
grinding. Of course before all this the spindle carrying the ring had been adjusted with great
accuracy to be respectively parallel and at right angles to the two motions of translation which
were to be used in generating the cylindrical and plane surfaces; it having been found before by
test that these two motions were themselves near enough mutually rectangular. The degree to
which various "taper" effects could be avoided was not, however, limited to the accuracy of
these preliminary tests and adjustments, for by means of weights and springs the relation of
various parts of the machine to each other could be altered during the grinding and any tendency
to cut "taper" minimized in this way. It is true that by so doing irregularities and tremors
were doubtless introduced which would have been absent with a properly constructed machine,
but with the arrangements at hand this was the best that could be done. Of course the design
of the several linear constraints on a milling machine are not at all what would be chosen for
work such as this, but by careful manipulation very satisfactory results were obtained.

In finishing a flat side, the surface was tested after every cut with a standard straightedge,
and the high spots were taken off on the next cut; these finishing cuts could not be measured,
but were probably about .1/'. In a similar way watch was kept for possible taper in the inside
hole, and no systematic variations in the inside diameter as great as 0.002 mm. were allowed.
After the surfaces were finished the ring would be turned over and again waxed down; failure
to be properly seated on the three steel points would be detected by the first cut or would be

VALUE OF ACCELERATION OF GRAVITY— MENDEXHALL. 15

shown by subsequent micrometer measurements. Such measurements showed that when tin-
lshed, there was with one ring- a maximum difference of about 0.001 mm. in thickness between
extremities of a diameter, and considerably less than this with the other. All the grinding was
done wet, and though chatter marks due to vibration of the machine were never eliminated, still
they were uniform and fine and the general surface had a surprisingly high polish (see pi. 2).
Though the process here described was slow (it took, with the unavoidable interruptions, about
a month to "finish." a ring), it proved capable of giving rings of sufficiently accurate figure for
the purpose in hand.

MEASUREMENT OF THE KINGS.

As before stated, measurements of internal diameter and thickness were made only with ordi-
nary micrometer gauges, care being taken about temperature disturbances, hut for the determina-
tion of the external diameter a special comparator was constructed. A few words will sufficiently
explain the points considered in its design (pi. 3). Since the general plan was to make contact
settings on the ring, these to be directly compared with a line-standard meter, the essential fea-
tures of the instrument are: A rigid end stop; accurate ways, on winch slide two carriages, one
(intermediate) carrying the ring (with its plane horizontal), the other a second end stop, and a
microscope focused on the standard bar. The one carriage has a transverse slide carrying the
ring, for the purpose of adjusting it so that its center is in line with the two stops. The support
is furthermore so arranged that the ring can be rotated around a vertical axis through its center
and perpendicular to its plane and to the ways (for testing "roundness"); and a vertical, linear
motion along this axis is provided so the diameter may be measured at various points from face
to face. The construction is such that to a sufficient degree of accuracy the plane of the ring-
is parallel to the ways and to the line of the contact points. The end stops are round steel rods,
hardened and ground, two sets of actual contact surfaces being provided, plane and spherical
(radius 4 inches). The practice was to have a spherical end abut against a plane face. There is
a chance for a constant error to enter here, in case the contact pieces are not symmetrical with
respect to the same axis, i. e., do not touch the ring and each other in the same way. Therefore
some measurements were also made with two plane faces abutting against each other, and. since
they agreed to within the limit of error with those made with one plane and one spherical surface.
it was concluded that this constant error was negligible. In general, "touch" contact was used
in bringing the ring against the fixed stop and electrical contact (single dry cell and volt-meter)
in bringing the moving point against the ring and against the fixed stop. The electrical method
is more delicate, but the other is quite satisfactory. During the observations the ring was
protected quite thoroughly by asbestos and cotton, and its temperature was given by two ther-
mometers resting directly on the upper surface.

Standard meter. — This was a new nickel-steel bar (H form), by the Geneva society, which
had just been calibrated by the National Bureau of Standards, Washington; the corrections
determined by them have been applied to all measurements. The temperature coefficient of the
bar is so small that no very special precautions were necessary to control its temperature under
the conditions of this work. In getting the final corrected value of the diameter, however, the
proper correction was applied to reduce the bar interval for the temperature at which it was
calibrated (15.9° C.) to the temperature of the measurements (23c ('.); this involves a slight
exterpolation of the temperature coefficient as given by the Bureau (for the interval 10 C. to
20° C), but no serious error is in all probability introduced thereby. The observing microscope
was of Geneva society construction, with micrometer eye-piece and objective illumination. The
micrometer screw was, unfortunately, not a very good one, but by using a group of one-tenth
mm. intervals, into which one millimeter space on the standard was divided, these being evaluated
by careful comparison with each other and with a known millimeter, it was possible to avoid
using any great interval of the screw, so that uncertainties from this source were very greatly
reduced.

16

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

The measurements made with this comparator may be grouped as follows:

1. Measurement of various diameters to test the

24

28

22

21

20

0.9

Fig. 9.

i
i
i

1

1
1
1
1

Expansion

of

Ring II

k

1
1

i
1
I

1
1

/

1
1
1
1
i
1
I

9j

1
1
1

1
1

1
1
1

i

28.849cm

roundness" of the ring. No variations
as great as 0.001 mm. could with cer-
tainty be detected, and the rings were
therefore considered round.

2. A series of measurements of a
single diameter of the rings at several
temperatures to determine the tem-
perature coefficient. It was not pos-
sible to work over a very large range
of temperatures, but the agreement of
the results is quite satisfactory, as can
be seen from figure 9. From figure 9
the uncorrected values of D, for the
standard temperature (23° C.) have
obtained, and in a similar way for Dr

3. Measurements of diameters at
various points between the two faces.
Differences were here found in each
ring ranging over about 0.01 mm., due
undoubtedly to errors in the vertical
guideways of the milling machine.
The following figure 10 shows the dis-
tribution of these variations, the quan-
tities plotted being differences in diam-
eter and the corresponding position

on the ring. A sufficiently exact allowance for these irregularities has been made, as follows:

Consider the actual ring as made up of a perfect
ring with a certain small mass, the irregular rim,
added:

Let d)n=this, small additional mass.
M = mass of actual ring.

H = minimum external radius of actual ring.

K = R+JR = radius of gyration of Am about the center

of ring.

J'R = an increment of R such that

R+ J'R = radius of a perfect ring equal as to mass

and moment of inertia to the real ring.

Then:

1.-.

,■

•^

A

Fig. 10.

■

-

Variation in diameter

1"

*

Ring I

•

Ordinates, 1 div.-l mm.

j

Abcissae, 1 div. = .002 mm

k

5

•■

\

O

.

■"

moment of inertia of the actual ring=s(M— Am)R.2-\-AmK."

= 3MR2

-|z////R2

= |mR8+^»iR2

-zb»R2-M-////RJR

[Neglecting terms of second order in Jm and JR.

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 17

Hence, to determine ^'R, we have

j;.M(R+J'R)2 = ^MR2+gJ///R'-
and —

A nt
The ratio y can be found by the aid of the graphical construction figure 10; in this way

the corrections ^'R, and J'R„ have been found, which are to be added to the minimum values of
R, and R2 to give the effective radii of the rings.

In all the length measurements it was the custom to make five or more successive contacts
and readings of the moving contact against fixed contact; the other carriage and ring would then
be put on the ways, and five or more contacts and readings taken of ring against end stop and
moving stop against ring; the ring would then be moved and another series of contacts taken of
stop against stop. In case the primary object happened to be to measure diffen noes in diameter,
zero readings (stop against stop) would be less frequently taken.

MEASUREMENT OF THE PERIOD.

The pendulums were swung in a brass air-tight case (see figure 11 page 18) on an agate knife
edge of 120° angle. This was given its final grinding and polishing by Mr. E. G. Fisher of the
United States Coast and Geodetic .Survey, whose kindness I am glad to acknowledge. A coinci-
dence method was used for comparing the period of the pendulums with the beat of the standard
mean solar clock of the Washburn Observatory, kindly made available by Prof. G. C. Comstock.
The arrangement was as follows: on the flat face of the pendulum toward the observer were etched
eight very fine radial lines about 3 mm. long, symmetrically distributed at intervals of 45°, and
at about the distance (2 cm.) from the outer circumference where, as determined above, their
effect on the period would be a minimum. Thus, while one line was immediately over the knife
edge, the opposite one was vertically underneath and executing the longest possible linear arc of
vibration. This line was observed with a telescope of considerable magnifying power, and was
brilliantly illuminated for an instant once every two seconds. This was very simply brought
about by the use of the flash apparatus belonging to one of the United States Coast and Geodetic
Survey one-half second pendulum outfits, loaned through the courtesy of Superintendent Titt-
man. The horizontal slit of the apparatus was periodically opened by the clock circuit, while on
the slit was focussed the horizontal image of a Nernst glower, in such a manner that the beam
afterwards fell upon the etched line on the ring. The linear amplitude at the beginning of a
swing was from S to 9.5 mm., and at the end from 3 to 5 mm.; with the magnification used, the
coincidence of the etched line with the cross wire of the telescope could lie determined with ample
accuracy. The times of coincidence were noted on a chronometer whose rate with respect to the
clock was followed closely, and all intervals reduced to clock seconds. Finally, from observations
for which I am indebted to Professor Comstock, the mean rate of the clock was determined and
the corresponding correction applied. As the observations extended almost continuously over a
period of more than two weeks, it is safe to say that diurnal variations of clock rate do not affect
the result.

Further points to be considered in connection with the determination of T are —

1. Adjustment of the ease and pendulum.

2. Temperature corrections.

3. Amplitude corrections.
1. Pressure corrections.

5. Corrections for vibration of the support.
1. The principal adjustments are to have the knife edge horizontal and the plane of the
pendulum at right angles to it. The leveling of the edge was tested with a 5" level supported on
80.369°— vol 10—11 2

n.

<^> — i

w

^

J.

Q}

T3

a
-

SB
S

18

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL.

19

the knife edge and reversed. The azimuth adjustment was tested by means of a similar level,
pivoted, and provided with a glass contact point which rested against the face of the ring over
the knife edge (see tig. 12). Evidently if the ring is not at right angles to the knife edge, a rota-
tion of it around the edge will result in a motion of the level bubble; and a simple calculation
shows that this device with a 5" level is more sensitive than is necessary to enable one to adjust
to within the limits (± 8') indicated as desirable in the discussion under theory. After the ring
was adjusted two stop screws (S, S,. fig. 11),
rigidly fastened to an axis fixed to the bot-
tom of the case, were swung into position
and set until they made simultaneous con-
tact with both sides of the ring. They
served to locate permanently the correct
plane, and the ring was always tested with
respect to them before and after each _ Line of
swing.

Mechanical arrangements were of course
provided for lowering, raising, and starting
the pendulum from outside the case, and
these operated without at all displacing the
ring from its proper position.

•2. Temperatun correction. — From the
pendulum formula:

Vnz^

J_L

( o )

rr

T2=KR

Fig. 12.

find:

AT

ffjer

_/~

s±

where 6 is the coefficient of thermal expan-
sion of the ring, and JT the small change
in period produced by the small changes in
temperature Ad. Using the measured co-
efficient of expansion for the two rings, the
values of AT have been calculated. There
were two thermometers in the pendulum
case, one near the bottom of the ring, the
other above the middle, and as they usually
differed by less than u. 1° (_'.. the mean (of
their readings at the beginning and end of
a swing) was taken as the temperature of
the ring.

3. Amjilit'iil, correction. — At the begin-
ning and end of each set of observations,
the double amplitude was measured and the
reduction to an infinitesimal arc obtained by graphical interpolation from the usual expression:

W

T

[jk (">

,u <", + ",)"-

I
L92

(«,-

,,]

The initial half amplitudes were about 1 12' and the final averaged about 35'.

■i. Pressun correction. — The average pressure inside the pendulum case during observations
was about 1 cm. of mercury, at which pressure corrections for buoyancy and entrained air are
negligible.

20 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

5. Correction for the vibration of the support. — The correction for the vibration of the knife-
edge support was determined by the method of Schuman." For this purpose the two rings were
supported side by side on a steel knife edge, which took the place of the usual agate one. One
pendulum, the "driving" one [Ring I] was given a vibration of about the usual amplitude, the
other, the "driven," having been brought to rest with the greatest care; and the operation con-
sisted in measuring the gradually diminishing amplitude of the driving pendulum and the grad-
ually increasing amplitude of the driven one. The period of Ring I was first adjusted by means
of small attached weights to agreement with that of Ring II to within 0s. 00002, and it was so
arranged that one of the etched lines on Ring II, and a tine wire attached to Ring I, could be
simultaneously observed with a high power telescope, and the amplitude measured with a micro-
meter eyepiece. These amplitudes, measured at known intervals of time after the starting of
Ring I, were found, when plotted, to be linear functions of the time. According to Schuman, if:

Wx, Sir],= amplitude of the driven pendulum at times tl and /.,.
$,, $2 = simultaneous amplitudes of the driving pendulum,
T= half-period of the pendulums.
ar=apparent lengthening of the driving pendulum on account of the

we have

vibrations of the case,

R-1MII

The values of Wand 4> were determined at an interval f.2 — £1=2408. by graphic interpolation
from the direct observations, and the following computed values of a obtained:

cm.

1. Top of pendulum case off. . . a= 0. 00063

2. Top of pendulum case off. . . «= 0.00065

3. Top of pendulum case on. . . a— 0. 00074

4. Top of pendulum case on. . . a— 0. 000756

To determine the corresponding change in period, we have, if—

T = observed period
T' = corrected period

T^27r^— l +g Ta

=T'+0.02«.

Hence, using the mean value of a with "top on" it is found that:

JrI\ = 0s. 0000150

To determine the corresponding correction for Ring II, /?, we can write, according' to
Schumann,

Q—a ';wn*'nliigu

miSiTi^i

where ?//,,///u = inasses of pendulums.

.s1.vH = distances of center of gravity from point of
support.
Ti,Tn= periods.
ei,*n= constants which depend on the form of the
pendulums and the support.

"Schumann, Zeits. f. Math, und Physik. 44 Jahrgang, pp. 124 to 126.

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL.

21

In the present ease it will be safe to assume:

and

So that

Sn_Tn_£n
*i _Tx -«,

= 1

— — = ratio of thicknesses,

111!

_14.2

l.vi

A T„ = 0s. (1000136.

For the determination of T the pendulums were allowed to vibrate uninterruptedly for from
six to nine hours, according to circumstances, a few coincidences being noted at the beginning
and end of this period, from which the coincidence interval and the period could be calculated in
the usual wa}'. Each ring was vibrated in eight different "positions," that is, with the. knife
edge bearing on eight different elements of the internal surface, corresponding to the eight
etched lines above referred to. The following tables summarize all the determinations of T for
both ring's, together with the corrections and reductions.

King I. — Mori mum ruriutioiis of opjioxU,x about 0.0000^6.
[Radius=14cm.409044. Thiekness = 15,mu.40.]

Date

Posi-
tion.

Mean
ampli-
tude.

Pres-
sure.

mm.

mm.

July 16 ..

1

6.20

11.5

July 19 ..

1

6.70

9.0

July 16 ..

2

7.00

20.0

July 19 ..

2

7.50

3.5

July 25 ..

2

5. 30

12.0

July 17 ..

3

7. GO

11.0

July 19 ..

3

9.80

7.0

July 20 ..

3

5.40

8.0

July 23 ..

3

6.05

10.0

July 24 ..

3

5.90

10.0

July 17 ..

4

7. Ill

10.0

July 20 ..

4

5.30

00.0

July 21 ..

4

6.20

7.0

July 25 ..

4

6.50

8.0

July 25 ..

4

3.70

11.0

July 17 ..

5

6.50

10.0

July 21 ..

5

5. 50

10.0

July 18 ..

6

5. 90

10.0

July 22 . .

6

5.70

24.(1

July is ..

/

6.50

S. II

July 22 ..

7

5.70

8.0

July 18 ..

8

6.50

8.0

July 23 ..

8

6.30

8.0

Duration of

swills;.

5 l_'«i 28

S 44 III)

4 11 00

5 33 00
ii 53 mi

8 15 00

4 29 411

9 59 00
9 44 00
9 16 00

3 56 00
9 42 12

5 33 00

7 03 00

4 03 00

6 31 00
9 50 00
9 53 00

10 06 00
6 35 00
9 49 00
6 31 00

8 37 00

Temper-
ature.

23. 15
23. 80

2:;. 45

23.70
23. 13
23. 10
23. 60
23. 30
22.70
2.".. 10
23. 30
27.90
23. 20
22. 50

22. 50
2:;. 65

23. 10
23. 40
23.20
23.60
23.05
23.80
22.85

Reduced

Weight.

i observed

Reduced

tn inli-

T.

to 23° C.

nites.

are.

1

L. 002508

2507

2504

1
1

2518
2525

2513
2523

2509

251!)

1
2
•>

2502
2509
2515

2499
2509
2515

2496
2496
2511

1
2

2
•>

2539
'j;,( IS
2493
2491

2536
2506
2493
2490

2527
2504
249"

2488

2

247H

2474

2470

1

2496

2496

2495

2

2457

2456

2453

3

2485

2488

2485

•>

2473

2476

2475

1

2476

2473

2470

1

2491

2491

2489

1

2474

2472

2470

1

2453

2451

2450

2

2449

2446

2445

3

2466

2466

24U4

2474

2469

2466

2501

2502

2499

Mean for !
eachposi- op]

2507
2507

2502

2476

2493

2483

2479

247!)

2480

2460

245D

~24S3"

Mean of all
positions.

1. 002483

Corrected

for clock

rate.

1.002432

Final corrected period=ls.0024165.

22 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 1.

Ring EL— Maximum difference {T6—Ti)=0.000875.
[Radius=14om.42580; thickness=14""".21.]

Posi-
tion.

Mean
ampli-
tude.

Pres-
sure.

Duration of
swing.

Tempera-
ture.

Observed
period.

Reduced
to 23° C.

Reduced
to infi-
nites,
are.

Mean for
each posi-
tion.

Mean of Mean of all
opposites. positions.

I lorrected for
clock rate.

1
1
2
3
3
4
5
6
7
7
8

mm.
6.0
7.0
6.5
6.5
6.0
6.0
5.6
6.5
7.0
6.6
6.2

mm.

9.0

1.2

8.0

10.0

13. 0

8.0

9.0

8.0

8.0

10.0

10. 0

h. m. s.
9 9 43
4 13 00
6 32 00
9 2s 00

6 48 00

7 2. 00
9 24 00
4 30 00
4 11 00
6 35 00

11 07 00

22.70
22. 50
22. 20
22. 70
22. 70
22. 30

22. 30
22.60

23. 00
33. 20
22. 45

1.002979
2966
2941
2972
2947
3083
3163
3219
3187
3173
3106

2981
2969
2946
2974
2949
3037
3167
3221
3187
3172
3109

2979
2965
2943
2971
2947
3035
3165
3218
3183
3169
3107

2972

3068

1.003071

1. 003020

294:;
2959

3080

3067

3035
3165
3218
Ml 76

3071

3107

Final corrected period=ls.0030069.

The first thing to be noticed is the much greater variation of T for different positions, in the
case of Ring II than Ring I; for Ring II the range being 0a.000275, and for Ring I, 0S.00005,
the latter being of the same order of magnitude as the accidental variations between individual
determinations at the same point. In both cases the variation with position is quite regular, a
minimum T on one side corresponding to a maximum at the opposite point, with intermediate
values between as would be expected; and it is very noticeable that the means of the periods
for diametrically opposite points agree almost as well for Ring II as for Ring I. The large vari-
ations for Ring II were quite unexpected, for its behavior in the course of construction had not
suggested that there was any great difference in the material at different points; and it would
seem probable that a difference in density which would produce the observed differences in
period would result in a difference in hardness or texture which the grinding wheel would be
sensitive to detect. The existence of actual flaws or crevices is unlikely, since the ring was
originally forged. Errors of figure which would produce these variations of period are:

(1) Eccentricity of inner and outer circumferences.

(2) Ellipticity.

(3) Nonparallelism of faces.

It is certain that neither (1) nor (2) i* present in sufficient magnitude to produce the observed
effects; (2) would have been detected by the direct measurements and (1) would have shown in
grinding.

As before stated, the faces of Ring II were slightly out of parallel, the maximum difference in
thickness being less than 0""".OOl; whereas, it was shown above that a difference of 0""".01 would
produce. onhr about one-quarter of the maximum observed difference in period, and would be
equivalent to a regular change in density in which the maximum variation in density was one

Ap
P '

one-thousandth of the mean density, i. e.

=0.001. One is apparently forced to the conclu-

Ap._

sion that Ring II is nonhomogeneous and that the ratio -- is, perhaps, 0.004. It should be

added that the ring was examined with a flip coil and a ballistic galvanometer, but no magnet-
ization was detected.

The calculation of the effect of a special case of nonuniform density (see p. 10 above) showed
that though the maximum difference of period for different positions might be considerable, the
mean period would differ by less than a tenth of this amount from the period of the correspond-
ing perfect ring; and also showed that (for the special case considered) the particular pair of
diametrically opposite periods (so to speak) which are equal to each other are, to a close approxi-
mation, equal to the period of a perfect ring. However, without knowing more about the real

VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 23

cause of the irregularities in Ring- II, it is impossible to draw any conclusions as to the magni-
tude or even the sign of the collection which should he applied to the observed period, and the
best that can be done is to take the mean.

To determine <j we have then the following corrected values:

K,

■ 14,409044:

T,

1.0024165

R,

= 14,42580

T

L. 0030069

r/U)

^'.iso.526

g CD

'.'so. 511

From these

Considering the irregular behavior of King II these values are in very satisfactory agreement.

The results of this work can be taken, it is hoped, both as throwing light on the reliability
and practicability of the method and as furnishing a new absolute determination of g, though in
order to compare the value here found with previous results, either the ring pendulum must be
swung in Washington or a relative determination made between there and Madison. It is
believed, however, that the work demonstrates:

(1) The possibility of making glass-hard rings of steel of sufficiently accurate figure for
the purpose.

(2) That some rings show a very satisfactory uniformity of period for different positions.

(3) That even where considerable asymmetry exists the mean period corresponds very
closely to the period of the corresponding perfect ring.

(4) That different rings will yield extremely concordent results.

(5) Finally, that with rings prepared with the degree of precision which has been attained,
the method will be valuable as a check upon determinations of gravity made by methods
hitherto in use.

In conclusion, I wish to acknowledge my indebtedness to the University of Wisconsin for
the facilities accorded for the work, and to Mr. H. G. Fisher, mechanician of the department
of physics, for faithful and painstaking assistance in the construction of most of the apparatus.

August, 1904.

Memoirs N'at. Acad. Sciences, Vol. X.

Plate 1.

FINISHED STEEL RING.

Memoirs N'nt. Acad Sciences, Y<>1 X.

Plate 2.

MILLING MACHINE ARRANGED FOR GRINDING.

-~-v

2

3)

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

Volume X.

SECOND MEMOIR.

WASHINGTON:
GOVERNMENT PRINTING OFFICE.

1905.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

SECOND MEMOIR.

CLAYTONIA GRONOV.

A MORPHOLOGICAL AND ANATOMICAL STUDY.

BY

THEODORE HOLM.

PRESENTED TO THE ACADEMY BY GEORGE L. GOODALE.

25

CLAYTONIA GRONOV. A MORPHOLOGICAL AND ANATOMICAL STUDY.

By Theo. Holm.

(With plates 1 and 2.)

I. CLAYTONIA AS A GENUS.

A glance at the literature and a consideration of the species themselves must necessarily
convince even the most critical systematic that Claytonia, as heretofore defined, can not possi-
blv be confounded with Montia, nor Montia with Claytonia. They both have been excellently
described and seemingly well understood now for at least a century and a half.

Sometimes the accumulation of new material with additional new species may alter the
views of the systematist in regard to the proper limitation of some genus, but this has not been
the ease with Claytonia. From the skillful treatment of such eminent systematists as Fenzl
and Gray, the genus has been received and explained as it always was, and has, of course, been
kept separate from the monotypic Montia. Though by no means a large genus, indeed rather a
small one, Claytonia represents an assemblage of species of marked variation in habit but with
the floral structure principally the same. As classified by Gray," the species are divided into
five sections based upon characters derived from the vegetative organs mainly: Euclaytonia,
the large-rooted C. megarrhiza, C Virginica, etc.; Limnia, the fibrous-rooted annual or peren-
nial C. Sibirica, C. perfoliata, etc.; Alsinastrum, the stoloniferous ('. Chamissonis; Naiocrene,
the bulbiferous C. parvifolia, and finally Montiastrum, the leafy-stemmed and alternate-leaved
annuals C. diffusa and C. linearis, of which the latter is, furthermore, distinct by the flowers
having the petals obviously unequal, but unguiculate as in the other species, and by the number
of stamens being sometimes reduced to only three.

While thus the vegetative organs exhibit a very pronounced variation in Claytonia, the
floral structure appears essentially the same. The position of the calyx leaves is the same in all
the species enumerated by Gray, the anterior covering the posterior. The petals are always
prominently unguiculate and more or less coherent at the very base; their relative length may
be somewhat different within the same flower, as noticed in C. linearis. The stamens, normally
five, are inserted near the base of the petals, and finally the ovary is ovoid, bearing a long style
with three short branches, papillose only on their inner surface. It will be seen from this that
the flower of Claytonia throughout the genus — from Euclaytonia to Montiastrum, inclusive —
shows the same diagram, and that the modification sometimes observable in the relative size of
the petals and in the number of stamens does not disturb the primary arrangement of the indi-
vidual parts of the flower.

It is now surprising to see that, notwithstanding such uniformity in floral structure, Claytonia
lias in late years6 been divided and a number of its species been referred to Montia, with which
they have nothing in common. Here again the literature and a renewed examination of Montia
would have shown what Montia is and how correctly it was described and understood by Linnseus.
Let us then recapitulate some of the most essential points in the flower by which the monotypic
Montia differs from " all the other genera of the order Poi'tulacacese.'''' The exactly opposite

"Proceed. Am. Acad., New Ser., Vol. 14, 1887, p. 278.

b Synoptical Flora of North America, Vol. I, 1895-97, p. 272.

27

28 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 2.

arrangement of the calyx leaves, the posterior of these covering the anterior;" the somewhai
zygomorphic, gamopetalous corolla with the three stamens inserted at the apex of the corolla tube;
the turbinate ovary with a minute style and three long, subplumose stigmata. Having advanced
these brief remarks upon the generic characters of Claytonia and Mbntia, we might now pro-
ceed to describe some morphological and anatomical points in Claytonia, and, of course, we
receive the genus in the same way as it was understood before and outlined so well in the works
of Gray, Fenzl, Jussieu, Bentham and Hooker, Exgler and Prantl, etc.

II. THE INFLORESCENCE.

The aerial stems are in Claytonia nearly always terminated by an inflorescence, usually pre-
ceded by one pair of opposite leaves, which by Wydler and Eichler have been defined as fore-
leaves; the flowers themselves are mostly destitute of such foreleaves, but there are species in
which one of these, the fertile, is readily visible as a minute bract, especially in the lower por-
tion of the inflorescence. Frequently the foreleaves are the only leaves of the aerial stems, but
in some few species the stems are quite leafy from the base to the inflorescence in C. Chamis-
aon/'s Esch., where the leaves are opposite, while in C. linearis Dougl. and C. parvifolia Moc.
they are alternate.

In regard to the inflorescence, this is of the cymose type, but seems never to be regularly or
completely developed in our genus. It sometimes begins as a very regular cyme, but the lateral
ramifications soon turn to monochasia of the type cicinnus or scorpioid cyme, as described by
Wydler*. Most complete is the cyme perhaps in ('. Sibirica L. ; the stem is terminated by a
flower, and a lateral inflorescence is developed in the axil of each of the two prophylla. The one
of these lateral inflorescences may continue this regular cymose ramification at least at intervals,
while the other, usually very soon, turns to a monochasium; nearly all the flowers are in this
species provided with one of the two foreleaves (the fertile), but they are relatively small,
especially in the monochasia. A like composition of the inflorescence may also be observed in
C. sarmentom Met., but in most of the specimens examined of this species a few-flowered
scorpioid cyme seemed to be the typical. In large specimens of C. linearis Dougl.. the inflo-
rescence begins as a cyme, but the lateral branches become immediately leafless monochasia of
the same type as described above; in small specimens, on the other hand, only one prophyllon is
developed, and the inflorescence consists only of one or four flowers representing a true
monochasium.

Partly a true cyme and partly a scorpioid cyme is the inflorescence of C. megarrhiza Parry
and ('. arctica Adams; an apparently regular cyme is to be found in C. Chamissonis, Esch., at
least in the lower portion, but while the one lateral branch becomes a four or five flowered leaf-
less monochasium. the other most frequently develops as a long vegetative shoot. In the other
species which we have examined a scorpioid cyme is the only kind of inflorescence represented,
mostly with the secondary prophylla entirely suppressed, as in C. Virginica L., C. Caroliniana
Michx., C. asarifolia Bong., < '. parritfora Dougl., C. lanceolata ■ Pursh, C. gypsqphiloides
Fisch. et Met., (\ spatkulata Dougl.. and C. arenicola Hend. ; the last species possesses long,
many-flowered monochasia in which all the flowers are provided with a prophyllon. In C.
parvifolia Moc. the inflorescence has only very few flowers, since the one of the two lateral
branches, as it seems, constantly develops into a vegetative shoot; this species is, furthermore,
peculiar by the two opposite prophylla being developed only as minute, hyaline, and scale-like
leaves, besides that the numerous stem leaves subtend small bulblets, which are said to fall off
and to develop new individuals.

"Almquist S. Om blomdiagrammet hos Montia (Botan. Notiser 1884: 156, and Botan. Centralbl. 21:91. 1885).
The fruit and the seeds in Moulin, as well as the mechanism by which the seeds are ejected, is carefully described by
Professor Urban (Jahrb. hot. Garten Berlin 4:256, 1886).

b Flora, 1851: 348.

CLAYTONIA GRONOV.— THEO. HOLM. 29

III. THE MORPHOLOGICAL STRUCTURE OF THE SHOOT.

The primary shoot represents a monopodium in nearly all the species. The main axi.s hears
in these only leaves, which are always green and developed as proper leaves; it is from the axils
of these that the flower-hearing- stems develop in the first year, when the species is an annual, but
much later if it is a perennial. A rhizome is often developed and in a very different manner,
which depends not only upon the structure of the rhizome itself, but also upon the structure of
the root system. The species of Claytonia exhibit altogether a striking diversity as far as
concerns their mode of growth, and it is strange to see how differently certain species behave in
this respect, although they are otherwise to be considered as near allies. A classification of the
species from a biological view point must, therefore, result in the separation of related types, at
least in some instances.

These biological types may be arranged as follows:

I. ANNUALS.

A. — The shoot ia terminated by an inflorescence (C. linearis Dougl., C. diffusa Nutt., C. dichotoma Nutt.).
B. — The apex of the shoot is vegetative, represented by a rosette of leaves ( C. Sibirica L., C. arenicola Hend.,
C. perfoliata Dow., (.'. parrijloni Docgl., ('. ijypsophil.oides Fisch. etMsy., C. spathulata Dougl. ).

2. PERENNIALS.

C. — As B, but with a fleshy, horizontal rhizome and filiform secondary roots (C. asarifolia Boko. ).

D. — As C, but the rhizome is very short and slender, and bulblets are developed in the axils of the stem leaves.
I ( '. parvifolia Moo).

E. — Monopodial, as those above (from B to D inclusive), but the rhizome is erect and short with a very large
root, the primary (('. Yirginlca L., C. Caroliniana Michx., C. lanceolata Pursh, C. rnegarrhiza Parry, ' '. arctica
Adams).

F. — Monopodial, with stolons above ground and slender root ( C. sarmentosa Mey. ).

< i. — Not monopodial, with filiform roots and stolons underground, i iften terminated by bulblets. ( ( '. Chamissonis
Esch.).

Seven well-marked biological types are thus characteristic of these eighteen species of
Claytonia. Let us examine these a little further.

Among the annuals, ('. linearis Dougl., C. diffusa Nutt., and ('. dichotoma Nutt., it
appears as if the primary axis becomes continued into an inflorescence. We use the expression
"appears" since the material which we have examined was not quite sufficient or satisfactory for
this purpose; moreover, only dried specimens were at our disposal. The larger specimens were
profusely branched in the first of these species, and the true ramification could not be made out
beyond that the leaves were all alternate and that there was no trace of any basal rosette, so
very distinct and readily observable in all the other annuals of the section B. In some small
specimens the cotyledons were still preserved, and they were linear and above ground. Only
two inflorescences were developed in these specimens, and from the same height, and either were
both axillary and pertaining to the cotyledons, or the one was axillary and the other one terminal.
The latter explanation seems to be the more probable, inasmuch as there was no evidence of any
rudimentary terminal bud. However, a renewed examination of fresh material may prove the
opposite.

All the other annuals which we have examined possessed a rosette of leaves from the
axils of which the flower-bearing stems had developed. The primary root is long and slender.
Claytonia Sibirica L. belongs to this category, but it appears as if this species also occurs as
perennial, judging from a note in Gray's paper cited above. This author states that it is "a pure
annual when it grows in exsiccated soil, but when better nourished it is more enduring and bears
offsets on stout stolons from the crown, and so, in the absence of much winter's cold, its life is
continued and extended from year to year." We have not been able to secure any material that
showed such modification, but it is interesting to know that a perennial form does exist of this
species, and that it is stoloniferous; in certain other genera and of remote orders similar per-

30 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 2.

ennial and stoloniferous specimens have been recorded of species that are otherwise typically
annual."

The next large group (2) comprises such species as are typically perennial, and the first of
these, C. asarifolia Bong., possesses a horizontally creeping and quite fleshy rhizome, the apex
of which bears a number of large leaves with axillary inflorescences. The primary root has van-
ished and is replaced by many filiform secondary ones, which proceed from the very short
internodes of the rhizome. A like but much more slender rhizome is developed in C. parvifolia
Moc, a species that is very characteristic by its alternate stem leaves and by the presence of
bulblets in the axils of these. The bulblets resemble very much those of Dentaria iulbifera,
Saxifraga cernua, etc. (PL 1, fig. 1.) We now pass to section E, in which the rhizome is
vertical and very short, but in which the primary root sometimes attains an enormous develop-
ment. To here belong ('. megarrhiza Parry. < '. Virginica L, and their allies. Of these the
former is the most remarkable of the genus. The very small seedling (PI. 1, tig. 2) has the
cotyledons raised above ground by a short but very distinct hypocotyl (H in rig. 2); the primary
root (R) is long and very slender with a few ramifications, densely covered with root hairs. At
this stage two leaves, succeeding the cotyledons, are already visible, and the plant is now ready
to meet the first winter. The first sign of change in the equipment of this little plant is the
loss of the cotyledons; thereupon follows a gradual wrinkling of the hypocotyl, by which the
apical bud becomes pulled down beneath the surface of the ground, and the root continues its
growth vertically and to a very considerable depth. In the following spring the leaves develop
and form soon a small rosette, while the hypocotyl and the basal portion of the root has com-
menced to increase in thickness; lateral, slender roots become also developed. (PI- 1. fig- 3.)
How soon the flowering begins we do not know, but it is very likely that it takes the plant three
or four years before it produces flowers.

In fully matured specimens the leafy rosette is very large, the hypocotyl still visible as a cylin-
dric, thick, and prominently wrinkled body above a long, very fleshy, and thick root, the primary;
the lateral roots persist also and increase quite considerably in thickness, but not to such an extent
as the main root (PI. 1, fig. 4). If we lay a longitudinal section through the rosette and the
hypocotyl, we notice at once a number of small, young inflorescences and leaves ready to push
out during next spring. These inflorescences are stalked and erect, and the young flowers are
covered by the (fore) leaves. The hypocotyl persists during the whole life of the plant, and
constitutes a portion of the wrinkled crown above the root. Characteristic of ('. megarrhiza
and arctica is, thus, the continuous growth in length and thickness of the primary root, besides
the overwintering of the leaves and inflorescences.

It is now interesting to study the morphological structure of C. Virginica L.. which no
doubt is a near ally of C. megarrhiza; biologically, however, they are very distinct. Let us
state at once that C. Virginica does agree with < '. megarrhiza as far as concerns the monopodial
shoot and the persisting primary root, though not the entire root. The development of the plant
is as follows:

As already described by GrONOVIXJS,* " Monocotyledonum instar protrudit unicuni foliolum,"
and so is the only sign of the seedling above ground a single leaf with a small blade borne on a
long, filiform petiole (PI. '2, figs. 10 and 12). This leaf is borne upon a small tuberous body
underground, which terminates into a long, filiform root (R in fig. 10) with a few ramifications
and densely clothed with hairs. An anatomical study of the tuberous body shows at once that
this is also a part of the root, and no hypocotyl is thus developed. The base of the petiole
closely surrounds a minute leaf (!,' in fig. 11). which sometimes develops during the first season
(/' in fig. 13). and this leaf resembles the proper leaves of the full-grown plant. During the first
season the base of the root increases rapidly in thickness, while the slender portion dies off and
no trace of this is to be found in the following spring. The development of leaves continues at
the same time as the root grows in thickness, forming a more or less globular body with many

"The author: On the vitality of some annual plants. (Am. Journ. of Sci., vol. 42, 1891, p. 304.
b Flora Virginica, Pare. I, 1743, p. 25.

CLAYTONIA GRONOV.— THEO. HOLM. 31

superficial, transverse wrinkles (PI. 'J, tig. 15), and with several long- roots developing in small
tufts from the sides. Some three or four years elapse before the flower- appear, and the fact that
the floral stems are not preceded by a leafy rosette, as in the former species, makes it somewhat
difficult to appreciate that the steins are actually axillary and that the shoot represents a monopo-
dium. But if we examine the apex of the tuberous body — the root — we readily notice that the
renter is occupied by minute leaves and inflorescences, the position of which answers that of a
monopodium and also that of a shoot of ( '. megarrhiza, with the exception that the leaves do not
winter over in ('. Virginica. In this way these two species show a marked distinction in respect
to the persistence of the entire root and the overwintering of the leaves in ('. megarrhiza in
contrast to the reduction of the root and the early fading away of the leaves in C. Virginica.

Judging from the appearance of the vegetative organs in ('. Caroliniana and ('. lanceolata,
these two species show evidently the same course of development as we have observed in < '. Vir-
ginica; but they ought to be studied.

The last perennial and monopodia 1 species is < '. sunn, ntnsa Mey. (PI. I, rigs. 5 and 6). This
is nearest related to ( '. m< garrhiza with which it has in common a long, perennial root, persisting
in its entire length, and an overwintering rosette of leaves. But it differs, and very prominently
so, by the main root being quite slender, by the leaf-bases being somewhat swollen, and by its
ability to wander by means of stolons above ground, developed from the axils of the leaves, in
our specimens of leaves from the previous year. The stolons consist either of one single inter-
node terminated by a rosette of leaves (tig. 5), or they bear several long-petioled leaves with
stretched internodes, preceding the terminal, vegetative bud (fig. 6). Secondary roots develop
from the internodes of these stolons (/• in rigs. 5-<J).

The successive development of inflorescences and leaves is, however, identical with thai of
< '. megarrhiza and ('. Virginica. We have thus in C. sarmentosa a truly stoloniferous species,
yet with the primary root persisting as in the other species, and with the shoot being monopodial.
Furthermore the monopodial structure of the primary axis becomes repeated in the axillary
branches, the stolons.

These species, described above, represent then several types of rhizomes, but only a tew of
these are stoloniferous, and the plants show but a very limited ability to wander, for instance,
('. asarifolia by its creeping rbotstock, < '. sarmentosa by its stolons, and ('. pawifolia by it-
deciduous bulblets. We now pass to describe the vegetative propagation of < '. Cliamissonis,
which in this particular respect appears to be the best equipped of all the members of the genus.
Besides propagating by seeds, this species gives, also, an excellent illustration of a stoloniferous
and bulbiferous plant. Our figure 7 on PI. 1 shows a small specimen, the smallest we could
find in order to represent the plant with its rhizome in natural size; nevertheless, it is perfectly
sufficient for giving an idea of the mode of growth.

A flower-bearing shoot has developed from a bulb, and the stem above ground is terminated
by a two-flowered inflorescence, preceded as usual by a pair of opposite leaves; but in contra-
distinction to most of the other Claytonise, the aerial stem i- leafy from the base to the flowers,
and all the leaves are opposite, including those of the subterranean stolons and bulbs. The root
system is poorly developed, there being onlj- some filiform, almost unbranched roots proceeding
from the minute internodes of the bulb, from which the shoot has developed. Long and slender
stolons with small, opposite, scale-like leaves are visible in the axils of the bulb scales and of
one of the lowermost leaves of the stem; these stolons, which are often branched, are either
terminated by a small, pointed bud or by an ovoid bulb with thick, fleshy scales of a crimson
color. Both forms of stolons are underground, and they both send up an aerial shoot in the
coming year. This kind of propagation takes place at a very early stage, already in the first
year when the seed has germinated. Such seedlings show, thus, a pair of small, hairy cotyledons
above ground, from the axils of which stolons develop. The immediate direction of these
stolons was. however, vertical instead of horizontal, since they were developed in some distance
above the surface of the ground, the cotyledons being epigeic, as described above; the primary
root is quite long, but very thin and slightly ramified; its duration does not exceed one season,

32 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 2.

since the floral shoots always die off after the ripening of the seeds while the stolons and the
bulbs winter over.

The structure of the seedling showed very plainly that the shoot is not monopodial but that
it is terminated by an inflorescence, as in the specimens that had developed from stolons, as
figured and described in the preceding.

If we now compare Gray's systematic classification of the species with our table, based upon
the structure of the shoot alone, it is evident that certain species, otherwise closely related, have
become separated from each other and referred to distinct sections, in some instances to sections
of their own — monotypic. The members of Euclaytonia have been divided, and both C.
sarmentosa and ('. asarifolia appear to be distinct from these and distinct among themselves.
Li in nia, on the other hand, stays unchanged, and so do the monotypic Aldnastrum and JVaiocrme,
besides Montwsbrwm,. So, after all, the systematic classification compares fairly well with our
arrangement of the species, and of the two the former is, no doubt, the most natural, even if
some of the species may represent very distinct biological types.

Nevertheless, several analogies exist by which these types pass over into each other, and
by which the genus becomes actually quite definite and naturally outlined. Not speaking of the
uniformity in floral structure observed in all the species, the shoot itself, with its branches and
root system, does also show some degree of uniformity, at least in a general way. The inflorescence
is of the cymose type throughout the genus; the monopodial structure is common to nearly all
the species, annuals as well as perennials; the primary root stays as a more or less typical taproot
in most of the species; finally, the tendency of developing bulblets is well expressed in some of
these plants.

IV. THE ANATOMICAL STRUCTURE OF THE VEGETATIVE ORGANS.

While dried and pressed material may be sufficient to the study of a part of the morphologi-
cal structure, it is seldom of much use for anatomical purpose, especially not when the plants
are more or less succulent, as in the present genus. We therefore regret that our material
preserved in alcohol only consists of a few species, collected from time to time; but whatever
importance may be attached to the result of our investigation, a brief sketch of the anatomical
peculiarities of some of these species may serve, at least, as a modest contribution to the
knowledge of these plants heretofore but little known from this particular point of view.

THE ROOT.

The somewhat modified structure of the roots in certain species necessitates the treatment of
these to themselves. We may begin with O. megarrhiza. In this the ultimate ramifications
of the lateral roots are the only ones wherein the primary arrangement of the tissues is still
preserved and of which the structure is identical with that of a normal root, We notice
here a hairy epidermis, covering a hypoderm of very wide cells, inside of which there is a
cortical parenchyma, consisting of only two layers, the innermost differentiated as a thin-walled
endodermis. The pericambium is similarly thin-walled and continuous, surrounding a central
linear group of very narrow scalariform vessels and two groups of leptome, the elements of
which are exceedingly narrow.

If we now examine the slender, apical portion of the primary root in its second or third
year of growth, we notice a marked difference from the former by the absence of all the tissues
from epidermis to the pericambium, inclusive. The root has grown in thickness, and the peri-
cambium has now. by rapid cell division, developed several (about five) peripheral strata of cork
and a secondary cortex, which consists of about twelve layers of starch-bearing cells. The inner-
most portion of the central cylinder shows a number of vessels, in the center of which the primor-
dial are quite distinct from the younger by their narrow lumen. The leptome is located outside
the wider vessels, separated from these by broad strata of eambial tissue, which extends also
between the leptomatic groups themselves, thus covering the oldest part of the hadrome— the
protohadrome vessels. This structure is, to some extent, also observable in the thickest roots.

CLAYTONIA GRONOV.— THEO. HOLM. 33

But in these we notice a more or less distinct layering, like annual rings, which have been pro-
duced by the continuous formation of independent groups of leptome with a few vessels in the
secondary cortex. These rays of collateral mestome-bundles are furthermore separated from
each other by broad rays of pith. The central cylinder, with the primordial groups of leptome
and hadrome, is hardly discernible in these thick roots; the entire central group of these tissues
is mostly destroyed, and the root shows generally a broad, hollow center.

While examining some older roots of this species we often noticed that the long, lateral
ramifications showed a tendency to grow together in several places, thence to become separated,
and sometimes to grow together again at a greater depth (pi. 1, tig. 4). The complete preser-
vation of the central cylinders in such roots, where they were free and where they had grown
together, seems to prove that a fusion had actually taken place rather than a cleaving of a single
root. Another peculiarity which was frequently observed in the very thickest portion of the
root was that the internal structure did not only show one central cylinder with its heavy mass
of secondary cortex, but also several much smaller and apparently independent mestome-cylinders.
Considering the fact that each of these mestome-cylinders possessed exactly the same structure
as that of a slender root, viz, that it was covered by several layers of cork surrounding a
secondary cortex and a central portion of leptome, cambium, and vessels, make us believe that
these represent lateral roots, and that they remain inclosed within the loose and very heavy coat
of cork layers, which is always noticeable in matured roots of this species. In some cases,
especially where several of these mestome-cylinders were massed together, some of these showed
the same tendency to melt together as the free roots; but also in these were the central cylinders
perfectly isolated, and the only tissues in which the fusion was observable was the cortex and
the cork, the latter forming one single coat around two of these mestome-cylinders. The thick
root of ('. megarrhiza thus represents the primary root of the plant, and it persists for several
years, with a gradual increase in thickness. The thickness, however, does not seem to be due
only to the formation of secondary tissues within the main root alone, but also to the develop-
ment of lateral roots, which not only increase in thickness themselves but which, furthermore,
remain inclosed and covered by the cork of the primary root.

Similar cases of roots being inclosed has been described as characteristic of some other
plants, for instance: Bromeliacese," Erioca/ulaceae,b and Ophrydese."

In Claytonia Virginia* L., the underground, dark-brown, tuberous body from which the flower-
ing stems and leaves proceed is generally described as a tuber, or sometimes as a conn, but, as
stated above, this organ represents a root, the base of the primary. The long, filiform apex of
the main root (PI. 2, tig. 10) dies off during the first season, while the basal portion persists, and
increases gradually in thickness; it soon becomes globular, but when it is fully matured it repre-
sents a more or less laterally compressed body, with a roundish outline. At this stage numerous
filiform lateral roots are observable; they appear in small tufts on the edges of the mother root,
which is yet very distinctly diarchic. The minor structure of these roots at their various stages
is as follows: The lateral roots are of two kinds, some that are capillary, smooth, and almost
unbranched, and others that are thicker, prominently wrinkled and ramified. Of these the latter
develop from the central cylinder of the mother root, while the former appear as basal lateral
ramifications of these. The wrinkled roots are able to increase in thickness, but only a little,
and they never attain the swollen appearance of the mother root. Their increase in thickness
depends upon the divisions of the pericambium developing a cork outward and a secondary
cortex inward, throwing off the older tissues from the epidermis to the endodermis inch; a
cambial tissue has also developed to the same extent as described under ( '. megarrhiza.

The most noticeable characteristic of these roots is their contractile power, which is effected
by means of a wrinkling of the cork layers, in which the radial cell walls show very distinct
undulations. A much more simple structure is possessed by the smooth and slender ramifica-

" Jorgensen, A.: Bidrag til Rodens Naturhistorie ( Bot. Tidsskr. Copenhagen, ser. 3, vol. 2. 1877-79. p. 150.

^The author: Eriocaulon decangulare L. (Bot. Gazette, vol. 31. 1901. p. 23).

,;Same: The root structure of North American terrestrial Orchidese (Am. Journ. of Sc, vol. IS. 1904. p. 208).

89369° — vol 30—11 3

34 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 2.

tions. In these the original structure remains unchanged (PL 2, tig. 18). The hairy epidermis
is thin-walled; the cortex (C in tig. 18), consists only of three layers, of which the innermost is
differentiated as an endodermis (End. in tig. 18); the pericambium (P) is continuous, and sur-
rounds two rays of hadrome alternating with two groups of leptome.

If we now examine the primary root we notice that the structure of its filiform apex, which
only persists during the first season, agrees exactly with that of the capillary lateral roots,
which have just been described. But the structure of the swollen base is different. In this the
pericambium becomes gradually very active, besides that a cambium develops inside the leptome
and extends from there around the primordial vessels. This increase continues from year to
year, accompanied by the development of collateral mestome-bundles in the starch-bearing cortex.
The mode of growth is like that observed in the main root of C. megarrhiza, though with the
important distinction that in this species the apex continues to grow, while it dies off in V. Vir-
ginica. Moreover, in the latter species the central cylinder persists for a very considerable
period, and the secondary cortex with its coat of cork layers remains active throughout the life
of the plant. The lateral roots are quite numerous in both, but in ( '. Virginica they do not
traverse the cortex vertically as fully developed roots, but they proceed at once to the periphery
until they become free, as is the usual course followed by lateral roots.

A very long, but relatively slender, primary root is possessed by C. sarmeiiiosa, and it
persists for several years. It is not contractile, but combines the functions of a storage and a
nutritive root. The increase in thickness is quite moderate, and the central cylinder, with its
mass of narrow vessels and groups of leptome, does not break down even in the older roots, while
the peripheral tissues- become replaced by layers of cork and starch-bearing secondary cortex.
Lateral roots occur, but they are scarce; the primordial tissues are all noticeable in these, even
if some, slight increase in thickness does take place; the endodermis is moderately thick-walled,
and the pericambium is continuous.

If we now examine the root system of one of the annual species — for instance, C. a/renicola —
we notice that both the slender, main root and its almost capillary ramifications are able to grow
in thickness.

The epidermis and hypodertn are thrown off very soon, together with the cortex, and are
replaced by two or three layers of secondary cortex, surrounding the central cylinder of hadrome
and leptome, besides some cambium. The lateral roots are all diarchic, but the very irregular
position of the numerous (about thirty) narrow vessels in the primary root made the number of
primordial rays indeterminable.

In species where an underground stem becomes developed — for instance in 0. parvifolia,
C. asarifolia, and ('. Ohamissonis — the primary root is no longer observable in matured speci-
mens, but is replaced by secondary, which proceed from the short internodes. The structure of
such roots is very simple, since they show no signs of increasing in thickness, and neither are
they contractile. They have an epidermis with many hairs, directly covering a cortex of about
five layers, inside of which is a thin-walled, or sometimes slightly thickened, endodermis; a
continuous pericambium surrounds two distinct hadromatic rays, alternating with two groups
of leptome,

In bringing these facts together it appears as if the root system of our species of < 'laytonia,
represents four physiological types: Nutritive, attachment, contractile, and storage roots. Of
these, the first type is well exemplified in the secondary roots of C. parvifolia, C. asarifolia,
and V. Ohamissonis ; the second in the annual C. arenicola; the third in the slender lateral roots
of ('. Virginica; while a combination of both contractile and storage roots may be observed in
the main root of C. Virginica and ('. megarrhiza. In ( '. sarmentdsa, on the other hand, the root
seems to combine the function of a nutritive with that of a storage root.

THE STEM.

The above-ground stem is of short duration in Claytonia, and lasts only one season. In
some species it bears only two large green leaves and an inflorescence (('. Virginica, etc.), in
others it bears several, but smaller, leaves, which are either alternate or opposite ( C. Ohamissonis),

CLAYTONIA GRONOV.— THEO. HOLM. 35

in the axils of which may be developed either inflorescences, vegetative shoots with distinct inter-
nodes, or small bulblets.

However, the stem structure is almost identical, and characteristic of the genus seems the
lack of collenchymatic and stereomatic tissue, as mentioned by Becker." The cuticle is always
distinct, and is prominently wrinkled in ('. Chamissonis, C. megarrhiza, and C. sarmentosa. In
regard to epidermis, we notice in ('. Virginica (PI. 2, fig. 17) an excessive thickening of the outer
cell wall, with numerous layerings; in the other species the outer cell-wall is generally thickened,
but only moderately. The cortical parenchyma is rather open from the intercellular spaces being
quite wide, and the innermost stratum is differentiated as an endodermis, usually thin walled
throughout, and showing the < 'asparvan spots very plainly; in ('. arenicola, however, the endo-
dermis showed the cell-walls slightly thickened. Inside the endodermis are four very broad
collateral mestome-bundles. separated from each other by thin-walled parenchyma, medullary
rays; besides that there is a narrow group of this same tissue in the center.

If we now compare the structure of the rhizomes, we find in the stolons of C. Chamissonis
almost the same development of the various tissues as in the stem above ground. But in the
stolons the cortex contains deposits of starch, and the endodermis has the inner cell-wall slightly
thickened; besides that, there is some thick-walled mestome-parenchyma between the leptome
and the endodermis. Of the four mestome bundles, the two are much broader than the others,
and the pith seems to be less developed than in the stem. The stolons of this species possess no
cambium, and are thus incapable of growing any further in thickness; they are not of any long
duration, either, since they evidently separate from the mother plant at the close of the first
season, when they are able to continue their growth independently.

A more developed structure is possessed by the above-ground stolons of C. sarmentosa. In
these the cuticle is thick and prominently wrinkled, covering an epidermis of small but somewhat
thick-walled cells; the cortex consists of about eight quite compact layers, but without starch.
The thin-walled endodermis surrounds a secondary cortex of about six layers, with abundant
deposits of starch, inside of which is a closed ring of several collateral mestome-bundles with
intrafascicular layers of cambium. The center of the stolon is occupied by a narrow cylinder of
starch-bearing pith. In this species the stolons are thus able, to increase in thickness, and our
material showed plainly that they remain active and in connection with the mother plant for at
least two or three years.

The horizontally creeping rhizome of < '. asarifolia persists for several years, and shows many
layers of cork, forming a thick coating around a broad, starch-bearing parenchyma of a secondary
cortex. The mestome-bundles are all collateral and arranged in a circle; they consist of leptome,
cambium, and man}' narrow vessels, especially pitted ducts. A very compact, starch-bearing pith
occupies the greater portion of the central cylinder.

In ( . parvifolia there is also a horizontal rhizome, but this is partly above ground, and of
a much weaker structure. The epidermis is at length thrown off without being replaced by
any layers of cork, while the cortex and endodermis persist; the former of these contains
chlorophyll. There are only five collateral mestome-bundles, without cambium, and these are
separated from each other by rays of the broad central pith.

A somewhat greater diversity in regard to the structure is thus observable in the rhizome
than in the flower-bearing stems, which is quite natural when we consider the various modifica-
tions exhibited by the former, viz: The perennial creeping rhizome of C. asarifolia, the annual
stolons of ('. Chamissonis, in contrast to the perennial ones of ('. sarmentosa.

THE LEAF.

We meet here with several, and quite important, modifications of structure, which is by no
means surprising, when we remember that the leaves winter over in some species. < '. megarrhiza,
('. arctica, and < '. sarmentosa, but die off in all the others before the summer has passed, not
speaking of such leaves as are developed as mere bulb scales, in C. Ghamisson'ix, for instance.

"Becker C: Beitrag zur vergleichenden Anatomie der Portulacaceen. tnaug. diss?. Miinchen, 1895.

36 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 2.

It may, therefore, be advisable to treat of some of these species by themselves, beginning with
C. Chamissonis. The stem bears many pairs of opposite leaves, which are held in an almost
vertical position, and their structure is as follows: The cuticle is distinct, wrinkled near the
margins of the blade, but is otherwise smooth. The outer cell-walls of epidermis are moderately
thickened, and the radial are more or less undulate, especially on the upper, the ventral face of
the blade. Stomata abound on both faces; they are raised a little, and possess two subsidiary
cells, which are parallel with the stoma, and the air chamber is wide and deep. No trichomes of
any kind were observed, but small, stiff hairs were, nevertheless, observed upon the earliest
leaves, succeeding the cotyledons. The chlorenchyma is differentiated into a typical palisade
tissue on the ventral part of the blade, and as an open pneumatic tissue on the dorsal. No
mechanical tissue, neither as stereome or collenchyma was observed, and the mestome-bundles are
only surrounded by a thin-walled parenchyma sheath, and deeply imbedded in the chlorenchyma.

In the bulb-scales of this same species the thin-walled epidermis lacks, of course, stomata,
and the mesophyll is merely represented as a homogenous tissue of closely packed roundish
cells tilled with starch. The mestome-bundles are very small and only three in number.

In C. Virginica the stomata are most abundant on the dorsal face of the blade, and they
have often two pairs of parallel subsidiary cells instead of but one; moreover, the cells of the
ventral epidermis are usually somewhat larger than those of the dorsal. In regard to the
chlorenchyma, this shows the differentiation as in the former species, but the pneumatic tissue
is still more open, on account of the very irregular shape of the cells, leaving very wide inter-
cellular spaces. The mestome-bundles are also small in this species and are not supported by
any kind of mechanical tissue. The basal leaves have very long and slender petioles, in which
there is a chlorophyll-bearing cortex with very wide intercellular spaces, besides lacunes. There
is one crescent-shaped central mestome-bundle and two small lateral, which are orbicular in
transverse sections; each of these is surrounded by a special thin-walled endodermis.

If we now examine the overwintering leaf of G. megarrhiza, we notice in this a very thick
and smooth cuticle, covering an epidermis, with the outer cell-walls prominently thickened, but
perfectly glabrous. The stomata (PI. 2, fig. 9 ) are somewhat- raised, and possess mostly two
pairs of subsidiary cells, more or less parallel with the stoma. They appear to be equally
distributed on both faces of the blade. A thick homogenous parenchymatic tissue represents
the chlorenchyma, the individual cells of which are shaped like, palisades, vertical on the leaf
blade and filled with chlorophyll. The mestome-bundles are small and deeply imbedded in this
tissue. No support of mechanical tissue was observed.

Although the leaves of C. sanm ittoxii are green during the winter, thick and fleshy like
those of C. megarrhiza, they nevertheless show a very different structure. The stomata are
almost exclusively confined to the dorsal face, and the cuticle is very thin. In this species the
chlorenchyma is plainly differentiated into a ventral palisade tissue and a dorsal pneumatic, which
consists of -irregularly branched cells, like those observed in < '. Virginica. Otherwise the struc-
ture of the mestome-bundles, etc., is like that of the previously described species.

The isolateral leaf-structure exhibited by ('. megarrhiza is a character that has been observed
in several other alpine species, pertaining to remote genera; the prominent development of the
chlorenchyma into a palisade tissue seems to confirm the general supposition that in alpine
plants the assimilation governs the structure of the chlorenchyma. On the other hand, the
plainly dorsiventral structure, with the very open pneumatic tissue, as represented by C. sar-
mentosa, is a good illustration of a plant adapted to an atmosphere charged with excessive mois-
ture. In this case the transpiration seems to be a more important factor than the assimilation, as
far as concerns the differentiation of the chlorenchyma into both a palisade and a pneumatic
tissue.

It is somewhat surprising to observe a very open pneumatic tissue in the leaf of C. Virgin-
ica, which is not an inhabitant of wet localities or is in any way exposed to a damp atmosphere.
Nevertheless, the leaf-structure of this species is more open than that of C. Chamissonis, a plant
that grows exclusively in very wet places — in beaver swamps or along creeks in the aspen zone

CLAYTONIA GRONOV.— THEO. HOLM. 37

of the Rocky .Mountains, for instance. Such controversies in structural respecl arc frequent-
very frequent, indeed — and the present knowledge of plant structures is yet much too incomplete
to enable us to oiler any plausible explanation.

It seems, however, as if the species of Claytonia which we have examined exhibit certain
structures which may be regarded as generic; for instance, the absence of stereomatic and col-
lenchymatic tissues, the structure of the stomata (in contrast to those of the monotvpic Montia),
the four mestome bundles in the stem, the diarchic root, the lack of trichomes, of reservoirs,
etc. By considering the external morphological structure of the various organs, we meet also
here with some certain degree of uniformity throughout, even if some of the species may be
regarded as very distinct from a biological point of view.

Brookland, D. C, October, 190^.

EXPLANATION OF PLATES.

PLATE 1.

Fig. 1. Bulblet of Claytonia parrifnliit, magnified.

Fig. 2. Claytonia megarrhiza, a seedling, natural size: Cot.=the cotyledons; H=the hypocotyl; R=the primary

root.
Fio. :i. Same species in the second year, natural size; letters as above.

Fig. 4. Same species, but at a later stage, natural size; the lateral roots have grown together with the primary.
Fk;. 5. Claytonia sarmi mosa, natural size; r=a secondary runt developed from the stolon.
Fig. 6. Same species; a leafy stolon, natural size; r=secondary roots.
Fig. 7. Claytonia Chamissonis, natural size, showing a plant developed from a bulb, and bearing three stolons, the

one of which is terminated by a bulb.
Fig. s. Claytonia diffusa ; a stem-leaf, natural size.

PLATE 2.

Fig. 9. Stomata of the leaf of Claytonia megarrhiza,'XS60.

Fig. 10. Claytonia Virginica, a seedling, natural size; Cot. =the cotyledon; R=the primary root.

Fig. 11. Same species; the tuberous portion of the primary root; P=the li •.«* leaf succeeding the cotyledon (Cot.);

/=lateral roots; magnified.
Fig. 12. Same species; the blade of the cotyledon, magnified.

Fig. 13. Same species; a seedling, showing the cotyledon and a proper leaf, ll; natural size.
Fig. 14. Same species in its second year, where the filiform apex of the primary root has fallen off; letters as above;

natural size.
Fig. 15. Same species, showing the globular, primary root (R) with several filiform, lateral roots of a specimen about

four years old; magnified three times.
"Fig. 16. Same species; the stomata of the leafx360.

Fig. 17. Same species; transverse section of the stem; Epid.=epidermis; Hyp. =the hypodenn. X480.
Fig. 18. Same species; transverse section of a filiform, lateral root; Ep.=epidermis; C=cortex; End. =endodermis;

P. =pericambium ; L. =leptome. X840.
Fig. 19. The diagram of the flower of Montia rivalaris; A=theaxis; C'=the posterior, C2=the anterior calyx-leaf;

copied from Almquist (I.e.).

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. VOL X.

PLATE I

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X

PLATE

Cot.

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

"Volume X.

THIRD MEMOIR.

WASHINGTON:

GOVERNMENT PRINTING OFFICE.

1905.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

THIRD MEMOIR.

A RESEARCH UPON THE ACTION OF ALCOHOL
UPON THE CIRCULATION.

BY

HORATIO C. WOOD,

Professor of Materia Medica and Therapeutics in the University of Pennsylvania,

DANIEL M. HOYT,

Assistant Demonstrator of Pharmacodynamics in the University of Pennsylvania

39

CONTENTS.

Pay1*

Introduction 43

Experimentation upon the Effect of Alcohol on the Arterial Pressure. : 44

First. Upon Normal Dogs 45

Second. Upon Dogs suffering from Infective Fevers 47

Third. Upon Dogs after section of the Spinal Cord 48

Fourth. Upon Dogs after tying of the Aorta 51

Experiments upon Normal Dogs with the Stroniuhr 51'

Experiments upon the Isolated Reptilian Heart 54

Discussion of these Experiments - 63

Relation of Results to the Work of Previous Experimenters 64

Conclusions as to the Action of Alcohol upon the Circulation of the Lower Animals 65

Plethysmography Experiments upon Man 65

Remarks upon the Results in Relation to the Action of Alcohol on the Nervous System 67

41

THE ACTION OF ALCOHOL UPON THE CIRCULATION.

By Horatio C. Wood and Daniel M. Hoyt.
INTRODUCTION.

When Dr. H. C. Wood graduated in medicine in 1862 the profession knew of but two
heart stimulants, namely, ammonia and alcohol; for it was taught that digitalis is a powerful
heart sedative, to be used in cases of excessive heart, excitement, and when, as in aneurism, it
was desirable to lessen the force of the blood current.

Not many years after the physiologists, and subsequently the clinicians, began to learn that
digitalis is not a cardiac depressant but a most powerful and useful cardiac stimulant — a stimu-
lant which for most purposes still stands at the head of the list of remedies of the class. Alco-
hol, on the other hand, yet remains a question of dispute, so far as concerns its action upon the
circulation. Probably since the days of Noah, certainly up to the present moment, whatever
the judgment of the profession may be, the action of the laity is that alcohol is a prompt heart
stimulant. If a man faints in a drug store, or in a public assembh*, or in the street, unless the
crowd be so far given to temperance principles that no whisky flask is available, said tiask is
forthcoming.

Nearly fifty years of medical life has led Dr. H. C. Wood to attach much importance to
widespread popular beliefs, not in regard to the truth of their theory but of their practical
results. For years the profession looked upon the mediaeval practice of the use of balsams on
wounds as a dirty, obnoxious procedure. Now we know that the old vulnarian used remedies
which were actively germicidal, and that in the midst of mediaeval tilth, with its hosts of hungry
organisms, he was practicing a rude antiseptic surgery.

For years indefinite there has been a widespread belief that fistula in ano and similar dis-
charging tubercular sores ought not to be healed in consumptive people; the profession decided
that they simply helped to exhaust the system and must be done away with; but the latest
specialists in tuberculosis have come to the belief that these tubercular sinuses may be really
curative by the antitoxin which they produce interfering with tubercular processes more
serious because situated in a more vital part. The facts that alcohol is used to the amount
of tons annually in diseased conditions affecting the circulation; that it is not powerless for
good or for evil; that the physiologists are in absolute discord in regard to its influence, upon
the circulation, and that the clinicians are becoming, in the presence of this physiological diversity
of opinion, doubtful and uncertain in the use of the drug, can not be gainsaid. As proof of the
divergency of opinion among competent pharmacologists, two quotations may be cited — one,
written in 1900, by H. C. Wood, professor of therapeutics in the University of Pennsylvania, as
follows;

Upon the heart the small dose of alcohol acts as a direct stimulant, the large dose as a depressant or paralyzant.
The influence of minute doses upon the vasomotor system is not thoroughly worked out, but there appears to be a
widening of the blood paths at a time when the heart is still stimulated, so that there is a marked quickening of the
blood movement. (Treatise on Therapeutics. J. B. Lippincott Co., 11th ed., p. 287.)

The other coming from the pen of John .1. Abel, professor of pharmacology in Johns Hopkins
University is:

So far as present experimental evidence goes, we may say: 1. That alcohol as such, that is, when it is introduced
into the circulation with the avoidance of local irritation, is not a circulatory "stimulant." 2. Alcohol in moderate
quantities, say a pint of wine, has no direct action on the heart itself, either in the way of stimulating or depressing

43

44 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

it. :>. Alcohol in moderate quantities has also no direct action on the walls of the 1>1 1 vessels, either on their

muscular portions or on the peripheral terminations of their vasomotor nerves. (Physiological Aspects of the
Liquor Problem. Houghton, Mifflin & Co., vol. 11, p. 91.)

Led by the importance of this subject, the authors of the present memoir applied to the
National Academy of Science for a grant from the Bache fund of $300; this sum of money has
become the basis of the present investigation. The literature of alcohol has been studied
over and over again, with impartiality and with partiality, with critical acumen, with partizan-
ship, with judicious candor, with shallowness and with thoroughness, and so variously that it has
seemed to us that the possibility of further usefulness in any such study is exhausted. In the
two works already cited the reader can find the past epitomized. The intent of the present
research is to investigate the question de novo, with mind kept as free as is humanly possible
from the predisposing effects of previous beliefs. The experiments are reported in the memoir
in unusual detail, so as to afford experts opportunity for studying the evidence which is
brought forward.

It is perhaps proper to state that although the actual work of making the experiments was
chiefly performed by Doctor Hoyt, Doctor AVood took part in and overlooked all experiments
of importance, so that the authors of this memoir are equally responsible for the accuracy of
the experimental work and of its results.

EXPERIMENTATION.

The experiments which we have made with alcohol bad for their intent the finding out of
certain facts, and therefore naturally arrange themselves into series, each series being directed
to the determining of an individual fact or of several facts closely allied. These series are —

First. Experiments made upon the uninjured animal to determine the effect of alcohol upon
the arterial pressure.

Second. Experiments made upon dogs suffering from an infective fever to determine
whether alcohol acts under these circumstances as it does upon the normal animal.

Third. Experiments made upon dogs with variously situated sections of the spinal cord, in
order to determine the effect of alcohol upon the arterial pressure when the general vascular
system has been separated from its dominant vasomotor centers.

Fourth. Experiments as to the effect of alcohol upon the arterial pressure after the aorta
has been tied in the middle thoracic or upper abdominal region.

Fifth. Experiments made upon normal dogs with the Ludwig stromuhr to determine the
effect of alcohol upon the rate of the blood flow.

Sixth. Experiments to determine the influence of alcohol upon the isolated reptilian heart.

SERIES FIRST.

In this series we performed two sets of experiments — those in which the alcohol was given
by inhalation and those in which it was administered intravenously.

In the inhalation experiments the method adopted was to allow the dog to breathe through
a tracheal tube which was connected with a double tube bottle in such way that the air had to
bubble through a considerable mass of SO per cent alcohol. It was found that under these
circumstances the air was loaded with the vapor of alcohol, whilst an abundant supply of air
was furnished the animal. Usually the inhalation was not accompanied by any struggling or
excitement, but it was not found possible to produce a complete amesthetic unconsciousness.
This was contrary to the result reached many years ago by Dr. H. C. Wood, that animals could
be anaesthetized with simple alcohol placed in an imperfectly closed inhaler.

It is evident that the anaesthesia which was produced in the earlier experiments of Doctor
Wood was largely the outcome of a slow asphyxiation due to an imperfect supply of air. Alcohol
when given in the method adopted in the present series of experiments usually failed to produce
rise of the arterial pressure, and in the exceptional case only caused such rise very late in the
poisoning, at a time when the respiration had been profoundly affected by pulmonary congestion

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

45

and oedema due to the local action of the alcohol upon the pulmonic mucous membranes. At

such times the pulse was slow and full, and it was clear that the circulatory changes were the
outcome of asphyxiation. In most of the experiments the animal died suddenly l>v respiratory
failure, there either being no unconsciousness until the act of death had been entered upon or
was about to begin. It has not .seemed to us necessary to report the experiments of this series
in detail, but we have tabulated one typical experiment, in which there was no rise of arterial
pressure.

Experiment 1. — Alcohol given by Inhalation. No morphia. Small amount of ether. Reflexes

normal befort beginning experiment.

Tinic in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0
.40
1.40
2.40

3.40

14.41)
L5.20

22.211 to 22 40

-■. .'.

126

113

Alcohol begun.

Pulse irregular. Animal per-
fectly quiet.

Reflexes active. Imperfect di-
astole every other heat.

Tendency to dicrotism.

Reflexes sluggish.

Sudden respiratory failure.
Postmortem, lungs oedema-
tous, the larger bronchial
tubes full of fluid.

126
120

117

99

110
115

115

112

57

1(1.",

The following experiments were directed simply to studying the effects of the intravenous
injection of alcohol upon the circulation in the normal dog. In all of the experiments ether was
used during the preparation of the artery and vein, care being taken to allow the effects of the
ether to go off before the first record of blood pressure. In a few instances a small amount of
morphia was also given to the animal operated upon.

Experiment 2. — Weight, 7\ kilos.

Alcohol, 10 per cent, until strength increased us given in
r< mark column.

Time in minutes ami
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0

0.20 to 1.40

2.20

3.00 to ."..20

3.40

5.20

6.20

8.50 to 9.10

9.30

10.10 to 10.30

10.50

11.50 to 12.10

1.", 10

15.10 to 15.30

16.10 to 16.30
17.10

18.10 to 18.30
3.710
38.10
42.10
42.10
43.10
43.50
44.50

48.50 to 49.10
49.10
49.30

C. r.

104

152

Animal very quiet.
Reflexes present.

20 per cent solution of alcohol.

33 per cent solution of alcohol.

5o per cent, alcohol. Clot formed.
50 percent alcohol.

5

90

146

5

90

90

78

143
155
145

10

75

149

11

87

152

5

75
72

151
151

5
5

84

140

5

110

i:,5

5

20

00
00

160

14S

20

12

12

72
60

60

115

46

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.
Experiment 3. — Alcohol 50 per cent.

Time in minutes and n

seconds. urug.

Pulse.

Pressure.

Remarks.

0

6.00 to 6.20

6.40

8.40 to 9.00

10.00

11.00 to 11.05

13.05 to 13.10

13.30

18.30 to 18.50

19.50 to 21.50

23.50

25.50 to 26.10

20 3o

28 30
28.30 to 28.50

29.50

29.50
30.50 to 31.10

31.30
34.30 to 35.10

35.30

36.30

38.30

38.30 to 38.40

39.40

40.20

40.40
41.40 to 42.00

43.00
43.20 to 43.40

c. c.

183

I4S

Clot.

No appreciable change.

Amount of injection not stated.

Amount of injection not stated.
Sudden fall of pressure; pro-
longed systole.

Figures as to amount of injec-
tion not clear.

Pulse full and slow; no prolon-
gation of systole.

Tendency to dicrotism.

Pressure fell at once to zen >.

4

210

157

4

210

166

4
4

186
225

165
165

6
6
6
8

168
192

150
186
162

139

L55

137
155
141

8
Inj

12

144

126

Inj

36

36

144

21

99
129

4
Inj

30

108

10

57

76

26

Experiment -t. — JV<

■null dog. Wright, 0 kilos. Rectal temperature, -IS-
morjihia gireii with ether. Alcohol, 50 per cent.

C. 8 centigram mes of

'Pi in minutes and

seconds.

Drug.

Pulse.

Pressure.

Remarks.

0
1.00 to 1.05
2.35

3.50 to 4.00

c. c.

70

98

Animal quiet.

Respiration stopped.
Prolonged systole.

5

72

72
70

96

102
108

0.00

6.30 to 7.00

10

7.30

86
80
72

113

98

120

9.00

10.30

12.30 to 13.10

15

14.10

106
86

135

96

15.40

10.17
18.00

20

19.30

74

63

An examination of the foregoing experiments will show that in Experiment 2 alcohol had
no distinct effect upon the arterial pressure until it was given in such amounts as to reduce the
pressure. In Experiment 3, there was a rise of the arterial pressure, 18 millimeters, in the
course of about as many minutes. In Experiment 4, a rise of the arterial pressure of nearly
4<t millimeters was reached. These experiments seem to show that alcohol has a tendency to
produce a slight rise in the arterial pressure in the normal dog, but that this tendency is not
pronounced and may fail to occur, even when small and carefully calculated doses are employed.

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

47

SERIES SECOND.

In this scries we made only two experiments, which were performed on doos suffering from
distemper accompanied with the usual systemic disorder and marked fever. These experiments
are as follows:

Experiment 5. — Dog suffering from distemper. Temperature, lfi.5 O. Very weak and ill.
Weight, \ kilns. Ether used. Alcohol, 50 per cent.

Time in minutes and

seconds.

Drug.

Pulse.

Pressure.

Remarks.

(1
1.00 to 1.10

1.20
3.20
4.20
4.30
4.40 to 4.50
7.50
19.50

r '■.

134

157

Howling.

Animal quiet before injection
was finished.

5

124
112

152
147

5

172

13S

5

124

14S

145
112

Experiment 6. — Dog suffering from distemper. Temperature, '/<>■■>' < '■ Weight, 7 kilos.

Ether used. Alcohol, 50 ji< r cent.

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0

1.02

4.00

6.00 to 6.30

8.00

10.00

12.00 to 12.10

16.10

16.40 to 16.50

18.20

18.50

19.20

19.30

20.30

21.30

22.30

r. .'.

136

185

Reflexes normal.

I'ulse dicrotic; respiration

( 'in pneumogastrics.
Animal killed.

slow.

15

136

195

10

lis
136

1S6
201

5

136

187

1

138

191

6
5

04

105

2 IS

225

An examination of the records just given will show that in Experiment 5 it was not possible
to cause rise of the arterial pressure by alcohol, whereas in Experiment 0 a slight but distinct
rise was produced, so that it would appear that in the dog suffering from the general prostration
and circulatory disturbance of an infective fever alcohol has no consistent pronounced influence
in elevating the blood pressure, but at times does have such effect. The drug therefore seemingly
acts upon the circulation in fever in no way differently from that in which it acts upon the
circulation in health.

A remarkable effect noted in these dogs, not connected with the circulation, was the influence
of the alcohol upon the nervous system, an influence so pronounced as to suggest that very
possibly in human fever alcohol is of service as a calmative agent. The animals were suffering
from fever and its discomforts; were of necessity restrained in the ordinary dog trough;
were violently restless and howling at the time of the intravenous injection of the alcohol.
The alcohol was not given in sufficient dose to produce a recognizable narcosis, yet within
two or three minutes after its injection the animal became perfectly quiet and apparently
blissful lv content.

48

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

SERIES THIRD.

In the experiments included in this series the spinal cord was always cut somewhere in the
cervical region, artificial respiration being maintained. Every effort was made to keep uniform-
ity of rate and activity in the respiratory movements, and in nearly all the experiments the
condition of the cord was tested by the effect of asphyxiation upon the circulation, so that it was
physiologically demonstrated that the vasomotor system was completely paralyzed. Further,
the completeness of the section of the cord was confirmed by post-mortem examination. The
section of the cord is a surgical procedure requiring so much cutting and time and involving
so much suffering that the animal was perforce thoroughly anaesthetized during the surgical
procedures, but in every experiment time was allowed after the operation for the effects of the
anaesthetic to disappear, so that the conjunctival reflexes were normal.

Experiment 7.-

Tbung, vigorous dog. Weight, If. kilos. Alcolwl used, 50 per cent.

in ii/i/K r cervical rnjiini.

Cord cut

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0
0.05

0.10 to 0.20
0.40

0.50 to 1.00
1.20
1.50

1.55 to 2.05
2.15
2.25
2.45

2.50 to 3.00
::.io
3.50

4.40 to 4.50
5.10

e. c.

198

150

32
32

4

180

50

3

134
156

60
50

3

144

80

4

160

60

5

120
120

90

70

5

84

40

Experiments. — Cord cut in lower cervical region. Much hemorrhage. At post-mortem sum, of
the extrein, anterior fihers not cleanly cut. Asphyxia, no rise. Alcohol, 50 per cent.

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0
1.00 to 1.20

1.25

2.25
4.55 to 5.00

5. 10
6.10 to 6.15

7.45

9.45 to 9.50

10.10 to 10.15

10.25
10.45 to 10.50

11.20

C. r.

100

58

5

30
46

47
70

2

82

59

5

50

72

2
2

26

50

2

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

49

Experiment 9. — Cord cut in th upper cervical region. Alcohol used, first injection, 50 per cent;
after that to tk end of tht experiment, 1$ per cent.

Time in minute and
seconds.

Dmg.

Pulse.

Pressure.

Remarks.

0.34
0.60
1.56
3.00
3.50
4.00
4.30
6.10
6.20
7.00

7.40
10.30

11.30

12.00 to 13.10
14.00

14.30 to 16.00
18.00
19.00

20.00 to 20.30
20.45
21.30

c. c.

57

70-80

Prolonged systolic and markedly
dicrotic pulse.

10

63

85
115
113
113
114

5

63

10

57
54

103

107

10

42
48

106
123

5

95
118

15

133

128

51

14

54

141)

13

57

140

6

18

6
12

71
61

Experiment 10. — Cord cut in lower cervical n gion. Alcohol us< d, 50 p< r •-, nt. There was much

. hemorrhag( .

Time in minuii- and
seconds.

Drug.

Pulse.

Pressure.

Remarks

0

0.60
2.00 to 2.20

2.20
3.20 to 3.40

3.50
4.00 to 4.20

4.20
5.40 to 5.50

5.50
5.50 to 6.50

6.50
7.50 to 8.00

8.00

c. c.

204
204

46
46

I'ulsc waves very small.

No appreciable change in pres-
sure at any time between in-
jpi'tions.

5

180

46

6

180

48

10

195

63

10

210

56

10

168

59

10

216

55

89369°— vol 10—11-

50 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X? NO. 3.

Experiment 11. — Cord cut in cervical region. Weight, 10 pound*.

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0
0.10 to 0.30

0.30

1.30
1.50 to 2.10

2.30
3.10 to 3.50

3.50

*'. c.

155

49

Amount of alcohol not recorded.
Clot forming.

8

153

141

69
52

Injection

144

50

4

132

55

Experiment 12.

- Weight of dog, 10.5 kilos. Cord cut in the lower cervical region,
hemorrhage during flu operation. Alcohol used, 50 j» r cent.

< 'misidi nrfile

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0

1.30 to 1.50

3.30

5.00

6.00

6.05 to 6.35

7.05 to 7.25

7.55

9.55 to 10.25

10.55

12.55

14.25 to 14.35

14.45

16.15 to 16.45

20.45 to 22.15

25.15

26.45 to 27.15

27.35

30.05

30.35 to 31.05

32.35

34.35 to 36.05

38.25

41.25 to 41.52

41.55

c:c.

58

67

The heart stopped apparently
in full diastole. The animal
was .supposed tn lie dead,
but the heart immediately re-
sumed action when the pneu-
mc pastries were cut.

Death during injection.

15

60 ! 90
60 83

3

64 70

5

70 82

11

50 54
62 ' 78

5

78 73

10
15

68

95

10

52
72

* 97
100

10

68

97

16

38

154

10

94

137

30

An inspection of those experiments will show that in Experiment 7, in which the dog- was
young and vigorous, the arterial pressure was raised over Km per cent in spite of the consentaneous
marked decrease in the rate of the pulse; that in Experiment 8 the pressure was raised about 25
per cent at the maximum in spite of the fact there had been a great deal of hemorrhage from the
operation; that in Experiment '.» the pressure was elevated as much as 50 per cent at the maxi-
mum, the pulse being reduced in frequency; that in Experiment It) although there was much
hemorrhage the elevation of pressure at the maximum was about 25 per cent; that in Experi-
ment 11 the maximum rise of pressure was about 4<i per cent; that in Experiment 12 the maxi-
mum rise of pressure under the use of alcohol was about 50 per cent.

In none of these cases was the arterial pressure kept for a great length of time at the highest
point, but there was always a prolonged maintenance of the pressure above the normal.

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

51

SERIES FOURTH.

In the present series of experiments the effort was made to study the action of alcohol upon
the blood pressure when the aorta had been previously tied.

Experiment 13. — Aorta tied aboV( renals and heloio diaphragm. Alcohol, 50 per cent.

Morphia us< </.

Time in minutes and
seconds.

Drug.

I'lllse

Pressure.

Remarks.

0

c. c.

80

200

Sudden death.

0. 30 to 0.40

5

3.40

68

199

3.40 to 4.10

5

8.10

53

205

9.10 to 9.40

10

10.40

52
74

143
202

14.40

14.40

10

17.40

84

68
66

196
189

188

21.40

24.40

26.40

30

Experiment 14. — Aorta tied above renals, below diaphragm.

no morphia.

Alcohol, 50 per cent. Ether hut

Time in minutes and
seconds.

Drug.

Pulse.

Pressure.

Remarks.

0

1.00 to 1.05

3.05

5.35

7.35

9.05 to 9.35

11.35

13.35

13.45 to 13.50

16.50

19.50 to 20.20

20.50

21.50

22.20
2H.2I)
27.20
32.20

c. c.

100

180

Animal restless.

Reflexes present. Animal cries.

3

120
136
132

185
186

is:.

3

140
126

175
175

4

Hill

176

Reflexes absent. Animal quiet.

5

Respiration stopped.
Slight respiratory effort.
Artificial respiration. Reflexes
absent.

Clot.
Death.

52

88

119
178

2
10

Experiment 15. — Aorta tied at tht diaphragm, which wax perforated. Ether used. Alcohol. 't.'

pi r <■> at .

Time in minutes and
seconds.

Drug.

Pulse.

Pressure

Remarks.

0
3.00 to 3.20

4.00

7.00

S.OOto S.20

11.50

11.20

11.50

11.50

12.50
13.20

c. c.

15S

Heart prolonged diastole. Cut
pneumogastrics. Respiration

stopped.

Artificial respiration.

L0

150
166

5

155

10

108

IO IO

o to

10 ic

52 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

An examination of the experiments of this series will show that alcohol under the circumstances
produced no constant influence upon the circulation. The results were very unsatisfactory so far
as the circulation is concerned, because of the enormous disturbance of the respiration and of
the general system produced by the tying of the aorta. There was so much unrest and motion,
and the circulation was so irregular, that the series is probably of no value as throwing light
upon the action of alcohol upon the circulation. These experiments ought to be repeated upon
curarized dogs, with artificial respiration, if any weight at all is to be attached to them.

The conditions under any circumstances, however, are so abnormal that it has not seemed
to us that any results reached would be of importance, and we have therefore not carried this
matter to a further conclusion.

STROMUHR.

Over twenty-five years ago Dr. H. C. Wood asked Professor Schmiedeberg, in his labora-
tory at Strassburg, to show him how to use Ludwig's stromuhr; the reply was, -v Nobody can
use the stromuhr except Professor Ludwig, and Ludwig himself could not do so if it woe not
for his diener Hans. So Doctor Wood went to Leipzig, told the story to Professor Ludwig,
who with considerable glee called Hans and said: '''Hans, Schmiedebekc says I could not use
the stromuhr if it was not for you; that you are the man who does it; so show the professor
how."

There are, however, no excessive practical difficulties in the use of the stromuhr, provided
complete destruction of the coagulability of the blood be secured. In the present work we found
great difficulty in preventing the coagulation of the blood in or about the tubes of the stromuhr.
The rabbit is so small an animal that it did not seem to us wise to employ it, so all our experi-
ments were made with dogs.

Wittee's peptone was given intravenously to the amount of over 3 grams per kilo to the
dog without sufficient result on the blood to make the experiment workable. Leech extract, or
the active principle of the leech salivary gland, we were unable to buy in the American market.
Following the method recommended by Franz as closely as we could did not bring the desired
result for reasons that are not clear to us. We succeeded, however, in getting successful
experiments by using the following plan, based upon the work of Franz: According to the
statements of Franz, the active anticoagulating principle of the leech is most largely situated
in the salivary glands anterior to the tenth ring, but is also to a greater or less extent diffused
through the rest of the body. We found it very difficult with our laboratory centrifuge to
properly act upon a large gummous mass such as that formed with the whole of the leech,
whereas the centrifuge acted well with the leech heads.

We therefore cut off the heads of the leeches, cut them into very small pieces, rubbed
them up with very tine sand, and to the mass added 5 c.c. of a seven-tenths per cent normal salt
solution for each leech represented. This was heated for twenty minutes over a wTater bath at
212°. The bodies of the leeches we treated in the same manner as the heads, and the two separate
masses were allowed to stand in a room of low temperature for twelve hours. The mass contain-
ing the leech heads was then centrifuged for twenty minutes; the sand contained in the lower
portion of the centrifuge was then washed, the wash liquid centrifuged, and the two fluids obtained
added together. The mass containing the bodies of the leeches was filtered through cheese cloth
under pressure; the filtrate was then centrifuged. The mass was again washed with salt solu-
tion, the filtrate centrifuged, and the two results obtained added. The fluids obtained from the
heads were now added to those derived from the bodies, and the two constituted the liquid leech
extract which was injected.

For obvious reasons no definite amount of the saline was used in making the leech extracts,
consequently the dose of the solution given to the dog was measured b}r the number of leeches
represented and not by the number of cubic centimeters of the solution injected. Franz states
three leeches per kilo as the amount necessary to prevent coagulation; the lowest amount with
which we were successful was three and a half leeches per kilo, but it is very probable that the
fresh European leech contains more of the active principle than do such travelled leeches as we

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

53

employed, since it may well be that the amount of active principle in the leech is lessened by the
transportation across seas and the necessary long keeping.

The stromuhr used in these experiments was connected with the carotid artery and the
jugular vein on the same side of the neck in the ordinary manner. Morphia was used in suffi-
cient amount to keep the animals perfectly quiet during the experiment. Ether was also admin-
istered during the insertion of the stromuhr, time being afterwards allowed for the influence of
the ether to be entirely dissipated before the stromuhr norm was taken. The alcohol was given
intravenously. The experiments were as follows:

In the details of the experiments the record of time during the experiment is in minutes,
that of the filling of the stromuhr in seconds. The alcohol used was always 25 per cent.

Experiment 16.

Time in
minutes.

Drug.

Stromuhr

time in
seconds.

Remarks.

0
2
3
4
8
10
12
17
19
22
24
25
29
30
33
35
39
41
43
45
47
50
53

c. c.

21

Norm.
Respirator)' death.

1

18
18
16

2

16

2

15

3

13

5

14

5

14

8

17

10

20

15

25

20

4:i

Experiment IT. — Wt ight of dog, 8.05 kilograms.

Time in „
minutes. < umg-

Stromuhr
time in
seconds.

Remarks.

0

1

3

4

5

6

7

8

9

10

11

12

14

15

19

20

24

28

32

c. <'.

22

Respiratory death.

2

20

2

17

2

15

3

14

4

14

5

14

10

14

20

14

12

21

54

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

Experiment 18. — Very young dog, weight 6.006 kilograms.

Time in
minutes and

seconds.

Pressure,

arteriiil.

Drug.

Rate of
pulse.

Stromuhr
time in
seconds.

Remarks.

0.30
2.30

18.30

19.00

c. r.

Respiratory curves absent or

slight.
Distinct respiratory curves.

81

63
68

130

144
154
152

35
35
35

19.30 70

20.00
20.30
21.30
22.30
24.30
25.30
26.30
31.30
32.00
40.00

1

66

68

"~69~~
72

144
152

17
17

2

156

20

16

4

60
61
53

138

30

148 29

166

74

In looking over the foregoing experimental record, it will be seen that in Experiment ltf,
under the influence of 8 c. c. of 25 per cent alcohol, there was a decrease in the time required to
till the stromuhr of from twenty-one to fourteen seconds, or, in other words, an increase of 33 per
cent in the rapidity of the. flow of the blood. This increase in the rapidity of the flow of blood
was maintained after the further injection of 5 c. c. of alcohol, but gradually lessened on the
repetition of the dosage, so that after 36 c. c. of the alcohol it had practically disappeared. The
paralyzant influence of the alcohol then became more and more apparent, and when 15 c. c. in
addition to that previously used had later been injected, the rate of flow through the artery was
less than half of the norm.

In Experiment 17, in a dog weighing S kilos, 9 c. c. of alcohol reduced the time necessary
for the tilling of the stromuhr from twenty-two to fourteen seconds- -i. e., increased the rapidity
of the blood flow a little over 33 per cent. It is remarkable that the further injection of 35 c. c.
of alcohol had no further effect upon the rate of the blood current, but when 12 additional c. c.
were subsequently given the flow came down to about the norm.

Experiment l!-i was a more complicated one than the others. In it the blood pressure was
studied at the same time as the rate of blood flow. The administration of 1 c. c. of alcohol
brought down the time necessary for the filling of the stromuhr from thirty-five to fifteen
seconds: in other words, more than doubled the rate of flow. When 6 c. c. of additional alcohol
had been given, the increase of the rate of flow decreased until finally the paralyzant effect of the
alcohol upon the circulation became very apparent, so that seventy-four seconds were required
to till the stromuhr instead of thirty-five, the norm. It should be noted that the changes in
the rate of flow were not paralleled by any changes in the arterial pressure. A peculiarity of
this experiment is the extraordinary effect reached by the injection of a very small amount of
alcohol. It should be noted, however, that the dog which was experimented upon was not only a
very small dog, weight 12 pounds, but that it was also a very young puppy, and therefore
presumably abnormally sensitive to the influence of drugs.

SERIES SIXTH.

In studying the action of alcohol upon the isolated frog's heart we have used successively
the various forms of apparatus known to us, in order to reach results which should be as far as
possible free from fallacies, and to discover the possible sources of the difference of the reports
made by other observers.

We have made a number of experiments with the ordinary Kroneker apparatus. Unfortu-
nately, in the moving from the old to the new University of Pennsylvania laboratories, all the rec-

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT. 55

ords of these experiments were lost. The tracings had, however, beeu studied, and the conclusion
reached that no constant effect was demonstrable in them as produced by alcohol, except that
very large doses of alcohol depressed the heart. It has seemed to us, as the result of our experi-
ments, that the Kroneker apparatus is not applicable to the study of problems like that which
we are considering, namely, whether a certain drug does or does not increase the heart work.
Under the best conceivable circumstances the isolated frog's heart is under conditions which are
unnatural, and which may seriously affect the influence of drugs upon the viscus. In most of
our experiments with Kroneker's apparatus, owing to the canula being inserted not into the
aorta but into the ventral or dorsal portion of the auricle, the ligature was so low down as to
compromit the ganglia lying in the lower third of the auricles, so that the preparation was
practically an apical one. The difference between such a preparation and that of the heart
proper is shown by the fact that whereas the frog's isolated heart ought to beat from 25 to 40
heats a minute, in our experiments with the Kroneker apparatus in most cases it beat 4 to 5
times a minute, and often would not rhythmically pulsate at all unless artificial stimulation was
applied to it.

It is true that in some cases we succeeded in tying above the ganglia, under which circum-
stances the preparation was one of the heart itself and not an apical one. and the viscus could
heat rhythmically. It is evident that with an apical preparation it is not possible to- satisfactorily
study a drug which may act upon the heart ganglia, and in any series of experiments with the
Kroneker apparatus confusion is liable to arise from an attempt to compare the results of
experiments in which the preparations have been really diverse, some with and some without
uninjured cardiac ganglia. Of course, exactness on the part of the experimenter will minify
this possible source of fallacy.

Moi'e serious objections to the Kroneker apparatus for use by the pharmacologist are the
following:

First. To maintain the slow circulation of the blood through the loose tissues of the frog
very little force is required,, so that the batrachian heart is arranged for and accustomed to but
little resistance to its efforts: in the Kroneker apparatus, during the period of record, the heart
is heating against a comparatively heavy column of mercury, and is therefore under unnecessarily
unnatural conditions.

Second. An objection which applies equally to the usual forms of the Williams apparatus as
to the Kroneker, is the difficulty of interpreting the graphic results. In the interpretation of the
writing the height of the wave is usually taken as the measure of the heart work; it is plain, how-
ever, that this height is chiefly the measure of the force of the current, since it is entirely possible
that the heart should not thoroughly empty itself in systole against the resistance of the mercu-
rial column: further, it is certainly conceivable (in our opinion must be) that a heart, wThich during
diastole is only partially dilated and therefore at the time of systole has in it comparatively
little blood, may by a sudden, sharp, very complete contraction raise the mercurial column higher
than, or at least as high as, it would be elevated by another heart which dilating very freely beats
with a slow, prolonged, hut not very forcible, contraction. In one case the graphic result would
he a high, narrow cone: in the other case it would he a broad, perhaps flat-topped, wave. The
second heart might he doing much more work than the first, although the ordinary method of
reading the graphic results would assign to the first heart the victory of doing the larger work.
In other words, it seems to us plainly possible that a drug may greatly increase the work done by
a heart without proportionately increasing the power of that heart to overcome resistanceand to
raise a column of mercury.

Third. A source of fallacy with the Kroneker apparatus is the varying condition of the heart
as to its blood supply: this is readily appreciated by reference to the following tig. 1. It will
he seen at once that when the stopcocks L and F are open the blood flows from burette B to
burette A, and the heart has through it a regular circulation: when, however, a record is
to he made the stopcocks L and F are closed, so that the heart is beating against the resistance
of the mercury column, and has no blood passing through it during the record period. After

56

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

the record has been made, the blood is again allowed to flow through the heart, and so with
alternate periods of feeding and starving the heart continues its movements as long as may be.
It is evident that the conditions under which the heart is doing its work are again unnecessarily
unnatural, and further, that it is not possible to make a continuous uniform application of the
drug under study to the heart.

Fourth. A possible source of fallacy is found in the difficulty of closing the stopcocks F
and L at exactly completed diastole, for it is evident that if in one record the heart had been
thoroughly dilated when closure was made, and in the other record the heart had been lacking
even 10 per cent of full dilatation, the rise of the mercurial column would be different in the
two records, although the real power of the heart is the same during the two periods.

The four considerations given above seem to us sufficient to prevent reliance on drug exper-
iments made with Kroneker apparatus, except when the influence of the drug is so overpowering
as to overcome the limit of error due to the conditions of the trial.

Flu. 1.

In the Williams apparatus a double cauula is placed in the ductus arteriosus and the whole
heart is employed, so that some of the difficulties of the cardiac study are avoided. Two forms
of the Williams apparatus have hitherto been in use, and have been supplied to the university
laboratories by the Harvard Apparatus Company.

In the first of these forms of apparatus the blood flows through the heart during the whole
experiment, avoiding in this way one of the difficulties of the Kroneker apparatus, and the
graphic record is made of the movements of the salt solution in the closed receptacle K. in which
the heart is placed. Two methods of study have been practiced in regard to these movements.
In one method the movement of the salt solution is simply measured by the eye, as the column
pulsates backward and forward over a graded scale. In the other method the movements arc
imparted to a comparatively heavy column of mercury which records them upon a revolving
drum. In the Harvard apparatus, fig. B, with which we experimented, the graphic method was
employed.

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND IIOYT.

0/

The objections to the first form of the Williams apparatus as supplied by the Harvard Com-
pany, are: First, the great nonintermittent outside pressure upon the heart, K, tig. 2, produced
by the liquid in which the heart is immersed and the column of mercury connected with that
liquid, in accordance with the ordinary laws of hydrostatics; second, the difficulty of interpreting
the graphic records, which has already been spoken of, applies to this as to all other graphic
methods of studying the frog's heart; third, at least in the individual form of apparatus supplied
by the Harvard Company as we put it up, the pressure on the inside of the heart is excessive.
due to the height of the reservoir above the heart.

The second form of the Williams apparatus seems to us to involve three inherent sources of
possible fallacy. First, the heart is working against excessive resistance in raising the column
of mercury; second, if by loosening of the clamp or in other method the size of the orifice at

A j^B

c\

kfj — h&{

If

mD h I H

E~jjp

fflf— \ 1

1 1t k Hi

which the blood escapes becomes in the slightest degree altered, an enormous effect must be
produced upon the mercurial column, since the movements of the mercurial column mark simply
the relation between the resistance at that point and at the point of pulsation:" third, close,
accurate interpretation of the graphic results is for reasons previously explained difficult if not
impracticable.

f In using this apparatus we found that much freer movements took place in the mercurial column when the
second valve at D, controlling the backward flow of the blood, was left open; the increased movements of the mercury
being evidently due to an increased fall of the column, the result of the reflux of the column of blood into the heart
during the diastolic period. It is plain, however, that under these circumstances the interna] pressure upon the
ventricles during diastole must equal the weight of the column of mercury, increased according to the laws of
hydrostatic pressure, and that in this fact is found a most unnatural condition, the effect of which can not lie
estimated. We have experimented with Williams's apparatus both with and without the distal valve: those
experiments which yielded the best-looking tracings were without the valve, but we are not at this time able to
trace out the differences in the. experimental results.

;>n

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

The force of the objections to even the best form of the Williams apparatus was not
appreciated by us until we had made a number of experiments upon the isolated heart of the
frog. The record of those experiments which we made with the second form of the Williams
apparatus are as follows:

Experiment 19.

Time in
minutes.

Rate.

Height.

Resultant.

Remarks.

1
3
4
5

6
9

56
56

14
14

784

7S4

i of 1 per cent of alcohol.

56

58
56

12
L2

12

672
696
672

Experiment 20.

Time in
minutes.

Rate

Height.

Resultant.

Remarks.

8

10
11
13
16
17
19
21
23
25
31
35

24
24

18
20

432
480

1 per cent of alcohol.
3 per cent of alcohol.

24
21
19
18

26
20
22

I'll

624
420
418
360

17
18
17
18

20

18
14
10

340
324
238
180

Experiment 21.

Time in
minutes.

Rate.

Heigh l.

Resultant.

Remarks.

2
3

5

6
11
12
14
16
22
24
26
28
30
32
35

• 24
21
20

32
32
32

768
672 '
ii4ll

} of 1 per cent of alcohol.

1 per cent of alcohol.
5 per cent of alcohol.

31
21
32
32
29

30

28
30
32
30

930

868
960

1,024
S70

25
26

30
30

750

7S0

21

20

30
28

630
560

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND IIOYT.

59

Experiment -2'2.

Timein ,
minutes.

Height.

Resultant.

Remarks

12
13
15
16

8

9

s

8
8

s

04
72

til

1 of 1 per cent of alcohol.

■1 of 1 |>cr cent of alcohol.
J of 1 jier cent of alcohol.

1 per cent of alcohol.

18
20
31
35

40

4;i

51
58

"i6"

9

Id
10
11
10

111

s
8
8
10
10
10
10

SO
72
80
100
110
100
100

61
68

75
84
87
89
100

9

111

90

9

s

6

8

54
64

8
8

6
8

48
64

Looking over the records of these experiments will show that in Experiment 19 the exhi-
bition of one-fourth of 1 per cent of alcohol was followed by a distinct fall of the heart work;
that in Experiment 20 the use of 1 per cent of alcohol was followed I >y a temporary rise, soon
giving way to a distinct fall, which became more accentuated when 3 per cent of alcohol was
Used; that in Experiment 21 one-fourth of 1 per cent of alcohol apparently produced a very
decided and persistent rise of heart work, which lasted until the alcohol was increased to 1 per
cent, when there was a pronounced fall, not, however, below the norm; whilst later 5 per cent
of alcohol rapidly decreased the heart work to below the norm; that in Experiment 22 the heart
work was distinctly and persistently increased by the exhibition of one-fourth of 1 per cent
of alcohol, the increase being maintained for over half an hour, until the exhibition of three-
fourths of 1 per cent of alcohol produced a fall below the norm.

On the whole these experiments seem to us to indicate that in small doses alcohol increases
the work of the isolated frog's heart, but the results obtained were distinctly discordant and
unsatisfactory. In all these experiments the hearts of small frogs were used, and after much
experience witli Kroneker's apparatus, Williams's apparatus, and the one shortly to be described,
it is clear to us that experimental results reached by the use of small hearts are not reliable.
The resistance in either the Kroneker or the Williams apparatus, when the small heart is used,
is out of all proportion to the cardiac power, and feeble muscle fiber may well stretch, give way,
or lose functional ability rapidly under the strain. Moreover, in the Williams apparatus, when
the heart is small it is difficult to avoid injury to it in the insertion and securing of the canula in
the truncus arteriosus, and we know of no way of judging with certainty whether the heart has or
has not been injured. Whatever the reasons may be, of this fact we are confident, namely, that
even with the best forms of "frog's heart apparatus,'" if the experimental results are to be per-
sistent in the one experiment and consistent in the various experiments, it is essential that the
hearts of very large bullfrogs or of large snakes or tortoises be employed. We believe that the
failure to obtain a rise in Experiment 19 from the one-fourth per cent of alcohol was probably
due to injury of the heart in the making of the preparation.

Led by what we consider to be the difficulties inherent to the older forms of apparatus, we
have devised and used one which is shown in tig. 3, an apparatus which is of course a modifica-
tion of the Williams apparatus. This apparatus consists, beginning at the left, in a pair of
Mariott bottles, united by a Y-shaped tube with a clip so arranged as to shut off either bottle at
will. Then, of the ordinary Williams apparatus, with this modification, that at the distal end
the blood is allowed to pass through a glass tube and to drop into a beaker glass for a fixed

60

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

period of time. In using this apparatus the pressure upon the heart can be varied by elevating
the bottles A and R and the resistance to the systole by elevating the drip tube II. We have
found in practice that the elevation to the bottles and to the drip tube must have such relation
that the drip tube\shall be at least as high as the pressure point in the bottles.

Our experience shows that in order to get the best results with this apparatus some care and
experience are necessary in so adjusting the height of the reservoir bottles above the heart that
the amount of pressure upon the heart during diastole and the amount of resistance to the heart
during systole shall be properly proportioned to the size and power of the organ. In the frog,

Fig. 3.

and probably other reptiles, the internal diastolic cardiac pressure is very slight, so that in the
isolated heart it is very easy to have conditions, both during diastole and systole, which are
entirely unnatural. "

" In trials with the pure Kinder solution as a nutrient fatigue developed so rapidly as, in our opinion, to make
trustworthy results impossible. The fluid which we finally used was similar to that originally employed by Williams,
except in the substitution of bullocks' for rabbits' blood. Our fluid consisted of a mixture of one part of defibrinated
bullocks' blood to two parts of a half per cent of saline solution. In order that the heart might have a constant
supply of oxygen, in no case was the same blood passed twice through the heart. In one of the large reservoir
bottles was placed the pure nutrient fluid, in the other nutrient fluid containing the required percentage of alcohol,
so that by simply changing the clip, without altering the pressure or in any way disturbing the heart condition,
pure nutrient fluid or alcoholized fluid could be run through the viscus at will. We had some difficulty in working
the Williams valve until our dinner, suggested the use of the skin of the frog, which we found when used fresh or
even after keeping in saline solution would do admirably.

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND IIOYT.

61

Experiment 23. — Moderately larg* frog.

Time in minutes and

secoinls.

Elate.

Amount.

Remarks.

2.58 to 3.03
3.03 to 3.08
3.08 to 3.13
3.13
3.13 to 3.18

3.28 to 3.33

3.33 to 3.38

3.44
3.46 to 3.51

3.51 to 3.56

3.57

4.01 to 4.06

4.10

4.12 to 4.17
4.17 to 4.22
4.22 to 4.27

4.31

4.34 to 4.39
4.39 to 4.44
4.44 to 4.49

4.49

4.52 to 4.57
4.57 to 5.02

5.02 to 5.07

5.07

5.13 to 5 L8
5.20 to 5.25

24
15
14

c. <-.
S4
99
105

| of 1 per cent alcohol.
< Hogged valve cleaned.

Blood without alcohol.
Heart irregular in action.

1 ot i per cent alcohol.

Air in tube since beginning taken
out.

Blood without alcohol.

J of 1 per cent alcohol.

Blood, 1 per cent alcohol.

Hi

112

120
152

65
84

85

111
107
103

99

95

100

109

110
96

56

4:;

Experiment 24. — Rather small frog.

Time in minutes and

seconds.

Elate.

Amount.

Remarks.

1.35 to 1.45
2.04 to 2.09

2.10 to 2.15

2.15
2.15 to 2.20

2.26 to 2.31

2.31 to 2.36

2.36
2.38 to 2.43
2.43 to 2.4s
2.4S to 2.53

2.5:; to 2.58

2.58

3.01 to 3.06

3.06 to 3.11

3.11 to 3.16

3.16
3.21 to 3.26
3.26 to 3.28

3.28
3.29 to 3.34
3.34 t.. 3.39

C. c.

\ of 1 per cent alcohol.

Apparatus out of order; 10 minutes
to get started.

Blood without alcohol.

Four minutes.

J of 1 per cent alcohol.

Blood without alcohol.

Two minutes.

1 per cent alcohol.

26
26

18
19

40
36

83

91

34
34
32
32

86

87
87
90

32
32
32

104

93
91

30

55

22

32

48
25

In the last experiment perhaps the alcohol used was too strong — one-half per cent instead of one-fourth. Much
fussing and use of heart, also, before last trial.

G2 MEMOIKS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

Experiment 25. — Large frog.

Time in minutes and
seconds.

Rate.

Amount.

Remarks.

3.03 to 3.08
3.os to 3.13
3.13 to 3.18

3.18
3.20 to 3.25
3.25 to 3.30
3.30 to 3.35
3.35 to 3.40

3.40
3.43 to 3.48
3.48 to 3.53

3.53
3.54 to 3.59
3.59 to 4.04

4.04 to 4.09

4.09
4.11 to 4.16
4.16 to 4.21

4.21
4.22 to 4.27
4.27 to 4.36

40
39
39

c c
90
91
93

} of 1 per cent alcohol.

Blooil without alcohol.
A of 1 per cent alcohol.

Blood without alcohol.
\ of 1 per cent alcohol.

40
38
40
38

101
102
103
102

37
38

92
92

36
38

97
96
95

36
36

88
86

36

36

86

68

Experiment 26. — Land tortoise.

Time in minutes and
seconds.

Rate.

Amount.

Remarks.

4.19 to 4.24
4.24 to 4.29

4.30
4.32 to 4.37
4.37 to 4.42

4.42
4.44 to 4.4!)

42

41

c. c.
149
149

j of 1 per cent alcohol.
Blood without alcohol.

41
36

175
175

39

125

Experiment 27. — Snaki .

Time in minutes and
seconds.

Rate.

Amount.

Remarks.

3.48 to 3.53
3.53 to 3.58

3.58 to 4.03

4.03
4.05 to 4.10
4. 10 to 4.15
4.15 to 4.20

4.20
4.22 to 4.27
4.27 to 4.32

4.32
4.34 to 4.39
4.39 to 4.44

4.45
4.47 to 4.52

4.:.:;

34
28

28

c. c.
55
60
60

2 of 1 per cent alcohol.

Blood without alcohol.
£ of 1 per cent alcohol.

25 66
28 68
33 ; 68

33 61
36 61

34
36

70
69

37

54

j of 1 per cent alcohol.

Blood without alcohol.
| of 1 per cent alcohol.

Blood without alcohol.

4.55 to 5.00

5.00 to 5.115

5.06 to 5.11

5.11

41
40
40

62
56
45

5.13 to 5.18

5.19 to 5.24

5.24

42
44

39
79

5.30 to 5.35
5.36 to 5.41

44

99
91

5.41

5.42 to 5.47

44

73

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND IIOYT.

63

Experiment 28.- Snapping turtle.

Time in minutes and
seconds.

Rate.

Amount.

Remarks.

4.05 to 4.10
4.10 to 4.15

4.16
4.17 to 4.22
4.22 to 4.27

4.27

9

r. r.

177

175

A of 1 per cent alcohol.

9
12.

197
213

In studying the experiments which have here been recorded in detail, it will he noted that in
Experiment 23 under the influence of one-fourth of 1 per cent of alcohol the heart work increased
from a maximum of 105 to 150 c. c, then on the withdrawal of the alcohol fell to 84 c. c, hut rose
again to 111 on the renewal of the alcohol, to fall again to 100 when the alcohol was withdrawn; to
rise to 110 again when the alcohol was added in half per cent, this rise being followed, however,
by a rapid fall in the amount of the heart work, which on the increase of the alcohol in the blood
to 1 per cent came down to 43 c. c. per minute. The technical details of this experiment were
not satisfactory in that at one time the apparatus had to be taken entirely apart on account of
coagulation of blood in it, and that later the process had to be again stopped in order to remove
air which had been shut in the tube.

In Experiment 24 the work of the heart rose from 10 c. C. during the prealcoholic period to
91 c. c. during the alcoholic period, tailing, however, very distinctly when the alcohol was
withdrawn from the blood; increasing later to 104 when the alcohol was increased to one-half
per cent, and falling rapidly to 22 when the alcohol was withdrawn, rising again on the addition
of 1 per cent of alcohol temporarily, the rise being followed by a fall. The first part of this
experiment was in its technique not thoroughly satisfactory and the alleged norm of 10 c. c. is
almost certainly incorrect. The apparatus in the beginning failed to work properly, for reasons
which were not clearly made out; requiring ten minutes for taking everything apart and getting
the tubes together again before the blood flowed freely. The original norm was probably
incorrect, but the subsequent readings were clearly accurate.

The two experiments, 2:; and 24, whose results we have just epitomized, were maae with
medium-sized hearts derived from frogs of corresponding size. For reasons which have been
heretofore assigned, it seems to be impossible to get with such hearts satisfactory results, and
we therefore do not think that very much weight can be given to these Experiments 23 and 24.

The remaining experiments of the series were made with powerful hearts, capable of over-
coming the resistance and other abnormal conditions of the heart under study.

In Experiment 25, under the influence of one-fourth percent of alcohol, the heart work rose
from 93 to 103; that is, 12 per cent; fell 12 per cent when the alcohol was withdrawn, rose about
5 per cent under the influence of one-third per cent of alcohol, fell to 10 per cent below the
original norm when the alcohol was withdrawn: the heart subsequently failing under the influence
of one-half of 1 per cent of alcohol.

In Experiment 26, made with a land tortoise, the norm of heart work was found to be 149
c. c, rising to 175 on the addition of one-half of 1 per cent of alcohol to the nutritive fluid, to
fall to 125 when the alcohol was withdrawn.

In Experiment 27. in which a snake was used, the heart work norm was 60 c. c. ; the addition
of one-half of 1 per cent of alcohol made it rise to 68 c. c, about 13 per cent: then the work fell
to the original norm when the alcohol was withdrawn, to rise again about 15 per cent on the
addition of one- half of I per cent of alcohol to the blood; to fall again In percent below the
norm when the alcohol was withdrawn, again to rise temporarily under the influence of two-
thirds of 1 per cent, of alcohol, to fall again much below the norm mi the withdrawal of the
alcohol, again to increase under the influence of two-thirds of 1 per cent of alcohol 16 per cent,
to finallv fall when the alcohol was withdrawn.

64 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

In Experiment 28, with the large heart of a good-sized snapping turtle, one-half of 1 per
cent of alcohol raised the heart work from 177 to 213, a gain of 20 per cent.

In addition to the experiments, the details of which have been given, we have made others
with the hearts of large frogs, in which the results reached were entirely concordant with those
just tabulated. It should be noted that in many of these experiments the alcohol was repeatedly
used and withdrawn and used again, and that each time the heart work rose and fell with the
giving and withdrawing of the alcohol, and that in no experiments with the large heart did the
alcohol fail clearly and positively to manifest its influence.

The results of all the experiments which we have made clearly establish that when the
isolated reptilian heart is placed under conditions as nearly natural as is possible, the amount of
blood which it will pump during a fixed period — i. e., the amount of work which it will do — is
increased usually from 10 to 15 per cent by the addition of one-quarter to one-half per cent of
alcohol to the nutrient fluid. In these experiments it was usually apparent that the increased
work was manifested by the increase in the amount of blood thrown out by the heart at one
systole, and it appeared to us that the alcohol increases the completeness of the diastole.

RELATION TO PREVIOUS INVESTIGATION.

The facts which we believe we have experimentally determined in regard to the action of
alcohol upon the circulation are:

First. In the normal dog alcohol does not usually, either in small or large dose, distinctly
increase the arterial pressure, although occasionally such an effect appears.

Second. The action of alcohol upon the circulation in dogs suffering from an infective fever,
at least so far as the blood pressure is concerned, is similar to its influence upon the normal dog.

Third. After section of the spinal cord in the cervical region, with artificial maintenance of
the respiration, alcohol distinctly and consistently increases the arterial pressure; in other words,
alcohol increases arterial pressure after the general vascular system has been separated from
its dominant vaso motor centers.

Fourth. (Series 5.) The exhibition of small doses of alcohol increases very markedly the
rate of flow of blood through the large arteries, as measured by Ludwig's stromuhr; this increase
of rate being consistently maintained under the repetition of the intravenous injection of alcohol
until the time comes when the rate of flow gradually lessens under the paralytic influence of the
toxic dose of alcohol upon the heart and blood vessel. The increase of the rate of flow is in
no wise dependent upon nor related to any elevation of the arterial pressure, as it may occur
without the pressure being sensibly affected.

Fifth. (Series (!.) One-quarter to one-half per cent of alcohol added to the nutritive fluid
feeding an isolated working reptilian heart markedly and persistently increases the amount of
the fluid pumped in a given length of time by the heart; that is, markedly increases the work
done by the heart. If one-half to 1 per cent of alcohol lie added to the nutritive fluid there may
be a primary condition of increase of work, followed in a few minutes by marked lessening of
the work clone. Larger percentages of alcohol immediately decrease the activity of the isolated
reptilian heart.

The first question which naturally arises at this point is as to how far the above facts which
we seem to have established agree with the results obtained by previous experimentators; let us
look at this matter in a consecutive manner.

First. Without more elaborate discussion we think that anyone conversant with the litera-
ture of the action of alcohol upon the blood pressure will acknowledge that the general drift of
the evidence is in accord with the results which we have reached. Most observers affirm they
have been unable to get any increase of the arterial pressure by the use of alcohol, whilst others
allege that they have obtained such increase. Attempts have been made by critics to reconcile
these differences by asserting the incompetence of one set of observers, the critic attributing
these qualities to one or the other set of observers according to his own opinion on the subject.
It seems to us much more probable that both sets of observers have recorded correctly their

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT. 65

observations, which were partial truths, the whole truth being' that alcohol does not commonly
elevate the blood pressure, but in some cases does so.

Second. We know of no experiments having been made as to the effect of the exhibition of
alcohol upon the blood pressure in dogs suffering- from an infective fever, but the results which
we have obtained in dogs are in close concord with those reached by Cabot upon human beings
suffering from various infective fevers.

Third. The only experiments with which we are familiar other than our own upon the action
of alcohol on the arterial pressure after section of the spinal cord are those which were made in
or about 1900 by Prof. John J. Abel, of Johns Hopkins University. In these experiments the
results were exactly like those which we have obtained. In a letter written in 1904 by Professor
Abel to Dr. H. C. Wood, Professor Abel states that in all his spinal-cord experiments with
alcohol great care was taken to see that the section of the cord was complete, and he further
states that except in certain experiments, when owing to the animal having been extremely feeble
and having suffered from violent hemorrhage during the operation, the blood pressure was almost
exhausted before the administration of the alcohol, alcohol always caused distinct elevation of
the arterial pressure after section of the spinal cord.

Fourth. In regard to the effect of alcohol upon the rate of the blood flow, the only experi-
mental record in literature with which we are familiar is that of John C. Hemmeter (N. Y. M. R.,
xl, 1891), who in a single experiment found that in the dog the blood flow was increased from
158 milligrammes per second to 399 milligrammes per second by the exhibition of alcohol. This
single experiment is evidently in accord with the results which we have obtained.

Fifth. In regard to the action of alcohol upon the isolated reptilian heart, much work has
been performed by various observers at various times, with results which have been discordant.
In our study of the effect of the drug upon the reptilian heart the attempt was made to discover
if possible the reason of this discordancy. The method of cutting the Gordian knot adopted by
some authorities, namely, the assertion that everybody, who had obtained results different from
those which they themselves had reached, did not know how to experiment properly, as already
stated, does not seem to us philosophic. Having, however, exhaustively studied this subject
already, we now merely state our conviction that the reasons of the discrepancies in literature
have been made apparent, and that our results are not exceptional in any way.

INTERPRETATION.

The interpretation of the experimental facts which have just been stated does not seem to
us difficult. The arterial pressure is the result of the interplay of two antagonistic forces, the
propelling power derived from the heart and the frontal resistance offered by the blood vessels.
If either of these forces be increased — that is. if the blood vessels be narrowed or the heart power
augmented — the arterial pressure will rise. If either of these forces be diminished the arterial
pressure will fall. If one of these forces be increased and the other diminished the arterial
pressure may rise, may fall, may remain as it has been, according as the balance between the
two forces rises, falls, or is maintained. The fact, therefore, that alcohol does not constantly
elevate the blood pressure is no proof that it does not stimulate either the heart or the blood
vessels, since it is evidently possible that it may stimulate one dominant factor of the blood
pressure and depress the other so equally as to maintain the balance. Further, the fact that
the influence of alcohol upon the blood pressure is not a constant one suggests the probability that
it does disturb one or other dominant blood pressure factor, and is unable always to accurately
keep the balance between the two altered forces.

The second fact in regard to alcohol and the blood pressure is that alcohol notably, consist-
ently, and persistently elevates blood pressure after paralysis of the vasomotor system by high-
up spinal section. This elevation of the blood pressure can not be due to a local action upon
the blood vessel walls, otherwise it would manifest itself before section of the spinal cord,
because any local action would necessarily show itself as much before as after removal of the
dominant vasomotor nerve control. It appears to us that the effects of alcohol upon the blood
89369°— vol 10—11 5

66 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. N, NO. 3.

pressure before and after section of the cervical cord are when taken together in themselves
sufficient to show that alcohol concentaneously stimulates the heart and depresses the vasomotor
centers. This conclusion is very strongly corroborated by the effect of alcohol in increasing the
rate of the blood flow in the arteries. The blood flow may be increased by augmenting the force
of the propelling power, or by diminishing the power of the resistance, or it may be enormously
increased by simultaneously increasing the propelling power and decreasing the resistance. We
have demonstrated that the rate of the blood flow is almost doubled by alcohol; indeed the
amount of this increase is so great as in itself to suggest that there must be a double factor in its
production. That the increased rate of blood flow is not caused by or consistently accompanied
with increase in the arterial pressure we have demonstrated. Either simply cardiac stimulation
or simple vasomotor constriction would increase the arterial pressure. Moreover, if an increase
of the blood flow produced by the drug were simply due to cardiac stimulation, such cardiac
stimulation would of necessity clearly register itself in the uninjured animal by a rise of the
blood pressure, and this alcohol does not do; further, if the increased blood flow were the out-
come of vascular depression, of necessity alcohol should in the uninjured animal produce fall of
the blood pressure.

These three facts taken together, namely, lack of power to consistently increase or decrease
blood pressure in the uninjured animal; possession of power to increase blood pressure after
centric vasomotor paralysis; possession of power to enormously augment the rate of the blood
flow, lead to one inevitable conclusion, namely, that a drug which possesses these things must
simultaneously stimulate the heart and widen the blood paths by depressing the vasomotor
centers. Such, then, must be the action of alcohol.

The correctness of this conclusion is further corroborated by the results of our study of the
action of alcohol upon the isolated reptilian heart. It would, apparently, have been in order to
have made studies upon the mammalian heart, but we have long since believed, as the result of
careful study of the experimental methods and results heretofore published, that such experi-
mentation is so surrounded with practical difficulties that the results reached are more apt to be
misleading than true guides. The delicacy of the organ, the violence done to its natural condi-
tions, the unexplainable results which have been reached by various experimenters seem to us to
show that until the technique of the method is radically improved little can really be learned
from such experiments unless in the case of a drug like digitalis, whose cardiac action is
overwhelming.

On the other hand, the power of the reptilian heart under favorable circumstances to con-
tinue at ordinary temperatures its functions for many hours regularly and without pronounced
abatement evinces a lack of sensibility and a robustness of resistance to unnatural conditions
which are the basis of successful experimentation. Moreover, all our physiological and pharma-
cological data show that, so far as quality of drug action is concerned, there is no difference
between the mammalian and reptilian heart. We can. therefore, confidently add to the facts
previously summarized the further fact that there is direct proof that alcohol increases the heart
work.

CONCLUSION.

Alcohol does not seriously affect in tin normal animal blood pressure; elevates the Hood pres-
sure after vasomotor paralysis from net inn of the cervical cord; increases enormously the rate of
the Hood flaw; directly stimulates th, heart; therefore the general action upon the circulation
of the moderate dose of alcohol is great increase in tin rapidity of the circulation caused by
cardiac xti /nidation, with eascular (Hiatal inn due to depression of the vasomotor centers.

Hainan experiments. — The conclusion just reached rests, as does most of our knowledge, in
regard to the physiological action of drugs, upon experiments made upon the lower animals;
but it has occurred to us that these results might with a certain measure of plausibility be tested
by plethysmographic studies upon human beings. Some experience with the plethysinograph
has led us to believe that with this instrument incorrect results can very readily be reached, and
that too much reliance can readily be placed upon its indications. When the arm is used as

ACTION OF ALCOHOL UPON CIRCULATION— WOOD AND HOYT.

67

ordinarily in the plethysmograph insensible movements backward or forward have an enormous
influence upon the lever which records the movements of the contained fluid. We have made
two experiments with the arm plethysmograph, using- every precaution to avoid fallacies, and
employing a person unaccustomed to the use of alcohol. In the first of these experiments
whisky was taken, in the second Mumm's extra dry champagne. In examining the results of
these experiments it must be remembered that although it is possible to make a plethysmograph,
the movements of the lever of which shall have an absolute value — in other words represent the
percentage of enlargement of the arm — such instrument must be made with great care and at
much expense.

The university laboratory does not own such an instrument, and our present purposes have
not required it; all that we have attempted to do is to show whether there is or is not a distinct
increase in the size of the arm following the ingestion of alcohol. In the following tables, when
the needle was above the norm, the amount of the ascent is given in millimeters preceded by
a +; when the needle was below the norm the descent is given in millimeters with a — . As
already shown these millimeters are no measure of the amount of expansion and contraction
of the volume of the arm.

A.

Time in
minutes.

Drug.

Plethysmo-
graph ic lever.

0
20
30
40
60

Sll

90

Whisky 50 c. c

Ni inn.

Norm.

13 mm.

L5 mm.

|- 7 mm.

5 mra.

1 mm.

.In

do

do

do

do

do

0
7
11
14
15
19
27
:;n

M

Champagne 198 c. c

do

Norm.
1'4 mm.
+ 13 mm.
—10 mm.
+27 ram.
-j 22 ram.
+27 ram.
\- 7 mm.
— 11 mm.

do

do

do

do

do

..do

..do

The above records are entirely concordant with one another, differing only in the fact, which
is constantly indicated in human lite, that distilled liquors like whisky act more slowly than does
champagne. In each experiment there was a distinct increase in the size of the arm — with the
whisk}' slowly and gradually, with champagne, rapidly — developed; and with whisky much more
permanently maintained than with champagne, the rise after a time being followed by a slight
decrease in the size of the arm below the normal.

The increase in the size of the arm in these experiments is not readily explainable except
with the supposition of increased amount of blood in the organ, due to dilatation of the arterioles
and the greater circulation through the vessels of the extremities, the blood not tarrying so long
in the great venous system of the abdomen and thorax. The results therefore are entirely
concordant and corroborative with those reached by experiments upon animals.

REMARKS.

The conclusions which we have established throw much light upon the practical problem of
the therapeutic effects and uses of alcohol, indicating that some results which have been supposed
to be due to a direct action of the drug are secondarily produced by the increase of the activitv

68 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 3.

of the circulation. A scientific journal like the present is hardly the place for a discussion of
problems of practical medicine, but it may be allowable to point out how this new knowledge
relates itself to the action of the drug upon the cerebrum. There is, on the one hand, at present-
no sufficient proof that alcohol is a direct cerebral stimulant such as caffeine, unless it be in
exceptional cases of exhaustion or of narcotic habit it does not sensibly augment the working power
of the brain. Again, so far as consciousness is concerned, its tendencies are to produce sleep
rather than wakefulness, whilst the true cerebral stimulant, augmenting the functional activity
of the cortical centers, lessens their tendency to go into a condition of functional rest, i. e., sleep.
On the other hand, any habitue* of feasts where alcoholic drinks circulate freely knows full well
the increase of amount and brilliancy of conversation which occurs pari passu with the flushing
of the cheeks. Evidently it is probable that this cerehral excitement and increased activity is
due not to the direct action of the drug upon the brain but to the enormously increased now of
blood running riot through the cerebrum.

EXPLANATION OF PLATES.

PLATE I.

Experiment 17. — Stromuhr.

Fig. 1. The norm, after the leech extract, lower line representing seconds, upper line the time required for the filling

of the stromuhr.

Fig. 2. Record two minutes after the injection of 2 c. c. of alcohol.

Fig. 3. One minute after the injection of a second 2 c. c. of alcohol, 4 in all.

Fig. 4. One and one-half minutes after fourth injection of alcohol, 9 c. c. in all.

Fig. 5. One and one-half minutes after the sixth injection of alcohol, 13 c. c. in all.

Fig. 6. After the injection of 28 c. c. of alcohol.

Fig. 7. After the injection of 48 c. c. of alcohol.

Fig. 8. After the injection of 60 c. c. of alcohol.

PLATE II.

Experiment 18.

Fig. 1. The norm, after the leech extract, showing pressure in the carotid artery and time required for the filling of

the stromuhr.
Fig. 2. After 3 c. c. of alcohol.
Fig. 3. After 7 c. c. of alcohol.

PLATE III.

Experiment 21. — Williams' s apparatus. Frogs heart.
Fig. 1. The norm.

Fig. 2. With the use of one-half per cent of alcohol.
Fig. 3. With the use of 1 per cent of alcohol.

70

Memoirs Nat. Acad. Sciences, Vol. X, No. 3.

Plate I.

i i r

m

Fig. I.

mi iiiiiiiiiiiiiiiiiiiiiiiiiii mm

Fig. V.

Illllllllllllllllillllllllilllllllllll

Fig- II.

Fig. VI.

llllllllllllllllllllllllllllllllllll Illlllllllllllll

Fig. III.

Illllllllllllllllllllllllllllllllllll HI

Fig. VII.

Illlllllllllllllllllllllllllllllllllllllllllllllllllllll
Fig. rv.

llllllliiilliillliliiiiliiiiilliiiiiiiiniililiiiiillllUllll

Fig. VIII.

EXPERIMENT 17.

Memoirs Nat. Acad. Sciences, Vol. X, No. 3.

_A

Plate II.

A

i i i i i i i i i ii i i i i i i i i

Fig. I.

T

V

T~

Fig. II.

~T

IS

y

1 1 1 1 1 ii M

Fig. III.
EXPERIMENT 18.

Memoirs Nat. Acad. Sciences, Vol. X, No. 3.

\/\

Plate III.

Fig. I.

Y Y V Y

\iV

(\Al\(\l*

Fig. II.

h

I

r V Y T V
Fig. III.

EXPERIMENT 21

V

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

Volume X.

FOURTH MEMOIR.

WASHINGTON:

GOVERNMENT PRINTING OFFICE.

1905.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

FOURTH MEMOIR.

PHORONIS ARCHITECT A:

ITS LIFE HISTORY, ANATOMY, AND BREEDING HABITS.

BY

WILLIAM KEITH BROOKS, LL. D.,

Henry Walters Professor of Zoology in the Johns Hopkins University,

AND

RHEINART PARKER COWLES, Ph. D.,

Adam T. Bruce Fellow in the Johns Hopkins University.

71

INTRODUCTORY NOTE BY W. K. BROOKS.

As my name appears on the title-page of this Memoir as joint author, I take this opportunity to say that my
own share in the work has been that of instructor and director only. The investigations are the exclusive work of
Dr. R. P. Cowles, and while I have followed them in detail, and hold myself responsible for their soundness and
accuracy, the credit for the research belongs to Doctor Cowles alone.

Dry Tortugas, Florida, July 3, 1905.

72

CONTENTS.

Pago.

Introductory note by Prof. W. K. Brooks 72

Introduction 75

Methods 76

Breeding habits 715

Laying of eggs 77

Fertilization 77

Segmentation 77

Gastrulation and further changes in the form of the larva 79

Formation of the mesoderm 80

Further growth of the young larva 82

General account 82

Nephridial pit 84

-Medullary plate 84

Trunk cavity 84

Fully developed Actinotrocha 85

Species A 86

Species B 86

Internal organization of the fully developed Actinotrocha 87

Subneural gland 87

Oral and atrial grooves 87

Neuropore _ 88

Subneural sinus 88

Stomach diverticula 88

Notochords 88

Nervous system 89

Muscular system 92

Body cavities, mesenteries, etc 93

Nephridia 95

Rudiments of the adult blood vessels in the Actinotrocha 96

Blood corpuscles and their origin 97

Rudiment of the "adult collar cavity" _ 98

Metamorphosis 98

Preoral lobe and tentacles 99

Ganglion 99

Ectodermal wall of collar 99

Perianal ciliated ring and ectodermal wall of the trunk 99

Cavity of the preoral lobe 99

Mesentery between the lobe and collar 99

Larval collar cavity 99

Adult collar cavity 100

Trunk cavity and cavity of the ventral pouch 100

Ventral and lateral mesenteries 100

Stomach diverticula 100

Digestive areas 1 00

Nephridia 100

Vascular system 101

Adult Phoronis architi eta 102

( ieneral account 102

Lophophoral organs 103

Vascular system 105

Nervous system 106

Nephridia 107

Reproductive organs 107

Ciliated ridge of the alimentary canal 107

Summary 107

References Ill

73

PHORONIS ARCHITECT.*: ITS LIFE HISTORY, ANATOMY, AND

BREEDING HABITS.

INTRODUCTION.

The study of Phoronis wrchitecta was begun in the summer of 1901 and continued in the
summer of 1902 at Beaufort. N. C. We are indebted to the Hon. G. M. Bowers, United States
Commissioner of Fisheries, for the privilege of working in the Commission's station at Beaufort,
where all the conveniences necessary for scientific investigation are at hand: to Prof. H. V.
Wilson, director of the station in 1901, and to Dr. Caswell Grave, director during L902, for
many kindnesses.

While the study of the live material was for the most part done at Beaufort, the rest of the
work was pursued in the zoological laboratory of the Johns Hopkins University.

Since the discovery of Phoronis hippocrepia by Wright in L856, the affinities of this inter-
esting genus have been more or less under discussion. Different investigators have sought to
ally the Phoronidse with the Bryozoa, the Brachiopoda, the Sipunculida, and other groups.

Roule (1*0) thinks that the Phoronidas should be placed next to the Bryozoa in a natural classi-
fication. He does not consider that they have any affinity to the Entt mjpm usta, but from a study
of the early stages of development he finds that they are related to the true Chordata (tunicates
and vertebrates). He says. "16mbryon de Vertebre est une Trochophore renversee."

Lankester and Mcintosh are inclined to consider Phoronis, < 'ephalodiscus, and Rhabdopleura
as related forms, while Harmer (7) makes a comparison of Phoronis with Oephalodiseus and
thinks that perhaps there may be some affinity.

Masterman (1."). 16) in a series of papers made a comparison of the actinotrocha larva of
Phoronis with Balanoglossus and its larva and also with Cephalodisous. In this paper, he arrives
at the conclusion that there is a close genetic relationship between the Phoronida>, Balanoglossus,
and Oephalodiseus. Since the appearance of Masterman's papers, Ikeda (9) has investigated the
develdpment of Phoronis ijimai and has made a careful study of several Actinotrochse found in
Japanese waters. Shortly after this, Longchamps (12) published a comparative study of the
early development of several species of Phoronis and also of several species of Acti/notrochse,
giving a very careful critical resume of the work done by different investigators.

Menon (17) has lately published a short paper on the Actinotrochse, in which he considers
the Phoronidse to be related to the Chordata, but thinks the relationship is to be traced through
a form like Rimini,, pi, urn.

This study of the development and anatomy of Phoronis architecta was begun before the
publication of the last four papers mentioned, and when they appeared the abandonment of this
investigation was seriously considered. However, since there seem to lie specific differences and
since there are several disputed points in the development, it seems best to publish the results of
this study.

It is hardly necessary lo enter into an historical account of the work that has been done on
the development and anatomy of the Phoronidse, since there are several papers which have
reviewed the subject exhaustively.

89369° — vol 10—11 G 75

76 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

METHODS.

Most of the material — eggs, larva?, and adults — was tixed in a saturated solution of corrosive
sublimate, to which had been added 2 per cent of glacial acetic acid. A fresh solution was made
as soon as tjie tine white precipitate appeared, which is usually present in old solutions. This
fixing agent gave very good results. Material fixed in Perenyi's fluid was found more valuable
in some few respects than the acetic sublimate. When segmentation stages were treated with a
5 per cent solution of formaldehyde, the blastomeres stood out almost as distinctly as in the
living material. The larger species of the two Actinotroch a found in Beaufort Harbor is muoh
more active than the other, and when it comes in contact with the fixing fluid the preoral lobe is
bent upward into an unusual position. Consequently a few drops of 4 per cent solution of
muriate of cocaine in 50 per cent alcohol was added to the water containing the Actinotrochse.
After this treatment they died in their usual form when put in the fixing fluid.

Flemming-'s fluid, as well as the acetic sublimate, was found to be a very valuable fixing
agent for the Acti/nolrocha . Heidenhain's iron hsematoxylin was used in staining sections of the
adult, and a secondary stain of alcoholic eosin or rubin gave very good results. The most satis-
factory stain for sections of young larvae and Actinotrochse was found to be a solution of safranin
in anilin water. Since it was very desirable to make a study of the adults throughout the year,
and as it was not possible to remain in Beaufort for this purpose during the winter and spring
months, specimens were collected and sent to Johns Hopkins University at different times.
Here they were placed in aquaria rilled with sea water, which was kept in good condition by
a rich growth of diatoms on top of a layer of sand. Not only did the diatoms keep the water
from becoming polluted, but they also afforded abundant food for the Phoronis, so that healthy
individuals with their lophophoral tentacles fully expanded were continually at hand for a live
study. The authors are much indebted to Dr. Caswell Grave, the originator of the diatom method
in rearing Echinoderm larvae, for the use of his aquaria. Drew's modification of Patton's method
for embedding and orienting eggs was used with fairly good success, although a large percentage
of the embryos were broken during the process. Most of the embryos were cut into sections 3
H thick, but for some purposes sections 2 /.i thick were used.

BREEDING HABITS.

Andrews's (1) observations on Phoronis architecta bring him to the conclusion that either the
sexes are separate in that species or that if the individuals are hermaphroditic the male and
female elements mature at different times. Many specimens examined by us during May, June,
July, August, September, and October, both by means of sections and when alive, showed in no
ease ovaries and testes occurring at the same time in an individual, but ovaries and testes
undoubtedly occur together in the same individual in /'. a'ustralis. Benham (2) has observed
this, as we have also, in material sent to us by Mr. Ikeda.

During the month of January the peritoneal tissues surrounding the blood caeca is very
abundant, but as a rule at this time no eggs or spermatozoa are found in it. In one individual
out of some 20 or 30 a few ovarian eggs were found, however. All of these specimens
collected in January were without lophophoral organs, and we kept many of them in aquaria until
the 1st of May. At this time lophophoral organs began to make their appearance in some,
while in others they were absent. In all the specimens, however, either ovaries or testes were
present, as was also the case in specimens collected at Beaufort in the early part of May.
Further reference will be made to the lophophoral organs and their relation to the breeding
season under the section which deals with the structure of the adidt.

The breeding season of Phoronis architecta extends from March or April to November or
December. Ikeda (9) has stated that "the breeding season of Phoronis ijimai ranges through
about half of the year, say from November to June or July." There seems to be a surprising
difference in the time of breeding between these two species. The Act/'/iotrochse at Beaufort are
found throughout the summer and autumn, but they are especially abundant during August and
September. Ikeda has suggested that Phoronis annually " changes its generation." It does not

PHORONIS ARCHITECTA— BROOKS AND COWLES. 77

seem probable that this is the case for Phoronis architecta, because full-sized adults are found
throughout the year in Beaufort Harbor, and specimens were kept alive for fifteen months in the
laboratory of Johns Hopkins University.

THE LAYING OF THE EGGS.

During low tide in the summer and autumn it was easy to colled from loo to 150 specimens
of Phoronis architecta during an hour or two. About one-half of these would usually have
male reproductive organs and the rest female reproductive organs. The Phoronis were placed
in glass crystallizing dishes and after about twenty-four hours many of the individuals began to
lay — usually at night — but the eggs were not retained among the tentacles in a mass, as described
by most investigators, but were swept gently away from the lophophoral crown by the ciliation
on the tentacles and on the anal region, so that they settled near by on the bottom of the dish.
Sometimes, however, the newly laid eggs were carried up and down the tentacles in currents
caused by the cilia, and occasionally a few eggs were found grouped near the tips of the tentacles,
being held there, loosely by a small quantity of mucus-like material. At no time, however, were
eggs and larvse aggregated in definite masses, as described by Ikeda (!*), nor were they brooded
among the tentacles, as Masterman (16) has observed in the case of Phoronis huskii. That eggs
and embryos were not found by Longchamps among the tentacles of " Phoronis <l Helgoland" is no
doubt due to the fact that the same habit prevails in the above form that does in Phoronis
architt eta.

While the adults were laying, they were examined under the compound microscope. They
showed large numbers of eggs which were floating freely back and forth in the body cavity as
the animal contracted and expanded. Sections of adults in this condition show that all these free
eggs contained the first polar body spindle. At intervals of about one minute an egg is extruded
with considerable force from the nephridial opening, and in no case do the eggs at this moment
have polar bodies. The wall of the nephridial ridge is transparent enough to see the eggs
as they slip through the larger part of the nephridium. While passing through, they are
pressed by the walls of the organ until they are about twice as long as broad (fig. 1). The fact
that Phoronis architecta does not keep its eggs in masses within the tentacular crown, together
with the fact that most of the individuals lay them at about the same lime at night, makes
it possible to preserve any one stage in the development of the embryo in sufficient quantity for
a thorough study.

FERTILIZATION.

Ikeda ('.») and Longchamps (12) made the observation that the eggs in the body cavity of the
parent showed the spindles of the first polar body. This I found to be the case in Phoronis
architecta (tig. 1). Eggs in the nephridia were found to be in the same stage, and in neither case
was there any sign of an entering spermatozoon or a male pronucleus (fig. 1). There is no doubt
of the fact that in Phoronis architecta the spermatozoon does not enter the egg until the latter
has been expelled from the nephridium. Ikeda observed this fact for Phoronis i/jimai.

SEGMENTATION.

The eggs of Phoronis architecta while still in the body cavity are somewhat irregular in
shape, and. as mentioned above, are decidedly so while passing through the nephridium.
However, after they are laid they become almost perfectly spherical and average loo /< in diam-
eter (fig. 2), thus measuring the same as the egg of "Phoronis </< X(i]il<*." (Longchamps (12).)
The egg is very opaque, being heavily laden with small yolk granules. It is surrounded by a
delicate membrane, which, however, is not very conspicuous, being closely applied to the sur-
face, but after fertilization it separates to some extent (fig. •!).

Observations on the segmentation of the egg of Phoronis are conflicting. This part of the
development of Phoronis seems to have been treated hastily by most observers, probably
because it is difficult to obtain sufficient material for its study. It is agreed that the segmenta-
tion is total. Foettinger (5) and E. Schultz (21) claim that the segmentation is unequal.

78 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

Caldwell (3) say* that in the four-cell .stage two smaller clear and two larger opaque cells are
present. Masterman (16) rinds that in the four-cell stage the blastomeres taper toward one pole,
and that this results, when the third furrow appears, in the upper four being less in bulk than
the lower four. Masterman's description, I rind, applies to the eggs of Phoronis australis.
Ikeda (9) did not discover any appreciable difference in the size of the hlastomeres until the
eio-ht-cell stage. At this time, he says, '"it will be seen that the upper four blastomeres are
very slightly smaller than the lower four."

In Phoronis architecta the first cleavage plane is meridional and usually divides the egg into
two practically equal blastomeres (rig. 3), although sometimes the division is decidedly unequal
(tig. 4). The cleavage furrow begins in the region of the polar bodies (tig. 5). After the com-
pletion of the first cleavage and sometimes before, the first polar body divides (fig. 6). In fig. 6
is seen the reconstruction of the nuclei after the first cleavage. Immediately before the second
cleavage the two blastomeres, which were closely applied to one another after the first cleavage,
come to overlap. About fifteen minutes after the first cleavage the second cleavage takes place.
It is meridional and at right angles to the first, dividing the two equal blastomeres into four
equal blastomeres. As Ikeda has observed, the cleavage does not occur simultaneously in both
blastomeres nor does it in later cleavages (tig. 7). The blastomeres of the four-cell stage which
at first overlapped soon become applied to one another so that the two meet in a cross furrow
(tig. 8). Shortly before the third cleavage occurs the cross furrow disappears and the blasto-
meres come to overlap. The third cleavage takes place fifteen minutes after the second cleavage,
and it is equatorial. The blastomeres become drawn out into a more or less ovoid shape and, as
division takes place, the upper four blastomeres become rotated in the direction of the hands of
a watch (fig. 9). The eight blastomeres are approximately the same size, as a rule, and there is a
small segmentation cavity present which from now on persists (rig. 10). The three polar bodies
are distinguishable at this stage sometimes within the blastoccele and sometimes on the surface
of the blastomeres. The blastocoele is open at the animal and vegetal poles. The sixteen-cell
stage arises from the eight-cell stage by a meridional division of each of its blastoLueres, but
they do not all divide simultaneously (tig. LI), although the difference in time is very slight.
After the sixteen-cell stage the individual blastomeres were not followed. The division takes
place rather irregularly, hut the blastomeres are all about of the same size.

The so-called "blastocoele pore." observed by Ikeda CM. was found occasionally in young

blastula?, but it does not seem to be of constant occurrence nor definite in position (figs. 12, 13).

Two hours after the first cleavage the blastula is composed of seventy or eighty cells, and it

is still inclosed in the egg membrane. Four hours later the membrane disappears, and the

ciliated blastula begins to swim (tig. 14).

The blastomeres were so much alike and so uniform in size that their individual history was
not traced. It would seem probable from Masterman's work on Phoronis oushii (16) that the
cell lineage might be followed in that form, for he rinds considerable difference in the size of
the blastomeres in the early stages of cleavage at least.

The apical pole of the ciliated blastula is provided with long cilia (rig. 14). The nuclei are
situated nearer the outer than the inner surface, and the inner ends of the cells are filled with
rather dense granules. In the segmentation cavity are found the so-called '"corpuscles." which
have been observed by most investigators working on the early stages of Phoronis. Caldwell's
(3a) view that they are not mesoderm cells is undoubtedly correct. Our observations agree with
those of Ikeda (9), for the "plasmic corpuscles" are much smaller than any of the cells of the
blastula, and none with nuclei were found. In Phoronis architecta they do not appear until the
late blastula stage (fig. 14). at which time the inner ends of the cells are densely granular. It
seems very probable that the corpuscles are pushed out from the densely granular part of the
cell, and that, as Caldwell and Ikeda have held, they are an extra supply of nourishment.

The blastuhe. gastruhe. and young larva' of Phoronis architecta are quite similar in appear-
ance to those of Phoronis oV Helgoland which Longchamps (12) has figured. The development is
more regular than that of most other species, which is probably due to the fact that the eggs
and embryos are not harbored in the tentacular crown.

PHORONIS ARCHITECTA— BROOKS AND COWLES. 79

GASTRULATION AND FURTHER CHANGES IN THE FORM OF THE LARVA.

In the blastula, which lnis just begun to invaginate, the invagination is eccentric, thus giv-
ing the first indication of the bilateral symmetry of the larva. This is further emphasized in
the young- gastrula of Phoronis architecta by a thickening- of the ectoderm cells, which becomes
the ganglion of the Actinot/rocha. The cells composing this thickening of the ectoderm are
at the apical pole in the blastula and they bear long cilia, but as gastrulation takes place and
as the embryo elongates the thickening comes to occupy a position nearer the anterior end of
the larva (figs. 15, 15a, 155). The published accounts seem to indicate that the ganglion
makes its appearance much later in most species than it does in Phoronis architecta, although
Roule (20) figures the "plaque cephalique" at a rather early stage in Phoronis sabatieri. The
changes which take place in the shape of the blastopore are much like those described by
other investigators. At the beginning of gastrulation the blastopore is wide open and circular in
outline. The lateral lips of the blastopore then gradually draw together in the posterior region,
inclosing that part of the wall of the archenteron between them (fig. 20c), which becomes a
solid mass of cells continuous with the cells of the fused lips of the blastopore (tigs. 18a", IV).
The cells of the solid mass are of the same character as those of the wall of the archenteron
where the blastopore is open. They are quite granular, except at the periphery, where they
project into the cavity of the blastocuele, and their nuclei are quite indistinct. Both of these
facts are characteristic of the cells, making up the archenteric wall (tig. 18c).

As a result of the closing iip of the blastopore posteriorly, the blastopore becomes oval in
shape, and an indication of a ventral furrow, first observed by Caldwell and called a "primitive
groove." appears. In Phoronis architecta this groove is only to be seen in one or two sections
back of the blastopore, after which the ventral surface is convex (figs. I8a'-20c). A "primitive
streak," as described by Caldwell (Mr/) could not lie made out. The gastrula. which is at first
circular in horizontal section, becomes slightly elongated when the blastopore takes on an oval
shape.

Gradually the blastopore lips close up more anteriorly until the blastopore becomes circular
in outline but much smaller than it was originally. At the same time the anterior end of the
larva begins to bend in a ventral direction Und the archenteron becomes elongated posteriorlv
(tig. 20).

Now the larva increases slightly in length (fig. 21). the blastopore assumes the form of a
transverse slit, the anterior end bends farther ventrally. and the posterior end of the enteron
becomes applied to the ectoderm at the posterior end of the larva (fig. 21).

Our observations on Phoronis architecta agree with the description of Masterman (Iti). Ikeda
(9), and Longchamps (12) in regard to the closure of the lips of the blastopore and the resulting
change in the shape of the latter, but in Phoronis architecta the definitive blastopore does not
seem to be pushed farther anteriorly by the special activity in the posterior region of the blast-
opore, as Ikeda has found to be the case for Phoronis ijimai. The definitive blastopore seems
to be represented by the anterior part of the wide circular blastopore of the young gastrula. Its
change in position with reference to the anterior end is due to an elongation of the posterior
portion of the embryo and the ventral flexure of its anterior end.

Our studies on the development of Phoronis architecta lead us to agree with Ikeda and
Longchamps as to the, fate of the cells in the posterior part of the blastopore and as to the ecto-
dermal origin of the " posterior pit.** The cells of the posterior part of the blastopore become
invaginated by the closure of the blastopore lips and form part of the ventral wall of the enteron,
while the •* posterior pit." which appears in Phoronis architecta shortly before the definitive
blastopore is formed, is of ectodermal origin and has no apparent relation to the ventral groove.
As Ikeda ('•») has stated, the pit is the beginning of the nephridium of the Actinotroeha. In a
recent paper .Masterman (1<;<M says that he ha- found the "posterior diverticulum" both in larva'
of P. /ins/,/',' and /'. hippocrepia and that he considers them to be the anlagen of the nephridia.

80 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

FORMATION OF THE MESODERM.

There is considerable difference of opinion among those who have investigated the embry-
ology of Phoronis as to the origin of the mesoderm, and there seem to be no two whose descrip-
tions agree, although Ikeda (9) and Longchamps (12), in their recent papers, arrive at the same
conclusions, generally speaking.

The study of the eggs and larvae of Phoronis architecta and those of Phoronis austral!*
show that the great difference in the origin of the mesoderm, as Roule (20) and Masterman (16)
see it, may be due, in a great part, to difference in the larva? themselves.

The eggs and embryos of Phoronis australis, for which we are indebted to Mr. Ikeda,
are very similar in appearance to those of Phoronis husk!!, judging from Masterman's figures
(16). Sections of the eggs and larvae of the former show the development to be of the same
general type as that of Phoronis !jlmal. which Ikeda (9) has described.

The eggs and larvae of Phoronis a/rchitecta are considerably different from those mentioned
above. They arc more regular in form, the blastocoele is much more spacious and the cells
themselves are more regular in shape and arrangement. They are most similar in appearance to
the early stages of Phoronis sabatieri studied and figured by Roule (20) and those of uPhoronis
d' Helgoland" figured by Longchamps (12).

The formation of the mesoderm begins in Phoronis architecta as soon as the flattened side of
the blastula begins to gastrulate. In a few cases round blastuhe are found, within the blastocoele
of which are rather large granular spherical bodies much larger than the plasmic corpuscles
described above. Each of these contains an opaque body which takes satfranin stain with readi-
ness. A comparison of these bodies with the nuclei of the cells of the blastula wall convinces
one at once that they are not nuclei. In tig. l-ia a section through such a blastula is shown in
which these bodies are seen within the wall of the blastula as well as inside the blastocoele. They
are embedded in the wall without reference to the limits of the cell and usually occupy the width
of two cells. The cells inclosing these peculiar bodies do not differ from the cells surrounding
them in that region and each has its own nucleus. These bodies are not the cut ends of amoeboid
processes which Caldwell (3a) and Roule (20) observed, for such processes do not occur in the
blastula? of Phoronis architecta. We are unable to make any positive statement as to their fate.
but it is very probable that they break up into the smaller plasmic corpuscles. Such bodies as
the former might easily be mistaken for mesoderm cells, and we suspect that the "mesoderm
cells" observed by Foettinger (5), Metschnikoff (18), and E. Schultz (21) in the round blastuhe
were of the same character.

The work on Phoronis architecta indicates that the mesoderm which forms the lining of the
preoral lobe and the collar cavities of the Actinotrocha arises from the lips of the blastopore.
As to the origin of the lining of the trunk segment, we are still in some doubt, but we are
inclined toward Longchamps's suggestion that some of the cells of the nephridial pit give rise to
it. Caldwell (3a) also holds that the mesoderm arises from the endoderm, assuming that the
"posterior pit" (nephridial diverticulum), which he considers to lie one point of origin of the
mesoderm, is of endodermal origin. Roule (20) derives most of the mesoderm from the endo-
derm. but also considers the "bandelettes mesoblastiques," which Schultz (21) first pointed out to
be the same as the posterior diverticulum of Caldwell, as giving rise to mesoderm.

As is seen on referring to tig. 15. the flattened part of the wall of the blastula has become
more than one cell thick. In fact active cell division has taken place. Yet most of these cells
are destined to become the wall of the archenteron, and only a few are to give rise-to mesoderm.
Careful examination of many sections fails to show that mesoderm cells ever have their origin
from the dorsal surface of the archenteron. In this respect the development of Phoronis archi-
tecta seems to agree with that of Phoronis kowalt vsMi as described by Caldwell (3a) and Long-
champs (12). and that of Phoronis host,-;;, which Masterman (16) investigated. In Phoronis
architecta, as in the form studied by Longchamps (12). the anterior and lateral borders of the
blastopore are most active in giving rise to mesoderm (tigs. 16 tf, 6, c, d, e,f). Most of it is

PHORONIS ARCHITECTA— BROOKS AND COWLES. 81

proliferated from the anterior end of the archenteron, and the power of producing the same
seems to diminish gradually toward the posterior end of the blastopore lips in those gastrula?
where the round blastopore is just beginning to close up (tigs. Hi a, h, c, d, <,/').

The mesoderm cells are very amoeboid in character and are often seen in living specimens and
sometimes in sections sending out long pseudopod-like prolongations, which become attached to
the walls of the gastrula. tty means of these amoeboid movements they are able to crawl up the
walls of the blastocoele.

We were unable to make out any structure in Phoronis architecta which could be interpreted
as "archenteric diverticula." such as figured by Caldwell (3a) and [keda (!»). Fig. L6c might be
interpreted as showing these diverticula, but the condition there is hardly different from the
arrangement of the mesoderm cells, which are being pushed out into the blastoctele in front of
the blastopore (figs. 1>'>. L6&). Caldwell first observed these structures in the gastrula? of Pho-
ronis kowalt vskii, but Longchamps (12). who has recently carefully studied the same species, has
been unable to rind them, [keda ('•»). however, finds very definite diverticula in the gtstruhe of
Phoronis ijimai, but he figures them as being in the region of the blastopore, while, according
to Caldwell's (3a) figures, they are found posterior to the blastopore.

Let us return again to the mesoderm cells which lie anteriorly to the blastopore. These
amoeboid cells undoubtedly multiply while in the blastocoele, ami in a gastrula where the blasto-
pore lips have (dosed up somewhat so as to give an oval outline to the blastopore (tig. I8f) these
cells have become arranged into a definite sac (figs. V.K 20a), which is later to form the lining of
the preoral lobe. In no case were we able to find the least indication of an anterior unpaired diver-
ticulum, which Mastennan (16) says exists in the gastrula of Phoronis husl-li. At this stage
the cavity of the sac is small and is present only in front of the blastopore. The walls, however,
are extended on each side into a lateral cord of mesoderm cells, which lies in the blastocoele at the
side of the blastopore (tig. L8/"). Some of the cells of the dorsal wall of the sat' send out pseu-
dopodia. which attach themselves to an ectodermal thickening, and this thickening will become
the ganglion of the Actinotrocha (tie-. L9).

The above condition continues until the oval blastopore becomes smaller and round in outline
(figs. 20, 20e), which change is also accompanied by further growth of the enteron in a posterior
direction until it almost touches the end of the larva. The cells of the two lateral cords of
mesoderm have now increased in number, have arranged themselves so as to inclose a cavity,
continuous with the cavity of the anterior one described above, and have become attached both
to the lateral ectodermal wall and the lateral endodermal wall (fig. 205). Anteriorly this sac,
which is now horseshoe shape (lie-. 20e), is still only attached to the ganglionic thickening and
the ventral ectodermal wall (fig. 20). The conditions just described are not due to the shrinkage
of the mesodermal lining away from the wall of the larva, for the transparency of the living
larva makes it possible to see the formation of the mesodermal sac. We have followed this
formation step by step many times in the living gastrula and larva, as well as in sections and
surface mounts.

As the anterior end of the larva bends farther Neutrally and becomes a definite preoral lobe,
the round blastopore assumes the shape of an oval with its major axis transverse to the lone- axis
of the larva (rig. 21). The posterior part of the larva increases in length and the enteron sends
out a posterior diverticulum, the beginning of the intestinal canal, whose blind end fuses with
the ectoderm of the posterior end of the larva. The walls of the mesodermal sac become applied
to the wTalls of the preoral lobe more generally, thus forming a definite mesodermal epithelium
for the cavity of the preoral lobe (figs. 23. 21, 22). Posteriorly, as Masterman (15) has described
for the fully developed Actinotrocha, the cavity is produced "'into two horns running back
laterally" (fig. 22a), but as yet there is no complete mesodermal lining in the cavity back of this
(figs. 22 b, c). The posterior wall of the mesodermal lining of the preoral lobe forms a definite
septum (tigs. 21, 21"), but it is not as yet, at least, composed of two layers, as Masterman finds
in the older Actinotrocha.

82 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

While the above changes have been taking place in the preoral end of the larva there has
also been some change in the postoral region. It is seen from tigs. 16 c, d, e, f that in the
young gastrula with the large circular blastopore mesoderm cells are being pushed out into
the blastocoele along both sides of the archenteric wall back almost to the posterior border of
the blastopore. At this stage large spherical cells with rather small, deeply staining nuclei
are sometimes seen floating freely in the blastocoele (tig. 17'/). These cells have their origin
in the wall of the archenteron (fig. 17) and are quite different from the bodies found in the
blastocoele of the blastula. They have a definite nucleus and they seem to be similar cells to
those found by Ikeda in the larva with one pair of tentacles. They certainly do resemble the
blood corpuscles found in the older larvae, only they are considerably larger. Ikeda (9) came to
the conclusion that these cells were the " mother cells of blood corpuscles which are found as
corpuscle masses in the collar cavity of the Actinotrocha." Since the publication of his paper
Mr. Ikeda has written that he considers his theory concerning the fate of these cells to be
incorrect. They are easily distinguishable from all other cells by the fact that the}' are larger
and that the cytoplasm does not stain. They have a nucleus which is rather small. We shall
return to a consideration of these cells when we describe the blood corpuscles of the Actinotrocha.

As the blastopore lips begin to close up posteriorly (figs. 18 d, e) the endoderm cells in that
region lose the power of giving rise to mesoderm cells, but they are still found arising in a more
anterior region.

At a little later stage, in which the blastopore has become circular again after the fusion of
the blastopore lips and the enteron has almost reached the posterior end, a few mesoderm cells
are seen lining the ventral ectoderm in the posterior region (tig. 20^). These cells, however,
do not have their origin from the wall of the posterior part of the enteron nor from the ventral
ectoderm which Caldwell (3a) would call the "primitive streak." The cells forming the ventral
ectoderm are very regularly arranged into a layer one cell thick and all the nuclei are in a resting
state. The mesoderm cells have either migrated from the cells of the lateral cords which arc
prolongations of the sac, forming the lining of the preoral lobe (tig. 20e), or from the region of
the blastopore, where some mesoderm cells are still arising. In general, our interpretation of
the faets bearing on the origin of the mesoderm in the posterior region of the larva agrees with
that of Longchamps (12) for Phoronix TcowdU vskii.

When the larva reaches the stage shown in fig. 21 where the blastopore is transverse and
the archenteron fuzes with the posterior ectoderm, the mesoderm cells are found to be more
numerous in the posterior region, and in nearly all cases they are applied to the ventral suface
of the blastocoele. At this time the proliferation of mesoderm cells from the endoderm has
ceased in the anterior region ami there is no indication of any mesoderm cells being given off
from most of the posterior region. At the extreme posterior end of the enteron, however, a
transverse section across the larva (fig. 22</) shows a mass of cells which might be taken for
proliferating mesoderm cells. Traced farther back, this mass of cells is found to be part of the
wall of the ••posterior pit," or. as Ikeda (!>) has called it, "the nephridial pit" (figs. 22 e,f, g).
The fate of the cells of the nephridial pit will be discussed in the description of the larva with
two tentacles.

Larvae like the one just described do not show the least trace of a mesentery between the
collar and trunk. In fact, one could hardly say that a trunk existed at this time. The oblique
strongly ciliated tract of ectoderm which indicates the line of origin of the larval tentacles has
not appeared.

FURTHER GROWTH OF THE YOUNG LARVA.

The flexure of the preoral lobe continues as the larva grows older (fig. 2-1). In this way a
vestibule is formed and the original blastopore becomes the part which connects the vestibule
and archenteron (fig. 24). This relation between the vestibule and blastopore has been recog-
nized by Masterman (16), Roule (2<>). Ikeda (9), and Longchamps (12). Longchamps speaks of it
as a "stomodanim," and Masterman does also, but the latter adds " oesophagus " after it. (If our

PHORONIS ARCHITECTA— BROOKS AND COWLES. 83

idea that a stomodseum is a pitting in of the ectoderm which finally breaks through into the
enteric cavity is correct, then Masterman's and Longchamps's use of the word is incorrect.)

Masterman speaks of a "slight ridge" running around the edge of the preoral hood and
then "downwards till it is lost on the surface of the tentacles.*' Such a ridge is not present in
the larva of Phoronis wrchitecta and there is no connection between the ciliated tract along the
line of which the larval tentacles arise and the ciliated edge of the preoral hood.

At this stage (tie-. 24) a definite intestinal canal is seen which, however, does not open 3*et to
i he exterior. The intestine, as described above, is not of ectodermal origin in the larva of Pho-
ronis architecta. There is no proctodeum. On this point our observations agree with those of
Masterman, Longchamps, and Ikeda.

Roule (20) says: " Lin anus et rectum se faconnent, aux depens de l'ectoderm, sur I'extremite
posterieure du corps " (p. L02), and Caldwell (3a) derives the intestine from the remains of the
"primitive streak."

As yet the anal papilla is not at all definite, but the ciliated band along which the larval
tentacles are to arise has now appeared. This is indicated in the sagittal section (tig. 24) by a
thickening of the ectoderm.

The mesoderm cells which in fig. 21 are seen applied to the ventral ectoderm of the larva
have now increased considerably in number and have become arranged at quite definite intervals
(titr. 24). If the ventral surface of the larva is examined, while the larva is alive, it will lie seen
that these cells have become simple muscle cells made up of two rather delicate fibres which
extend from a large nucleus situated near the mid-ventral line. These fibres run parallel to one
another around the wall of the larva (tie-. 25).

The whole body cavity back of the mesentery between the cavities of the collar and lobe
represents the larval collar cavity of the Actinotrocha, and although its somatic walls are not
lined by a perfectly continuous mesodermal epithelium, yet there are indications that such a
lining is being formed. The ventral and lateral walls of the stomach, however, are perfectly
free from any epithelial covering. In fact, in all the Actinotrocha' examined no mesodermal
epithelium covering the ventral and lateral walls of the stomach in the collar region could lie
found. We have never seen any sign of mesodermal sac-like formation such as occurs in the

preoral lobe.

Roule (20, p. 112) has described in a considerably older larva than the one with which we
are dealing certain mesodermal cells to which he has given the name " coniunctivo-musculaires
elements." These he represents as spindle-shaped cells terminated by long fibre-like prolonga-
tions and he has figured them as being quite numerous in the "plasma, transparent et con-
sistant." of the coelomic cavity. While the young larva of Phormiis architecta bears a close
resemblance to that of Phoronis s<ih<if;,ri described by Roule (20), yet at no time during the
life of the larva have we seen these cells suspended in the body cavity in such numbers as he has
shown. Spindle-shaped cells with long prolongations are quite numerous, but they are usually
found applied to the somatic walls of the larva.

Although recent investigators have thrown some doubt on the existence of the lobe-collar
septum, yet such a septum unquestionably exists in the larva of Phoronis architecta. Ikeda
CM has shown that it is incomplete in the old actinotrocha and our observations agree with his.
but it is a fact, nevertheless, that the septum is continually present throughout the larval life of
Phoronis architecta and that it makes its appearance at a very early stage in the life history.

Longchamps (12) says: "Si une subdivisions plus ou moins complete s'e"tablissait, entre ces
deux regiones, elle ne seriat en tout cas que sccondaire, et la cloison s'&lifierait aux depends de
mesenchyme." It is plain from what has been said that we can not agree with Longchamps
in his statement that the septum is secondary. It must be admitted, however, that the septum
between the lobe and the collar is often considerably thinner than that between the collar and
the trunk. If its origin had not been followed from the earliest stages by means of sections
in three different planes, whole mounts and live material, we should not have been inclined to
consider it a primary and constant organ of the larva.

84 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

We had confidently expected to find in the larva of the stage represented in fig. 24 some
indication of the mesentery between the collar and the trunk, but were disappointed. Although
the ciliated tract along which the tentacles are to arise has made its appearance and extends
obliquely around the body proper of the larva, indicating a line just a little above the line of
separation of the cavities of the trunk and collar in the older actinotrocha. yet examination
of sections does not show the least sign of the mesentery or its fundament.

Ikeda (9) has found mesoderm cells connecting the nephridial canals with the splanchnic
walls, and he thinks they arc the first indication of the septum between the collar and trunk
cavities. We have not been able to find the paired masses of "hypoblast cells" which
Masterman (16) says give rise to the trunk cavities, although it is true that mesoderm cells
were found lying on the dorsal wall of the intestine. Masterman does not follow the fate of
these masses, but in the larva with three pairs of tentacles he speaks of "the two mesocceles
pushing dorsally, their walls forming a pair of conspicuous mesenteries with the walls of the
inetacoeles" (p. 395).

As has been said, the masses of cells that Masterman (16) speaks of have not been found,
but we do not deny that the condition which he describes may exist in the larva of Phoronis
busMi with three pairs of tentacles.

" Nephridial pit" (Ikeda). — A structure of the larva of Phoronis which has given rise to
considerable controversy is the •■nephridial pit" ("posterior, anal, ectoblastic pit," "posterior
diverticulum"). It seems safe to assume that such a structure exists in the young larvae of all
species of Phoronis. It lias been seen by Caldwell (3a) in P. kowalevskii, by Ikeda (9) in /'. ijimai,
by Longchamps (12) in /'. howalt vskii, by Masterman (16«) in P. buskii and /'. hippocrepia, and by
us in /'. architecta. Although Roule (20) has not observed the pit in /'. sabatieri, it seems
probable that such a structure will he found there on further investigation. It is difficult to
believe that Roule's understanding of the origin of the nephridia from two cell masses of
somatopleure symmetrically placed at the sides of the larva is correct. As stated above, we

consider the pit to 1 f ectodermal origin (fig. 24). Further study of the structure leads us

to agree with Ikeda that it divides into two lateral branches, each of which becomes a nephridial
canal of the actinotrocha (figs. 25, 26, 27, 28). In tig. 25, which is a drawing made from a living
larva, the canals, which in a little younger stage were practically the same diameter throughout
their length, have become tipped at their distal ends with a bunch of cells which, we believe,
are later to form the excretory cells of the nephridium.

No positive statement concerning the origin of these cells can be made, since it is difficult
to obtain many larva' of /'. architecta which are old enough to show these bunches of cells in the
process of formation. The sections examined afford no evidence that they are formed by free
mesoderm cells attaching themselves to the internal ends of the nephridial canals, and we are
rather inclined to consider them as arising from the cells of the internal blind ends of the
nephridial canals (tigs. 25-28). Ikeda's description (9) of the way the nephridial tubes arise
from the ectodermal pit— i. e., by tin' " reevagination of the distal unpaired portion of the
nephridial pit"— seems to be correct. Longchamps's (12) interpretation of the change in form of
the "ectodermal pit" agrees quite closely with Ikeda's description.

"Medullary plat< " (Roule).- When the young larva of Phoronis architecta has reached the
two-tentacle stage cross sections show that there is a definite ventral ciliated band extending from
the mouth to the ciliated tentacular band (tigs. 29, /<. c, <l. - ). This ventral ciliated band has
been observed by Roule (20) in the larva of /'. sabatieri, but it has not been described for any
other species. Roule has homologized it with the medullary plate or medullary groove of the
annelid larva.

" Trunk cavity." — Longchamps has drawn attention to a figure of an Actinotrocha published
in Hatschek's" Lehrbuch der Zoologie." In this figure are represented two ctelomic sacs sur-
rounding the intestine. Ilatschek does not describe the origin of these sacs, but Longchamps
(p. 555) proposes the question, "Si les canaux ne derivaient pas des expansions laterals du
diverticule ectoblastique, chacun des canaux restant en rapport avec Texterieur par un orifice

PHORONIS ARCHITECTA— BROOKS AND COWLES. 85

resultant du dedoublement de I'orifice primitif et median, tandis que le restant <lu diverticule
ectoblastique deviendrait la cavite posterieure du corps."

Such an origin for this posterior cavity would seem to be a possible one and would give an
easy explanation for the origin of the collar trunk and ventral mesenteries.

We believe that the cavity of the trunk is formed in the following manner: As the tentacles
grow out and increase in number the posterior region of the larva about the tectum increases
greatly in length. In doing the latter the mesodermal lining of the collar is drawn away from
the somatic wall in the region back of the tentacular band, and a cavity is left containing the rec
turn, part of the stomach, and the proximal part of the nephridial diverticula. At the same time
this is taking place certain cells which seem to arise from the base of the nephridial diverticula
give rise to the lining of the cavity of the trunk. As to the manner of origin of these cells
we are still in doubt. We have not found two ccelomic sacs which Hatschek (8) seems to have
figured (it is possible that his figure is meant to represent a single sac cut at two places).
and we have hunted for them in larva1 where the diverticula are just beginning to form and
also in larvaa with two, four, and six tentacles. In one specimen with two tentacles, however
(fig. 30), an arrangement of mesodermal cells on the dorsal side of the intestine which seems
to be the beginning of a sue is found; this, however, is not paired. Whether or not this sac
and its cavity give rise to the lining and cavity of the trunk we can not say. for we have found
but one specimen in which this condition exists.

One thing is certain, the fully developed trunk cavity of the Actinotrocka has a distinct
mesodermal lining, consisting of a somatic and a splanchnic layer. As far as we know all Actino-
trochse have a ventral mesentery, which tends to support the view that the lining of the cavity
of the trunk has its origin in a sac which grows around the rectum and posterior part of the
stomach. Whether or not the fact that there is an indication of a dorsal mesentery in the pos-
terior region of some of the fully developed Actinotrochx, Species 15.. has any bearing on the
double origin of the cavity of the trunk we can not say. for we have never seen the very young
larva? of this form.

The youngest larva taken from the tow had three pairs of tentacles, with beginnings of the
fourth pair. In this larva the tentacles had grown considerably in length, and the posterior
region had become somewhat elongated (tig. 31). Only one specimen of this age was obtained.
and it was only studied while alive. The mesentery between the collar and lobe was plainly
seen, and there seemed to be a thin mesentery between the region of the collar and the younger
trunk region. The nephridial canals were seen with difficulty, but the rounded bunches of
excretory cells forming the internal ends of the canals were plainly visible.

When the larva of Phoronis architecta has five pairs of tentacles (tig. 32) the trunk region is
elongated considerably and constitutes about one-half the length of the larva. In fact, the larva
at this stage looks much like the fully developed Actinotrocha. The •"retractors"' described by
Ikeda (9) are now present and the body wall in the anal region shows a thickening which is to
become the perianal ciliated band. 'Phis larva shows clearly the presence of two mesenteries.

In tin' larva with six pairs of tentacles (tig. 33) till of the organs of the fully developed
Actinotrocha arc present. The ventral pouch begins to invaginate (tig. :!:-'>) and sections usually
show that the blood corpuscle masses are forming.

FULLY DEVELOPED ACTINOTROCHA.

There are two species of Actinotrochm found in the waters of Beaufort Harbor, and they are
very similar, if not identical, with the two species that E. B. Wilson (24) observed in Chesapeake
Bay. From the latter part of May until the latter part of September both species are fairly
abundant in the tow.

Wilson has designated the two species found in Chesapeake Bay as Species A. and Species
B., and because of the general agreement between our observations and his descriptions the
Beaufort Actinotrochse will be designated as Species A. and R, although we are satisfied that
Species A. is the larva of P. architecta.

86 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL X, NO. 4.

Species A. — Species A. (tig-. 34) is somewhat smaller than Species B. and its average length is
1.03 mm. The trunk is quite stout, the intestine is short, and the posterior end of the stomach
readies as far as two-thirds of the length of the trunk cavity. When about ready to metamor-
phose, this larva usually has 18 larval tentacles and an equal number of young- adult tentacles.
The adult tentacles do not usually appear until the larva has is larval tentacles (its full number)
and they arise as thickenings on the under side of the liases of the larval tentacles. In this
respect the larva resembles one of the actinotrocha? which Ikeda (9) has described. The blood
corpuscles are found in two masses usually applied to the ventro-lateral surface of the stomach,
and they make their appearance in the larva with 12 or 14 tentacles. A pair of muscles which
Ikeda has been the first to describe, and which he has called " retractor muscles," are always
present; although they have not been made out in younger larvse than those with 10 tentacles.
This species is without the so-called "stomach diverticula." Pigment cells are found rather
irregularly scattered on the wall of the body cavity. There are definite aggregations of these at
the bases of the tentacles, and a few pigment cells are seen on the surface of the blood corpuscle
masses. Usually there are quite a number in the wall of the posterior portion of the trunk.

This Actinotrocha is not as active as Species IS. and it docs not, as a rule, turn up its preoral
hood when irritated. Its metamorphosis usually takes place quickly, fifteen or twenty minutes
being- required for its completion. Actinotrocha Species A. is, no doubt, the actinotrocha of
P. architecta.

Species Ii. {fig. 35). — This Actinotrocha is larger than Species A., and when about ready
to metamorphose it has an average length of 1.22 mm., and has at least 26 tentacles. (Wilson
(24) figures the Actinotrocha Species IS., ready to metamorphose, with 22 tentacles.) The differ-
ence in appearance between this larva and Species A. is rather striking. Beside being- somewhat
longer, it is slightly narrower in the collar region and decidedly so in the trunk region, which
gives it a much more graceful appearance than that of Species A. The intestine is quite long,
extending throughout the posterior two-thirds of the trunk cavity.

M. Longchamps has kindly pointed out to me that the "adult tentacles appear bilaterally,
the mid-ventral line being, at first, free of the buds." They do not arise, however, as thicken-
ings on the under side of the bases of the larval tentacles as in Species A. They have their
origin at the base of the larval tentacles, but they are separate from them, and they appear first
in the larva with 24 tentacles.

This Actinotrocha differs in three important respects from Actinotrocha Species A. In the
first place it has its blood corpuscles aggregated into four masses, two of which are usually in
the same position as the pair in the smaller species. The other two, however, are found, as a
rule, more anteriorly in the collar cavity, and are applied to the dorso-lateral walls of the stomach.
The posterior pair lying on the ventro-lateral sides of the stomach make their appearance during
the 18 or 20 tentacle stage, hut the other pair do not appear until about the 22-tentacle stage.
This larva also has retractors extending from the ganglion to the region of the first and second
pair of tentacles.

A second point of difference is the fact that Actinotrocha Species B. possesses a pair of
diverticula at the anterior end of the stomach. These are present as early as the 22-tentacle
stage. This larva can further be distinguished from the other species by the fact that there
is found in the older larva- a sensory papilla on the mid-dorsal surface of the preoral lobe.

Actinotrocha Species IS. is much more active when irritated than the other species. The
least irritation causes it to turn up its hood and to assume attitudes like those figured by
Masterman (15). In fact, judging by the figures and text of Masterman's paper, it seems that
there is considerable similarity between this larva and the one he has described. The two larvse
are very much alike in shape and both have the lateral stomach diverticula, but the form that
Masterman describes has only two masses of Mood corpuscles. The two species are not identical,
nor is Actinotrocha Species IS identical with Actinotrocha ivanchiata from the North Sea, for, as
Longchamps has pointed out to us, the latter has but two blood corpuscle masses. Long-champs
has informed us that in Actinotrocha Species IS. the adult tentacles make their appearance in the

PHORONIS ARCHITECTA— BROOKS AND COWLES. 87

same special way that they do in Actinotrocha oranchiata (found near Helgoland and described
l>v J. Midler (19); and Masterman (15) says in his paper that the form he worked on "does not
appear to differ in any essential respect" from Actinotrocha oranchiata. There seems, however,
to be considerable difference in size between Actinotrochaoranchiata and Actinotrocha Species B.,
for, according to Longchamps, the best-developed specimen that he obtained of this species
measured 2 nun., while the length of Actinotrocha Species B. averages 1.22 nun.

Although Actiiiotrnrlin Species A. seems to metamorphose without any difficulty when
brought into the laboratory, yet we have never been able to induce Actinotrocha Species B. to
do so. Specimens have been kept for ten days or more (the pouch and blood corpuscles being
well developed) and in some cases they succeeded in evaginating the ventral pouch, but they
were never able to complete the metamorphosis.

As far as we know, the adult of this Actinotrocha has never been found, but probably it lives
under quite different conditions from Phoronis architecta, and it is not improbable that it may be
found as a deep-water form.

INTERNAL ORGANIZATION OF THE FULLY DEVELOPED ACTINOTROCHA.

•• ShIiiii in-ill ijliiinj" (.Masterman). — Masterman (15) has described a depression in the dorsal
wall of the buccal cavity which he terms a "subneural gland" and which he compares with the
gland of the same name in the Tunicata and also possibly with the hypophysis of the Vertebrata.

Roule (2d) anil Ikeda (9) are of the opinion that this depression is a product of the fixino-
method.

Longchamps (12) does not consider it to be an accidental structure, but he does not agree
with Masterman's view as to its theoretical significance.

Menon (17) says that the •'subneural gland" first appears in connection with the collar and
that during development it shifts forward into the preoral lobe, but in another part of his paper
he says the (esophagus is often folded transversely (this also the case in the young Phoronis) into
pouches and the "subneural gland" is a diverticulum of its dorsal wall.

While in examining sections we have frequently found a depression in the region that Mas-
terman (15) indicates, we have never found it in the living larva. Only in very poorly killed
larvae have we found the depression to be as deep as Masterman has shown, and in all cases the
structure of the wall is practically like that of the oesophagus.

In the Actinotrochse Species A. and B. there is no depression in the living larva which might
be homologized to the subneural gland of higher animals, and we are forced to agree with Roule
and Ikeda in their belief that the so-called "subneural gland" which Masterman describes is a
product of fixation.

•• Oral mill atrial grooves" (Masterman). — Masterman (15) has observed a mid-ventral
ciliated area leading into the mouth from the preoral lobe in front and a broad ciliated area
depressed into two oral grooves leading into it from the ventral surface of the collar area. He
has also seen two so-called "atrial grooves" leading into the dorsolateral corners of the mouth.
Masterman says he does not find gill-slits in the Actinotrocha, nor does he find structures that
he considers to be their homologues. "The atrial grooves" of the Actinotrocha, he says, how-
ever, are the analogues of gill-slits (15, p. 319). On page 358 (15), however, he says that
"tentatively, I would regard the atrial grooves of the Actinotrocha as the early rudiments of
pharyngeal clefts as found in Cephalodiscus."

His "oral grooves." he says, correspond to the oral grooves in Cephalodiscus.

Roule (20) does not find the "atrial grooves." but finds two lateral grooves, which he con-
siders to be formed by the insertion of the hood on to the collar wall.

Ikeda (9) and Longchamps (12) are of the opinion that these grooves do not normally exist.

We have made a careful study of the live Actinotrocha and of surface mounts, but have not
been able to make out these grooves in either Species A. or Species 15. Sections, however, show
that the "oral grooves" are present, and that in most preparations where the preoral hood has
been turned upward by violent contraction (due to the fixing agent) there are two short grooves

88 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X. NO. 4.

in the position in which Masterman finds the "atrial grooves." In those ruses in which the hood
remains in its normal position we have seldom found Masterman's so-called "atrial grooves,1' and
even in a few cases where the. hood is turned upward they have been absent.

The ventral wall of the hood just as it passes into the wall of the (esophagus not infrequently
shows a pair of bilaterally situated grooves which are similar to those found on the ventral collar
wall.

" Neuropore" (Masterman). See section on the nervous system.

" Subneural sinus" (Masterman). — Another organ whieli Masterman (15) has described is a
sinus immediately below the nerve ganglion, caused by the want of contiguity between the
mesoblastic wills of the preoral cavity and the collar cavity. This sinus, he claims, is closed
except for a fissure which leads eventually into the dorsal blood vessel. He compares this sinus
to the heart of Balanoglossus.

Menon (19), as far as we know, is the only other worker on the Actinotrocha who claims that
there is a definite vesicle beneath the ganglion and he has discovered no connection between its
cavity and the dorsal blood vessel.

Roule, Longchamps, and Ikeda do not rind this organ, but the latter recognizes the existence
of a space ("posterior recess") free from mesenchymatous fibres, which is the posterior part of
the preoral lobe. This, however, he says, does not connect with the dorsal blood vessel.

From the study of the early development of Phoronis architecta and the origin of the
mesentery between the hood and the collar, we have come to the conclusion that no vesicle is
formed in that species between the two layers of the mesentery (if two layers exist). The
mesentery which forms the posterior wall of the preoral lobe cavity is found attached just back
of the ganglion in the median line and there is not the least sign of a vesicle other than the
cavity of the preoral lobe (tig. 21).

In neither Actinotrocha Species A. nor Actinotrocha Species B. have we found a vesicle below
the ganglion, although in both cases there is a space such as Ikeda (9) has seen, free from mesen-
chymatous fibres. The anterior boundary of this space is rather sharply defined and occasionally
among longitudinal sections a fibre with a nucleus is seen running vertically from the dorsal to
the ventral wall of the hood, giving the appearance of an anterior wall to the space. These
fibres, however, are very much more delicate than the wall of the collar lobe septum, and what is
more, they occur only occasionally and are evidently not sections through a membrane.

In the Actinotrocha!, which we have examined, there does not exist any vesicle beneath the
nerve ganglion nor any structure which could be likened to the heart vesicle of Balanoglossus. For
the supposed relation of the dorsal blood vessel to the '•subneural sinus." see Blood system.

•• Stomach Diverticula" (Ikeda. Longchamps, and Menon).

" JVotochords" (Masterman and Roule).

Ever since Johannes Midler (19) saw the paired "blinddarme" in Actinotrocha hranchiata
nearly all of those who have studied Actinotrochse have observed the same structures. Some
have considered them to be liver diverticula, others have described them as dark masses with
globules and as brown specks. Wilson calls them •"glandular lobes of the stomach."

Ikeda (9), Longchamps (12), and Menon (17) speak of them as "stomach diverticula," but
they do not ascribe any function to them. Masterman (15) and Roule (20) look upon them as
rudimentary notochords. Roule. Ikeda. and Longchamps have studied larvae in which the
diverticulum was not paired and lateral, but unpaired and medio-ventral. The latter investigator
has observed larva- of both types.

We find that in Species A. the diverticulum is undeveloped even at the time of metamorphosis
while in Species B. the diverticulum is paired, well developed, and ventrolateral.

Longchamps has very justly objected to Masterman's use of the name liDiplochorda," under
which the latter includes the Phoronida> and Cephalodiseus.

The diverticula of Species B. do not show the regularly arranged vacuoles which Masterman
has described for the Actinotrocha from St. Andrews Bay. In fact, we agree with Longchamps's
(12) observations in finding the histological characters absolutely different in Species A. and B.
from the histology of notochords, and there is not the least indication of supporting tissue.

PHORONIS ARCHITECTA— BROOKS AND COWLES. 89

However, larvae which we have examined, fixed in Flemming's fluid, have not shown the vacuoles
to be tilled with fat droplets as Longebamps states.

Sections tli rough the diverticula of quite old larvae (fig. 35) stained with iron hsematoxylin
show columnar cells, nearly every one of which contains a deeply staining body about one-quarter
the size of the nucleus. The bodies are not found in the wall of the stomach proper, and we
believe that they give the yellowish-brown color to the diverticula of the live Actinotrocha.

In some cases we have found old larvse in which the cells of the diverticula were vacuolated,
but in these cases we have also found that the entire stomach wall was vacuolated. The vacuoles
were never large enough or numerous enough to alter the natural position of the nuclei.

According to Masterman's description, the first vacuoles are formed at the distal ends of the
cells and more vacuoles arise later between these and the inner ends of the cells. As far as we
know, the origin of vacuolated tissue in vertebrates is the reverse of this, the vacuolization
beginning at the center of the cord and traveling outward.

The specimens of Actinotroch.se of Phoronis sabatieri which we have examined show the struc-
ture of the stomach diverticulum to be very similar to that of the diverticulum in the Actino-
trocha Species B. The diverticulum, however, is somewhat more vacuolated in the former than
in the latter, but it does not show the peculiar structure which Masterman has described for the
"notochord" of the species from St. Andrews Bay.

It is hard to see what use the Actinotrocha has for any organ of support in the region where
the diverticula are found and it seems much more probable that they have a glandular function.

Nervous system. — It is generally admitted among investigators who have studied the
anatomy of the Actinotrocha carefully, that the creature has a subepidermal layer of nervous
tissue throughout the body which is fibrillar in character. This nervous tissue assumes the form
of quite definite tracts in certain parts of the body in Actinotrocha Species Ii. and fairly well-
developed nerves can be said to twist. The most conspicuous ones are found in the median
dorsal line of the preoral hood as three distinct longitudinal bundles of nerve fibres extending
from the ganglion to the anterior edge of the hood. There are other tracts which, though they
are not as definitely marked out as the above, are undoubtedly nerves.

Masterman (15) in his work on the anatomy of the Actinotrocha from St. Andrews Bay has
described a complicated nervous system, but the investigations of Roule (20), Ikeda (It), and Long-
champs (12) have thrown considerable doubt on the correctness of his observations. Whether
these differences have been due to differences in the Actinotroch.se. studied by these workers or
whether they are due to the technique it is impossible to say. but. judging from the difference
in the degree of development between the nervous system in Species A. and Species B., we all-
ied to believe that the disagreements are due partly to the fact that no two of these investigators
have studied the. same specie- of Actinotrocha.

While the nervous system of Species A. can with careful study be shown to be very similar
to that of Species B., yet it is so feebly developed that without first having studied Actinotrocha
Species B. we should not have been able to see the similarity in the disposition of the different
nervous tracts. The ganglion with its three dorsal longitudinal nerves running along the median
line of the hood is easily seen in the live larva of Species A., but in sections we have found it
impossible to trace the latter. The sensory papilla mentioned in the description of the Actino-
trocha Species B. is absent in this species.

We are pleased to be able to confirm, to some extent, Masterman's (15) description of the
nervous system of the Actinotrocha, especially since a shadow of doubt has been cast upon his
work by some who have studied the Actinotrocha.

Partly because Species B. seems to be a much more highly developed ActinoProcha than
Species A., and partly because of its similarity to the one that .Masterman studied (which is of so
much theoretical interest), we shall confine the description and figures to the nervous system of
Species B., although we are convinced that this Actinotrocha is not that of Phoronis architected
but of an adult that has not been discovered.

90 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

We must admit that we have been very unsuccessful in the attempt to study the nervous
system of the Actinotrocha by means of methylene blue and ammonium molybdate. Gold
chloride has given no better results than staining- with iron hematoxylin.

If the dorsal surface of the hood of a live Actinotrocha Species B. be examined, one will find
that there are a great many fibres winch run in more or less definite tracts (tig. 36). Many of
these fibres have nuclei along their course and are undoubtedly muscle fibres, while others run to
the edge of the hood and there seem to be continuations of certain cell-like bodies which Ikeda
was the first to describe (fig. 37). Although we have seen these bodies on all occasions in surface
views stained with methylene blue, yet in sections we have never been able to make them out, if
they are nerve cells. It must be mentioned, however, that in transverse sections through the
edge of the hood every 3 n section shows at least one nucleus closely applied to the ring of
nervous tissue running round the edge of the hood (tig. 43). These occup3T the same position
with reference td the edge of the hood that the cell-like bodies do which are seen in surface views,
but we take them to be the nuclei of muscle cells, and frequently we have traced deeply stained
muscle fibres arising from them (fig. 43). Within the nervous tissue of the preoral ring we have
found no structures which we could consider to be the cell-like bodies mentioned by Ikeda (9).

Ikeda has figured a great many fibres arising from the ganglion, but in the Actinotrocha
that we have examined we have not been able to see the connections; however, we do not wish
to deny that they exist.

The three median nerves arising from the anterior side of the ganglion and running forward
to the edge of the hood, and two longitudinal tracts of nerve fibres arising from the posterior
side of the ganglion, can be easily made out, but the large majority of fibres which compose the
broad tract shown in tig. 36 are not connected with the nerve ganglion. There are some indi-
vidual differences in the arrangement of the above tracts, but in general they are about as shown
in fig. 36.

On each side of the medio-dorsal line in the region of the youngest tentacles a tract of fibres
can be seen running longitudinally. In the region where the edge of the preoral hood is inserted
into the collar a small tract made up of a few fibres branches off from the dorsal longitudinal
tract and passes into the edge of the preoral lobe. Somewhat farther forward each dorsal longi-
tudinal trunk spreads out sometimes into three rather indefinite tracts, most of whose fibres seem
to reach the edge of the hood. Many of the fibres of the anterior branch appear to end in the
region at the sides of the ganglion, but no connection with the latter could be found.

Immediately posterior to the ganglion a tract of fibres (fig. 36) is seen which runs for a short
distance transversely to the long axis of the Actinotrocha. On both sides the fibres of this tract
soon diverge from one another and in this way distribute themselves over the anterior part of
the hood, ending at the edge of the latter (tig. 36).

Masterman (15) has figured (PI. XVIII, fig. 2) certain nerve tracts to the right and left of
the three nerves arising from the anterior end of the ganglion and finds that these "run
forward and outward and then bend backward and take a course to the posterior corner of
flic hood."

A lateral view of the hood of Actinotrocha Species B. shows sometimes fibres gathered
together in trunks, but these never take the direction as shown by Masterman. They diverge
rather regularly and end all along the edge of the hood instead of at the posterior corners of the
same (fig. 37). They are in no way associated with the ganglion and do not have the appearance
of being even when the hood is turned upward out of its usual position.

For several reasons we believe that the complicated tracts of fibres seen in a surface view of
a live Actinotrocha Species B. are not nerve fibres but muscle fibres. First, many of them show
along their course nuclei resembling nuclei of muscle cells. Second, cross sections through the
hood show that there is a rather heavy lining of muscle tibres which run in the same general
direction as do the fibres shown in the surface view. Third, there is no connection between
these fibres and the nerve ganglion.

PHORONIS ARCHITECTA— BROOKS AND OOWLES. 91

From the posterior side of the ganglion two tracts of nerve fibres pass out and can be traced
backward some little distance, but they are soon lost to view, as Lkeda (9) has found to be the
case when studying methvlene-blue preparations.

Sections through Actinotrocha Species B. bring out quite plainly certain nervous tracts which
appear as thickenings of the subepidermal nervous tissue and which correspond in a large part
to the principal nerves described by Masterman.

Anterior to the ganglion a section through the hood shows the parallel nerves which run
from the anterior side of the ganglion to the anterior edge of the hood. The boundary of these
nerves, as shown in fig. 4-1, is a little too definite. The subepidermal nerve tissue, which forms
a thin layer below the ectoderm cells, is not shown in the series of sections to be described.

Following the sections posteriorly we come to the ganglion, which in this specimen has
become invaginated. together with the overlying epidermis, so as to form a pit. A cross section
through this pit is shown in fig. 44/;. The cavity of the pit is lined by epidermis, while periph-
erally the wall of the pit consists of the ganglion cells and the nerve fibres of the ganglion (tigs.
38— 44/<). The nuclei of the ganglia are easily made out. but it is only after staining very deeply
with iron hematoxylin that the cytoplasm can be seen. The imagination in the region of the
ganglion is unusual and is brought about by the violent contraction of the hood when immersed in
the fixing fluid. This undoubtedly is the same condition that Masterman (15) has described and
the same structure that he has homologized to the '"neuropore" of the Chordata, or that he lias
compared to the tubular dorsal nervous system of the same type as that of Balanoglossus. (Q. J.,
Vol. XL. page 2;»5, 296.) It should be mentioned, however, that Masterman (Ub) in his answer
to Roule has admitted the error of his rather hasty conclusion.

Menon(lT) ha-- recently described a tubular nerve ganglion for a certain Actinotrocha, but
the structure i> probably due to fixation.

Immediately posterior to the ganglion a cross section shows two thickenings of the sub-
epidermal nervous system. These thickenings are what Masterman has described as the
dorsal longitudinal nerves and they can be traced from the ganglion. They are almost exactly
between the dorsal muscle tract and the epidermis of the dorsal wall. A little farther back these
so-called nerves are not quite as distinct, but when the region of the first pair of tentacles is
reached they become more prominent again and diverge, passing down the lateral walls along
the bases of the tentacles (tig. 41). They meet in the ventral region and thus form a ring-like
thickening of the subepidermal nervous system, which is undoubtedly the same that Masterman
has described as the ■"collar nerve ring" (tig. 42). Ganglion cells are demonstrable in this nerve
ring by staining deeply with iron hematoxylin (tig. 39). As we shall show in the account of
I lie muscular svstem there is a ring of muscle fibre which follows the nerve ring".

Masterman says that "fibers pass mid dorsally as a pair of tracts, giving off branches to
the body wall and terminating in a nervous ring just anterior to the perianal band." In his
figures of sections, however, the pair of tracts does not show back of the most dorsal pair of
tentacles. In Actinotrocha Species B. there are no definite tracts of nerve fibres running longi-
tudinally from the region where the collar nerve ring passes obliquely downward from the dorsal
surface of the collar. Nerve fibres are undoubtedly present all along the dorsal wall, but these
are not massed together in tracts and are simply the fibres of the ordinary subepidermal nervous
tissue. The nervous ring in front of the perianal band is not present in the Actinotrochse that we
have studied.

Masterman (15) finds that part of the nerve ring around the edge of the hood passes up to
the nerve ganglion when it reaches the insertion of the hood, and that numerous fibres also appear
to pass on to the ventral surface of the collar region. Live Actinotrochse. (Species A. and Species
B.), when examined under the microscope, do not show a branch of the nerve ring of the lobe
passing upward to the nerve ganglion. Sections also fail to show this condition, which is very
necessary to Masterman's comparison of the nervous system of Balanoglossus and the Actino-
trocha. Fibres from the nerve ring do, however, pass on to the ventral surface of the collar
region.

S9369 i-oj 10—11 T

92 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

Numerous fibres, which Masterman speaks of as passing down on to the ventral collar wall,
are massed in the Actinotrocha Species B. into two definite thickenings which are seen in rig. Me
and rig. 40. These thickenings of the nervous tissue gradually approach one another as we trace
the sections backward and come to run along the same line as do the two ventral muscle tracts
of the collar, hut before the line of insertion of the ventral tentacles is reached these thicken-
ings are lost in the subepidermal nervous tissue.

We have not been able to make out either in sections or in surface mounts any definite nervous
tract running from the collar nerve ring along the ventral region of the trunk, although, as
before said, there is a subepidermal network of nervous tissue throughout the wall. It
will be remembered, however, that above we have described two longitudinal dorso-lateral tracts
of muscle fibres, and there are quite numerous longitudinal muscle fibres in the ventral wall of
the trunk. There is also a fairly well-developed layer of circular muscles, and these, together
with the longitudinal muscles, give the appearance in surface views of the longitudinal tracts
giving off branches.

The nervous system of the Actinotrocha of JPhoronis sabatieri is less highly developed,
judging from the specimens we have examined, than that of cither Species A. or Species B. The
ganglion, or, as Roule (20) calls it, the " plaque cephalique," contains ganglion cells like those we
have found in other Actinotrochse, which shows that there is something more present than a
simple subepidermal nervous system, such as Roule has described, in the Actinotrocha of Phoro-
nis sabatieri.

Muscular systt /a. — There is no doubt but that there is some diversity in the arrangement of
muscle fibres in the different species of Actinotrochse. A study of the two species, A. and B., as
well as the description of different species by other investigators, convinces us of this.

In the study of the muscular system the best results were with material rixed in Flem-
ming's strong solution and stained with Haidenhain's iron ha'inatoxylin. These solutions make
the muscle fibres stand out very distinctly, whereas material rixed and stained with other fluids
shows them so feebly that the muscle tracts might easily be overlooked.

Ikeda (9) has described a pair of bundles of muscle fibres springing from "the hind lateral
corners of the ganglion and running divergently downward until they insert themselves in the
collar walls between the first and second tentacles." These muscles, to which he has given the
name of "retractors,"'' are present in the Actinotrochse Species A. and Species B. (figs. 34, 35. 45,
45a).

The "retractors" that Ikeda figures in the trunk cavity of one of the Japanese Actino-
trochse were not found in either Actinotrocha Species A. or Species B.

Another pair of bundles of muscle fibres is found in Species B. They spring from the
wall of the hood at the sides of the ganglion, traverse the cavity of the hood and become
inserted on its ventral wall directly under the ganglion (rig. 45a).

Certain tracts of muscle fibres are very highly developed in Species B. Transverse sections
(stained with iron hematoxylin) through the wall of the hood in front of the ganglion show
black dots spread over the internal dorsal surface of the hood, and these seem to be embedded
in the mesodermal lining. These dots are the cut ends of muscle fibres, and as the sections are
followed posteriorly, these dots gradually become massed about halfway between the ganglion
and the sensory papilla and represent the sectioned ends of a pair of longitudinal muscle tracts
which are bilaterally placed on the right and left of the median dorsal line (rig. 44). These two
thick tracts of muscle fibres extend posteriorly in the dorso-lateral regions of the Actinotrocha
and do not disappear until the perianal ring is reached. They are very characteristic structures
in Species B. (rigs. 44 to 44//). but we have not been able to make them .out in Species A.

These muscle bands, no doubt, serve to draw the anal end of the body of the Actinotrocha up
to the oral end during the metamorphosis. They are the most highly developed muscle tracts in
the body of the Actinotrocha and their course is almost identical with the course of the "dorsal
nerves" that Masterman describes.

Examination of cross sections of Species B. in the region of the vestibule shows the cut ends
of numerous muscle fibres which are spread over the ventral surface of the collar. Passing

PHORONIS ARCHITECTA— BROOKS AND COWLES. 93

posteriorly, these fibres become massed into definite muscle tracts, about halfway back from the
vestibule to the ventral insertion of collar-trunk mesentery (figs. 44r, 44(/). These two ventral
longitudinal tracts, which are bilaterally placed one on each side of the ventral median line,
become separated, in most cases at least, from the ventral body wall in the region of the posterior
pair of blood corpuscle masses and the latter become rather closely associated with them (fig. 4('i).
We could not discover that these fibres were in any way related to the nephridia as has been
described for some species.

In the region of the insertion of the ventral tentacles the muscle fibres of the ventral tracts
become again applied to the ventral body wall, but definite tracts are no longer present. How-
ever, in the trunk region these fibres form a definite tract, which is confined to the ventral body
wall, and it does not disappear until the perianal ring is reached (figs. 44 g, Ii, i).

Another tract of muscle fibres present in species B., which does not seem to be developed in
other Art)noti'och;i', judging from existing descriptions, is that found in the region of the bases
of the tentacles. From the dorsal muscle tracts, where the most dorsal and anterior pair of
tentacles arises, muscle fibres are given off, which follow the bases of the tentacles and which
form a well-developed ring of muscle fibres. In other words, there is a ring of muscle fibres
which follows the line of insertion of the mesentery between the collar anil trunk cavities
(fig. 44e).

A tract of muscle fibres, which also seems to occur only in Species B., is one composed of
only a few fibres, which are found running around the edge of the hood on the internal wall of
the same (tigs. 44 '/, h). Where the edge of the hood passes into the wall of the collar cavity
these fibres are seen to run on to the internal surface of the lateral wall of the collar and to
mingle finally with the fibres of the dorsal tract. The direction these fibres take when they pass
on to the wall of the collar reminds one very much of the fibres which Masterman (15) figured as
nerve fibres.

On the internal ventral surface of the hood in both species of Actinotrochae there is a system
of muscle fibres arranged concentrically. They run almost parallel with one another and with
the edge of the hood (figs. 47 and 44<').

Beside the tracts of muscle fibres which have been described there are, lining the walls of the
collar and trunk, circular muscle fibres lying between the longitudinal muscle fibres and the
ectoderm. These have been generally observed by previous workers as have also the muscular
covering of the ventral pouch and the muscle cells of the dorsal blood vessels.

Body cavities, mesenteries, etc. — Much difference of opinion exists as to the origin and limits
of the body cavities in the Actinotrocha and also as to the value of these cavities in determining
the phylogenetic history of Phoronis.

Roule (20) stands alone in considering the Actinotrocha to have but one body cavity, which
is lined by an epithelium formed from mesenchymatous cells. He absolutely denies the presence
of any mesenteries.

Through the kindness of Mr. Longchamps we have been able to study the Actinotrocha of
Phoronis sabatieri, and have found that the mesentery between the collar and trunk is present,
although it is less highly developed than in other species. We are unable, with the material at
hand, to give any opinion as to the presence of a mesentery between the preoral lobe and collar
cavities.

Caldwell (3) claims that there are but two body cavities, and that these are separated by a
mesentery (collar-trunk mesentery of Masterman).

Longchamps (12) is inclined toward the view of Caldwell, while Ikeda (!») finds the mesentery
dividing the lobe and collar, which, however, he says, is incomplete. Both of these investigators
recognize the presence of the ventral mesentery.

Menon (17) finds three body cavities (preoral, collar, and trunk), a ventral mesentery, and
indications of a dorsal mesentery in the trunk.

Masterman (1(>) considers that the Actinotrocha have five body cavities — an unpaired lobe
cavity, a paired collar cavity, and a paired trunk cavity. This idea is based on his study of the

94 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

early development of the body cavities and not on the adult organization of the Actinotrocha,
for in the collar he finds only a dorsal mesentery (no other investigator has seen this), and in the
trunk only a ventral mesentery.

While it is possible that the mesoderm arises as diverticula from the enteron, as Caldwell
and Masterman have described, yet Longchamps (12), who has recently reinvestigated the early
embryology of the form that Caldwell worked on {Phoronis kowaU vskii), denies the origin of the
cavity in front of the collar trunk mesentery from enteric diverticula. Ikeda (it), who recognizes
the "anterior diverticula" of Caldwell in the Japanese species, nevertheless holds that the body
cavities do not arise from anterior diverticula, but are simply produced by mesoblast cells apply-
ing themselves to and forming the lining of the ectoblastic and entoblastic wall.

In the section on the mesoderm we have stated that in the embryo of Phoronis architecta we do
not find that the mesoderm arises from enteric diverticula, There can not be the least doubt,
however, that the preoral lobe at an early stage becomes lined by a sac of mesoderm cells and
that the wall of this sac gives rise to the mesentery. Furthermore, this sac is extended postero-
lateral^ into two horns winch are characteristic of the cavity of the preoral lobe, according to
Masterman, Ikeda, and Menon. It must be admitted, however, that this sac does not seem to
retain its character as a sac. but that the cells become separated and apply themselves here and
there to the walls of the preoral lobe. The mesentery remains intact and can not be considered
as a secondary structure as has been suggested by Longchamps. Although we agree with Ikeda's
statement that the mesentery between the lobe and the collar is incomplete laterally in the fully
developed Actinotrocha, yet in the Actinotrocha of Phoronis architecta, at least, it must be
considered as a definite mesentery.

The fully formed Actinotrochse (Species A. and Species B.) do not show a complete epithe-
lial lining to the preoral lobe, but the mesoderm cells are arranged as described in the young
larva.

It is stated above in tin' part on the mesoderm that we do not find that the lining of the collar
cavity is of enteroccelic origin in Phoronis architecta. However, in the fully formed Actino-
trocha there is an undoubted mesodcrmic ephithelium lining the somatic wall. This layer is very
conspicuous immediately before metamorphosis, because it becomes separated from the somatic
wall prior to becoming transformed into the ring vessel of the adult (tigs. 51;/, 51^).

The splanchnic wall of the collar cavity in the Actinotrochse, that we have examined is devoid
of a mesodermal lining, and the occurrence of mesoderm cells on the wall is very infrequent.
This condition of affairs in the well-developed Actinotrocha is what one would expect from the
disposition of the mesoderm cells in the very young larvse of Phoronis architecta, where it is
only very seldom that any are found on the stomach wall (tig. 24).

The absence of a mesodermal lining on the splanchnic wall of the collar cavity is made all
the more evident by the examination of cross sections showing the collar-trunk mesentery
(figs. f>lg, 51/0- When the mesentery reaches the stomach wall, instead of dividing into two
layers, one of which would be continued into the mesodermal lining of the stomach wall of
the collar cavity, it turns abruptly upon itself and becomes the lining of the stomach wall
of the trunk. We have never found the least indication in the collar cavity of a dorsal mesentery
such as Masterman (15) has described in the Actinotrocha from St. Andrews Bay. The trunk
cavity is lined throughout by a sac of mesodermal epithelium, and the mesentery is plainly seen
to be continuous with the lining of the somatic wall and with the lining of the wall of the gut.
The ventral mesentery of the trunk is present in Species A. and Species B., and while there
is no dorsal mesentery we have found indications of it in two specimens only (Species B.) at the
posterior end of the trunk. We can not say. however, that it has any ontogenetic significance
( tigs. 18, 41/, 44;/). We have also found the ventral mesentery to be present in the Actinotrocha of
Phoronis sabatii ri.

The ventral pouch fills a large part of the trunk cavity in the fully formed Actinotrocha, and
just before metamorphosis it frequently pushes the collar trunk mesentery well forward into the
collar cavity, thus making the study of the relation of the different parts quite difficult. Both

PHORONIS ARCHITECTA— BROOKS AND COWLES. 95

the externa] opening of the ventral pouch and the nephridial openings are found on the ventral
wall of the trunk just posterior to the insertion of the mesentery as in other species.

Nephridia. — Wagener (2:i) was the first to observe the •"nephridial bouquets," but Caldwell
(3) was the first to publish a careful study of the, nephridia of the Actinotrocha. Goodrich" (6)
has recently published a paper on the excretory organs of Amphioxws, and lie adds a note on the
nephridium of the Actinotrocha which confirms Caldwell's view. The two latter investigators
agree that the nephridium ends blindly without funnels; that there are tubular processes, each
one containing a lumen and tipped with an excretory cell, and that these processes radiate out
from the blind inner end of the nephridial canal.

Longfchamps (12) is inclined to accept Caldwell's view of the subject. Roule (20) and Ikeda
(9) seem to hold the view that the nephridial canal ends blindly without branching, and that the
blind end is tipped with excretory cells, which, however, are not perforate.

Masterman (15) and Menon (17) have another view. They both think that the nephridial
canal terminates internally as two (Menon) or more (Masterman) funnels, and they recognize the
existence of long processes without lumens attached to the ends of the funnel.

We have not been able to make a study of the nephridia of the living Actinotrocha, but we have
investigated them by means of sections in Species A. and Species B. For this purpose we have
used material fixed in Flemming's fluid and also in corrosive acetic. The sections were stained
with iron hematoxylin. Our work has been done with very high powers (Zeiss obj. TV and No.
12 Zeiss compensating occulare).

The nephridia of the two Acti/notrochst have much the same structure, but in Species A.
we have been unable to find that the internal end of the nephridial canal branches, while in
Species B. the internal end divides into two short branches.

Figs. 52, 52«, 52J represent three transverse sections through the anterior part of the
nephridium of Species B. Fig. .">2 is through the nephridial canal just posterior to its inter-
nal end. Darkly staining dots seen in the lumen represent cross sections of long flagella such as
Goodrich (G) has described in the " solenocytes " of AmpMoxus.

Fig. b2<i shows a section through the nephridial canal a few sections anterior to that of fig.
52, and at the same time it shows the lower or most posterior branch with a few excretory cells
and their processes.

In tig. 525, which is a section through the tip of the upper or anterior branch of the nephrid-
ium, the lumen of the nephridial canal is reduced to a very small (dear space.

If a section is taken in a longitudinal direction through the nephridial canal and its excretory
processes (fig. 52g), it is seen that the distinct walls of the nephridial canal disappear when the
" bouquet" of excretory cells is reached, but that the end is blind and that it is merely a thin
walled bulb from whose surface radiate the processes of the excretory cells. The structure of
these processes is the same in both species that we have examined except that in Species A. they
are much shorter, which might account for the different descriptions we find in the literature.
We are convinced that in both species the excretory processes contain lumens, that these lumens
are continuous with the lumen of the nephridial canal, and that they contain flagella.

Each of the excretory processes is tipped by a body the distal end of which is drawn out
into a sharp-pointed process. The outline of only one cell could be seen in the body. Some-
times it contains but one nucleus, which may be oval in shape or bent almost at right angles
(tig. 52</), but in the majority of cases there are undoubtedly two nuclei (fig. 52c). Fig. 52(
shows a cross section through one of these bodies. If a transverse section of the nephridial
processes is taken (tig. 52/), it is seen that each has a definite wall and that inside there is a
definite dot which we take to be a cross section through the flagelluni. This Hagellum has its
origin from the cell body at the end of the process, and the indications are that the Hagellum
extends throughout the length of the process into the lumen of tin1 nephridial tube.

"Since writing this paper a description of the nephridia of the Actinotrocha by Goodrich (6a) lias come to our
notice. Our account agrees to a large extent with his.

96 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

We are not prepared to say that the cell bodies at the end of the excretory processes are
composed of two cells, but it is a fact that two nuclei exist, and this conclusion is not based
on sections through bent nuclei which might lead one to think that there were two when only
one existed. It will be seen from this description that the anatomy of the excretory cells and
processes of the Actinotrochse which we have studied resembles that of similar structures
described by Goodrich for Amphioxus.

There is nothing now to add concerning the nephridial canal except that a longitudinal
section through it, which has been stained with iron hematoxylin, shows long flagella extending
some distance from the distal end into its lumen (fig. 52^).

Sections of the Acti/notrocha of Phoronis sabatieri show that the nephridia resemble those of
other Actinotrochse studied, although they do not seem to be as well developed as those of
Species A. and B. The specimens at hand show that the internal opening in the collar cavity is
situated at about the same level as in other Actinotrochse, and not at the level of the oesophagus,
as Koule (20) has indicated.

The course which the canal takes is like that which has been described by other investigators,
and we agree with the observation of others in regard to the nephridial canal opening to the
exterior at the sides of the ventral pouch opening.

Masterman (15) describes a pair of ciliated pores opening to the exterior on the dorsal surface
of the preoral lobe. These, he finds, lead into tubes closely similar in cross section to the cross
section of canals of the collar nephridia. and these tubes have an internal opening into the preoral
lobe cavity. He compares the external pores to the proboscis pores of Cephalodiscus. In the
Zoologisher Anzeiger, 1901, Volume XXIV, page 231, he admits that their occurrence is variable.
No other investigators have found these organs. Ikeda mentions the fact that flask-shaped
glands on the upper face of the preoral lobe occur in one larva studied by him, but he denies
that the}' are such organs as Masterman describes.

Masterman (15) also finds thin-walled organs lying in the hsemoccele space immediately below
the anal ciliated band. Speaking of these (15) he says: "A pair of organs which I have not fully
made out, but they may be the rudiments of the trunk nephridia." Masterman, however, denies
their existence in a later paper, and no one else has seen the organs, as far as we know.

Rudiments of the adult blood vex*//* hi tl>, Actinotrocha. — Many investigators of the Act i-
notrocha have recognized the beginnings of the adult blood vessels, but E. B." Wilson (21) is the
first one who clearly states the fact that the cavity containing the blood corpuscle masses gives
rise to the ring vessel of the adult, although Metschnikoff seems to have had some such idea.
Caldwell (3) and Ikeda (!») confirm the statement of Wilson with reference to the origin of the
ring vessel of the adult.

While Masterman (15) describes a much more complicated vascular sj'stem for the Actino-
trocha from St. Andrews Bay than that of all the Actinotrochse examined, yet we agree with
him in his view that the cavities of the blood vessels may be considered as vestiges of the
segmentation cavity.

Above we have given our opinion that the "subneural sinus" (Masterman) does not exist in
the Actinotrochse that we have examined, and that although there is a space beneath the ganglion
it has no connection with the dorsal blood vessel.

The blood vessels of the adult are represented in the Actinotrochae Species A. and B. by a
dorsal vessel (figs. 31, 35) extending along the median dorsal line of the intestine, from the
mesentery between the collar and trunk almost to the posterior end of the stomach, where there
are small ca?cal outpushings of the splanchnic mesodermal walls of the end of the stomach. This
dorsal blood vessel, although it is a completely formed vessel, has arisen from a proliferation of
the cells of the splanchnic mesodermal wall along the dorsal median line of the stomach, and its
lumen is really a part of the blastocoele — i. e., it is a part of the space, between the splanchnic
mesodermal lining and the wall of the stomach. Posteriorly, the dorsal blood vessel becomes
indefinite and passes into the ordinary splanchnic mesodermal lining, thus really being open pos-
teriorly into the space between the wall of the stomach and the mesodermal lining.

PHORONIS ARCHITECTA— BROOKS AND COWLES. 97

At the time of metamorphosis in the Actinotroohae Species A. and Species B., there is no
sign of a ventral blood vessel along- the stomach, such as Masterman (15) and Roule (20)
describe.

We have been unable to find the "ring sinus" which, according to Masterman, connects the
dorsal vessel with the ventral vessel at the end of the stomach, nor have we seen the "postoral
ring sinus" connecting the dorsal vessel with the ventral vessel.

Masterman's "postoral ring sinus." •■ventral blood vessel," and •"ring sinus" (situated at
the junction between the stomach and intestine) will l>e discussed in the section on the metamor-
phosis.

There is undoubtedly a space between the wall of the perianal ring and its mesodermal lining
(tig. 49) in preserved specimens which seems to be what Masterman calls the " haemal ring."
but it does not become any organ of the adult.

As stated above, we believe with Wilson, Caldwell, and Ikeda that the cavity of the collar
and its somatic mesodermal lining become the ring vessel of the adult.

We shall continue the discussion of the further development of the dorsal blood vessel into
the efferent and afferent vessels of the adult in the section on the metamorphosis.

Masterman speaks of haemal sinuses passing down the tentacles, but says that they are not
very decided. Ikeda has. however, investigated these structures carefully, and we thoroughly
agree with his view that the cavity of the collar, together with its somatic lining, extends into
the tentacles, and that these prolongations become the tentacular vessels of the adult. This
condition is shown very plainly in a dorso-lateral section of the Actinotrocha Species A. (tig. 50).

Ill, „h! corpuscles and their origin. — E. R. Wilson (2-4) has touched upon the origin of the
blood corpuscles, and according to him they develop in solid masses adhering to the stomach
walls near the base of the tentacles. Caldwell (:!) finds that the corpuscle masses "arise from
the mesoblast cells in front of the septum," but he has nothing further to say about their
position or origin. Ikeda (9) describes the blood corpuscles as arising from "gigantic meso-
blast cells in the body cavity of the larvae with one or two pairs of tentacles." Since the
publication of this paper, Ikeda has rejected this view, although he has published nothing on the
subject. Menon (17) thinks that the blood corpuscles arise from the splanchnopleure covering
the stomach and its diverticulum. According to Cori (1), the blood corpuscles in the adult are
formed from the endothelium of the blood vessels.

In the Actinotrocha Species A. (probably that of Phoronis architecta) the blood corpuscles
usually make their appearance during the 14-tentacle stage, as in "Type A" described by Ikeda,
although we have found larva' of this stage in which definite blood corpuscles were not present.

Actinotrocha Species A. with It! tentacles invariably has blood corpuscles, and they are
present in the so-called collar cavity as two masses more or less closely applied to the ventro-
lateral walls of the stomach (figs. 51 ,/. /<). In some cases, however, they are separated from the
wall by a considerable space.

The transverse section of a larva with 12 tentacles in a plane just posterior to the base of
the tentacles, but anterior to the mesentery, always shows two masses of cells bilaterally placed
and closely applied to the mesoderm lining the ventro-lateral somatic wall (tig. 53). Occasionally
cells are found in these masses, situated very close to the mesodermal lining, which are
decidedly spindle-shaped in form and whose nuclei resemble those of the cells of the mesodermal
lining, both in shape, size, and internal structure. These cells are not very rich in cytoplasm.
Most of the cells, however, are almost three times the size of the cells lining the somatic wall,
the cytoplasmic part of the cell having increased in size to a greater extent than the nucleus.
Most of the nuclei have large deeply staining nucleoli (tig. 51).

In some specimens parts of these masses of cells are apparently in the act of wandering
across the body cavity to the position the blood-corpuscle masses occupy in the fully formed
Actinotrocha.

Some 15 or 20 larva' with 12 or 11 tentacles have been sectioned, and with one exception we
have found that when the mesodermal masses are present on the ventral body wall there are no
blood-coi'puscle masses present in the larva, and that when the blood-corpuscle masses are

98 MEMOIRS NATIONAL ACADEMY OF SCIENCES. VOL. X, NO. 4.

present there are no mesodermal masses. In this exception small blood-corpuscle masses were
found applied to the stomach wall, and masses of cells bilaterally placed were found on the
ventral somatic wall, but these cells had already taken <>n the character of blood corpuscles.

Ikeda (9) has described a "mesoblastic cell mass" which he evidently considers as giving
rise to the adult body cavity, and its position is very similar to that of the mesoblastic masses
described above. They are both products of the mesoblastic lining of the ventral somatic wall
and are situated between the plane of the bases of the tentacles and the plane of the somatic
insertion of the mesentery between the collar and trunk. Although Ikeda does not touch upon
the very early origin of the adult body cavity, yet it seems probable that he considers it as arising
from a single mass of cells. The mesoblastic masses described above are paired and bilaterally
placed, and they are present only in the young larva of L2 or 14 tentacles. Furthermore, in
the larva with 12 or 14 tentacles there is no sign of the beginning of the adult body cavity.
Although these mesodermal masses which, according to our observations, give rise to the blood
corpuscles have a similar position to the fundament of the young adult body cavity, yet we are
convinced that they do not give rise to it.

In Species A. there is no intimate relation between the masses of blood corpuscles and the
nephridia. such as has been described by Masterman (15) for the'species from St. Andrews Bay,
and by Longchamps ( L2) for Actinotrocha branchiata. In the larva of 16 tentacles the blood-cor-
puscle masses are. however, closely applied to the stomach wall in the region of the digestive
area. There is no mesodermal epithelium covering that part of the surface of the stomach which
lies within the collar cavity, and the blood corpuscles seem to be so intimately related to the
digestive areas that we are inclined to believe that they receive nourishment from them.

While the blood corpuscles vary in size and undoubtedly multiply by karyokinetic division,
yet we have never found the "large and somewhat coarsely granular" and the •"smaller finely
granular" corpuscles that Ikeda (!>) speaks of. nor in this species have we found any "gigantic
mesoderm cells" in the region of the blood-corpuscle masses. Very large cells in close relation
to the blood corpuscle masses are found in some specimens of Actinotrocha Species B. (tig. 44/').
These cells resemble the cells described in the old gastrula of Species A. as arising from the wall
of the archenteron, only they are not as coarsely granular as the latter. While in Actinotrocha
Species B. the cells are found in most cases closely associated with the blood corpuscles, we have
never seen them in the process of division and do not believe that they give rise to blood
corpuscles. Their occurrence is quite variable, but as far as has been observed they are not
present in the Actinotrochst which are ready to metamorphose. They are not phagocytes, nor are
they pigment cells, and the only name which we feel justified in giving them is large free
mesoderm cells. Frequently they are also found in the posterior end of the trunk cavity (fig. 41/).

Roule (-20) holds that the nephridia end internally at the level of the (esophagus, and he
shows this in a figure. We have made cross sections through this region and have found masses
of cells in much the same place as Roule has shown. These cells seem to be blood corpuscles,
but very few specimens have been examined, and only one of these showed these masses of cells.

Rudiment <>ff/i< ■■mini! collar cavity" (Ikeda).— Ikeda has observed a mesodermal cell mass
on the ventral somatic wall just under the second tentacle in rather young specimens of all the
Japanese Actinotrocha. He has traced the development of this mass of cells and finds that a
cavity arises in it which, before metamorphosis, becomes quite spacious and extends into the
tentacles. We are able to confirm Ikeda's view that this cavity is the rudiment of the "adult collar
cavity," or "supraseptal cavity" of the adult, as it is usually called (tigs. 50, 48, 51//. 45/'. 46).

METAMORPHOSIS.

Several investigators have carefully described the external characteristics of the metamor-
phosis of the Actinotrocha, so it is unnecessary to enter into a detailed description.

Wilson (24) studied the metamorphosis of Act) notrnrhte Species A. and Species B., which are
found in Chesapeake Bay. but he did not cut sections of his material. Ikeda (9), however, has
investigated the internal changes which take place during metamorphosis and has added a val-

PHORONIS ARCHITECTA— BROOKS AND COWLES. 99

uable contribution to the subject. The behavior during metamorphosis of Actinotrochas Species
A. and Species IS. from Beaufort Harbor seems to be quite the same as that of the two Actino-
trochse which Wilson has observed, and there is little doubt but that they are of the same species.

As Wilson has stated, the metamorphosis of Actvnotrocha Species A. (tig. 'Si) takes place
much more quickly than that of Species IS. (fig. 35). In fact, we have never obtained a completely
metamorphosed specimen of the latter, although many times we have found specimens of this
species with the ventral pouch well evaginated (tig. 55). We have tried to make the conditions
favorable for the completion of the metamorphosis by covering the bottom of the aquarium with
a layer of sand rich in diatoms and also by changing the water frequently. Under these
conditions the larva' (Species IS.) would invariably sink to the bottom and move around on the
sand apparently in search of a favorable place to finish the metamorphosis. The latter never
occurred, however, although sometimes the larva1 would attach the end of the ventral pouch to
the bottom of the dish. In this way the creature would often remain for days and although the
preoral lobe and larval tentacles would degenerate the anal end of the larva would never become
turned upward so as to lie in close proximity to the mouth.

As we have said before, we are inclined to think that the Actinotrocha Specie-, B. belongs to
au adult which lives under different conditions from that of PJwronis architecta, and we should
not be surprised if it were found to be the Actinotrocha of a deep-water form. Although
( 5 rianthus occurs in Beaufort Harbor, we have never found Phoronis australis associated with it.

Actvnotrocha Species A., as a rule, metamorphoses in about twenty minutes (tigs. 56, 56a,
."><;/<). and usually just before this takes place it sinks to the bottom of the dish, but occasionally
metamorphosis occurs on the vertical side of the dish near the surface of the water, the young
Phoronis remaining tixed where the metamorphosis takes place.

Preoral I<>1>- mill t> iitiivles. — Usually the larval or distal part of the tentacles (Species A.) and
the preoral lobe are swallowed during metamorphosis. The proximal parts of the tentacles
become directed upward and constitute the tentacles of the adult. They always number 18 in
the very young Phoronis (Species A.) and there is an indication of the horseshoe arrangement
which is found in the adult (tig. ."><;/>).

The preoral lobe does not give rise to the epistome of the adult, for as Menon (17) has
correctly observed, this structure is not present in the very young Phoronis. However, the
epistome. which is of ectodermal origin, soon makes its appearance, -and when the creature has 30
tentacles it is a very conspicuous organ (tig. 57).

Ganglion. -The ganglion on the dorsal surface of the hood is lost when the preoral lobe is
swallowed, and hence does not give rise to the so-called brain ganglion of the adult.

Ectodermal mall of collar. —Although the preoral lobe degenerates, the wall of the collar
does not, but becomes drawn inside the body of the young Phoronis and forms the wall of the
oral end of the gut.

Perianal ciliated ring and ectodermal wall of th trunk. — When the critical point in the
metamorphosis is reached — that is. when the posterior end becomes drawn up to the region of the
mouth — the perianal ciliated ring is usually seen as a protuberance in that region (Wilson's rig.
12), but shortly after this it becomes drawn in, and, together with some of the ectoderm, becomes
the lining of that part of the rectum which is near the anal opening. The drawing in take- place
to such an extent that most of the ectodermal wall of the trunk of the Actinotrocha becomes
incorporated in the wall of the rectum, as Caldwell has observed.

This process, together with the drawing in of the ectodermal wall of the collar to form the
wall of the oral end of the gut, seems to cause a change in the position of the nephridial canals.
(See section on nephridia.)

Cavity of the preoral lobe. — Since the preoral lobe is lost during the metamorphosis, its cavity
does not take part in the structure of the adult.

M ki at, rij h, I m, , u (/,, lull, mid collar. — This mesentery does not persist.

Larval collar cavity. — As has been stated by other investigators, and as we have observed, the
larval collar cavity with its mesodermal wall becomes the ring vessel of the adult. This organ
will be discussed further in the section on the vascular system.

100 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

" Adult collar cavity" (Ikeda). — This cavity, which is found in the well-developed Actinotrocha,
undoubtedly becomes the "adult collar cavity" or supraseptal cavity of the adult, as Ikeda says.
In the young Phoronis it is seen as a cavity which occupies all the region anterior to the trans-
verse septum and which is prolonged into the tentacles. It is lined by a mesodermal epithelium
and coutains the ring vessel with its tentacular vessel.

Trunk cavity <tn<l cavity of the ventral pouch. — These cavities become the infraseptal cavity
of the adult.

Ventral mesentery. — The ventral mesentery of the Acti/notrocha no doubt becomes the mes
entery in the adult which Cori calls the " hauptmesenterium " and which Benham names the
"oesophageal" and "rectal" mesenteries. Mesenteries are present in the very young Phoronis
(just after the completion of the metamorphosis), which are found in the exact position that one
would expect the ventral mesentery of the Actinotrocha to assume after metamorphosis. Ikeda's
figures indicate that he considers the longitudinal mesenteries of the very young Phoronis to be
the same as the ventral mesentery of the Actinotrocha^ for he gives them the same name.

We can not otter any observation on the origin of the lateral mesenteries of the adult except
that they are not present in the very young Phoronis that we have examined. They undoubtedly
arise later in the life history.

Stomach diverticula. — This structure is not present in the Actinotrocha Species A., so we are
not able to give any information on the subject. It seems to be the general opinion among those
who have studied the metamorphosis that it does not persist as an organ in the adult.

Dig, stir, areas. —While these organs persist for some little time after metamorphosis, they
arc not evident as organs in the adult Phoronis architecta.

Nephridia. — Caldwell (3), Ikeda (9), Longchamps (V2). and Menon (17) have all observed the
change in position of the larval nephridial canals which is due to the changes taking place during
the critical period of the metamorphosis, and it is a quite well-established fact that the external
ends of the larval nephridial canals come to be situated near the anal opening.

.lust after the critical period a cross section through the anterior end of the young Phoronis
cuts the transverse septum ("diaphragm," "collar trunk mesentery"), which runs obliquely and
passes through the supraseptal and infraseptal cavities. It shows a transverse section through the
nephridial canals, which are still attached to the mesentery, as in the Actinotrocha . Following
the sections anteriorly, the canals are seen to open into the supraseptal cavity (" larval collar
cavities," " ring vessel of the adult"), and they are still found in possession of their excretory
cells. Posteriorly the sections show that the nephridial canals leave the septum and pass between
the wall and the mesodermal lining of the infraseptal cavity (tig. 59). At this time their external
openings are situated on the lateral epidermal wall in a transverse plane which is somewhat below
the transverse plane of the anus, and they are by no means as near to the latter as they are in
the adult Phoronis. It is seen from this description that during the critical period there is very
little change in the structure of the larval nephridiaor in their position, although the evagination
of the ventral pouch and the drawing in of the ectoderm of the trunk to form the end of the.
rectum causes the anus to become rather closely approximated to the external nephridial openings.

Caldwell (3) says that the whole of the larval nephridial canals remains as the paired nephridia
of the adult, while Ikeda thinks it probable that only the parts of the nephridial canals lying in
the wall of the trunk persist. He assumes that the nephridial funnels of the adult, which both
open into the infraseptal cavity, are secondary outgrowths of the above remnants of the nephridial
canals.

As the metamorphosis continues, sections show that the excretoiy cells and that part of the
nephridial canals situated in the larval body cavity have become obliterated, together with the
portion of the nephridial canals running in the septum. While we do not wish to deny that
the remnants of the nephridial canals and their external openings, situated originally in the
trunk cavity of the Actinotrocha. become part of the nephridia of the adult, yet in the stage
under consideration they could not be found. So far as we know, Ikeda is the only investigator
who has given us figures illustrating the relation between the larval nephridia and the nephridia
of the adult. While his tig. 64e shows the larval nephridial canals, his tig. 66, which is a cross

PHORONIS ARCHITECT A— BROOKS AND COWLES. 101

section through the anterior end of a young Phoronis and which shows a section through the
young nephridium of the adult, does not prove that he is dealing with the same structure.

Vascular system. — It will be remembered that the vascular system of the fully developed
Actmotrocha Species A. consisted of a dorsal blood vessel (tigs. 51/'. g, //) running along the
median line of the stomach from the dorsal insertion of the mesentery, between the collar and
trunk, to the posterior end of the stomach, its lumen being a part of the segmentation cavity; a
bunch of blood caeca formed at the posterior end of the stomach as evaginations of its splanchnic
mesodermal covering and a loose sac of mesodermal tissue arising on the somatic wall of the collar
segment and inclosing the larval collar cavity (tigs. 50, 51 f, </. //). (See below for discussion of
the " post-oral ring sinus," ventral vessel and the "ring sinus" at the junction of the stomach
and intestine.)

There are several important points in the vascular system of the Actinotrocha which must
be taken into account in order to understand its metamorphosis into the vascular system of the
young Phoronis. First, that the dorsal blood vessel, which is formed from the splanchnic meso-
dermal lining of the trunk cavity, incloses a part of the space between the lining and the wall of
the alimentary canal — i. e., the segmentation cavity — second, that this vessel dwindles away pos-
teriorly and opens into the space between the lining and the wall of the alimentary canal; third,
that the wall of the stomach in the collar segment is practically free from mesodermal lining
(tigs. 51 ij. /i). and that the larval collar cavity, with its somatic mesodermal lining, is a blood
sinus; fourth, that the larval collar cavity is a part of the segmentation cavity; and, fifth, that
during metamorphosis the act of drawing the stomach and intestine into the cavity of the ventral
pouch causes pressure to be exerted on the larval collar cavity.

When the critical stage is being passed through, the blood-corpuscle masses break up and
they are driven by the pressure on the collar cavity to the points of least resistance. As a rule
some of the blood corpuscles are squeezed up into the dorsal region of the collar cavity where
the dorsal blood vessel ends, and invariably some of the blood corpuscles pass from the larval
collar cavity into the cavity between the wall of the alimentary canal and its mesodermal covering.
In fact, as soon as the critical stage occurs, the splanchnic mesodermal lining in all regions
becomes separated from the wall of the alimentary canal and thus allows the blood corpuscles t >
move about between these two layers throughout the extent of the alimentary canal.

The dorsal blood vessel (" mediangefasz" (Cori), "afferent vessel*' (Benham), and the ring
vessel with its tentacular vessel are completely formed structures at this stage. The dorsal
vessel is still freely open posteriorly into the space or sinus between the stomach wall and its
mesodermal covering and blood corpuscles are carried back and forth from it to the sinus by the
contraction and expansion of the former. Anteriorly the dorsal vessel can plainly be seen
opening into the ring vessel (larval collar cavity.)

The origin of the connection between the dorsal vessel and the ring vessel and the manner
in which the blood corpuscles find their way into the former are questions which have not been
very satisfactorily elucidated. Actiiiotrni-lm Species A., does not present any great difficulties
in the way of understanding how these processes take place. The dorsal blood vessel opens
posteriorly into the sac-like sinus around the loop of the alimentary canal, and it seems probable
from an examination of sections of the critical stage that it is also open anteriorly. Assuming
that such is the condition, it will open into the space between the mesodermal lining and the wall
of the gut. This space, however, is in free communication with the larval collar cavity (adult
ring vessel) which contains the blood corpuscles. Under these conditions the blood corpuscles
can pass into the dorsal blood vessel from either end.

Masterman (15) and Roule (20) both describe a vessel on the ventral stomach wall of the
Actmotrocha. We have not found this vessel in the Actinotrocha, nor do we find it in sections of
the critical stage.

At this time there is but one ring vessel in the supraseptal cavity, but we consider that it
represents both the receiving and distributing vessels of the adult Phoronis.

Shortly after the critical point in the metamorphosis, the mesodermal lining on the left side
of the oral limb of the U-shaped alimentary canal begins to show indications of becoming a blood

102 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

vessel, and when the metamorphosis is completed a definite vessel is seen, which opens posteri-
orly into the spacious blood sinus around the loop of the alimentary canal. Anteriorly before
reaching- the transverse septum, it divides into two branches, which run obliquely upward along
the sides of the alimentary canal, almost encircling- the same; these finally open into the ring-
vessel of the supraseptal cavity (tig. 00). The vessel described becomes the efferent vessel of the
adult (figs. 7s. 77. 7.">, 66) and its branches become part of the recipient vessel.

As Ikeda has pointed out, the efferent vessel of the adult corresponds to the ventral vessel
which Masterman (15) and Roule (20) have found in the Actinotrochse before metamorphosis.

In all the completely metamorphosed Actinotrochse that have been sectioned there is but one
ring vessel, but the young Phoronis, when it is 12 hours old, possesses both the recipient and
distributing vessels; these vessels, we believe, arise from the single ring- vessel of the metamor-
phosing Actinotrocha by the fusion of its walls and by the subsequent separation of the two
parts along the line of fusion.

Masterman, in his description of the blood system of the Actinotrocha, speaks of a "ring
sinus" at the anterior end of the intestine which connects the dorsal and ventral vessels. He
also says that there are two lateral branches of the dorsal vessel in the region of the pharynx
which pass downward around the oesophagus ("l post-oral ring sinus") and become continuous
with the ventral vessel.

The former undoubtedly represents the sinus surrounding the loop of the alimentary canal
in the young- Phoronis, while the latter, no doubt represents the branches of the efferent vessel
which become part of the recipient vessel of the adult. Masterman says that these branches
open into the dorsal blood vessel, but such is not the case in the completely metamorphosed
Actinotrocha.

From a comparison of Masterman's description of the vascular system of the Actinotrocha
and Ikeda's and our own description of the same before and after metamorphosis, it is seen at once
that this system develops more precociously in the form that Masterman studied. This condition,
together with the facts that the lumen of the blood vessels are parts of spaces between the wall
of the gut and its mesodermal lining- and that the mesodermal lining of the alimentary canal tits
loosely while the blood system is developing, gives additional weight to Masterman's statement
that the dorsal vessel opens into the so-called "subneural sinus." However, in the Actinotrocha.
that we have examined such a connection does not exist, and. as stated above, a "subneural sinus"
or cavity caused by a lack of contiguity between the mesodermal wall of the preoral lobe and
that of the collar cavity is not present.

THE ADULT PHORONIS ARCHITECTA.

Phoronis architecta was discovered by Andrews (1) in June, 1885, at Beaufort, N. C, and
he described it as a new species, giving it the specific name "architecta,'1 on account, no doubt,
of its building a beautiful, straight tube. He finds that the tubes are made up of a clear, firm,
chitin-like membrane covered with small, clear grains of sand, and he thinks that these grains
are selected by the animal. Specimens collected from different localities in Beaufort Harbor
vary considerably in regard to the character of the sand grains and quite often small fragments
of dark shells are found mixed in with the latter. Occasionally two tubes occur cemented
together; but this condition is rare, for they are usually isolated and embedded perpendicularly
in the sand. When the specimens are brought into the laboratory and put into aquaria with
sand and water, they usually crawl out of their tubes and begin to form new ones. Long-
champs (13) has lately pointed out that the tube is formed by a secretion from the posterior end
of the animal and not from the anterior end, as Cori has said. This is the case for /'. wrchitecta.

Above it is stated that the tubes are straight, but where new tubes are formed in the aquaria
they are always twisted to a considerable extent, and they are attached firmly to the bottom
of the jar. In its natural habitat, Phoronis architecta does not have a firm substratum to which
to cement its tube, but it is seen from the above observation that when a solid surface presents
itself, the tube may take on the condition found in some of the other species of Phoronis which
are attached to rocks and shells.

PHORONIS ARCHITECTA^BROOKS AND COWLES. 103

Phoronis architecta lives :it about low-water mark on the sand shoals, which are very
numerous in Beaufort Harbor, and. as a rule, the individuals' occur in patches. Three or four
hundred specimens are often found within a radius of 4 or 5 feet, but one is very apt to find
isolated specimens while digging in the sand anywhere in the harbor.

Only rarely do the tubes project above the surface of the sand as Andrews ( 1 ) has described,
and in these cases the condition was due to disturbances of the surface of the sand, such as
hollows made by Oallinectes. Usually the upper end of the tube is from 3 to 5 cm. below the
surface of the sand.

The average length of these tubes is 13 cm., and the average width a little over 1 nun. The
adult when removed from its tube is about 1 mm. in diameter in tin' posterior one-third, and
slightly less in the anterior two-thirds (fig. t!l). The length of specimens taken out of the tidies
varies with the amount of contraction from 20 to 25 mm., which figures are considerably lower
than the length given by Andrews (about 50 mm.). The specimens which Andrews described
must have been considerably more extended than any we have preserved. When the animal is in
its natural habitat and undisturbed, however, it is capable of great extension, stretching the whole
length of the tube and even considerably farther, so that its lophophoral end may project above
the surface of the sand and reach for some considerable distance along its surface. We have not
been able to preserve specimens in their extended condition, and they usually contract to from
20 to 25 mm. in length.

The anterior two-thirds of the living specimen has a flesh color, while the posterior one-third
is dark-yellowish red and quite opaque, which is due to (he fact that the gonads and blood caeca
are situated in this region. In preserved specimens, the body wall is annulated (tig. 61), but
such is not the case probably in the fully extended individual.

The crown of tentacles is quite simple compared to the crown of tentacles in /'. australis,
P. buskii, and /'. pacifica. A cross section shows that it is crescentric and that the ends are not
spirally coiled (tig-. *>2. 63, <i4).

Andrews (1) has given us a description of the principal points in the anatomy of Phoronis
architecta, which he has undoubtedly made brief because of the resemblance to the anatomy of
Phoronis australis as described by Benham ('2). In general our observations agree with those
of Andrews, but there are a few points which merit discussion.

Lophophoral o/yaw*.— These peculiar organs (tig. 62) have been observed in several different
species of Phoronis, and although functions for them have been suggested, the observations do
not seem to have extended over a long enough period in the adult life of the worm to warrant a
definite1 statement as to their function.

The lophophoral organ.- (tig. 62) lie one on each side of the median line within the concavity
of the lophophore. They are outgrowths from the base of the inner row of tentacles, and, in
some species at least, are quite conspicuous organs, but they do notarise until the Phoronis has
reached its adult size. Organs located in the above region have been described for eight species,
but the size and shape do not seem to be the same in all. Whether these differences are specific
or whether the observations have been made at different periods in the adult life it is hard to
say. Lophophoral organs like those present in Phoronis architecta are found in /'. psammophila,
P. pacifica, P. mulleri, and, «o doubt, in some other species also. It seems, however, prob-
able from the description of the anatomy of /'. buskii and /'. australis that in these species
the lophophoral organs are much less highly developed than in the smaller species with fewer coils
in the lophophoral crown. We have examined several specimens of J', australis with ami without
genital products, but in no case have we seen organs such as are present in /'. architecta.

Various functions have been assigned to the lophophoral organs. Mcintosh (14), working
with /'. busMi, considers that they are sensory in function, while Masterman (l'i), who has studied
the same species, says that they are glandular and that they give rise to mucus which serves to
hold the embryos together in masses. In other words, he considers them to be "subsidiary repro-
ductive organs." Benham (-2), who worked on /'. australis, and Cori (4), who investigated
P. psammophila, both give these organs a glandular function, while Andrews (1) thinks that

104 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

in P. a/rchitecta they are used in building the tubes. II. B. Torrey (22) has made the interest-
ing-observation that in some specimens of P. pacifica the lophophoral organs are like those in
P. australis, while in others they are like those in /'. architecta. It is probable that in part of
the specimens which Torrey examined the lophophoral organs were not full grown, while in the
rest they had reached their full development.

Our observations indicate that Andrews" supposition concerning the tube-building function
of the lophophoral organs can not be held. Individuals without the lophophoral organs
build new tubes covered with sand grains just as do those with the organs, and young specimens
of Phoronis architecta, which are in possession of tubes, never have lophophoral organs. These
two facts prove quite conclusively that the lophophoral organs of Phoronis architecta are not
used for tube building.

Masterman's view that the lophophoral organs of P. buskii are glandular, and that they fur-
nish mucus to hold the eggs and embryos in masses can not be applied to P. architecta, for in
this species the eggs and embryos are not held in masses.

Specimens ai Phoronis architecta have been examined during almost every month in the year
in order to discover whether or not there is any relation between the lophophoral organs and the
breeding season During the months of dune, July. August, September, and October examina-
tion of many specimens of Phoronis architecta shows that more than one-half are with lopho-
phoral organs — i. e., with the "carpel-like organs" and the "'spherical sense lobes" (Andrews).
Examination of specimens taken during these months shows that some contain ovaries and eggs
while others do not, and that all contain spermatozoa in the body cavity, but that only those
without ovaries contain testes. Occasionally an egg floating freely in the body cavity is found
in specimens with testes. These facts are correlated with the presence or the absence of the
lophophoral organs, for these organs are present in specimens with testes and without ovaries
and absent in specimens with ovaries and without testes.

During the latter part of December and the tirst part of January specimens of J', architecta,
some of which were collected in Beaufort Harbor at that time and some of which had been kept
alive in the laboratory of Johns Hopkins University since the summer months were examined.

Many of these specimens (Ho or 40) were examined by crushing the posterior end and also
by cutting sections, but with one exception all of these individuals were found to be without
ovaries and testes. In the case of the exception, a few ovarian eggs were present, but the ovaries
were still very young. The blood ca*ca at this time are surrounded by a great abundance of the
peculiar peritoneal tissue, which later gives rise to the reproductive organs. Lophophoral organs
were absent both in specimens collected at Beaufort during the first part of January and in speci-
mens collected during the summer and kept in the laboratory.

During the months of February, March, and April the specimens in the aquaria at Johns
Hopkins University were examined quite frequently, but until March or April there was no sign
of lophophoral organs. Then they began gradually to develop in some specimens until by the
first of May they were full size. At this time another lot of live material was received from
Beaufort which afforded some very interesting observations. The number of individuals with
and without lophophoral organs were in about the same ratio as during the summer months.
At this time, in specimens with lophophoral organs, the testes are 'present but the ovaries are
not, while specimens without lophophoral organs possess ovaries and contain ovarian eggs.
Quite of ten specimens with lophophoral organs have large bunches of spermatozoa floating freely
in the body cavity, and in some cases these occur inside the nephridia. In one individual a large
bunch of spermatozoa was found lodged in the end of the lophophoral organ's pocket-like
cavity.

Judging from our observations, it seems that the relation of the lophophoral organs to the
breeding season is as follows: Some adults are giving rise to eggs throughout the months of
May, June, July. August, September, and October. None of the individuals arising from
these eggs become sexually mature until March or April of the next year. Those which are
the oldest — i. e., those born in the early months of the year before — develop testes and lopho-
phoral organs in March or April. Then they lose their lophophoral organs, the testes disap-

PHORONIS ARCHITECTA— BROOKS AND COWLES. 105

pear and ovaries begin to develop about the first of May. While this is going on, individuals
which were born later in the summer of the year before begin to develop testes and lophophoral
organs, and thus we have individuals with lophophoral organs and testes occurring at the same
time of the year as individuals without lophophoral organs and with ovaries.

While there is no absolute proof, the upper part at least of the lophophoral organs prob-
ably functions as a kind of seminal receptacle. We are led to this conclusion by these facts:
First, that the organs appear only when the testes are present; second, that large bunches of
spermatozoa have been found in the body cavity, in the nephridia, and in the cavity of the lopho-
phoral organs; and, third, that there are ciliated grooves leading from the nephridial pores to the
cavities of the lophophoral organs.

Vascular systt m. —Nearly all of the early investigators of the anatomy of Phoronis recognize
the existence of an efferent and afferent vessel which are in connection with vessels running up
into the tentacles.

Caldwell's (3) description, although brief, is complete, and differs very little from later ones.
Cori's (4) account seems to be about the same as Caldwell's; however, he recognizes one ring
vessel instead of two and describes in more detail the relation between the tentacular vessels and
the ring vessel.

In Phoronis a/ustralis, Benham (2) finds the circulatory system much the same as Caldwell
does in the form that he worked on. Practically the only point of difference is that he describes
the tentacular vessels as dividing iido two branches, one opening into the distributing vessel
(inner) and the other into the recipient vessel (outer).

Andrews (1) finds that the vascular system of P. architecta, as far as he has determined, is
like that of P. australis, while Ikeda (!>) says that Benham's description holds good for /'. ijimai
and /'. hippocrepia.

A transverse section through the lophophoral crown of /'. architecta (fig. 63) shows that the
cavity of each tentacle contains a blood vessel which is attached to the inner surface of the wall.

At the base of the tentacles a cross section shows that there are two blood vessels running
parallel to one another through most of their course around the cavity of the lophophore (tigs. 65
to 71). These vessels are distinct, although closely applied to one another, thus differing from
what Cori finds in /'. psammophila. The outer vessel and inner vessel (figs. «>.">. liti) are, respec-
tively, the "recipient" and "distributing" vessels which Benham describes. In fig. S3 is shown
a cross section through the base of the tentacles. Throughout most of the section the tentacular
vessels open into the outer or recipient vessel, but at one end the tentacular vessels open into
the inner or distributing vessel. This section, together with sections anterior and posterior to
it, show conclusively that the tentacular vessel has two separate openings, one into the distribu-
ting vessel, the other into the recipient vessel, and that the distributing and recipient vessels are
completely separate. A longitudinal section through the anterior end of Phoronis architecta
shows conclusively that the tentacular vessel divides into two branches, one opening into the
recipient vessel and the other into the distributing vessel.

A little more posteriorly the ring like distributing vessel opens into a median longitudinal
vessel lying between the oesophagus and rectum but (dose to the wall of the former (tigs. <!7. 68).
Th'.s vessel, which is the afferent vessel, pierces the transverse septum (fig. «;;)) and runs
posteriori}- (within the rectal or posterior chamber) between the two arms of the alimentary
canal. At the point where the vessel passes through the septum there is a thick layer of muscle
fibres surrounding the former which undoubtedly has the power of shutting off the blood supply
to the tentacles and which may be very necessary to prevent the animal from bleeding to death
when the lophophoral crown is cast away (figs. 68 to 71).

The two sides of the ring-like recipient vessel do not pass into a single vessel while they are
within the supraseptal cavit\ (tigs. 67 to 71). but after they have pierced the transverse septum
the right side of the ring i.s seen to pass diagonally across the oesophagus and to meet the left
side of the rine- (rigs. 75 to 78). From this point the two become one vessel, the efferent vessel,
which runs posteriorly within the left body cavity. In the posterior part of the body, where
the alimentary canal makes a loop, the efferent and afferent vessels are continuous and open into

IOC) MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. N, NO. 4

a sinus around the .stomach. Along- most of the course of the efferent vessel blood caeca are
given off, and a large bunch also arises from the sinus.

X, mm* system. — We have found that the nervous system of the Acti/noProcha is more
highly developed in some species than in others and that it is subepidermal in character. In the
different species of the adult we also find that there is considerable difference in the degree of
development of the nervous system and that it is largely subepidermal.

Caldwell (3) was the first to give a good description of the nervous system, although
Kowalevsky (11) recognized the existence of a lateral nerve and ganglion. Caldwell found the
ring nerve, a hollow nerve cord on the left side, and he speaks of two ciliated pits consisting of
nerve cells, ganglion, and nerve fibres. The description is so brief, that one can not say whether
or not the ganglion that he speaks of represents the ganglion that Kowalevsky (11) and Cori (-1)
describe.

Benhain (2) finds no ganglion in /'. austraUs, but describes two small areas which, it seems
probable, are the same as Caldwell's "" ciliated pits." He is the first to recognize the existence
of a lateral nerve on the right side as well as on the left, and he finds a nerve ring with a nerve
to each tentacle arising from it.

Cori (4) describes a definite ganglion, a lateral nerve on the left side only and tentacular
nerves. He is the only investigator who has published anything on the distribution of the ner-
vous tissue in the lophophoral organ.

Andrews (1), Torrey (22), and Ikeda (9) have given very brief descriptions of the nervous
system, but the two former recognize the existence of a short lateral nerve on the right side as
well as a long one on the left side, while the latter speaks of a so-called brain ganglion and
nerve ring.

The account which Andrews gives of the nervous system of P. architecta is very brief,
since Ins paper deals only with the description of a new species. He only speaks of the lateral
nerve and makes no mention of a brain ganglion, ring nerve, tentacular nerves, or nerves to the
lophophoral organ.

In general our observations on the lateral nerve of /'. a/rchitecta agree with those of Andrews
and Torrey. The lateral nerve of the left side is quite conspicuous and extends from the anterior
end to a point about one-third from the posterior end of the animal. It runs along the lateral
body wall until it is almost in the region of the transverse septum, then it gradually passes
obliquely upward in close proximity to the left nephridial canal, and finally is seen embedded in
tin1 ectoderm at the side of the anal papilla. From this point it passes around the base of the
anal papilla between the anus and the mouth, and then it begins to take the same course close to
the nephridial tube on the right side as it did on the left side, but it soon grows much smaller in
diameter and finally disappears (figs. 78 to <>7). A longitudinal section passing through the mouth
and anus shows the relation which the nerve cord bears to the ganglion and nerve ring (tig. 84).
Cori (4) figures such a section through JP. psammophila, but he seems to have overlooked the
nerve cord or axis cylinder in this region. It is closely associated with the cells of the ganglion
and lies just a little below the latter. In an oral direction from the ganglion is seen a section
through the nerve ring.

If a cross section (fig. 85) is taken through the ganglion so as to cut longitudinally through
the nerve cord and if the section is stained deeply with iron hsematoxylin and eosin, it will show
plainly that there is no cavity in the cord, but that it is made up of a mass of fibres surrounded
by a nucleated sheath. Caldwell (3) considers the structure to be a hollow nerve cord; Benhain
d') says that it has semifluid contents and that he has been unable to make out any punctated
nerve substance; and Cori (4) states that it is an axis cylinder.

We have endeavored to find some connection between the cord and the ganglion, but have not
been very successful. In the region of the ganglion — i. e., between the mouth and the anus —
the sheath of the nerve cord does not seem to differ in thickness or character from the same
structure in other parts. The cells of the ganglion, however, send out processes which in
sections are frequently seen applied to tin1 sheath, but no connection between the fibres of the
nerve ring and those of the cord could be made out.

PHORONIS ARCHITECTA— BROOKS AND COWLES. 107

Kowalevsky (11), Cori (-1), and Torrey (22) have all found the nerve ganglion, while Benham
(2) denies its existence in /'. auxtralix. It undoubtedly exists in P. architecta, is situated at the
base of the anal papilla between the anus and the mouth, and lies above the nerve cord between
the anal papilla and the nerve ring- (fig. 84).

The ganglion consists of nerve fibres and nerve cells and the latter have at least two
processes. While it is a definite structure back of the anal papilla, on the sides it diminishes in
size until its cells become indistinguishable from those of the nerve ring. in fact, all of the
ectoderm forming the sides of the groove between the anal papilla and the base of the lophophore
is rich in nerve fibres and cells.

The nerve ring follows the base of the lophophore on the outer side throughout its extent,
and in the inner part of the horseshoe it is quite rich in nerve cells whose processes can be seen
penetrating into the mass of fibres (figs. 67 to 74). This ring represents the collar nerve ring of
the Actinotrocha.

There is a definite tract of nervous tissue running up the inner side of the tentacle, but we
are not prepared to say that it is a nerve running from the ring, although it is nervous tissue
which is undoubtedly continuous with that of the nerve ring.

Cori (-4) has carefully studied the anatomy of the lophophoral oi'gan of /'. pxanimophUa and
we have nothing to add to his description at present. We are also unprepared to say whether or
not the second layer of the lophophoral organ consists of nerve cells. As he has described, they
have long prolongations which extend from the cells of the inner layer to the outer, and these
processes form a rather marked layer just below the epidermis on the outer surface of the organ.
At the base of the lophophoral organ these prolongations seem to be intimately associated with
nerve fibres which can be traced to the nerve ring.

Throughout the body wall of the trunk there is a subepidermal layer of nervous tissue.

Nephridia. — We have nothing new to add concerning the adult nephridia, but our observations
on 1'. architecta confirm those of Benham {•!) for /'. australis. The nephridial canals lie embedded
in the ectodermal wall in the region of the rectum. Each opens to the exterior through a pore
at the side of the anal papilla. Following the canal from the nephridial pore, we see that it
passes downward — i. e., posteriorly — for a short distance and then bends upon itself running
upward parallel to the descending arm. A short distance above the bend it opens by one funnel
into the lateral body cavity (fig. 72) and by another into the rectal body cavity (fig. 70).

Reproductive organs. — Ikeda's recent paper (10) on the reproductive organs of Phoronis
gives a good account of the anatomy and development so we shall not enter into a description of
them. We are able to confirm Andrews's observations that the male organs develop at a different
time from those of the female.

OiUated 'ridge of the alimentary canal. — Andrews has described a ridge running along the
inner wall of the oral branch of the alimentary canal (tig. 81). H. B. Torrey has found the
same structure in /'. pacifica, and we can confirm Andrews's observation for P. architecta. This
ridge does not seem to have any rudiment in the Actinotrocha, and it is not present just after
metamorphosis.

SUMMARY.

The male and female reproductive organs do not develop at the same time in P. architecta,
and the indications are that it is a protandrous animal.

Fertilization is external and the eggs are not held in lophophoral masses by the tentacles.

Segmentation is holoblastic and equal, but cleavage does not occur simultaneously in all the
blastomeres. During the division of the four-cell stage into the eight-cell stage, the upper four
blastomeres rotate in the direction of the hands of a watch. The sixteen-cell stage arises from
the eight-cell stage by a meridional division of each blastomere.

The blastopore is eccentric from the beginning of gastrulation and the ganglion of the
Actinotrocha makes its appearance at this time. As development proceeds, the blastopore gradu-
ally closes up from the posterior end toward the anterior end of the larva until finally it becomes
a transverse slit.

89369°— vol 10—11 S

108 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 4.

The "primitive streak" of Caldwell does not seem to be present in the larva of P. architecta.

The "nephridial pit" is of ectodermal origin.

The mesoderm arises, for the most part, from the lips of the blastopore. Archenteric
diverticula are not present in the larva of /'. architecta, but there is a sac-like formation of
mesoderm cells in the anterior end which forms the lining of the preoral lobe and which gives
rise to a mesentery between the lobe and collar cavities.

The lining of the collar cavity does not arise from a mesodermal sac. It is formed by
isolated mesoderm cells which arrange themselves on the somatic wall leaving the splanchnic wall
practically without any lining.

In the larva of /'. archit, ,■/</ the mesodermal lining of the trunk cavity is complete, covering
both the somatic and splanchnic walls, and it seems probable that it arises from cells forming the
base of the nephridial diverticula-. There is a mesentery between the cavities of the trunk and
collar.

A stomodseum and proctodseum are not present. The blastopore becomes the mouth, the
anus arises quite late in the early life of the embryo, and the rectum is formed as an outgrowth
of the blind end of the archenteron.

The nephridial canals, at least, have their origin in a single median pit which soon branches
into two intercellular tubes. We have not found anv evidence that the excretory cells of the
nephridia are formed from free mesoderm cells attaching themselves to the blind end of the
nephridial canals.

The " aeuropore" and "subneural gland," which Masterman has described, do not exist in the
Actinotrochse examined, although imperfectly preserved specimens show unusual structures which
might be taken for these organs.

Masterman's "subneural sinus" is not present either, although there is a space below the
ganglion which is free from mesodermal strands. The '■'atrial grooves" which Masterman says
exist are present in the larvse we have studied, but we can not consider that they have the signifi-
cance that he assigns to them. Occasionally grooves are found which might be comparable to
Masterman's "oral grooves," but they are due to imperfect fixation. The stomach diverticula
exist in one species that we have examined, but they do not impress us as being of notochordal
nature, as Roule and Masterman have claimed.

There is a subepidermal layer of nervous tissue throughout the body. Extending anteri-
orly from the ganglion, which is situated on the median dorsal surface of the hood, are three
longitudinal nerves, which finally become continuous with a nervous ring running around the
edge of the hood. From the posterior side of the ganglion two parallel tracts of nerve fibres
issue and pass posteriorly along the dorsal collar wall until they reach the circle of tentacles,
where most of them follow the line of insertion of the collar trunk mesentery, and give rise to a
collar nerve ring. The nerve fibres from the edge of the preoral hood do not pass up to the
ganglion from the point of attachment of the hood on to the collar wall, as Masterman has
described, but they make a sharp turn, running posteriorly and obliquely along the lateral and
ventral wall of the collar, where they form two definite nerve tracts which become, lost in the
region of the collar nerve ring. While there may be nerve fibres passing from the ganglion out
in all directions over the surface of the hood, we have not been able to make them out, nor do we
find any definite nervous tract running along the dorsal or ventral wall of the trunk segment.

There is one pair of retractor muscles extending from the region of the ganglion to the
collar walls, in the region of the first and second pairs of tentacles, and besides these, in one
Actinotrocha that we have examined, there is another pair extending from the sides of the ganglion
to the ventral wall of the hood. In this latter Actinotrocha there is an extensive layer of muscle
fibres in the wall of the hood and also a ring of fibres around the edge of the latter. A pair of
longitudinal muscle tracts extend from the region of the ganglion, along the dorsal wall of the
Actinotrocha, to the perianal ring, and there is a similar pair of tracts extending along the ventral
wall of the collar and trunk. A ring of muscle fibres run parallel with the ring nerve, between
the collar and trunk segments. Beside these muscle tracts there is a layer of circular fibres in

PHORONIS ARCHITECTA— BROOKS AND COWLES. 109

the wall of the collar and trunk, lying between the longitudinal fibres and the ectoderm. There
is also a covering- of muscle cells on the ventral pouch and on the wall of the dorsal blood vessel.

The nephridia have much the same structure as those of Amphioanus, as described by Good-
rich. In one of the Actinotrocha from Beaufort Harbor the nephridial canal branches, but in the
other it does not. Nephridial funnels do not exist, but the ends of the canals open into tubular
cells, and the lumen of each cell contains a flagellum. The nephridial canals open to the exterior,
at the sides of the orifice of the ventral pouch. The nephridia, which Masterman describes for
the preoral hood and trunk, are not present in any Actinotroch.se that we have examined.

The bloodvessels of the Actinotrocha are formed from the splanchnic mesodermal lining and
they inclose part of the blastocoele. There isa dorsal blood vessel opening ('() anteriorly into the
space between the stomach wall and the splanchnic lining. At the posterior end of the stomach,
where the dorsal vessel ends, there are caecal vessels formed as evaginations of the mesodermal
lining of the stomach. The dorsal vessel becomes the afferent vessel of the adult, while the
efferent vessel does not arise until just after metamorphosis. The collar cavity, which isa part
of the blastocoele, becomes the ring vessels and tentacular vessels of the adult. There is no
connection between the dorsal blood vessel and Masterman's "subneural sinus."

The blood corpuscles arise from the somatic mesodermal lining of the ventro-lateral collar
wall just in front of the septum. The\ make their appearance as two masses of cells bilaterally
placed, one on each side of the median ventral line, and as they develop they migrate across the
collar cavity and become applied to the naked walls of the stomach.

The rudiment of the supraseptal or collar cavity of the adult makes its appearance in about
the same region as do the blood corpuscles but a little later in the life history of the Actinotrocha.

During metamorphosis the following organs are lost: The preoral lobe, the ganglion, and
the larval tentacles. The ectodermal wall of the collar cavity, the stomach diverticula, the
digestive areas, and the perianal ciliated ring are not destroyed, but they lose their identity.
The subepidermal nervous layer of the trunk and ventral pouch becomes part of the same
tissue in the adult, but the larger part of this tissue, as well as the lateral nerve, the ganglion,
and the nerves to the lophophoral organs are new formations.

All of the nervous structures of the collar and trunk are lost during metamorphosis, except
the collar trunk nerve ring, which persists as the nerve ring of the adult.

The ventral mesentery becomes the oesophageal and rectal mesenteries of the adult, and the
cavities of the trunk and ventral pouch are transformed into the infraseptal cavity.

At least the greater part of the nephridia is lost during metamorphosis.

The lophophoral organs arise late in the adult life and are present only in individuals which
are with testes and without ovaries. They probably serve as seminal receptacles.

The vascular system of the adult consists of an efferent and afferent vessel, which are
continuous posteriorly by means of a sinus around the loop of the alimentary canal; of caeca!
vessels as outgrowths from the afferent vessel and the blood sinus; of a distributing and recip-
ient ring vessel, the former opening into the afferent vessel and the latter into the efferent vessel;
and of tentacular vessels, each of which divides into two short branches, one opening into the
distributing vessel and the other into the recipient vessel.

There is a ciliated ridge extending along part of the inner wall of the alimentary canal.

The nervous system of the adult is to a great extent subepidermal. There is a nerve with
a nucleated sheath extending along the left side of the animal. Anteriorly it bends around the
anal papilla and continues as a short nerve on the right side. There is a ganglion between the
mouth and anus. A nerve ring extends around the base of the lophophore and it gives off
nerves to the lophophoral organs. There is nervous tissue in the walls of the tentacles.

The excretory organs are paired and each nephridium consists of a tube bent upon itself.
One end opens to the exterior, while the other is continued into two funnels, one communicating
with the rectal and the other with the lateral body cavity.

The reproductive organs arise from the lining of the caeca] blood vessels, and the male organs
develop at a different time from those of the female.

.Johns Hopkins University, March. 190^.

REFERENCES.

1. Andrews, E. A. On a New American Species of the Remarkable Animal Phoronis. Ann. and Mag. of Nat. Hist.

6th series, vol. 5, 1890.

2. Benham, W. B. The Anatomy of Phoronis Australia. Quart. Journ. Micro. Science, new series, vol. 30, 1889.

3. Caldwell, W. H. Preliminary Note on the Structure, Development, and Affinities of Phoronis. Proc. of the

Roy. Soc., vol. 34, 1882-1883.
3a. Caldwell, \V. II. Blastopore, Mesoderm, and Metameric Segmentation. Quart. Journ. Micro. Science, vol.
25, 1885.

4. Com, C. J. Untersuchung iiber die Anatomic und Histologic der Gattung Phoronis. Zeit. fur Wiss. Zoologie,

vol. 51, 1891.

5. Foettinoee, A. Note sur la Formation du Mesoderme dans la Larva de Phoronis hippocrepia. Arch, de Biologie,

vol. 3, 1882.

6. Goodrich, E. S. On the Structure of the Excretory Organs of Amphioxus. Quart. Journ. Micro. Science, vol.

45, 1902.
6a. Goodrich, E. S. On the Body Cavities and Nephridia of the Actinotrocha Larva. Quart. Journ. Micro.
Science, vol. 47, 1903.

7. Harmer, S. F. Appendix to Report on Cephalodiscus dodecalophus, by \V. C. M'Intosh. Chal. Report, vol.

20 — Zoology.

8. Hatsciiek, B. Lehrbuch der Zoologie. 1888-1893.

9. Ikeda, I. Observations on the Development, Structure, and Metamorphosis of Actinotrocha. Journ. of the Col.

of Sci., Imperial Univ. Japan, vol. 13, pt. 4, 1901.

10. Ikeda, I. On the Development of the Sexual Organs and of their Products in Phoronis. Annot. Zoo. Japan,

vol. 4, pt. 4, 1903.

11. Kowai.evsky, A. Anatomy and Development of Phoronis. St. Petersburg, 1807. See Arch, fiir Naturgesch.,

vol. 2, 1807; Leuckart's Bericht.

12. Longchamps, M. de Selys. Recherches sur le Developpement des Phoronis. Arch, de Biologie, vol. 18, 1902.

13. Longchamps, M. de Selys. Beitrage zur Meeresfauna von Helgoland. Oldenburg, 1903.

14. M'Intosh, W. C. Report on Phoronis buskii. Chal. Report, vol. 27.

15. Masterman, A. T. On the Diplochorda. Quart. Journ. Micro. Science, vol. 40, 1897.

Hi. Masterman, A. T. On the Diplochorda: III. The Early Development and Anatomy of Phoronis buskii
M'Intosh. Quart. Journ. Micro. Science, vol. 43, 1900.

16«. Masterman, A. T. Review of Mr. Iwaji Ikeda's Observations on the Development, Structure, and Metamor-
phosis of Actinotrocha. Quart. Journ. Micro. Science, vol. 45, 1902.

16ft. Masterman, A. T. Professor Roule upon the Phoronidea. Zool. Anz., No. 642, 1901.

17. Menon, K. R. Notes on Actinotrocha. Quart. Journ. Micro. Science, vol. 45, 1902.

18. Metschnikoff, E. Uber die Metamorphose einiger Seethiere. III. Uber Actinotrocha. Zeit. fiir Wiss.

Zoologie, vol. 21, 1871.

19. Mtii.i.ER, J. Bericht iiber einige neue Thierformen der Nordsee. Arch, fiir Anat. und Physiol., 1846.

20. Roule, L. Etude sur le Developpement Embryonnaire des Phoronidiens. Ann. des Sci. Naturelles de

Zoologie, 8th series, vol. 11, 12, 1900-1901.

21. Schultz, E. Uber Mesodermbiidung bei Phoronis. Trav. Soc. Natural. St. Petersburg, vol. 28, 1897.

22. Torrev, II. B. On Phoronis pacifica, sp. now Bio. Bui., vol. 2, No. 6, 1901.

23. Wagener, K. Uber den Ban der Actinotrocha branch iata. Arch, fiir Anat. und Phys., 1847.

24. Wilson, E. B. The Origin and the Significance of the Metamorphosis of Actinotrocha. Quart. Journ. Micro.

Science, vol. 21, 1881.

25. Schdltz, E.a Aus dem Gebiete der Regeneration. III. liber Regenerationserscheinuugen bei Phoronis

mulleri Sel. Long. Zeit. fiir Wis*. Zoo., Bd. 75, 1903.
20. Cowi.es, R. P. Origin and Fate of the Body Cavities and the Nephridia of the Actinotrocha. Johns Hopkins

University Circular, April, 1904.
27. Cowles, R. P. Origin and Fate of the Blood Vessels and Blood Corpuscles of the Actinotrocha. Zoo. Anz.,

Bd. NXVII, No. 19, vom. 3. Juni 1904.

"Received after completion of paper.

HI

REFERENCE LETTERS FOR FIGURES.

a aim.-.

a. c. i- adult collar cavity (Ikeda).

at', v afferent blood vessel.

al. c alimentary canal.

a. p anal papilla.

art artefact.

a. t adult tentacle.

a. t. m transverse septum of adult.

b. c blood corpuscles.

1). c. m blood corpuscle masses.

b. t basement tissue ( Benham).

ca? blood caecum.

c. c collar cavity.

eg ciliated groove ( Andrews i.

c. \v collar wall.

d. a digestive area.

d. in. t dorsal muscle tract.

d. v dorsal vessel ( afferent ).

d. ve distributing vessel.

ef. v efferent vessel.

eg egg.

e. b edge of hood.

ep epistome.

ex. c excretory cell.

H flagellum.

g ganglion.

g. c ganglion cell.

g. m. c giant mesoderm cell.

in. c infraseptal cavity.

int intestine.

lat. n lateral nerve.

1. 1. c left lateral cavity.

1. 1. m left lateral mesentery.

1. 1. n lateral longitudinal nerve.

1. in longitudinal muscle.

1. r. m ring muscle tract of lobe.

1. r. n ring nerve tract of lobe.

1. t larval tentacle.

m mesoderm.

in.1 mesentery between preoral

lobe and collar cavities.

m.2 mesentery between collar

and trunk cavities.

m. c. m mesodermal cell mass giv-
ing rise to blood corpus-
cles.

in. f muscle fiber.

m. 1. n median longitudinal nerve.

m. s mesodermal sac of preoral

lobe.

n. c nepliridial canal.

neph nephridium.

EXPLANATION

neph. o nepliridial opening.

n. f nerve fiber.

n. f.1 nepliridial funnel into rec-
tal body cavity.

n. f.- nepliridial funnel into lat-
eral body cavity.

n. p nepliridial pit.

nu nuclei of ciliated cells of

perianal ring.

ces. m oesophageal mesentery.

p. an. s perianal space.

pig pigment.

p. o. c preoral body cavity.

p. o. 1 preoral lobe.

p. r perianal ring.

p. re posterior recess I Ikeda).

subneural sinus (Master-
man ).

r rectum.

r. b. v ring blood vessel.

r. c rectal cavity.

r. d. in rudimentary dorsal mesen-
tery.

ret retractor muscle.

r. 1. c right lateral cavity.

r. in rectal mesentery.

r. n ring nerve.

r. ve recipient vessel.

sen. p sensory papilla.

sp. in sphincter muscle.

st stomach.

sup. c supraseptal cavity.

t tentacle.

t. b. v tentacular blood vessel.

t. c trunk cavity.

th ventral thickening of ecto-
derm.

t. in. t tentacular ring muscle tract.

t. n. t tentacular ring nerve tract.

t. r tentacular ridge.

v vestibule.

ves glandular vesicles in ecto-
derm.

v. in ventral mesentery.

v. in. t ventral muscle tiact.

v. n. t ventral nerve tra;t.

v. p ventral pouch.

v. p. 0 ventral pouch opening.

v. v ventral blood vessel (effer-
ent i.

v. w. h ventral wall of hood.

OF FIGURES.

The objectives used in this work are the jj and J Spencer and the ,'_. Zeiss Oil Immersion. The occulares used
are the " X4" and " X 8 " Spencer and the No. 12 Zeiss Compensating.

113

PLATE I.

115

PLATE I.

Fig. 1. — Transverse section through nephridium of adult. rV Ob. X4 0c. Camera. X 440.

Fk;. 2. — Unsegmented egg with one polar body. (From life. ) J Ob. X 8 Oc. Camera. X 360.

Fig. ■'!. — Two-cell stage, showing equal blastomeres. ( From life. ) £ Ob. X 8 Oc. Camera. X 360.

Fig. 4. — Two-cell stage, showing unequal blastomeres. (From life. ) 5 Ob. X8 0c. Camera. X 360.

Fig. 5. — Beginning of two-cell stage. (From life.) £ Ob. X8 0c. Camera. X 360.

Fig. 6. — Section through two-cell stage. Chromosomes have lost their identity and granular vesicles have made
their appearance. Granular character of the yolk only shown in part of one blastomere. ,', Oil
Immersion. X 8 Oc. Camera. X 704.

Fig. 7. — Beginning of four-cell stage. (From life.) J Ob. X 8 Oc. Camera. X 360.

Fig. 8. — Four-cell stage, showing polar furrow. (From life.) ,} Ob. X 8 Oc. Camera. X 360.

Fig. 8a. — Section through four-cell stage, showing granular vesicles which make their appearance after the dis-
appearance of the chromosomes. ,'2 Oil Immersion. X8 0c. Camera. X 704.

Fig. 9. — Four-cell stage passing into eighth-cell stage. Seen from above and showing the twisting of the blasto-
meres. I Ob. X 8 Oc. Camera. X 360.

Fig. 10. — Eight-cell stage, showing rotation of blastomeres. (From life.) | Ob. X8 0c. Camera. X360.

Fig. 1 1. — Section of eight-cell stage ready for sixteen-cell stage. Position of mitotic figures indicate meridional divi-
sion, y'j Oil Immersion. X 8 Oc. Camera. X 704.

Fig. 12. — Young blastula showing "blastoccele pore." (From life.) ,\ Ob. x 8 Oc. Camera. X360.

Fig. 13. —Section through young blastula showing blastocrele pore. rV Oil Immersion. X8 0c. Camera. X 704.
116

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE I.

Fif. 2.

Fig. 4.

Pig. 8.

Fig. 7.

Fig. 10.

Fig. 8 (o

Fit.'. 18.

Fig. 12.

PHORONIS ARCHITECTA

PLATE II.

PLATE II.

Fig. 14.— Optical section of an old blastula. (From life.) J Ob. X 8 Oc. Camera. X 360.

Fig. 14a. — Section through an old blastula showing endodermal bodies in blastoccele. y'rr Oil Immersion. X 8 Oc.

Camera. X 704.
Fig. 15. — Longitudinal section through older blaatula than that of tig. 14a showing proliferation of endoderm cells.

y1. Oil Immersion, x 8 Oc. Camera, x 704.
Fig. 15a. — Transverse section through a gastrula which is just beginning to gastrulate. Taken through ganglionic

thickening. ^ Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 156. — Transverse section through same specimen as that of rig. 15a. Taken through the middle of the gastrula.

T'j Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 16. — Longitudinal section through a gastrula which has begun to elongate. fa Oil Immersion. X8 Oc.

Camera. X 704.
Fig. 16a. — Transverse section through anterior end of a gastrula which was a little younger than that of tig. 16.

Taken just back of the ganglion, ,'j Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 166. — Transverse section through same specimen as that of tig. 16a. Taken just in front of anterior end of the

archenieron. Shows mesoderm arising from the latter. TV Oil Immersion. X 8 Oc. Camera. X 704.

Fig. 16c. — Continuation of above series. Taken through anterior part of archenteron. T'j Oil Immersion, x 8

Oc. Camera. X 704.
Fig. 16d. — Continuation of above series. Taken through middle of archenteron. ,V Oil Immersion. X8 Oc.

Camera. X 704.
Fig. 16e. — Continuation of above series. Taken through posterior part of archenteron. j\ Oil Immersion.

X 8 Oc. Camera. X 704.
Fig. 16/. — Continuation of above series. Taken through the region where the lips of the blastopore are closing up.

yV Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 16g. — Horizontal section through a gastrula of the same age as that of tig. 16. T\ Oil Immersion. X8 Oc.

Camera. X 704.
Fig. 17. — Transverse section through a gastrula showing peculiar granular cells arising from the endoderm. Tlj Oil

Immersion. X 8 Oc. Camera. X 704.
118

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE

Kit'. II f«

FIk. 15.

Fig. 15 (6)

Fill. 18.

Fig. 15 («)

Big, lit ,„,, in

Fife'. 16 (C)

Pig. 16 (6)

Fig1. 17.

PHORONIS ARCHITECTA

"om.ss.JJri.

PLATE III.

119

PLATE III.

Fig. 17'/. — Same as tig. 17, showing one of the peculiar cells set free in the blastocoele. ,'.. Oil Immersion. X 8 Oc.

Camera. X 704.
Fig. IS. — Transverse section through the anterior end of a young larva, which is slightly younger than the specimen

of which tig. lit is ,\ longitudinal section. Blastopore is slightly oval in outline. Taken through the

ganglion. TV Oil Immersion. X 8 Oc. Camera. X 704.
Fig. ISc;. — Continuation of above series. Taken just in front of archenteron. ,\ Oil Immersion, x 8 0c. Camera.

X 704.
Fig. 186. — Continuation of above series. Taken through anterior part of blastopore. Tl, Oil Immersion. X 8 I »c.

Camera. X 704.
Fig. 18c. — Continuation of above series. Taken through posterior part of blastopore. j5 Oil Immersion. X 8 Oc.

Camera. X 704.
Fig. 18d. — Continuation of above series. Taken immediately posterior to the blastopore. Lips have grown together

and there is a straight furrow corresponding to Caldwell's "primitive groove." rj Oil Immersion.

X 8 Oc. Camera. X 704.
Fig. 18c. — Continuation of above series. Taken posteriorly to section 1S</. No sign of Caldwell's "primitive groove

or streak." -fa Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 18/. — Horizontal section through same stage as 18 a, b, c, etc. fa Oil Immersion. X 8 0c. Camera. X 704.
Fig. 19. — Sagittal section through larva which is a little older than that of series 18 a, 6, c, etc. Shows mesodermal

preoral sac. jV Oil Immersion. X 8 Oc. Camera. X 704.
Fio. 20. — Sagittal section through a larva somewhat older than that of tig. 19. Blastopore has become circular again,

but much smaller than originally, TV Oil Immersion. X S Oc. Camera. X 704.
Fig. 20a. — Transverse section through larva of same age as that of fig. 20. Taken just posterior to the ganglion.

TV Oil Immersion. X S ( >c. Camera. < 704.
Fig. 206. — Continuation of series. Taken through blastopore. T'5 Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 20c. — Continuation of series. Taken just posterior to the blastopore. Slight indication of groove. T'o Oil

Immersion. X 8 Oc. Camera. X 704.
Fig. 20rt\ — Continuation of series. Taken near posterior end of larva. Xo groove. T'5 Oil Immersion. X 8 Oc.

Camera. X 704.
Fig. 20e. — Horizontal section through a larva of the same age as that of figs. 20 a, 6, etc. Shows mesodermal sac

with posterior prolongations. ,\, Oil Immersion. X 8 Oc. Camera. X 704.
120

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE III.

mg. 17 („>

Kill. 18,

Kit:. 18 (ft)

W\g. 18 (o)

Fitr. ' ■

Pig. in.

Big. 18 (/)

Kl(f. 20.

Fife'. 20 («)

Kilt. -

Pig. 20 (d)

Fig. 20 («)

PHORONIS ARCHITECTA

plate rs;

T

i-ji

PLATE IV.

Fig. 21.-

Fig. 21,1.
Fig. 22.-

FiG.22a.

Fig. 226.

Fig. 22c.

Fig. 22d
Fig. 22e.

Fig. 22/

Fig. 22^.

Fig. 23.-

Fig. 23a.
Fig. 24.-

Fig. 25.-

-Sagittal section through a larva somewhat older than that of fig. 20 a, h, c, etc. Blastopore oval and

transverse. Nephridial pit present at this stage. Archenteron has fused with posterior ectodermal

wall, jj Oil Immersion, x 8 Oc. Camera. X 704.
— Continuation of above. Taken longitudinally and lateral to that of fig. 21. TV Oil Immersion. X 8 Oc.

Camera. X 704.
-Transverse section through a larva of the same age as the one shown in figs. 21 and 21a. Taken just pos-
terior to ganglion. -,-'-, Oil Immersion. X 8 Oc. Camera. X 704.
— Continuation of above series. Taken through blastopore. t't Oil Immersion. X80c. Camera. X 704.
— Continuation of above series. Taken just posterior to blastopore. T\ Oil Immersion. X 8 Oc. Camera.

X 704.
— Continuation of above series. Taken halfway between the blastopore and the posterior end. Shows the

mesoderm cells on the ventral ectoderm. T'j Oil Immersion. x8 0c. Camera. X 704.
— Continuation of above series. Taken through rectum. j*j Oil Immersion. X 8 Oc. Camera. X704.
— Continuation of above series. Next section posterior to that of fig. 22rf. T\s Oil Immersion. X 8 Oc.

Camera. X 704.
— Continuation of above series.

T'j Oil Immersion. X 8 Oc.
—Continuation of above series

X704.
■Horizontal section through a larva i if the same age as that of fig. 21

X704.
—Same as fig. 23, but more ventral, ,'j Oil Immersion. X8 Oc.
-Longitudinal section through a larva somewhat older than that of fig. 21.

just made its appearance. rV Oil Immersion. X 8 Oc. Camera. X 704
-Larva with two pairs of tentacles. (From life. ) J Ob. X4 0c. Camera.
122

Next section posterior to that of fig. 22e,
Camera. X 704.
Section through nephridial pit.

Through wall of nephridial pit.
ya Oil Immersion. X 8 Oc. Camera.
TV Oil Immersion. X 8 Oc. Camera.
( lamera.

X704.

Not quite sagittal.

X225.

Anus has

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE IV

Pig. 21 a

Fin. 21.

Fig. aa tbi

Fig. aa („,)

Pig.

Fig. 22 {d)

n,l

Pig. aa.

Pig. 22 (C)

Pig. 22 (/)

Fig. 2a

PHORONIS ARCHITECTA

PLATE V.

89369°— vol 1 < i — 1 1 9 123

PLATE V.

Fig. 26. — Horizontal section through a larva somewhat older than that, of tig. 24, but younger than that of fig. 25.
Shows the separation of the cells of the nephridia] pit into two wings. ,',- Oil Immersion. X 8 Oc.
Camera. X 704.
Fig. 27. — Horizontal section of posterior end showing slightly older stage in the development of the nephridia than

that of fig. 26. j5. Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 28. — Horizontal section through a larva with beginnings of two tentacles. Shows nephridia. ,'2 Oil Immersion.

X 8 Oc. Camera. X 704.
Fig. 29a. — Transverse section through posterior end of a larva with two pairs of tentacles. TW Oil Immersion. X 8

Oc. Camera. X 704.
Fig. 29b. — Continuation of series 29a. Taken through the region of the rectum. tl. Oil Immersion. X 8 Oc.

Camera. X 704.
Fig. 29c. — Continuation of series 29«. Taken through the middle of the larva. T*.v Oil Immersion. X8 Oc.

Camera. X 704.
Fig. 29c. — Continuation of series 29a. Taken through the hotly proper and the lower part of the hood. TK Oil

Immersion. X 8 Oc. Camera. X 704.
Fig. 29r/. — Continuation of series 29n. Taken through body and hood near the region of the mouth. ^ Oil

Immersion. X 8 Oc. Camera. X 704.
Fig. 30. — Almost a sagittal section through a larva with two tentacles. rl2 Oil Immersion. X 8 Oc. Camera. X 704.
Fig. 31. — Larva with three pairs of tentacles. Outline drawing from life. 1 Ob. < 4 Oc Camera. X 225.
Fie. 32. — Larva with five pairs of tentacles. Outline drawing from life. | Ob. < S Oc. Camera. X 202.
Fig. 33. — Larva with six pairs of tentacles. Outline drawing from life. s Ob. X 8 Oc. Camera. X 202.
124

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE V.

Fig. 26.

Fig. 27

Fig. 28.

Fig. 29 {d)

Fig. :

juj.l.

t.r.

Fig. 30.

Fig. 29 lb)

ret.

t.r.

Fig. 29 («)

m'

jng.

Fig. 32.

Fig. 81.

PHORONIS ARCHITECTA

PLATE VI.

125

PLATE VI.

Fig. 34.— Actinotroeha Species A. ( Drawn from life. ) £ Ob. X 8 Or. Camera. X 135.
Fig. 35.— Actinotrocha Species B. ( Drawn from life. ) j Ob. X 8 Oc. Camera. X 135.

126

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE VI

O
Ld
H

I
O

<
03

z
o
tr
o

1

CL

PLATE VII.

127

PLATE VII.

Fig. 36. — Nervous and muscular tracts of the dorsal surface of the hood. Aetinotrocha Species B. (Drawn from

living specimen.)
Fig. 37. — Lateral view of anterior part of Aetinotrocha Species B., showing muscle tracts. (Drawn from living

specimen. )
Fig. 38. — Longitudinal section through the ganglion of an Aetinotrocha. r'j Oil Immersion. 12 Zeiss Occulare.

Camera. X 665.
Fig. 39. — Section through a ganglion cell in the collar nerve ring. Aetinotrocha Species B. T'2 Oil Immersion. X 81

Oc. Camera. X 469.
Fig. 40. — Transverse section through the nerve tract of the ventral collar wall. Aetinotrocha Species B. fa Oi

Immersion. 12 Zeiss Occulare. Camera. X 665.
Fig. 41. — Transverse section through the dorsal nerve tract where it passes down along the liases of the tentacles.

Aetinotrocha Species B. ^ Oil 1 lersion. 12 Zeiss Occulare. Camera. X 665.

Fig. 42. — Transverse section through the collar nerve ring. Aetinotrocha Species B. ,'_. Oil Immersion. 12 Zeiss

Occulare. Camera. X 665.
Fig. 43. — Transverse section through the nerve tract around the edge of the hood. Aetinotrocha Species B. T\ Oil

Immersion. 12 Zeiss Occulare. Camera. X 665.
Fig. 44. — Transverse section through the hood of Aetinotrocha Species B. Taken through the sensory papilla. Hood

flattened out, J Oh. X 4 Oc. Camera. X 300.
Fig. 44a. — Continuation of series 44. Taken through the anterior part of the ganglion. J Ob. X4 Oc. Camera.

X 300.
Fig. 4ib. — Continuation of series 44. Taken through the ganglion which is invaginated by the action of fixing

agents. J, Ob. X 4 Oc. Camera. X 300.
128

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X,

si II ]>

hi' /

Kig. 42.

''•"*■ iiH. ''"-*■

^m^M'

l.r.,i.

"itmiuiiiiii,f. . iu

*""/..,,. f

Fig. 44 (6)

PHORONIS ARCHITECTA

PLATE VIII.

129

PLATE VIII.

Fig. 44c. — Continuation of series 44. Taken through the region where the edge of the hood passes into the collar

wall, i Ob. <4 0e. Camera. X 300.
Fig. 44(7. — Continuation of series 44. Taken through the middle of the collar segment. J Ob. X -1 Oc. Camera.

X 300.
Fig. 44c — Continuation of series 44. Taken through the bases of the ventral tentacles of the collar, i Ob. X 4 Oe.

Camera. X 300.
Fig. 44/. — Continuation of series 44. Taken immediately posterior to that of tig. 44c. i Ob. x4 Oc. Camera.

X 300.
Fig. 44'/. — Continuation of series 44. Taken in the anterior part of the trunk segment. J Ob. X S Oc. Camera.

■ 480.
Fig. 44/i. — Continuation of series 44. Taken through the rectum, i Ob. X 8 Oc. Camera. X 480.
Fig. 44/. — Continuation of series 44. Taken through the anterior part of the perianal ring. }, Ob. X 8 Oc.

Camera. X 4S0.
Fig. 44/. — Continuation of series 44. Taken through the posterior part of the perianal ring. ^ Ob. X 8 Oc.

Camera. X 4S0.
1311

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE VIII

il.m.t.

Fig. 44 (d)

Fiir. 44 /,

r.,l.m. :::r ~

Fif. 44 (j)

Fig. 44 :,.

PHORONIS ARCHITECTA

PLATE IX.

131

PLATE IX.

Fig. 45. — Longitudinal section through the ganglion, showing lobe collar mesentery. rV Oil Immersion. X 4 Oc.

Camera. X 293.
Fir. 45«. — Longitudinal section through ganglion, showing retractor and mesentery. TV Oil Immersion. X 4 Oc.

Camera. X 293.
Fig. 456. — Longitudinal section through the Actinotrocha, showing incomplete part of lobe collar septum. J Ob.

X 4 Oc. Camera. X 200.
Fig. 4fi. — Horizontal section through Actinotrocha Species B. I Ob. X 4 Oc. Camera. X 200.
Fig. 47. — View showing muscles of inner surface of hood. From living specimen. | Ob. X 8 Oc. Camera.
Fig. 48. — Sagittal section through Actinotrocha Species B. I Ob. X 4 Oc. Camera. X 150.
Fig. 49. — Longitudinal section through the posterior end of Actinotrocha Species B. T\, Oil Immersion. X 4 Oc.

Camera. X 293.
Fig. 50. — Longitudinal section through Actinotrocha Species A., showing relations of larval oollar cavity and adult

collar cavity, i Ob. X 4 Oc. Camera. X 200.
132

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. VOL X.

PLATE IX

p.r e.

V "

■'/■: / X* % Ki;.'. 45 (6)

p.o.c.

Pig. M.

Fill- 50.

PHORONIS ARCHITECTA

PLATE X.

133

PLATE X.

Fig. 51. — Transverse section through Actinotrocha Species A. Taken through ganglion. J Ob. X4 0c. Camera.

X 225.
Fig. 51a. — Continuation of series 51. J Ob. X4 0c. Camera. X 225.
Fig. 516. — Continuation of series 51. J Ob. X4 0c. Camera. X 225.
Fig. 51c. — Continuation of series 51. | Ob. X4 0c. Camera. X225.
Fig. 51 d. — Continuation of series 51. J Ob. X4 0c. Camera. X225.
Flo. oli-. — Continuation of series 51. \ Ob. X 4 Oe. Camera. X 225.
Fig. 51/. — Continuation of series 51. ^ Ob. X4 0c. Camera. X225.
Fio. olg. — Continuation of series 51. Taken through the collar segment. Showing the lining drawn away from the

ectodermal wall. \ Ob. -4 0c. Camera. X 225.
Fig. 51h. — Continuation of series 51. Taken through collar region just anterior to bases of the ventral tentacles.

i Ob. ■ 4 Dr. Camera. ■ 225.
Fig. 52. — Transverse section through the nephridial canal. Actinotrocha Species B. ,'. oil Immersion. 12 Zeiss

Comp. Occulare. Camera. -1400.
Fig. 52a. — Continuation of series 52. Taken through the lower branch of the nephridial canal, ,'j Oil Immersion.

12 Zeiss Com]). Occulare. Camera. X 1400.
Fut. 526. — Continuation of series 52. Taken through the end of the upper branch of the nephridial canal, /.oil

Immersion. 12 Zeiss Comp. Occulare. Camera. .1000.
Fio. 52c. — Longitudinal section through one of the cellular processes at the end of the nephridium. Showing two

nuclei. rV Oil Immersion. 12 Zeiss Comp. Occulare. Camera. X 1000.
Fnt. 52d. — Same as fig. 52c. Showing one nucleus, j1. Oil Immersion. 12 Zeiss Comp. Occulare. Camera.

X 1000.
Kiit. 52c — Transverse section through the end of a process. ,'. Oil Immersion. 12 Zeiss Comp. Occulare. Camera.

X 1000.
Fig. 52/. — Transverse section through the proximal half of the processes. ,-'..- oil Immersion. 12 Zeiss Comp.

Occulare. ( iamera. X 1000.
Fnt. 52g. — Longitudinal section through anterior end of a nephridium. Actinotrocha Species B. f'j Oil Immersion.

12 Zeiss Com]). Occulare. Camera. X 1000.
134

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE X

Fig. 52 <£>

Fig. M</)

Big. 52 (a)

PHORONIS ARCHITECTA

PLATE XI.

135

• PLATE XI.

-Transverse oblique section through Actinotrocha Species A. Taken through region of origin of blood

corpuscles. 14 tentacles, j'j Oil Immersion. X 4 Oc. Camera. X 293.
-Transverse section through ventral collar wall. Same specimen as that of fig. 53. Showing origin of blood

corpuscles. T'j Oil Immersion. 12 Zeiss Comp. Occulare. Camera. X 935.
-Actinotrocha Species B with ventral pouch evaginated. f Ob. X 8 Oc. Camera. X 45.
-Actinotrocha Species A. Immediately before metamorphosis. § Ob. X 4 Oc. Camera. X 56.
— Actinotrocha Species A. Shortly after the beginning of metamorphosis. § Ob. X 4 Oc. Camera. X 56.
—Metamorphosed A ctinotrocha Species A. § Ob. X4 0c. Camera. X56.
-Young specimen of Phoronis architecta (?) with 30 tentacles. § Ob. X 4 Oc. Camera. X 28.
-Metamorphosed Actinotrocha Species A. Transverse section through the region of the transverse septum,
i Ob. X 8 Oc. Camera. X 240.
Fig. 60. — Completely metamorphosed Actinotrocha Species A. Transverse section in region of branching of efferent

vessel. I Ob. X 8 Oc. Camera. X 240.
Fio. 61. — Adult Phoronis architecta removed from tube. X8. '
136

Fig.

53.-

Fig.

54.-

Fig.

55.-

Fig.

56.-

Fig.

56a.

Fig.

566.

Fig.

57.-

Fig.

59.-

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE XI.

in/ill.

m.l.

M

i

%

Pig. 54

1 1. rill

at.

I.I.

■

n/'.i:

'l/'.r.

Fly. 57.

~1

%»li*t*

&.V.
Pig. 80.

/•.//.

Ii.c.iii.

y '■'■
at.

p.o.l.

Fig. 56 (ft)

// ffih ,

:. .

Pig. 56 (a)

V

p.r.

b.c.

t.lu:

8Up.C.

Fit'. 01

Fig. 51).

PHORONIS ARCHITECTA

t.DlL

PLATE XII.

137

PLATE XII.

Fig. 62. — Tentacular crown of Phoronis architecta. Showing lophophoral organs, epistome, and mouth. Drawn from
a living tentacular crown which had been constricted off from the animal. X 100.

138

MEMOIRS OF THE NATIONAL ACADEMY Of SCIENCES, VOL. X

PLATE XII.

Fig. 62

PHORONIS ARCHITECTA

PLATE XIII.

89369 —vol Tii— 11 in 139

PLATE XIII.

Fig. 63. — Transverse section through Phoronis

X130.
Fig. 64. — Continuation of series 63.
Fig. 65. — Continuation of series 63.
Fig. 66. — Continuation of series 63.
Fig. 67. — Continuation of series 63.
Fig. 68. — Continuation of series 63.

| Ob. X8 Oe. Camera
140

chitecta. Taken through tentacles. ; OI>.

8 Oc. Camera.

Taken near base of tentacles. | Ob. X 8 Oc. Camera. X 130.
Taken through epistome. f, Ob. X 8 Oc. Camera. X 130.
Taken through anal papilla. § Ob. X 8 Oc. Camera. X 130.
Taken through nephridial opening, 'i Ob. X 8 Oc. Camera. X 130.

Taken through the transverse septum and below the nephridial openings.
. X 130.

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE XIII.

Fig. 63.

d.ve.

d.ve.

Fig. 01.

d.ve.

Ntip.C.

Fig. 64.

Fig. 66.

d.ve.

d.ve.

Fig. 68.

;/.(•('.

PHORONIS ARCHITECTA

PLATE XIV.

141

PLATE XIV.

Fig. 69. — Continuation of series 63. Taken a little posteriorly to that of fig. *>S. ji Ok X 8 < to. Camera.
Fa;. 70. — Continuation of series 63. Taken through the nephridial funnel that opens into the rectal cavity

X8 0c. Camera. X 130.
Fig. 71. — Continuation of series 63. Taken a little posteriorly to that of fig. 70. H Ok x8(>c Camera.
Fig. 71'. — Continuation of series 63. Taken through the funnel opening into the lateral cavity. $ Ob.

Camera. X 130.
Fig. 73. — Continuation of series 63. Taken through the loop in the nephridium. § Ob. X 8 Oc. Camera,
Fig. 74. — Continuation of series 63. Taken through the oral side of the nerve ring. § Ob. X8 Oe.

X130.
142

X 130.

. I Ob.

X 130.

X 8 ( >c.

X 130.

( lamera

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X

PLATE XIV

tl.rt .

Fig. 69.

Fig. 70.

Fig. 71.

Ba v.n.

Fig. 72.

In /. n.

In/, n.

Vig. 7:t.

I ut. ii.

Fig. 74.

PHORONIS ARCHITECTA

PLATE XV.

143

PLATE XV.

Fki. 75. — Continuation <>f scries 63.
Fk(. 70. — Continuation of series <>:;.
around the oesophagus.
Fig. 77. — Continuation of series 63.
Fig. 7S. — Continuation of series <>:'..
Fig. 79. — Continuation of series 63.
Fig. 80. — Continuation of series 63.
144

Taken a little posteriorly to that of fig. 7*. | Ob. X 8 Oc. Camera. X 130.
Taken through the region where the branches of the efferent blood vessel pass
| Oh. X8 0c. Camera. X 130.

Taken a little posteriorly to that of fig. 7<i. jj Ob. X 8 Oc. Camera. X 130.
Taken a little posteriorly to that of fig. 77. | Ob. X 8 Or. Camera. X 130.
Longitudinal muscles begin to appear, jj Ob. X 8 Oc. Camera. X 130.
Taken a little posteriorly to that of fig. 79. j Ob. X 8 Oc. Camera. X 130.

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL X.

PLATE XV.

I11l.11

mg. 75.

Fig. 7(i.

Fig. 77.

hit.ii

Fig. 78.

tfi Fig. 80.

PHORONIS ARCHITECTA

PLATE XVI.

145

PLATE XVI.

Fig. 81.— Continuation of series 63. Taken a little posteriorly to that of fig. 80. s Ob. X 8 Oc. Camera. X 130.
Fig. 82. — Continuation of series 63. Typical transverse section through the middle of the trunk, 'i Ob. XS Oc.

Camera. X 130.
Fig. 83. — Longitudinal section through the recipient and distributing vessels. J Ob. x 4 Oc. Camera. X 450.
146

MEMOIRS OF THE NATIONAL ACADEMY Of SCIENCES, VOL X

PLATE XVI

Fisr. 81.

/././//.

hit.ii.

PHORONIS ARCHITECTA

r^r.rrc^ r)rr

PLATE XVII.

147

PLATE XVII.

Fig. S4. — Longitudinal section through the anal region. Showing the ganglion and its relation to the lateral nerve

cord. ,\ Ob. X 4 Oc. Camera. X 450.
Fig. 85. — Transverse section through the region of the anal papilla. Showing the relation of the nerve ring to th»
lateral nerve. J Ob. X 4 Oc. Camera. X 450.
148

MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES, VOL. X.

PLATE XVII.

Big. 84

Pig. 85.

PHORONIS ARCHITECTA

&3j)K/..

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

Volume X.

FIFTH MEMOIR.

WASHINGTON:
GOVERNMENT PRINTING OFFICE.

1906.

NATK )NAL ACADEMY OF SCIENCES.

Volume X.

FIFTH MEMOIR.

THE AFFINITIES OF THE PELAGIC TUNICATES.

No. 1. ON A NEW PYROSOMA.
(Dijil' urosoma tllijifica.)

BY

WILLIAM KEITH BROOKS,

HENRY WALTERS PROFESSOR OF ZOOLOGY IN THE JOHNS HOPKINS UNIVERSITY.

149

THE AFFINITIES OF THE PELAGIC TUNICATES.

(Presented to the National Academy, November, l'.tt>4.)

No. i. ON A NEW PYROSOMA.
( Dipleurosoma elliplica. )

By William Keith Bhuoks, LL. D.,
Henry Walters Professor of Zoology in the Johns Hopkins University.

Part I.— INTRODUCTORY.

I am indebted to Dr. Caswell Crave for the opportunity to study the Pyrosoma that is here
described. The specimens were collected in the Gulf Stream oti' Beaufort, North Carolina, by
the United States Commission of Fish and Fisheries, and were brought to the marine laboratory
of the Commission at Beaufort. They were intrusted to me for study by Doctor Grave, the
director of the laboratory. The illustrations that accompany the memoir were drawn by Mr.
Carl Kellner.

While all the species of Pyrosoma that have been described arc circular in cross section, the
cross section of the one that is to be described is a flattened ellipse, so that the colony has two
broad sides (tig. 4) and two narrow edges (tig. .">).

Except for this flattening, it does not differ in any essential way from other Pyrosomus.
which are tubular colonial ascidians that float or swim in the water of the ocean, usually at
considerable depth below the surface, but often at or very near it. As their name expresses,
thev are among the most brilliantly luminous of marine animals, glowing witli an intense white
light that is notable even under the noonday sun of the tropical ocean. The light, which is
under the control of the organism, is emitted by a pair of luminous organs (tig. 2 and tig. 8, /').
on each side of the pharynx, near the mouth, and in the coelomic cavity.

The basis or foundation of the colony, that binds the ascidians together into an organized
whole, is a hollow tube of cellulose (ties. 2 and 4) (dosed at one end. A. and opened at the other,
B. The open end carries a muscular diaphragm, by which the aperture may be reduced or
enlarged.

The ascidian units, or ascidiozooids, many hundreds or thousands in number, are so placed
that their mouths </, are on the outer service of the tube, while their cloacal apertures, c, open
into the cavity of the tube, or common cloaca (tig. 3, CC), which again opens to the external
water through the terminal opening which may be reduced in size. or. perhaps, completely
closed by the muscular diaphragm.

The members of the community breathe and obtain their food, like other ascidians, by draw-
ing water through the mouth (tig. 8, d) into the pharynx or gill-chamber (fig. S, <•) bythe vibration
of the cilia around the gill slits. The waste water is discharged from the body through the cloaca]

151

152 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 5.

aperture, and. as the cloaca of each ascidiozooid opens into the common cloaca, this becomes filled
with water, which, overflowing through the open end, tends to drive the colony through the
water in the opposite direction. This current is modified and controlled bv the diaphragm, and
by the movements of the ascidiozooids, so that the progress through the water is not slow and
continuous, but rapid and intermittent. A muscle, shown near the cloacal aperture in figure 8,
extends from each ascidiozooid to those adjacent to it and binds all the units of the colony
together, so that they are able to make concerted movements, and thus to control the expulsion
of the locomotor current.

The structure and the development of Pyrosoma have been well described by many natural-
ists, and a good account of the more essential features is to be found in the text-books. Those
who wish for a more complete account should consult the memoirs of Herdman (Report on
the Tunicata collected during the voyage of H. M. S. "Challenger," XXVI-XXVIII), of
Salensky (Beitrage zur Embryonalentwicklung der Pyrosomen. Zool. Jahrb. IV and V), and of
Seeliger (Zur Entwicklungsgeschiehte der Pyrosomen. Jenaische Zeitschr. fur Wiss. Naturw.
XXIII.. and Die Pyrosomen., Leipzig, 1895).

The subject of this memoir is a new form of Pyrosoma, which seems to me to be generically
different from all that have been described; but, as its differences from the forms that are
known do not involve its fundamental structure, I have little to add to the published accounts,
although a brief sketch of the origin of the colony will be the most satisfactory way to explain
the meaning of the terms that are to be used in describing the species.

The egg of Pyrosoma gives rise to an embryo which, while it acquires some indications of
ascidian structure, remains rudimentary and quickly degenerates. It is commonly called by the
name Cyathozooid, given to it by Huxley. It is shown, in an advanced stage of degeneration, at
ey in figure 1. Before it begins to degenerate, it gives rise to a tubular outgrowth, which becomes
divided, by constrictions, into four segments, each of which ultimately becomes an ascidian.
The four segments are in a row at first but as they grow and develop into ascidians they twist so
as to form a zone or girdle around the rudimentary Cyathozooid, as is shown in figure 1. These
four primary ascidiozooids are the foundation of a new colonial Pyrosoma. As figure 1 shows,
they are inclosed in a common mantle of cellulose, and are arranged in a circlet around a common
cloaca into which the cloaca of each opens, while the mouths are on the outer surface. The sur-
face that is below in figure 1 is the closed end of the colonial tube, while the opening is above in
the figure, in the center of the rosette of eight tubular processes that are shown in the figure.
In all ordinary Pyrosomas, the circlet that is formed by the four primary ascidiozooids is a
circle, but in the species that is the subject of this paper it is an ellipse; the ascidiozooid marked
/id 1 and its fellow lying in the long axis of the ellipse, and the one marked pa 2 and its fellow
in the short axis. They are also shown, at a later stage, at pa 1 and pa 2, in figure 2.

The four primary ascidiozooids soon begin to multiply by budding, and thus to lay the
foundation for a new colony, which may ultimately consist of thousands of ascidiozooids, all
produced, either immediately or indirectly, as buds, by the four primary ascidiozooids. As
each ascidiozooid that arises as a bud soon begins to produce buds in its turn, only a few
of those that enter into the structure of an adult colony arise immediately from the primary
ascidiozooids.

Few young colonies, large enough to have all the characteristics of the full-grown colony,
and yet small enough and transparent enough to be studied with a microscope, have been found,
and none have been adequately figured.

Among Doctor Grave's specimens is one, about half an inch long, which he had stained and
mounted in balsam. It is shown in figure 2, with one of its flat sides toward the observer. As
it is small enough to lie studied as a transparent object under the microscope, and is yet, in all
essential particulars, a fully developed Pyrosoma, it presents a more complete picture of the
organization of the colony than any drawing that has been published. The colony is represented
with its closed end below, and the open end with its diaphragm above. It consists of seventy
ascidiozooids, arranged in seven rows or verticils, and of numerous buds. There are four
ascidiozooids — the primary ascidiozooids — in the first row, eight in the second, ten in the third,

AFFINITIES OF THE PELAGIC TUNICATES— BROOKS. L53

twelve in the fourth, twelve in the fifth, fourteen in the sixth, and ten in the seventh. The
ascidiozooids in the first row are the largest, and there is a gradual decrease in size to the last
row, in which they arc no larger than the buds, /', that are carried by those in the first and second
rows. All are placed with their dorsal surfaces and brains toward the open end of the colony,
and their ventral surfaces and endostyles toward the closed end. The new buds arise at the
aboral end of the endostyle, on the ventral surface, as shown at /' in figure 8, and in figure 2.

As the smallest and youngest aseidiozooids are nearest the open end, while they arise on the
surface of the zooid that is nearest the closed end, it is clear, from the figure, that a migration
must take place from the region where new buds arise to the region where they complete
their growth and development, and that this migration must, in some cases, be from one end of
the colony to the other. Each young ascidiozooid has two tubular processes, like those that are
shown in figure 1, on the region of the body that is nearest the open end of the colony. These
processes lengthen until they reach and enter into the diaphragm, where they are shown in figure :.'.
With a microscope they may be traced inward among the zooids and buds, although the com-
ponents of the colony are so crowded, and the tubes so delicate, that I have not been able to follow
any of them to the end, except the ones that end in the zooids in the row nearest the opening.
The number of tubes in the diaphragm, at the stage shown in figure 2, is nearly equal to the
number of zooids. but somewhat less, so that some of them must fail to reach the diaphragm, or
else degeneiate and disappear after they have reached it. The walls of the tubes are muscular,
and they are, no doubt, concerned in the opening of the diaphragm, and in the migration of the
zooids, although it is not probable that they bring about the migration by direct muscular con-
traction, since the distance that the zooids move seems to be too great to be brought about in this
way. It is more probable that the tubes become shortened by some structural change, which,
aided, it may be, by their muscular contractions, draws the new ascidiozooid into the region of
the colony where there is most room for it. In young: colonies there is most room at the open or
growing end, and the colony grows by the addition of new whorls of zooids at this end, and the
zooids are arranged in verticils. As the colony grows, new zooids become fitted into the spaces
between the old ones, and the verticillated arrangement which is so notable in the young colony
is no longer recognizable (fig. 4).

Part II. -DESCRIPTIVE.

DIPLEUROSOMA, genus nov.
DIAGNOSIS OF THE GENUS.

Colony bilaterally symmetrical with reference to one of the planes that pass through the
principal axis, la cross section the colony is elliptical, with the common cloaca, or central
chamber, reduced to a narrow slit in the long axis of the ellipse.

DIPLEUROSOMA ELLIPTICA, nov. sp.

Figures 4, 5, tf, 7, and 8.

DESCRIPTION OF THE SPECIES.

Distribution. — Found in the Gulf Stream off Beaufort, North Carolina. It is, no doubt,
widely distributed in the waters of the Gulf Stream.

Length if colony. — Twenty-two centimeters.

Greatest diameter of colony. — Fifty-seven millimeter-.

Least diameter of colony. — Twelve millimeters.

Ratio between tin long axis and tht short axis of tht elliptical cross section. — About one to
four.

Distribution of the ascidiozooids. —Regularly verticillated in small colonics, irregular in large
ones.

Outer surfact of mantle. — Smooth in young colonies, thickly set in large ones, with
tubercles that are very variable, usually conical and symmetrical but often with a tongue-like
projection on the dorsal side.

Oral tube. —Conical, axial, nearly as wide as long.

Mouth. — In long axis and usually horizontal or at right angles to the long axis. In young
colonies, and in many of the zooids of large colonies, it is at the bottom of a shallow conical pit.
In most of the ascidiozooids in large colonies it is at the end of a conical process; in a few, on
the ventral surface and near the tip of a tongue-shaped process.

Branchial chamber.— Not narrowed at inner end.

QUI slits. — Thirty-seven or more.

Longitudinal folds of branchial rhumhi-r. — Eighteen or more.

Endostyle. Nearly straight.

Testis. — In a pouch that protrudes beyond the general outline, with from seven to nine lobes.

< 'loacal nvuscli . Long.

Dorsal tentacles of pharynx. — About seven, variable and irregular.

Oral processes. — The writers on Pyrosoma attribute great taxononiic importance to the
absence or presence or shape of the oral processes on the outer surface of the colony, since these
structures arc conspicuous when present and easy to sketch and to describe.

In many species they are. no doubt, characteristic, affording a ready means of identification,
hut in others they are too irregular and variable to have any systematic value.

154

AFFINITIES OF THE PELAGIC TUNICATES— BROOKS. 155

In the species that is here described the outer surface of the test is smooth in young colonies,
and the mouths are at the bottoms of conical pits, figure 2, as they are in some of the zooids of
old colonies. Most of the zooids of older colonies have processes that are conical and symmetrical,
and the mouths are terminal, figure 8. There is nothing distinctive in the length of the processes,
for some are short and some long. While they are usually conical and symmetrical with reference
to the long axis of the aseidiozooid, they are sometimes elongated on the side that is dorsal to the
mouth, winch is thus oblique and on the ventral side of the process at some distance from its tip.

DipL Ural symmetry. — The dipleural symmetry that characterizes this species is recognizable
in the embryo, becoming more marked with the growth of the colony.

The embryonic colony of four primary ascidiozooids, figure 1, is nearly circular, although the
two ascidiozooids. pa 1, that are to occupy the sides of the colony, are easy to distinguish from
the two. jut 2, that are to lie on the edges.

The young colony, with seventy ascidiozooids shown in side view in figure 2 and in transverse
section in figure ?>, exhibits marked dipleuralism.

There are seven ascidiozooids on each edge, or fourteen in all, and twenty-seven on each side,
or fifty-four in all, and the four primary ascidiozooids, pa 1 and/A/ 2, are readily distinguishable.
The diagrammatic section, figure 3, is through the verticil that is fourth from the closed end
in figure 2. As the diagram shows, there is one zooid on each edge at this level, and there are
five on each side, or twelve in all, and the thickness of the colony is about equal to one-half its
breadth, so that the ratio of thickness to breadth is one-half.

In the adult colony, shown in side view in figure -t, in end view in figure 6. in edge view in
figure 5. and in section in figure 7, there are about sixty zooids in each cross section, and the
thickness of the colony is to its breadth about one to four.

VertidUation. — In the full-grown colony there is no visible trace of an arrangement of the
zooids in rings, although this arrangement is regular and conspicuous in the young colony shown
in figure 2.

In this there are seven rings, with four zooids in the first, eight in the second, ten in
the third, twelve in the fourth, twelve in the fifth, fourteen in the sixth, and ten in the seventh,
or seventy in all. The regular verticillation is obliterated, in older colonies, by the interpolation
of new buds between the rings.

N'JoG'.l0— VOL 10—11 11

EXPLANATION OF THE PLATES.

REFERENCE LETTERS.

a. The closed end of the colony,
as. An ascidiozooid.

b. The open end of the colony.

c. The cloaca of the ascidiozooid.
CC. The common cloaca of the colony.
d. The mouth.

f. The mantle of cellulose.

g. The endostyle.

h. The luminous organ.

i. The testis.

j. A bud.

k. The stomach.

1. The intestine.

n. First oral muscle.

o. Second oral muscle.

p. The oesophagus.

pa. 1. The primary ascidiozooid on the edge of the colony.

pa. 2. The primary ascidiozooid on the side of the colony.

FIGURES.

F„;. i. — The cyathozooid and the four primary ascidiozooids of Dipleurosoma elliptica.

Fig. 2.— A young colony of Dipleurosoma elliptica, with seven verticils of ascidiozooids

Fig. 3. — Transverse section of the colony shown in figure 2.

Fig. 4. — Side view of a fully grow n colony of Dipleurosoma elliptica.

Fig. 5. — Edge view of same.

Fig. (i. — The open end of same.

Fig. 7. — Transverse section of same.

Fig. S. — A single ascidiozooid from a fully grown colony of same.

156

Hll.ll

Et)A

C. KELLNE

DIPlEUROSOMA

PLATE II

C. KEUNEK. DEL.

MEMOIRS

OF THE

NATIONAL ACADEMY OF SCIENCES.

"VoLume X.

SIXTH MEMOIR.

WASHINGTON:
GOVERNMENT PRINTING OFFICE.

1906.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

SIXTH MEMOIR.

COMMEL1NA0E.E.

MORPHOLOGICAL AND ANATOMICAL STUDIES OF THE VEGETATIVE

ORGANS OF SOME NORTH AND CENTRAL

AMERICAN SPECIES.

BY
THEODORE HOLM.

PRESENTED TO THE ACADEMY BY GEORGE I_. GOODALE.

157

COMMELINACE^E.

MORPHOLOGICAL AND ANATOMICAL STUDIES OF THE VEGETATIVE ORGANS OF SOME
NORTH AND CENTRAL AMERICAN SPECIES.

Hv Theodore Holm.

(With Plates I- VIII.)

Characteristic of the families that constitute the order Enantioolasta& is the atropous ovule."
The flowers are hypogynous; in some of the families the general monocotyledonous type with live
trimerous whorls completely developed may be readily recognized, while in others the flowers
arc so much reduced that the type is difficult to trace, as, for instance, in Restionacese and Cen-
trolepidacese. The habit of these plants is somewhat peculiar, and it seems as if a certain struc-
ture in regard to inflorescence, ramification of shoot, shape of leaves, etc., is prevalent in most
of these families. The Mayacacest show a habit unlike that of any other aquatic plants; the Xyri-
dacese with their cone-shaped inflorescences, the Eriocaulacese with their capitula, the Rapatean ;>
and the Restionacese represent types of very distinct and characteristic aspect. In the Commeli-
nacese, on the other hand, the structure of the flower exhibits a very pronounced variation from
actinomorphic (Tradescantia) to zygomorphic (Commelina); the foliage is also to some extent
different within certain genera ( Tradescantia), besides that the rhizomes exhibit several types of
growth characteristic of certain genera, or of species within the same genus. In other words,
the Comvielinacese do not possess a habit of their own or of so special and well-marked peculiarity
as the other families of the Enantioblastse; nevertheless the family seems to be a very natural one,
and, to use the words of Bentham and Hooker: "Ordo totus optime limitatus, nee cum ullo alio
generibus intermediis junctus." Several and very excellent monographs have been published on
some of these families. Masters has treated the Restionacese ;b Hieronymus the C'entrolepi-
</</<■< ,'iV Seubert the Xyridacese and Mayacacese.; d Bongard/ Kcernicke/ and Ruhland? the
Eriocaulacese; Hasskarl* and Clarke' the Commelinacese,. Besides these works a few papers
have also been published on the morphology and anatomy of these plants, for instance, by Cili;.-'
NlLSSON,* Poulsen.' Van Tieghem,'" and the author."

" In a recently published paper, " Beitriige zur Morphologie der Commelineen " (Flora 1904, p. 512), Mr. J. Clark
stales that the atropous ovule is only characteristic of the genus Tradescantia as far as concerns the Commelinaeeie,
while this type of ovule occurs merely as an exception in "all the other genera of the order." Nevertheless the
ovules of Weldenia are certainly atropous, and we hope that some future investigator will undertake the study of this
particular point in respect to our native representatives.

''In De Candolle: Monographic Phanerog. Vol. I. p. L'ls.

= Abhdl. Naturf. Gesellsch. Halle. Vol.12. 1873.

''In Martins: Flora I'.rasil. Vol.111. 1842-1871. Pars. I, pp. 211-227.

< Mem. de l'Acad. imp. de St. Petersbourg. 1831 cet.

/In Martius: Flora Brasil. Vol. III. 1842-1871. Pars. I, p. 273.

PlnEngler: Das Pflanzenreich. 1903.

h Commelinacese Indies. 1870.

»In De Candolle: Monogr. Phanerog. Vol. III. 1881.

-/Beitriige zur vergleichenden Anatomic der xerophilen Familie der Restiacess. Inauj;. diss. Leipzig. 1891.

*Studien ueber die Xyrideen. Kgl. Sv. Vet. Akad. Hdlgr. Vol.24. 1892.

' Anatomiske Studier over Eriocaulaceerne. Thesis. Kjobenhavn. 1888.

Anatomiske Studier over Xiyra-Slaegtens vegetative organer. Vidensk. Medd. naturh. For. Kjobenhavn. 1891.

Anatomiske Studier over Mayaca Aubl. Overs. Kgl. D. Vid. Forhdlgr. 1886.

'" Structure de la racine et disposition des radicelles dans les ( V ntmlr/iiilrta, .lour/?*, Mayaaea el XyricUes. Journ.
de Botan. 1887.

n Eriiji-ntdoii dernntjulare L.; an anatomical studv. Bot. Gaz. 1901.

159

160 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

In speaking- more particularly of the ' ■ Commelinacese, this family figures quite often, and
sometimes very prominently so, in works on anatomical botany. De Bart" mentions several
points of great interest, derived from this family: The peculiar arrangement of the vascular
system; the structure of epidermis with the stomata; the occurrence of crystals; the root-
structure, etc. Falkenberg6 describes the stem-structure of Tradescantia argi ntea and crassula,
also of Commelina Africa mi. Schwendenee" calls attention to the occurrence of collenchyma
and discusses the development of the mechanical tissue in some of the species. Van Tieghem''
refers often to the Commeliinn; :> as a family of importance in anatomical respect. Furthermore
has Eberhard' described the structure of leaf and stem of a few species of Tradescantia,
Dichorisandra , ( 'am/nilu, and Sjiinmema, besides the distribution of starch, tannin, and chloro-
phyll in these species. The most comprehensive paper, however, is by Gravis', in which
Tradescantia Virginica is discussed from a morphological, anatomical, and physiological point
of view. Among the works dealing more particularly with the morphology of the family may be
mentioned those by Eichlerc and Schumann*, in which the diagram of the flower and the
structure of the inflorescence have been described and explained. Finally, in regard to the
germination may be cited Mirbel', who described seedlings of Commelina communis and
cristata, and Klebs-7, who has offered a most excellent contribution to the knowledge of the
morphology and biology of the germination.

It is thus evident that the Commelinacea have already been studied from various viewpoints
and by authors of prominence. De Bary, Falkenberg, and Schwendener have no doubt
demonstrated the most interesting points to be observed in the anatomical structure: The fibro-
vascular system and the mechanical support. Eichleb and Schumann have elucidated the very
difficult points in respect to the flowers and inflorescences; in regard to the systematic treatment
of the family Hasskarl and Clarke have furnished us with specific diagnoses and sectional
divisions of the species, besides notes on the general habit and geographical distribution of these
interesting plants.

However, when we examine the literature and consider the species that have been studied
more critically, it is readily noticed that relatively only a few species have been treated, and that
these, are mostly such as are frequently cultivated as ornamental plants. This is not so strange,
however, when we remember the exceedingly delicate structure of most of these plants, which
makes it necessaiy that they must either be studied from living specimens or from alcoholic
material. When plants of this family are pressed and dried for herbaria they lose their
structure to a very great extent, and this is the reason why so very few species have been more
closety investigated. The systematic treatment of the family may as far as concerns the external
character of flowers, fruits, and leaves be well drawn from herbarium specimens but, as in so
many other instances, the parts underground are seldom preserved, and are consequently passed
by in diagnoses. The rhizome and the roots have, as a matter of fact, received very little
attention; the ramification of the shoot and the anatomical structure of the vegetative organs in
general are, on the other hand, well known in some species, but entirely unknown in others.

It would thus appear as if there is still something to be done in regard to investigating the
Commelinacese, and having had the opportunity of observing and collecting several species in the
field, and preparing these for further studies, we do not hesitate to present the results of our
investigations as acontribution to the knowledge of the family. As will be seen from the following

« Vergleichende Anatoniie der Vegetationsorgane der Phanerogamen und Fame. 1877.

'' Vergleichende Untersuchungen neber den Bau der Vegetationsorgane der Monocotyledonen. 1876.

cDas mechanische Princip. 1871.

''Traitc de Botanique. 1884.

' Beitrage zur Anatomie und Entwickelung der Commelynaceen. [naug. diss. Hannover, 1900.

/Rcrhi-ivlics aiiatoniiques et physiologiques sur le Tradescantia Virginica L. Bruxelles, 1S98.

9 Bluthendiagramme. Leipzig, 1875.

'' Neue Untersuchungen ueber den Bluthenanschluss. Leipzig, 1890.

I Ann. duMus. d' hist. nat. Vol. 13, p. 54. 1809.

3 Beitrage zur Morphologie und Biologie der Keimung. Untersuch. Hot. Inst. Tubingen. Vol. 1. L881-1885.

NORTH AND CENTRAL AMERICAN COMMELINACE/E— HOLM. 161

pages, the writer has endeavored to include as much as possible of the structural peculiarities, but
in some cases our material proved to be insullicient, thus we felt obliged to confine ourselves to
the external structure alone. The object of our research has been to illustrate some biological
features of these plants, as, for instance, their life under ground; the development of a rhizome;
the contractile power of the roots, besides their ability to store nutritive matters; furthermore,
the mechanical support possessed by stem and leaf, the organization of the leaf, with the differen-
tiation of the chlorenchyma; the stomata and the various types of hairs, etc.

Among the plants which have been studied by the writer are two that actually represent the
very rarest members of the family: Weldenia and Tradescantia Warszewicziana, both from
Guatemala. The material of these was carefully collected and preserved by Mr. Wm. R. Maxon,
who so very kindly gave us the privilege of using it for our present investigation.

The species which we have examined belong to the genera Commelina, Aneilema, Tmantia,
Tradescantia, and Weldenia:

Commelina nudiflora L. District of Columbia: thickets in Brookland.
C. Virginiea 1.. District of Columbia: among rocks on the Potomac shore.
C. erecta L. Florida: near Eustis.

C. hirtella Vaiil. District of Columbia: sandy river shore near Marshall Hall.
C. dianihifolia D. ('. Texas.

Aneilema nudiflorum R. Br. Georgia: near Thomasville, introduced.

Tinantia <<n<>mi\Ui (Torr.) Clarke Texas: at Kerrville, 1,600-2,000 feet altitude, and Alamo Heights. San Antonio.
Tradescantia rosea Vent. Florida: in sandy soil near Lake Dot, Eustis.
T. Virginica L. District Columbia: among rocks on the Potomac shore.
T. seopulorum Rose. Arizona: Oak Creek.

T. sp. Colorado: in alkaline soil, plains near Denver, 5,000 feet altitude.
T. crassifolia Cav. Mexico: Barranca of < luadelajara, 5,000 feet altitude.

T. pinelorum Greene. Arizona: Kincon Mountains, 7,500 feet altitude, and Huachuca Mountains.
T. Floridana Wats. Florida: Hammocks, Lee County.
T. micrantha Torr. Texas: Corpus Christi.

T. Warszewicziana K. et B. Guatemala: Santa Rosa, dry rocks in the open.

Weldenia Candida S< hult. pil. Guatemala: Volcan de Agua, in line, hard-packed sand, .on rocky slopes within the
crater, about 3,600 meters altitude.

Commelina nudiflora L.

The Germination.

Seedlings of C. com munis and cristata were described by Miubel (1. a), and by Klebs (1. c.)
referred to his second type, where the sheath of the cotyledon becomes very much prolonged and
forms a threadlike organ with the apex remaining inclosed in the seed; other representatives
of this same type are: Asphodelus, Dianella, Aristea, and Tradescantia.

Our figure 1 on Plate I shows the seedling of CoimueHim n "</'T>'>ra, and we notice at once
the long, threadlike portion between the sheath (S) and th.1 apex inclosed in the seed (C); this
filiform poition may develop from the side of the sheath, as figured, or near the apex of same.
There is a distinct hypocotyl (H), from the middle of which a whorl, of three secondary roots have
developed, while several others proceed from the base of the hypocotyl. The primary root (R)
persists for a few months and ramifies but sparingly (/■)• At this stage of growth we notice, also.
the first internode (I1) with the first leaf (L1). The internal structure of the various organs of
the seedling may be described as follows:

The secondary roots (fig. 14. PI. Ill) are very hairy, but possess no exoderm; the cortex (C)
consists only of three layers, and the endodermis (End.) is very thin walled. The pericambium
(P) is continuous and surrounds three rays of hadrome (H) alternating with three groups of
leptome, of which the proto-leptome cells are plainly visible (PL); the center of the root is
occupied by a wide vessel.

A still more delicate structure is observable in the lateral roots (tig. 15, PI. Ill), where
there are only two layers of cortical parenchyma (C) immediately inside the epidermis; the endo-
dermis (End.) is also here thinwalled with the Casparyan spots plainly visible, but the pericam-

162 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

bimn (P) is here interrupted by the two proto-hadroine vessels. This root is diarchic and there
are thus only two groups of leptome.

The cotyledonary sheath is very thin and perfectly glabrous; the epidermis is thinwalled on
both faces and covers a few, two to six, layers of chlorenchyma with chlorophyll. There are
only two collateral mestome-bundles containing a broad group of leptome, but only a few vessels.
No mechanical tissue was observed. In the cylindrical threadlike portion of the cotyledon the
epidermis is also thinwalled, but is here provided with stomata. Two very small collateral
mestome-bundles are located in a thinwalled, compact parenchyma of about twenty layers.

The hypocotyl, of which we have figured half of the central cylinder (PI. IV, tig. 19) has
also a thinwalled epidermis covered by a thin, smooth cuticle. The cortex consists of eight
layers of roundish cells with narrow intercellular spaces, surrounding a thinwalled endoder-
mis (End., fig. 19.) Four collateral mestome-bundles traverse the central cylinder, of which the
innermost portion is occupied by a pith. Secondary roots develop on the hypocotyl, in whorls
of three or four, from outside the leptome, but inside the endodermis.

These parts of the seedling, the cotyledon, the hypocotyl, and the first developed system of
roots are only of short duration. Thus when the plant commences to bloom they have mostly
faded away, while the first internode ( I1 in fig. 1) is generally to be observed as the basal stem-
portion in matured specimens.

The Ramification of the Shoot.

The species is an annual and possesses no rhizome, the basal stem-internodes being above
ground. The weak ascending main axis is. however, supported by a system of relatively strong-
roots, which develop in whorls of about five from the basal nodes. (PI. 1, fig. 2.) A profuse
development of lateral shoots takes place at an early stage. Thus the plant become- able to spread
over the surface of the ground, the branches being more or less decumbent or ascending. The
leaves are alternate and nearly all subtend axillary shoots sometimes accompanied by an acces-
sory bud, which is situated at the side of the shoot. Such collateral buds are also known from
various Liliaceat and Aracese, for instance.

Each fully developed and matured shoot becomes, however, terminated by an inflorescence,
and the small, leafy shoots which so abundantly occur in this species are only apparently vege-
tative, the floral apex having become arrested in its further development.

The lateral axes are readily distinguished from the main one by the presence of a fore-leaf,
which is membranaceous, colorless, and partly tubular, and which occupies the same position as
in most of the other monocotyledonous plants, turning its back toward the mother-axis. By
studying the composition of a number of shoots of C. nudiflora, we have observed the following
arrangement to be the prevalent.

Our figure 3 (PI. I) represents a stem-portion (A) with a leaf (L1), in the axil of which a
shoot is developed with two leaves (LJ and L3), besides two inflorescences (I' and P), while the
fore-leaves are not visible, being hidden within the sheaths of the green leaves. A diagram of
this same shoot-complex (fig. i) may show the exact position of the leaves much better, and we
notice here that the axillary branch (B in fig. 3) commences with a fore-leaf (P1) which alternates
with the green leaf L1, and bears a leaf L\ turned ninety degrees to the side of L1 and P1.
Above this leaf (L2) is an inflorescence (I1) with its large green spathe, alternating with the leaf
(L2); this inflorescence terminates the shoot (B). Another shoot is visible in the axil of leaf L\
which, like the former, begins with a fore-leaf (P2) alternating with the leaf L2. This little
shoot bears, also, a green leaf (L3), which shows the same turning to the side as the leaf L2, thus
forming an angle of ninety degrees with the fore-leaf (P2); an inflorescence, I2, terminates the
shoot and the spathe alternates with the green leaf, L".

While thus the fore-leaves alternate with the leaf of the mother-shoot, the succeeding green
leaf becomes turned ninety degrees to the side, a structure that seems to he typical of ( '. nudifiora.
When more than one green leaf is developed on the shoot, a corresponding number of axillary
branches is to be observed, in which the same disposition of fore-leaves and spathes becomes

NORTH AND CENTRAL AMERICAN COMMELINACEiE— HOLM. 163

repeated, as described above, with the only difference that the upper portion of the shoot may
show a turning of somewhat less than ninety degrees from the axis.

It has been mentioned above that accessory buds occur, and these are to be found within the
fore-leaves of first or second order, though not in the axils of these; they are usually collateral,
when considered in connection with the other shoots, and begin, like these, with a fore-leaf pre-
ceding a green leaf and sometimes a rudimentary inflorescence.

The Internal Structure of the Vecetative Orcans.
the roots.

All the roots of O. mid/flora are nutritive. As shown in our figure 2, there are several
secondary roots developed at the basal nodes of the stem, and these bear lateral ramifications in
some distance from the surface of the soil. Of these the secondary are naturally the strongest
developed and are quite thick. The epidermis (Ep. in fig. 17, PI. Ill) is thinwalled and hairy:
it surrounds a thinwalled exodermis (Ex. in fig. 17). the cells of which arc much larger than those
of epidermis. Between the exodermis and the cortex arc usually two layers of stereomatic cells
with the cross- walls distinctly oblique. The cortical parenchyma consists of about ten strata of
very thinwalled cells which decrease in size toward endodermis; the cortex is quite solid, the
intercellular spaces being very narrow. The endodermis (End. in figs. 16 and 18) shows a more
or less prominent thickening of the radial and inner cell walls, but contains no starch. In regard
to the pericambium the structure was observed to be somewhat variable in a number of roots.
It was either thinwalled throughout or thickwalled outside the hadromatic rays; moreover it was
found to be continuous in some roots, hut interrupted by the proto-hadrome in others, while in
some roots it was continuous near the apex, but interrupted at the base. It would therefore
appear as if 'he pericambium shows no constant structure in our plant, even if we did observe
that it was continuous in most of the roots that were examined. Similar irregularities in the
structure of the pericambium we have observed in other plants, for instance. Eriocaulon,a various
Carices,b Graminese," etc. The leptome, when viewed in transverse sections, forms large and
broad groups, with the proto-leptome cells plainly visible. The hadrome consists mostly of five
rays, but six or seven were also occasionally observed; the peripheral scalariform vessels are
either single or two arranged side by side; the innermost vessels are very wide and reticulated,
and one of these may sometimes occupy the center of the root. The conjunctive tissue is thin-
walled in some roots, hut more or less thickened in others.

If we compare now the structure of these secondary roots with that of their lateral ramifica-
tions, we notice only a very few deviations. These consist, in the absence of stereomatic tissue.
in the more delicate structure of the endodermis; besides in the smaller number of vessels. But
in respect to the pericambium we noticed exactly the same variations as in the secondary roots.

THE STEM.

The basal internodeof a flowering specimen (I1 in tig. 2, PI. I) shows the following structure:
A thin and smooth cuticle covers the epidermis, of which the outer cell-walls are slightly
thickened; then follows a collenchymatic tissue of two or three layers bordering on a thinwalled
cortex of about six strata, with small, but distinct, intercellular spaces.

An endodermis (End. in fig. 2(> on PI. IV) with heavily thickened inner and radial walls
surrounds the central cylinder, which is furthermore strengthened by a closed ring of stereome
bordering directly on endodermis, and which consists of a single layer outside the leptome
of the four peripheral mestoine-bundles, but of several between these. There are only four
mestome- bundles in which the hadrome of wide reticulated and narrower scalariform vessels

a Botanical Gazette, vol. 31, 1901, p. 17.
b Am. Journ. Sc, vol. 10. 1900. p. 278.
'Bot Gaz., vol. 39, 1905, p. 131.

164 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

surround the leptome in the shape of a V. The innermost part of the central -cylinder is occupied
hv a thinwalled solid pith with no deposits of starch.

In passing to the second internode (Is in fig. 2) we notice the same structure of epidermis,
collenchyma, cortex, endodermis and stereome as described above, but the number of mestome-
bundles is different, there being three concentric bands of five bundles in each of the two outer
ones and of four in the innermost. Of these the peripheral correspond with those observed in
the first internode, while those of the two inner bands, which are located in the pith, exhibit a
much weaker structure. The stereome is here reduced to a few cells on the hadrome-side or
entirely absent as in the innermost; the leptome shows the same development as in the peripheral,
while the vessels are much reduced in number; a large lacune, with remnants of some annular
vessels, forms a very conspicuous portion of the innermost mestome-bundles. All these
mestome-bundles are collateral.

The third internode (I3 in fig. 2) shows about the same structure, but the number of
mestome-bundles has increased now till eight in the outermost band, alternating with six in the
following, while there are six others near the center of the pith. Of these the innermost are
arranged in two parallel lines close to each other.

These basal internodes thus show a very simple structure of epidermis, but in regard to the
other tissues these exhibit relatively the same development as the uppermost portion of the stem.
Let us examine the internode B, figured on Plate I, figure :!. The cuticle is smooth and the epider-
mis is rather small-celled, as in the basal portions. Rut stomata are present (tig. 21, PI. IV), and
these are surrounded by four cells, two parallel with the stoma and two vertical on this; the sto-
mata are level with epidermis and arranged in longitudinal rows. Hairs are frequent, consisting
of two cells with the apex obtuse, but no glandular were observed. Two layers of collenchyma
separate the epidermis from a chlorophyll-bearing thinwalled cortex of about five strata. The
(>ndodermis is very thinwalled and surrounds directly the peripheral band of sixteen collateral
mestome-bundles of the characteristic V-shape. but lacking the support of stereome. The pith
contains small deposits of starch, and we find here about rive somewhat irregular bands of smaller
mestome-bundles, each with one narrow annular and one wide reticulated vessel with some lep-
tome, but destitute of any mechanical support.

THE LEAVES.

The stem leaves, for instance L' in our figure 3. Plate I. have large blades and a tubular
sheath.

The epidermis of the blade, viewed en face, consists of polygonal cells with straight radial
walls, becoming much narrower above ami below the mechanical tissue. Stomata occur on both
faces of the blade, but are, however, most numerous on the lower; they are projecting and are
surrounded by two pairs of subsidiary cells. (PI. V. fig. '24:.) The outer cell-wall of epidermis
(Pi. IV. rig. 22) is distinctly thickened on the dorsal face, much less so on the ventral. Epider-
mal projections of two kinds cover both faces, viz. small wartlike (fig. 30) and long clavate of
three cells in one row, which abound on the dorsal face. A large mass of hypodermal water-
storage-tissue occurs on the leptome-side of the midrib, but is absent from the hadrome. The
chlorenchyma consists of a very open pneumatic tissue on the dorsal face of the leaf-blade
(PI. IV, fig. 23), and of one single stratum of palisade cells on the ventral. Cells containing
raphides occur in both of these tissues, and arc located directly beneath epidermis: they are
very long (PI. V, fig. 25) when viewed in superficial sections, and are more or less parallel with
the veins.

A rather poorly developed collenchymatic tissue of one or two strata is to be observed in
the midvein and below the larger parallel secondary veins, but there is none in the leaf-margins.

The mestome bundles occur as about seven almost parallel veins that traverse the entire
length of the blade, and as numerous very short anastomoses. Of these the midrib is the
strongest developed (PI. V, tig. 26); there is a thinwalled completely closed parenchyma-sheath,
but no mestome-sheath. The leptome represents -a roundish group with sieve-tubes and com-

NORTH AND CENTRAL AMERICAN COMMELINACE.E-- HOLM. 165

panion cells well differentiated; the hadrome consists of two reticulated and one ring-vessel.
Two very small mestome- strands are located in the leaf-margins, and their structure is very
simple (PI. V, fig. 27); the parenchyma-sheath (P). of which two cells are moderately thickened,
surround a group of leptome and one or seldom two reticulated vessels.

A somewhat similar structure is to be observed in the green spathe which surrounds the
inflorescence. The dorsal face of this leaf is very scabrous from numerous short pointed and
somewhat curved hairs, accompanied by the same kind of wartlike and clavate which were
noticed on the stem-leaves. The epidermis is otherwise thinwalled and covers a chlorenchvma
of two to three strata of open pneumatic tissue, but no palisades; raphide-cells are very numer-
ous, but much shorter than those in the stem-leaves. No collenchyma accompanies the veins,
the minor structure of which agrees with that of the veins of the other leases.

The fore-leaves are tubular and membranaceous, almost colorless. Epidermis is thinwalled
on both faces, and lacks the pointed hairs and the papillae, while a few clavate were observed on
the dorsal face. This tissue, the dorsal and ventral epidermis, is the only one of these [eaves
except around the nerves, where a few parenchymatic cells form an incomplete sheath; the
mestome-bundles, eight in all. contain mostly leptome, and are not supported by any cover of
collenchymatic tissue.

Although no chlorophyll was observed in the fore-leaf, a few stomata were, nevertheless,
noticed, and these showed the same structure as those of the green leaves.

Commelina Virginica L.

The Rhizomk.

A rhizome is developed in this species, but it is short and condensed (PI. II, fig. 8); it con-
sists of a few erect internodes, each of which represents the base of an erect aerial shoot with
usually two roots. These roots develop from the ventral face of the internodes; they are thick,
dark brown, and densely covered with hairs. They branch but sparingly, and the lateral ramifi-
cations are more slender and of a lighter color. The rhizome has no horizontal internodes, and
its further growth is only secured by the development of a bud in the axil of a scale-like leaf,
situated near the base of the short, erect internode. This bud is developed on the side of the
shoot, alternately to the right or left; thus the rhizome grows out in a zigzagged direction.
This structure of the rhizome may he more easily understood if we examine the smaller specimen
drawn on the same plate (fig. 10) with its diagram (tig. 11). The base of the old shoot (A) repre-
sents only one internode, and the leaves have faded away completely. A lateral branch has
pushed out (A1) which bears a bicarinate foreleaf (P1) and two scale-like membranaceous basal
leaves (L1 and L2). Of these the foreleaf turns its back towards the mother-axis (A), while the
two other leaves are turned ninety degrees to the side of this, alternating with each other, as
seen in the diagram (tig. 11). Two axillary buds (B' and B2) are visible, and it is the latter of
these (B2) which develops into an aerial shoot during the succeeding year, while the other one
(B1) stays dormant.

If we return now to the larger rhizome (ties. 8 and 9), we notice the same arrangement of
leaves and position of buds, besides that the lateral, aerial branch (A2) from the axil of leaf (L3)
does also bc<jin with an addorsed fore-leaf (P2).

It seems, thus, characteristic of the rhizome of this species that no horizontal internodes occur,
that the growth takes place in a zigzagged direction, and that the laid in the axil of leaf (L1) remains
dormant.

The Aerial Shoot.

It is not uncommon to find specimens with a simple, erect stem terminated by an inflorescence
and with no indication of lateial Moral or vegetative shoots. Most frequently, however, the stem
is branched and often very profusely so. Lateral shoots may thus develop from the axils of
nearly all the stem-leaves, and these lateral shoots are again terminated by an inflorescence, besides
that a few, two or three, inflorescences of third order may be observed near the apex of each lateral

166 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

branch. Purely vegetative .shoots are frequent; they are developed on the lateral shoots and
contain no rudiments of flowers.

If we examine the ramification we notice an addorsed bicarinate foreleaf at the base of each
lateral branch and at the base of each axillary inflorescence. The diagram of the shoot agrees
very well with that of C. nudiflora, described above, but there is no stem-leaf situated directly
on the floral shoot; thus the foreleaf is the only loaf below the spathe. By comparing the exact
position of the foreleaf with that of the spathe we noticed that the latter was turned ninety
degrees to the side of the former, as iu Commelina rmdiflora.

The Internal Structure of the Vegetative Organs,
the roots.

As described above, the secondary roots are quite thick and densely covered with root-hairs;
the}7 represent a combination of two types, since they are contractile and contain large deposits
of starch. Epidermis is thinwalled, and the cells are stretched radially. (PI. VII, fig. 41, Ep.)
There is an exodermis (Ex. in fig. 41) of one layer, with the cells stretched in the same way, and
of which the cell-walls show numerous foldings when examined in longitudinal radial sections.
About four strata of slightly thickened stereomatic tissue separate the exodermis from the
cortex proper. These stereomatic cells are much shorter than typical stereome, and their cross-
walls are horizontal instead of oblique.

The cortex represents a broad tissue of about thirty layers, the cells of which are thinwalled
and round when viewed in transverse sections, and they are filled with starch. The cortical
parenchyma exhibits a very regular radial arrangement with rhombic intercellular spaces.
Numerous crystal-ducts occur in the cortex. They are very long, but much narrower than the
surrounding cortical cells and contain bundles of raphides.

Endodermis is small-celled and thinwalled, with the Casparyan spots plainly visible, but
contains no starch. The pericambium consists of a single layer, and is continuous in some roots,
but interrupted by the proto-hadrome in others. The hadrome forms twelve short rays, with
the proto-hadrome vessels single or two or three together arranged side by side. The leptome
is well developed in broad groups, separated from the center by several layers of thinwalled
conjunctive tissue.

The lateral roots are much more slender, and they are not contractile; otherwise the epidermis
and exodermis show the same structure as observed in the secondary roots. Cortex consists
here of only five layers, with no deposits of starch and with no crystals. Endodermis is thin-
walled, or the inner and radial walls may be slightly thickened. The pericambium is continuous
and surrounds five to six very short rays of hadrome with the proto-hadrome-vessels mostly
single; a very wide reticulated vessel occupies the center of the root. The leptome is well
developed, but the proto-leptome cells less distinct than in the thick roots.

THE RHIZOME.

The basal persisting internode shows the following structure: Epidermis is moderately7
thickened on all the cell-walls, perfectly glabrous and covered by a smooth, thick cuticle. The
cortex is moderately thickwalled and consists of numerous layers filled with starch; tubular
raphide-eells abound here. Two almost concentric rings of mestome-strands are located in the
cortex; they are collateral, and each is surrounded by a sheath of cells which are distinctly
smaller than the surrounding cortex and contain no starch. The innermost portion of the inter-
node is occupied by a solid parenchyma of the same structure as the cortex and with similar
deposits of starch.

THE STEM ABOVE GROUND.

Epidermis is here thinwalled and quite hairy from small four-celled hairs with the apical
cell somewhat curved, thus they represent minute hooks; stomata are present with two pairs of
subsidiary cells very plainly differentiated. (PI. VII, fig. 40.) The cortex is thinwalled except

NORTH AND CENTRAL AMERICAN COMMELINACEjE— HOLM. 167

where it is developed as a collenchymatic tissue of four to live hypodermal strata, and the cortex
proper contains much chlorophyll, besides raphides in long tubular cells. Inside the cortex is
a closed sheath of thickwalled cells which reminds of an endodermis. but they did not resist the
effect of concentrated sulphuric acid. This sheath surrounds several strata of typical stereome,
which forms a massive closed ring around the mestome-bundles. Some of these about twenty
five, are arranged in a peripheral band bordering directly on the stereome. while the others,
about twenty, are scattered very irregularly in the pith. Of these the peripheral possess a very
large group of leptome. two wide pitted ducts, and one annular vessel located between two
scalariform. No parenchyma- or mestoine-sheath was observed.

The innermost mestome-bundles have only one. but very wide, pitted duct and sometimes an
annular and a scalariform vessel, but they lack the support of stereome.

A pith of large roundish cells occupies the center of the stem; it contained very much starch,
and tubes with raphides were also observed.

THE STEM-LEAVES.

The blade is held in a horizontal position and is very hairy. Epidermis of the ventral face.
when viewed en face, consists of penta- or hexagonal cells (PI. VI, tig. 37) with many pointed
hairs of only two cells, but with very few stomata. The dorsal face, on the contrary, is almost
glabrous, but amply provided with stomata of the same structure as those of the stern. (PI. VII,
fig. 40.) A cross-section of the leaf -blade shows a thin and smooth cuticle on both faces. The
outer cell-wall of epidermis is moderately thickened, and the lumen of the cells, which is rather
narrow above and below the midrib, increases in size from there toward the margins of the
blade: the stomata are seen now to be somewdiat projecting, and their air-chamber is deep and
quite wide. A single stratum of collenchyma is noticeable above and below the midrib, which is
prominent only on the lower face of the blade. This collenchyma passes gradually over into a
layer of colorless cells on the ventral face of the midvein. while on the dorsal there is a mass of
similar colorless tissue, the function of which is evidently to store water. This colorless tissue,
together with the collenchyma, is thus confined to the two faces of the midvein alone.

The chlorenchyma consists of a dense palisade tissue of one layer and of a very open pneu-
matic tissue of very irregular cells in several strata. Cells with raphides are scattered on the
ventral face beneath the epidermis.

The stereome is weakly developed and occurs as small strands on the leptome-side of the
mestome-bundles except the midvein; no stereome was observed on the hadrome-side or in the
margins of the blade.

The mestome-bundles are almost orbicular in cross-section; they an1 surrounded by a thin-
walled, colorless, parenchyma-sheath. No mestome-sheath is developed, but the leptome is,
nevertheless, covered and protected by a layer of thickwalled mestome-parenchyma. The leptome
is well developed, and the hadrome has. at least in the largest veins, two very wide pitted ducts,
one annular and two or three scalariform vessels.

The leaf-sheath is tubular and densely covered by long, hooked hairs. (PI. VII, tig. 39.) The
collenchyma is here only developed on the dorsal face of the midvein, and the chlorenchyma is
traversed by broad lacunes beneath the ventral epidermis. No palisades are developed, and the
mestome-bundles are somewhat weaker than in the leaf-blade.

Commelina erecta L.

Having been unable to detect any points by which this species may be distinguished from
C. Virginica L.. as far as concerns the ramification of rhizome and aerial shoots, we will confine
ourselves to describe the internal structure alone.

168 MEMOIKS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

THE ROOTS.

The roots are quite long and more slender than in the preceding species; they are very hairy
and represent also here a combination of two types, contractile- and storage -roots. The exoder-
mis consists of large, pentagonal cells with the radial walls very prominently folded. The cor-
tex consists of fifteen layers, which are quite compact and contain large deposits of starch; some
cells were noticed to contain tannin. The cortical parenchyma is thinwalled throughout, and no
stereomatic strata are developed in this species beneath the exodermis. Endodermis is thinwalled,
with the Caspai-yan spots plainly visible; the pericambium is thinwalled and continuous, sur-
rounding five short rays of hadrome with the two to three proto-hadrome vessels situated side
by side. The leptome constitutes broad groups, and the conjunctive tissue is thinwalled, but
occupies only a very small portion of the central cylinder, since the center contains a very wide
vessel.

THE STEM ABOVE GROUND.

In the uppermost internodes below the inflorescence the epidermis is covered by a thick
and smooth cuticle, and the cellwalls, especially the outer, are distinctly thickened: pluricellular,
strongly curbed hairs abound, and the stomata are level with epidermis. Beneath epidermis are
several isolated groups of collenchyma, separated from each other by narrow rays of the green
cortex, which forms also a closed ring of about three layers around the stereome and the
mestome-strands. There is also in this species a sheath like an endodermis which separates the
stereome from the cortex proper, but it was very thinwalled in ( '. < recta. The stereome is not
very thickwalled, but incloses the peripheral band of mestome-bundles completely. The number
of mestome-bundles is rather small, there being about sixteen peripheral and a very few located
in the pith, and their structure is exactly the same as noticed in the preceding species. The
pith represents a very large thinwalled parenchyma, but contained no starch.

THE STEM-LEAVES.

The leaf -blade is very hairy on both- faces, especially on the ventral; these hairs are short and
clavate or somewhat longer and with the apical cell strongly curved. The cuticle is smooth or
wrinkled outside the subepidermal collenchyma. Epidermis has the outer cell-wall slightly
thickened on the dorsal face, much less so on the ventral; the lumen of the cells is large on
both faces except above the midrib. Stomata abound on the dorsal face; they are level with
epidermis and are surrounded by four cells.

There are hypodermal layers of collenchyma above and below the midrib, which on the
dorsal face passes over into a water-storage tissue of thinwalled colorless cells. Similar groups
of collenchyma were also noticed at the other large veins. Besides this support of collenchyma
the mestome-bundles possess also a little stereome on the leptome-side, separated from the
collenchyma by a single stratum of chlorenchyma; a few cells of stereome were, furthermore,
observed in the margins of the blade. The chlorenchyma is differentiated into one layer of
palisades on the ventral face, very compact and full of chlorophyll, and into a more open
pneumatic tissue on the dorsal. Cells with raphides were observed in both of these tissues.

The mestome-bundles are surrounded by a thin-walled parenchyma sheath and show the same
structure as described above for ('. Virginica.

Commelina hirtella Yahl.

The Rhizome.

A rhizome of a flowering specimen is figured on our Plate I. figure 5. It is perennial,
horizontally creeping, with distinct, more or less stretched internodes. the leaves of which are
membranaceous and tubular, when young. The roots are hairy, somewhat fleshy, but never
tuberous; they are sparingly branched and develop in a number of three or five at the nodes,
above the insertion of the leaves. The ramification of the rhizome is sympodial. and the lateral

NORTH AND CENTRAL AMERICAN COMMELINACEiE— HOLM. 169

branches begin with an addorsed foreleaf. Dormant buds occur in the leafaxils. The length of
the complete rhizome is very variable, and we have noticed as many as nine internodes between
two flower-bearing shoots, representing the growth of one season.

THE RAMIFICATION OF THE AERIAL SHOOT.

The species is more robust and taller than the others, but the stem is less branched. Vege-
tative shoots may develop near the base, but seldom at the upper part, and a few inflorescences
are to be observed at the apex. The stem-leaves are ample and provided with large sheaths;
they are on the lateral shoots preceded by a small tubular foreleaf, which is bicarinate. and slit
on the frontal face. (PI. I, figs. 6 and 7.)

By examining the position of the leaves, foreleaves. and spathes in a lateral shoot we notice
that the green leaves are turned 90 degrees to the side of the foreleaf, as in the species described
above. As many as three green leaves may be observed on a single, flowering, lateral shoot,
alternating with each other and supporting lateral inflorescences, each of which begins with an
addorsed foreleaf and where the spathe is turned 90 degrees to the side of this.

The Internal Structure of the Vegetative Organs.

the ROOTS.

As mentioned in the preceding the roots of this species are somewhat fleshy, but not tuber-
ous; they may be designated as "nutritive" and at the same time "contractile." but not as
-forage roots.

The thinwalled epidermis shows a profuse development of hairs. An exodermis of a single
layer of, in transverse sections, polygonal thinwalled cells separate epidermis from the cortex;
viewed in longitudinal sections the cell-walls of the exodermis show numerous foldings. (PI. V,
fig. 29.) The cortical parenchyma constitutes a homogeneous thinwalled tissue, which fre-
quently collapses tangentially; or the peripheral strata of the cortex may consist of thickwalled
cells, stereoinatic, with the lumen quite narrow; these cells are, however, relatively short and
the cross-walls horizontal instead of oblique as in typical stereome.

Endodermis is mostly thinwalled, but we observed, also, cases where the inner and radial
cell-walls were moderately thickened. The pericambium consists of a single layer and we noticed
no instances in the secondary roots where it was interrupted by the proto-hadrome vessels. (PI.
VI, fig. 34.) The leptome occurs as broad groups as in the other species examined, and the
hadrome constitutes a very variable number of rays from four to eight, but five being the most
frequent; the rays are very short, and the innermost vessels, which are reticulated, are the
widest. One of these may occupy the center of the root, but very seldom. The proto-hadrome
vessels (PII in tig. 34) are very narrow and either single or two together. The conjunctive tis-
sue is often more or less thickwalled, and extends to the center of the root.

If we now examine the much thinner lateral roots, we notice only a few layers of thinwalled
cortical parenchyma which do not collapse. The number of hadromatic rays may lie reduced to
only two, of which the proto-hadrome vessels border directly on endodermis; when four or five
rays were developed, these vessels were located inside the pericambium as in the mother-root.
But otherwise the structure of the lateral roots appeared to be very uniform with epidermis,
exodermis, endodermis. and the conjunctive tissue thinwalled throughout.

It would thus appear as if the pericambium is continuous in the secondary roots, judging
from the large number of roots that have been studied and at different places, but sometimes
interrupted in the lateral. Finally may be mentioned that " thyllen" were observed in the reticu-
lated vessels of some of these roots.

THE RHIZOME.

The horizontal internodes show the following structure: A thin, smooth cuticle covers
epidermis, from which numerous clavate hairs are developed. The cortex is differentiated into
a hypodermal collenchyma of about three strata, and a cortex proper of about twenty layer-:

170 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

the latter contains raphides and tannin, and the intercellular spaces are often very wide,
especially near the endodermis. A thinwalled endodermis with the Casparvan spots plainly
visible surrounds the central cylinder and borders directly on a continuous ring of stereome.
This stereome is rather thinwalled and incloses the peripheral mestome-strands completely; it
occurs also around the inner mestome-bundles, but is weakly developed. The collateral mestome-
bundles are arranged in four bands, which are barely concentric: the peripheral are the highest
developed, consisting of a large group of leptome and several vessels, two wide reticulated, one
annular, and a few scalariform. The inner mestome-bundles, which are located in the pith,
possess also a large leptome, but only one very wide reticulated vessel. A thinwalled pith
with large deposits of starch occupies the greater portion of the central cylinder.

THE STEM ABOVE GROUND.

The basal internodes show the same structure as the rhizome, but with the collenchyma much
more typically developed and with the stereome more thickwalled.

By examining the upper internodes. which are completely covered with the leaf-sheaths, we
notice the same structure; epidermis, however, is more hairy, and besides the clavate hairs there
are also some that are sharply pointed. (PI. VI, fig. 35.) Stomata are frequent and show
variation in regard to the position of the surrounding cells. (PI. V, fig. 28, and PI. VI, tig. 33.)
Viewed en face the cells of epidermis are short and broad in the stomatiferous strata, but narrower
between these; the cell-walls are thin throughout.

Beneath the epidermis are several isolated groups of collenchyma of very thickwalled cells
in five or six strata. The cortex contains chlorophyll and is developed as dense palisades between
the collenchymatic groups, but inside it represents a very open tissue of in transverse section
roundish cells. Raphides in long tubular cells are frequent in the cortex, besides large globose
crystals of Calcium oxalate. (PI. VI, tig. 36.)

A thinwalled endodermis surrounds the central cylinder in which we notice the same structure
as in the rhizome — a continuous ring of thinwalled stereome, four bands of mestome strands, and
a pith. The last of these, the pith, contains no starch, but numerous crystals and raphides.
(PI. VII, tig. 38.) It is a rather open tissue with the intercellular spaces very wide.

If we now examine the nodus, we find the same structure as described above in regard to
epidermis, collenchyma, cortex, endodermis, and stereome, but the mestome-bundles show
naturally a somewhat modified structure. The peripheral mestome -strands are almost orbicular,
when viewed in cross-sections, and the leptome is on both sides covered by several reticulated
vessels. The mestome-strands of the inner bands ai'e larger than the peripheral, since some
of these have fused together, forming bicollateral and perihadromatic strands; the pith was
observed to be moi'e solid than in the internode.

The aerial shoot is actually terminated by a single Hower borne upon a slender, glabrous
peduncle; a lateral and much thicker peduncle proceeds from the base of the terminal, and bears
usually two or three flowers. The internal structure, of these two peduncles is almost identical,
with the exception of the arrangement and number of the mestome-strands. There are only
four or five peripheral strands in the terminal, while the lateral contains three almost concentric
hands of collateral mestome-bundles, about fifteen in all. The epidermis is thinwalled and bears
many pointed hairs; the cortical parenchyma, which occupies most of the cross-section, is very
open from the presence of wide lacunes. An endodermis surrounds the central cylinder with a
closed ring of stereome, the mestome-bundles, and the solid, but thinwalled pith.

THE STEM-LEAVES.

The green leaves are provided with a long, tubular sheath and a flat blade, held in a hori-
zontal position.

The sheath is very veiny and covered with hairs on the outer face. These hairs represent
three kinds: Very long and sharply pointed, consisting of four cells, which are located along the
ventral suture and around the orifice of the sheath; some that are very short, but pointed like

NORTH AND CENTRAL AMERICAN" COMMELINACE^E— HOLM. 171

the others, and which occur in rows near the sfcomatiferous strata: finally clavate hairs are very
abundant and show the same distribution as the short ones. The epidermis is thinwalled on
both faces, and is covered by a smooth cuticle. A collenchymatic tissue is developed as a few
layers on the dorsal face of the largest veins. There is a homogeneous chlorenchyma of, in trans
verse sections, roundish cells with wide intercellular spaces near the ventral face (the inner) of
the sheath. Druids, but no raphides, were observed in the chlorenchyma. The stereome is
poorly represented, and occurs as a few cells on both faces of the veins, and is more thickwalled
on the leptome-side than on the badrome; in no instances was the stereome observed to be sub-
epidermal. In regard to the mestome-bundles, these are collateral and of the usual structure, as
described above.

The leaf blade is scabrous on the ventral face and along' the margins; the midvein is thick
and very prominent on the dorsal face. Clavate and two-celled, pointed hairs abound on the
ventral face, but only the clavate are frequent on the dorsal. Stomata were observed on both
faces, but they are most numerous on the dorsal; they are generally surrounded by four cells
(PI. VI, fig. 32) or, though seldom, by five (fig. 31); the guard-cells are conspicuously larger on
the leaf-blade than on the stem and the sheath. Viewed en face the cells of epidermis are mostly
pentagonal or hexagonal, with the radial walls straight, a structure that was observed on both
faces of the blade. Examined in transverse sections epidermis consists of a double layer above the
middle portion of the blade, covering the midrib, and also above some of the larger veins. But
otherwise there is only one stratum of epidermis, and the cell-walls are thin. The epidermis of
the lower face consists of a single layer throughout: the cells are thinwalled and very small
underneath the veins, but larger between these.

A collenchymatic tissue of one layer covers the leptome-side of the midvein and of some of
the larger, but there is none on the hadrome-side. The chlorenchyma is differentiated into one
stratum of long palisades on the ventral face of the blade, and a pneumatic tissue on the dorsal.
The palisade-tissue is quite compact; it contains tannin, but no cells with crystals were observed.
The pneumatic tissue, on the other hand, is very open on account of the very irregular shape of
the cells, and raphides and crystals were observed here.

The mestome-bundle> are collateral; they possess a colorless parenchyma-sheath, which i<
generally thinwalled; a few layers of thickwalled mestome-parenchyina occurs, sometimes, on
the leptome-side. or on both the leptome- and the hadrome-side. The primary veins have a large
group of leptome, and several wide vessels.

THE 8PATHE.

The structure of the spathe is more simple than that of the .stem-leaves. While the ventral
face is destitute of stomata and hairs, the dorsal has numerous stomata and short, pointed hairs
in abundance; epidermis is thinwalled on both faces and represents the on!}' tissue in the leaf-
margins which are grown together, thus the spathe is partly closed. The chlorenchyma is only
developed as a pneumatic tissue, which is very open. No collenchyma was observed, but the
mestome-bundles are supported by a few strata of thickwalled mestome parenchyma. Druids
and single crystals occur in long, narrow cells beneath the epidermis.

Commelina dianthifolia D. C.

The ramification of the Shoot.

The parts underground consist of a few vertical internodes covered by leaf-sheaths and
bearing many fleshy, brown roots with slender lateral ramifications. Our dried material showed
no stems from the previous year, but it appears, nevertheless, as if the species is perennial. The
aerial stem is quite tall, erect, and profusely branched, each branch being terminated by an
inflorescence. These axillary shoots bear membranaceous, tubular fore-leaves and show the same
89369°— vol 10—11 12

172 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

disposition of the leaves as described above. The number of green leaves on the lateral shoots
is somewhat variable, from two to four on the basal, and only one on the uppermost of these.
The flowers are surrounded by a large, green spathe, which is relatively long and acuminate in
this species.

The Internal Structure of the Vegetative Organs.

the roots.

The fleshy, secondary roots are very hairy. An exodermis of one layer of thinwalled cells
with prominent foldings surrounds a cortical parenchyma of large size. This parenchyma consists
of about twenty strata thinwalled cells with narrow intercellular spaces and tilled with starch.
The endodermis and the pericainbium are thinwalled and surround six broad groups of leptome
alternating with six short rays of hadrome; the exact position of the proto hadrome vessels could
not be ascertained, since the roots had been pressed and dried. A thinwalled conjunctive tissue
occupied the center of the root.

THE STEM ABOVE GROUND.

The internodes are smooth and minutely hairy from small, clavate hairs. The cuticle is
thick and smooth, and covers a thickwallcd epidermis; stomata are frequent and are arranged in
longitudinal rows, where the cortical parenchyma extends to epidermis. Inside the epidermis
are three layers of very thickwallcd eollenchyma, which is frequently interrupted by the cortex,
as mentioned above. The cortex constitutes a rather narrow zone of thinwalled cells containing
chlorophyll. A thinwalled endodermis surrounds the central cylinder and borders directly on a
closed sheath of stereome of three layers. The mestome-bundles are collateral and are arranged
in three concentric bands. Of these the peripheral are very numerous and they are completely
surrounded by stereome. The inner band consists of ten mestome-bundles with a smaller number
of vessels and the innermost of only three. While the stereome is usually confined to the
peripheral mestome-bundles in the species of Commelina, described above, we noticed in
the present species, C. dianthifolia, that a small group of this tissue was also developed on the
leptome-side of all the inner mestome-strands. The pith is thinwalled and tilled with starch.

THE STEM-LEAVES.

The leaf-blade is scabrous on both faces and along the margins from two-celled, short, but
sharply pointed hairs and one-celled, roundish, very thickwallcd warts. Besides these some
clavate hairs were also observed, but only on the ventral face of the blade, and not in any large
number. The cuticle is thick and smooth. Viewed en face the cells of epidermis are mostly
octagonal; in transverse sections the cells show a wide lumen and the outer walls are moderately
thickened. Stomata are distributed over both faces of the blade; they are level with epidermis
and have two pairs of subsidiary cells parallel with the stoma. Thickwallcd eollenchyma was
observed on the leptome-side of the larger veins, and in the margins. The stereome is weakly
developed as a few strata on the leptome- and hadrome-side of the larger mestome-bundles,
separated from the eollenchyma by a few layers of chlorenchyma. The chlorenchyma consists
of one single layer of palisades, vertical on the ventral face, and of a more open pneumatic tissue
near the dorsal portion of the blade. Many cells were observed to contain tannin. The structure
of the leptome and hadrome showed nothing "I' particular interest.

THE SPATHE.

The structure of the spathe is almost identical with that of the leaf-blade in regard to
epidermis with the stomata and hairs; the wartlike papilhe were, however, not observed. The
mechanical tissue is somewhat poorer developed, there being only a small group of eollenchyma
on the leptome-side of the midvein, and stereome is totally absent. But in regard to the. chloren-
chyma and the minor structure of the mestome-strands we did not notice any important difference
between the spathe and the stem-leaf.

NORTH AND CENTRAL AMERICAN COMMELINACE.E— HOLM. 173

Aneilema nudiflorum R. Br.

The Ramification of the Shoot.

The species is ;in annual with decumbent stems rooting at the lower nodes. The narrow
leaves are alternate with distinct sheaths which inclose the axillary buds; the fore-leaf is mem-
branaceous, tubular with the apex extended into two small, green teeth. Nearly all the shoots
are terminated by an inflorescence borne on a long, slender scape. In regard to the arrangement
of the leaves, the diagram is the same as that figured on our Plate II <>f Tradescantia rosea, i. e.,
a regular alternation of the green stem-leaves and the fore-leaf.

The Internal Structure of the Vegetative Organs.

the roots.

Two to three slender and sparingly branched roots are developed on the lower face of the
nodes. Their structure is as follows: Epidermis is hairy, and covers an exodermis of one layer
of thinwalled, pentagonal cells, which are larger than those of epidermis and the adjoining cortex;
no foldings of the cell-walls were observed. The cortical parenchyma consists of ten strata, of
which the four peripheral are persisting, while the others were collapsed- tangentially; no starch
was observed. The endodermis and the continuous pericambium are thinwalled. There are five
short hadromatic rays with one very wide, reticulated vessel in the center, and two to three
narrower, spiral in each ray. The leptome is well developed, and the conjunctive tissue, which
occupies only a small portion of the central cylinder, is thinwalled.

the stem.

The structure of the stem could not he studied satisfactorily, since the material had been
pressed and dried. We noticed, however, that a continuous sheath of hypodermal collenchyma
surrounded a narrow zone of green cortical parenchyma, and that the peripheral mestome-bundles,
located inside the cortex, had a support of stereomatic tissue on the leptome side.

the stem-leaves.

Viewed en face epidermis of the dorsal face consists of rectangular cells with some few rows
of clavate hairs between the stomatiferous strata. The stomata have one pair of subsidiary cells
and are slightly raised above the adjoining epidermis. The outer cell-wall of epidermis exhibits
a number of longitudinal ridges, which are covered by the thin but distinct cuticle.

The ventral epidermis shows the same structure, but has no stomata. Along the margins of
the blade are minute, one-celled warts, but no hairs or prickle-like projections. Viewed in
ti'ansverse sections the leaf shows a large-celled epidermis on both faces, and the stomata have
deep and wide air-chambers. Underneath the ventral epidermis is a water-storage tissue of two
layers of very large .thinwalled cells, which covers the chlorenchyma. This tissue represents a
homogeneous, open pneumatic tissue, since no distinct palisades were noticed. The mestome-
bundles are very thin, and only the mediane has a support of hypodermal collenchyma on the
leptome-side; some of the other veins, had a small group of stereome on the leptome- but none
on the hadrome-side, and some few layers of this tissue were, furthermore, observed in the leaf-
margins.

Tinantia anomala (Torr.) Clarke.

This plant was originally described by Torrey" as a Tradescantia "anomala" and his
material came from the shady woods on the Blanco, Comale, and other rivers in Texas. As
stated by Torrey, "the species is intermediate between Tradescantia and Commelina, resembling

«U. S. and Mex. Bound. Survey under Lieut. Emory. Washington, 1858, p. 225.

174 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

tlu> latter in the unequal petals and difformed stamens as well as in the terminal leaf or bract
(which is like a spatha laid open), and the former in the six fertile stamens with bearded filaments."
Several years later the species became transferred to the genus Tinantia by C. B. Clarke (1. c).

The Ramification of the Shoot.

The. species is an annual with an ascending stem; the roots are very slender, much branched,
and develop from the very base of the stem. The lowest leaves, one to three, are lanceolate, the
others ovate to cordate and acuminate. Axillary shoots develop from the basal leaves and also
from some of the higher situated. It seems characteristic of this plant that the axillary buds break
through the sheath of the supporting leaf. However, as will be shown later, we noticed the same
peculiarity in Traih'xraiitia Flm'idana, and Clarke (1. c.) describes the same as characteristic of
Polyspatha paniculata Benth. and Buforrestia Mannii Clarke.0

The accompanying diagram of the shoot of Tinantia (PI. VIII. fig. -M5) shows the arrangement
of the leaves. L'-L3 are alternating stem-leaves; a lateral shoot is developed in the axil of L3,
and the fore-leaf (P1) alternates with this, while the succeeding green leaves (L4 and L5) are
turned 90° to the side, as in < 'ommelina. In the axil of W are two shoots developed; the main
one of these commences with the fore-leaf P2, upon which two green leaves (L6-L7) follow; the
secondary, which belongs to the axil of the fore-leaf (P2) begins, also, with a fore-leaf (P3)
succeeded by a green leaf (L*). We notice thus in these three shoots exactly the same position
of the leaves as in Corrwndina, described above; furthermore, the fore-leaves in Tinantia support
lateral ramifications.

Although axillary buds are present on the secondary branches, it seems as if these stay
dormant, unless the terminal inflorescences should become injured. In the specimens which we
have examined the main stem was invariably terminated by an inflorescence. There were,
furthermore, two or three long, lateral branches, all of which bore several green leaves and were
terminated by a few-flowered inflorescence. In no instance did we observe that the small buds
(in the axils of L4-L8) attained any further development. Thus we presume they are merely
auxiliary.

The Internal Structure of the Vegetative Organs.

the roots.

A haiiy epidermis covers a thinwalled exodermis of a single layer and of which the cell-walls
show nc foldings. The cortical parenchyma consists of eight compact strata, showing a very
regular radial arrangement of the cells; the parenchyma is thinwalled throughout, and no deposits
of starch were, observed. The endodermis and the continuous pericambiutn are thinwalled.
Seven short rays of hadrome alternate with seven roundish groups of leptome. A wide,
reticulated vessel occupies the center of the root, and the proto-hadrome-vessels are mostly
only one in each ray. The conjunctive tissue is thinwalled and sparingly represented.

THE STEM.

The glabrous internodes are covered by a thick, smooth cuticle. Epidermis is thinwalled,
and the stomata are arrangfed in longitudinal, very narrow rows outside the narrow hypodermal
rays of cortical parenchyma. The stomata have one pair of subsidiary cells, parallel with the
stoma, and they are sunk below the surrounding epidermis; the air-chamber is wide, but rather
shallow. A collenchymatic tissue is well developed, and represented by many hypodermal groups
of one or two layers; the cells are very thickwalled and of a regular stellate shape. The cortex
consists only of a few layers of thinwalled cells filled with chlorophyll, and, as stated above, this
tissue extends to epidermis between the groups of collenchyma. No raphides were observed.
Inside the cortex is a single layer of very large, thinwalled cells, which doubtless represents an

"It, moreover, occurs in TradescanMa genieulata Jacq. and in Campelia Zanonia H. B. K., besides that Sehiinland
mentions it as common to several species of Dichorisandra. (Natiirl. Pflanzenfam., II, 4, p. 68.)

NORTH AND CENTRAL AMERICAN COMMELINACEiE— HOLM. 17.")

endodermis. It borders on a closed ring of thinwalled stereome, which surrounds the peripheral
mestome-bundles completely and separates the cortex from the pith. The peripheral mestome-
strands are thus supported by stereome on all sides; they are collateral and have many very wide
vessels, which cover the sides of the Ieptome in the shape of the letter V. The thinwalled pith
contains no starch or raphides. but is traversed by a few mestome-bundles, with a little stereome
on the leptome-side.

THE LEAVES.

The stomata show the same structure as those of the stem, and they occur only on the dorsal
face of the blade. No hairs were observed, but along the margins the epidermis is extended into
roundish warts, which are quite thickwalled. The chlorenchyma contained many cells with
raphides, but we were unable to ascertain whether a palisade-tissue was developed, since our
material had been dried and pressed. The midrib is slightly thicker than the other veins on
account of the presence of a group of collenchyma and water-storage tissue on the leptome-side.

Tradescantia rosea Vent.

The Rhizome.

This species possesses a horizontally creeping rhizome with stretched internodes partly
covered with membranaceous, scale-like leaves and provided with fleshy roots. The ramification
is, as may be seen from our figure (PI. II, fig. 12), monopodial, until the partly subterranean
stem becomes terminated by an inflorescence (I6). The internodes I1 to I' are all horizontal, while
the long internode P is vertical and constitutes the base of an aerial, flowerbearing shoot. Four
axillary, flower-bearing shoots (S'-S1) are developed in this specimen, and the basal internodes
of these have partly fused together with the respective main axes the internodes I3 to P; these
axillary shoots are, of course, aerial and ascending, hut in order to facilitate the view of the
complete rhizome we have drawn all the axes, the main and the lateral, in one plane. Thick and
fleshy roots develop at the nodes of the main rhizome, while some more slender ones are to he
observed at the nodes of the axillary shoots.

The Ramification of the Shoot.

If we examine one of the axillary shoots, for instance, S!. we notice the following structure
(tig. 13): / signifies the scale-like leaf, from the axil of which the shoot has developed: P is the
internode above this leaf. As normally in monocotyledonous plants the first leaf of the lateral
shoot is an addorsed fore-leaf (P1), succeeded by a green leaf (L1), while an inflorescence (S3)
terminates the shoot. In the axil of L', however, another shoot is visible, which also commences
with an addorsed fore-leaf (P'~), succeeded by two alternating green leaves L2 and L3. which sur-
round a minute inflorescence of third order; this inflorescence stays dormant until the following
season. If we compare now the diagram of Tradescantia (tig. 13) with those of Commelina (tigs.
9 and 11), we notice at once that all the leaves, the fore-leaves and the green ones, alternate with
each other in Tradescantia, while in Commelina the green leaves are turned 90 to the side of
the fore-leaf.

The Internal Structure of the Vegetative Organs.

the roots.

A thick, secondary root, examined near the apex, shows the following structure: The thin-
walled epidermis is exceedingly hairy, and covers an exodermis, which consists of a single layer
and of which the cellwalls are folded and very slightly thickened. The cortex is represented by
about eight strata with narrow intercellular spaces and with large deposits of starch. The
endodermis is moderately thickened and surrounds a thinwalled pericambium, which is continu-
ous in some of these secondary roots, but interrupted in others. When such interruptions were

176 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

noticed, it was generally only a few of the proto-hadrome vessels that had broken through the
pericambium— for instance, two rays in pentarchic roots. The hadromatic rays are short, con-
sisting only of one wide, central, reticulated, and a few much narrower scalariform vessels.
Theleptome is well developed and the proto-leptome cell plainly visible. By examining this same
root near the base we noticed that the cortex and endodermis had become considerably thick-
walled and porous. (PI. VII, fig. 42. ) The somewhat thinner lateral roots show the same
structure as the secondary, described above, with the only exception that the cortical paren-
chyma is less developed, and consists of only two or three strata; moreover, the pericambium is
mostly interrupted by all the proto-hadrome- vessels. These interruptions of the pericambium
appear, however, as being very .irregular, and we noticed, for instance, that in one root this
tissue was continuous in some places, but interrupted in others, besides that it was either inter-
rupted by all the proto-hadrome vessels or only by two or three of these in tetrarchic roots.

The roots, especially the secondary, of Tradescantia rosea arc thus contractile, and at the
same time storage-roots.

THE KHIZOME.

The structure of the horizontal internodes is identical and may be described as follows: The
internodes are cylindric and smooth, covered by a thick, wrinkled cuticle. The outer cell-walls
of epidermis are moderately thickened, and stomata with the guard-cells raised (PI. VII, tig. 45)
occur on the upper face of the rhizome, where also chlorophyll was observed. There is no col-
lenchyma. and the cortex borders thus directly on epidermis. The cortical tissue is slightly thick-
walled and quite compact; it contains starch and raphides. The mestome-strands are arranged
in two concentric bands, sixteen peripheral and live near the center. Of these the peripheral are-
supported by one or sometimes two layers of thickwalled cells, which resemble stereome; the lep-
tome is mostly covered by the hadrome on the sides. In regard to the inner band of mestome-
bundles these show the same structure, bat their mechanical support is much weaker and each
contains a wide lacune with an annular vessel. The pith is thinwalled and contains no starch.

The sixth internode (I11 in tig. 12) is almost above ground and differs from the others,
the horizontal, by being hemic ylindric and densely hairy. The cuticle is thick and prominently
wrinkled. Epidermis is quite thickwalled and the outer cell-walls show several and very
distinct longitudinal ridges; stomata and clavate hairs were observed. Two to three layers of
collenchyma in isolated groups are located beneath the epidermis. The cortical parenchyma is
thinwalled and very open from wide intercellular spaces; ii contains a little chlorophyll and
passes gradually over into the central pith, the cells of which are much larger. Two concentric
bands of mestome-bundles traverse this internode, there being eighteen peripheral and about five
near the center. The peripheral are located in the cortex in the same radius as the groups of
collenchyma. though separated from these by the cortex, and several of these are almost lepto-
centric, since the leptome is more or less surrounded by the vessels; no stereome was observed.
The innermost mestome-strands are all collateral and somewhat larger than the peripheral; they
are located in the pith, which is thinwalled and which contains no deposits of starch.

THE STEM ABOVE GROUND.

The basal internodes show exactly the same structure as the sixth internode of the rhizome,
described above. If we, on the other hand, examine the upper portion of the stem near the
inflorescence we notice some slight modification in structure, which principally depends upon
the number of the mestome-bundles. These are present in a smaller number, only nine periph-
eral and seven near the center; they constitute two bands, which are not quite concentric, but
the mestome shows the same position as described above, the leptome being almost surrounded
by the hadrome in the peripheral as well as in the central strands. The upper internodes are
cylindric, glabrous, and smooth, but exhibit otherwise the same structure as the basal in regard
to cuticle, epidermis, collenchyma, cortex, and pith. No stereome was observed, and the cortical
parenchyma did not show the innermost stratum differentiated as an endodermis.

NORTH AND CENTRAL AMERICAN COMMELINACE^E— HOLM. 177

THE LEAVES.

The green leaves are very narrow, with a broad hut shallow groove on the upper face. The
cuticle is thin and wrinkled. Epidermis, viewed en face, consists of rectangular cells and has no
hairs or stomata on the upper face of the blade. On the lower face of the leaf-blade epidermis
shows the same structure outside the collenchyma, hut not where it covers the chlorenchyma.
Because we notice here that the cells are more quadratic; besides that stomata and hairs occur in
abundance. The stomata have two subsidiary cells parallel with the stoma and are level with
epidermis; the air-chamber is shallow, but wide. Hairs of two kinds were observed — short, cla-
vate and long, straight, sharply pointed, four-celled; these hairs, (specially the clavate, cover
the lower surface of the blade, especially underneath the chlorenchyma.

A transverse section of the blade shows that the cells of epidermis are much smaller on the
dorsal face than on the ventral, besides that the outer cell-walls are moderately thickened.
Beneath the entire ventral epidermis is a large water -storage tissue, which only consists of two
layers, but of which the cells are very large and thinwalled. Tin1 ventral face of the blade is
thus occupied by a large-celled epidermis and a hypodermal water-storage tissue, which reminds
very much of some bulliform cells of certain <• 'nimin, ;<-, Cyperacea?, etc.

The chlorenchyma represents an almost homogeneous tissue of somewhat oblong or roundish
cells (in transverse sections) and with wide intercellular spaces. It is developed as a very open
pneumatic tissue underneath the water-storage tissue on the ventral face, but near the margins
where this tissue ceases a few palisade cells were observed. On the dorsal face of the blade the
chlorenchyma is more compact, and some of the cells show actually the shape of true palisades,
vertical on the leaf-surface. Near the mestome-bundles the chlorenchyma shows also here and
there some palisades, but we can not say that a typical palisade-tissue was developed in any parts
of the leaf-blade.

The mestome-bundles are arranged in one plane and are supported by a few cells of hypo-
dermal collenchyma on the leptome-side. The mestome-strands are thus embedded in the chlo-
renchyma. and are surrounded by a colorless, thinwalled parenchyma-sheath. The midvein is
larger than the others and is not projecting. There are fourteen mestome-bundles in the blade,
seven large and seven much smaller, arranged very regularly in alternation with each other: the
leptome is rather small in comparison with the hadrome, which contains about live scalariform
vessels and a large lacune with an annular.

Toward the apex of the blade the margins become involute, forming an almost closed channel
on the ventral face.

THE FORE-LEAVES.

A fore-leaf of a 3Toung. vegetative shoot from near the base of a flower-bearing stem is
tubular, membranaceous, and hyaline. The cuticle is thin, but wrinkled (PI. VII, tig. -14); epi-
dermis is thinwalled and glabrous; it constitutes the only tissue between the two ribs and has
but a few stomata. The chlorenchyma is very poorly developed as an open tissue, almost desti-
tute of chlorophyll, and is only to be observed around the mestome-strands. which form two
prominent keels, one on each side of the tube. The leptome and hadrome are quite well differen-
tiated and surrounded by a colorless parenchyma-sheath, but without any support of mechanical
tissue such as collenchyma or stereome. The fore-leaf has thus two projecting ribs, of which
the one is somewhat more conspicuous than the other, since it contains a small mestome-strand
besides the larger one; the leaf is, therefore, actually three-nerved instead of two-nerved, the
latter being, however, the most common case among the Monocotyledon.es.

Tradesccmtia Virginica L.

The Rhizome.

The minor structure of the rhizome has been very carefully described and figured by Gravis
(1. c). who studied the development of the stem from seedling to matured plant. When culti-
vated in gardens our species grows in dense tufts and the rhizome is thus very densely matted.

178 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

But in its natural .surroundings, in woods or among rocks on the river-shores, the plant does not
show such profuse development of shoots, and the rhizome is consequently much less branched.
However, the principal features of the structure are identical, and the following characteristics
may be mentioned: The rhizome is at Hist creeping, and during the life of the plant some of the
shoots develop in this manner with horizontal internod.es, while the majority of the buds under-
ground develop immediately into ascending shoots. The internodes of the rhizome are usually
short and densely covered with membranaceous, sheathing leaves like the base of the aerial stem.
All these leaves subtend axillary buds, and the biseriate arrangement of the leaves is readily
recognized by the very regular position of the buds upon the rhizome in two rows. The root-
system is represented by numerous fleshy though rather slender roots, which develop from all
sides of the nodes.

The Internal Structure of the Vegetative Organs.
the ROOTS.

The secondary roots are quite long, rather slender and sparingly branched; their color is
dark brown, and their surface shows a very pronounced wrinkling. They represent a combination
of contractile- and storage-roots. Lateral roots occur, but these are mostly filiform and of short
duration.

In the secondary roots the epidermis is thinwalled and hairy: it becomes suberized at an
early stage and covers the old roots as a stratum of partly collapsed cells. Inside the epidermis
is an exodermis of a single layer, the cells of which are thinwalled and in which the radial walls
are very prominently folded (PI. VII, fig. -±3). The cortical parenchyma consists of many strata
of thinwalled cells with distinct intercellular spaces and sometimes with lacunes near the
periphery; deposits of starch and cells with raphides were observed in the cortex. A thinwalled
endodermis with the Casparyan spots plainly visible surrounds the central cylinder. The peri-
cambium, which is thinwalled, was found to. be continuous in all the secondary roots examined.
The hadrome forms about ten rays, of which the innermost vessels are reticulated and very wide,
surrounding a central group of thinwalled conjunctive tissue. The leptome is well developed
and shows the proto-leptome cell very plainly.

A similar structure was noticed in the lateral roots, but only in some of these was the
exodermis observed. We might also mention that the center of these roots was constantly
occupied by a wide reticulated vessel and that the pericambium was interrupted by some of the
proto-hadrome vessels. These interruptions appeared, however, as being very irregular; in
lateral roots of first order one proto-hadrome vessel out of six rays had broken through, while
in lateral roots of second order two vessels out of four rays were bordering on endodermis.

THE STEM ABOVE GROUND.

The basal internode is smooth and glabrous. A thin, smooth cuticle covers the epidermis,
of which the outer and partly also the radial cellwalls are somewhat thickened. About four
strata of thickwalled collenchyma separate epidermis from the cortex, which constitutes about
six quite compact layers, rilled with chlorophyll and some raphides. Inside the cortex is a
closed sheath of stereome in one to two layers, which surround the niestome-bundles. These are
arranged in three almost concentric bands; those of the peripheral band border directly with
their leptome on the stereome. They are often approximately perihadromatic, due to anasto-
moses, and the hadrome contains several wide reticulated, some narrower scalariform, besides an
annular vessel in a lacune. The niestome-bundles of the innermost two bands are not so numer-
ous as the peripheral; they are mostly collateral and are very conspicuous by containing large
lacunes with remnants of annular vessels. "Thyllen" were frequently observed in these vessels.

The mestome-strands are thus located in the pith, and none of these were surrounded by
parenchyma- or by mestome-sheaths. The pith is thinwalled, and shows very distinct intercellu-
lar spaces; cells containing raphides were observed in the pith, but no starch.

NORTH AND CENTRAL AMERICAN COMMELINACEjE— HOLM. 179

The third internode above the basal bears a green leaf with an axillary, small inflorescence.
The structure of the cuticle, epidermis, and collenchyma is as described above, but the cortex is
more open. The stereome surrounds here four concentric bands of mestome-bundles, which are
mostly regularly collateral.

The upper internodes are hairy from two-celled hairs, of which the apical cell is very long
and pointed, straight or slightly curved, but not hooked as we noticed in Commelina. Stomata
abound, and are located in longitudinal rows. They have one pair of subsidiary cells parallel
with the stoma. Otherwise the epidermis shows the same structure as in the lower internodes.
The cortex is very open and borders outward on a collenchymatic tissue, inward on a sheath of
stereome. The mestome-bundles are also here arranged in four almost concentric bands, but are
mostly perihadromatic. The pith is thinwalled and not broken.

THE FLOWERING PEDUNCLE.

The stem-structure is readily recognized in the peduncle, since the tissues are arranged in
the same manner, but developed somewhat differently. Epidermis is much more hairy from
very long, pointed hairs, mixed with some glandular. The collenchyma and stereome are both
quite thinwalled, and the mestome-bundles occur here in only two concentric bands, of which
the peripheral are more or less fused together, two and two.

THE STEM-LEAVES.

The green leaves are smooth and glabrous on the ventral, but hairy on the dorsal face.
Viewed en face the radial cell-walls of epidermis are straight, not undulate: the hairs are short
and pointed. Stomata occur on both faces of the blade, but are most numerous on the dorsal.
They are surrounded by four cells, of which the one pair is parallel with the stoma. The guard-
cells are mostly raised a little above the surrounding epidermis. Viewed in cross-sections the
cells of epidermis are quite large on both faces, especially on the ventral, where it covers three
to four strata of colorless thinwalled cells above the midrib. Similar but smaller groups of
colorless cells were, furthermore, noticed between the other veins, but only on the ventral face.
A collenchymatic tissue of two or three strata is developed below the midrib and the stronger
veins, but is entirely absent from the ventral portion of the leaf-blade.

The mesophyll represents an almost homogeneous tissue of irregular cells with wide inter-
cellular spaces. Some few palisade cells were observed, however, on the ventral face, but only
in the lateral parts of the blade, and without forming a distinct tissue, ('ells with raphides
abound in the mesophyll. especially near epidermis.

The mestome-strands possess a thinwalled parenchyma-sheath, which does not contain
chlorophyll, and is therefore readily distinguished from the surrounding cells of the mesophyll.
The midvein is barely larger than the others, but is prominent by its larger support of collen-
chyma. The leptome and hadrome are w?ell developed, and show the usual structure, the
mestome-bundles being all collateral.

Tradescantia scopulorum Rose.

The Ramification of the Shoot.

The rhizome is very short and bears many slender, but somewhat Meshy roots, which are
almost unbranched; it resembles that of T. Virginica. The aerial stems are erect and branched
from near the base. These lateral branches begin, as usually, with an addorsed fore-leaf, tin1
shape of which is quite characteristic; it is membranaceous and consists of u tubular sheath and
a very distinct blade, reaching until 15 milimeters in length. This fore-leaf is thus only partly
covered by the sheath of the stem-leaf, which supports the lateral branch. The other leaves of
the branches are green and alternate with the fore-leaf, showing the same position as described
above under Tradescantia rosea. It appears us if the branches become terminated by inflores-
cences, but these are usually not so rich-flowered as the one that terminates the main shoot.

180 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

The Internal Structure of the Vegetative Organs.

the roots.

The secondary roots show the structure as follows: The epidermis is hairy and covers au
exodermis of large cells with the walls thin and distinctly folded. The cortex is differentiated
into three zones, a peripheral which consists of about four strata of relatively small cells, an inner
of about ten layers of large cells tilled with starch, and finally an endodermis. The endodermis
is thinwalled, showing the Casparyan spots very plainly: it did not contain starch. The
pericambium is thinwalled and continuous. The hadrome forms eight short rays, in which the
protohadrome vessels were observed to be mostly single or sometimes two arranged side In side.
Broad groups of leptome alternate with the hadromatic rays, and a few strata of thinwalled
conjunctive tissue surround the two central, reticulated and very wide vessels.

THE STEM ABOVE GROUND.

The internodes from the middle of the stem are cylindric, furrowed, and hairy. The hairs
are of the same kind as observed in 7. Virginica, lone- and pointed or short and clavate.
Epidermis is moderately thickened and covered by a thin, smooth cuticle. A thickwalled
collenchyma of about six layers, but in isolated groups, separate the epidermis from the cortical
parenchyma. The cortex is very thinwalled and consists of only four or five layers; it contained
chlorophyll. Inside the cortex is a closed sheath of stereome in one or two layers, but the cells
are rather thinwalled. Three almost concentric bands of mestome-bundles traverse the inner
part of the stem: the peripheral border directly on the stereome with their leptome, while the
two inner hands are located in the pith.

THE STEM-LEAVES.

The blade is glabrous and smooth, with a thin, but distinct cuticle. Epidermis consists of
large cells on both faces of the blade, and the outer cell-walls are slightly thickened on the dorsal:
stomata occur on both faces and the subsidiary cells are raised above the surrounding epidermis.
Prominent groups of thickwalled collenchyma cover the leptome-side of the larger mestome-
bundles; besides that an isolated group of this tissue occupies the outermost portion of the leaf-
margin. The chlorenchyma is poorly developed, and consists only of a few laj'ers of roundish
cells. The mestome-strands possess a thinwalled parenchyma-sheath, and show the same structure
as observed in T. Virginica.

Tradescantia sp. — While the specimens of T. scopulorum, described above, were collected in
the mountains of Arizona, there is still another western member of the genus which inhabits the
alkaline plains of Colorado. This Tradescantia is by Mr. Rose included in his scopulorum, but
it appears to be distinct from this. It is a much coarser plant, with larger flowers and broader
leaves; the fore-leaves are destitute of blades, and the broad calyx-leaves and peduncles are very
hairy. The anatomical structure is somewhat different and may be described as follows:

THE HOOTS.

The secondary roots are fleshy, but slender and ramify but sparingly. Epidermis is thin-
walled and very hairy; it covers an exodermis of large, pentagonal cells, the walls of which are
thin ami prominently folded. The cortex consists of twelve compact layers of thinwalled
parenchyma, filled with starch. Endodermis and the pericambium are thinwalled, continuous.
There are six short, hadromatic rays alternating with six broad groups of leptome; the proto-
hadrome-vessels are very narrow, and are present in the number of two or three situated side by
side. The conjunctive tissue is thinwalled. and does not extend to the center of the root, which
is occupied bjr three wide, reticulated vessels.

NORTH AND CENTRAL AMERICAN COMMELIXACE.E— HOLM. 181

THE STEM ABOVE liKOUND.

The stem is cylindric, deeply furrowed. The, smooth cuticle covers a very thickwalled
epidermis with stomata, but without hairs. A very thickwalled collenchyma occurs as isolated
groups beneath the epidermis and borders on a narrow zone of thinwalled cortical parenchyma.
A closed ring of rather thinwalled stereome surrounds the central cylinder in which the mestome-
bundles are arranged in a few bands of the same structure as described above. The pith is thin-
walled and does not contain starch.

THE STEM-LEAVES.

The ventral face "I' the blade is smooth and glabrous, while the dorsal is distinctly furrowed.
Stomata with one pair of subsidiary cells occur on both faces; they arc level with epidermis,
but the subsidiary cells were observed to be somewhat raised on the ventral face. The cuticle is
smooth and very distinct. Epidermis consists of large cells on both faces, and the outer walls
are quite thick on the dorsal, but thin on the ventral face. Two or three strata of colorless cells
(water-storage tissue) arc located beneath the entire ventral epidermis. A few, one or two,
layers of thickwalled collenchyma were observed on the leptome-side of the larger veins, but
separated from these by small groups of water-storage tissue; no collenchyma or stereome was
observed on the ventral face of the blade, but a few layers of the former occupy the margins.
The chlorenchynia contains much chlorophyll and represents a homogeneous tissue of oblong
cells, but of no palisades. A thinwalled colorless parenchyma-sheath surrounds the mestome-
bundles in which the leptome and hadrome are well developed in the larger of these. No
lacunes were observed in the leaf; thus the structure is quite compact throughout.

Tradescantia crassifolia (Javan.

The species is perennial with erect or ascending villous stems, simple or branched. The
leaves are oblong, acute, densely villous, and thick. There are about five sessile inflorescences,
one terminal and four axillary, remote. The roots are fusiform, very thick, and develop from
the basal nodes. Our specimens were dried, thus we were unable to examine the internal
structure, of the parts above, ground, but we succeeded in preparing some of the roots so as to
study their structure.

The roots are tuberous at the middle, but rather slender toward the base and apex. Epider-
mis is very hairy and covers an exodermis of a single layer of thinwalled cells; no foldings were
observed. Inside the exodermis are five to six strata of sterei'ds, which are not very thickwalled
and of which the cross-walls are barely oblique. These tissues show the same structure in the
slender and tuberous portions of the root, but the cortex and the pith are somewhat different.
The cortical parenchyma consists of ten layers in the tuberous portion: the cells are thinwalled
with narrow intercellular spaces. The innermost four layers were tilled with starch, bordering
on a thinwalled endodermis. A thinwalled pericambium surrounds numerous very short rays of
hadrome. alternating with broad groups of leptome; the position of the proto-hadrome vessels
could not be ascertained. The pith occupies the larger part of the central cylinder, and consists
of numerous compact strata of which the peripheral, two or three, are densely filled with starch.

If we now examine the slender portions of these roots, we notice the complete absence of
starch in the cortex and in the pith; moreover the pith occupies here only a small portion of the
central-cylinder, while the number of layers in the cortical parenchyma is the same, but the
lumen of the cells much smaller. The roots of this species represent, thus, a combination of two
types — nutritive and storage roots.

Tradescantia pinetorwm Greene.

(T. tuberosa Greene — non Roxb.)

This species possesses a long, creeping rhizome with cylindrical, stretched internodes from
3 to 5 centimeters in length. There are roots, from one to three at each node, which are very
thick and hairy; they vary from oblong to fusiform at the base and are terminated by a long,

182 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

very slender apex with several lateral ramifications; the length of the tuberous portion is about
2 centimeters, the thickness about 1 centimeter. Besides these there are, furthermore, some
that are filiform in their whole length. The leaves of the rhizome are membranaceous and buds
were observed in the axils of these. The stem above ground is the direct continuation of the
rhizome and all the internodes, even the basal, are stretched; it is erect and bears several leaves
with narrowly linear, conduplicate blades. Vegetative shoots are sometimes developed in the
axils of the lowest stem-leaves and there is usually only one terminal inflorescence unless the
lateral shoots develop further and become flower-bearing. The arrangement of the leaves is the
same as that described above as characteristic of the genus.

Tradescantia Florid ana Wats.

The Ramification of the Shoot.

The species shows the habit of Commelina nudiflora; there is no rhizome, and the long,
slender stem is creeping with the lateral branches erect or ascending; the stem-leaves are sessile
with short sheaths and ovate blades. The lateral branches bear a short, membranaceous and
tubular fore-leaf at the base and it seems characteristic of this species that the lateral shoots,
although strictly axillary, break through the base of the sheath of the supporting leaf, thus the
shoot with its fore-leaf becomes perfectly free. The other leaves of the shoots show the same
shape as the supporting leaf, but it was frequently observed, however, that the first leaf above
the proph3'llon was merely developed as a sheath with a minute, rudimentary blade. In regard
to the diagram of the axillary shoot, we noticed exactly the same position of the leaves as
described under Commelina. The small inflorescence is terminal, sometimes accompanied by a
few lateral, developed in the axils of the uppermost leaves. The stems are rooting, one to two
secondary roots being developed at each node.

The Internal Structure of the Vegetative Organs.

the ROOTS.

The secondary roots are very thin and ramify freely: they are very hairy and the thinwalled
epidermis covers a large-celled exodermis, of which the outer cellwalls are slightly thickened;
no foldings were observed, thus the root is not contractile. The cortex consists of three compact
strata of thinwalled cells, and the endodermis is moderately thickened on the inner and radial
walls. The pericambium is thinwalled and continuous. Six very short rays of hadrome alter-
nate with six broad groups of leptome. while the center is occupied by two very wide, reticulated
vessels. The conjunctive tissue is poorly represented and very thinwalled.

THE STEM.

Clavate hairs abound, and the outer cellwall of epidermis shows numerous longitudinal ridges,
covered by the thin and smooth cuticle. A collenchymatic tissue was observed beneath the
epidermis, but very poorly developed. The cortex constitutes a narrow zone of parenchyma,
containing chlorophyll. No stereome was observed, thus the thinwalled endodermis surrounds
the central-cylinder directly. Two bands of mestome-bundles traverse the stem, the peripheral
bordering on endodermis, while the innermost are located in the thinwalled but solid pith.

THE STEM-LEAVES.

Viewed en face epidermis of both faces of the blade shows the same structure, viz: Polyedric
cells with tin1 walls straight and very thin. Clavate hairs abound on the dorsal face together
with the stomata, which possess two pairs of subsidiary cells parallel witli the stoma; two-celled,
sharply pointed hairs cover the margins, rendering these very scabrous. Viewed in transverse
sections epidermis shows large cells on both faces, and the outer wall is extended into a
number of minute, wartlike papillre, covered by a thin and smooth cuticle; these papillae

NORTH AND CENTRAL AMERICAN COMMELINACELE— HOLM. 183

occur, however, only on the ventral face of the blade. No collenchvnia and no stereome was
observed, and the chlorenchyma represents a homogeneous tissue of mostly roundish cells, tilled
with chlorophyll and raphides. The veins arc very tine and possess no mechanical support.

Tradescantia micrantha Torr.

The stems are weak, decumbent, and often rooting at the nodes. The small, ovate leaves are
alternate, and the species reminds very much of the former, T. Floridana, in respect to its habit.
The roots, about live at each node, are very thin and show several minute ramifications; they are
not confined to the one face of the nodes, but develop all around these. The stems are profusely
branched, and the axillary branches begin with a fore-leaf, which is membranaceous, very short,
tubular, and truncate. In regard to the axillary buds, these do not break through the sheath of
the supporting leaf, and the diagram of the shoot with its leaves and inflorescence corresponds
with that of Tradescantia rosea, as described in the preceding.

In some of the specimens which we have examined the lateral branches bore a number of
leaves, developed as mere sheaths with minute blades, as if they were subterranean.

Tradescantia Warszewicziana Kunth et Bouche.

This remarkable Tradescantia is figured in Curtis's Botanical Magazine." and one of the
figures shows an entire plant with "the stem stout, forked, terete, having a subarborescent
character, and marked with the scars of fallen leaves. The branches are leaf}', chiefly toward
the apex/' The peduncle is figured and described as ""axillary, 1 to 1£ feet long, terete, purplish
above, fcniing a not very copiously branched panicle of purple-lilac densely crowded but small
flowers." The habit of the plant, considering the stem and the foliage, is thus much more like
that of an Aloe or a Draca mi than of a Tradescantia. The internodes of the stem are exceedingly
short, and the leaves are crowded. The relatively short and compact inflorescence is borne upon
a long, naked scape, which is axillary. The bracts that subtend the inflorescential branches are
very short and broad. In regard to the flowers, the sepals and petals are uniform and purplish,
the latter the largest; the stamens are all uniform and beardless. In spite of these very pronounced
habital characters the .species is by Clarke placed in his section: Eutradescantia; we do not
consider this classification a natural one, for even if the floral characters may be identical, to some
extent, the habit of the plant in connection with certain points in its anatomical structure make
us believe that the species really represents a section of its own.

With Planchon our species was a Dichorisamlra; with Hasskarl a Spirmn ma (fide Clarke 1. c. ).

The Internal Structure of the Vegetative Organs.

the ROOTS.

Numerous long, whitish and somewhat fleshy secondary roots are developed from the
nodes, and they are amply ramified. Their structure is as follows:

The epidermis is very hairy, and there is an exodermis of one layer of pentagonal cells with
the outer walls moderately thickened, and with the radial walls very distinctly folded. Cortex
consists of about ten layers of thinwalled cells arranged radially toward endodermis. No starch
or raphides were observed. The endodermis is thickwalled in the manner of an U-endodermis
and is very porous. A thinwalled, continuous pericambium surrounds sixteen short rays of
hadrome with some narrow (spiral) and a few wider (reticulated) vessels; the proto-hadrome-
vessels were noticed to be single in each ray. The leptome is well developed and represents
round groups in transverse sections, with the proto-leptome cell plainly visible. The center of
the root is occupied by a narrow group of thickwalled conjunctive tissue.

a Vol. 16, Tab. 5188.

184 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

THE STEM.

The stout stem, which bears the rosette of leaves, is cylindrical. In the older internodes
several strata of cork have replaced the epidermis, while in the younger portions the epidermis
is still preserved and consists of thinwalled cells. From epidermis to the center of the internode
a large parenchyma is developed of very uniform structure, and not interrupted by any sheaths
of collenchyma, endodermis or stereome. In other words the peripheral cortex passes insensibly
over into the central pith. Both tissues are thinwalled and contain raphides and deposits of
starch, but in some of the outermost strata of the cortex (in younger internodes) chlorophyll
was, also, observed. The outer mestome-bundles are arranged in several peripheral and concen-
tric bands, while the inner ones, the most numerous, are scattered among each other in no order.
A thinwalled parenchyma-sheath is developed around each mestome-bundle, but otherwise their
structure is somewhat different. The peripheral bands are of more or less typical, collateral
structure, while the inner ones are very variable, representing several transitions from almost
collateral to strictly lepto-centric, with a number of wide, reticulated vessels inclosing the
leptome completely. The structure of the older internodes, which we have thus examined
reminds more of that of a rhizome than of a stem above-ground; we mention this, because Mr.
Maxon, who collected the specimens and who found the plant in great abundance, did not notice
any such large stem-portion above ground as figured in Curtis's Botanical Magazine (1. a). The
stems were in accordance with his observations mostly subterranean, and the leaves of the
rosette were not recurved, but ascending to almost erect.

THE SCAPE.

The long internode that bears the inflorescence is cylindric and almost glabrous. A thin
but distinct cuticle covers the epidermis, consisting of long rectangular cells when viewed en
face. Stomata with one pair of subsidiary cells parallel with the stoma are arranged in
longitudinal rows alternating with strata in which clavate hairs and short, roundish papillae
occur. In cross-sections the cells of epidermis show a prominent thickening of the outer walls.
Underneath epidermis are many broad groups of thickwalled collenchyma. The cortex contains
much chlorophyll, but occupies only a small portion of the scape; it extends to the epidermis
between the collehchymatic strands. A sheath of very thinwalled stereome surrounds the central
cylinder and borders directly on the innermost strata of the cortical parenchyma; it consists
of about four layers and separates the cortex from the pith. The mestome-bundles constitute
one peripheral band of about thirty-five, and several inside these, but apparently scattered. The
peripheral are approximately V-shaped and contain several wide reticulated vessels and a lacune
with the remnants of a ring-vessel; besides being surrounded by the stereomatic sheath, as
mentioned above, they have, furthermore, a few layers of more thickwalled stereome on the
leptome-side. The central mestome-bundles did not show any mechanical support; they traverse
the pith, which is compact but very thinwalled.

THE LEAVES.

The green leaves have a broad lanceolate and acuminate blade and a short sheath; their
length averages about 15 centimeters, their width about -i centimeters. Epidermis of the dorsal
face shows a very characteristic structure. Viewed en face the outer wall of many of the cells
shows a number of minute roundish warts (PI. VIII, fig. 48) covered by a thin, perfectly smooth
cuticle; the shape of the cells is hexagonal with straight radial walls. Stomata abound on this
fare of the blade (the dorsal); they have one pair of subsidiary cells parallel with the stoma, and
one pair vertical on this, thus the stoma is surrounded by four cells, all containing chlorophyll.
Hairs are frequent; they are composed of three cells, of which the apical is quite long and obtuse.
Besides these obtuse hairs, some others with the apical cell sharply pointed and curved occur
along the leaf-margins, rendering these very scabrous. The ventral epidermis shows the same
structure of the cells, but no stomata or hairs were observed here.

NORTH AND CENTRAL AMERICAN COMMELINACEiE— HOLM. 185

A transverse section of the blade shows the following- structure: Epidermis consists of rathei
low cells on both faces (tig. -±7), and the thickening of the outer walls is very distinct in some of
the cells; the stomata are level with epidermis, and the air-chamber is wide, but shallow. Under-
neath the ventral epidermis is a large water-storage-tissue, which occupies the entire upper face
of the blade without being interrupted by the chlorenchyma or by any strands of mechanical
tissue. It reaches its highest development above the middle portion of the blade and decreases
in thickness toward the margins. This water-storage-tissue consists of three layers of cells that
are much larger than those of epidermis: the innermost layer is the thickest on account of the
greater height of the cells. When exposed to a dry atmosphere the cells of this tissue shrink
rapidly by foldings of the radial cell-walls. A like tissue, but of smaller dimensions, occurs
also beneath the dorsal epidermis. The chlorenchyma is differentiated into one to two layers
of short palisades on the ventral face and a larger pneumatic tissue on the dorsal. The
palisades are best developed near the margins of the blade where the water-storage-tissue is not
so thick. The cells of the pneumatic tissue are somewhat irregular, more or less star-shaped,
and they contain much chlorophyll. Cells with r aphides were observed inside the ventral
water-storage-tissue and above the palisades. While the chlorenchyma on the ventral face of the
blade is completely separated from epidermis by the continuous strata of water-storage- tissue, it
does reach the dorsal epidermis by narrow rays, which thus interrupt the colorless-tissue, but
only here and there between the veins. The mechanical tissue is weakly developed as an isolated
strand of stereome in each margin and as a few layers on the leptome-side of the veins. No
collenchyma was observed. The mestome-bundles are collateral and very small; they possess a
thinwalled parenchyma-sheath, a small group of leptome, and a few vessels.

Weldenia c<ni<li<l<< Schtjlt. fil.

The first description and illustration of this remarkable plant was published in Flora
(January, 1829), by J. H. Schultes. jr., who received a specimen from Mexico collected by
v. Karbinsky. The genus is dedicated to Baron v. Welden, an Austrian botanist. Ten years
later the plant was described by Bentham" as a new genus Lampra volca/nica, and his material
came from Volcan de Agua. at an elevation of about 14.0o0 feet, in Guatemala. Since then the
plant has been collected in a few other places, in Sierra delas Cruces and Ojo Caliente, Zacatecas,
both in Mexico. It is fairly well illustrated by Sir Joseph Hooker.'' but the drawing, which
was based upon dried material, does not show the petals correctly. The petals are not spreading,
but almost erect in accordance with a photograph taken by Macgraw Coxe, United States
minister to Guatemala and Honduras (IsHT).

The Ramification' of the Shoot.

The plant is a perennial herb provided with a dense cluster of fusiform roots developed from
the basal nodes of the shoot. The shoot is single, judging from the material that has been exam-
ined, and consists of a few short or sometimes more or less stretched internodes which bear mem-
branaceous sheathing leaves without blades. Two buds, one larger and one smaller, and both
evidently dormant, are generally found at the base of the flowering shoot: these buds are situ-
ated somewhat lower than the flowering shoot, and they belong to basal leaves of the shoot
of the previous year. If we now examine the structure of the flowering shoot of this season we
notice (PI. VIII, fig. 49) five membranaceous leaves alternating with each other (/'-/); the inter-
nodes, especially the basal, are very short, while the upper ones (between I3 and Is) are longer,
from two to five cm. in length. Three axillary buds are developed, and these belong to /'. /',
and /3; it appears as if the bud in the axil of /3 is the one that will develop) into a floral shoot dur-
ing the succeeding year, and that the two others correspond with the two dormant ones at the
base of the shoot of last year's growth. The other leaves of the flowering shoot form a rosette

oPlantse Hartwegianse. London. 1839.

&Icones plantarum. S;er. 3, vol. 3, 1S77-1S7H, p. 28, tab. 1236.

186 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

and are provided with green blades, but onlv the first one of these, L1, alternates with the
membranaceous; the four succeeding are turned 90° to the side (L2-L5), and we noticed, fur-
thermore, that the two outermost (L2 and L3) were united at the base, forming a closed sheath
around the inner ones. Wh-ile thus the leaves described above are arranged alternately, but
in two planes, the succeeding (6-13) represent a spiral and surround the terminal inflorescence.
The numerous flowers are almost sessile and are destitute of bracts and fore-leaves; the central
is the first one to bloom, and judging from the rudimentary stage of the peripheral flower-buds
the time of flowering must extend to several months with onlv a few (two ?) flowers developed
at the same time.

While thus the subterranean stem-portion of Weldenia often possesses a few stretched inter-
nodes, the aerial shoot is merely represented by a dense rosette of green leaves surrounding the
sessile many-flowered inflorescence, which is of the centrifugal type.

The Internal Structure of the Vegetative Organs.

the roots.

Most of the roots are thick and fusiform, but some few thin and cylindric ones were also
observed. These slender roots were developed at the base of the dormant buds, and they show
the structure as follows: The thinwalled and hairy epidermis covers an exodermis of two la}Ters,
of which the cellwalls are not contractile. The cortex consists of ten layers; the cells are very
thinwalled and are arranged radially toward the endodermis. Deposits of starch were observed
in the innermost strata of the cortical parenchyma. Endodermis is thinwalled and shows the
Casparyan spots very plainly. The pericambium is thinwalled and continuous; it surrounds nine
broad groups of leptome alternating with nine very short rays of hadrome, which consist of one
or, seldom, two spiral proto-hadrome vessels and a single, wide, scalariform inside. A thinwalled
pith without starch occupies the greater part of the central cylinder. No raphides or crystals
were observed.

The fusiform roots consist of a short, slender base, a long tuberous portion, that averages
from 4 to 7 centimeters in length and 6 to 10 millimeters in thickness, and finally of a long,
slender apex.

The slender, basal portion of these fusiform roots is hairy and the exodermis is contractile.
The cortical parenchyma is composed of numerous layers, but only the three innermost are
preserved and contain starch; the others are collapsed. Endodermis is thinwalled and shows
prominent tangential foldings; the pericambium is also thinwalled and continuous. In regard
to the leptome and hadrome we noticed the same structure as described above, but the number of
rays is larger, there being 21, alternating with a corresponding number of leptomatic strands.
The thinwalled pith represents a broad parench}Tma containing starch.

In passing to describe the swollen portion of these same roots, we might state at once that
the structure in general is identical with that of the slender base; the larger dimensions depend
merely upon a larger size of the cells in the cortical parenchyma and in the pith, while the number
of strata is the same. The cortex is, moreover, solid in this portion of the root, and not collapsed.
In the slender apical portion of these same roots the structure is almost the same. However the
exodermis showed no foldings of the cell-walls; the cortex consisted of only 12 layers filled with
starch; the number of hadromatic rays was only 12, and the pith represented a smaller parenchyma.

In regard to the proto-leptome cells the accompanying drawings (PI. VIII, figs. 50 and 51)
illustrate two cases from the swollen portion of these roots. The leptomatic groups are some-
times very broad, and in such cases it appears as if two proto-leptome cells were developed
instead of but one, when the groups are narrower.

the rhizome.

One of the basal stretched internodes shows the following structure. It is cylindric, with a
shallow and narrow groove on the one side. The cuticle is thin and smooth, and covers a thin-
walled epidermis of small cells; viewed en face the cells are narrow and rectangular. A few

NORTH AND CENTRAL AMERICAN COMMELINACE^E— HOLM. 187

stomata, but no hairs, were observed. Cortex consists of ten strata of thinwalled cells, with narrow
intercellular spaces; no starch, but raphides and very little chlorophyll, was observed. The
cortex is not separated from the broad central mass of parenchyma by any sheath of stereome or
by any stratum that might be distinguished as an endodermis. Nevertheless we did notice one
or sometimes two layers of cells that were more closelj- connected with each other than those
of the cortex, and these bordered on the leptome-side of the peripheral mestome-bundles.
Examined in longitudinal sections these cells did not differ from those of the adjoining paren-
chyma, nor did they resist concentrated sulphuric acid any better.

The peripheral mestome-bundles (twenty-five) are arranged in a circle. They are relatively
small and almost orbicular in transverse sections; they are collateral and contain only a few
vessels and a small group of leptome. Resides these regularly arranged peripheral mestome-
strands we find in the central portion of the pith about forty others, which are apparently
scattered and not arranged in any order. These mestome-bundles are larger, since they posses
more leptome and much wider vessels, but they are all collateral like the others. The pith is
thinwalled, quite solid, and contains many raphides, but no deposits of starch.

Characteristic of the stem of Weldenia is the absence of collenchyma and stereome. We
must remember, however, that the stem is subterranean and of relatively short duration.

THE GKEEN LEAVES.

The lanceolate blades are quite thick and smooth. Viewed en face the ventral epidermis
consists of very regular hexagonal cells, some of which are developed into four-celled hairs with
the apical cell very long and obtuse. (PI. VIII, fig. 52.) On the dorsal face the cells show the
same shape, but are much shorter in the stomatiferous strata than between these. The stomata
(PI. VIII, fig. 53) are arranged in longitudinal rows parallel with the longitudinal axis of the
blade; the}' have one pair of subsidiary cells and are slightly raised above the surrounding
epidermal cells: the air-chamber is broad and deep. Between the stomatiferous strata are longi-
tudinal rows of hairs of the same type as described above, but these are very numerous on this
face of the blade, the dorsal, and they are often developed in small tufts of four or five together.
These hairs occur, furthermore, along the margins of the blade. Viewed in transverse
sections the epidermis-cells are thinwalled and rather small on both faces; the cuticle is thin and
smooth. Underneath the ventral epidermis is a large tissue of colorless, thinwalled cells in about
live strata above the middle portion of the blade, but of only one near the margins. This tissue,
composed of large cells, represents a water-storage-tissue and is distributed over the entire ventral
face of the blade, but decreases in thickness toward the apex and the margins. A much narrower
portion of the leaf-blade is occupied by the chlorenchyrna. This consists of two layers of short
palisades which border on the water-storage tissue and of a pneumatic tissue of star-shaped cells
with broad intercellular spaces. The latter tissue is thus located near the dorsal epidermis, from
which it is separated by groups of collenchyma which support the larger veins, while it borders
directly on the epidermis between these. The collenchyma is very thickwalled and is confined
to the leptome side of the mestome bundles. No stereome was observed. Cells with raphides
abound in the chlorenchyrna.

There are ten almost parallel veins which traverse the chlorenchyrna from the base of the
blade to the apex; they are connected with each other by numerous fine anastomoses. The larger
veins are collateral, with the leptome and hadrome well developed and surrounded by a thinwalled,
colorless parenchyma-sheath, but they have no mestome-sheath and no thickwalled niestome-
parenchyma. Tin' anastomoses are much smaller and orbicular in transverse sections.

If we examine the small leaves that surround the inflorescence, we find the same structure as
described in the preceding, but the blade is thinner on account of the lesser development of the
water-storage tissue.

89369°— vol in— n 13

188 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL X, NO. 6.

THE MEMBRANACEOUS LEAVES.

These leaves have a tubular sheath and a minute free blade, and they cover the subterranean
internodes of the stem. They arc perfectly glabrous and smooth, and contain no chlorophyll.
The epidermis is very thinwalled and consists of large cells on both faces, somewhat higher on
the dorsal than on the ventral face. A few layers of a homogeneous chlorenchyma surround the
veins, but between these the leaf consists only of the two epidermes. No collenchyma or
stereome was observed, and the mestome- rands are very thin, but surrounded by a parenchyma
sheath. In regard to the structure of the mestome-bundles we noticed that the hadrome was
better represented than the leptome.

SUMMARY.

These species of C«mmeUnaceae, which we have described in the foregoing pages, thus repre-
sent different types of biological interest: Commelina nudifiora, Tinantia, and Aneilema are
annual; all the others are perennial. Among the latter are some of which the habit resembles
that of the annual species, but which, nevertheless, are able to persist throughout the winter-
months, at least in the southern parts of this continent: Tradescantia Floridana and micrantha;
these maj' be designated as photophilous, their vegetative propagation being secured by axillary
buds developed wholly above ground. The other perennials (except Trad. Warssewicziana) are
scotophilous," in which the herbaceous stems die to the surface of the soil each year, and in which
the vegetative propagation takes place by means of buds developed upon rhizomes. In regard
to Tradescantia Warssewicziana, we feel uncertain about its manner of growth, even if we did
observe that the stem bears some buds underground.

If we now examine and compare the external structure of the rhizomes and the roots with
that of the foliage, we do not notice any definite correlation between these. In our species of
Commelina the foliage is the same whether the species arc annual or perennial, and whether the
rhizomes are horizontally creeping with slender roots (('. hirtella) or very short and provided
with fleshy, thick roots (C. Virginica, etc.). In the genus Tradescantia we meet with species of
which the leaves are long and narrow and of which the rhizomes are either creeping and bearing
tuberous roots (T. jpinetorum) or very compact, with tuberous (7\ crassifolia) or more slender
roots ( T. Virginica, scopulorum). In Weldenia and T. Warszea'ieziana the leaves are fleshy and
arranged in a rosette; in the former the roots are thick and fusiform, in the latter they are
slender and much branched. In some of the other Tra<l>sc,i,ifi;e the habit becomes more like that
of Commelina, -especially iu T. Floridana and micrantha, with their short and broad leaves and
decumbent stems, or with the stems more ascending or erect as in T. eoininelinciides K. et S.,
pulchella H. B. K., and disgrega Ki nth. The position of the leaves, as shown in the diagrams,
and the axillary shoots perforating the leaf-sheaths are also characteristic of certain members of
the family.

While thus several variations exist in regard to the development of the foliage, stems, and
roots, we shall now extend the comparison to the structural peculiarities possessed by the same
organs as represented by these species.

THE ROOTS.

Simply nutritive roots were observed in Cminm Una nmlifftira, Tinantia, Aneilema, and
Tradescantia Florida na ; the slender roots of Weldenia belong to this same category. Nutritive
and at the same time conti-actile are characteristic of T. Warssewicziana and C. hirtella.
Nutritive and at the same time storage-roots were found in Tradiseantia crassifolia. In the
remaining species the roots showed a combination of contractile- and storage- roots. An
exodermis was observed in all the species, and it consists of two layers in Weldenia. Stere'ids
occur in Commelina nudiflora, Virginica, Tradescantia Fl<nii<hni<i and crassifolia; they attain
the highest development in the last species. The cortical parenchyma is partly collapsed in

"Goebel, K., Organographie der Pflanzen, Jena, 1900, p. 645.

NORTH AND CENTRAL AMERICAN COMMELINACEiE— HOLM. 189

Aneilema, but not so in the others. Endodermis was observed to lie. more or less thickwalled in
Connnelhui nudif^ra. Trad< xcantia Floridana, rosea, and Warszewicziana, but thinwalled in the
others. The pericambium is represented by a single layer and is thinwalled in all the species;
it was found to be interrupted by the proto-hadrome in Commelina nudifiora, Virginica, and
Tradescantia rosea. The number of hadromatic rays is, of course, very variable, and the
largest number (twenty-one) was observed in Weldenia. In this same genus the pith is very
well developed and occupies the greater portion of the central-cylinder. In the other species
the pith is generally very little developed.

THE RHIZOMES.

In Tradescantia rosea the cuticle is quite thick and wrinkled, but lather thin and smooth in
the others. Hypodermal strands of collenchyma were observed in Commelina hirtella, but not
in any of the others. The cortical parenchyma is moderately thickwalled in < 'pmm< Una I irginica
and Tradescantia rosea; an endodermis was only noticed in Commelina hirtetta. A continuous
sheath of stereome surrounds the peripheral mestome-bundles in C. hirtella, while in T. rosea
this tissue occurs only as a few layers on the leptome-side. The mestome-bundles of the
peripheral bands are collateral in contrast to some of those of the inner bands, which are very
irregular and more or less leptocentric in T. Warszt wicziana. The pith contains deposits of
starch in Commelina Virginica, hirtella and in T. Warszewicziana, but not in the others; starch
was. furthermore, observed in the cortex of the last species, in C. Virginica and T. rosea.

THE STEM ABOVE O ROUND.

Several hypodermal strata of more or less thickwalled collenchyma was observed in all the
species examined. The innermost layer of cortex is differentiated as an endodermis in the
species of Commelina and Tinantia, also in Tradescantia Floridana, but not in the others. A
closed sheath of stereome surrounds the mestome-bundles in the species of Commelina, Tinantia,
and Tradescantia, with the exception of T. Floridana and rosea. In Aneilema the stereome
occurs only as a few isolated strata on the leptome-side. The mestome-bundles are collateral
and mostly arranged in several concentric bands. Deposits of starch were found in the pith of
C. Virginica and dianthifolia.

THE GREEN LEAVES.

The leaves are dorsiventral in the species of Commelina, and in Tradescantia Warszewi-
cziana, besides in Wrldmia; they are almost dorsiventral in T. Virginica, but isolateral in T.
scopulorum, Floridana, and in Aneilema. These dorsiventral leaves are held in a horizontal
position.

In T. Virginica the chlorenchyma is imperfectly developed as palisades, and in the isolateral
leaves the palisades are totally absent. The leaves of these Tradescantia' are also held in an
almost vertical position, except in T. Floridana; in this species we were unable to discover any
trace of palisades, but our material, having been dried and pressed, was not quite suitable for this
purpose, and it would seem somewhat strange if the leaves of this species, which are held in
horizontal position, should really be isolateral instead of dorsiventral.

In regard to the palisade-tissue, we might state that the palisades observed in '/'. rosea were
not typically7 developed. The pneumatic tissue attains its highest development in Weldenia and
T. Warszewicziana. where it is composed of star-shaped cells, while in the others the shape is
more irregular, but always with wide intercellular spaces.

The mechanical tissue is. to some extent, well represented in the leaves. Collenchyinatic
strands were thus observed above and below the midvein in Commelina nudiflora, Virginica, and
erecta, or below this in Am ilt ma; or only on the leptome-side of the larger veins in C. hirti lla,
dianthifolia, T. rosea, Virginica, scopvlorum, Weldenia, and Tinantia; or in the leaf margins, as
in C. dianthifolia. Stereome was observed in T. Warszewicziana on the leptome-side and in the
margins; on the leptome-side alone in Aneilema and C. Virginica; or on both faces of the veins
in C. dianthifolia.

190 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

The water-storage-tissue reaches a high development in several of these plants. It is always
hypodermal and covers the entire ventral face of the leaf in Tradescantia Warszt wicziana, besides
that it is very amply represented on the dorsal face, but interrupted here and there by narrow
strata of chlorenchyma, inside the stoinatiferous strata of the epidermis. In T. rosea, Am /'/, ma,
and Weldenia it is distributed over the entire ventral face of the blade. It occurs as a large
group below the midvein in ( '. n udiflora ; above the larger veins in ( '. hirtellq ; above and below
the midvein in ( '. erecta and Virginica, or only above this; as in T. Virginica.

Finally, the epidermis, witli its various kinds of projections, as warts, obtuse, pointed, or
curved hairs, and the stomata do also show several modifications within the family. The number
of subsidiary cells appears to be constant, at least in the leaves, and it deserves notice that
Tradescantia Floridana is the only species of the genus in which two pairs of subsidiary cells
were observed; all the Commetinas have two pairs, while the Tradescantim and Weldenia only one.

We might ask now whether it is possible to classify these plants as Xerophytes, Mesophytes,
or Hydrophytes. Judging from the nature of the habitat where these plants occur, it appears
as if we might consider, for instance, T. Warszewicziana, T. sp. (from Colorado) and Weldenia
as xerophilous, but from higher elevations. T. rosea from low sandy woods in subtropical
Florida is not exactly a xerophyte in the stricter sense of the word. T. Virginica appears
intermediate between a mesophyte and xerophyte. Aneilema on the other hand may be well
classified among the hydrophytes. In regard to Commelina hirtella from sandy river-shores, it
seems difficult to express any opinion whether this is to be considered a hydrophyte or a
mesophyte.

Corresponding difficulties are met with when we examine and compare the dominating
features of the leaf-structure of these same species, if these are to be brought in connection with
the nature of the habitat. They may he enumerated as follows:

Aneilema: Leaf isolateral; water-storage-tissue over entire ventral face; collenchyma ami stereome on leptome-side of

midrib.
( 'ommelina hirtella: Leaf dorsiventral; water-storage-tissue above the larger veins; collenchyma on leptome-side.
Tradescantia Virginia:: Leaf partly dorsiventral; water-storage-tissue above midvein; collenchyma on leptome-side.
V. sp. (Colorado): Leaf isolateral; water-storage-tissue over entire ventral face and on leptome-side; collenchyma on

leptome-side.
T. rosea: Leaf almost isolateral; water-storage-tissue over entire ventral face; collenchyma on leptome-side.
Weldenia: Leaf dorsiventral; water-storage-tissue over entire ventral face; collenchyma on leptome side.
Tradescantia Warszewicziana: Leaf dorsiventral; water-storage-tissue over both faces of the blade; stereome on leptome-

aide and in margins.

Of these tissues the water-storage-tissue is somewhat unequally developed so far as concerns
T. Virginica, since it is so very prominent in the other species. It is very scantily represented
in Camim Una hirtella, but, as we'remember from the foregoing, none of the other species pos-
sessed any large quantity of this tissue. The presence of a large water-storage-tissue in the
isolateral leaf of Aneilema is a frequent occurrence among hydrophilous plants. In regard to
the other species, the great development of this tissue may be well brought in connection with
the nature of the habitat.

The collenchyma is absent from the leaf of T. Warszewicziana, but is replaced by stereome;
it is present in all the others, accompanied by stereome in Am il, nm. It seems strange that this
tissue is not developed in the leaf of T. Warszt wicziana, since it is so well represented in the
scape. It seems also strange that stereome occurs in Aneilt ma, but not in the species of Trades-
cantia from Colorado, Florida, or District of Columbia.

The collenchymatic tissue is evidently a character of the family; the water-storage-tissue an
epharmonic.

But from the present knowledge of these plants we dare not enter any further into a discus-
sion of their classification as members of certain associations, mesophilous, hydrophilous, or
xerophilous. To fully appreciate the importance of the morphological and anatomical structures
which we have described above it seems necessary to study many of the other representatives of
the family. We hope that the present investigation may prove useful to future studies as a con-
tribution to the knowledge of these interesting plants.

Brookland, D. C, March, 1906.

PLATE I.

Fig, 1. Commelina nudiflora L. A seedling, natural size. C=the seed with the apex of the cotyledon inclosed;

H = the hypocotyl; S=the sheath of the cotyledon ; R=the primary root; r=two lateral roots; P=the

first stem-internode; L1 and La=the first green leaves.
Fig. 2. Same species. Basal portion of a flowering specimen, natural size. I'-P=the first three stem-internodes.
Fig. 3. Same species. A flower-bearing shoot, natural size. A=internode of main stem; B=internode of axillary

shoot; L'=leaf borne on main stem; I1-I2=inflorescences.
Fig. 4. Same species. Diagram of the shoot B. For explanation see the text.
Fig. 5. Rhizome of Coinimiiini hiiiilln Vaiil, natural size.
Fig. 6. Same species; a fore-leaf, seen from the front, natural size.
Fig. 7. Same species; a fore-leaf, removed from the branch and seen from the back, natural size.

PLATE II.

Fig. 8. Commelina Virginwa L. The rhizome with the base of an aerial shoot, natural size. P1-P2=fore-leaves;

A'=continuation of main stem; A2=an axillary stem; L1-L2=scale-like leaves; L3=scar of stem-leaf.
Fig. 9. Same species. Diagram of the aerial shoot, figured in Fig. 8. For explanation see the text.
Fig. 10. Same species. A rhizome, natural size. A =basal stem-internode from the previous year; A1 =basal portion

i if aerial stem of this year; P=the fore-leaf; L1-L2=scale-like leaves.

Fig. 11. Same species. Diagram of the si t, figured in Fig. 10. For explanation see the text.

Fig. 12. Tradescantia rosea Vent., a rhizome, natural size. I1-l5=the intemodes of the rhizome; I6=the basal

internode (above ground) of the main stem; S'-S*=axillary floral shoots; P= fore-leaves; L1-L2=green

leaves.
Fig. 13. Same species. Diagram of the axillary floral shoot S3 figured in Fig. 12. For explanation see the text.

PLATE III.

Fig. 14. Commelina nudiflora L. A secondary root of the seedling, transverse section. End.=endodermis; P=Peri-
cambium; II = hadrome; PH = proto-hadrome; PL=proto-leptome. X 744.

Fig. 15. Same species. A lateral root of the seedling; letters as above. X 744.

Fig. 16. Same species. A secondary root of fullgrown specimen, transverse section; letters as above. X 744.

Fig. 17. Same species. A secondary root of fullgrown specimen, transverse section. Ep. =epidermis; Ex.=exo-
dermis. X 480.

Fig. 18. Same species. A secondary root, transverse section; letters as above. All the proto-hadrorue-vessels are
located inside the pericambium. X 744.

PLATE IV.

Fig. Id. Commelina nudiflora L. The hypocotyl of the seedling, transverse section. End.=endodermis. X 480.

Fig. 2o. Same species. The basal internode I1, transverse section. End. =endodermis. X 480.

Fig. 21. Same species; stomata from the stem. X 360.

Fig. 22. Same species; transverse section of part of stem-leaf. Ep.=epidermis. X 744.

Fig. 23. Same species; transverse section showing the pneumatic tissue. X 480.

PLATE V.

Fig. 24. Same species; stomata of the leaf. X 360.

Fig. 25. Same species; raphide-rells from the leaf. X 480.

Fig. 26. Same species; the midrib of the leaf, transverse section; P=parenehyma sheath. y 744.

Fig. 27. Same species; transverse section of a marginal vein from the leaf, letter ;is above. ■ 744.

Fig. 28. Commelina hiriella V ahl. A stoma from the stem. X 480.

Fig. 29. Same species. Tangential section of root, showing a cell of exodermie with foldings. X 480.

191

192 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 6.

PLATE VI.

Fig. 30. Commelina nudiflora L. Epidermis with warts, from dorsal face of leaf. X 480.

Fig. 31. Commelina hirtella Vahl. Stoma from the leaf. X 360.

Fig. 32. Same species. Stoina from the leaf. X 360.

Fig. 33. Same species. Stoma from the stem. X 360.

Fig. 34. Same species. A secondary root, transverse section; C = the cortex; End. = endodermis; P = pericam-

bium; PL = proto-leptome; PH = proto-hadrome. X 480.
Fig. 35. Same species. Epidermis from the stem, showing stomata and two kinds of hairs. X 360.
Fig. 36. Same species. Cells with crystals from the stem (cortex). X 480.
Fig. 37. Commelina Virginica L. Epidermis of ventral face of leaf-blade. X 360.

PLATE VII.

Fig. 38. Commelina hirtella Vahl. Transverse section of inner portion of stem, showing the pith, with crystals and

very wide intercellular spaces. X 360.
Fig. 39. Commelina Virginica L. Hair from the leaf-sheath. X 360.
Fig. 40. Same species. Stomata from the leaf. X 360.
Fig. 41. Same species. Transverse section of the root, showing epidermis (Ep. ), exodermis (Ex.), and sterei'ds.

X 360.
Fig. 42. Tradescantia rosea Vent. Transverse section of the root. End. = endodermis; P = pericambium; PH —

proto-hadrome; PL = proto-leptome. X 480.
Fig. 43. Tradescnutin Virginicul^. A cell of exodermis of root, showing the foldings of the wall. X "44.
Fig. 44. Tradescantia rosea Vent. Transverse section of fore-leaf, showing epidermis and cuticle. X 840.
Fig. 45. Same species. A stoma from the rhizome. X 360.

PLATE VIII.

Fig. 46. Tinantia anomala (Tore.) Clarke. Diagram of the shoot. L'-L" = green leaves ; P'-P3 = fore-leaves; there
is one shoot in the axil of L2, beginning with the fore-leaf P1, and another shoot in the axil of L3,
beginning with the fore-leaf P2. In the axil of P2 is a third shoot, which begins with the fore-leaf P3.

Fig. 47. Tradescantia Warszewicziana K. et B. Epidermis of leaf, transverse section. X 480.

Fig. 48. Same species. Epidermis of leaf, viewed en face. X 480.

Fig. 49. Weldenia Candida Schult. fil. Diagram of the shoot; /'-/5 = scale-like leaves of stem underground; L'-L5 =
green leaves; 6-13 = the innermost leaves, which surround the inflorescence.

Fig. 50. Same species. Transverse section of central-cylinder of root. Letters as above. X 480.

Fig. 51. Same species. Transverse section of central-cylinder of root. Letters as above. There are two proto-leptome-
cells (PL). X 480.

Fig. 52. Same species. Hair from the leaf. X 360.

Fig. 53. Same species. Stoma from the leaf. X 360.

Memoirs Nat. Acad. Sciences, Vol. X. 6th Mem.

Plate I.

1 i

Auctor a>l nut. delin.

COMMELINACE/E.

Memoirs Nat. Acad. Sciences, Vol. X, 6th Mem
A.i...^ _L»

Plate II.

Auctor "il not. </< tin.

COMMELINACE/E.

Memoirs N.ii. Acad. Sciences, Vol. \, 6tli M> m.

Plate III.

14

18

J UCtor <fl it"! (it h it

COMMELINACE^.

Memoirs Nat. Acad. Sciences, Vol, X. 6th Mem.

EP. .

23

.1 tictoi ad n<xt. di tin.

-A

21

COMMELINACE/E.

Memoirs Nat. Apart, Sciences, Veil. X, (»1h Mei

Plate V.

A actor (ul mil. <l> Hit.

COMMELINACE>£

Memoirs Nat. Acad, Sciences, Vol. X, 6th Mem.

Plate VI.

Auctor ad not. deliu.

COMMELINACE>€.

Memoirs Nat. Acad. Sciences, Vol. X, 6th Me

Plate VII.

Auctor -Hi not. del in

COMMELINACE/<£.

Memoirs Nat. Acad. Sciences, Vol. X, 6th Mem.

Plate VIII.

AtlCtOT a-/ not. '/' I) ii

COMMELINACE/t.

MEMOIRS

NATIONAL ACADEMY OF SCIENCES.

Volnnie ]X.

SEVENTH MEMOIR.

WASHINGTON:
GOVERNMENT PRINTING OFFICE.

1910.

NATIONAL ACADEMY OF SCIENCES.

Volume X.

SEVENTH MEMOIR.

TABLES OF MINOR PLANETS DISCOVERED BY JAMES C. WATSON.

(93) MINERVA.

(101) HELENA.

(103) HERA.

(105) ARTEMIS.

PART I.

TABI, ES OF

(115) T.IIYRA.

(119) ALTHAEA.

(128) NEMESIS.

(133) CYRENE.

BY

(139) JUEWA.

(161) ATHOR.

(174) PHAEDRA.

(179) KLYTAEMNESTRA.

ARMIN O. LEUSCHNER,

WITH THE ASSISTANCE OP

R. T. CRAWFORD, FRANK ROSS, BURT L. NEWKIRK,
ADELAIDE M. ROBE, KSTELLE GLANCY, AND OTHERS,

BEING IN PART A CONTINUATION OF PREVIOUS INVESTIGATIONS BY
E. BECKER, W. S. EICHELBERGER, WILLIAM MCKNIGHT RITTER, and G. K. LAWTON.

193

NATIONAL ACADEMY OF SCIENCES.
MEMOIRS.

Volume X.
SEVENTH MEMOIR.

Published under the Watson Trust.

Trustees:

SIMON NEWCOMB, Chairman.
LEWIS BOSS.
WILLIAM L. ELKIN.

194

CONTENTS.

Page.

Preface by Simon Newcomb 197

Introduction 199

Explanation of the tables 201

General plan of the tables 201

General tables 201

Tables of Jupiter's mean anomaly, g' (Table A) 201

Traverse tables (Table B) 201

Elements (Table C) 202

Special tables for the twelve planets 202

Arguments g and g' of the perturbations 203

Tables of eight planets: (105) Artemis, (115) Thyra, (128) Nemesis, (133) Cyrene, (139) Juewa, (161) Alitor,

(174) Phaedra, (179) Klytaemnestra 204

Nonsecular portion of the perturbations 204

Secular portion of the perturbations 204

Arrangement of the tables 205

Directions for computing the perturbations nil:, o log r=log (1+v), and d/3 205

Example

Tables of three planets: (101) Helena, (103) Hera, (119) Althaea 208

Nonsecular portion of the perturbations 208

Secular portion of the perturbations 20S

Arrangement of the tables 209

Directions for computing the perturbations nSz, 3 log r=log (1+v), and «/? 209

Example 209

Tables of (93) Minerva 210

Nonsecular portion of the perturbations 211

Secular portion of the perturbations 212

The long-period term in nSz 212

Arrangement of the tables 213

Directions for computing the perturbations no:, n log r=log (1+v), and dp 213

Example 213

Directions for the computation of a geocentric position referred to the mean equinox and equator for the

beginning of the year, from .1/, » log r. and ofi 215

Example 215

Table A. — Jupiter's mean anomaly 217

Table B.— Traverse tables 218

Table < ' —Elements 234

Tables of (105) Artemis 236

Tables of (115) Thyra 246

Tables of (128) Nemesis 255

Tables of (133) Cyrene 265

Tables of (139) Juewa 278

Tables of (161) A thor 29 1

Tables of (174) Phaedra 301

Tables of (179) Klytaemnestra 313

Tables of (101) Helena 327

Tables of (103) Hera 338

Tables of (119) Althaea 348

Tables of (93) Minerva 359

195

ERRATA.

Page 200, line 21: For "Bitter", read "Eichelberger".

Page 211, line 28: In argument of cos for "g' — g", read "«/' — Mg".

Page 216, line 7 from bottom: For "9.60706", read "9.60706 n".

Page 234, Foot-note : After the words "osculating for the epoch" insert "(excepting (93)
Minerva, for which the date of osculation is 1S72, Nov. 2.0, Gr. M. T.)"

Page 359, line 3: For i-\ai + {Mi)ty\ read ~[ai + (4ai),y\

Page 361, line 3: For "Epoch and Osculation", read "Epoch".

Page 361, under line 3: Insert "Date of Osculation = 1872, Nov. 2.0, Gr. M. T."

Page 362, first column: For "Arg. tg — i'gf,\ read "Arg. (/—/'/<) f —/'(/- /<</)".

Page 363, first column: For "Arg. / g-ig'J\ read "Arg. {I— i' p) s— i'(g' — M ^)".

Page 361, last line: For "[a« + (^i<) ]", read " [as, + (^a*),] ".

Page 364, last line: For "[Ji+^W, read " fo + (^JAJ ".

Pages 305-372, inclusive, last line of each: For " [at + (^)j] ", read " [a< + (^«j) J ".

196

TABLES OF MINOR PLANETS DISCOVERED BY JAMES C. WATSON.

By Armin O. Leuschner.
PREFACE.

By the will of James C. Watson, who died in 1880, a fund was bequeathed in trust to the
National Academy of Sciences for the purpose of promoting astronomical research. Objects
specifically designated were the awarding of a medal not oftener than once in two years for
important astronomical works and the construction of tables of the minor planets discovered
by the testator. The expenditures were to be made under direction of a board of three trustees.
The first board was named in the will, the members being J. E. Hilgard, John H. C. Coffin,
and Simon Newcomb. At the present time, March, 1908, the members of the board are:
Simon Xewcomb, chairman: William L. Elkin, and Lewis Boss.

The construction of the tables was long delayed by the difficulty of finding computers
competent to carry the work through in a satisfactory way. To lessen this difficult}- an
arrangement was made with Prof. E. Becker, director of the Strassburg observatory, for sup-
plying a complete form for computing the perturbations according to Hansen's method, in
which the eccentric anomaly was taken as the independent variable. An example was also
supplied lr\T Professor Becker in the form of a computation of the perturbations of Eurynome by
Jupiter. Tables of Minerva were completed and published on this plan by Dr. W. S. Eichel-
berger.

The conclusion subsequently reached was that the system of employing the eccentric
anomaly was not a desirable one, and that it was better to adhere to the use of the time as the
fundamental variable. Several experts were engaged in computing the perturbations of different
asteroids by Jupiter under the general direction of the writer, but in no case except that of
Minerva were the processes of tabulating the perturbations and correcting the elements brought
to a satisfactory conclusion.

The slow progress of the work made it evident that it must be prosecuted in a more sys-
tematic way under the personal direction of a leader who would bring it to a conclusion. After
a careful survey of the field, Prof. Armin O. Leuschner, of the University of California, was
selected as the leader, and all the papers were placed in his hands. He undertook to construct the
tables with the aid of the students and assistants in the Berkeley Astronomical Department of the
University of California. The system agreed upon was that the tables should be carried only to the
degree of precision necessary for finding ephemerides. The only perturbations then required
would be those of the first order by Jupiter, though approximate quantities of higher order
would in some cases be advisable. The construction of even these approximate tables proved
vastly more laborious than had been expected, owing to circumstances set forth by Professor
Leuschner in the introduction. As the general outcome of the work up to the present time,
tables of twelve of the asteroids in question are herewith presented, with the hope that they
will be sufficiently accurate for as long a period as if entire theoretical precision had been aimed
at in their construction. The remaining tables are in an advanced state, and it is expected
that they will be completed and published at no distant day with the single exception of Aethra
which must await rediscovery.

Simon Newcomb.

Washington, 190S, March.

197

INTRODUCTION.

The results recorded in these pages are the outcome of an effort to supplement the author's
lectures on celestial mechanics in the University of California by extensive numerical application
in the field of perturbations.

During the summer of 1901 the Watson trustees of the National Academy of Sciences
agreed to engage students and graduates of the University of California in the work of computing
the perturbations of the minor planets discovered by Watson on condition that the author
would assume the immediate direction of the work and sole responsibility to the trustees for its
success. The original scope of the undertaking as fixed by Prof. Simon Newcomb, chairman
of the Watson trustees, was to embrace the numerical development of the perturbations,
including terms only of the first order with respect to the mass of Jupiter, by Hansen's method;
a correction of the elements by means of the differences between the computed and observed
positions for all available oppositions; and the construction of tables to facilitate the computa-
tion of positions to the nearest minute of arc, from the date of discovery to 1930.

As the undertaking is now nearing completion, it is deemed advisable to make the tables
available to astronomers in advance of the details of the investigations. The present series,
containing the tables of twelve planets, is to be followed by several others, which will contain
the tables of the remaining planets, and possibly also the detailed investigations.

Many difficulties of a theoretical as well as a practical nature were encountered during the
progress of the work, necessitating departures from the general program for individual planets,
particularly for planets of the Hecuba type.

It is unnecessary to enter here upon a discussion of the progress and organization of the
investigation. It is sufficient to say that all computations were done independently by two
computers.'frequently by different methods, and that the system of checks used makes it highly
probable that the results are free from numerical error. Particular attention was paid to the
investigation of the differences between the theoretical and observed positions. The origin
of all unusually large residuals has been traced. When they occur they are, in general, accounted
for by higher order perturbations of Jupiter, or by perturbations of other major planets, or by
the fact that sufficiently accurate initial elements of the disturbed planet were not available
for the rigid computation of the coefficients of the perturbations. Corrections to the perturba-
tions, due to the differences between the initial and final elements of a planet may be included,
if it be deemed necessary, in subsequent series. Much useless labor has been caused by
erroneous identifications of the Watson planets on the part of the observers. A comparison
of the tables with future observations will be necessary to decide whether all erroneous
observations have been eliminated.

Actual work was commenced in August, 1901, with Dr. Russell Tracy Crawford and
Dr. Frank Elmore Ross as computers. They continued in the work for one year, and in that
time computed, under the author's direction, the perturbations of ten planets in duplicate, by
Hansen's method. Tables of seven of these are included in the present series: (105) Artemis,
(128) Nemesis, (133) Cyrene, (139) Juewa, (161) Aihor, (174) Phaedra, and (179) Klytaemnestra.
Since then the computations have been carried on almost entirely by university students, except
that Dr. Burt L. Newkirk was appointed in September, 1903, a special assistant and was
assigned with Miss Adelaide M. Hobe chiefly to take charge of some twelve piece computers
in revising perturbations, correcting elements, and constructing tables. Doctor Newkirk
and Miss Hobe have also developed the perturbations of (115) Thyra and (93) Minerva. The
tables of Minora, however, contained in this series, are based on a previous investigation by

Dr. W. S. ElCHELBEKGER.

199

200 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Several interruptions, of which one lasted for nearly a year, were caused by the resignation
of assistants who were called to permanent positions elsewhere. Thus Doctor Crawford, Doctor
Ross, Doctor Newkirk, and Miss Kobe were lost in turn to the work. Other interruptions arose
from the necessity of temporarily employing the Watson computers as assistants in the regular
departmental work of instruction. So far three distinct sets of computers have been trained
in succession for the work. At present, the investigations are progressing with Miss Estelle
Glancy, a graduate'student in the university, as chief computer.

The original program, which included only those planets for which the investigation of the
general perturbations had not been undertaken by other astronomers, has since been extended
by the trustees, at their own initiative, to embrace the publication of tables of all of the
twenty-two Watson planets excepting (132) Aeihra, which is lost. Investigations, however,
by Mr. A. J. Champreux, which are under way, point to the possibility of deciding the fate of
this planet.

To enable the author to prepare all the available material for publication, the Watson
trustees placed in his hands such original computations and manuscripts as were in their pos-
session. These included, in the main, perturbations and tables of (103) Hera and (119) Althaea
by William McKnight Ritter; perturbations and tables of (93) Minerva by Dr. W. S.
Eichelberger; perturbations of (101) Helena by Ritter, tables by Eichelberger, and
fragments of a comparison between theory and observation by G. K. Lawton; development
of the perturbations and partial comparison between theory and observation for (79) Eurynome
by Prof. E. Becker, continued by Ritter.

In regard to these planets, the trustees desired that certain discrepancies between theory
and observation should be investigated, that such revision of the results be made as might seem
necessary, and that the tables which in general gave the theoretical positions to a tenth of a
second of arc, should be abridged to correspond to the limits of accuracy fixed by the method
of investigation used in each case.

This task proved far more laborious than was anticipated. In the case of (93) Minerva
the perturbations were checked by a complete independent development. Yet, it has ulti-
mately been possible to preserve, in the main, the original results of the author's predecessors
in the work, and thus to secure for them the credit which is their due. No change whatever
has been made in Eichelberger' s results on (93) Minerva.

The aim of the trustees was not that a theoretical study should be undertaken of the rela-
tive merits of the various methods of developing the perturbations of the minor planets, but
that tables of the Watson planets be produced in the most expeditious manner. It was there-
fore not within the scope of this work to arrange for practical application to the minor planets
such analytical methods as have been made available by Poincare, E. W. Brown, and others,
in a manner similar to that employed by Brendel in his "Theorie der Kleinen Planeten,"
which is based on Gylden's researches.

Furthermore, Hansen's and Bohlin's methods have so far been found eminently suitable
for the objects aimed at. Nevertheless, the details of. the investigation to be published later
will furnish abundant material for studies of a purely analytical nature.

The length of time required to develop perturbations by Hansen's method is not such an
important factor after all in these considerations, for after gaining the necessary experience
Crawford and Ross were able to completely develop the perturbations of the first order in
normal cases in from forty to sixty hours.

For three, planets of the Hecuba type the development of the perturbations remains to be
made. Preparatory to this, special tables for the group i have been computed on the basis
of the method employed by Bohlin for the group J in his "Formeln und Tafeln zur gruppen-
wrisse Berechnung der allgemeinen Storungen benachbarter Planeten" and "Sur le developpe-
ment des Perturbations Planetaiics."

The tables for the group \ were barely completed when similar tables by H. von Zeipel
appeared in the Memoires de I'Academie Imp6riale des Sciences de St. Petersbourg, VIII serie,

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 201

Classe Pkysicomathematique, Volume XII, No. 11, under the title "Angenaherte Jupitersto-
rungen fur die Hecuba-Gruppe."

A thorough comparison of v. Zeipel's and the author's tables for the group J remains to
be undertaken before either are applied to the development of the perturbations of the three
planets belonging to the Hecuba type.

Acknowledgment is due to Prof. Simon Newcomb, chairman of the Watson trustees of
the National Academy of Sciences, for his constant efforts in promoting this investigation.

Acknowledgment is also due to Professor Bohli.n for facilitating the construction of the
special tables for the group \ by placing his revised computations for tables of group \ in
the author's hands; to Director Campbell, of the Lick Observatory of the University of Cali-
fornia, and to Superintendents Asa Walker and W. J. Barnette, of the United States
Naval Observatory, for furnishing especially needed observations, and finally to the author's
coworkers, particularly to Messrs. Crawford, Ross, and Newkikk, and Misses IIobe and
Glancy, for their untiring devotion to the numerical work connected with this undertaking.

EXPLANATION OF THE TABLES.
GENERAL PLAN OF THE TABLES.

The tables consist of general tables and special tables. The general tables are those tables
which are required for all planets in the computation of a geocentric position. The tabular
values were computed to one more figure than given in the tables, to insure correctness of the
last tabulated figure. Decimals of a degree are used throughout and computations may be
readily conducted on the basis of these tables with the aid of Bremiker's five-place logarithmic
tables.

The perturbations, excepting those of (93) Minerva, are developed with the argument
dg—i'g'), and a uniform plan is adopted for the special tables of the various planets, except for
those, planets for which the development of the perturbations and the construction of tables
was originally undertaken elsewhere. In these latter cases the original plan of tabulation has
been adhered to to avoid laborious and unnecessary transformations.

GENERAL TABLES.

In the general fables are included tables of Jupiter's mean anomaly from 1863, the year of
discovery of the first Watson planet, to 1930: Traverse Tables giving the products « sin ^4 and a
cos ^4; and a table of Elements. All other general tables necessary for the computation of a
geocentric position may be found in Bauschixger's "Tafeln zur Theoretischen Astronomie"
and in Tietgex's "Tafel zur Bereclmung der Wahren Anomalie," which may be used in connec-
tion with the tables here given. The particular tables to be employed at various stages of the
computation of a geocentric position are referred to in the example given on page 215.

TABLES OF JUPITER'S MEAN ANOMALY, g' (TABLE A).

The values of g' are tabulated from 1863 to 1930. They are taken from Hill's Tables of
Jupiter and Saturn," Tables VIII to XII. The values of g' contained in g—g', Table I of (93)
Minerva, however, do not correspond to the values of g' in Table A, since the value of g' used
by Eichelberger in building the table g—g' is the undisturbed mean anomaly of Jupiter.
It can be obtained by multiplying Arg. I of Hill's Tables for the date +6d.6 by the mean
motion 299".1283756.

It should also be noted that the dates for which the values of g' and g are given in Tables A
and I refer to Berlin mean time, except in case of (93) Minerva, for which Table I refers to
Greenwich mean time.

TRAVERSE TABLES (TABLE B).

These tallies are to facilitate the formation of the products of the form a sin .4 and a cos A,
which occur in the periodic parts of the perturbations, ami are designated, at the foot of "the

" Astronomical Papers prepared for the use of the American EphenierU and Nautical Almanac. Vol. VII.

202 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

tables of each planet, by a{ sin ig and bt cos ig or at sin k and b{ cos ie. They are to be entered
with a=ai and A = ig or is as arguments. The products are tabulated for every degree of A
from 1 ° to 90°, and for every unit of a from 1 to 100. For a = 1, the products are given to five
decimals: from a = 2 to a = 9 to four decimals, and from a = 1 1 to a = 100 to one decimal. This
latter part of the Traverse Tables has been copied from Table II of The American Navigator
by Nathaniel Bowditch. The at and b{ coefficients are tabulated to one decimal of the
adopted unit of 0?001 for noz and u/cos i, and to one decimal of 0.00001 for dlog r. The
products may be taken directly from the tables by double interpolation for values at and bt up
to 100.0 units in each case, i. e., for coefficients not exceeding 0?1 or 0.001 , respectively. If the
coefficients be larger, the products may be conveniently found in parts with the aid of that
portion of the table which is given to four and five decimals. Example : Required the product—

a sin A = - 2479.6 X sin 306?3S ; Unit of a = 0?001

Since the angle is in the fourth quadrant, the algebraical sign of the product is +. The
numerical part may be taken from the Traverse Tables in the form :

(1000 X 2 + 100 X 4 + 79.6) cos 36?3S)

1000X2 cos36?38 =1610.1 Table B, page '-'is

100X4 cos 36.38 = 322.0 Table B, page 219

79. 6 cos 36 . 38 = 64.1 Table B, page 230

-2479. 6 sin 306. 38 =1996.2 units=l?9962

With Bremiker's five-place tables the product is found to be 1996.3, which agrees with the
former result within the accuracy of the computation.

ELEMENTS (TABLE C).

In this table are given the final elements of the twelve planets and the quantities m0 and g
for computing the magnitude at opposition, the latter being taken from the Berliner Astro-
nomisches Jahrbuch.

SPECIAL TABLES FOR THE TWELVE PLANETS.

The special tables for the twelve planets are arranged in three groups.

The first group contains eight planets for which the argument of the developments is
(ig-i'g'), and for which the perturbations are tabulated in the form:

2',(«j sin ig + bt cos ig) +cT

where the coefficients au b(, and e are functions of coefficients of the original developments;
a{ and bt are also functions of g' , while e is a function of g.

The second group contains three planets for which the argument of the developments is
also (ig-i'g'), but in which all terms having (ig-i'g') or a multiple of (ig-i'g') as argument
are combined in the tables for particular values of i and i' under a single argument (ig-i'g').

If we denote the three components ndz, log (1 + v) and <?/?, by the symbol j, then the per-
turbations are tabulated in the form

r = -iri + rtT-c'r

where i is the numerical designation of the various arguments and cr is a constant.

The third group contains but one planet, (93) Minerva, for which the argument of the
developments is (i—i'/i)e—i'(g' —fig), ami for which the perturbations arc tabulated in the form

2'i<ii sin ie + J,-&,- cos is + (Jl>„ ),

where the at and bt are functions of coefficients of the original developments and of the argu-
ment N = s-g'-/ie sin s, and where (J6„)( is the nontrigonometrical secular part of the per-
turbations. Explicit directions for the use of the tables and an example are given with each
group.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 203

The special tables for each planet are preceded by the adopted elements, a list of the
auxiliary quantities needed in ((imputing a geocentric position, and by the developments of ndz,
v, and u/cos i.

The arrangement of the tables for the different planets has been rendered as uniform as
seemed expedient, without too extensive transformation, considering the diversity of the
original plans adopted by Eichelberger, Ritter, and the author. The angles throughout
are expressed in decimals of a degree. Table I of every planet gives the mean anomaly. Tables
II-IV give the nonsecular portion of the perturbations. In the tables these are designated as
periodic terms. Table V gives the secular portion of the perturbations. Table VI gives the
constants for the equator. For the first group, containing eight planets, the perturbation in
the third component is tabulated in the form u/cos i, for all others in the form d^=au/cos i.
The unit of the tabular values is printed at the head of each table.

For (93) Minerva, for which e was kept explicit in the plan adopted for tabulation by
Eichelberger, a Table VII is added, giving the reduction of the mean to the eccentric anomaly.
This table also contains part of the argument N of Tables II-IV of Minerva. Table I of Minerva
contains the other part of this argument.

Tables for the equation to the center and the logarithm of the radius-vector are not given,
as Bauschinger's "Tafeln zur Theoretischen Astronomie" and Tietjen's "Tafel zur Berech-
nung tier Wahren Anomalie" answer all requirements.

The perturbations of the first group, containing eight planets, were developed to the nearest
second of arc, while the tables give the perturbations to one decimal of the adopted units 0?001
and 0.00001. These tabular values were computed only to the last figure given in the tables.
The last figure is, therefore, not exact, but was retained to insure greater exactness of the per-
turbations to the nearest 0?001 and 0.00001. The tables, therefore, give the perturbations of the
first order well within the originally contemplated limit of one minute of arc-. For the remaining
four planets the accuracy is still greater, the perturbations having been developed to the nearest
tenth of a second of arc and the values in the tables having been computed to one more decimal
than tabulated. The mean anomaly and the constants to the equator have been computed
to one and two more places than tabulated to facilitate later correction of the elements.

ARGUMENTS g AND g> OF THE PERTURBATIONS.

The perturbations are based on the initially adopted elements of a minor planet and Jupiter.
They are corrected only for the finally adopted mean mean motion of the planet. The values of
the mean anomaly given in Table I for each planet are based on the finally adopted values of the
mean mean motion and of the mean anomaly <70 at the epoch, as deduced by the Method of
Least Squares from the differences between the theoretical and observed positions.

In general the absolute corrections to g0 and it can not be obtained with accuracy from the
Least Squares reduction. When they are large they usually are numerically nearly equal and of
opposite sign. The position, however, of the planet in its orbit does not depend so much on
the absolute values of Aga and Jtt as on their sum Ju-\-Jg„, which is of greater accuracy.

Whatever uncertainty may remain in the tabulated values of g is therefore almost wholly
eliminated in the undisturbed positions through the constants for the equator, which are based
on the value of z resulting from the Least Squares solution. But, in general, this will not be
the case for the perturbations, because their coefficients are based on the initial value of n for
each planet.

Theoretically, for attaining the highest accuracy, the coefficients should have been corrected
to correspond to the final value of - (and of the other elements), if the arguments were to be
based directly on the g in Table I. But within the accuracy aimed at in these tables it is suffi-
cient to correct the values of g in Table I by J-=-—n0 when they are to serve as arguments,
and to use them as they stand when they are to serve as mean anomalies. This correction
arises from the consideration that the perturbations depend in part on 7t+g0, for which the
initial and final values are

"0 + ^0)0 and -0 + J7z-\-(g(l)„ + Jg„=~0 + l(g0)0+Jg0 + J7T'].
89369°— vol 10—11 14

204 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X. NO. 7.

Thus, since Jg„ appears in Table I and since the coefficients of the perturbations depend on
^0, the correction An may be allowed for in the main by adding the same to the values of g as
given in Table I when the g are to serve as arguments. In cases where Jr is small and the
perturbations do not vary rapidly with g, the correction may be neglected. But with large
values of Jr. and rapid variation of the perturbations the omission of this correction may intro-
duce comparatively large errors of the second order in the residuals, through the consequent
inaccuracy of the arguments of the perturbations.

TABLES OF EIGHT PLANETS.- -| 105 1 ARTEMIS. 1 115 1 THYRA, (128) NEMESIS, ( 133 1 CYRENE, (139)
JUEWA, <i6i> ATHOR. (174) PHAEDRA, (179) KLYTAEMNESTRA.

The elements of these planets are mean elements.
.The expressions for ndz, v, and w/cos i are developed in the following form:

ndz = nz -g0- nt = I^i-A \< sin ( ig - i'g' ) + Zt 1^ cos (ig - i'g' )
+ (t-t0) { lid sin ig + Z \Dt cos ig)
v=B°0 + 2tZ*A!< sin {ig - i'g' ) + !£<&< cos (ig - i'g' )
+ (t-t0){D0 + lid sin ig + J2A cos ig}
w/cos i=Bl + lil^A1,' sin (ig — i'g') + Z^Z^B',' cos (ig —i'g')
+ (t-t0){D0 + Ita sin ig + IiDi cos ig)

i varying from — so to +00, and i' from 0 to 00, except that the constants Bl and D0 are segre-
gated from the sums. Before tabulation, the expression for v was transformed into an expression
for log (1 +v) =<5 log r by multiplying the expression for v by Mod. sin 1" and adding the higher
powers of v where they were appreciable.

For tabulation the perturbations are segregated into their nonsecular and their secular
portions.

NONSECULAR PORTION OF THE PERTURBATION.

The nonsecular portion of the expression is:

Bl + IilfA1^ sin (ig-i'g^+JjIfBi- cos (ig-i'g').

For ndz, Bt = D0=0, these constants being contained in the elements g and n, respectively. Let

A','=m!f cos Ml'
B\i =m'e sin M\>

where m'> may always be taken positive. Then the perturbations may be written in the form

Bl + ZiZf M'e m'e sin (ig-i'g' + MV)

or also

Z(Zr m'f sin ig cos ( .!/;< - i'g') + ZfZ? m'< cos ig sin (Mi-— i'g')

if B„ be omitted for the present.

As a first step in the construction of the tables each coefficient m'- and angle Mi were com-
puted from the corresponding coefficients A\> and B\- of sin (ig — i'g') and cos (ig — i'g').

For a particular value of i the foregoing double sum becomes

sin ig Z^ml^ cos ( M\- — i'g' ) + cos ig Zvm\> sin ( M \> — i'g' )

where i is to be taken both positive and negative, while i' is always positive.
Let

a+0) represent the coefficient of sin ig.
a_,,, represent the coefficient of sin ( — ig).
6+(() represent the coefficient of cos ig.
&_,„ represent the coefficient of cos ( — ig).

MINOR PLANETS DISCOVERED BY WATSON LKrsCIINER. 205

Then the nonsecular portion of the perturbations becomes for a particular numerical value
of i, i now positive only,

ndz = a+li) sin ig + a-i(l sin ( — ig) + &+(t)cos ig + b-(i) cos (—ig)
= (ani> -a.(i)) sin ig + (b+lil + 6_(t)) cos ig
=at sin ig + bi cos ig
where

at=Ii-m+ii cos ( M+it —i'g") —S^rnr't cos (M~\> — i'g')
bt = 2i-m+\- sin ( M+\ -i'g') +Ii>nrli- sin (M^-i'g')

if Bl be again omitted in v and w/cos i.

The o, and 6, are therefore functions of the original A\ and B\> coefficients and of the argu-
ment g' . They are tabulated for each positive value of i at intervals of 6° of g' from g' = 0 to
^'=360°, or where the perturhations vary rapidly at intervals of 3°. The difference in the
a, and b, Tor one degree is also given, higher differences having been considered when necessary.
The constant B I occurring in v and u/cos i is included in b0. It is not necessary to compute
a0 since this is multiplied by sin OXg.

SECULAR PORTION OF THE PERTURBATIONS.

This is of the form

T{D„ + IfOi sin ig + I^D, cos ig}
where T=t—t0 in Julian years, and may be written

Tc

where

c =D0 + IjCj sin ig + IfDt cos ig.

c is a function of g and is tabulated for every 6° thereof in Table V.

g was kept explicit in preference to g , as more terms could thus be combined in the tabu-
lated values of a, and b,. These coefficients were also found to converge more rapidly with g
explicit.

The complete tabulation of the perturbations of this" group of eight planets is, therefore,
in the form

.Tta, sin ig + -fit cos ig + cT

for each of the components \\dz, log (1 +v) =3 log /■, and u/cos i.

ARRANGEMENT OF THE TABLES.

Table I gives the values of the mean anomaly g for January 0.0 of every common }*ear and
for January 1.0 of every leap year from the date of discovery to 1930, and their changes for the
different months and days.

Tabh II gives the coefficients at and /*, of the periodic parts of the perturbation ndz with
the argument g' in units of 0?001 and one decimal thereof.

Table III gives the coefficients at and &,• of the periodic parts of the perturbation log
(l+v)=d log r with the argument g in units of the fifth place and one decimal thereof.

Table IV gives the coefficients a, and 6,- of the periodic parts of the perturbation u/cos i
with the argument g' in units of 0?001 and one decimal thereof.

Table V gives the coefficients c of the secular parts of the perturbations for all three com-
ponents with the argument g.

Table VI gives the constants for the equator for the beginning of every year from the date
of discovery to 1930, inclusively of the logarithms of the epiantities cos a, cos b, and cos c, by
which the perturbation 3p must be multiplied to obtain the corrections Ax, Ay, and Az to the
heliocentric ecpiatorial coordinates x, y, and z.

206 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

DIRECTIONS FOR COMPUTING THE PERTURBATION adz, S log r=log (1 + v), and 6/3.

The perturbations ndz, 3 log r, and u/cos i are each of the form

-i a( sin ig + It bt cos ig + cT

Hence the following directions apply alike to each of the three components:

Let t0 be the epoch of the mean anomaly g0, and let t be the date for which the perturba-
tions are to be computed. Let g' be Jupiter's mean anomaly at the date. Let g be the planet's
undisturbed mean anomaly at the date. For the date t take g' and g from tables A and I,
respectively. To form the argument g of the perturbations in Tables II-IV, apply to Table I
the correction An=n — h0. (See p. 203.)

Form as many multiples of the corrected g as there are subscripts i in the tables of at and bit
Tables II-IV.

Express T=t — t„ in Julian years and decimals thereof.

With argument g' take at and bit the coefficients of the periodic terms, from Tables II-IV,

With argument g take the secular terms c from Table V.

By means of the Traverse Tables B form the periodic terms:

at sin ig and at cos ig

Form the secular terms c(t — t0) =cT.

Sum the periodic terms and the secular terms for each component.

Compute djJ = -„ „-

cos i
The disturbed mean anomaly is

M= nz = g + ndz.

EXAMPLE.

As an example for the use of the tables of this group of eight planets, the perturbations
of (179) lUytaemnestra will be computed for 1907, September 26.5, Berlin mean time.

g, Table I

g', Table A.

L907 .0

Sept. 0.0

26.0

0.5

9, <f

An

Arg. g, g'

302?31498

46. 72370

4. 99924

0. 09614

78?06
20. 191
2.161
0. 042

t-t„

g

2g

3g

4g
5g
6g

+14. 1 years.
353?66
347. 32
340. 99

334. 65
32S. 31
321.97

354. 1341

- 0. 4719

353. 662

100. 454
100. 454

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

PERTURBATIONS.

207

Arg. g'.

nSz

log(l + ")

u/cos i

Table II, Unit=0?001.

Table III, Unit=0. 00001.

Table IV, Unit=0?001.

i

Ci

h

"i

h

"i

h

0
1
2
3
4
5
6

-203. 2
-136. 7
- 24.3
+ 1.4
1.5
+ 0.7

-9.3
+507. 5
+249. 1
+ 17.9
5.3
+ 0.7
+ 0.3

+ 50.3
+106. 6
+ 10.9
-2.6
+ 0.4

+ 0.1
+ 11.4
+58. 4
-12.3
- 0.8
+ 1.0

+7.5
+5.8
+ 1.6

+3.1
+1.9
-4.2
-3.2

Arg. (/.—TABLE V

C

-2.49

+0.01

+0.02

FROM TRAVERSE TABLES, TABLE B.

i

nSz

log(l+")

u/cos l

m sin ig

6{ cos ig

a; sin ig

6; cos ig

«, ,sin ig

6j cos ig

0

1

2
3
4
5
6

+22.4
+30.0
+ 7.9

- 0.6
+ 0.8

- 0.4

-9.3
+504. 4
+242. 9
+ 16.9
-4.8
+ 0.6
+ 0.2

- 5.5
-23.4

- 3.6
+ 1.1

- 0.2

+ 0.1
+11.3
+57. 0
—11.6

- 0.7
+ 0.8

-0.8
-1.3
-0.5

+3.1
+ 1.9
-4. 1
-3.0

+160.1

+750. 9

-31.6

+56. 9

-2.6

-2.1

Sum
c(t-t0)

+811.0
- 35. 1

+ 25.3
+ 0.1

-4.7
+0.3

+775. 9
= +0?7759
=ndz

+ 25.4

= +0.000254

=log(l+v)

-4.4
= -0?0044

= u/cos i

The perturbations are:

a u

n&=+0?7759; log(l +v) =o log r= +0.00025; ^ = 573cosi = -0.00023

and

M = nz=g + ndz = 354° 9100

As an example for the computation of a geocentric position with the aid of I/, log(l +v) =51og
?-, and 5/9, the geocentric right ascension and declination of this planet, referred to the mean
equinox and ecliptic 1907.0, are derived for the date of the perturbations on page 215.

208 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF THREE PLANETS.— ( IOI ) HELENA, (103) HERA, AND (119) ALTHAEA.

The elements of these planets are osculating0 elements.

The perturbations are developed in sines and cosines of (ig — i'g'). The form of develop-
ment is the same as for the foregoing group of eight planets, see page 202.

Before tabulation, the expression for v was transformed into an expression for log
(1 +]/) = 8 log r by multiplying the expression for v by Mod. sin 1" and adding the higher powers
of v wherever they were appreciable. Similarly the expression for uj cos i was transformed
into an expression for <?/? by multiplying the expression for u/ cos i by a sin 1". «

For tabulation the perturbations are segregated into their nonsecular and their secular
portions.

NONSECULAR PORTION OF THE PERTURBATIONS.

In accordance with the plan adopted by the original computers for tabulating the non-
secular perturbations of these planets, all terms having (ig — i'g') or multiples thereof for
particular values of i and %' as argument are tabulated under the single argument (ig — i'g')
for the three components in Tables II, III, and IV, respectively. The original numerical
designation of the arguments (ig — i'g') for particular values of i and i' has also been adhered
to, and differs for the three planets. The numerical designation of the different arguments
and the numbers added to make all quantities positive are given separately for each planet.
In Tables II, III, and IV the headings of the terms depending on a particular argument i are
(ndz)i, (d log r)i, and (<J/?)4-.

SECULAR PORTION OF THE PERTURBATIONS.

This is tabulated in the same manner as for the preceding group of eight planets, in Table
V, and is denoted by (ndz)t, (3 log r)t, and (dfj)t, respectively. The argument to be used for
each planet is indicated in the table. (ndz)t, (o log r)t, and (<??),. must be multiplied by T=t — tg
in Julian years.

From the sum of the perturbations for each component taken from Tables II-V must be
subtracted the sum of the constants added to make all quantities positive. The constant
terms of the developments are not included in the tables and must also be applied. For each
component the algebraic sum of the constants to be applied is given separately with the tables
of each planet, and is designated by cz, cr, c„ for the three components, respectively.

Besides the constants introduced to make all the values of d log r positive, and the constant
corresponding to the absolute term in the development of v, cr also contains the correction
which it is necessary to apply to d log r when the geocentric places are computed with the
value of the semimajor axis a which corresponds to the mean mean mption. It is to be observed
that in Hansen's theory the disturbed positions must be computed with constant elements.
The constant in the development of v corresponds to the value of the semimajor axis a, com-
puted from the osculating mean motion. The value a, however, given with the elements
and in the auxiliary quantities in these tables, corresponds to the mean mean motion. That
part of cr which is due to the introduction of the semimajor axis a, corresponding to the mean
mean motion in place of the osculating value of a, is indicated for each planet.

Thus, in the tables for Althaea, page 348, the sum of the constants added to make
all numbers of Table III positive is 107.5 units of the fifth decimal place. The constant term
in v, page 350, is +27". 4, and the correction of this constant necessitated by the use of the
mean instead of the osculating value of the semimajor axis a is —38". 4. The algebraic sum
of this latter correction and of the constant in v is — 11".0, or — 11". 0 sin 1" Mod. = —2.3 units
of the fifth decimal place in d log r. The total number of units of the fifth decimal place to
be subtracted from d log r is, therefore, 110 units = cT, as given on page 348, of the tables of
(119) Althaea.

" It is to be observed, however, that the elements g0 and n contain the constant and the nontrigometrical secular
parts of ndz, respectively.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNEK. 209

The complete tabulation of the perturbations of (101) Helena, (103) Hera, and (119)
Althaea, is, therefore, as follows

ndz = (ndz), + (ndz)2 + etc + {ndz)tT—cz

3 log r = (3 log /■), + (<} log r), + etc . - + (8 log r)tT-Cr

dp = (£/?), + (<?/?), + etc. . . . + (*/?), T- o

ARRANGEMENT OF THE TABLES.

Table I gives the values of the mean anomaly g for January 0.0 of every common year,
and for January 1.0 of every leap year from the year of discovery to 1930, and its variations
for the different months and days.

Table II gives the periodic parts of the perturbations of the mean anomaly, designated
by (noz)^ (ndz),, etc., for arguments 1, 2, etc., in units of 0?001 and one decimal thereof.

Table ///gives the periodic parts of the perturbations of the radius vector, designated by
(8 log r)lt (3 log r),, etc., for arguments 1, 2, etc., in units of the fifth place and one decimal
thereof.

Table IV gives the periodic parts of the perturbations u c<>s i multiplied by a sin 1",
designated by (8p)u (o^),, etc., in units of the fifth decimal place and one decimal thereof.

Table V gives the perturbations of the mean anomaly, of the radius vector, and of the third
coordinate, arising from the terms to be multiplied by T, the time from the epoch expressed in
Julian years. These coefficients of the secular parts of the perturbations are designated by
(ndz)t, (8 log r)t, and (#),.

Table VI contains the constants for the equator for the beginning of every year from the
date of discovery to 1930, inclusively of the logarithms of the quantities cos a and cos b and
cos e, by which the perturbation 8$ must be multiplied to obtain the corrections Jx, Jy, Az to
the heliocentric equatorial coordinates ,r, y, and z.

DIRECTIONS FOR COMPUTING THE PERTURBATIONS n<5z, S log r=log lltl'l, and S/S.

Let /0 be the epoch of the mean anomaly g0, and let t be the date for which the perturba-
tions are to be computed. Let g' be Jupiter's mean anomaly at the date. Let g be the planet's
undisturbed mean anomaly at the date. For the date t take g' and g from the Tables A and I,
respectively. To form the argument g of the perturbations in tables II-V, apply to Table I the
correction J-=r— k0. (See p. 203.)

Form the necessary arguments (ig—i'g') for Tables II to V as indicated on pages 327, 338,
or 348.

Express T=t—t0 in Julian years and decimals thereof.

From Tables II-IV take the periodic, parts (n8z)i, (8 log r)it and (8p)f of the perturbations
with the arguments (ig—i'g'), in accordance with their designations on pages 327, 338, or 348.

From Table V take the values of (noz)t, (o log r)t, and (33)t, to be multiplied by T= (t — t0)
in Julian years and perform the multiplication.

Form the sums ndz, 8 log /•, and 8j3, of the periodic and secular parts of the perturbations.

Subtract the constants cz, cr, and c^, given on pages 327, 338, or 348.

The disturbed mean anomaly is:

M=nz=g + n8z.

EXAMPLE.

As an example of the use of the tables of (101 ) Helena, (103) Hera, and (119) Althaea, we
shall compute the perturbations of (119) Althaea for 1907, December 2.7535, Berlin Mean Time.

210

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

g, Table I.

g', Table A.

1907.0

324-83910

78?06

t

1907. 922

Dec. 0.0
2.0

79. 36264
0. 47523

27. 752
0. 166

1894. 643

+ 13.28 Julian

0.7535
9, 9'

0. 17904

0. 063

years.

44. 8560

106. 04

At,

- 0.0261

Arg. g, g'

44. 830

106. 04

PERTURBATIONS.

(ndz)i

(d log r)i

W)i

Arguments.

Table II,
Unit=0?001.

Table III,
Unit =0.00001.

Table IV,
Unit =0.00001.

9

9- 9'

9-3 g'

9-2 g'

2 9-3 9'

2 9- 9'

3 9-2 g'

3 9—4 .'/

4 9—3 9'

- 9'
-9- 9'

44?83
298. 79

86. 71
192. 75
131. 54
343. 62
282. 41

70.33
221. 20
253. 96
209. 13

1

9
3
4
5
6
7
8
9

10
11

217.6
90.6

224.6
39,0
1.4
2.1
0.0
0.5
0. 1
0. 1
0.5

21.5
71.2
3.9
18.0
1.7
1.6
1.2
0.0

1.3

25.9
5.7
11.4
14.2
28.1
4.6

3.5

27.2
3.9

Arg. 1, c={ndz)t, etc., Table V.

Sum
c (t-t0)

+ 576. 5

17.8

- 407. 2

+ 120. 4
-2.7
-109. 8

+ 124. 5
- 69.5
-161.4

(ndz)t

(a log r)(

W)i

+ 151.5
= (ndz)

+ 7.9
=0 logr

-106.4
=8p

-1.34

-0.20

-5. 23

The perturbations are

ndz = +0?1515; 8 log r= +0.00008; 5/3= -0.00106
and

M=nz=g + ndz = 45?0075.

For an example for the computation of a geocentric position with the aid of M, d log r, and
dp, see the example of (170) IUytaerrmestra, page 215.

TABLES OF (g3) MINERVA.

The elements of Minerva are osculating" elements. The tables of Minerva are reproduced
from a manuscript by Eichelberger. The original tables were merely abridged and rearranged
to conform as much as possible to the general plan adopted for the tables of the minor planets
discovered by Watson.

a It is to be observed, however, that the elements gQ and n contain the constant and nontrigonometrical parts of
ndz, respectively.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 211

The tables are based upon the "General Perturbations of Minerva by Jupiter," published by
Eichelberger in the Memoirs of the National Academy of Sciences, Volume III, Tbird Memoir.

Except for some minor changes, due mainly to the adoption of a different epoch and of a
slightly different value of Jupiter s mass, the perturbations and elements given on pages 361.
362, and 363 are the same as those originally published by Eichelberger.

The expressions ndz, v, and u/cos i are developed in the form:

ndz = nz -ga- nt = ZfZ^A \> sin [ (i - i'ft)e - i' (g' - fig)] +
ZilfB): cos [(i-i',i)s-i'(g' -fig)] +
■ (t-t0){IiCi sin ie + liDi cos (s}

v-Bi+ItlrAl ^n [{i-i' n)s-i'{g' -fig)] +

Zili&t cos [(i-i'fi)s-i'(g'-fig)] +
(t - ta) {D0 + Z4 Ci sin is + ZiDi cos is }

u cos i=Bl + ZiZ?A\> sin [(i-i' n)s-i'{g' —fig)] +
liZiB1, cos [(i-i'fi)s-i'(g' -fig)] +
(t - t0) {D0 + liCt sin is + J,Z>,- cos is }

i varying from — oo to + <x> , and i' from 0 to oo , except that the constants Bl and Dn are
segregated from the double sums.

Before tabulation, the expression for v was transformed into an expression for log (1 +v) =
3 log /• by multiplying the expression for v by Mod. sin 1", the higher powers of v being inappre-
ciable within the accuracy of the tables. Similarly the expression for u/cos i was transformed
into an expression for 3t3 by multiplying the expression for u/cos i by a sin 1".

For tabulation the perturbations are segregated into their secular and nonsecular portions.
The long period term in ndz is

+ 11". 1 cos [5s - U(g' + ue sin s)] + 4".() sin [5s - 1 3 (g' + fie sin s)]

and is also segregated from the periodic portion.

NONSECULAR PORTION OF THE PERTURBATIONS.

The nonsecular portion of the perturbations has the form

Bl + ZiZfM. sin [ti-i'u)s-i'(g' -pgfi+SJfB, cos [(i-i' fi)s -i'(g' -g)]

for all three components. For ndz, Bt and Z)IJ=0, these constants being contained in the
elements g0 and n, respectively.
By writing the argument

(i — i'fi)s — i' ig' — fig)
in the form

i'(s-g' -fie sin e) + (i-i')s = i'AT+ (i-i')e
where

V= (g -g') + (s -g - ae sin s) = (g -g') +J(g -g')
and where

J (g — g ) = s — g — fie sin s

we obtain for the nonsecular portion of the perturbations the expression

SiSgA^ sin [i X + (i - i' )s] + ZilfB'e cos [i' N+(i- %' )e]

where B\ is omitted for the present.

If we write (i) for (i— %'), and expand the sines and cosines, the expression becomes for a
particular value of (i)

Zi'A"i'.+i' sin i'N cos (i)s + ZVA^.*V cos i X sin (i)s
+ Zi-BW,+* Cos i' N cos (i)s - J'i5';.,+'" sin i' N sin (i)s

= cos (i)eZi{Ay+i' sin V X + B'^*' cos i'AT + sin (i)eZi'[A^+e cos i'N-B",^'' sin i'N]
where, as before, i' is always positive, and where (i) = (i—i') may be either positive or negative.

212 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Let, in the foregoing expression,

a-Hj, represent the coefficient of sin ( + (i)s).
(i-Ut represent the coefficient of sin ( — (i)e).
b+(i) represent the coefficient of cos ( + (i)s).
b-fi) represent the coefficient of cos ( — (i)s).

Then the nonsecular portion of the perturbations becomes for a particular value of (i)

(o+rt)— o_w) sin (i)£ + (b+d)+b-(i)) cos (i)e

where (i) is always positive.

Changing the notation by letting

a{=(a+ii) -a_(i)) ; ft, = (b+li) -J_(i))

we obtain the following form for the nonsecular portion of the perturbations for a particulai

value of (i),

a, sin is + bt cos is

where

a, = 2VU+,?+;' cos i' V-5+';:+'' sin i'JV] - Z^A'^' cos i' N-B~^+i' sin i'A]
&< = 2,^+(49+*' sin i'N+B+y+i' cos i'A] + J,-[^-';.,+''' sin i'N+B-^' cos i'iV]

Tlie nonsecular portion of the perturbations have thus been reduced to the form

Jjfflj- sin ie + Ifii cos is, i always positive.

The a, and bt coefficients are functions of the original A\ and J5;< coefficients, as given on
pages 362, 363, and of the argument N, where

N=g-g'+J(g-g')
and

J(ij —g1) =e—g — fte sin e.

The a, and 6, coefficients are tabulated for the nonsecular parts of the perturbations with
the argument N in Tables II, III, and IV for all three components, the intervals being so chosen
as to facilitate interpolation. The difference for one degree is also given wherever necessary.
The constant Z?J occurring in v and w/cos i, is included in b0. It is not necessary to compute
a0 since this is multiplied by sin OXg.

SECULAR PORTION OF THE PERTURBATIONS.

This is of the form

T{D„ + 1 iC, sin ie + Ifi, cos is}

where T=t— 10, and may be written

(A\)t + ZiiAaJt sin ie + Zt{dhi)t cos is
where

UK), = TDn; (Ja,)t = TOs: (Jb,), = TD,.

The secular terms are thus reduced to the same form as the nonsecular terms. The values of
(Jb0)t, (Ja,),, and (J&,-)t are tabulated in Table V for all three components for the beginning of
every second year from 1865-1930, together with the changes for various intervals, to facilitate
their computation for any date within the table. The term (Jb0)t in ndz is contained in the
element n, and need not be tabulated. This heading has, therefore, been adopted for the long-
period term.

THE LONG-PERIOD TERM IN rniz.

The long-periodic term in ndz has been computed for every two years from 1865-1930,
and is tabulated in Table V in the block ndz under the heading (Jb0)t. Owing to its slow varia-
tion its changes are not given.

The complete tabulation of the perturbations of Minerva is, therefore, in the form

(Jb„)t +-!>, + (Ja,)t] sin u + I$b,+ (Al,)d cos ie
for each of the components ndz, log (1 +v)=d log r, and dp.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

213

ARRANGEMENT OF THE TABLES.

'fable I gives the values of the mean anomaly g and of (g—g') for January 0.0 of every
common year and for January 1.0 of every leap year from 1865 to 19:50, and their changes for
the different months and days.

Table II gives the coefficients a, and b, of the periodic parts of the perturbations ndz, with
the argument N, hi units of 0?001 and one decimal thereof, where

N=(g-g') + J(g-g').

Table III gives the coefficients a, and b, of the periodic parts of the perturbations log
(1 +y) =o log r with the argument N in units of the fifth decimal place and one decimal thereof.

Table IV gives the coefficients a, and />, of the periodic parts of the perturbations <5;? with
the argument N in units of the fifth place and one decimal thereof.

Table V gives the coefficients (Jb0)t, (Jat)t, and (J6,-)« of the secular parts of the perturba-
tions for all three components for the beginning of every second year from 1865 to 1930, together
with their changes for one year, thirty-one days, thirty days, twenty-eight days, and one day.
The coefficient (4b0)t for ndz represents the long-period term.

Table VI gives the constants for the equator for the beginning of every year from date of
discovery to 1930, inclusively of cos a, cos b, cos c, by which the perturbations d.3 must be multi-
plied to obtain the corrections Jx, Jy, Iz to the heliocentric equatorial coordinates x, y, and z.

Table VII gives the values of J(g —g') =e—g — ue sin s and the values of the reduction (s —g)
from mean to eccentric anomaly for the argument g.

DIRECTIONS FOR COMPUTING THE PERTURBATIONS n,)z, o log r=log (l+u), and oj).

Let t be the date for which the perturbations are to be computed. Let g' be Jupiter's
mean anomaly at the date. Let g be the planet's undisturbed mean anomaly at the date. For
the date / take g and g—g' from Table I. Greenwich mean time is used for this table.

With g + -l~ as argument take J (g—g') and (e— g) from Table VII.

Form the multiples of s up to 5s, where £ =g + (s — g).

With N=(g -g')+J(g -g')+J- as argument take the coefficients a„ bt of the periodic part
of the perturbations from Tables II, III, and IV, where i has every value from 0 to 5.

For the date t take the coefficients (Ja,),, (Jb,)t from Table V for each of the three com-
ponents. Form the coefficients (a)i=ai + (Ja,)t and (b)i = bt + (Jbi)t-

By means of the traverse tables, Tables B, form the products

[a,- + (Ja,)t] sin is and [b, + (Jfr,)<] cos is.

Form the sum of the products for each component. The resulting sums are the desired
values. of ndz, <Hogr, and d,3. The disturbed mean anomaly is M'=nz=g + ndz.

EXAMPLE.

As an example of the use of the tables, the perturbations of Minerva will be computed for
1874, January 15.0, Greenwich mean time.

Table I.

Table VII.

9

9-9'

Argument g.

1874.0
Jan. 0.0
15 days

199?86574
0. 00000
3. 23301

43?455
0.000
1.987

1(9-9')
(s-g)

-1?717
-2. 795

9
(e-9)

€

2e
3e
4«

5£

203? 165
-2. 803

(9-9')

Mg-g')

J-

Arg. A'

45. 442

-1. 717
+0.067

200. 36
40.72

241. 09
81.45

281. 81

J-
Arg. g

203. 09875
+0. 0666
203. 1651

45.442

43. 792

214

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

PERTURBATIONS.

nSz

log (1+v)

3P

Arg. N

Table II, Unit=0?001.

Table III, Unit=0.00001.

Table IV, Unit=0.00001.

i

<H

h

dj

bi

<H

ft,

0

- 69.8

+30.4

-31.4

1

+199. 8

-329. 5

-22.3

+70.0

+ 9.2

+21.2

2

-100.0

- 34.0

-3.4

- 6.0

+22.3

+51. 9

3

-133. 5

- 13.6

+ 0.4

-7.8

- 2.0

+ 9.3

4

4.9

+ 1.6

+ 0.3

- 2.4

+ 1.6

-2.6

5

+ 2.6

+ 3.9

+ 0.1

- 0.2

- 0.1

- 0.9

TABLE V (T = 1874, JAN. 15.0).

i

Uii)t

(A-)<

U<H)t

(A)l

{A<H)t

(Od*

0

+2.9

+0.3

1

-0.7

+3.9

+1.5

+0.3

—11.9 —1.8

2

-0.1

Applying these secular terms to the corresponding periodic coefficients just preceding, and
then multiplying by the sines and cosines of the proper multiples of e, we obtain the following
perturbations by means of the Traverse Tables, Tables B:

FROM TRAVERSE TABLES. TABLE B.

i

nSz

log (1+v)

gfi

<ij sin ie

bi cos ie

<Zj sin it

bi COS M

ai sin u

6j cos ie

0
1
2
3
4
5

•

- 69.3

- 65. 1
+ 116.7

- 4.8
-2.5

- 66.8
+305. 4

- 25. 9
+ 6.6
+ 0.3
+ 0.8

+7.3
-2.2
-0.3
+0.3
-0. 1

+30.4
-66.0
-4.6
+ 3.8
- 0.4

+ 0.9
+14.5
+ 1.7
+ 1.6
+ 0.1

-31. 1

-17.8
+39.4
-4.5

- 0.4

- 0.2

- 25. 0

+220. 4

+4.9

-36.8

+ 18.8

-14.6

Sum

+195. 4

-31.9

+4.2

The perturbations are

ndz= +0?1954; log (1 +v)

-0.00032; £/? =+0.00004;

and

M = nz = g + ndz = 203 ?2942.

For an example for the computation of a geocentric position with the aid of M, log (1+v)
d log r, and dp, see the example of (179) Klytaemmstra , page 215.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER. 215

DIRECTIONS FOR THE COMPUTATION OF A GEOCENTRIC POSITION REFERRED TO
THE MEAN EQUINOX AND EQUATOR FOR THE BEGINNING OF THE YEAR, FROM

M, 5 log r, AND 5,3.

To the undisturbed g, i. e., the value taken directly from Table I, the perturbations no:
have been added to form the disturbed mean anomaly,

M=nz = g + ndz.

From M, the true anomaly./1 may be conveniently computed by means of Tietjen's "Tafe
zur Berechnung der Wahren Anomalie." "

Compute the radius vector corresponding to f by the formula

V
r = -

1 +e cosy

where p and e are to be found with the Auxiliary Quantities.
Compute /-, the disturbed radius vector by the formula

r=r(l +v).

Take from the table of the Constants for the Equator, Table VI, the values A', B' , C , log
sin a, log sin b, log sin c, for the beginning of the year and compute the heliocentric coordinates
by the formulae,

x=r sin a sin (A' +j).
y = r sin b sin (B' +/')■
z — r sin c sin ( C +f) .
Compute

Ax = cos a dj3
Ay =cos b 5/3
Az =cos c dj3

where cos a, cos b, cos c, are given in Table VI.

Form the geocentric coordinates by the formulae,

$=x + Jx + A
rl=y+Jy+T

£=2 +AZ + Z

in which X, Y, and Z are the solar coordinates at the date referred to the mean equator and
equinox at the beginning of the year.

Compute a and d for the beginning of the year in the usual way from

p cos 3 cos « = ?

p cos d sin a = Tj

psind =C

EXAMPLE.

As an example, the geocentric right ascension and declination of (179) IUytaemnestra will
be computed for September 26.5, 1907, Berlin mean time, referred to the mean equinox and
ecliptic for the beginning of the year, with the aid of the perturbations derived on page 206, etc

a Veroffentlichungen des Koniglichen Astronomischen Rechen-Instituts zu Berlin. No. 1.

216 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

o

9

354. 1341

a

log cos/

9. 99728

nSz

+ 0. 7759

.£

log e cos /

9. 04693

g-\-n8z=M1

354. 9100

S

log ( 1+e cos/)

0. 04587

Arg. M1=2tc-M,

5. 0900

\

c

<5

log/-

0. 42182

dM°

+ 0. 0900

a

log (1 +y)

26

dM'

+

5.40

log r

0. 42208

<f>

6. 4371

is

d<j>'

+

6.23

■a

dv/d<j>

+ 0. 2320

bo
O

(D dvld<j>)dM'
A<f>d<y /20

+ 42

i

+ 6

a

a
a

log 5/3

6. 358n

Zd$'

+

1.48

d(v—M)jdM

+ 0. 2542

3

1/2 Dmd M°

0

CSJ

log e, log p, and log a from elements

ZdM'

+

1.37

"5

and auxiliary quantities, page 313.

v-M

+ 1

16.55

v,-M,

\ 1. 3233

19.40

»!■=/

353. 5867

H

a Veroffentlichungen des Koniglichen Astronomischen Rechen-Instituts zu Berlin, No. 1.

c

1

c

A', B', C

84?0995

351?2146

12?5988

Table VI.

A'+f, etc.

77. 6862

344. 8013

6. 1855

log sin a, etc.

9. 99630

9. 97007

9. 58154

Table VI.

log sin (A'-\-f), etc.

9. 98989

9. 41857n

9. 03240

log x, y, z

0. 40826

9. 8107 In

9. 03601

log cos a, etc.

9. lJ4n

9. 555n

9.966

Table VI.

log Jr. Ay, J:

5.472

5.913

6. 32 In

x, y, z

+ 2.56012

- 0. 64674

+ 0. 10864

Ax, Ay, J:

+ 3

+ 8

21

x, v. z

- 1.00115

- 0.04320

- 0.01875

[Berliner Astro-
\ nomiscb.es Jhar-
1 buch, 1907.

f> v, c

+ 1.55900

- 0. 68986

+ 0.08968

logf

log COS il
log sin <t

log 7)

log tg a
a, 1907.0

0. 19285
9.96118
9. 60706
9. 83874n
9. 64589n
336?1319
=22h 24m 31?7

log p cos 3
log cos 3
log sin 3

logC
log tg 8
3 1907.0
logp

0. 23167
9. 99940
8. 72043
8. 95270
8. 72103
3?0113
0. 23227

a =22" 24m 32s)

M 907.0
3=3° 0'.7 1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLE A.— JUPITER'S MEAN ANOMALY, (g')

217

Jan. 0.0 of

common years; Jan. 1.0 of leap years

Table for beginning of
month

Year

9'

Year

'/

Month

9'

1863
B 4

O

182. 91
213. 29

1900
1

O

225. 68
256. 01

Jan. {°;°

O

| 0. 000

5

243. 57

o

286. 36

™- {?:J5

1 2. 576

6

273. 84

3

316. 71

7

304. 11

B 4

347. 12

Mar. 0.0

4. 902

B 8

334. 49

5

17. 1-1

Apr. 0.0

7.478

9

4.82

6

47. 75

May 0.0

9. 971

1370

35. 18

7

78. 06

June 0.0

12. 547

1

65.58

B 8

108. 46

July 0.0

15. 030

B 2

96.04

9

138. 79

Aug. 0.0

17. 015

3

126. 43

1910

169.12

Sept. 0.0

20. 191

4

156. 78

1

199. 46

Oct. 0.0

22. 684

5

187. 10

B 2

229. 88

Nov. 0.0

25. 259

B 6

217. 47

3

260. 22

Dec. 0.0

27. 752

7

247. 74

4

290. 54

8

278. 00

5

320. 86

9

303. 28

B 6

351.26

B1880
1
2

338. 68

9.02

39.41

7
8
9

21.57
51.89
82.22

Change for n daysa

3

69.80

B1920

112.65

n

9'

n

9'

B 4

5

100. 24
130. 58

1
2

143.01
173. 36

6

160. 89

3

203. 69

7

191. 18

B 4

234. 06

1

0.083

16

1.330

B 8

221.56

5

264. 33

2

0. 166

17

1.413

9

251.87

6

294. 60

3

0.249

18

1.496

1890

282. 19

7

324. 87

4

0.332

19

1.579

1

312. 53

B 8

355. 26

5

0.416

20

1.662

B 2

342. 97

9

25. 60

6

0.499

21

1.745

3

13. 34

1930

55.97

7

0. 582

22

1.828

4

43.70

1

86. 36

8

0. 665

23

1.911

5

74.03

B 2

116.83

9

0.748

24

1.994

B 6

104. 45

3

147.21

10

II S3!

25

2.078

7

134. 76

4

177.56

11

0.914

26

2.161

8

165. 05

1935

207. 86

12

0.997

27

2. 244

1899

195. 36

13
14
15

1.080
1.163
1.247

28
29
30

2.327
2.410
2.493

a]

^or dates during January

and

February of leap years

subt

ract one day before enter-

ing

he table.

218

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLE B. TRAVERSE TABLES.

Giving the products a jL" A with the arguments a and .4.

a

1

2

3

a

A

Bin

COS

sin

COS

sin

cos

A

0°

0.00000

1. 00000

0. 0000

2. 0000

0. 0000

3. 0000

90°

1745

15

349

3

524

5

1

0. 01745

0. 99985

0. 0349

1. 9997

0. 0524

2. 9995

89

1745

46

349

9

523

13

2

0. 03490

0. 99939

0. 0698

1. 9988

0. 1047

2. 9982

88

1744

76

349

15

523

23

3

0. 05234

0. 99863

0. 1047

1. 9973

0. 1570

2. 9959

87

1742

107

348

22

523

32

4

0. 06976

0. 99756

0. 1395

1. 9951

0. 2093

2. 9927

86

1740

137

348

27

522

41

5

0. 08716

0. 99619

0. 1743

1. 9924

0. 2615

2. 9886

85

1737

167

348

34

521

50

6

0. 10453

0. 99452

0. 2091

1. 9890

0: 3136

2. 9836

84

1734

197

346

39

520

60

7

0. 12187

0. 99255

0. 2437

1. 9851

0. 3656

2. 9776

S3

1730

228

346

46

519

68

8

0. 13917

0. 99027

0. 2783

1. 9805

0. 4175 '

2. 970S

82

1726

258

346

51

518

77

9

0. 15643

0. 98769

0. 3129

1. 9754

0. 4693

2. 9631

81

1722

2S8

344

58

516

87

10

0. 17365

0. 98481

0. 3473

1. 9696

0. 5209

2. 9544

80

1710

318

343

63

515

95

11

0. 19081

0. 98163

0. 3816

1. 9633

0. 5724

2. 9449

79

1710

34S

342

70

513

105

12

0. 20791

0. 97815

0. 4158

1. 9563

0. 6237

2. 9344

78

1704

37S

341

76

oil

113

13

0. 22495

0. 97437

0. 4499

1. 9487

0. 6748

2. 9231

77

1697

407

339

si

510

122

14

0. 24192

0. 97030

0. 4838

1. 9406

0. 7258

2. 9109

76

1690

437

338

87

507

131

15

0. 25882

0. 96593

0. 5176

1. 9319

0. 7765

2. 8978

75

1682

467

337

94

504

140

16

0. 27564

0.96126

0. 5513

1. 9225

0. 8269

2. 883S .

74

1673

496

334

99

502

149

17

0. 29237

0. 95630

0. 5847

1.9126

0. 8771

2. 86S9

73

1665

524

333

105

500

157

18

0. 30902

0. 95106

0. 6180

1. 9021

0. 9271

2. 8532

72

1655

554

331

111

496

166

19

0. 32557

0. 94552

0.6511

1. 8910

0. 9767

2. 8366

71

1645

583

329

116

494

175

20

0. 34202

0. 93969

0. 6840

1. 8794

1. 0261

2. 8191

70

1U35

011

327

122

490

184

21

0. 35837

0. 93358

0. 7167

1. 8672

1. 0751

2. 8007

69

1624

640

325

128

487

191

22

0. 37461

0.92718

0. 7492

1. 8544

1. 1238

2. 7816

6S

1612

668

323

134

484

201

23

0. 39073

0. 92050

0. 7815

1. 8410

1. 1722

2. 7615

67

1601

696

320

139

480

209

24

0. 40674

0. 91354

0. 8135

1. 8271

1.2201'

2. 7406

66

1588

723

317

145

477

217

25

0. 42262

0. 90631

0. 8452

1.8126

1. 2679

2. 7189

65

1575

752

315

1511

472

225

26

0. 43837

0. 89879

0. 8767

1. 7976

1.3151

2. 6964

64

1562

778

313

150

469

234

27

0. 45399

0. 89101

0. 9080

1. 7820

1. 3620

2. 6730

63

1548

806

309

161

464

242

28

0. 46947

0. 88295

0. 9389

1. 7659

1. 4084

2. 6488

62

1534

B33

307

167

460

249

29

0. 48481

0. 87462

0. 9696

1. 7492

1. 4544

2. 6239

61

1519

859

304

171

456

258

30

0. 50000

0. 86603

1. 0000

1. 7321

1. 5000

2. 5981

60

1504

886

301

178

451

266

31

0. 51504

0. 85717

1. 0301

1. 7143

1. 5451

2. 5715

59

1488

912

297

182

447

274

32

0. 52992

0. 84805

1. 0598

1. 6961

1. 5898

2. 5441

58

1472

938

295

188

441

281

33

0. 54464

0. 83867

1. 0893

1. 6773

1. 6339

2. 5160

57

1455

963

291

192

437

289

34

0. 55919

0. 82904

1. 1184

1. 6581

1. 6776

2. 4871

56

1439

9S9

288

198

431

296

35

0. 57358

0. 81915

1. 1472

1. 6383

1. 7207

2. 4575

55

1421

1013

284

203

427

304

36

0. 58779

0. 80902

' 1.1756

1. 6180

1. 7634

2.4271

54

1403

1038

280

207

420

312

37

0. 60182

0. 79864

1. 2036

1. 5973

1. 8054

2. 3959

53

1384

1063

277

213

416

319

38

0. 61566

0. 78801

1. 2313

1. 5760

1. 8470

2. 3640

52

1366

L086

273

217

410

326

39

0. 62932

0. 77715

1. 2586

1. 5543

1. 8880

2. 3314

51

1347

1111

270

222

404

333

40

0. 64279

0. 76604

1. 2856

1. 5321

1. 92S1

2. 2981

50

1327

1133

265

227

398

340

41

0. 65606

0. 75471

1.3121

1. 5094

1. 9682

2. 2641

49

1307

1157

262

231

392

347

42

0. 66913

0. 74314

1. 3383

1. 4863

2. 007 1

2. 2294

48

1286

1179

257

230

3S6

353

43

0. 68199

0. 73135

J . 3640

1. 4627

2. 0460

2. 1941

47

1267

1201

253

240

380

361

44

0. 69466

0. 71934

1. 3893

1. 4387

2. 0840

2. 1580

46

1245

1223

249

245

373

367

45

0. 70711

0.70711

1.4142

1.4142

2. 1213

2. 1213

45

A

cos

sin

cos

sin

cos

sin

A

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

219

Table B. — Traverse Tables — Continued.

Giving the products a. SJ[ A with the arguments a and A.

a

4

5

6

a

A

sin

COS

sin

COS

sin

eos

A

0°

0. 0000

4. 0000

0. 0000

5. 0000

0. 0000

6. 0000

90°

698

6

873

8

1047

9

1

0. 0698

3. 9994

0. 0873

4. 9992

0. 1047

5. 9991

89

698

18

872

">'?

1047

28

2

0. 1396

3. 9976

0. 1745

4.9970

0. 2094

5. 9963

88

697

31

872

38

1046

45

3

0. 2093

3. 9945

0. 2617

4. 9932

0. 3140

5. 9918

87

697

43

871

54

1045

64

4

0. 2790

3. 9902

0. 3488

4. 9878

0. 4185

5. 9854

86

li'.tii

54

870

68

1044

B2

5

0. 3486

3. 9848

0. 4358

4. 9810

0. 5229

5. 9772

85

695

67

868

84

1043

101

6

0.4181

3. 9781

0. 5226

4. 9726

0. 6272

5.9671

84

694

79

867

99

1040

118

7

0. 4875

3. 9702

0. 6093

4. 9627

0. 7312

5. 9553

83

692

91

S66

114

1038

137

8

0. 5567

3. 9611

0. 6959

4. 9513

0. 8350

5.9416

82

690

103

m,:;

129

1036

155

9

0. 6257

3. 9508

0. 7822

4. 9384

0. 9386

5. 9261

81

689

116

Mill

144

1033

173

10

0. 6946

3. 9392

0. 8682

4. 9240

1.0419

5. 90S8

80

list;

127

858

159

1030

190

11

0. 7632

3. 9265

0. 9540

4. 9081

1. 1449

5. 8898

79

684

139

856

174

1026

209

12

0. 8316

3. 9126

1. 0396

4. 8907

1. 2475

5. 8689

78

0S2

151

852

190

1022

227

13

0. 8998

3. 8975

1. 1248

4. 8718

1. 3497

5. 8462

77

679

163

848

203

1018

244

14

0. 9677

3. 8812

1. 2096

4. 8515

1. 4515

5. 8218

76

676

175

845

219

1014

262

15

1. 0353

3. 8637

1. 2941

4. 8296

1. 5529

5. 7956

75

672

187

841

233

1009

280

16

1. 1025

3. 8450

1. 3782

4. 8063

1. 6538

5. 7676

74

670

198

836

248

1004

298

17

1. 1695

3. 8252

1. 4618

4. 7815

1. 7542

5. 7378

73

666

210

833

262

999

315

18

1. 2361

3. 8042

1. 5451

4. 7553

1. 8541

5. 7063

72

662

oo x

827

277

993

332

19

1. 3023

3.7821 ""

1. 6278

4. 7276 "

1. 9534

5. 6731

71

658

233

823

291

987

349

20

1/3681

3. 7588

1.7101

4. 6985

2. 0521

5. 6382

70

654

245

817

306

981

367

21

1.4335

3. 7343

1.7918

4. 6679

2. 1502

5. 6015

69

649

256

812

320

974

384

22

1. 4984

3. 7087

1. 8730

4. 6359

2. 2476

5. 5631

68

645

267

806

334

968

401

23

1. 5629

3. 6820

1. 9536

4. 6025

2. 3444

5. 5230

67

640

278

801

348

960

417

24

1. 6269

3. 6542

2. 0337

4. 5677

2. 4404

5. 4813

66

636

290

794

362

953

435

25

1.6905

3. 6252

2. 1131

4. 5315

2. 5357

5.4378

65

630

300

787

375

945

450

26

1. 7535

3. 5952

2. 1918

4. 4940

2. 6302

5. 3928

64

625

312

782

390

937

467

27

IS 160

3. 5640

2. 2700

4. 4550

2. 7239

5. 3461

63

619

322

774

403

929

484

28

1. 8779

3. 5318

2. 3474

4.4147

2. 816S

5. 2977

62

613

333

"60

416

921

500

29

1. 9392

3. 4985

2. 4240

4. 3731

2. 9089

5. 2477

61

MIS

344

760

430

911

515

30

2. 0000

3. 4641

2. 5000

4. 3301

3. 0000

5. 1962

60

602

354

752

443

902

532

31

2. 0602

3. 4287

2. 5752

4. 2858

3. 0902

5. 1430

59

595

365

744

456

893

547

32

2. 1197

3. 3922

2. 0496

4. 2402

3. 1795

5. 0883

58

589

375

736

468

883

563

33

2. 1786

3. 3547

2. 7232

4. 1934

3. 2678

5. 0320

57

58''

385

728

482

874

578

34

2. 2368

3. 3162

2. 7960

4. 1452

3. 3552

4. 9742

56

575

396

719

494

863

593

35

2.2943

3. 2766

2. 8679

4. 0958

3. 4415

4. 9149

55

568

405

710

507

852

608

36

2.3511

3. 2361

2. 9389

4. 0451

3. 5267

4. 8541

54

562

414

702

519

842

623

37

2. 4073

3. 1945

3. 0091

3. 9932

3. 6109

4. 7918

53

553

425

692

531

831

637

38

2. 4626

3. 1520

3. 0783

3. 9401

3. 6940

4. 7281

52

547

434

683

543

819

653

39

2. 517::

3. 1086

3. 1466

3. 8858

3. 7759

4. 6029

51

538

444

673

556

808

666

40

2.5711

3.0642

3. 2139

3. 8302

3. 8567

4. 5963

50

531

454

664

566

797

IWI

41

2.6242

3. 0188

3. 2803

3. 7736

3. 9364

4. 5283

49

523

462

653

579

7S4

694

42

.2. 6765

2. 9726

3. 3456

3. 7157

4. 0148

4. 4589

48

515

472

644

5S9

772

708

43

2. 72S0

2. 9254

3.4100

3. 6568

4. 0920

4. 3881

47

506

4 so

633

601

759

721

44

2. 7786

2. 8774

3. 47:;:;

3. 5967

4. 1679

4.3160

46

498

490

622

612

747

734

15

2. 8284

2. S2S4

3. 5355

3. 5355

4. 2426

4. 2426

45

A

cos

sin

cos

sin

cos

sin

A

S'XW.)

-VOL 10—11-

220 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

Giving the products o *J". A with the arguments a and A.

0°

1

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

sin

0. 0000
0. 1222
0. 2443
0. 3664
0. 4883
0. 6101
0. 7317
0. 8531

0. 9742

1. 0950
1. 2155
1. 3357
1. 4554
1. 5746
1. 6934
1.8117

1. 9295

2. 0466
2. 1631
2. 2790
2. 3941
2. 5086
2. 6222
2. 7351
2. 8472

2. 9583

3. 0686
3. 1779
3. 2863
3. 3937
3. 5000
3. 6053
3. 7094
3. 8125

3. 9144

4. 0150
4. 1145
4. 2127
4. 3096
4. 4052
4. 4995
4. 5924
4. 6839
4. 7740
4. 8626
4. 9497

1222
1221
1221
1219
1218
1216
1214
1211
1208
1205
1202
1197
1192
1188
1183
1178
1171
1165
1159
1151
11-15
1136
1129
1121
1111
1103
1093
1084
1074
1063
1053
1041
1031
1019

mi hi

995
982
909
956
943
929
915
901
886
871

COS

7. 0000
6. 9989
6. 9957
6. 9904
6. 9829
6.9734
6. 9616
6. 9478
6. 9319
6. 9138
6. 8936
6. 8714
6. 8470
6. 8206
6. 7921
6. 7615
6. 7288
6. 6941
6. 6574
6. 6186
6. 5778
6. 5351
6. 4903
6. 4435
6. 394S
6. 3442
6.2916
6. 2370
6. 1806
6. 1223
6. 0622
6. 0002
5. 9365
5. 8707
5. 8033
5. 7341
5. 6631
5. 5904
5. 5161
5. 4400
5. 3623
5. 2830
5. 2020
r, 1 195
5. 0354
4. 9497

n

32
53
75
95
118
138
159
181
202
222
244
264
285
306
327
347
307
388
408
427
448
468
487
506
526
546
564
583
601
620
039
056
674
692
710
727
743

810
825

841

sin

0. 0000
0. 1396
0.2792
0. 4187
0. 5581
0. 6972
0. 8362

0. 9750

1. 1134
1. 2515
1. 3892
1. 5265
1. 6633
1. 7996

1. 9354
2. 0706

2. 2051
2. 3390
2. 4721
2. 6045
2. 7362
2. 8669

2. 9969
3. 1258

3. 2539
3. 3809
3. 5070
3. 6319
3. 7558

3. 8785
4. 0000
4. 1203

4. 2394
4. 3571
4. 4735
4. 5886
4. 7023
4. 8145

4. 9253

5. 0346
5. 1423
5. 2485
5. 3530
5. 4560
5. 5573
5. 6568

1396
1396
1395
1394
1391
1390
1388
1384
1381
1377
1373
1368
1363
1358
1352
1345
1339
1331
1324
1317
1307
1300
1289
1281
1270
1261
1249
1239
1227
1215
1203
1191
1177
1104
1151
1137
1122
1108
1093
1077
1002
1045
1030
1013
995

8. 0000

7. 9988
7. 9951
7. 9890
7. 9805
7. 9696
7. 9562
7. 9404
7. 9222
7. 9015
7. 8785
7. 8530
7. 8252
7. 7950
7. 7624 '
7. 7274 '
7.6901 '
7. 6504 '
7. 6084
7. 5642
7. 5175
7. 4686
7. 4175
7. 3640
7. 3084
7. 2505
' 7. 1904
7. 1281
7. 0636
6. 9970
6. 9282
6. 8574
6. 7844
6. 7094
6. 6323
6. 5532
6. 4721
6. 3891
6.3041
6. 2172
6. 1284
6. 0377
5. 9452
5. 8508
5. 7547
5. 6568

sin

207

230

278
302

907
925

0. 0000

0. 1571
0.3141
0. 4710
0. 6278
0. 7844

0. 9408
1. 0968

1. 2526
1. 4079
1. 5628
1.7173

1. S712

2. 0246
2. 1773
2. 3294
2. 4807
2.6313
2. 7812

2. 9301
3.0782

3. 2253
3. 3715
3. 5166
3. 6606
3. 8036

3. 9453

4. 0859
4. 2252
4. 3633
4. 5000
4. 6353
4. 7693

4. 9018

5. 0327
5. 1622
5. 2901
5. 4163
5. 54 L0
5. 6639

5. 7851
5.9045
(i. 0222

6. 1380
■ 6. 2519

6. 3640

1545
1539

1534
1527

1521
1513

1500

1489
1481

1402

1440
1430

1417

1295

1247

1158
1139

9. 0000
8. 9986
8. 9945
8. 9877
8. 9781
8. 9658
8. 9507
8. 9329
8. 9124
8. 8892
8. 8633
8. 8347
8. 8033
8. 7693
8. 7327
8. 6933
8. 6514
8. 6067
8. 5595
8. 5097
8. 4572
8. 4022
8. 3446
8. 2845
8. 2219
8. 1568
8. 0891
8. 0191
7. 9466
7. 8716
7. 7942
7. 7145
7. 6324
7. 5480
7.4613
7. 3724
7. 2812
7. 1877
7. 0921
6. 9943
6. 8944
6. 7924
6. 6883
6. 5822
6. 4741
6. 3640

14
41
68
90
123
151
178
205
232
259
286
314
340
306
394
419
447
472
498
525
550
576
601
626
651
677
700
725
750
774
797
821
S44
867
889
912
935
956
978

1041
1061

1081
1101

a
A

90°

89

88

87

86

85

84

83

82

81

80

79

78

77

76

75

74

73

72

71

70

69

68

67

66

65

64

63

62

61

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

221

Table B. — Traverse Tables — Continued.

Giving the products a *'" A with the arguments a and A.

'

11

12

13

14

15

16

17

a

A

sin

COS

Bin

COS

sin

cos

sin

cos

sin

cos

sin

COS

sin

cos

A

0°

0.0

11.0

0.0

12.0

0.0

13.0

0.0

14.0

0.0

15.0

0.0

16.0

0.0

17.0

90°

1

0.2

11.0

0.2

12.0

0.2

13.0

0.2

14.0

0.3

15.0

0.3

16.0

0.3

17.0

89

2

0.4

11.0

0.4

12.0

0.5

13.0

0.5

14.0

0.5

15.0

0.6

16.0

0.6

17.0

88

3

0.6

11.0

0.6

12.0

0.7

13.0

0.7

14.0

0.8

15.0

0.8

16.0

0.9

17.0

87

4

0.8

11.0

0.8

12.0

0.9

13.0

1.0

14.0

1.0

15.0

1.1

16.0

1.2

17.0

86

5

1.0

11.0

1.0

12.0

1. 1

13.0

1.2

13.9

1.3

14.9

1.4

15.9

1.5

16.9

85

6

1. 1

10.9

1.3

11.9

1.4

12.9

1.5

13.9

1.6

14.9

1.7

15.9

1.8

16.9

84

7

1.3

10.9

1 5 11. 9

1.6

12.9

1.7

13.9

1.8

14.9

1.9

15.9

2.1

16.9

83

8

1.5

10.9

1.7 11.9

1.8

12.9

1.9

13.9

2. 1

14.9

2.2

15.8

2.4

16.8

82

9

1.7

10.9

1.9 11.9

2.0

12.8

2. 2

13.8

2.3

14.8

2.5

15.8

2.7

16.8

81

10

1.9

10.8

2. 1 11. 8

2.3

12.8

2.4

13.8

2.6

14.8

2.8

15 s

3.0

16.7

80

11

2.1

10.8

2.3

11.8

2.5

12.8

2. 7 13. 7

2.9

14.7

3.1

15.7

3.2

16.7

79

12

2.3

10.8

2.5

11.7

2.7

12.7

2.9

13.7

3.1

14.7

3.3

15.7

3.5

16.6

78

13

2.5

10.7

2.7

11.7

2.9

12.7

3.1

13.6

3.4

14.6

3.6

15.6

3.8

16.6

77

14

2.7

10.7

2.9

11.6

3.1

12.6

3. 4 13. 6

3.6

14.6

3.9

15.5

4.1

16.5

76

15

2.8

10.6

3.1

11.6

3.4

12.6

3.6

13.5

3.9

14.5

4. 1

15.5

4.4

16.4

75

16

3.0

10.6

3.3

11.5

3.6

12.5

3.9

13.5

4.1

14.4

4.4

15.4

4.7

16.3

74

17

3.2

10.5

3.5

11.5

3.8

12.4

4.1

13.4

4.4

14.3

4.7

15.3

5.0

16.3

73

18

3.4

10.5

3.7

11.4

4.0

12.4

4.3

13.3

4.6

14.3

4.9

15.2

5.3

16.2

72

19

3.6

10.4

3.9

11.3

4.2

12.3

4.6

13.2

4.9

14.2

5.2

15. 1

5.5

16.1

71

20

3.8

10.3

4.1

11.3

4.4

12.2

4.8

13.2

5.1

14. 1

5.5

15.0

5.8

16.0

70

21

3.9

10.3

4.3

11.2

4.7

12.1

5.0

13.1

5.4

14.0

5.7

14.9

6.1

15.9

69

22

4.1

10.2

4.5

11.1

4.9

12.1

5.2

13.0

5.6

13.9

6.0

14.8

6. 4 15. 8

68

23

4.3

10. 1

4.7

11.0

5. 1

12.0

5.5

12.9

5.9

13.8

6.3

14.7

6. 6 15. 6

67

21

4.5

10.0

4.9

11.0

5.3

11.9

5.7

12.8

6.1

13. 7

6.5

14.6

6. 9 15. 5

66

25

4.6

10.0

5.1

10.9

5.5

11.8

5.9

12.7

6.3

13.6

6.8

14.5

7.2

15.4

65

26

4.8

9.9

5. 3 10. 8

5.7

11.7

6.1

12.6

6.6

13.5

7.0

14.4

7.5

15.3

64

27

5.0

9.8

5. 4 10. 7

5.9

11.6

6.4

12.5

6.8

13.4

7.3

14.3

7.7

15.1

63

28

5.2

9.7

5. 6 10. 6

6.1

11.5

6.6

12.4

7.0

13.2

7.5

11. 1

8. 0 15. 0

62

29

5.3

9.6

5. 8 10. 5

6.3

11.4

6.8

12.2

7.3

13.1

7.8

14.0

8.2

14.9

61

30

5.5

9.5

6. 0 10. 4

6.5

11.3

7.0

12.1

7.5

13.0

8.0

13.9

8.5

14.7

60

31

5.7

9.4

6.2

10.3

6.7

11. 1

7.2

12.0

7.7

12.9

8.2

13.7

8.8

14.6

59

32

5.8

9.3

6.4

10.2

6.9

11.0

7.4

11.9

7.9

12.7

8.5

13.6

9.0

14.4

58

33

6.0

9.2

6.5

10. 1

7. 1

10.9

7.6

11.7

8.2

12.6

8.7

13.4

9.3

14.3

57

34

6.2

9.1

6.7

9.9

7.3

10.8

7.8

11.6

8.4

12.4

8.9

13.3

9.5

14.1

56

35

6.3

9.0

6.9

9.8

7.5

10.6

8.0

11.5

8.6

12. 3

9.2

13.1

9.8

13.9

55

36

6.5

8.9

7. 1 9. 7

7.6

10. 5

8.2

11.3

8.8

12.1

9.4

12.9

10.0

13.8

54

37

6.6

8.8

7. 2 9. 6

7. S

10.4

S. 4

11.2

9.0

12.0

9.6

12.8

10.2

13.6

53

38

6.8

8.7

7.4

9.5

8.0

10. 2

8.6

11.0

9.2

11.8

9.9

12.6

10.5

13.4

52

39

6.9

8.5

7.6

9.3

8.2

10.1

8.8

10.9

9.4

11.7

10.1

12.4

10.7

13.2

51

40

7.1

8.4

7.7

9.2

8.4

10.0

9.0

10. 7

9.6

11.5

10.3

12.3

10.9

13.0

50

41

7.2

8.3

7.9

9.1

8.5

9.8

9.2

10.6

9.8

11.3

10.5

12.1

11.2

12.8

49

12

7.4

S. 2

8.0

8.9

8.7

9.7

9.4

10.4

10.0

11. 1

10.7

11.9

11.4

12.6

48

43

7.5

8.0

8.2

8.8

8.9

9.5

9.5

10.2

10.2

11.0

10.9

11 7

11.6

12.4

47

44

7.6

7.9

8.3

8.6

9.0

9.4

9.7

10. 1

10.4

10.8

11. 1

11.5

11.8

12.2

46

45

.1

7.8

7.8

8.5

8.5

9.2

9.2

9.9

9.9

10. 6

10.6

11.3

11.3

12.0

12.0

45

.'us

sin

cos

sin

cos

sin

CM,-

sin

cos

sin

cos

sin

cos

sin

1 A

222

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B.

— Trc

/oer&e

Table

s — Continu

ed.

Giving the products

"cos^ wi,h tlle arBuments o and A-

a

18

19

20

21

22

23

24

a

A

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

COS

sin

cos

A

0°

0.0

18.0

0.0

19.0

0.0

20.0

0.0

21.0

0.0

22.0

0.0

23.0

0.0

24.0

90°

1

0.3

18.0

0.3

19.0

0.3

20.0

0.4

21.0

0. 4 22. 0

0.4

23.0

0.4

24.0

89

2

0.6

18. 0

0.7

19.0

0. 7

20.0

0.7

21.0

0. 8 ; 22. 0

0.8

23.0

0.8

24.0

88

3

0.9

18.0

1.0

19.0

1.0

20.0

1. 1

21.0

1.2 22.0

1.2

23.0

1.3

24 0

87

4

1.3

18.0

1.3

19.0

1.4

20.0

1.5

20.9

1. 5 | 21. 9

1.6

22. 9

1.7

23.9

86

5

1.6

17.9

1.7

18.9

1. 7

19.9

1.8

20.9

1.9 21.9

2.0

22.9

2.1

23.9

85

6

1.9

17.9

2.0

18.9

2.1

19.9

2.2

20.9

2. 3 21. 9

2.4

22.9

2.5

23.9

84

7

2.2

17.9

2.3

18.9

2.4

19.9

2.6

20.8

2. 7 21. 8

2.8

22.8

2.9

23.8

S3

8

2.5

17.8

2.6

18.8

2.8

19.8

2.9

20.8

3.1

21.8

3.2

22. 8

3.3

23.8

82

9

2.8

17.8

3.0

18.8

3.1

19.8

3.3

20.7

3.4

21.7

3.6

22.7

3.8

23.7

81

10

3.1

17.7

3.3

18.7

3.5

19.7

3.6

20.7

3.8

21.7

4.0

22.7

4.2

23.6

so

11

3.4

17.7

3.6

18.7

3.8

19.6

4.0

20.6

4.2

21.6

4.4

22.6

4.6

23.6

79

12

3.7

17.6

4.0

18.6

4.2

19.6

4.4

20.5

4.6

21.5

4.8

22.5

5.0

23.5

78

13

4.0

17 5

4.3

18.5

4.5

19.5

4.7

20.5

4.9

21.4

5.2

22.4

5.4

23.4

77

14

4.4

17.5

4.6

18.4

4.8

19.4

5.1

20.4

5.3

21.3

5.6

22.3

5.8

23.3

76

15

4.7

17.4

4.9

18.4

5.2

19.3

5.4

20.3

5.7

21.3

6.0

22.2

6.2

23.2

75

16

5.0

17.3

5.2

18.3

5.5

19.2

5.8

20.2

6. 1

21.1

6.3

22.1

6.6

23.1

74

17

5.3

17.2,

5.6

18.2

5.8

19. 1

6.1

20. 1

6.4

21.0

6.7

22.0

7.0

23.0

73

18

5.6

17. 1

5.9

18.1

6.2

19.0

6.5

20.0

6.8

20.9

7.1

21.9

7.4

22.8

72

19

5.9

17.0

6.2

18.0

6.5

18.9

6.8

19.9

7.2

20. 8

7.5

21.7

7.8

22.7

71

20

6.2

16.9

6.5

17.9

6.8

18.8

7.2

19.7

7.5

20.7

7.9

21.6

8.2

22.6

70

21

6.5

16.8

6.8

17.7

7.2

18.7

7.5

19.6

7.9

20.5

8.2

21.5

8.6

22.4

69

22

6.7

16.7

7. 1

17.6

7.5

18.5

7.9

19.5

8.2

20.4

8.6

21.3

9.0

22.3

68

23

7.0

16.6

7.4

17.5

7.8

18.4

8.2

19.3

8.6

20. 3

9.0

21.2

9.4

22. 1

67

24

7.3

16.4

7. 7

17.4

8.1

18.3

8.5

19.2

8.9

20.1

9.4

21.0

9.8

21.9

66

25

7.6

16.3

8.0

17.2

8.5

18.1

8.9

19.0

9.3

19.9

9.7

20.8

10.1

21.8

65

26

7.9

16.2

8.3

17. 1

8.8

18.0

9.2

18.9

9.6

19.8

10.1

20.7

10.5

21.6

64

27

8.2

16.0

8.6

16.9

9. 1

17.8

9.5

18.7

10.0

19.6

10.4

20.5

10.9

21.4

63

28

8.5

15.9

8.9

16.8

9.4

17.7

9.9

18.5

10.3

19.4

10.8

20.3

11.3

21.2

62

29

8.7

15.7

9.2

16.6

9.7

17.5

10.2

18.4

10.7

19.2

11.2

20.1

11.6

21.0

61

30

9.0

15.6

9.5

16.5

10.0

17.3

10.5

18.2

11.0

19.1

11.5

19.9

12.0

20.8

60

31

9.3

15.4

9.8

16.3

10.3

17.1

10.8

18.0

11.3

18.9

11. 8

19. 7

12.4

20.6

59

32

9.5

15.3

10. 1

16. 1

10.6

17.0

11.1

17.8

11.7

18.7

12. 2

19.5

12.7

20.4

58

33

9.8

15.1

10.3

15.9

10.9

16.8

11.4

17.6

12.0

18.5

12.5

19.3

13.1

20.1

57

34

10.1

14.9

10.0

15.8

11.2

16.6

11.7

17.4

12.3

18.2

12.9

19.1

13.4

19.9

56

35

10.3

11.7

10.9

15. (i

11.5

16.4

12. 0 17. 2

12.6

18.0

13.2

18.8

13.8

19.7

55

36

10. 6 14. 6

11.2

15.4

11.8

16.2

12.3 17.0

12.9

17.8

13. 5

IS. 6

14.1

19.4

54

37

10.8

14.4

11. 4

15.2

12.0

16.0

12. 6 16. 8

13. 2 17. 6

13.8

18.4

14.4

19.2

53

38

11.1

14. 2

11.7 15.0

12. 3

L5.8

12. 9 16. 5

13.5

17.3

14.2

18.1

14.8

18.9

52

39

11.3

14.0

L2 I) 14.8

12.6

15. 5

13.2

16.3

13.8

17.1

14.5

17.9

15.1

18.7

51

40

11.6

13.8

12. 2

14.6

12.9

15.3

13.5

16. 1

14. 1

16.9

14.8

17.6

15.4

18.4

50

41

11.8

13. 6

12.5

14.3

13.1

15. 1

13.8

15.8

14.4

16.6

15. 1

17.4

15.7

18.1

49

42

12.0

13.4

12.7

14. 1

13.4

14.9

14. 1

15.6

n. 7

16. 3

15. 4

17.1

16.1

17.8

48

43

12.3

13.2

13.0

13.9

13.6

14. 6

14.3

15.4

15 . 0

16. 1

15. 7

16.8

16.4

17.6

47

44

12.5

12.9

13.2

13.7

13.9

14.4

14.6

15.1

15.3

15.8

16. 0

16.5

16.7

17.3

46

45

12. 7

12. 7

13.4

13.4

14. 1

14. 1

14.8

14.8

15.6

15.6

16.3

16.3

17.0

17.0

45

A

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

A

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

223

Table B.

-Tn

ir, 1 si

Table

s—Cc

uitim

ed.

Giving the products a ^1 A with the

irguments a and A.

a

25

26

27

28

29

30

31

a

A

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

COS

sin

COS

A

0°

0.0

25.0

0.0

26. 0

0.0

27.0

0.0

28.0

0.0

29.0

0.0

30.0

0.0

31.0

90°

1

0.4

25.0

0.5

26.0

0.5

27.0

0.5

28.0

0.5

29.0

0.5

30.0

0.5

31.0

89

2

0.9

25.0

0.9

26. 0

0.9

27.0

1.0

28.0

1.0

29.0

1.0

30.0

1. 1

31.0

88

3

1.3

25.0

1.4

26.0

1.4 27.0

1.5

28.0

1.5

29.0

1.6

30.0

1.6

31.0

87

4

1.7

24.9

l.S

25 9

1.9 \ 26.9

2.0

27.9

2. 0 28. 9

2. 1

29.9

2. 2

30.9

86

5

2.2

24.9

2.3

25 9

2. 1 26. 9

2.4

27.9

2. 5 28. 9

2.6

29.9

2.7

30.9

85

6

2.6

24.9

2.7

25.9

2. 8 26. 9

2.9

27.8

3.0

28.8

3.1

29.8

3.2

30.8

84

7

3.0

24.8

3.2

25 s

3.3

26.8

3.4

27.8

3. 5

28.8

3.7

29.8

3.8

30.8

83

8

3.5

24.8

3.6

25. 7

::. 8

26. 7

3.9

27.7

4.0

28.7

4.2

29.7

4.3

30.7

82

9

3.9

24.7

4. 1

25. 7

4.2

2i ; 7

4.4

27.7

4.5

28.6

4.7

29.6

4.8

30.6

81

10

4.3

24.6

4.5

25.6

4. 7

26.6

4. 9 27. 6

5.0

28.6

5.2

29.5

5.4

30.5

80

11

4. 8 24. 5

5.0

5.2

26.5

5. 3 27. 5

5.5

28. 5

5. 7 29. 4

5.9

30.4

79

12

5.2

24.5

5.4

25. 4

5.6

26, I

5.8

27.4

6.0

28.4

6. 2 29. 3

6.4

30.3

78

13

5.6

24.4

5.8

25. 3

6. 1

26, ;;

6.3

27.3

6.5

28.3

6.7

29.2

7.0

30.2

77

14

6.0

24.3

6.3

25. 2

6.5

26. 2

6.8

27.2

7.0

28.1

7.3

29.1

7.5

30.1

76

15

G. 5

24.1

6.7

25. 1

7.0

26. 1

7.2

27.0

7.5

28.0

7.8

29.0

8.0

29.9

75

16

6.9

24.0

7.2

25.0

7.4

26. 0

7.7

26.9

S. 0

27.9

8.3

28.8

8.5

29.8

74

17

7.3

23.9

7.6

24.9

7.9

25.8

8.2

26.8

8.5

27.7

8.8

28.7

9.1

29.6

73

18

7.7

23.8

8.0

24.7

8.3

25.7

8.7

26.6

9.0

27.6

9.3

28.5

9.6

29 5

72

19

8.1

23.6

8.5

24.6

8.8

25. 5

9.1

26.5

9.4

27.4

9.8

28.4

10.1

29.3

71

20

8. .6

23.5

8.9

24.4

9 2

25 1

9.6

26.3

9.9

27.3

10.3

28.2

10.6

29. 1

70

21

9.0

23.3

9.3

24.3

9.7

25. 2

10.0

26. 1

10.4

27. 1

10.8

28.0

11.1

28.9

69

22

9.4

23.2

9.7

24.1

10. 1

25. 0

10.5

26.0

10.9

26.9

11.2

27.8

11.6

28.7

68

23

9.8

23.0

10.2

23.9

10.5

24.9

10.9

25.8

11.3

26. 7

11.7

27.6

12. 1

28.5

67

24

10.2

22.8

10.6

23.8

11.0

24. 7

11.4

25.6

11.8

26.5

12.2

27.4

12.6

28.3

66

25

10.6

22.7

11.0

23.6

11.4

21 5

11.8

25.4

12.3

26.3

12. 7

27.2

13.1

28.1

65

26

11.0

22.5

11.4

23.4

11.8

24. 3

12.3

25 2

12.7

26. 1

13.2

27.0

13.6

27, 9

64

27

11.3

22.3

11.8

23.2

12.3

24. 1

12.7

24.9

13.2

25.8

13.6

26.7

14.1

27.6

63

28

11.7

22. 1

12.2

23.0

12.7

23.8

13.1

24.7

13.6

25.6

14.1

26.5

14.6

27.4

62

29

12.1

21.9

12.6

22.7

13.1

23.6

13.6

24.5

14.1

25.4

11.5

26.2

15.0

27. 1

61

30

12.5

21.7

13.0

22. 5

13.5

23.4

1 1 (I

24. 2

14.5

25.1

15. 0

26.0

15. 5

26.8

60

::i

12.9

21.4

13.4

22. 3

13 9

2:1. 1

14.4

24.0

14.9

24.9

15. 5

25.7

16.0

26.6

59

32

13.2

21. 2

13.8

22. 0

14.3

22. it

11 s

23.7

15.4

24.6

15.9

25 1

16.4

26.3

58

33

13.6 21.0

14.2

21.8

11.7

22. 6

15.2

23.5

15. 8 24. 3

16.3

25.2

16.9

26.0

57

34

14.0 20 7

14.5

21. 6

15.1

22. 4

15.7

23.2

16. 2 24. 0

16.8

24.9

17.3

25.7

56

35

14. 3 20. 5

14.9

21.3

15.5

22. 1

16. 1

22.9

16. 6 23. 8

17.2

24.6

17.8

25.4

55

36

14. 7 20. 2

15.3

21. o

15.9

21. S

16. 5 22.7

17.0

23.5

17, 6

24.3

18.2

25.1

54

37

15. 0 20. 0

15.6

20.8

16.2

21.6

' 16. 9

22. 4

17.5

23. 2

is 1

24.0

18.7

24.8

53

38

15. 4 19. 7

16.0

2(1. 5

hi, 6

21.3

17.2

22.1

17.9

22. 9

18.5

23.6

19.1

24.4

52

39

15.7

19.4

16.4

•_'ii 2

17 0

21.0

17. 6 21. S

18. 3. 22. 5

18.9

23.3

19. 5

24.1

51

40

16.1

19.2

16. 7

19.9

17,4

2(1. 7

18.0

21.4

18.6

22.2

19.3

23.0

19.9

23.7

50

41

16.4

18.9

17.1

19.0

17.7

20. 4

18.4

21.1

19.0

21. 9

19.7

22.6

20.3

23.4

49

12

16.7

18.6

17.4

19.3

IS. 1

20. 1

18.7

20.8

19.4

21. 6

20.1

22. 3

20.7

23.0

48

43

17.0

18.3

17. 7

19.0

18.4

L9. 7

19.1

20.5

19.8

21.2

20.5

21.9

21. 1

22. 7

47

11

17.4

18.0

18.1

18.7

18.8

19.4

19.5

20.1

20.1

20.9

20.8

21.6

21.5

22. 3

46

45

17.7

17.7

IS. 4

18.4

19.1

19.1

19.8

19.8

20.5

20.5

21 2

21.2

21.9

21.9

45

'

cos

sin

COS

sin

cos

sin

cos

sin

. cos

sin

cos

sin

cos

sin

A

224

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

0

32

33

34

35

36

37

38

a

A

sin

COS

sin

COS

sin

COS

sin

cos

sin

cos

sin

"cos

sin

cos

A

0°

0.0

32.0

0.0

33.0

0.0

34.0

0.0

35.0

0.0

36.0

0.0

37.0

0.0

38.0

90°

1

0.6

32.0

0.6

33.0

0.6

34.0

0.6

35.0

0.6

36.0

0.6

37.0

0. 7

38.0

89

2

1. 1

32.0

1.2

33.0

1. 2

34.0

1.2

35.0

1.3

36.0

1.3

37.0

1.3

38.0

88

3

1.7

32.0

1.7

33.0

1.8

34.0

1.8

35. 0

1.9

36.0

1.9

36.9

2.0

37.9

87

4

2.2

31.9

2.3

32. 9

-2.4

33.9

2.4

34.9

2.5

35.9

2.6

36.9

2.7

37.9

86

5

2.8

31.9

2.9

32.9

3.0

33.9

3.1

34.9

:;. i

35.9

3.2

36.9

3.3

37.9

85

6

3.3

31.8

3.4

32.8

3.6

33.8

3.7

34.8

3.8

35.8

3.9

36.8

4.0

37.8

84

7

3.9

31.8

4.0

32.8

4. 1

33.7

4.3

34.7

4.4

35.7

4.5

36.7

4.6

37.7

83

8

4.5

31.7

4.6

32.7

4.7

33.7

4.9

34.7

5.0

35.6

5.1

36.6

5.3

37.6

82

9

5.0

31.6

5.2

32.6

5.3

33.6

5.5

34.6

5.6

35.6

5.8

36.5

5.9

37.5

81

10

5.6

31.5

5.7

32.5

5.9

33. 5

6.1

34.5

6.3

35.5

6.4

36.4

6.6

37.4

80

11

6.1

31.4

6.3

32.4

6.5

33.4

6.7

34.4

6.9

35.3

7. 1

36 3

7.3

37.3 '

79

12

6.7

31.3

6.9

32.3

7. 1

33.3

7.3

34.2

7.5

35. 2

7.7

36.2

7.9

37.2

78

13

7.2

31.2

7.4

32. 2

7.6

33.1

7.9

34. 1

8.1

35. 1

8.3

36.1

8.5

37.0

77

14

7.7

31.0

8.0

32. 0

8.2

33. 0

8.5

:;i o

8.7

34.9

9.0

35.9

9.2

36.9

76

15

8.3

30.9

8.5

:;i 9

8.8

32,8

9. 1

33.8

9.3

34. s

9.6

35.7

9.8

36.7

75

16

8.8

30.8

9. 1

31.7

9.4

32.7

9.6

33. 6

9.9

34.6

10.2

35.6

10.5

36.5

74

17

9.4

30. 6

9.6

31.6

9.9

32.5

10. 2

33. 5

10.5

34.4

10.8

35.4

11. 1

36. 3

73

18

9.9

30.4

10.2

31.4

10.5

32. 3

10.8

33. 3

11. 1

34.2

11.4

35.2

11.7

36. 1

72

19

10.4

30.3

10.7

31.2

11.1

32.1

11.4

33. 1

11.7

34.0

12.0

35.0

12.4

35.9

71

20

10.9

30.1

11.3

31.0

11.6

31.9

12.0

32. 9

12.3

33.8

12.7

34. S

13.0

35.7

70

21

11.5

29.9

11.8

30.8

12.2

31.7

12.5

32. 7

12.9

33.6

13.3

34. 5

13.6

35. 5

69

22

12.0

29.7

12.4

30.6

12. 7

31.5

13. 1

32. 5

L3.5

33.4

13.9

34. 3

14.2

35. 2

68

23

12. 5

29.5

12.9

30.4

13.3

31.3

13.7

32. 2

14. 1

33.1

14.5

34. 1

11 s

35.0

67

24

13.0

29.2

13.4

30. 1

13.8

31.1

14.2

32.0

14.6

32.9

15.0

33.8

15. 5

34.7

66

25

13.5

29.0

13.9

29.9

14.4

30.8

14.8

31.7

15.2

32.6

15.6

33.5

Hi. 1

34.4

65

26

14.0

28.8

14. 5

29.7

14.9

30.6

15. 3

31.5

15. S

32.4

16.2

33.3

16.7

34. 2

64

27

14.5

28.5

15.0

29.4

15.4

30.3

15. 9

31.2

Hi. 3

32.1

16.8

33.0

17.3

33.9

63

28

15.0

28.3

15.5

29.1

16.0

30.0

16.4

30.9

16.9

31.8

17.4

32. 7

17.8

33.6

62

29

15.5

28.0

16.0

28.9

16.5

29.7

17.0

30. 6

17.5

31.5

17.9

32. 1

18 1

33.2

61

30

16.0

27.7

16.5

28.6

17.0

29.4

17.5

30.3

18.0

31. 2

18.5

32.0

19.0

32.9

60

31

16.5

27.4

17.0

28.3

17.5

29.1

18.0

30.0

18.5

30.9

19. 1

31.7

19.6

32.6

59

32

17.0

27. 1

17 5

28.0

18.0

28.8

18.5

29.7

19.1

30.5

19.6

31.4

20. 1

32. 2

58

33

17.4

26.8

18.0

27. 7

18.5

28.5

19. 1

29. 4

19.6

30.2

20.2

31.11

20.7

31.9

57

34

17.9

26.5

is. 5

27.4

19.0

28. 2

L9. i;

29.0

20. 1

29.8

20.7

30. 7

21.2

31.5

56

35

18.4

26.2

18.9

27.0

19. 5

27.9

20. 1

28.7

20.0

29. 5

21. 2

30. 3

21.8

31.1

55

36

18.8

25.9

19.4

26.7

20. 0

27.5

20.6

28. 3

21 2

29.1

21.7

29.9

22. 3

30.7

54

37

19.3

25.6

19.9

26.4

20. 5

27. 2

21. 1

28.0

21. 7

28.8

22. 3

29.5

22.9

30.3

53

38

19. 7 25. 2

20. 3

26. 0

20.9

26.8

21.5

27. Ii

22. 2

28.4

22.8

29. 2

23. 4

29.9

52

39

20.1

24.9

20.8

25. 6

21.4

. 26. 4

22.0

27. 2

22.7

28.0

23.3

28.8

2::. 9

29.5

51

40

20.6

24. 5

21 2

21.9

26.0

22. :.

2i ;. s

23.1

27. Ii

23.8

28. 3

21.4

29.1

50

41

21.0

24.2

21.6

24. 9

22. 3

25.7

23.0

26. 1

2:;, ii

27.2

24.3

27.9

24.9

28.7

49

42

21.4

23.8

22 1

24.5

22. 8

25.3

23. 1

26. 0

24.1

26.8

24.8

27.5

25. 4

28.2

48

43

21.8

23.4

22. 5

24. 1

2:!. 2

24.9

2::. ii

25.6

24.6

26.3

25. 2

27. 1

25.9

27.8

47

44

22.2

23.0

22.9

23.7

23.6

24.5

24.3

25. 2

25. 0

25.9

25.7

26.6

26.4

27.3

46

45

22.6

22.6

23. 3

23.3

24.0

24.0

24.7

24. 7

25.5

25.5

20.2

26.2

26.9

26.9

45

A

cos

sin

cos

sin

COS

sin

cos

sin

cos

sin

cos

sin

cos

sin

A

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

225

Table B. — Traverse Tables — Continued.

a

39

40

41

42

43

44

45

a

.1

sin

cos

sin

COS

sin

cos

sin

cos

sin

COS

.-ill COS

sin

cos

A

0°

0.0

39.0

0.0

40.0

0.0

41.0

0.0

42.0

0.0

43.0

0.0 44.0

0.0

45.0

90°

1

0.7

39.0

•0.7

40.0

0.7

41.0

0.7

42.0

0.8

13,11

0. S 41.0

0.8

45.0

89

2

1.4

39.0

1.4

40.0

1.4

41.0

1.5

42.0

1.5

13.0

1. 5 41. 0

1.6

45.0

88

3

2.0

38.9

2.1

39. 9

2.1

40.9

2.2

41.9

2.3

42.9

2.3

43.9

2.4

44.9

87

4

2.7

38.9

2.8

39.9

2.9

40.9

2.9

41.9

3. 0

42. !l

3. 1

43.9

3.1

44.9

86

5

3.4

38.9

3.5

39. s

3.6

40.8

3.7

41.8

3.7

42.8

3.8

43. S

3.9

44.8

85

6

4. 1

38.8

4.2

39.8

4.3

40.8

4.4

41.8

4.5

42.8

4.6

43.8

4.7

44.8

84

7

4.8

38.7

4.9

39.7

5.0

40.7

5.1

■11. 7

5.2

12. 7

5.4

43. 7

5.5

44.7

83

8

5.4

38.6

5.6

3!). 6

5.7

40.6

5.8

41. (i

6.0

42. 6

6. 1

43.6

6.3

44.6

82

9

6.1

3S.5

6.3

39.5

6.4

40.5

6.6

11.3

6.7

■12.5

6.9

43.5

7.0

11 1

M

10

6.8

38.4

6.9

39. 1

7.1

40.4

7.3

41.4

7.5

42.3

7.6

43.3

7.8

44.3

80

11

7.4

38.3

7.6

39.3

7.8

10.2

8.0

41.2

8.2

42.2

8.4

43.2

8.6

44. 2

79

12

8.1

38. 1

8. 3 39. 1

S.5

40.1

8.7

41. 1

8.9

42.1

9.1

43.0

9.4

44.0

78

13

8.8

38.0

9.0

39.0

9.2

39.9

9.4

40. 9

9.7

41.9

9.9

42.9

10.1

43.8

77

14

9.4

37. 8

9.7

38.8

9.9

39.8

Ki.2

40.8

10. 4

41.7

10. 6

42.7

10.9

43, 7

76

15

10.1

37.7

10.4

38.6

10. 6

39.6

10.9

40.6

11.1

41.5

11.4

42.5

11. 6

43.5

75

16

10. 7

37.5

11.0

3S.5

11.3

39.4

11.6

40.4

11.9

41.3

12.1

42.3

12.4

43.3

74

17

11.4

37.3

11.7

38.3

12.0

39.2

12.3

40. 2

12.6

41. 1

12. 9

42. 1

13. 2

43.0

73

18

12. 1

37.1

12. 1 38. 0

12.7

39.0

13.0

39.9

13. 3

40.9

13,0

41.8

13.9

42.8

72

19

12. 7

36.9

13.0

37.8

13.3

38.8

13.7

39.7

11.0

40.7

14.3

41.6

14. 7

12. 5

71

20

13.3

36.6

13. 7

37.6

14.0

38.5

14.4

39. 5

11.7

40.4

15. 0

41.3

15. 1

42. 3

70

21

14.0

36. -1

14.3

37.3

14.7

38.3

15.1

39. 2

15.4

40. 1

15.8

41. 1

16. 1

42. 0

69

22

14.6

36.2

15. 0

37.1

15. 1

38.0

15.7

38.9

Hi. 1

39.9

16.5

10. s

16.9

41.7

68

23

15. 2

35.9

15.6 36.8

16.0

3,7. 7

16. 4

38.7

16.8

39.6

17.2

40.5

17.6

41. 1

07

24

15.9

35. 6

16.3

36.5

16.7

37. 5

17.1

38.4

17.5

39.3

17.9

40.2

IS. 3

41. 1

66

25

16. 5

35. 3

16. II

36.3

17.3

37.2

17.7

38.1

is. 2

39.0

18.6

39.9

19.0

40.8

65

26

17. 1

35. 1

17 5

36.0

18.0

36.9

is. 1

37.7

18.8

38. o

1!». 3

39.5

19.7

40.4

64

27

17.7

34. 7

18.2

35.6

18.6

36.5

19. 1

37.4

19.5

38. 3

20. 0

3!l. 2

20.4

40. 1

63

28

18.3

34.4

is. s

35.3

19.2

36. 2

19.7

37. 1

20. 2

38.0

20. 7

38.8

21.1

39. r

62

29

18.9

34.1

I'l. 1

35.0

19. 9

35.9

20. 4

3,6. 7

20.8

3,7, 6

21.3

38. 5

21. s

39.4

61

30

19.5

33.8

20.0

34.6

20.5

35. 5

21.0

3,1,. 1

21.5

37. 2

22 0

38. 1

22.5

39.0

60

31

20. 1

33.4

20.6

34.3

21. 1

35. 1

21.6

36.0

22. 1

311 9

22. 7

37.7

23.2

38.6

59

32

20.7

33. 1

21. 2

33.9

21. 7

34.8

22.3

35. 6

32 s

30. 3

23, 3,

37. 3

23, s

38.2

58

33

21.2

32. 7

21.8

33.5

22.3

34.4

22.9

35. 2

23. 4

3,1,. 1

24.0

36.9

21. 5

37.7

57

34

21.8

32. 3

22. 1

33.2

22.9

34.0

23.5

34.8

24.0

35.6

21.6

36.5

25.2

37.3

56

35

22. 1

31.9

22. 9

32.8

23.5

33. 6

24.1

3,1, 1

21. 7

35. 2

25. 2

36.0

25.8

36. 9

55

36

22. >.)

31.6

23.5

32.4

24.1

3,3. 2

24.7

34.0

23. 3,

3,1. S

25.9

35.6

26.5

2,6 !

54

37

23. 5

31.1

21. 1

31.9

21. 7

32.7

23. 3

33. 5

23. II

3,1.3

26. :,

35. 1

27. 1

35.9

53

38

24.0

30.7

21.6

31.5

25.2

32.3

25.9

33. 1

26.5

33.9

27. 1

34.7

27.7

35. 5

52

39

24. 5

30.3

25. 2

31.1

25.8

31.9

26. 1

32. 0

27. 1

:,:, i

27.7

34.2

28. 3,

35.0

51

40

25. 1

29.9

2.-,. 7

30.6

26.4

31.4

27.0

32. 2

27 li

32.9

28.3

33.7

28.9

34.5

50

41

25.6

29.4

26. 2

30.2

26.9

30.9

27. i;

31.7

28. 2

32. 5

28.9

33.2

29. 5

34. 0

49

42

26. 1

29. 0

26.8

29.7

27.4

30. 5

28. 1

31.2

28.8

32.0

29. 4

32.7

30. 1

33. 4

is

43

26.6

28.5

27.3

29.3

28.0

30.0

28.6

3,(1. 7

29. 3

3,1 1

30.0

32.2

30.7

32.9

47

44

27. 1

28. 1

27. s

28.8

28.5

29.5

29.2

30. 2

29. it

30.9

30. 6

31.7

31.3

32. 1

46

45

27.6

27. 6

28.3

28.3

29.0

29.0

29. 7

29. 7

30. 4

311. 1

sin

31.1

31. 1

31.8

31.8

45

A

cos

sin

cos

sin

cos

sin

cos

sin

cos

COS

sin

cos

sin

.1

226

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

Giving the products a jj'" A with the arguments a and A.

a

46

47

48

49

50

51

*52

a

A

sin

COS

sin

cos

sin

C08

sin

COS

sin

cos

sin

cos

sin

cos

A

0°

0.0

46.0

0.0

47.0

0.0

48.0

0.0

49.0

0.0

50.0

0.0

51.0

0.0

52.0

90°

1

0.8

46.0

0.8

47.0

0.8

48.0

0.9

49.0

0.9

50.0

0.9

51.0

0.9

52.0

89

2

1.6

46.0

1.6

47.0

1.7

48.0

1.7

49.0

1.7

50.0

1.8

51.0

1.8

52.0

88

3

2.4

45.9

2.5

46.9

2.5

47.9

2.6

48.9

2.6

49.9

2.7

50.9

2.7

51.9

87

4

3.2

45.9

3.3

46.9

3.3

47.9

3.4

48.9

3.5

49.9

3.6

50.9

3.6

51.9

86

5

4.0

45.8

4. 1

46.8

4.2

47.8

4.3

48.8

4.4

49.8

4.4

50.8

4.5

51.8

85

6

4.8

45.7

4.9

46.7

5.0

47.7

5.1

48.7

5.2

49.7

5.3

50.7

5.4

51.7

84

7

5.6

45.7

5.7

46.6

5.8

47.6

6.0

48.6

6. 1

49.6

6.2

50.6

6.3

51.6

83

8

6.4

45.6

6.5

46.5

6.7

47.5

6.8

48.5

7.0

49.5

7.1

50.5

7.2

51.5

82

9

7.2

45.4

7.4

46.4

7.5

47.4

7.7

48.4

7.8

49.4

8.0

50.4

8.1

51.4

81

10

8.0

45.3

8.2

46.3

8.3

47.3

8.5

48.3

8.7

49.2

8.9

50. 2

9.0

51.2

80

11

8.8

45. 2

9.0

46. 1

9.2

47.1

9.3

48.1

9.5

49.1

9.7

50.1

9.9

51.0

79

12

9.6

45.0

9.8

46. 0

10.0

47.0

10.2

47.9

10.4

48.9

10.6

49.9

10.8

50.9

78

13

10.3

44.8

10.6

45.8

10.8

46.8

11.0

47.7

11.2

48.7

11.5

49.7

11.7

50.7

77

14

11.1

44.6

11.4

45.6

11.6

46.6

11.9

47.5

12.1

48.5

12.3

49.5

12.6

50.5

76

15

11.9

44.4

12.2

45.4

12.4

46.4

12.7

47.3

12.9

48.3

13.2

49.3

13.5

50.2

75

16

12.7

44.2

13.0

45.2

13.2

46.1

13.5

47. 1

13.8

48. 1

14.1

49.0

14.3

50.0

74

17

13.4

44.0

13.7

44.9

14.0

45.9

14.3

46.9

14.6

47.8

14.9

48.8

15.2

49.7

73

18

14.2

43.7

14.5

44.7

14.8

45.7

15.1

46.6

15. 5

47.6

15.8

48.5

16.1

49.5

72

19

15.0

43.5

15.3

44.4

15.6

45.4

16.0

46.3

16.3

47.3

16.6

48.2

16.9

49.2

71

20

15.7

43.2

16. 1

44.2

16.4

45.1

16.8

46.0

17.1

47.0

17.4

47.9

17.8

48.9

70

21

16.5

42.9

16.8

43.9

17.2

44.8

17.6

45.7

17.9

46.7

18.3

47.6

18.6

48.5

69

22

17.2

•42.7

17.6

43. 6

18.0

44.5

18.4

45.4

18.7

46.4

19.1

47.3

19.5

48.2

68

23

18.0

42.3

18.4

43.3

18.8

44.2

19.1

45.1

19.5

46.0

19.9

46.9

20.3

47.9

67

24

18.7

42.0

19.1

42.9

19.5

43.9

19.9

44.8

20.3

45.7

20.7

46.6

21.2

47.5

66

25

19.4

41.7

19.9

42.6

20.3

43.5

20.7

44.4

21.1

45.3

21.6

46.2

22.0

47.1

65

26

20.2

41.3

20.6

42.2

21.0

43.1

21.5

44.0

21.9

44.9

22.4

45.8

22.8

46.7

64

27

20.9

41.0

21.3

41.9

21.8

42.8

22.2

43.7

22.7

44.6

23.2

45.4

23.6

46.3

63

28

21.6

40.6

22.1

41.5

22.5

42.4

23.0

43.3

23.5

44.1

23.9

45.0

24.4

45.9

62

29

22.3

40.2

22.8

41.1

23.3

42.0

23.8

42.9

24.2

43.7

24.7

44.6

25.2

45.5

61

30

23.0

39.8

23.5

40.7

24.0

41.6

24.5

42.4

25.0

43.3

25.5

44.2

26.0

45.0

60

31

23.7

39.4

24.2

40.3

24.7

41.1

25.2

42.0

25.8

42.9

26.3

43.7

26.8

44.6

59

32

24.4

39.0

24.9

39.9

25.4

40.7

26.0

41.6

26.5

42.4

27.0

43.3

27.6

44.' 1

58

33

25.1

38.6

25.6

39.4

26.1

40.3

26.7

41.1

27. 2

41.9

27.8

42.8

28.3

43.6

57

34

25.7

38.1

26.3

39.0

26.8

39.8

27.4

40.6

28.0

41.5

28.5

42.3

29.1

43.1

56

35

26.4

37.7

27.0

38.5

27.5

39.3

28.1

40.1

28.7

41.0

29.3

41. S

29.8

42.6

55

36

27.0

37.2

27.6

38.0

28.2

38.8

28.8

39.6

29.4

40.5

30.0

41.3

30.6

42.1

54

37

27.7

36.7

28.3

37.5

28.9

38.3

29.5

39.1

30.1

39.9

30.7

40.7

31.3

41.5

53

38

28.3

36.2

28.9

37.0

29.6

37.8

30.2

3S. 6

30.8

39.4

31.4

40.2

32.0

41.0

52

39

28.9

35.7

29.6

36.5

30.2

37.3

30.8

38.1

31.5

38.9

32.1

39.6

32.7

40.4

51

40

29.6

35.2

30.2

36.0

30.9

36.8

31.5

37.5

32.1

38.3

32.8

39.1

33.4

39.8

50

41

30.2

34.7

30.8

35.5

31.5

36.2

32.1

37.0

32.8

37.7

33.5

38.5

34.1

39.2

49

42

30.8

34.2

31.4

34.9

32.1

35.7

32.8

36.4

33.5

37.2

31.1

37.9

34.8

38.6

48

43

31.4

33.6

32.1

34.4

32.7

35.1

33.4

35.8

34.1

36.6

34.8

37.3

35.5

38.0

47

44

32.0

33. 1

32.6

33.8

33.3

34.5

34.0

35.2

34.7

36.0

35.4

36.7

36.1

37.4

46

45

32.5

32.5

33.2

33.2

33.9

33.9

34.6

34.6

35.4

35.4

36.1

36.1

36.8

36. »

45

1

1 A

cos

sin

cos

sin

cos

sin

COS

sin

"cos

sin

cos

sin

cos

sin

A

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

227

Table B. — Traverse Tables — Continued.

a

53

54

55

56

57

58

59

a

A

sin

COS

sin

cos

sin

COS

sin

COS

sin

cos

sin

cos

sin

cos

A

0°

0.0

53.0

0.0

54.0

0.0

55.0

0.0

56.0

0.0

57.0

0.0

58.0

0.0

59.0

90°

1

0.9

53.0

0.9

54.0

1.0

55.0

1.0

56.0

1.0

57.0

1.0

58.0

1.0

59.0

89

2

1.8

53.0

1.9

54.0

1.9

55. 0

2.0

56.0

2.0

57.0

2.0

58.0

2.1

59.0

88

3

2.8

52.9

2.8

53.9

2.9

54.9

2.9

55.9

3.0

56.9

3.0

57.9

3.1

58.9

87

4

3.7

52.9

3.8

53.9

3.8

54.9

3.9

55. 9

4.0

56.9

4.0

57.9

4.1

58.9

86

5

4.6

52. s

4. 7

53.8

4.8

54.8

4.9

55.8

5.0

56.8

5.1

57.8

5.1

58.8

S5

6

5.5

52. 7

5.6

53. 7

5.7

54.7

5.9

55.7

6.0

56.7

6.1

57.7

6.2

58.7

84

7

6.5

52.6

6.6

53.6

6.7

54.6

6.8

55.6

6.9

56.6

7.1

57.6

7.2

58.6

83

8

7.4

52. 5

7.5

53. 5

7.7

54.5

7.8

55. 5

7.9

56.4

8.1

57.4

8.2

58.4

82

9

8.3

52.3

8.4

53.3

8.6

54.3

8.8

55.3

8.9

56.3

9.1

57.3

9.2

58.3

si

10

9.3

52. 2

9.4

53.2

9.6

54.2

9.7

55.1

9.9

56.1

10.1

57.1

10.2

58.1

80

11

10.1

52.0

10.3

53.0

10.5

54.0

10.7

55.0

10.9

56.0

11.1

56.9

11.3

57.9

79

12

11.0

51.8

11.2

52.8

11.4

53.8

11.6

54.8

11.9

55.8

12. 1

56.7

12.3

57.7

78

13

11.9

51.6

12.1

52.6

12.4

53.6

12. 6

54.6

12.8

55.5

13.0

56.5

13.3

57.5

77

14

12.8

51.4

13.1

52.4

13.3

53.4

13.5

54.3

13.8

55. 3

14.0

56.3

14.3

57.2

76

15

13.7

51.2

14.0

52. 2

14.2

53.1

14.5

54.1

14.8

55.1

15.0

56.0

15.3

57.0

75

16

14.6

50.9

14.9

51.9

15.2

52. 9

15.4

53.8

15. 7

54.8

16.0

55.8

16.3

56.7

74

17

15.5

50.7

15.8

51. 6

16.1

52.6

16.4

53.6

16.7

54.5

17.0

55.5

17.2

56.4

73

18

16.4

50.4

16.7

51.4

17.0

52.3

17.3

53.3

17.6

54.2

17.9

55.2

18.2

56.1

72

19

17.3

50.1

17.6

51.1

17.9

52.0

18.2

52.9

18.6

53.9

18.9

54.8

19.2

55.8

71

20

18.1

49.8

18.5

50.7

18.8

51. 7

19. 2

52.6

19.5

53.6

19.8

54.5

20.2

55.4

70

21

19.0

49.5

19.4

50.4

19.7

51.3

20.1

52.3

20.4

53.2

20.8

54.1

21. 1

55.1

69

22

19.9

49.1

20.2

50.1

20.6

51.0

21.0

51.9

21.4

52.8

21. 7

53.8

22.1

54.7

68

23

20.7

48.8

21.1

49.7

21.5

50.6

21.9

51. 5

22.3

52.5

22.7

53.4

23.1

54.3

67

24

21.6

48.4

22.0

49.3

22.4

50.2

22.8

51.2

23.2

52.1

23.6

53.0

24.0

53.9

66

25

22.4

48.0

22.8

48.9

23.2

49.8

23.7

50.8

24.1

51.7

24.5

52. 6

24.9

53.5

65

26

23.2

47.6

23.7

48.5

24.1

49.4

24.5

50.3

25.0

51. 2

25.4

52.1

25.9

53.0

64

27

24. 1

47.2

24. 5

48.1

25.0

49.0

25.4

49.9

25.9

50.8

26.3

51.7

26.8

52.6

63

28

24.9

46.8

25.4

47.7

25.8

48.6

26.3

49.4

26.8

50.3

27.2

51.2

27.7

52.1

62

29

25. 7

46.4

26.2

47.2

26.7

48.1

27.1

49.0

27.6

49.9

28.1

50.7

28.6

51.6

61

30

26.5

45.9

27.0

46.8

27.5

47.6

28.0

48.5

28.5

49.4

29.0

50.2

29.5

51.1

60

31

27.3

45.4

27.8

46.3

28.3

47. 1

28.8

48.0

29. 4

48.9

29.9

49.7

30.4

50.6

59

32

28.1

44.9

28.6

45.8

29.1

46.6

29.7

47.5

30.2

48.3

30.7

49.2

31.3

50.0

58

33

28.9

44.4

29.4

45. 3

30.0

46. 1

30.5

47.0

31.0

47.8

31.6

48.6

32. 1

49.5

57

34

29.6

43.9

30.2

44.8

30.8

45.6

31.3

40.4

31.9

47.3

32.4

48.1

33.0

48.9

56

35

30.4

43.4

31.0

44.2

31.5

45.1

32.1

45.9

32.7

46.7

33.3

47.5

33.8

48.3

55

36

31.2

42.9

31.7

43.7

32.3

44.5

32.9

45.3

33.5

46.1

34.1

46.9

34.7

47.7

54

37

31.9

42. 3

32.5

43.1

33.1

43.9

33.7

44.7

34.3

45.5

34.9

46.3

35. 5

47.1

53

38

32.6

41.8

33.2

42.6

33.9

43.3

34. 5 44. 1

35.1

44.9

35.7

45.7

36. 3

46.5

52

39

33.4

41.2

34.0

42.0

34. (i

42.7

35.2

43.5

35.9

44.3

36.5

45. 1

37.1

45.9

51

40

34. 1

40.6

34.7

41.4

35. 4

42. 1

36.0

42.9

36.6

43.7

37.3

44.4

37. 9

45.2

50

41

34.8

40.0

35. 4

40.8

36. 1

41.5

36.7

42. 3

37.4

43.0

38.1

43.8

38.7

44.5

49

42

35.5

39. 1

36.1

40. 1

36.8

40.9

37.5

41.6

38. 1 42. 4

38.8

43.1

39.5

43.8

48

43

36.1

38.8

36.8

39.5

37.5

40. 2

38. 2

41.0

38. 9 11.7

39.6

42.4

40.2

43.1

47

44

36.8

38.1

37.5

38.8

38.2

39.6

38.9

40.3

39.6 41.0

40.3

41.7

41.0

42.4

46

45

37.5

37. 5

38.2

38.2

38.9

38.9

39.6

39.6

40. 3 40. 3

41.0

41.0

41.7

41. 7
sin

45

A

cos

sin

cos

sin

cos

sin

cos

sin

cos sin

cos

sin

cos

A

228

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

Giving the products a ^ .4 witn the arguments a and A.

a

60

61

6

2

63

64

65

66

a

A

sin

COS

sin

COS

sin

COS

sin

cos

sin

COS

sin

COS

sin

COS

A

0°

0.0

60.0

0.0

61.0

0.0

62.0

0.0

63.0

0. 0

64. 0

0.0

65.0

0.0

66.0

90°

1

1.0

60.0

1. 1

61.0

1. 1

62.0

1.1

63.0

1.1

64.0

1.1

65.0

1.2

66.0

89

2

2. 1

60.0

2.1

61.0

2. 2

62.0

2.2

63.0

2.2

64.0

2.3

65,0

2.3

66.0

88

3

3.1

59.9

3.2

60.9

3.2

61.9

3.3

62.9

3.3

63. 9

3.4

64. 9

3.5

65.9

87

4

4.2

59.9

4.3

60.9

4.3

61.8

4.4

62.8

4.5

63.8

4.5

64.8

4.6

65.8

86

5

5.2

59.8

5.3

60.8

5.4

61.8

5.5

62.8

5.6

63.8

5.7

64.8

5.8

65.7

85

C

6.3

59.7

6.4

60.7

6.5

61.7

6.6

62. 7

6.7

63.6

6.8

64.6

6.9

65.6

84

7

7.3

59. 6

7.4

60.5

7.6

61.5

7.7

62.5

7.8

63.5

7.9

64.5

8.0

65.5

83

8

8.4

59.4

8.5

60. 4

8.6

61.4

8.8

62.4

8.9

63. 4

9.0

64.4

9.2

65.4

82

9

9.4

59.3

9.5

60.2

9.7

61.2

9.9

62.2

10.0

63. 2

10.2

64.2

10.3

65.2

81

10

10.4

59.1

10. 6

60. 1

10.8

61.1

10.9

62.0

11.1

63.0

11.3

64.0

11.5

65.0

SO

11

11.4

58.9

11.6

59.9

11.8

60.9

12.0

61.8

12. 2

62.8

12.4

63.8

12.6

64.8

79

12

12. 5

58.7

12.7

59.7

12.9

60.6

13.1

61.6

13.3

62.6

13.5

63.6

13. 7

64.6

78

13

13.5

58. 5

13.7

59.4

13.9

60.4

14.2

61.4

14.4

62.4

14.6

63.3

14.8

64.3

77

14

14. 5

58.2

14. S

59.2

15.0

60.2

15.2

61.1

15.5

62.1

15.7

63. 1

16.0

64.0

76

15

15.5

58.0

15.8

58.9

16.0

59.9

16.3

60.9

16.6

61.8

16.8

62.8

17. 1

63.8

75

16

16.5

57.7

16.8

58.6

17.1

59.6

17.4

60.6

17.6

61.5

17.9

62.5

18.2

63.4

74

17

17.5

57.4

17.8

58.3

18.1

59.3

18.4

60.2

18.7

61.2

19.0

62.2

19.3

63.1

73

18

18.5

57.1

18.9

58.0

19.2

59.0

19.5

59.9

19.8

60. 9

20. 1

61.8

20.4

62.8

72

19

19.5

56.7

19.9

57.7

20.2

58.6

20.5

59.6

20.8

60.5

21.2

61. 5

21.5

62.4

71

20

20.5

56.4

20.9

57.3

21. 2

58.3

21.5

59.2

21.9

60. 1

22. 2

61. 1

22.6

62.0

70

21

21.5

56.0

21.9

56.9

22. 2

57.9

22.6

58.8

22.9

59.7

23. 3

60.7

23.7

61.6

69

22

22.5

55. 6

22.9

56.6

23. 2

57.5

23.6

58.4

24.0

59. 3

24.3

60.3

24.7

61.2

68

23

23.4

55.2

23.8

56.2

24.2

57.1

24.6

58.0

25.0

58. it

25. I

59.8

25.8

60.8

67

24

24.4

54.8

24.8

55. 7

56.6

25.6

57.6

26.0

58.5

26.4

59.4

26.8

60.3

66

25

25.4

54.4

25.8

55. 3

26. -J

56.2

26.6

57. 1

27.0

58.0

27. 5

58.9

27.9

59.8

65

26

26.3

53. 9

26. 7

54.8

27.2

55.7

27. 6

56.6

28.1

57.5

28.5

58.4

28.9

59.3

64

27

27.2

53.5

27.7

54. 4

28.1

55.2

28.6

56.1

29.1

57.0

29. 5

57. 9

30.0

58.8

63

28

28.2

53.0

28.6

53. 9

29.1

54.7

29.6

55.6

30.0

56. 5

30.5

57.4

31.0

58.3

62

29

29. 1

52. 5

29.6

53.4

30.1

54.2

30.5

55. 1

31.0

56.0

31.5

56.9

32.0

57.7

61

30

30.0

52.0

30. 5

52.8

31.0

53.7

31.5

54.6

32.0

55. 1

32.5

56.3

33.0

57.2

60

31

30.9

51.4

31.4

52.3

31.9

53.1

32.4

54.0

33.0

54.9

33.5

55. 7

34. 0

56. 6

59

32

31.8

50.9

32.3

51.7

32.9

52.6

33.4

53.4

33.9

54. 3

34.4

55.1

35.0

56.0

58

33

32. 7

50.3

33.2

51.2

33.8

52.0

34.3

52.8

34.9

53.7

35.4

54. 5

35.9

55. 4

57

34

33. 6

49.7

34.1

50. 6

34.7

51.4

35.2

52.2

35.8

53. 1

36. 3

53.9

36.9

54.7

56

35

34.4

49. 1

35.0

50.0

35.6

50.8

36. 1

51.6

36.7

52.4

37.3

53.2

37.9

54.1

55

36

35. 3

48.5

35.9

49.4

36.4

50.2

37.0

51.0

37.6

51.8

38.2

52.6

38.8

53.4

54

37

36. 1

47.9

36.7

48. 7

37.3

49.5

37.9

50.3

38.5

51. 1

39.1

51.9

39.7

52.7

53

38

36. 9

47.3

37.6

48. 1

38.2

48.9

38.8

49.6

39.4

50. 4

40. 0

51. 2

40.6

52.0

52

39

37.8

46.6

38.4

47.4

39.0

48.2

39.6

49.0

40. 3

49.7

40.9

50.5

41.5

51.3

51

40

38.6

46.0

39.2

46.7

39.9

47.5

40.5

48.3

41. 1

49.0

41.8

49.8

42.4

50.6

50

41

39.4

45.3

40.0

46.0

40.7

46.8

41.3

47.5

42.0

48.3

42. 6

49. 1

43.3

49.8

49

42

40.1

44.6

40.8

45.3

41.5

46. 1

42. 2

46.8

42.8

47.6

43.5

48.3

44.2

49.0

48

43

40.9

43.9

41.6

44.6

42.3

45.3

43.0

46. 1

43.6

46.8

4 1. 3

47.5

45.0

48.3

47

44

41.7

43.2

42.4

43.9

4I3. 1

44.6

43.8

45.3

44.5

46. 0

45.2

46.8

45.8

47.5

46

45

42.4

42.4

43.1

43. 1

43.8

43.8

44.5

44.5

45.3

45.3

46.0

46.0

46. 7

46.7

45

1 A

cos

sin

COS

sin

cos

sin

cos

sin

cos

sin

COS

sin

COS

sin

1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

229

Table B. — Traverse Tables — Continued.

Giving the products

asm A
cos

with the

arguments a an

1 A.

a

6

7

68

69

70

71

72

73

a

A

sin

cos

sin

COS

sin

COS

sin

cos

sin

COS

sin

COS

sin

COS

A

0°

0.0

67.0

0.0

68.0

0.0

69.0

0.0

70.0

0.0

71.0

0.0

72.0

0.0

73.0

90°

1

1.2

67.0

1.2

68.0

1.2

69.0

1.2

70.0

1.2

71.0

1.3

72.0

1.3

73.0

89

2

2.3

67.0

2.4

6S.0

2. 1

69.0

2.4

70.0

2.5

71.0

2.5

72.0

2.5

73.0

88

3

3.5

66.9

3.6

67.9

3.6

68.9

3.7

69.9

3.7

70.9

3.8

71.9

3.8

72.9

87

4

4.7

66.8

4.7

67.8

4.8

68.8

4.9

69.8

5.0

70.8

5.0

71.8

5.1

72.8

86

5

5.8

66. 7

5.9

67.7

6.0

68.7

0.1

69.7

6.2

70.7

6.3

71.7

6.4

72.7

85

6

7.0

66.6

7. 1

67.6

7.2

68.6

7.3

69.6

7.4

70.6

7.5

71.6

7.6

72.6

84

7

8.2

66.5

8.3

67.5

8.4

68. 5

8.5

69.5

8.7

70.5

8.8

71.5

8.9

72.5

83

8

9.3

66.3

9.5

67.3

9.6

68.3

9. 7 69. 3

9.9

70.3

10.0

71.3

10.2

72.3

82

9

10.5

66.2

1(1.6

67.2

10.8

68.2

1 1. 0 69. 1

11. 1

70. 1

11.3

71. 1

11.4

72. 1

81

10

11.6

66. 0

11.8

67.0

12.0

68.0

12.2

68.9

12.3

69.9

12.5

70.9

12.7

71.9

80

11

12.8

65.8

13.0

66.8

13.2

67.7

13.4

68.7

13.5

■69.7

13.7

70. 7

13.9

71.7

79

12

13.9

65.5

14. 1

66.5

14.3

67.5

14.6

68.5

14.8

69.4

15.0

70.4

15.2

71.4

78

13

15.1

65.3

15.3

66.3

15.5

67.2

15.7

68.2

16. 0

69.2

16.2

70.2

16.4

71. 1

77

14

16.2

65.0

16.5

66.0

16.7

67.0

16.9

67.9

17.2

68.9

17.4

69.9

17.7

70.8

76

15

17.3

04.7

17.6

65.7

17.9

66.6

18.1

67.6

18.4

68.6

18.6

69.5

18.9

70.5

75

16

18.5

64.4

18.7

i.:.. 1

19.0

66. 3

19.3

67.3

19.6

68.2

19.8

69.2

20.1

70.2

74

17

19.6

64.1

19.9

65. o

20. 2

66. 0

20.5

66.9

20.8

67.9

21. 1

68.9

21.3

69.8

73

18

20.7

63.7

21.0

61. 7

21.3

65.6

21. 6 66. 6

21.9

67.5

22.2

68.5

22. 6

69.4

72

19

21.8

63. 3

22. 1

64.3

22. 5

65.2

22. 8 66. 2

23.1

67. 1

23.4

68. 1

23.8

69.0

71

20

22.9

63.0

23.3

63.9

23. 6

64.8

23. 9 , 65. S

24.3

66.7

24.6

67.7

25.0

68.6

70

21

24.0

62.5

24.4

63.5

24.7

64.4

25. 1 65. 4

25.4

66.3

25.8

67.2

26.2

68.2

69

22

25. 1

62.1

25.5

63.0

25.8

64.0

26.2

64. 9

26.6

65.8

27.0

66.8

27.3

67.7

68

23

26.2

61.7

26.6

62.6

27.0

63.5

27.4

64.4

27.7

65.4

28.1

66.3

28.5

67.2

67

2 1

27.3

61.2

27. 7

62. 1

28.1

63.0

28.5

63.9

28.9

64.9

29.3

65.8

2!). 7

66.7

66

25

28.3

60.7

28. 7

61. 6

29. 2

62.5

29.6

63.4

30.0

64.3

30.4

65. 3

30. 9

66.2

65

26

29. 1

60.2

29.8

61. 1

30. 2

62.0

30.7

62.9

31.1

63.8

31.0

64. 7

32. 0

65.6

64

27

30.4

59.7

30.9

60. 6

31.3

61.5

31. 8 62. 4

32.2

63.3

32.7

64.2

33.1

65.0

63

28

31. 5

59.2

31.9

60. 0

32. 4

60. 9

32. 9 61. 8

33. 3

62.7

33.8

63.6

34.3

64.5

62

29

32. 5

58.6

33.0

59. 5

33. 5

60.3

33.9 61.2

34.4

62.1

34.9

63.0

35. 4

63.8

61

30

33.5

58.0

34.0

58.9

34. 5

59.8

35.0

60.6

35. 5

61.5

36.0

62. 1

36.5

63.2

60

31

34. 5

57.4

35. 0

58.3

35. 5

59. 1

36.1

60. 0

36.6

60.9

37.1

61.7

37.6

62.6

59

32

35. 5

56. 8

36.0

57. 7

30. 6

58.5

37. 1

59.4

37.6

60.2

38.2

61. 1

38.7

61.9

58

33

36.5

56.2

37.0

57.0

37.6

57.9

38.1

58.7

38.7

59. 5

39 :

60. !

39.8

61.2

57

34

37.5

55. 5

3S.0

56.4

38.6

57.2

39.1

58.0

39.7

58.9

40.3

59.7

40.8

60.5

56

35

38.4

54.9

39.0

55.7

39.6

56. 5

40.2

57.3

40.7

58.2

41.3

59.0

41.9

59.8

55

36

39.4

54. 2

40.0

55.0

40.6

55. 8

11. 1

56.6

41.7

57.4

42. 3

58.2

42. 9

59. 1

54

37

40.3

53.5

40.9

54.3

41.5

55. 1

42.1

55. 9

42.7

56. 7

43.3

57.5

43.9

58.3

53

38

41.2

52.8

41.9

53.6

42. 5

54. 4

43.1

55. 2

43.7

55.9

44.3

56. 7

44.9

57.5

52

39

42.2

52.1

42.8

52. S

43.4

53. 6

44.1

54.4

44.7

55.2

15. 3

56.0

45.9

56.7

51

40

43.1

51.3

43. 7

52. 1

44.4

52.9

45.0

53. 6

45.6

54.4

46.3

40.9

55. 9

50

41

44.0

50.6

44.6

51.3

45. 3

52. 1

45.9

52.8

46.6

53.6

47.2

54.3

47.9

55.1

49

42

44.8

49.8

45. 5

50.5

46. 2

51.3

46.8

52.0

47. 5

52.8

48.2

53. 5

48.8

54.2

48

43

45.7

49.0

46. I

49.7

47. 1

50. 5

47.7

51.2

48.4

51.9

49. 1

52.7

49.8

53.4

47

44

46.5

48.2

47.2

48.9

47.9

49.6

48.6

50.4

49.3

51. 1

50.0

51.8

50.7

52. 5

46

45

47.4

47.4

48.1

48.1

48.8

48.8

49.5

49.5

50.2

50.2

50.9

50.9

51. 6

51.6

45

A

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

COS

sin

COS

sin

.4

230

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

Giving the products a^'" A with the arguments a and A.

a

74

75

76

77

78

79

80

a

A

sin

COS

sin

cos

sin

cos

sin

cos

sin

cos

sin

COS

sin

COS

A

0°

0.0

74.0

0.0

75.0

0.0

76.0

0.0

77.0

0.0

78.0

0.0

79.0

0.0

80.0

90°

1

1.3

74.0

1.3

75.0

1.3

76.0

1.3

77.0

1.4

78.0

1.4

79.0

1.4

80.0

89

2

2.6

74.0

2.6

75.0

2.7

76.0

2.7

77.0

2.7

78.0

2.8

79.0

2.8

80.0

88

3

3.9

73.9

3.9

74.9

4.0

75.9

4.0

76.9

4.1

77.9

4.1

78.9

4.2

79.9

87

4

5.2

73.8

5.2

74.8

5.3

75.8

5.4

76.8

5.4

77.8

5.5

78.8

5.6

79.8

86

5

6.4

73.7

6.5

74.7

6.6

75.7

6.7

76.7

6.8

77.7

0.9

78.7

7.0

79.7

85

6

7.7

73.6

7.8

74.6

7.9

75.6

8.0

76.6

8.2

77.6

8.3

78.6

S.4

79.6

84

7

9.0

73.4

9. 1

74.4

9.3

75.4

9.4

76.4

9.5

77.4

9.6

78. 4

9.7

79.4

83

8

10. 3

73.3

10.4

74.3

10. 6

75.3

10.7

76.3

10.9

77.2

11.0

78.2

11.1

79.2

82

9

11.6

73.1

11.7

74. 1

11.9

75.1

12.0

76.1

12.2

77.0

12.4

78.0

12.5

79.0

SI

10

12. S

72.9

13.0

73.9

13.2

74.8

13. 4 75. 8

13.5

76.8

13.7

77.8

13.9

78.8

80

11

14.1

72.0

14.3

73.6

14.5

74.6

14.7

75.6

14.9

76.6

15.1

77.5

15.3

78.5

79

12

15.4

72.4

15.6

73.4

15.8

74.3

16.0

75.3

16.2

76.3

16.4

77.3

16.6

78.3

78

13

16.6

72. 1

16.9

73. 1

17. 1

74. 1

17.3

75.0

17.5

76.0

17.8

77.0

18.0

77.9

77

14

17.9

71.8

18. 1

72.8

18.4

73.7

18.6

74.7

18.9

75.7

19.1

76.7

19.4

77.6

76

15

19.2

71.5

19.4

72.4

19.7

73.4

19.9

74.4

20.2

75.3

20.4

76.3

20.7

77.3

75

16

20.4

71. 1

20.7

72. 1

20.9

73.1

21.2

74.0

21.5

75.0

21.8

75.9

22. 1

76.9

74

17

21.6

70.8

21.9

71.7

22.2

72.7

22.5

73.6

22.8

74.6

23.1

75.5

23.4

76.5

73

18

22.9

70.4

23.2

71.3

23. 5

72.3

23.8

73.2

24.1

74.2

24.4

75.1

24.7

76.1

72

19

24. 1

70.0

24.4

70.9

24.7

71.9

25.1

72.8

25. 1

73.8

25.7

74.7

26.0

75.6

71

20

25.3

69.5

25.7

70.5

26.0

71.4

26.3

72.4

26.7

73.3

27.0

74.2

27.4

75.2

70

21

26.5

69. 1

26.9

70.0

27.2

71.0

27.6

71.9

28.0

72.8

28.3

73.8

28. 7

74.7

69

22

27.7

68.6

28. 1

69.5

28.5

70.5

28.8

71.4

29. 2

72.3

29.6

73.2

30.0

74.2

68

23

28.9

68. 1

29.3

69.0

29.7

70.0

30. 1

70.9

30.5

71.8

30.9

72.7

31.3

73.6

67

24

30.1

67.6

30.5

68.5

30.9

69.4

31.3

70.3

31.7

71.3

32. 1

72.2

32.5

73.1

66

25

31.3

67.1

31.7

68.0

32.1

68.9

32.5

69.8

33.0

70.7

33.4

71.6

33.8

72.5

60

26

32.4

66.5

32.9

67.4

33.3

68.3

33. S

69.2

34.2

70. 1

34.6

71.0

35.1

71.9

64

27

33.6

65.9

34.0

66.8

34.5

67.7

35.0

68.6

35.4

69.5

35.9

70.7

36.3

71.3

63

28

34.7

65.3

35.2

66.2

35.7

67. 1

36.1

68.0

36.6

68.9

37. 1

69.8

37.6

70.6

62

29

35.9

64.7

36.4

65.6

36.8

66.5

37.3

67.3

37.8

68.2

38.3

69.1

38.8

70.0

61

30

37.0

64.1

37.5

65.0

38.0

65.8

38.5

66.7

39.0

67.5

39.5

68.4

40.0

69.3

60

31

38.1

63.4

38. 6

64.3

39. 1

65.1

39.7

66.0

40.2

66.9

40.7

67.7

41.2

68.6

59

32

39.2

62. 8

39.7

63. 6

40.3

64.5

40.8

65.3

41.3

66. 1

41.9

67.0

42.4

67.8

-,s

33

40.3

62. 1

40.8

62.9

41.4

63. 7

41.9

64.6

42.5

65.4

43.0

66.3

43.6

67. 1

57

34

41.4

61.3

41.9

62. 2

42.5

03.0

43.1

63.8

43.6

64.7

44.2

65.5

44.7

66.3

56

35

42.4

60.6

43.0

61.4

43.6

62.3

44.2

63. 1

44.7

63.9

45.3

64.7

45.9

65. 5

55

36

43.5

59.9

44. 1

60. 7 11.7

61.5

45.3

62.3

45.8

63.1

46.4

63.9

47.0

64.7

54

37

44.5

59. 1

45. 1

59.9

45.7

60. 7

46.3

61.5

46.9

62.3

47.5

63.1

48.1

63.9

53

38

45.6

58.3

46.2

59. 1

46.8

59.9

47.4

60.7

48.0

61.5

48.6

62.3

49.3

63.0

52

39

46.6

57.5

47.2

58.3

47.8

59.1

48.5

59.8

49.1

60.6

49.7

61.4

50.3

62.2

51

40

47.6

56.7

48.2

57. 5

48.9

49.5

59.0

50.1

5S.8

50.8

60.5

51.4

61.3

50

41

48.5

55.8

49.2

56.6

49.9

57.4

50.5

58.1

51.2

58.9

51.8

59.6

52.5

60.4

49

42

49.5

55.0

50.2

55. ;

50.9

56.5

51.5

57.2

52.2

58.0

52.9

58.7

53.5

59.5

48

43

50.5

54.1

51. 1

54.9

51.8

55. 6

52.5

56.3

53.2

57.0

53.9

57.8

54.6

58.5

47

44

51.4

53. 2

52. 1

54. 0

52.8

54.7

53.5

55.4

54.2

56. 1

54. 9

56.8

55.6

57.5

46

45

52.3

52.3

53.0

53.0

53.7

53.7

54.4

54.4

55. 2

55.2

55.9

55.9

56.6

56.6

45

A

cos

sin

COS

sin

COS

sin

cos

sin

cos

sin

cos

sin

COS

sin

A

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

231

Table B. — Traverse Tables — Continued.

a

81

82

83

si

85

86

8

7

a

A

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

COS

sin

cos

A

0°

0.0

81.0

0.0

82.0

0.0

83.0

0.0

84.0

0.0

85.0

0.0

86.0

0.0

87.0

90°

1

1.4

81.0

1.4

82.0

1.4

83.0

1.5

84.0

1.5

85.0

1.5

86.0

1.5

87.0

89

2

2.8

81.0

2.9

82.0

2.9

82.9

2.9

83.9

3.0

84.9

3.0

85.9

3.0

86.9

88

3

4.2

«0.9

4.3

81.9

4.3

82.9

4.4

83.9

4.4

84.9

4.5

85.9

4.6

86.9

87

4

5.7

80.8

5.7

81.8

5. 8 82. 8

5.9

83.8

5.9

84.8

6.0

85.8

6. 1

86.8

86.

5

7.1

80.7

7. 1

81.7

7.2

82.7

7.3

83.7

7.4

84.7

7.5

85.7

7.6

86.7

85

6

8.5

80.6

8.6

81.6

8.7

82.5

8.8

83.5

8.9

84.5

9.0

85.5

9.1

86.5

84

7

9.9

80.4

10. 0

81.4

10.1

82.4

in. 2

83.4

10.4

84.4

10.5

85.4

10.6

86.4

83

8

11.3

80.2

11.4

81.2

11.6

82.2

11.7

83.2

11.8

84.2

12.0

85.2

12.1

86.2

82

9

12. 7

80.0

12.8 81.0

13.0

82.0

13.1

83.0

13.3

84.0

13.5

84.9

13.6

85.9

81

10

14.1

79.8

14.2

80.8

11.4

81.7

14.6

82.7

14.8

83.7

14.9

84.7

15. 1

85. 7

80

11

15.5

79.5

15.6

80.5

15.8

81.5

16.0

82.5

16.2

83.4

16.4

84.4

16.6

85.4

79

12

16.8

79.2

17. 0 80. 2

17.3

81.2

17.5

82.2

17.7

83.1

17.9

84.1

18.1

85.1

78

13

is. 2

78.9

18.4

79.9

18.7

80.9

18.9

81.8

19.1

82.8

19. 3 83. 8

19.6

84.8

77

14

19.0

78.6

19.8

79.6

20. 1

80.5

20.3

81.5

20.6

82. 5

20.8

83.4

21.0

84.4

76

15

21.0

78.2

21.2

79.2

21.5

80.2

21.7

81.1

22.0

82.1

22.3

83.1

22.5

84.0

75

16

22.3

77.9

22.6

78.8

22. 9

79.8

23. 2

80.7

23.4

81.7

23.7

82.7

24.0

83.6

74

17

23.7

77.5

24.0

78.4

24. 3

79.4

24.6

80.3

24 9

81.3

25.1

82.2

25.4

83.2

73

18

25. 0

77.0

25.3

78.0

25.6

78.9

26.0

79.9

26. :',

80.8

26.6

81.8

26.9

82.7

72

19

26.4

76.6

26.7

77.5

27.0

78.5

27.3

79.4

27. 7

80.4

28.0

81.3

28.3

82.3

71

20

27.7

76. 1

28.0

77.1

28.4

78.0

28.7

78.9

29.1

79.9

29.4

80.8

29.8

81.8

70

21

29.0

75. 6

29.4

76.6

29.7

77.5

30. 1

78.4

30.5

79.4

30.8

80.3

31.2

81.2

69

22

30.3

75. 1

30.7

76.0

31.1

77.0

31. 5

77.9

31.8

78.8

32. 2 79. 7

32.6

80.7

68

23

31.6

74.6

32.0

75.5

32.4

76.4

32.8

77.3

33.2

78.2

33. 6 79. 2

34.0

80. 1

67

24

32.9

74.0

33.4

74.9

33. 8 75. 8

34. 2

76. 7

34. 6 77 7

35. 0 78. 6

35.4

79.5

66

25

34.2

73.4

34.7

74.3

35. 1 75. 2

35.5

76. 1

35.9

77.0

36. 3 77. 9

36.8

78.8

65

26

35.5

72.8

35.9

73.7

36. 4 74. 6

36.8

75.5

37.3

76.4

37. 7 77. 3

38.1

78.2

64

27

36.8

72.2

37. 2 73. 1

37. 7 74. 0

3S. 1

74.8

38.6

75. 7

39. 0 76. 6

39.5

77.5

63

28

38.0

71.5

38.5

72.4

39. 0 73. 3

39.4

74.2

39. 9 75. 1

40.4 75.9

40.8

76.8

62

29

39.3

70.8

39.8

71.7

40. 2 72. 6

40.7

73.5

112 74.3

41. 7 75. 2

42.2

76.1

61

30

40.5

70. 1

41.0

71.0

41.5 71.9

42.0

72. 7

42.5

73.6

43. 0 74. 5

43.5

75.3

60

31

41. 7

69.4

42. 2 70. 3

42.7 71.1

43.3

72.0

43.8

72.9

44. 3 73. 7

44.8

74.6

59

32

42.9

68. 7

43. 5 69. 5

44. 0 70. 4

44.5

71.2

45. 0 72. 1

45.6

72.9

46.1

73.8

58

33

44. 1

67.9

44. 7 68. s

45. 2 69. 6

45. 7

70.4

46.3 71.3

46. 8 72. 1

47.4

73.0

57

34

45.3

67.2

45.9

68.0

46. 4 68. 8

47.0

69.6

47. 5 70. 5

4S. 1 71.3

48.6

72.1

56

35

46. 5

66. 1

47.0

67.2

47.6 68.0

48.2

68.8

48. 8 ! 69. 6

49.3 70 1

49.9

71.3

55

36

47. 6

65.5

48.2

66.3

48. 8 67. 1

49.4

68.0

50. 0 ' 68. 8

50.5

69.6

51.1

70.4

54

37

48.7

64. 7

49.3

65.5

50. 0 66. 3

50.6

67.1

51.2 67.9

51.8

68.7

52.4

69.5

53

38

49.9

63.8

50.5

64.6

51. 1 65. 4

51.7

66.2

52. 3 67. 0

52.9

67.8

53.6

68.6

52

39

51.0

62.9

51.6

63.7

52. 2 ^4. 5

52. 9 65. 3

53. 5 66. 1

54.1

66.8

54.8

67.6

51

40

52. 1

62.0

52. 7 62. 8

53. 4 63. 6

54.0

64.3

54. 6 65. 1

55. 3 65. 9

55.9

66.6

50

41

53.1

61. 1

53. 8 61. 9

54. 5 62 6

55. 1

63.4

55. S 64. 2

56. 4 64. 9

57.1

65.7

49

42

54.2

60.2

54. 9 60. 9

55.5 61.7

:.n 2

62.4

56. 9 63. 2

57.5

63.9

58 2

64. 7

48

43

55.2

59.2

55. 9

60.0

56. 6 60. 7

57. 3

61.4

58. 0 62. 2

58.7

62.9

59.3

63.6

47

44

56.3

58.3

57.0

59.0

57. 7 59. 7

58.4

60.4

59.0

61. 1

59.7

61.9

60.4

62.6

46

45

57.3

57.3

58.0

58.0

58. 7 58. 7

59.4

59.4

60. 1

60.1

60.8

60.8

61.5

61.5

45

A

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

A

232

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Table B. — Traverse Tables — Continued.

a

88

89

90

91

92

93

94

a

A

sin

COS

sin

COS

sin

cos

sin'

cos

sin

cos

sin

cos

sin

cos

A

0°

0.0

88.0

0.0

89.0

0.0

90.0

0.0

91.0

0.0

92.0

0.0

93.0

•o.o

94.0

90°

1

1.5

88.0

1.6

89.0

1.6

90.0

1.6

91.0

1.6

92.0

1.6

93.0

1.6

94.0

89

2

3. 1

87.9

3. 1

88.9

3.1

89.9

3.2

90.9

3. 2 91. 9

3.2

92.9

3.3

93.9

88

3

4.6

87.9

4.7

88.9

4.7

89.9

4.8

90.9

4.8 91.9

4.9

92.9

4.9

93.9

87

4

6. 1

87.8

6.2

88.8

6.3

89.8

6.3

90.8

6. 4 91. 8

6.5

92.8

6.6

93.8

86

5

7.7

87.7

7.8

88.7

7.8

89.7

7.9

90.7

8. 0 91. 6

8.1

92.6

8.2

•93.6

85

6

9.2

87.5

9.3

88.5

9.4

89.5

9.5

90. 5

9.6

91.5

9.7

92.5

9.8

93.5

84

7

10. 7

87.3

10.8

88.3

11.0

89. 3

11. 1

90.3

11.2

91.3

11.3

92.3

11.5

93.3

83

8

12.2

87.1

12.4

88.1

12.5

89. 1

12.7

90.1

12.8

91. 1

12.9

92.1

13.1

93.1

82

9

13.8

86.9

13.9

87.9

It. 1

88.9

14.2

89.9

14.4

90.9

14.5

91.9

14.7

92.8

81

10

15.3

86.7

15.5

87.6

15.6

88.6

15.8

89.6

16. 0 90. 6

16. 1

91.6

16.3

92.6

80

11

16.8

86.4

17.0

87.4

17.2

88.3

17.4

89.3

17.6

90.3

17.7

91.3

17.9

92.3

79

12

18.3

86. 1

18.5

87.1

18.7

88.0

18.9

89.0

19.1

90.0

19.3

91.0

19.5

91.9

78

13

19.8

85.7

20.0

86.7

20.2

87.7

20.5

88. 7

20.7

89.6

20.9

90.6

21.1

91.6

77

14

21.3

85.4

21.5

86.4

21.8

87.3

22.0

88.3

22.3

89.3

22.5

90.2

22.7

91.2

76

15

22.8

85.0

23.0

86.0

23.3

86.9

23.6

87.9

23.8

88.9

24.1

89:8

24.3

90.8

75

16

24.3

84.6

24.5

85.6

24.8

86.5

25. 1

87.5

25.4

88.4

25. 6

89.4

25.9

90.4

74

17

25.7

84.2

26. 0

85.1

26.3

86.1

26.6

87.0

26.9

88.0

27.2

88.9

27.5

89.9

73

18

27.2

83.7

27.5

84.6

27.8

85.6

28. 1

86.5

28.4

87.5

28.7

88.4

29.0

89.4

72

19

28.7

83.2

29.0

84.2

29.3

85.1

29.6

86.0

30.0

87.0

30.3

87.9

30.6

88.9

71

20

30.1

82.7

30.4

83.6

30.8

84.6

31.1

85.5

31.5

86.5

31.8

87.4

32.1

88.3

70

21

31.5

82.2

31.9

83. 1

32.3

84.0

32.6

85.0

33.0

85.9

33.3

86.8

33.7

87.8

69

22

33.0

81.6

33.3

82.5

33.7

83.4

34.1

84.4

34.5

85.3

34.8

86.2

35.2

87.2

68

23

34.4

81.0

34.8

81.9

35.2

82.8

35. 6

83.8

35.9

84. 7

36.3

85.6

36.7

86.5

67

24

35.8

80.4

36.2

81.3

36.6

82.2

37.0

83. 1

37.4

84.0

37.8

85.0

38.2

85.9

66

25

37.2

79.8

37.6

80.7

38.0

81.6

38.5

82.5

38.9

83.4

39.3

84.3

39.7

85.2

65

26

38.6

79. 1

39.0

80.0

39.5

80.9

39.9

81.8

40. 3

82.7

40.8

83.6

41.2

84.5

64

27

40.0

78.4

40.4

79.3

40.9

80.2

41.3

81.1

41.8

82.0

42.2

82.9

42. 7

83.8

63

28

41.3

77.7

41.8

78.6

42.3

79.5

42.7

80. 3

43.2

81.2

43.7

82. 1

44. 1

83.0

62

29

42.7

77.0

43. 1

77.8

43.6

78. 7

44. 1

79.6

44.6

80.5

45.1

81.3

45.6

82.2

61

30

44.0

76.2

44.5

77. 1

45.0

77.9

45. 5

78.8

46.0

79.7

46.5

80.5

47.0

81.4

60

31

45.3

75.4

45.8

76.3

46.4

77. 1

46. 9

78.0

47.4

78.9

47.9

79. 7

48.4

80.6

59

32

46.6

74.6

47.2

75.5

47.7

76.3

48.2

77.2

48.8

78.0

49.3

78.9

49.8

79.7

58

33

47.9

73.8

is 5

74.6

49. 0

75.5

49.6

76.3

50.1

77. 2

50.7

78.0

51.2

78.8

57

34

49.2

73.0

19 s

73.8

50.3

74. 6

50.9

75.4

51.4

76. 3

52.0

77. 1

52.6

77.9

56

35

50.5

72.1

51.0

72.9

51.6

73.7

52. '2

74.5

52.8

75.4

53.3

76.2

53. 9

77.0

55

36

51.7

71.2

52.3

72.0

52.9

72.8

53.5

73.6

54.1

74.4

54.7

75.2

55.3

76.0

54

37

53. 0

70.3

53.6

71. 1

54.2

71.9

54.8

72.7

55.4

73.5

56.0

74.3

56.6

75.1

53

38

54.2

69.3

54.8

70. 1

55.4

70.9

56.0

71.7

56.6

72.5

57.3

73.3

57.9

74.1

52

39

55.4

68.4

56.0

69. 2

56.6

69.9

57.3

70.7

57.9-

71.5

58.5

72.3

59. 2

73. 1

51

40

56.6

67.4

57. 2

68. 2

57.9

68.9

58.5

69.7

59. 1

70.5

59.8

71.2

60.4

72.0

50

41

57.7

66.4

58.4

67.2

59.0

67.9

59.7

68.7

60.4

69.4

61.0

70.2

61.7

70.9

49

42

58.9

65.4

59.6

66. 1

60. 2

66.9

60.9

67.6

61.6

68.4

62.2

69. 1

62.9

69.9

48

43

60.0

64.4

60.7

65.1

61.4

65.8

62. 1

66. 6

62.7

67.3

63.4

68.0

64. 1

68.7

47

41

61. 1

63.3

61.8

64.0

62.5

64.7

63.2

65.5

63.9

66.2

64.6

66.9

65.3

67.6

46

15

62. 2

62.2

62.9

62.9

63.6

63.6

64.3

64.3

65. 1

65. 1

65.8

65.8

66.5

66.5

45

A

COS

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

cos

sin

A

MINOR PLAXETS DISCOVERED BY WATSON— LEUSCHNER.

233

Table B. — Traverse Tables — Continued.

a

95

96

97

98

99

100

a

A

sin

COS

sin

cos

sin

cos

sin

COS

sin

cos

sin

COS

A

0°

0.0

95.0

0.0

96.0

0.0

97. 0

0.0

98.0

0.0

99.0

0.0

100.0

90°

1

1.7

95.0

1. 7

96.0

1.7

97.0

1.7

98.0

1.7

99.0

1.7

100.0

89

2

3.3

94.9

3.4

95.9

3.4

96.9

3.4

97.9

3.5

98.9

3.5

99.9

88

3

5.0

94.9

5.0

95.9

5.1

96.9

5. 1

97.9

5.2

98.9

5.2

99.9

87

4

6.6

94.8

6.7

95. 8

6.8

96.8

6.8

97.8

6.9

98.8

7.0

99.8

86

5

8.3

94.6

8.4

95.6

8.5

96. 6

8.5

97.6

8.6

98.6

8.7

99.6

85

6

9.9

94.5

10.0

95.5

10. 1

96.5

10.2

97. 5

10. 3

98.5

10.5

99.5

84

7

11.6

94.3

11.7

95.3

11.8

96.3

11.9

97.3

12. 1

98.3

12. 2

99.3

S3

8

13. 2

94. 1

13.4

95.1

13. 5

96. 1

13. 6

97.0

13.8

98.0

13.9

99.0

S2

9

14.9

93.8

15.0

94.8

15. 2

95.8

15. 3

96.8

15.5

97.8

15.6

98.8

si

10

16.5

93.6

16. 7

94.5

16.8

95.5

17.0

96.5

17.2

97.5

17.4

98.5

80

11

18.1

93.3

18.3

94.2

18.5

95.2

18. 7

96.2

18.9

97. 2

19.1

98.2

79

12

19.8

92.9

20.0

93.9

20.2

94.9

20.4

95.9

20.6

96.8

20.8

97.8

78

13

21.4

92.6

21.6

93.5

21.8

94.5

22.0

95.5

22.3

96.5

22.5

97.4

77

14

23.0

92.2

23.2

93.1

23.5

94.1

23.7

95.1

24.0

96. 1

24. 2

97.0

76

15

24 il

91.8

24. S

92.7

25. 1

93.7

25.4

94.7

25.6

95.6

25.9

96.6

75

16

26. 2

91.3

26.5

92.3

26.7

93.2

27.0

94.2

27.3

95.2

27.6

96. 1

74

17

27.8

90.8

28. 1

91.8

28.4

92.8

28.7

93.7

28.9

94.7

29.2

95.6

73

18

29.4

90.4

29.7

91.3

30. 0

92.3

30.3

93.2

30.6

94.2

30.9

95.1

72

19

30.9

89.8

31.3

90.8

31. 6

91.7

31.9

92.7

32.2

93.6

32. 6

94.6

71

20

32. 5

89.3

32.8

90.2

33. 2

91.2

33.5

92. 1

33. 9

93.0

34.2

94.0

70

21

34.0

88.7

34.4

89.6

34.8

90.6

35.1

91.5

35. 5

92.4

35.8

93.4

69

22

35.6

88.1

36.0

89.0

36.3

89.9

36.7

90.9

37. 1

91.8

37.5

92.7

68

23

37.1

87.4

37.5

88.4

37.4

89.3

38.3

90. 2

38.7

91.1

39.1

92. 1

67

24

38.6

86.8

39.0

87.7

39. 5

88.6

39.9

89.5

40.3

90. 4

40.7

91. 1

66

25

40. 1

86. 1

40.6

87.0

41.0

87.9

41.4

88.8

41.8

89.7

42.3

90. 6

65

26

41.6

85. 4

42. 1

86.3

42.5

87.2

43.0

88. 1

43.4

89.0

43.8

89.9

64

27

43. 1

84. 6

43. 6

85.5

44.0

86.4

44.5

87.3

44.9

88.2

45.4

89.1

63

28

44.6

83.9

45. 1

84.8

45.5

85.6

46.0

86.5

46. 5

87.4

46.9

88.3

62

29

46. 1

83.1

46.5

84.0

47.0

84.8

47.5

85.7

48.0

86.6

48.5

87.5

61

30

47.5

82.3

48.0

83.1

48.5

84.0

49.0

84.9

49.5

85.7

50.0

86.6

60

31

48.9

81.4

49.4

82.3

50.0

83.1

50.5

84.0

51.0

84.9

51.5

85.7

59

32

50. 3

80.6

50.9

81.4

51.4

82.3

51.9

83.1

52.5

84.0

53.0

84.8

58

33

51.7

79. 7

52.3

80.5

52.8

81.4

53. 4

82.2

53.9

83.0

54. 5

83.9

57

34

53.1

78.8

53.7

79 6

54. 2

80.4

54.8

81.2

55.4

82. 1

55.9

82.9

56

35

54.5

77.8

55. 1

78.6

55. 6

79.5

56.2

80.3

56.8

81. 1

57.4

81.9

55

36

55.8

76.9

56. 4

77.7

57. 1)

78.5

57.6

79.3

58. 2

80. 1

58.8

80.9

54

37

57.2

75.9

57.8

76.7

58.4

77.5

59. 0

78.3

59.6

79. 1

60.2

79.9

53

38

58.5

74.9

59.1

75.6

59. 7

76.4

60.3

77.2

6L. 0

78.0

61.6

78.8

52

39

59.8

73.8

60. 4

71. li

61.0

75. 4

61. 7

76. 2

62. 3

76.9

62. II

77. 7

51

40

61. 1

72.8

61. 7

73. 5

62. 4

74.3

63. 0

73 1

63.6

75.8

61.3

76.6

50

41

62. 3

71. 7

63.0

72.5

>,:,. 6

73.2

64.3

7 1.(1

64. 9

74. 7

65. 6

75.5

49

42

63 6

711.6

64.2

71.3

64.9

72. 1

65.6

72. s

66.2

73.6

66. 9

74.3

48

43

64.8

69.5

65. 5

70.2

66. 2

70.9

66. S

71.7

67. 5

72. 1

68. 2

73.1

47

44

66.0

68.3

66.7

69. 1

67.4

69.8

68. 1

70. 5

68.8

71.2

69.5

71.9

46

45

67, 2

67.2

67.9

67.9

68. 6

68.6

69.3

69 3,

70. 0

70.0

70.7

70.7

45

.4

COS

sin

COS

sin

cos

sin

cos

sin

cos

sin

cos

sin

A

234

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

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V. z— ■

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J3 3 *

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TABLES

(10.1) ARTEMIS.
(115) THYRA.
(128) NEMESIS.
(133) CYRENE.

OF

(139) JUEW \. I

(161) VTHOR. I

(174) PHAEDRA.
(179) KLYTAEMNESTRA.

?tdz, 3 log r, and w/cos i are tabulated in the
form 2{ di sin ig + 2i bt cos ig + cT.

89369°— vol 10—11 16

235

236 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF (105) ARTEMIS.

MEAN ELEMENTS.

Epoch, 1896, Nov. 20.0, M. T. Berlin=1896.887, M. 1

. Berlin.

9a

o / // o
=353 59 41=353. 9948

CO

= 54 48 51= 54. 8142]

Q

=188 7 15=188. 1208 [Mean equinox and ecliptic 1900.0

i

= 21 30 0= 21. 5000 J

<P

= 10 6 12= 10. 1032

n

=970".4380 = 0. 26956611

The elements are based on oppositions extending from 1868 to 1900 anc:

on the perturbations of the first

order by Jupiter, as given on page 237.

AUXILIARY QUANTITIES.

log «=0. 37536 log 57. 296 «=1. 00221 h)trJl~e_„ q9„„9
log e=9. 24408 log p =0.36178 logy — — ». a^suz

TABLE I.— MEAN ANOMALY (g).

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Month

9

Year

9

Year

9

Jan. go

O

\ 0. 00000

B

1868

O

29. 80279

1899

O

201. 83028

69

128. 19442

1900

300. 22191

Feb. {0;0

| 8. 35655

1870

226. 58605

1

38. 61354

71

324. 97768

2

137. 00517

Mar. 0.0

15. 90440

B

72

63. 63888

3

235. 39680

Apr. 0.0

24. 26095

73

162. 03051

B 4

334. 05800

May 0.0

32. 34793

74

260. 42214

1905

72. 44963

June 0.0

40. 70448

1875

358. 81377

6

170. 84126

July 0.0

48. 79146

B

76

97. 47496

7

269. 23289

Aug. 0.0

57. 14801

77

195. 86659

B 8

7. 89409

Sept. 0.0

65. 50456

78

294. 25822

9

106. 28572

Oct. 0.0

73. 59154

79

32. 64985

1910

204. 67735

Nov. 0.0

81. 94809

B

1880

131. 31105

1

303. 06898

Dec. 0.0

90. 03508

81
82
83

• 229. 70268

B 2

41. 73017

328. 09431
66. 48594

3

4

140. 12180
238. 51343

B

84

165. 14714

1915

336. 90506

Change for n daysa

1885

263. 53877

B 6

75. 56626

86

1. 93040

7

173. 95789

?l

a n

9

B

87
88

100. 32203
198. 98322

8
9

272. 34952
10. 74115

\f

89

297. 37485

B 1920

109. 40234

o

O

IN'.KI

35. 76648

1

207. 79397

1

0. 26957

16

4. 31306

91

134.15811

2

306. 18560

2

0. 53913 17

4. 58262

B

92

232. 81931

3

44. 57723

3

0. 80870 18

4. 85219

93

331.21094

B 4

143. 23843

4

1.07826 19

5. 12175

94

69. 60257

L925

241. 63006

5

1. 34783 ; 20

5.39132

imi;,

167. 99420

6

340. 02169

6

1. 61740 21

5. 66089

B

96

266. 65539

7

78. 41332

7

1.88696 22

5. 93045

97

5. 04702

B 8

177. 07452

8

2. 15653 23

6. 20002

98

103. 43865

9

275. 40615

9

2. 42609 24

6. 46958

99

201. 83028

1930

13. 85778

10
11

2. 69566
2. 96523

25
26

6. 73915

7. 00872

12

3. 23479

27

7. 27828

N

OTE . — W

nen g is used as an argument of the perturbations

13

3. 50436

28

7. 54785

add to the a

of this table J7r=r—ii0=+0?1631. For explana-

14

3. 77392

29

7. 81742

tion

see page

203.

15

4. 04349

30

8. 08698

a]

''or days during January and

Febi

uary of leap years, substractone

day

jefore entering this table.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

237

Tables of (105) Artemis — Continued.

PERTURBATIONS.

nSz

V

u/cos i

Arg.

ig— i'g'

sin

cos

sin

cos

sin

cos

i if

n

II

n

II

a

II

0 0

4

+ 3

0 0

0. 14nt

- 1.05nt

+1 0

— 2

+ 4

+1

+ 4. 14nt

- 4. 38nt

- 2. 19nt

2. 07nt

- 6.23nt

+ 3.94nt

+ 2

+ 3

+ 2

- 1

+2

0. ISnt

0. Hint

0. 19nt

0. 18nt

- 0.54nt

+ 0.34nt

3

+ 0.02nt

0.02nt

0. 02nt

0. 02nt

- 0.07nt

4- 0.04nt

+4 0

- O.Olnt

+ O.Olnt

-2 -(-I

- 1

- 1

-1

+ 8

9

4- 5

+ 4

7

+ 3

0

f 21

+ 2

1

+ 3

- 9

+ 4

+ 1

+ 43

53

f 20

- 16

+ 7

- 8

+2

1

2

2

- 2

- 5

+3 +1

+ 1

1

-1 +2

+ 2

1

+ 1

- 3

- 1

0

f 23

7

+ 4

+ 7

-13

- 9

+ 1

- 18

+ 239

f 64

7

14

+13

+ 2

- 20

r 120

r 74

V 13

f 6

+ 1

3

+ 8

8

+ 1

+ 1

+4 +2

+ 1

1

-1 +3

+ 2

+ 1

- 1

— 2

0

27

+ 1

h 12

-14

-19

+1

-256

+1356

f 81

f 28

- 5

- 2

+2

-272

f 312

^162

+ 139

f 3

+50

+3

- 2

10

• + 11

•5

- 1

+ 5

+4 +3

+ 1

+ 1

+ 1

0 -4

— 2

1

1

+ 3

+ 1

- 22

21

5

5

- 2

+ 2

+2

f 69

39

17

- 30

• 5

- 9

+ 3

14

2

1

- 10

1

- 3

i -1

1

1

0 +5

1

+1

3

- 5

+ 1

1

- 1

+2

+ 31

3

- 10

+ 2

- 1

+3

+ 11

+ 5

+ 3

- 8

f 3

+4 +5

2

1

- 1

+1 +6

1

1

- 1

1

+2

9

6

+ 1

3

- 1

+3

+ 3.

+ 3

+ 9

10

4

+ 1

+4

1

1

+5 +6

1

238 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (105) Artemis — Continued.

TABLE II.— n<5z.

PERIODIC TERMS.

Unit of a and 6=09001.

i

0

1

2

9'

bo

Diff.forl°

ai

Diff.forl0

b,

Diff.forl0

a..

Diff.forl0

62

Diff . for 1°

O

0

- 1.4

-0.67

- 73.6

+22. 36

+454. 5

+ 4.01

- 50.8

+4.64

+ 107. 6

+1.82

6

-5.4

-0.64

+ 62.4

+22. 71

+458. 5

- 2.72

- 22.4

+4.71

+114.8

+0.68

12

- 9.1

-0.55

+194. 8

+21.01

+421.9

- 9.41

+ 5.7

+4.62

+115.8

-0.31

18

-12.0

-0.44

+310. 6

+17. 30

+347. 2

-15.26

+ 33.0

+4.44

+111. 1

-1.24

24

—14.4

-0.33

+399. 3

+12. 01

+241. 5

-19.71

+ 59.0

+4.16

+ 100.9

-2.18

30

-16.0

-0.17

+452. 4

+ 5.47

+ 114.3

-22.31

+ 82.9

+3.72

+ 85.0

-3.16

36

-16.4

0.00

+464. 9

- 1.36

— 22.1

-22. 83

+ 103.7

+3.05

+ 63.0

-4.17

42

-16.0

+0.14

+436. 1

- 8.16

-155.3

—21. 16

+ 119.5

+2.01

+ 35.0

-5.07

48

-14.7

+0. 28

+368. 6

-14. 10

-272. 1

-17.48

+ 127.8

+0.58

+ 2.2

-5.72

54

-12.6

+0.40

+269. 8

-18. 61

-361. 9

-12. 26

+126. 4

—1.12

- 33.6

-5.97

60

- 9.9

+0.48

+ 149.3

-21. 19

-417.0

- 5.85

+ 114.3

-2.93

- 69.4

-5.62

66

- 6.8

+0.51

+ 19.6

-21.71

-432. 1

+ 0.83

+ 91.2

-4.66

-101.0

-4.65

72

- 3.8

+0.50

-107. 1

-20. 13

-407. 0

+ 7.36

+ 58.4

-6.02

-125.2

-3. 10

78

- 0.8

+0.46

-218. 2

-16. 63

-345. 4

+13. 00

+ 19.0

-6.82

-138.2

-1.08

84

+ 1.7

+0.37

-303. 8

-11.69

-253. 8

+17.22

- 23.4

-6.94

-138.2

+ 1.12

90

+ 3.6

+0.24

-356. 5

- 5.64

-142.4

+ 19.60

- 64.3

-6.29

-124.8

+3.25

96

+ 4.6

+0.12

-371.5

+ 0.61

- 22.5

+20. 01

- 98.9

-4.96

- 99.2

+5.08

102

+ 5.0

0.00

-349. 2

+ 6.72

+ 93.9

+ 18.46

-123.8

-3.12

- 63.8

+6.40

108

+ 4.6

-0.14

-292. 5

+11. 94

+ 195.5

+ 15. 15

-136. t

-0.93

- 22.4

+7.02

114

+ 3.3

-0. 24

-208. 5

+15. 82

+272. 9

+ 10.43

-135.0

+ 1.33

+ 20.4

+6.90

120

+ 1.7

-0.30

-106.0

+17.97

+318. 9

+ 4.76

-120.4

+3.42

+ 60.4

+6.10

126

- 0.3

-0.34

+ 3.6

+18. 29

+333. 0

- 1.06

— 93.9

+5. 16

+ 93.6

+4.64

132

- 2.4

-0.32

+ 109.9

+ 16.77

+306. 1

- 6.75

- 58.5

+6.29

+116.0

+2.71

138

- 4.2

-0.29

+201. 5

+13. 51

+250. 6

-11.59

- 18.4

+6.74

+126. 1

+0. 52

144

- 5.9

-0.22

+269. 9

+ 9.06

+ 169.6

-15. 15

+ 22. 4

+6.48

+122. 4

-1.70

150

(i 8

-0. 11

+308. 6

+ 3.68

+ 72.0

-17.09

+ 59.4

+5.50

+105. 7

-3.69

156

-7.2

+0.01

+314. 1

- 1.87

- 31.9

-17.23

+ 88.4

+3.90

+ 78.1

-5.29

162

-6.7

+0.12

+286. 2

- 7.27

-131.3

-15.61

+106.2

+ 1.90

+ 42.2

-6.13

168

-5.7

+0.21

+228. 4

-11. 83

-216.2

-12.47

+ 111.2

-0.29

+ 4.5

-6.25

174

-4.2

+0.20

+ 146.6

-15. 19

-278. 4

- 8.04

+102. 7

-2.40

- 32.8

-5.74

180

- 2.6

+0.30

+ 49.2

-16.94

-311.3

- 2.78

+ 82.4

-4.12

— 64.4

-4.48

186

- 0.6

+0.31

- 53.4

-17.00

-311.7

+ 2.63

+ 53.2

-5.31

- 86.6

-2.74

192

+ 1.1

+0.27

-151.5

-15.35

-279. 7

+ 7.91

+ 18.7

-5.82

- 97.3

-0.73

198

+ 2.6

+0.21

-234. 6

-12. 14

-218.4

+12. 33

- 16.8

-5.61

- 95.4

+ 1.27

204

+ 3.6

+0.12

-294. 7

- 7.91

-134. 1

+15. 57

- 48.6

-4.76

- 82.1

+3.05

210

+ 4.0

+0.02

-325. 6

- 2.43

- 34.6

+17.26

- 73.9

-3.41

- 58.8

+4.42

216

+ 3.8

-0.08

-323. 9

+ 3.02

+ 69.7

+ 17.22

- 89.5

-1.72

- 29.0

+5.23

222

+ 3.0

-0.11

-289. 3

+ 8.40

+ 168.7

+15. 49

- 94.5

+0.12

+ 4.0

+5.48

228

+ 2.5

-0.18

-224. 7

+12.92

+252. 5

+12. 18

- 88.0

+1.91

+ 36.7

+5.15

234

+ 0.8

-0.23

-136. 6

+ 16.25

+312. 3

+ 7.57

- 71.6

+3.49

+ 65.8

+4.27

240

- 0.3

-0. 17

- 32.8

+ 17.99

+341. 7

+ 2.05

- 46.1

+4.77

+ 88.0

+2.93

246

- 1.2

-0. 12

+ 75.8

+17. 96

+336. 9

- 3.64

— 14.4

+5.56

\ 101.0

+1.28

252

- 1.8

-0. 03

+ 179. 1

+16.11

+298. 0

- 9.22

+ 20.6

+5.82

+ 103.3

-0.62

258

- 1.6

+0.08

+265. 8

+12. 54

+227. 8

-13.97

+ 55.4

+5.45

+ 93.6

-2.56

264

- 0.9

+0.17

+327. 0

+ 7.64

+133. 0

-17.36

+ 86.0

+4.44

+ 72.6

-4.33

270

+ 0.4

+0.26

+356. 1

+ 1.86

+ 22.4

-19.15

+ 108. 7

+2.84

+ 41.6

-5.75

276

+ 2.2

+0.35

+349. 3

- 4.15

- 93.1

-19.02

+120. 1

+0.79

+ 3.6

-6.57

282

+ 4.6

+0.42

+306. 3

-10.01

-202. 1

-19.01

+118.2

-1.49

- 37.2

-6.60

288

+ 7.2

+0.44

+230. 9

-14. 95

-293. 7

-13.20

+102.2

-3.72

- 75.6

-5.83

294

+ 9.9

+0.42

+ 129.5

-18.58

-357. 9

- 8.05

+ 73.6

-5.57

-107.2

-4.33

300

+ 12.3

+0.38

+ 11.6

-20. 36

-388. 6

- 1.98

+ 35.4

-6.76

-127.6

-2.21

306

+ 14.5

+0.29

— 111.0

-20. 23

-381.6

+ 4.29

- 7.5

-7.11

-133. 7

+0.20

312

+ 15.8

+0. 16

-227. 4

-18.21

-337. 1

+10. 39

- 49.9

-6. 59

-125.2

+2.53

318

+16.4

+0.02

-325. 9

-14.33

-258. 6

+15. 54

- 86.6

-5.29

-103.3

+4.50

324

+16.1

-0. 12

-396. 6

- 9.06

-153. 2

+19. 37

-113.4

-3.45

- 71.2

+5.82

330

+15.0

-0.28

-432. 7

- 2.78

- 29.7

+21.42

-128.0

-1.38

- 33.5

+6.38

336

+12.8

-0.42

-429. 9

+ 3.74

+ 99.9

+21.47

-130.0

+0.62

+ 5.3

+6.21

342

+ 9.9

-0.52

-387. 8

+10. 18

+224. 1

+19.57

-120.6

+2.32

+ 41.0

+5.47

348

+ 6.5

-0.61

-309. 4

+ 15.72

+331. 0

+15. 77

-102.2

+3.54

+ 70.9

+4.33

354

+ 2.6

-0.66

-201.8

+ 19.95

+410. 4

+10. 47

- 78.1

+4.28

+ 93.0

+3.06

360

- 1.4

-0.67

- 73.6

+22. 36

+454. 5

+ 4.01

- 50.8

+4.64

+107. 6

+ 1.82

[ndz, 3 log r, and u/eos i are to be computed m the form l'i ai sin ig+Si bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

239

Tables of (105) Artemis — Continued.
TABLE II.— vSz— Continued.

PERIODIC TERMS.

rnitofa and 6=09001.

X

3

4

9'

«3

Diff. for 1°

h

Diff. fori0

<»4

Diff. fori0

b<

Diff. for 1°

O

0

+ 7.5

+0.38

+ 6.4

-0.58

-0. 1

-0.07

-0.0

+0.01

6

+ 8.9

+0.06

+ 2.6

-0.64

-0.5

-0. 00

-0.3

+0. 05

12

+ 8.2

-0. 25

- 1.3

-0.58

-0.8

II 02

0.0

+0.07

18

+ 5.9

-0.47

- 4 3

-0.36

-0.8

+0.02

+0.5

+0.08

24

+ 2.6

-0.52

- 5.6

II (is

-0.5

+0.08

+0.9

+0.06

30

- 0.4

-0.45

- 5.2

+0.21

+0.1

+0. 10

+ 1.2

+0.02

36

- 2.8

-0.26

- 3.1

+0.40

+0.7

+0.08

+ 1.1

-0.04

42

- 3.5

+0.02

- 0. 1

+0. 45

+1.1

+0.07

+0.7

-0.&8

48

- 2.5

+0.27

+ 2.3

+0.35

+1.5

+0.02

+0.2

-0.09

54

- 0.3

+0.41

+ 3.8

+0.12

+1.4

-0.03

-0.4

-0. 10

60

+ 2.4

+0.42

+ 3.8

-0. 12

+1.1

-0.08

-1.0

-0.08

66

+ 4.8

+0.32

+ 2.4

-0.33

+0.5

-0.10

-1.3

-0.02

72

+ 6.3

+0.12

- 0.2

-0.48

-0.1

-0. 09

-1.3

+0.01

78

+ 6.2

-0.14

- 3.4

-0.48

-0.6

-0.07

-1.2

+0.04

84

+ 4.6

-0.36

- (i. 0

-0.35

-0.9

-0.03

-0.8

+0.08

90

+ 1.9

-0.51

- 7.6

-0.17

—1.0

0.00

-0.3

+0.08

96 ■

- 1.5

-0.52

- 8.0

+0.07

-0.9

+0.03

+0.1

+0.06

102

— 4.4

-0. 4 1

- 6.8

+0.28

-0.6

+0.04

+0.4

+0.03

108

-6.4

-0.23

-4.6

+0.42

-0.4

+0. 04

+0.5

0.00

114

-7.2

-0.06

- 1.7

+0.47

-0.1

+0. 03

+0.4

-0.02

120

- 7. 1

+0.12

+ 1.0

+0. 42

0.0

+0.01

+0.3

-0.01

126

— 5.8

+0.28

+ 3.3

+0.32

0.0

+0.01

+0.3

-0.02

132

- 3.8

+0.32

+ 4.7

+0. 15

+0.1

+0.01

+0.1

-0.02

138

- 1.9

+0.32

+ 5.1

+0.01

+0.1

-0.01

0.0

-0.01

144

+ 0.1

+0.29

+ 4.8

-0.10

0.0

-0.01

0.0

+0.01

150

+ 1.6

+0.21

+ 3.9

-0.16

0.0

0.00

+0.1

-0.01

156

+ 2.6

+0.11

+ 2.9

-0. 19

0.0

-0.01

-0.1

-0.02

162

+ 2.9

+0.03

+ 1.6

-0.21

-0.1

0.00

-0.1

+0.01

168

+ 3.0

-0.02

+ 0.4

-0.18

0.0

0.00

0.0

+0.01

174

+ 2.6

-0.09

- 0.6

-0.17

-0.1

-0.01

0.0

0.00

180

+ 1.9

-0.12

- 1.6

-0. 12

-0.1

0.00

0.0

+0.01

186

+ 1.1

-0.16

- 2.0

-0.04

-0.1

-0.01

+0.1

+0.02

192

0.0

-0.17

- 2. 1

0.00

-0.2

+0.01

+0.2

0.00

198

- 0.9

-0. 15

- 2.0

+0.06

0.0

+0.01

+0.1

-0.01

204

-1.8

-0.11

- 1.4

+0.13

-0.1

+0.01

+0.1

+0.01

210

2. 2

-0. 05

- 0.4

+0.16

+0.1

+0.02

+0.2

0.00

216

-2.4

+0.01

+ 0.5

+0.13

+0.1

0.00

+0.1

-0.01

222

- 2. 1

+0.08

+ 1.2

+0.13

+0.1

0. 00

+0.1

-0.01

228

- 1.5

+0.12

+ 2. 1

+0.12

+0.1

-0.01

0.0

+0.01

234

- 0.7

+0. 12

+ 2.6

+0.03

0.0

0.00

+0.2

+0.02

240

0.0

+0.14

+ 2.5

+0.02

+0.1

+0.01

+0.2

+0.01

246

+ 1.0

+0.16

+ 2.8

+0.01

+0.1

+0.02

+0.3

+0.01

252

+ 1.9

+0.13

+ 2.6

-0. 05

+0.3

+0.02

+0.3

-0.01

258

+ 2.6

+0.14

+ 2.2

-0.10

+0.4

+0.03

+0.2

-0. 02

264

+ 3.6

+0.14

+ 1-4

-0.15

+0.7

+0.03

0.0

-0.04

270

+ 4.3

+0.09

+ 0.4

-0.20

+0.8

0.00

-0.3

-0.06

276

+ 4.7

+0.04

- 1.0

-0.25

+0.7

-0.03

-0.7

-0.06

282

+ 4.8

-0.04

- 2. li

-0.30

+0.4

-0. 00

-1.0

-0.03

288

+ 4.2

-0.18

- 4.6

-0.32

0.0

-0.08

-1.1

-0.01

294

+ 2.6

-0.34

- 6.5

-0.26

-0.5

-0.08

-1.1

+0.02

300

+ 0.1

-0.47

- 7.7

-0. 12

-1.0

-0.07

-0 9

+0.07

306

- 3.0

-0. 52

- S.O

+0.08

-1.3

-0 02

-0.3

+0.10

312

-6.2

-0.49

-6.7

+0.30

—1.3

+0.03

+0.3

+0.08

318

-8.9

-0.34

- 4.4

+0. 52

-0.9

+0. 06

+0. li

+0. 06

324

-10.3

-0.08

- 0.4

+0.69

-0.6

+0.08

+ 1.0

+0.04

330

-9.9

+0. 21

+ 3.9

+0.66

0.0

+0.09

+1.1

-0.02

336

- 7.8

+0.47

+ 7.5

+0. 51

+0.5

+0.06

+0.7

-0.07

342

-4.3

+0.67

+ 10.0

+0. 28

+0.7

+0.01

+0.3

-0.08

348

+ 0.2

+0.72

+10. 8

-0.03

+0.6

-0 03

-0.2

-0.06

354

+ 4.4

+0.61

+ 9.6

-0.37

+0. 3

-0. 06

-0.4

-0. 03

360

-+ 7.5

+0.38

+ 6.4

-0 58

-0.1

-0.07

-0.6

+0.01

[ndz, 3 log r, and M/eos i are to lie computed in the form li at sin ig+Ii hi cos ig+cT.

240 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (105) Artemis — Continued.

PERIODIC TERMS.

TABLE III.— S log r.

Unit of o and 6=0.00601.

i

)

]

2

9'

K

Diff. for 1°

a,

Diff. for 1°

h

Diff. for 1°

a2

Diff. for 1°

h

Diff. fori0

O

0

+3.6

-0. 05

+32.4

+0. 18

+ 4.8

-1.40

+47. 1

+0.94

+23.0

-2.06

6

+3.1

-0.08

+32.4

+0. 18

- 3.7

-1.41

+51.0

+0.38

+10.2

-2.18

12

+2.6

-0. 12

+30. 3

-0.52

-12.1

-1.32

+51.7

-0. 16

- 3.2

-2.18

18

+ 1.7

-0.15

+26.1

-0.85

-19.6

-1.15

+49. 1

-0.67

-15.9

-2.03

24

+0.8

-0. 18

+20. 1

-1. 10

-25.9

-0.91

+43.7

-1.12

-27.6

— 1.82

30

-0.4

-0.19

+12.9

-1.24

-30. 5

-0.60

+35. 6

-1.55

—37.7

-1.53

36

-1.5

-0.18

+ 5.2

-1.32

-33. 1

-0.28

+25.1

-1.91

-46.0

-1. 15

, 42

-2.5

-0. 15

- 3.0

-1. 33

-33.8

+0.06

+12. 7

-2. 21

-51. 5

—0.64

48

-3.3

-0. 12

-10.8

-1.22

-32.4

+0. 40

- 1.4

-2.38

-53.7

-0.03

54

-4.0

-0.09

-17.7

-1.06

-29.0

+0.70

-15. 9

-2.38

-51. 9

+0. 63

60

—4.4

-0.05

-23.5

-0.82

-24.0

+0.94

-29.9

-2. 18

-46.1

+1.31

66

-4.6

0.00

-27.6

-0. 53

-17.7

+1.12

-42.0

-1.75

-36.2

+ 1.92

72

—4.4

+0. 05

-29.9

-0.22

-10.5

+ 1.20

-50.9

-1.14

-23.0

+2.42

78

-4.0

+0.09

-30. 2

+0. 13

-3.3

+ 1. 19

-55.7

-0.37

-7.2

+2.69

84

-3.3

+0. 13

-28.3

+0. 45

+ 3.8

+ 1. 10

-55.3

+0.48

+ 9.3

+2.70

90

-2.4

+0. 15

-24.8

+0.70

+ 9.9

+0.92

-49.9

+ 1.28

+25. 2

+2.45

96

-1.5

+0. 15

-19.9

+0.89

+ 14.8

+0. 68

-39.9

+1.99

+38.7

+ 1.94

102

-0.6

+0.14

-14.1

+ 1.02

+18.0

+0.37

-26.0

+2.49

+48. 5

+ 1.22

108

+0.2

+0.12

-7.7

+1.03

+19.2

+0.05

-10.0

+2.72

+53.4

+0.38

114

+0.8

+0.10

- 1.7

+0. 94

+ 18.6

-0.24

+ 6.7

+2.68

+53.1

-0.48

120

+1.4

+0.06

+ 3.6

+0.78

+16.3

-0.49

+22.1

+2.35

+47.6

-1.29

126

+1.5

0.00

+ 7.7

+0. 55

+12.7

-0.69

+34.9

+ 1.81

+37.6

-1.94

132

+1.4

-0.03

+ 10.2

+0.28

+ 8.0

-0. 79

+43.8

+ 1.08

+24.3

-2.38

138'

+ 1.1

-0.08

+ 11. 1

-0.02

+ 3.2

-0. 78

+47.9

+0.25

+ 9.1

—2.56

144

+0.5

-0.10

+ 10.0

-0.28

- 1.3

-0. 68

+46.8

-0.57

-6.4

-2.46

150

—0.1

-0. 11

+ 7.7

-0.48

- 5.0

-0. 50

+41. 1

-1.31

-20.4

-2.09

156

-0.8

-0. 11

+ 4.2

-0.60

-7.3

-0.27

+31. 1

-1.91

-31.5

-1.53

162

-1.4

-0. 10

+ 0.5

-0.61

-8.2

-0.01

+18.2

-2.27

-38.8

-0.80

168

-2.0

-0.09

- 3.1

-0. 58

-7.4

+0.25

+ 3.9

-2.35

-41.1

+0.02

174

-2. 5

-0.06

-6.4

-0. 43

-5.2

+0.46

-10.0

-2.17

-38.6

+0.79

180

-2.7

-0.02

-8.3

-0.22

- 1.9

+0.58

-22. 1

-1.73

-31.6

+ 1.48

186

-2.7

+0.02

- 9.1

+0.01

+ 1.7

+0.63

-30.8

-1.12

-20.9

+ 1.94

192

-2.4

+0.06

-8.2

+0.24

+ 5.7

+0.62

-35.6

-0.38

-8.3

+2. 18

198

-2.0

+0.08

-6.2

+0. 45

+ 9.2

+0.50

-35. 3

+0.42

+ 5.3

+2. 16

204

-1-. 5

+0. 10

-2.8

+0.62

+ 11.7

+0.31

-30.5

+ 1. 12

+17.6

+1.86

210

-0.8

+0.09

+ 1.2

+0.67

+12.9

+0.08

-21.8

+ 1.69

+27.6

+1.33

216

-0.4

+0.08

+ 5.2

+0.65

+12.7

-0.17

-10.2

+2.05

+33.6

+0. 66

222

+0.1

+0.06

+ 9.0

+0 58

+10.9

-0.39

+ '2.8

+2. 15

+35. 5

-0.09

228

+0.3

+0.02

+ 12.1

+0.40

+ 8.0

-0. 58

+ 15. 6

+ 1.97

+32.5

-0.83

234

+0.4

0.00

+13.8

+0. 15

+ 3.9

-0.71

+26.4

+1.58

+25. 5

-1.44

240

+0.3

-0.05

+ 13.9

-0.10

- 0.5

-0. 74

+34.6

+ 1.02

+ 15 2

-1.92

246

-0.2

-0.08

+12.6

-0. 35

- 5.0

-0.70

+38.7

+0.32

+ 2.5

-2.18

252

-0.6

-0.08

+ 9.7

-0.58

- 8. 9

-0.58

+38.4

-0.42

-10.9

-2. 19

258

-1.2

-0.10

+ 5.6

-0.77

-11.9

-0.38

+33.6

-1. 15

-23.8

-1.98

264

-1.8

-0. 10

+ 0.5

-0. 89

-13.5

-0. 12

+24.6

-1.76

-34.6

-1.52

270

-2.4

-0.09

- 5.1

-0.91

- 13.3

+0. 18

+12.5

-2.20

-42. 1

1) ss

276

-2.9

-0.07

-10.4

-0.84

-11.3

+0.47

- 1.8

-2.43

-45.2

-0. 12

282

-3.2

-0.03

-15.2

-0.68

-7.7

+0 73

-16.7

-2.39

-43. 5

+0.68

288

-3.3

+0.01

-18.6

-0.44

- 2.5

+0.93

-30.5

-2.09

-37. 1

+1.44

294

-3.1

+0.06

-20.5

-0. 15

+ 3.5

+ 1.08

-41.8

-1.54

—26.2

+2.08

300

-2.6

: II (Ml

-20.4

+0. 18

+ 10. 4

+ 1.12

-49.0

-0.79

-12. 1

+2. 50

306

-2.0

+0. 12

-18.3

+0. 52

+16.9

+ 1.02

-51.3

+0.02

+ 3.8

+2.65

312

-1.1

+0.15

-14.2

+0 81

+22.7

+0.87

-48. 7

+0.87

+ 19. 7

+2. 51

318

-0.2

+0. 15

-8.6

+ 1.03

+27.3

+0.62

-40.9

+ 1.63

+33.9

+2. 11

324

+0.7

+0.16

- 1.8

+ 1 20

+30.2

+0.30

-29. 1

+2. 18

+45.0

+1.48

330

+ 1.7

+0. 15

+ 5.8

+1.28

+30. 9

-0.07

-14 7

+2.48

+51. 6

+0.72

336

+2.5

+0.12

+ 13. 5

+1.22

+29. 4

-0.42

+ 0.6

+2.55

f 53. 7

-0.03

342

+3.1

+0.09

+20. 5

+ 1.07

+25.8

-0.77

+15.9

+2.38

+51.2

-0.76

348

+3.6

+0.05

+26.3

+0.81

+20.2

-1 06

+29.1

+ 1.98

+44.6

-1.36

354

+3.7

0.00

+30.2

+0.51

+13.1

-1.28

+39.7

+1.50

+34.9

-1.80

360

+3.6

-0. 05

+31'. 1

+0. 18

+ 4.8

-1.40

+47.1

+0.94

+23.0

-2 06

[ndz S log r, and u/cos i aro to he computed in the form St a, sin ig+St Oi cos ig+cT.\

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (105) Artemis — Continued.

241

PERIODIC TERMS.

TABLE III.— d log r— Continued.

Unit of a and 6=0.00001.

i

3

4

9'

"3

Diff. for 1°

h

Diff. for 1°

"t

Diff. for 1°

b<

Diff. for 1°

O

0

+6.3

-0.41

-A.l

-0.39

0.0

0.00

0.0

+0. 02

6

+3.3

-0. 54

-6.4

-0. 13

0.0

+0.01

+0.1

+0.02

. 12

-0.2

-0.49

-6.3

+0. 15

+0.1

+0.02

+0.2

+0.01

18

-2.6

-0.28

-4.6

+0.37

+0.2

+0.02

+0.2

-0.01

24

-3.6

-0.03

-1.9

+0.42

+0.4

+0.02

+0.1

-0.02

30

-3.0

+0. 21

+0.5

+0.32

+0.5

0.00

-0.1

-0.03

3G

-1. 1

+0. 35

|-2 11

+0.12

+0.4

-0.02

-0.3

-0.03

42

+ 1.2

+0.34

+2.0

-0. 12

+0.3

-0.02

-0.5

-0.03

4S

+3.0

+0. 18

+0.5

-0.33

+0.2

-0.04

-0.7

-0.02

54

+3.4

-0.06

-2.0

-0.39

-0.2

—0. 05

-0.7

0.00

60

+2.3

-0.29

-4. 2

-0.32

-0.4

-0.03

-0.7

+0.02

66

-0. 1

-0.43

-5.8

-0.12

-0.6

-0.02

-0.5

+0.04

72

-2.9

-0. 45

-5.6

+0.14

-0.6

-0.02

-0.2

+0. 05

78

-5.5

-0.32

-4.1

+0.35

-0.8

-0.01

+0.1

+0.04

84

-6.8

-0.09

-1.4

+0.47

-0.7

+0.02

+0.3

+0.03

90

-6.6

+0.13

+1.5

+0. 45

-0.5

+0.04

+0.5

+0. 02

96

-5. 2

+0. 31

+4.0

+0. 32

-0. 2

.11 1.1

+0.6

0.00

102

-2.9

+0.40

+5.3

+0.12

0.0

+0.03

+0.5

-0.01

108

-0.4

+0.36

+5.5

-0.08

+0.2

+0.02

+0.5

-0.02

114

+ 1.4

+0.22

+4.4

-0.21

+0.3

+0. 02

+0.3

-0.02

120

+2. 3

+0.09

+3.0

-0.24

+0. 4

0. 00

+0. 2

-0.02

126

+2. 5

-0.02

+ 1.5

-0.20

+0.3

-0.02

+0.1

-0.02

132

+2.0

+0.6

-0.10

+0.2

-0.01

-0.1

-0.02

138

+ 1.1

-0.08

+0.3

0.00

+0.2

-0.01

-0.2

-0.01

144

+ 1.1

0.00

+0.6

+0.04

+0.1

-0.01

-0.2

+0.01

150

+ 1.4

+0.08

+0.8

0.00

+0.1

-0.02

-0. 1

+0.02

156

+2.0

+0. 10

+0. 6

-0. 08

-0.1

-0.02

0.0

+0.01

162

+2.6

+0.03

-0.2

-0.17

-0.1

+0.02

0.0

0.00

168

+2.4

-0.07

-1.4

-0.20

+0.1

+0.01

0.0

+0.01

174

+1.8

-0. 17

-2.6

-0.16

0.0

-0.01

+0.1

0.00

180

+0.4

-0.27

-3.3

-0.06

0.0

0.00

0.0

-0.02

186

-1.4

-0.28

-3.3

+0.09

0.0

+0.01

-0.1

0.00

192

-3.0

-0.21

-2.2

+0.24

+0.1

-0.01

0.0

+0.01

198

-3.9

-0.05

-0.4

+0.34

-0. 1

-0.02

0.0

+0.01

204

-3.6

+0. 13

+ 1.9

+0.32

-0.1

■ 11 n_>

+0.1

+0.01

210

-2.3

+0.28

+3.5

+0.21

+0.1

+0.02

+0.1

+0.01

216

-0.2

+0.37

+4.4

+0.04

+0.1

+0.01

+0.2

+0.01

222

+2.1

+0.32

+4.0

-0.14

+0.2

+0.01

+0.2

-0.01

228

+3.7

+0. 20

+2. 7

-0.28

+0.2

+0.01

+0.1

-0.02

234

+4.5

+0.03

+0.6

-0.34

+0.3

+0. 02

-0.1

-0.02

240

+4.1

-0. 12

-1.4

-0.29

+0.4

0.00

-0.2

-0.02

246

+3.0

-0.22

-2.9

-0.18

+0.3

-0. 02

-0.3

-0.02

252

+1.4

-0. 24

-3.5

-0.02

+0.2

-0.02

-0.5

-0.02

258

+0.1

-0.18

-3.2

+0.08

0.0

-0.03

-0.5

-0.01

264

-0.8

0 (l<!

-2.6

+0. 10

-0.2

-0.04

-0.6

0.00

270

-1.0

0.00

-2.0

II IIS

-0.5

-0.04

-0.5

+0. 02

276

-0.8

+0.01

-1.6

0.00

-0.7

-0.02

-0.3

+0.03

2S2

-0.9

-0.04

-2.0

-0.06

-0.8

+0.01

-0. 1

+0.04

288

-1.3

-0. 12

-2.3

-0. 05

-0.6

+0.02

+0.2

+0.05

294

-2.4 •

-0.22

-2.6

+0.02

-0.6

+0.02

+0.5

+0.04

300

-4.0

-0. 25

-2.0

+0.17

-0.4

+0.03

+0.7

+0.02

306

-5.4

-0.18

-0.6

+0.32

-0.2

+0. 05

+0.7

0.00

312

-6.1

0.00

+1.8

+0.44

+0. 2

+0.04

+0.7

-0.02

318

-5.4

+0.23

+ 1-7

+0.44

+0.3

+0.02

+0.5

-0.03

324

-3.3

+0.46

+ 7. 1

+0.30

+0. 4

+0.02

+0.3

-0. 03

330

+0.1

: il ",s

+8.3

+0.07

+0.5

0.00

+0.1

-0.03

336

+3.6

+0. 55

+7.9

-0. 22

+0.4

-0.02

-0.1

-0.02

342

+6.7

+0.41

+5.6

-0 47

+0.2

-(1. 112

-0.2

-0. 01

348

+8.5

+0. 12

+2.3

-11 61

+0.1

-0. 02

-0.2

354

+8.2

-0.18

-1.7

-0. 58

0.0

-0.01

-0.1

+0. 02

360

+6.3

-0.41

-4.7

-0.39

0.0

0.00

0.0

+0.02

[nil, S log r, and u/cos i are to be computed in the form Si at sin ig+Ii bi cos ig+cT.]

242 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (105) Artemis — Continued.

PERIODIC TERMS.

TABLE IV.— u/cos

Unit of a and 6=09001.

i

0

1

2

9'

6o

Diff. for 1°

"i

Diff. for 1°

&.

Diff. for 1°

a2

Diff. for 1°

h

Diff. for 1°

O

0

- 5.0

+0.35

+ 9.6

+0.17

+ 1.9

-0.12

+ 4.5

+0.52

+ 9.6

-0. 20

6

- 2.8

+0.42

+ 10.4

+0.12

+1.1

-0.16

+ 7.4

+0.42

+ 8.0

-0.35

12

0.0

+0.47

+11.0

+0.06

0.0

-0.20

+ 9.5

+0.30

+ 5.4

-0.45

18

+ 2.8

+0.47

+11.1

-0.07

-1.3

-0.22

+11.0

+0.18

+ 2.6

-0.50

24

+ 5.6

+0.47

+ 10.2

-0.19

-2.7

-0.22

+11.6

+0.03

- 0.6

-0.53

30

+ 8.4

+0.40

+ 8.8

-0.29

-4.0

-0.20

+ 11.4

-0.10

-3.8

-0.53

36

+10.4

+0.32

+ 6.7

-0.35

-5.1

-0. 12

+ 10.4

-0. 25

- 7.0

-0.49

42

+ 12.3

+0.24

+ 4.6

-0.40

-5.5

-0.02

+ 8.4

-0.38

-9.7

-0.42

48

+13.3

+0. 12

+ 1.9

-0.41

—5.4

+0. 05

+ 5.9

-0.47

-12.0

-0.31

54

+ 13.6

-0.01

- 0.3

-0.35

-4.9

+0.08

+ 2.8

-0.55

-13.4

-0. 17

60

+13.2

-0.13

- 2.3

-0.31

-4.5

+0. 10

- 0.7

-0.58

-14.0

-0.02

66

+12.0

-0.25

- 4.0

-0.23

-3.7

+0.12

-4.2

-0.61

—13.7

+0.13

72

+10.2

-0.34

- 5.1

-0.19

-3.1

+0.08

- 8.0

-0.58

-12.4

+0.29

78

+ 7.9

-0.39

- 6.3

-0.16

-2.7

+0. 06

-11.2

-0.48

-10.2

+0.43

84

+ 5.5

-0.42

- 7.0

-0.11

-2.4

+0. 05

-13.8

-0.36

- 7.2

+0.58

90

+ 2.8

-0.43

-7.6

-0.08

-2.1

+0.06

-15.5

-0.18

- 3.2

+0.68

96

+ 0.3

-0.40

- 8.0

-0.08

-1.7

+0. 06

-16.0

+0.02

+ 1.0

+0. 75

102

- 2.0

-0.32

-8.6

-0.08

-1.4

+0.07

-15.2

+0.25

+ 5.8

+0.76

108

-3.6

-0.22

-8.9

-0.01

-0.9

+0.10

-13.0

+0.49

+ 10.1

+0.63

114

-4.7

-0.12

-8.7

+0. 03

-0.2

+0.12

-9.3

+0.68

+13.4

+0.48

120

- 5.0

0.00

- 8.5

+0.05

+0.5

+0. 11

-4.8

+0.81

+15.8

+0.25

126

-4.7

+0.10

- 8.1

+0.08

+ 1.1

+0.10

+ 0.4

+0.88

+ 16.4

-0.05

132

- 3.8

+0.18

-7.5

+0.09

+1.7

+0.10

+ 5.7

+0.83

+ 15.2

-0.32

138

- 2.5

+0.24

- 7.0

+0. 09

+2.3

+0.11

+ 10.4

+0.68

+12.5

-0.58

144

- 0.9

+0.28

- 6.4

+0.08

+3.0

+0.12

+ 13.8

+0.43

+ 8.2

-0.78

150

+ 0.8

+0.25

- 6.1

+0.08

+3.7

+0.11

+ 15.6

+0.14

+ 3.1

-0.88

156

+ 2.1

+0.21

- 5.4

+0. 11

+4.3

+0.11

+15. 5

-0.15

-2.3

-0.87

162

+ 3.3

+0.15

- 4.8

+0.12

+5.0

+0. 12

+13.8

-0.42

- 7.3

-0.76

168

+ 3.9

+0.06

-3.9

+0.17

+5.8

+0.10

+ 10.4

-0.66

-11.4

-0.58

174

+ 4.0

-0.04

- 2.8

+0.21

+6.2

+0.06

+ 5.9

-0.79

-14.2

-0.32

180

+ 3.4

-0.15

- 1.4

+0.23

+6.5

+0.01

+ 0.9

-0.84

-15.2

-0.03

186

+ 2.2

-0.22

0.0

+0.25

+6.3

-0.06

-4.2

-0.78

—14.6

+0. 25

192

+ 0.8

-0. 25

+ 1.6

+0.24

+5.8

-0.15

-8.5

-0.65

-12.2

+0.48

198

- 0.8

-0.27

+ 2.9

+0.20

+4.5

-0.24

-12.0

-0.49

-8.8

+0.65

204

- 2.4

-0.25

+ 4.0

+0.16

+2.9

-0.26

-14.4

-0.23

- 4.4

+0.77

210

- 3.8

-0.20

+ 4.8

+0.08

+1.4

-0.25

-14.8

+0.03

+ 0.4

+0.78

216

-4.8

-0. 12

+ 4.9

0.00

-0.1

-0.26

-14.0

+0.27

+ 5.0

+0.74

222

- 5.3

-0. 02

+ 4.8

-0.04

-1.7

-0. 24

-11.6

+0. 51

+ 9.3

+0.64

228

- 5.1

+0.09

+ 4.4

-0.08

-3.0

-0. 20

-7.9

+0.68

+12.8

+0.45

234

-4.2

+0.19

+ 3.9

-0.11

-4.1

-0. 14

- 3.4

+0.78

+14.7

+0.20

240

- 2.8

+0.25

+ 3.1

-0.16

-4.7

-0. 10

+ 1.5

+0.82

+ 15.2

-0. 06

246

— 1.2

+0.30

+ 2.0

-0.17

-5.3

-0.07

+ 6.4

+0.76

+ 14.0

-0.33

252

+ 0.8

+0.32

+ 1-1

-0.16

-5.5

-0.01

+10.6

+0. 62

+11.2

-0.57

258

+ 2.7

+0.29

+ 0.1

-0.18

-5.4

+0.06

+13.8

+0.40

+ 7.2

-0.75

264

+ 4.3

+0.24

- 1.1

-0.19

-4.8

+0.12

+15.4

+0.12

+ 2.2

-0.83

270

+ 5.6

+0. 17

- 2.2

-0.14

-3.9

+0.16

+15.3

-0.18

- 2.8

-0.82

276

+ 6.3

+0.07

-2.8

-0.08

-2.9

+0.19

+13.3

-0.42

-7.6

-0.72

282

+ 6.4

-0.06

-3.2

-0.06

-1.6

+0.22

+ 10.2

-0.64

-11.4

-0. 52

288

+ 5.6

-0.18

- 3.5

+0.01

-0.3

+0.23

+ 5.6

-0.78

—13.8

-0.25

294

+ 4.3

-0.27

- 3.1

+0.10

+1.2

+0.21

+ 0.9

-0.78

—14.4

+0.02

300

+ 2.4

-0.33

- 2.3

+0.17

+2.2

+0.14

-3.8

-0.71

-13.6

+0.27

306

+ 0.3

-0.37

- 1. 1

+0.21

+2.9

+0.11

-7.6

-0. 56

-11.2

+0.50

312

- 2.0

-0.37

+ 0.2

+0.21

+3.5

+0.03

-10.5

-0.37

-7.6

+0.62

318

- 4.1

-0.34

+ 1-4

+0.22

+3.3

-0.02

-12.0

-0.11

- 3.7

+0.67

324

- 6.1

-0.29

+ 2.8

+0.22

+3.2

-0.02

-11.8

+0.10

+ 0.4

+0.65

330

-7.6

-0.20

+ 4.1

+0. 18

+3.1

-0.01

-10.8

+0.27

+ 4.1

+0.57

336-

-8.5

-0.09

+ 5.0

+0.16

+3.1

-0. 02

- 8.6

+0.44

+ 7.2

+0.43

342

-8.7

+0.03

+ 6.0

+0.18

+2.8

-0.04

- 5.5

+0.53

+ 9.3

+0.27

348

— 8. 1

+0.14

+ 7.2

+0.20

+2.6

-0.02

- 2. 2

+0. 57

+10.4

+0.09

354

- 7.0

+0.26

+ 8.4

+0.20

+2.5

-0.06

+ 1.3

+0. 56

+10.4

-0.07

360

- 5.0

+0.35

+ 9.6

1

+0.17

+1.9

-0.12

+ 4.5

+0.52

+ 9.6

-0.20

[nSz, d log r, and u/cos i are to be computed in the form It ai sin ig+Zi 6< cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

243

PERIODIC TERMS.

Tables of (105) Artemis — Continued.
TABLE IV.— « .us i— Continued. ,

I'nit of a and 6=09001.

i

3

4

9'

"3

Diff.forl0

h

Diff.forl0

"4

Diff.forl0

».

Diff.forl0

O

0

+1.2

+0.02

+ 1.0

-0. 10

+0.2

-0. 01

+0.1

-0. 02

6

+1.1

-0.04

+0.2

-0. 11

+0.1

-0.01

0.0

-0.02

12

+0.7

-0. 08

-0.3

i

+0.1

-0.02

-0.1

+0.01

18

+0.2

ii ii'i

-0.5

+0.02

-0. 1

-0.01

+0.1

+0.02

24

-0.4

-0.06

-0.1

+0.07

0.0

+0.02

+0.1

+0.01

30

-0.5

+0.01

+0.3

+0.07

+0.1

+0.02

+0.2

+0.01

36

-0.3

+0.08

+0.7

+0.08

+0.3

+0.02

+0.2

-0.01

42

+0.4

+0.12

+ 1.2

+0.04

+0.3

+0.02

+0.1

-0.02

48

+1.1

+0.12

+ 1.2 •

-0.04

+0.5

+0.01

-0.1

-0.03

54

+ 1.8

+0.09

+0.7

-0.12

+0.4

-0.02

-0.3

-0.03

60

+2.2

+0.02

-0.2

-0.15

+0.2

-0.04

-0.5

-0.02

66

+ 2.0

-0.06

— 1. 1

-0. 15

-0.1

-0.04

-0.6

0.00

72

+1.5

-0.13

-2.0

-0.12

-0.3

-0. 03

-0.5

+0.02

78

+0.4

-0.18

-2.6

-0. 05

-0.5

-0. 02

-0.3

+0.03

84

-0.6

-0. 18

-2.6

+0.04

-0.6

0.00

-0.1

+0.04

90

-1.7

-0. 13

-2.1

+0.12

-0.5

+0.02

+0.2

+0.04

96

-2.2

-0.08

—1.2

+0.17

-0.3

+0.03

+0.4

+0.02

102

-2.7

-0.02

-0.1

+0.17

-0.1

+0.03

+0.5

-0.01

108

-2.4

+0.08

+0.8

+0.14

+0.1

+0. 02

+0.3

-0. 02

114

-1.8

+0. 12

+ 1.6

+0.11

+0.2

+0.01

+0.3

-0.02

120

-0.9

+0. 14

+2.1

+0.04

+0.2

-0.01

+0.1

-0.02

126

-0.1

+0. 12

+2.1

-0.02

+0.1

-0.01

0.0

-0.02

132

+0.6

+0.10

+1.9

-0.07

+0.1

-0. 02

-0.1

+0.01

138

+1.1

+0.07

+ 1.3

-0.08

-0.1

-0.01

+0.1

+0.02

144

+ 1.4

+0.03

+ 1.0

-0.08

0.0

+0. 02

+0.1

+0.01

150

. +1. 5

+0.01

+0.4

-0.10

+0.1

+0.02

+0.2

+0.(11

156

+1.5

-0.01

-0.2

-0.08

+0.3

+0.02

+0.2

-0.01

162

+1.4

-0.02

-0.5

-0. 06

+0.3

+0.02

+0.1

-0.02

168

+ 1.3

-0. 05

-0.9

-0.08

+0.5

+0.01

-0. 1

-0.03

174

+0.8

-0.08

-1.4

-0.06

+0.4

-0. 02

-0.3

-0.03

180

+0.4

-0.09

-1.6

-0.02

+0.2

0 III

-0.5

-0.02

186

-0.3

-0.11

-1.6

+ 0.01

-0.1

-0.04

-0.6

0.00

192

-0.9

-0.09

-1.5

+0.04

-0.3

-0.02

-0.5

+0.02

198

—1.4

-0.08

-1.1

+0.08

-0.5

-0.02

-0.3

+0.03

204

—1.8

-0.04

-0.5

+0.10

-0.6

0.00

-0.1

+0.04

210

-1.9

+0.01

+0.1

+0. 12

-0.5

+0. 02

+0.2

+0.04

216

-1.7

+0.06

+0.9

+0.11

-0.3

+0. 03

+0.4

+0.02

222

-1.2

+0.09

+1.4

+0.07

-0.1

+0.03

+0.5

-0.01

228

-0.6

+0. 10

+1.7

+0.02

+0.1

+0.02

+0.3

-0.02

234

0.0

+0. 10

+1.7

-0.01

+0.2

+0.01

+0.3

-0.02

240

+0.6

+0.08

+ 1.6

-0.03

+0.2

-0.01

+0.1

-0.02

246

+ 1.0

+0.06

+1.3

-0.07

+0.1

-0.01

0.0

-0.02

252

+1.3

+0.02

+0.8

-0.08

+0.1

-0.02

-0.1

+0.01

258

+1.3

+0.01

+0.4

-0.05

-0.1

-0.01

+0.1

+0.02

264

+ 1.4

0.00

+0.2

-0.04

0.0

+0.02

+0.1

+0.01

270

+ 1.3

0.00

-0.1

-0.07

+0.1

+0.02

+0.2

+0.01

276

+ 1.4

0.00

-0.6

-0.07

+0.3

+0.02

+0.2

-b. oi

282

+ 1.3

-0.02

-0.9

-0. 05

+0.3

+0.02

+0.1

-0.02

288

+1.2

-0.04

—1.2

-0. 08

+0.5

+0.01

-0.1

^0.03

294

+0.8

-0.09

—1.8

-0. 08

+0.4

-0.02

-0.3

-0.03

300

+0.1

-0.12

-2. 1

-0.02

+0.2

-0.04

-0.5

-0.02

306

-0.7

-0. 12

-2.1

+0.03

-0.1

-0.04

-0.6

0.00

312

-1.4

-0. 12

—1.7

+0.08

-0.3

-0.03

-0.5

+0. 02

318

-2. 1

-0.08

— 1. 1

+0.12

-0.5

-0. 02

-0.3

+0.03

324

-2.4

-0.02

-0.2

+0. 14

-0.6

0.00

-0.1

+0.04

330

-2.3

+0.06

+0.6

+0. 15

-0.5

'

+0.2

+0.04

336

-1.7

+0. 11

+1.6

+0. 12

-0.3

+0. 03

+0.4

+0.02

342

-1.0

+0. 15

+2.1

+0. 02

-0.1

+0. 03

+0.5

-0.01

348

+0.1

+0.15

+1.9

-0.06

+0.1

+0.02

+0.3

-0.02

35 1

+0.8

+0.09

+1.4

-0.08

+0.2

+0.OL

+0.3

-0. 02

360

+ 1.2

+0.02

+ 1.0

-0. 10

+0.2

-0.01

+0.1

-0.02

[no2, 1 log r, and a/cos i are to be computed in the form It a,- sin ig+St t>i cos ig-i-cT.)

244

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (10,5) Artemis — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T = (t — 1„| IN JULIAN YEARS.

nSz

o logr

u/cos i

9

Unit of

:=0?001

Unit of c

=0.00001

Unit of

-=0?001

c

Diff. for 1°

c

Diff. for 1°

c

Diff. for 1°

O

0

-2. 18

+0. 038

-0.86

-0.017

+ 1.56

-0. 063

6

-1.95

+0. 042

-0.96

-0. 015

+ 1. 16

-0. 067

12

-1.68

+0. 046

-1.04

-0.012

+0.76

-0. 070

18

-1.40

+0. 048

— 1. 11

-0.010

+0.32

-0. 073

24

-1.10

+0. 051

-1. 16

-0. oos

-0. 12

-0. 072

30

-0.79

+0. 052

-1.20

-0. 004

-0.54

-0. 070

36

-0.47

+0. 054

—1.21

-0. 002

-0.96

-0. 070

42

-0. 14

+0. 052

-1.22

0.000

-1.38

-0. 068

48

+0. 16

+0. 052

-1.21

+0. 003

-1.78

-0. 062

54

+0.48

+0. 052

-1.18

+0. 006

-2.13

-0. 057

60

+0.79

+0. 049

— 1. 14

+0. 008

-2.46

-0. 054

66

+ 1.07

+0. 048

-1.08

+0.010

-2.78

-0. 048

72

+ 1.36

+0.014

-1.02

+0.010

-3.04

-0. 040

78

+ 1.60

+0. 040

-0.96

+0.013

-3.26

-0. 035

84

+ 1.84

+0. 037

-0. 86

+0.016

-3.46

-0. 030

90

+ 2. 04

+0. 032

-0.77

+0. 014

-3.62

-0. 022

96

+2. 23

+0. 030

-0.69

+0. 015

-3. 72

-0. 015

102

+2. 40

+0. 026

-0. 59

+0. 017

-3.80

-0.011

108

+ 2.54

+0. 020

-0.49

+0. 018

-3.85

-0. 006

114

+ 2. 64

+0.015

-0.38

+0.017

-3.87

-0. 001

120

+2.72

+0. 012

-0.29

+0. 018

-3.86

+0. 006

126

+2.78

+0. 006

-0.17

+0.018

-3.80

+0.011

132

+ 2. 79

+0. 001

-0.08

+0.016

-3. 73

+0.014

138

+2.79

-0. 004

+0.02

+0. 017

-3.63

+0.019

144

+2.74

-0. 008

+0.12

+0. 016

-3.50

+0. 024

150

+ 2.70

-0.011

+0.21

+0. 017

-3.34

+0. 028

156

+ 2.61

-0.017

+0.32

+0.016

-3. 16

+0. 032

162

+2. 50

-0.021

+0.40

+0. 014

-2. 96

+0. 035

168

+2.36

-0. 025

+0.49

+0. 013

-2.74

+0. 039

174

+ 2. 20

-0. 028

+0. 56

+0.012

-2.49

+0. 042

180

+ 2.02

-0. 032

+0. 64

+0. 012

-2.23

+0. 044

186

+ 1.82

-0. 035

+0.71

+0.011

-1.96

+0. 046

192

+ 1.60

-0. 038

+0.77

+0. 009

-1.68

+0. 050

198

+ 1.36

-0. 040

+0.82

+0. 008

-1.36

+0. 052

204

+ 1.12

-0. 042

+0.87

+0. 008

-1.06

+0. 052

210

+0.85

—0. 046

+0.91

+0. 006

-0.74

+0. 053

216

+0. 57

-0. 046

+0. 94

+0. 004

-0.42

+0 053

222

+0.30

-0. 046

+0.96

+0. 003

-0. 10

+0. 053

228

+0.02

-0. 047

+0.98

+0. 002

+0. 22

+0. 053

234

-0.26

-0. 048

+0.99

-0.001

+0. 54

+0. 053

240

-0.55

—0. 048

+0.97

-0. 002

+0.86

+0. 052

246

-0.83

-0. 048

+0.96

-0. 002

+ 1. 16

+0. 050

252

-1.12

-0. 046

+0.94

-0. 004

+ 1.46

+0. 048

258

-1.38

-0. 043

+0.91

-0. 008

+ 1.74

+0. 047

264

-1.64

-0. 042

+0.85

-0. 010

+ 2.02

+0. 045

270

-1.88

-0. 039

+0.79

-0.009

+2. 28

+0. 042

276

-2.11

-0. 037

+0.74

-0. 012

+2. 52

+0. 037

282

-2. 32

-0. 032

+0. 65

-0.015

+ 2.72

+0. 031

288

-2. 50

-0. 028

+0.56

-0. 016

+ 2. 89

+0. 027

294

-2.66

-0. 023

+0.46

-0.017

+3.04

+0. 021

300

-2.78

-0. 018

+0.36

-0. 019

+3. 14

+0.013

306

-2.88

-0.014

+0. 23

-0. 020

+3.20

+0. 006

312

-2.95

-0. 008

+0. 12

-0.019

+3.21

-0. 002

318

-2.97

-0.001

0.00

-0. 022

+3.18

-0. 009

324

-2.96

+0. 002

-0. 14

-0. 022

+3.10

-0. 020

330

-2.94

+0. 009

-0. 27

-0. 022

+ 2.94

-0. 028

336

-2. 85

+0.017

-0.41

-0. 022

+ 2.76

-0. 035

342

-2.74

+0. 022

-0. 54

-0. 020

+2.52

-0. 043

348

-2.58

+0. 028

-0. 65

-0. 018

+2. 24

-0. 050

354

-2.41

+0. 033

-0.76

-0. 018

+ 1.92

-0. 057

360

-2.18

+0. 038

-0.86

-0.017

+ 1.56

-0.063

[ndz, d log r, and u/cos ; are to be computed in the form li at sin ig+Si bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSC'IIXER.

245

Tables of (106) Artemis — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B'

c

log sin a

log sin b

log sin c

1868. 0

O

331.9602

O

241. 8561

o

294. 7577

9. 99948

9. 99970

8. 78814

9

. 9732

S6S9

.8123

48

70

. 78868

1870

331.9862

241.8817

294. 8667

9. 99948

9. 99970

8. 78922

1

331. 9992

.8945

. 9209

47

70

. 78976

2

332.0122

.907;;

294. 9750

47

70

. 79030

3

. 0252

.9201

295.0291

47

70

. 79084

4

.0382

.9328

.0831

47

70

. 79138

1875

332. 0513

241. 9456

295. 1371

9. 99947

9. 99970

8. 79192

6

. 0643

.9584

. 1910

46

70

. 79246

7

.0773

. 9712

.2448

46

70-

. 79300

8

. 0903

.9840

. 2985

46

70

. 79354

9

. 1033

241. 9968

.3519

46

70

. 79409

1880

332. 1163

242. 0096

295. 4053

9. 99946

9. 99970

8. 79463

1

. 1293

.0224

. 4585

45

70

. 79517

2

. 1424

. 0352

.5116

45

70

.79571

3

.1554

.0480

. 564S

45

70

. 79625

4

.1684

.0608

. 6177

45

70

. 79679

1885

332. 1814

241. 0736

295. 6706

9. 99945

9. 99970

8. 79733

6

. 1944

.0863

. 7234

44

70

. 79787

7

. 2074

. 0991

. 7759

44

70

. 79841

8

.2204

.1119

. 828 1

44

70

. 79895

9

. 2334

.1247

8807

44

70

. 79J49

1890

332. 2465

242. 1375

295. 9329

9. 99944

9. 99970

8. 80003

1

.2595

. 1503

295. 9851

44

70

. 80057

2

. 2725

.1031

296. 0372

43

70

.80111

3

2855

. 1759

OS9I

43

70

. 80166

4

.2985

.1887

. 1409

43

70

. 80220

1895

332.3115

242. 2014

296. 1926

9. 99943

9. 99970

8. 80274

6

. 3245

.2142

.2441

43

70

. 80328

7

.3376

.2270

. 2955

42

70

. 80382

8

. 3506

.2398

.3468

42

70

. 80436

9

.3636

.2526

.3979

42

70

. 80490

1900

332. 3766

242. 2654

296. 4489

9. 99942

9. 99970

8. 80544

1

. 3896

.2782

.4999

42

70

. 80597

2

.4026

.2910

. 5507

41

70

. 80650

3

. 4157

.3038

.6014

41

70

. 80703

4

.4287

. 3165

.6520

41

70

. 80755

190.-,

332.4417

242. 3293

296. 7026

9. 99941

9. 99969

8. 80808

6

. 4547

. 3421

.7530

41

69

. 80861

7

.4677

. 3549

.8034

40

69

. 80914

8

.4807

.3677

. 8536

40

69

. 80967

9

.4938

.3805

.9037

40

69

.81019

1910

332. 5068

242. 3933

296. 9537

9. 99940

9. 99969

8. 81072

1

. 5198

.4061

297. 0036

40

69

.81125

2

. 5328

.4188

. 0533

39

69

.81178

3

. 5458

.4316

. 1030

39

69

.81231

4

55S8

. 4444

. 1526

39

69

. 81284

1915

332. 5719

242. 4572

297. 2022

9. 99939

9. 99969

8. 81336

6

.5849

.4700

.2516

39

69

.813S9

7

. 5979

.4828

.3009

38

69

. 81442

8

. 6109

. 4956

.3502

38

69

. 81495

9

.6239

. 5084

.3992

38

69

. 81548

1920

332. «369

242.5211

297. 4482

9. 9938

9. 99969

S. S1601

1

. 6500

. 5339

.4971

38

69

. 81653

2

.6630

. 5467

. 5457

37

69

. 81706

3

. 6760

. 5595

.5945

37

69

. 81759

4

. 6890

. .-,723

.6431

37

69

.81812

1925

332. 7020

242. 5851

297. 6916

9. 99937

9. 99969

8. 81865

6

. 7150

.5979

.7400

37

69

.81917

7

. 72S1

.6107

. 7ss_>

36

69

. 81970

8

.7411

. 6234

. 8362

36

69

.82023

9

. 754 1

.6362

.8842

36

69

. 82076

1930

332. 7671

j 242. 6490

297. 9319

9. 99936

9. 99969

8. 82129

Year

log

:os a

log

cos b

log

cos c

U

S68. 0

8.

G90

8.5

70 n

9.

999

1<

130.0

8.

736

8.5

70 n

9.

999

246 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF (115) THYRA.

MEAN ELEMENTS.

Epoch, 1890,

Jan., 0.0372. M. T. Berlin = 1890.000, M. T. Berlin.

O

0o=299

/ //

32 18=299?5382

oi= 94

15 37= 94.26041

£=309

12 2=309. 2006 [Mean equinox and ecliptic 1900.0

i= 11

35 8= 11. 5856 J

<p= 11

6 59= 11.1164

n=966"

3084 = 0. 26841901

The elements are based on

oppositions extending from 1871 to 1904 and on the perturbations of the

first order by Jupiter, as given

on page 247.

AUXILIARY QUANTITIES.

loga=0.37659 log 57.2958e=1.04324 log../1—e=9 91521
log e=9. 28511 log p =0.36014 v 1+e

TABLE I.— MEAN ANOMALY (g).

Jan., 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Month

9

Year

9

Year

9

Jan{o:o

O

| 0. 00000

O

O

1871

236. 70020

1901

297. 76735

B 2

334.94160

2

35. 74029

™{l°o

} 8. 32099

3

72. 91454

3

133.71323

4

170. 88748

B 4

231. 95458

Mar. 0.0

15. 83672

5

268. 86042

5

329. 92752

Apr. 0.0

24. 15771

B 6

367. 10178

6

67. 90046

May 0.0

32. 21028

7

105. 07472

7

L65. 87340

June 0.0

40. 53127

8

203. 04766

B 8

264. 11476

July 0.0

48. 58384

9

301. 02060

9

362. 08770

Aug. 0.0

56. 90483

B 1880

39. 26195

1910

100. 06064

Sept. 0.0

65. 22582

1

137. 23489

1

198. 03358

Oct. 0.0

73. 27839

2

235. 20783

B 2

296. 27493

Nov. 0.0

81. 59938

3

333. 18077

3

34. 24787

Dec. 0.0

89. 65195

B 4
5
6

71. 42213
169. 39507
267. 36801

4

5

B 6

132. 22081
230. 19375
328.43511

Change for n daysa

7

5. 34094

7

66. 40805

B 8

103. 58230

8

Kit. 38099

9

201. 55524

9

262. 35393

n

9

n

9

1890

1

299. 52818
37.50112

B 1920
1

0. 59528
98. 56822

B 2

135. 74248

2

196.54116

3

233. 71542

3

294.51410

1

0. 26842

16

4.29472

4

331. 68836

B 4

32. 75546

2

0. 53684

17

4.56314

5

69. 66130

5

130. 72840

3

0. 80526

18

4. 83156

B 6

167. 90265

6

228. 70134

4

1. 07368

19

5. 09998

7

265. 87559

7

326. 67428

5

1. 34210

20

5. 36840

8

3. 84853

B 8

64. 91563

6

1. 61052

21

5. 63682

9

101. 82147

9

162. 88857

7

1. 87894

22

5. 90524

1900

199. 79441

1930

260. 86151

8

2. 14736

• 23

6. 17366

9

2. 41578 24

6. 44208

10

2. 68420 i 25

6. 71050

11

2. 95262 26

6. 97892

Note. — W
add to the

len g is used as ai
g of this table i

argument of the perturbations,
te=.T-n0=+0?1367. For ex-

12
13

14

3. 22104
3. 48946
3. 75788

27
28
29

7. 24734
7. 51576
7. 78418

planation se<

i page 203.

15

4. 02630

30

8. 05260

° For days during January and

February of leap years subtract one

day before entering this table.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHXEK.

247

Tables of (115) Thyra— Continued.

PERTURBATIONS.

in

2

i-

u/cos (

Arg.

ig—iY

sin

COS

sin

cos

sin

cos

i V

//

//

//

//

//

//

0 0
0 0

- 3

+ 0. 03nt

+3
+0. 15nt

+1 o

+1
+ 2
+2
+3 0

0. 83nt
0.04nt

4. 84nt

- 0. 23nt

- 0. 02nt

- 2. 42nt

- 0. 23nt
0. 03nt

+ 3

+ 0.42nt

+ 1

+ 0.04nt

- 5.36nt

- 0. 51nt

- 0. 07nt

-0. 52nt

—0. 05nt
-O.Olnt

-1 +1

0
+ 1
+2 +1

+ 4

- 2

- 87

- 4

+ 1

- 9

- 55

3

1

- 21
_ 2

+ 2
+ 2

+32
+ 4

+ 2
+ 5
- 6

_ 2

-2
—7

+8
+3

-1 +2

0
+ 1
+2
+3
+4 +2

9

+ 115
+ 64

+ 5

+ 1

- 1
- 14
^236
+ 121
8
+ 1

+ 1

6

f 65

4- 75
• 9

+ 1

- 4
-33
-40
- 5

- 9
+ 10
+ 5

- 1

+4
-6
-1

0 +3
+1
+2
+3
+4 +3

- 5

+488

+110

5

+ 1

4- 5
+ 84
-217

+ 2

+ 1

_ 9

- 7

—112

1

- 2
-29
-58

- 5

- 1

+ 3
+ 8
-37

- 3

- 1

+4
-1
-1

+1 +4

+2

+3

+4 +4

2

+ 7
- 1

- 3

f 7
4

+ 1

+ 2
■ 2

+ 1

— 1

— 8
- 5

- 1

— 1

-2
—1

+2 +5

+3

+4 + 5

- 2

+ 2

- 1

- 2

— 1

+ 1
- 1

+1

+ 2 +6
+3 +6

1

- 1

- 1

248

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {115) Tliyra— Continued.

TABLE II.— n3z.

PERIODIC TERMS.

Unit of a and 6=09001.

i

0

1

2

9'

K

Diff. for 1°

a,

Diff. fori0

6,

Diff. for 1°

a..

Diff. for 1°

b.

Diff. fori0

0

0

-5.0

+0. IS

+141. 8

+3.15

+ 72.8

-7.77

+ 51. 9

-1.89

-26.2

-2.48

6

-3.9

+0. 18

+153. 5

+0.73

+ 24.5

-8.22

+ 38.3

-2.50

-39.1

-1.68

12

-2.9

+0. 17

+150. 6

-1.68

- 24.3

-7.90

+ 21.9

-2.80

-46.4

-0.72

18

—1.9

+0. 16

+ 133.4

-3.86

- 68.9

-6.78

+ 4.7

-2.78

-47.7

+0.27

24

—1.0

+0. 13

+ 104.3

-5.60

-105. 7

—5. 20

- 11.5

-2.44

-43.2

+ 1. 15

30

-0.3

+0. 12

+ 66.2

-6.75

-131.3

-3.18

- 24.6

-1.81

-33.9

+1.86

36

+0.4

+0.10

+ 23.3

-7.38

-143.9

—1.01

- 33.2

-1.01

-20.9

+2.34

42

+0.9

+0.07

- 20.8

-7.20

-143. 4

+ 1.21

- 36.7

-0.11

-5.8

+2.51

48

+ 1.2

+0.07

- 61.6

-6.23

-129. 4

+3.25

- 34. 5

+0.82

+ 9.2

+2.32

54

+1.7

+0.06

- 95.6

-4.84

-104. 4

+4.86

- 27.0

+ 1.59

+22.0

+1.84

60

+1.9

+0.03

-119.7

-3.05

- 71.1

+5.92

- 15.4

+2. 18

+31.3

+1.15

66

+2.1

+0.04

-132. 2

-1.08

- 33.3

+6.41

- 1.0

+2.48

+35.8

+0.28

72

+2.4

+0. 04

-132.6

+0. 98

+ 5.8

+6.26

+ 14.2

+2.44

+34.7

-0.66

78

+2.6

+0.03

-121.3

+2.71

+ 41.9

+5. 51

+ 28.3

+2.11

+27.8

-1.58

84

+2.8

+0.04

-100. 1

+4.15

+ 71.9

+4.22

+ 39.5

+ 1.49

+15.9

-2.29

90

+3.1

+0.04

- 71.5

+5.11

+ 92.6

+2. 59

+ 46.2

+0.62

+ 0.3

-2.76

96

+3.3

+0.02

- 38.8

+5.46

+103.0

+0.83

+ 46.8

-0.43

-17.2

-2.92

102

+3.3

-0.01

- 6.0

+5.19

+102.6

-0.96

+ 41.0

-1.48

-34.7

-2.73

108

+3.2

-0.01

+ 23.5

+4.39

+ 91.5

-2.54

+ 29.0

-2.39

-50.0

-2. 16

114

+3.2

-0.02

+ 46.7

. +3. 15

+ 72.1

-3.72

+ 12.3

-3.08

-60.6

-1.29

120

+3.0

-0. 05

+ 61.3

+1.60

+ 46.8

-4.42

- 8.0

-3.48

-65.5

-0.24

126

+2.6

-0.08

+ 65.9

-0.80

+ 19.1

-4.54

- 29.4

-3.50

-63. 5

+0.92

132

+2.0

-0.10

+ 60.3

-1.70

-7.7

-4.08

- 50.0

-3.14

-54.5

+2.06

138

+ 1.4

-0.12

+ 45.5

-3.06

- 29.9

-3.12

- 67.1

-2.42

-38.8

+3.04

144

+0.6

-0. 13

+ 23.6

-4.01

- 45.2

-1.76

- 79.1

-1.42

-18.0

+3.73

150

-0.2

-0.12

-2.6

-4.44

- 51.0

-0.08

- 84.1

-0.21

+ 6.0

+4.07

156

-0.9

-0.12

— 29.7

-4.28

— 46.1

+1.63

- 81.6

+1.02

+30.9

+4.06

162

-1.7

-0.11

- 53.9

-3.52

- 31.4

+3.22

- 71.8

+2.22

+54.7

+3.65

168

-2.2

-0.08

- 71.9

—2. 25

- 7.5

+4.49

- 55.0

+3. 25

+74.7

+2.88

174

-2.6

-0.05

- 80.9

-0.59

+ 22.5

+5.29

- 32.8

+3.99

+89.2

+ 1.82

180

-2.8

0.00

- 79.0

+1.30

+ 56.0

+5.52

- 7.1

+4.41

+96.6

+0.61

186

-2.6

+0.06

- 65.3

+3.18

+ 88.7

+5.09

+ 20.1

+4.47

+96.5

-0. 65

192

-2.1

+0. 10

- 40.8

+4.92

+117. 1

+4.06

+ 46.5

+4.12

+88.8

-1.90

198

—1.4

+0. 14

- 6.2

+6.29

+137.4

+2.47

+ 69.5

+3.43

+73.7

-3.03

204

-0.4

+0.18

+ 34.7

+7.09

+146. 7

+0.46

+ 87.7

+2.48

+52. 4

-3.88

210

+0.7

+0.20

+ 78.9

+7.37

+ 142.9

-1.78'

+ 99.2

+ 1.29

+27.1

-4.41

216

+2.0

+0.22

+121.7

+7.80

+ 125. 3

-3.97

+103. 2

+0.01

- 0.5

-4.59

222

+3.3

+0.20

+ 159.2

+5.46

+ 95.3

-5. 98

+ 99.3

-1.26

-28.0

-4.41

22S

+4.4

+0.18

+ 187.2

+3.63

+ 53.6

-7.59

+ 88.1

-2.41

-53.4

-3.88

•1M

+5.5

+0. 16

+202. 8

+1.38

+ 4.2

-8.69

+ 70.4

-3.36

-74.6

-3.06

240

+6.3

+0.10

+203. 8

-1.15

- 49.4

-9.02

+ 47.8

-4.03

-90.1

-2.00

246

+6.7

+0.04

+ 189.0

-3.68

-102. 5

-8.54

+ 22.0

-4.38

-98.5

-0.82

252

+6.8

-0.02

+159. 6

—6.01

-150.4

—7. 22

-4.8

-4.39

-99.9

+0.40

258

+6.4

-o.os

+ 116.9

-7.92

-189. 1

—5! 35

- 30.7

-4.08

-93.8

+ 1.57

264

+5.8

-0. 15

+ 64.5

-9.34

-214.7

-2.96

- 53.7

-3.46

—81.1

+2.56

270

+4.6

-0.22

+ 6.3

-9.88

-224. 6

-0.29

— 72. 2

-2.59

-63.1

+3.34

276

+3.2

-0.24

- 52.6

-9.64

-218.2

+2.49

- 84^8

-1.57

-41.0

+3.88

282

+1.7

-0.27

-107.8

-8.64

-195.9

+4.94

- 91.0

-0.48

-16.5

+4.12

288

0.0

-0.29

-154.7

-6.76

I.-.S !l

+7.22

- 90.4

0 66

+ 8.4

+4.02

294

—1.8

-0.28

-188.9

-4.45

-110.7

+8.80

- 83.0

+1.76

+31.8

+3.62

300

-3.4

-0.27

-208. 1

-1.83

- 54.8

+9. 66

- 69.4

+2.67

+51.9

+2.96

306

-5.0

-0.23

-210. 9

+0.91

+ 3.5

+9. 66

- 51.0

+3.33

+67.3

+2.07

312

-6.2

-0. 18

-197.2

+3. 55

+ 59.5

+8.89

- 29.4

+3.71

+76.7

+1.01

318

-7.1

-0. 13

-168. 3

+5.84

+108. 7

+7.28

- 6.5

+3. 77

+79.4

-0.11

324

-7.8

-0.08

-127. 1

+7.70

+146. 8

+5.21

+ 15.9

+3.52

+75.4

-1.18

330

-8.0

-0.01

- 77.4

+8.77

+ 171.2

+2.76

+ 35.7

+2. 94

+65. 2

-2.12

336

-7.9

+0.04

- 23.5

+9.00

+ 179.9

+0. 14

+ 51.2

+2.09

+49. 9

-2.86

342

-7.5

+0. 09

+ 29.2

+8.39

+ 173.0

-2.43

+ 60.8

+ 1.08

+30. 9

-3.28

348

-6.8

+0. 12

+ 77. 1

+7.21

+150. 7

-4.72

+ 64. 2

+0.02

+ 10.5

-3.34

354

-6.0

+0. 15

+ 115.7

+5.39

+116.3

-6.49

+ 61.0

-1.02

-9.2

-3.06

360

-5.0

+0. 18

+141.8

+3.15

+ 72.8

-7.77

+ 51.9

-1.89

-26.2

-2.48

[ndz, 3 log r, and m/cos I are to bo computed in the torm It oj sin ig+ It 6< cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

249

PERIODIC TERMS.

Tables of (115) Thyra — Continued.
TABLE II.— nSz— Continued.

Unit of a and 6=09001.

i

3

4

.<?'

«3

Diff. for 1°

63

Diff. for 1°

at

Diff. for 1°

*4

Diff. for 1°

O

0

+3.9

-0.05

+0.7

-0. 18

+0.9

+0.05

+0.9

-0.05

(i

+3.5

-0.08

-0.2

-((. 12

+ 1.1

+0. 02

+0.5

-0.07

12

+3.0

-0.09

-0.8

-0.08

+ 1.1

-0.01

0 1

-0.06

18

+2.4

-0.08

-1. 1

-0.05

+ 1.0

-0.02

-0.2

-0.04

24

+2.1

-0.06

-1.4

-0.04

+0.8

-0.03

-0.4

-0.03

30

+1.7

-0.07

-1.6

-0.02

+0.6

-0.03

-0.6

-0.02

36

+ 1.3

-0.07

-1.6

-0.02

+0.4

-0.03

-0.7

0.00

42

+0.9

-0.06

-1.9

-0.03

+0.2

-0.02

-0.6

+0.02

48

■ ii 6

-0.07

-2.0

0.00

+0.1

-0.01

-0.5

0.00

54

+0.1

II IIS

-1.9

+0.02

+0.1

-0.01

-0.6

-0.01

(iO

-0.3

-0.05

-1.7

+0.04

0.0

-0. 02

-0.6

0.00

66

-0.5

-0.02

-1.4

+0.05

-0. 2

-0.02

-0.6

-0.01

72

-0.6

0.00

—1.1

+0.04

-0.3

-0.02

-0.7

0.00

78

-0.5

+0.02

-0.9

+0.02

-0.4

-0. 03

-0.6

+0.02

84

-0.3

+0.02

-0.8

-0.02

-0.7

-0.04

-0.5

+0.02

90

-0.3

0.00

-1. 1

-0.05

-0.9

-0. 02

-0.3

+0.05

96

-0.3

-0.03

-1.4

-0.05

-0.9

-0.01

+0.1

+0.06

102

-0.7

-0.08

-1.7

-0.03

-1.0

+0.02

+0.4

+0. 05

KIS

-1.3

-0. 12

-1.8

+0.01

-0.7

+0. 05

+0.7

+0.05

114

-2. 1

-0. 12

-1.6

+0.07

-0.4

+0.06

+ 1.0

+0.02

120

-2.7

-0.08

-1.0

+0.12

0.0

+0.07

+ 1.0

-0.01

126

-3.1

-0.04

-0.2

+0. 15

+0.4

+0. 06

+0.9

-0. 02

132

-3.2

+0.02

+0.8

+0.18

+0.7

+0. 03

+0.7

-0.06

138

-2.9

+0. 09

+ 1.9

+0. 16

+0.8

+0. 02

+0.2

-0.08

111

-2.1

+0.15

+ 2. 7

+0.12

+0.9

-0.02

-0.2

-0.07

150

— 1. 1

+0.17

+3.3

+0. 06

+0.6

-0. 06

-0.6

-0.05

156

-0.1

+0.17

+3.4

-0.02

+0.2

-0.07

-0.8

-0.02

162

+0.9

+0.16

+3.0

-0.08

-0.2

-0.08

-0.8

+0.02

168

+ 1.8

+0.10

+2.4

-0.12

-0.7

-0. 06

-0.5

+0.04

174

+2.1

+0.04

+1.6

-0. 14

-0.9

-0.02

-0.3

+0.07

180

+2.3

0.00

+0.7

-0.13

-0.9

+0.02

+0.3

+0.08

186

2 1

-0.06

0.0

-0.09

-0.7

+0. 05

+0.7

+0.05

L92

+ 1.6

-0.09

-0.4

-0.06

-0.3

+0.08

+0.9

+0.04

198

+1.0

-0. 09

-0.7

-0.02

+0.2

+0.08

+1.2

+0.01

204

ii :,

-0.08

-0.6

+0.02

+0.6

+0.07

+ 1.0

-0.05

210

ii 1

-0. 05

-0. 4

+0.07

+ 1.0

+0. 05

+0.6

-0.08

216

-0.1

0.00

+0.2

+0.09

+ 1.2

0.00

+0.1

-0.09

222

+0.1

+0.06

+0.7

+0.07

+ 1.0

-0.02

-0.4

-0.08

228

+0.6

+0.10

+1.0

+0. 05

+0.9

-0.04

-0.7

-0. 06

234

+1.3

+0.12

+1.3

+0.01

+0.5

-0.08

-1.0

-0.02

240

+2.1

+0.13

+ 1.1

-0.08

0.0

-0.08

-1.0

+0.02

246

+2.9

+0.12

+0.4

-0.15

-0.4

-0.06

-0.8

+0.04

252

| 3 6

+0.07

-0.7

-0.21

-0.7

-0.02

-0.5

+0.05

258

+3.7

-0. 02

-2. 1

-0.24

-0.6

+0.02

-0.2

+0.05

264

+3.3

-0. 13

-3.6

-0. 25

-0.5

+0. 02

+0.1

+0.04

270

+2.1

-0.25

-5.1

-0.20

-0.3

+0. 05

+0.3

+0.02

276

+0.3

-0.33

-6.0

-0. 10

+0.1

+0.04

+0.3

-0.01

2S2

-1.9

-0.37

-6.3

. +0.03

+0.2^

+0.02

+0.2

-0. 03

288

-4.1

-0. 35

-5.6

+0.19

+0.3

0.00

-0.1

-0. 05

294

-6.1

-0.25

-4.0

+0.32

+0.2

-0. 02

-0.4

-0.04

300

-7.1

-0.10

-1.8

11 111

0.0

-0. 05

-0.6

-0.02

306

-7.3

+0.04

+0.8

+0.42

-0.4

-0.06

-0.7

+0.01

312

-6.6

+0.18

+3.2

+0. 36

-0.7

-0. 05

-0.5

+0. 04

318

-5. 1

+0.32

+5.1

+0. 26

-1.0

-0.03

-0.2

+0.06

324

-2.8

+0.37

+6.3

+0.12

-1.1

0.00

+0.2

+0.07

330

-0.7

+0.34

+6.5

-0.02

-1.0

+0.02

+0.6

+0.07

336

+1.3

+0.30

+6.0

-0. 14

-0.8

+0. 05

+1.0

+0.05

3 12

+2.9

+0.21

+4.8

-0.22

-0.4

+0.08

+1.2

+0.02

348

+3.8

+0.10

+3.4

-0.23

+0.1

+0.08

+1.3

-0.01

354

+4.1

+0.01

+2.0

-0.22

+0.5

+0.07

+ 1.1

-0.03

360

+3.9

-0.05

+0.7

-0.18

+0.9

+0. 05

+0.9

-0.05

[n3z, 3 log r, and ujcos i are to be computed in theform l'i <n sin ig+Ii bi cos ig+cT.]

250

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

PERIODIC TERMS.

Tables of (115) Thyra — Continued.

TABLE III.— S log r.

Unit of a and 6=0.00001.

i

0

1

2

9'

6o

Diff. for 1°

a,

Diff. for 1°

6,

Diff. for 1°

<h

Diff. for 1°

h

Diff. for 1°

O

0

-1.4

-0.02

+ 7.7

-0.46

-5.7

-0.32

-7.7

-1.02

-21.2

+0.64

6

-1.5

-0.01

+ 4.7

-0.50

- 7.1

-0. 16

-13.1

-0.72

-16.5

+0.90

12

-1.5

0.00

+ 1.7

-0. 49

-7.7

-0.04

-16.4

-0.38

-10.4

+ 1.05

18

-1.5

+0.01

- 1.2

-0.47

-7.6

+0.10

-17.6

0.00

-3.9

+ 1.04

24

—1.4

+0. 02

- 3.9

-0. 42

-6.4

+0.23

-16.4

+0.37

+ 2.1

+0.93

30

-1.3

+0. 02

- 6.2

-0. 32

- 4.8

+0.30

-13.2

+0.64

+ 7.3

+0.73

36

-1.1

+0.02

-7.7

-0.21

-2.8

+0.36

- 8.6

+0.83

+10.9

+0.42

42

-1.1

+0.02

-8.7

-0.10

- 0.5

+0.38

-3.2

+0.89

+12.4

+0.07

48

-0.8

+0.03

- 8.8

+0.02

+ 1.8

+0.37

+ 2.1

4-0. 82

+11.7

-0.28

54

-0.7

+0.02

- 8.4

+0. 10

+ 3.9

+0.34

+ 6.7

+0.68

+ 9.1

-0.57

60

-0.6

+0. 02

-7.7

+0.15

+ 5.9

+0.29

+10.2

+0.42

+ 4.9

-0.78

66

-0.5

+0.01

- 6.6

+0.20

+ 7.4

+0.22

+ 11.7

+0.06

- 0.3

-0.89

72

-0.5

+0.02

-5.3

+0.22

+ 8.6

+0.18

+ 10.9

-0.30

- 5.8

-0.86

78

-0.3

+0.02

- 3.9

+0.24

+ 9.6

+0.12

+ 8.1

-0.62

-10.6

-0.70

84

-0.2

+0.01

- 2.3

+0.23

+ 10.0

+0.08

+ 3.5

-0.87

-14.2

-0.47

90

-0.2

0.00

- 1. 1

+0.22

+ 10.5

+0.05

- 2.3

-1.03

-16.2

-0.14

96

-0.2

+0.02

+ 0.3

+0.22

+ 10.6

+0.02

- 8.9

-1.08

-15.9

+0.26

102

0.0

+0.02

+ 1.6

+0.20

+ 10.7

0.00

-15.2

-0.95

-13.1

+0.64

108

+0.1

+0.02

+ 2.7

+0.19

+ 10.6

-0.02

-20.3

-0.71

-8.2

+0.98

114

+0.2

+0.01

+ 3.9

+0.21

+ 10.5

0.00

-23.7

-0. 38

- 1.4

+ 1.21

120

+0.2

0.00

+ 5.2

+0.22

+ 10.6

—0.02

-24.9

+0.01

+ 6.3

+ 1.32

126

+0.2

+0.02

+ 6.5

+0.25

+ 10.3

-0.05

-23. 6

+0.46

+14.5

+ 1.32

132

+0.4

+0.01

+ 8.2

+0.28

+10.0

-0.08

-19.4

+0.88

+22.2

+ 1.16

138

+0.3

-0.02

+ 9.9

+0.29

+ 9.3

-0.14

-13.0

+1.24

+28.4

+0.84

144

+0.2

-0.01

+ 11.7

+0.31

+ 8.3

-0.19

- 4.5

+ 1.50

+32.4

+0.47

150

+0.2

-0.02

+ 13.6

+0.32

+ 7.0

-0.28

+ 5.0

+ 1.62

+34.0

+0. 02

156

-0.1

-0.05

+ 15.5

+0.29

+ 5.0

-0.38

+ 14.9

+1.60

+32.6

-0.49

162

-0.4

-0.06

+ 17.1

+0.22

+ 2.5

-0.45

+24.2

+ 1.41

+28.1

-0.96

168

-0.8

-0.06

+ 18.2

+0.16

' - 0. 4

-0.52

+31.8

+ 1.10

+21.1

-1.33

174

-1.1

-0.05

+ 19.0

+0.08

- 3.8

-0.58

+37.4

+0. 70

+ 12.1

-1.63

180

-1.4

-0.06

+ 19.1

-0.04

- 7.5

-0.64

+40.2

+0.21

+ 1.5

-1.80

186

-1.8

-0.08

+ 18.5

-0.19

-11.5

-0.67

+39.9

-0.31

-9.6

-1.81

192

-2.3

-0.07

+16.8

(i 32

-15.4

-0.63

+36.5

-0.81

-20.2

-1.68

198

-2.6

-0.04

+ 14.6

-0.48

-19.1

-0.58

+30.2

-1.25

-29.6

-1.38

204

-2.8

-0.03

+ 11.1

-0.63

-22.3

-0.48

+21.5

-1.59

-36.8

-1.01

210

-3.0

-0.02

+ 7.0

-0. 72

-24.8

-0.35

+ 11.1

-1.82

-41.7

-0.55

216

-3.0

+0.01

+ 2.5

-0.79

-26.5

-0.18

- 0.3

-1.90

-43.4

-0.02

222

-2.9

+0. 02

- 2.5

-0.85

-26.9

+0.01

-11.7

is:;

-41.9

+0.50

228

-2.7

+0.05

-7.7

-0.85

-26.4

+0.21

-22.3

-1.62

-37.4

+0.97

234

-2.3

+0.06

-12.7

-0.81

-24.4

+0.41

-31.2

-1.31

—30.3

+ 1.37

240

-2.0

+0.08

-17.4

-0. 72

-21.5

+0.57

-38.0

-0.90

-21.0

+ 1.67

246

-1.4

+0.09

-21. 3

-0.58

-17.6

+0.74

-42.0

-0.41

-10.3

+1.82

252

-0.9

+0.09

-24. 3

-0.39

-12.6

+0.86

-42.9

+0.11

+ 0.9

+1.86

258

-0.3

+0.09

-26.0

-0.19

-7.3

+0.93

-40.7

+0.59

+12.0

+ 1.74

264

+0.2

+ 0.08

-26.6

+0.02

- 1.5

+0.96

-35.8

+ 1.03

+21.8

+ 1.52

270

+0.7

+0.08

-25.8

+0.23

+ 4.2

+0.92

-28.3

+ 1.38

+30.2

+ 1.18

276

+ 1.1

+0.06

-23.8

+J>.42

+ 9.6

+0.83

-19.2

+ 1.62

+35.9

+0.72

282

+1.4

+0.04

-20.7

+0.59

+ 14.2

+0.70

-8.9

+ 1.74

+38.9

+0.26

288

+ 1.6

+0.02

—16.7

+0.73

+ 17.9

+0.52

+ 1.7

+ 1.71

+39.0

-0.22

294

+ 1.6

0.00

-12.0

+0.81

+20.5

+0.34

+ 11.6

+1.56

+36.2

-0.68

300

+1.6

-0.02

- 7.0

+0.83

+22.0

+0.12

+ 20.4

+ 1.29

+30.8

—1.07

306

+1.4

-0.04

- 2.0

+0. 81

+22.0

-0. 10

+27.1

+0.90

+23.4

-1.35

312

+1.1

-0.05

+ 2.7

+0.74

+20.8

-0.28

+31.2

+0.48

+ 14.6

-1.52

318

+0.8

-0.06

+ 6.9

+0.61

+ 18.6

-0.47

+32.8

+0. 03

+ 5.2

-1.54

324

+0.4

-0.07

+ 10.0

+0.44

+ 15.2

-0.58

+31.6

-0.41

- 3.9

—1.44

330

0.0

-0.07

+ 12.3

+0.28

+ 11.6

-0.63

+27.9

-0.79

-12.1

—1. 22

336

-0.4

-0. 06

+ 13.3

+0.08

+ 7.6

-0.67

+22.1

-1.09

-18.6

-0^91

342

-0.7

-0.06

+ 13.3

-0.08

+ 3.6

-0.64

+ 14.8

-1.28

-23.0

-0.52

348

-1.1

-0.05

+12.3

-0.26

- 0.1

-0.57

+ 6.8

-1.30

-24.9

-0. 10

354

-1.3

-0.02

+10.2

-0.38

-3.2

-0.46

- 0.8

-1.21

-24.2

+0.31

360

-1.4

-0.02

+ 7.7

-0.46

- 5.7

-0.32

-7.7

-1.02

-21.2

+0.64

[nSz, d log t, and u,cos i are to be computed in the form J» n, sin ig + Sibicos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

251

PERIODIC TERMS.

Tables of (115) Thyra — '. ontinued.
TABLE III.— d log r— Continued.

Unit of a and 6=0X0001.

i

3

4

9'

"3

Din", for 1°

63

Diff. for 1°

a,

Diff. for 1°

&»

Diff. for 1°

0

0

+ 1.0

-0.15

-3.0

0.00

+0.5

-0.04

-0.5

-0.02

6

+0.2

-0. 12

-2.8

+0.03

+0.2

-0.04

-0.6

0.00

12

-0.4

-0. 10

-2.6

+0.06

0.0

-0.03

-0.5

+0.01

18

—1.0

-0.07

-2. 1

+0.08

-0.2

-0.02

-0.5

+0.02

24

—1.2

-0. 04

-1.7

+0.08

-0.3

-0. 02

-0.3

+0.02

30

-1.4

-0.02

-1. 1

+0.08

-0.4

0.00

-0.2

+0.02

36

-1.4

+0.01

-0.8

+0.06

-0.3

+0.02

-0.1

+0.02

42

—1.3

+0.02

-0.5

+0.04

-0.2

+0.01

+0.1

+0.02

48

-1.2

+0.02

-0.2

+0.02

-0.2

+0.01

+0.2

+0.01

54

—1.0

+0.03

-0.1

+0.02

-0. 1

+0.01

+0.2

-0.01

60

-0.8

+0.02

0.0

+0.01

-0. 1

+0.02

+0.1

-0.01

66

-0.8

0.00

0.0

-0.01

+0.1

+0.02

+0.1

-0.01

72

-0.8

0.00

-0.1

-0.01

+0.1

-0.02

0.0

-0.01

78

-0.8

-0.01

-0.1

+0.01

-0.1

-0.01

0.0

-0.01

84

-0.9

-0.02

0.0

+0.01

0.0

+0.01

-0.1

0.00

90

— 1. 1

-0.03

0.0

+0.02

0.0

0.00

0.0

+0.02

96

-1.3

-0.02

+0.2

+0.04

0.0

-0.01

+0.1

0.00

102

—1.4

-0.01

+0.5

+0. 05

-0.1

+0.01

0.0

-0.01

108

-1.4

+0.01

+0.8

+0.07

+0.1

+0.02

0.0

-0.01

114

-1.3

+0.02

+ 1.3

+0.08

+0.1

-0.02

-0.1

-0.01

120

— 1. 1

+0.06

+ 1.7

+0.08

-0.1

-0.02

-0.1

-0.01

126

-0.6

+0.09

+2.2

+0.06

-0.1

-0.01

-0.2

-0.01

132

0.0

+0. 10

+2.3

+0.02

-0.2

-0.01

-0.2

+0.01

138

+0.6

+0. 11

+2.3

-0.02

-0.2

-0.01

-0.1

+0.02

144

+1.3

+0.11

+2.2

-0.04

-0.3

-0.02

+0.1 -

+0.02

150

+ 1.9

+0.08

+1.8

-0.08

-0.4

0.00

+0.2

+0.02

156

+2.3

+0.06

+ 1.2

-0. 11

-0.3

+0.02

+0.3

+0.02

162

+2.6

■ 0.02

+0.5

-0. 12

-0.2

+0.02

+0.5

+0.02

168

+2.6

-0.02

-0.2

-0. 11

0.0

+0.03

+0.5

+0.01

174

+2.3

-0.06

-0.8

-0.08

+0.2

+0.04

+0.6

0.00

180

+1.9

-0.08

-1.3

-0.07

+0.5

+0.04

+0.5

-0. 02

186

+1.4

-0.08

—1.6

-0.04

+0.7

+0.02

+0.3

-0.02

192

+ 1.0

-0.08

—1.7

+0.8

-0.02

+0.1

-0.04

198

+0.5

-0.06

-1.7

+0.02

+0.6

-0.02

-0.2

-0.04

204

+0.3

-0.02

—1.5

+0.02

+0.6

-0.02

-0.5

-0.04

210

+0.2

-0.03

-1.4

+0.01

+0.4

-0.03

-0.7

-0. 02

216

-0.1

-0.01

-1.4

0.00

+0.2

-0.05

-0.7

0.00

222

+0.1

-0.01

-1.4

-0.02

-0.2

-0.04

-0.7

+0.02

228

-0.2

-0.02

—1.6

-0.02

-0.3

-0.02

-0.5

+0.03

234

-0.2

-0.04

-1.7

-0.03

-0.4

-0. 02

-0.3

+0.02

240

-0.7

-0.08

-2.0

-0.02

-0.5

0.00

-0.1

+0.03

246

—1.2

-0.09

-2.0

0.00

-0.4

+0.02

+0.1

+0.02

252

-1.8

-0. 12

-2.0

+0.03

-0.2

+0.02

+0.2

+0.01

258

-2.6

-0.12

—1.6

+0.09

-0.1

+0.02

+0.2

-0.01

264

-3.2

-0.08

-0.9

+0.13

0.0

+0.01

+0.1

-0.02

270

-3.6

-0.04

0.0

+0.17

0.0

0.00

0.0

-0.02

276

-3.7

+0.01

+1.1

+0.18

0.0

-0.01

-0.1

-0.02

282

-3.5

+0.08

+2.2

+0.18

-0.1

-0.02

-0.2

-0.01

288

-2.7

+0. 15

+3.3

+0. 15

-0.2

-0.02

-0.2

+0. 01

294

— 1.7

+0. 18

+4.0

+0. 10

-0.4

-0.02

-0.1

+0.02

300

-0.5

+0.22

+4.5

+0.04

-0.5

0.00

+0.1

+0.03

306

+0.9

+0.22

+4.5

-0.04

-0.4

+0.02

+0.3

+0.02

312

+2.1

+0. 19

+4.0

-0. 11

-0.3

+0.02

+0.5

+0.03

318

+3.2

+0.15

+3.1

-0. 18

-0.2

+0.04

+0.7

+0.02

324

+3.9

+0.08

+2.0

-0.20

+0.2

+0. 05

+0.7

0.00

330

+4.2

0.00

+0.8

-0.20

+0.4

+0. 03

+0.7

-0.02

336

+3.9

-0.05

-0.5

-0.18

+0.6

+0.02

+0.5

-0.04

342

+3.6

-0.08

—1.4

-0. 16

+0.6

+0.02

+0.2

-0.04

348

+2.9

-0. 13

-2.3

-0.12

+0.8

+0.01

-0.1

-0.04

354

+2.0

-0.16

-2.8

-0.06

+0.7

-0.02

-0.3

-0.02

360

+1.0

-0. 15

-3.0

0.00

+0.5

-0. 04

-0.5

-0.02

[n)z, 3 log r, and u/cos > are to be computed in the form £x at sin 1'9+Jj 61 cos ig+cT.]
89309"— vol. 10—11 17

252

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

PERIODIC TERMS.

Tables of (115) Thyra^- Continued.

TABLE IV — u cos i.

Unit or a and 6=09001.

{

0

1

2

3

K

Diff.

Diff.

&.

Diff.

Diff.

h

Diff.

Diff.

K

Diff.

g'

fori0

«i

fori3

fori0

Q2

fori0

fori0

"3

fori0

fori0

o

0

+ 1.1

+0.02

+3.4

-0.02

-0.4

-0.18

-9.8

-0. 06

- 0.3

+0.50

-1.4

+0.01

0.0

+0.08

6

+1.1

-0.01

i 3. 2 -0.08

-1.4

-0.16

-9.6

+0.13

+ 2.8

+0.51

-1.3

+0.03

+0.5

+0.07

12

+ 1.0

-0.02

+ 2. 5

-0. 13

-2.3

-0.10

-8.2

+0.28

+ 5.8

+0. 45

-1.0

+0.04

+0.8

+0.04

18

+0.8

-0.04

+ 1.6

-0. 17

-2.6

-0.06

-6.2

+0.40

+ 8.2

+0. 33 -0. 8

+0. 05

+1.0

+0.02

24

+0.5

-0.04

+0.5

-0. 18

-3.0

ii in

- 3.4

+0. 50

+ 9.8

+0. 19 -0. 4

+0.06

+1.1

+0.02

30

+0.3

ii ii:,

-0.6

-0.18

-3.1

+0.02

- 0.2

+0. 53

+10.5

+0. 02 ' -0. 1

+0. 05

+ 1.2

+0.01

36

-0.1

-0.05

-1.7

-0. 18

-2.7

+0.08

+ 3.0

+0.52

+ 10. 1

-0. 16

+0.2

+0. 05

+1.2

-0.02

42

-0.3

-0. 05

-2.7

-0.16

-2.1

+0.12

+ 6.0

+0.44

+ 8.6

-0.30

+0.5

+0.03

+0.9

-0.03

48

-0.7

-0.04

-3.6

-0.11

-1.2

+0.17

+ 8.3

+0.32

+ 6.5

-0.43

+0.6

+0.04

+0.8

-0.02

54

-0.8

-0. 02

-4.0

-0. 05

-0.1

+0.18

+ 9.8

+0.18

+ 3.4

-0.53

+ 1.0

+0.04

+0.0

-0.03

60

ii 9

-0.02

-4.2

0.00

+ 1.0

+0.18

+10.4

+0.01

+ 0.1

-0. 54

+ 1.1

+0.01

+0.4

-0.05

66

-1.0 0.00

-4.0

+0.06

+2.2

+0.18

+ 9.9

-0.19

- 3. 1

-0. 51

+1.1

-0.01

0.0

-0.07

72

-0. 9 0. 00

-3.5

+0. 10

+3.3

+0.15

+ 8.1

-0.34

- 6.0

-0.43

+1.0

-0.01

-0.4

-0.05

78

— 1. 0 0. 00

-2.8

+0.17

+4.0

+0.12

+ 5.8

-0.44

-8.3

-0.31

+1.0

-0.02

-0.6

-0.04

84

-0.9

+0.01

-1.5

+0.21

+4.8

+0.09

+ 2.8

-0.53

- 9.7

-0.13

+0.7

-0.06

-0.9

-0.04

90

-0.9

+0.01

-0.3

+0.21

+5.1

+0.03

- 0.6

-0. 55

-9.9

+0.04

+0.3

-0.06

-1. 1

-0.02

96

-0.8

0.00

+1.0

+0. 22

+5.2

-0.01

-3.8

-0. 52

- 9.2

+0.21

0.0

-0.06

-1.2

+0.01

102

-0.9

0.00

+2.4

+0.22

+5.0

-0.08

- <;. s

-0.41

-7.4

+0.36

-0.4

-0.07

-1.0

+0.03

108

-0.8

-0.01

+3.6

+0. 18

+4.2

-0. 12

- 8.7

-0.26

-4.9

+0.48

-0.8

-0.06

-0.8

+0.05

114

-1.0

-0.02

+4.6

+0.18

+3.5

-0.13

- 9.9

-0.12

- 1.7

+0. 54

-1. 1

-0.02

-0.4

+0.06

120

-1.1

-0.01

+5.7

+0.13

+2.6

-0. 16

-10. 1

+0.06

+ 1.6

+0.55

-1.0

+0.02

-0. 1

+0.06

126

-1.1

0.00

+6.2

+0.08

+1.6

-0.17

-9.2

+0.25

+ 4.9

+0.52

-0.9

+0.02

+0.3

+0. 07

132

-1.1

+0.01

+6.6

+0. 05

+0.6

-0.18

- 7. 1

+0.39

+ 7.8

+0.40

-0.7

+0.04

+0.7

+0.04

138

-1.0

+0.01

+6.8

0.00

-0.5

-0.18

-4.5

+0.48

+ 9. 7

+0.26

-0.4

+0.07

+0.8

+0.02

144

-1.0

+0.03

+6.6

-0.04

-1.4

-0.13

-1.3

+0.55

+10.9

+0. 11

+0.1

+0.07

+0.9

-0.01

150

-0.6

+0.06

+6.3

-0.08

-2.1

-0.10

+ 2.1

+0.56

+ 11.0

-0.08

+0.4

+0.04

+0.7

-0. 03

156

-0.3

+0.08

+5.8

-0.09

-2.6

-0.08

+ 5.4

+0. 52

+10.0

-0. 25

+0.6

+0.03

+0.5

-0. 06

162'

+0.3

+0.11

+5.2

-0. 10

-3.0

-0.04

+ 8.4

+0. 42

+ 8.0

-0.39

+0.8

0.00

0.0

-0.06

168

+ 1.0

+0.13

+4. 6 -0. 10

-3.2

-0.02

+ 10.4

+0.28

+ 5. 3

-0.50

+0.6

-II. 02

-0.2

-0.05

174

+1.9

+0.14

+4.0

-0. 10

-3. 1

+0. 02

+ 11.7

+0.13

+ 2.0

-0.55

+0.6

-0.03

-0.6

-0.03

180

+2. 7 1 +0. 15

+3.4

-0. 10

-3.0

+0.02

+ 12.0

-0.04

- 1.3

-0. 57

+0.2

-0.06

-0.6

+0.01

186

+3.7

+0.16

+2.8

-0.09

-3.0

+0.02

+ 11.2

-0. 22

-4.8

-0.54

-0. 1

-0.05

-0.5

0.00

192

+4.6

+0. 14

+2.3

- (1. (IT

-2.7

+0.03

+ 9.4

-0. 35

-7.8

-0.43

-0.4

-0. 02

-0.6

+0. 02

I'.IN

+5.4

+0.14

+2.0

-0.07

-2.6

+0.01

+ 7.0

-0.47

-10.0

-0.32

-0.4

-0. 02

-0.2

+0.04

204

+6.3

+0.11

+ 1.5

-0.08

-2.6

+0.01

+ 3.8

-0. 53

-11.6

-0.18

-0.6

-0.01

-0.1

+0.03

210

+6.7

+0.07

+ 1.0

-0.07

-2.5

+0.01

+ 0.6

-0.55

-12. 1

-0.01

-0. 5

+0.03

+0.2

+0.02

216

+7.1

+0. 03

+0.7

-0.08

-2.5

-0. 02

- 2.8

-0. 53

-11.7

+ 0. 16

-0.2

+0.03

+0.2

+0.01

222

+ 7.1

-0.02

+0.1

-0. 11

-2.7

-0.03

- 5.8

-0.46

-10.2

+0.30

-0.1

+0.02

+0.3

0. 00

228

+6.9

-0.06

-0.6

-0. 12

-2.9

-0.03

- 8.3

-0.37

- 8.1

+0.42

0.0

+0.01

+0.2

-0.01

234

+6.4

-0.10

-1.4

-0.13

-3.1

-0.02

-10.2

-0.22

- 5.2

+0.48

0.0

+0.01

+0.2

-0.02

240

+5.7

-0.13

-2.2

-0.15

-3.2

-0.02

-11.0

-0.06

-2.3

+0.52

+0.1

-0.01

0.0

-0.03

246

+4.8

-0.17

-3.2

-0.16

-3.4

+0.01

-10.9

+0. 09

+ 1-1

+0.52

-0. 1

-0.02

-0.2

0.00

252

+3. 7 -0. 18

-4. 1

-0.13

-3.1

+0. 05

-9.9

+0.22

+ 4.0

+0.45

-0.2

-0.02

0.0

+0.02

258

+2. Ii -0. 20

-4. 8 i -0. 16

-2.8

+0.06

-8.2

+0.36

+ 6.5

+0.38

-0.4

-0.01

0.0

+0.02

264

+1.3 -0. 19

5 9

-0. 14

-2.4

+0.09

- 5.6

+0. 45

+ 8.5

+0. 25

-0. 3

+0.01

+0.3

+0.04

270

+0.3 -0. 18

-6.5

-0.09

-1.7

+0.13

-2.8

+0.48

+ 9.5

+0.09

-0.3

fO.Ol

+0.5

+0.04

276

-0.8

-0. 15

-7.0

-0. 06

-0.8

+0. 14

+ 0.2

+0.50

+ 9.6

-0.08

-0.2

+0.04

+0.8

+0.02

282

—1.5

-0.12

-7.2

-0.02

0.0

+0.15

+ 3.2

+0.44

+ 8.6

-0.21

+0.2

+0. 05

+0.8

0.00

288

— 2. 2

-0.09

-7.2

+0. 05

+ 1.0

+0. 18

+ 5.5

+0.36

+ 7.1

-0. 32

+0.4

+0.06

II s

-0.02

294

-2.6

0 in

-6. 6

+0. 09

+2.1

+0.17

+ 7.5

+0. 25

+ 4.7

-0.42

+0.9

+0.07

+0.6

-0.04

300

-2.7

-0.01

-6.1

+0.12

+3.0

+0. 12

+ 8.5

+0.09

+ 2.0

-0.47

+ 1.2

+0.03

+0.3

-0.06

306

-2.7

+0. 02

-5.2

+0.18

+3.6

+0.10

+ 8.6

-0.07

- 0.9

-0.48

+1.3

-0.01

-0. 1

-0.08

312

-2.5

+0.06

-4.0

+0.22

+4.2

+0.08

+ 7. 7

-0. 21

-3.8

-0.43

+1.1

-0.02

-0.7

-0.08

318

-2.0

+0.09

-2.6

+0.23

+4.5

+0.03

+ 6.1

-0.33

- 6. 1

-0.34

+1.0

-0. 05

-1.0

-0. 05

324

—1.4

+0.08

-1.2

+0.22

+4.6

-0.02

+ 3. 7

-0.43

-7.9

-0.22

+0.5

-0.08

-1.3

—0.03

330

-1.0

+0.09

+0.1

+0. 22

+4.3

-0.07

+ 0.9

-0.48

-8.8

-0.08

0.0

-0.08

-1.4

-0.02

336

-0.3

+0. 09

+ 1.4

+0. 19

+3.8

-0.12

- 2.0

-0.49

-8.8

+0. 10

-0.4

-0.07

-1.5

+0.02

342

+0.1

+0.08

+2.4

+0. 13

+2.8

-0. 15

- 5.0

-0.43

- 7.6

+0. 24

-0.8

-0.07

-1.2

+0.06

348

+0.6

+0.07

+3.0

+0.08

+2.0

-0.17

-7.2

-0.32

-5.9

+0.37

-1.2

-0. 05

-0.8

+0.07

354

+0.9

+0.04

+3.4

+0.03

+0.8

-0.20

-8.9

-0.22

-3.2

+0.47

-1.4

-0.02

-0.4

+0.07

360

+ 1.1

+0.02

+3.4

-0.02

-0.4

-0.18

-9.8

-0.06

- 0.3

+0.50

-1.4

+0. 01

0.0

+0.08

[ndz, S log r, and u/cos i are to be computed in the form Ii at sin ig + S, 6i cos ig+cT.\

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (115) Thyra— Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 10) IN JULIAN YEARS.

253

noz

o log r

U rOS i

9

Unit of

•=0?001

Unit of c

=0.00001

Unit of

•=0°001

c

Diff. for 1°

c

Diff. fori0

e

Diff. for lJ

O

0

—2. 42

-0. 008

+0. 17

-0. 01 s

-0.20

-0. 054

6

-2. 44

-0. 002

+0.07

-0.018

-0. 52

-0. 053

12

-2 15

+0. 002

-0. 05

-0. 020

-0.84

-0. 052

18

-2. 12

+0. 008

-0. 17

-0. 018

1 1 1

-0. 048

24

-2. 35

+0. 013

-0.27

—0. 016

-1.41

-0.011

30

-2. 26

+0. 01S

-0. 36

—0.017

-1.67

-0. 040

36

-2. 14

+0. 022

-0.47

-0.018

-1.89

-0. 034

42

-1.99

+0. 026

-0.57

-0. 013

-2.08

-0. 029

48

1 83

+0. 029

-0.63

-0. 010

-2.24

-0. 023

54

-1.64

+0. 032

-0.69

-0. 010

-2.36

-0.0IS

60

-1.44

+0. 035

-0.75

-0. 009

—2. 46

—0.012

66

— 1. 22

+0. 038

-0.80

-0.007

-2. 51

-0. 006

72

-0.99

+0. 038

-0. 83

-0. 004

-2. 53

-0. 002

78

-0.76

+0. 038

-0. 85

-0. 002

-2. 53

+0. 003

84

-d 53

+0. 040

-0.86

-0. 002

-2.49

+0. 008

90

-0. 2S

+0. 041

-0.87

' -0.001

-2.43

+0.012

96

-0. 01

+0. 039

-0.87

+0. 002

-2.34

+0.016

102

+0. 19

+0. 039

-0.85

+0. 003

—2. 24

+0. 020

108

+0. 43

+0. 039

-0. 83

+0. 004

-2. 10

+0. 023

114

+0. 06

+0. 037

-0.80

+0. 005

-1.96

+0. 026

120

+0.87

+0. 034

-0.77

+0. 008

-1.79

+0. 028

126

+ 1.07

+0. 032

-0.71

+0. 008

-1.63

+0. 029

132

+1.26

+0.031

-0.67

+0. 008

-1.44

+0. 032

138

+1.44

+0. 029

-0.61

+0. 010

-1.24

+0. 033

144

+1.61

+0. 026

-0. 55

+0. 010

. -1.04

+0. 035

150 ■

+ 1. 75

+0. 022

-0. 49

+0.011

-0.82

+0. 036

156

+1.88

+0. 020

-0.42

+0.011

-0.61

+0. 03(1

162

+1.99

+0. 017

-0. 36

+0. 011

-0.38

+0. 038

168

+2.08

+0. 013

-0. 29

+0. 013

-0. 15

+0. 038

174

+2. 15

+0. 010

-0.20

+0. 013

+0.07

+0. 038

180

+2.20

+0. 006

-0.13

+0. 012

+0.30

+0. 038

186

+2.22

+0. 002

-0. 05

+0. 012

+0. 52

+0. 037

L92

+2. 23

0.000

+0.02

+0. 013

+0.74

+0. 037

198

+2. 22

-0. 005

+0.11

+0. 013

+0.96

+0.036

204

+2. 17

-0. 008

+0.18

+0.012

+ 1. 17

+0.034

210

+2.12

-0.011

+0.26

+0.012

+1.37

+0. 033

216

+2. 04

-0.016

+0. 33

+0. 012

+1. 57

+0. 031

221'

+ 1.93

-0. 019

+0.41

+0. 012

+ 1.74

+0. 028

228

+ 1.81

-0. 02 1

+0. 18

+0. 011

+ 1.90

+0. 028

234

+1.68

-0. 024

+0. r,i

+0.011

+2.07

+0. 025

240

+1.52

-0. 028

+0. 61

+0. 011

+2.20

+0. 022

246

+ 1.34

-0. 031

+0.67

+0.010

+2.33

+0. 019

252

+1. 15

-0. 033

+0. 73

+0. 008

+2.43

+0.015

258

+0. 94

-0. 035

+0.77

+0. 008

+2.51

+0. 012

264

+0. 73

-0. 038

+0.82

+0. 008

+2. 57

+0. 008

270

+0. 50

-0. 039

+0.86

+0. 006

+2.(11

+0. 004

276

+0. 26

-0. 039

+0.89

+0.(KII

+2.62

0.000

282

+0.03

-0. 01 1

+0.91

+0. 002

+2.61

-0. 005

288

-0.23

-0. 042

+0. 92

+0. 001

+2. 56

-0.011

294

-0. 48

-0. 042

+0.92

-0. 002

+2. 48

-0. 016

300

-0. 73

-0. 041

+0.90

-0. 003

+2.37

-0. 021

306

-0.97

-0. 039

+0. 88

— 0. 004

+2. 23

-0. 026

312

-1.20

-0. 038

+0.85

-0. 007

+2.06

-0. 031

318

-1.42

-0. 038

+0.80

-0. 009

+1.86

-0. 037

324

-1.65

-0. 034

+0.74

-0. 012

+ 1.62

-0. 042

330

—1.83

— 0. 029

+0. 66

-0. 013

+1.36

-0. 046

336

-2. 00

-0. 027

+0.58

-0.014

+ 1.07

-0. 050

342

-2. 15

-0. 022

+0.49

—0. 016

+0.76

-0. 052

348

2. 26

-0.017

+0. 39

-0. 018

+0. 45

-0. 052

354

- 2. 35

-0.013

+0.28

-0. 018

+0. 13

-0 054

360

-2. 42

-0. 008

+0. 17

-0. 018

-0. 20

-0 054

[niz, o log r, and u/cos i are to be computed in the form J; a; sin ig + Zi bi cos ig t cT.\

254

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (115) Thyra — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B'

c

log sin a

log sin b

log sin c

1871.0

O

133. 6335

O

38. 3091

o

58. 3609

9. 99462

9. 93598

9. 72345

2

.6475

.3237

.3709

62

97

347

3

.6615

.3383

. 3810

62

96

349

4

.6755

.3529

.3910

62

95

351

1875

133. 6895

38. 3674

58. 4010

9. 99462

9. 93594

9. 72353

6

.7035

. 3820

.4111

62

93

355

7

.7175

•3966

.4211

63

92

357

8

.7315

. 4112

.4312

63

91

359

9

.7455

. 4257

. 4412

63

90

361

1880

133. 7595

38. 4403

58. 4512

9. 99463

9. 93589

9. 72363

1

.7735

.4549

.4613

64

88

365

2

. 7876

.4695

. 4713

64

87

367

3

.S016

.4840

. 4814

64

86

369

4

.8156

.4986

.4914

64

85

371

i ss;>

133. 8296 .

38. 5132

58. 5014

9. 99464

9. 93584

9. 72373

6

.8436

.5278

. 5115

64

83

375

7

. 8576

.5424

.5215

65

82

377

8

.8716

.5569

.5316

65

81

379

9

. 8856

.5715

.5416

65

80

381

1890

133. S996

38. 5861

58. 5516

9. 99465

9. 93579

9. 72383

1

.9136

.6066

.5616

66

78

385

2

. 9276

.6152

.5717

66

77

387

3

.9416

.6298

.5818

66

76

389

4

.9556

.6444

.5918

66

75

391

1895

133. 9696

38. 6590

58. 6018

9. 99466

9. 93574

9. 72393

6

.9836

.6735

.6119

66

73

395

7

133. 9976

.6881

. 6219

67

72

397

8

134.0117

.7027

.6320

67

71

399

9

. 0257

.7172

.6420

67

70

401

1900

134. 0397

38. 7318

58. 6520

9. 99468

9. 93568

9. 72403

1

.0537

.7464

.6621

68

67

405

2

.0677

.7610

.6721

68

66

407

3

. 0817

.7757

.6822

68

65

409

4

. 0958

.7903

.6922

68

64

411

1905

134. 1098

38. 8049

58. 7023

9. 99468

9. 93563

9. 72413

6

. 1238

.8195

.7123

69

62

415

7

. 1378

.8342

.7224

69

61

417

8

.1518

.8488

.7324

69

60

419

9

.1659

.8634

.7425

69

59

421

1910

134. 1799

38. 8780

58. 7526

9. 99470

9. 93558

9. 72423

1

.1939

. 8926

.7626

70

57

425

2

.2079

.9072

.7726

70

56

427

3

.2220

.9218

.7827

70

55

429

4

. 2360

.9365

.7928

70

54

431

1915

134. 2500

38. 9511

58. 8028

9. 99470

9. 93553

9. 72433

6

.2640

.9657

.8129

71

52

435

7

.2780

.9803

.8229

71

51

437

8

. 2921

38. 9949

.8330

71

50

439

9

. 3061

39. 0096

.8430

71

49

441

1920

134. 3201

39. 0242

58. 8531

9. 99472

9. 93548

9. 72443

1

.3341

.0388

.8631

72

47

445

2

.3482

.0534

.8732

72

46

447

3

. 3622

.0680

.8832

72

45

449

4

.3762

.0826

.8933

72

44

451

1925

134. 3902

39. 0972

58. 9033

9. 99472

9. 93543

9. 72453

6

. 4042

.1119

.9134

73

42

455

7

.4183

.1265

.9234

73

41

457

8

. 4323

. 1411

. 9335

73

40

459

9

.4463

.1557

.9435

73

39

461

1930

134. 4603

39. 1703

58. 9536

9. 99474

9. 93537

9. 72463

Year

lOg C

os a

log c

os 6

log c

OS c

18

71.0

9. 19

46 n

9.70

35 n

9.9

287

19

30.0

9. 18

95n

9. 70

53n

9.9

283

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLES OF (128) NEMESIS.

255

MEAN ELEMENTS.

Epoch, 1896, July 3.0, M. T. Berlin = 189(i.504, M. T. Berlin

Of// 0

00=101 41 9=101?6858

<u=299 56 32=299. 9422]

& = 76 39 30= 76. 6584 [Mean equinox and eclipl

ic 1900.0.

i= 6 15 18= 6. 2551 J

<p= 7 16 50= 7.2805

ri=777. "8761 = 0. 21607669

The elements are based on oppositions extending from 1872 to 1899 and

on the perturbations of the first

order by Jupiter, as given on page 256.

AUXILIARY QUANTITIES.

log a =0.43940 log 57. 2958e=0. 86099 , /T— 1 Q „..„„
log e=9. 10287 log p =0.43236 10*V T+e

TABLE I.— MEAN ANOMALY (g).

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Year

!/

Year

9

Month

9

B 1872

O

327. 7994

1902

0
175. 13562

Jan. g;[

O

| 0. 00000

3

46. 66739

3

254. 00361

4

125. 53538

B 4

333. 08768

*Mi!

1 6. 69837

5

204. 40338

5

51. 95568

B 6

283. 48744

6

130. 82367

Mar. 0. 0

12. 74852

7

2. 35544

7

209. 69166

Apr. 0. 0

19. 446S9

8

81. 22343

B 8

288. 77573

May 0. 0

25. 92919

9

160.09142

9

7. 64372

June 0.0

32. 62756

B 1880

239. 17549

1910

86.51171

July 0. C

39. 10986

1

318. 04348

1

165. 37970

Aug. 0. 0

45. 80823

2

36. 91147

B 2

244. 46377

Sept. 0. C

52. 50660

3

115. 77947

3

323. 33176

Oct. 0. C

58. 98890

B 4

194. 86354

4

42. 19976

Nov. 0.0

65. 68727

5

273. 73153

5

121. 06775

Dec. 0. C

72. 16964

6

352. 59952

B 6

200. 15182

7
B 8

71. 46751
150. 55158

7
8

279. 01981
357. 8S780

9

229.41957

9

76. 75579

Change for n daysa

1890
1

308. 28756
27. 15556

B 1920
1

155. 83986
234. 70786

B 2

L06. 23962

2

313. 57585

n

g

n

g

3

185. 10762

3

32. 44384

4

263. 97561

B 4

111.52791

5

342. 84360

5

190. 39590

0

0

B 6

61. 92767

6

269. 26389

1

0. 21608

16

3. 45723

7

140. 79566

7

348. 13188

2

0. 43215

17

3. 67330

8

219. 66365

B 8

67. 21595

3

0. 64823

18

3. 88938

9

298. 53165

9

146. 08394

4

0. 86431

19

4. 10546

1900

17. 39964

1930

224. 95194

5

1. 08038

20

4. 32153

1

96. 26763

6

7
8

1. 29646
1. 51254
1. 72861

21
22
23

4. 53761
4. 75369
4. 96976

Note.— W

len g is used as an argument of the perturbations,

9

1. 94469

24

5. 18584

add tci the<7 <>

i this table Jn=n— jt0=0?3894. For explanation

10

2. 16077

25

5. 40192

see page 203

11

2. 37684

26

5. 61799

12

2. 59292

27

5. 83407

13

2. 80900

28

6. 05015

14

3. 02507

29

6. 26622

15

3. 24115

30 6. 48230

1

aj

'or days dm

ing January and

.

Febr

uary of leap y

ears substract one

day 1

jefore enterin

g this table.

256

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {128) Nemesis — Continued.

PERTURBATIONS.

Arg
ig—i'g'

ndz

0
0

+ 1
+1
+2
+2
+3

0

-1 +1
0

+1

+2 +1

0 +2
+ 1

42
+3

+ 4 +2

0 +3

+1
+2
+3
+4 +3

+2 +4

+3

+4

+ 5 +4

+2 +5

+3

+4

+5 +5

0. 43nt
0. Olnt

+ 1

7

9

- 16

+ 581
+457
+ 17

+ 1

+ 30
+ 117
f- 44
+ 2

+ 1
- 14

+ 8
+ 1

+

ii cos i

7. 22nt

1

0. 22nt

O.Olnt

1

3

19

+ 102

+ 71
+ 3

- 2

- 19

+ 44

h 10

+ 1

3

+ 10
+ 11

1

+ 1

- 3. 61nt

- 0.22nt

- 0.02nt

+ 1

- 5

+ 18

+ 41

f 3

+ 1
+ 3
+20

— 1

- 3

+ 2

+ 1
+ 6

6

7

0. 21nt

O.Olnt

+ 2
+ 75

7

6

107

263

- 18

_ 9

1
55
32

3

+

3

1

+3. 08nt

+0. 19nt
+0. 02nt

+1
+3
—1

+2

-2

+2

+ 1

-1

+6
+1

2

0. 38nt

2. 03nt

0. 13nt
O.Olnt

1
4
4
2

6
6
4
1

- 1

- 3

+15
+ 1

- 3

+ 2
- 1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHXER.

Tables of {128) Nemesis — Continued.

257

PERIODIC TERMS.

TABLE II.— nSz.

Unit of a and 6=09001.

i

0

1-

2

. 9'

K

Diff. fori0

«i

Diff. fori0

6,

Diff. fori0

a.

Diff. fori0

h

Diff. fori"

O

0

-1.0

+0. 19

+108 5

+0.62

+ 17.9

-5. 00

+ 156. 4

+1.48

+ 33.3

-5. 96

6

+0.1

+0. 18

+ 108.6

-0.56

- 12.5

-4. 96

+ 161.2

+0. 03

-3.7

-6.20

12

+1.2

+0. 18

+101.8

-1.72

- 41.6

-4.67

+ 156.8

—1.47

- 41.1

-6.10

18

+2.3

+0.18

+ 88.0

2. 7S

- 68.5

-4. 14

+ 143.5

-2.94

- 76.9

-5. 62

24

+3.3

+0.16

+ 68.5

-3.65

- 91.3

-3.37

+ 121.5

-4.24

-108.6

-4.73

30

+4.2

+0. 12

+ 44. 2

-4.38

-108.9

-2. 42

+ 92.6

-5.26

-133. 6

-3.56

36

+4.8

+0.09

+ 16.0

-4.83

-120.3

-1.36

+ 58.4

-5.92

-151.2

-2.12

42

+5.3

+0.07

- 13.8

-5.03

— 125.2

-0.23

+ 21.5

-6. 65

-159. 2

-0.58

48

+5.6

+0. 02

- 44.4

-4.98

-123. 1

+0.92

- 16.3

-6.09

-158.2

+0.92

54

+5.6

-0.02

- 73.7

-4.71

—114.2

+2.00

- 51.6

—5. 54

-148. 1

+2. 35

60

+5.4

-0. 05

-100.9

—4. 22

- 99.1

+3.02

- 82.8

-4. 72

-130.0

+3.52

66

+5.0

-0.08

-124.3

-3. 51

- 77.9

+3.91

-108.2

-3.63

-105.8

+4.40

72

+4.4

-0.12

-143.0

-2. 63

- 52.2

+4. 61

-126.4

—2. 42

- 77.2

+4.94

78

+3.5

-0.14

-155.9

-1.63

- 22.6

+5. 11

-137.2

-1. IS

- 46.4

+5.18

84

+2.7

-0. 15

-162.6

-0. 57

+ 9.1

+5. 39

-140. 6

+0.02

- 15.0

+5.13

90

+ 1.7

—0. 16

-162.7

+0.54

+ 42.1

+5. 48

-136. 9

+1.08

+ 15.2

+4.82

96

+0.8

-0.14

-156. 1

+ 1.63

+ 74.8

+5. 32

-127.6

+ 1.97

+ 42.8

+4.30

102

0.0

-0.14

-143. 1

+2.68

+ 105.9

+4. 95

-113.2

+2.72

+ 66.8

+3.66

108

-0.9

-0.14

-124. 0

+3.62

+ 134.2

+4.41

- 94.9

+3.30

+ 86.8

+2. 95

114

-1.7

-0. 11

- 99.6

+4.43

+ 158.8

+3.68

- 73.5

+3.71

+ 102.2

+2. 14

120

-2.2

-0.08

- 70.8

+5.12

+ 178.3

+2.78

- 50.2

+3.96

+112.5

+ 1.32

126

-2.6

-0.04

- 38.2

+5. 62

+192. 1

+1.80

- 26.0

+4.03

+ 118.0

+0.51

132

-2.7

-0.01

-3.4

+5.91

+ 199.9

+0.74

- 1.8

+3.98

+118.6

-0.28

138

-2.7

+0.02

+ 32. 7

+6.00

+201. 0

-0.38

+ 21.7

+3.73

+ 114.6

-1.06

144

-2.4

+0.06

+ 68.6

+5.88

+195. 4

-1.49

+ 43.0

+3.34

+105. 9

-1.77

150

-2.0

+0. 07

+ 103.3

+5.58

+ 183. 1

-2.58

+ 61.8

+2. 85

+ 93.4

-2. 36

156

-1.6

+0. 09

+ 135.5

+5.08

+ 164.3

-3.60

+ 77.2

+2. 25

+ 77.6

-2. 78

162

-0.9

+0. 12

+ 164.2

+4.35

+ 139.9

-4. 51

+ 88.8

+ 1.58

+ 60.0

-3. 05

168

-0.1

+0. 12

+ 187.7

+3.47

+ 110.2

-5. 28

+ 96.2

+0.93

+ 41.0

-3. 16

174

+0.6

+0. 1 2

+205. 8

+2. 48

+ 76.5

-5. 88

+ 100.0

+0.30

+ 22. 1

-3.11

180

+1.4

+0. 12

+217. 5

+1.37

+ 39.7

-6.30

+ 99.8

-0. 25

+ 3.7

-2.96

186

+2.1

+0. 10

+222. 2

+0.16

+ 0.9

-6.49

+ 97.0

-0.63

- 13.4

—2. 72

192

+2. 6

+0.08

+219! 4

-1.07

- 38.2

-li. 45

+ 92.2

-0.98

- 29.0

-2^48

198

+3.1

+0.08

+209. 4

-2. 26

- 76.5

-6.19

+ 85.2

-1.28

- 43.2

—2. 28

204

+3.5

+0.04

+ 192.3

-3.38

-112.5

—5. 68

+ 76.9

-1.47

- 56.4

-2.08

210

+3.6

+0.01

+ 168. 8

-4.42

-144.7

-4.95

+ 67.6

-1.69

- 68.2

-1.93

216

+3.6

-0.01

+ 139. 2

-5. 32

-171.9

-4.02

+ 56.6

-1.98

- 79.6

—1.82

222

+3.5

-0.03

+105. 0

-5.98

-193.0

-2.93

+ 43.8

-2. 35

- 90.0

-1.63

228

+3.2

-0.08

+ 67.4

-6. 44

-207. 1

—1.71

+ 28.4

—2.75

- 99.2

-1.34

234

+2.6

—0. 10

+ 27.7

-6.64

-213.5

-0.42

+ 10.8

-3.16

-106. 1

-0.93

240

+2.0

-0. 10

— 12.3

-6. 57

-212. 1

+0.90

- 9.5

-3.57

-110.4

-0.36

246

+1.4

-0. 12

- 51.1

-6. 24

-202. 7

+2.18

- 32.0

-3.84

-110.4

+0.40

252

+0.6

-0.14

- 87.2

-5.62

-186.0

+3.35

- 55.5

-3.88

-105. 6

+ 1.28

258

-0.3

-0.14

-118.5

-4.77

-162.4

+4.41

- 78.6

-3. 72

- 95.0

+2. 23

264

—1.1

-0.15

—144.4

-3.73

-133.1

+5. 22

-100.2

-3.29

- 78.8

+3. 17

270

-2. 1

-0. 16

-163. 3

—2.52

- 99.7

+5. 82

-118.1

-2.55

- 57.0

+4. 03

276

-3.0

-0.14

-174.7

— 1.23

- 63.2

+6.14

-130. 8

-1.61

- 30.4

+4.66

282

-3.8

-0. 12

-178. 1

+0.09

- 26.0

+6.17

-137.4

-0.48

— 1.1

+5. 04

288

-4.5

-0.11

-173.6

+1.41

+ 10.8

+5.92

-136. 6

+0. 74

+ 30.1

+5.16

294

-5.1

-0. 09

-161.2

+2. 62

+ 45.0

+5. 38

-128.5

+1.93

+ 60.8

+4.92

300

-5.6

-0.06

-142.2

+3.68

+ 75.3

+4. 59

-113.4

+3.04

+ 89.1

+4.38

306

-5.8

-0.04

-117.0

+4.53

+100.1

4-3.58

- 92.0

+4.02

+113.4

+3.62

312

-li. 1

-0.02

- 87.8

+5.11

+ 118.3

+2. 42

- 65. 1

+4.82

+132.5

+2.65

318

-6.1

+0.02

- 55.7

+5.43

+129. 2

+ 1.18

- 34.2

+5.34

+145. 2

+ 1.52

324

-5.8

+0.06

- 22.6

+5.47

+ 132.4

-0.09

- 1.0

+5. 60

+150. 7

+0.29

330

-5.4

+0.08

+ 9.9

+5.21

+ 128.1

-1.34

+ 33.0

+5. 60

+ 148. 7

-0.98

336

-4.8

+0.10

+ 39.9

+4.68

+ 116.3

-2.49

+ 66.2

+5.32

+ 139.0

—2.26

342

-4.1

+0.14

+ 66.0

+3.90

+ 98.2

-3.46

+ 96.8

+4. 73

+ 121.6

-3.45

348

-3.1

+0. 16

+ 86.7

+2.93

+ 74.8

-4.22

+123. 0

+3. 88'

+ 97.6

-4.49

354

—2. 2

+0.18

+101. 2

+ 1.82

+ 47.5

-4.74

+143. 4

+2.78

+ 67.9

-5.36

360

-L0

+0.19

+108. 5

+0.62

+ 17.9

-5.00

+156.4

+ 1.48

+ 33.3

-5.96

[n3z, 3 log r. and u/cos t are to be computed in the form Si ai sin ig+^i bi cos ig+c'I'.]

258

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (128) Nemesis — Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6=0?0Ot

i

3

4

5

Diff.

b3

Diff.

Diff.

bt

Diff.

Diff.

&5

Diff.

g'

«3

fori0

fori0

«4

fori0

fori0

<*5

fori0

for 1°

o

0

+ 14.8

+0.30

+ 4.8

-0.68

+2.5

+0.04

+0.6

-0.15

+0.8

+0.02

+0.3

-0.06

6

+ 16.0

+0. 08

+ 0.3

-0.78

+2.6

-0.02

-0.4

-0.15

+0.9

-0.01

-0.1

-0.07

12

+ 15.7

-0.18

- 4.5

-0.78

+2.3

-0.08

—1.2

-0. 13

+0.7

-0.04

-0.5

-0.06

18

+ 13.8

-0.43

- 9.0

-0.68

+1.6

-0.12

-2.0

-0.09

+0.4

-0.06

-0.8

-0.03

24

+ 10.5

-0.63

—12.7

-0. 51

+0.9

-0.12

-2. 3

-0.04

0.0

-0.08

-0.9

0.00

30

+ 6.2

-0. 75

-15.1

-0. 28

+0.2

-0.14

-2.5

-0.01

— 0. 5

-0.06

-0.8

+0.03

36

+ 1.4

-0.79

-16.0

-0.01

-0.8

-0.15

-2.4

+0.05

-0.7

-0.03

-0.5

+0.06

42

- 3.3

-0.72

-15.2

+0. 23

—1.6

-0.11

-1.9

+0.10

-0.9

-0.01

—0.1

+0.08

48

-7.2

-0.58

—13. 2

+0.42

-2.1

-0.06

-1.2

+0.13

-0.8

+0. 03

+0.4

+0.07

54

—10.2

-0.40

-10.2

+0.55

-2.3

-0. 02

-0.3

+0.14

-0.5

+0.05

+0.7

+0.04

60

-12.0

-0.22

- 6.6

+0.59

-2.2

+0.03

+0.4

+0.14

-0.2

+0.07

+0.9

+0.01

66

-12.8

-0.03

- 3.1

+0.58

—1.9

+0.10

+1.4

+0.12

+0.3

+0.07

+0.8

-0.02

72

-12.4

+0.12

+ 0.4

+0.52

-1.1

+0.13

+1.8

+0.07

+0.6

+0.04

+0.6

-0. 05

78

—11.5

+0.20

+ 3.2

+0.44

-0.3

+0.14

+2.2

+0.02

+0.8

+0.02

+0.2

-0.07

84

-10.0

+0.28

+ 5.7

+0.38

+0.6

+0.13

+2.0

-0. 05

+0.8

-0.02

-0.2

-0.06

90

-8.2

+0. 32

+ 7.8

+0.32

+1.3

+0. 11

+ 1.6

-0.09

+0.6

-0.04

-0.5

-0.04

96

-6.2

+0.38

+ 9.5

+0.24

+ 1.9

+0.06

+0.9

—0.14

+0.3

-0.06

-0.7

-0.02

102

- 3.7

+0.45

+ 10.7

+0. 16

+2.0

-0.01

-0.1

-0.16

-0. 1

-0.06

-0.7

+0.01

108

- 0.8

+0.51

+11.4

+0.08

+1.8

-0.08

—1.0

-0.13

—0.4

-0.04

-0.6

+0.03

114

+ 2.4

+0. 55

+ 11.6

-0.06

+ 1.1

-0.13

-1.7

-0.08

-0.6

-0.02

-0.3

+0.05

120

+ 5.8

+0.56

+10.7

-0.25

+0.2

-0.15

-1.9

-0.02

-0.7

+0.01

0.0

+0.05

126

+ 9.1

+0.49

+ 8.6

-0.44

-0.7

-0.14

-1.9

+0.04

-0.5

+0.03

+0.3

+0.04

132

+ 11.7

+0. 34

+ 5.4

-0.62

-1.5

-0.12

-1.4

+0.11

-0.3

+0.04

+0.5

+0.02

138

+13.2

+0.11

+ 1.2

-0. 75

-2.0

-0.04

-0.6

+0.16

0.0

+0.05

+0.6

0.00

144

+13.0

-0. 18

-3.6

-0.78

-2.0

+0. 02

+0.5

+0.17

+0.3

+0.03

+0.5

-0.02

150

+11.0

-0.48

-8.2

-0.68

—1.8

+0.08

+ 1.4

+0.13

+0.4

+0. 02

+0.3

-0.04

156

+ 7.2

-0.73

-11.9

-0.48

-1.0

+0.15

+2.1

+0.08

+0.5

0.00

0.0

-0.04

162

+ 2.2

-0.89

—14.0

-0.16

0.0

+0.17

+2.4

+0.01

+0.4

-0.02

-0.2

-0.03

168

- 3.5

-0.92

-13.8

+0.22

+1.0

+0.17

+2.2

-0.07

+0.2

-0.03

-0.4

-0. 02

174

- 8.8

-0.79

-11.4

+0.57

+2.0

+0.13

+1.6

-0.13

0.0

-0.03

-0.4

+0.01

180

-13.0

-0.52

- 7.0

+0.86

+2.5

+0.05

+0.6

-0.18

-0.2

-0.02

-0.3

+0.02

186

—15.0

-0.11

— 1.1

+ 1.01

+2.6

-0.03

-0.6

-0.18

-0.3

-0.01

-0.1

+0.03

192

-14.3

+0.32

+ 5.1

+0.99

+2.1

-0.12

—1.6

-0.15

-0.3

+0.01

+0.1

+0.02

198

-11.2

+0.70

+10.8

+0.80

+1.2

-0.17

-2.4

-0.09

-0.2

+0.02

+0.2

+0.02

204

- 5.9

+0.97

+14.7

+0. 46

+0.1

-0.18

-2.7

-0.01

0.0

+0.02

+0.3

0.00

210

+ 0.4

+ 1.08

+16.3

+0. 04

-1.0

-0.18

-2.5

+0.0S

+0.1

+0.02

+0.2

-0.02

216

+ 7.0

+1.01

+15.2

-0.41

-2.0

-0.13

—1.8

+0.15

+0.3

+0. 02

+0.1

-0.02

222

+ 12.5

+0.77

+11.4

-0. 78

-2.6

-0.04

-0.7

+0.18

+0.3

-0.01

-0.1

-0.02

228

+16.2

+0.41

+ 5.8

-1.02

-2.5

+0.04

+0.4

+0.18

+0.2

-0.02

-0.2

-0. 02

234

+17.4

-0.02

- 0.8

-1.07

-2.1

+0.11

+ 1.5

+0. 15

+0.1

-0.03

-0.3

-0.01

240

+16.0

—0.42

- 7.0

-0.96

-1.2

+0.17

+2.2

+0.09

-0.2

-0.03

-0.3

+0.01

246

+ 12.4

-0.73

-12.3

-0.72

-0.1

+0.19

+2.6

+0.01

-0.3

-0.02

-0.2

+0. 02

252

+ 7.2

-0.92

-15.6

-0.38

+1.1

+0.17

+2.3

-0.08

-0.4

-0. 02

0.0

+0.03

258

+ 1.3

-0. 95

-16.8

—0.02

+1.9

+0.11

+1.6

-0.14

-0.4

+0.02

+0.2

+0.03

264

— 4.2

-0.84

-15.9

+0.30

+2.4

+0.05

+0.6

-0.17

-0.2

+0.03

+0.4

+0.02

270

- 8.8

-0.65

-13.2

+0. 53

+2.5

-0.02

-0.4

-0.18

0.0

+0.04

+0.5

+0.01

276

-12.0

—0.41

-9.5

+0.66

+2.1

-0.11

-1.5

-0.16

+0.3

+0.04

+0.5

-0.02

282

-13.7

-0. 15

-5.3

+0.69

+ 1.2

-0.16

-2.3

-0.09

+0.5

+0.02

+0.3

ii ill

288

-13.8

+0.06

— 1.2

+0.64

+0.2

-0.18

-2.6

-0.02

+0.6

+0.01

0.0

-0.05

294

-13.0

+0.18

+ 2.4

+0. 54

-0.9

—0.16

-2.5

+0. 06

+0.6

-0.02

-0.3

-0.05

300

—11.6

+0.28

+ 5.3

+0.42

—1.8

—0.13

-1.9

+0. 12

+0.3

-0.04

-0.6

-0.03

306

- 9.7

+0.32

+ 7.4

+0.32

-2.5

-0.08

-1.1

+0. 16

+0.1

-0.05

-0.7

-0.01

312

-7.7

+0.36

+ 9.2

+0. 27

-2.7

0.00

0.0

+0. 18

-0.3

-0.06

-0.7

+0. 02

318

- 5.4

+0.38

+10.6

+0.20

-2.5

+0.07

+1.0

+0.16

-0.6

-0.03

-0.4

+0.05

324

- 3.2

+0.40

+ 11.6

+0.17

-1.9

+0.11

+1.9

+0. 12

-0.7

-0.02

-0.1

+0.06

330

- 0.6

+0.47

+12. 6

+0.11

—1.2

+0.14

+2.4

+0.07

-0.8

+0.02

+0.3

+0.06

336

+ 2.4

+0.53

+ 12. 9

-0.02

-0.2

+0.17

+2.7

+0.02

-0.5

+0.04

+0.6

+0.04

342

+ 5.8

+0.58

+12.4

-0.16

+0.8

+0.16

+2.6

-0.05

-0.2

+0.06

+0.8

+0. 02

348

+ 9.3

+0. 55

+11.0

-0.33

+1.7

+0.12

+2.0

-0. 10

+0.2

+0.07

+0.8

-0.02

354

+12.4

+0.46

+ 8.4

-0. 52

+2. 2

+0.07

+1.4

—0.12

+0.6

+0.05

+0.6

-0.04

360

+14.8

+0.30

+ 4.8

-0.68

+2^5

+0.04

+0.6

-0. 15

+0.8

+0.02

+0.3

-0. 06

[ndz, J log r, and u/cos i are to be computed in the form Jj a* sin ig+2i 6» cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNEK.

259

PERIODIC TERMS.

Tables oj {128) Nemesis — Continued.

TABLE III.— $ log r.

Unit of a and 6=0.00001.

i

0

1

2

g'

''0

Diff for 1°

"i

Diff. for 1°

6,

Diff. for 1°

<h

Diff. for 1°

6,

Dili', for 1°

o

0

—2. 2

0.00

+ 3.2

-0.48

- 5.0

-0.14

+13.0

-2.48

-65.3

-0. 54

6

2. 2

.+0. 01

+ 0.1

-0. 52

-5.5

-0.02

-2.3

-2.54

-66.8

+0.06

12

-i.\

+0.02

- 3.0

-0.52

- 5.2

+0.12

-17.5

-2.47

-64.6

+0.66

18

-2.0

+0.02

- 6.1

-0.47

- 4.1

+0.26

-31.9

-2. 24

—58.8

+ 1.22

24

-1.8

+0.02

- 8.6

-0.38

- 2.1

+0.37

-44.4

-1.89

—49.9

+1.72

30

-1.7

+0.04

-10.6

-0.28

+ 0.3

+0.47

—54.6

-1.42

-38. 2

+2.11

36

-1.4

+0.04

-12.0

-0.17

+ 3.4

+0.56

-61.6

-0.88

-24. 6

+2.37

42

-1.2

+0.04

-12.6

-0.02

+ 7.0

+0.61

-65. 1

-0.30

-9.8

+2.48

4S

-0.9

+0.04

-12.3

+0.12

+10.7

+0.62

-65.2

+0.28

+ 5.3

+2. 45

54

-0.7

+0.04

-11.1

+0.27

+14.4

+0. 59

-61.7

+0. 85

+ 19.6

+2.28

60

-0.5

+0.03

- 9.1

+0.42

+ 17.8

+0. 54

-55.0

+ 1.31

+32.7

+2.01

66

-0.3

+0.02

- 6.1

+0. 57

+20. 9

+0.46

-45.8

+1.71

+43. 7

+1. 60

72

-0.2

+0.02

- 2.3

+0.68

+23.3

+0.34

-34.5

+1.98

+51.9

+1.13

78

-0.1

+0.02

+ 2.0

+0. 77

+25. 0

+0.19

-22.0

+2.16

+57.3

+0.66

84

0.0

+0.01

+ 6.9

+0.82

+25. 6

+0. 04

— 8.6

+2.18

+59. 8

+0. 16

90

0.0

-0.01

+11.8

+0.82

+25. 5

-0. 12

+ 4.2

+2. 10

+59. 3

-0. 32

96

-0.1

-0.02

+16.8

+0.83

+24. 1

-0.32

+16.6

+ 1. 95

+55. 9

-0.75

102

-0.3

-0.02

+21.8

+0.78

+21.7

-0.48

+27.6

+ 1.68

+50. 3

-1.12

108

-0.4

-0.03

+26.1

+0.67

+18.3

-0. 65

+36.8

+ 1.37

+42. 5

-1.41

114

-0.7

-0.04

+29.7

+0. 55

+13.9

-0.78

+44.0

+ 1.00

+33.4

-1.61

120

-0.9

-0.04

+32.7

+0.39

+ 8.9

-0.88

+48.8

+0.62

+23.2

-1.74

126

-1.2

-0. 05

+34.4

+0.21

+ 3.4

-0.96

+51. 5

+0.26

+12.4

-1.78

132

-1.5

-0. 05

+35.2

+0. 03

-2.6

-1.02

+51.9

-0. 10

+ 1.9

— 1.72

138

-1.8

-0.06

+34.8

-0. 17

-8.7

-1.02

+50.3

-0.43

- 8.2

-1.62

144

-2.2

-0. 05

+33.2

-0.35

-14.8

-0.98

+46.7

-0.72

-17.6

-1.46

150

—2.4

-0.04

+30.6

-0.52

-20.6

-0.90

+41.7

-0.95

-25.7

-1.23

156

-2.7

-0.04

+26.9

-0.70

-25. 6

-0.78

+35. 3

-1.13

-32.4

—1.01

162

-2.9

^0.02

+22. 2

-0.84

-30.0

-0.66

+2N. 1

-1.24

-37.8

-0.78

168

-3.0

-0.02

+16^8

-0.95

-33. 5

-0.48

+20.4

-1.32

-41.7

-0. 52

174

-3.1

-0.01

+10.8

-1.02

-35.8

-0.29

+12.3

-1.35

-44.1

-0.28

180

-3.1

0.00

+ 4.4

-1.07

-37.0

-0. 12

+ 4.2

-1.34

-45. 1

-0.06

186

-3.1

+0.02

- 2.0

-1.08

-37.2

+0.08

-3.8

-1.32

—44.8

+0. 14

192

-2.9

+0.02

- 8.5

-1.03

-36.0

+0. 27

-11.6

-1.27

—43.4

+0. 35

198

-2.8

+0.02

-14.4

-0.94

-34.0

+0. 45

-19.0

-1.19

-40.6

+0.55

204

-2.6

+0. 04

-19.9

-0.84

-30.6

+0.62

-25. 9

-1. 11

-36.8

+0.72

210

-2.3

+0.05

-24.6

-0.72

-26.5

+0. 74

-32. 3

-1.01

-32.0

+0.89

210

-2.0

+0. 05

-28.5

-0.57

-21.7

+0.86

—38.0

-0.88

—26.1

+ 1.08

222

-1.7

+0. 05

-31.4

-0.40

-16.2

+0.91

-42.8

-0. 70

-19.0

+1.27

228

-1.4

+0.06

-33.3

-0.22

-10.8

+0.95

-46.4

-0.50

-10.9

+ 1.42

234

-1.0

+0.05

-34.1

-0.02

-4.8

+ 1.06

-48.8

-0.24

- 2.0

+ 1.53

240

-0.8

+0.04

-33.7

+0.14

+ 1.9

+0.95

—49.3

+0.08

+ 7.5

+ 1.62

246

-0.5

+0.06

-32.4

+0.28

+ 6.5

+0.80

-47.9

+0.42

+ 17.4

+ 1.64

252

-0.2

+0.02

-30.2

+0.43

+11.5

+0.80

-44.3

+0.76

+27.2

+1.59

258

-0.1

+0.02

-27.2

+0. 55

+ 16.1

+0.68

-38.8

+1.09

+36.5

+1. 45

264

4-0.2

+0. 02

-23.6

+0.66

+ 19.7

+0.52

-31.2

+ 1.42

+ 44.6

+ 1.22

270

+0.2

0.00

-19. 3

+0.72

+22.4

+0.39

-21.7

+ 1.72

+51.1

+0.92

276

+0.2

0.00

-14.9

+0.76

+24.4

+0. 24

-10.5

+1.93

+55.6

+0. 55

282

+0.2

-0. 01

-10.2

+0.77

+25. 3

+0.09

+ 1.5

+2.05

+57.7

+0. 11

288

+0.1

-0.02

- 5.7

+0. 75

+25. 5

-0.06

+14. 1

+2.08

+56.9

-0. 36

294

-0.1

-0.04

- 1.2

+0.68

+24.6

—0.21

+26. 5

+ 1.99

+53. 4

-0.82

300

-0.4

-0.02

+ 2.5

+0.61

+23.0

-0.33

+38.0

+1.80

+47.0

-1. 28

306

-0.5

-0.04

+ 6.1

+0.52

+20. 6

-0.45

+48. 1

+1.50

+38.1

— 1.68

312

-0.8

-0.06

+ 8.7

+0.39

+ 17.7

-0. 52

+56. 0

+1.10

+ 26. 9

-2.02

318

—1.1

-0.04

+10.8

+0.28

+ 14.4

-0. 57

+61.3

+0. 65

+ 13.9

-2.25

324

-1.3

-0. 03

+12.0

+0. 12

+ 10.9

-0.58

+63.8

+0.11

- 0.1

-2.37

330

-1.5

-0.03

+12.1

-0.03

+ 7.4

-0.58

+62. 6

-0.47

-14.5

—2.37

336

-1.7

-0.04

+11.6

-0. 14

+ 3.9

-0.54

+58. 2

—0.99

-28.5

-2.23

342

-2.0

-0.02

+ 10.4

-0.27

+ 0.9

-0.48

+50. 7

-1.49

-41.3

-1.97

348

-2.0

-0.02

+ 8.4

-0. 3S

- 1.8

-0.39

+40. 3

—1.92

-52.1

-1.58

354

-2.2

-0. 02

+ 5.9

-0.43

-3.8

-0. 27

+27.6

-2.28

-60.3

-1. 10

360

-2.2

0.00

+ 3.2

-0.48

- 5.0

-0. 14

+13. 0

—2.48

-65.3

-0. 54

[ndz, 3 log, r and u/cos i are to be computed in the form £i a* sin ig+2i 6* cos ig+cT.}

260

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (128) Nemesis — Continued.
TABLE III.— a log r— Continued.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

3

4

5

</

«3

Diff.
(or 1°

l>3

Diff.
for 1°

"4

Diff.
fori0

K

hiii
for 1°

a5

Diff.
for L°

fc5

Diff. for 1°

O

0

+ 2.9

-0.42

-9.5

-0. 18

+0.7

-0.12

-2.3

-0.03

+0.2

-0.04

-0.6

-0.02

6

+ 0.2

(i 16

-10.2

-0.04

-0.2

-0.14

-2.4

+0.01

-0. 1

-0.05

-0.7

+0.01

12

-2.6

0.47

-10.0

+0.11

-1.0

-0.12

-2.2

+0. 06

-0.4

-0.04

-0.5

+0.03

18

- 5.4

-0.42

-8.9

+0. 25

-1.7

-0.09

-1.7

+0.09

-0.6

-0. 02

-0.3

+0.04

24

-7.7

-0. 32

- 7.0

+0.37

-2. 1

-0. 06

-1. 1

+0. 12

-0.7

0.00

0.0

+0.06

30

-9.2

-0.20

- 4.5

+0.44

-2.4

-0.02

-0.3

+0. 13

-0.6

+0. 02

+0.4

+0.04

36

-10.1

-0. 06

- 1.7

+0.49

-2.3

+0.03

+0.5

+0.13

-0.4

+0.04

+0.5

+0.02

42

-9.9

+0. 10

+ 1.4

+0.47

-2.0

+0. 08

+ 1.3

+0. 11

-0. 1

+0. 06

+0.7

+0.01

48

-8.9

+0.22

+ 3.9

+0.38

-1.3

+0.12

+1.8

+0.07

+0.3

+0. 05

+0.6

-0. 02

54

-7.2

+0.32

+ 6.0

+0.29

-0.5

+0.12

+2.1

+0.02

+0.5

+0.03

+0.4

-0.04

60

- 5.2

+0.36

+ 7.4

+0.18

+0.2

+0.12

+2. 1

-0.02

+0.7

+0.01

+0.2

-0. 05

66

-2.9

+0.38

+ 8.2

+0.08

+1.0

+0. 10

+1.8

-0.07

+0.6

-0.02

-0.2

-0.05

72

- 0.6

+0.37

+ 8.3

-0.02

+ 1.4

+0. 06

+ 1.2

-0.12

+0.5

-0.04

-0.5

-0.03

78

+ 1-5

+0.32

+ 8.0

-0.11

+1.7

+0.02

+0. 5

-0. 12

+0.2

-0. 05

-0.6

-0.01

84

4-3.3

+0.28

+ 7.0

-0.18

+ 1.7

-0. 02

-0.2

-0. 10

-0.2

0.04

-0.6

+0.01

90

+ 4.8

+0. 22

+ 5.8

-0. 22

+ 1.4

-0.08

-0.8

-0.08

-0.4

-0.02

-0.5

+0.03

96

+ 6.0

+0. 17

+ 4.4

-0.27

+0.8

-0.10

-1.2

-0. 05

-0.5

-0.01

-0.2

+0.04

102

4-6.8

+0.09

+ 2.6

-0.30

+0.2

-0.10

-1.4

+0.01

-0.5

0.00

+0.1

+0.04

108

+ 7.1

+0.02

+ 0.8

-0. 32

-0.5

-0.10

-1. 1

+0. 05

-0.5

+0.02

+0.3

+0.02

114

4-7.0

-0.06

— 1.2

-0. 33

-1.0

-0.06

-0.8

+0. 08

-0.2

+0.04

+0.5

+0.02

120

4- 6.4

-0. 16

- 3.2

-0.30

— 1. 1

0.00

-0.2

+0. 10

0. 0

+0.03

+0.5

0.00

126

4- 5.1

-0.27

- 4.9

-0.25

—1.0

4-0.03

+0.4

+0.09

+0.2

+0.03

+0.4

-0.02

132

+ 3.2

-0.33

- 6.2

-0.16

-0.7

+0.07

+0.9

+0. 06

+0.4

+0.02

+0.2

-0.03

138

+ 1.1

-0.38

- 6.8

-0.04

-0.2

+0. 10

+ 1.1

+0.02

+0.5

0.00

0.0

-0.03

144

- 1.4

-0.39

-6.7

+0.09

+0.5

+0.08

+ 1.1

-0.02

+0.4

-0.02

-0.2

-0.02

150

- 3.6

-0.32

- 5.7

+0.24

+0.9

+0.07

+0.8

-0. 06

+0.2

-0.03

-0.3

-0. 02

156

- 5. 3

-0.22

-3.8

+0.36

+1.3

+0.04

+0.5

-0.08

0.0

0 02

-0.4

0. 00

162

-6.2

-0.07

-1.4

+0.42

+ 1.4

-0.02

-0.2

-0. 10

-0 2

-0.02

-0.3

+0. 02

168

- 6.1

+0.09

+ 1.2

+0. 42

+1.2

-0. 05

-0.8

-0.10

-0.3

-0.02

-0.2

+0. 02

174

- 5.1

+0. 26

+ 3.6

+0. 35

+0.8

-0.08

-1.4

-0.05

-0.3

+0.01

0.0

+0.02

180

- 3.0

+0. 39

+ 5.4

+0.22

+0.2

-0.10

-1.4

-0.01

ii 2

+0.02

+0.2

+0.02

186

- 0.4

+0. 45

+ 6.2

+0.04

-0.5

-0.10

-1.5

+0.02

-0. 1

+0.02

+0.2

0.00

192

+ 2.4

+0.44

+ 5.9

-0. 15

-1.0

-0.08

-1. 1

+0.07

+0.1

+0.02

+0.2

0.00

198

+ 4.9

+0.34

+ 4.4

-0.32

-1.4

-0.04

-0.7

+0.09

+0.2

+0.02

+0.2

-0. 02

204

+ 6.5

+0. 18

+ 2.0

-0.44

— 1.5

0.00

0.0

+0. 11

+0. 2

0.00

0.0

-0.02

210

+ 7.1

-0.01

- 1.(1

-0.49

-1.4

+0.03

+0.6

+0.08

+0.2

-0.01

-0.1

-0.02

216

+ 6.4

-0. 22

3.9

-0.45

-1.0

+0.09

+1.0

+0.06

+0.1

-0.02

-0.2

-0.01

222

+ 4.5

-0.38

-6.4

-0.34

-0.3

+0.10

+1.3

+0.03

-0. 1

-0.02

-0.2

0.00

228

+ 2.0

-0.47

- 8.0

-0. 17

+0.2

+0.08

+1.4

-0.02

-0.2

-0.01

-0.2

+0. 01

234

- 1. 1

-0.52

-8.4

+0.03

+0.7

+0.08

+1.1

-0.08

-0.2

0.00

-0.1

+0.02

240

-4.2

-0.47

- 7.6

+0.21

+1.1

+0. 05

+0.5

-0.09

-0.2

0.00

+0.2

+0. 02

246

- 6.7

-0. 36

- 5.9

+0.37

+1.3

-0.01

0.0

-0.08

-0.2

+0.02

+0.2

+0.02

252

- 8.5

-0. 18

:;. 2

+0.47

+1.0

-0.05

-0.6

-0.09

0.0

+0.02

+0.3

+0.01

258

-8.9

-0.01

- 0.3

+0.48

+0.7

-0.07

-1.1

-0. 05

+0.2

+0.02

+0.3

-0.02

264

-8.6

+ 0. 12

+ 2.5

+0. 45

+0.2

-0.10

-1.2

-0.01

+0.3.

+0.02

+0.2

-0.02

270

-7.4

+0.26

+ 5.0

+0.36

-0.5

-0. 10

-1.2

+0. 02

+0.4

+0.01

0.0

-0.02

276

-5.5

+0.34

+ 6.8

+0.24

-1.1

-0.08

-0.9

+0.06

+0.4

-0.02

-0.2

-0.03

282

-3.3

+0. 38

+ 7.9

+0.12

-1.5

-0.03

-0.5

+0.08

+0.2

-0.03

-0.4

-0.02

288

- 0.9

+0.38

+ 8.3

+0.02

-1.5

+0.01

+0.2

+0. 10

0.0

-0.03

-0.5

0.00

294

+ 1.2

+0.34

+ 8.2

-0. 08

-1.4.

+0. 03

+0.8

+0. 10

-0.2

-0.04

-0.5

+0.02

300

+ 3.2

+0.28

+ 7.4

-0.14

-1. 1

+0.08

+1.4

+0.08

-0.5

-0. 02

-0.2

+0.02

306

+ 4.6

+0. 24

+ 6.5

-0.18

-0.5

+0.11

+1.7

+0. 05

-0.5

0.00

-0.1

+0.03

312

+ 6.1

+0. 21

+ 5.2

-0.24

+0.2

+0.12

+2.0

0.00

-0.5

+0.02

+0.2

+0.04

318

+ 7.1

+0. 15

+ 3.6

-0.26

+0.9

+0.11

+1.7

-0. 05

-0.3

+0.03

+0.5

+0.02

324

+ 7.9

+0.11

+ 2.1

-0.29

+1.5

+0.09

+1.4

-0. 08

-0. 1

+0.04

+0.5

+0.02

330

+ 8.4

+0.05

+ 0.1

-0.32

+2.0

+0.06

+0.8

-0.10

+0.2

+0.06

+0.6

-0.01

336

+ 8.5

-0.03

-1.8

-0.35

+2.2

+0.02

+0.2

-0. 12

+0.5

+0.03

+0.4

-0.04

342

+ 8.0

-0. 12

- 4. 1

-0.37

+2.3

-0.04

-0.7

-0.12

+0.6

+0.01

+0.2

-0.04

348

+ 7.0

-0.23

-6.2

-0.32

+1.8

-0.08

-1.3

-0. 11

+0.6

-0.02

-0.2

-0. 05

354

+ 5.2

-0.34

- 8.0

-0.28

+ 1.3

-0.09

-2.0

-0.08

+0.5

-0.03

-0.5

-0.03

360

+ 2.9

-0.42

-9.5

-0.18

+0.7

-0.12

-2.3

-0.03

+0.2

-0.04

-0.6

-0.02

[niz, S log r, and u/cos i are to be computed in the form n ai sin ig+Ix bt cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

261

Tables of {128) Nemesis — Continued.

TABLE IV.— u cos i.

PERIODIC TERMS.

Unit of aand 6=0¥0I)1.

z

0

1

2

9'

&o

Diff. for 1°

a,

Diff. for 1°

6,

Diff. for 1°

a.

Diff. for 1°

6,

Diff. fori0

0

0

—1.5

0.00

-0.4

0.00

+0.2

+0.02

+2.3

+0.24

+4.7

-0.09

6

-1.5

+0.02

-0.4

0.00

+0.4

0. 00

+3.6

+0.19

+4.0

-0. 17

12

—1.3

+0.03

-0.4

0.00

+0.2

-0. 02

+4.6

+0. 16

+2.7

—0. 22

18

— 1. 1

+0.04

-0.4

+0.02

+0. 2

0.00

+5.4

+0.0S

+ 1.3

-0. 25

24

-o.s

+0.04

-0.2

+0.02

+0.2

-0.01

+5.6

0.00

-0.3

-0.27

30

-0.6

+0.05

-0.2

0.00

+0.1

-0. 02

+5.4

-0.08

-1.9

-0. 26

36

-0.2

+0. 06

-0.2

+0.01

0.0

-0. 02

+4.6

-0. 16

-3.4

-0.22

42

4-0.2

+0.04

-0. 1

+0.01

-0. 2

-0. 03

+3.5

-0.20

-4.5

-0.16

48

+0.3

+0.03

-0. 1

■ n in

-0.4

-0.03

+ 2.2

- 0, 21

-5.3

-0. 09

54

+0.6

+0.03

0.0

-0.01

-0. ii

-0.05

+0.6

-0.26

-5.6

-0.02

60

+0.7

+0.02

-II. 2

-0.02

-1.0

-0. 05

-0.9

-0. 25

-5.6

+0.07

66

+0.8

0.00

-0.3

-0.02

-1.2

-0.04

-2.4

-0.22

-4.8

+0.13

72

+0.7

-0.01

-0.4

-0.02

-1.5

0 01

-3.6

-0.17

-4.0

+0.17

78

+0.7

-0.02

-0.6

-0.04

-1. 7

-0. 02

-4.4

-0. 10

-2.8

+0.22

84

+0.4

-0.04

-0.9

-0.06

-1.8

-0.02

-4.8

:

-1.4

+0.23

90

+0.2

-0.05

—1.3

-0.07

-1.9

-0.01

-4.8

+0. 05

0.0

+0.22

96

-0.2

-0.06

-1.7

-0.06

-1.9

II III

1. 2

+0. 10

+1.3

+0.20

102

-0.5

-0. 06

-2.0

-0.06

—1.8

+0.02

-3.6

+0. 15

+2.4

+0.15

108

-0.9

-0.08

-2.4

-0.07

—1.6

+0. 05

-2.4

+0.20

+3.1

+0.09

114

-1. 1

-0.07

-2.8

-0. 05

-1.2

4 0 07

-1.2

+0.19

+3.5

+0.02

121)

— 1. 7

-0.07

-3.0

-0.02

-0.8

■ II lis

-0.1

• 0 IS

+3.4

-0.04

126

— 2. 2

-0.07

-3.1

0.00

-0.2

+0.10

+1.0

+0.17

+3.0

-0.09

132

-2. 5

-0. 05

-3.0

+0.01

+0.4

+0. 10

+1.9

+0.12 •

+2.3

-0.15

138

-2. 8

-0.04

-3.0

+0.03

+ 1.0

+0 10

+2.5

+0.06

+ 1.2

-0.18

144

-3.0

-0.03

-2.6

+0.08

+ 1.6

+0.10

+2.6

-0.01

+0.1

-0.18

150

-3.2

-0.02

-2.0

+0.09

+2.2

+0.09

+2.4

-0. 05

-0.9

-0. 17

156

-3.2

0.00

-1.5

+0. 10

+ 2.6

+0.06

+ 2.0

-0.12

-1.9

-0. 13

162

-3.2

0.00

-0.8

+0. 11

+2.8

+0. 03

+ 1.0

-0. 17

-2.5

-0.09

168

-3.2

+0.01

-0.2

+0. 13

+3.0

+0.03

0.0

- 0. is

-3.0

-0.03

174

-3. 1

. II 01'

+0.8

+0.13

+3.2

0.00

—1.1

-0. 19

-2.9

+0.04

180

-2.9

o ii,;

+1.4

+0.10

+3.0

-0. 05

-2.3

-0. 18

-2.5

+0.09

L86

-2. 7

+0. 03

+2.0

+0. 10

+2.6

-0. 05

-3.2

-0.12

-1.8

+0.15

192

-2.5

ii ii:,

+2.6

+0. 10

+2.4

-0.07

-3.8

-0.08

-0.7

+0.19

198

-2. 1

0 (III

+3. 2

+0.07

+ 1.8

-0. 10

-4.2

-0. 02

+0.5

+0.20

204

—1.8

■ ii in;

+ 3.4

+0.03

+ 1.2

-0.09

-4.0

+0.07

+1.7

+0.22

210

—1.4

+0.07

+3.6

+0. 02

+0.7

-0.10

-3.4

+0.12

+3.1

+0. 19 .

216

-1.0

+0.07

+3.6

-0.01

0.0

-0. 11

-2.5

+0.18

+4.0

+0.13

222

-0.6

0 OS

+3.5

-0.02

-0.6

-0.08

-1.3

+0.21

+4.7

+0.09

22S

-0. 1

+0.07

+3.3

-0.06

-1.0

-0.07

0.0

+0.22

+5.1

+0.02

234

+0.2

- n 06

+ 2.S

-0.08

-1.4

-0. 05

+ 1.4

+0.24

+5.0

-0.00

240

+0.6

+0.07

+2.4

-0.07

-1.6

-0.03

+2.9

1-0. 21

+4.4

-0. 13

246

+1.0

+0.06

+2.0

II lis

-1.8

-0.02

+4.0

+0.16

+3.4

-0.18

252

+1.3

+0.04

+ 1.4

II IIS

-1.7

+0.01

+4.8

+0.10

+2.2

-0. 22

258

+1.5

+0.04

+ 1.0

-0. 07

—1.7

+0.01

+5.2

+0.03

+0.8

-0. 25

2)14

+1.8

+0. 03

+0. 6

-0. 05

-1.6

o n;;

+ 5.2

-0.03

-0.8

0. 25

270

+1.9

+ 0.02

+0.4

-0. 05

—1.3

+0.04

+4.8

-0.12

-2.2

0. 22

276

+2.0

0.00

0.0

-0.05

— 1. 1

+0.04

+3.8

-0.18

-3.5

-0. 18

2,S2

+1.9

0 02

-0. 2

-0.03

-0.8

+0.06

+ 2.6

-0.22

-4.4

-0.12

2SS

+ 1.7

-0.02

-0. 4

0 02

-0.4

+0.06

+ 1.2

-0.25

-4.9

-0.04

294

+1.6

-0.03

-0.4

0. 00

-0.2

+0.03

-0.4

-0.26

-4.9

+0.02

300

+1.3

-0.05

-0.4

+0. 01

0.0

+0.04

-1.9

-0.23

-4.6

+0.11

306

+1.0

-0.07

-0.3

+0.01

+0.3

+0.03

-3.2

-0. 18

-3.6

+0.18

312

+0.5

-0.07

-0.3

+0.01

+0.4

+0.02

-4.1

-0.12

-2.5

+0.22

318

+0.2

-0.06

-0.2

- II III

+0.4

0.00

—4.7

-0. 06

-1.0

+0. 25

324

-0.2

-0.07

-0.2

0.00

+0.4

0.00

-4.8

+0.02

+0.5

+0.26

330

-0.6

-0.07

-0.2

0.00

+0.4

0.00

—4.4

+0.10

+2.1

+0.23

336

-1.0

-0.05

-0.2

0.00

+0.4

0.00

-3.6

+0.17

+3.3

+0.18

342

-1.2

II 1)3

-0.2

0.00

+0.4

-0.01

-2. 4

+0. 23

+4.3

+0.13

348

-1.4

-0.02

-0.2

-0.02

+0.3

-0. 02

-0.8

+0.26

+5.0

+0.07

354

-1.5

-0.01

-0.4

-0.02

+0.2

-0.01

+0.7

+0. 26

+5.1

-0.02

360

—1.5

0.00

-0.4

0.00

+0.2

+0.02

\ 2. :;

+0.24

+4.7

-0.09

\n8z, d log r, and u/cos i are to be computed in the form Ii a% sin ig+Ii bi cos ig+cT.]

262

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

PERIODIC TERMS.

Tables of (128) Nemesis — Continued.
TABLE IV.— m/cos i— Continued.

Unit of a and 6=09001.

i

3

4

9'

"3

Diff. for 1°

b3

Diff. for 1°

«3

Diff. for 1°

b4

Diff. for 1°

O

0

+0.3

-0.01

-0.5

-0.01

0.0

-0.03

-0.3

0.00

6

+0.2

-0.02

-0.5

-0.01

-0.2

-0.02

-0.3

+0.01

12

+0.1

-0.01

-0.6

-0.01

-0.3

-0.01

-0.2

+0.02

18

+0.1

-0.02

-0.6

+0.01

-0.3

0. 00

0.0

+0.03

24

-0.1

-0.03

-0.5

+0.01

-0.3

+0.01

+0.2

+0.02

30

-0.3

-0.03

-0.5

+0.01

-0.2

+0.02

+0.3

+0.01

36

-0.5

-0.02

-0.4

+0.02

0.0

+0.03

+0.3

0.00

42

-0.6

-0.01

-0.2

+0.03

+0.2

+0.02

+0.3

-0.01

48

-0.6

+0.01

0.0

+0.02

+0.3

+0.01

+0.2

-0.02

54

-0.5

+0.02

+0.1

+0.02

+0.3

0.00

0.0

-0. 03

CO

-0.3

+0.03

+0.3

+0.02

+0.3

-0.01

-0.2

-0.02

66

-0.1

+0.02

+0.3

0.00

+0.2

-0.02

-0.3

-0.01

72

0.0

+0.01

+0.3

-0.02

0.0

-0. 03

-0.3

0.00

78

0.0

+0.01

0.0

-0.04

-0.2

-0.02

-0.3

+0.01

84

+0.1

-0.01

-0.2

-0.02

-0.3

-0.01

-0.2

+0.02

90

-0.1

-0.03

-0.3

-0.02

-0.3

0.00

0.0

+0.03

96

-0.3

-0.03

-0.4

+0.02

-0.3

+0.01

+0.2

+0.02

102

-0.5

-0.04

-0.2

+0.04

-0.2

+0.02

+0.3

+0. 01

108

-0.8

-0.03

+0.1

+0.06

0.0

+0.03

+0.3

0.00

114

-0. 9

+0.02

+0.5

+0.07

+0.2

+0.02

+0.3

-0.01

120

-0.7

+0. 04

+0.9

+0.07

+0.3

+0.01

+0.2

-0.02

126

-0.4

+0.08

+ 1.3

+0.04

+0.3

0. 00

0.0

-0.03

132

+0.2

+0. 10

+1.4

+0. 01

+0.3

-0.01

-0.2

-0.02

138

+0.8

+0.09

+ 1.4

-0.02

+0.2

-0. 02

-0.3

-0.01

144

+1.3

+0.08

+1.1

-0.08

0.0

-0.03

-0.3

0.00

150

+1.7

+0. 04

+0.5

-0.11

-0.2

-0.02

-0.3

+0.01

156

+1.8

-0.01

-0.2

-0.12

-0.3

-0.01

-0.2

+0.02

162

+ 1.6

-0. 05

-0.9

-0.11

-0.3

0. 00

0.0

+0.03

168

+1.2

-0.09

—1.5

-0.08

-0.3

+0. 01

+0.2

+0.02

174

+0.5

-0. 12

-1.8

-0.03

-0.2

+0.02

+0.3

+0.01

180

-0.3

-0.12

-1.9

+0.02

0.0

+0.03

+0.3

0.00

186

—1.0

-0. 10

—1.5

+0. 08

+0.2

+0.02

+0.3

-0.01

192

—1.5

-0. 06

-1.0

+0. 11

+0.3

+0.01

+0.2

-0.02

198

-1.7

0.00

-0.2

+0.12

+0.3

0. 00

0.0

-0.03

204

—1.5

+0. 05

+0.5

+0.11

+0.3

-0.01

-0.2

-0.02

210

— 1. 1

+0. 08

+1.1

+0.08

+0.2

0.02

-0.3

-0.01

216

-0.5

+0.11

+1.4

+0.02

0.0

-0. 03

-0.3

0.00

222

+0.2

+0.11

+1.4

-0.02

-0.2

-0.02

-0.3

+0.01

228

+0.8

+0.08

+ 1.2

-0.08

-0.3

-0.01

-0.2

+0.02

234

+ 1.1

+0.04

+0.5

-0.11

-0.3

0. 00

0.0

+0.03

240

+ 1.3

0.00

-0. 1

-0. 10

-0.3

+0.01

+0.2 •

+0.02

246

+ 1.1

-0. 06

-0.7

-0.08

-0.2

+0.02

+0.3

+0.01

252

+0.6

-0. 09

-1.1

-0. 06

0.0

+0. 03

+0.3

0.00

258

0.0

0.09

—1.4

-0. 01

+0.2

+0.02

+0.3

-0.01

264

-0.5

-0. 09

-1.2

+0.04

+0.3

+0.01

+0.2

-0.02

270

-1.1

-0.07

-0.9

+0.07

+0.3

0.00

0.0

-0.03

276

-1.3

-0.02

-0.4

+0.09

+0.3

0.00

-0.2

-0.02

282

-1.3

+0.01

+0.2

+0.09

+0.2

-0.02

-0.3

-0.01

288

—1.2

+0. 05

+0.7

+0.08

0.0

-0.04

-0.3

0.00

294

-0.7

+0.08

+1.1

+0.05

-0.2

-0.02

-0.3

+0.01

300

-0.3

+0. OS

+ 1.3

+0.02

-0.3

-0.01

-0.2

+0.02

306

+0.2

+0. 07

+ 1.3

-0. 02

-0.3

0. 00

0.0

+0.03

312

+0.5

+0.04

+ 1.0

-0.04

-0.3

+0. 01

+0.2

+0.02

318

+0.6

+0. 02

+0.8

-0.06

-0.2

+0.02

+0. 3

+0.01

324

+0.8

+0. 02

+0.3

-0. 06

0.0

+0. 03

+0.3

0.00

330

+0.9

0.00

+0.1

-0.04

+0.2

+0.02

+0.3

-0.01

336

+0.8

-0. 02

-0.2

-0.03

+0.3

+0.01

+0.2

-0.02

342

+0.6

-0.02

-0.3

-0.01

+0.3

0.00

0.0

-0.03

348

+0.5

-0.02

-0.3

-0.01

+0.3

-0.01

-0.2

-0.02

354

+0.3

-0.02

-0.4

-0. 02

+0.2

-0.02

-0.3

-0.01

360

+0.3

-0.01

-0.5

-0.01

0.0

-0.03

-0.3

0.00

\ndz, 8 log r, and k/cos i are to be computed in the form Si at sin ig+Ii &( cos ig-i-cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

26:; -

Tables of (128) Nemesis — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 1„) IN JULIAN YEARS.

ndz

u log r

it/cos i

9

Unit of

0. mil

Unit of c

=0.00001

Unit of

•=0?001

c

Diff. for 1°

c

Dili', for 1°

c

Diff. for 1°

O

0

-2. 85

0.00

+0.06

-0. 02

+0.68

+0.02

0

-2.85

0.00

-0.05

-0.02

+0.81

+0.02

12

-2.81

0.00

-0.18

-0.02

+0. 93

+0.02

18

-2. 75

+0.01

-0.30

-0.02

+ 1.04

+0.02

24

-2. 65

+0. 02

-0.42

-0.02

+ 1.12

+0.01

30

-2.52

+0.02

-0.54

-0.02

+ 1.20

+0.01

36

-2.36

+0. 02

ii i,::

-0.02

+1.26

+0.01

42

-2. 18

+0.03

-0.73

-0.02

+ 1.28

0.00

48

—1.97

+0.04

-0.81

-0.01

+ 1.30

0.00

54

-1.74

+0. 04

-0.88

-0.01

+1.31

0.00

liO

-1.49

+0. 04

-0.93

-0.01

+ 1.28

0.00

66

-1.22

+0.04

-0. 99

-0.01

+ 1.25

-0.01

72

-0. 95

+0. 05

-1.02

-0.00

+1.20

-0.01

78

-0.66

+0.05

-1.04

-0.00

+1.15

-0.01

84

-0.37

+0T05

-1.05

-0.00

+ 1.06

-0.02

90

-0. 09

+0. 05

-1. 05

-0.00

+0.96

-0.02

96

+0.20

+0. 05

-1.04

-0.00

+0.87

-0.02

102

+0. 50

+0. 05

-1.01

-0.00

+0.78

-0.02

108

+0. 76

+0.04

-0.98

+0.01

+0.64

-0.02

114

+ 1.03

+0.04

-0.94

+0.01

+0.52

-0.02

120

+1. 28

+0.04

-0.89

+0.01

+0.41

-0.02

126

+ 1. 52

+0.04

-0.83

+0.01

+0.28

-0.02

132

+ 1.74

+0.04

-0.77

+0.01

+0. 15

-0.02

138

+1. 95

+0.03

-0.70

+0.01

+0.01

-0.02

144

+2. 12

+0.03

-0.61

+0.01

-0.13

-0.02

150

+2.28

+0.02

-0. 53

+0.01

-0.26

-0.02

156

+2.40

+0. 02

-0. 45

+0.02

-0.39

-0.02

162

+2.52

+0.02

-0.35

+0. 02

-0. 52

-0.02

168

+2.60

+0.01

-0.26

+0.02

-0. 65

-0.02

174

+2.66

+0.01

-0.15

+0.02

-0.77

-0.02

180

+2.69

+0.01

-0.06

+0.02

-0.88

-0.02

186

+2.69

0.00

+0.04

+0.02

-0.99

-0.02

192

+2.67

0.00

+0. 14

+0.02

-1.09

-0. 02

198

+2.61

-0.01

+0.24

+0.02

-1.18

-0.01

204

+2.53

-0.01

+0.33

+0.02

-1.26

-0.01

210

+2.44

-0.02

+0.43

+0.02

-1.34

-0.01

216

+2. 30

-0.02

+0. 52

+0.02

-1.40

-0.01

222

+2. 16

-0.03

+0. 61

+0.01

-1.44

-0.01

228

+ 1.97

-0. 03

+0.69

+0.01

-1.48

-0.01

234

+ 1.78

-0. 03

+0.76

+0.01

-1. 51

0.00

240

+ 1. 56

-0.04

+0.83

+0.01

-1. 52

0.00

246

+ 1.32

-0.04

+0.89

+0.01

1 51

0.00

252

+ 1. 07

-0.04

+0.94

+0.01

-1. 50

0.00

258

+0.80

-0.04

+0.98

+0.01

-1.47

+0.01

264

+0.53

-0. 05

+1.02

+0.01

-1.42

+0.01

270

+0. 25

-0. 05

+1.05

0.00

-1.36

+0.01

276

-0.04

-0. 05

+ 1.05

0.00

-1.29

+0.01

282

-0.36

-0. 05

+ 1.05

0.00

-1.22

+0. 02

288

-0.62

-0. 05

+1.04

0.00

-1.10

+0. 02

294

-0. HI

-0.05

+ 1.03

0.00

-0. 98

+0.02

300

-1.20

-0. 05

+ 1.00

-0.01

-0.87

+0.02

306

-1.46

-0.04

+0.94

-0.01

-0.74

+0.02

312

-1.72

-0.04

+0.89

-0.01

-0. 59

+0.03

318

-1.95

-0.04

+0.82

-0.01

-0. 43

+0.03

324

-2.16

-0. 03

+0.74

-0. 02

-0.27

+0.03

330

-2. 35

-0.03

+0.64

-0. 02

-0.12

+0.03

336

-2. 50

-0. 02

+0. 54

—0.02

+0.05

+0.03

342

-2.64

-0.02

+0.42

-0. 02

+0.22

+0.03

348

-2. 74

-0.02

+0.32

-0.02

+0.37

+0.02

354

-2.82

-0.01

+0.18

-0. 02

+0.52

+0.03

360

-2. 85

0.00

+0.06

-0.02

+0.68

+0.02

[ndz, 3 log r, and u/cos i are to be computed in the form Si ai sin ig+Si b% cos ig+cT.]

264

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {128) Nemesis — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B'

C"

log sin a

log sin b

log sin c

1872. 0

O

106. 1307

O

IS. 9491

o

3. 3092

9. 99755

9. 95800

9. 63598

3

.1447

.9631

. 3217

55

01

596

4

.1587

.9771

.3342

55

01

594

1875

106. 1728

18.9910

3. 3467

9. 99755

9. 95802

9. 63592

6

.1868

19. 0050

. 3592

55

02

589

7

.2008

.0190

.3717

55

03

587

8

.2149

.0330

.3842

55

03

585

9

.2289

.0470

.3967

55

04

583

1880

106. 2429

19. 0610

3. 4092

9. 99755

9. 95804

9. 63581

1

. 2570

. 0750

.4217

55

05

579

2

.2710

.0890

.4342

55

05

577

3

.2850

.1030

.4467

55

06

574

4

.2990

. 1170

. 4592

55

06

572

1885

106. 3131

19. 1310

3.4717

9. 99755

9. 95807

9. 63570

6

.3271

. 1450

.4842

55

07

568

7

.3411

. 1590

. 1967

55

08

565

8

. 3552

. 1730

. 5092

55

09

563

9

.3692

. 1870

.5217

55

09

561

1890

106. 3832

19. 2010

3. 5342

9. 99755

9. 95810

9. 63559

1

.3973

. 2150

. 5467

55

10

557

2

.4113

.2290

. 5592

55

11

555

3

. 4253

. 2129

. 5717

55

11

553

4

.4393

. 2569

. 5842

55

12

550

1895

106. 4534

19. 2709

3. 5967

9. 99755

9. 95812

9. 63548

6

.4674

. 2849

. 6092

55

13

546

7

.4814

. 2989

. 6217

55

13

544

8

. 4955

.3129

. 6312

55

14

542

9

. 5095

.3269

Ollis

55

14

■ 540

1900

106. 5235

19. 3409

3. 6593

9. 99755

9. 95815

9. 63538

1

.5376

. 3549

.6718

54

16

535

2

. 5516

.3689

.6843

54

16

533

3

5650

.3829

.6968

54

17

531

4

.5797

.3969

.7093

54

17

529

1905

106. 5937

19.4109

3. 7218

9. 99754

9. 95818

9. 63527

(i

. 6078

.4249

.7343

54

18

525

7

.6218

I3S9

.7468

54

19

522

8

. 6358

. 4529

. 7594

54

19

520

9

. 6499

.4669

. 7719

54

20

518

1910

106. 6639

19.4810

3. 7844

9.99754

9. 95820

9.63516

1

.6780

. 1950

.7969

54

21

514

2

.6920

. 5090

.8094

54

21

512

3

. 7060

. 5230

.8219

54

22

510

4

. 7201

. 5370

s:;n

54

22

503

1915

106. 7341

19.5510

3. 8470

9. 99754

9. 95823

9. 63505

0

. 7182

. 5650

. 8595

54

23

503

7

. 7622

. 5790

. 8720

54

24

501

8

. 7762

. 5930

. 8845

54

24

499

9

. 7903

.6070

. 8970

54

25

497

1920

106. 8043

19.6210

3. 9096

9. 997:. 1

9. 95825

9. 63495

1

.8184

. 6350

. 9221

54

26

492

2

. 8324

. 6490

. 9346

54

26

490

3

.8464

. 6631

.9471

54

27

488

4

. 8605

. 6771

. 9596

54

27

486

1925

106. 8745

19.6911

3. 9721

9. 99754

9. 95828

9. 63484

6

.8886

. 7051

. 9847

54

29

482

7

. 9026

. 7191

3. 9H72

54

29

4S0

8

.9166

. 7331

4. 0097

54

30

477

9

. 9307

. 7(71

. 0222

54

30

475'

1930

L06. 9447

19.7611

4. 0347

9. 99754

9. 95831

9. 63473

Year

log cos a

log cos b

log COS ('

1S72.0
1930. 0

9. 025 n
9. 026 n

9. 623 n

9. 621 n

9. 955
9. 955

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLES OF (133) CYRENE.

265

MEAN ELEMENTS.

Epoch, 1896, Dec. L0.0, M. T. Berlin=1896.942, M. T. Berlin.

0 / //

#,,=204 8 9=204?1357

w=285 19 53=285.3314]

&=32] 10 39=321. 1770 Mean equinox and eclipt

ic 1900.0.

i= 7 13 53= 7. 2315 1

<p= 7 49 26= 7.8239

,1= 661". 6605= 0.18379457

The elements are based on oppositions extending from 1873 to 1S94 and on the perturbations of the first

order by Jupiter, as given on page 266.

AUXILIARY QUANTITIES.

log a=0.48625 log 57. 2957 e=0. 89207 lo„ /
log 1 9. L3395 log p =0.47812 "V

~=9. 94051

+e

TABLE I.— MEAN ANOMALY (g).

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Month

g

Yea r

9

Year

9

t JO. 0
Jan. { . „

[ 0. 00000

O

O

1873

36. 85220

1902

183. 42049

\1.0

4

103. 93722

3

250. 50551

Feb.{°;°

1 5. 69763

5

171. 02224

B 4

317. 77!:12

B (i

238. 29105

5

24. 85934

Mar. 0.0

10. 84388

7

305. 37607

6

91. 9^436

Apr. 0.0

16. 54151

8

12. 16108

7

L59. 02938

May 0.0

22. 05535

9

79.54610

B 8

226. 29819

June 0.0

27. 75298

B1880

146.81492

9

293. 38321

July 0.0

33. 26682

1

213. 89993

1

0. 46823

Aug. 0.0

38. 9(1145

2

280.98495

1

67. 55324

Sept. O.o

44.66208

3

348.06997

B 2

134.82206

Oct. 0. 0

50. 17592

B 4

55. 33878

3

201.90708

Nov. 0.0

55.87355

5

122.42380

4

268. 99209

Dei'. 0.1

61. 38739

6

7
B 8

189 ..0882
256.59384
323. 86265

,5

336 (17711

B (i

7

43. 34592
110.43094

9

30.94767

8

177.51596

( hange for n days"

IS! Ml
1

98. 03269
lli5. 11770

9
B 1920

244.60098
311. 86979

n

9

IX

9

B 2

232.38652

1

18. 95481

3

299.47154

2

86. 03983

4

6. 55655

3

153. 12484

O

O

5

73.64157

B 4

220. 39366

1

0. 18379

16

2. !I4064

B 6

1 10.91038

5

287. 47868

2

0. 36758

17

3. 12443

7

207. 99540

6

354.56369

3

0. 55137

is

3. 30822

8

275.08042

7

61.64S71

4

0.73516

19

3.49201

9

342. L6544

B 8

128.91752

5

0. 91895

20

3. 67580

1900

49. 25046

9

L96. 00254

6

1. II 1271

21

3. 85959

1

116.33547

1930

263.08756

7

8

9

10

1.28653
1. 47032
I.li5411
1. s:(790

22
23
24

25

1 04338

1. 22717
4.41096
4. 59475

Note. When g is used as an argument of the perturbations

add to the g of this table J- = -— -0=a?0139. For explanation

11

2.02169

26

1. 77854

see page 203.

12

2.20548

27

4. 96233

13

2. 38927

28

5. 14012

14

2. 57306

29

5. 32991

15

2. 75685

30 5.51370

a ]

or days dm

ing .la ntiary and

Febr

uarj nf leap

year subtract one

day

lefore enteric

g this table.

266

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (133) Gyrene— Continued.

PERTURBATIONS

ndz

;

u/cos i

Arg.
ig—i'g'

sin

cos

sin

cos

sin

cos

i V

//

//

//

//

//

ii 0

- 10

— 8

0 0

0. 06nt

- 0.74nt

+ 1 o

+ 8

+1

l.SOnt

17. 25nt

8. 62nt

0. 90nt

+11. 34nt

+ 3. 49nt

+2

1

+ 1

— 1

+ 2

+ 2

+ 0. 06nt

0. 60nt

0. 60nt

- 0. 06nt

+ 0.79nt

+ 0. 24nt

+3

0. 04 nt

0. 06nt

+ O.OSnt

+ 0. 03nt

+4 0

O.Olnt

+ O.Olnt

-1 +1

2

+ 1

1

1

+ 3

- 6

0

+ 68

54

9

+ 13

+16

-20

+ 1

r 240

+ 287

Mi

- 71

-17

+ 13

+ 2

+ 10

+ 7

6

— 7

-11

+ 5

+3 +1

4- 1

1

+ 1

1

-1 +2

+ 1

_ 2

+ 2

+ 1

f 5

- 1

I)

+ 18

43

+ 22

+ 8

+65

-11

+ 1

-1110

+5920

+436

+ 87

-24

+ 8

+2

- 484

4-1900

+978

250

-59

-20

+ 3

21

+ 75

+ 75

4 21

- 1

+4

1

5

+ 8

+ 2

+5 +2

+ 1

0 +3

- 3

+ 3

1

- 1

- 5

- 3

+ 1

78

+ 74

- 23

- 23

-13

-11

+2

+ 486

- 405

-150

-182

-21

-24

+3

+ 97

46

- 32

- 68

+ 3

+ 6

+ 4

+ 8

3

- 3

9

2

+5 +3

+ 1

1

+1 +4

19

+ 5

1

- 9

-11

+2

+ 875

68

-118

+ 1

+ 7

+3

f 370

+ 84

+ 44

-198

- 5

+29

+4

1

5

- 3

3

+ 1

+5 +4

I

1

1

+ 1 +5

+ 3

+ 2

+ 2

+ 72

4- 53

- 12

f 20

- 6

+ 6

+3

- 163

- 193

- 82

+ 68

+ 14

-14

+4

— 22

- 42

- 29

+ 15

+ 5

— 4

+5

1

+ 2

+ 1

+ 1

+6 +5

+ 1

+ 1

. +2 +6

+' 1

+ 10

3

+3

14

- 169

- 34

+4

+ 15

85

- 46

8

J- 9

+ 2

+5

4

+ 7

+ 4

+ 3

- 1

+6 +6

+ 1

— 1

+3 +7

4- 36

71

+ 6

+ 6

+ 1

+ 1

+4

93

+ 81

+ 38

+ 44

- 6

— 6

+5

17

+ 8

+ 6

+ 11

- 1

+6 +7

+ 3

2

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHXER.

267

PERIODIC TERMS.

Tables of {133) Oyrene — Continued.

TABLE U.—nSz.

Unit of a and 6=09001.

i

0

1

2

9'

bo

Diff.forl0

Oj

Diff.forl0

b,

Diff.forl0

a2

Diff.forl0

h

Diff.forl0

0

0

+ 3.5

-0. 45

- 262.0

+58. 78

+ 1715.0

+ 10. 82

+264. 8

+12. 68

+411. 1

-20. 85

3

- 83.7

+59. 74

+1738. 2

+ 4.58

+295. 7

f 8.07

+346. 8

-21. 53

6

+ 1.0

-0.40

+ 96.4

+60. 04

+ 1742.5

- 1.72

+313. 2

+ 3. 55

+281. 9

-21. 20

9

+ 276.5

+59. 66

+ 1727. 9

- 7. 98

+317. 0

- 0.65

+219.6

-19. 98

12

- 1.3

-0. 35

+ 454.4

+58. 59

+1694. 6

1 1 23

+309. 3

- 4.38

+162. 0

-17.90

15

+ 628.0

+56. 86

+1642. 5

-20. :r,

+ 290. 7

- 7.48

+112. 2

-15. 15

18

-3.2

-0.28

+ 795.5

+54. 52

+ 1572. 5

-26. 23

+264. 4

- 9.72

+ 71. 1

-11.85

21

+ 955. 1

+51. 56

+ 1485. 1

-31. 82

+232. 4

-11. 15

+ 41. 1

- 8.20

24

- 4. 7

-0.23

+ 1104.8

+47. 94

+ 1381.6

-37. 08

+ 197. 5

-11. 63

+ 21.9

- 4.42

27

+ 1242. 7

+43. 80

+ 1262.6

-41. 97

+ 162.6

—11. 25

+ 14.6

- 0.72

30

- 6.0

-0. 19

+ 1367. 6

+39. 22

+ 1129.8

-46. 37

+ 130.0

- 9.95

+ 17.6

+ 2.67

33

+ 1478.0

+34. 20

+ 984.4

-50. 26

+ 102.9

- 7.83

+ 30.6

+ 5.60

36

- 7.0

-0. 12

+1572. 8

+28. 74

+ 828. 2

-53. 60

+ 83.0

- 5.03 '

+ 51.2

+ 7.93

39

+1650. 4

+22. 92

+ 662.8

-56. 34

+ 72.7

- 1.76

+ 78.2

+ 9.53

42

— 7.4

-0.07

+ 1710.4

+16. 92

+ 490. 2

-58. 42

+ 72. 4

+ 1.80

+108. 4

+10. 18

45

+1752. 0

+ 10. 72

+ 312.3

-59. 85

+ 83.5

+ 5.48

+ 139. 3

+ 9.93

48

— 7.8

-0.04

+ 1774.7

+ 4.33

+ 131. 1

-60. 66

+ 105.3

+ 9.07

+ 168.0

+ 8.73

51

+ 1778. 0

- 2.02

51.6

—60. 75

+ 137. 9

+12. 32

+ 191.7

+ 6. 70

54

- 7.9

0. 00

+1762. 6

- 8.33

- 233.4

-60. 14

+ 179.2

+15. 00

+208. 2

+ 3.78

57

+1728. o

-14. 60

- 412.4

-58. 88

+227. 9

+ 17.00

+214. 4

+ 0.20

60

— 7.8

+0.02

+1675.0

-20. 65

- 586.7

-56. 97

+281. 2

+18. 18

+209. 4

- 3.82

63

+ 1604.1

-26. 45

- 754.2

-54. 42

+337. 0

+18. 50

+191.5

- 8. 10

66

— 7. 7

+0.02

+ 1516.3

-32. 00

- 913.2

-51. 28

+392. 2

+ 17. 80

+160. 8

-12. 48

69

+ 1412. 1

-37. 15

-1061.9

-47. 62

+443. 8

+ 16.13

+ 116.6

— 16. 73

72

— 7.4

+0.03

+ 1293. 4

-41. 80

-1198.9

-43. 40

+489. 0

+ 13. 50

+ 60.4

-20. 68

75

+ 1161.3

-46. 00

-1322.3

-38. 68

+524. 8

+ 10.08

- 7.5

-24. 12

78

- 7.3

+0. 01

+ 1017.4

-49. 70

-1431.0

-33. 62

+549. 5

+ 5.87

- 84.4

-26. 82

81

+ 863. 1

-52. 84

-1524.0

-28. 23

+560. 0

+ 1.08

-168.4

—28. 67

84

- 7.3

-0.01

+ 700.4

-55. 36

-1600.4

-22. 53

+556. 0

- 4.03

-256. 4

-29. 55

87

+ '531. 0

-57. 24

-1659.2

-16.60

+535. 8

- 9.33

-345. 7

-29. 47

90

-7.4

-0. 05

+ 357.0

-58. 16

-1700.0

-10.52

+500. 0

-14. 63

-433. 2

—28. 30

93

+ ISO. 3

-59. 06

-1722.3

- 4.37

+448. 0

-19. 70

-515. 5

-26. 17

96

- 7.9

-0. 10

+ 2.6

-59. 10

-1726.2

+ 1.80

+381. 8

-24. 28

-590. 2

-23. 10

99

- 174.3

-58. 46

-1711.5

+ 7.90

+302. 3

-2S. 30

-654. 1

—19. 20

102

-8.6

-0. 14

- 348. 1

-57. 10

—1678. 8

+ 13.82

+212.0

-31. 58

-705.4

—14. 58

105

- 516.9

-55. 16

-1628. 4

+19. 60

+112. 8

-34.00

—741. 6

- 9.48

108

-9.6

-0.21

- 679.0

-52. 64

-1561. 2

+25. 14

+ 8.0

-35. 43

-762. 3

- 3.98

111

- 832.8

-49. 63

-1477. (1

+30. 37

- 99.8

-35. 90

-765. 5

+ 1.70

114

—11. 1

-0. 27

- 976.8

-46. 07

-1379.0

+35. 22

-207. 4

-35. 32

-752. 1

+ 7.32

117

-1109.2

-42. 03

-1266.3

+39. 67

-311. 7

-33. 84

-721. 6

+12. 76

120

-12. 8

-0.28

-1229.0

—37. 58

-1141.0

+43. 67

-410. 4

-31. 46

-675. 5

+17. 83

123

-1334.7

-32. 77

-1004.3

+47. 17

-500. 5

-28. 30

-614. 6

+22. 37

126

-14. 5

-0. 32

-1425.6

-27. 65

- 858.0

+50. 12

-580. 2

—24. 45

-541.3

+26. 25

129

-1500.6

-22. 26

- 703.6

+52. 56

-647. 2

-20. 06

-457. 1

+29. 42

132

-16.7

-0.37

-1559.2

-16. 63

- 542. 7

+54. 40

-700. 6

-15.28

-364. 7

+31. 78

135

-1600.4

Hi m;

- 377.2

+55. 66

-738. 9

-10. 30

—266. 4

+33. 28

138

-18.9

-0.38

-1624.4

- 5.05

- 208.8

+56. 32

-762. 4

- 5.25

-165. 0

+33. 87

141

-1630. 7

+ 0.78

- 39.3

+56. 40

-770. 4

- 0.25

- 63. 2

+33. 67

144

—21.2

-0.38

-1619.7

+ 6.62

+ 129. 6

+55. 87

-763. 9

+ 4.53

+ 37.0

+32. 78

147

-1591.0

+ 12.35

+ 295.9

+54. 74

-743. 2

+ 8.95

+133. 5

+31. 24

150

-23.5

-0.36

-1545.6

+ 17.86

+ 458. 0

+53. 02

—710. 2

+12. 90

+224. 4

+2S. 95

153

-1483.8

+23. 22

+ 614.0

+50. 77

-665. 8

+ 16.36

+307. 2

+26. 12

156

-25. 5

-0.29

-1406. 3

+28. 38

+ 762. 6

+4S. 00

-612.0

+ 19. 26

+381. 1

+22. 97

159

-1313. 5

+33. 15

+ 902.0

+44. 70

-550. 2

+21. 57

+415. 0

+ 19. 55

162

-27.0

-0.21

-1207. 4

+37. 50

+ 1030. 8

+40. 92

—482. 6

+23. 18

+498. 4

+15. 95

165

-1088. 5

+41.47

+1147. 5

+36. 74

-411. 1

+24. 20

+540. 7

+12.33

168

-28.0

-0.12

— 958.6

4-44. 98

+ 1251.2

+32. 18

-337.4

+24. 62

+572. 4

+ 8. 7S

171

- 818.6

+48. 08

+1340. 6

+27. 27

-263. 4

+24. 53

+593. 4

+ 5.40

174

-28.4

-0.01

- 670. 1

+50. 62

+1414. 8

+22. 03

-190.2

+23. 97

+604.8

+ 2. 27

177

- 514.9

+52. 56

+ 1472.8

+16. 60

-119.6

+23. 00

+607. 0

- 0.57

180

-28. 1

+0. 12

- 354.8

+53. 90

+ 1514. 4

+11.03

- 52.2

+21. 70

+601. 4

- 3. 05

[■nSz, 3 log r, and u/cos i are to be computed In the form £{ a, sin ig+Si bi cos ig+cT.]
89369°— vol 10—11 18

268 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (133) Gyrene — Continued.

TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6= 09001 .

i

0

1

2

g'

K

Diff.forl0

a,

Diff.forl0

b,

Diff.forl0

«2

Diff.forl0

b2

Diff.forl0

o

180

-28. 1

+0.12

- 354.8

+53. 90

+1514. 4

+11.03

- 52.2

+21. 70

+601. 4

- 3.05

183

— 191.5

+54. 66

+1539. 0

+ 5.32

+ 10.5

+20. 17

+588. 7

- 5.18

186

-27.0

+0. 25

- 26. 8 1

+54. 88

+1546. 3

- 0.48

+ 68.8

+18. 53

+570. 3

- 0.88

189

+ 137. 8

+54. 50

+1536. 1

- 6.22

+121. 8

+16. 86

+547. 4

- 8.25

192

- 25. 1

+0.38

+ 300.2

+53. 46

+ 1509.0

-11.87

+ 170.0

+15. 20

+520. 8

- 9.28

195

+ 458. 6

+51. 86

+1464. 9

-17.42

+213. 0

+13. 57

+491. 7

- 9.98

198

-22. 4

+0. 52

+ 611.4

+49. 67

+1404. 5

-22. 76

+251. 4

+12. 10

+460. 9

-10. 36

201

+ 756. 6 !

+46. 93

+1328. 3

-27. 87

+285. 6

+10. 80

+429. 5

1(1. 55

204

-IS. 9

+0. 65

+ 893.0

+43. 72

+1237. 3

-32. 65

+316. 2

+ 9.72

+397. 6

-10.00

207

+1018.9

+40. 00

+1132. 1

37. 02

+343. 9

+ 8.83

+365. 5

-10.72

210

—14.0

+0. 74

+ 1133.0

+35. 82

+ 1015.2

-40. 96

+369. 2

+ 8. 15

+333. 2

-10.70

213

+ 1233. 8

+31. 28

+ 886. 6

-44. 50

+392. 8

+ 7.63

+300. 9

-10. 83

216

-10.0

+0.82

+1320. 7

+26. 42

+ 74S. 2

-47. 53

+415. 0

+ 7.28

+268. 2

-11.02

219

+1392. 3

+21. 25

+ 601.4

-50.04

+436. 5

+ 7.00

+234. 8

-11.30

222

- 4.S

+0.88

+ 1448. 2

+15. 82

+ 448.0

-51. 94

+457. 0

+ 6.72

+200. 0

-11.90

225

+1487. 2

+ 10. 20

+ 289.8

-53. 23

+476. 8

+ 6.38

+163.4

-12. 00

228

+ 0.6

+0.91

+ 1509.4

+ 4. 52

+ 128.3

54.04

+495. 3

+ 5.97

+124. 4

-13.45

231

+1514. 3

- 1.20

— 34.4

-54. 18

+512.6

+ 5.40

+ 82. 7

-14.43

234

+ 6.1

+0.92

+1502. 2

- 6.92

- 196.8

-53. 76

+527. 7

+ 4.58

+ 37.8

-15. 05

237

+1472. 8

-12. 57

- 357.0

■52. 73

+540. 1

+ 3. 52

- 11.2

-16. 95

240

+11.6

+0. 90

+ 1426.8

-18. 03

- 513.2

—51. 09

+548. 8

+ 2. 12

- 63.9

-18. 15

243

+1364. 6

-23. 30

- 663.5

-48. 90

+552. 8

+ 0.40

-179. 2

—19. 22

246

+ 16.9

+0. 83

+ 1287.0

-28. 33

- 806.6

-46.22

+551. 2

- 1.63

—157. 2

—20. 22

249

+ 1194.6

-33.06

- 940.8

-43.03

+543. 0

- 4.02

-241. 4

-21. 00

252

+21.6

+0.73

+ 1088. 6

-37. 42

-1064. 8

-39. 36

+527. 1

- 0.73

-305. 2

-21. 43

255

+ 970. 1

-41. 36

-1177.0

-35. 20

+502. 6

- 9.63

-370. 0

-21.48

258

+25. 7

+0.64

+ 840.4

-44. 88

-1270.0

-30. 68

+469. 3

-12. 68

-434. 0

-21.00

261

+ 700.8

-47. 90

-1361.1

-25. 90

+426. 5

-15.82

-496.0

-20. 07

264

+29.3

+6.52

+ 553.0

-50. 40

-1431.4

-20. 75

+374. 4

-19. 03

-554. 4

-IS. 63

267

+ 398.4

52. 36

-1485. 6

-15.36

+312.3

-22. 12

-607. 8

-10.63

270

+32. (1

+0. 38

+ 238 8

-53. 76

-1523. 6

- 9.83

+241. 7

- 24. 90

-054. 2

I:; 9s

273

+ 75.8

-54.60

-1544. (i

- 4.17

. +162.9

-27.38

-691. 7

-10.80

276

+33.9

+0. 25

- 88.8

54.85

-1548. 6

+ 1. 55

+ 77. 4

-29. 43

-719.0

- 7.17

279

- 253.3

-54. 55

-1535.3

+ 7. 27

- 13.7

-30. 96

-734. 7

- 3.15

282

+35.0

+0. 1 1

- 416. 1

-53. 65

-1505.0

+12.95

-108.4

-31.88

-737.9

+ 1.27

285

- 57.-.. 2

■52.08

-1457. 6

+ 18. 53

-205. 0

-32. 10

-727. 1

+ 5.90

288

+35. 2

-0. 02

- 728. 6

-49. 95

-1393. 8

+23. 90

-301.0

-31.50

-702. 5

+10. 62

291

- 874.9

-47. 35

-1314.2

+29. 03

-394. 0

-30. 15

-063. 4

+15.32

294

+34.7

-0. 15

-1012.7

-44.22

-1219.6

+33. 92

-481. 9

-28. 03

-610. 6

+19. 85

297

-1140.2

-40. 55

-1110.7

+38.46

-562. 2

-25. 15

-544. 3

+24. 07

300

+33.4

-0. 27

-1256.0

-36. 42

- 988.8

+42. 62

-632. 8

—21. 53

-466. 2

+27. 80

303

-1358. 7

-31.87

- 855.0

+46. 35

-691.4

-17.30

-377. 5

+30. 95

306

+31. 5

-0.38

-14-17. 2

-26. 93

- 710. 7

+49. 56

-736. 6

-12. 52

-280. 5

+33. 42

309

-1520. 3

-21. 70

- 557. 6

+52. 25

-766- 5

- 7.37

-177.0

+35. 06

312

+28.9

-0. 45

-1577.4

-16.18

- 397.2

+54. 44

-780. 8

- 1.93

- 70.1

+35. 80

315

-1017.4

-10.43

- 231.0

+50. 04

-778. 1

+ 3. 00

+ 37.8

+35. 65

318

+26.1

-0.49

-1640.0

- 4. 55

- 61.0

+57. 02

-759. 2

+ 9.03

+143. 8

+34. 50

321

-1644. 7

+ 1.42

+ 111.1

+57. 38

-723. 9

+14. 20

+244. 8

+32. 47

324

+23.0

-0.53

-1631.5

+ 7.43

+ 283. 3

+57. 12

-674.0

+ 18.95

+338. 6

+29. 64

327

-1000. 1

+13. 42

+ 453.8

+56. 22

-610. 2

+23. 16

+422. 6

+26. 04

330

+19.7

-0. 56

-1551.0

+19.28

+ 620. 6

+54. 66

-535. 0

+26. 65

+494. 8

+21. 65

333

—1484.4

+25. 02

+ 781.8

+52. 50

-450. 3

+29. 30

+552. 5

+ 16.75

336

+ 10.3

-0.58

-1400.9

+30. 52

+ 935.6

+49. 75

-359. 2

+30. 98

+595. 3

+11. 52

339

-1301.3

+35. 66

+1080. 3

+46. 46

•264. 1

+31.70

+621. 6

+ 6. 13

342

+12.8

-0.56

-1186.9

+40. 45

+1214.4

+42. 64

-169.0

+31. 38

+632. 1

+ 0.78

345

-1058.6

+44. 82

+1336. 1

+38. 30

76. 1

+30. 13

+626. 3

- 4.38

348

+ 9.6

-0.53

- 918.0

+48. 73

+1444.2

+33.48

+ 11.8

+27. 96

+605. 8

- 9. 10

351

- 766 1'

+52. 15

+ 1537. 0

+28. 26

+ 91.7

+24. 83

+571. 7

-13.23

354

+ 0.4

-0.51

- 605. 1

+54. 96

+1613.8

+22. 72

+ 161.8

+21. 15

+526. 4

-16.03

357

- 430.4

+57. 18

+ 1673.3

+ 10. 86

+219. 6

+17. 16

+471. 9

-19. 22

360

+ 3.5

-0. 45

- 262.0

+58. 78

+1715.0

+ 10. 82

+264. 8

+12. 68

+411. 1'

-20. 85

[niz, d log r, and u/cos i are to be computed in the form li m sin ig+Ii bi cos ig+cT.]

PERIODIC TERMS.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (133) Cyrene— Confirmed.
TABLE II.— noz— Continued.

2<;<j

Unit of a and 6=09001.

i
9'

3

i

3

°3

Diff. for ]°

h

Diff. for 1°

9'

":i

Diff. tor 1°

h

Diff. for 1°

O

0

+ 82. 6

-10. 17

- 89.2

5 112

O

ISO

+100. 6

+ 5.35

+ 85. 0

- 7.82

3

+ 50. 7

-10.60

- 98.8

1 66

183

+ 114.0

+ 3. 53

+ 59. 7

- 8.82

6

+ 19. (i

- 9. 93

- 99. 2

+ 1.47

186

+ 121.8

+ 1.50

+ 32.1

- 9.33

9

- 8. 9

- 8. 40

- 90.0

+ 4. 20

189

+ 1 23. 0

- 0.67

+ 3.7

- 9.37

L2

- 31. 1

- 6. 13

— 74.0

+ 6. 18

192

+ 117. s

- 2.82

- 24.1

- 8.97

15

- 45. 7

- 3. 17

- 52. !l

+ 7. 33

1115

+106. 1

- 4.83

- 50. 1

- 8.08

18

- 52. 2

- ii. 65

- 30.0

+ 7. 10

l!IS

+ 88.8

- 6.62

- 72.6

— 6.62

21

- 49.6

+ 1.93

S. 5

+ 0.63

2111

+ 66.4

- 8.00

- 89.8

— 4.77

24

- 40.6

+ 3.87

+ 9.8

+ 5.05

204

+ 40.8

- 8. 85

-101.2

- 2. 65

27

- 26. 1

+ 5. 17

+ 21.8

+ 2. 93

2(17

+ 13.3

- 9. 17

-105.7

- 0.40

30

- 9. 6

+ 5. 63

+ 27.4

+ 0. 52

210

- 14.2

- 8.90

-103.6

+ 1.87

33

+ 7.4

+ 5. 28

+ 24.9

1.S5

213

- 40. 1

- 8. 10

— 94.5

+ 4.02

3(5

+ 22. 1

+ 3.97

+ 16.3

;;. 85

216

- 62. 8

- 6. 75

- 79.5

+ 5.88

39

+ 31. 2

+ 2.02

+ 1.8

5. 28

219

- SO. 6

- 5.03

- 59.2

+ 7.38

42

+ 34.2

- o, 35

- 1 5. 1

- 5.83

222

05.11

- 3.03

- 35. 2

+ 8.33

45

+ 29. L

- 2. 7S

- 33.2

- 5.58

225

- 98. s

- 0.87

9.2

+ 8.75

48

+ 17.5

- 4. lis

- 48.9

- 4.38

228

- 98.2

+ 1.33

+ 17.3

+ 8.60

51

- 0.8

- 6. lis

- 511. 5

- 2.52

251

- 90.8

+ 3.40

+ 42. 4

+ 7.95

54

- 22. 6

— 7. 65

- 64.0

- 0.03

234

— 77.8

+ 5. 17

+ 65.0

+ 6.83

57

- 46.7

- 7.83

- 59. 7

+ 2.75

237

- 59.8

+ 6.60

+ 83. 1

+ 5.42

60

- 69. 6

— 6. SS

— 47.5

+ 5.47

240

- 38. 2

+ 7.62

+ 97.5

+ 3.68

63

- ss.o

- 5. L5

- 26.9

+ 7.85

243

- 14. 1

+ 8.23

+105. 5

+ 1.78

66

-100.5 '

- 2. 03

- 0.4

+ 9.60

246

+ 11.2

+ 8.42

+108. 2

- 0.07

69

-103.8

+ 0. in

+ 30. 7

+10. 53

249

+ 36. 4

+ 8.18

+ 105.1

- 1.90

72

- 98. 1

+ 3.63

+ 62.8

+10. 38

252

+ 60.3

+ 7. 58

+ 96.8

- 3. 63

75

- 82.0

+ 6. 78

+ 93.0

+ 9.30

255

+ 81.9

+ 6. 72

+ 83.3

— 5.20

78

- 57.4

+ 9. 58

+118.6

+ 7. 23

258

+100.6

+ 5.55

+ 65.6

- 6.48

81

- 24.6

+ 11.70

+ 136.4

+ 4.47

261

+ 115.2

+ 4. 17

+ 44.4

- 7.53

84

+ 12.8

+ 12. 82

+145. 4

+ 1.05

264

+ 125.6

+ 2.63

+ 20.4

- 8.33

87

+ 52. 3

+12.97

+142. 7

- 2.58

267

+ 131.0

+ 0.95

5. 6

- 8.88

90

+ 90 6

+12.03

+129. 9

- 6.07

270

+ 131.3

ii 83

- 32.9

- 9.17

93

+124.5

+10. 22

+106. 3

9. 25

273

+ 126.0

- 2. (is

- 60.6

- 9.08

96

+ 151.9

+ 7. 52

+ 74.4

LI. 80

276

+ 115.2

- 4.60

- 87. 4

- 8.63

99

+169. 6

+ 4. 22

+ 35. 5

-13.53

279

+ 98. 1

- 6.47

- 112. 4

- 7.80

102

+ 177.2

+ 0.57

6.8

-14. IS

282

+ 76.4

- 8.17

-134.2

- 6.55

105

+ 173.0

- 3. 10

- 49. 6

-13.90

285

+ 49.4

11.67

-151.7

- 4.93

108

+158.6

— 6. 45

- 90.2

-12.66

2ss

+ 18.4

10.95

-I65.S

- 2.90

111

+134. 3

- 9.33

-125, 6

-10.66

291

- 16.5

-11.83

-169. 1

- ii 53

114

+ 102. 6

-11.56

-154.2

- 8.00

294

52. 6

-12. 10

- 167.(1

+ 2.15

117

+ 64.9

-13.05

-173. 6

- 4.93

297

- ss. o

-11.75

-156. 2

+ 4.97

120

+ 24. 3

-13. 58

-183.8

1 67

300

1 !3 1

-10.67

-137.2

+ 7. 73

123

- 16.6

-13.38

-183.6

+ 1.57

303

152 !i

- 8.92

-109.8

+10. 27

126

- 56.0

-12.42

-174.4

. + 4. 50

306

-176.6

- 6.43

- 75.6

+ 12.40

129

- 91. 1

-III. S3

-156. 6

+ 7.03

309

191.5

- 3.40

- 35.4

+13. 93

132

-121.0

- 8. 78

-132.2

+ 9.02

312

■197.0

+ 0.02

+ 8.0

+14. 62

135

-143. 8

- 6. 10

-102.5

+ 10.47

315

-191.4

+ 3. 57

+ 52. 3

+14.43

138

-159.4

- 3.88

(ill 1

+ 11. 28

3 IS

175.6

+ 7.07

+ 94.6

+13. 28

141

-167.1

- 1.36

- 34. 8

+11. 55

321

-149.0

+ 10.23

+132.0

+11.28

144

-167. 6

+ 1.02

0. 1

+11.26

324

-114.2

+ 12.78

+162. 3

+ 8.38

147

-161.0

+ 3. 23

+ 32. S

+ 10. 53

327

- 72.3

+14. 53

+182. 3

+ 4.90

150

-148. 2

+ 5. 17

+ 63.1

+ 8.57

330

27.0

+15. 20

+191.7

+ 1.02

153

-130. 0

+ 6.77

+ 84.2

+ 7.98

333

+ 18.9

+14.86

+188. 4

- 2.90

156

-107.0

+ S.02

+111.0

+ 7.18

336

+ 62.2

+13.42

+174.3

- 6.55

159

- 81.9

+ 8.93

+127. 3

+ 4.53

339

+ 99.4

+11.06

+ 149. 1

- 9.68

162

- 54.0

+ 9.52

+ 138. 2

+ 2.68

342

+ 128.6

+ 7.88

+110.2

-11.97

165

- 24.8

+ 9.77

+143. 4

+ 0.77

345

+ 146. 7

+ 4.27

+ 77.3

-13.33

IDS

+ 4.6

+ 9.62

+ 142.8

- 1.20

348

+ 154. 2

+ 0.48

+ 36.2

-13.53

171

+ 32.9

+ 9.07

+136.2

- 3. 15

351

+149. 6

- 3. 17

-3.9

-12. 72

174

+ 59.0

+ 8.17

+123.9

- 4.93

354

+ 135.2

- 6.32

- 40.1

-10.80

177

+ 81.9

+ 6.93

+ 106. 6

- 6.48

357

+ 111.7

- 8.77

- 68.7

- 8.18

180

+ 100. 6

+ 5.35

+ 85. 0

- 7.82

360

+ 82.6

-10. 17

- 89.2

- 5.02

[ndz, i log r, and u/cos i are to be computed in the form Ii at sin ig+Ii bi cos ig+cT.]

270 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (133) Gyrene— Continued.
TABLE II.— noz— Continued.

PERIODIC TERMS.

Unit of a and 6=09001.

i

4

5

6

I

Diff.

b4

Diff

Diff.

h

Diff.

Diff.

h

Diff.

9'

«4

for 1°

for 1°

«5

for 1°

for 1°

"6

for 1°

for 1°

O

0

-27.0

-0.80

-13.2

+3.22

-6.3

+0.47

+4.5

+0.68

+ 1.1

0.00

0.0

-0.12

0

25 it

+ 1. 27

+ 5.0

+2. 58

-2.0

+0.81

+7.6

+0.19

+0.8

-0.08

-0.7

-0.09

12

-13.8

+2.17

+ 16.0

+0.95

+3.4

+0.74

+6.8

-0.36

+0.2

-0. 12

-1.1

-0.02

18

- 1.4

+1.76

+ 16. 4

-0. 62

+6.9

+0. 32

+3.3

-0.73

-0.6

-0.10

-0.9

+0.06

24

+ 6.0

+0.63

+ 10. 2

-1.25

+7.3

-0.22

-2.0

-0.79

-1.0

-0.03

-0.4

+0.11

30

+ 6.2

-0.44

+ 3.3

-0.78

+4.3

-0. 66

-6.2

-0.45

-1.0

+0. 05

+0.4

+0.12

30

+ 2.2

-0.65

+ 0.8

+0.02

-0.6

-0.81

-7.4

+0.10

-0.4

+0.10

+1.0

+0.05

42

0.0

+0.07

+ 3.5

+0.71

-5.4

-0. 57

-5.0

+0.58

+0.2

+0.10

+ 1.0

-0.03

48

+ 3.0

+0.88

+ 7.8

+0.51

-7.4

-0. 03

-0.5

+0.78

+0.8

+0.07

+0.6

-0.08

54

+ 10. 5

+ 1.39

+ 8.0

-0.60

-5.8

+0.49

+4.4

+0.62

+1.0

-0.01

0.0

-0.11

60

+17.8

+0.80

+ 0.6

-1.S3

-1.5

+0.76

+7.0

+0. 15

+0.7

-0.08

-0.7

-0.08

66

+18.4

-0.77

- 12.6

-2.37

+3.3

+0.68

+6.2

-0.38

0.0

-0. 10

-1.0

-0.01

72

+ 8.6

-2.48

-25.2

-1.54

+6.6

+0.27

+2.4

-0.70

-0.5

-0.08

-0.8

+0.07 .

78

-9.6

-3.33

-28.9

+0.52

+6.5

-0.26

-2.2

-0.68

-0.9

-0.02

-0.2

+0.10

84

-28.3

-2. 56

-19.0

+2.75

+3. 5

-0.63

-5.8

-0.36

-0. 7

+0.05

+0.4

+0.08

90

-37.5

-0. 18

+ 2. 4

+4. 13

— 1. 1

-0.70

-6.5

+0. 14

-0.3

+0.08

+0.8

+0.03

96

-30.4

+2.61

+ 27. 2

+3.70

-4.9

-0.42

-4. 1

+0. 55

+0.3

+0.08

+0.8

-0.03

102

-7.7

+4.66

+43. 2

+ 1.31

-6.2

+0.02

+0.1

+0.66

+0.7

+0.03

+0.4

-0.08

108

+21.8

+4.74

+41.2

-1.92

-4.6

+0.44

+3.8

+0.46

+0.7

-0.02

-0.2

-0.08

114

+45.0

+2.56

+20.2

-4. 76

-0.9

+0.62

+5.6

+0.07

+0.4

-0.07

-0.6

-0.04

120

+50.0

-0.95

-12.2

-5.54

+2.9

+0.48

+4.6

-0.34

-0.1

-0.08

-0.7

+0.02

126

+33.6

-4.36

-41.6

-3.80

+4.9

+0. 12

+1.5

-0.57

-0.6

-0.04

-0.4

+0.06

132

+ 1.0

-6.00

-54. 6

-0. 22

+4.4

-0.27

—2. 2

-0.48

-0.6

+0.02

0.0

+0.07

138

-33.2

-4.86

-44. 2

+3. 58

+1.7

-0.50

-4. 2

-0.15

-0.4

+0.05

+0.4

+0.05

144

-53.2

-1.53

-14.5

. ;, S'l

-1.6

-0. 45

-4.0

+0. 22

0.0

+0.07

+0.6

0.00

150

-50.3

+2.51

+21.6

+5. 53

-3.7

-0. 17

-1.6

+0.44

+0.4

+0. 05

+0.4

-0.05

156

-25.2

+5. 41

+47.2

+2.61

-3.6

+0.18

+ 1.3

+0.42

+0.6

0.00

0.0

-0.06

162

+10. 1

+5. 80

+50. 8

—1.44

—1.6

+0.41

+3.4

+0.18

+0.4

-0. 05

-0.3

-0.04

168

+39.4

+3.46

+ 31.2

-4.80

+ 1.3

+0.42

+3.4

-0. 16

0.0

-0.07

-0.5

0.00

174

+48.6

-0.47

- 2.5

-5.82

+3.4

+0. 18

+1.5

-0.39

-0.4

-0.04

-0.3

+0.04

180

+33.8

-4.15

-33.4

-4.01

+3.5

-0.15

-1.3

-0.41

-0.5

0.00

0.0

+0.05

186

+ 2.6

-5.71

-47.0

-0.26

+1.6

II 38

-3.4

-0.21

-0.4

+0.04

+0.3

+0.04

192

-29.6

-4.47

-36.5

+3.58

-1.0

-0.41

-3.8

+0.12

0.0

+0.07

+0.5

0.00

198

-47.0

-0.93

-7.4

+5.62

-3.3

—0.24

-1.9

+0.38

+0.4

+0.05

+0.3

-0.04

204

-40.8

+2.96

+25.8

+4.89

-3.9

+0.08

+0.8

+0.42

+0.6

0.00

0.0

-0.06

210

-14.2

+5.46

+46.9

+1.79

-2.3

+0.36

+3.2

+0.25

+0.4

-0. 05

-0.4

-0.05

216

+19.8

+5.28

+45.6

-2.25

+0.4

+0.42

+3.8

-0.05

0.0

-0.07

-0.6

0.00

222

+44.4

+2.52

+22.0

-5. 17

+2.7

+0.27

+2.6

-0.32

-0.4

-0.05

-0.4

+0.05

228

+47.8

-1.47

-11.8

-5. 54

+3.6

-0.01

-0.1

-0.42

-0.6

-0.02

0.0

+0.07

234

+28.1

-4.74

-39.4

-3.19

+2.6

-0.29

-2.4

-0.28

-0.6

+0.04

+0.4

+0.06

240

-4.6

-5.60

-47.2

+0.67

+0.1

-0.41

-3.4

0.00

-0. 1

+0.08

+0.7

+0.02

246

-34.0

-3.71

-31.4

+4.25

-2.3

-0.26

-2.4

+0.27

+0.4

+0.07

+0.6

-0.04

252

-45.8

0.00

- 0.2

+5.64

-3.0

+0.02

-0.2

+0.40

+0.7

+0.02

+0.2

-0.08

258

-34.0

+3.80

+31. 1

+4.23

-2. 1

+0.28

+2.4

+0.28

+0.7

-0.03

-0.4

-0. OS

264

-3.7

+5.74

+46.6

+0.62

+0.3

+0.40

+3.2

-0.02

+0.3

-0.08

-0.8

-0.03

270

+29.5

+4.80

+38.6

-3.28

+2.7

+0.28

+2.1

-0.01

-0.3

-0.08

-0.8

+0.03

276

+49.6

+1.54

+ 10.0

-5. 75

+3.7

-0.02

-0.5

-0.44

-0.7

-0. 05

-0.4

+0.08

282

+46.4

-2.55

-25. 4

-5.48

+2.4

-0.36

-3.2

-0.32

-0.9

+0.02

+0.2

+0.10

288

+21.0

-5.53

-51.0

-2.62

-0.6

-0.51

-4.4

0.00

-0.5

+0.08

+0.8

+0.07

294

-15.4

-6.04

-54.6

+1.38

-3.7

-0.39

-3.2

+0.37

0.0

+0.10

+1.0

-0.01

300

-46.4

-3.81

-34.4

+4.92

-5.3

-0. 05

0.0

+0.58

+0.7

+0.08

+0.7

-0.08

306

-58.0

+0.08

+ 0.4

+6. 17

-4.3

+0.38

+3.7

+0.49

+1.0

+0.01

0.0

-0.11

312

-45.4

+3.86

+34.6

+4.72

-0.8

+0.63

+5.9

+0.16

+0.8

-0.07

-0.6

-0.08

318

-15.2

+5.71

+53.4

+1.28

+3.3

+0.60

+5.6

-0.29

+0.2

-0.10

-1.0

-0.03

324

+18.6

+5.11

+49.9

-2.40

+6.4

+0.28

+2.4

-0.67

-0.4

-0.10

-1.0

+0.05

330

+42.3

+2.44

+27.0

-4.81

+6.7

-0.22

-2.4

-0.72

-1.0

-0. 05

-0.4

+0. 12

336

+46.4

-1.00

-3.6

-4.93

+3.8

-0.64

-6.3

—0.42

-1.0

+0.03

+0.4

+0.11

342

+31.9

-3.53

-28.3

-3.00

-1.0

-0.79

-7.4

+0.09

-0.6

+0.10

+0.9

+0. 06

348

+ 7.4

-4.24

-37.8

-0.20

-5.7

-0. 55

-5.2

+0.58

+0.2

+0.12

+ 1.1

-0.02

354

-15.4

-3.04

-30.7

+2.27

-7.6

-0. 05

-0.5

+0.81

+0.8

+0.08

+0.7

-0. 09

360

-27.0

-0.80

-13.2

+3.22

-6.3

+0.47

+4.5

+0.68

+1.1

0.00

0.0

-0.12

[n3z, 3 log t, and w/cos i are to be computed in the form 1% a* sin ig + Ii bi cos ig+cT.

PERIODIC TERMS.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (183) Gyrene— Continued.

TABLE III.— B log r.

271

Unit of a and 6=0.00001.

i

0

1

2

9'

&o

Diff.fnrl0

"i

Diff.forl0

b,

Diff.fnrl0

0,

Diff.forl0

62

Diff.forl0

O

0

+ 2.0

-0. 12

+106. 7

+0.04

1.0

-3.32

+ 163. 7

-1.66

- 10.9

-4.94

6

+ 1.3

-0. 12

+ 105. 1

-0.58

- 20.8

-3.24

+ 151.6

-2.26

- 38.1

-4.13

12

+ 0.5

-0.12

+ 99.7

-1. 17

- 39. 9

-3. 08

+ 136. 6

-2. 62

- 60. 5-

-3.37

18

- 0.2

-0. 12

+ 91. 1

-1.70

- 57. 7

-2. 79

+ 120.2

-2.75

- 78.5

-2. 72

24

- 1.0

-0. 12

+ 79. 3

-2. 18

- 73. 4

-2. 12

+103. (i

-2.77

- 93. 2

-2. 21

30

— 1.7

-0. 11

+ 65. 0

-2.56

- 86.7

-2.00

+ 87. 0

-2.78

-105. 4

-1.88

36

-2.3

+ 48 :

-2. 88

- 97.4

-1.51

+ 70. 2

-2.82

-115.7

-1.62

42

-2.9

-0.08

+ 30. 5

-3. 10

-104. 8

-0.98

+ 53. 1

-2.H2

-124. S

-1.48

48

-3.3

-0. 05

+ 11.5

3. 2:;

-109.2

-0.41

+ 35.2

-3. 16

-133.4

-1.33

54

-3.5

-0. 02

-8.3

-3.28

-109. 7

+0.20

+ 15.2

-3.54

-140. 8

-1. 10

60

-3.6

- 27. 9

-3.21

-106.7

+0. 79

-7.3

-3.98

-146. 6

-0. 73

66

-3.6

+0.02

- 46.8

-3. 05

- 100. 2

+1.38

- 32. (1

-4.47

-149.6

-0. 18

72

- 3.4

+0.04

- 64 5

-2.79

- 90. 1

+ 1. 93

- 60.9

-4.95

-148. 8

+0. 60

78

- 3.1

+0.07

- 80.3

-2. 40

- 77.0

+2. 16

- 92. 0

-5.26

-142.4

+ 1.68

84

-2.6

+0.08

- 93. 3

-1.91

- 60.6

+2.92

-124.0

-5. 27

-128.7

+2.98

90

- 2. 1

+0.09

-103.2

-1.33

- 41.9

+3. 26

-155. 3

-4.93

-106.6

+4.44

96

- 1.5

+0.11

-109. 3

-0.68

- 21.5

+3. 51

-183. 2

-4. 11

- 75.4

+5. 92

102

- 0.8

+0.12

—111.3

+0.01

+ 0.2

+3. 62

-204. 6

—2.76

- 35.5

+7.26

108

- 0.1

+0.10

-109.2

+0.75

+ 22.0

+3. 56

-216.3

-0.94

+ 11. 7

+8. 22

114

+ 0.4

+0. 10

-102.3

+1.49

+ 42.9

+3.33

-215.9

+ 1.21

+ 63.1

+8. 62

120

+ 1-1

+0. 08

- 91. 3

+2. 16

+ 62.0

f 2. 9:.

-201.8

+3. 54

+115. 1

+8.37

126

+ 1.4

+0. 06

- 76.4

+2.72

+ 78.3

+2.43

-173.4

+5.78

+ 163.6

+ 7.44

132

+ 1.8

+0.04

- 58. 6

+3.16

+ 91.2

+1.79

-132.4

+7.70

+204. 4

+5. 81

138

+ 1.9

0.00

- 38.5

+3.46

+ 99.8

+ 1.01

- 81. 0

+9.10

+233. 3

+3.63

144

+ 1.8

-0.04

- 17.1

+3.58

+103. 7

+0.25

- 23.2

+9.80

+248. 0

+ 1. 17

150

+ 1.4

-0.08

+ 4.4

+3. 51

+102. 8

-0. 55

+ 36.6

+9. 75

+247. 3

-1.41

156

+ 0.9

-0. 10

+ 25.0

+3. 28

+ 97. 1

-1.30

+ 93.8

+S. 99

+231. 1

-3.81

162

+ 0.2

-0. It

+ 43.7

+ 2.87

+ 87.2

-1.96

+144. 5

+7. 62

+201. 6

—5.84

168

- 0.8

-0. L6

+ 59. 4

+2.32

+ 73. 6

-2. 52

+185. 2

+5.81

+ 161.0

-7. 37

174

- 1.7

-0. L8

+ 71.6

+ 1.70

+ 57.0

-2.93

+214. 2

+3.78

+ 113.2

-8.26

ISO

- 3.0

-0.21

+ 79.8

+0. 99

+ 38.4

-3. is

+230. 6

+1.72

+ 61. 9

-8. 62

186

-4.2

-0.20

+ 83.5

+0.27

+ 18.9

-3. 29

+234. 8

-0.22

+ 9. 7

-8. .".2

L92

-5.4

-0.21

+ 83.0

-0.44

1. L

-3. 22

+ 228.0

-1.96

- 40.3

-7.98

198

-6.7

-0.20

+ 78.2

-1.13

- 19.8

-3.00

+211.3

-3.43

- 86.1

-7. L9

2(11

-7.8

-0. 17

+ 69. 1

-1.72

- 37.1

-2. 67

+ 186.8

-4.62

-12£. 6

-6.23

210

-8.7

-0. 15

+ 57. 5

-2. 25

- 51.8

-2.18

+ 155.8

-5.62

-160.9

-5. 17

216

- 9.6

-0. 12

+ 42. 4

-2. 68

- 63.3

-1.64

+ 119.3

—6.44

-188.6

-4. 02

222

-10.2

-0.07

+ 25.3

-2.94

- 71.5

-1.00

+ 78.5

-7.08

-209. 1

-2.78

228

-10.4

-0.02

+ 7. 1

-3.08

- 75. 4

-0. 29

+ 34.3

-7.58

-222.0

-1.41

234

-10.5

+0.02

- 11.6

-3.09

- 75.0

+0.41

- 12.4

-7.89

221;. 11

+0.11

240

-10.2

+0.08

- 30.0

-2.93

- 70.5

+ 1. 09

— 60.4

-7.93

-220. 7

+ 1. 72

246

-9.6

+0.11

- 46.8

-2.61

- 61.11

+1.76

-107.6

-7.62

-205. 4

+3.44

252

-8.9

+0. 15

- 61. 3

-2. 16

- 49.4

+2. 33

-151.8

-6.89

-179.4

+5. 20

258

-7.8

+0.18

- 72. 7

-1.59

- 33.9

+2. 78

-190.4

-5. 72

-143.0

+6.84

264

-6.7

+0.19

- 80. 4

-0. 95

- 16.0

+ 3. 12

-220. 4

-4.04

- 97.3

+8. 19

27(1

-5.5

f 0. 22

- 84. 1

-0.21

+ 3. (1

+3.28

-23S. 9

-2.00

- 44.7

+9.12

276

- 4. 1

+0.22

- 82. 9

+0. 56

+ 23.4

|-3. 28

-244.4

+ 0. 3.'

+ 12. 1

+9. 50

282

-2.8

+0.22

— 77. 4

+ 1.28

+ 42. 9

+3. 10

-235. 1

+2. 73

+ 69.3

+9.21

288

- 1.4

+0.22

- 67. (i

+ 1.97

+ 60. (i

+2. 73

-211.6

+5. 00

+122. 6

+8. 25

294

- 0.2

+0. 19

- 53.8

+2. 52

+ 75. 7

f 2. 27

-175. 1

+6. 92

+168. 3

+6. 68

300

+ 0.9

+0.18

- 37. 3

+2.96

+ 87.8

+1.68

-128.6

+8. 29

+202. 7

+4. 60

306

+ 1.9

+0. 15

- 18.3

+3.25

+ 95.8

+0. 97

- 75. (i

+9. 01

+223. 5

+2. 25

312

+ 2.7

id L2

+ 1.7

+3.38

+ 99. 1

+0. 24

- 20. 5

+9. 02

+229. 7

-0. 12

318

+ 3.3

+0.08

+ 22. :;

+3.37

+ 98.7

-0. 50

+ 32. 7

+8.38

+222. 0

-2.34

324

+ 3.6

+0. 05

+ 42. 1

+3. 17

+ 93. 1

-1.2(1

+ SO. 0

+ 7. 17

+201. 6

—4.20

330

+ 3.9

+0.02

+ 60. 3

+2. 83

+ 84.3

-1.82

+ 118.7

+5. 58

+171.6

-5.51

336

+ 3.8

-0.02

+ 76. 1

+2.41

+ 71.6

-2. 37

+147. 0

+3.82

+135. 5

-6.28

342

+ 3.6

0 n i

+ 89. 2

+ 1.89

+ 55.9

-2. 79

+164.6

+2. 12

+ 96.3

-6. 50

348

+ 3.2

-0. 08

+ 98.8

+1.28

+ 38. 1

:; (is

+172. 3

+0.58

+ 57.5

-6.26

354

+ 2.7

-0. 10

+101 6

+0.66

+ 19.0

-3. 26

+ 171.5

II. 72

+ 21.2

-5. 70

360

+ 2.0

-0. 12

+106. 7

+0. 04

1.0

3. 32

+ 163 7

-1.66

- 10.9

-4.94

[n8z, d log r, and u/cos i are to be computed in the form l'i ai sin ig - 1 ~t hi cos ig+cT.]

272 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (133) Cyrene — Continued.

TABLE III— d log r— Continued.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

t

4

9'

a3

Diff.forl0

b3

Diff.forl0

",

Diff.forl3

K

Diff.forl0

O

0

- 6.7

-1.92

-34. 1

+1. 28

- 6.1

+1.10

+ 9.5

+0.44

6

-15.4

-1. 02

-24.6

+1.62

+ 0.9

+0.98

+ 9.7

-0.28

• 12

-19.0

-0.27

-14.7

+1. 53

+ 5.6

+0.45

+ 6.1

-0.69

18

—18.6

+0.22

- 6.2

+ 1.21

'+ 6. 3

-0.08

+ 1.4

-0. 65

24

—16.3

+0.42

- 0.2

+0.82

+ 4.7

-0. 32

- 1.7

-0. 29

30

-13.6

+0.43

+ 3.6

+0.55

+ 2.5

-0.25

- 2. 1

+0. 02

36

-11.1

+0.40

+ 6.4

+0.47

+ 1-7

-0.02

- 1.5

+0.08

42

-.8.8

+0.43

+ 9.2

+0. 50

+ 2.3

+0. 13

- 1.2

-0.09

48

- 5.9

+0.63

+ 12.4

+0. 55

+ 3.3

+0.02

- 2.6

-0. 35

54

- 1.2

+0.97

+15. 8

+0.44

+ 2.6

-0.34

- 5.4

-0.44

60

+ 5.7

+ 1.34

+ 17.7

+0.07

- 0.8

-0.73

-7.9

-0. 17

66

+14.9

+ 1.55

+16.6

-0. 58

- 6 2

-0. 82

- 7.4

+0.41

72

+24.3

+ 1.38

+10.8

-1.40

-10.7

-0.44

- 3.0

+0.98

78

+31.5

+0.78

- 0.2

-2. 18

-11.5

+0.30

+ 4.4

+ 1. 21

84

+33.7

-0.25

-15. 3

-2. 65

- 7. 1

+1.11

+ 11.5

+0.88

90

+28.5

-1.58

-32.0

-2.70

+ 1.8

+1. 55

+ 14.9

-0.01

96

+ 14.8

-2.88

—46.4

-1.S6

+ 11.5

+1.29

+ 11.4

—1.09

102

- 6.0

-3.87

-54.3

-0.48

+17.3

+0.37

+ 1.8

-1.79

108

-30.2

-4.03

-52.2

+ 1.30

+ 15.9

-0.88

-10. 1

-1.74

114

-52.6

-3.30

-38.7

+3. 08

+ 6.8

-1.87

-19. 1

-0.89

120

-68.1

—1.61

-15.3

+4. 52

- 6.5

-2. 12

-20.8

+0.48

126

-71.9

+0.47

+ 13.9

+5. 00

-18.6

-1. 45

-13.4

+ 1.75

132

-62.5

+2.61

+42.8

+4. 44

-23.9

-0.09

+ 0.2

+2.32

138

-40.6

+4.41

+65. 3

+2.78

-19.7

+ 1.38

+ 14.4

+ 1.90

144

-11.4

+5. 19

+76.1

+0.66

-7.4

+2.26

+23.0

+0.68

150

+ 19.6

+4. 95

+73.2

-1.57

+ 7.4

+2. 17

+22.6

-0.86

156

+45. 9

+3.63

+57.3

-3. 52

+18.6

+1. 14

+12.7

-1.98

162

+61.9

+ 1.62

+32.7

-4.53

+21.1

-0.35

- 1.2

-2. 16

168

+65.3

-0.41

+ 4.9

-4. 56

+ 14.4

-1. 59

-13.2

-1.38

174

+57. 0

-2. 13

-20.2

-3.56

+ 2.0

-2. 05

-17.7

+0.01

180

+39.7

-3.34

-37.8

-2.11

-10.2

-1.49

-13.1

+1.31

186

+ 18.5

-3. 62

-45.5

-0. 42

-15. 9

-0.20

- 2.0

+1.92

192

- 2.2

-3.07

-42.9

+1.10

-12.6

+ 1.14

+ 9.9

+1.54

198

-18.3

-2.08

-32. 3

+2. 15

- 2.2

+ 1.88

+ 16.5

+0.36

204

-27. 1

-0.78

-17.1

+2.62

+ 9.9

+ 1. 67

+14.2

-0.98

210

-27.7

+0.49

- 0.8

+2. 53

+17.8

+0.62

+ 4.8

-1.84

216

—21. 2

+ 1. 56

+ 13.3

+1.93

+17.3

-0.78

-7.9

-1.82

222

- 9.0

+2. 26

+22.4

+0.95

+ 8.5

-1.76

-17.0

-0.87

228

+ 5.9

+2. 51

+24.7

-0.23

-3.8

-1.88

-IS. 3

+0.49

234

+21.1

+2. 21

+19.6

-1.45

-14.0

-1.08

-11.1

+ 1.59

240

+32.4

+1. 35

+ 7.3

-2.48

-16 7

+0.26

+ 0.8

+ 1.86

246

+37.3

+0.08

-10.1

-3.07

-10.9

+ 1.43

+11.2

+ 1.18

252

+33.4

-1.40

-29.5

-3.16

+ 0.5

+1.87

+15. 0

-0. 10

258

+20.5

-2.88

-46.5

-2.38

+ 11. 5

+ 1.32

+10.0

-1.38

264

— 1. 1

-4.04

-56. 7

-0.84

+ 16.2

+0.04

- 1.5

-1.97

270

-26.4

-4.28

-56. 6

+1.01

+ 12. 0

-1.33

-13.6

-1.57

276

-50.8

-3. 63

-44.6

+2.90

+ 0.2

-2.16

-20. 3

-0.32

282

-68.3

-2.00

-21.8

+4.48

-13.9

-1. 96

-17.5

+1.18

288

-74.8

+0.07

+ 7.6

+5. 16

-23.4

-0.84

- 6.2

+2.22

294

-67.5

+2.29

+37.9

+4.72

-24.0

+0.72

+ 9.1

+2.33

300

-47.3

+4.22

+62.2

+3.13

-14. 7

+2. 02

+21.8

+1.45

306

-18.7

+5. 14

+75. 5

+ 1.08

+ 0.2

+2. 47

+26. 5

-0. 05

312

+12.3

-+ 5. 00

+75. 2

-1.13

+ 14.9

+1.92

+21.2

-1.50

318

+39.4

+3.88

+61.9

-3. 11

+23. 3

+0.64

+ 8.5

-2. 28

324

+57.5

+2. 02

+39.3

-4. 28

+ 22. 6

-It. SI

- 6.1

-2.08

330

+63.7

+0. 05

+ 12.6

-4.42

+ 13.6

-1.78

-16.4

-1.10

336

+58.1

— 1. 65

-12.0

-3.56

+ 1.2

-1.92

-19. 3

+0.18

342

+43.9

-2.84

-30. 1

-2.29

- 9.4

-1.28

-14.2

+1.19

348

+25.6

-3.02

-39.5

-0.82

-14. 1

-0.24

- 5.0

+ 1.55

354

+ 7.7

-2. (ill

-40.0

+0. 45

-12.3

+0.67

+ 4.4

+ 1.21

360

-6.7

-1.92

• —34. 1

+1.28

- 6. 1

+ 1. 10

+ 9.5

+0.44

[n<Jz, d log r, and u/cos i are to be computed in the form -i'i a( sin ig+ Jj b{ cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of {133) Cyrene— Continued.

1*73

PERIODIC TERMS.

TABLE III.— 3 log r— Continued.

t'nit of a and 6=0.00001.

i
9'

1

{

°5

Diff.forl°

65

Diff.forl0

«6

Diff.forl0

6«

Diff.forl0

O

0

+2.3

+0.34

+3.2

-0. 25

+0.2

-0.07

-0. 5

-0.02

6

+3.9

+0.12

.11 :i

-0.41

-0.2

-0. 05

-0.5

+0.02

12

+3.7

-0. is

-1.7

-0.38

-0.4

-0.02

-0.3

+0.05

18

+1.8

-0.38

-3.6

-0.18

-0.5

+0.02

+0.1

+0. 05

24

-0.8

-0.39

-3.8

+0. 11

-0.2

+0.05

+0.3

+0.02

30

-2.9

ii 23

-2.3

+0.33

+0.1

+0.04

+0.3

-0.01

36

-3.6

+0.02

+0.2

+0.40

+0.3

+0.01

+0.2

-0.03

42

-2. (i

+0. 28

+2. 5

+0.27

+0.2

-0.02

-0. 1

-0.03

48

-0.2

+0. 39

+3.4

+0.02

+0.1

-0. 03

-0.2

-0.02

54

+2.1

+0.31

+2. 7

-0.24

-0.2

-0.03

-0.3

+0.01

60

+3. 5

+0.08

+0.5

-0.38

-0.3

-0.01

-0. 1

+0.04

66

+3.0

-0. 19

-1.8

-0.32

-0.3

+0.02

+0.2

+0. 05

72

+ 1.2

-0. 35

-3.4

-0.12

-0.1

+0.05

+0.5

+0.02

78

-1.2

-0.36

-3.3

+0. 13

+0.3

+0. 05

+0.4

-0. 02

S4

-3. 1

-0. 18

—1.8

+0. 32

+0.5

+0.02

+0.2

-0. 05

90

-3.4

+0.07

+0.5

+0. 35

+0.5

-0.02

-0.2

-0.07

96

-2.3

+0.26

+2.4

+0.21

+0.2

-0.06

-0.6

-0.04

102

-0.3

+0.32

+3.0

-0.01

-0.2

-0.06

-0.7

+0.01

108

+ 1.6

+0. 22

+2.3

-0.21

-0.5

-0. 05

-0.5

+0.07

114

+2.4

+0.02

+0.5

-0.28

-0. 8

-0.01

+0.1

+0.09

120

+ 1.9

-0. 17

-1. 1

-0. 21

-0.6

+0. 05

+0.5

+0.06

126

+0.4

-0.25

-2.0

-0.04

-0.2

+0.08

+0.8

+0.02

132

—1.1

-0.20

-1.6

+0. 14

+0.4

+0.08

+0.7

-0. 03

138

-2.0

-0. 05

-0.3

+0.24

+0.7

+0.03

+0.4

-0.08

144

—1.7

+0. 14

+ 1.3

-11 -jo

+0.8

-0.02

-0.2

-0.08

150

-0.3

+0.23

+2.1

+0.04

+0.5

-0.06

-0.6

-0. 05

156

+ 1.1

+0.19

+1.8

-0. 12

+0.1

-0. OS

-0.8

+0.01

162

+2. 0

+0.08

+0.6

-0. 22

-0.5

-0.07

-0.5

+0.05

168

+2. 0

-0. 10

-0.9

-0. 21

-0. 7

-0.01

-0.2

+0.06

174

+0.8

-0. 22

-1.9

-0. 09

-0.6

+0.04

+0.2

+0.06

180

-0. 7

-ii 21

-2.0

+0. OS

-0.2

+0.07

+0.5

+0.02

186

-1.7

-0.08

-0.9

+0. 22

+0.2

+0.05

+0.5

-0.02

L92

-1.7

+0.07

+0.6

+0.22

+0.4

+0.02

+0.3

-0.05

198

-0.9

1-0. 18

+1.7

+0. 12

+0.5

-0.02

-0.1

-0.05

204

. u -,

+0. 22

+2.0

11 0:,

+0.2

-0. 05

-0.3

-0.02

210

+ 1.8

+0. 12

+1.1

-0. 20

-0. 1

-0.04

-0.3

+0.01

216

+2.0

-0. 05

-0.4

-0. 22

-0.3

-0.01

-0.2

+0.03

222

+1.2

-0.18

-1.6

-0. 13

-0.2

+0.02

+0.1

+0.03

228

-0. 1

-0. 22

-2.0

+0.02

-0.1

- 11 DM

+0.2

+0.02

234

—1.4

-0. 14

-1.4

+0. 15

+0.2

+0.03

+0.3

-0.01

240

-1.8

+0.02

-0. 2

+0. 21

+0.3

■

+0.1

-0.04

246

-1.2

+0. 17

+ 1.1

+0. 13

+0.3

-0.02

-0.2

-0.05

252

+0.2

+0.20

+ 1.4

-0.02

+ 0. 1

-0.05

-0.5

-0.02

258

+ 1.2

+0.11

+0.9

-0.17

-0.3

-0.05

-0.4

+0.02

264

+1.5

-0.03

-0. 5

-0.22

11 5

-0.02

-0.2

+0.05

270

1) s

-0.19

-1.7

-0.12

-0.5

+0.02

+0.2

+0.07

276

-0.8

-0.26

-2.0

+0.03

-0.2

+0.06

+0.6

+0.04

282

-2. 3

-0. 17

-1.3

+0. 21

+0.2

+0.06

+0.7

-0.01

288

-2.8

+0.02

+0.5

+0.29

+0.5

+0.05

+0.5

-0.07

294

-2. 1

+0. 22

+2. 2

11 _•:;

+0.8

+0.01

-0. 1

-0.08

300

-it. 2

+0.33

+3' 3

+0.04

+0.6

-0.05

-0.5

-0.06

306

1 9

+0.29

+2.7

-0.19

+0.2

-0.08

-0.8

-0.02

312

+3.3

+0. 11

+ 1.0

-0.34

-0.4

-0.08

-0.7

+0.03

318

+3.2

-0. 15

-1.4

-0. 34

-0.7

-0.03

-0.4

+0.08

324

+ 1.5

-0. 33

-3.1

-0.17

-0.8

+0. 02

+0.2

+0.08

330

-0.8

-ii. 38

-3.3

+0.09

-0.5

+0. hi;

+0.6

+0. 05

336

-3.0

-0. 24

-2. 0

+0.32

-0. 1

+0.08

+0.8

-0.01

342

-3.7

+0. 03

f0 5

+0.39

+0.5

+0.07

+0.5

-0. 05

348

-2.6

+0. 30

+2. 7

II L'S

+0.7

+0.01

+0.2

-0. 06

354

-0.2

+0.41

+3. 9

+0.04

+0.6

-0.04

-0.2

-0. 06.

360

+2. 3

+0.34

+3.2

-0. 25

+0.2

-0.07

-0.5

-0. 02

[ndz, 3 log r, and u/coa i are to be computed in the form Jj dt sin ig+J2{ bi cos ig + cT.]

274

,

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (138) Cyrene — Continued.

PERIODIC TERMS.

TABLE IV.— u/cos i.

Unit of o and 6=09001.

t

0

1

2

9'

K

Diff. for 1°

«L

Diff. for 1°

6i

Diff. for 1°

a2

Diff. fori0

b..

Diff. foi 1°

O

0

—11.7

-0. 64 '

-17.0

-0.19

-2.5

+0.42

-15.8

+0.47

+ 6.8

+0.44

6

-15. 4

-0.58

-17.8

-0. 05

+ 0.3

+0. 54

-12.7

+0. 52

+ 8.8

+0.25

12

—18.7

-0. 51

-17.6

+0.14

+ 4.0

+0. Ill

- 9.0

+0.48

+ 9.8

+0.07

18

—21. 5

-0.41

-16.1

+0. 35

+ 7.6

+0.61

- 7.0

+0.34

+ 9.6

-0. 12

24

-23.6

-0. 31

-13.4

+0. 53

+ 11.3

+0. 56

- 5.5

+0. 18

+ 8.4

-0. 19

30

—25.2

-0.21

-9.7

+0.69

+ 14.3

+0.42

-4.8

+0.02

+ 7.3

-0. 15

36

-26.1

-0.09

- 5. 1

+0. 82

+16.3

+0.24

- 5.2

-0. 12

+ 6.6

-0.06

42

-26.3

+0.02

+ 0.2

+0.88

+ 17.2

+0. 06

- 6. 2

-0. 10

+ 6.6

+0.10

48

-25. 8

+0. 1 1

+ 5.4

+0.85

+ 17.0

-0.17

- 7.1

-0. 13

+ 7. S

+0.29

54

-24. 0

+0. 27

+ 10.4

+0. 75

+15. 2

-0. 38

-7.8

-0.01

+10.1

+0.45

60

-22.6

+0.38

+ 14.4

+0.58

+12.5

-0.52

-7.2

+0.22

+13.2

+0.51

66

-20.1

+0.47

+ 17.4

+0.38

+ 9.0

-0.61

-5.2

+0.45

+ 16.2

+0.48

72

-17.0

+0.56

+ 19.0

+0.17

+ 5.2

-0.63

- 1.8

+0.66

+ 19.0

+0.35

78

-13.4

+0.62

+ 19.4

-0.05

+ 1.4

-0.62

+ 2.7

+0.81

+20.4

+0. 12

84

-9.6

+0.66

+ 1S. 1

-0.26

-2.2

-0.52

+ 7.9

+0.88

+20.4

-0. 12

90

— 5. 5

+0.69

+16.3

-0.40

-4.8

-0.37

+ 13.3

+0.84

+ 18.9

-0.42

96

— 1.3

+0.68

+ 13. 6

-0.48

-6.6

-C. 20

+ 18.0

+0.68

+ 15.3

-0.69

102

+ 2.7

+0.66

+ 10.6

-0.50

-7.2

-0.04

+ 21.4

+0.46

+ 10.6

-0.86

108

+ 6.6

+0. 62

+ 7.6

-0.48

- 7. 1

+0.08

+23. 5

+0.18

+ 5.0

-0.93

114

+ 10. 1

+0. 53

+ 4.9

-0.40

-6.2

+0.21

+23. 6

-0.08

- 0.6

-0.93

120

+13.0

+0. 43

+ 2.8

-0.29

-4.6

+0.28

+22.6

-0.31

- 6.2

-0.88

126

+ 15.3

+0.31

+ 1.4

-0.18

-2.8

+0. 30

+ 19.9

-0. 52

-11.2

-0.72

132

+ 16.7

+0.17

+ 0.6

-0.08

- 1.0

+0.20

+ 16.4

-0.62

-14.8

-0. 56

138

+ 17.3

+0.04

+ 0.5

0.00

+ 0.3

+0. 21

+ 12.4

-0.70

-17.9

-0. 40

144

+17.2

-0. 10

+ 0.6

+0.06

+ 1.5

+0. 14

+ 8.0

-0.72

-19.6

-0.24

150

+ 16. 1

-0. 24

+ 1.2

+0.07

f- 2.0

+0.03

+ 3.8

-0.73

-20.8

-0.10

156

+ 14.3

-0. 37

+ 1.4

+0. 05

+ 1.9

-0.03

- 0.8

-0.75

-20.8

+0. 04

162

+ 11.7

-0.48

+ 1.8

+0.02

+ 1.6

-0.08

- 5.2

-0.75

-20.3

+0.16

168

+ 8.5

-0.56

+ 1.7

-0.02

+ 1.0

-0.09

- 9.8

-0. 74

-18.9

+0.32

174

+ 5.0

-0.60

+ 1.5

-0.04

+ 0.5

-0.09

-14.1

-0.67

—16.4

+0.49

180

+ 1.3

-0.63

+ 1.2

-0.06

- 0. 1

-0. 07

-17.8

-0.57

-13.0

+0.67

186

-2.6

-0. 62

+ 0.8

-0.07

- 0.3

-0. 02

-20.9

-0.41

- 8.4

+0.83

192

- 6.1

-0.56

+ 0.4

ii in

- 0.4

+0. 01

-22.8

-0.20

- 3.0

+0.94

198

- 9.3

-0.49

+ 0.3

-0.02

- 0.2

-, 0. 02

—23. 1

+0.06

+ 2.9

+ 1.02

204

-12.0

-0.39

+ 0.2

+0.02

- 0.1

+0.04

—22. 1

+0. 37

+ 9.2

+0.99

210

-14.0

-0. 26

+ 0.5

+0.0S

+ 0.3

+0. 04

-19! 0

+0.62

+14.8

+0.85

216

-15. 1

-0.11

+ 1.1

+0. 11

+ 0.3

-0. 02

-14.6

+0.87

+19.4

+0.65

222

—15. 3

+0.04

+ L.8

+0. 12

0.0

-0.06

- S. li

+ 1.02

+22.6

+0.38

228

-14.6

+0. Ill

+ 2. li

+0.12

- 0.4

-0.08

- 2.3

+ 1.07

+24. 0

+0.08

234

-13.0

+0.32

+ 3.2

+0.07

- 1.0

-0. 14

+ 1.2

+ 1.03

+23.5

-0.25

240

-10.8

+0.42

+ 3. 1

+0.01

- 2.1

-0. 17

+ 10. 1

+0.88

+21.0

-0.51

246

-7.9

+0.52

+ 3.3

-0.06

- 3.0

-0. 14

+ 11. S

+0. 69

+ 17.4

-0.70

252

-4.6

+0. 58

+ 2.7

-0.11

-3.8

-0.13

+ 1S. 4

+0.46

+12.6

-0.83

258

- 1.0

+0. 62

+ 2.0

-0.16

-4.6

-0.12

+20. 3

+0.21

+ 7.4

-0.87

264

+ 2.8

+0.61

+ 0.8

-0.21

-5.2

-0.07

+20.9

0.00

+ 2.2

-0.84

270

+ 6.3

+0.58

- 0.5

-0.22

- 5.4

+0. 02

+20.3

-0. 18

— 2. 7

-0.76

276

f 9.7

+0. 52

- 1.8

-0.21

- 5.0

+0.05

+ 18.8

-0. 31

-6.9

-0.69

282

+ 12.5

+0.41

- 3.0

-0.17

- 4.8

+0. 06

+ 10.6

-0.42

-11.0

-0.61

288

+ 14.6

+0. 28

- 3.8

-0. 12

-4.3

+0. 08

+ 13.7

-0.52

-14.2

-0.48

294

+ 15.9

+0. 17

- 4.5

-0. OS

-3.8

+0. 06

+ 10.4

-0.61

—16.8

-0.38

300

+ 16.6

+0. 03

- 4.8

-0.04

-3.6

+0.03

+ 6.4

-0.68

-18.8

-0.27

306

+ 16.3

-0. II

- 5.0

-0.05

-3.4

-0.02

+ 2.3

-0. 74

-20.0

-0.13

312

+ 15.3

-0. 23

- 5.4

-0.06

-3.8

-0.09

- 2.4

-0.78

-20. 4

+0.04

318

+13. 5

-0. 38

— 5. 7

-0.10

-4.5

-0.12

- 7.0

-0. 75

-19.5

+0.23

324

+ 10. s

-0. 18

- (i. (i

-0. is

- 5.3

—0. 12

-11.4

-0.68

-17.6

+0.42

330

+ 7.7

-0. 56

- 7.8

-0.23

- 6.0

-II. 12

-15.2

-0. 55

-14.4

+0.60

336

+ -t-1

-0. 62

- 9. 1

-0.32

- (i. s

-0.08

-IS. 0

-0.37

-10.4

+0.72

342

+ 0.3

-0. 65

-11.6

-0.34

- 0.9

+0.03

-19.0

-0.13

-5.7

+0.79

348

-3.7

-0.68

-13.5

-0.32

-6.4

+0. IS

-19.0

+0.11

- 0.9

+0.76

354

- 7.8

-0.67

-15.5

-0.29

-4.7

+0.32

- 18. 3

+0.32

+ 3.4

+0.64

360

—11.7

-0.64

-17.0

— 0. in

- 2.5

+0.42

-15.8

+0.47

+ 6.8

+0.45

I ;m , . log 1 . and u cos i are to be computed in the form Si aj sin ig+Ii 6j cos ig +cT.)

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (133) Cyrene — Continued.
TABLE IV.— u cos i— Continued.

275

PERIODIC TERMS.

Unit of a and 6=09001.

i

3

4

9'

°3

Diftforl0

63

Diff.forl0

'<->

Diff. for 1°

b,

Dill, for 1°

O

0

+ 3.5

+0.31

+ 5.8

-0. 28

+2.6

-0.26

-2.8

-0.20

6

+ 4.8

+0. 15

+ 4.0

-0. 32

+0.8

-0.29

-3.5

-0.03

12

+ 5.3

+0.03

+ 2.0

-0.32

-0.9

-0.23

-3.2

+0. 10

IS

+ 5. 2

-0.04

+ 0.1

-0. 27

-2. 0

-0. 14

-2.3

+0. 18

24

+ 4.8

-0.10

-1.2

-0.21

-2.6

-0.06

— 1. 1

+0. Ill

30

+ 4.0

-0. 12

-2.4

-0.17

-2.7

+0.01

0.0

+0. is

36

+ 3.3

-0. 12

-3.2

-0.13

-2.5

| II lis

+ 1.0

+0. 16

42

+ 2. 5

-0. 17

- 4.0

-0.13

-1.8

+0.12

+ 1.9

+0.13

48

+ 1.3

-0.22

-4.8

-0.12

—1.1

+0.16

+2.6

+0. 08

54

- 0.1

-0.28

- 5.4

-0. 06

+0.1

+0.22

+2.9

-0.01

GO

- 2.0

-0.32

- 5.5

+0.03

+1.6

+0.23

+2.5

-0.11

66

- 4.0

-0.32

- 5.0

+0. 16

+ 2. 9

+0.16

+1.6

-0.21

72

- 5.9

-0.29

-3.6

+0.32

+3.5

-0.01

0.0

-0. 30

78

- 7.5

-0. 17

- 1.1

+0.40

+2.8

-0. IS

-2.0

-0. 28

84

- 7.9

+0. 05

+ 1.9

+0. 52

+ 1.3

-0.31

-3.3

-0.12

90

- 6.9

+0.28

+ 5.2

+0. 51

-0.9

-0.36

-3.4

+0. 10

96

- 4.6

+0.48

+ 8.0

+0.37

-3.0

-0.23

-2.1

+0. 28

102

- 1. 1

+0.64

+ 9.6

+0.13

-3.7

+0.02

0.0

+0.38

L08

+ 3.1

+0.69

+ 9.6

-0.15

-2.8

+0.26

+2.5

+0. 32

114

+ 7.2

+0.58

+ 7.8

-0. 46

-0.6

+0.41

+3.9

+0. 09

120

+ 10. 1

+0. 33

+ 4.1

-0. 69

+2.1

+0.40

+3.6

-0.20

126

+ 11.2

0.00

- 0.5

-0.79

+4.2

+0.20

+1.5

-0. 42

132

+10. 1

-0.36

- 5. 4

-0.74

+4.5

-0. 12

—1.4

-0.48

138

+ 6.9

-0.66

- 9.4

-0.52

+2.8

-0.39

-4.3

-0.32

144

+ 2. 2

-0.85

-11.7

-0.18

-0.2

-0.52

-5.2

0.00

150

- 3.3

-0. 85

-11.6

+0. 22

-3.4

-0.44

-4.3

+0. 32

156

- 8.0

-0.66

- 9.0

+0.59

-5.5

-0.16

-1.4

+0.52

162

—11. 2

-0.34

- 4.5

+0.84

-5. 3

+0. 19

+2.0

+0. 52

168

-12. 1

- II lis

+ 1.1

+0.90

-3.2

+0. 45

+4.8

+0. 29

174

-10.3

+0.48

+ 6.3

+0.78

+0.1

+0. 53

+5.5

-0. 07

180

- 6. 3

+0.79

+ 10.4

+0.48

+3.2

+0.39

+4.0

-0. 35

186

- 0.8

+0.92

+12.0

+0. 05

+4.8

+0.09

+1.3

-0.47

192

+ 4.7

• +0. 83

+ 11.0

-0.38

+4.3

-0.23

-1.6

-0.40

198

+ 9.2

+0.58

+ 7.5

-0.72

+2.0

-0.41

-3.5

-0. 16

2(11

+ 11.6

+0.18

+ 2.4

-0.89

-0.6

-0.38

-3.5

+0. 14

210

+ 11.4

-0.26

-3.2

-0.88

-2. 5

-0.18

-1.8

+0.34

216

+ 8. :.

-0. 64

-8.2

-0.67

-2.7

+0.09

+0.6

+0. 32

222

+ 3.7

-0.87

-11.2

-0.28

-1.4

+0.30

+2.1

+0. 15

22.S

- 1.9

-0.90

-11.6

+0.15

+0.9

+0.32

+2.4

-0.08

234

- 7. 1

-0.72

-9.4

+0.54

+2.5

+0. 16

+1.1

- 0. 29

240

-10.6

-0.39

- 5.1

+0.82

+2.8

-0.08

— 1. 1

-0. 34

246

—11.8

+0.02

+ 0.4

+0. 91

+1.5

-0.31

-3.0

-0. 21

252

-10.3

+0.44

+ 5.8

+0.79

-0.9

-0.39

-3.6

+0.05

258

- 6.5

+0.75

+ 9.9

+0.49

-3.2

-0.27

-2.4

+0.31

264

— 1.3

- II. Ss

+ 11.7

+0.09

-4.1

-0.01

+0.1

+0.43

270

+ 4.1

- II S_'

+11.0

-0.31

-3.3

+0.26

+2.8

+0. 35

276

+ 8.6

+0. 58

+ 8.0

-0.63

-1.0

+0.44

+4.3

+0.10

282

+11.1

+0.22

+ 3.4

-0.83

+2.0

+0.42

+4. 0

-0.18

288

+11.3

-0.16

- 2.0

-0.83

+4.0

+0.18

+2.1

-0.41

294

+ 9.2

-0. 50

-6.6

-0. 64

+4. 2

-0.11

-0.9

-0.46

300

+ 5.3

-0.72

-9.7

-0. 36

+2.7

-0.33

-3.4

-0. 29

306

+ 0.6

-0.77

-10.9

-0.01

+0. 2

11. 13

-4.4

0.00

512

- 3.9

-0.68

-9.8

+0.32

-2.5

-0. 37

-3.4

+0. 28

318

- 7.5

-0.46

- 7.0

1 11 ;,ii

1. 2

-0. 12

— 1. 1

+0. 42

324

- 9.4

-0. 15

- 3. 1

+0.67

-4.0

+0.17

+1.6

+0. 40

330

- 9.3

+0. 13

+ 1.0

+0.62

—2. 2

+0.36

+3.7

+0. 23

336

- 7.8

+0.36

+ 4.4

-Ml IS

+0^3

+0.41

+ 4.4

-0. 04

342

- 5.0

+0.49

+ 6.7

+0.28

+2.7

+0.31

+3. 2

-0. 27

348

- 1.9

+0. 51

+ 7.7

+0. 05

+4.0

+0.10

+1.2

-0. 36

354

+ 1.1

+0. 45

+ 7.3

-0.16

;; :i

-0.12

—1.1

-0.33

360

+ 3. 5

+0.31

+ 5.8

-0.28

+2.6

-0.26

-2.8

-0.20

[no:, d log t, and u/cos i are to be computed in the form Ji a% sin ig+I{ bi cos ig +cT.]

276 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {loo) Cyrene — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 1„) IN JULIAN YEARS.

ndz

3 log r

it/cos i

9

Unit of

c=0?001

Unit of

c=0.0001

Unit of

c=0?001

c

Diff. for 1°

c

Diff. for 1°

c

Diff. for 1°

o

0

-5.82

+0.011

-0.25

-0. 043

+0.98

+0. 075

6

-5.72

+0. 023

-0. 51

-0. 042

+ 1. 42

+0. 072

12

-5.54

+0. 034

-0. 76

-0. 040

+1.84

+0. 068

18

-5. 31

+0. 044

-0.99

-0. 038

+2.23

+0. 061

24

-5.01

+0. 056

-1.22

-0. 036

+2.57

+0. 054

30

-4.64

+0. 065

-1.42

-0. 032

+2.88

+0. 048

36

-4.23

+0. 072

-1.61

-0. 029

+3. 14

+0. 040

42

-3.77

+0. 080

-1.77

-0. 024

+3. 36

+0. 032

48

-3. 27

+0. 087

-1.90

-0. 020

+3. 52

+0. 022

54

-2.73

+0. 092

-2. 01

-0. 016

+3.63

+0. 015

60

-2. 17

+0. 095

-2.09

-0.011

+3.70

+0.007

66

—1.59

+0. 098

-2. 14

-0. 008

+3.71

-0.002

-•2

-1.00

+0. 100

-2.18

-0. 002

+3.68

-0. 009

78

-0.39

+0. 100

-2.17

+0. 002

+3.60

-0. 015

84

+0. 20

+0. 098

-2.15

+0. 005

+3.50

-0. 022

90

+0.79

+0. 097

-2. 11

+0. 008

+3.34

-0. 028

96

+ 1.36

+0. 092

-2. 05

+0. 012

+3. 16

-0. 035

102

+ 1.90

+0. 089

-1.96

+0.016

+2.92

-0. 039

108

+2.43

+0. 086

-1.86

+0. 018

+2.69

-0. 041

114

+2.93

+0. 079

-1.74

+0.021

+2.43

-0. 046

120

+3. 3S

+0. 072

-1.61

+0. 022

+2.14

-0. 049

126

+3.80

+0. 067

-1.47

+0. 026

+ 1. 84

-0. 053

132

+4. 18

+0. 059

-1.30

+0. 028

+ 1. 50

-0. 056

138

+4.51

+0. 052

— 1. 14

+0. 028

+ 1.17

-0. 058

144

+4.80

+0. 043

-0.96

+0. 030

+0.82

(i o:,s

150

+5.03

+0. 034

-0.78

+0. 031

+0. 47

-0. 060

156

+5. 21

+0. 028

-0. 59

+0. 031

+0. 10

-0. 059

162

+5. 36

+0. 018 •

-0.41

+0. 032

-0.24

-0. 058

168

+5.43

+0.008

-0.20

+0. 033

-0.60

—0. 060

174

+5. 45

-0. 001

-0.01

+0. 032

-0. 96

-0. 058

180

+5. 42

-0. 009

+0. 19

+0. 033

-1.30

-0. 057

186

+5.34

-0. 018

+0.39

+0. 032

1 61

-0. 055

192

+5. 20

-0. 028

+0. 58

+0. 032,

1 96

-0. 052

198

+5. 01

-0. 036

+0.77

+0. 031

-2. 27

-0. 051

204

+4.77

-0. 044

+0. 95

+0. 029

-2. 57

-0. 048

210

+4.48

-0. 052

+1.12

+0. 027

-2. 84

-0. 042

216

+4. 15

-0. 059

+ 1.27

+0. 026

-3.08

-0. 038

222

+3.77

-0. 067

+1.43

+0. 025

-3.30

-0. 035

228

+3. 35

-0. 073

+ 1.57

+0. 023

-3. 50

-0. 031

234

+2.89

-0. 078

+ 1.71

+0. 021

-3. 67

.-0. 026

240

+2.41

-0. 084

+ 1.82

+0. 017

-3.82

-0. 020

246

+1.89

-0. 089

+ 1.91

+0. 014

-3.91

-0. 013

252

+ 1.34

-0. 093

+ 1.99

+0. 012

-3.98

-0. 009

258

+0.77

-0. 095

+2. 05

+0. 008

-4. 02

-0. 003

264

+0.20

-0. 097

+2.09

+0. 005

-4.02

+0. 003

270

-0.39

-0. 09S

+2. 11

+0. 002

-3.98

+0. 010

276

-0.98

-0. 098

+2.11

-0. 002

-3.90

+0. 018

282

-1. 56

-0. 096

+2.08

-0. 007

-3. 76

+0. 024

288

-2.13

! 091

+2.03

-0.010

-3. 61

+0. 031

294

-2.69

-0. 091

+ 1.96

-0. 015

-3. 39

+0. 039

300

-3. 22

-0. 086

+ 1.85

-0.019

-3. 14

+0. 044

306

-3. 72

-0. 080

+ 1. 73

-0. 022

-2.86

+0. 052

312

-4.18

-0. 072

+ 1.58

-0. 027

-2. 52

+0. 059

318

-4.59

-0. 065

+ 1.41

-0. 031

-2.15

+0. 065

324

-4.96

-0. 057

+ 1.21

-0. 035

-1.74

+0. 070

330

-5.27

-0. 046

+0.99

-0. 037

— 1.31

+0. 073

336

-5.51

-0. 036

+0.77

-0. 038

-0.86

+0. 074

342

—5. 70

-0. 025

+0.53

-0. 042

-0.41

+0. 077

348

-5. 81

-0. 012

+0.27

-0. 043

+0. 06

+0. 078

354

-5.85

-0. 001

+0. 01

-0. 043

+0.52

+0. 077

360

-5.82

+0.011

-0. 25

-0. 043

+0.98

+0. 075

[ndz, d log r, and u/cos i are to b • computed in the form 2* at sin ig+Ii bi cos ig+cT,]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHXER.

Tables of {133) Cyrene — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

I i

i

Year

.1'

B'

C"

log sin a

log sin 6

log sin c

1873. 0

O

336. 3562

O

243. 8244

o

254. 5000

9. 99861

9. 94195

9. 69090

4

.3701

.8390

.5112

61

94

091

1875

336.3841

243. '8536

254. 5224

9. 99862

9.94194

9. 69092

6

3980

.8682

. 5336

62

93

093

7

.4120

. S.S27

. 5448

62

93

095

8

. 4259

.8973

. 5560

62

92

096

9

.4398

.9119

. 5672

62

92

097

1880

33G. 4538

243. 9265

254. 5784

9. 99862

9. 94192

9. 69098

1

.4677

.9411

. 5S96

62

91

100

o

.4810

. 9556

.6008

62

91

101

3

. 4956

.9702

. 6120

62

91

102

4

5095

!IS.|K

. 6232

62

90

103

1885

336. 52:;:>

243. 9994

254. 6344

9. 99862

9. 94190

9. 69104

6

. 5374

244. 0139

. 6456

63

89

106

7

. 5513

. 0285

. 6569

63

88

107

8

. 5653

. 0431

.6681

63

88

Ills

9

. 5792

. 0577

.6793

63

87

109

1890

336. 5931

244.0722

254. 6905

9. 99863

9. 941S7

9. 69110

1

.6071

(is.;.

. 7017

63

86

112

2

.6210

. 1014

. 7129

63

86

113

3

. 6350

1 mil

. 7241

63

85

114

4

. 6489

.1306

. 7353

63

85

116

1895

336. 6628

244. 1451

254. 7465

9. 99864

9. 94184

9.69117

6

.6768

. 1597

. 7577

64

84

118

7

.6907

. 1743

.7689

64

83

119

8

. 7046

l.SS'l

.7801

64

83

120

9

.7186

. 2034

.7913

64

82

122

1900

336. 7325

244. 2180

254. 8025

9. 99864

9. 94182

9. 69123

1

7464

. 2325

.8137

64

82

124

2

. 7604

.2471

. 8249

64

81

1 25

3

. 7743

.2616

. 8360

64

81

127

4

7882

. 2702

.8472

64

80

128

L905

336. 8022

244. 2907

254. 8584

9. 99864

9. 94180

9.6912H

6

.816]

. 3053

K090

65

79

130

7

. 8300

. 3198

.8808

65

79

132

8

. 8439

. 3344

.8919

65

78

133

9

.8579

. 3489

. 9031

65

78

134

l'.UO

336. S71S

244. 3635

254.9143

9. 99865

9.94177

9. 69135

1

.8857

. 3780

9255

65

77

137

2

.8997

. 3926

:i:;i;7

65

■76

L38

3

.9136

.4071

. 9478

65

76

139

4

. 9275

.1217

. 9590

65

75

140

L915

336.9414

244. 4362

254. 9702

9. 99866

9. 94175

9. 69141

6

. 9554

i;,iis

.9814

66

7:.

143

7

!ir,!i:;

in:.:;

254. 9926

66

74

144

8

.9832

.4798

255. 0037

66

74

145

9

336. 9972

.4944

.0149

66

73

146

1920

337.0111

244. 50S9

255. 026 1

9. 99866

9. 114173

9. 69148

1

. 0250

. 5235

.0373

66

72

149

2

. 0390

. 5380

. 0485

66

72

150

3

0529

. 5526

0596

66

71

151

4

.0668

. 5671

.0708

66

71

152

1925 '

337. 0808

244. 5817

255. 0820

9. 99866

9. 94170

9.69151

6

.0947

. 5962

. 0932

67

70

155

7

. 1086

lilllS

. 1044

67

69

1*56

8

. 1225

. 6253

. 1155

67

69

157

9

. 1365

.6399

. 1267

67

68

159

1930

337. 1504

244. 65 1 1

255. 1379

9. 99867

9. 94168

9. 69160

Year

log cos a

log cos 6

log cos c

1873. 0
1930. 0

8. 902 n
8. 893 n

9. 685 n
9. 686 n

9.940
9.940

278 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF (139) JUEWA.

MEAN ELEMENTS.

Epoch, 1897, Jan. 29.0, M. T. Berlin=1897.079, M. T. Berlin.

o / //

00=155 29 57 = 155?4991
<u=162 12 34 = 162.20941

Q,= 2 27 38= 2. 4604 Mean equinox and eclipt

ic 1900.0.

i= 10 55 12= 10.9200J

<p= 10 2 40= 10.0443

?i=764". 1684 = 0. 21226900

The elements are based on oppositions extending from 1874 to 1898 and on the perturbations of the

firsi

order by Jupiter, as given on page 279.

AUXILIARY QUANTITIES.

log a=0. 44454 log 57. 2958 e=0. 99970 log./1-'
log e=9. 24158 logp =0.43113 »l+«

=9. 92347

TABLE I. — MEAN ANOMALY (g).

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Month

9

Year

9

Year

9

T 10.0

o

| 0. 00000

O

O

1S74

166. 07140

1902

176.73419

5

243. 54958

3

254. 2 12: is

*M?:8

} 6. 5S034

. B

6

321.24004

B 4

331. 90283

7

38. 71822

5 49.38102

Mar. 0.0

12. 52387

8

116. 19641

6 126. 85920

Apr. 0.0

19. 10421

9

193. 67459

7

204. 33739

May 0.0 25.47228

B

1880

271. 36505

B 8

282. 027S4

Juiie 0.0 32. 05262

1

348. 84323

9

359. 50603

■

July 0.0

38. 42069

2

66. 32142

1910

76.98421

Aug. 0.0

45. 00103

3

143. 79960

1

154.46240

Sept. 0.0

51. 58137

B

4

221. 49006

B 2

232. 15285

Oct. 0.0

57. 94944

5

298. 96824

3

309.63104

Nov. 0.0

64. 52978

6

16. 44643

4

27. L0922

Dec. 0.0

70. 89785

7

93.92461

5

104. 5S741

B

8

171. 61507

B 6

182. 27786

9

249. 09325

7

259. 75604

Change for n days a

1890
1

326 57144
44. 04962

8
9

337.23423
54. 71242

B

2
3

4

121. 7400S
199.21826
276. 69644

B 1920
1
2

L32. 40287

209. SSI 05
287.35924

n

9

n

9

O

5

354. 17463

3

4. 83742

B

6

71. 86508

B 4

82. 52788

1

0.21227

16

3. 39632

7

149. 34327

5

L60. 00606

2

0. 42454

17

3. 60859

8
9

226. 82145
304. 29964

6

7

237. 18425
314.96243

3
4

0. 63681
0. 84908

18
19

3. 82086

4. 03313

1900

21. 77782

B 8

32. 65289

5

1.06135

20

4. 24540

1 ,

99. 25601

9

110. 13107

6

1.27362

21

4. 45767

1930

187. 60926

7
8
9

10
11

1. 48589
1.69816

1. 91043

2. 12270
2. 33497

22
23
24
25
26

4. 66994

4. 88221

5. 09448
5. 30675
5. 51902

Is

OTE. — W

ion q is used as an argument of the perturba-

lions add 1

o the g of this table 4n=iz— ?r0=+0?2733.

12

2. 54724

27

5. 73129

For

explam.t

ion see page 203.

13

2. 75951

28

5. 94356

14

2.97178

29

6. 15583

15

3. 18405

30

6. 36810

op

or days during January and

Febr

uary of leap years subtract one

day 1

before entering this table.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (189) Juewa — Continued.

279

PERTURBATIONS.

ndz

V

ft/cos i

Arg.
%g~%'g'

sin

cos

sin

cos

sin

cos

i V

//

//

//

//

/f

//

0 0

6

+ 1

0 0

+ 0.08nl

+ 2. Olnt

+ 1 o

+ 9

+1

2. Olnt

17. 75nt

- 8. 87nt

+ 1. OOnt

- 2. 44nt

— 7. 76nt

+2

+ 1

1

1

+ 2

— 1

+2

0. 08nt

0. 76nt

0. 7(int

+ 0. 08nt

- 0. 21nt

- 0. 67nt

+3

0. Olnt

0. 07nt

0. lOnt

+ 0. Olnt

- 0. 03nt

- 0. 09nt

+4 0

0. Olnt

0. Olnt

- 0. Olnt

-2 +1

+ 1

+ 1

+ 1

—1

+ 14

+ 1

+ 9

+ 7

- 1

0

+ 5G

• 28

+ 3

+ 8

+ 9

- 3

+ 1

+ 215

- 100

- 33

- 71

- 1

+2 +1

+ 12

- 7

■ 5

9

+ 6

- 4

-1 +2

+ 2

- 1

+ 1

+ 2

+ 5

- 2

0

+ 23

+ 3

- 3

+ 8

+21

-16

+1

+ 703

- 042

-161

-111

-16

+13

+2

+ 2S4

- 410

-235

-163

+ 1

- 6

+3

+ 14

— 22

- 23

- 15

- 1

+ 1

+4 +2

+ 1

_ 2

3

_ 2

-1 +3

- 1

- 1

+ 1

0

4

_ 2

3

- 7

+ 10

+ 1

+ 173

- 424

+ 69

+ 23

- 4

+ 11

+2

- 177

+ 645

+283

+ 76

+ 10

-26

+3

- 11

+ 62

+ 50

+ 9

+ 1

- 2

+4

1

+ 5

+ 7

+ 1

- 1

+5 +3

+ 1

+ 1

0 +4

+ 1

_ 2

+ 1

+ 2

+ 1

+ 2

18

+ 7

+ 9

+2

+ ii;

+ 267

+ 74

5

- 9

+3

+ 20

+ 90

+ 55

- 11

- 5

+4 +4

2

■ 2

+ 1

- 1

0 +5

+ 2

+ 1

13

16

+ 8

— 7

+ 6

+26

+2

+2034

+5210

ISO

- 78

+ 3

+ 2

+3

+ 395

+ 645

+343

210

-21

-49

+4

+ 8

+ 18

+ 22

- 12

2

- 3

+5

+ 2

+ 3

+ 4

3

+6 +5

+ 1

+ 1

+ 1

1

+ 1 +6

2

4

+ 2

- 1

+2

.+ 17

+ 26

■ 6

+ 6

_ 2

- 4

+3

- 72

62

- 23

+ 28

+ 4

+ 4

+4

17

12

- 7

+ 12

+ 2

+ 1

+5 +6

+ 2

_ 2

+2 +7

0

5

+ 2

+ 1

+3

• 86

42

4

+ 19

+4

40

- 8

- 5

+ 21

+5

+ 3

- 1

+6 +7

•

- 1

+ 1

+3 +8

• SO

- 13

+4

+ 71

17

9

- 32

+5

+ 9

- 3

- 2

7

— 1

+6 +8

- 1

+ 1

+ 1

+ 1

280 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (139) Juewa — Continued.

TABLE II.— n<5z.

PERIODIC TERMS.

Unit of a and 6=09001.

i

0

1

2, 3

i

Diff.

Diff.

6,

Diff.

Diff.

1

Diff.

9'

bo

fori0

«i

fori0

for 1°

ai

fori0

for 1°

O

0

-8.3

-0.45

+294. 8

-16.55

-417.2

-10.05

+ 5.6

-0.72

-4.8

-1.06

6

-10. 9

-0.41

+ 190. 2

-18. 08

—464. 4

- 5. 63

- 1.6

-1.40

- 8. 1

+0.12

12

-13.2

-0.37

+ 80.3

-18. 35

-484. S

- 1. 16

- 9.2

-0.85

- 3.4

+1. 35

18

—15.3

-0.32

- 27.7

-17.47

—478. 3

+ 3. 12

— 10.2

+0. 59

+ 6.6

+1.73

24

-17.0

-0.26

-127.6

-15.68 !

-447. 3

+ 6.99

- 2. 1

+ 1.98

+15. 0

+0.76

30

-18.4

-0. 22

-214.3

-13.02

-395. 8

+ 10.07

+11.4

+2.17

+ 14.2

-1.06

36

-19.6

-0. 18

-283. 8

- 9.99

-328. 0

+12.35

+20.9

+0.74

+ 2.3

-2.62

42

-20.5

ii 1 I

-334. 2

- 6.68

-249. 2

+ 13. 82

+18.8

-1.39

-14.5

-2.61

48

-21.3

-0. 11

-364. 0

- 3.23

-163.8

+ 14.43

+ 4.2

-3. 15

-25.9

-0.86

54

-21.8

-0.07

-373. 0

+ 0. 12

- 77.6

+ 14.23

-15. 8

-3.06

-23. 4

+1. 72

60

-22.1

-0.02

::i;2 i;

+ 3.21

+ 5.5

+ 13. 32

-29. 0

— 1. 05

-6.6

+3. 58

60

-22.1

+0.03

-334. 5

f 5 94

+ 80.8

+ 11.62

-26. 8

+1.83

+16.0

+3.44

72

-21. 7

+0.10

-291.3

+ 8.26

+144. 9

+ 9.51

-8.6

+3.85

+30.8

+1.18

78

-20.9

+0. 16

-236. 7

+ 9.80

+194. 9

+ 7.00

+15.4

+3.68

+28.6

-1.89

84

-19.8

+0. 22

-175. 0

+10. 63

+228. 9

+ 4.28

71'

+31.6

+1.33

+ 9.8

-4. 02

90

-18.2

+0.30

-110.6

+10. 75

+246. 2

+ 1.58

<M

+29. 8

-1.89

-15.4

-3. 82

96

—16.2

+0.38

- 47.4

+10. 06

+247. S

- 0.92

-o
c

c4

+ 10.8

—4.04

-32.0

-1.40

102

—13.7

+0.44

+ 10.2

+ 8.85

+235. 1

- 3.03

-14.4

-3.85

-30.7

+ 1. 85

108

-10.9

+0.48

+ 58.8

+ 7. 29

+211. 4

- 4.62

CO

-31.4

-1.47

-12.0

+3. 96

114

-7.9

+0.49

+ 97.7

+ 5. 55

+ 179.6

- 5.65

C-1

-30.6

+ 1.69

+12. 5

+3.74

120

- 5.0

+0.49

+ 125.4

+ 3.79

+143. 6

- 6. OS

m

-13.1

+3.74

+29.0

+ 1.29

126

- 2.0

+0.48

+ 143.2

+ 2.22

+106. 7

- 6.02

be

+ 10.0

+3.41

+28.0

-1.63

132

+ 0.7

+0. 42

+ 152.0

+ 0.88

+ 71.3

5. (17

P.

+24.4

+ 1.04

+ 11.7

-3.39

138

+ 3.1

+0.36

+ 153. 8

- 0.09

+ 38.7

- 5. 1 1

o

+22. 5

-1.62

-8.6

-2.89

144

+ 5.0

+0.29

+150. 9

- 0.72

+ 10.0

- 4. 4S

XI

+ 7.2

-3.02

-19.7

—0.56

150

+ 6.6

+0. 22

+145. 1

- 1.07

- 15.0

— 3.95

Gv

-10.2

-2.32

-15.3

+1.89

156

+ 7.7

+0.14

+138. 1

- 1.29

— 37.4

- 3.60

60

-17.6

+0. 06

+ 0.4

+2.90

162

+ 8.3

+0.07

+129. 6

- 1.48

- 58.2

- 3.43

—

- 9.5

+2.39

+ 15. 7

+ 1.78

168

+ 8.5

+0. 02

+ 120.3

- 1.71

- 78. 6

- 3.40

cc

+ 8.0

+3.01

+ 19.2

-0. 71

174

+ 8.5

-0.01

IIMI 1

- 2. 10

- 99.0

- 3.47

+22.8

+ 1. 51

+ 7.2

-3.00

180

+ 8.4

-0.02

+ 95.0

- 2.68

-120. 2

- 3.53

>

+23.8

-1.20

-13.4

-3.36

186

+ 8. 3

-0. 02

+ 76.8

- 3.46

-141.4

- 3.47

-'

+ 8.4

-3. 54

-29.1

-1.48

192

+ 8.2

-0.02

+ 53. 5

- 4.38

-161.8

- 3. 22

Js

-15.0

-3. 73

-29.0

+1.60

198

+ 8.1

0.00

+ 24.3

- 5.41

-180.0

- 2.66

c

-32. 2

-1.58

-11.4

+3.87

204

+ 8.2

+0.02

- 11.4

— 6.42

-193. 7

- 1.73

0)

>

-32.1

+1.61

+13.6

+3.98

210

+ 8.4

+0. 05

- 52.7

- 7.27

-200. 8

- 0.48

'&

-14.4

+3.96

+32.2

+1.78

216

+ 8.8

+0. 09

- 98.6

- 7.82

-199. 4

+ 1.12

X

+11.4

+4.08

+33.1

-1.49

222

+ 9.5

+0. 11

-146.6

- 8.05

-187. 4

+ 3.00

V.

+30.4

+1.88

+15.9

-3.86

228

+10. 1

+0.11

-195. 2

- 7.82

-163. 4

+ 5.00

+32.2

-1.34

-9.3

-4.03

234

+10.8

+0. 12

-240. 4

— 6.98

-127. 4

+ 7.01

CO

+ 16.0

-3.65

—28.2

—1.89

240

+ 11.5

+0.12

-279. 0

- 5.64

- 79.3

+ 8.91

■d

-7.6

-3.75

-30.2

+1.19

246

+12.3

+0.13

-308. 1

- 3.79

- 20.5

+ 10.57

<3

-25.2

-1.77

-15.6

+3.31

252

+13. 1

+0. 12

-324. 5

- 1.49

+ 47.5

+ 11.78

<M

-27.4

+ 1.01

+ 5.8

+3.38

258

+13.7

+0. 11

-326. 0

+ 1. 16

+ 120. 9

+ 12. 44

Jl

-14.6

+2.90

+21.5

+ 1.47

264

+14.4

+0.12

-310. 6

+ 4.07

+ 196. 8

+ 12. 65

u

+ 4.0

+2.90

+23. 4

-0.89

270

+15.2

+0.10

-277. 2

+ 7.08

+271. 2

+ 11.97

&

+17. 2>

+1. 18

+12.4

-2.47

276

+15.6

+0. 06

-225. 6

+10. 00

+339. 0

+ 10. 59

+18.2

-0. 85

-3.2

-2. 35

282

+15.9

+0.04

-157. 2

+12. 65

+396. 7

+ 8.43

+ 8.6

-2.06

-13.3

-0.80

288

+16. 1

0.00

- 73.8

+ 14.99

+438. 6

+ 5. 39

— 3. 8

-1.74

—12.8

+0.92

294

+15.9

-0. 06

+ 21.3

+16. 58

+461. 4

+ 1.87

-10.4

-0.34

-3.9

+ 1.74

300

+15.4

-0.12

+ 123.2

+17. 21

+461. 0

- 2. 16

-7.9

+1.04

+ 5.7

+1.20

306

+14.4

-0. 19

+225 8

+ 16. 84

+435. 5

- 6.39

+ 0. 4

+1.46

+ 9.0

—0. 10

312

+13.1

-0. 26

+323. 0

+ 15.33

+384. 3

-10. 58

+ 7.6

+0.66

+ 4.5

—1.22

318

+11.3

-0.32

+ 407.4

+ 12.61

+308. 5

-14.47

+ 8.3

-0.45

-3.8

—1.28

324

+ 9.2

-0.41

+ 472. 3

+ 8.89

+212. 2

-17.49

+ 2.2

-1.28

- 9*1

-0.31

330

+ 6.4

-0. 46

+512. 5

+ 4.32

+ 100.6

-19.49

-5.4

-1.07

-7.5

+0.72

336

+ 3.7

-0.48

+524. 1

- 0.56

- 19.0

-20. 13

-9.2

-0.02

- 0.4

+1.32

342

+ 0.7

-0. 52

+505. 8

- 5.46

-138. 2

-19. 36

-5.7

+ 1.03

+ 6.5

+0.70

348

-2.5

-0. 52

+458. 6

-10. 08

-248. 8

-17.31

+ 1.6

+ 1. 20

+ 8.0

—0.31

354

- 5.5

-0.48

+386. 4

-13.82

-343. 8

-14. 17

+ 7.0

+0.33

+ 2.8

—1.23

360

-8.3

-0.45

+294. 8

-16. 55

-417. 2

-10.05

+ 5.6

-0.72

-4.8

-1. 06

[noz, I log r, and u/cos i are to be computed in the form Si ai sin ig+Si bt cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER,

Tables of (139) Juewa — Continued.
TABLE II.— nSz— Continued.

281

PERIODIC TERMS.

Unit of a and o=0°.001.

i

2

3

g'

a2

Diff.forl°

b2

Diff.forl0

«3

Kill. fori0

63

Diff.forl0

0

0

+ 636.4

+143. 41

+ 1661.9

- 52. 73

+ 53.6

+ 14. 67

+ 190. 9

- 2.32

3

+1040. 7

+125. 49

+1447. 6

- 87. 73

+ 99.5

+ 15.20

+178. 5

5 'is

6

+ 1380. 8

+ 98.69

+1141. 6

-116. 15

+ 143.3

+ 13. 73

+155. 0

- 9. 92

9

+ 1626. 8

+ 65.96

+ 756. 2

-137.99

+ 181.9

+ 11. 15

+ 119.0

-13.63

12

+ 1772. 2

+ 28.66

+ 323. 2

-149. 59

+212. 0

+ 7.88

+ 73. 2

-16. 83

15

+ 1797. 1

- 10. 13

- 132.0

-152. .05

- 229. 2

+ 3. 42

+ 18.0

- 19.36

18

+ 1711.4

- 48. 29

- 578 7

-143. 70

+ 232. 5

- 1. S3

- 41.6

20. 26

21

+ 1510. 5

83 22

- 985 1

-126. 75

+218. 2

- 7. 35

-102. 1

- L9 76

24

+1218.0

-111.94

-1330.7

-100.91

+188. 4

-12. 6S

L58 1

-17.42

27

+ 846.0

-133 7(1

-1584.8

- 69. 12

+ 142. 1

-17. 35

-205. 2

-13. 67

30

+ 425. 1

-145. 78

-1741.0

- 32. 69

+ 84. 3

-21. 14

239. (i

- S. 25

33

- 19. 5

-lis 88

-1779. 2

+ 5. 33

+ 17.0

-23. 11

-254. 7

- 2. 23

36

- 458.0

-141.37

-1709.0

+ 41' 7'.(

- 51. 4

-21. 69

252. 1

+ 4. 22

39

- 85S. 9

-125.23

-1525.5

+ 77. 13

-111. 8

-19. 00

-229.4

+10.48

42

-1201. 0

-100.38

-1252.0

+105. 44

-165. 1

-17. 16

IS9 5

+ 15.92

45

-1455.2

611 (IS

- 899. 8

+126. 99

-213.4

-14.07

-133.9

+20. 38

48

-1614. (i

- 34.33

499. 2

+ 139. (1.;

-246. 4

- 6.67

69 11

+22. 74

51

-1659.5

+ 2. 53

74. 6

+142. 25

-253. 4

+ 0.97

+ 0.8

+23.41

54

-1599. 4

+ 38. 85

- 344. 3

+135. 02

-240. 6

+ 7. 12

+ 69. 4

+21. 89

57

-1429. 4

+ 72. 1 1

+ 727.0

+ 119. 47

-208 9

+ 12. 97

+ 130. 5

+ 1S. 79

60

-1172. 4

+ 99. 1 1

+1052 '(

+ 95.30

-162.8

+ 17. 57

+ 180. 6

+ 13.90

63

- 839. 6

+ 120.09

+ 1293. 3

+ 65. 51

Kit. '.i

+20. 57

+213. 9

+ 8.33

66

- 460.8

+ 131.44

+ 1441. 7

+ 31. 24

- 41.2

+21. 62'

+230. 6

+ 2.30

69

- 59.8

+ 134. 17

+ 1479. 1

— 4.47

+ 23. 2

+21. 09

+ 227. 7

- 3.70

72

+ 334. 4

+ 12(1 65

+ 1414.9

- 39. 57

+ S3. 6

+18. 53

+208. 4

- 9.03

75

+ 691. 7

+ 110. 92

+ 124 1. 7

- 71.56

+ 134.4

+15. 03

+ 173.5

-13.50

78

+ 991. 9

+ 86. 81

+ 99 1 . 2

- 97 63

+ 173.8

+ 10. 55

+ 127. 4

L6. 68

81

+1207. 0

+ 57 26

+ 665. 7

-117.06

+ 197. 7

+ 5.50

+ 73.4

-18. 83

84

+1331.4

+ 23.47

+ 297. 8

-127. 14

206. s

+ 0. 32

+ 16.0

-IS. 92

S7

+ 1346. 1

- 11.57

- 88.4

-128. 68

+ 199. 6

- 4.67

- 40. 1

-17.97

90

+ 1262. 0

- 45 86

- 464.6

-120. 17

+178. s

- 9.03

- 91. 8

-15. 78

93

+ 1074.4

- 76. 87

- 801. 2

-103. 67

+ 145.4

-12. 67

-134. S

-12.67

96

+ 806. 6

-101.81

-1078. 7

- 78.90

+ 102. 8

-15. 28

-167.8

- 8.83

99

+ 470. 4

—120. 03

-1269. 1

- 48.74

+ 53.7

-16. 87

-187.8

- 4.55

102

+ 95.3

-128. 99

-1367.4

- 14.43

+ 1-6

-17. 30

-195. 1

- 0. 10

105

- 294. 8

I I'll 37

-1355.7

+ 20. 50

- 50.1

-16. 70

-1SS. 4

+ 4.32

108

— 671 2

-119.59

-1244.4

+ 54. 78

- 98. 6

-15. OS

-169. 2

+ 8.40

111

-1004. 2

—101. 87

-1030.3

- S5 (i'_>

-140. 6

-12. 5:;

-138. 0

^11.97

114

-1274. 6

- 75. 98

736.6

+ 110.25

-173.8

- 9. 10

- 97.4

+14. 80

117

-1454. 7

- 44. 82

- 375. 8

+128. 01

-195 2

- 5.05

- 49.2

+16. 77

120

-1539. 8

9. 60

+ 22. 4

+136. 33

-204. 1

- 0.60

+ 3.2

+17. 72

123

-1512. 3

+ 26. 17

+ 433. 3

+ 135 96

-198.8

+ 3.98

+ 57.1

-J-17.57

126

-1382 8

+ 61 28

+ 828. 4

+ 125 13

-ISO. 2

+ 8.50

+ 108.6

+16. 15

129

-1148.1

+ 92. 79

+ 1177.6

+ 106. 81

-117. S

+12. 57

+ 154.0

+ 13.63

132

- 832. 2

+117. 91

+1461. 4

+ 80.03

-104. 8

+ 15. S7

+ 190.4

+ 9. 98

135

- 447. 8

+136. 06

+1652. 3

+ 47 93

- 52 6

+ 18. 23

+213. 9

5. 57

138

- 25. 0

+144. 66

+1745. 2

+ 11. 67

+ 4.6

+19. 57

+223. 8

+ 0.60

141

+ 411. 2

+144. 51

+ 1722. 3

- 25. 13

+ 63.5

+19. 39

+217. 5

- 4. 57

144

+ S32. 2

+134. 12

+1594. 4

- 61. 24

+ 119.4

+17. 37

+ 196.4

- 9.60

147

+1207. 5

+115. 50

+1358. 3

- 93. 77

+ 167. 7

+ 14. 32

+ 159.9

-14. 07

150

+1517. 2

+ 88.53

+1037. 8

-119.97

+205. 3

+10. 15

+ 112.0

-17. 48

153

+ 1733. 1

+ 56. 11

+ 645. 6

-139. 16

+228. 0

+ 5. 15

+ 55.0

111 116

156

+ 1850. 0

+ 19.67

+ 212.0

-148. 78

+235. 6

- 0.38

-6.2

-20. 61

159

+1849. 8

- 17.88

- 238. 1

-149.59

+225. 7

- 5. S3

- 67.2

-19.84

162

+ 1742. 7

- 54.66

- 675. 6

-140.06

+200. 6

-10. 87

-123.6

-17.18

165

+1525 2

- 87.94

-1070.0

-122. 29

+ 160.5

-15.32

-170. 3

-13. 60

168

+ 1221.0

-115.05

-1401.2

- 96.05

+ 110.0

-18. 24

-205.2

- 8.97

171

+ 842. 0

-135.25

-1640.6

- 64. 21

+ 52. 4

-19. 87

-224. 1

- 3. 77

174

+ 418.6

-145.96

-1782.6

- 28. 26

-7.6

-19. 82

-227. 8

+ 1.55

177

- 24.8

-147. 93

-1808. 7

+ 9.02

- 65. -'

-IS. 27

-214.8

+ 6.63

180

- 459.0

-139. 54

-172s. 5

+ 45. 61

-117.2

-15. 63

-188.0

+ 11.07

[ruiz, 3 log r, and u/cos i are to be computed in the form Jt o-i sin ig+ J\ 6» cos ig+cT.]

282 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (139) Juewa — Continued.

TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6=09001

i

2

3

9'

a2

Diff. fori0

b2

Diff. fori0

Q3

Diff. fori0

h

Diff. fori0

O

180

- 459.0

-139.54

-1728. 5

+ 45. 61

-117.2

—15. 63

-188. 0

+ 11.07

183

- 853. 6

-122.93

-1538. 2

+ 78. 92

-159.0

-12.00

—148.4

+ 14.60

186

-1188.4

- 97.84

-1260. 8

+106. 17

-189. 2

- 7.60

-100.4

+ 16. 85

189

-1434.9

- 61. 16

- 908.0

+126. 72

-204. 6

— 2.87

- 47.3

+17. 92

192

-1587. 2

- 32. 21

- 509.4

+137. 95

-206. 4

+ 1.82

+ 7.2

+17.72

195

-1626. (i

+ 4.10

- 89.1

+ 140. 54

-193. 7

+ 6.23

+ 59.0

+16.42

198

-1562.6

+ 39. 77

+ 324. 0

+ 132. 86

-169.0

+ 10.02

+ 105. 7

+ 14. 10

201

-1391.0

+ 72.32

+ 699.7

+117.00

-133.6

+ 13. 07

+143.6

+ 10. 95

204

-1134.3

+ 99.00

+1018.0

+ 92. 82

- 90.6

+15. 22

+ 171.4

+ 7. 20

207

- 803. 8

+ 119.05

+ 1251.0

+ 63. 11

- 42.3

+ 16.43

+ 186.8

+ 3. 10

210

- 428. 9

+ 129.82

+1392. 6

+ 29. 13

+ 8.0

+ 16.55

+ 190.0

- 1. 10

213

- 33. 6

+132. 08

+1424. 3

- 6.17

+ 57.0

+15.70

+ 180.2

- 5.20

216

+ 353.9

+ 124.25

+1355. 6

- 40. 81

+ 102. 2

+ 13.97

+ 158.8

- 8.98

219

+ 703.7

+ 108. 38

+ 1182.5

- 72. 31

+ 140. 8

+ 11. 40

+ 126. 3

-12. 27

222

+ 996. 3

+ 84. 29

+ 927.4

- 97.91

+ 170. 6

+ 8.00

+ 85. 2

-14.92

225

+ 1203.9

+ 54. 74

+ 601. 8

-116.85

+ 188.8

+ 4.00

+ 36.8

-16. 72

228

+1320. 8

+ 21.07

+ 235. 1

-126.59

+ 194.6

- 0. 52

- 15. 1

—17.48

231

+1329. 0

- 13.73

- 149. 1

-127.88

+ 185.7

- 5. 17

— 68.1

-17. 15

234

+ 1238.4

- 47. 83

- 522.5

-119.08

+163.6

- 9.67

-118.0

-15. 52

237

+ 1045. 2

- 78. 64

- 855.4

-102.30

+127. 7

-13. 73

-161.2

-12. 73

240

+ 772.4

-103.41

-1128.5

- 77.38

+ 81.2

-17.08

-194. 4

- 8.77

243

+ 431. 7

-121.42

-1314.2

- 47. 11

+ 25. 2

-19. 63

-213.8

- 3.97

246

+ 52. 9

-130. 04

-1407.4

- 12. 71'

- 35.0

-20. 40

-218. 2

+ 1.53

249

- 339. 8

-130. 12

-1390. 5

+ 22. 27

- 95.7

-19.74

-204. 6

+ 7.20

252

- 718. 1

-120. 09

-1273. 8

+ 5li' 65

-151.8

-17.34

-175.0

+ 12. 60

255

-1052. 1

-102.04

-1054.0

+ 87. 51

-198. 3

-13. 54

-129.0

+ 17.27

258

-1322. 5

- 75.82

- 754.8

+112.06

-231. 6

- 8.03

- 71. 4

+20. 92

261

-1501. 6

- 44.35

- 388. 7

+129. 69

-246. 5

- 1. 95

- 5.0

+22. 89

264

-1584. 8

- 8.73

+ 14.2

+137. 79

-243. 3

+ 4.57

+ 64.0

+22. 82

267

-1554.0

+ 27. 63

+ 429. 1

+137. 13

-219. 1

+ 10. 88

+ 130. 1

+21.01

270

-1420.4

+ 62. 72

+ 827. 0

+ 126.07

-178.0

+ 16.42

+ 188. 1

+17. 10

273

-1181. 3

+ 94. 26

+1177.2

+ 106.88

-120.6

+21. 08

+231. 3

+11.65

276

- 861.0

+119. 37

+ 1460.4

+ 79.49

- 53.4

+23. 56

+258. 0

+ 5.32

279

- 472. 4

+ 137.29

+ 1648.7

+ 46. 76

+ 18.9

+24. 26

+263. 2

- 1.48

282

- 46.7

+145.42

+1737. 2

+ 9.90

+ 90.0

+22. 67

+249. 1

- 8. 10

2S5

+ 391.0

+ 144.67

+170S. 1

- 27. 63

+153. 2

+ 19.41

+214. 6

-14.28

288

+ 811.2

+ 133. 36

+1572. 8

- 63. 91

+204. 8

+ 14. 23

+ 164.8

-18. 89

291

+1182. 6

+113. 67

+1328. 3

- 96. 58

+238. 6

+ 8.33

+ 102.9

-21. 93

294

+1485. 1

+ 85. 53

+ 999. 7

-122. 61

+254. 8

+ 2.00

+ 35.2

-22. 87

297

+ 1G90. 2

+ 51. 92

+ 600. 1

—141. 35

+250. 6

4 22

- 32. 6

—22. 13

300

+ 1792.8

+ 14. 12

+ 161.2

-150.09

+229. 5

- 9^73

- 95.8

-19. 27

303

+ 1774. 9

- 24.40

- 291. 1

-149. 70

+ 192.2

-14. 48

-148. 2

-15. 43

306

+1647. 8

- 61. 67

- 726. 7

-138. 56

+ 144. 2

-17.36

-188. 4

-10.72

309

+1408.6

- 95. 30

-1113.8

-118.95

+ 89.4

-18.95

-212.5

- 5.60

312

+1082. 4

-122. 28

-1432. 1

- 90.68

+ 32. 1

-18.62

-222. 0

- 0.57

315

+ 682.5

— 141. 89

-1652. 1

- 56.78

- 22. 3

-17.32

-215. 9

+ 4.03

318

+ 240.8

-151. 39

-1768. 8

- 18. 55

- 71.8

-15. 02

-197.8

+ 7.68

321

- 216.4

-151.66

-1763. 4

+ 20. 30

-112.4

-12.07

-169.8

+ 10. 47

324

- 658.8

-141.11

—1647. 0

+ 58.46

-144. 2

- S. 88

-135.0

+12. 23

327

-1054. 2

—121. 88

-1416. 3

+ 92. 84

-165. 7

- 5.65

- 96.4

+ 13. 22

330

-1381. 6

- 93.85

-1096. 4

+120. 54

-17S. 1

2. 72

- 55. 7

+ 13. 40

333

-1611.4

- 60.07

- 700.6

+140. 85

-182.0

- a 02

- 16.0

+13. 05

336

-1737.9

- 22.00

- 260. 9

+151. 18

-178.2

+ 2. 32

+ 22. li

+ 12. 43

339

-1742. 0

+ 17.25

+ 197.0

+151' 24

-168. 1

+ 4.42

+ 58.6

+ 11. 53

342

-1634.4

+ 55.68

+ 642.0

+142. 29

-151.7

+ 6.37

+ 91.8

+10. 53

345

-1411.4

+ 90.51

+1041. 8

+ 123. 61

-129.9

+ 8. 15

+121.8

+ 9.33

348

—1097. 6

+ 118.79

+1375. 2

+ 96. 13

-102. 8

+ 9.93

+ 147.8

+ 7.92

351

- 7011. 1

+139. 76

+ 1612.6

+ 62. 79

- 70.3

+11.63

+169. 3

+ 6.13

354

— 268. 6

+150. 79

+1747. 6

+ 24. 93

- 33.0

+ 13.63

+184. 6

+ 3.85

357

+ 189.2

+152. 59

+ 1760.6

- 14.28

+ 11.5

+ 14.43

+ 192. 4

+ 1.05

360

+ 636.4

+ 143.41

+ 1661. 9

- 52. 73

+ 53.6

+ 14.67

+190. 9

- 2.32

[ndz

(J log t, and u/cos i are lo be computed in the form J| ai sin ig+2{ bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of {139) Juewa — Continued.

i>s:;

TABLE II.— ndz— Continued.

PERIODIC TERMS.

Unit of a ami o=0?0Ol.

i

5

6

/

«5 !

Diff. for 1°

h

Diff. for 1°

«6

Diff. for 1°

&6

Diff. for 1°

O

0

+4.5

-0.02

0.0

-0. 52

-0.6

+0.03

+0.3

+0.07

6

+3.1

-0. 36

-2.9

-0.32

-0.2

+0.08

+0.6

+0.02

12

+0.2

0 16

-3.9

+0.02

+0.3

+0.07

+0.6

-0.04

IS

-2.4

-0. 28

-2.6

+0.31

+0.6

+0. 02

+0. 1

-0.07

24

-3.1

+0. 04

-0.2

+0.38

+0.5

-0. 03

-0. 2

-0.06

30

-1.9

+0. 28

+1.9

+0. 22

+0.2

- II 1)7

-0. 6

-0.02

36

+0.2

+0. 31

+2.5

-0.06

-0.3

-0. 06

-0.5

+0.03

42

+1.8

+0.13

+1.2

-0. 26

-0.5

-0. 01

-0. 2

+0.07

48

+ I.S

-0. 12

-0.6

-0.25

—0.4

+0.03

+0.3

+0.06

54

+0.4

0. 26

—1.8

-0.08

-0. 1

+0.05

+0.5

+0.01

60

—1.3

—0. 22

-1.5

+0. L6

+0.2

+0. 04

+0.4

-0.03

66

—2. 2

0.00

+0.1

+0.28

+0.4

+0.01

+0.1

-0. 05

72

—1.3

+0.22

+1.8

+0.19

+0.3

-0.03

-0.2

-0.03

78

+0. 4

+0.29

+2.4

-0.03

0.0

-0.04

-0.3

0.00

84

+2.2

+0.19

+ 1.4

-0. 25

-0.2

-0.02

—0.2

+0.02

90

+2.7

-0.05

-0.6

-0.31

-0.3

0.00

0.0

+0.03

96

+ 1.6

—0. 28

-2.3

-0. 18

-0.2

+0.02

+0.2

+0.02

102

-0.6

-0 32

-2.7

+0.07

0.0

+0.03

+0.3

-0.01

108

-2. 3

-0. 15

—1.5

+0.27

+0.2

+0.01

+0.1

-0.02

114

-2.4

+0.08

+0.5

+0.28

+0.1

-0.01

0.0

-0.02

120

—1.3

+0. 23

+1.9

+0.13

+0.1

-0.02

-0. 1

—0.01

126

+0.4

+0.25

+2.1

-0.08

-0.1

-0.02

-0. 1

+0.01

132

+ 1.7

+0. 09

+0.9

-0.22

-0.1

+0.01

0.0

+0.02

138

+1.5

-0. 12

-0.6

-0.19

0.0

+0. 02

+0.1

+0.01

144

+0.3

-0.20

—1.4

-0.02

+0.1

+0.01

+0.1

-0.02

150

-0.9

-0. 13

-0.9

+0.15

+0.1

-0.01

-0.1

-0.02

156

—1.3

+0.04

| 0.4

+0. 20

0.0

-0.02

-0.1

-0.01

162

-0.4

+0.19

+1.5

+0.08

-0. 1

-0.02

-0.2

+0.01

168

+1.0

+0. 17

+ 1.4

-0.11

-0.3

-0.01

0.0

+0.03

174

+2.0

+0.02

+0.2

-0.25

-0.2

+0.02

+0.2

+0.02

180

+ 1.7

-0.16

-1.6

-0.24

0.0

o ii.;

+0.3

0.00

1S6

+0.1

-0.31

-2.7

-0.04

+0.2

+0.02

+0.2

-0.02

192

-2.0

-0. 25

-2. 1

+0.21

+0.3

0.00

0.0

ii in

198

-2.9

-0.02

-0.2

+0. 34

+0.2

-0.03

-0.3

—0.03

204

-2.3

+0. 22

+2.0

+0.28

-0.1

-0. 05

-0.4

+0.01

210

-0.3

+0.34

+3.1

+0. 04

-0.4

-0.03

-0. 2

+0.04

216

+1.8

+0.28

+2.5

-0.21

-0.5

+0.01

+0.1

+0. 05

222

+3.0

+0. 05

+0.6

-0.33

-0.3

+0. 06

+0.4

+0.03

228

+2.4

-0. 20

-1.5

-0.28

+0.2

+0.07

+0.5

—0.01

234

+0.6

-0. 31

-2. 6

-0.03

+0.5

+0.03

+0.3

—0.06

240

-1.3

(1 22

-1.9

+0.20

+0.6

-0.02

-0.2

-0.07

246

-2.0

0.00

-0.2

+0.26

+0.2

-0.06

-0.5

-0.03

252

-1.3

+0. 18

+1.2

+0.13

-0.1

-0.07

-0. 6

+0.02

258

+0.2

+0.21

+1.4

-0.07

-0.6

-0.04

-0.3

+0.07

264

+1.2

+0.08

+0.4

-0.20

-0.6

+0. 02

+0.2

+0.08

270

+1.1

-0. 12

-1.0

-0.18

-0.3

+0.07

+0.6

+0.03

276

-0.3

-0.26

—1.7

+0.01

+0.2

+0.08

+0.6

—0.02

282

-2.0

-0. 17

-0.9

+0.23

+0.6

+0.03

+0.3

-0.08

288

-2.3

+0. 08

+ 1.1

+0.32

+0.6

-0.02

-0.3

-0.08

294

-1.0

+0.32

+ 2. 9

+0. 17

+0.3

-0.08

-0.6

-0.03

300

+1.5

+0.38

+3.1

-0.13

-0.3

-0.08

-0.7

+0.02

306

+3.6

+0.20

+1.3

-0.38

-0.7

-0.03

-0.3

+0.08

312

+3.9

-0. 11

-1.5

-0.44

-0.7

+0.04

+0.2

+0.08

318

+ 1.9

-0.43

-4.0

-0.26

-0.2

+0.08

+0.7

+0.04

324

-1.3

-0. 50

-4.6

+0. 12

+0.3

+0.08

+0.7

-0.03

330

—4.1

-0.30

-2. 5

+0.48

+0.7

+0.02

+0.3

-0.08

336

-4.9

+0.09

+1.0

+0. 54

+0.6

-0. 03

-0.3

-0.08

342

-3.0

+0.44

+3.9

+0. 32

+0.3

II lis

-0.6

-0.02

348

+0.4

+0. 53

+4.S

-0.06

-0.3

-0.08

-0.6

+0. 03

354

+3 4

+0. 34

+3.2

-0.40

-0.6

-0.02

-0.2

+0.08

360

+4.5

-0. 02

0.0

-0.52

-0. 6

+0. 03

+0.3

+0.07

[ndz, 3

log r, and ulc

as i are to be

computed in t

he form 2i at

sin ig+Zi bi

cos ig+cT.]

89369°— v

284 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (189) Juewa — Continued.

TABLE III.— 3 log r.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

0

1

2

9'

K

DifUorl"

«1

Diff. for 1°

'>,

Diff. for 1°

a2

Diff. for 1°

b..

Dili, fori0

O

0

+1.4

0.00

-23. 0

-1.00

-31. 1

+0.27

+ 63.' 2

- 1 . 66

- 35.8

-5.82

6

+ 1.4

0.00

-29.4

-1.09

-28. 9

+0.49

+ 45.0

-4.28

- 67.6

-4.51

12

+1.4

0.00

-3d. 1

-LOS

- 25. 2

+0.78

+ 13.5

-6.00

- 88.2

-2. 12

18

+1.3

-0.02

-42. 3

-0.93

Ml 11

+1.08

- 24. 6

-11. 45

- 93.2

+0. 58

24

+1.2

-0. 02

-47.3

-0. US

-12.2

+ 1.34

- 61. 6

-5.65

- 81.3

+3.29

30

+1.1

-0.02

-50. 5

-0.37

- 3.5

+1. 50

- 90.4

-3.68

- 55.0

+5.27

36

+0.9

-0.03

-51. 7

+0.02

+ 5.8

+ 1.58

-105. 7

-1.2S

- 19. 9

+6.23

42

+0.7

-0. 04

-50. 3

+0.40

+15. 5

+ 1.55

-105. 7

+ 1. 15

+ 17.5

+6.01

48

+0.4

-0. 06

-46.9

+0.74

+24.4

+1.40

— 91.9

+3.25

+ 50.2

+4.64

54

0.0

-0.08

-41.4

+ 1.03

v +32.3

+ 1.19

- 68.4

+4.39

+ 73.2

+2.88

. 60

-0.5

-0. 09

-34. 5

+1.27

+38.7

+0.96

- 41.0

+4.58

+ 84. 7

+ 1.02

66

-1.1

-0.10

-26. 2

+ 1.45

+43.8

+0.68

- 15.0

+3.89

+ 85.4

-0.52

72

-1.7

-0.11

-17. 1

+1.55

+46.8

+0.37

+ 5.7

+2.85

+ 78.4

-1.54

78

-2.4

-0. 11

-7.6

+ 1.61

+ 48. 2

+0.06

+ 111. 2

+ 1.77

+ 68.4

-1.62

84

-3.0

-0.10

+ 2. 2

+ 1. 63

+47.6

-0.28

+ 26.9

+1.03

+ 59. 0

-1.27

90

-3.6

-0.10

+ 12.0

+1.58

+44.9

-0.63

+ 31.6

+0.84

+ 53.2

-0. 65

96

-4.2

-0.08

+21. 1

+ 1.44

+40.0

-0.98

+ 37.0

+ 1.21

+ 51. 2

-0.22

102

-4.6

-0.06

+29. 3

+ 1.21

+33. 2

-1.31

+ 46.1

+1.94

+ 50.6

-0.26

108

-4.8

-0.03

+35. 6

+0. ss

+24. 3

-1.62

+ 60.3

+2.69

+ 48.1

-0.92

114

-5.0

-0. 02

+39.9

+ 0. 46

+13.7

-1.82

+ 78.4

+3.16

+ 39.6

-2. IS

120

-5.0

+0.02

+41. 1

-0.04

+ 2.4

-1.90

+ 96.8

+2.84

+ 22.0

-3.73

126

-4.7

+0.07

+39.4

II .Mi

- <). 1

-1.86

+110. 7

+ 1.61

5.2

-5. 21

132

-4. 2

+0.08

+34.4

-1.05

-HI. II

-1.66

+114.(1

-0. 50

Hi.:.

-6.28

138

-3.7

+0.08

+26.8

-1.46

-29. 0

-1.30

+ 104. 7

-2.92

- 78. 7

-6.24

144

-3.2

+0.09

+ 16.9

-1.78

-35. 5

-0.83

+ 79.6

-5. 28

-113.4

-5.13

150

-2.6

+0.10

+ 5.5

-1.94

-Mi). 0

-0.31

+ 41.4

-7.20

-13S. 2

-2.97

156

-2.0

+0.09

- (i. 4

-1.93

39. 2

+0.23

- 4. S

8 Id

-147. 7

-0.08

162

-1.5

+0.07

-17.7

-1. 79

-36.2

+0. 75

- 53 1

-7 5(1

-139.3

+2.80

168

-1.2

+0. 06

-27. 9

- 1 . 52

-30. 2

+ 1.22

— 93. 1

-5. S3

-114. 1

+5.40

174

-0.8

+0.04

-35. 9

-1 13

-21. 5

[ 1 56

-121. (1

-3.33

- 76.2

+6.99

180

-0.7

+0.02

-41. .".

-II. IIS

-11.5

+ 1. 7S

-133.4

-ii. 58

32 i;

+7.36

186

-0.5

0.00

-44. 1

-I). Id

- 0.1

+ 1.91

— 128. 6

+2.01

+ 9.7

+6.51

192

-0.7

-0.02

-43.8

+0. 29

+ 11.4

+1.88

-110.5

+3.81

+ 44.0

+4. 76

198

-0.8

-0.03

io i;

+0. 74

+22. 5

+ 1.75

- 84. 7

+4.61

+ 66.8

+2.75

204

-1. 1

-0. 03

-34. 9

+ 1.13

+32.4

• L51

- 57.0

+4.44

+ 77.0

+0.88

210

-1.2

-0.03

-27.0

-t 1.46

+ 40. 11

+ 1.21

- 33.0

+3.44

+ 77.3

-0. 54

216

1.5

-0.04

-17.4

+ I.6S

+46.9

+0. 85

- 15. 7

+2.32

+ 71.9

-1.11

222

-1.7

-0.03

- 6.9

+ 1.82

• +50. 8

li Hi

- 5. 2

+ 1.39

+ 65. 4

-0.87

228

-1.9

-0.03

+ 4. 5

+ 1. 90

+ 52. 4

+0.06

+ 10

+0.96

+ 61. 5

-0.30

234

-2. 1

-0.03

+ 15. 9

- 1 . 85

+51.5

-II. 34

+ 6.3

+ 1. 15

+ 61.8

+0.29

240

-2.3

-0.02

+26. 7

+] 73

+4S. 3

-0. 72

+ 14.8

+ 1.S3

+ 65.0

+0. 52

246

-2.4

-0.01

+36. 7

+1.53

+42.9

-1.07

+ 28.3

+2.69

+ 6S. 1

+0.13

252

-2.4

-0.01

+4.\ 1

-1 l'ii

+35. 5

-1. 38

+ 47. 1

+3.38

+ 66.6

-0.91

25S

-2. 5

0.00

+51.8

+26.4

-1.62

+ OS. 8

+3.57

+ 57. 2

-2.38

264

-2.4

+0.02

+56. 3

+0. 55

+16.1

-1.7(1

+ 8S. 3

+2. 81

+ 3S. 1

-3.93

270

-2.3

+0.02

+58. 4

+0.10

+ 5.3

-1.83

+100. 8

+ 1.13

+ 10.0

-5.26

276

-2.1

+0.03

+57. 5

0 32

- 5.9

-1. 78

+ 101.9

-0. 95

- 23.5

-5. 67

282

-1.9

+0.03

+54. li

-0.71

-16.1

-1.59

+ 89. 1

-3.15

- 56.4

-5.15

288

-1.7

+0.06

+49. 0

-I.IIS

-25. 0

-1.33

+ 04.1

-5. 11

- 83.2

-3.59

294

-1.2

+0.07

+41.7

-1.31

-32.1

-II. IIS

+ 29.6

-6.21

- 97.8

-1. 15

300

-0.9

+0.06

+3:i 3

-1.39

-30.8

-0.61

-8.3

-6.18

- 97.0

+ 1.42

306

-0.5

+0. 06

+25. 0

-1.36

-39. 4

ii 28

- 42. 2

— 1. 112

- 80.6

+3.86

312

-0.2

+0. OS

+17.0

-1.211

-40. 1

. II 111'

- 65 5

-2. 112

- 52.1

+5.49

318

+0.4

+0.08

+ 9.9

-1.08

-39. 1

+0. 22

- 73. 7

+0. 02

- 17.0

+6.00

324

+0.8

+0. 00

+ 4.0

-0. 89

- 37. 4

+0.29

- 65. 3

+ 2. 58

+ 17.4

+5.25

330

+ 1.1

+0.03

- 0.8

-0 72

-35. 6

1-0.27

- 42.7

| 1 711

+ 43.7

+3.30

336

+ 1.2

+0.02

- 4. 7

-0. 114

-34. 2

+0. 22

- Ill li

5.66

+ 55. 7

+0.64

342

+ 1.4

+0.02

- s. r,

-0.64

-33.0

+0.13

+ 22. 7

+5.30

+ 51.4

-2.06

348

+ 1.5

0.00

-12.4

-0. 74

-32.6

+0.08

+ 50.3

+3.67

+ 31.0

-4.48

354

+ 1.4

-17.4

0. 88

-32. 1

+0. 12

+ 61.11

+ 1.08

- 0.3

-5. 79

360

+ 1.4

0.00

-23. 0

-1.00

ill 1

+0.27

+ 63.2

-1.66

- 35.8

-5. 82

[ndz, 0 log t, and k/cos i are to be computed in the lorm Si at sin ig+It bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of {139) Juewa — Continued.
TABLE III.— o log r— Continued.

285

PERIODIC TERMS.

Unit of a and 6=0.0(1001.

i

3

4

9'

<h

Diff. for 1°

6

Diff. for 1°

«4

Diff. for 1°

b<

Diff. for 1°

O

0

+85. 7

-3. 39

-41.7

-7.03

+ 1. 1

-0.28

- 2.3

+0. 05

6

^i. :;i

-77.2

1. 55

-0.1

-0. 02

-1.0

+0.22

12

+ 13.0

-7.67

'il 1

- 1.01

+ 0.8

+0.22

+ 0.3

+0. 06

18

-32 ;

-7. 24

-89. 7

+2.56

+ 2.6

+0. 23

- 0.3

-0.28

24

-70. 6

-5. 14

63 i

+5. 78

.; i,

-0. 10

- 5. 1

-0.53

30

-92. 0

-1.72

-23.0

+7.49

+ 1.4

-0. 60

- 6.7

- 0. 39

36

-91.3

■ I. 96

+22. S

+ 7.46

- 3.6

ll ss

- 7.8

+(). 17

42

-us 5

i 37

+62. 9

+5. 58

9.2

0. (i.s

- 4.7

+0. 84

48

-29.4

+ 7. 42

+87. 0

+2. 13

-11.7

II III!

+ 2.4

+ 1.22

54

+16.8

+ 7. 57

1.70

S. 5

1 II 95

+ 10.0

+0. 96

60

+57. 5

+ 5. 62

+66.6

5 55

- il. 3

f 1.45

+ 13.8

+0.09

66

' +81.2

+ 1.96

+27.0

7.49

+ S. 9

, +1.20

+11.1

-0. 95

72

+81.0

-2. 05

-19. 1

7.45

+ 11. 1

■ 0. 28

+ 2.4

-1.58

78

,i, i,

— 5. 75

-58. 1

5. 15

+ 12.3

-o. si;

- 7.9

-1.37

84

+ 15.4

-7.58

-77. S

-1.18

3 s

-i.i;i

-14.0

-0.41

90

-29. 9

-7.05

72. 2

+3. 04

- 7.0

-1.50

(2 s

+0.79

96

-65. 0

-1. 29

-43.0

ii 36

1 1. 1

II 55

-4.5

+ 1.58

102

78. 7

-0.13

+ 0.5

+ 7.64

-13. (i

+0.68

+ 6.2

+ 1.52

108

-66. 6

+4. 02

- 11 1

+6. 53

- 6. 1

+ 1.4S

+13.8

+0.68

114

-33.0

+6. S3

+ 74.9

+ 3.41

+ 4.2

+1.48

+14.4

II IS

120

+ 11.4

, 58

S3 2

-0. 63

+11.8

•o 76

+ 8.1

-1.29

L26

+53. S

+6. 17

+67. 3

-4.47

+ 13.3

-0.28

- 1. 1

- 1 . 34

132

+S2. 2

■ 3.05

+32. 1

6.93

-0.98

- S. 0

II i;s

138

+89.0

-0.74

-12.3

7.48

+ 1.5

-0. 99

-9.3

+0.18

144

+73.3

-4.30

-53. 9

-6. 1 1

- 3.4

-0. 42

- 5.9

+0.68

150

+39. 6

—6.67

-82.9

3.31

- 3.6

+0.26

- 1.2

+0. 58

156

- 3.6

-7.40

-92.2

+0.24

- 0. 3

+0. 52

+ 1.0

+0.01

L62

-45. 9

-6. 42

-80.0

+3.74

+ 2.8

+0. 22

- 1. 1

-0. 54

168

-77.6

-:;. 90

-49.0

+ 6. 35

+ 2.4

-0. 11

- 5.5

-0.61

174

-90.8

-0.36

-6.7

+7.47

2.6

-0. 96

- 8.4

-0.08

180

-81.9

+3.32

+37.1

+6.77

- 9. 1

-o. 87

- 6.5

+0.74

I. si;

-52. 4

+6.28

+ 71.1

+4. 25

15.0

-0. 15

+ 0.5

+1.31

192

- 9.6

+7.63

+85. 8

+0. 46

-10.9

+0.86

+ 9.2

+1.18

IIIS

+35. (I

+6.83

+76.6

-3. 50

-2.7

+ 1.52

+ 14.7

+0.34

204

+68. 5

+3.99

+45. 6

-ii. 58

+ 7.4

+ 1.41

+ 13.3

n rs

210

+80.5

-0. 14

+ 1.4

-7.71

+ 14.2

+0.53

+ 5.3

- 1 . 54

216

+66.8

-4.29

-42.4

6.46

+13.8

-0. 04

- 5.2

-1.50

222

+31.5

-7.10

-72.2

3. 1 1

+ 6.5

-1.46

-12.7

0. lis

228

-14. 1

-7.67

-77. s

+ 1.20

3.8

1 52

13. 4

+0.48

234

-55. S

-5. 78

-57, S

+5. 24

11.7

-0.77

- 7.0

+ 1.33

240

so ii

-1.97

-18.0

| 7. 57

-15.0

+0. 55

+ 2.6

-M.43

246

-79.4

+ 2. 29

+28.5

+ 7.48

— 7. 7

+ 1. 14

+ 10.2

+0.79

252

55. 9

+5. 93

+ 67. 6

+5.19

+ 0. S

+ 1.28

+ 12. 1

-o. 17

258

-11.7

+7.73

+87.9

+ 1.32

+ 7.7

+0.78

+ 8.2

-0. 90

264

+34.7

+ 7.33

|-83 5

-2. 76

+ 10.0

-0.02

+ 1.3

-1.06

270

+72. 5

+4.97

51,. :,

6.00

+ 7. 4

-0. 112

- 4.5

o. 65

276

+91.9

+ 1.31

+14.6

7.6]

+ 2.6

ii 7:;

-6.5

-0. 02

282

+88. 2

-2. 49

-51. 1

-7. 27

- 1.4

-0.43

-4.8

+0.39

288

+63.4

5 Ii]

-69 5

5. Ill

-2.6

+0. oj

- 1.8

+0.40

294

+23. 5

-7. 38

-91. 1

-1.86

- 1.2

+0. 26

0.0

+0. 12

300

-21.8

-7.42

-91. (i

+1.69

+ 0. 5

+0. 14

- 0.4

-0. 17

306

-62. 2

-5. 74

-70. S

+ 0. 5

-0. 17

- 2.0

-0.22

312

-88.0

-2.60

-33. 5

i 7. 1 1

- 1.5

-0.37

- 3. 1

0.00

318

-93. 4

+0. 94

+ 11.8

+ 7. 63

- 5,9

-o. 28

- 2.0

+0.35

324

-70. 7

+4.49

+54. 6

+6. 33

- 4.9

+0.05

+ 1.1

: 0.52

330

-41. 5

+6.95

+84.7

+3.46

- 3.3

+0.41

+ 4.2

+0.37

336

+ 3 ii

+ 7.79

+94.4

-o. 28

0.0

+0.55

+ 5.5

-0,01

342

+4S. 1

+6. 77

+81.3

-3.99

+ 5. 3

+0. 38

+ 4.1

ii ;-;s

348

+81. ii

+4. 03

+48. 5

-6.7]

+ 4.5

0.00

+ 0.9

-0.48

354

+95. 0

+0. 34

+ 3.9

7. 82

+ 3. 5

-0. 28

- 1.6

-0.26

360

+85.7

-3.39

-41. :

-7. ii:;

+ 1.1

0 |{

- 2. il

+0.05

[ntz, S log r. and u cos i are to he computed in the form _y, a< sin iti - 1, ii cos ig+cT.'

286

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (139) Juewa — Continued.
TABLE III.— 3 loer— Continued.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

5

6

9'

%

Dii'f. for 1°

h

Dift for 1°

a<s

Dift for 1°

h

Diff. for 1°

O

0

+0.6

-0.32

-2.9

-0.02

+0.5

+0.1

6

-1.3

-0. 23

-2. 3

+0.18

+0.5

-0.2

12

-2. 2

-0.02

-0.7

+0.27

+0.2

-0.5

IS

-1.6

+0.14

+0.9

+0. 18

-0.2

-0.6

24

-0.5

+0.19

+1.4

+0.01

-0.5

-0.4

30

+0.7

+0.12

+1.0

-0.13

-0.6

0.0

36

+ 1.0

-0.03

-0.2

-0. 15

-0. 5

+0.4

42

+0.3

-0.12

-0.8

-0. 05

-0.2

+0.5

48

-0.5

-0.12

-0.8

+0.08

+0.2

+0.5

54

-1. 1.

-0.01

+0.2

+0. 16

+0.5

+0.3

GO

-I). 6

+0. 13

+1.1

+0.09

+0.5

0.0

66

+0.5

+0.17

+ 1.3

-0. 05

+0.4

-0.3

72

+ 1.4

+0. OS

+0.5

-0.18

+0.2

-0.3

78

+ 1.5

-0.08

-0. 8

-0.18

0.0

-0.3

84

+0.5

-0.19

-1.7

-0.08

-0.2

-0.2

90

-0. S

-0.21

-1.7

+0.08

-0.2

-0.2

96

-2.0

-0. 10

-0.7

+0.22

-0.2

0.0

102

-2.0

+0. 09

+0.9

+0.22

-0.2

+0.1

108

-0.9

+0.22

+2.0

+0.09

-0.2

+0.2

114

+0. 7

+0.22

+2.0

-0.08

-0.1

+0.3

120

+1.7

+0.09

+ 1.1

-0.20

+0.1

+0.3

126

+ 1.8

-0.06

-0.4

-0.20

+0.3

+0.2

132

+1.0

-0. 16

-1.3

-0.08

+0.4

0.0

138

-0. 1

-0. 15

-1.4

+0.07

+0.3

-0.2

144

-0.8

-0.03

-0. 5

+0.12

+0.2

-0.3

150

-0.5

+0. 08

+0.2

+0. 08

-0.1

-0.3

156

+0.2

+0.12

+0.5

-0.02

-0.2

-0:2

162

+0.9

+0. 05

0.0

-0.13

-0.3

-0.1

168

+0.8

-0.10

-1.1

-0.13

-0.2

+0.2

174

-0.3

-0. 19

-1.6

-0.01

-0.1

+0. 2

180

-1.5

-0.18

-1.2

+0. 15

0.0

+0.1

186

-2.4

-0.02

+0.2

+0.24

0.0

+0.1

192

-1.7

+0.16

+ 1.7

+0.20

-0. 1

+0.1

198

-0.4

+0.27

+2.6

+0. 05

-0.1

+0.2

204

+1.5

+0.24

+2.3

-0.16

0.0

+0.2

210

+2.5

+0.07

+0.7

-0.28

+0.3

+0.3

216

+2.3

-0.12

-1. 1

-0.25

+0.5

+0.1

222

+1.1

-0.25

-2.3

-0.08

+0.5

-0.2

228

-0.7

-0.23

-2.1

+0. 12

+0.2

-0.6

234

-1.7

-0.08

-0.9

+0.22

-0.2

-0.6

240

-1.7

+0.08

+0.5

+0.18

-0.6

-0.5

246

-0.8

+0. 18

+ 1.3

+0. 05

-0.7

-0.1

252

+0. 4

+0. 14

+ 1. 1

-0.07

-0.6

+0.5

258

+0.9

+0. 02

+0. 5

-0.12

-0.2

+0.8

264

+0.6

-0.08

-0.4

-0. 08

+0.3

+0.7

270

-0. 1

-0. 09

-0. 5

+0.04

+0.7

+0.3

276

-0.5

l) in

+0.1

+0. 11

+0.7

-0.2

282

-0.2

+0.11

+0. 8

+0. 06

+0.4

-0.5

288

+0.8

+0.15

+0.8

-0 06

-0.2

-0.6

294

+ 1.6

+0. 05

+0.1

II IS

-0.4

-0.5

300

+ 1.4

-0.11

-1.3

-0.20

-0.5

0.0

306

+0.3

-0. 23

-2.4

-0.08

-0. 3

+0.2

312

-1.4

-0.28

-2.4

+0.12

-0. 1

+0.3

318

-3.0

-0. 14

-0. 9

+0.30

+ 0. 2

+0.2

324

-3.1

+0. 11

+ 1.3

+0.33

+0.2

0.0

330

-1.7

+0.32

+3.1

+0.19

0.0

-0.2

336

+0.8

+0.37

+ 3. 6

-0.07

-0. 2

-0. 1

342

+2.7

+0.22

+2.3

-0.28

-0.2

+0.2

348

+3.5

-0.01

+0.2

-0.36

0. 0

+0.3

354

+ 2. 6

-0.24

-2.0

-0. 26

+0.2

+0.3

360

+0.6

-0.32

-2.9

-0.02

+0.5

+0.1

[ndz, J log r, and u/cos i are to be computed in the lorra Jj oi sin ig+Ii 6> cos ig+cT.l

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

287

PERIODIC TERMS.

Tables of (189) Juewa — Continued.

TABLE IV.— u/cos i.

Unit of a and 6=0°00L

i

0

1

2

9'

K

Diff. for 1°

"x

Diff. for 1°

5,

Diff. fori0

a2

Diff. fori0

b.2

Diff. for 1°

O

0

- 0.5

-0.15

-7.4

+1.06

+15.8

+0.02

+ 5.2

-0.70

-13.7

-0.21

6

— 1.8

—0.22

- 0.9

+0. 96

+ 14.6

-0. 39

+ 0.8

-0.69

-14.1

+0.07

12

- 3.2

-0. 26

+ 4.2

+0. 64

+11. 1

-0.72

- 3.1

-0.59

-12.11

+0.28

18

- 4.9

-0.28

+ 6.8

+0.28

+ 6.0

-0.87

- 6.3

-0.46

-10.8

+0.42

24

- 6.6

-0. 25

+ 7.5

-0.08

+ 0.7

-0.78

- 8.6

-0. 28

- 7.S

+0.52

30

-7.9

-0.20

+ 6.0

-0.34

-3.4

-0. 56

- 9.'6

-0.08

-4.6

+0.53

36

- 9.0

-0. 12

+ 3.5

-0.47

- 5.9

-0. 22

- 9.6

+0.08

- 1.4

+0.51

42

- 9.4

-0.02

+ 0.4

-0.42

- 0.1

+0.08

- 8.7

+0.20

+ 1.5

+0.44

48

- 9.4

+0.06

-1.6

-0.22

-4.9

+0.30

-7.2

+0.31

+ 3.9

+0. 35

54

- 8.8

+0.13

- 2.2

+0.04

-2.6

+0.42

- 5.0

+0.39

+ 5.7

+0.24

60

- 7.8

+0.21

— 1.1

+0.32

+ 0.2

+0.36

- 2.5

+0.42

+ 6.8

+0. 11

66

- 6.3

+0.26

+ 1.7

+0.51

+ 1.7

+0.15

+ 0.1

+0.43

+ 7.0

-0.03

72

-4.7

+0.28

+ 5.0

+0. 55

+ 2.0

-0.08

+ 2.7

+0.41

+ 6.4

-0.18

78

- 3.0

+0.29

+ 8.3

+0.44

+ 0.7

-0.34

+ 5.0

+0.34

+ 4.9

-0.32

84

- 1.2

+0.30

+ 10.4

+0.18

- 2.1

-0.50

+ 6.8

+0.21

+ 2.6

-0.41

90

+ 0.6

+0.30

+ 10. 5

-0. 14

- 5.3

-0.52

+ 7.5

+0.02

0.0

-0.45

96

+ 2.4

+0.30

+ 8.7

-0.41

- 8.4

-0.42

+ 7.1

-0.13

-•2.8

-0. 42

102

+ 4.2

+0.27

+ 5.6

-0.58

-10.4

-0. 17

+ 5.9

-0.29

- 5.1

-0.32

108

+ 5.6

+0.22

+ 1.7

-0. 65

-10.4

+0.13

+ 3.6

-0.38

-6.7

-0.20

114

+ 6.9

+0. IS

— 2.2

-0.55

- 8.8

+0.40

+ 1.3

-0.38

- 7.5

-0.03

120

+ 7.8

+0.12

-4.9

-0. 33

-5.6

+0. 57

- 0.9

-0.34

- 7. 1

+0.12

126

+ 8.3

+0.02

-6.2

-0. 07

- 2.0

+0.58

- 2.8

-0.23

- 6.0

+0.22

132

+ 8.2

-0.08

- 5.7

+0.19

+ 1.4

+0.48

- 3.7

-0.11

- 4.5

+0.24

138

+ 7.5

-0.17

-3.9

+0.36

+ 3.8

+0.27

— 4. 1

-0.03

- 3.1

+0.21

144

+ 6.2

-0. 25

- 1.4

+0.42

+ 4.6

-0. 02

- 4. 1

+0.02

- 2.0

+0.13

150

+ 4.5

-0.32

+ 1-1

+0. 32

+ 3.6

-0. 28

- 3.8

+0.04

- 1.5

+0.07

156

+ 2.3

-0.39

+ 2.5

+0. 12

+ 1.3

— 0. 41

-3.6

+0.02

- 1.2

+0.04

162

- 0.2

-0.39

+ 2.5

-0. 13

- 1.3

—0.41

- 3.7

-0.06

- 1.0

+0. 06-

168

- 2.4

-0.37

+ 0.9

-0. 34

-3.6

-0. 31

-4.3

-0. 11

- 0.5

+0.12

174

-4.6

-0.32

-1.6

-0. 44

- 5.0

-0.08

- 5.0

-0.09

+ 0.4

+0.21

180

-6.3

-0. 23

-4.4

-0.42

-4.6

+0.22

- 5.4

0.00

+ 2.0

+0.29

186

-7.4

-0.14

-6.7

-0. 25

-2.4

+0. 46

- 5.0

+0.14

+ 3.9

+0.31

192

- 8.0

-0.06

-7.4

+0.02

+ 0.9

+0. 58

- 3.7

+0.29

+ 5.7

+0.26

198

- 8.1

+0.02

- 6.5

+0.29

+ 4.6

+0. 58

- 1.5

+0.41

+ 7.0

+0. 14

204

-7.6

+0.12

-3.9

+0.54

+ 7.9

+0. 43

+ 1-2

+0.46

+ 7.4

-0. 05

210

- 6.7

+0.18

0.0

+0.67

+ 9.8

+0. 18

+ 4.0

+0.42

+ 6.4

-0.25

216

- 5.4

+0.24

+ 4.1

+0.65

+10. 1

-0. 10

+ 6.2

+0.28

+ 4.4

-0.41

222

-3.8

+0. 28

+ 7.8

+0. 52

+ 8.6

-0.34

+ 7.3

+0.07

+ 1.5

-0.48

228

- 2.0

+0.30

+ 10.4

+0.27

+ 6.0

-0.47

+ 7.0

-0. 12

- 1.3

—0.47

234

- 0.2

+0.33

+11.0

-0.04

f 3. 0

-0. 50

+ 5.8

-0.29

- 4.1

-0.38

240

+ 2.0

+0. 35

+ 9.9

-0.29

0.0

-0.39

+ 3.5

-0.41

- 5.8

-0. 19

246

+ 4.0

+0.34

+ 7.5

-0.42

- 1.7

-0. 13

+ 0.9

-0.43

- 6.4

-0.02

252

+ 6.1

+0.32

+ 4.8

-0.45

- 1.6

+0 11

— 1.7

-0.39

- 6.0

+0.14

258

+ 7.8

+0. 26

+ 2.1

-0.32

- 0.4

+0.30

-3.8

-0.31

-4.7

+0.27

264

+ 9.2

+0.20

+ 1.0

-0.07

+ 2.0

1 o :;s

- 5.4

-0.19

- 2.8

+0.34

270

+10.2

+0.10

+ 1.3

+0.16

+ 4.1

+0. 28

- 6.1

-0. 06

- 0.6

+0. 35

276

+10.4

0.00

+ 2.9

+0.34

+ 5.3

+0.09

- 0.1

+0. 05

+ 1-4

+0. 34

282

+ 10. 2

-0.08

+ 5.4

+0.38

+ 5.2

-0. 19

-5.5

+0.12

+ 3.5

+0.32

288

+ 9.4

-0.18

+ 7.5

+0.27

+ 3.0

-0. 52

-4.6

+0.20

+ 5.3

+0.30

294

+ 8.1

-0.25

+ 8.6

+0.02

-1.0

-0.72

- 3.1

+0.29

+ 7.1

+0.27

300

+ 6.4

-0.27

+ 7.8

-0.33

-5.6

-0.77

— 1.1

+0.38

+ 8.5

+0.19

306

+ 4.9

-0.25

+ 4.6

-0.69

-10.2

-0.67

+ 1.4

+0.45

+ 9.4

+0.08

312

+ 3.4

—0.22

- 0.5

-0.90

-13.6

-0. 37

+ 4.3

+0. 51

+ 9.5

-0.06

318

+ 2.3

-0.17

-6.9

-1.08

-14.6

+0. 05

+ 7.5

+0.52

+ 8.7

-0.22

324

+ 1.4

-0.12

-13.4

-0. 98

-13.0

+0. 50

+10. 5

+0.44

+ 6.8

-0.42

330

+ 0.9

-0. 05

-18.7

-0. 69

-8.6

+0.88

+12.8

+0.31

+ 3.7

-0. 60

336

+ 0.8

-0.01

-21.7

-0.27

-2.4

+ 1.06

+14. 2

+0.09

- 0.4

-0. 69

342

+ 0. S

-0. 02

-21.9

+0. 23

+ 4.1

+1.05

4-13.9

-0. 18

-4.6

-0.68

348

+ 0.6

-0.07

-18.9

+0.69

+ 10.2

+0.86

+ 12.0

-0.39

- 8.5

-0.58

354

0.0

-0.09

-13.6

+0. 96

+ 14.4

+0.47

+ 9.2

-0.57

-11.6

-0. 43

360

- 0.5

-0. 15

-7.4

+1.06

+15.8

+0.02

+ 5. 2

-0.70

-13.7

-0.21

[noz, 3 log r, and u/cos i are to be computed in the form li a.\ sin ig+2i bj cos ig+cT.]

288 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (139) Juewa — Continued.

PERIODIC TERMS.

TABLE IV.— u/cosi— Continued.

Unit of a and 6=09001.

!

3

4

ft

<h

Diff. fori0

b3

Diff . for 1°

«4

Diff. for 1°

K

Diff. for 1°

o

0

-4.8

-1.13

-14.1

+0.37

-0. 1

-1.0

6

-11.0

-0.81

-10.2

+0.88

—0.5

—1.0

12

-14.5

-0.30

-3.5

+1. 18

-0.9

-0.6

18

-14.6

+0.31

+ 4.0

+1.17

—1.2

-0.1

24

-10.8

+0.85

+10.5 .

+0.87

—1.2

+0.5

30

-4.4

+ 1.16

+ 14.4

+0.36

-0.8

+1.0

36

+ 3.1

+1.19

+14.8

-0. 26

-0.2

+1.3

42

4- 9.9

+0. 92

+11.3

-0.81

+0.5

+1.3

48

+14.1

+0.39

+ 5.1

—1.16

+1.1

+0.9

54

4-14.6

-0.24

-2.6

-1.22

+1.5

+0.1

60

4-11. 2

II Sll

- 9.5

-0.92

+1.4

-0.5

66

4-5.0

-1.16

-13.7

-0.39

+0.9

-1.2

72

- 2. 7

-1.21

-14.2

+0.25

+0.1

-1.5

78

- 9.5

-0.91

-10.7

+0.82

-0.7

-1.4

84

-13.6

-0.38

-4.4

+1.18

—1.3

-0:8

90

-13.9

+0.28

+ 3.4

+ 1.22

—1.5

0.0

96

-10.2

+0.88

+ 10. 2

+0.88

-1.3

+0.8

102

- 3.4

+ 1.22

+ 14.0

+0.31

-0.6

+1.3

108

+ 4.5

+1.21

+13.9

-0. 35

+0.2

+1.5

114

+ 11.1

+0.86

+ 9.8

-0.94

+ 1.0

+ 1.1

120

+ 14.8

+0.27

+ 2.6

-1.28

+1.3

+0.5

126

+14.3

-0.44

- 5.6

\ 22

+1.4

-0.5

132

+ 9.5

-1.02

-12.1

-0^82

+0.9

—1.1

138

+ 2.1

-1.30

-15.5

-0.22

+0.2

-1.4

144

- 6. 1

-1.23

-14.7

+0.49

-0.7

-1.3

150

-12.7

-0. 82

- 9.6

+1.08

—1.2

-0.8

156

-15.9

-0. 17

-1.8

+1.33

-1.4

0.0

162

-14.7

+0.54

+ 6.4

+1. 22

-1.5

+0.8

168

-9.4

+ 1.09

+ 12.8

+0.77

-0.5

+1.4

174

- 1.6

+ 1.32

+15. 6

+0.11

+0.4

+1.3

180

+ 6.4

+1.18

+ 14. 1

-0. 58

+1.1

+1.0

186

+ 12.6

+0.72

+ 8.6

-1.08

+1.5

+0.3

192

+ 15. 1

+0. 05

+ 1.1

-1.28

+1.3

-0.6

198

+ 13.2

-0.62

- 6.8

-1.13

+0.8

-1.3

204

+ 7.6

—1.10

-12.5

-0.68

0.0

-1.5

210

0.0

-1.26

-14.4

+0.02

-0.8

—1.2

216

- 7.5

-1.05

-12.2

+0.66

-1.4

-0.7

222

-12.6

-0.57

-6.5

+1.11

-1.5

+0.1

228

-14. 3

+0.05

+ 1.1

+1.24

-1.2

+0.9

234

-12.0

+0.71

+ 8.4

+1.02

-0.5

+1.3

240

-5.8

+1.15

+13.3

+0.51

+0.2

+1.5

246

+ 1.8

+ 1. 22

+14.5

-0. 12

+0.9

+1.0

252

+ 8.9

+0.99

+11.8

-0.72

+1.3

+0.5

258

+ 13.7

+0. 51

+ 5.9

-1.13

+1.3

-0.2

264

+ 15. 0

-0.12

-1.8

-1.24

+0.9

-0.8

270

+ 12. 3

-0.73

- 9.0

-1.00

+0.5

—1.2

276

+ 6.2

— 1. 12

-13.8

-0.52

n 1

—1.2

282

- 1.2

—1.21

-15.2

+0.09

-0.6

-0.9

288

- 8.3

-1.02

-12.7

+0.68

-1.0

-0.5

294

-13.5

-0. 58

- 7.0

+1.08

-1.0

-0.1

300

-15.2

+0.03

+ 0.2

+1.20

-0.9

+0.5

306

-13.1

+0.61

+ 7.4

+1.06

-0.6

+0.7

312

-7.9

+ 1.03

+12.9

+0.62

-0.3

+0.9

318

- 0.7

+1.20

+14.9

+0.04

+0.2

+0.8

324

+ 6.5

+ 1.07

+13.4

-0. 52

+0.5

+0.7

330

+12. 1

+0.68

+ 8.6

-0.97

+0.8

+0.4

336

+ 14.7

+0.13

+ 1.8

-1.18

+0.8

0.0

342

+13.7

-0.46

- 5.6

-1.12

+0.9

-0.4

348

+ 9.2

-0.92

-11.6

-0. 75

+0.7

-0.6

354

+ 2.6

— 1. 17

-14.6

-0.21

+0.4

-0.9

360

-4.8

-1.13

-14.1

+0.37

-0.1

-1.0

[ndz, 3 log r, and u/cos i are to be computed in the form J,- at sin ig+Ii bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

289

Tables of (139) Juewa — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 10) IN JULIAN YEARS.

ndz

3 log r

II cos i

9

Unit of

•=0°001

Unit of c

=0.00001

Unit of

[i.iiiii

c

Diff. for 1°

c

Dig. for 1°

c

Dill fori0

O

0

-7.00

-0. 013

+0.33

-0. 052

-2.44

-.019

6

—7.04

0.000

+0.02

-0. 052

-2.53

-.012

12

-7.00

+0. 015

-0.30

-0. 052

-2.57

-.002

18

-6. 86

+0. 030

-0.61

-0. 052

-2. 56

+.006

24

-6. 64

+0. 044

-0.92

-0. 050

-2. 52

+.012

30

-6. 33

+0. 057

-1.2]

-0. 045

-2.42

+ .019

36

-5. 96

+0. 068

-1.46

-0.0 12

-2.29

+.026

42

-5. 52

+0. 080

-1.70

-0. 038

-2. 11

+ .032

48

-5. 01

+0. 090

-1.91

-0. 032

—1.91

+.036

54

-4. 44

+0. 098

-2.08

-0. 026

-1.68

+.042

60

—3. SI

+0. 103

-2.22

-0. 022

-1.40

+.046

66

-3.20

+0. 109

-2. 35

-0. 018

-1.12

+.048

72

-2.53

+0. 112

-2. 43

-0. 010

■I) .S3

+.050

78

-1.86

•+0. 114

-2.47

-0. 006

-0.53

+.052

84

-1. 16

+0. 117

-2.50

-0. 002

-0.21

+.052

90

-0.46

+0. 116

-2.50

+0. 002

+0. 10

+.052

96

+0. 23

+0. 115

-2. 47

+0. 007

+0. 42

+. 052

102

+0.92

+0. 112

-2.42

+0. 010

+0.72

+.050

108

+1.58

+0. 108

-2. 35

+0. 015

+1.02

+.049

114

+2. 22

+0. 104

-2.21

+0. 01S

+1.31

+.047

120

+2. 83

+0. 099

-2. 13

+0. 020

+ 1. 58

+.046

126

+3.41

+0. 092

-2.00

+0. 023

+1. 86

+.043

132

+3.94

+0. 086

-1.85

+0. 026

+2. 10

+.040

138

+4.44

+0. 079

-1.69

+0. 028

+2.34

+.038

144

+4. 89

+0. 070

-1.52

+0. 030

+2.56

+.035

150

+5. 28

+0. 062

-1. 33

+0. 034

+2.76

+.030

156

+5. 63

+0. 052

-1. 11

+0. 035

+2.92

+.029

162

+5.91

+0. 042

-0.91

+0. 034

+3.11

+.027

li is

+6. 14

+0. 033

-o. 70

+0. 037

+3.24

+.021

174

+6. 31

+0. 023

-0.47

+0. 038

+3.36

+.018

180

+6.42

+0.012

-0.24

+0. 038

+3. 46

+.014

186

+6. 46

+0. 002

-0.02

+0. 038

+3.53

+.010

192

+6.44

-0. 008

+0. 21

+0. 039

+3.58

+.006

198

+6. 36

-0. 020

+0.45

+0. 039

+3. 60

+.002

204

+6. 20

-0.031

+0.68

+0. 037

+3.60

-.002

210

+5. 99

-0. 040

+0.89

+0. 036

+3.56

-.008

216

+5. 72

-0. 049

+1.11

+0. 036

+3.51

-.011

222

+5.40

-0. 059

+ 1. 32

+0. 034

+3.43

-. 015

228

+5. 01

-0. 070

+1. 52

+0. 032

+3. 33

-.019

234

+4.56

-0. 078

+1.71

+0. 029

+3.20

-.024

240

+4.08

-0. 085

+1.87

+0. 027

+3.04

-.028

246

+3.54

-0. 092

+2. 03

+0. 026

+2.86

-.032

252

+2.97

-0. 098

+2. 18

+0. 022

+2.65

-.036

258

+2. 36

-0. 104

+2. 30

+0.019

+2.43

-.038

264

+1.72

-0. 110

+2.41

+0. 017

+2. 19

-.042

270

+1.04

-0. 114

+2. 50

+0. 012

+1. 92

-.048

276

+0. 35

-0. 117

+2. 56

+0. 008

+1. 62

-. 050

2S2

-0.36

-0. 11 :i

+2.60

+0. 004

+1.32

-.052

288

-1.08

-0. 118

+2.61

-0. 002

+1.00

-.056

294

-1.78

-0. 118

+2.58

-0. 006

+0.65

-.057

300

-2.49

-0. 116

+2. 54

-0.012

+0.32

II.-.6

306

-3. 17

-0. Ill

+2.44

-0. 018

-0.02

-.058

312

-3.82

-0. 106

+2.32

-0. 022

-0.38

-.058

318

-4.44

-0. 099

+2. 18

-0. 028

-0. 72

-.055

324

-5. 01

-0. 090

+ 1.99

-0. 034

-1.04

-.053

330

-5.52

-0. 080

+ 1.77

-0. 039

-1.36

-.048

336

—5. 97

-0. 069

+ 1.52

-0. 044

-1.62

-.044

342

-6. 35

-0. 056

+ 1.24

-0. 047

-1.89

-.040

348

-6.64

-0. 044

+0. 96

-0. 049

-2. 10

-.034

354

-6.88

-0. 030

+0.65

-0. 052

-2.30

-.028

360

-7.00

-0. 013

+0.33

-0. 052

-2.44

-.019

[ndz, d log r, and u/cos i are to be computed in the form li at sin ig+It 6< C03 ig+cT.}

290 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (139) Juewa — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B'

C

log sin a

log sin b

log sin c

1874. 0

O

254. 2692

O

164. 5411

O

163. 6877

9. 99999

9. 91669

9. 75166

5

254. 2829

164. 5566

163. 6975

9. 99999

9. 91669

9. 75166

6

2966

5721

7074

99

69

65

7

3103

5876

7172

99

69

65

8

3240

6031

7271

99

70

65

9

3377

6186

7370

99

70

65

1880

254. 3514

164. 6341

163. 7468

9. 99999

9. 91670

9. 75165

1

3651

6496

7567

99

70

65

o

3788

6651

7666

99

70

65

3

3! 125

6806

7764

99

70

65

4

4062

6961

7863

99

70

65

1SS5

254. 4199

164. 7116

163. 7961

9. 99999

9. 91670

9. 75164

6

4336

7271

8060

99

70

64

7

4473

7 125

8159

99

70

64

8

4610

7580

8257

99

70

64

9

4747

7735

8356

99

70

64

1890

254. 4884

L64. 7890

163. 8455

9. 99999

9.91670

9. 75164

1

502 L

8045

8554

99

70

64

o

5I5S

8200

8652

99

70

64

3

5295

8355

8751

99

71

64

4

5432

8510

SS5I)

99

71

64

1895

251.5569

164. 8665

163. 8948

9. 99999

9.91671

9. 75164

6

5706

8820

9047

99

71

63

7

5S13

8975

9146

99

71

63

8

5980

9130

9214

99

71

63

9

6117

92S5

9343

99

71

63

1900

254. 6254

164. 9440

163. 9441

9. 99999

9.91671

9. 75163

I

6391

9595

9540

99

71

63

2

(i52S

9750

9638

99

71

63

3

6665

164. 9905

9737

99

71

63

4

lisn::

165. 0060

9836

99

71

63

1905

254. 6940

165.0215

163. 9934

9. 99999

9. 91671

9. 75162

6

71177

0370

164. 0033

99

71

62

7

721 1

(1525

0131

99

71

62

8

7351

IICS]

0230

99

72

62

9

7488

0836

0329

99

72

62

1910

254.7625

L6 5.0991

164. 0427

9. 99999

9. 91672

9. 75162

1

7762

1146

0526

99

72

62

2

79(10

1301

0625

99

72

62

3

S037

1456

0723

99

72

62

4

8174

1611

0822

99

72

62

1915

254. 83, II

165. 1766

164. 0920

9. 99998

9.91672

9. 75162

6

84 is

1921

1019

98

72

61

7

S5S5

2076

1118

98

72

61

8

8722

2231

1216

98

72

61

9

SS59

2386

1315

98

72

61

1920

254. 8997

165.2541

164. 1414

9. 99998

9. 91672

9. 75161

1

9134

2696

1512

98

72

61

2

927 1

2852

1611

98

72

61

3

9408

3007

1710

98

73

61

4

9545

3162

LSI IS

98

73

61

1925

254. 9682

165.3317

164. 1907

9. 99998

9. 91673

9. 75160

6

9819

3472

2005

. 98

73

60

7

254. 9957

3627

2104

98

■ 73

60

8

255. 0094

3782

2203

98

73

60

9

(123,1

3937

2301

98

73

60

1930

255. 0368

165. 4092

164. 2400

9. 99998

9. 91673

9. 75160

Year

log cos a

log cos 6

log (us c

1874. 0
1930.(1

7. 824 n
7. 978 n

9. 752 ii
9. 752 n

9.917
9.917

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLES OF (161) ATHOR.

291

MEAN ELEMENTS.

Epoch, 1896, Apr. 14.0, M. T. Berlin=1896.285, M. T. Berlin.

O / //

ff0= 72 49 13= 72?8202

«=291 46 24 = 291.77331

Q= 18 39 54= 18.6651 1 Mean equinox and ecliptic 1900.0.
i= it 3 26= 9.0573 J

q>= 7 57 47= 7.963]

n= 966".6573 = 0.26851592

The elements are based on oppositions extending from 1S76 to 1903 and on the perturbations of the

first order by Jupiter, as given on page 292.

AUXILIARY QUANTITIES.

log a=0.37649 lug 57.2958 , =0.89968 lo„A/IEf =9 93945
loge=9.14156 logp =0.36807 io* v 1+e

TABLE I. -MEAN ANOMALY (g).

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of morilh

Year

9

Year

9

Month

9

B

1876

7

O

243.38573
341. 39404

1903
B 4

O

10.95271
109. 22953

Jan. {0;°

O

| 0. 00000

8
9

79. 40235
177. 41066

5
6

207. 23784
305. 24616

<*•$

1 8. 32399

B

I SMI

275. 68749

7

43. 25447

Mar. 0.0

15.8421!

1

L3. 69580

B 8

141. 53129

Apr. 0.0

24. 16643

2

111.70411

9

239. 53960

May 0.0

32. 22191

3

209. 71242

1910

337. 54792

June 0.0

40. 54590

B

4

307. 98925

1

75. 55623

July 0.0

48. 60138

5

45. 99756

B 2

173. 83305

Aug. 0.0

56. 92537

6

144. 00587

3 271.84136

Sept. 0.0

65. 24936

7

242.01418

4 9. 84968

Oct. 0.0

73. 30484

B

8

340.291(11

5 107. 85799

Nov. 0.0

81. 62883

9

78. 29932

B 6

206. 13481

Dec. 0.0

89. 68431

1890
1

176.31176:;
274.31594

7
8

304. 14312
42. 15144

B

■>

12. 59277

9

140. 15975

Change for n days0

3

110. 60 11 IS

B 1920 238. 43657

4

•jus. 60939

1 336. 44488

5

306. 61770

2 74. 45320

n

9

• 71

9

B

6

44. 89453

3 172. 46151

7

142. 90284

B 4 270. 73833

8

240.91115

5 8. 74664

O

o

9
1900

1
2

3

338.91946

76. 92777

174.93608

272. 94440

10. 95271

6 106. 75496

7 204. 76327
B 8 303. 04009

9 41.04840
L930 139.05672

1

2
3
4
5

0. 26852 16
0. 53703 17
0. 80555 18
1.07406 lil
1.34258 20

A. 29(126

4. 56 1 i 7
4.83329

5. 10180

5.37(1:12

6

L. 61112 21 5. 638S4

Note. — When g is used as an argument of the perturba-

7

B7961 22 5.90735

tions add to the g of this table J x=r.— x0=— 0?0716.

8

2. 14813

23

6. 17587

Fur explanation see patre 203.

9

2.41664

24

6. 44438

111

2. (is:, 16

25

6. 71290

11

2. 95368

26

6. 9SI 12

12

3. 22219

27

7. 24993

13

3. 49071

28

7. 51845

14

3. 75922

29

7. 78696

15

4. 02774

30

8. 05548

« For days during January and

February of leap years subtract

one day before entering this table.

292

MEMOIKS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (161) Athor— Continued.

PERTURBATIONS.

Arg.

ndz v

u/cos i

ig—i'g'.

sin

cos

sin

cos

sin

cos

i V
0 0
0 0

+ 1 o

+1

+ 2

+3 0

0 +1
+1
+2 +1

0 +2

+ 1
+2
+3 +2

0 +3
+ 1
+2
+3
+4 +3

+ 2 +4

+3

+4 +4

+3 +5

+4

+5 +5

//

+ 0. 46nt
+ O.Olnt

- 10

- 49
_ 2

+ 6
-128

- 78

- 1
+ 55
+ 181

- 7

- 7

- 20

- 3

- 1

+ 4

- 2

//

- 4. 78nt

- 0. 16nt

- O.Olnt

+ 23
+ 103

+ 4

+ 4
-152
-113

- C

+ 6
-502
-200

- 6

- 1

- 12

- 10
+ 3

- 1

//

- 2. 39nt

- 0. 16nt

- 0. Olnt

+ 38
+ 4

- 3

- 39

- 70

- 6

- 3

- 32
-103

- 6

- 1

5

- 6

+ 2

- 1

+ 1

//

- 4

- 0. 02nt

+ 4

- 0. 23nt

- O.Olnt

+17
+ 1

+ 3

+37
+49

+ 4

- 7
-92
+ 3

+ 1

+ 9

+ 2

+ 1

2

+ 2

+ 3.24nt
+ 0. 22nt
+ 0.02nt

+ 5

- 2

- 1

+ 3

- 1

- 3

- 1

+ 18
+ 1

+ 1

//

- 0. 35nt

+ 1.69nt
+ 0. 12nt
+ O.Olnt

- 1

+ 5

- 7

- 3

- 4
+21

+ 1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (161) Athor— Continued.

293

PERIODIC TERMS.

TABLE II.— noz.

Unit of a and 6=09001.

i

0

1

2

9'

K

Diff. for 1°

«,

Diff. for 1°

6,

Diff. tor 1°

(In

Diff. for 1°

b.

Diff. for 1°

O

0

+9.1

+0.01

-126.8

-8.01

-287.0

+0.70

+ 19.1

-4. 12

- 93.1

-1.46

6

+9.0

-0. 04

-174.8

-7.72

-275. 2

+3.14

-7.2

-4.42

- 98.1

-o. is

12

+8.6

-0. 08

-218. 0

-6.47

-249. 3

+5.36

- 34.0

-4.33

- 95.2

+1.12

18

+8.0

-0. 12

-252. 4

-4.68

-210. 9

+ 7. 18

- 59.2

-3.87

- 84.6

+2. 34

24

+7.2

-0.13

-274. 2

-2.42

-163.2

+8.51

- 80.4

-3.07

- 67.1

+3.38

30

+6.4

-0. 17

-281.5

+0.11

-110.2

+9.02

- 96.1

-2.02

- 44.1

+4. 15

36

+5.2

-0. IS

-272.9

+2. 72

- 56.6

+8.74

-104.6

-0.78

- 17.3

+4.58

42

+4.2

-0. 15

-248. 8

+5. 12

6.8

+7.71

-105.4

+0. 52

+ 10.9

+4.62

48

+3.4

-0. 12

-211.4

+ 7.12

+ 34.5

+5. 87

- 98.4

+ 1.80

+ 38.1

+4.31

54

+2.7

-0. L2

L63.3

+8.69

+ 63.6

+3. 66

- 83.8

+2.92

+ 62.6

+3.68

60

+ 1.9

-0.10

-108. 6

+9. 42

+ 78.4

+ 1. 13

- 63.4

+3. si

+ 82.3

+2.74

66

+1.5

-0. 05

- 51.8

+9.38

+ 77.2

-1. 53

- 38.1

+4.43

+ 95.5

+1.61

72

+ 1.3

-0. 02

+ 2.4

+8.57

+ 60.0

-4. 05

- 10.2

+4.71

+ 101. 6

+0.34

78

+1.2

-0. 01

+ 49.6

+6. 95

+ 28.6

-6. 22

+' 18. 4

+4. 62

+ 99.6

-0.96

84

+ 1.2

+0.02

+ 85. 8

+4.88

- 14.6

-7.94

+ 45.2

+4.18

+ 90.1

-2.17

90

+1.4

+0.04

+108. 2

+2.48 ■

- 65.4

-8.90

+ 68.6

+3.43

+ 73.6

-3. 22

96

+1.7

+0.04

+115. 5

-0.08

-119.9

-9.11

+ 86.4

+2.43

+ 51.4

-4. 03

102

+1.9

+0.02

+ 107.2

-2. 54

-173.2

-8.52

+ 97. S

+ 1. 25

+ 25. 2

-4.52

108

+2.0

+0.01

+ 85.0

-4. 70

-220. 8

-7. 17

+ 101.4

-0.07

-2.9

-4.66

114

+2.0

-0.02

+ 50.8

-6.38

-259. 2

-5.38

+ 97.0

-1.34

- 30.8

-4.46

120

+1.7

-0. 05

+ 8.4

-7. 53

285. t

-3.20

+ 85.3

-2.51

- 56.5

-3. 90

126

+1.4

-0.08

- 38.2

-7.90

-297. 6

-0.88

+ 66.9

-3.48

- 77.6

-3. 01

132

+0.8

-0.12

- 84.8

-7.38

-296. 0

+1.38

+ 43.6

-4.14

- 92.6

-1.90

138

0.0

-0. 14

126 S

-6. 35

-281. 0

+3.42

+ 17. 2

-4.46

-100.4

—0. 65

144

-0.9

-0.16

-161.0

-4.81

-255. 0

+4.97

9.9

-4.41

Hill 1

+0.65

150

-1.9

-0.18

-184. 5

-2.88

-221. 4

+5.93

- 35.7

-3.99

- 92.6

+1.88

156

-3.1

-0. 19

-195. 6

-0.81

-183.8

+6.36

- 57.8

-3. 21

- 77.8

+2.92

162

-4.2

-0.18

-194. 2

+ 1.20

-146.4

+5.90

- 74.2

-2. Hi

- 57.6

+3.66

168

-5.2

-0.16

-181. 2

+2. 96

-113.0

+4.96

- 83.7

-0.95

- 33.9

+4.06

174

-6.1

-0. 14

-158. 7

+ 4. 30

- 86.9

+3.53

- 85.6

+0.32

8.9

+4.07

180

-6.9

-0. 12

-129. 6

+5.08

- 70.6

+1.77

- 79.9

+ 1.52

+ 14.9

+3.68

186

-7.6

-0. 09

- 97.8

+ 5. 23

- 65. 6

-0.12

- 67.4

+2.52

+ 35.2

+2.96

192

-8.0

-0. 05

- 66.8

+4.78

- 72.0

-1.93

- 49.6

+3.23

+ 50.4

+1. 95

198

-8.2

-0.02

- 40. 1

- 3 75

- 88.8

-3.47

- 28.6

+3. 57

+ 58.6

+0.78

204

-8.2

+0.02

- 21.8

+2.29

-113.6

-4.55

- 6.8

+3. 52

+ 59.7

-0.41

210

-8.0

+0. 05

- 12.9

+0. 56

-143.4

-5. 10

+ 13.7

+3.10

+ 53.7

-1.52

216

-7.6

+0.07

- 15.1

-1.28

-174. 9

-5.07

+ 30.4

+2.32

+ 41.5

-2.41

222

-7. 2

+0.07

- 28.2

-2.98

-204. 2

-4.42

+ 41.6

+1.32

+ 24.8

-2. 97

228

-li. 8

+0. OS

- 50.8

-4.38

-227. 8

-3. 22

+ 46.3

+0.20

+ 5.9

-3.15

234

-6.2

+0.09

- 80.7

-5. 32

-242. 8

-1.63

+ 44.0

-0.91

- 13.0

-2.95

240

-5.7

+0.08

-114.6

-5. 69

-247. 4

+0.20

+ 35. 4

-1.88

- 29.5

-2.38

246

-5.3

+0.07

-149.0

-5. 47

-240. 4

+ 2.08

+ 21.5

-2. 58

- 41.5

-1.52

252

-4.9

+0. 08

-180. 2

-4.62

222 5

+3.78

+ 4.4

-2 112

- 47.8

-0. 49

258

-4.4

+0. 08

-204. 5

-3.25

-195.0

+5.16

- 13.6

-2.88

- 47.4

+0.64

264

-4.0

+0.07

-219. 2

-1.51

-160. 6

+6.03

- 30.2

-2.48

- 40.1

+1.67

270

-3.6

+0.08

-222. 6

+0.46

-122. 6

+6.30

- 43.4

-1.73

- 27.4

+2.47

276

-3.1

+0.09

-213.7

+2.45

- 85.0

+5.94

- 51.0

-0.73

- 10.4

+2.98

282

-2.5

+0.11

-193.2

+4.22

- 51.3

+4.97

- 52.2

+0.38

+ 8.4

+3. 11

288

-1.8

+0. 12

-163.0

+5. 63

- 25.3

+3.44

— 46.4

+1. 50

+ 26.9

+2.85

294

—1.0

+0.14

-125.6

+6. 52

- 10.0

+1. 54

- 34.2

+2.46

+ 42.6

+2.23

300

-0.1

+0.17

- 84.8

+6.86

- 6.8

-0. 55

- 16.9

+3.16

+ 53.7

+1.30

306

+ 1.0

+0. 19

- 44.6

+6.32

- 16.6

-2.67

+ 3.7

+3.52

+ 58.2

+0. 17

312

+2.2

+0.20

9.0

+5.23

- 38.8

-4. 58

+ 25.4

+3.47

+ 55.7

-1.02

318

+3.4

+0.19

+ 18.2

+3.60

- 71.6

-6.07

+ 45.4

+3.02

+ 46.0

-2.17

324

+4.5

+0.19

+ 34.2

+ 1.56

-111.6

-6.98

+ 61.7

+2.26

+ 29.7

-3.12

330

+5.7

+0.20

+ 36.9

+0.72

-155.4

-7.37

+ 72.5

+1. 19

+ 8.6

-3.76

336

+6.9

+0.18

+ 25.6

-2. 98

-198. 6

-6.92

+ 76.0

-0.04

— 15.4

-4.03

342

+7.8

+0. 12

+ 1-1

-5. 03

-237. 0

-5. 64

+ 72.0

-1.30

- 39.8

-3. 91

348

+8.4

+0.09

- 34.8

-6. 65

-266. 3

-3.88

+ 60.4

-2.48

- 62.3

-3.41

354

+8.9

+0.06

- 78.7

-7.77

-283. 6

-1.72

+ 42.2

-3.44

- 80.7

-2. 57

360

+9.1

+0.01

-126. 8

-8.01

-287. 0

+0.70

+ 19.1

-4.12

- 93.1

-1.46

[ndz, 3 log r, and u cos i are to be computed in the form Z\ a% sin ig+ J( 6( cos ig+cT.]

294 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (161) Athor— Continued.

PERIODIC TERMS.

TABLE II.— ndz— Continued.

Unit of o and 6-09001.

1

3

4

g'

«3

Diff.forl0

63

Diff.forl0

a4

Diff.forl0

b4

Diff.forl0

o
0

-2.8

-0. 35

-6.5

+0.08

-1.0

+0.02

+0.'4

+0.08

6

-4.8

-0.31

-5.6

+0.22

-0.8

+0.06

+0.8

+0.05

12

-6.5

-0.22

-3.8

+0. 33

-0.3

+0.08

+1.0

+0.02

18

-7.4

-0.08

-1.6

+0.39

+0.2

+0.08

+1.0

-0.02

24

-7.5

+0.06

+0.9

+0.42

+0.6

+0.06

+0.8

-0. 05

30

-6.7

+0.20

+3.4

+0.37

+0.9

+0.03

+0.4

-0.07

36

-5. 1

+0.33

+5.4

+0.28

+ 1.0

-0.01

0.0

-0.08

42

-2.7

+0.42

+6.6

+0. 11

+0.8

-0. 05

-0.5

-0.07

4S

-0. 1

+0. 42

+6.7

-0.06

+0.4

-0.07

-0.8

-0.03

54

+2.3

+0. 36

+5.9

-0.19

0.0

-0.08

-0.9

0.00

60

+4.2

+0.24

+4.4

-0.30

-0.5

-0.06

-0.8

+0.03

66

+5.2

+0.10

+2.3

-0.38

-0.7

-0.03

-0.5

+0.07

72

+5.4

-0.06

0.0

-0.38

-0.9

-0.01

0.0

+0.08

78

+4.5

-0. 20

-2.1

-0.30

-0.8

+0.04

+0.5

+0.07

84

+3.0

-0.29

-3.6

-0. 18

-0.4

+0.07

+0.8

+0.04

90

+ 1.0

-0.31

-4.2

-0.02

0.0

+0.07

+ 1.0

0.00

96

-0.7

-0.28

-3.9

+0. 11

+0. 4

+0. 07

+0.8

-0. 04

102

-2.2

-0. 19

-2.9

+0.21

+0.8

+0. 06

+0.5

-0.06

108

-3.0

-0.08

—1.4

+0. 25

+1.1

+0. 02

+0.1

-0.08

114

-3.1

+0. 05

+0.1

+0. 25

+1.0

-0.03

-0.4

-0.08

120

-2.4

+0. 16

+ 1.5

+0. 19

+0.7

-0.07

-0.8

-0. 05

> 126

-1.2

+0.22

+2.3

+0.08

+0.2

-0.08

-1.0

-0.02

132

+0.2

+0.22

+2.5

-0.02

-0.3

-0.08

—1.0

+0.01

138

+ 1.5

+0.20

+2.1

-0.12

-0.7

-0.06

-0.9

+0.04

144

+2.5

+0. 10

+1.1

-0.18

-1.0

-0.03

-0.5

+0.08

150

+2.7

0.00

-0.1

—0.21

— 1. 1

+0.01

0.0

+0.08

156

+2.5

-0.07

-1.4

-0. 18

-0.9

+0.04

+0.5

+0.08

162

+ 1.9

-0.13

-2.3

-0. 12

-0.6

+0. 05

+0.9

+0.04

168

+0.9

-0. 18

-2.9

-0. 06

—0.3

+0.07

+1.1

+0.01

174

-0.2

-0. 18

-3.0

+0.02

+0.2

+0.08

+ 1.0

-0.02

180

-1.2

-0. 13

—2. 7

+0.08

+0.6

+0. 05

+0. s

-0. 05

186

-1.8

-0.08

-2.0

+0.12

+0.8

+0.02

+0.4

-0.07

192

-2. 1

-0.02

-1.2

+0.12

+0.9

0.00

0.0

-0. 05

198

-2.0

+0.02

-0.6

+0.09

+0.8

-0.02

-0.2

-0.03

204

-1.8

+0.06

-0. 1

+0.07

+0.6

-0.04

-0.4

-0.03

210

—1.3

+0.08

+0.2

+0. 02

+0.3

-0.05

-0.6

-0.02

216

-0.9

+0. 05

+0.2

-0.02

0.0

-0.04

-0.6

+0.01

222

—0.7

+0.02

0.0

-0.04

-0.2

-0.02

-0.5

+0.02

228

-0.7

-0.02

-0.3

-0.04

-0.2

0.00

-0.4

+0. 02

234

-0.9

-0.04

-0.5

-0.01

-0.2

-0. 01

-0.3

+0.02

240

—1.2

-0. 06

-0.4

+0.02

-0.3

-0.01

-0.2

+0.02

246

—1.6

-0.05

-0.3

+0. 05

-0. 3

-0. 1

+0.02

252

-1.8

-0. 02

+0.2

+0.0S

-0.3

-0.01

0.0

0.00

25S

-1.9

0. 00

+0.7

+0.08

-0.4

-0.01

-0.1

0.00

264

-1.8

+0.02

+1.2

+0.09

-0.4

0.00

0.0

+0.02

270

-1.6

+0. 07

+1.8

+0. 09

-0.4

0.00

+0.2

+0.03

276

-1.0

+0.10

+2.3

+0.08

-0.4

+0. 02

+0.4

+0. 02

282

-0.4

+0. 12

+2.7

+0. 04

-0.2

+0.02

+0.5

+0.02

288

+0.4

+0.12

+2.8

0.00

-0. 1

+0.03

+0.7

+0.02

294

+1.1

+0.13

+2.7

-0.02

+0.2

+0. 05

+0.8

-0.01

300

+2.0

+0. 14

+2.5

-0. 05

+0.5

+0. 05

+0.6

-0.03

306

+2.8

+0. 13

+2.1

-0.10

+0.8

+0.03

+0.4

-0. 05

312

+3. 6

+0.11

+1.3

-0.15

+0. 9

+0. 01

0.0

-0.06

318

+4.1

+0. 08

+0.3

-0.18

+0.9

-0.01

-0.3

-0.06

324

+4.5

+0.02

-0.9

-0.22

+0.8

-0. 05

-0.7

-0. 06

330

+4.3

-0. 05

-2.3

-0. 24

+0.3

-0. 08

-1.0

-0.03

336

+3.9

-0. 12

-3.8

-0.23

-0.1

-0.08

— 1. 1

+0.01

342

+2.9

-0. 22

-5. 1

-0.19

-0.6

-0.07

-0.9

+0.04

348

+ 1.3

ii 23

-6.1

-0.12

-0.9

-0.03

-0.6

+0.06

354

-0. 6

-0.34

-6.6

-0. 03

-1.0

-0.01

-0.2

+0.08

360

-2.8

-0. 35

-6.5

+0. 08

-1.0

+0.02

+0.4

+0.08

{■ndz, 3 log r, and tt/cos ! are to be computed in the form I, at sin i</+Zi bj cos ia+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of {161) Aihor— Continued.

295

PERIODIC TERMS.

TABLE III.— ,51ogr.

Unit of a and 6=0.001)01.

i

0

1

2

9'

bo

Diff.forl0

"i

Diff.forl0

6)

Diff.forl0

«2

Diff.forl0

62

Diff.forl0

O

0

+26.4

+0.04

-58. 5

+0.26

+45.8

+0. 51

-39.8

-0. 51

-4.4

+1.64

6

+26.7

+0. 05

-56. 5

+0.40

+48.7

+0.42

-41.4

0.00

+ 6.2

+ 1.78

12

+27.0

+0.03

-53. 7

+0. 54

+50.9

+0. 32

-39. 8

+0. 52

+17.0

+ 1.72

18

+ 27.1

+0. 02

-50.0

+0. 65

+52.6

+0. 19

-35.2

+ 1.00

+26.9

+ 1.53

24

+27.2

0.00

-45. 9

+0.70

+53.2

+0.02

-27. 8

+ 1.41

+35.4

+ 1.22

30

+27.1

-0. 02

-41.6

+0.72

+52.8

-0.16

-18.3

+ 1.71

+41.5

+0.78

36

+27.0

-0.02

-37. 3

+0. 68

+51.3

-0. 35

- 7.3

+1.88

+44.8

+0.28

42

+26.8

-0. 04

-33.4

+0.59

+4S. 6

—0. 55

+ 4.2

+ 1.90

+44.9

-0. 26

48

+26.5

-0.05

-30.2

-i). 16

+44.7

-0.68

+ 15. 5

+ 1.78

+41.7

-0.78

54

+26.2

-0. 05

-27.9

+0.30

+40. 5

—0.78

+25.5

+ 1.50

+35. 5

-1.22

60

+25 9

-0. 06

-26.6

+0. 10

+35. 3

-0.87

+33. 5

+ 1.12

+27. 0

-1.58

66

+25.5

-0.00

-26.6

-0. 12

+30.1

-0.87

+38.9

+0. 64

+ 16.5

-1.83

72

+25.2

-0. 05

-28.0

-0.32

+24.9

-0.82

+41.2

+0.12

+ 5.0

-1.96

78

+24.9

-0. 04

-30. 5

-0.49

+20.2

-0. 72

+40.3

-0.40

- 7.0

-1.93

84

+24.7

-0.02

-33.9

-0.63

+16.2

-0. 60

+36.4

-0.92

-18.2

-1.74

90

+24.6

-0.02

-38.1

-0.77

+ 13.0

-0. 42

+29.3

-1. 35

—27.9

-1.42

90

+24.4

-0.01

-43. 1

-0.84

+11.1

-0.22

+20.2

-1.60

-35.3

-1.02

102

+24.5

+0.02

-48.2

-0.84

+ 10.3

-0.04

+ 9.2

-1.88

-40.1

-0. 52

108

+24.6

+0.02

-53.2

-0.80

+ 10.6

+0.14

-2.4

-1.92

-41.5

+0.02

114

+24.8

+0.03

-57. 8

-0.72

+ 12.0

+0.32

-13.9

-1.84

-39.8

+0. 54

120

+25. 0

+0.03

-61.9

-0. 62

+14.4

+0.47

-24. 5

—1.62

-35. 0

+1.01

126

+25.2

+0.04

-65.3

-0.47

+ 17.6

+0. 57

-33.4

-1.26

-27.7

+ 1.40

132

+25. 5

+0. 05

-67. 5

-0. 32

+21.2

+0.62

-39.6

-0.80

-18.2

+1.68

138

+25. 8

+0. 05

-69.1

-0.17

+25. 0

+0.62

-43.0

-0.30

- 7.5

+1.82

144

+26.1

+0.03

-69. 5

-0. 01

+28.7

+0.60

-43. 2

+0. 22

+ 3.6

+1.79

150

+26.2

+0.02

-69. 2

+0. 12

+32.2

+0. 55

-40.3

+0.71

+14.0

+1.62

156

+26.4

+0.02

-68.1

+0.21

+35. 3

+0.46

-34.7

+ 1.12

+23.1

+1.32

162

+26. 5

+0.01

-66.7

+0.28

+37.7

+0.37

-26.8

+ 1.42

+29.9

+0.92

168

+26.5

0.00

-64.8

+0.32

+39.7

+0.27

-17.6

+ 1. 59

+34.1

+0.44

174

+26.5

-0.01

-62.9

+0.31

+40.9

+0. 15

-7.7

+ 1.60

+35.2

-0. 06

180

+26.4

-0.01

-61.1

+0.29

+41. 5

+0.08

+ 1.6

+1.47

+33.4

-0. 52

186

+26.4

-0.02

-59.4

+0.24

+41.8

+0.02

+ 9.9

+1.18

+29.0

-0.92

192

+26.2

-0.02

-58.2

+0.18

+41.7

-0.02

+15. 8

+0.79

+22.4

-1.20

198

+26.2

-0.01

-57. 2

+0.14

+41.5

-0.04

+ 19.4

+0.37

+ 14.6

-1. 33

204

+26.1

-0.02

-56. 5

+0.08

+41.2

-0. 05

+20.2

-0.08

+ 6.4

-1.32

210

+25.9

—0.02

-56.2

+0. 05

+40.9

-0.02

+18.4

-0. 50

- 1.2

-1.18

216

+25.9

0.00

-55. 9

+0.02

+40.9

+0.02

+ 14.3

-0.82

-7.7

-0.90

222

+25. 9

0.00

-55. 9

+0.02

+41.2

+0. 05

+ 8.5

-1.04

-12.0

-0. 52

228

+25. 9

0.00

-55. 6

+0.06

+41.5

+0.08

+ 1.8

-1.12

-13.9

-0.12

234

+25. 9

0.00

-55. 2

+0.08

+42.1

+0.11

-4.9

-1.05

-13.4

+0.28

240

+25.9

-0.01

-54.7

+0.12

+42.8

+0.10

-10.8

-0.85

-10.5

+0.62

246

+25.8

0.00

-53.7

+0.18

+43.3

+0.08

-15. 1

-0. 54

- 5.8

+0.89

252

+25.9

0.00

-52. 5

+0.21

+43.8

+0.04

-17.3

-0.14

+ 0.2

+1.02

258

+25. 8

-0. 01

-51.2

+0.22

+43.8

-0.02

-16.8

+0.26

+ 6.4

+0.99

264

+25.8

0.00

-49.8

+0.23

+43. 5

-0.08

— 14.2

+0. 60

+12.1

+0.84

270

+25.8

-0. 02

-48.4

+0.22

+42.9

-0.14

- 9.6

+0. 90

+ 16.5

+0.58

276

+25.6

-0.03

-47.1

+0.18

+ 41.8

-0.22

- 3.5

+1.07

+ 19.0

+0.20

282

+25.4

-0. 02

-46.2

+0.11

+40.3

-0.26

+ 3.2

+1.09

+ 18.9

-0. 22

288

+25.3

-0.02

-45. 8

+0. 02

+38. 7

-0. 29

+ 9.6

+ 1.00

+ 16.4

-0.61

294

+25. 1

-0. 02

-45. 9

-0.06

+36. 8

-0. 31

+15. 1

+0. 75

+ 11.6

-0.95

300

+25.0

-0.02

-46. 5

-0. 14

+35. 0

-0.28

+18.6

+0.38

+ 5.0

-1.19

306

+24.9

-0.01

-47.7

-0.23

+33. 5

-0.22

+19.7

-0.04

-2.7

-1.32

312

+24.9

0.00

-49.3

-0.30

+32.4

-0.12

+ 18.1

-0.48

-10.8

-1.28

318

+24.9

0.00

-51.3

-0.36

+32. 0

-0.03

+13.9

-0.89

-18.1

-1.09

324

+24.9

+0. 01

-53.6

-0.37

+32.0

+0.08

+ 7.4

-1.24

-24. 0

-0.78

330

+25.0

+0.03

-55. 7

-0. 34

+33.0

+0.22

- 1.0

-1. 48

-27. 5

-0. 37

336

+25. 3

+0.04

-57. 7

-0.28

+34. 6

+0. 32

-10.3

-1.58

-28.4

+0.11

342

+25. 5

+0.04

-59. 0

-0. 17

+36.8

+0.42

-19.9

-1.51

-26.2

+0.58

348

+25. 8

+0.06

-59. 7

-0. 05

+39.6

+0.48

-28.4

-1.28

-21.4

+1.05

354

+26.2

+0. 05

-59.6

+0.10

+42.6

+0. 52

-35.3

-0. 95

—13.6

+ 1.42

360

t

+26.4

+0. 04

-58. 5

+0.26

+45.8

+0.51

-39.8

-0. 51

— 4.4

+ 1.64

[ndz, d logr, and u/cos i are to be computed in the form Si <n sin ig+Ii bi cos tg+cT

296 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {161) Athor— Continued.

TABLE III.— flog r— Continued.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

9'

3

4

"3

Diff.forl0

h

Diff.forl0

at

Diff.forl0

b,

Diff.forl0

O

0

-4.3

+0.08

+1.9

+0.22

+0.2

+0.07

+0.8

-0.02

6

-3.6

+0. 12

+3.0

+0.18

+0.6

+0.05

+0.6

-0.04

12

-2.8

+0.18

+4.0

+0.13

+0.8

+0.02

+0.3

-0. 06

18

-1.4

+0. 22

+4.0

+0.06

+0.8

-0.02

-0.1

-0.06

24

-0.1

+0.23

+4.7

-0.02

+0.6

-0.03

-0.4

-0.05

30

+1.4

+0.21

+4.3

-0.10

+0.4

-0.05

-0.7

-0.03

36

+2.4

+0.16

+3.4

-0.16

0.0

-0.07

-0.8

0.00

42

+3.3

+0. 10

+2.3

II 20

-0.4

-0. 05

-0.7

+0.03

48

+3.6

0.00

+1.0

-0.22

-0.6

-0.02

-0.4

+0.06

54

+3.3

-0.08

-0.3

-0. 20

-0.7

0.00

0.0

+0. 06

60

+2.7

-0.13

-1.4

-0. 1 1

-0.6

+0.02

+0.3

+0.04

66

+1.7

-0.16

-2.1

-0.08

-0.4

+0. 04

+0.5

+0.03

72

+0.8

-0.17

-2.3

0.00

-0. 1

+0.07

+0.7

+0.01

78

-0.3

-0. 15

-2.1

+0.04

+0.4

+0. 00

+0.6

-0.02

84

—1.0

-0. 09

-1.8

+0. 08

+0.6

+0.02

+0.4

-0.04

90

-1.4

-0.04

— 1. 1

+0.12

+0.7

0.00

+0.1

-0.06

96

-1.5

0.00

-0.5

+0. 10

+0.0

-0.02

-0.3

-0. 05

102

-1.4

+0.03

+0.1

+0.06

+0.4

-0.04

-0.5

-0.04

108

—1.1

+0. 06

+0.3

+0.02

+0.1

-0.06

-0.8

-0.02

114

-0.7

+0.07

+0.5

+0.01

-0.3

-0. 05

-0.8

+0.02

120

-0.3

+0.04

+0.4

-0.02

-0.5

-0. 04

-0.5

+0.05

126

-0.2

+0.01

+0.1

-0. 05

-0.8

-0.02

-0.2

+0.06

132

-0.2

-0.02

-0.2

-0.05

-0.8

+0.01

+0.2

+0.06

138

-0.4

-0. 05

-0. 5

-0. 03

-0.7

+0. 03

+0.5

+0.05

144

-0.8

-0.06

-0.6

0.00

-0.4

+0. 00

+0.8

+0.02

150

—1.1

-0.06

-0. 5

+0.02

0.0

+0. 07

+0.8

-0.01

156

-1.5

-0.05

-0.4

+0. 05

+0.4

+0. 05

+0.7

-0.02

162

-1.7

-0. 02

+0.1

+0.08

+0.6

+0.03

+0.5

-0.04

168

-1.7

+0.01

+0.5

+0.07

+0.8

+0.02

+0.2

-0. 05

174

-1.6

+0.02

+0.9

+0.07

+0.8

-0. 02

-0.1

-0. 05

180

-1.3

+0.06

+1.3

+0. 05

+0.5

-0.04

-0.4

-0.04

180

-0.9

+0.07

+ 1.5

+0. 01

+0.3

— 0. 02

-0.6

-0.02

192

-0.5

+0. 06

+1.4

— 0. 1 12

+0.1

-0.04

-0.6

+0.01

198

-0.2

+0.03

+1.3

— 0. 02

-0.2

-0. 03

-0.5

+0.02

204

-0.1

+0.02

+1.1

-0. 04

-0.3

-0.02

-0.5

+0.02

210

0.0

+0.01

+0.8

-0.03

-0.4

-0.02

-0.2

+0.04

216

0.0

-0.01

+0.7

-0.02

-0.5

0.00

0.0

+0.02

222

-0.1

-0.02

+0. 5

-0.02

-0.4

+0. 02

+0.1

+0,01

228

-0.2

-0.02

+0.5

+0.01

-0.3

+0.02

+0.1

+0.01

234

-0.3

-0.02

+0.6

+0.02

-0.2

+0.01

+0.2

+0.01

240

-0.4

0.00

+0.7

+0.02

-0.2

+0.01

+0.2

0.00

246

-0.3

+0.02

+0.9

+0.02

-0. 1

+0.01

+0.2

0.00

252

-0.2

+0.03

+ 1.0

+0.02

-0. 1

0.00

+0.2

+0.01

258

+0.1

+0. 05

+1.1

+0.01

-0. 1

+0.01

+0. 3

+0.02

264

+0.4

+0. 05

+1.1

-0.01

0.0

+0.02

+0.4

+0.01

270

+0.7

+0. 04

+ 1.0

-0. 02

+0.1

+0.02

+0.4

-0.01

276

+0.9

+0.03

+0.8

-0.04

+0.3

+0.02

+0.3

-0.02

282

+1.1

+0.03

+0.5

-0.06

+0.5

+0. 02

+0.2

-0.01

288

+ 1.3

+0. 02

+0.1

-0.08

+0.5

+0.02

+0.2

-0.03

294

+1.4

+0.01

-0.5

-0.09

+0.6

0.00

-0.2

-0. 05

300

+1.4

-0. 02

-1.0

-0.08

+0.5

02

-0.4

-0. 03

306

+1.1

-0.06

-1.4

-0.08

+0.3

-0.04

-0.6

-0.03

312

+0.7

-0.08

-2.0

-0.09

0.0

-0.04

-0.8

-0.02

318

+0.1

-0. L2

-2.5

-0. 00

-0.2

-0. 04

-0.8

+0.02

324

-0.8

-0.15

— 2. 7

-0. 02

-0.5

-0. 05

-0.6

+0. 04

330

—1.7

-0. 15

-2.7

+0. 02

-0.8

-0. 02

-0.3

+0.06

336

-2.6

-0. 15

-2.3

+0. 08

-0.8

0.00

+0.1

+0.06

342

-3. 5

-0. 13

-1.7

+0.14

-0.8

+0. 02

+0.5

+0.05

348

—4. 2

-0.08

-0.7

+0.18

-0. 5

+0.05

+0.7

+0. 02

354

-4.5

-0.01

+0.5

+0. 22

-0.2

+0.06

+0.8

+0.01

360

-4. 3

+0. 08

+1.9

+0. 22

+0.2

+0.07

+0.8

-0.02

[nSz, (5 log r, and u/cos i are to Le computed in the form li ai sin ig+^i bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (161) Ath or— Continued.

297

TABLE IV.— u cos i.

PERIODIC TERMS.

Unit ol a and b= 09001.

i

0

1

2

9'

K

Diff.forl0

a,

Diff.forl0

6,

Diff.forl0

a.

Diff.forl0

b,_

Diff.forl0

0

0

+1.7

0.00

+6.4

-0.13

-8.4

0.00

+5.3

+0.28

+4.7

-0.26

6

+1.7

0.00

+5. 6

-0.12

-8.3

+0.02

+6.7

+0. 19

+2.8

-0.33

12

+ 1.7

-0. 02

+5.0

-0.11

-8.1

+0. 06

+7.6

+0.07

+0.7

-0.36

IS

+1.5

-0. 03

+4.3

-0. 09

-7.6

+0.08

+7.5

-0.07

-1.5

-0.38

24

+ 1.3

-0.04

+3.9

-0.08

-7.2

+0.09

+6.8

-0.17

-3.8

-0.37

30

+1.0

-0.07

+ 3. 5

-0.04

-6.5

+0.12

+5.5

-0.28

-5.8

-0.28

36

+0. 5

-0.08

+3.4

-0.01

-5.8

+0.11

+3.5

-0. 35

-7.1

-0.18

42

0.0

-0. 10

+3.4

+0.01

-5.2

+0.10

+ 1.3

ii 38

-8.0

-0.08

48

-0.7

-0. 1 1

+3. 5

+0. 03

-4.6

+0.11

-1.1

-0.40

-8.0

+0.06

54

-1.3

-0. 10

+3.8

+0.06

-3.9

+0.09

-3.5

-0. 37

-7.3

+0.18

60

-1.9

-0.09

+4.2

+0.08

-3. 5

+0.06

-5. 5

-0.29

-5.8

+0.29

66

-2. 4

-II. IIS

+4.7

+0.08

-3.2

+0. 05

-7.0

-0.20

-3.8

+0.36

72

—2. 9

—0.08

+5.1

+0.08

-2.9

+0.03

-7.9

-0.07

-1.5

+0.40

78

-3.3

-0. 06

+5.7

+0. 08

-2.8

+0.01

-7.8

+0.07

+ 1.0

+0. 42

84

-3. 6

-0. 02

+6.1

+0. 08

-2.8

-0. 02

-7.1

+0.18

+3. 6

+0.39

90

-?,. 6

0.00

+6.6

+0.08

-3.0

-0. 02

-5. 7 -

+0.29

+5.7

+0. 31

96

-3.6

+0. 02

+7.0

+0.04

-3.1

-0.02

-3.6

+0.37

+7.3

+0.21

102

-3.3

+0.06

+7.2

+0. 04

-3.3

-0.04

-1.3

+0. 42

+8.2

+0.09

108

-2.9

+0. 08

+7.5

+0.03

-3.6

-0. 05

+ 1.4

+0.43

+8.4

-0.04

114

-2. 4

+0.08

+7.6

+0. 02

-3.9

-0.04

+3.9

+0.39

+7.7

-0.17

120

—1.9

+0.09

+7.7

+0. 02

-4.1

-0. 02

+6.1

+0.33

+6.4

-0.28

120

-1.3

+0. 10

+7.8

: u IIJ

-4.2

-0. 03

+7.9

+0. 23

+4.3

-0. 37

132

-0.7

+0.11

+7.9

■ II ill

-4.5

-0. 03

+8.9

+0.10

+2. (1

-0.41

138

0.0

+0. 10

+7.9

+0.01

-4.6

-0.02

+9.1

-0.03

-0.6

-0.42

144

+0. 5

+0.08

+8.0

ii in

-4.8

-0.02

+8.5

-0. 15

-3.1

-(1.40

150

+ 1.0

+0.07

+8.0

+0.01

-4.9

-0.03

+ 7.3

-0.27

-5.4

-0. 33

156

+1.3

+0.04

+ S. 1

+0.02

-5. 2

-0. 04

+5.3

-0.36

-7.1

-0.23

162

+ 1.5

+0. 03

+8.2

+0.01

-5.4

-0.04

+3.0

—0.41

-8.2

-0. 12

168

+ 1.7

+0.02

+8.2

0.00

-5.6

-0. 05

+0.4

-0.42

-8.6

+0. 01

174

+ 1.7

0. 00

+8.2

0.00

-6.0

-0. 05

-2. 0

-0.39.

-8.1

+0.14

180

+1.7

0.00

+8. 2

-0.02

-6. •_•

0.06

-4.3

0. 34

-6.9

+0.26

186

+1.7

-0.02

+8.0

-0. 03

-6.7

-0.06

-6.1

-0. 24

-5.0

+0. 35

192

+1.5

-(1, (13

+7.8

-0.04

—6. 9

-0.04

-7.2

-0. 12

-2. 7

+0.39

198

+1.3

-0.03

+7.5

-0.06

-7.2

-0.04

-7.5

+0.02

-0.3

+0.41

204

+1.1

-0.02

+7.1

-0.07

-7.4

-0.04

-7.0

+0. 13

+2.2

+0.39

210

+1.0

-0.02

+6.7

ii us

-7. 7

-0. 03

-5.9

+0. 21

+4.4

+0. 32

216

+0.9

0.00

+6.2

-0.09

-7.8

+0.01

-4.1

+0. 33

+6.1

+0.23

222

+1.0

+0. 01

+5.6

-0.09

-7.6

+0.03

-1.9

+0.38

+7.2

+0. 12

228

+1.0

+0. 01

+5.1

-0.08

-7.4

+0.04

+0.5

+0.40

+7.6

-0.01

234

+ 1.1

0.00

+4.6

-0.08

-7. 1

+0.06

+2.9

+0.38

+7.1

-0.14

240

+1.0

+0.01

+4.2

-0.00

-6.7

+0.09

+5.1

+0.32

+6.0

-0.24

246

+1.2

+0.02

+3.9

0.02

-6.0

+0.10

+6.8

+0.23

+4.2

-0.32

252

+1.3

+0.01

+3.9

0.00

-5.5

+0.10

+7.9

+0. 12

+2.1

-0.37

258

+1.3

+0.01

+3.9

+0. 02

-4.8

+0.11

+8.2

-ii 02

-0.2

-0. 39

264

+ 1.4

+0.01

+4.1

+0.04

-4.2

+0.10

+7.7

-0. 12

-2.6

-0.38

270

+1.4

0.00

+4.4

+0.08

-3.6

+0.09

+6.7

-0. 22

-4.7

0.31

276

+ 1.4

-0.01

+5.0

+0.10

-3.1

+0.06

+5.0

-0.32

-6.3

-0. 22

282

+ 1.3

-0.01

+5.6

+ 0. 1 1

-2.9

+0. 02

+2.9

-0.37

-7.4

-0. 12

288

+1.3

-0.01

i; 3

+0. 12

-2.8

+0. 02

+0.6

-0.38

-7.8

+0. 01

294

+ 1.2

-0.02

+7.0

+0.12

-2.7

ii HI

-1.7

-0. 36

-7.3

+0. 13

300

+1. 1

-11.01

+ 7.7

+0.10

-2.9

-0.06

-3.7

-0.30

-li. 2

+0. 2:;

306

+ 1. 1

-0.02

+8.2

+0.08

-3.4

-0.08

-5.3

-0. 22

-4.5

+0. 32

312

-j-0. 9

-0.01

+8.7

+0.08

-3.9

-11. 10

-6.3

-0.10

-2.4

+0. 36

318

+1.0

0.00

+9.1

+0. 04

-4. 6

-0. 12

-6. 5

+0.03

-0.2

+0. 38

324

+0. 9

0.00

+9.2

+0.01

-5. 4

-0. 12

-5. 9

+0.13

+2.1

+0. 35

330

+1.0

+0.02

+9.2

-0.02

-ii. 1

-0. 12

-4.9

+0.23

+4.0

+0.28

336

+1.1

+0.02

1 v 9

-0.07

1, s

-ii. 11

-3. 1

+0.32

1 5. 5

+0.2O

342

1-1.3

+0.03

+8.4

-0. 09

-7.4

II lis

-1.0

+0.36

+6. -1

-0.09

3 is

+ 1-5

+0.03

+7.8

-a io

-7.8

II. (IS

+ 1.2

+0.37

+6.6

-0. 04

354

+ 1.7

| u 02

+7.2

-0. 12

-8.3

-0.05

+3.4

+0.34

+5. 9

-o. in

360

+ 1.7

0.00

+6.4

-0. 13

-8.4

0.00

+5.3

+0.28

+4.7

-0. 2(1

[ndz, 3 log r, and u/cos i are to be computed in the form It at sin ig+£i bt cos ig-i-cT.]

298 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (161) Aihor — Continued.

TABLE IV.— m/cos i— Continued.
PERIODIC TERMS. Unit ot o and 6=09001.

i

3

9'

«3

Diff.forl0

h

Diff.forl0

°
0

+0.2

+0.2

6

+0.3

+0.1

12

+0.2

-0.1

18

+0.2

-0.1

24

+0.1

-0.2

.SO

-0.2

-0.2

36

-0.2

-0.2

42

-0.3

-0.1

48

-0.3

+0.1

54

-0.2

+0.2

60

-0.2

+0.4

66

-0.1

+0.4

72

0.0

+0.5

78

+0.2

+0.3

84

+0.3

+0.3

" 90

+0.4

+0.2

96

+0.5

+0.1

102

+0.5

0.0

108

+0.3

-0.2

114

+0.3

-0.2

120

+0.2

-0.4

126

+0. 2

-0.4

132

0.0

-0.4

138

0. 0

-0.2

144

0.0

-0.2

150

-0.2

-0.2

156

-0.1

-0.2

162

-0.1

-0. 2

168

-0.1

-0.2

174

-0.1

-0.3

180

-0.2

-0.2

186

-0.3

-0.1

192

-0.4

-0. 1

198

-0.4

-0.1

204

-0.5

0.0

210

-0.6

+0.2

216

-0.4

+0.4

222

-0.3

+0.5

228

-0.3

+0.7

234

0.0

+0.8

241)

+0.2

+0.8

246

+0.5

+0.6

252

+0.6

+0.5

25S

+0.8

+0.3

264

+0.9

+0.1

270

+0.8

-0.2

276

+0.7

-0.5

282

+0.5

-0.6

288

+0.3

-0.8

2!) 4

+0.1

-0.8

300

-0.2

-0.8

"

306

-0.4

-0.6

312

-0.6

-0.4

318

-0.6

-0.2

324

-0.6

0.0

330

-0.6

+0.2

336

-0.3

+0.4

342

-0.1

+0.4

343

-0.1

+0.4

354

+0.1

+0.3

360

+0.2

+0.2

\nSz, S\ogr, and u/cos i are to be computed in thelorm of 2i<n sin ig+Zibi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (161) Athor— Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T= (t— 1„) IN JULIAN YEARS.

299

noz

d log r

u cos i

g

Unit of i

=0?001

Unit of c

=0.00001

Unit of <

•=0?001

c

Diff. for 1°

c

Diff. for 1°

<•

Diff. fori0

o

0

-2.35

+0. 003

-0.09

-0. 018

+0.69

+0. 032

6

-2. 32

+0. 009

-0.20

-0. 01S

+0.88

+0. 029

12

-2. 24

+0. 014

-0.30

-0. Oil)

+ 1.04

+0. 025

18

-2. 15

+0. 018

-0.39

-0. 015

+1.18

+0. 022

24

-2.03

+0. 021

-0. 48

-0. 01 1

+ 1.31

+0. 020

30

-1.90

+0. 025

-0.56

-0. 013

+ 1.42

+0. 017

36

-1.73

+0. 030

-0.64

-I). 012

+ 1. 51

+0. 012

42

— 1. 54

+0. 032

-0.70

-0.010

+ 1.56

+0. 008

48

-1.34

+0. 034

-0.76

-0. 008

+ 1.60

+0. 005

54

—1.13

+0. 037

-0.80

-0. 008

+ 1.62

+0. 002

60

-0.90

+0. 039

-0.85

-0. 006

+ 1.62

-0. 002

66

-0.66

+0. 040

-0.87

-0. 002

+ 1.59

-0. 007

72

-0. 42

+0. 039

-0.88

-0. 001

+ 1. 54

0 oii'i

78

-0. 19

+0. 040

-0.88

0.000

+ 1.48

-0. 012

84

+0. 00

+0. 041

II. NS

+0. 002

+1.40

-0. 016

90

+0. 30

+0.01D

-0.86

+0. 003

+1.29

-0. 018

96

+0. 54

+0. 038

-0.84

+0. 005

+ 1.18

— 0. 019

102

+0. 70

+0. 036

-0.80

+0. 007

+ 1.06

-0. 021

108

4-0.97

+0. 034

- II. 76

+0. 008

+0.93

— 0. 022

114

+1.17

+0. 032

-0.71

+0. 008

+0.79

-0. 024

120

+ 1.36

+0. 030

-0.66

+0. 010

+0.64

-0. 025

126

+ 1.53

+0. 027

-0. 59

+0.011

+0.49

-0. 025

132

+1.68

+0. 024

-0.53

+0. 011

+0.34

-0. 027

138

+1.82

+0. 021

-0.46

+0. 012

+0.17

-0. 027

144

+ 1.93

+0. 018

-0.39

+0. 012

+0.02

-0. 026

150

+2.03

+0. 014

-0.31

+0. 013

-0.14

-0. 028

156

+2. 10

+0. 011

-0.23

+0. 012

-0.31

-0. 028

162

+2. 16

+0. 008

-0.17

+0. 012

-0.48

-0. 026

168

+2.20

+0. 003

-0.09

+0. 013

-0.62

-0. 025

174

+2.20

-0. 001

-0.01

+0. 014

-0.78

-0. 024

180

+2.19

-0. 003

+0.08

+0. 013

-0.91

-0. 023

186

+2. 16

-0. 008

+0. 15

+0. 012

-1.06

-0. 022

192

+2.10

-0.011

+0. 22

+0. 012

-1.18

-0. 020

198

+2.03

-0. 014

+0. 30

+0. 012

-1.30

-0. 019

204

+ 1.93

-0. 018

+0.37

+0. 012

—1.41

-0. 018

210

+1.82

-0. 020

+0.44

+0. 012

-1.52

-0. 017

216

+1.69

-0. 023

+0. 51

+0. 011

-1.61

-0. 013

222

+1. 54

-0. 028

+0. 57

+0. 010

-1.68

-0. 012

228

+1. 36

-0. 029

+0.63

+0. 009

-1.74

-0. 010

234

+ 1.19

-0. 032

+0.68

+0. 009

-1.80

-0. 008

240

+0.98

-0. 034

+0.73

+0. 008

-1.84

-0. 004

246

+0.78

-0. 035

+0.77

+0. 006

-1.85

0.000

252

+0. 56

-0. 038

+0.80

+0. 005

-1.84

+0. 001

258

+0.33

-0. 038

+0.83

+0. 004

-1.84

+0. 003

264

+0. 10

-0. 039

+0. 85

+0. 002

-1.80

+0. 008

270

-0. 14

-0. 040

+0.85

+0. 001

-1.75

+0. 010

270

-0.38

-0. 040

+0. 86

0.000

-1.68

+0. 012

282

-0.62

-0. 039

+0.85

-0. 003

-1.60

+0. 016

288

-0. 85

-0. 038

+0.82

-0. 005

-1.49

+0. 019

294

-1.07

-0. 036

+0.79

-0. 006

-1.37

+0. 022

300

-1.28

-0. 035

+0. 75

-0. 008

-1.22

+0. 025

306

-1.49

-0. 033

+0.70

-0. 009

-1.07

+0. 027

312

-1.68

-0.029

+0.64

-0.011

-0.90

+0. 030

318

-1.84

-0. 026

+0.57

-0. 012

-0.71

+0. 032

324

-1.99

-0. 022

+0. 49

-0. 014

-0.52

+0. 032

330

-2.11

-0. 019

+0.40

II 015

-0.32

+0. 034

336

-2.22

-0. 016

+0.31

-0. 016

-0.11

+0. 035

342

-2.30

-0. 010

+0.21

-0.017

+0.10

+0. 034

348

-2.34

-0. 005

+0.11

-0. 017

+0.30

+0. 033

354

-2.36

-0. 001

+0.01

-0.017

+0. 50

+0. 032

360

-2.35

+0. 003

-0.09

-0. 018

+0.69

+0. 032

[ndz, d log t, and u/cos i are to be computed in the form of liat sin ig+Zibi cos ig+cT.]
89369°— vol 10—11 20

300 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (161) Athor— Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

V

C

log sin a

log sin b

log sin e

1876. 0

O

39. 8897

o

311. 6661

O

305. 3692

9. 99947

9. 92836

9. 72625

7

9035

6811

3796

47

36

625

8

9173

6962

3900

46

37

624

9

9311

7112

4005

46

37

623

[SMI

39. 9450

311. 7262

305. 4109

9. 99946

9. 92837

9. 72623

1

9588

7413

4213

46

38

622

2

9726

7563

4317

46

38

621

3

39. 9864

7714

4421

46

38

621

4

40. 0002

7864

4525

46

39

620

1885

40. 0141

311. 8015

305. 4630

9. 99946

9. 92839

9. 72619

6

0279

8166

4734

46

39

619

7

0417

8316

4838

46

40

618

8

0555

8467

4942

46

40

618

9

0693

8617

5016

46

40

617

1890

40. 0832

311. 8768

305. 5150

9. 99946

9. 92841

9. 72616

1

0970

8919

5255

46

41

616

2

1108

9070

5359

46

41

615

3

1246

9220

5463

45

42

614

4

1384

9371

5567

45

42

614

1895

40. 1523

311.9522

305. 5671

9. 99945

9. 92842

9. 72613

6

1661

9672

5775

45

43

613

7

1799

9823

5SS0

45

43

612

8

1937

311. 9974

5984

45

43

611

9

2075

312.0124

6088

45

44

611

1900

40. 2214

312. 0275

305. 6192

9. 99945

9. 92844

9. 72610

1

2352

0426

6296

45

44

609

2

2490

0576

6400

45

45

609

3

2628

0727

6504

45

45

608

4

2767

0878

6609

45

45

607

1905

40. 2905

312. 102S

305. 6713

9. 99944

9. 92846

9. 72607

6

3043

1179

6817

44

46

606

7

3181

1330

6921

44

47

606

8

3319

1480

7025

44

47

605

9

:;|.-,s

1631

7130

44

47

604

1910

40. 3596

312. 1782

305. 7234

9. 99944

9. 92848

9. 72604

1

3734

L932

7338

44

48

603

2

3872

2083

7442

44

48

602

3

4011

2234

7546

44

49

602

4

4149

2384

7650

44

49

601

1915

40. 4287

312. 2535

305. 7755

9. 99943

9. 92850

9. 72600

6

4425

2686

7859

43

50

9. 72600

7

4563

2836

7963

43

50

9. 72599

8

4702

2987

8067

43

51

599

9

4841

3138

8171

43

51

598

1920

40. 4979

312. 3288

S276

9. 99943

9. 92851

9. 72597

1

5117

3439

83S0

43

52

597

2

5256

3590

8484

43

52

596

3

539 1

3740

858S

43

52

595

4

5532

3891

S692

43

53

595

1925

40. 5670

312. 4042

305. 8797

9. 99942

9. 92853

9. 72594

6

5809

4192

8901

42

54

594

7

5947

4343

9005

42

54

593

8

6085

4494

9109

42

54

592

9

622:-;

Hi 15

9213

42

55

592

1930

40. 6362

312. 4795

305. 9318

9. 99942

9. 92855

9. 72591

Year

log cos a

log cos 6

log cos c

1876.0
1930. 0

8. 696 9. 724 n

8. 712 9. 724 n

9.928
9.928

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLES OF (174) PHAEDRA.

301

MEAN ELEMENTS.

Epoch, 1893, Nov. 16.0, M. T. Berlin = 1893.876, M. T. Berlin.

O / // O

0O=2O1 5 28 = 201°0912

« = 280' 3 40=286.0611]

&=328 42 26 = 328. 7073 [Mean equinox and ecliptic 1900.0.

i= 12 7 3= 12. 117.",J

0= 8 18 11= 8.3030

n = 733. "4324 = 0.20373123

The elements are based on oppositions extending from 1877 to L901 and on the perturbations of the

first order by Jupiter, as given on page 302.

AUXILIARY QUANTITIES.

log a=0. 45643 log 57. 2958e=0. 91772 wjl^-q qofi„4
log e=9. 15959 log p =0. 44728 , IogV T+~e y,i()8*

TABLE I.— MEAN ANOMALY igi.

Jan. 0.0 of common years; Jan. 1.0 of leap years

Table for beginning of month

Month

g

Year

9

Year

9

Jan. \ , „

0
\ 0. 00000

0

0

1877

25. 29186

1905

308.64741

11.0

8

99. 65375

6

23. 00931

Feb.j0'^ 6.31567

9

174. 01565

7

97.37121

U-0

B 1880

248. 58128

B 8

171. 93684

Mar. 0.0

12. 02014

1

322. 94318

9

246. 29874

Apr. 0.0

18. 33581

2

37. 30508

1910

320. 66064

May 0.0

24. 44775

3

111. 66698

1

35. 02254

June 0.0

30. 76342

B 4

186. 23261

B 2

109. 58817

July 0.0

36. 87535

5

260.59451

3

183. 95007

Aug. 0.0

43. 19102

6

334.95641

4

258.31197

Sept. 0.0

49. 50669

7

49. 31831

5 332. 67387

Oct. 0.0 55.61863

B 8

123.88394

B 6 47. 23950

Nov. 0.0 61. 93429

9

198. 245S4

7 121. 60139

Dec. 0.0 68. 04623

1890

1
B 2

272 60774

8 IflR QR39Q

346. 96964

9

270. 32519
344. 89082

61.53527 B 1920

3

135.89716 1

59. 25272

Change for n days a

4
5

210. 25906 2 133. 61462
284. 62096 3 207. 97652

yi

9

fl

9

B 6

359. 18659

B 4 282. 54215

7

73. 54849

5 356. 90405

8

147. 91039

6 71. 26595

0

0

9

222 27229

7

145. 62785

1

0. 20373

16

3. 25970

1900

296. 63419

B 8

220. 19348

2

0. 40746

17

3. 46343

1

10. 99609

9

294. 55538

3

0. 61119

18

3. 66716

2

85. 35799

1930

8. 91727

4

0. 81492

19

3. 87089

3

159. 71989

5

1. 01866

20

4. 07462

B 4

234. 28552

6

1. 22239

21

4. 27836

1905

308. 64741

7
8
9

1.42612
1. 62985
1. 83358

22
23
24

4. 48209
4. 68582
4. 88955

Note. — W"

len g is used as an argument of the perturba-

10

2. 03731

25

5. 09328

tions add to

the g of this table ^7r=^— tt0= +091151. For

11

2. 24104

26

5. 29701

explanation

see page 203.

12

2. 44477

27

5. 50074

13

2. 64851

28

5. 70447

14

2. 85224

29

5. 90821

15

3. 05597

30

6. 11194

0 For dates during January and

February of leap years, subtract one

day before entering this table.

302

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (174) Phaedra — Continued.

PERTURBATIONS.

ndz

i

m/cos i

Arg.

ig-'g'

sin

cos

sin

cos

sin

cos

//

//

//

//

//

//

0 0
0 0

•

— 7

+ 0. 01 nt

- 7

- 0. 7H nt

+ 1 o

+i

+2
+2
+3 0

0. 14 nt

_ 2

8. 61 nt
_ 2

- 0. 30 nt

— 0. 02 nt

4. 30 nt
1

— 0. 30 nt

- 0. 03 nt

+ 4

+ 0. 07 nt

+ 1

+11. 22 nt

-1

+ 0. 80 nt

+ 0. 09 nt

+ 3. 58 nt
+ 1

+ 0. 26 nt
+ 0. 03 nt

-1 +1
0

+1
+2
+3 +1

- 4
+ 20
+122
+ 5

- 4
+ 22
+ 198

+ 1

+ 2

+ 63
+ 1
+ 1

- 3

+ 2

- 37

- 4

+ 3
+17
-17
-10
- 1

- 6
-16
+12
+ 3

-1 +2

0
+ 1
+2
+3
+4 +2

+ 4
-637
-358

- 17

- 1

_ 2
- 48
+1132
+ 549
+ 24
+ 2

+ 2
+ 21
+157
+306
+ 25
+ 3

+ 2
+ 87
+ 199

+ 18

+ 2

+ 3
+30
-25
-21
- 1

+ 5
- 2
—15

+ 1

0 +3

+1
+2
+3
+4 +3

- 4
-165
+465
+ 59

+ 5

+ 72
- 124

+ 1

- 13
- 50

_ 2

- 33
-198

- 44

- 6

- 4

- 7
+11
+ 1
+ 1

- 4
-14
+37
+ 5
- 1

+1 +4

+2

+3

+4

+5 +4

- 19
+ 155
+ 68

- 8
+ 76
+ 71

5

- 1

+ 3
+ 22
+ 42

- 3

- 1

- 8

- 41

- 41

+ 1

- 3

- 9

- 6
+ 7
+10

+1 +5

+2

+3

+4

+5 +5

+ 10
+654

- 29
+ 4

- 1

+ 14
+1442

- 519

33

- 1

- 7

- 54
-263

- 28

- 2

+ 5
+ 21
+ 14
- 2

+ 1

- 8
-19
+85
+ 9

+ 1

+ 3

- 4
+ 1

+2 +6

+3

+4

+5 +6

+ 18
+ 15
- 4

+ 2

- 33

10

- 11

- 6

- 7

- 8
+ 2

+ 3
+ 2

+ 3
+ 2
- 1

+3 +7

+4

+5

+6 +7

- 7
+ 30
2

+ 6
- 3

+ 1

+ 3
- 2

+ 1

- 16

+ 1

+ 1

- 2

+ 7

- 1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (174) Phaedra — Continued.

TABLE II.— ndz.

303

PERIODIC TERMS.

Unit of a and 6=« 09001.

1

0

1

9'

&o

Diff.forl"

»i

Diff.forl0

b,

Diff.forl

0

0

- 7.3

-0.09

-189. S

+13. 04

+388. 2

+ 8.04

6

- 7. 6

ii in

—105.5

+ 14. 82

+428. 1

+ 5.02

12

-7.2

+0. 10

- 13.4

+15. 7 1

+448. 5

+ 1.69

18

- li. 4

+0. 15

+ 81.8

+ 15. 86

+448.4

- 1.78

24

- 5. l

+0.19

+ 175.2

+ 15. 17

+427. 2

- 5. 1 7

30

- 4. 1

+0.23

+262. 4

+13. 76

+386. 4

- 8.32

36

- 2. 6

+0. 28

+339. 0

+ 11.58

+ 327. 4

-11. 12

42

- 0. 8

+0.28

+401. 2

+ 8.90

+252. 9

-13. 38

48

+ 0.8

+0. 27

+443. 8

+ 5. SI

+166. 9

-15. 13

54

+ 2.4

+0.26

+470.0

+ 2.44

+ 72. S

-16.05

60

+ 3.9

+0.23

+475. 1

- 1.09

- 24.2

-16. 19

tie

+ 5. 2

+0.19

+457.8

- 4.58

-119.9

— 1 5. 55

72

+ 6. 2

+0.12

+420 2

7. 80

209. 2

-1 1 (10

78

+ (i. 8

i

+ 304. 2

-10. 59

- 287. 5

-11.82

84

| ii 'i

(i mi

+293. 1

-12.89

-351. 0

- 9.11

90

- 6 -

-0. 06

+ 211.0

-14.37

-396. s

- 6.00

96

+ 6.2

-0. 15

+ 122.2

-15.08

-123. 0

- 2.65

102

+ 5.0

-ll. 21

+ 31. S

1 1 'in

-428. o

+ 0.68

10S

+ 3.7

-O. 25

- 55.0

-13.85

-414. 9

+ 3. 73

114

- 2.0

-0. 32

-134.4

12. 32

-383. 8

+ 6.41

120

- 0. 1

-ll. 37

-202. s

-10.30

-338. 0

+ 8. 54

126

- 2.4

-0. 42

258 ii

- 7.95

2s l . 3

+10. 05

132

- 5. 1

. -0.43

-298. 2

- 5.48

-217.4

+10. 96

L38

7 ii

-0. 42

-323.8

- 3.07

1 lii. 8

+ 11.33

144

-10. 2

-0.42

-335.0

(1 so

- 81.4

+ 11.23

150

-12.6

I) 111

-333. 4

+ 1. 28

- 14.8

+10. 77

156

-15. 0

(i 35

-319.7

+ 3. 17

+ 47.8

+ 9. 07

L62

-16.8

-0. 27

-295.4

+ 4. 78

+ 104.8

+ 8. OS

168

-18.2

ii 19

-202. 4

+ 6. 17

+ 155.5

+ 7.80

174

-19. 1

-0. 11

-221. 4

+ 7.40

+198.4

+ 6. 44

180

-19.5

+0. 01

-173. i;

+ 8.40

+232. s

+ 4. 92

186

-19. 0

+0. 12

-120.6

+ 9. 13

+257. 4

+ 3. 22

192

-IS. 0

+0.22

- 64.0

+ 9. 58

+271. 5

+ 1.38

198

-16.4

+0. 33

- 5. 6

+ 9. 07

+274.0

- 0.56

204

-14.0

+0.42

+ 52 ii

+ 9.37

+264. 8

2. 33

210

-11.3

+0. 52

+106. 8

+ s. ii:;

+243 0

- 4.46

216

- 7.S

+0.59

+155. 0

+ 7.47

+211. 3

- 6.13

222

- 4.2

+0. 63

+196. 4

+ 5. 98

+ 170.0

- 7. 33

228

- 0.2

+0. 65

+227 1

+ 4. 22

+ 120.9

- S. 02

234

+ 3. 6

+0.64

+247. 1

+ 2. 28

+ 66.5

- 0. 28

240

• '■

+0. 02

+251. s

+ 0. 31

+ 9.6

- 9.47

246

+ 11.0

+0.56

+250 8

- 1.02

- 47.1

- 9. 27

252

+14.2

+0.48

+2:;:.. i

:; 13

-101. 0

- s. 76

258

+16.8

+0.38

+200. 6

- 5.09

- 1 52. 2

- 7.90

264

+18. 7

+0. 27

+ 174. 3

i, 57

196. 1

- 6. 80

270

• 20.0

+0. 14

+130. 8

- 7.S2

23:; s

- 5.50

270

+20.4

+0. 02

+ 80. 3

- 8.00

-2112.4

i. 00

282

+ 20. 2

-0.11

+ 24.0

- 9. 70

-2SI.S

- 2. 20

2SS

+ 19. 1

—0. 22

- 30. 8

- in 33

- 289. 'i

ii 33

294

+17. 6

11 311

-100.0

- III. .v,

-285.8

+ 1. 711

300

+15.5

-0.38

-163.4

-10. 38

-268.4

+ 4.07

306

+ 13.0

-0. 45

-224. 0

- 9. 73

-237. II

0. 38

312

+ 10. 1

-0. 50

280.2

- S. 47

191.8

+ 8. 65

318

+ 7.0

-6.49

-320. 2

i, i,:;

L33 2

+ 10. 72

324

+ 4. 2

-0.48

-359. 8

- 4. 28

63 2

+ 12. 38

I |i i

+ 1.2

ii. 47

-377 6

1 Hi

+ 13.4

+13. 112

336

-1.4

-0. 40

-377 3

+ 1. 65

+ 98.8

+ 14.IH

342

-3.6

ii 32

-357. 8

+ 4. 86

+ 182.4

+ 13. 72

348

- 5. 2

0. 24

-319.0

+ 7. 98

+ 201. S

+ 12. 30

354

- 0.5

-0.18

-262.0

+10. 77

+331. 0

+ 10. 53

360

- 7.3

-0.09

-ISO. s

+13. 04

+38S. 2

+ 8.04

[■adz, S log r, and it/cos i are to lie computed in the form ii a,- sin ig+1 i In cos ig+cT.)

304 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {174) Phaedra — Continued.

PERIODIC TERMS.

TABLE II.— ndz— Continued.

Unit of a and 6=09001.

i

2

3

9'

a,

Di ft. fori0

62

Diff. fori0

«3

Diff. fur 1°

63

Diff. for 1°

O

0

+207. 9

+42. 19

+565. 7

-23. 00

+ 25.2

-12.16

-131.5

- 1.58

3

+384. 3

+35. 30

+480.6

-32. 79

- 11.7

-12.00

-130. 8

+ 1.78

6

+477.4

+26. 04

+371.0

-40. 23

- 46.8

-10. 92

-120.8

+ 4.90

9

+539. 0

+ 15. 10

+241.6

-45. 30

- 77. 2

- 9.10

-101.4

+ 7.62

12

+568. 0

+ 3.50

+ 102. 2

-47. 24

-101.4

- 6.60

- 75.1

+ 9.70

15

+560. 0

- 8.22

- 39.0

-46.41

-116.8

- 3.70

- 43.2

+ 11. 05

18

+518. 7

-19.32

-173.2

-42. 43

-123.5

- 0. 53

-8.8

+11. 50

21

+444. 1

-29. 46

-291.0

-35. 93

-120. 0

+ 2. 62

+ 25.8

+ 11.16

24

+344. 0

-37.27

-386. 4

-26. 94

-107.8

+ 5.52

+ 58.2

+ 9.94

27

+222. 8

—42. 80

-451. 1

-16.27

- 86.9

+ 8.00

+ 85.4

+ 8.00

30

+ 90.2

-45. 22

—484. 0

— 4.78

- 59.8

1 + 9. 85

+106. 2

+ 5.47

33

— 45. 6

-44. 78

-479. 8

+ 6.93

- 27.8

+ 11.00

+ 118.2

+ 2.53

36

-17.-.. 1

-41. 13

-442. !

+18. 10

+ 6.2

+ 11.23

+121.4

- 0. 57

39

-289.8

-34. 97

-371. 2

+28.41

+ 39. 6

+ 10. 63

+114. 8

- 3.60

42

-382. 8

-26. 28

-273. 9

+36. 1 1

+ 70.0

+ 9. 18

+ 99.8

- 6.36

45

-445. 8

-15. 75

-154.9

+42. 16

+ 94.7

+ 7. 10

+ 76.6

- 8.67

48

-477.3

- 4. 35

- 23.9

+44. 80

+ 112.6

+ 4. 48

+ 47.8

-10. 26

51

-471. 9

+ 7.37

+ 111. 1

+44. 69

+ 121.6

+ 1.53

+ 15.0

-11. 15

54

-433. 1

+18. 60

+241. 2

+41. 38

+ 121.8

- 1.58

- 19.1

-11. 13

57

-3(11). 3

+29.01

+356. 8

+35. 52

+ 112. 1

- 4. (ill

- 51.8

-10. 33

60

—260. !»

+37. 30

+451. 8

+26.99

+ 91. 2

- 7.28

- 81.1

- 8. 74

63

—138.8

+43. 36

+517. 0

+ 16.55

+ (iS. 1

- 9.43

-104.2

- 6.50

66

- 3.7

+46. 35

+551. 1

+ 5.23

+ 37.6

-10.87

-120.1

- 3.73

69

+ 136.5

+46. 59

+548. 4

- 6.48

+ 3.2

-11.57

-126.6

- 0. 62

72

+272. S

+43. 65

+512. 2

-17.82

- 31.8

-11.35

-123.8

+ 2.58

75

+395. 8

+38. 15

+441. 5

-28. 13

- lit. !l

-10.33

-111.1

+ 5. 62

78

+499. 2

+ 30.02

+343. 4

-37. 00

- 93.8

- s. 50

- 90. 1

+ 8.22

81

+574. 2

+ 19.96

+221.7

-43. 43

-115.9

- 11.07

- 61. 8

+10. 28

84

+619. 0

+ 8.94

+ 85. 6

-46. 94

-130.2

- 3. 12

- 28.4

+ 11.65

87

+ 627. 8

- 2. 62

- 57.2

—47. 76

-134.0

+ 0. 13

+ 8.1

+ 12. 20

90

+603. 3

-13.90

-198.0

-45.46

-12:i 1

+ 3.40

+ 44.8

+11. 85

93

+544. 1

—24.54

-327. 1

-40. 59

-114.2

+ 6.48

+ 79.2

+10. 65

96

+457. 8

-33. 22

-439. 1

-33. 16

- 90.5

+ 9. 17

+ 108. 7

+ 8. (iO

99

+ 347. 2

-39. S6

—524. 6

-24.00

- 59.2

+ 11.25

+ 130. 8

+ 5. 95

102

+221. 3

-43. 73

-581.8

-13.36

- 23.0

+ 12.56

+ 144.4

+ 2.78

105

+ 87. t

-45. 06

-604. 8

- 2.43

+ 16. 1

+ 13.03

+ 147. 5

- 0.58

108

- 4(1 2

-43. 40

-596. 4

+ 8.27

+ 55. 2

+ 12.52

+140. 9

- 3.97

111

-170.5

-39. 25

-555. 2

+ 18. 12

+ 91.2

+ 11.16

+123. 7

- 7.15

114

-279.3

-32. 60

-487. 5

+26. 72

+ 122.2

+ 9.02

+ 98.0

- 9.90

117

-364. 4

-24. 10

396. 8

+33 15

+145. 3

+ 6. 23

+ 64.3

— 12. 08

120

-423. !)

-14.62

-291.2

+36. 01

+ 159.6

+ 2. 95

+ 25. 5

-13.35

123

-452. 1

- 4.65

-177.6

+38. 34

+ 163. 0

- 0.57

- 15.8

-13. 73

126

-451. 8

+ 5.08

- 64.0

+36. 81

+ 156. 2

- 4.08

- 56.9

-13. 23

129

-421. 6

+ 14. 26

+ 40.9

+32. 99

+138. 5

- 7.37

- 95.2

-11.92

132

-367. 8

+21. 68

+ 131. 7

+26. 85

+ 112.0

-10. IS

-128.4

- 9.68

135

-293. 4

+27. 29

+200. 4

+18. 95

+ 77.4

-12.38

-153.3

- 6.80

L38

-206. 5

+30. 36

+245. 4

+ 10.20

+ 37.7

-13.73

-169. 2

- 3.48

141

-113.6

+31. 07

4 261.6

+ 1.07

- 5.0

-14.25

-174.2

+ 0.03

144

- 22.7

+29. 00

+251. 8

- 7. 73

- 47. S

-13.78

-169.0

+ 3. 58

147

+ 58. 2

+24. 77

+ 215. 2

-15.90

- 87. 7

-12.46

-152. 7

+ 6.93

150

I 123. 9

+18.40

+ 158. 0

-22. 27

-122. (i

- 10. 35

-127.4

+ 9.85

153

+ 167.2

+10. 48

+ 83. 5

-26. 78

-149.8

- 7.60

- 93.6

+ 12. 12

156

+ 186. 8

+ 1.77

0.2

-28. 72

-168.2

- 4.30

- 54.7

+13. 53

159

+ 177.8

- 7. 18

- si;. 5

—28. 37

-175.6

- 0. 76

— 12.4

+14. 18

162

+ 143.7

L5 63

-167. 8

-25. 26

-172.8

+ 2. 7..

+ 30.4

+ 13.88

165

+ 84. 0

-23. 34

-235.9

-20. 03

-159.1

+ 6.07

+ 70.9

+ 12. 72

168

+ 5.4

-29. 07

-286.0

- 12. 70

-136. 4

+ 8.95

+ 106. 7

+10. 72

171

- 88. 1

- 32. so

-310. 8

- 3.93

-105. 4

+11.28

+135. 2

+ 8.13

174

-188. 9

:::: mo

-309. 6

+ 5.47

- lis. 7

+ 12. 83

+ 155. 5

+ 5. 03

177

-289. 4

-32. 66

-27S. 0

+15. 02

- 28. 1

+ 13.58

+ 165.4

+ 1.67,

180

-382. 1

-28. .".1

-219.5

+23. '1.

+ 12.8

+ 13.43

+ 165. 5

- 1.72

[ndz, 3 log r, and B/cos i are to be computed iu the form Zi a* sin iy+Ii bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (174) Phaedra— Continued.
TABLE II.— ndz— Continued.

305

PERIODIC TERMS.

Unit of a and 6=09001.

i

2

i

■y

"j

Di£f.forl°

62

Diff.forl0

Q3

Diff.forl0

b3

Diff.forl0

0

180

-382. 1

-28. 54

-219. 5

+23. 98

+ 12.8

+ 13. 43

+ 165. 5

- 1.72

183

-458. 4

-22. 21

-134. 1

+32. 10

+ 52. 2

+ 12. 50

+155. 1

- 4.98

186

-513. 4

-13. 82

- 28.8

+38. 04

+ 87.8

+ 10. 75

+ 135.6

- 7. 90

189

-540.0

- 4.00

+ 92.0

+41. 87

+116. 7

+ 8. 37

+107. 7

-10.25

192

-537. 1

+ 6.50

+219. 8

+42. 95

+ 138. 0

+ 5. 52

+ 74. 1

-11.87

195

-501. 0

+ 17. 15

+347. 1

+41.46

+ 149. 8

+ 2. 37

+ 36. 5

-12. 75

198

-434. 5

+27. 18

+465. 7

+36. 98

+152. 2

- 0.93

- 2. 1

-12. 80

201

-337. 9

+36. 31

+566. 7

+30. 28

+ 144 2

- 4.13

- 40.3

-12. 10

204

-218.6

+43. 20

+645. 2

+21.34

+127. 4

- 0 '.17

— 75. 0

-10. 57

207

- 81.0

+47.86

+693. 3

+ 10. 80

+ 102. 4

- 9.33

-103. 7

- 8. 38

210

+ 65.8

+49. 66

+710.0

- 0. 50

+ 71. 4

-11. 10

-125.3

- 5. 70

213

+214. 3

+48. 86

+690. 3

L2 mi

+ 35.8

-12. 17

-137.9

2 OS

216

+356. 0

+44. 99

+0?s 0

-22.88

- 1.6

-12.37

-141. 4

+ 0.48

219

+481. 8

+38. 74

+553. 0

32 93

- 38.4

-11.80

-135.0

+ 3. 60

222

+586. 2

+30. 12

+442. 3

-40. 87

- 72.4

-10. 15

-11!). S

+ 6.47

225

+660. 9

+ 19. 75

+310. 0

-46. 63

-101. 1

- 8. 17

- 96. 2

+ 8. 93

228

+704. 7

+ 8. 55

+ 165. 3

-49.51

-123. 2

- 5. 92

- 66. 2

+10. 80

231

+712. 2

- 2.97

+ 15.6

-49. 77

-136. 6

- 2.97

- 31.4

+ 12. 00

234

+686. 9

-14. 03

-130. 4

-46.94

-141.0

+ 0.22

+ 5.8

+ 12.40

237

+628. 0

-24. 40

263 6

-41.68

-135.3

+ 3.38

+ 43.0

+ 12. 02

240

+542. 3

-32. 72

-37S. 2

-34. 04

-120. 7

+ 6.35

+ 77.9

+ 10. 78

243

+433. 7

-39. 02

-466. 2

-24.63

- 97.2

+ 8.98

+ 107. 7

+ 8.87

246

+310. 8

-42. 55

-526. 0

-14.30

- 66.8

+ 11.03

+ 131. 1

+ 6.37

249

+181. 0

-43. 51

-552. 0

— 3. 57

- 31.0

+ 12. 40

+ 145.9

+ 3. 42

252

+ 52.6

-41. 50

-547. 4

+ 6.80

+ 7.6

+ 12.95

+ 151. 6

+ 0. 13

255

- 65.6

-37. 18

-511.2

+ 16. 52

+ 46. 7

+ 12. 70

+ 146. 7

- 3. 20

258

-168.2

-30. 52

-449. 9

+24. 40

+ 83.8

+ 11.58

+132. 4

- 6. 35

26 1

-217. 1

-22. 10

-366. 8

+30. 35

+ 116. 2

+ 9.73

+108. 6

- 9. 17

26 1

-300. 8

-12.85

-270. 4

+33. 59

+ 142. 2

+ 7. 17

+ 77.4

-11.43

267

-324. 2

- :: 25

-167. 7

+34. 44

+159. 2

+ 4. 10

+ 40.0

-13.03

270

-320. 3

+ 6.03

- 66. 4

+32.51

+ 160 s

+ 0. 70

- 0.8

-13.78

27::

-288. 0

+14. 73

+ 25. 1

+28. 38

+163. 4

- 2.78

- 42.7

-13.65

276

-233. 6

+ 21.52

+101. 7

+ 22. 02

+ 150. 1

- 6.13

- 82.7

-12.55

279

-160.8

+26. 44

+155. 7

+ 14.02

+126. 6

- 9. 18

-118.0

-10. 72

282

- 77.5

+28. 73

+185. 8

+ 5. 32

+ 95. 0

-11.70

-147.0

- 8. 17

285

+ 9.2

+28. 68

+187. 6

- 3.63

+ 50. 1

-13.45

-167.0

- 5.05

288

+ 92. 0

+25. 96

+164.0

-12. 13

+ 14. 3

-14.32

-177.3

- 1. 53

291

+ 162. 8

+21.11

+ 114. S

-19.91

- 29. 5

-14.35

-176 2

+ 2. 12

294

+216. 7

+ 14.23

+ 46.3

-25. 72

- 71.8

-13. 38

-164. 6

+ 5. 70

297

+246. 8

+ 5.85

- 37.5

-29. 53

-109. 8

-11.60

-142.0

+ s. 92

300

+251. 8

- 3. 15

-128.4

-30. 78

-141.4

- 8.98

-111. 1

+ 11.50

303

+ 227. 9

-12.20

-219. 8

-29. 67

-163. 7

- 5.80

- 73.0

+ 13. 40

306

+178. 6

-20. 70

-303. 8

-25. 79

-176.2

- 2.23

- 30.7

+ 14.36

309

+ 103. 7

28 ;; i

-372. 4

-19. 85

-177. 1

+ 1.48

+ 13. 2

+ 14.45

312

+ 10. 4

-33. 81

-420. 9

-11.63

-167. 4

+ 5.07

+ 56.0

+13. 55

315

- 97.0

-37. 19

-442. 2

- 2. 52

-146.7

+ 8.32

+ 94. 5

+ 11.80

318

-210. 1

-37. 82

-436. 0

+ 7.35

-117.5

+ 10.97

+ 126. 8

+ 9.23

321

-321. 4

-35. 95

-398. 1

+ 17. 23

- 80.9

+ 12.88

+ 149. 9

+ 6. 10

324

-423. 1

-31.27

-332. 6

+26. 42

- 40. 2

+13. 87

+163. 4

+ 2.58

327

-506. 8

-24. 14

-239. 6

+34. 64

+ 2.3

+13. 97

+ 165 1

- 1.07

330

-567. 7

-15.27

-126.8

+40. 50

+ 43.6

+13. 05

+157. 0

- 4. 57

333

-59.S. 4

- 5.18

+ 1.1

+44. 12

+ 80. 0

+11. 30

+ 138.0

- 7. 75

336

-598. 8

+ 5.67

+ 135.2

+44. 90

+ 111 1

+ 8. 78

+110. 5

-10.30

339

-564. 4

+ 16. 55

+267. 8

+43.01

+ 133.3

+ 5. 73

+ 70. 2

-12. 12

342

-499. 5

+26. 85

+390. 4

+38. 11

+ 145 8

+ 2. 32

+ 37. S

-13. 05

345

-404. 6

+35. 70

+494.2

+30 98

+ 147. 2

- 1. 17

- 2. 1

-13. 05

348

-287. 3

+42. 42

+574. 2

+ 21 66

+ 138.8

i 50

- 40.5

-12.05

351

-152.4

+ 46. 82

+ 1122. S

+ lo. S3

+ 120. 2

- 7. is

- 74. 1

-10. 28

354

- 9 3

+48. 15

+639. 2

- 0. 70

+ 93. 9

- 9. 82

-102.2

- 7 82

357

+133. 6

+ 46. 69

+61S 6

-12.25

+ 61.3

-11. 15

-121.3

- 4.88

360

+267. 9

+ 42. 19

+565. 7

-23. 00

+ 25. 2

-12. 16

-131.5

- 1.58

[n3z. 3 lu£ r, and u cos i are lu lie computed in the form Si a* sin ig+Ji bi cos ig*j-cT.

306

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (174) Phaedra— Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6=09001.

i

4

5

9'

"4

Diff.forl0

b4

Diff.forl0

Q5

Diff.forl0

h

Diff.forl0

0

0

4-14.6

-0.93

—10.9

-1.60

-2.0

-0. 12

—1.2

+0.18

6

+ 5.8

-1.72

-18.4

-0.70

-2.3

+0.03

+0.1

+0.22

12

- 6.0 .

-2.00

-19.3

+0.48

-1.6

+0. 16

+1.5

+0.17

18

-16.8

—1.31

-12.6

+ 1.58

-0.4

+0. 22

+2.1

+0.02

24

—21.7

-0.13

- 0.3

+2.24

+1.0

+0. 19

+1.8

-0.11

30

-IS. 4

+ 1.18

+12.6

+ 1. 89

+ 1.9

+0.08

+0.8

-0.20

36

-7.5

+2.20

+21.3

+0.78

+2.0

-0.08

-0.6

-0.19

42

+ 6.4

+2.26

+21. 9

-0. 59

+ 1.0

-0. 18

-1.5

-0.11

48

+ 18.0

+1.36

+14.2

-1.91

-0.2

-0.20

-1.9

+0.02

54

+22. 7

+0.06

+ 0.8

-2.37

-1.4

-0. 13

—1.3

+0.16

60

+18.7

-1.24

-12. 4

-1.76

—1.8

-0.01

0.0

+0.20

66

+ 7.8

-2. 15

-20.3

-0.66

-1.5

+0.12

+1.1

+0.15

72

-5.4

-2.06

-20. 3

+0.63

-0.3

+0.19

+ 1.8

+0.04

78

-15. 5

-1. 12

-12. 7

+ 1. 70

+0.8

+0. 18

+1.6

-0.10

84

-18.9

+0. 03

- 1.4

+ 1. 90

+1.8

+0.08

+0.6

-0.18

90

-15.1

+ 1.07

+ 9.4

+ 1.38

+1.8

-0.07

-0.6

-0. 18

96

- 6.1

+ 1.66

+ 15. 1

+0.42

+1.0

-0.17

-1.6

-0.12

102

+ 3.4

+1.34

+14.5

-0. 52

-0.2

-0. 18

-2.0

+0.02

108

+ 10.0

+0.69

+ 8.8

—1.10

—1.2

-0. 13

-1.3

+0. 15

114

+ 11.7

-0. 10

+ 1.3

— 1. 12

-1.8

-0.03

-0.2

+0.18

120

+ 8.9

-0.66

- 4.7

-0.71

-1.6

+0. 09

+0.9

+0.14

126

+ 3.9

-(I 78

-7.2

-0.12

-0.7

+0. 17

+ 1.5

+0.05

132

- 0.6

-0. 52

- 6.2

+0.31

+0.4

+0. 16

+ 1.5

-0. 05

138

- 2. 5

-0.12

- 3.5

+0.41

+1.2

+0.08

+0.9

-0.13

144

- 2.0

+0. 15

- 1.3

+0.22

+ 1.4

-0.02

-0. 1

-0. 14

150

- 0.7

+0. 15

- 0.8

-0.06

+ 1.0

-0.09

-0.8

-0.08

156

- 0.2

-0.06

- 2.0

- 0. 22

+0.3

-0. 12

-1. 1

0.00

162

- 1.4

-0.34

-3.4

-0.09

-0.5

-0. 10

-0.8

+0.07

168

-4.3

-it 13

- 3. 1

+0.22

-0.9

-0.02

-0.3

+0.09

174

-6.6

-0.21

- 0.7

+0.55

—0.7

+0. 06

+0.3

+0.08

180

-6.8

+0.22

+ 3.5

+0.69

-0.2

+0.08

+0.6

+0.02

186

- 4.0

+0.67

+ 7.6

+0.47

+0.3

+0.07

+0.6

-0.04

192

+ 1.2

+0.88

+ 9.1

+0.07

+0.6

+0.01

+0.1

-0.08

198

+ 6.6

+0.68

+ 6.8

-0.63

+0.4

0.03

-0.3

-0.06

204

+ 9.3

+0.13

+ 1.5

-0. 95

+0.2

-0. 06

-0.6

-0.01

210

+ 8.2

-0. 50

-4.6

-0.87

-0.3

-0. 07

-0.4

+0.03

216

+ 3.3

-0.97

-8.9

-0.36

-0.6

-0.02

-0.2

+0.04

222

- 3.4

-0. 98

-8.9

+0.34

-0.6

+0. 03

+0.1

+0.06

228

-8.4

-0. 54

-4.8

+0. 91

-0.2

+0. 05

+0.5

+0.03

234

-9.9

+0. 11

+ 2.0

+ 1.08

0.0

+0.03

+0.5

-0.01

240

-6.7

+0.79

+ 8.2

+0.74

+0.2

+0.02

+0. 4

-0.03

246

- 0.4

+1.09

+ 10.9

+0.09

+0.3

+0.01

+0.1

-0.03

252

+ 6.4

+0.92

+ 9.3

-0.58

+0.3

-0. 01

0.0

-0.01

258

+10.7

+0.38

+ 3.9

-0. 99

' +0.2

-0.01

0.0

0.00

264

+10.9

-0.28

-2.6

-0.96

+0.2

+0.02

0.0

0.00

270

+ 7.3

-0.75

-7.6

-0.58

+0.4

+0.03

0. 0

0. 02

276

+ 1.9

-0.82

- 9.5

-0.02

+0.6

0.00

-0.2

-0. 03

282

-2.6

-0. 58

- 7,!l

+0.40

+0.4

-0. 05

-0.4

-0.06

288

- 5.0

-0. 19

- 4.6

+0.52

0.0

-0.08

-0.9

-0. 05

21)4

- 4.9

+0.13

-1.7

+0.34

-0.6

-0. 10

-1.0

+0.03

300

- 3. 1

+0.18

- 0.5

+0.08

—1.2

-0.08

-0.5

+0.09

:;imi

-2.8

-0.03

- 0.8

-0. 06

—1.5

0.00

+0.1

+0.13

312

-3.8

-0. 26

- 1.2

+0.04

—1.2

+0.09

+1.1

+0. 13

318

-5.9

-0.32

- 0.3

+0.34

-0.4

+0. 17

+ 1.7

+0. 05

324

-7.6

-0. 05

+ 2.9

+0.68

+0.8

+0. is

+ 1.7

-0.04

330

- 6. 5

+0. 49

+ 7. s

+0.78

+1.8

+0. 11

+1.2

-0. 15

336

- 1.7

+1.02

+ 12.2

+0. 42

+2.1

-0.01

-ill

-0.22

342

+ 5.8

+ 1.23

-1 1 2. 8

-0.32

+1.7

-0.12

-1.4

-0.17

348

+ 13.1

+0.93

+ 8. 3

-1. 11

+0.7

-0.22

-2. 1

-0.06

354

+17.0

+0.12

- 0.5

-1.60

-0.9

— 0. 22

-2.1

+0.08

360

+14. 6

-0.93

-10.9

-1.60

-2.0

-0. 12

-1.2

+0.18

[ndz, .? log r, and u/cos i are to be computed in the form It at sin ig+Si bi cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

307

PERIODIC TEEMS.

Tables of (174) Phaedra — Continued.

TABLE III.— 3 log r.

Unit of a and 6=0.00001.

i

0

1

2

9'

K

Diff.forl0

"i

Diff.forl0

b,

Diff.forl0

Oj

Diff.forl0

62

Diff.forl0

O

0

-1.0

-0.16

+41.9

+0.12

+ 3.2

—1.18

+ 47.4

-0.91

-4.5

-1.06

6

-2.0

-0. 15

+42.1

-0.04

-3.9

—1.17

+ 42. 1

-0.81

- 9.5

-0. 72

12

-2.8

-0. 13

+41.4

-0.22

-10.8

-1. is

+ 37. 7

-0.62

- 13.2

-0. 56

18

-3.6

-0. 12

+39. 5

-0.39

- L8.0

— 1. 12

+ 34.6

-0.51

- 16.2

-0. 52

24

-4. 2

-0.09

+36.7

-0. 57

-24.3

-1.02

+ 31.6

-0.47

- 19.4

-0. 55

30

-4.7

-0.07

+32. 7

-0.74

-30.3

-0. 94

+ 29.0

-0.48

— 22.8

-0. 57

36

-5.0

-0.04

+27.8

-0.88

-35. 6

-0.79

+ 25.8

-0.60

- 26.2

-0.54

42

-5.2

-0.02

+22. 1

-1.00

-39.8

-0.62

+ 21.8

-0.68

- 29.3

-0.47

48

-5.2

+0.01

+15. 8

-1.10

-43.0

-0.42

+ 17.6

-0.70

- 31.8

-0.35

54

-5.1

+0.(13

+ 8.9

-1. 15

-44.9

-0.23

+ 13.4

-0.68

- 33.5

-0.28

60

-4.8

+0.06

+ 2.0

-1.16

-45. 8

-0.05

+ 9.5

-0.61

- 35.2

-0. 25

66

-4.4

+0.08

- 5.0

-1. 14

-45. 5

+0. 13

+ 6.1

-0. 54

- 36. 5

-0.28

72

-3.9

+0. 09

-11.7

-1.12

-44.2

+0.31

+ 3.0

-0.61

- 38.5

-0. 43

78

-3.3

+0.11

—18. 5

-1.09

-41.8

+0.48

- 1.2

-0.80

- 41.7

-0.60

84

-2.6

+0.12

-24.8

-1.05

-38.4

+0.63

-6.6

-1. 14

- 45.7

-0.68

90

-1.9

+0.12

-31. 1

-1.00

-34.2

+0.80

- 14.9

— 1. 65

- 49.9

-0. 58

96

-1.1

+0.12

-36.8

-0. 91

-28.8

+1.01

- 26.4

-2.16

— 52 6

-0.20

102

-0.4

+0.12

-42.0

-0.76

-22. 1

+ 1.22

- 40.8

-2. 58

- 52! 3

+0.47

108

+0.3

+0.12

-45.9

-0.50

—14.2

+1.41

- 57. 3

-2.76

- 47.0

+ 1.37

114

+ 1.0

+0.10

-48.7

-0.31

-5.2

+ 1.57

- 74.0

-2. 56

- 35.9

+2.42

120

+ 1.5

+0.08

-49.6

+0.04

+ 4.6

+ 1.66

- 88.1

-1.92

- 18.0

+3. 44

126

+ 1.9

+0.07

-48. 2

+0.42

+14.7

+ 1.66

- 97. 0

-0.86

+ 5. 5

+4. 22

132

+2.3

+0.04

-44. 5

+0.80

+24. 5

+1.54

- 98.4

+0.54

+ 32.7

+4.61

138

+2.4

+0.01

-38. 6

+ 1. 17

+33.2

+ 1. 32

- 90.5

+2.06

+ 60.8

+4.48

144

+2.4

-0.01

-30. 5

+ 1. 48

+40.4

+1.00

- 73.7

+3.45

+ 86. 4

+3.78

. 150

+2.3

-0.04

-20.8

+ 1.68

+45.2

+0.59

- 49.1

+4. 56

+ 106. 1

+2. 59

156

+1.9

-0.08

-10. 5

+1.73

+47.5

+0.16

- 18.9

+5. 20

+117. 5

+1. 09

162

+1.4

-0. 10

0.0

+1.68

+47.1

-0.30

+ 13.3

+5. 26

+119.2

—0. 55

168

+0.7

-0.12

+ 9.7

+ 1.50

+43.9

-0.70

+ 44. 3

+4.79

+110. 9

-2.07

174

-0.1

-0. 14

+ 18.0

+ 1.24

+38.7

-1.00

+ 70.8

+3.86

+ 94.4

-3. 26

180

-1.0

-0.16

+24. 6

+0.92

+31.8

— 1. 23

+ 90.6

+2.67

+ 71.8

-4. 05

186

-2.0

-0.17

+29. 1

ii ;,s

+23. 9

-1.34

+102. 8

+1.42

+ 45. 8

-4. 35

L92

-3.0

-0. 16

+31. 5

+0. 23

+ 15. 7

-1.37

+ 107.6

+0.24

+ 19.6

-4. 26

198

-3.9

-0.14

+31.H

i

+ 7.5

— 1. 32

+ 105. 7

-0.73

- 5. 3

-3. 91

204

-4.7

-0.13

+30.8

-0 32

- 0.2

-1.22

+ 98.8

-1.42

- 27. 3

-3.38

210

-5. 5

-0.11

+28.0

-0. 55

- 7.1

-1.09

+ 88.7

-1.87

15.9

-2. 87

216

-6.0

-0.08

+24. 2

-0. 73

-13.3

-0. 94

+ 76.4

—2.20

- 61.7

— 2. 42

222

-6.4

—0.05

+19. 2

-0.91

-18.4

-0.74

+ 62.3

-2 47

- 75.0

-2. 03

228

-6.6

-0. 02

+13.3

-1.04

-22. 2

-0. 56

+ 46.8

-2. 78

- 86.1

-1.71

■s:a

-6.6

+0. 03

+ 6.7

-1.16

-25. 1

-0. 32

4 29.0

-3.18

- 95. 5

— 1. 32

240

-6.2

+0.08

- 0.6

-1.24

-26. 1

-0.03

+ 8.6

-3.60

-101. 9

-0.73

246

-5.6

+0.11

-8.2

-1.27

-25.5

+0. 25

- 14. 2

-3.97

-104.3

+0. 02

252

-4.9

+0.13

-15. 8

— 1. 22

-23. 1

+0. 58

- 39.1

-4. 15

—101.6

+1.03

258

-4.0

+0.16

-22. 9

-1.08

-18.6

+0.90

- 64.0

-4.01

- 91.9

+2. 22

264

-3.0

+0.18

-28.7

- 0.82

-12.3

+1.20

- 87. 2

-3. 45

75.0

+3.40

270

-1.9

| ii. L9

-32.7

-0.51

- 4. 2

+ 1.42

-105 1

-2.94

- 51. 1

+4. 42

276

-0.7

+0.19

-34.8

-0.13

+ 4.8

+1. 53

-116. I

-1.08

- 21.9

+5. 10

282

+0.4

+0.18

-34. 3

+0.30

+14.2

+1. 55

-118.4

+0.49

+ in. 2

+5. 26

288

+ 1.4

+0. 15

-31.2

+0.71

+23. 4

+ 1.42

-110.5

+2.08

+ 41.2

+4.88

294

+2.2

+0.12

-25. S

• I.liii

+31.3

+ 1. 17

- 93.4

+3. 43

+ 68.7

+3.98

300

+ 2. 9

+0.10

-18. 5

+ 1.32

+37.4

+0.84

- 69. 3

+4.38

+ 89.0

+2. 64

306

+3.4

+0.06

- 9.9

+ 1.48

+41.4

II. is

- 40.9

+4. 80

+100. 4

+1.12

312

+3.6

+(). 02

- 0.7

+1.52

+43.1

+0.10

- 11.7

+4. 62

+ 102 5

-0.39

318

+3.6

-0.01

+ 8.3

+ 1.45

+42. 6

-0.27

+ 14.6

+3.98

+ 95. 7

-1.68

324

+3.5

-0. 05

+10. 7

+ 1.31

(-39.9

-0. 58

+ 36. 1

3 02

+ 82.3

-2. 57

330

+3.0

-0.09

+24.H

1. II

+35. 7

0 82

+ 50.9

+1.88

+ 64.9

-3.01

336

+2.4

-0.11

+30. 0

+0.89

+30. 1

-0.98

+ 58.7

+0.81

+ 46. 2

-3. 01

342

+1.7

-0.13

+34.7

+ 0. 70

- 23.9

-1.08

+ 60.6

— 0. 04

+ 28.8

! 66

348

+0.8

-0. 15

+38.4

+0.49

+ 17.1

— 1. 14

+ 58. 2

-0. 62

+ 14.3

-2. 13

354

-0.1

-0. 15

+40.6

+0.29

+10.2

-1.16

+ 53.0

-0. 90

■ 3.2

— 1. 57

360

-1.0

-0.16

+41.9

+0.12

+ 3.2

-1.18

+ 47.4

-0.91

4.5

-1.06

[ntiz, S log r, and 1/ cos i are to lie computed in the form Ii at sin ig+Ii &i 00s ig+cT.

308 , MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (174) Phaedra— Continued.
TABLE III.— S log /—Continued.

PERIODIC TERMS.

Unit of a and 6=0.00001.

i

3

4

5

„/

Diff.

b,

Diff.

Diff.

6,

Diff.

Diff.

h

Diff.

9

«3

fori"

fori0

«4

fori0

for 1°

«5

for 1°

for 1°

O

0

-52. 8

-0.38

-3.5

+4.76

- 6.5

-0.64

- 6.4

+0. 57

-0.9

+0.09

+0.9

+0.08

6

-47.5

+2. 00

+24.4

+4.28

- 9.4

-0.22

- 1.7

+0. S8

-0.3

+0.12

+ 1.2

+0.02

12

-28.8

+3.97

+45.6

+2.63

- 9.1

+0.34

+ 4.2

+0.88

+0.6

+0.11

+1.1

-0.05

18

- 2.0

+4.73

+54. 6

+0. 26

- 5.3

+0.82

+ 8.9

+0. 55

+1.0

+0.04

+0.6

-0.11

24

+25.5

+4.18

+48.7

-2.07

+ 0.8

+ 1.02

+ 10.8

-0. 02

+1.1

-0.02

-0.2

-0. 11

30

+46.0

+2.40

+29.8

-3.94

+ 7.0

+0.83

+ 8.6

-0. 65

+0.8

-0.08

-0.7

-0. 06

36

+54. 3

+0.18

+ 3.6

-4.61

+10.8

+0.32

+ 3.0

-1.03

+0.1

-0.11

-0.9

-0.01

42

+48.2

—2. 02

-23.0

-3.99

+10.8

-0. 33

- 3. S

-1.02

-0.5

-0.08

-0.8

+0. 05

48

+30.0

-3.80

-42.2

-2.19

+ 6. S

-0.88

- 9.3

-0.63

-0.8

-0.02

-0.3

+0.08

54

+ 4.8

- 1. 32

-49.3

-0. 05

+ 0. 3

-1.08

-11.4

+0.01

-0.7

+0.05

+0.2

+0.07

60

—19.4

-3.60

-42. 8

+2. 15

- 6.1

-0.87

- 9.2

+0. 62

-0.2

+0.08

+0.5

+0.03

66

-36. 4

-1.82

-24.8

+3.63

-10. 1

-0.33

- 4.0

4-0. 'J7

+0.2

+0.06

+0.6

-0. 02

72

-41.2

+0. 31

- 1.4

+3.97

-10.1

+0. 30

+ 2.4

+0. 96

+0.5

+0.02

+0.2

- 0. 07

78

-32.7

+2. 39

+20. 5

+3.11

- 6.5

+ 0. 76

+ 7.5

+0. 58

+0.5

-0.02

-0.2

-0. 06

84

-14. 1

+3.63

+34.1

+ 1.22

- 1.0

+0. 90

+ 9.4

+0.02

+0.3

-0. 06

-0.5

-0. 02

90

+ 8.7

+3.79

+35.2

-0.90

+ 4.3

+0.72

+ 7.7

-0.48

-0.2

-0.08

-0.5

+0. 02

96

+29. 0

+2. 69

+23. 3

-2.91

+ 7.6

+0.29

+ 3.6

-0.74

-0.6

—0.04

-0.3

+0. 05

102

+39.3

+0. 65

+ 2.0

-4.00

+ 7.8

-0.18

- 1.2

-0.70

-0.7

+0.01

+0.1

+0.07

108

+36.8

-1.52

-22.4

-3.91

+ 5.5

-0. 51

-4.8

-0.43

-0.5

+0.06

+0.5

+0.06

114

+21.1

-3. 57

-42.6

-2. 62

+ 1.7

-0. 59

- 6.4

-0.08

0.0

+0.08

+0.8

0.00

120

-4.2

—4.62

-52. 0

-0. 38

- 1.6

-0. 45

- 5.8

+0. 22

+0.5

+0.06

+0.5

-0.05

126

-32.0

-4. 42

-47. 1

+1.98

-3.7

-0.22

-3.8

+0. 37

+0.7

+0.01

+0.2

-0.07

132

-54. 9

-2.97

-28.3

+4.16

-4.3

-0.02

- 1.4

+0. 33

+0.6

-0.03

-0.3

-0.07

138

-66.0

-0. 58

+ 0.8

+5. 27

- 4.0

+0.08

+ 0. 2

+0. 22

+0.3

-0.07

-0.6

-0.02

144

-61.8

+1.98

+ 32. t

+5.08

- 3.3

+0.09

+ 1.1

+0. 12

-0.2

-0.07

-0.6

+0.02

150

-42.3

+4. 34

+59. 3

f-3. 65

-2.9

+0.07

h 1.7

+0. 12

-0.5

-0.03

-0.3

+0.06

156

—11.7

+5. 66

+ 74. 3

+ 1. 16

- 2.5

+0.08

+ 2.5

+0. 15

-0.6

+0.01

+0.1

+0.06

162

+23.1

+5.68

+73.2

-1. 53

- 1.9

+0.17

+ 3.5

+0. 17

-0.4

+0. 05

+0.4

+0.04

168

+53. 8

+4.34

+55. 9

-4.06

- 0.5

+0.30

+ 4.5

+0. 12

0.0

+0.06

+0.6

0.00

174

+73.1

+ 1.90

+26.2

-5. 63

+ 1.7

+0.38

+ 5.0

-0.04

+0.3

+0.04

+0.4

-0. 05

ISO

+76.6

-0.83

- 9.1

-5.88

+ 4.1

+0.34

+ 4.0

-0. 28

+0.5

+0.02

0.0

-0.06

186

+63.1

-3. 51

-41.7

-4. 75

+ 5.8

+0. 15

+ 1.6

-0.47

+0.5

-0.03

-0.3

-0.04

192

+36.2

-5. 22

-64.1

-2.48

+ 5.9

-0.14

- 1.6

-0. 50

-r-0.1

-0.06

-0.5

-0. 02

198

+ 2.8

—5.70

-71.4

+0.18

+ 4.1

-0. 42

-4.4

-0. 35

-0.2

-0. 05

-0.5

+0.02

204

-29.7

-4.86

-62. 0

+2.83

+ 0.8

-0. 56

- 5.8

o o:;

-0. 5

-0.02

-0.2

+0.06

210

—53.4

-2. 76

-38.9

+4.69

-2.6

-0.47

-4.8

+0.32

-0.5

+0.01

+0.2

+0.06

216

-62. S

-0. 23

- 8.0

+5.20

-4.8

—0.18

- 2.0

+0. 52

-0.4

+0.04

+0.5

+0.03

222

•-56.2

+2. 26

+23.0

+4.70

-4.7

+0.20

+ 1.5

+0. 52

0.0

+0.06

+0.6

0.00

228

—35.7

+4.27

+46. 2

+2.77

-2.4

+0.48

+ 4.3

+0. 29

+0.3

+0.04

+0.5

-0.03

234

- 7.1

+5. 05

+56.2

i). :;s

+ 1.1

+0.58

+ 5.0

0 I.S

+0.5

+0.02

+0.2

-0.04

240

+22.4

+4.51

+50. 8

-2. 05

+ 4.5

+0. 42

+ 3.3

-0.41

+0.5

-0.01

0.0

-0.04

246

+44.9

+2.81

+31.6

-4.07

+ 6.1

+0.08

+ 0.1

-0. 58

+0.4

-0.02

-0.3

-0.03

252

+54.8

+0.38

+ 4.0

-4.92

+ 5.4

-0. 29

-3.6

-0. 53

+0.2

-0.02

-0.4

-0.02

258

+49.5

-2.02

-24. 9

-4. 45

+ 2.6

-0. 54

-6.3

-0.27

+0.2

-0.03

-0.5

0.00

264

+30.5

-4.06

-47. 1

-2.81

- 1. 1

-0. 58

- 6.8

+0. 08

-0.2

-0.03

-0.4

+0.02

270

+ 2. 8

-4.93

-57. 2

-0.39

-4.3

-0.42

- 5.3

o :;.;

-0.2

-0.02

-0.4

+0.01

276

-26. 2

-4. 50

-51. 8

+2. 02

- 6.1

-0. 15

- 2.5

+0.48

-0.5

-0.02

-0.3

+0.02

2S2

-48.9

-2.89

-33. 0

+4. 05

- 6.1

+0.11

+ 0.5

+0. 43

-0.5

-0.01

-0.1

+0.04

288

-59. 4

-0.48

- 5.1

+4. 99

-4.8

+0. 25

+ 2.7

+0. 28

-0.6

-0.01

+0.2

+0. 04

21 14

-54. 7

-1.97

+24.4

+4.60

- 3.1

+0.27

+ 3.9

+0. 12

-0.6

+0. 03

+0.4

+0. 05

300

-35. 8

+ 4.04

+47.8

+2. 99

- 1.6

+0. 22

+ 4.2

+0.02

-0.2

+0.07

+0.8

+0.04

306

- 8.3

+4.94

+58.8

+0. 57

- 0.5

+0.19

+ 4.2

+0. 01

+0.2

+0.08

+0.9

0.00

312

+21. 1

+4.60

+54. 6

-1.S6

+ 0.7

+0.21

+ 4.3

0.00

+0.8

+0. OS

+0.8

-0. 06

318

+44.5

+3.00

+36. 5

-3.91

+ 2.0

+0. 26

+ 4.2

-0. 05

+ 1.1

+0.02

+0.2

-0.11

324

+ 55. 6

+0.60

+ 9. 6

-4.87

+ 3.8

+0. 32

+ 3.7

-0. 18

+ 1.1

-0.02

-0.5

-0. 11

330

+51. 7

-1.82

-19.5

-4. 52

+ 5.8

+0.24

+ 2.0

-0. 39

+0.8

-0.09

-1.1

-0.07

336

+33. 8

-3.89

-42. 3

-2. 90

+ 6.7

+0. 02

- 1.0

-0. 56

0.0

-0. 12

-1.3

-0.01

342

+ 7.1

-4.79

-52. S

-0.51

+ 6.0

-0.31

-4.7

-0. 55

-0.7

-0. 10

-1.2

+0. 06

348

-21. 2

-4. 37

-48. 1

+ 1.88

+ 3.0

-0.64

- 7.6

-0.32

-1.2

-0.06

-0.6

+0.12

354

-43.0

-2. 75

-30. 2

+3.92

-1.7

-0.79

- 8.5

+0.10

-1.4

+0. 02

+0.2

+0.12

360

-52. 7

-0. 38

- ?,. 5

+ 4. 76

- 6. 5

-0.64

- 6.4

+0.57

-0.9

+0.09

+0.9

+0.08

[nSz, ii log r. and it/cos i are to be computed in the form Si at sin ig+Ii In cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSOX— LEUSCHNER.

309

PERIODIC TERMS.

Tables of (174) Phaedra — Continued.

TABLE IV.— u cos i.

I'nit of a and 6-09001.

i

0

1

2

9'

K .

Diff.forl0

<*,

Diff.forl0

6,

Diff . for 1 '-

a.

Diff.forl0

b.

Diff.forl0

O

0

- 6.2

-0. 32

-17.2

-0. 17

-3.7

+0. 57

-12. 2

+0.55

+ 9.6

+0.61

6

- 8.1

-0. 29

-17.7

+0.02

0.0

+0.61

- 8. 1

+0.70

+12.6

+0. 34

12

-9.7

-0. 26

-16.9

+0.21

+ 3.6

+0. 56

- 3. 1

+0.84

+13.7

0.00

18

-11.2

-0. 2::

-15.2

+0. 34

+ 6,7

+0.49

+ 2. 0

+0.76

+12.6

-0.36

21

-12.5

-0.20

-12. S

+0.45

+ 9.5

+0.39

+ 6.0

+0. 52

+ 9.4

-0.66

30

-13.6

-0. Hi

- 9.8

+0.52

+ 11.4

+0.28

+ 8.2

+0.18

+ 4.8

-0. M

36

-14.4

-0. 12

- 0.6

+0.54

+ 12.8

+0.18

+ 8.2

-0. 21

- 0.3

-0. 78

42

-15. 0

-0. 08

- 3.3

+0. 56

+ 13.6

+0.08

+ 5.7

-0. 57

- 4.6

-0 01

48

-15. 3

-0.112

+ 0.1

+0. 54

+13.8

+0. 02

+ 1-4

-0.78

- 7.6

-0.28

54

-15. 3

+0. 02

+ 3.2

+0. 52

+13.8

-0.03

- 3.7

-0.83

- 8.0

+0. 13

60

-15. 1

+0.07

+ 6.3

+0. 51

+ 13.4

-0.12

- 8.6

-0.72

- 6.0

+0. 51

66

-14. 5

+0. 12

+ 9.3

+0.50

+12.4

-0.20

-12.3

-0. 43

- 1.9

+0.80

72

-13.6

+0. 18

+12.3

+0.45

+ 11.0

-0.30

-13. 8

-0.05

+ 3.6

+0. 94

78

-12.3

+0. 22

+ 11.7

+0.37

+ 8.8

-0.39

-12.9

+0.36

+ 9.4

+0.89

84

-10.9

+0. 2i,

+16.7

+0.26

+ 6.3

-0.48

- 9.5

+0.71

+14.3

+0. 68

90

-9.2

+0.22

+17.8

+0.08

+ 3.0

-0.54

-4.4

+0. 92

+17. 5

+0. 35

96

- 7.1

+0. 34

+ 17.7

-0.10

- 0.2

-0.53

+ i.o

+0.98

+18.5

-0 02

102

- 5.1

+0. 35

+16. 6

-0.27

- 3.4

-0.48

+ 7. 1

+0.87

+ 17. 2

-0.38

108

-2.9

+0.38

+14. 5

-0.40

- 5. 9

-0.36

+12.0

+0.62

+13.9

-0. 05

114

- 0.6

+0. 38

+11.8

-0.49

— 7. ,

-0.21

+ 14.9

+0. 33

+ 9.4

-0. 7s

120

+ 1-7

+0. 35

+ 8. 6

-0. 55

8.4

u in

+ 10. 0

+0. 05

+ 4.6

-0.77

126

+ 3.6

+0. 32

+ 5. 2

-0.49

- 7.0

+0. 17

+15.5

-0.18

+ 0.2

-0.65

132

+ 5.5

+0.28

+ 2.7

-0. 36

- 6.4

+0. 27

+ 13.9

-0.32

- 3.2

-0. 48

138

+ 6.9

+0. 21

+ 0.9

-0. 22

-4.4

+0. 35

+ 11.7

-0. 36

- 5.6

-0. 32

144

+ 8.0

+0. 15

0.0

-0.08

- 2.2

+0.32

+ 9.6

-0. 32

- 7.0

-0.21

150

+ 8.7

+0.08

0.0

+o. oi ;

- 0.5

+0. 25

+ 7.8

0 27

- 8.1

-0.14

156

+ 8.9

-0.01

+ 0.7

+0. 12

+ 0.8

+0.12

+ 6.4

-0. 23

- 8.8

-0. 14

162

+ 8.6

-0.09

+ 1.5

+0.14

+ i.o-

-0.01

+ 5.0

-0. 25

- 9.8

-0.18

168

+ 7.8

-0.16

+ 2.4

+0.10

+ 0.7

-0.08

+ 3.4

-0. 31

-11.0

-0.20

174

+ 6.7

-0. 22

+ 2.7

-0. 02

0.0

-0.15

+ 1.3

-0.42

-12. 2

-0. IS

180

+ 5. 2

-0. 27

+ 2.1

-0. 12

- 1.1

-0. 15

- 1.6

-0.58

-13. 2

-0.08

L86

+ 3.5

-0.29

+ 1.3

-0. 17

- 1.8

-0.09

-5.7

-0. 68

-13.2

+0.10

L92

+ 1-7

-0.29

+ 0.1

-0. 22

- 2.2

+0.01

-9.7

-0. 00

-12.0

+0.37

L98

0.0

-0.28

- 1.3

-0. 18

- 1.7

+0.11

-13.6

-0.56

- 8.8

+0.63

204

- 1. 7

-0. 27

- 2.0

-0.09

- 0.9

+0.16

-16. 4

-0. .',2

-4.4

+0.83

210

- 3.2

-0. 21

-2.4

+0.02

+ 0.2

+0.21

-17. 1

-0.01

+ 1-2

+0.98

216

- 4.2

-0. 15

- 1.8

+0. 14

+ 1.6

+0. 17

-16.5

+0.36

+ 7.3

+0.95

222

- 5.0

-0.09

- 0.7

+0.21

+ 2. 2

+0.07

-13.1

+0.71

+ 12. 6

+0. 76

228

- 5.3

-0.01

+ 0.7

+0.22

+ 2^4

+0. 05

- 8.0

o \i:\

+16. 4

+0. 45

234

- 5.1

| 0.07

+ 2.0

+0.23

+ 1.6

-0.17

- 1.9

+ 1.02

+18.0

+0.08

240

- 4.5

+0.13

+ 3.5

+0. 14

+ 0.4

-0.23

+ 4.2

: 0 'iv

+17.4

-0. 29

246

- 3.5

+0.19

+ 3.7

-0.02

- 1.2

-0.30

+ 9.9

+0.80

+ 14.5

-0. 02

252

- 2. 2

+0. 23

+ 3.3

-0. 15

- 3.2

-0. 28

+13.8

+0.48

+10.0

-0.81

258

- 0.7

+0. 26

+ 1.9

-0.25

- 4.6

-0. 19

+ 15. 7

+0.16

+ 4.8

-0.88

264

+ 0.9

+0. 28

+ 0.3

-0. 29

- 5.5

-0. 07

+15. 7

-0. 10

- 0.5

-o 82

270

+ 2.6

+0. 27

- 1.6

-0. 30

- 5.4

+0. 06

+13.8

-0.39

- 5. 1

-0. 0.5

276

+ 4.1

+0.24

-3.3

-0. 22

- 4.8

+0.15

+11.0

n 50

-8.3

-0.42

2S2

+ 5.5

+0 20

- 4.3

-0.08

- 3.6

+0.21

+ 7.8

-0. 52

-10.2

-0. 22

288

+ 6.5

+0. 14

- 4.3

+0. 05

- 2.3

+0.19

+ 4. 8

—0.46

-11.0

-0.07

294

+ 7.2

+0.08

- 3.7

+0. 11

- 1.3

+0.11

+ 2. 3

-0. 37

-11.0

+ 0. 02

300

+ 7.5

+0. 02

- 3.0

+0. 14

- 1.0

-0. 02

+ 0.4

-0.30

-10.7

+0.05

306

+ 7.4

-0.05

- 2.0

+0.16

- 1.6

-0. 17

- 1.3

-0.28

-10. 4

+0.02

312

+ 6.9

-0. 11

- 1.1

+0.06

:; o

-0. 28

- 2 9

-0. 28

—10.^4

0.00

318

+ 6.1

-0.18

- 1.3

-0.09

- 5.0

-0. 34

— 4. 7

0 16

-10.4

+0.03

2,21

+ .4-8

-0. 23

-2.2

-0. 24

- 7. 1

-0. 32

- 7.2

-0. 42

-10.0

+0. 12

330

+ 3.3

-0. 28

- 4.2

-0.39

- 8.9

-0.24

- 9. S

o 13

- 9.0

+0.28

336

+ 1.5

-0.31

- 6.9

-0. is

— 10.0

-0.09

-12. 4

-0.40

-6.6

+0.47

342

- 0.4

0 32

- 9.9

-0.51

-10.0

+0. OS

-14. 0

-0. 27.

- 3.4

+0.62

348

- 2.4

0 12

-13.0

-0.48

- 9.0

+0. 27

-15.4

-0.01

+ 0.8

+0.72

354

-4.3

-0.32

-15. 7

-0. 35

- o 8

+0.44

-14.7

+0. 27

+ 5.3

+0. 73

360

- 6. 2

-0. 32

-17. 2

-o 17

-3.7

+0. 57

-12 2

+0. 55

+ 9.6

+0. 01

log r. and u cos i are to be computed in the form li ai sin ig+li bi cos ig + cT.]

310 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (174) Phaedra — Continued.

PERIODIC TERMS.

TABLE IV— u/cos i— Continued.

Unit of a and 6=09001.

i

3

4

9'

«3

Diff.forl0

h

Diff.forl0

«4

Diff.forl0

bt

Diff.forl0

O

0

+22.0

+0.18

+ 3.6

-1.88

+3.4

+0.27

+2.3

-0.28

6

+ 19.9

-0.78

- 8.0

-1.68

+4.5

+0.06

0.0

-0.42

12

+12.7

-1.48

-16.6

-1.02

+4.1

-0.22

-2.7

-0.39

18

+ 2.2

-1.78

-20.3

-0.10

+ 1.9

-0.42

-4.7

-0.22

24

- 8.7

-1.55

-17.8

+0.82

-1.0

-0.49

-5:3

+0.06

30

-16.4

-0.88

-10.5

+1.47

-4.0

-0.38

-4.0

+0.28

36

-19.3

+0.02

- 0.2

+1.71

-5.5

-0.08

—1.0

+0.52

42

-16.1

+0.90

+ 10.0

+1. 45

-5.0

+0.21

+2.2

+0.47

48

- 8.5

+ 1.51

+ 17.2

+0.77

-3.0

+0.43

+4.6

+0.26

54

+ 2.0

+1.72

+19.2

-0.14

+0.2

+0.50

+5.3

-0.04

60

+12. 1

+1.40

+15. 5

-1.02

+3.0

+0.37

+4.1

-0.32

66

+18.8

+0.68

+ 7.0

-1.62

+4.6

+0.10

+1.5

-0.46

72

+20.2

-0.27

- 3.9

-1.75

+4.2

-0.18

—1.4

-0.40

78

+15. 6

— 1. 15

-14.0

-1.38

+2.5

-0.34

-3.3

-0.20

84

+ 6.4

-1.72

-20.5

-0.62

+0.1

-0.38

-3.8

+0.04

90

- 5.1

-1.83

-21.5

+0. 33

-2.1

-0.25

-2.8

+0.25

96

-15. 6

-1.44

-16.5

+1.26

-2.9

-0.04

-0.8

+0.32

102

-22.4

-0. 63

-6.4

+ 1.86

-2.6

+0.12

+1.0

+0.23

108

-23.2

+0. 43

+ 5.8

+1.95

-1.4

+0.23

+2.0

+0.09

114

-17.2

+ 1.38

+ 17.0

+ 1.50

+0.2

+0.22

+2.1

-0.05

120

-6.7

+ 1.93

+23.8

+0. 61

+ 1.2

+0.11

+1.4

-0.14

126

+ 6.0

+2.02

+24.3

-0.46

+1.5

-0.01

+0.4

-0.14

132

+ 17. 6

+ 1.55

+18.2

-1.42

+1.1

-0.07

-0.3

-0.08

138

+24.6

+0.63

+ 7.2

-2.00

+0.7

-0.06

-0.5

-0.02

144

+25. 2

-0.45

- 5.8

-2.07

+0.4

-0.03

-0.5

+0.01

150

+19.2

-1.43

-17.6

-1.59

+0.3

+0.02

-0.4

0.00

156

+ 8.0

-2. 02

-24.9

-0.67

+0.6

+0.02

-0.5

-0.06

162

- 5. 1

-2.09

-25.6

+0.42

+0.5

-0.05

—1.1

-0.09

168

-17. 1

-1.62

-19.9

+1.38

0.0

-0.13

-1.6

-0.06

174

—24.6

-0.72

- 9.1

+ 1.99

—1.1

-0. IS

—1.8

+0.04

180

-25.8

+0.36

+ 4.0

+2.08

-2.2

-0.15

—1.1

+0.17

186

-20.3

+1.31

+ 15.9

+1.63

-2.9

-0.04

+0.2

+0.25

192

-10. 1

+ 1.91

+23.6

+0.80

-2.7

+0.15

+1.9

+0.26

198

+ 2.6

+2. 05

+25.5

-0.23

— 1. 1

+0.29

+3.3

+0.15

204

+14.5

+1.67

+20.8

-1.19

+0.8

+0. 32

+3.7

-0.04

210

+22. 6

+0.87

+11.2

-1.85

+2.8

+0.26

+2.8

—0.24

216

+24.9

-0.14

— 1.4

-2.04

+3.9

+0.07

+0.8

-0.35

222

+20.9

-1. 10

-13.3

-1.68

+3. 6

-0.14

—1.4

-0.33

228

+11.7

— 1. 76

-21.6

-0.94

+2.2

-0.30

-3.2

-0.19

234

- 0.2

-2.00

-24.6

+0.04

0.0

-0.33

-3.7

+0.02

240

-12.3

— 1. 75

-21.1

+1.02

-1.8

-0.25

-2.9

+0.20

246

-21.2

-1.02

-12.4

+1.72

-3.0

-0.08

—1.3

+0.29

252

-24.6

-0.03

- 0.5

+2.02

-2.8

+0.11

+0.6

+0.27

258

-21. 6

+0.95

+11.8

+1.80

—1.7

+0.21

+1.9

+0.13

264

-13.2

+1.72

+21. 1

+ 1.11

-0.3

+0.22

+2.2

-0.02

270

- 1.0

+2.07

+25. 1

+0.11

+0.9

+0.13

+1.6

-0.13

276

+11.6

+1.87

+22.4

-0.92

+1.3

+0.02

+0.6

-0.15

282

+21.4

+1.17

+14.1

-1.72

+1.2

-0.06

-0.2

-0.10

288

+25. 6

+0. 17

+ 1.8

-2.11

+0.6

-0.10

-0.6

-0.02

294

+23. 4

-0.89

-11.2

-1.92

0.0

-0.05

-0.5

+0.03

300

+ 14. 9

-1.72

-21. 2

-1.22

0.0

+0.01

-0.2

+0.02

306

+ 2.8

-2.10

-25. 9

-0.22

+0.1

+0.03

-0.2

-0.02

312

-10. 3

-1.95

-23.8

+0.86

+0.4

0.00

-0.5

-0.06

318

-20.6

— 1. 25

-15.6

+1.68

+0.1

-0.08

-0.9

-0.05

324

-25.3

-0.23

-3.6

+2. 07

-0.6

-0. 13

—1.1

+0.01

330

-23. 4

+0.80

+ 9.2

+1.89

—1.5

-0.13

-0.8

+0.12

336

-15.7

+1.61

+ 19.1

+ 1.23

—2. 2

-0. 03

+0.3

+0.22

342

— 4. 1

+2.00

+24.0

+0.25

-1. 9

+0.12

+1.9

+0.22

348

+ 8.3

+ 1..S2

+22.1

-0. 79

-0.8

+0.27

+3.0

+0.12

354

+ 17.8

+ 1. 14

+ 14.5

-1.54

+1.3

+0.35

+3.4

-0. 00

360

+22.0

+0.18

+ 3.6

-1.88

+3.4

+0.27

+2.3

-0.28

[nSz, o log r, and ucos i are to be computed in the form li at sin ig+2i 6j cos ig+cT.]

.MINOR PLANETS DISCOVERED BY WATSON— LEUSCHXER.

311

Tables of (174) Phaedra — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 10) IN JULIAN YEARS.

noz

o log: r

m/cos i

9

Unit of £

=0?001

Unit of c

=0.00001

Unit of

-=0?001

c

Diff. for 1°

c

Diff. for 1°

c

Diff. for 1°

O

0

-3.22

-0.001

+0.02

-0. 022

+ 1.11

+0. 082

6

-3.21

+0. 005

-0.12

-0. 024

+ 1. 59

+0. 078

12

-3.16

+0. 012

-0.26

-0. 023

+2.04

+0. 073

18

-3.06

+0. 020

-0.40

-0. 022

+2.47

+0. 067

24

-2.92

+0. 024

-0.53

-0. 022

+2.84

+0. 059

30

-2.77

+0. 029

-0.66

-0.019

+3.18

+0. 052

36

-2. 57

+0. 036

-0.76

-0. 017

+3.46

+0. 042

42

-2.34

+0. 040

-0.86

-0. 017

+3.69

+0. 034

48

-2.09

+0. 042

-0.96

-0. 013

+3.87

+0. 024

54

-1.83

+0. 047

-1. 02

-0.010

+3.98

+0. 015

60

-1.53

+0. 050

-1.08

-0. 008

+4. 05

+0. 008

66

-1.23

+0. 052

-1. 12

-0. 005

+4.07

-0. 002

72

-0.91

+0. 053

— 1.14

-0. 004

+4.03

-0. Oil'

78

-0.59

+0. 053

—1.17

-0. 002

+3. 94

-0. 018

84

-0.27

+0. 054

-1.17

+0. 001

+3.81

-0. 025

90

+0. 06

+0. 054

-1.16

+0. 002

+3.64

-0. 031

96

+0.38

+0. 052

— 1. 14

+0. 004

+3.44

-0. 038

102

+0.68

+0. 051

— 1. 11

+0. 006

+3.18

-0. 044

108

+0.99

+0. 049

— 1.07

+0. 008

+2.91

-0. 048

114

+1.27

+0.047

-1.02

+0. 009

+2.61

-0. 051

120

+ 1.55

+0. 044

-0.96

+0. 012

+2.30

-0. 054

126

+ 1.80

+0. 040

-0.88

+0. 012

+ 1.96

-0. 059

132

+2.03

+0. 038

-0.81

+0. 012

+1.59

-0. 062

138

+2. 25

+0. 035

-0.73

+0. 014

+1.22

-0. 062

144

+2.45

+0. 029

-0.64

+0. 016

+0.84

-0. 064

150

+2.60

+0. 024

-0. 54

+0. 017

+0.46

-0. 066

156

+2. 74

+0. 021

-0.44

+0. 017

+0.05

-0. 066

162

+2.85

+0. 016

-0. 34

+0. 017

-0.33

-0. 064

168

+2.93

+0. 011

-0. 24

+0. 018

-0.72

-0. 065

174

+2.98

+0. 006

-0. 12

+0. 018

—1.11

-0. 064

180

+3.00

+0. 001

-0.02

+0. 018

-1.49

-0. 062

186

+2.99

-0. 004

+0.09

+0. 018

-1.85

-0. 059

192

+2.95

-0. 009

+0.20

+0. 018

-2.20

-0. 058

198

+2.88

-0. 014

+0. 31

+0. 018

-2. 55

-0. 055

204

+2.78

-0. 019

+0.41

+0. 017

-2.86

1) u.M

210

+2. 65

-0. 022

+0.51

+0. 016

-3.16

-0.047

216

+2.51

-0. 028

+0.60

+0. 016

-3.42

-0. 042

222

+2. 32

-0. 033

+0.70

+0. 016

-3.67

-0. 039

228

+2.11

-0. 036

+0.79

+0. 013

-3.89

-0. 032

234

+1.89

-0. 038

+0.86

+0. 012

-4.06

-0. 027

240

+1.65

-0. 043

+0.94

+0. 012

-4.21

-0. 022

246

+1.37

-0. 048

+1.00

+0. 009

-4.33

-0. 017

252

+1.08

-0. 048

+1.05

+0. 009

-4.41

-0.009

258

+0. 79

-0. 049

+1.11

+0. 008

-4.44

-0.002

264

+0.49

-0. 052

+1. 14

+0. 005

-4.43

+0. 005

270

+0.16

-0. 054

+ 1. 17

+0. 002

-4.38

+0.011

276

-0.16

-0. 053

+1. 17

0.000

-4.30

+0. 020

282

-0.48

-0. 054

+ 1. 17

-0. 001

-4. 14

+0. 029

2SS

-0.81

-0. 054

+ 1. 16

-0. 002

-3.95

+0. 036

294

—1.13

-0. 052

+ 1.14

-0. 004

-3.71

+0. 042

300

-1.43

-0. 051

+ 1.11

-0. 008

-3. 44

+0. 049

306

-1.74

-0. 048

+ 1.05

-0.011

-3.12

+0. 059

312

-2.01

-0. 044

+0.98

-0. 013

-2. 73

+0. 067

318

-2.27

-0. 042

+0.89

-0. 016

-2.32

+0.071

324

-2.51

-0. 038

+0.79

-0. 018

-1.88

+0. 075

330

-2.72

-0. 031

+0.68

-0. 019

-1.42

+0. 081

336

-2.88

-0. 026

+0.56

-0. 021

-0.91

+0. 084

342

-3.03

-0. 021

+0.43

-0. 022

-0.41

+0. 084

348

-3.13

-0. 014

+0. 30

-0. 023

+0.10

+0. 085

354

-3.20

-0. 008

+0.15

-0. 023

+0.61

+0. 084

360

-3.22

-0. 001

+0.02

-0. 022

+1.11

+0. 082

[7io2, 3 log r, and u/cos i are to be computed in the form of Ji a* sin ig+ J* bt cos ig+cT.]

312 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (174) Phaedra — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

1877. 0

8

9
1880

1

2

3

4
1885

6

7

8

9
1890

1
. 2

3

4
1895

6

7

8

9
1900

1

2

3

4
1905

6

7

8

9
1910

1

2

3
4

1915
6
7
8
9

1920
1
2
3
4

1925
6
7
8
9

1930

A'

47. 1139
0995
0852

47. 0708
0565
0422
0278
0135

II, <l!l<!|
9S4S
9704
9561
9417

46. 9274
9130
8987
8844
8700

46. 8557
8412
8269
8125
7982

46. 7839
7695
7552
7408
7265

46. 7122
6978
6835
6691
6548

46. 6404
6261
6118
5974
5831
HI. 56S7
5544
5401
5257
5114

46. 4970
4827
4684
4540
4397

46. 4253
4110
3967
3823
3680
46. 3536

B'

250. 8059
8211
8363

250. 8515
8668
8820
8972
9124

250. 9277
9429
9581
9733

250. 9886

251. 0038
0190
0342
0495
0647

251. 0799
0952
1104
1256
1408

251. 1561
1713
1865
Jills
2170

251. 2323
2475
2628
2780
2932

251.3084
3237
3390
3542
3695

251. 3847
3999
4152
4304
4457

251. 4609
4762
4914
5066
5219

251. 5371
5524
5676
5829
5981

251. 6133

264. 3497
3593
3690

264. 3787
:issi
3981
4078
4174

264. 4271
4368
4465
4562
4658

264. 4755
1S52
4949
5046
5142

264. 5239
5336
5433
5530
5627

264. 5724
5820
5917
6014
6111

264. 6208
6304
6401
6498
6595

264. 6692
6788
6885
6982
7079

264. 7175
7272
7369
7466
7563

264. 7659
7756
7853
7950
8047

264. 8143
8240
8337
8434
8529

264. 8627

9. 99736
36
36

9. 99736
36
37
37
37

9. 99737
37
38
38
38

9. 99738
38
39
39
39

9. 99739
39
40
40
40

9. 99740
41
41
41
41

9. 99741
42
42
42
42

9. 99742
43
43
43
43

9. 99743
44
44
44
44

9. 99744
45
45
45
45

9. 99745
40
46
46
46

9. 99746

log sin b log sin c

9. 92070
69
68

9. 92068
67
66
65
64

9. 92063
62
62
61
60

9. 92059
58
57
56
56

9. 92055
54
53
5,2
51

9. 92051
50
49
48
47

9. 92040
46
45
44
43

'i 921142
41
41
40
39

9. 92038
37
36
35
35

9. 92034
33
32
31
30

9. 92030
29
28
27
26

9. 92025

9. 75124
25
27

9. 75128
29
30
31
33

9. 75134
35
36
38
39

9. 75140
41
42
44
45

9. 75146
47
48
50
51

9. 75152
53
54
56
57

9. 75158
59
60
61
63

9. 75164
65
66
67
69

9. 75170
71
72
73
74

9. 75176
77
78
79
80

9. 75182
83
84
85
86
9. 75188

Year

log cos a

log cos 6

log cos c

1877. 0
1930. 0

9. 043 n
9. 033 n

9. 743 n
9. 744 n

9.917
9.917

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
TABLES OF (179) KLYTAEMNESTRA.

313

MEAN ELEMENTS.

Epoch, 1893, Sept. 17.0, M. T. Berlin=1893.712, M. T. Berlin.

O / //

g0 = 89 22 45= 89?3792

w=100 51 4S = 100.86321

gj=253 17 5=253.2848 } Mean equinox and ecliptic 1900.0.

i= 7 47 18= 7.7882J

<p= i; 26 14= 6.4371

n= 692". 2030= 0.19227861

The elements are based on oppc wit ions extending from 1877 to 1899 and on the perturbations of the first

ordei

by Jupiter, as given on page 314.

AUXILIARY QUANTITIES.

loga=0.47318 log 57.2957 <=0^0777 IogJEL9.95110
log e=9.04965 l"g /» =0.46ib9 °Vj[4f

TABLE I.— MEAN ANOMALY ig).

Jan. 0.0 of common years: Jan. 1.0 of leap years

Table for beginning of month

Month

g

Year

9

Year

9

T /0.0

Jan. \l0

0
| 0. 00000

1877

O

355. 71052

1905

O

161. 95159

8

65. 89222

6

232. 13328

**.{!J

| 5. 96064

9

136. 07391

7

302. 31498

B

lssii

206. 44788

B 8

12. 68895

Mar. 0.0

11.34444

1

276. 62957

9

82. 87064

Apr. 0.0

17. 30507

2

346.81127

1910

153. 05233

May 0.0

23. 07343

3

56. 99296

1

223. 23403

June 0.0

29. 03407

B

4 127. 36693

B 2

293. 60800

July 0.0

34. 80243

5

197. 54862

3

3. 78969

Aug. 0.0

40. 76306

6

267. 73032

4

73. 97138

Sept. 0.0

46. 72370

7

337.91201

5

144. 15307

Oct. 0.0

52. 49206

B

8

48. 28598

B 6

214. 52705

Nov. 0.0

58. 45270

9

118.46767

7

284. 7087 1

Dec. 0.0

64. 22105

ISill)

1

188. 64937
258.83106

8
9

354. 89043
65. 07212

B

2

329. 20503

B 1920

135. 44610

3

39. 38672

1

205. 62779

Change for n days0

4
5

109. 56841
179. 75011

2
3

275. 80948
345. 99117

B

6

7
8

250.12408

320. 30577

30. 48746

B 4

5

56. 36514
126.54684

n

9

n

9

6

196. 72853

9

100. 66916

7

266. 91022

1

0. 19228

16

3. 07646

1900
1

170. 85085
241. 03254

B 8
9

337. 2S419
47. 46589

2
3

0. 38456
0. 57684

17

18

3. 26874
3. 46101

2

311. 21423

1930

117. 64758

4

0. 76911

19

3. 65329

3

01 qq=;qq

5

0. 96139

20

3. 84557

B

4 91. 76990
1905 161. 95159

6
7
8
9
10

1. 15367
1. 34595
1. 53S23
1. 73051
1. 92279

21
22
23
24
25

4. 03785
4. 23013
4. 42241
4. 61469
4. 80696

N

ote. — When g is used as an argument of the perturbations

add

to the q of this table An=n— r.0= —049719. For ex-

11

2. 11506

26

• 4.99924

planation see page 203.

12

2. 30734

27

5. 19152

13

2. 49962

28

5. 38380

14

2.69190

29

5. 57608

15

2. 88418

30

5. 76836

" For days during January and

February of leap years subtract one

day before entering this table.

314 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (179) Klytaemnestra — Continued.

PERTURBATIONS.

?!<

h

V

» cos i

Arg.
ig-i'g'

sin

cos

sin

cos

sin

COS

//

//

//

//

ff

//

0 0
0 0

- 8

0. 02nt

+ 3

+ 0. 20nt

+1 0

+1
+2
+2
+3 0

+ 0. 75nt

- 1

+ 0. 02nt

7. 06nt

- 0. 20nt
0. 01 nt

- 3. 53nt

- 0. 20nt

- 0. Olnt

+ 3

— 0. 37nt

- 0. 02nt

- 9. 05nt

- 0. 52nt

- 0. 04nt

- 1. 19nt

- 0. 07nt

- 0. Olnt

-1 +1

0
+ 1
+2
+3 +1

+ 5

- 285

- 10
_ 2

- 3

+ 14
+ 93
+ 4

+ 2
- 2
+ 28
+ 3

+ 3

+ 3

+ 87

+ 7
+ 1

_ 2
- 8
+ 6
+ 1

- 2
-13
+ 9

+ 7

0 +2

+1

+2
+3
+4 +2

- 24
+1354
+ 925

4- 32
+ 2

+ 24
-1107

- 678

23

- 2

- 12
-117
-371

- 23

- 3

- 12
-147
-508

- 32

4

+16
-12
-14

+ 8
-11
-15

+ 1

+1 +3

+2

+3

+4 +3

+ 18-
+ 13
+ 46
+ 3

- 1
- 138

65

- 3

- 56

- 45

4

+ 3
9

- 32
3

+ 7
-20
- 4

+ 1
- 8

+2 +4
+3

+4

+5 +4

+ 26
+ 13
+ 6
+ 1

- 16
+ 46

- 15

- 2

+ 2
+ 25
- 11
_ o

4
9
5

- 1

+10
- 1

+3 +5

+4

+5

+6 +5

+ 4
+ 4

- 4

+ 7

- 4

- 1

- 2
+ 4

- 4

- 1

- 2

- 3

+ 1

+4 +6

+5

+6 +6

+ 1
+ 2
- 1

+ 1
+ 2
- 2

+ 1

- 1

— 1

+ 1

+3 +7
+4
+5
+6

+7 +7

- 293
+ 10

+ 1

+ 78

2

+ 1

1

- 1

- 1

- 4

- 4

- 1

+ 1

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (179) Klytaemnestra — Continued.

315

TABLE II .— n<Jz.

PERIODIC TERMS.

Unit of a and 6=09001.

i

0

1.

2

9'

K

Diff.forl0

"i

Diff.forl0

h

Diff.forl0

(I.,

Diff.forl0

b2

Diff.forl0

O

0

+ 10.6

+0.23

+308. 9

—10. 44

-289. 8

-12. 24

+268. 5

- 8.90

-233. 0

- 9.68

6

4-11.8

+0. 16

+238. 0

-12.92

-356. 5

- 9.72

+208. 6

-10. 75

-284. 4

- 7.30

12

+12.6

+0.10

+ 153. 9

-14.90

-406. 4

- 6.72

+ 139. 5

-12. 10

-320. 6

- 4.62

18

+13.0

+0.02

+ 60. 4

-lti. 10

-437. 0

- 3. 35

+ 64.9

-12. 60

-339. 8

- 1.75

24

+ 13.0

-0.04

- 38.0

-16.60

-446. 6

+ 0.18

- 10.6

—12. 36

-341. 6

+ 1.07

30

+ 12.5

-0. 12

-137. 0

-16.30

-434. 8

+ 3. 73

- 83.4

-11.57

-327. 0

+ 3.73

36

+11.6

-0.19

-231. 8

-15. 20

-401. 8

+ 7.18

-149. 4

-10. 19

-296. 8

+ 6. 10

42

+ 10.2

-0.26

-318. 0

-13.31

-348. 7

+10. 34

—205. 7

- 8. 42

253 8

+ 7.93

48

+ 8.5

-0.30

-391. 5

-10.89

-277. 7

+13.04

-250. 4

- 6.36

-201. 6

+ 9.25

54

+ 6.6

-0.34

-448. 7

- 7.97

-192. 2

+15. 30

—282. 0

- 4. L5

, —142.8

+ 10. 12

60

+ 4.4

-0.38

-1ST. 2

- 4.64

- 95.5

+16. 80

-300. 2

- 1.90

- 80.2

+10. 45

66

+ 2.1

-0.38

-504. 1

- 1.03

+ 7. S

+ 17. 50

-304. 8

+ 0. 25

- 17. 4

+10. 28

72

- 0.2

-0.39

-499. 6

+ 2. 63

+ 113.4

+ 17.50

-297. 2

+ 2. 20

+ 43. 2

+ 9.76

78

-2.6

-0.38

-472. S

+ 6.23

+216. 4

+ 16. 70

-278. 4

+ 3.90

+ 99. 7

+ 8.90

84

-4.7

-0.34

-424. 8

+ 9.60

+312. 6

+15. 20

-250. 4

+ 5. 35

+150. 0

+ 7.79

90

-6.7

-0. 30

-357. 6

+12. 57

+397. 5

+12. 88

-214. 2

+ 6.57

+ 193.2

+ 6.53

96

-8.3

-0. 24

-274.0

+ 15.02

+467. 2

+10. 11

-171.6

+ 7.50

-228.4

+ 5. 16

102

-9.6

-0.18

—177.4

+ 17. 00

+518. 8

+ 6.88

-121 2

+ 8.20

+255. 1

+ 3.71

108

—10.5

-0.12

- 71.8

+18. 10

+549. 7

+ 3.32

- 73. 2

+ 8.65

+272. 9

+ 2.22

114

-11.0

-0.05

+ 38. 4

+18. 50

+558. 6

- 0.38

- 20.4

+ 8.90

+281. 7

+ 0.68

120

—11.1

+0.02

+14s 5

+18. 10

+545. 1

- 4.07

+ 33.6

+ 8. 92

+281. 0

- 0.96

126

—10.7

+0. 10

+254 1

+16. 90

+509. 8

- 7.63

+ 86.6

+ 8.66

+270. 2

- 2.57

132

-9.9

+0.16

+350. 2

+14.95

+453. 5

-10. 90

+137. 5

+ 8. 17

+25D. 2

- 4. 14

138

-8.8

+0.20

+433. 5

+12.50

+379. 0

-13. 66

+184. 6

+ 7.39

+220. 5

- 5. 67

144

-7.5

+0.25

+500. 2

+ 9. 52

+289. 6

-15. 90

+226. 2

+ 6.32

+182. 1

- 7.07

150

-5.8

+0.28

+547. 7

+ 6.13

+188. 2

-17. 60

+260. 4

+ 4.92

+135. 6

- 8.32

156

- 4. 1

+0.30

+573. 8

+ 2. 52

+ 79.4

-18. 50

+285. 2

+ 3.23

+ 82. 2

- 9.33

162

-2.2

+0.31

+577. 9

- 1.19

- 31.9

-18. 60

+299. 2

+ 1.32

+ 23.6

- 9.98

168

- 0.4

+0.28

+559. 5

- 4.83

-141.8

-17. 90

+301. 0

- 0.73

- 37.6

-10. 22

174

+ 1.2

+0.27

+519.9

- 8. 27

-245. 6

-16.60

+ 290.4

- 2.86

- 99.0

-10. 03

180

+ 2.8

+0.23

+460. 3

-11.36

-339. 3

-14.44

+266. 7

- 4. 95

-158.0

- 9.38

186

+ 4.0

+0.18

+383. 5

-13. 95

-418. 9

-11. 82

+231. 0

- 6.89

-211.6

- 8.27

192

+ 5.0

+0. 13

+292. 9

-15. 94

-481. 2

- 8.78

+184.0

- 8.61

-257. 3

- 6.73

198

+ 5.6

+0.07

+ 192. 2

-17. 43

-524.2

- 5.40

+ 127. 7

- 9.94

-292. 4

- 4.81

204

+ 5.8

+0.01

+ 85 2

-IS. 10

-546. 0

- 1.82

+ 64. 7

-10. 84

-315. 0

- 2.64

210

+ 5.7

-0. 05

— 23. 2

-18. 00

546 0

+ 1.80

- 2.4

-11.26

-324. 1

- 0.30

216

+ 5.2

-0. 11

-129. 0

-17.12

-524. 4

+ 5.31

- 70. 4

-11. 15

-318. 6

+ 2. 11

222

+ 4.4

-0. 16

-227. 2

-15. 46

-482. 3

+ 8.58

-136.2

-10. 55

-298. 8

+ 4.44

228

+ 3.3

-0.20

-314. 6

-13.34

-421.4

+ 11.44

-197.0

- 9.43

-265.3

+ 6.60

234

+ 2.0

-0.24

-387. 3

-10.65

—345. 0

+ 13. 77

-249. 4

- 7. §8

-219.6

+ 8.49

240

+ 0.4

-0. 26

-412 1

- 7.56

-256. 1

+ 15.70

-291. 6

- 5.98

-163. 4

+10. 04

246

- 1. 1

-0. 25

-478. 0

- 4.18

-158. 4

+ 16. 70

-321. 2

- 3.77

- 99. 1

+11. 15

252

-2.6

-0. 26

-492. 6

- 0.65

- 56. <;

+17.10

-336. 8

- 1.35

- 29.6

+11.77

258

-4.2

-I). 24

-485. 8

+ 2.85

+ 45. 2

+16. 70

-337. 4

+ 1.16

+ 42. 1

+ 11.88

264

- 5. 5

-0.21

-458. 4

+ 6. 20

+ 142. 8

: 15 lid

-322. 9

+ 3. 67

+113. 0

+ 11.47

270

-6.7

-0. 17

-411.4

+ 9.23

+231.7

+13. 78

-293. 4

+ 6.08

+179. 8

+ 10. 54

276

-7.5

-0. 11

-347. 6

+11.83

+308. 2

+ 11.44

-250. 0

+ 8.26

+239. 5

+ 9.12

282

- 8.0

-0. 05

-269. 1

+14. 00

+369. 0

+ 8.61

-194.3

+10. 12

+289 2

+ 7. 22

288

- 8. 1

+0.02

-180. 6

+ 15. 40

+411.5

+ 5.40

-128. 6

+11.54

+326. 1

+ 4.92

294

-7.8

+0.08

- 85. 4

+ 16.10

+433. 8

+ 2.02

- 55 8

+12.48

+348. 2

+ 2.32

300

- 7. 1

+0.14

+ 11.7

+16. 10

+435. 7

- 1.43

+ 21 2

- 1 2. 82

+354. 0

- 0.48

306

- 6.1

+0.20

+ 106. 7

+ 15. 40

+416.6

- 4. 85

+ 98.0

+12. 50

+342. 4

- 3.33

312

- 4. 7

+0.26

+ 195. 0

+13. 82

+377. 5

- s 05

+171.2

+ 11.56

+314. 0

- 6.06

318

- 3.0

+0.30

+ 272. 6

+ 11. 73

+320. 0

-10.81

136.8

+ 10. 00

+269. 7

- 8.54

324

- 1. 1

+0.33

135. 8

+ 9. 11

+247. S

-13. 05

+291. 2

+ 7.87

+211.5

-10. 62

330

+ 1.0

+0. 35

+381.9

+ 6.05

+163.4

-14.80

+331. 2

+ 5. 27

+ 142.2

-12. 30

336

+ 3.1

+0.35

+408. 4

+ 2. 70

+ 71.0

-15. 80

+354. 4

+ 2. 37

+ 65. 1

-13. 24

342

+ 5.2

+0.34

+414. 3

- 0.78

- 24. 9

-16. 00

+359. 6

- 0.68

- 15. 2

-13. 43

348

+ 7.2

+0.32

+399. 1

- 4. 25

-120.0

- 15 50

+346. 2

- 3.68

- 94. 6

—12. 88

354

+ 9.0

+0.28

+363. 3

- 7. 52

-209. 6

- 1 l 30

+315. 4

- 6.48

-168.3

-11. 53

360

+10.6

+0.23

+308. 9

-111. 44

-289. 8

-12.24

+268. 5

- 8.90

-233. 0

- 9.68

[n$z, ■> log r, and u cos i are to be computed in the form It at sin \g+Z\ o
89369°— vol 10—11- -23

316 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (179) Klytaemnestra — Continued.

TABLE II.— n3z— Continued.

PERIODIC TERMS.

Unit of a and 0=09001.

i

3

4

9'

<>3

Din". fori0

h

Diff.forl0

«4

Diff.forl0

bt

Diff.forl0

O

0

-22.5

+ 1.09

+ 0.2

+4.11

+6.7

-0.23

-4.0

-0. 54

6

- 4.8

+3.88

+21.5

+1.85

+4.2

-0.50

-6.9

-0.35

12

+24.0

+4.29

+22.4

-1.80

+0.7

-0.62

-8.2

-0.06

18

+46.7

+2.02

- 0.1

-4.90

-3.3

-0. 56

-7.6

+0.25

24

+48. 2

-1.93

-36.4

-5. 66

-6.0

-0.34

-5.2

+0.48

30

+23.5

-5.59

-68.0

-3. 45

-7.4

-0.06

-1.8

+0.57

36

-18.9

-7.02

—77.8

+0.72

-6.7

+0.22

+1.6

+0.46

42

-60.8

-5.39

-59.3

+4.92

-4.8

+0.35

+3.7

+0.26

48

-83.6

-1.44

-18.8

+7.22

-2.5

+0.37

+4.8

+0.08

54

-78.1

+3.04

+27.4

+6.53

-0.4

+0.30

+4.7

-0.07

60

-47.1

+6.01

+59.6

+3.18

+ 1.1

+0.22

+4.0

-0. 12

66

- 6.0

+6.09

+65. 6

-1.08

+2.2

+0.15

+3.2

-0.13

72

+26.0

+3.53

+46.6

-4.20

+2.9

+0.11

+2.4

-0.16

78

+36.4

-0.22

+ 15.2

-4.75

+3.5

+0.10

+1.3

-0.21

84

+23.4

-3.16

-10.4

-2.68

+4.1

+0.04

-0.1

-0.28

90

- 1.5

-3. 72

-17.0

+0.68

+4.1

-0.09

-2.0

-0.33

96

-21.3

-1.74

-2.2

+3.42

+3.0

-0.28

-4.1

-0.29

102

-22.4

+1*64

+24.0

+3.90

+0.8

-0.43

-5.5

-0.13

108

- 1.6

+4.48

+44.6

+1.73

—2. 2

-0.48

-5.7

+0.12

114

+31.4

+5.09

+44.8

-1.98

-5.0

-0.38

-4.0

+0.38

120

+59. 5

+2. 90

+20.8

-5. 32

-6.8

-0.16

-1.1

+0.57

126

+66.2

-1.19

-19.0

-6.45

-6.9

+0.19

+2.8

+0.61

132

+45. 2

-5.22

-56.6

-4.60

-4.5

+0.50

+6.2

+0.42

138

+ 3.6

-7.15

-74.2

-0.48

-0.9

+0.65

+7.8

+0.08

144

-40.6

-6.01

-62.4

+4.03

+3.3

+0.59

+7.2

-0.28

150

-68.5

-2. 30

-25.8

+6.82

+6.2

+0.35

+4.5

-0. 53

156

-68.2

+2. 29

+ 19.5

+6.62

+7.5

+0.02

+0.8

-0.61

162

-41.0

+5.65

+53.6

+3.59

+6.5

-0. 29

-2.8

-0.50

168

- 0.4

+6.25

+62.6

-0.70

+4.0

-0.46

-5.2

-0.25

174

+34.0

+4. 01

+45. 2

-4.15

+1.0

-0.46

-5.8

+0.02

180

+47.7

+0.23

+ 12.8

-5.19

-1.5

-0.33

-5.0

+0.21

186

+36. 8

■ -3.06

-17. 1

-3.52

-3.0

-0. 17

-3.3

+0.30

192

+ 11.0

-4. IS

-29. 4

-0.20

-3.5

-0.02

-1.4

+0.26

198

-13.3

-2.68

-19.5

+2. 85

-3.3

+0.06

-0.2

+0.18

204

-21.1

+0. 52

+ 4.8

+3.88

-2.S

+0. OS

+0.8

+0.13

210

•— 7. 1

+3.55

+27.0

+2.27

-2.4

. II IIS

+1.4

+0.10

216

+21. 5

+4. lil

+32.0

—1.11

-1.9

+0. 08

+2.0

+0.12

222

+48.2

+2.96

+ 13.7

-4.45

-1.4

+0.15

+2.9

+0.13

228

+57. 0

-0.72

-21.4

-5. 88

-0.1

+ 0.27

+3.6

+0.08

234

+39. 6

-4.62

—56.8

-4.47

+1.8

+0.33

+3.9

-0.08

240

+ 1.5

-6.75

-75. 0

-0.75

+3.9

+0.28

+2.6

-0.28

246

-41.4

-5. 96

-65. 8

+3.58

+5.1

+0.10

+0.6

-0.40

252

-70.0

-2. 55

-32.0

+6.45

+5.1

-0.13

—2. 2

-0.46

258

-72.0

+1.90

+11.6

+6.46

+3.5

-0.37

-4' 9

-0.32

264

-47.2

+5.26

+45.5

+3.63

+0.7

-0. 50

-6.1

-0. OS

270

- 8.9

+5. 91

+55.2

-0.58

-2.5

-0.48

-5.8

+0.20

276

+23. 7

+3. 69

+38.6

-4. 05

-5.0

-0. I'll

-3.7

+0.41

282

+35.4

-0.19

+ 6.6

-5. 13

-6.0

-0.02

-0.9

+0.47

288

+21.4

-3.71

-23. 0

-3.32

-5.2

+0. 22

+1.9

+0.38

294

- 9.1

-5. 01

-33. 2

+0.40

-3.4

+0.33

+3.6

+0. 17

300

-38.7

-3.44

-18.2

+4.00

-1.2

+0. 31

+3.9

-0.03

306

-50. 4

+0.21

+14.8

+5.62

+0.3

+0. 16

+3.2

-0. 16

312

-36.2

+4.07

+49.2

+4.33

+0.7

0.00

+2.0

-0.15

318

— 1.6

+6.12

+66.8

+0.82

| i) 3

-0.08

+1.4

-0.02

324

+37.2

+5. 34

+59. 0

-3. 20

-0.3

-0.02

+1.8

+0.12

330

+62.5

+2. 17

+28.4

-5. 77

0.0

+0. 13

+2.9

+0.17

336

+63.2

-1. si

-10.2

-5. 60

+ 1.3

+0. 29

+3.8.

+0.08

342

+40.4

-4. 63

-38.8

-2. 87

+3.5

+0.38

+3.8

-0. 12

348

+ 7.6

1.86

-44.6

+0.92

+5.8

+0.29

+ 2.4

-0. 35

354

-17.9

-2. 51

-27. 8

+3.73

+7.0

+0.08

-0.4

-0.53

360

- 22.5

+ 1.09

+ 0.2

1

+4. 11

+ 6. 7

-0.23

-4.0

-0. 54

[nSz, s

log r. andu/c

os i are to be

computed in

the form li a

sin ig+Si 6i

cos ig+cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

317

Tables of (179) Klytaemnestra — Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6=09001.

i

5

6

9'

a5

D iff. fori0

b,

Dili .fori"

°o

Diff.forl0

K

Diff.forl0

O

0

+0.9

-0.07

-1.0

-0.08

0.0

-0.08

-0.8

-0.01

6

+0.3

-0.11

-1.4

-0.04

-0.5

-0.08

-0.8

+0.03

12

-0.4

-0.12

-1.5

+0.02

-0.9

-0.03

-0.4

+0.08

18

-1.1

-0.09

-1. 1

+0.08

-0.9

+0.02

+0.2

+0.09

24

-1.5

-0.05

-0.5

+0.12

-0.7

+0.06

+0.7

+0.07

30

-1.7

+0.02

+0.3

+0.15

-0.2

+0.09

+1.0

+0.02

36

-1.3

+0.10

+1.3

+0.12

+0.4

+0.09

+0.9

-0.04

42

-0.5

+0.14

+ 1.7

+0.04

+0.9

+0. 05

+0.5

-0.08

48

+0.4

+0.15

+1.8

-0.04

+1.0

-0. 02

-0.1

-0.10

54

+1.3

+0.12

+1.3

-0.11

+0.7

-0.07

-0.7

-0.08

60

+1.8

+0.04

+0.5

-0.16

+0.2

-0.09

-1.0

-0.02

66

+1.8

-0.05

-0.6

-0. L6

-0.4

-0.08

-0.9

+0.05 '

72

+1.2

-0. 12

-1.4

-0.10

-0.8

-0.04

-0.4

+0.08

78

+0.3

-0.16

-1.8

-0.02

-0.9

+0.02

+0.1

+0.08

84

-0.7

-0. 15

-1.7

+0.07

-0.6

+0.08

+0.6

+0.06

90

-1.5

-0.08

-1.0

+0.14

0.0

+0.08

+0.8

+0.01

96

-1.7

+0.01

0.0

+0.16

+0.4

+0.06

+0.7

-0.05

102

-1.4

+0.08

+0.9

+0.12

+0.7

+0.02

+0.2

-0.08

108

-0.7

+0.14

+1.5

+0. 05

+0.6

-0. 02

-0.3

-0.07

114

+0.3

+0.15

+1.5

-0.03

+0.4

-0.07

-0.6

-0.02

120

+1.1

+0.10

+ 1.1

-0. 10

-0.2

-0.08

-0.6

+0.02

126

+1.5

+0.02

+0.3

-0. 15

-0.5

-0.03

-0.4

+0. 05

132

+ 1.3

-0.06

-0.7

-0.12

-0.6

+0.02

0.0

+0.07

138

+0.8

-0.12

-1.2

-0.07

-0.3

+0.05

+0.4

+0. 05

144

-0.1

-0. 15

-1.5

+0.01

0.0

+0.06

+0.6

0.00

150

-1.0

-0. 11

-1.1

+0.09

+0.4

+0.04

+0.4

-0. 05

156

-1.4

-0.03

-0.4

+0.14

+0.5

+0.01

0.0

-0.06

162

-1.4

+0.04

+0.6

+0.13

+0.5

-0.03

-0.3

-0.04

168

-0.9

+0.11

+1.2

+0.08

+0.1

-0.07

-0.5

-0.02

174

-0.1

+0.15

+ 1.5

+0.02

-0.3

-0.06

-0. 5

+0.02

180

+0.9

+0.13

+1.4

-0.08

-0.6

-0.02

-0.2

+0.06

186

+1.5

+0.06

+0.6

-0. 14

-0.5

+0.02

+0.2

+0.07

192

+1.6

-0.01

-0.3

-0.14

-0.3

+0.05

+0.6

+0.03

198

+ 1.4

-0.09

-1.1

-0.12

+0.1

+0.07

+0.6

-0.01

204

+0.5

-0.16

-1.7

-0.04

+0.5

+0.00

+0.5

-0. 05

210

-0.5

-0.15

-1.6

+0. 05

+0.8

+0.01

0.0

-0.07

216

-1.3

-0.10

-1.1

+0.11

+0.6

-0.04

-0.3

-0.06

222

-1.7

-0.02

-0.3

+0.14

+0.3

-0.07

-0.7

-0.03

228

-1.6

+0.05

+o. 6

+0.13

-0.2

-0.07

-0.7

+0.02

234

-1.1

+0.12

+ 1.3

+0.08

-0.5

-0. 05

-0.5

+0.06

240

-0.2

+0.14

+ 1.6

+0. 01

-0.8

-0. 01

0.0

+0.07

246

+0.6

+0.12

+1.4

-0. 06

-0.6

+0.03

+0.3

+0. 05

252

+1.2

+0.08

+1.0

-0.10

-0.4

+0.06

+0.6

+0.03

258

. +1. 5

+0.01

+0.2

-0.12

+0.1

+0.07

+0.7

0.00

264

+1.3

-0. 05

-0.5

-0.10

+0.4

+0.04

+0. 6

-0.04

270

+0.9

-0.08

-1.0

-0.06

+0.6

+0.02

+0.2

-0.06

276

+0.3

-0.09

-1.2

-0.01

+0.6

-0.01

-0.1

-0.05

2S2

-0.2

-0.08

-1.1

+0.02

+0.5

-0. 03

-0.4

-0.03

288

-0.7

-0.06

-0.9

+0.05

+0.2

-0.06

-0.5

-0.02

294

-0.9

-0.02

-0.5

+0.07

-0.2

-0.05

-0.6

+0.01

300

-0.9

0.00

-0.1

+0.07

-0. 4

-0.02

-0. 1

+0.03

306

-0.9

+0.02

+0.3

+0. 05

-0.5

-0. 02

-0.2

+0. 05

312

-0.7

+0.04

+0. 5

+0.04

-0.6

0.00

+0.2

+0. 05

318

-0.4

+0.05

+0. 8

+0.03

-0.5

+0. 03

+0.4

+0.03

324

-0.1

+0. 05

+0.9

+0. 01

-0.2

+0.06

+0.6

+0.02

330

+0.2

+0.06

+0.9

-0.01

+0.2

+0.06

+0.6

0.00

336

+0.6

+0.07

+0.8

-0.02

+0.5

: O 01

+0.6

-0.04

342

+1.0

+0. 04

+0.6

-0.07

+0.7

+0.02

+0.1

-0.08

348

+ 1.1

+0.01

0.0

-0.09

+0.7

-0.02

-0.3

-0.07

354

+1.1

-0.02

-0.5

-0.08

+0.5

-0.06

-0.7

-0.04

360

+0.9

-0.07

-1.0

-0.08

0.0

0 Os

-0. 8

-0.01

[na

iz, S log r, and u/cos i are to be computed in the form It a, sin ig + Ii bt cos ig+cT.]

318 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (179) Klytat mnestra — Continued.

PERIODIC TERMS.

TABLE III 3 log r.

Unit of a and 6=0.00001.

i

0

1

2

0'

K

Diff.forl0

«,

Diff.forl0

6,

Diff.forl0

a2

Diff.forl0

b.

In tY. fori0

o

0

-3.6

+0.08

-19.6

-0. 72

-10.9

+0.74

- 88.0

—3. 7S

-107.0

+3.24

6

-3.0

+0. 1 1

-23.2

-0. 52

-5.8

+0.92

-108.5

-2. 97

- 85.1

+3.98

12

-2.3

+0. 13

-25. 9

-0. 32

+ 0.2

+ 1.02

-123. 6

-2. 01

- 59.3

+4. 50

IS

-1.4

+0.12

-27.1

-0. 08

+ 6.5

+ 1.08

-132. 6

-0.98

- 31.1

+4.78

24

-0.8

+0.12

-26. S

+0.17

+13.2

+ 1. 10

-135.4

+0.08

2.0

+4.83

30

0.0

+0. 12

-25. 1

+0.42

+ 19.7

+1.08

—131. 7

+ 1.12

+ 26.9

+4.65

36

+0.7

+0. 12

-21. 7

+0.68

+26. 1

II IIS

-122. 0

+ 2.06

+ 53.8

+4.24

42

+ 1.4

+0.10

-17.0

+0.88

+31. 5

us:;

-107.0

+2.88

+ 77.8

+3.65

48

+ 1.9

+0.07

-11. 1

+ 1.08

+36.1

n li.",

- 87.3

+3. 56

+ 97.6

+2.92

54

+ 2.2

+0.04

- 4.1

+ 1.22

+39.3

+0.40

- 64.3

+4.02

+ 112.9

+2.08

60

+2.4

+0.02

+ 3.6

+ 1.32

+40.9

+0. 15

- 39.1

+4. 30

+ 122.6

+1.16

66

+ 2.5

0.00

+11.8

+ 1.37

+ 41. 1

-0. 11

- 12.7

+4.38

+ 126.8

+0. 24

72

+2.4

-0.02

+20.0

+ 1.36

+39.6

-0.38

+ 13.5

+4. 27

+ 125. 5

-0.64

78

+2 2

-0.06

+2S. 1

+ 1.29

+36. 5

-0.66

+ 38.5

+3.98

+ 119.0

-1.48

84

+L7

-0.08

+35.5

+ 1.16

+31. 7

-0. 93

+ 61.2

+3. 54

+ 107.8

-2. 21

90

+ 1.3

-0.08

+42.0

+0.98

+25.3

-1.17

+ 81.0

+3. 00

+ 92.5

-2.82

96

+0.7

-0.12

+47. 2

+0.76

+ 17.7

-1. 35

+ 97.2

+2.35

+ 73.9

-3.31

102

-0.1

-0.13

+51.1

+0. 50

+ 9.1

-1.50

+ 109.2

+ 1.62

+ 52.8

—3.66

108

-0.9

-0.13

+53. 1

+0.20

- 0.3

-1.58

+ 116.7

+0.88

+ 30.0

-3.87

114

-1.7

-0.13

+53.5

-0.11

-9.9

-1.62

+ 119.8

-0.15

+ 6.4

-3.93

120

-2.5

-0. 13

+51.8

-0. 42

-19.7

-1.60

+118.5

-0.60

- 17.2

-3.87

126

-3.3

-0.12

+48.4

-0.70

-29.1

-1. 52

+ 112.6

-1.32

- 40.0

-3.67

132

-4.0

-0.11

+43.4

-0.99

-37.9

-1. 35

+ 102.6

-1.97

- 61.2

-3.33

138

-4.6

-0.08

+36.5

-1.24

-45.3

-1.13

+ 89.0

-2.58

- 80.0

-2. 91

144

-5.1

-0.07

+28.5

-1.45

-51. 5

-0.88

+ 71.7

-3.11

- 96.1

-2.40

150

—5.4

-0.04

+ 19. 1

-1.61

-55. 9

ii i,ii

+ 51.7

-3. 52

-108.8

-1.78

156

-5.6

-0.02

+ 9.2

-1.70

-58. 7

-0.29

+ 29.4

-3.82

-117.5

-1.08

162

-5. 6

+0.01

- 1.2

-1.72

-59. 4

+0.04

+ 5.8

-4.00

—121.7

-0. 32

168

-5.5

+0.03

-11.4

-1.67

-58. 2

+0.37

- 18.6

-4.05

-121.4

+0.47

174

-5.2

+0.06

-21. 2

-1.58

-55. 0

+0.68

- 42.8

—3. 92

-116. 1

+1.28

180

-4.8

+0.08

-30.3

-1. 42

-50. 0

+0.97

- 65. 7

-3.64

-106.0

+2.06

186

-4.3

+0.10

-38.2

-1.21

-43.4

+ 1.27

- 86.5

-3.21

- 91.4

+2. 78

192

-3.6

+0. 11

—44.8

-0. 93

-35.3

+1.42

-104.2

-2. 62

- 72.6

+3. 42

198

-3.0

+0. 11

-49.4

-0. 64

-26.4

+ 1.58

-118.0

-1.88

— 50.3

+3.94

204

-2.3

+0. 12

-52. 5

-0.35

-16.5

+ 1.66

-126. 8

-1.04

- 25.3

+4.31

210

-1.5

+0. 12

-53. 6

-0.02

- 6.5

+ 1.64

-130. 5

-0. 14

+ 1.4

+4.50

216

-0.8

+0. 11

-52.8

+0.31

+ 3.2

+ 1.59

-128.4

+0.83

+ 28.7

+4.48

222

-0.2

+0. 10

-49. 9

+0. 61

+ 12.6

+1.49

-120. 5

+ 1.77

+ 55. 2

+4.27

228

+0.4

+0.08

-45. 5

+0.86

+21.1

+ 1.32

-107.2

+2.65

+ 79.9

+3.83

234

+0.8

+0.06

-39.6

+ 1.09

+28.5

' +1. 10

- 88. 7

+3. 45

+ 101.2

+3.21

240

+1.1

+0. 04

-32. 4

+ 1. 25

+34.3

+0.83

- 65.8

+4.11

+ 118.4

+2.43

246

+1.3

+0.01

-24.6

+ 1.35

+38.5

+0. 55

- 39.4

+4.58

+ 130. 4

+1.52

252

+1.2

-0. 02

-16.2

+1.38

+40.9

+0.27

- 10.9

+4.82

+ 136. 6

+0.50

258

+1.1

-0.02

- 8.0

+ 1.38

+41.7

-0.02

+ 18.5

+4.85

+136. 4

-0.56

264

+0.8

-0. 06

+ 0.3

+1.31

+40.6

-0.32

+ 47. 3

+4. 65

+ 129. 9

-1.60

270

+0.4

-0.08

+ V. 7

+ 1.18

+37.9

-0. 55

+ 74.3

+4. 23

+117.2

-2. 58

276

-0.1

-0.09

+ 14.4

+0.99

+34. 0

-0.78

+ 98.1

+3.58

+ 98.9

-3.45

282

-0.7

-0. 11

+ 19.6

+0. 76

+28.6

-0. 95

+ 117.3

+2. 75

+ 75.8

-4.17

288

-1.4

-0. 11

+23. 5

+0. 52

+22. i;

-1.08

+ 131. 1

+1.80

+ 48. 9

-4.68

294

-2.0

-0.10

+25. 9

+0.28

+ 15. 7

-1.14

+ 139.0

+0.74

+ 19.6

-4.98

300

-2.7

-0.11

+ 26. 8

0.00

+ 8.9

-1. 12

+ 140.0

-0.38

- 10. S

-5. 04

306

-3.3

-0. 10

+25. 9

-0.28

+ 2.3

-1.06

+ 134. 5

-1.46

- 40.9

-4. 85

312

-3.9

-0.08

+23.5

-0.48

- 3. S

-0.98

+ 122. 5

-2. 49

- 69.0

-4.41

318

-4.3

-0.06

+20. 1

-0.68

- 9.4

ii s2

+104. li

-3.38

- 93.8

-3.78

324

-4.6

-0. 04

+ 15.3

-0.87

-13. 7

n 62

+ 81. 9

-4.13

-114.3

-2. 95

330

-4.8

-0.02

+ 9.7

-0.98

-Hi. 9

-0.41

+ 55.0

-4.68

-129. 2

-1.96

336

-4.9

+0.01

+ 3.6

-1.02

-IS. li

-0. II

+ 25.8

-4.98

-137. 8

-0.88

342

-4.7

+0.03

-2.6

-1.03

-18.6

+0. 08 .

- 4.7

-5. 05

-139.8

+0.24

348

-4.5

+0.06

-8.8

-1.00

-17. (i

+0. 32

- 34. 8

-4.88

-134.9

+ 1.32

354

-4.0

+0.08

-14.6

-0. 90

-14. 7

+0. 56

- 63. 1

-4. 43

-124.0

+2.32

360

-3.6

+0.08

-19.6

-0. 72

-10.9

+0.74

- 88.0

- 3. 78

-107.0

+3.24

[ndz, 5 log r, and u/c-os i are to be computed in the form It ai sin ig+Ii bi cos ig+cT.)

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

319

PERIODIC TERMS.

Tables of (179) Klytaemneslra — Continued.
TABLE III.— 3 log r— Continued.

Unit of a and 6-d.OOOOL

i

3

4

5

n'

Diff.

63

Diff.

Diff.

b<

Diff.

Dili.

bs

Diff.

9

a3

forl°

fori0

at

fori0

fori0

as

fori0

fori0

O

0

-9.2

-0. 83

-16.4

+0.32

-3.1

-0.30

-4.1

+0. 18

-1.0

-0.02

-0.5

+0.08

6

-14. 1

-0.72

-13.6

+0.62

-4.7

-0. 19

-2.6

+0.30

-1. 1

-0.01

+0.2

+0.09

12

-17.9

-0. 50

- 9.0

+0.84

-5.4

-0.02

-0.4

+0.38

-1. 1

+0.04

+0.6

+0.07

18

-20.1

-0. 19

-3.5

+0.94

-4.9

+0.15

+2.0

+0.33

-0.6

+0.09

+ 1.0

+0.06

24

-20.2

+0.13

+ 2.4

+0.97

-3.6

+0.27

+3.6

+0.21

0.0

+0.10

+1.3

+0.01

30

-18.5

+0.38

+ 8.1

+0.88

-1.7

+0.32

+4.5

+0.06

+0.6

+0.08

+1.1

-0. 05

36

-15. 6

+0.60

+12.8

+0.70

+0.3

+0.28

+4.3

-0.09

+1.0

+0.06

+0.7

-0.08

42

-11.3

+0.78

+16. 5

+0.49

+1.7

+0.18

+3.4

-0. 18

+ 1.3

+0.02

+0.2

-0.10

48

-6.2

+0.88

+18.7

+0.27

+2.4

+0.08

+ 2.1

-0.19

+ 1.2

-0.04

-0.5

-0. 10

54

- 0.8

+0.91

+ 19. 7

+0.03

+2.7

+0.02

+1.1

-0.18

+0.8

-0.08

-1.0

-0.06

60

+ 4.7

+0.89

+19.1

-0.24

+2.6

(i (i:,

0.0

-0. 14

+0.2

-0.11

—1.2

-0.01

66

+ 9.9

+0.82

+16.8

-0.52

+2.1

-0.08

-0.6

-0.11

-0.5

-0.09

-1. 1

+0.03

72

+ 14.5

+0.63

+12.9

-0.75

+ 1.7

-0.08

-1.3

-II. HI

-0.9

-0.06

-0.8

+0.08

78

+ 17.5

+0.34

+ 7.8

-0.93

+ 1.2

-0. 12

-1.8

-0.08

-1.2

-0. 02

-0.2

+0. 11

84

+ 18.6

+0.01

+ 1.7

-1.02

+0.3

-0. 17

-2.2

-0.03

-1. 1

+0. 05

+0.5

+0.08

90

+17.6

-0. 35

— 4.4

-0.94

-0.8

-0. 18

-2.2

+0.04

-0.6

+0. 08

+0.8

+0. 05

96

+14.4

-0.67

-9.6

-0.72

-1.8

-0. 16

-1.7

+0.14

-0.1

+0.09

+1.1

+0.01

102

+ 9.6

-0.86

-13.0

-0.40

-2.7

-0.08

-0.5

+0. 23

+0.5

+0.08

+0.9

-0.05

108

+ 4.1

-0.91

-14.4

-0.05

-2.8

+0.06

+ 1.1

+0. 20

+0.8

+0.03

+0.5

-0.08

114

- 1.3

-0.81

-13.6

+0.28

-2. 0

+0.20

+2.6

+0.21

+0.9

0.00

-0.1

-0.08

120

- 5.6

-0. 58

-11. 1

+0.52

-0.4

+0.30

+3.6

+0.08

+0.8

-0. 05

-0.5

-0.06

126

- 8.3

-0.30

-7.3

+0.68

+ 1.6

+0.31

+3.5

-0. 10

+0.3

-0.08

-0.8

-0.02

132

-9.3

-0. 05

- 3.0

+0.68

+3.3

+0.23

+2.4

-0.27

-0.2

-0.08

-0.8

+0.02

138

-8.9

+0.18

+ 0.9

+0.59

+4.4

+0. 05

+0.3

-0. 35

-0.6

-0.04

-0.5

+0.07

144

- 7.0

+0.39

+ 4.1

+0.46

+3.9

-0. 14

-1.8

-0.32

-0.7

0.00

0.0

+0.08

150

-4.2

+0.49

+ 6.4

+0.29

+2.7

-0.28

-3. 5

-0.20

-0.6

+0.03

+0.5

+0.06

156

- 1.1

+0.58

+ 7.6

+0.08

+0.5

-0.33

-4.2

-0.02

-0.3

+0.07

+0.7

+0.02

162

+ 2.7

+0.60

+ 7.4

-0.14

-1.3

-0.26

-3.7

+0. 14

+0.2

+0.08

+0.7

-0.02

168

+ 6.1

+0.51

+ 5.9

-0.36

-2.6

-0.15

-2.5

+0.24

+0.6

• 0. (i,-,

+0.5

-0.06

174

+ 8.8

+0. 35

+ 3.1

-0.56

-3.1

-0.01

-0.8

+0.25

+0.8

+0.01

0.0

-0.08

180

+ 10.3

+0.10

- 0.8

-0.71

-2.7

+0.08

+0.5

+0.18

+0.7

-0.03

-0.5

-0.07

186

+ 10.0

-0.20

-5.4

—0.74

-2.0

+0.16

+ 1.4

+0.09

+0.4

-0.08

-0.8

-0.03

192

+ 7.9

-0. 50

-9.7

-0.63

-0.8

+0. 15

+ 1.6

0.00

-0.2

-0.08

-0.9

+0.01

198

+ 4.0

-0.74

-13.0

-0.40

-0.2

+0.08

+ 1.4

-0.04

-0.6

-0.06

-0.7

+0. 06

204

- 1.0

-0.88

-14.5

-0.08

+0.2

+0.04

+ 1.1

-0. 05

-0.9

-0.02

-0.2

+0.08

210

-6.5

-0.84

-13.9

+0.29

+0.3

+0.03

+0.8

-0.02

-0.9

+0.02

+0.2

+0.08

216

-11.1

-0.65

-11.0

+0. 59

+0.6

+0.04

+0.8

-0.02

-0.7

+0.06

+0.7

+0.08

222

-14.3

-0.39

-6.8

+0.76

+0.8

+0.04

+0.5

-0. 05

-0.2

+0.08

+ 1.1

+0.02

228

-15.8

-0.08

- 1.9

- II VJ

+1.1

+0.04

+0.2

-0.08

+0.3

+0.08

+ 1.0

-0.03

234

-15.4

+0.18

+ 3.0

+0.75

+ 1.3

-0.02

-0.6

—0.13

+0.8

+0.07

+0.7

-0.06

240

-13.6

; u :is

+ 7.1

+0.62

+0.9

-0.11

-1.4

-0.12

+1.1

+0.02

+0.3

-0.08

246

-10.8

+0.49

+ 10.4

+0.46

0.0

—0. 17

-2.0

+0. 05

+1.1

-0.02

-0.2

-0. 09

252

-7.7

+0. 55

+ 12.6

+0.29

-1.1

-0.19

-2.0

11 07

+0.8

-0.07

-0.8

-0.08

258

-4.2

+0.59

+ 13.9

+0.14

-2.3

-0.16

-1.2

+0. 18

+0.3

-0.08

-1.1

-0.02

264

- 0.6

+0. 59

+ 14.3

0.00

-3.0

-0. 05

+0.1

+0.23

-0.2

-0.08

-1. 1

+0.02

270

+ 2.9

+0.57

+ 13.9

-0.13

-2.9

+0.10

+ 1.6 •

+0.23

-0.6

-0.07

-0.8

+0. 05

276

+ 6.2

+0.52

+ 12.7

-0.25

-1.8

+0.20

+2.9

+0.16

-1.0

-0.04

-0.5

+0.07

282

+ 9.1

+0.43

+ 10.9

(i. :;s

-0.5

+0.23

+3.5

+0.03

-1.1

+0.02

0.0

+0.08

288

+11.4

+0.31

+ 8.2

-0.48

+ 1.0

+0.22

+3.3

-0.08

-0.8

+0.04

+0.5

+0.07

294

+ 12.8

+0.16

+ 5.1

-0. 52

+2.2

+0.14

+ 2.4

-0.17

-0.6

+0. 05

+0.8

+0.04

300

+ 13.3

+0.02

+ 2.0

-0.50

+2.7

+0.04

+ 1.3

-0. 16

-0.2

+0.08

+ 1.0

+0.01

306

+13.1

-0.08

- 0.9

-0.48

+2.7

-0.03

+0.5

-0.13

+0.3

+0.08

+0.9

-0.02

312

+12.4

-0.14

-3.6

-0.42

+2.3

-0. 05

-0.3

(1 (Is

+0.7

+0.05

+0.8

-0. 04

318

+ 11.4

-0.18

-5.9

-0.37

+2.1

-0.01

-0.5

-0.04

+0.9

+0.02

+0.4

-0.07

324

+10.3

-0.21

- S.O

-0.36

+2.2

+0.02

-0.8

-0.06

+ 1.0

0.00

0.0

-0.08

330

+ 8.9

-0.27

-10.2

-0.38

+2.3

+0.02

-1.2

-0. 10

+0.9

-0.02

-0.5

-0. 07

336

+ 7.1

-0.37

-12.6

-0.40

+2.4

-0.03

-2.0

-0.18

+0.6

-0.06

-0.8

-0. 05

342

+ 4.5

-0.54

-15.0

-0.34

+1.9

-0.13

-3. 3

-0. 18

+0.2

-0.08

-1.1

—0.02

348

+ 0.6'

-0.72

-16.7

-0. 20

+0.8

-0.25

-4.2

-0. 12

-0.3

-0.08

-1.1

+0.02

354

- 4.1

-0.82

-17.4

+0.02

-1. 1

-0.32

-4.7

+0.01

-0.8

-0. 06

-0.9

+0. 05

360

- 9.2

-0.83

-16.4

+0.32

-3.1

-0.30

-4.1

+0.18

-1.0

-0.02

-0.5

+0.08

[ndz, d log r, and u'cos i are to be computed in the form i1* a* sin ig+Ii bi cos ig+cT.]

320 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (179) Klytaemnestra — Continued.

PERIODIC TERMS.

TABLE IV.— u/cos :

Unit of a and 6=09001.

i

0

1

9'

&0

Diff. for 1°

a.

Diff. fori0

&>

Diff. fori0

O

0

- 0.5

-0.12

+1.1

-0.04

-0.8

-0.01

6

-1.2

-0. 12

+0.8

-0.04

-0.8

+0.02

12

- 1.9

-0. 12

+0.6

-0. 06

-0.6

+0.02

18

- 2.7

-0. 12

+0.1

-0.07

-0.5

+0.04

24

-3.4

-0. 10

-0.2

-0.04

-0.1

+0.08

30

-3.9

-0.08

-0.4

-0.02

+0.5

+0.10

36

-4.3

-0.06

-0.5

0.00

+1.1

+0.10

42

-4.6

-0.03

-0.4

+0.02

+ 1.8

+0. 12

48

-4.7

+0.02

-0.2

+0. 05

+2.5

+0. 12

54

-4.4

+0. 05

+0.2

+0.08

+ 3.3

+0. 12

60

- 4. 1

+0.08

+0.9

+0. 12

+4.0

+0. 11

66

- 3.4

+0.12

+1.7

+0. 16

+4.6

+0.06

72

-2.8

+0.14

+2.8

+0.18

+4.7

0.00

78

- 1.7

+0.18

+3.9

+0.18

+4.6

-0.02

84

- 0.6

+0.20

+5.0

+0.18

+4.4

-0.07

90

+ 0.7

+0.22

+6.1

+0. 17

+3.8

-0. 13

96

+ 2.1

+0.22

+7.0

+0. 12

+ 2.8

-0. 18

102

+ 3.4

+0.22

+7.6

+0.08

+ 1.6

-0.22

108

+ 4.8

+0.22

+8.1

+0. 05

+0.1

-0.26

114

+ 6.1

+0.20

+8.2

-0.02

-1.5

-0.27

120

+ 7.2

+0. 18

+7.8

-0. 10

-3. 1

-0.28

126

+ 8.2

+0. 15

+7.0

-0. 17

-4.8

-0.25

132

+ 9.0

+0. 12

+5.8

-0.22

-6. 1

-0.21

138

+ 9.6

+0. 08

+4.4

-0.26

-7.3

-0. 18

144

+ 9.9

+0.03

+2.7

-0.30

-8.2

-0.12

150

+ 10.0

-0.01

+0.8

-0.33

-8.7

-0. 05

156

+ 9.8

-0. 05

-1.3

-0.33

-8.8

+0.02

162

+ 9.4

-0.08

-3.2

-0.30

-8.5

+0.10

168

+ 8.7

-0. 13

-4.9

-0.28

-7.6

+0. 15

174

+ 7.8

—0. 17

-6.5

-0.23

-6.7

+0. 20

180

+ 6.7

-0.20

-7.7

-0. 18

-5.2

+0.26

186

+ 5.4

-0.22

-8.6

-0. 11

-3.6

+0.24

192

+ 4.1

-0.22

-9.0

-0.04

-2.2

+0.26

198

+ 2.7

-0.22

-9.1

+0.02

-0.5

+0.26

204

+ 1.4

-0.22

-8.8

+0.08

+0.9

+0.23

210

+ 0.1

-0.21

-8.2

+0. 12

+2.3

+0.20

216

- 1. 1

-0. 19

-7.3

+0.17

+3.3

+0.16

222

-2.2

-0.17

-6.2

+0. 18

+4.2

+0.12

228

- 3.1

-0. 13

-5.2

+0. 18

+4.7

+0.06

234

-3.8

-0.10

-4.0

+0.19

+4.9

+0.01

240

-4.3

-0.07

-2.9

+0. 19

+4.8

-0.04

246

-4.6

-0.02

-1.7

+0. 16

+4.4

-0.06

252

-4.6

+0.01

-1.0

+0. 12

+4.1

-0.07

258

-4.5

+0.04

-0.3

+0. 10

+3.6

-0.09

264

- 4. 1

+0.07

+0.2

+0.07

+3.0

-0. 12

270

- 3.7

+0.08

+0.5

+0.03

+2.2

-0. 10

276

- 3. 1

+0.11

+0.6

+0.02

+1.8

-0. 08

2S2

-2.4

+0.12

+0.8

+0.02

+ 1.2

-0. 08

L'SS

- 1.6

+0. 12

+0.9

0.00

+0.9

-0.04

294

- 0.9

+0. 12

+0.8

-0.01

+0.7

-0. 05

300

- 0.2

+0. 11

+0.8

0.00

+0.3

-0.02

306

+ 0.4

+0.10

+0.8

+0.02

+0.4

-0.02

312

+ 1.0

+0.08

+ 1.0

+0.02

+0.1

-0.02

318

+ 1.4

+0.04

+ 1.0

+0.01

+0.1

-0.01

324

+ 1.5

+0.02

+1.1

+0.02

0.0

-0.02

330

+ 1.6

-0.01

+ 1.2

+0.02

-0. 1

-0.02

336

+ 1.4

-0.03

+1.3

+0.02

-0.2

-0.02

342

+ 1.2

-0. 06

+ 1.4

0.00

-0.3

-0.03

348

+ 0.7

-0.08

+ 1.3

-0.01

-0.6

-0.03

354

+ 0.2

-0. 10

+ 1.3

-0.02

-0.7

-0.02

360

- 0.5

-0.12

+ 1.1

-0.04

-0.8

-0.01

[ndz, 3 logr, and u/cos i are to be computed In the form Jia<sin ig+St bt cos ig+cT.''

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (179) Klytaemnestra — Continued.
TABLE IV.— u/coa i— Continued.

321

PERIODIC TERMS.

Unit of a and 6=09001.

1

2

3

9'

a2

Dili', for 1°

62

Diff . for 1°

«3

Diff. for 1°

"

Diff. for 1°

o

0

-9.2

-0.22

-4.4

+0.42

+ 1.7

+0.01

+0.2

-0. 12

6

-10.2

-0. 10

- 1.8

+0.46

+ 1.6

-0.06

-0.6

-0.12

12

-10.4

+0.03

+ 1.1

+0.47

+ 1.0

-0. 12

-1.3

-0.08

18

-9.8

+0.17

+ 3.8

+0.43

+0.2

-0.13

-1.7

-0. 02

24

- 8.4

+0. 28

+ 6.3

+0.38

-0.6

-0.12

-1.6

+0.05

30

-6.5

+0.36

+ 8.4

+0.29

-1.2

-0.10

-1. 1

+0. 10

3G

- 4. 1

+0.42

+ 9.8

+0.17

-1.8

-0.06

-0.4

+0.12

42

- 1.5

+0.43

+ 10.4

+0.05

-1.9

+0.02

+0.4

+0. 15

48

+ 1-1

+0.42

+ 10.4

II (IS

-1.6

+0.08

+ 1.4

+0.13

54

+ 3.6

+0.39

+ 9.5

-0.18

-1.0

+0.13

+2.0

+0.08

60

+ 5.8

+0.31

+ 8.2

-0.25

0.0

+0.17

+2.3

+0.03

66

+ 7.3

+0.22

+ 6.5

-0.32

+ 1.0

+0.18

+2.4

-0.02

72

+ 8.4

+0. 12

+ 4.4

-0.36

+2.1

+0.15

+2.0

-0. 12 •

78

+ 8.8

+0.02

+ 2.2

-0.36

+2.8

+0.08

+ 1.0

-0. 18

84

+ 8.6

-0.08

+ 0.1

-0.34

+3.2

+0.01

-0.2

-0.20

90

+ 7.9

-0.15

— 1.9

-0.29

+2.9

-0.08

-1.4

-0. 19

96

+ 6.8

-0.21

-3.4

-0.21

+2.3

-0. 13

-2.5

-0. 17

102

+ 5.4

-0.24

-4.4

-0.12

+ 1.3

-0.21

-3.4

-0. 10

108

+ 3.9

-0.24

-4.9

-0.05

-0.2

-0.23

-3.7

-0.01

114

+ 2.5

-0.22

- 5.0

+0.02

-1.5

-0.22

-3.5

+0.08

120

+ 1.2

-0.18

-4.7

+0.07

-2.8

-0.18

-2.7

+0.16

126

+ 0.3

-0. 12

-4.2

+0. 11

-3.7

-0. 10

-1.6

+0.22

132

- 0.3

-0.07

- 3.4

+0.13

-4.0

-0.01

-0.1

+0.25

138

- 0.5

-0.01

-2.6

+0.12

-3.8

+0. OS

+ 1.4

+0.24

144

- 0.4

+0.04

- 1.9

+0.09

-3.1

+0.17

+2.8

+0.19

150

0.0

+0.08

- 1.5

+0.05

-1.8

+0.23

+3.7

+0. 11

156

+ 0.5

+0.08

-1.3

-0.01

-0.3

+0. 25

+4.1

+0.02

162

+ 1.0

+0. OS

- 1.6

-0.06

+ 1.2

+0.24

+3.9

-0.08

168

+ 1-4

+0. 04

- 2.0

-0.10

+2.6

+0. 19

+3.2

-0. 17

174

+ 1.5

0.00

- 2.8

-0. 13

+3.5

+0.11

+ 1.9

-0. 23

180

+ 1.4

-0.06

-3.6

-0.13

+3.9

+0.02

+0.4

-0.24

186

+ 0.8

-0.12

-4.4

-0. 14

+3.8

-0.08

-1.0

-0.22

192

0.0

-0. 17

-5.3

-0.12

+3.0

-0.17

-2.3

-0. 19

198

— 1.2

-0.23

- 5.8

-0. 05

+1.8

-0.22

-3.3

-0. 11

204

-2.8

-0.26

- 5.9

+0.02

+0.4

-0.23

-3.6

0.00

210

-4.3

-0.26

-5.6

+0.08

-1.0

-0.22

-3.6

+0.08

216

- 5.9

-0. 25

-4.8

+0.18

-2.2

-0.16

-2.6

+0.14

222

-7.3

-0.20

- 3.4

+0.25

-2.9

-0.08

-1.6

+0.20

228

-8.3

-0.12

- 1.8

+0.31

-3.2

-0.01

-0.2

+0.22

234

-8.8

-0.04

+ 0.3

+0.37

-3.0

+0.08

+ 1.0

+0.19

240

- 8.8

+0.06

+ 2.6

+0.37

-2.2

+0. 15

+2.1

+0. 15

246

- 8.1

+0. 17

+ 4.7

+0. 35

-1.2

+0.19

+2.8

+0.08

252

-6.8

+0.26

+ 6.8

+0. 31

+0.1

+0.20

+3.0

-0.02

258

- 5.0

+0.35

+ 8.4

+0.22

+ 1.2

+0.18

+2.6

-0.10

264

-2.6

+0.41

+ 9.5

+0. 12

+2.2

+0.12

+1.8

-0. 15

270

- 0.1

+0.43

+ 9.9

+0.01

+ 2.7

+0.04

+0.8

-0.18

276

+ 2.6

+0.42

+ 9.6

-0.11

+2.7

-0.03

-0.3

-0.18

282

+ 5.0

+0.38

+ 8.6

-0.22

+2.3

-0.11

-1.4

-0. 15

288

+ 7.1

+0.31

+ 6.9

-0.33

+1.4

-0.15

-2. 1

-0.09

294

+ 8.7

+0.21

+ 4.6

-0.42

+0.5

-0.17

-2.5

-0. 03

300

+ 9.6

+ 0. 08

+ 1.9

-0.45

-0.6

-0.17

-2.5

+0.04

306

+ 9.7

-0.04

- 0.8

-0.46

—1.5

-0.12

-2.0

+0.12

312

+ 9.1

-0. 17

-3.6

-0.43

-2.0

-0.06

-1.1

+0. 15

318

+ 7.7

-0.29

- 6.0

-0.36

—2. 2

-0.01

-0.2

+0.16

324

+ 5.6

-0.39

-7.9

-0.28

-2.\

+0. 05

+0.8

+0. 14

330

+ 3.0

—0.44

-9.3

-0. 17

-1.6

+0.12

+1.5

+0.09

336

+ 0.3

-0.47

-9.9

-0.02

-0.7

+0.15

+ 1.9

+0.03

342

- 2.6

-0. 46

-9.6

+0.11

+0.2

+0.14

+ 1.9

-0.02

348

- 5.2

-0.41

- 8.6

+0.23

+ 1.0

+0. 11

+ 1.6

-0.08

354

-7.5

-0.33

- 6.8

+0.35

+ 1.5

+0.06

+0.9

-0. 12

360

-9.2

-0.22

- 4.4

+0.42

+ 1.7

+0.01

+0.2

-0. 12

[ndz, <J log r, and u/cos ! are to be computed in the form J,- a\ sin ig+Ii bt cos ig+cT.]

322 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tatkes of {179) Klytaemnestra — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T = lt-t„) IN JULIAN YEARS.

ndz

o log r

w/cos i

9

Unit, of c

=0?001

Unit of c

=0.00001

Unit of c

=0?001

c

Diff. for 1°

c

Diff. for 1°

c

Diff. for 1°

O

0

-2.48

+0. 004

-0.11

-0. 018

-0.36

-0. 061

6

-2.44

+0. 010

-0.21

-0. 018

-0. 73

-0. 059

12

-2. 30

+0. 015

-0.32

-0.018

-1.06

-0. 056

18

-2.26

+0. 018

-0.42

— 0. 016

-1.40

-0. 054

24

-2. 14

+0. 023

-0.51

-0. 015

-1.72

-0. 052

30

-1.98

+0. 028

-0.60

-0. 013

-2.02

—0. 045

36

-1.80

+0. 030

-0.67

-0. 012

-2.26

-0. 038

42

-1.62

+0. 033

-0.74

-0.011

-2.48

-0. 034

4S

-1.40

+0. 037

-0.80

-0. 008

-2.67

-0. 028

54

—1.18

+0. 038

-0.84

-0. 008

-2.82

-0. 022

60

-0.94

+0. 041

-0.89

-0. 006

-2.94

-0. 017

66

-0.69

+0. 042

-0.92

-0. 003

-3.02

-0. 010

72

-0. 44

+0. 042

-0. 93

-0. 001

-3.06

-0. 004

78

-0. 18

+0. 042

-0.93

0.000

-3.07

+0. 002

84

+0.07

+0. 042

-0. 93.

+0. 002

-3.04

+0. 008

90

+0.32

+0. 042

-0.91

+0. 003

-2.98

+0. 013

96

+0. 57

+0. 040

-0.89

+0. 006

-2.88

+0. 018

102

+0.80

+0. 038

-0.84

+0. 008

-2.76

+0. 022

108

+ 1.03

+0. 038

-0.80

+0. 008

-2.62

+0. 027

114

+ 1. 25

+0. 034

-0.76

+0. 008

-2.44

+0. 032

120

+1.45

+0. 032

-0.70

+0. 010

—2.23

+0. 035

126

+1. 64

+0. 029

-0.64

+0. 01 1

-2.02

+0. 038

132

+1.80

+0. 025

-0.57

+0. 012

— 1. 78

+0. 043

138

+ 1. 94

+0. 022

-0.50

+0.012

—1.50

+0. 043

144

+2.07

+0. 019

-0.42

+0. 014

-1.26

+0. 043

150

+2.17

+0. 015

-0.33

+0. 014

-0.98

+0. 047

156

+2. 25

+0. 012

-0.25

+0. 013

-0.70

+0. 047

162

+2.31

+0. 008

-0.17

+0. 013

-0.42

+0. 048

168

+2. 34

+0. 003

-0.09

+0. 014

-0.13

+0. 048

174

+2.35

0.000

0. 00

+0. 014

+0. 16

+0. 049

180

+2.34

-0. 004

+0.08

+0. 014

+0.46

+0. 049

186

+2.30

-0. 008

+0.17

+0. 013

+0.75

+0. 048

192

+2.24

-0. 012

+0.24

+0. 013

+ 1.03

+0. 046

198

+2. 16

-0. 015

+0.33

+0. 013

+ 1.30

+0. 044

204

+2. 00

-0. 020

+0. 40

+0. 013

+ 1.56

+0. 043

210

+ 1.92

-0. 023

+0.49

+0. 012

+ 1.82

+0. 040

216

+1.78

-0. 025

+0.55

+0.011

+2.04

+0. 036

222

+1.62

-0. 028

+0.62

+0.011

+2.26

+0. 034

228

+ 1.44

-0. 032

+0.68

+0. 010

+2. 45

+0. 032

234

+ 1.24

-0. 035

+0.74

+0. 009

+2.64

+0. 028

240

+ 1.02

— 0. 038

+0. 79

+0. 008

+2.80

+0. 023

246

+0. 79

-0. 038

+0.83

+0. 006

+2. 92

+0. 018

252

+0. 56

-0. 039

+0.86

+0. 005

, +3. 02

+0.016

258

+0. 32

-0. 041

+0.89

+0. 003

+3.11

+0. 012

264

+0.07

-0. 042

+0.90

+0. 002

+3. 16

+0. 004

270

-0.18

-0. 042

+0.91

0.000

+3. 16

-0. 002

276

-0.43

-0. 042

+0.90

-0. 002

+3. 14

-0. 007

282

-0.68

-0. 042

+0.89

-0. 002

+3.08

-0. 012

288

-0.93

-0. 041

+0.86

— 0. 005

+3. 00

-0. 017

294

— 1. 17

-0. 038

+0.83

-0. 007

+2.88

-0. 024

300

-1.39

—0. 036

+0.78

-0. 008

+2.71

-0. 030

306

-1.60

-0. 034

+0.73

-0. 010

+2.52

-0. 036

312

-1.80

-0. 031

+0.66

-0. 012

+2.28

-0. 043

318

-1.97

-0. 028

+0.59

-0. 014

+2.00

-0. 047

324

-2. 13

-0. 023

+0.49

-0. 016

+1.72

-0. 050

330

-2.25

-0. 018

+0.41

-0.016

+ 1.40

-0. 053

336

-2.35

-0. 015

+0. 31

-0.017

+ 1.08

-0. 055

342

-2.43

-0.011

+0.21

-0.017

+0.74

-0. 059

348

-2.48

-0. 005

+0. 11

-0. 018

+0.37

-0. 062

354

-2.49

0.000

0.00

-0. 018

0.00

-0. 060

360

-2.48

+0. 004

-0. 11

-0. 018

-0.36

-0. 061

[ndz, (J log r, and u/cos i are to be computed in the form 1't at sin ig+li bi cos ig-t-cT.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

323

Tables of (179) EJytaemnestra — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

log cos a

log (•( is b

log cos c

1877. 0
1930. 0

9. 113 n
9. 115 n

9. 554 n
9. 556 n

9.966
9.966

Year

A'

B'

C"

log sin a

log sin b

log sill C

1877.0

O

83. 6776

O

350. 8069

o

12. 1875

9. 99632

9. 97022

9. 58051

8

.6917

. 8205

20 12

32

022

054

9

. 7058

.8341

.2149

31

021

058

1880

83.7198

350. 8477

12. 2286

9.99(131

9.97021

9. 58061

1

. 7339

.8613

2423

31

020

064

2

.7480

. 8749

. 2560

31

020

068

3

. 7(120

KSN5

. 2697

31

019

071

4

. 7761

. 9021

2S3I

31

019

074

1S85

S3. 7901

350.9157

12.2971

9. 99631

9. 97018

9. 58078

6

. 8042

. 9292

3109

31

018

081

7

.8183

.9428

. 324(1

31

017

085

8

. 8324

.9564

. 3383

31

017

088

9

. 8465

.9700

. 3520

31

016

092

1890

83. 8605

350. 9836

12.3657

9. 99631

9. 9701(1

9. 58095

1

.8745

350. 9972

.3794

31

015

099

2

SSM,

351. 0108

3931

31

015

102

3

.9027

.0244

.4068

30

014

106

4

.9167

o:js(i

. 4205

30

014

109

1895

83.9308

351. 0516

1 2. 1342

9. 99630

9. 97013

9. 58113

6

.9448

.0651

.4480

30

013

116

7

. 9589

.0787

. 4617

30

012

119

8

.9730

. 0923

. 4754

30

012

123

9

83. 9870

. 1059

ism

30

011

126

1900

84. 0011

351. 1195

12. 5028

9. 99630

9. 97011

9. 58130

1

.0152

. 1331

. 5165

30

010

133

2

.0292

. 1467

. 5302

30

010

137

3

.0433

.1603

. 5439

30

009

140

4

. 0574

. 1739

. 5576

30

009

144

1905

84. 0714

351. 1875

12.571:;

9. 99630

9. 9700S

9. 58147

6

. 0855

.2010

585 1

30

008

151

7

. 0995

.2146

. 5988

30

007

154

8

. 1136

. 22S1J

.6125

29

007

158

9

. 1277

. 2418

. 6262

29

006

161

1910

84. 1417

351. 2554

12. 6399

9. 99629

9. 9700(1

9. 58165

1

. 1558

.2690

.6536

29

005

168

2

. 1699

.2826

. 6(173

29

005

171

3

. 1839

2962

.6810

29

004

175

4

. 1980

mas

.6947

29

004

I7S

1915

84. 2120

351. 3234

12. 7084

9. 99(129

9. 97003

9. 58182

6

. 2261

. 3369

. 7222

29

003

185

7

.2402

. 3505

. 7359

29

002

188

8

. 2512

. mm

. 7496

29

002

192

9

.2683

.3777

. 7633

29

001

195

1920

84. 2821

351. 3913

12. 7770

9. 99629

9. 97001

9. 58199

1

. 2961

.4049

. 7907

29

000

203

2

. 3105

1 1 85

son

29

9. 97000

206

3

3246

1321

.8181

28

9. 96999

210

4

.3386

1 157

. 8318

28

999

213

1 925

84. 3527

351. 4593

12. 8455

9. 99628

9. 96998

9. 582 1 7

6

. 36(17

. 4728

. 8593

28

998

220

7

.3808

4864

. 8730

28

997

223

8

.3949

. 5000

.8867

28

997

227

9

.4089

. 5136

.9004

28

996

230

1930

84. 4230

351. 5272

12.9141

9. 99628

9. 96996

9. 58234

TABLES

OF

(101) HELENA. (103) HERA. (119) ALTHAEA.

The perturbations are tabulated in the forms
ndz = (noz)1 + (noz)2 + .... + (ndz)tT— cz
d log r={d log r), + (d log r)2 + . . . + (8 log r), T- cT

325

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

327

TABLES OF (101) HELENA.

OSCULATING ELEMENTS.

Epoch ami osculation, L877, Dec. 10.0, M. T. Berlin=1877.042, M. T. Berlin.

o / //

0O= 99 46 33= 99?7757

w=343 57 7=343.9519]

fi=343 39 43=343. 6620 Mean equinox and ecliptic 1880.0.

i= 10 9 51= 10. 1642 J
= 7 55 16= 7.9210

n=854. "4377 = 0.23734381

g0 and n are mean elements.
The elements are based on oppositions extending from 1868 to 1899 and on the perturbations of the first
order by Jupiter, as given on page 329.

AUXILIARY QUANTITIES.

loga=0.41222
log e=9.13928

log 57
log p

2958e=0.89740
=0.40389

Log fi

+e

=9.93977

NUMERAL DESIGNATION OF THE ARGUMENTS FOR TABLES II-V.

1= g-ty'

2= 9
3= g- 9'

4= g-2g'
b=2g-Sg'
6= - ;,'
7=2g- g'

8= g-ig'
9= 2g-bg'
10= Zg—4g'
11= Sg-bg'
12= 4g-:lg'
13= 3g-2g'
14=-jr- g>

15= 4g-bg'
16= 4g-lg'
17= bg-4g'
18= bg-6g'
19= bg-Za'
20= -g-2g'
21= g—bg

CONSTANTS TO BE SUBTRACTED FROM THE TABULATED PERTURBATIONS.

cz=0?9227 cr=0.00224 c,j=0.00263

Derivation of c-. cr, c. (See also page 208)

Arg.

n8z

0 log r

s?

Arg.

71(52

0 log T

Sp

s

p
B

1-11

Unit=0?001

Unit=0.00001

Unit=0.00001

11-21

Unit=0?001

Unit=0.00001

Unit=0.00001

"3

1

307. 97

11.4

17.9

sum

916.46

213.8

243. 8

M ■

2

231. 97

87.5

87.7

12

0.78

0.7

0.9

3

102. 78

37. 8

9.8

13

3.22

■1. 7

1.2

4

106. 58

16.4

IS. 9

14

1.03

0.5

4.4

o ^

5

148. 00

.".4. 6

82.4

15

0.72

0.4

0.5

^a

6

5.67

0.9

16.5

16

II 17

0. 1

.8 £

12 -^

7

2. 39

1.6

4.4

17

0. 14

0.1

8

0.44

0. 1

1.0

18

0. 22

0.1

9

3.47

0.3

0.2

19

0.1

QQ

10

4.36

2. 1

2.2

20

1. 1

a

11

2.83

1. 1

2.8

21

2.1

o
O

Sum

916. 46

213. 8

243. 8

Sum

922. 7

218.5

254. 0

c2=0?9227

er=0. 002185— (constant part of o log r+correction for difference between mean and
osculating values of semi-major axis)
=0. 002185-(-112".33+88//.49)sin 1" Mod.
=0.002185+0.000050.
=0. 00224

c„=0. 002540— (constant part oi Bp)
'=0.002540+0.000087
=0. 00263

328 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (101) Helena— Continued.

TABLE I.— MEAN ANOMALY (gj.

Jan. 0.0 of common year

s; Jan

1.0 of leap years

Table for beginning of month

Year

g

Year

9

Month

9

B 1868

o

317. 98033

1900

O

211. 81744

t /0.0
Jan. |x Q

O

]■ 0. 00000

9

44. 61082

1

298. 44793

1870

131. 24131

2

25. 07842

Feb.{°;°

\ 7. 35766

1

217.87180

3

111. 70891

B 2

304. 73964

B

4

198. 57674

Mar. 0.0

14. 00328

3

31. 37013

5

285. 20723

Apr. 0.0

21. 36094

4

118. 00062

6

11. 83772

May 0.0

28.48126

5

204.63111

7

98. 46821

June 0.0

35. 83892

B 6

291. 49894

B

8

185. 33605

July 0.0

42. 95923

7

18. 12943

9

271. 96654

Aug. 0.0

50. 31689

8

104. 75992

1910

358. 59703

Sept. 0.0

57. 67455

9

191. 39041

1

85. 22752

Oct. 0.0

64. 79486

B 1880

278. 25825

B

2

172. 09536

Nov. 0.0

72. 15252

1

4. 88874

3

258. 72585

Dec. 0.0

79. 27283

2

3

B 4

91. 51923
178. 14972
265. 01756

4

5
6

345. 35634

71.98683

158. 85466

B

5

351.64805

7

245. 48515

Change for n days a

6

7

78. 27854
161.90903

8
9

332. 11564
58. 74613

y

/),

9

B 8

251. 77686

B

1920

145.61397

9

338. 407:;:.

1

232. 24445

1890

65. 03784

2

318. 87495

0

o

1

151.66833

3

45. 50544

1

0. 23734

16

3. 79750

B 2

238. 53612

B

4

132. 37327

2

0. 47-169

17

4. 03484

3

325. 16666

5

219.00376

3

0. 71203

18

4. 27218

4

51.79715

6

305. 63426

4

0. 94937

19

4. 50953

5

138. 42764

7

32. 26475

5

1.18671

20

4. 74687

B 6

225. 29547

B

8

119. 13258

6

1.42406

21

4. 98422

7

311.92596

9

205. 76307

7

1.66140

22

5. 22156

8

38. 55646

1930

292. 39356

8

1. 89874

23

5. 45890

1899

125. 18695

9
10
11

2. 13609
2. 37343
2. 61078

24
25
26

5. 69625
5. 93359
6. 17094

Note.— Wh

en g is used us ai

argument, of th

e perturbations.

12

2.84812

27

6. 40828

add to the g o

f this table An=

rt— 7i0 =

= +0?1071

For explana-

13

3.08546

28

6.64562

tion see page

203.

14
15

3. 32281
3. 56015

. 29
30

6. 88297

7. 12031

" for days during January and

February of leap years subtract one

day before entering this table.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

339

Tables of (101) Helena — Continued.

PERTURBATIONS.

Arg.

noz

V

tt/C08 i

sin

cos

sin

cos

sin

cos

i V

//

// ,

//

//

//

//

0 -0

-112.33

- 6.97

0 -0

+ 0. 241nt

+ 1 o

+

832.0

+ 76.4

+ 37.9

-412. 5

+53.6

+44.4

+1

+

0. CiOsiii

7. 382nt

:;. 691nt

0. 304nt

+ 1. 158nt,

+ 3. OOOnt

+2

+

1.2

- 0.0

0.0

- 1. 1

- 0.4

+ 0.0

+2

+

0.021m

0. 161 111!

I). I60nt

0.021m

+ 0. 079nt

+ 0. 206nt

+3 0

+

0.2

+ 0. 0

0. 1

+ 0.2

-2 -1

—

0.2

+ 0. 1

0. 1

+ 0.1

- 0. 1

-1

—

2.8

+ 2.4

- 1.6

- 1.8

+ 2.4

- 2.5

0

—

0.8

+ 17.3

- 1.3

+ 1.4

+ 7.2

- 4. 1

+ 1

—

103.6

+ 114.9

+ 40.4

+ 36.3

- 5.4

+ 0.2

+ 2

—

4.2

+ 6. S

+ 5. 1

+ 3.3

+ 1.6

- 3.2

+3 -1

—

0. 1

+ 0.2

+ 0.2

- 0.2

-1 -2

+

0.4

+ 0.6

(i. 2

+ 0.2

- 0. 1

+ 0.9

0

+

3.1

- 1. 1

0. 9

+ 1.3

- 1.8

+ 9.6

+1

—

48.3

-365.0

- 81.8

+ 9.9

+ 7.4

-13.0

+ 2

—

13.4

-257.2

-152.4

+ 7.9

- 0.8

- 2.0

+ 3

- Il.fi

- 12.6

0. 2

- 0.1

- 1.0

+4 -2

—

0.1

1.0

1.5

+ 0.1

- 0. 1

0 -3

—

1.5

- 3. 6

+ 1.9

0.9

+ 4.7

+ 1.4

+ 1

+ 104

-462. 3

+ 15. 1

+ 50.8

+ 8.7

+ 10.9

+2

—

532. 0

- 17.5

- 10. 1

+ 258.5

-40.8

-51.9

+3

—

35.5

- Hi. 6

- 12.3

+ 30. 2

- 2.5

- 3.7

+4

—

2.4

- 1.4

1.6

+ 3.2

- 0.5

- 0.5

+5 -3

—

0.3

II. 2

- 0.2

+ 0. 5

+ 1 -4

+

1.6

+ 0.1

- 0.4

+ 0.2

+ 0.3

+ 0.7

+2

+

10.8

- 18.0

- 6.9

4.3

- 3.0

- 1.8

+3

+

11. 1

- 11.0

7.3

6.8

- 1.8

+ 0.1

+4

—

4.5

■ 0.2

0. :'.

+ 3.5

+ 0.2

- 0. 1

+5

—

0.6

0. 1

0. 1

+ 0.6

- 0.1

+6 -4

—

0. 1

+ 0.1

+ 1 -5

- 1.7

+ 2

+

6.1

+ 10.8

+ 1.3

0.5

+ 0.1

+ 0.3

+3

+

3.8

+ 9. 1

+ 5.2

- 2. 1

- 0.1

+ 2. 2

+4

+

0.1

2.6

1.8

+ 0.4

- 0. 1

+5

—

0.8

+ 0.9

+ l',7

+ 0.8

+6 -5

—

0.2

+ 0.1

+ 0.1

+ 0.2

+2 -6

—

15.6

- 27. 4

+ 1.0

- 1.8

- 0.3

- 0. 1

+3

+

8.3

0.5

0.2

4.0

+ 1.1

+ ii. :;

+4

+

1.5

+ 0.4

+ 0.2

1.0

+ 0.3

+ 0.2

+5

—

0.6

— 0. 6

0.4

+ 0.4

- 0.1

+6

+ 0. 4

0.3

+ 7 -6

+ 0. 1

+ 0.1

+ 4 -7

0.4

+ 0.4

+ 0.2

+ 0.2

- 0.1

+ 5

+

o. :;

0. 2

- 0. 1

— 0.2

+ 0.1

+ 0

—

0.3

+ 0.2

+7 -7

+

0.1

+ 0.1

+ 0. 1

■ 0. 1

+5 -8

+ 0. 1

+ 0. 1

+ 6

- 0. 1

- (1. 1

+ 7 -8

—

0.1

+ 0.1

+ 0. 1

+ 0.1

+ 7 -9

0.1

1). 1

+8 -9

+ 0. 1

The constant part in n8z is included in the element g0.

The nontrigonometrical term multiplied by the time in ndz is included in the element n.

The ciinstanl part of v is included in the constant cr.

The constant part of u cos i is included in the constant c».

All other terms are contained in Tables II-V.

330

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.
Tables of (101) Helena — Continued.

TABLE II.— doc

Args.1-5

(nBz)l

Diff. for 1°

(ndz).

Diff. for 1°

(ndz)3

Diff

fori0

i nSz)t

Diff. for 1°

- ndz i,

Diff. fori"

o

0

172.0

+ 17.59

253.1

+ 14. 50

58.9

4.48

0.0

-0. 10

143. 3

-9.22

6

202.1

+ 18.56

277. 2

+ 14.29

53.0

—

2.52

0.6

+0.70

127.9

-9.17

12

233. 7

+ 19.36

300. 7

+13. 96

50.7

—

0.30

2.3

+ 1.42

112.7

-8.98

18

266. 5

+19.91

323. 6

+ 13. 49

52.1

+

2.01

5.3

+2. 12

98.0

-8.70

24

299.9

+20. 20

345. 5

+12. 79

57.3

+

4.15

9.3

+2. 72

83.8

-8.33

30

333.7

+20. 30

366.2

+11. 96

65.8'

+

5.94

14.3

+3.26

70.3

-7.88

36

367. 1

+20. 17

385.2

+10. 96

77.0

+

7.50

20.1

+3.70

57.6

-7.34

42

400. 8

+19.81

402. 7

+ 9.93

90.5

+

8 46

26.6

+4.04

45.9

-6. 67

48

433.3

+ 19.18

418.2

+ 8.71

104.8

+

8.70

33.6

+4.46

35. 3

-6. 02

54

464.6

+18. 27

431. 6

+ 7.47

119.1

+

8.29

41.4

+4.78

25. 9

-5. 26

60

494. 1

+ 17. 15

443. 1

+ 6.10

132. 3

+

7. 07

49.5

+5. 03

17.9

-4.40

66

521. 6

+15. 84

151. 9

+ 4. 63

143. 5

+

5. 94

58.1

+5. 27

11.2

-3.54

72

546.8

+ 14. 28

458.5

+ 3.22

151. 9

+

4. 04

67. 1

+5. 46

6.0

-2. 63

78

569. 1

+12. 52

462. 6

+ 1.66

156. 8

+

1.81

76.4

+5.71

2.5

-1.70

84

588. 4

+10. 66

464. 1

+ 0. 14

L57.8

—

0.53

86.1

+5. 86

0.4

-0. 73

90

604. 5

+ 8. 62

163. 1

- 1.32

155. 1

—

2.78

95.9

+5. 92

0.1

+0. 26

96

617. 1

+ 6.48

459. 6

- 2.87

148.6

—

4.96

105.8

+6.05

1.3

+1.24

102

626 1

+ 4.24

453. 5

- 4.38

138.8

—

6.78

116.0

+6.08

4.2

+2.20

108

631.2

+ 1.93

445. 1

- 5.80

126 2

—

8.29

126.0

+5. 96

8.6

+3. 12

114

632.3

- 0.33

434.2

- 7.14

111.4

—

9.36

135. 8

+5. 84

14.6

+4.03

120

030. 1

- 2.62

421.3

- 8.48

95.2

—

9.95

145. 5

+5. 66

22. 1

+4.90

126

623.8

- 4.88

406.1

- 9.70

78.4

10.14

154. 6

+5. 37

30.9

+5. 72

132

613.8

- 7.05

389. 1

-10.71

61.7

—

9.82

163. 3

+5. 01

41.1

+6. 42

1 18

600. 3

- 9. 12

370. 5

-11.65

45.9

—

9.06

171. 3

+4. 58

52.3

+ 7.11

144

583. 5

-11.03

350. 3

-12.55

31.7

—

7.95

178. 6

+4.08

64.7

+ 7. 74

150

563. 6

-12.80

328.8

-13.22

19.6

—

6.53

|S1 II

+3.54

78 0

+8.23

156

541. 0

-14.36

306.3

-13.80

10.1

—

4. SI

190.4

+3. 03

92.1

+8. 65

162

515. 8

- 15. 75

282.9

-14.23

3.6

—

2.94

195. 0

+2. 46

106.8

+8.96

168

488 5

-16. 97

259. 0

-14.48

0.4

—

0. 96

198.6

+1.87

121. 9

+9. 24

174

459. 4

-17.93

234. 8

-14.54

0.4

+

1.04

201. 2

+ 1.38

137. 4

+9.33

180

128. 8

-18.70

210. 6

-14. 4S

3.8

+

2.93

203. 1

+0.76

153. 0

+9. 31

186

397.1

-19.24

186.6

1 1. 26

10.2

+

4.73

203.9

+0.26

16S. 4

+9.24

192

361 S

19 57

Id:; 2

-13. s7

19.4

+

6.30

204. 0

0. 2.".

is:; 7

+9.07

198

332. 1

-19.65

140.4

-13. 40

31.0

+

7. 58

203. 1

-0. 78

198.6

+8. 76

201

299.4

-19.53

118.6

-12.71

44.6

+

s 65

201.4

-1. 22

212 9

+8.38

210

267. 1

-19.20

98.1

-11.85

59. 7

+

9.40

199.0

-1.73

226.5

+7. 92

216

235. 5

-18. 70

79. 2

-10.92

75. 7

+

9.81

195. 6

-2.23

239. 2

+ 7.34

222

204.9

-IS. 1)1)

61.8

- 9.89

92. 2

+

9.98

191. 5

-2.73

250. 9

+6.68

228

175. 6

-17. 14

46.2

- 8.71

108.8

+

'1 ss

IS!, :,

-3.28

261.4

+5.97

234

147. S

-16. 12

32.8

- 7. I'l

125. 0

+

9.52

ISO. 6

-3.80

270.8

+5. 18

240

121.9

-14. 95

21.3

- 6. 13

140.4

+

8.90

173. 9

-4. 34

27S. 7

+4. 34

246

98.1

-13.71

12.4

- 4. 67

154. 6

+

8.10

166. 1

-4.88

285. 2

+3.46

252

76.3

-12. 28

5.8

- 3.20

167.3

+

7.12

157. 6

5. 38

290.2

+2. 53

258

57. 2

-10. 76

1.7

- 1.74

L78. 2

+

5.94

148.2

-5. 92

293. 6

+ 1.58

264

lii 5

- 9.18

0.0

- 11.21

187. 0

+

4. 57

137. 9

-6.32

295. 4

+0.60

270

26.6

- 7.51

0.9

+ 1.26

193. 4

+

3.08

127. 1

-6.69

295. 7

-0. 33

276

15.5

- 5.76

4.2

+ 2.80

197. 2

+

1 . 57,

115. 6

7 Oil

294. 3

-1.31

282

7.3

- 4.01

10.2

+ 4.30

198. 5

0.08

103.8

-7.22

291.3

-2.28

288

2.1

- 2.19

18.5

+ 5. 71

197.0

—

1.6S

91.6

-7. 31

286. 8

-3. 1!)

294

0.1

- 0.33

29. 1

+ 7.07

192. I)

—

3.27

79.5

-7.22

2S0. 7

-4. OS

300

1. 1

+ 1. 53

42.1

+ 8.40

1S6. 0

—

4.83

ii7 i;

-7.04

273.2

-4. 93

300

5.2

+ 3.41

57.1

+ 9.62

176.9

—

6. 13

5(1, 1

-6. 7 1

264.3

-5. 71

312

12.4

+ 5. 25

74.1

+ 10.70

165. 7

—

7. 32

45. 2

-6.32

254. 2

-6. 43

318

22. 7

+ 7.07

92.7

+ 11.07

152. 6

—

8.29

35.1

-5. 73

242. 9

-7.07

324

36! 0

+ 8.88

112.9

+ 12. 56

L38 2

—

8.89

26. 2

-5.04

230. 6

-7.70

330

52. 2

+10. 58

134. 5

+ 13.15

123. 1

—

!). 16

18.3

-4. 30

217.3

-8.20

336

71.2

+ 12. 25

157. 0

+ 13. 82

107. 9

—

9.09

11.9

-3. 50

203. 1

-8. 54

342

92. 9

+ 13. 75

180. 5

+ 14.28

93. 1

—

8.58

6.7

-2.65

188.9

-8.90

348

117. 1

+ 15. 23

20 1 5

+ 14.57

79. 5

—

7.61

3. 1

-1.74

173. S

-9.17

35 1

1 13 6

+ 16. 19

228.9

+ 14.59

67 9

—

6.23

0.9

o. 92

158. 6

-9.18

360

172.0

+ 17 59

253.1

+ 14. 50

58. 9

1. 48

0.0

-0.10

143.3

-9.22

[>?2=(

iaz)i+(na

• ., ■

lT-cz.]

PERIODIC TERMS.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (101 1 Helena — Continued.
TABLE II.— ndz— Continued.

331

Unit=0°001.

Aig's.

6-18

(n8z)6

(nSz)l2

O

0

9.2

4.0

o. 5

li. 5

1.3

5. 4

0.4

0.0

1.7

0.0

0 3

0. 1

0. 1

10

9.3

3.8

0. li

(i. 7

1.9

-, i.

0.3

0.0

1.6

0 0

0.3

0.1

0.0

20

9.6

3.6

0.6

6.9

2. i;

•V 7

0.2

0.2

1.4

0. 1

0.3

0.1

0. 0

30

9.9

3.3

0.7

6.9

3 .;

r,. i;

0.1

0.4

1.2

0.2

0. 2

0.0

0.0

40

10.1

3.0

0.8

6.9

4.0

0.1

0.8

1. 1

o 2

0.2

0.0

0.0

50

10.1

2.8

0.8

li. 7

I 8

5.3

0.0

1. 1

0.9

0.3

0.2

0.0

0.0

60

9.8

2.5

0.8

6.4

5.1

0.0

1.6

0.7

0.4

0.1

0.0

0.0

70

9.0

2.1

0.9

6. 1

ii 2

4.7

0.0

2.1

0.5

0.5

0.1

0.0

0.0

80

7.8

1.9

0.9

5.7

6.9

4.3

0. 1

2.7

0.4

0.6

0.1

0.0

0.0

90

6.2

1.6

0. 9

7 1

:: 9

(1. 1

;; 2

0.3

0.8

0.1

0.0

0.1

100

4.5

1.2

0.9

4.6

7.9

3.4

0.2

3.8

0.1

0.9

0.1

0.0

0.1

110

2.S

0.9

0.9

4. 1

8.3

2. 9

0.3

1 . :;

0.1

1.0

0.1

0.0

0.1

120

1.5

0. (i

0.9

3.4

s. .:

2.4

0.4

4.8

0.0

1.1

0.0

0.0

0.2

130

0.5

0. 3

0.8

2.8

8.7

1.9

0.5

5.3

0.0

1.2

0.0

0.0

0.2

140

0.1

0.1

0.8

2. :;

8.7

1.5

0.7

5.7

0.0

1.3

0.0

0.1

0.3

150

0.1

0.0

0.7

1.7

8.6

1.1

0.8

6. 0

0.1

1.4

0.0

0. 1

0.3

160

0.4

0.0

0.6

1.2

8.3

0.7

0.9

6.3

0.1

1.4

0.0

0. 1

0.3

170

1.0

0.1

0. 6

0.8

7.9

0.4

1. 1

6. 1

0.3

1.4

0.0

0.1

0.4

180

1.6

0.2

0.5

0.5

7.4

0.2

1.2

li. 4

0.4

1.4

0.1

0.2

0.4

190

2.0

0.5

0.4

0.2

6.8

0. 1

1.3

6.4

0.5

1.4

0.1

0.2

0.4

200

2.4

0.8

0.3

0.1

6.2

0. 0

1.4

6.3

0.7

1.4

0.1

0.2

0.4

210

2.6

1.2

0.3

0.0

."». 1

0.0

1.5

'6.0

0.8

1.4

0.1

0.3

0.4

220

2.8

1.6

0. 2

0.1

4.7

0. 2

1.5

5.7

1.0

1.3

0.1

0.3

0.4

230

3.0

2.1

0.2

0.2

3.9

0.3

1.5

5.3

1.2

1.2

0. 2

0.3

0.4

240

3.4

2.6

0.1

0. 5

3.2

0.6

1.6

4.8

1.4

1.1

0.2

0.3

0.4

250

3.9

3.0

0. 1

0. S

2.5

0.9

1.5

4.3

1.5

0.9

0.2

0.3

0.4

260

4.8

3.5

0.0

1.3

1.8

1 . 3

1.5

3.8

1.7

0.8

0.3

0.3

0.4

270

5.8

3.8

0.0

1.8

1.3

1.8

1.4

3.2

1.8

0.7

0.3

0.3

0.4

280

6.9

4. 1

0.0

2.3

0.8

2.3

1.3

2.7

1.9

0.6

0.3

0.3

0.4

290

7.9

4.3

0.0

2. 9

0.4

2.8

1.2

2.1

2.0

0.4

0.3

0.3

0.3

300

8.7

4.5

0. 1

3.5

0. 1

3.2

1.2

1.6

2.0

0.3

0.3

0.3

0.3

310

9.2

4.6

0. 1

4. 1

0.0

3. 7

1.0

1.1

2.1

0.2

0.3

0.3

0.2

320

9.5

4.5

0.2

4.7

0.0

4.2

0.9

0.8

2.1

0.1

0.3

0.2

0.2

330

9.4

4.5

0.3

5.2

0.2

4.5

0.8

0.4

2.0

0.1

0.3

0.2

0.2

340

9.3

4.3

0.3

5.7

0.4

4.9

0.6

0.2

1.9

0.1

0.3

0.2

0.1

350

9.2

4.1

0.4

6.1

0.8

5. 2

0.5

0.0

1.8

0.0

0.3

0.1

0.1

360

9.2

4.0

0.5

6.5

1.3

5.4

0.4

0.0

1.7

0.0

0.3

0. 1

0.1

[nc5z=(n<Jz)14-(n<?2),+ -4- (nSz)t T— cz.]

S9369° — vol 10—11-

332

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

PERIODIC TERMS.

Tables of (101) Helena— Continued.

TABLE III.— 3 log r.

Unit-0.00001.

0

O

o

o

<m"

„

M

r-l

„,

"5

1—1

n

r-\

rH

t>

t-t

f— 1

*~

f-.

O

s~

t.

O

*~

O

*~

O

GQ

M

bo

<*-

so

be

£+H

CO

bio

t*-l

CO

bo

<4—

"&

_o

_o

as

_o

o

d

bb

o

ad

fab

o

as

f->

<

S-

"z

5

'o

'c

JL

<

«e

s

<

'o

a

O

0

21.7

0.4

+0.13

16. 8

108.8

-0.04

0

0

54.3

-1.09

o

192

13.7

-0.90

10

22. 1

3.0

4-0.41

13.4

107.5

-0. 19

8

44.8

-1.22

200

7.4

-0.67

20

22. :;

8.4

4-0. 65

10.4

104. 8

-0. 36

16

34.7

-1.26

208

3.0

-0.42

30

22.2

16.2

+0.88

7.8

100. 5

-0.50

21

24.9

-1.13

216

0.5

-0.19

40

21.7

26. 1

+ 1.07

5. 7

94.8

-0. 63

32

16. 8

-0.86

224

0.0

+0. 42

50

20.9

37.8

+1.26

4.0

87.9

-0.74

40

11.4

-0.46

232

1.3

+0.25

00

19.8

51. 1

+ 1.39

2.5

80.0

-0.84

48

9.5

0.00

240

4.1

+0.44

70

IS. -1

65. 4

+ 1.47

1.4

71.3

-0. 90

56

11.3

+0.46

248

8.3

+0.61

80

16.8

80. 1

+ 1.51

0.6

62. 2

-0.94

CI

L6.8

+0.88

256

13.9

+0.76

90

14. 9

95. (i

+ 1.51

0.1

52.7

-0. 94

72

25. o

+ 1. 13

261

20.3

+0.84

100

L2.9

no. 5

+1.47

0.0

43. 2

-0. 92

80

34. 8

+ 1.30

272

27.5

+0.92

110

10.8

L24.7

+ 1.36

0. 5

34. 1

-0.88

88

45.5

+ 1.30

280

35.2

+0.99

120

s. s

137. 7

+ 1.24

L.3

25.7

-0.80

96

55. 6

+ 1.18

288

43.2

+0.99

130

0.8

14!). 3

+ 1.07

2.7

18.0

-0.71

104

64. 2

+0.94

296

51.0

+0. 94

140

4.9

158.8

+0. 86

4.6

11.5

II 511

112

70.5

+0. 63

304

58. 1

+0.82

150

3.3

166.2

+0.63

6. S

6.3

-II 14

120

7 1. 1

+0. 25

312

64. J

+0.65

160

2.0

171.3

+0.38

9.2

2. 6

-0.29

I2S

74.5

-0. 13

320

68. 3

+0.42

170

1.0

173.9

+0.13

11.7

0.5

-0.13

130

72. 1

-0.48

328

70.6

+0.13

180

0.3

L73.8

-0. 13

14.2

0.0

-0.04

144

66.8

-0.80

336

70.3

-0. 19

190

0.0

171.1

-0.40

16.8

1.2

+0.21

L52

59. 1

-1.03

344

67. 1

-0. 52

200

0.1

L65.9

-0. 65

L9 1

1 1

+0.36

160

50.4

L. 20

352

62. 0

-0. 82

210

0.5

15S. 3

II. Sli

21.6

8.5

+0. 52

L68

40.5

-1.24

360

54. 3

-1.09

220

1.3

148.6

-1.07

23 9

14.3

+0. 65

176

30.7

-1.20

230

2.3

137.0

- 1 . 24

26.2

21.4

+0. 76

IS-1

21.6

-1.07

240

3.6

123. it

-1.36

28. 6

29. 1

+0. 84

250

5.1

109.8

-1.47

30.9

38. 2

+0. 90

260

6.8

94.8

-1.51

32.9

17. 5

+ 0.114

270

8.6

79.6

-1.51

34. 5

57.0

+0. 94

280

10.4

61.7

-1.47

35. 5

66. 3

+0.92

290

12.2

50. 4

-1.39

35.6

75. 3

+0.88

300

14.0

37.3

-1.24

34 9

S3. S

+ o. 80

310

15.7

25. 5

-1.07

33. 2

91.2

+0.69

320

17.3

15.7

-0.88

30. 8

97.5

+0. 57

330

18.7

8.1

-0.65

27. 7

102.6

+0.44

340

19.9

2.9

-0.40

24. 1

106.3

+0.29

350

20.9

0.3

-0. 13

20. 1

L08. 3

+ 0. 13

360

21. 7

0.4

+0.13

L6. 8

Mis. s

-0.04

[S log r=(,; log r\ + [o Inn ,-i,,+ -)-,,; log r\, T—cr.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

333

PERIODIC TERMS.

Tables of (101) Helena — Continued.
TABLE III.— 5 log ^-Continued.

Unlt=0.00001.

OB

i— 1

'O

r-

00

o

-

_

2

n

«

■2

_-

,-

00

:»

CO

>~

t*

K

&.

3~

■-

i~

*~

s~

K

*~

K

*~

K

m

be
o

sjo

be
o

o

6/.

o

bt
o

be
o

60

c

bC
O

60

be

M

o

<

«=

'O

CO

'o

'o

'o

t

«z

'o

'<3

«©

«o

<"o

o
0

1.3.

2.3

0. 1

0.2

0.7

0.8

1.4

2. i;

0. 1

0.4

0. 1

0.3

0.2

0.2

L5

1.4

2.4

0.1

(i ;;

ii. 3

1. 1

1.3

1.9

0. 1

0.3

0. 1

0.3

0.2

0.2

30

1.4

2.4

0. 1

0.3

0. 1

1.3

1. 1

1.3

0. 0

0.2

0. 1

0.2

0.2

0.2

45

1.2

2.5

0. 1

0.4

I), ii

1.6

ii 9

O.S

0.0

(1. 1

0.2

0.2

0.1

0.1

60

0.7

2.6

0.0

0.5

ii. 1

1.9

0.8

o. 3

0.0

0.0

0. 1

0.2

0. 1

0.1

75

0.3

2.7

0.0

ii. 5

0.3

2. 1

0.6

0. 1

0. 1

0.0

0.1

0.1

0. 1

0.1

90

0.0

2.7

0.0

ii. c

0. 5

<2-3

0.4

0.0

(1. 2

0. 0

0. 1

0.1

0.0

0.0

105

0.1

2. i;

0.0

0.6

1.0

2.4

0.2

0. 1

0.3

0.0

0.1

0.1

0.0

0.0

L20

0.4

2.4

0.0

0.6

1.:.

2. 3

0.1

(1. 1

0.4

0.0

0. 1

0.0

0.0

0.0

135

0.9

2.2

O. II

0.0

2 ii

2.3

0.0

(I.N

0.5

0.1

0. 1

0.0

0.0

0.0

150

1.3

1.8

0.0

0 ,

2. 1

0.0

1.4

0 6

0.2

0.1

0.0

0.0

0.0

L65

1.3

1.3

0.0

0.5

3.0

1.9

0.0

2.0

ii 8

0.3

0. 1

0.0

0.0

0.0

180

1. 1

0.9

0. 1

ii. 1

3 i

l.tl

0.1

2.7

0.9

0.4

0.0

0.0

0.0

0.0

195

0.7

0.5

0.1

(i. 3

3.8

1 :;

0.2

3.4

0.9

0.5

0.0

0.0

0.1

0.0

210

1) 1

0.2

0.1

(i. 3

4.(1

1 ii

ii 3

4.0

1.0

0.5

0.0

0.0

(1. 1

0.0

225

o. 3

0.0

0.1

0. 1

4. 1

0.7

0.5

4.5

1.0

0.6

0.0

0.1

0. 1

0.1

240

0.5

0.0

II. 1

0. 1

4. 1

0.5

0.7

5. 0

1.0

0.7

0.0

0. 1

0.1

0.1

255

0.9

0.2

0.1

0. 1

:; 'i

0. 2.

0.9

5.2

0.9

0.7

0.0

0.1

0.2

0.1

270

1.3

0. 5

0.1

0.0

3 6

(1. 1

1. 1

5.3

0.8

0.7

0.0

0.1

0.2

0.2

285

1.5

O.S

0. 1

0.0

?,. 2

0.0

1.2

5.2

0.7

0.7

0. 1

0.2

0.2

0.2

300

1.5

1.2

(1.2

0.0

2.7

0. 0

L.4

4.9

0. (i

0.7

0.1

0.2

0.2

0. 2

315

1.4

1.6

(1. ]

0.0

2. 1

0. 1

1.5

1.5

0.5

0.6

0.1

0.2

0.3

0.2

330

1.3

1.9

0.1

0. 1

1.6

0.2

1.5

3.9

0.4

0.5

0.1

0.3

o. 3

0.2

345

1.2

2.1

0. 1

0.1

1. 1

0.5

1.5

3. :;

0.3

0.4

0.1

0.3

0.3

0. 2

360

1.3

2.3

0.1

(1. 2

(1.7

0.8

1.4

2. 6

0.1

0.4

0.1

0.3

0.2

0.2

[3 log r=(d log ;•), + (,? log r),+ +(log r)t T-cr.]

334 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (101) Helena — Continued.

TABLE IV.— 3/3.
PERIODIC TERMS. Unit=0.00001.

Arg's. 1-6

(»«i

m*

w

(W«

(Wa

(<5/3)B

o

0

31.6

143.2

2.9

0.9

17.5

25.0

10

33.2

153. 7

0.4

2.1

9.8

27.9

20

34.3

162. 6

0.1

4.1

4.3

28.4

30

34.9

168.8

1.5

6.5

0.9

26.6

40

35.0

172.8

3.8

9.4

0.0

22.4

50

34.7

174.3

6.5

12.6

1.9

17.2

60

33.8

173.1

8.9

16.3

5.8

12.0

70

32.6

169. 5

10.3

20.4

12.0

8.3

80

30.9

163.2

10.0

24.7

20.5

6.5

90

28.8

154.8

8.8

28. 1

30.9

7.8

100

26.3

144.3

6.5

33.2

42.8

11.6

110

23.8

132. 2

4.0

37.0

56.1

17.5

120

20.8

118.4

1.6

39.8

70.1

24.5

130

17.8

103.8

0.5

41.5

84.4

31.2

140

14.8

88.7

0.8

42.0

98.7

36.5

150

11.8

73.6

2.5

41.1

112.8

39.3

160

9.0

58.9

5.4

39.0

126. 0

39.2

170

6.4

44.9

8.6

35.8

137.5

36.5

180

4.3

32.2

11.8

32.4

147.5

31.8

190

2.4

21.4

13.9

28.8

155.6

26.2

200

1.1

12.3

14.6

25. 4

161.3

19.9

210

0.3

5.8

14.5

22.5

mi. i

14.5

220

0.0

1.5

13.3

20.4

165. 3

10.4

230

0.4

0.0

12.0

IS. 7

163.4

7.1

240

1.3

1.5

11.1

17.3

159. 1

5.0

250

2.8

5.4

11.5

16.2

152. 6

3.5

260

4.6

11.9

13.3

14.9

143.8

2.4

270

7.0

20.5

15.9

13.3

133.1

1.5

280

9.6

31.3

18.8

11.4

121.0

0.5

290

12.5

43.7

21.3

9.1

107.5

0.0

300

15.7

57.6

22.4

6.8

93.7

0.6

310

18.8

72.4

22.0

4.4

79.3

2.1

320

21.8

87.7

19.5

2.4

65.1

5.3

330

24.8

102.5

15.8

1.0

51.5

9.8

340

27.3

117.0

11.1

0.1

38.6

15.2

350

29.7

130.9

6.6

0.3

27.3

20.6

360

31.6

143.2

2.9

0.9

17.5

25.0

[<?/?=(

Wi+(W2+

.... +(*£)« 5

p-c0-]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (101) Helena — Continued.

335

PERIODIC TERMS.

TABLE IV.— 8/3— Continued.

Unit=0.00001.

Arg's.

7-15,

(»07

(W.

W)„

W)n

(Wis

(Wu

(#)l5

(<5£),o

(8(1)21

20,21

O

0

0.4

1.9

0.8

2.4

5.5

0.2

0.0

1.2

0.4

2.2

0.0

15

1.0

2.0

0.8

3.0

5.5

0.1

0.0

2.1

0.5

2.2

0.0

30

2.0

1.9

0.8

3.5

5.0

0.1

0.0

3.2

0.6

2.0

0.2

45

3.0

1.9

0.8

4.0

4.5

0.0

0.2

4.2

0.8

1.9

0.6

60

4.1

1.8

0.6

4.4

4.0

0.0

0.5

5.5

0.8

1.6

1.0

75

5.4

1.6

0.6

4.5

3.4

0.1

0.8

6.5

0.9

1.2

1.5

90

6.4

1.4

0.5

4.5

2.6

0.2

1.1

7.4

1.0

1.0

2.1

105

7.4

1.1

0.4

4.5

1.9

0.5

1.5

8.0

1.0

0.8

2.8

120

8.2

1.0

0.4

4.1

1. 1

0.8

1.8

8.5

1.0

0.4

3.2

135

8.8

0.6

0.2

3.8

0.6

1.0

2.0

8.8

1.0

0.1

3.6

150

8.8

0.4

0.0

3.2

0.2

1.1

2.2

8.5

0.9

0.0

4.0

165

8.8

0.2

0.0

2.8

0.0

1.4

2.5

8.1

0.8

0.0

4.2

180

8.4

0.1

0.0

2.1

0.0

1.5

2.5

7.5

0.6

0.0

4.2

195

7.8

0.0

0.0

1.5

0.0

1.6

2.5

6.6

0.5

0.0

4.2

210

6.8

0.1

0.0

1.0

0.5

1.6

2.5

5.5

0.4

0.2

4.0

225

5.8

0.1

0.0

0.5

1.0

1.8

2.2

4.4

0.2

0.4

3.6

240

4.8

0.2

0.1

0.1

1.5

1.8

2.0

3.2

0.2

0.6

3.2

255

3.5

0.4

0.1

0.0

2.1

1.6

1.8

2.2

0.1

1.0

2.8

270

2.4

0.6

0.2

0.0

2.9

1.5

1.4

1.1

0.0

1.2

2.1

285

1.4

0.9

0.4

0.0

3.6

1.4

1.0

0.8

0.0

1.5

1.5

300

0.5

1.0

0.5

0.4

4.2

1.0

0.8

0.2

0.0

1.9

1.0

315

0.0

1.4

0.5

0.8

4.9

0.8

0.5

0.0

0.0

2.1

0.6

330

0.0

1.6

0.8

1.1

5.2

0.6

0.2

0.2

0.1

2.2

0.2

345

0.0

1.8

0.8

1.8

5.5

0.4

0.0

0.6

0.2

2.2

0.0

360

0.4

1.9

0.8

2.4

5.5

0.2

0.0

1.2

0.4

2.2

0.0

3=(5/9)1+(5ft)+ +W)t T-

336 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (101) ETelena — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t-tJ IN JULIAN YEARS.

Arg.

(ndz)t

Arg.

(8 log r)

Arg.

(SB ,

2.

TJnit=0?001.

2.

Unit=0.00001.

2.

Unit=0.00001.

o
0

-3.17

0

180

+3.06

O

0

-0. 10

O

180

+0.10

O

0

+6.00

O

180

-5. 25

10

-3.06

190

+2.94

15

-0.40

195

+0.36

15

+6.62

195

-5.62

20

-2.89

200

+2.78

30

-0.71

210

+0.63

30

+6.38

210

-5.62

30

-2.58

210

+2. 53

45

-0. 92

225

+0.84

45

+5. 62

225

-5.38

40

-2.22

220

+2.22

60

-1.09

240

+ 1.01

60

+4.62

240

-4.88

50

-1.81

230

+1.81

75

-1.18

255

+ 1. 13

75

+3.38

255

-3.88

GO

-1.31

210

+ 1.36

90

-1.18

270

+ 1.18

90

+ 1.75

270

-2.50

70

-0.75

250

+0.86

105

-1.09

285

+1.13

105

+0.13

285

-1. 12

80

-0.22

260

+0.33

120

-0.92

:;iiii

+ 1.01

120

-1.38

300

-0. 62

90

4-0.31

270

-0.19

135

-0.71

315

+0.80

135

-2.62

315

+2. 38,

100

+0.83

L'SII

-0. 72

150

-0.46

330

+0.55

150

-3.62

330

+3.88

110

+ 1.36

290

-1.25

L65

-0. 19

345

+0.23

165

-4.62

345

+5. 12

120

+ 1.81

300

-1.75

180

+0. 10

360

-0. 10

180

-5.25

360

+6.00

130

+2.19

310

-2.19

140

+2. 56

320

-2. 56

150

+2.81

330

-2.86

160

+2.94

340

-3.00

170

+3.06
+3.06

350

-3. 17

180

360

-3. 17

Thf perturbations are to be computed in the form —

7idz=i /i.i.-), + ( nSz)2+ +i n8z)t T—ct.

8 log ;■=((! log r),+(<3 log )■)., + +(d lug ;•), T— cT.

dB=(38)l + (d3\,+ +(83), T-cg.

MINOR PLAXETS DISCOVERED BY WATSOX— LEUSCHNER.

387

Tables of (101) Helena — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

-1'

B'

C

log sin a

log sin /;

log sin c

1868. 0

O

57.6916

O

325.8120

o

332.0712

9. 99945

9. 92280

9. 73980

9

. 71 15 (

. 8272

.0813

45

79

81

1870

57. 7 I'll

325.8425

332.0914

9. 99945

9. 9227H

9.73H81

1

. 7329

. 8578

L015

46

79

82

2

. 7467

.8730

.1116

46

78

83

3

7605

.8883

. 1217

46

78

83

4

. 7743

.9036

. 1318

46

78

84

1875

57. 7880

325. 9188

332. 1419

9. 99946

9. 112277

9. 73984

6

.8018

. 934 I

. L520

46

77

85

7

.8156

.9494

. 162]

46

76

85

S

8294

9646

. 1722

If',

711

86

9

3431

. 9799

. 1823

46

75

87

isso

57. 8569

325.9952

332. L924

9. 999411

9. 92275

9. 73987

1

. S707

326. 0104

JUL1',

46

75

88

2

. 8845

.1)2:.:

.2126

47

74

88

3

. vis:;

.0410

. 2227

47

74

89

4

.9120

.0562

2328

47

74

89

1885

57. 9258

326.0715

332. 2429

9. 99947

9. 92273

9. 73990

6

.9396

. 0868

2530

47

73

91

7

. 9534

. L020

.2631

47

72

91

8

. 967]

.1173

2732

47

72

92

9

.9809

. 1326

,2s:;:;

47

72

92

|S!I(I

57. 9947

326. 1478

332. 2934

9. 99947

9. 92271

9. 73993

1

58. 0085

.1631

3035

47

71

93

2

.0223

. L784

3136

47

71

94

3

.0360

1936

. 3236

4>

70

95

4

.0498

.2089

. 3337

48

70

96

1895

58. 0636

326.2212

332.3438

9. 9994S

9. 9226!)

9. 73996

6

.(177-1

. 2394

. 35311

48

69

96

7

.0911

. 2547

. 3640

48

69

97

8

.1049

.2699

3741

48

68

97

9

.1187

.3842

48

68

98

1900

58. 1324

326. 3005

332. 3943

9. 99948

9. 92268

9. 73998

1

. L462

.3158

4044

48

67

99

2

.1600

33io

.4145

18

67

4000

3

.1738

.3463

. 4246

48

66

00

4

.1876

.3616

1347

48

66

01

1905

58. 2013

326. 3769

332. 4 1 18

9. 99949

9. 92266

9. 74001

6

. 2151

.3921

. $549

49

65

02

7

2289

.4074

. 4650

49

65

03

8

.2427

. 4227

. 47.". 1

49

65

03

9

. 2565

.43711

. 4852

49

64

04

nun

58. 2702

326. 1532

332. 4953

9. 99949

9. 92264

9. 74004

l

. 2840

. 4685

. 5054

49

63

05

o

. 2978

. 1838

. 5155

49

63

05

3

.3116

.4990

. 5256

49

63

06

4

. 3254

. 5143

. 5357

49

62

07

1915

58. 3391

326. 5296

332. 5458

9. 99949

9. 92202

9. 74007

6

. 3529

. . 5449

.5559

50

61

08

7

.3667

.5601

. 5660

50

61

08

8

.3805

5754

.5761

50

61

09

9

.3943

. 5907

. 5862

50

60

10

1920

58. 4080

326. 6060

332. 5963

9. 99950

9. 92260

9. 74010

1

.4218

.6212

.6064

50

59

10

2

. 4356

. 6365

. 6165

50

59

11

3

.4494

. 6518

. 6266

50

59

12

4

.4632

.6670

.6367

50

58

12

1925

58. 4769

326. 6823

332. 6468

9. 99950

9. 92258

9. 74013

6

.4907

.6976

. 6569

50

57

14

7

. 5045

.7129

.6669

51

57

14

8

. 5183

. 7281

. 6770

51

57

15

9

. 5321

.7434

.6871

51

56

15

1930

58. 5458

326. 7587

332. 6972

9. 99951

9. 92256

9. 74016

Year

log cos a

log cos 6

log cos c

1868. 0
1930. 0

8. 699 n
8. 678 n

9. 738 n
9. 739 n

9.922
9.922

338 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF (103) HERA.

OSCULATING ELEMENTS.

Epoch and osculation, 1895, Nov. 26.0, M. T. Berlin=1895.904,M. T. Berlin.

o / //

g„= 76 9 2= 76? 1506

o,=185 15 25=185.2569)

£2 = 136 12 23 = 136. 2063 Mean equinox and ecliptic 1895.0.
i= 5 24 39= 5. 4107 J

cp= 4 34 6= 4.5682

,! = 798//.6939 = 0. 22185943

ga and n are mean elements.

The elements are based on oppositions extending from 1868 to 1902 and on the perturbations of the first
order by Jupiter, as given on page 340.

log a=0. 43175
log e=8. 90116

AUXILIARY QUANTITIES.

log 57. 2958e=0. 65928
log p =0. 42898

log

A

1+e

=9.96534

NUMERICAL DESIGNATION OF THE ARGUMENTS FOR TABLES II-IV.

1=9-9'

■2=9-29'

3=<7

4=9-3<7'

b=2g—3g'

6=

-9

7=

=*9-

-9'

8=

=-'</-

-bg'

9=

=3(7-

-2g>

10=

=30-

-V

ll=3p — bg'

12=4r/-:V
13=43-5(7'
14 = 5f/-6</
15= -g-g'

CONSTANTS TO BE SUBTRACTED FROM THE TABULATED PERTURBATIONS.

cz=0?5356 cr=0.001447 ^=0.000653

Derivation of cz, er, o„. (See also page 208.)

CO

Arg.

ndz
TJnit=0?001

3 log T
Unit=6.00001

Sp
Unit =0.00001

a

a

_

1

147.94

57.5

3.2

C3

2

93.31

13.5

6.9

CD
^4

3

168. 53

63.3

14.2

0

4

35.58

2.9

2.0

5

63.36

22.3

20.4

6

5.08

0.7

8.8

-r-

7

1.75

1.1

2.9

T3 2

8

2.69

-7J ft.

9

2.69

2 2

0.7

10

5.36

2.6

2.2

,C

11

6.69

2.3

3.1

o

12

0.42

0.4

13

1.72

0.9

0.7

c

14

0.33

0.2

CS

c
o

15

0. 17

1.0

Sum

535.6

169.9

66.0

c-=0?5356

cr=0. 001699 — (constant part of o log r -f- correction for difference between mean and
osculating values of semimajor axis)

=0. 001699-(+133.6"-13.8//) sin 1" Mod.

=0.001699-0.000252
(>=0. 001447

c„=0. 000660-(constant part of dp)

=0. 000660-0. 000007
c„=0. 000653

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

339

Tables o/( 103) Hera— Continued.

TABLE I.— MEAN ANOMALY (g).

Jan. 0.0 of common years; Ja

n. 1 .0 of leap years

Table for beginning of month

Year

9

\ ear

9

Month

9

B 1868

O

335. 18115

1899

O

327. 07362

T (0.0

•Ia"-|i.o
,. , (0.0

Feb-(i.o

Mar. 0.0
Apr. 0.0
May 0.0
June 0.0
July 0.0
Aug. 0.0
Sept. 0.0
Oct. 0.0
Nov. 0.0
Dec. 0.0

O

| 0. 00000

1 6. 87764

13.08970

19. 96734
26. 02313
33. 50077
40. 15656
47.03420
53. 91 1st
60. 5i,7i, 2
07. 44527
74. 10105

9

50. 15984

1900

48. 05231

L870

137. 13853

1

129.03100

1
B 2
3
4
5
B 6
7
8
9

218. 11722
299. 31778

20. 29643
101.27516
L82. 25385
263. 15440
344. 43310

65. 41179
146. 39048

B
B

2

3
4
■J
6
7
8
9
1910

210.00969

290. 98839

12.18894

93. 16763

174. 14632

255. 12501

336. 32556

57. 30426

L38. 28295

B 1880
• 1

227. 59103
308. 56972

B

. 1

219.26164

300. 40219

2

29. 54842

3

21. 440K8

3

B 4

110.52711
191,72766

4
5

102. 41958

IV 1.39827

5

272. 70635

B

6

2(14. 598S2

( lhange for n days0

6

7

353.68504

71. 1111374

7
8

345. 5,751
66. 55620

B 8

155.86429

9

147.53490

n g

n

g

9

230. S429K

B

1920

228. 73545

1890

317 82167

1

309. 71414

1

38. 80036

2

30. 692S3

O

o

B 2

120. 00091

3

111. 67152

1

0. 22186

16

3. 54975

3

200. 97961

B

4

192. 87208

2

0. 44372

17

3.77161

4

2.s 1.95830

5

273. 85077

3

0. 66558

18

3. 99347

5

2. 93699

6

354. S2946

4

0. 88744

19

4. 21533

B 6

84. 13754

7

75. 80815

5

1. 10930

20

4.43719

7

165. 11623

B

8

157. 00870

6

1.33115

21

4. 65905

8

246. 09493

9

237. 98739

7

1. 55301

22

4. 88091

1S99

327. 07362

1930

318. 96609

8

9

10

1. 77487
1. 99673

2. 21859

23
24
25

5. 10277
5. 32463
5. 54648

Note. — Wl

len ;/ is used as

.in argument o

! the perturba-

11

2. 44045

26

5. 76834

tions, add to

the g of this table

J-=.-

-*,=-<]

:2:i(i. Forex-

12

2. 66231

27

5. 99020

planation se«

■ page 203.

13

14
15

2.88417
3. 10603
3. 32789

28
29
30

6. 21206
6. 43392
6. 65578

° For days during January and

February of leap years subtract one

day before entering this table.

340

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X. N< ).

Tables of (103) Hera — Continued.

PERTURBATIONS.

ndz

V

u/cos i

Arc.
ig- i',/'

sin

cos

sin

COS

sin

cos

i i'

//

//

/t

//

//

/'

0 0

+ 133.6

+0.5

0 0

- 0. 107 t

+0. 481 t

+ 1 o

+ 89.0

-588. 7

-295. 0

- 42. 1

+ 10. 8

-1.4

+1

+ 2. 334 t

■ - 6. 424 t

3. 212 t

- 1. 167 t

- 0. 391 t

-4.034 i

+2

+ 1.9

- 11.9

- 11.9

- 1. 8

+ 0.5

-0. 1

+2

+ 0. 046 t

0. 127 t

- 0. 127 t

0. 046 t

- 0. 016 t

-0. Hill t

+3 0

0.4

+ 0.3

+ 0.4

+ 0. 5

-1 -1

- 0. 1

+ 0.6

- 0.4

- 0.3

+0.8

0

+ 9.7

+ 14.9

- 1. 3

+ 3.0

- 3.4

3.3

+ 1

-128.1

+ 163.4

+ 55. -1

+ 43.4

+ 1.6

-0.3

+2 -1

2.7

+ 5.3

+ 4.0

+ 2.2

- 1.1

+ 1.8

0 -2

+ 0.2

+ 2.3

- 1.3

+ I). 3

- 1.6

-2. S

+1 '

-127.0

-294. 6

- 58. 2

+ 22. 1

+ 1.0

+6.2

+2

- 84.0

-382.0

-221. 1

+ 48. 5

- 1.0

+ 1.0

+3

1.5

9.6

- 10.2

+ 1.8

+ 0.2

+0.5

+4 -2

0. 1

0.4

- 0. 7

+ 0.1

0 -3

+ 0.7

0.6

+ 0.3

+ 0. 3

- 0.4

+0.7

+1

+ 39.7

-123.5

+ 12. 6

+ 5.8

- L 1

-1. ]

+2

-172.6

+ 149.2

+ 67.2

+ 80. 5

+ 13. 4

+ 7.9

+3

- 35.2

- 13.6

- 11.4

+ 26.0

+ 0.0

+0.4

+4 -3

1.2

0.8

0.8'

+ 1.6

+ 1 -4

+ 0.0

0. 1

+ 0.2

+ 2

- 13.4

6.0

- 2.5

+ 4.1

+ 0.3

+ 1.0

+ 3

0.6

- 19.3

- 12. 2

+ 0.9

- 1. 0

+0.6

+4

7.3

+ 2.7

+ 2 II

+ 5.9

+5 -4

0.5

0.1

+ 0.2

+ 0.5

+2 -5

+ 1.9

9.5

+ 0.4

+ 0.1

+3

- 21. 1

+ 11.5

+ 5.1

+ 9.8

+ 2.1

+ 1.3

+ 4

5. 1

3.5

- 2. 1

+ 3.8

- 0. 1

+0.5

+5

1.0

+ 2.8

+ 2.3

+ 0. 9

+6 -5

0. 1

+ 0.2

+ 0.3

+ 0.1

+4 -6

+ 0.2

1.2

0.8

0. 1

+5

1.1

+ 0.2

+ 0.2

+ 0.9

+6 -6

+ 0.4

+ 0.6

+ 0.6

0.3

+6 -7

0.2

+ 0.4

+ 0.3

+ 0. 1

+ 7 -7

+ 0.3

+ 0.1

- 0.2

The constant part in ndz is included in the element g0.

The nontrigonometrical term multiplied by the time in ndz is included in the element n.

The constant part of v is included in the constant cy.

The constant part of k/cos i is included in the constant c„.

All other terms are included in Tables II-V.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCIIXEK.

341

Tables of (103) Hera— Continued.

TABLE II.— n<Jz.
PERIODIC TERMS. rnit=09001.

Arg's.

Diff.

(ndz)3

Diff.

1. 3

(nSz\

for r

fori0

O

0

85.0

-2.08

1.8

+0. 44 •

G

, i 5

-1.36

5.4

+0. 75

L2

68. 8

-0. 53

10.9

+ 1.06

IS

68. 2

+0.36

18.2

+1.36

21

73. 1

+1.25

27. 3

+ 1. 61

30

83.1

+2.08

38.0

+ 1.89

36

97.8

+2.78

50.1

+2. 14

Il-

116.1

+3.28

63.6

+ 2.33

ls

L36 6

+3. 56

78.2

+ 2. 53

54

158 1

+3.56

93.8

+ 2. 67

60

I7S.II

+3.31

110.2

+2. 78

66

197.3

+2.81

127. 1

+ 2.86

72

212.3

+2. 17

144.5

+2. 92

78

222.11

-1 .36

162 ii

+2. 92

84

228. 1

+0. 50

179.4

+2. 89

90

228.8

-0. 36

196.7

+2. S3

96

223. it

-1.22

213. 5

+2. 75

102

214. 1

-2.00

229. 7

+2.64

108

200. 0

-2.69

245. 0

+2.50

114

182.0

-3. 25

259. 6

+2.33

120

161. 1

-3.61

273.0

+2. 14

126

l:;n ii

-3.81

285. 2

+ 1.94

132

115.11

-3.89

296.2

| l 69

138

92. 7

-3.81

305. 7

+ 1.47

144

70. 6

-3.56

313.8

+ 1.22

150

50.2

-3. 19

320. 3

+0.94

156

32.6

-2.69

325. 2

+0.69

162

18.1

-2.08

328.6

+0.42

168

7.6

-1.39

330. 3

+0.14

174

1,5

-0.64

330.3

.-0. 14

ISO

0. 1

+0.19

328. 7

-0.42

186

3.8

+ 1.03

325. 4

-0. 67

192

12. 1

+ 1.75

320.6

ii 'il

198

2-1. s

+2. 44

314.1

-1.19

204

41.4

+3.06

306.1

-1.44

210

61.3

+3. 56

296.7

-1.69

216

84.0

-1-3.94

285. 9

-1.92

222

108.6

+4. 22

27:; B

-2. 11

22S

134.4

+4.33

260. 6

-2.31

234

160. 1

+4.33

246.3

-2.47

210

186.2

+4.19

231. 1

-2.47

246

210 5

+3.92

215. 1

-2.61

252

232.8

+3.53

198.5

-2.81

258

252. 5

+3.00

181.6

-2.86

264

268.6

+2.39

164 :;

-2.89

270

2S0.il

+1.72

147.0

-2.86

276

289.1

+ 1.00

129.8

-2.83

2S2

292 S

+0.22

113.0

-2. 75

288

291.9

-0. 50

96.8

-2.67

294

2S6 S

-1.22

81.1

-2.53

300

277. 3

-1.94

66.4

-2.36

306

263. 8

-2. 56

52.9

-2. 17

312

246. 7

-3.11

40.6

-1.94

318

226. S

-3.50

29.5

-1.69

324

205. 1

-3.75

20.2

-1.42

330

IS2.2

-3.86

12.6

-1. 14

336

159. 2

-3.78

6.6

-0.83

342

137.3

-3. 56

2.5

-0.53

348

116.9

-3.19

0.3

-0.19

354

99.2

-2.67

0.1

+0. 1 1

360

85.0

-2.08

1.8

+0.44

(ndz), + (r

idz), + ...

■ +(ndz)t T

-<*.]

342

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (103) Hera— Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit=0?001.

Are's.

Diff. for

(ndz)t

Diff. for

Diff. for

2. 4-8

(ndz)2

1°

1°

(nSz)5

1°

(ndz)6

(ndz)7

(ndz)a

o

0

9.6

-0. 75

1.7

+0.19

104.5

-0.83

9.7

3. 1

0.1

10

3.5

(I. 11

4.1

- (i 28

95. 5

-0.94

10.2

3.0

0.2

20

0.4

-0.17

7.5

+0. 39

85. 7

-1.03

10.5

2. S

0.4

30

0.4

+0.17

11.7

+0.47

75. 1

-1.08

10.5

2.6

0.0

40

3.7

+0.47

16.7

+0. 53

64.2

-1.08

10.3

2.4

1.0

50

10.0

+0.78

22. 1

■ 0.56

53 1

-1.08

9.9

2. 1

1.4

60

19.2

+ 1.06

28. 1

+0.61

42.7

-1.03

9.3

1.9

1.8

70

30.8

+ 1.28

34.3

+0.61

32.7

-0. 94

8.0

1.6

2. 2

SO

44.4

+ 1.44

40.4

+0.61

23.7

-0.86

7.8

1.4

2. 7

90

59.6

+ 1.56

46. 5

+0.58

15. 7

-0.72

6.9

1.1

3.2

100

75.6

+1.61

52.2

■ ii r,t;

9.2

-0. 58

6.2

0.9

3.7

110

91.8

+1.61

57.4

+0.47

4.4

i). ;,!i

5.5

0.6

4.1

120

107.8

+ 1.56

61.9

+0.42

1.3

-0.22

4.9

0.4

4.5

130

122.9

+1.47

65.8

■ (i :;:;

0.0

-0.03

4.3

0.2

4.8

110

136.9

+ 1.31

(is 5

+0.22

0.7

+0.17

3.8

0.1

5. 1

150

149. 1

+ 1. 14

70. 1

+0. 14

3.4

+0. 36

3.3

0.0

5.2

1G0

L59 5

+0.94

71.2

+0.03

7.8

+0. 53

2.8

0.0

5.4

170

167.7

+0.72

7(1. S

-0.08

13.9

+0.69

2 3

0. 1

5.4

ISO

173.8

+0. 50

69.5

-0. 19

21.6

+0.83

1.8

0.2

5.3

l!l()

177.5

+0.25

67.1

-0.28

30.6

+0.94

1.2

0.3

5.2

200

17S. 9

+0. 03

63.7

-0. 39

40.6

+1.03

0. 7

0.5

5.0

210

178.1

-0.19

59.5

-0.44

51.3

+ 1.08

0.3

0.8

4.8

22(1

175. 0

-0. 42

54. 5

-0. 53

62.4

+ 1.11

0. 1

1. 1

4.4

230

169. 8

-0.61

49.0

-0. 58

73.5

+1.11

0.0

1.4

4.0

240

162.7

-0.81

43.0

-0.61

84.3

+ 1.06

0.2

1.8

3.6

250

153. 5

-1.00

36.9

-0.61

94.5

+0.97

0.6

2.1

3.1

260

142. 7

-1.17

30.7

-0.61

103.7

+0.86

1.2

2.4

2.7

270

130. 4

-1.31

21. 7

-0. 58

111.6

+0.72

1.9

2.6

2.2

280

116.8

-1.42

19.0

-0.56

118.1

+0.56

2. S

2.9

1.7

290

102. 2

-1.50

13.8

-0.50

122. s

+0.39

3.7

3. 1

1.3

300

86.9

-1.53

9.2

-0.42

125.8

+0.19

4.6

3.2

0.9

310

71.6

-1.53

5.5

-0.33

126.8

0.00

5.6

3.3

0.6

320

56.6

-1.47

2. 6

-0. 22

125. 9

-0. 19

6.6

3.4

0.3

330

42.3

-1.36

0.8

-0.14

123.1

-0.36

7.4

3.4

0.1

340

29.4

— 1. 22

0. 0

-0.03

118. 5

-0.56

S. 3

3.3

0.0

350

18.2

-1.00

0.3

+0.08

112.2

-0.69

9. 1

3.2

0.0

360

9.6

-0.75

1.7

+0. 19

104.5

-0.83

9. 7

3. 1

0.1

[ndz=(ndz), + (ndz)2 + +{ndz)t T- c,]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

34:;

PERIODIC TERMS.

Tables of {103) Hera— Continued.
TABLE U-^n3z— Continued.

rnit.=ii?ooi.

Atgs.
9-15

n

(no:

1 nSz)13

{nSz)u

,,,,; ,.

O

0

0.0

0.0

9 9

0.2

0. 8

0.4

0.3

10

0.0

0.1

8.9

0.1

0.5

11 3

0.3

20

0.1

0.3

7. 7

0. 1

0.3

11 3

0.3

30

0.2

0. 6

6. 6

0.1

0. 2

n 2

0.3

40

0.4

1.2

5.4

0.0

0.1

11. 2

0.3

50

0.7

1.8

■I. 3

0.0

0.0

0. 1

0.3

60

1.0

2.5

3 2

II. II

0.0

0. 1

0.2

70

1. 1

3.4

2.3

0.0

0.1

0. 1

11. 2

80

1.8

4.2

1.5

0. 1

0.2

0.0

0.2

III)

2.3

5.2

0.9

II. 1

0.3

0.0

n. 2

100

2.8

6.1

0.4

0. 1

0.5

0.0

0. 1

110

3.2

7.1

0. 1

0.2

0.7

0.0

0. 1

L20

3.7

7.11

0.0

0.2

1.0

0. 0

0.1

130

4. 1

B ;

0.2

0.3

1.2

0. 1

0.1

140

4.5

9. I

0.5

0.4

1.6

II. 1

0.0

150

4.8

9. 9

1.0

0.4

1.9

0. 1

0.0

100

5.1

10.4

1.7

0.5

2.1

11. 2

0.0

170

5. 2

10.6

2.5

0.6

_'. 1

0.2

0.0

180

5. 4

10. 7

3. 5

0.6

2.7

0.3

0.0

190

5.3

10.6

4.5

0.7

2.9

0.3

0.0

200

5.2

10.4

5.7

0.8

3. 1

0.4

0.0

210

5.0

11). 1

6.9

0.8

3.3

11. 1

0.0

220

4.7

9 6

S.O

0.8

3.4

0.5

0.0

230

4.4

8.9

9.1

0.8

3.4

0.6

0.1

240

4.0

8.2

10. 2

0.8

3.4

0.6

0.1

250

3.6

7.4

11. 1

0.8

3.4

0.6

0.1

260

3.2

6.5

11.9

0.8

3.3

0.6

0. 1

270

2.7

5.5

12. 5

0.8

3.1

0.6

0.2

280

2.2

4.6

13.0

0.7

2.9

0.6

0.2

290

1.8

3.7

13.3

0.7

2.7

0.7

0.2

300

1.4

2.8

13.4

0.6

2.5

0.6

0.2

310

1.0

2.0

13.2

0.5

2. 2

0.6

0.3

320

0.7

1.4

12.9

0.5

1.9

0.6

0.3

330

0.4

0.8

12.4

0.4

1.6

0.6

0.3

340

0.2

0.4

11.7

0.3

1.3

0.5

0.3

350

0.1

0.1

10.8

0.2

1.0

0.4

0.3

360

0.0

0.0

9.9

0.2

0.8

0.4

0.3

[n3z=(n5z),+(n1Jz);.+ +(ndz)t T-ct]

344

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

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MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (103) Hera— Continued.

345

PERIODIC TERMS.

TABLE IV.— 3/3.

Unit=0.00001.

Arg's.

1-7,
9-11,

mi

(a/3)3

(5/5)4

(W 5

(We

M>7

(*«•

(«7>)io

(»««

(#)»

13, 15

0
0

4.6

16.4

12.3

0.6

30. 7

10.4

5.3

1.4

3.0

4.8

1.4

2.0

10

4.9

16.5

H.li

0.4

33.7

S. 7,

4.9

1.4

2.6

5. 2

1.4

1.9

20

4.6

16. 4

17. Ii

0.2

36.2

6.8

1.4

2.2

5. ii

1.3

1.8

30

4.2

15.7

20. 1

0.0

38. 1

5. 8

4. 1

1.4

l.s

5. 9

1.2

1.7

40

3 6

14.7

22. 5

0.0

39. ■'.

5.7

3.8

1.4

1.4

6. 1

1.2

1.5

50

3.0

13. 6

24.4

0.0

40. 3

5.8

3.3

1.3

1. 1

6.2

1. 1

1.4

60

11.8

26.1

0.1

40.6

6. 1

2.8

1.2

0.8

6 2

1.0

1. 2

70

2.4

10.1

27. 3

0.2

40. 4

6 'i

2.4

1. 1

0. 5

ii. 1

0.9

1.0

80

2.6

8.5

28.0

0.3

39. 3

7.9

1.9

1.0

0.3

6.0

0.8

90

3.3

6.9

28. 3

0.5

37 E

8.6

1.5

0.9

0. 1

5. 7

0.7

0.6

100

4.1

5.5

28. 2

0.8

35. -

1. 1

0.8

0.0

5. 1

0.6

0.4

110

5.3

4.2

27.7

1. 1

33.3

• i

0. 7

0.7

0.0

5.1

0. 5

0.3

L20

6.3

3.1

26. 7

1.4

30.3

7.5

0. 1

0.6

0.0

4.7

0.4

0. 2

130

7.0

2. 1

25. 4

l.s

27.0

5.9

0. '_'

o. 1

0. 1

4. 1

ii .;

0. 1

140

7.4

1.3

23.9

■> ■>

23. 6

4.0

0. 1

o 3

0. 3

3 i

0. 2

0.0

150

7.0

0.7

22. 1

LM,

20. 2

2.4

0.0

0.2

0.5

3 ii

0. 1

0.0

160

6.6

0.5

20.2

2. S

16.6

1.1

0.2

0.2

0.7

2.4

0.0

0.0

170

5.6

0.3

18.1

3.1

13.2

0.3

0 l

1.0

1.9 •

0.0

0.0

ISO

4.4

0. 1

15.9

3.4

10.0

0 0

0.5

n «i

1.4

1.4

0.0

o.o

190

3.2

0.0

13.7

3.6

7.0

0. 7

0.9

ii 0

I 8

1.0

0. 0

0.0

200

2.1

11.(1

11.4

4.6

LM)

1.3

0 0

2 2

0.6

0. 1

0 2

210

1.3

0.1

9.3

4.0

2.6

1 0

1.7

0.0

lm;

0.3

0. 2

0.3

220

0.6

0.4

7.3

4.0

1.2

ti. 5

2.0

0.0

3.0

0.1

0.2

0.4

230

0.3

0.8

5.4

4.0

0.4

9.0

2. 5

0. 1

3.3

0.0

0. 1

0.6

240

0.1

1.3

3.7

3.9

0.0

11.4

3.0

0.2

:; 6

0.0

0.5

0.8

250

0.0

2. 1

2.1

3 i

0.4

13.3

3. 5

0.3

3.9

0. 1

0.0

1.0

260

0.1

3.1

1.0

3.7

1.4

14.!)

0. I

4.1

0 2

0.8

1. 2

270

0.3

4.2

0.3

2.9

4.3

4.2

0. 1

0.8

1.4

280

0.5

5.6

n n

3.1

5.0

17.2

4.7

0.6

4.3

0. 7

0. 'i

1.6

290

0.7

7. 1

0. 1

2. 9

7 5

17. 7

5.1

0. 7

4.4

1. 1

1.0

l.s

300

1. 1

8. 7

0.7

17. ii

5. 1

n S

4. 3

1.5

1.1

I.S

310

1.8

in. 5

1.6

2.2

17.2

1.1

4.2

2. 1

1.2

1.9

320

2.6

12. ]

3.1

l.s

L7. 2

16. 5

5. 7

1. 1

4. 1

2.7

1.4

2.0

330

3.3

13. s

4.9

1.4

15. 5

1.2

3.9

3.3

1.4

2.0

340

.; >i

L5 ii

7. -1

1.2

24.2

14. 1

5. 6

1.2

3.7

3.8

1. 4

2.0 !

350

4.4

.

9.7

1.0

27. 6

12.3

1.3

3.4

l.:i

1.4

2.0

360

4.6

16. 5

12. 3

0.6

30. 7

LO 1

1.4

3.0

l 8

1.4

2.0 j

[a/3=(a/3),-+-

i i I

:;4i;

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {108) Hera — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 10) IN JULIAN YEARS.

Arg.

(ndz).

Arg.

(S log r)t

Arg.

(#>«

3

Unit=0?001

3

Unit=0.00001

3

Unit=0. 00001

O

0

-1.82

O

180

+ 1.75

O

0

-0.28

O

180

+0.21

O

0

-4.84

O

180

+5. 68

6

-1.74

L86

+ 1.68

6

-0. 35

186

+0.28

6

-4. 86

186

+5. 71

12

-1.64

192

+ 1.58

12

-0. 42

192

+0.34

12

-4.82

192

+5. 69

18

-1.52

I9S

+ 1.4S

18

-0.49

I9S

+0.40

18

-4. 71

198

+5.61

24

— 1. 38

204

+ 1.35

24

-0. 55

204

+0. 45

24

-4. 52

204

+5.51

30

-1.23

210

+ 1.21

30

-0.60

2111

+0. 50

30

-4.29

210

+5. 34

36

-1.06

216

+ 1.06

36

-0.65

216

+0. 55

36

-4.01

216

+5. 14

42

-0. 88

222

+0.90

42

-0.69

222

+0. 59

42

-3.64

222

+4. 87

48

-0. 09

228

+0.73

48

-0.72

228

+0.62

48

-3.24

22S

+4.55

54

-0. 50

234

+0.54

54

-0.74

234

+0.65

54

-2.81

234

+4.21

GO

-0.30

240

+0.35

6(1

—0. 75

240

+0. 67

60

-2. 34

240

+3.82

66

-0.10

246

+0. 16

06

-0.76

246

+0.68

66

-1.84

246

+3.38

72

+0.10

252

-0.03

72

-0.75

252

+0.69

72

-1.32

252

+2.91

78

+0.30

258

-0.23

78

-0.74

258

+0. 69

78

-0.75

258

+2. 41

84

+0.49

264

-0.42

84

-0. 72

264

+0.68

84

-0. 21

264

+ 1.90

90

+0.68

270

-0.61

90

-0.69

27(1

+0. 67

90

+0.33

270

+ 1.36

96

+0.86

276

-0.80

96

-0. 65

276

+0. 64

96

+0. S7

276

+0.80

102

+ 1.03

282

-0.98

L02

-0.61

2S2

+0.61

102

+1.42

282

+0.23

108

+ 1. 19

288

-1.14

108

-0.57

288

+0.57

108

+ 1.94

288

-0. 35

114

+1.33

294

-1.30

114

-0.52

291

+0. 52

114

+ 2. 45

294

-0. 92

120

+ 1.46

300

-1.45

120

-0. 46

300

+0.47

120

+2.94

300

-1.47

126

+ 1.57

306

-1.57

126

-0.40

306

+0.41

126

+3.39

306

-2.00

132

+ 1.66

312

-1.69

132

-0.33

312

+0.34

132

+3.81

312

-2. 51

138

+1.74

318

—1.78

138

-0. 27

318

+0. 28

138

+4.19

318

-2. 98

144

+ 1.80

324

-1.85

144

-0. 20

324

+0.20

144

+4. 54

324

-3.40

150

+ 1.84

330

-1.90

150

-0.13

330

+0.12

150

+4. SI

330

-3.79

156

+ 1.86

336

-1.93

156

-0.06

336

+0.04

156

+5. 10

336

-4.12

162

+ 1.86

342

-1.93

162

+0.01

342

-0.04

162

+5. 32

342

-4.39

L68

+ 1.84

348

-1.92

168

+0. 08

348

-0.12

168

+5.48

348

-4.60

174

+ 1.80

354

-1.88

174

+0. 15

354

-0.20

174

+5.62

354

-4.76

180

+ 1.75

360

-1.82

180

+0.21

360

-0.28

180

+5.68

360

-4. 8 1

The perturbations are to be computed in the form—

nBz=(nSz)l-\-ndz)2+ -\-(ndz)t T—ct

8 log r=(S log ''),+(,<? logr).,+ +(o log r)t T—cr

5/5=(5/?),+(^)2+ + (3/?), T-cB

MINOR PLAXETS DISCOVERED BY WATSON— LEUSCHNER.

347

Tables of (103) Hera — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B'

C"

log sin n

log sin h

log sin c

1868. 0

O

51. 2144

O

322.5520 '

O

31. 7396

9. 99906

9. 97429

9. 53220

69

. 2283

.5656

. 7557

06

29

218

1870

. 2423

. 5792

.7717

06

29

216

1

. 25(12

. 5927

.7878

06

29

214

2

. 27(12

. 6063

.8038

06

29

212

3

. 284 1

,619s

.S]!I9

06

29

209

4

29NI

.6334

. 8359

06

29

207

1875

51.3120

322. 6469

310. 8520

9. 99906

9. 97430

205

6

. 3260

. 6605

.8680

06

30

203

7

.3399

. 6740

.8841

06

30

201

8

.3539

. (1X75

.9002

06

30

198

9

. 3678

.7011

.9162

06

31

196

1880

51. 3818

322. 7146

310. 9323

9. 99907

9. 97431

9. 53194

1

.3957

. 7282

. 9483

07

31

192

2

.4097

. 7117

9644

07

31

190

3

. 4236

. 755:;

.9804

07

32

187

4

1376

. 7688

310. 9965

07

32

1S5

1885

51.4515

322. 7823

311.0126

9. 99907

9. 97432

183

6

. 4655

. 7959

.0286

07

32

181

7

.4794

. 8094

.0447

07

33

179

8

. 4933

.8230

. 0607

07

33

176

9

.5073

. 8365

.0768

07

33

171

1890

51.5212

322.8501

311.0928

9. 99907

9. 97433

9.53172

1

. 5352

m,:;i;

.1088

07

34

170

2

.5491

.8771

. 1249

07

34

167

3

.563]

.8907

.1409

07

34

165

4

. 5770

.9042

.1570

07

34

163

IS95

51. 5910

322. 9 1 78

311.1730

9. 99907

9. 97435

160

6

li

.9313

.1891

07

35

158

7

.6189

.9449

. 2051

07

35

156

8

.6328

.9584

. 22 1 2

07

35

151

9

.6467

.9719

.2373

07

36

151

1900

51. 6607

322. 9855

311.2534

9. 99908

9. 97436

9. 53149

1

.6747

322. 9990

. 2695

08

36

147

2

6SS6

323.(1126

. 2856

08

36

145

3

. 7026

.0261

.3017

08

37

142

4

. 7 1 65

.0397

.3177

08

37

140

1905

51. 73(15

323. 0532

311.3338

9. 99908

9. 97437

138

6

. 741 1

.0668

. 3499

ON

37

136

7

. 7584

.0803

. 3660

08

38

134

8

. 7723

.0938

. 3821

08

38

131

9

.7863

. 1074

.3982

08

38

129

1910

51.80(12

323. 1209

311.4143

9. 99908

9. 97438

9. 53127

1

.8142

. 1345

.4304

08

39

125

2

.8281

.1480

.4464

08

39

123

3

.8421

. 1616

. 4625

08

39

120

4

. 8560

. 1751

.4786

08

39

118

1915

51. 8700

323. 1886

311. 4947

9. 99908

9. 97440

116

6

. SS39

.2022

. 5108

08

40

114

7

.8979

.2157

.5269

08

40

112

8

.9119

. 2293

. 5430

08

40

109

9

.9258

. 242S

. 5591

08

41

107

1920

51. 9398

323. 2564

311. 5751

9. 99908

9. 97441

9. 53105

1

. 9537

. 2699

. 5912

09

41

103

2

.9677

.2834

. 6073

09

41

101

3

.9816

.2970

.6234

09

42

098

4

51. 9956

. 3105

. 6395

09

42

096

1925

52. 0095

323. 324 1

311. 6556

9. 99909

9. 97442

094

6

.0235

.3376

.6717

09

42

092

7

.0374

.3512

.6877

09

42

090

8

.0514

.3647

.7038

09

43

087

9

. 0653

.3782

.7199

09

43

085

1930

52. 0793

323. 3918

311. 7360

9. 99909

9. 97443

9. 53083

Year

log cos a

log cos b

log cos c

1870. 0
1930. 0

8.816
8.812

9. 524 n
9. 523 n

9.973
9.973

89309°— vol 10—11-

-2:::

348 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLES OF (119) ALTHAEA.

OSCULATING ELEMENTS.

Epoch and Osculation, 1894, Aug. 23.0. M. T. Berlin=1894.643, M. T. Berlin.

o„=332 43 50=332?7306

w=168 2 24 = 168.04001

& = 203 54 3=203.9008 Mean equinox and ecliptic 1S94.0.
i= 5 43 54= 5.7317J

cp= 4 36 2= 4.6006

n=855."4057 = 0.23761270

g0 and n are mean elements.

The elements are based on oppositions extending from 1872 to 1900 and on the perturbations of the
first order by Jupiter, as given on page 350.

AUXILIARY QUANTITIES.

log 57. 2958 c=0. 66234

log p =0.40909 •°yi.

NUMERICAL DESIGNATION OF THE ARGUMENTS FOR TABLES II-V.

log a=0.41189
log e=8. 90422

log \ — -=

9. 96509

1=9

2=<7-<?'
3=9-3/
4=7— 2o'

5=2*7— 3c'
6=29-0'
7=3o-23'
8=3ff-4o'

9= 4o-3o'
10= -g'
n=-g-g>

CONSTANTS TO BE SUBTRACTED FROM THE TABULATED PERTURBATIONS.

c2=0?4072 cr=0. 001098 cfi=0. 001607

Derivation of cz, cr, c„. (See also page 208.)

"3

M ■

Arg.

ndz
Unit=0?001

0 log r
Unit=0. 00001

57?
Unit=0. 00001

1

117.78

46. 1

69.3

2-~

2

106. 47

42.6

5.8

3

115. 08

3.0

5.9

° 8

4

51. 28

9.0

9.4

"C Pi
0 m

5

10. 56

3.4

51.5

■a £

6

1.47

0.9

2.8

CS.S

7

1.89

1.5

"3 S

8

0.36

0.2

1.8

C3 C

9

0.25

«

10

1.86

0.8

13.5

O

11

0.25

2 2

Q

Sum.

407.2

107. 5

162.2

rz=0?4072.

er=0. 001075— (constant part 0 log r + correction for difference between mean and
osculating values of semimajor axis).

=0. 001075-(27/'4-38."4) sin I" Mod.

=0.001075+0.000023.
cr=0. 001098.

c-=0. 001622— (constant part of 5/3).
=0. 001622-0. 000008.
=0.001614.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.
Tables of (119) Althae a— Continued.

TABLE I. — MEAN ANOMALY (g).

349

Jan. 0.0 of common years; Jan

1 .0 of leap years

Table for beginning of month

Year

9

Year

9

Month

9

B 1872

0

167. 67357

1901

O

164. 22968

Jan. /O.O
\1.0

0

]■ 0.00000

3

254. 40221

2

250. 95831

4

341. 13084

3

337. 68695

Feb. f 0.0

5

67. 85948

B

4

64. 65320

il.O

/ '""^

B 6

154. 82573

5

151. 38183

Mar. 0. 0

14.01915

7

241. 55436
328. 28300

6

238. 11047

Apr. 0.0

21. 38514

8

7

324. 83910

May 0. 0

28. 51352

9

55. 01163

B

8

51. 80535

June 0.0 35.87952

B 1880

141. 97788

9

138 53399

July 0. 0 43. 00790

1

228. 70652

1910

225. 26262

Aug. 0.0 50.37389

2

315. 43515

1

311. 99126

Sept. 0. 0 57. 73989

3

42. 16379

B

2

38. 95751

Oct. 0. 0 64. 86827

B 4

129. 13004

3

125.68614

Nov. 0.0

72. 23426

5

215. 85867

4

212. 41478

Dec. 0.0

79. 36264

6

302. 58731

5

299. 14341

7 '
B 8

29. 31594
116. 28219

B

6

7

26. 10966
112. 83830

9

203. 010S3

8

199. 56693

Change for n days °

1S90

289. 73946

9

286 29557

1

16. 46810

B

1920

13. 26181

n

n

9

B 2

103. 43434

1

99. 99045

9

3

190. 16298

2

186. 71909

4

276. 89162

3

273. 44772

o

O

5

3. 62025

B

4

0. 41397

1

0. 23761

16

3. 80180

B 6

90. 58650

5

87. 14260

2

0. 47523

17

4. 03942

7

177. 31513

6

173. 87124

3

0. 71284

18

4. 27703

8

264. 04377

7

260. 59988

4

0. 95045

19

4. 51464

9

350. 77241

B

8

347. 56612

5

1. 18806

20

4. 75225

1900

77. 50104

9

74. 29476

6

1. 42568

21

4. 98987

1930

161. 02340

7
8
9

1. 66329
1. 90090
2. 13851

22
23
24

5. 22748
5. 46509
5. 70270

Note. — W

len g is used as arj

argument of th

e perturbations

10

2. 37613

25

5. 94032

add to the g

of this table J

;r=;r—

!r0= -0?0261. For ex-

11

2. 61374

26

6. 17793

planation see

page 203.

•

12
13
14
15

2. 85135
3. 08897

3. 32658
3. 56419

27
28
29
30

6. 41554
6. 65316

6. 89077

7. 12838

a For days during January and

Febr

nary of leap years subtract one

day before entering this table.

350 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {119) Althaea — Continued.

PERTURBATIONS.

Arg.

ig-ig'

ndz

V

tt/coa i

sin

cos

sin

cos

sin

cos

i V

//

//

//

//

//

//

0 0
0 0

+ 27.4

+ 0. 051nt

+ 0.7

+ 0. 362nt

+1 o

+1

+2

+2 0

+418.6

- 1. 218nt
+ 8.2

- 0. 024nt

+7S. 9

- 3. 238nt
+ 1.3

- 0. 065nt

+39.9

- 1. 619nt

+ 1.4

+ 0.065nt

-207. 5

+ 0. 609nt,

-8.2

+ 0. 024nt

-43.0

- 1.346nt

- 1.5

- 0. 054nt

- 4.0

- 3. 004nt

- 0.2

- 0. 120nt

0 -1
0 -2
0 -3

+ 3.1
- 3.0

+ 0.2

- 3. 1
+ 1.9

- 1.8

— 1.5

- 1.0

+ 0.9

+ 2.1
-1.3

+ 0.1

-10.2
+ 1.3
- 0.4

-4.4
+ 0.6
+ 0.2

+ 1 -1
+ 2 -2
+3 -3
+4 -4

-174.6
+264. 0
+ 25.2
+ 5.7

+ 2.0
-7.2

- 0.8

- 0.4

+ 0.8
-4.2

- 0.6

- 0.3

+ 61.2
-156.2
- 18.3
-4.7

+ 2.7
-1.2
— 1.6

+ 1.3

- 0.6

- 0.6

+5 -5

+6 -6
+2 -1
+ 1 -2

+2 -4

+ 1.6
+ 0.5
5.2
+185. 2
- 1.1

— 0.1

+ 0.9
+ 2.1

- 0.7

- 0.1

+ 0.6
+ 0.1

- 1.4

- 0.5
+ 4.0

- 43.3
+ 0.4

- 2.0
-6.6

- 0.5

+ 1.0

-2.7
- 0.2

+1 -3

+2 -3

+3 -2

+404. 9
- 37.2

+ 6.8

-87.1
+ 8.0

+ 3.2
+ 3.8

+ 14.6
+ 16.1
- 7. 1

+ 4.4
-38.2
- 0.5

+ 1.7
-14.9
+ 0.2

+3 -4
+4 -3
-1 -1

+ 0.9
+ 0.9
+ 0.2

- 0.9

- 0.9

- 0.7
0.0

+ 0.6

- 1.0

- 0.7
+ 0.2

+ 1.3

— 0.2

- 1.6

+ 0.5
- 0.6

The constant part in ndz is included in the element g0.

The nontrigonometrical term multiplied by the time in ndz is included in the element n.

The constant part of v is included in the constant cr.

The constant part of u/cos i is included in the constant c»

All other terms are contained in Tables II-V.

MINOR PLANETS DISCOVERED BY WATSON— EEUSCHNER.

Tables of (119) Althaea — Continued.
TABLE II.— ndz.

351

PERIODIC

TERMS.

nnit=o?noi.

Arg. 2

(n3z),, Dili, lor 1

Arg. 2

(n3z)2 Di£f.forl°

O

0

104.7

+2.22

0

180

104.0

+3.14

3

111.3

+2.17

183

113.3

+ 3. 14

6

117.!)

+2.14

186

122. 6

+3. 06

9

L24. 3

+2.08

189

131. S

■ 3.06

12

130. 3

+ 1.94

192

140. 8

+2.97

15

135.8

+ 1.75

195

149. 1

+2.83

18

1 III s

+ 1.58

198

157. 9

+2. 69

21

145.2

+ 1.33

201

165.8

+2.58

24

148.8

+ 1. 19

204

173.3

+2.42

27

151. 7

+0.92

207

180.3

+2. 22

30

153.6

+0. 50

210

L86.8

+2. 03

33

154. 8

+0.22

213

192.6

+1. 86

36

155. 0

0.00

216

L97.8

+ 1.60

39

L54. 1

-0.28

219

202.2

+1.33

42

152. 9

-0.64

222

205. 9

+ 1.06

45

L50 5

-0.97

225

208. 8

+0.83

48

147.4

- 1 22

228

211.0

+0.61

51

143.4

-1.39

231

212. 2

+0.33

54

138. 8

-1.61

234

212.8

+0.08

57

133. 5

-1.89

237

212.4

-0. 22

(iO

127. 6

-2.08

240

211.4

-0.50

03

L21. 2

-2. 17

243

209.4

-0.75

66

114.3

-2. 31

246

206.8

-0.97

69

107.2

-2.44

249

203. 5

-1.25

72

99.7

-2.56

252

199.4

-1.47

75

92. 0

2. 58

255

194.7

-1.67

78

SI. 2

-2.58

258

189.4

-1.75

81

76. 1

-2.58

261

183.6

-1.97

84

cs. 5

-2.58

264

197.3

-2.17

87

60.8

- 2. 56

267

170. 5

-2.31

90

53.3

-2.44

270

163.4

-2. M

93

46.0

-2. 36

273

155.9

-2. 50

96

39. 1

-2.28

276

148.3

-2.56

99

32.5

-2.14

279

1 10. :.

■J. (II

102

26.4

-1.95

282

132. 6

-2.64

105

20.8

-1.7.".

285

124.7

-2.58

108

15.8

-1.58

288

116.9

-2.58

111

11.4

-1.39

291

109. 3

-2. 50

in

7.6

-1. 11

294

101. 9

-2.42

117

4.6

-0.89

297

94.7

-2.31

120

2.3

-0.64

300

88. 1

-2.14

123

0.8

-0.36

303

81.9

-2. 00

126

0.1

-0.08

306

76.2

-1.81

129

0.2

+0. 19

309

71.2

-1.53

132

1.1

+0.42

312

66.8

-1.31

135

2.8-

+0.69

315

63.3

-1.06

138

5 3

+0.97

318

60.5

-0.78

141

8.6

+ 1.25

321

58.5

-0. 50

144

12.6

+ 1.47

324

57.4

-0.22

147

17.4

+ 1.72

327

57.3

+0.08

150

22.9

+1.94

330

58.0

+0.42

153

29.0

+2.14

333

59. <;

+0.69

156

35.8

+2.31

336

62.1

+0.92

159

43.0

+ 2. 50

339

65. 4

+ 1.20

162

50.8

+ 2. 64

342

69.4

+ 1.47

165

59. 0

+2.78

345

74.2

+ 1.67

168

67.4

+ 2. 92

348

79.5

+1.89

171

76.4

+3.00

351

85.3

+2.03

174

85.5

+ 3.06

354

91.5

+2. 14

177

94. 7

1-3.06

357

98.0

+2.17

180

104.0

+ 3.14

360

104.7

+2.22

[ndz=(n

Sz)l+(ndz)2

+ . • • -r

(ndz)tr-C;

1

:',:,•_'

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of {119) Althaea— Continued.

TABLE II.— ndz— Continued.

PERIODIC TERMS.

Unit=0?001.

Arg's.
1,3-5

(ndz),

Dill, fori0

(ndz)3

Diff. fori0

(ndz)t

Diff. fori0

(«d2)5

O

0

140.0

+2. 14

91. 1

+1.94

51.7

+0.89

12.8'

11

152.8

+ 2.06

102.8

+ 1.97

57.0

+0.89

11.7

12

1(14. 4

+ 1.94

114.7

+2.00

62.2

+0.89

10.6

IS

176. 1

+ 1.89

126.7

+ 1.97

67.4

+0.86

9.5

24

187. 0

+ 1.72

138.3

+ 1.94

72.4

+0.81

8.4

30

196. 9

+ 1.61

150. 0

+ 1.89

77. 1

+0.78

7.3

30

206. 1

+ 1.44

161.1

+1.81

SI. 0

+0.72

6.3

42

214. 2

+ 1. 25

171.7

+ 1. 72

85.8

+0.67

5.3

48

221. 1

+ 1.06

181.7

+ 1.61

89.6

+0. 01

4.3

54

226.9

+0.89

190.8

+ 1.47

93.0

+0. 50

3.5

GO

231.7

1-0.01

199. 4

+ 1.33

95.9

+0.45

2.7

66

234. 1

+ 0. 30

206.9

+ 1.17

9N 1

+0.37

2.0

72

236.1

+0.19

213. 3

+0.97

LOO. 3

+0.28

1.4

78

236. 7

0.00

218.6

+0.81

101.8

+0. 23

0.9

84

236. 1

-0.22

223. 1

+0.61

102.6

+0.10

0.5

90

233. 9

-0.47

220. 1

+0.42

102. 9

0.00

0.2

90

230.6

-0.64

22S. 1

+0.23

102. 6

-0. 10

0. 1

102

226. 1

-0.89

228.6

0.00

101. S

-0.16

. 0.0

L08

220.0

-1.06

228. 3

-0. 19

100. 3

-0.28

0.0

114

213.3

-1.19

220. 4

-0. 42

98.4

-0.37

0.2

120

205. 6

-1.36

223. 3

-0. 61

95.9

-0.45

0.5

L26

196. 9

-1.53

219. 2

-0.81

92.9

-0.53

■ 0.9

132

187. 2

- 1 . 07

213. 0

-1.00

89.4

-0.64

1.4

138

1711.9

-1.75

207.2

-1. 17

85.6

-1). 07

2.0

144

L66. 1

-1.81

199.7

-1.33

81.3

-0.75

2.7

150

155. 3

-1.89

191.4

-1.44

76.7

-0.81

3.4

156

143. 6

-1.94

182.2

-1.61

71.8

-0.83

4.3

162

131. 9

-1.97

172.2

-1.72

66. 7

-0.86

5. 2

168

120.0

-2.00

161.7

-1.81

01. 1

-0. 92

6.2

174

107.8

-2.00

150. 6

-1.89

55. 9

-0.92

7.2

ISO

96. 1

-1.94

139. 2

-1.94

50. 5

-0. 92

8.3

186

84.4

-1.89

127.2

-2.00

45.1

-0.92

9.4

192

73.3

-1.81

115.3

-1.97

39.7

-0.89

10.5

198

62.8

-1.72

103.6

-1.97

'34.5

-0. SO

11.6

204

52.5

-1.69

91.7

-1.94

29.5

-0.81

12. 7

210

42.5

-1.56

80.3

-1.89

24.7

-0.78

13.8

216

33.9

-1.39

69.2

-LSI

20. 2

-0.72

14.8

222

25. 8

-1.25

58.6

-1.72

10.1

-0. 04

15.8

22S

18.9

-1.04

48.4

-1.01

12. 4

-0.58

16.8

234

13.1

-0.92

39.2

-1.44

9. 1

-0. 50

17.6

240

7.8

-0.78

30.8

-1.33

6.3

-0.45

18.4

246

3.9

-0.50

23. 3

-1.17

4.0

-0.37

19. 1

252

1.6

-0.33

16.7

-1.00

2.1

-0.25

19.7

258

0.0

-0.14

11.4

-0.81

0. 9

-0.17

20.2

264

0.0

+0. 08

6.9

-0.61

0.2.

-0.07

20.6

270

1. 1

+0.28

3.9

-0.42

0.0

-0.03

20.9

276

3.3

+0.50

1.9

-0.22

0. 0

+0.11

21.1

282

7.2

+0.75

1.4

0.00

1.4

+0.17

21.1

288

12.2

+0.92

1.9

+0.22

2.9

+0.30

21. 1

294

18.3

+ 1.17

3.9

+0.42

4.9

+0.39

20.9

300

26. 1

+ 1.33

6.9

+0.01

7.4

+0. 44

20.6

306

34.2

+ 1.47

11.1

+0.78

10.4

+0.53

20. 2

312

43.9

+ 1.67

16.4

+0.97

13.8

+0.61

19.7

318

54.2

+1.75

22.8

+ 1.17

17.6

+0.64

19.1

324

65.0

+ 1.86

30.3

+ 1.33

21.8

+0.72

18.4

330

76.4

+2. 00

38.9

+ 1.47

26.2

+0.78

17.7

336

89.2

+ 2. 11

48.1

+ 1.58

31.0

+0.81

16.8

342

101.7

+ 2.11

57.8

+ 1.72

35.9

+0.83

15.9

348

114. 4

+ 2.14

68.6

+ 1.81

41.1

+0.89

14.9

354

127. 2

+ 2.14

79.5

+ 1.89

46.4

+0.89

13.8

360

140.0

+2. 14

91.1

+ 1.94

51.7

+0.89

12.8

[ndz=(ndz)i + (n8z)2+

+ (ndz)tT-cz]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (119) Althaea— Continued.
TABLE II.— viz— Continued

:;:>:;

PERIODIC TERMS.

Unit-09001

Arg's. 6-11

" ;-)o

(nSz)7

(noz)s

i iiu:).,

[nSz)i0

{ndz)lt

0

0

1.7

1.9

0.1

0.3

1. 1

0.0

ID

L.5

2. 2

0. 2

(i. 3

1.0

0. 0

20

1.2

2. 5

(I. 2

n. ::

1.0

0.0

30

1.0

2. S

0.3

0.4

I. 1

0.0

40

0.8

3. 1

0.3

(i. -1

1 3

II. 1

50

ii 5

3 :;

ii. 1

0.4

1.5

0. 1

60

ii :;

3. 5

0.4

ii. 5

1. 7

0. 1

70

0.2

3. 7

0.5

0.5

1.9

0.2

SO

ii 1

:;. s

II. ii

0.5

2. 1

0. 2

90

0.0

3. 8

0.6

0. 7.

2. 2

O. 3

100

0.0

3 8

0.7

o 5

2. 1

o. 3

11(1

II II

3.7

0. 7

0.5

2. 7

ii 3

120

0. 1

3.5

0.7

0.5

3. o

0.4

130

0.2

3.3

0.7

ii \

:; l

0.4

140

0.4

3.1

0. 7

0. 1

3. 8

0.4

150

0. 5

2.8

0.7

0. 4

Id

0.5

160

0.8

2. ."i

0.7

0.3

4. 2

0.5

170

1.0

2.2

0.6

0.3

4. 1

0.5

180

1.2

1.9

0.6

0. 3 '

3. 8

ii 5

190

1.5

1.(1

0.6

0.2

3 3

0.5

200

1.7

1.3

0. 5

0.2

2. 7)

0.5

210

2.0

0.9

0. 4

0.1

1. s

0.5

220

2 2

0.7

0.4

0. 1

1.0

ii 1

230

'_'. 1

0.4

0.3

O. 1

0.4

0.4

240

2. (i

0.3

0.3

0. o

0. 1

0.4

250

2.8

0.1

0.2

0.0

0.0

0.3

260

2. S

0.0

0.2

0.0

I) 2

0.3

270

2.9

II ii

0.1

0.0

II 5

0.3

280

_' 'l

0.0

0.1

0.0

0.9

0.2

290

2 9

0. 1

0.0

0.0

1.3

0. 2

300

2.8

0. 3

I). 0

0. 1

1 7

0. 1

310

2.7

0.4

0.0

II 1

l.S

0. 1

320

2 ii

II. 7

0.0

0. 1

l.s

0.1

330

2.4

0.9

0.0

0. 1

1.7

0.0

340

2. 2

1.3

0. 1

0.2

1.5

0.0

350

2.0

1.6

0.1

0. 2

1.3

0.0

360

1.7

1.9

0. 1

0.3

1. 1

0.0

[no:

= (no:)l + (r

():),+ . .

+(ndz)tT

-ej

354

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

I'KRIUI«IC Tl K MS

Tables of (119) Althaea — Continued.

TABLE III— 3 log r.

Unit=0.00001.

Arg's.
1-8, 10

(3 lug r),

(3 log r)2

(3 log r)3

(3 log r)t

(3 log r)5

(3 log r),.

(3 log r).

(8 log r)8

(3 log r),„

O

0

0.6

17.5

6.1

0.0

6.8

1. 7

0.0

0.0

1.0

10

. 3.0

19.9

6.2

0.1

6.9

1. 7

0.0

0.0

1.0

20

6.8

27.0

6.2

0.5

6.8

1. 7

0. 1

0.0

0.9

30

11.9

37. 4

6.1

1.2

6.7

1.6

0.2

0.0

0.9

40

18.1

49. 1

5.8

2.1

6.5

1. 6

0.4

0.0

0.8

50

25.1

60.2

5.5

3.3

6.2

1.5

0.5

0.0

0.7

60

32.7

69. 1

5.2

4.6

5.8

1.4

0.8

0.0

0.6

70

40.6

74. 7

4.8

6.0

5.3

1.3

1.0

0.0

0.6

80

48.6

76.5

4.3

7.5

4.8

1.2

1.2

0.1

0.6

90

56.3

74. 7

3.7

9.1

4.2

1.0

1.5

0.1

0.6

100

63.7

69.5

3.2

10.7

3.6

0.8

1.7

0. 1

0.6

110

70.4

60.9

2.7

12.2

3.0

0.7

2.0

0.2

0.6

120

76.3

50.3

2.1

13.6

2.4

0.5

2.2

0.2

0.7

130

81.1

38. 6

1.6

15.0

1.8

0.4

2.5

0.3

0.6

140

84.8

26.7

1.1

■ 16. 1

1.3

0.3

2.6

0.4

0.6

150

87.2

16.1

0.7

17.0

0.9

0.2

2.8

0.4

0.5

160

88.7

7.6

0.4

17.6

0.5

0. 1

2.9

0.4

0.4

170

88.9

2. 1

0.2

18.0

0.2

0.0

3.0

0.4

0.2

180

87.8

0.0

0.0

18.2

0.0

0.0

3.0

0.5

0. 1

190

85.8

1.5

0.0

18.1

0.0

0.0

3.0

0.5

0.0

200

82.8

6.5

0.0

17.6

0.0

0.0

2.9

0.5

0.0

210

78.8

14.6

0. 1

17.0

0. 1

0. 1

2.8

0.5

0. 1

220

73.7

25.0

0.3

16.1

0.3

0. 1

2.6

0.5

0.2

230

67.9

36. s

0.6

15.0

0.6

0.2

2.4

0.5

0.5

240

61.4

48.8

0.9

13.6

1.0

0.3

2.2

0.5

0.8

250

54.3

59. 7

1.4

12.2

1. 5

0.4

2.0

0.5

1.2

260

46.7

68. 7

1.9

10.7

2.0

0. 6

1.7

0.4

1.4

270

39.1

74. 7

2.4

9.1

2.6

0. 7

1.5

0.4

1.6

280

31.6

77.2

2.9

7.5

3.2

0.9

1.2

0.4

1. 7

290

24.5

75.8

3.5

6.0

3.9

1.0

1.0

0.3

1.6

300

17.9

70.6

4.0

4.6

4.5

1. 1

0.8

0.3

1.6

310

12.0

62.0

4.5

3.3

5.0

1.3

0.6

0.2

1.4

320

7. 1

50.9

5.0

2.1

5.5

1.4

0.4

0. 1

1.4

330

3.3

39.0

5.4

1.2

5.9

1.5

0.2

0. 1

1.2

340

0.9

28. 1

5.7

0.5

6.3

1.6

0. 1

0. 1

1. 1

350

0.0

20.5

6.0

0.1

6.6

1.6

0.0

0. 1

1.0

360

0.6

17.5

6. 1

0.0

6.8

1. 7

0.0

0.0

1.0

log r=(3 log r)t+(3 log r)a+ + (3 log r)t T—cT.]

PERIODIC TERMS.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (119) Althaea — Continued.
TABLE IV.— SB.

355

UDit=0.00001.

Arg's. 1-6,
8, 10. 11

(SB),

(SB),

(Wh

(Sp)<

m,

(SB)n

m>

(<WlO

(Wu

O

0

64.3

5.8

7.!)

6.0

32 9

4.0

2.4

9.0

1.5

10

54. 6

5. 1

8.9

4.4

24.8

3.6

2.6

7. 1

1 2

20

44.9

4.8

9. 7

3.0

17.5

3.0

2.9

5.4

0.9

30

36.4

5. 1

10.4

1.9

11.4

2.6

3.0

3. 7

0.6

40

28.9

6. 1

10. 9

0.9

6.3

2.2

3.3

2. 2

0.4

50

22.7

7.6

11.4

0.2

2.6

1.6

3.4

1. 2

0.3

60

18.5

9. 1

11.5

0. 1

0. li

1.2

3.5

0.5

0.1

70

15. 9

10.5

ll.fi

0. 1

0. 0

0.8

3.5

0.1

0.0

80

14. 5

11.5

11.5

0.4

0.9

0.4

3.5

0.0

0. 1

90

15.4

11.8

11.3

1. 1

3.5

0.3

3.4

0.4

0.2

100

17.4

11.2

10.8

2.0

7.5

0. 1

3.3

1. 1

0.4

110

21.6

10. 1

10.2

3.1

12. S

0.0 :

3. 1

2.3

0.6

120

26.8

8.6

9.5

4.4

19.4

0.0

2.9

3.7

0.9

130

33. 1

7.1

8.6

5.8

26.8

0. 1

2.6

5.5

1.2

140

40.2

5.7

7.6

7.3

35.0

0.3

2.2

7.8

1.6

150

48.3

4.7

6.6

8.6

43.8

0.5

2.0

10.5

1.9

160

56.8

4.3

5.6

10.0

52. 7

0.8

1. 7

13.4

2.3

170

65.6

4. 1

4.6

11.5

61. ii

1. 1

1.4

16.4

2.6

180

74.4

4.0

3.6

12.8

70.4

1.5

1. 1

19.5

3.0

190

83.0

3.8

3.6

13.9

78.4

1.9

0.9

22.4

3.3

200

91.2

3.5

3.8

15.0

85.6

2.5

0.6

24.9

3.6

210

99.1

2.9

3.9

15.9

91.8

3.0

0.5

26.9

3.9

220

106.2

2.1

4. 1

16.7

96.8

3.5

0. 3

28.2

4. 1

230

112.3

1. 1

4.3

17.3

100.4

3.9

0. 1

28.8

4.2

240

116. 9

0.3

4.7

17. 7

102.4

4.3

0.0

28.5

4.4

250

120.3

0.0

5.0

17.9

103. 0

4. 7

0.0

27.7

4.5

260

122.8

0.0

5.4

17.9

102. 0

5.0

0.0

26.5

4.4

270

123 ::

1.0

5.7

17. 7

99.5

5.2

0. 1

25.1

4.2

280

122.3

2.3

6. 1

17.1

95.5

5.4

0.2

23.3

4. 1

290

119.6

4.0

6.5

16.3

90. 1

5.4

0.4

21.5

3.9

300

115. 2

5.9

6.8

L5. -1

83.8

5.4

0.6

19.8

3.6

310

109.4

7.2

7. 1

14.2

76.2

5.4

0.9

18.1

3.2

320

102.0

8.1

7.3

12.7

68.1

5.2

1.2

16.3

2.9

330

93.6

8.3

7.5

11.1

59.3

5.0

1.5

14.7

2.6

340

84.4

7.7

7.7

9.5

50.4

4.7

1.8

12.9

2.2

350

74.4

6.9

7.8

7.7

41.3

4.3

2. 1

11. 1

1.9

360

64.3

5.7

7.9

6.0

32. 5

4.0

2.4

9.0

1.5

[8B=(33)l + (Wh+ +(SB)t T-c„.]

356 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of 119 Althaea — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T = (t— 10) IN JULIAN YEARS.

Arg.

(nSz)t

Arg.

(3 log r)

Arg.

(30)t

1

Unit=0?001.

1

Unit=0.00001.

1

Unit=0.00001.

O

0

-1.39

O

180

+ 1.33

O

0

+0.21

O

180

-0. 17

O

0

-5.25

O

180

+6.15

6

-1.44

186

+ 1.38

10

+0. 12

190

-0.08

10

-5.61

190

+6.47

12

-1.47

192

+ 1.41

20

+0.02

200

+0.02

20

-5.78

200

+6.69

18

-1.48

198

+ 1.42

30

-0.07

210

+0.11

30

-5.74

210

+6.68

24

-1.48

204

+ 1.42

40

-0.16

220

+0.20

40

-5.46

220

+6.54

30

-1.46

210

+ 1.41

50

-0. 25

230

+0.29

50

-4.98

230

+6.23

36

-1.42

216

+ 1.38

60

-0.33

240

+0.37

60

-4. 35

240

+5.77

42

-1.37

222

+ 1.34

70

-0.40

250

+0.44

70

-3.54

250

+5.15

48

-1.30

228

+1.28

80

-0.45

260

+0. 49

80

-2.64

260

+4.38

54

-1.22

234

+ 1.21

90

-0. 50

270

+0.54

90

-1.63

270

+3.47

60

-1.12

240

+ 1.13

100

-0.52

280

+0.56

100

-0.59

280

+2.46

66

-1.01

246

+ 1.03

110

-0.53

290

+0.57

110

+0.46

290

+ 1.39

72

-0.89

252

+0.92

120

-0.52

300

+0. 56

120

+1.52

300

+0.27

78

-0.76

258

+0.80

130

-0.50

310

+0.54

130

+ 2. 52

310

-0.87

84

-0.62

264

+0.68

140

-0.46

320

+0.50

140

+3.46

320

-1.97

90

-0.48

270

+0.54

150

-0.41

330

+0.45

150

+4.31

330

-3.00

96

-0.34

276

+0.40

160

-0. 34

340

+0.38

160

+5. 05

340

-3.92

102

-0. 19

282

+0.25

170

-0. 26

350

+0.30

170

+5.69

350

-4.67

108

-0.04

288

+0. 10

180

-0.17

360

+0.21

180

+6. 15

360

-5. 25

114

+0. 11

294

-0.06

120

+0.26

300

-0.21

126

+0.41

306

-0.37

132

+0.54

312

-0. 52

138

+0.68

318

-0.66

144

+0.80

324

-0.80

150

+0.92

330

-0.92

L56

+ 1.02

336

-1.04

162

+ 1. 12

342

-1.15

16S

+1. 21

348

-1.24

174

+ 1.28

354

-1.32

180

+ 1.33

360

-1.39

The perturbations are to be computed in the form-

ndz=(ndz)1-\-(ndz).,+

d log r=(3 log r), + (<)"log r),+ .
30=(3P)l + (dP),+

.+(nSz)t T-cz.
.+(3 log r)t T-
. + (5/3), T-Cg.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (119) Althaea— Continued.

TABLE VI — CONSTANTS FOR THE EQUATOR.

357

Year

A'

B>

C

log sin a

log sin b

log sin c

1872.0

O

101.5286

O

10. 7759

o

18. 4605

9.99965

9.97775

9. 49775

3

.5425

.7894

.4780

65

75

777

4

. 5564

.8028

. 4956

65

75

779

1875

101.5703

10.8163

18. 5131

9. 99965

9.97775

9.49780

6

.5842

. 8297

. 5307

65

75

782

7

. 5981

. 8432

.51S2

65

75

783

8

.6120

. 8567

. 5658

65

75

785

9

. 6260

.8702

. 5833

65

71

787

1880

101. 6399

10. 8837

18. 6009

9. 99965

9. 97774

9.497S9

1

.i;;.:;n

.8971

.6184

65

74

790

2

. 6677

. 9105

.6360

65

74

792

3

. 6816

.9240

. 6535

65

74

793

4

. 6955

.937.-.

.6711

65

74

795

1885

101. 7094

10. 9510

18. 6886

9. 99965

9.97774

9.49796

6

.7233

.9644

. 7061

65

73

9. 19798

7

. 7372

.9779

.7237

65

73

9. 49800

8

.7512

10. 9914

.7412

65

73

801

9

.7651

1 1 0048

. 7588

65

73

803

1890

101.7790

11.0182

18.7763

9. 99965

9.97773

9. 49805

1

. 7929

.0317

. 7939

65

73

806

2

.sons

.0451

.8114

64

73

808

3

. 8207

. 0586

. S290

64

72

810

4

. S346

.0720

. .SO, 5

64

72

811

1895

101. 8485

11.0855

18. 8640

9. 99964

9.97772

9. 49813

6

.862-1

. 0989

.8816

64

72

814

7

.8763

.1124

. S992

64

72

816

8

. 8902

. 1259

.9167

64

72

818

9

90-11

. i:;:i:;

.9312

64

72

819

1900

101.9180

11. 1527

18. 9518

9. 99964

9. 97772

9.49S21

1

. 9319

.1662

.9693

64

71

823

2

.9458

.1796

18. 9868

64

71

824

3

. 9597

. 1931

19.0043

64

71

826

4

.9736

20(15

.0219

64

71

828

190.-.

101.9875

11.2200

19.0394

9. 99964

9. 97771

9. 49829

6

102.0014

. 2330

. 0569

64

71

831

7

.0153

.2470

.0744

64

71

833

8

.0292

.2605

.0919

64

71

834

9

.0432

.2739

.1094

64

70

836

1910

102.0571

11.2873

19. 1270

9. 99964

9.97770

9. 49838

1

.0710

.3008

. 1445

64

70

839

2

.0849

.3142

.1620

64

70

841

3

.0988

.3277

. 1795

64

70

842

4

. 1127

.3411

.1970

64

70

■ 844

1915

102. 1266

11. 3546

19.2145

9.99964

9. 97770

9.49846

6

. 1405

.3681

.23,21

64

69

847

7

.151-1

.3815

.2496

64

69

849

8

.1683

. 3950

.2671

63

69

851

9

. 1822

.4084

. 2S46

63

69

852

1920

102. 1962

11.4219

19.3021

9. 99963

9. 97769

9. 49854

1

.2101

.4354

.3196

63

69

856

2

.2240

.4488

. 3372

63

69

857

3

. 2379

. 4623

. 3547

63

68

859

4

.2518

.4757

. 3722

63

68

861

1925

102. 2658

11.4892

19.3897

9. 99963

9. 97768

9. 49862

6

.2797

.5027

.4072

63

68

864

7

.2936

.5161

.4247

63

68

866

8

.:;o75

.5296

.4423

63

68

867

9

.3214

. 5431

. 4598

63

68

869

1930

102. 3354

11. 5567

19.4773

9. 99963

9. 97767

9. 49871

Year

log cos a

log cos b

log COB C

1872.0
1930. 0

8. 602 n
8. 615 n

9. 494 n
9. 495 n

9.977
9.977

TABLES OF (93) MINERVA.

ndz, S log r, and o3 are tabulated in the form
li [a{+ Ubt),] sin is + It [bt+ (Jbt),] cos is+ (Jb0)t.

359

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

361

TABLES OF (93) MINERVA.

OSCULATING ELEMENTS.
Epoch and osculation, Jan. 0.0, M. T. Greenwich = 1875.0, M. T. Greenwich.

o / //

g„=278 32 8=278?5356
w=269 44 33=269.74261
JJ= 5 7 8= 5. 1189 iMean equinox and ecliptic 1875.0.

i= 8 36 20= 8. 6055 J
<p= 8 4 54= 8.0816
n= 775". 9214= 0.21553373

ga and n are mean elements.

The elements are based on oppositions extending from 1867 to 1902 and on the perturbations of the first order
by Jupiter, as given on page 362.

loga=0.44013
log e =9.14793

AUXILIARY QUANTITIES.

log 57.2958 e=0. 90606
log p =0.43146

log J\- '=9.93854
v 14- f.

1+e

TABLE I.— MEAN ANOMALYig,; AND (g-g'l.

Jan. 0.0 of common years; Jan. 1.0 of leap years.

Year.

1865
6
7

B 8

9

1870

1

B 2

3

4

1875

B 6
7
8
9

B1880
1
2

3
B 4

1885

6

7

B 8

9

1890

1

B 2

3

4

1895

B 6

7

9-9

211. 40636

290. 07617

8. 74598

87. 63133
166.30114
244. 97096
323. 64077

42. 52612
121. 19593
199. 86574
278. 53556
357. 42090

76.09071
154. 76053
233. 43034
312. 31569

30. 98550
109. 65531
188. 32512
267. 21047
345. 88028

64. 55010
143. 21992
222. 10527
300. 77508

19. 44489

98. 11470
177. 00005
255. 66986
334. 33967

53. 00949

131. 89484

210. 56465

289. 23446

7. 90427

328. 117

16. 458

64. 800

113. 274

161. 615

209. 957

258. 298

306. 772

355. 114

43. 455

91. 797

140. 271

188. 612

236. 954

285. 295

333. 769

22. Ill

70. 452

118. 794

167. 268

215. 609

263. 951

312. 292

0.766

49. 108

97. 449

145. 791

194. 265

242. 606

290. 948

339. 289

27. 763

76. 105

124. 446

172. 788

Year.

1900
1
o

3

B 4

1905

6

7

B 8

9

1910

1

B 2

3

4

1915

B 6

7

8

9

B 1920

1

2

3

B 4

1925

6

B

8

9

1930

86.
165.
243.
322.

41.
120.
198.
277.
356.

75.
153.
232.
311.

29.
108.
187.
266.
344.

63.
142.
221.
299.

18.

97.
175.
254.
333.

51.
130.
209.
288.

57408
24389
91370
5S352
46S87
13868
80849
47830
36365
03346
70327
37309
25843
92824
59805
26787
15322
82303
49284
16266
04801
71782
38763
05744
9 1279
61260
28241
95222
83757
50738
17720

9-9

221. 129
269. 471
317.812
6.154
54. 628
102. 969
151.311
199. 653
248. 126

296. 168

344. 810

33. 151

81. 625

129. 967

178. 308

226. 650

275. 124

323. 465

11.807

60. 148

His i;22

156. 964

205. 305

253. 647

302. 121

350. 462

38. 804

87. 146

135. 620

183. 962

232. 304

Note. — When g is used as an argument of the perturbations,
add to the g of this table Jk=k— ro=+0?0666. For explana-
tion see page 203.

Table for beginning of month.

Month.

9

9-9'

t JO.O
Jan. jj Q

O

| 0. 00000

1 6. 68154
12. 71649

O

0.000

Feb.{°;°

Mar. 0.0

4.106

7.814

Apr. 0.0

19. 39804

11. 920

May 0.0

25. 86405

15. 893

June 0.0

32. 54559

19. 999

July 0.0

39.01160

23. 972

Aug. 0.0

45. 69315

28. 078

Sept. 0.0

52. 37470

32. 184

Oct. 0.0

58. 84071

36. 157

Nov. 0.0

65. 52226

40. 263

Dec. 0.0

71. 98827

44. 236

Change for n days °

21553
43107
64660
86213
07767
29320
50874
72427
93980
15534
37087
58640

Ml 19 1

01747
23301

9-9'

n

0

0.132

16

0. 265

17

0.397

18

0.530

19

0.662

20

0. 795

21

0. 927

22

1.060

23

1.192

24

1.324

25

1.457

26

1.589

27

1.722

28

1. 854

29

1.987

30

44854
66407
87961
09514
31067
52621
74174
95728
17281
38834
60388
81941
03494
25048
16601

9-9

2.119
2.252
2.384
2.516
2.649
2.781
2.914
3.046
3. 179
3.311
3.444
3.576
3.708
3.841
3.973

a For days during January and February of
leap year subtract one day before entering
this table.

362 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tahltx of (93) Minerva — Continued.

PERTURBATIONS.

ndz

i

m/cos i

Are.
ig—i'g'

sin

cos

sin

cos

sin

cos

i i'

//

//

//

//

//

//

0 0

9.5

-9.4

0 0

0. 195 T

- 0. 198 T

+ 1 o

-104.9

-516.3

-259.0

+ 57.9

+43.8

+50.6

+1

+ 2. 746 T

- 14. S32T

- 7. 416 T

1. 387 T

+ 9. 290 T

+ 1. 409 T

+2

+ 2.4

+ 17.9

- 0.2

+ 0.9

- 0.3

+ 0.6

+ 2

■ 0. 098 T

+ 0. 521 T

+3 0

+ 0.1

-2 -1

+ 0.1

+ 0.2

- 0.1

+ 0.1

- 0.1

+ 0.1

-1

0.2

2.5

+ 1.3

+ 0.3

+ 4.0

- 2.8

0

+ 26.2

+ 37.9

+ 1.1

+ 3.7

+12.7

- 4. 1

+ 1

+ 36.2

+214. 2

+ 71.3

- 11.9

-12.0

+ 3.9

+2

+ 1.2

-2.2

+ 2.7

- 1.4

- 5.6

+ 0.1

+3 -1

■ 0.2

+ 0.2

+ 0.3

+ 0.3

-1 -2

0.4

- 0.1

+ 0.2

+ 0.3

+ 0.5

+ 0.3

0

+ 6.5

+ 2.2

+ 3.0

+ 12.5

+10.7

+13.7

+1

—768. 8

+307. 1

+ 55. 1

+151. 3

- 7.1

-13.1

+2

-431.7

+119.4

+ 70.8

+253. 7

-6.2

—11.1

+3

+ 17.5

- 5.7

- 0.7

- 0.2

+ 0.2

+ 1.3

+4 -2

+ 0.2

- 0.2

- 0.1

-1 -3

+ 0.3

+ 0.1

+ 0.1

+ 0.1

0

2.6

- 1.5

+ 1.8

-3.2

+ 1.2

-5.4

+1

-235. 6

- 74.9

+ 25.8

- 47.6

+ 6.1

- 6.9

+2

+374. 1

+301. 7

+139.6

—170. 1

-25.3

+20. 2

+3

+ 3.6

+ 26.7

+ 26.0

- 11.2

- 1.3

+ 1.1

+4

- 1.0

- 1.4

+ 0.3

+ 0.2

+ 0.4

- 0.1

+5 -3

- 0.1

- 0.1

0 -4

- 0.1

+ 0.2

+ 0.3

- 0.1

+ 1

1.0

-4.2

+ 4.4

- 0.4

+ 3.0

0.0

+2

+ 1.6

+ 106. 3

+ 34.1

+ 2.4

- 5.0

- 1.1

+3

- 27.5

+ 44.4

+ 28.9

+ 16.2

-3.8

-3.4

+4

+ 8.5

6.4

- 3.5

— 5.9

+ 0.4

+ 0.3

+5 —4

- 0. 1

+ 0.3

- 0.2

- 0. 1

- 0.1

The constant part in nSz is included in the element g0.

The nontrigonometrical term multiplied by the time in nSz is included in the element n.
All other terms are contained in Tables II-V.

The constant part of v contains the correction due to difference between mean and osculating values of the semi-
major axis.

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

3G3

Tables of (98) Minerva — Continued.
PERTURBATIONS— Continued.

ndz

V

a cos i

Arg
iff—19'

sin

cos

sin

.,!<

sin

cos

i i'

//

tr

//

//

//

//

+ 1 - 5

+ 2.2

1.5

+ 1.7

+ 2.5

+2.3

+ 2.7

+2

-332. 4

+320. 7

+17. 5

+30.0

-1. 1

+ 1.2

+3

-178.9

— 24. 6

+14. 3

+93.8

+2.4

-21. 1

+4

+ 15.6

+ 2.7

+ 2.4

- 6.5

-0.5

+ 0.9

+5

- 1.9

- 2.1

- 1.6

+ 1.3

+0.1

- 0.2

+6-5

+ 0.1

- 0.1

+1 - 6

0.1

- 0.1

- 0.1

+2

-3.6

■ 0.6

+ 0.8

-1.6

+0.5

- 0.5

+3

+ 17.4

+ 14.!)

+ 6.6

- 7.0

-1.8

+ 1.2

+4

+ 1.8

+ 7.3

+ 4.8

- 1.6

-1.2

+5

+ 0.6

- 3.1

- 2.2

- 0.5

+0.3

+ 0.1

+•

- 0.6

+ 0.7

+ 0.5

+ 0.5

-0.1

+ 7-6

+ 0.1

+2 - 7

- 0.3

+ 0.3

+0.3

+3

+ 0.8

+ 10.2

+ 2.6

+ 0.3

-0.3

+4

-4.6

+ 6.7

+ 3.9

+ 2.4

-0.9

- 1.0

+5

+ 2.1

- 1. 1

- 0.7

— 1.3

+0.1

+ 0.3

+ <i

- 1. 1

0.1

- 0. 1

+ 0.8

- 0. 1

+7 - 7

+ 0.3

+ 0.2

+ 0.2

— 0. 2

+2-8

- 0. 1

+ 0.1

- 0.1

- 0.1

-0.1

- 0.1

+3

- 10.7

+ 12.0

- 0.8

- 1.5

- 0.3

+4

+ 13.0

- 2.0

- 0.9

- 6.3

-0.3

+ 1.9

+5

+ 0.8

+ 0.7

+ 0.3

- 0.8

-0.2

+ 0.2

+6

- 0.5

- 0.7

- 0.5

+ 0.3

+0.1

+7

+ 0.4

+ 0.3

+8-8

- 0.1

- 0.1

+3-9

- 0.1

- 0.1

+4

+ 1.1

+ 0.8

+ 0.3

- 0. 4

-0.1

+ 0.1

+5

+ 0.2

+ 0.9

+ 0.5

- 0.2

-0.2

+6

+ 0.1

- 0.5

- 0.3

- 0.1

+0.1

+7

— 0.2

+ 0.2

+ 0.2

+ 0.2

+8-9

+ 0.2

0.0

- 0.1

+4 -10

+ 0.6

+ 1.8

+ 0.3

+5

- 0.7

+ 1.1

+ 0.6

+ 0.4

-0.2

- 0.2

+6

+ 0.2

- 0.1

- 0.1

- 0. 1

+ 0.1

+7 -10

— 0.2

+ 0.1

+5 -11

+ 0.4
+ 4.0

- 0. 1
+ 11.1

- 0.2

- 0.2

+5 -13

+6 -13

+ 0.5

- 1. 1

- 0.5

— 0. 2

+0.2

+ 0. 2

included in the clement n.

The constant part in ndz is included in the element ga.
The nontrigonometrical term multiplied by the time 111 ndz
All other terms are contained in Tables II-V.

The constant part of. v contains the correction due to difference between mean and osculating values of the semi-
major axis.

S93600— vol 10—11 24

364

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (93) Minerva — Continued.

PERIODIC TERMS.

TABLE II.— n3z.

Unit of a and 6=09001.

Arg.

«.

Diff. f..rl°

5,

Diff. for 1°

Arg.

a.

Diff. for 1°

6.

Diff. for 1°

O

0

+ 81.5

+ 8. 48

+ 45.9

- 1.90

180

+311.8

- 0.85

-142.2

-13.71

3

+ 106. 9

+ 8.43

+ 38.5

- 3.10

183

+306. 5

- 2.67

-182.8

-13.33

6

+ 131.9

+ 8.20

+ 27.3

- 4.32

186

+295. 9

— 4.41

-221. 9

-12.72

9

+ 155.9

+ 7.77

+ 12.5

- 5.54

189

+280. 2

- 6.02

-258. 9

-11.87

12

+178.3

+ 7. 15

5.9

- 6.72

192

+259. 9

- 7.48

-292. 9

-10. 82

15

+19S. 6

+ 6.34

- 27.7

- 7.83

195

+235. 5

- 8.75

-323. 6

- 9.59

18

+216.2

+ 5.34

- 52.8

- 8.85

198

+207. 7

- 9.81

-350. 3

- 8. 22

21

+230. 5

+ 4.18

- 80.7

- 9. 72

201

+176. 9

-10.64

-372. 8

- 6.73

24

+241.1

+ 2.88

-111.0

-10. 45

204

+144. 0

-11.25

-390. 6

- 5. 17

27

+247. 6

+ 1.46

-143. 2

-10. 99

207

+109. 7

-11.61

-403. 8

- 3.58

30

+249. 8

- 0.06

-176.7

-11.33

210

+ 74.6

-11.73

-412.1

- 1.99

33

+247. 2

- 1.64

-210. 9

-11.45

213

+ 39.5

-11.61

-415.8

- 0.44

36

+240. 0

— 3.22

-24:.. 2

-11.36

216

+ 5.1

-11.28

-414. 8

+ 1.01

39

+227. 9

- 4. SI

-278. 8

-11.02

219

- 27.9

-10. 74

-409. 6

+ 2.41

42

+211. 1

- 6.42

-311. 1

-10.45

222

- 59.1

-10.02

-400. 5

+ 3.64

45

+189. 9

- 7.81

-341. 3

- 9.68

225

- 87.9

- 9.15

-387.9

•+ 4. 73

48

+164.4

- 9.08

-368. 9

- 8.69

228

-113.9

- 8.17

-372.3

+ 5.64

51

+ 135. 2

-10. 33

-393. 3

- 7.52

231

-136.8

- 7.10

-354. 3

+ 6.35

54

+ 102. 6

-11.33

-413.9

- 6.18

234

-156.4

- 5.96

-334. 4

+ 6.90

57

+ 67.4

-12. 13

-430. 2

- 4.72

237

-172. 6

- 4.80

-313. 1

+ 7.26

60

+ 30.1

-12.71

-442. 1

- 3. 15

240

-185.3

- 3.66

-291.0

+ 7.41

63

- 8.7

-13. 07

--449. 1

- 1.51

243

-194. 6

— 2.54

-268.8

+ 7.40

66

- 48.1

-13.19

-451. 1

+ 0.13

246

-200. 6

- 1.48

-246. 8

+ 7.23

69

- 87.6

-13. 08

-448. 3

+ 1.78

249

-203. 5

- 0.51

-225.5

+ 6.91

72

-126.4

-12. 74

—440.5

+ 3.40

252

-203. 7

+ 0.36

-205. 4

+ 6.47

75

-163. 8

-12. 19

-427. 9

+ 4.94

255

-201.5

+ 1.11

1S6. 8

+ 5.92

78

—199. 3

-11.46

-410. 9

+ 6.39

258

-197.2

+ 1.73

—169. 9

+ 5.31

81

-232. 4

-10. 54

-389. 8

+ 7.71

261

-191.2

+ 2.21

-155. 0

+ 4.65

84

-262. 4

- 9. 48

-364. 8

+ 8.91

264

-184.0

+ 2.56

-142.1

+ 3.96

87

-289. 1

- 8.29

-336. 4

+ 9.97

267

-176.0

+ 2.77

-131.2

+ 3.27

90

-312. 1

- 6.99

-305. 2

+10. 86

270

-167.6

+ 2.85

-122.4

+ 2.60

93

-331.0

- 5.60

-271. 4

+ 11.61

273

-159.0

+ 2.81

-115.6

+ 1.99

96

-345. 6

- 4. 15

-235. 7

+12. 19

276

-150. 8

+ 2.67

-110.4

+ 1.44

99

-355. 8

- 2.64

-198.4

+12. 61

279

-143. 1

+ 2.44

-106.8

+ 0.98

102

-361.4

- 1.09

-160. 2

+12. 86

2S2

-136. 2

+ 2.13

-104. 5

+ 0.61

105

-362. 4

+ 0. 48

-121.4

+ 12.95

285

-130.4

+ 1.78

-103.1

+ 0.34

108

-358. 6

+ 2.06

- 82. 7

+ 12.87

288

-125. 6

+ 1.41

-102. 3

+ 0.18

111

-350. 0

+ 3.63

- 44.4

+ 12. 62

291

-121.9

+ 1.03

-101. 9

+ 0. 15

114

-336. 8

+ 5.18

- 7.1

+12. 20

294

-119.4

+ 0.66

-101.3

+ 0.21

117

-319.0

+ 6.69

+ 28.6

+11.59

297

-117.9

+ 0.34

-100.5

+ 0.37

120

-296. 8

+ 8.13

+ 62.3

+10. 81

300

-117.3

+ 0.07

- 99.0

+ 0.62

123

-270. 3

+ 9.48

+ 93.3

+ 9.86

303

-117.4

- 0. 11

- 96.7

+ 0.95

126

-240.0

+10. 72

+ 121.2

+ 8.73

306

-117.9

- 0.22

- 93.3

+ 1.35

129

-206. 1

+ 11.84

+145. 6

+ 7.44

309

-118.7

- 0.24

- 88.6

+ 1.78

132

-169. 1

+12.77

+165. 7

+ 5.99

312

-119.2

- 0.15

- 82.6

+ 2.23

135

-129.6

+13. 56

+181.4

+ 4.42

315

-119.4

+ 0.07

.- 75.2

+ 2.68

138

- 88.1

+ 14. 08

+192. 1

+ 2.74

318

-118.7

+ 0.39

- 66.6

+ 3.10

141

— 45.4

+ 14.39

+197. 7

+ 0.98

321

-116.9

+ 0.81

- 56.6

+ 3.49

144

- 2.1

+ 14.46

+198. 0

- 0. S3

324

-113.8

+ 1.33

- 45.7

+ 3.82

147

+ 41. 1

+14. 28

+ 192. 8

- 2.64

327

-108. 9

+ 1. 94

- 33.8

+ 4.05

150

+ 83.4

+13. 84

+182. 2

- 4.44

330

-102.1

+ 2.62

- 21. 5 .

+ 4.18

153

+ 123.9

+ 13. 15

+166.2

- 6. 16

333

- 93.1

+ 3.36

- 8.9

+ 4.19

156

+ 162.0

+12. 23

+145. 3

- 7.78

336

- 81.9

+ 4.13

+ 3.6

+ 4.06

159

+ 197.0

+11.07

+119.7

- 9.28

339

- 68.3

+ 4.91

+ 15.4

+ 3.80

162

+228. 2

+ 9.72

+ S9. 9

-10. 59

342

— 52.4

+ 5.68

+ 26.2

+ 3.39

165

+255. 2

+ 8.20

+ 56.4

-11.70

345

- 34.2

+ 6.41

4- 35. 6

+ 2.82

168

+277.3

+ 6.52

+ 19.9

-12.61

348

- 14.0

+ 7.06

+ 43.0

+ 2.11

171

+ 294. 2

+ 4.74

- 19.0

-13. 27

351

+ 8.0

+ 7. 62

+ 48.1

+ 1.28

174

+305. 7

+ 2.90

- 59.5

-13. 67

354

+ 31.0

+ 8.05

+ 50. 6

+ 0.31

177

+311.6

+ 1.02

— 100. 8

-13. 82

357

+ 56.2

+ 8.35

+ 49.9

- 0.76

180

+311.8

- 0.85

-142. 2

-13.71

360

+ 81.5

+ 8.48

+ 45.9

- 1.90

\niz,S logr, and iS/? are to be computed in the form Ji[ai+(Jbi)t]sinic+£i[bi-t-(4bi)i]coa h+(Jbo)t.)

MINOR PLANETS DISCOVERED BY WATSON— LEU.SCHNER.

365

Tables of (98) Minerva — Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of a and 6=09001.

Arg.

K

Diff.

Diff.

6,

Diff.

Diff.

bt

Diff.

Diff.

h

Diff.

fori0

<h

fori"

fur 1°

"4

fori0

forl°

«5

fori0

Cor 1°

0

0

+ 98.0

-3.85

+112.7

+ 1.72

+ 22.0

-7. 56

-3.6

+0.25

+1.9

+0.48

+2.9

+0.54

+3.8

-0.40

5

4- 78. 0

-4.13

+114.4

1 IIS

- 16.9

-7.81

-1.6

+0. 52

. :: s

+0.22

+4.7

+0.14

+1.0

-0.66

10

4- 56.9

-4.30

+102. 1

-3.79

- 54. 3

-6.99

+1.2

n 55

+4.0

-0.16

+4.2

-0.32

-2.3

-0.60

15

4- 35.2

-4.34

+ 77.3

-6.01

- 85.2

-5.24

+3.6

+0.33

+2.3

-0.49

+ 1.7

-0.64

—4.5

-0.24

20

4- 13.6

-4. 26

+ 43.3

-7.42

-105. 6

-2.81

+4.2

-0.06

-0.5

-0.60

—1.7

-0.64

-4.5

+0.24

25

■ 7.2

-4.06

+ 4.7

-7.85

-112.8

-0. 05

+3.0

—0.44

-3.3

-0.43

-4.2

-0. 33 -2. 3

+0.60

30

- 26.8

—3.75

- 33.4

-7.25

-106. 2

+ 2. 62

+0.2

-0.63

-4.5

-0. C6

-4.7

+0.14

+1.0

+0.67

35

- 44. 6

-3.33

66.3

-5.76

- 87.3

+4.83

-2. 9

—0. 55

-3.7

+0.37

-2.9

+0. 54

+3.8

+0.41

40

- 59.9

—2.82

— 89.9

-3.61

- 59.1

+6.31

-4.9

—0.19

—1.0

+0.66

+0.2

+0.67

+4.8

-0.04

45

- 72.6

-2. 22

-101. 9

-1. 17

- 25.8

+6.86

-4.6

+0.28

+2.4

+0.66

+3.3

+0.48

+3.4

-0.46

50

- 82.0

-1.54

-101.7

+1.18

+ 7.9

+6.46

-2.2

+0. 65

+5.1

+0.36

+4.7

+0.00

+0.5

-0.66

55

- 87.9

ii s2

- 90.8

+3. 12

+ 37.8

+5. 33

+1.4

+0.76

+5.7

-0. 13

+3.9

-0.37

-2.0

-0. 54

GO

- 90.1

-0.04

- 71.7

+4.37

+ 60.4

+3. 65

+4.9

ii -,l

+3.8

-0. 59

+ 1.3

-0.62

-4.5

-0. 17

65

- 88.4

+0. 74

- 48.3

+4. 85

+ 74.0

+1.79

+6.5

+0.07

+0.1

-0.83 -1.9

-0.58

-4.2

+0. 20

70

- 82.7

+ 1.51

- 24. 4

+4.59

+ 78.5

+0.27

+5.5

-0.46

-4.0

-0. 74 —4.1

-0.28

-2.0

+0. 57

75

- 73.3

+2. 24

-3.2

+3.79

+ 75.4

-1.23

+2.2

-0.83

-6.8

-0. 32 -4. 4

+0. 15

+ 1.1

+0.01

80

- 60.5

+2. 88

+ 13.1

+2. 70

+ 67.1

-1.96

-2.3

-0.88

-0.9

4-0. 24 -2. 7

+0. 51

+3.7

+0.37

85

- 44.7

+3.41

+ 23.8

+ 1.63

+ 56.7

-2.11

-6.1

-0.58

-4.4

+0. 73 +0. 2

+0.62

+4.5

-0.04

90

- 26.7

+3.77

+ 29.8

+0.82

+ 46. 7

-1.82

-7.7

-0.02

0.0

+0. 95

+3.1

+0.46

+3.3

-0.42

95

-7.3

+3.96

+ 32. 7

+0. 44

+ 38.9

-1.30

-6.3

+0.55

+4.5

+0.79

+4.5

+0.09

+0.6

-0.62

100

+ 12.6

+3. 95

+ 34. 9

+0. 51

+ 33.6

-0.83

-2.5

+0.91

+7.4

+0.32

+3.9

-0.32

—2.4

-0.53

105

+ 31.9

+3. 74

+ 38.3

+0.89

+ 30. 1

-0.64

+2.3

+0.93

+7.5

-0. 28

+ 1.5

-0.59

-4.3

-0.20

110

+ 49.7

+3.35

+ 44.0

+ 1.38

+ 26. 5

-0.88

+6.2

+0. 58

+4.8

-0. 7s -1.6

-0.59

-4.3

+0.22

115

+ 65.1

+ 2. SI

+ 51.9

+ 1.71

+ 20.6

— 1. 54

+7.8

+0.01

+0.2

-0. HO -4.0

-0.32

—2.3

+0. 55

120

+ 77. 6

+2.14

+ 60.4

+1.63

+ 10.6

-2.51

+6.4

-0. 55

-4.3

-0.77—4.6

+0.10

+0.8

+0.63

125

+ 86.4

+1.39

+ 67.2

+1.00

-4.6

-3.53

+2.6

-0.89

-7.1

-0. 30 -3. 0

+0.49

+3.6

+0.42

130

+ 91.4

+0.60

+ 69.5

-0.18

- 24.3 -4.33

-2.0

-0.87

-7.1

+0.28

0.0

+0.66

+4.7

+0.01

135

+ 92.4

-0.19

+ 64.7

-1.82

- 46.9

-4. 55

-5.6

-0.52

-4.5

+0.72

+3.1

+0.51

+3.7

-0.42

140

+ 89.5

-0.96

+ 51. 1

-3.62

- 69.2

-4. 11

-6.9

+0.01

-0.3

+0.86

+4.8

+0.12

+0.8

-0.66

14.'.

+ 82.9

-1.68

+ 28. 7

-5. 28

- 87.4

-3.00

-5. 5

+0. 51

+3.6

+0.66

+4.2

-0.33

-2.5

-0.59

150

4- 72. 9

-2.32

-0.9

-6.45

- 97.9

— 1.11

-2.2

+0.76

+5.9

+0.22

+1.6

-0.64

—4.6

-0.23

1 55

+ 59.8

-2.90

- 34. 5

-6.87

- 97.8

+1.21

+1.6

+0.71

+5.7

-0. 27

-1.8

-0.64

-4.6

+0.24

1G0

+ 44.1

-3.37

- 68.1

-6. 38

- 85. 6

- 3 66

+4.4

+0.36

+3.4

-0.01 -4.3

-0.33

-2.3

+0.61

165

-I- 2(3. 2

-3. 74

- 96.8

-4. 96

- 61.6

+5.88

+5.1

-0.08

0.0

-0. 66 -4. 8

+0.15

+1.1

+0.68

170

+ 6. S

-4. 02

-116.3

-2. 75

- 27.9

+7. 45

+3.7

-0.44

-2. S

-0.44—3.0

+0.56

+4.0

+0.41

175

- 13.7

-4.18

-123.4

-0.04

+ 11.5

- s. 1,|

+1.0

-0. 58

-4.1

— 0. 06 +0. 3

+0.69

+4.9

-0.07

180

- 34.8

-4. 23

-116.5

+2.82

+ 51. 9

+7.82

-1.7

-0.44

-3.4

+0. 30! +3. 5

+0.49

+3.5

-0.49

L85

- 55.8

-4. 17

- 95. 8

+5.39

+ 88.0

+6. 40

-3.1

-0.12

—1.3

+0. 48' +4. 9

+0.05

+0.4

-0.69

190

- 76.3

-4. 00

- 63.6

+ 7. 32

+ 115. 0

+4.22

-2.9

+0.21

+ 1.0

-11.41 +3.9

-0.41

-2.9

-0. 54

195

- 95.6

-3. 73

- 24. 1

+8.32

+ 129.3

+ 1.42

—1.2

+0.41

+2.5

+0. 16 +1.1

-0.66

-4.7

-0. 14

200

-113.4

-3.36

+ 17.7

+ 129. 0

-1.54

+0.8

+0.39

+2.5

-0. 10 -2.2

-0.59

-4.2

+0.32

205

-129. 1

—2. 90

+ 56.3

+ 7. 06

+ 114.3

—4.26

+2.3

+0.17

+1.1

-0. 30 -4. 3

-0.23

-1.7

+0.61

210

-142.2

-2.36

+ 86.8

+5. 00

+ 87.5

-6.32

+2.4

-0.12

-0.8

-0.37

-4.3

+0.22

+1.5

+0.60

215

-152.5

-1.75

+105. 4

+2.37

+ 52.6

-7. 40

+1.2

—0.34

-2.3

-0.19

-2.3

+0. 55

+3.9

+0.31

220

-159. 7

-1.09

+ 110.2

-0.43

+ 14.7

-7. 53

-0.7

-0.37

-2.6

+0.09

+0.7

+0.60

+4.4

-0. 12

225

-163. 4

-0.39

+ 101.5

-2. 98

- 21.0

—6.57

-2.2

-0.22

-1.5

+0.31

+3.3

+0.38

+2.8

-0.47

230

-163. 5

+0.34

+ 81.4

- 1.91

- 49. 6

-4.78

-2.7

+0.04

+0.3

+0.38

+4.2

-0.01

0.0

-0. 58

235

-160.0

+1.08

+ 53.9

—5. 93

- 67.9

—2.46

—1.9

+0.27

+1.9

+0. 251 +3. 2

-0.37

-2.6

-0.42

240

-152. 7

+1.82

+ 23. 8

-5.98

- 74.1

-0.04

-0.2

+0.36

+2.6

+0. 02 +0. 8

-0.54

-3.9

-0.09

245

-141.9

+2. 52

-4.3

-5.11

- 68.8

+2.07

+1.5

+0.28

+2.1

-0.22 -1.9

-0.47

-3.5

+0.27

250

-127. 6

+3. 18

— 26.2

-3.54

- 54. 5

+3.57

+2.3

+0.06

+0.6

-0. 34 -3. 6

-0.19

—1.5

+0.49

255

-110 2

+3.76

— 39.1

-1.61

- 34.5

+4.25

+2. 0

-0.17

-1.0

-0. 28 -3. 6

+0.16

+1.1

+0.48

260

- 90.1

+4.27

- 42.3

+0.32

- 13.4

+4.04

+0.8

-0. 29

—1.9

-0. OS -2. 1

+0.42

+3.1

+0.28

265

- 117. 7

+4.67

- 36.6

} l.ss

+ 4.7

+3.09

-0.6

-0.26

-1.8

+0. 13; +0. 2

+0.49

+3.7

-0.04

270

— 43.6

+4.96

- 24. (i

+ 2.78

+ 16.6

+1.61

-1.6

-0.09

-0.8

+0. 26 +2. 5

+0.36

+2.7

-0.33

275

- 18.3

+5. 13

- 10.1

+2.91

+ 20. 5

-0.04

-1.5

+0.11

+0.6

+0. 24 +3. 6

+0.08

+0.6

-0.48

280

+ 7.5

+ 5. 18

+ 3.2

+2. 27

+ 16.5

-1.51

-0.5

+0.24

+ 1.4

+0.08

-0.24

—1.8

-0.42

285

+ 33.2

+5. 09

+ 11 6

+ 1.01

+ 6.2

-2. 50

+0.7

+0.22

+1.3

-0.13 +1.4

-0.46

—3.4

-0.19

290

+ 58.1

+4.87

+ 12.8

-0. 56

- 7.4

-2. 78

+1.5

+0.06

+0.3

-0.25 — 1. 1

-0.48

-3.6

+0.14

295

+ 81.7

+4. 52

+ 6.1

-2.10

- 20.3

-2. 26

+ 1.3

-0. 14

—1.0

-0. 23 -3. 1

-0.29

-2.1

+0.42

300

4-103. 2

+4.07

- 7.6

-3.28

- 28. S

-1.04

+0.2

-0.28

—1.8

-0. 06 -3. 8

+0.03

+0.3

+0. 52

305

+122. 2

+3.51

- 25.7

-3.80

- 29.9

+0.66

-1.2

-0.26

-1.5

+0. 13 —2. 8

+0.36

+2.7

4 0.39

310

+ 13S. 1

+2.86

— 44.3

-3. 51

- 22.0

+2.50

-2.2

-0.09

-0.3

+0.31 -0.4

+0.54

+3.9

+0.08

315

4-150. 6

+2. 14

- 59.3

-2.43 ■ 5.2

+4. 12

-2.0

+0.16

+1.4

+0. 32 +2. 2

+0.48

+3.4

-0.29

320

+ 159.4

+ 1.38

- 66.9

-0.57

+ 18. 3

+ 5.20

-0.7

+0. 35

+2.6

+0.14 +4.0

+0.18

+1.2

-0.54

325

+164.4

+0.59

- 64.4

+ 1.62

+ 45.2

+5.42

+ 1.3

+0.38

+2.6

-0. 14

-0.22

—1.7

-0.55

330

+165. 3

-0.20

— 50.8

+3.82

+ 70. 9

+4.72

+ 2.9

+ 0. 22

+1.3

-0.3S +1.9

-0.53

—3.9

-0.28

335

+162.4

-0.96

- 26. 8

+5.65

+ 90.9

+3.12

+3.2

-0.08

-0.9

-0.45-1.1

-0. 60

-4.3

+0.14

340

+ 155.8

-1.69

+ 4.5

+6.74

+101. 1

+0.86

+2.1

-0.36

-2. 9

-0.31—3.7

-0. 3S

-2.6

+0.50

345

+145. 6

-2.36

+ 39.0

■ (, Nil

+ 98. 9

-1.73

-0.2

—0.50

-3.7

-0.01 -4.0

+0.04

+0.4

+0.65

350

+132. 3

-2. 95

+ 71.7

+ 6.02

! + 83. 8

-4.26

-2.6

-0.41

-2.9

+0. 32 -3. 2

+0.46

+3.3

+0.47

355

+ 116.2

-3. 45

+ 97.6

+4.21

+ 57. 1

-6.32

-3.9

—0.11

-0.7

+0. 52 -0. 3

+0.66

+4.7

+0.50

360

+ 98.0

-3.85

+112.7

+ 1.72

j + 22. 0

-7.56

-3.6

+0.25

+1.9

+0.48 +2.9

+0.54

+3.8

-0.40

[n.52 .J log r, and Ware to be computed in the form 2i[ai + (Jbi)i] sin ic+Zi[bi+(Jbi)]t cos it+(Jbo)t-]

366

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (93) Minerva — Continued.
TABLE II.— nSz— Continued.

PERIODIC TERMS.

Unit of o ando=.0?001.

Arg.

«3

Diff.forl0

h

Diff.forl0

Arg.

«3

Diff.forl0

h

Diff.forl0

0

0

4- 89.6

+ 8.34

+ 93.5

- 7.73

O

180

- 99.0

- 7.59

- 87.3

+ 8.76

3

+ 111.3

+ 6.06

+ 67.3

- 9.68

183

-118.0

- 5.02

- 58.4

+ 10. 40

6

+125. 5

+ 3.33

+ 36.1

-10.97

186

-128. 8

- 2. 13

- 25.6

+11.31

9

+ 131.1

+ 0.35

+ 2. 2

-11.51

189

-130. 6

+ 0.89

+ 8.7

+11.44

12

+ 127. 6

- 2.68

- 32. 1

-11.24

192

-123. 5

+ 3. 82

+ 42.2

+10. 76

15

+ 115.2

- 5.54

- 64.5

-10. 18

195

-108.0

+ 6.47

+ 72.6

+ 9. 30

18

+ 94.7

- 8.04

- 92.5

— 8.40

198

- 85.2

+ 8.64

+ 97.8

+ 7.33

21

+ 67. 5

- 9.99

-114.3

- 6.03

201

- 56.7

+ 10. 20

+116. 1

+ 4.81

24

+ 35.4

-11. 24

-128.3

- 3.22

204

- 24.7

+ 11.05

+126. 4

+ 2.00

27

+ 0.8

-11.71

-133. 4

- 0.16

207

+ 8.8

+ 11.14

+ 128.0

- 0.93

30

- 34. 1

-11.37

-129.2

+ 2.91

210

+ 41.4

+ 10.47

+ 120. 9

- 3. 76

33

- 66.6

-10. 23

-116. 1

+ 5.80

213

+ 71.0

+ 9.10

+105. 7

- 6.32

36

- 94.7

- 8.36

- 94.8

+ 8.29

216

+ 95.4

+ 7.13

+ 83.4

- 8.41

39

-116.2

- 5.90

- 66.9

+10. 19

219

+113.3

+ 4.69

+ 55.8

^- 9.91

42

-129.7

- 3.04

— 34.4

+ 11.39

222

+123. 3

+ 1.97

+ 24.7

-10. 73

45

-134. 2

+ 0.04

+ 0.6

+ 11.78

225

+125. 0

- 0.85

- 7.9

-10.82

48

-129. 5

+ 3.12

+ 35.5

+ 11.36

228

+118.3

- 3.59

- 39.6

-10. 18

51

-115.8

+ 5.98

+ 68.0

+ 10. 15

231

+103. 7

- 6.06

- 68.3

- 8.88

54

- 94.0

+ 8.41

+ 95. 7

+ 8. 22

234

+ 82. 4

- 8.09

- 92.2

- 6.99

57

- 65.9

+10. 26

+116.8

+ 5. 75

237

+ 55.7

- 9.56

-109.8

- 4.66

60

- 33.2

+ 11.39

+ 129.8

+ 2. 91

240

+ 25. 6

-10.40

-119.9

- 2.04

63

+ 1-7

+11.72

+133. 9

- 0. 2(1

243

-5.9

-10.53

-122. 0

+ 0.68

66

+ 36.3

+11. 26

+128. 7

- 3. 22

246

- 36.8

- 9.95

-116.0

+ 3.32

69

+ 68.4

+ 10.01

+ 114.8

- 6.02

249

- 64.9

- 8.74

-102.3

+ 5.72

72

+ 95.8

+ 8.09

+ 93.0

- 8.41

252

— SS. 6

- 6.96

- 82.1

+ 7.72

75

+116. 5

+ 5.63

+ 64.9

-10. 20

255

-100.2

- 4.74

- 56.5

+ 9. 20

78

+129. 2

+ 2.79

+ 32.5

-11.29

258

-116.8

- 2.24

- 27.4

+10. 07

81

+133. 1

- 0.22

- 2.1

-11.62

261

—119.6

+ 0.39

+ 3.2

+10. 27

84

+127. 9

- 3.22

- 36.4

-11. 35

264

-114.5

+ 2. 98

+ 33. 5

+ 9.81

87

+113. 9

- 5.99

- 68.3

- 9.94

267

-101.9

+ 5.36

+ 61.4

+ 8.71

90

+ 92.3

- 8. 34

- 9.",. 4

- 8.04

270

- 82.7

+ 7.37

+ 85. 2

+ 7.06

93

+ 64.4

-10. 14

-116.0

- 5.61

273

- 58.2

+ 8. 91

+103. 3

+ 4. 95

96

+ 32. 2

-11. 24

-128.7

- 2.80

276

- 29.9

+ 9.86

+ 114.6

+ 2.53

99

— 2.2

-11.58

-132.6

+ 0.20

279

+ 0.4

+10. 18

+ 118.4

- 0.05

102

- 36.5

-11.14

L27.5

+ 3. IS

282

+ 30.5

+ 9.83

+114.3

- 2.64

105

- 68.3

- 9.94

-113.7

+ 5.96

285

+ 58. 7

+ 8.84

+102. 7

- 5.04

108

- 95.5

- 8.07

- 92.1

+ 8.34

288

+ 83.0

+ 7.28

+ 84.4

- 7.13

111

-116.2

— 5.64

- 61.2

+10. 15

291

+101. 9

+ 5. 24

+ 60.4

- 8.77

114

-128.9

- 2.82

- 31.9

+11.28

294

+ 114.1

+ 2.85

+ 32.3

- 9.83

117

-132.9

+ 0. 20

+ 2.7

+11.64

297

+ 118.8

+ 0.26

+ 2.1

-10.25

120

-127.7

+ 3.22

+ 37.2

+11. 20

300

+115.6

- 2.38

- 28.5

-10.02

123

-113.8

+ 6.03

+ 69.1

+ 9.99

303

+104. 7

- 4.88

- 57.4

- 9.11

126

- 91.9

+ 8.44

+ 96.4

+ 8.09

306

+ 86.7

- 7.06

- 82.6

- 7.58

129

- 63. 7

+10. 28

+117.1

+ 5.62

309

+ 62.7

- 8.81

-102. 4

- 5.55

132

- 31.0

+11.39

+129. 8

+ 2.76

312

+ 34.4

- 9.99

-115. 5

- 3.12

135

+ 3.9

+11. 73

+133. 5

- 0.32

315

+ 3.4

-10. 50

-120. 9

- 0.44

138

+ 38.6

+11. 26

+ 127.9

- 3.38

318

- 27.9

-10.31

-118. 1

+ 2.28

141

+ 70.6

+ 9.99

+ 113.4

- 6.20

321

- 57.8

- 9.44

-107.4

+ 4.87

144

+ 97.8

+ 8.03

f 91.1

- 8.61

324

- 83.9

- 7.90

- 89.2

+ 7.18

147

+118.2

+ 5.49

+ 62.4

-10.41

327

-104.6

- 5.81

- 61. S

+ 9.03

150

+ 130.4

+ 2.60

+ 29.4

-11.48

330

-118.3

- 3.30

- 35.6

+10. 28

153

+133. 5

- 0.52

5.7

-11. 76

333

-124. 1

- 0. 52

-3.8

+ 10. 83

156

+127.3

- 3.58

- 40.4

-11. 21

336

-121.4

+ 2.31

+ 28.7

+10. 66

159

+112.2

- 6.39

- 72.2

- 9.87

339

-110. 4

+ 5.02

+ 59.5

+ 9.75

162

+ 89.4

- 8.74

- 98.9

- 7.84

342

- 91.6

+ 7.42

+ 86. 5

+ 8.16

165

+ 60.4

-10.48

-118.7

- 5.27

345

- 66.3

+ 9.33

+107.8

+ 5.98

168

+ 27.3

—11.47

-130. 2

- 2.33

348

- 36.2

+10. 63

+121. 9

+ 3.36

171

-7.6

-11. 65

-132.6

+ 0. 7 1

351

-3.2

+11.19

+127. 8

+ 0.48

174

- 41.8

-11.02

-125. 8

+ 3. 75

354

+ 30.2

+10. 98

+124. 8

— 2.46

177

- 73.0

- 9.64

-110.3

+ 6.49

357

+ 61.9

+10. 01

+113. 1

- 5. 26

180

- 99.0

- 7.59

- 87.3

+ 8.76

360

+ 89.6

+ 8.34

+ 93.5

- 7.73

[nSz, 5 log r, and V are to be computed in the form -r,[a<+(J6i)i]sin ii+Ii[bi+(Jbi)t] cos ii+(Jba)t-]

PERIODIC TERMS.

MINOR PLANETS DISCOVERED BY WATSON -LEUSCHNER.

Tables of (93 1 Mi n < rva — Cont inued .

TABLE III. — rj logr.

367

Unit of a and 6-0.00001.

Arg.

K

Diff. for 1

"i

Diff. for 1°

b,

Dill.
fori0

"j

Diff.

for 1°

62

Diff. for 1°

O

0

+45. 6

+ 1.00

-nil.:,

-0. 64

+ 10.8

-17.3

+1.28

+ 12.6

+1. 15

10

+52.8

+0.41

-101. 1

+0. 73

+36.1

+ 2. 55

+1.48

+ 17.4

-0. 19

20

+53.6

-0.24

- 87. 2

+2.01

+59.2

+ 1.96

+ 8.7

+0.63

+ 10.2

-1. 12

30

+48.0

II ss

62 5

+2. 82

+ 73. 2

f-0. 78

+ 9.2

-0. 52

- 1.3

-1.00

40

+36. 2

^1.44

- 33.1

+2. 93

+ 73. 7

-ii, 69

+ 0.5

-1.06

- 6.8

-0.03

50

+ 19.6

-1.85

-6.3

+2.30

+ 59.9

-2.03

- 8.5

-0.57

- 1.7

+0.97

60

+ 0.1

-2.02

+ 11.0

+ 1.10

+34.9

-2.86

- 8.6

+0.59

+ 9.8

+ 1. 15

70

-19.8

-1.90

+ 15.0

-0.30

+ 5.0

- 3.0]

+ 2. 5

+ 1.49

+ 17. 6

+0.24

80

-36.7

-1.44

+ 5.7

-1.51

-23.2

-2.53

+17.5

+1.30

+ 13.0

-1.15

90

-47.6

-0.69

- 14. 1

-2.35

-44. :;

-1.66

+24. 7

0.00

-3.4

-1.92

100

-50. 1

+0. 22

- 40.1

-2.81

-55. 8

-0.61

+ 16.7

1 53

-21.0

-1.39

110

-43.5

+ 1.07

- 69. (i

-2.90

-56. 3

+0. 51

- 2.5

-2.08

-27.6

+0.16

120

-29.4

+1.70

- 96.8

-2. 57

-45.4

+ 1.67

-20.4

-1.19

-18.2

+ 1. 59

130

-10.6

+2.00

-118.7

-1.71

— 23. 2

+2.70

-2:.. i;

+0.26

+ 0.4

+ 1.90

140

+ 9.5

+ 1.98

-129.4

-0.36

+ 7. 2

+3.28

-16.4

+ 1.43

+ 15. 6

+0.99

150

+28. 1

+1. 71

-125.2

+ 1.29

+40.0

+3.15

- 0.8

+1.47

+ 18.6

-0.37

160

+42.8

+ 1.22

- L06.2

+2. 54

+ 67. 7

+2. 27

+ 9.8

+0. 53

+ 9.9

-1.20

170

+52. 0

+0.62

- 76.3

+3.31

+83.7

+0.84

+ 9.1

0.62

- 1.8

-0. 96

180

+54. 9

+0.04

- 42.5

+3.30

+83.8

-0.82

- 0.2

-1.07

- 6.5

+0.08

190

+51.2

-0.08

- 13.0

+2.49

+68.3

-2.22

-8.7

-0. 47

- 0.5

+ 1.04

200

+41.6

-1.23

+ 5.2

+ 1.09

+41.3

-3.05

-7.6

+0.73

+11.2

+1.11

210

+27. 1

-1.65

+ 8.1

-0. 50

+10.1

-3.05

+ 4.6

+ 1.56

+18.1

+0.05

220

+ 9.2

-1.89

- 3.8

-1.82

-17.1

-2.27

+20.0

+1.30

+12.1

-1.29

230

-10.1

-1.95

- 26. 2

-2.53

-33. 7

-0.99

+26.9

-0. 05

- 5.5

-2.07

240

-29.0

-1.80

- 52.0

-2.49

-36.5

+0.42

+ 18.1

-1.66

-24.8

-1.56

250

-45. 6

-1.49

- 73.6

-1.73

-26.3

+1. 54

- 3.5

-2.44

-33.0

+0. 05

260

-58. 3

-1.03

- 85.3

-0.56

-7.9

+2. 03

-25. 9

-1.80

-23.1

+1.83

270

-65.9

-0.47

- 84.8

+0.63

+12.0

+ 1.82

-35.6

-0.01

+ 0.4

+2. 65

280

-67.7

+0.13

- 73. 9

+1.46

+26. 5

+1.01

-25.9

+ 1.86

+24. 6

+ 1.93

290

-63.5

+0.71

- 57. 7

+1.66

+31.2

-0.09

- 2.1

+ 2. 67

+35. 2

+0.08

300

-53. 6

+1. 23

- 42.8

+1.20

+25. 0

-1.10

+21.1

+1.92

+26.2

-1.78

310

-39. 2

+ 1. 63

- 35.3

+0. 25

+10.9

-1.63

+32.8

+0.12

+ 3.4

-2. 54

320

-21.5

+ 1.88

- 38.4

-0.86

— 5. 4

-1. 51

+ 24. 6

-1.63

-19.4

-1.79

330

-2.2

+1.94

- 51.6

-1.72

-17.3

-0.76

+ 3.8

-2.28

-29.2

-0. 10

340

+16.6

+1.80

- 71.0

-2.03

-19.3

+0.39

-16.4

-1.54

-21.8

+ 1.46

350

+33.1

+ 1.47

- 89.8

-1.64

- 9.4

+ 1.57

-24. 3

0.00

-3.7

+ 1. 93

360

+45. 6

+ 1.00

-101.5

-0.64

+10.8

+2.38

-17.3

+1.28

+ 12.6

+ 1. 15

tndz, d log r, and if are to be computed in the form J,fai+(J(>j)j] sin U+I4bi+VK)i\ cos ii+(.Jbo)t-]

368

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

Tables of (93) Minerva — Continued.
TABLE III.— S log r— Continued.

PERIODIC TERMS.

Unit of a and J>=0.00001.

Arg.

«3

Diff.

for 1°

b3

Diff.

fur 1°

«4

Diff.
forl°

bt

Diff.
forl°

"S

Diff.
fori0

h

Diff. for 1°

o

0

-7.2

+0.40

+4.5

+0.65

-1.0

-0.19

-1.2

+0.11

-0. 1

-0.04

-0.3

+0.02

10

-0.9

+0.78

+8.5

+0.08

-1.7

+0.07

+0.8

+0. 23

-0.3

+0. 01 0. 0

+0.04

20

+6.2

+0.53

+5.8

-0.59

+0.3

+0.27

+2.2

-0.01

-0.1

+0.03

+0.2

0.00

30

+8.2

-0.18

-1.6

-0.78

+2.3

+0.07

+0.5

-0.28

+0.2

i) 02

+0.2

-0.02

40

+3.3

-0.73

-7.5

-0.24

+1.3

-0.25

-2.1

-0.16

+0.2

-0.02

-0.1

-0. 02

50

-4.2

-0.65

-6.8

+0.42

-1.4

-0.22

-1.9

+0. 19

0.0

-0.04

-0.3

0.00

60

-7.8

-0.04

-0.5

+0.74

-2.1

+0.10

+0.6

+0.26

-0.3

-0.01

0.0

+0.04

70

-5.0

+0. 56

+6.0

+0.46

-0.1

+0. 25

+2.0

-0.01

-0.1

+0.05

+0.4

+0.02

80

+ 1.7

+0.67

+7.6

-0. 15

+1.5

+0.04

+0.6

-0. 21

+0.4

+0.04

+0.2

-0.05

90

+6.9

+0.31

+3.6

-0.59

+0.7

-0.16

-1.1

-0.07

+0.2

-0.05

-0.4

-0.03 •

100

+7.3

-0.23

-2.9

-0.63

-0.7

-0.08

-0.6

+0.14

-0.3

-0.04

-0.3

+0.04

110

+2.8

-0.63

-7.6

-0. 25

-0.4

+0.12

+0.7

II OS

-0. 3 +0. 04

+0.3

+0. 05

120

-3.9

-0.64

-7.3

+0.31

+0.8

+0.08

+0.4

-0. 13

+0.2

+0. 05

+0.3

-0.04

130

-8.2

-0.18

-1.8

+0.72

+0.6

-0. 14

-1.1

-0.10

+0.3

-0.03

-0.2

-0.04

140

-6.7

+0.47

+5.3

+0.60

-1.2

-0.16

-1.0

+0.14

-0.1

-0. 05

-0.3

+0. 02

150

+0.1

+0.79

+8.6

0.00

-1.6

+0.11

+1.1

+0.21

-0.3

+0.02

+0.1

+0.04

160

+6.9

+0.46

+5.0

-0.65

+0.6

+0. 27

+2.1

-0. 05

0.0

+0.05

+0.3

0.00

170

+8.0

-0.26

-2.6

-0.75

+2.4

+0.03

+0.2

-0.29

+0.2

+0.01

■o 1

-0.02

180

+2.4

-0. 75

-7.8

-0.21

+ 1.0

(I. 2S

-2.2

-0.13

+0.2

-0.02

-0.2

-0.01

190

-4.9

-0. 59

-6.3

+0.49

-1.7

-0.19

-1.7

+0.22

-0.1

-0.03

-0.2

+0.01

200

-7.8

+0. 05

+0.4

+0.74

-2.0

+0.14

+ 1.0

+0.24

-0.3

0.00

0.0

+0.04

210

-4.2

+0. 61

+6.4

+0.38

+0.2

+0.24

+ 1.9

-0.06

-0.1

+0.04

+0.4

+0.02

220

+2.6

+0.64

+7.1

-0.25

+1.5

-0.01

+0.3

-0. 20

+0.4

+0.03

+0.2

-0. 05

230

+7.0

+0.19

+2.3

-0. 62

+0.4

-0.16

-1.0

-0.02

+0.2

-0.06

-0.4

-0.04

240

+6.0

-0. 35

-3.7

-0. 50

-0.6

-0.03

-0.3

O 12

-0.4

-0.05

-0.3

+0.06

250

+1.2

-0.55

-6.7

-0.07

0.0

+0.11

+0.5

+0.01

-0.3

+0.06

+0.4

+0.05

260

-3.7

-0.39

-5.3

+0.31

+0.7

0.00

-0.1

-0. 12

+0.4

+0.06

+0.4

-0.06

270

-6.0

-0.07

-1.2

+0. 55

-0.1

-0.13

-0.9

-0.01

+0.4

-0.06

-0.4

-0.06

280

-5.2

+0.21

+3.0

+0.36

-1.1

-0.03

-0.1

+0.14

-0.4

-0.06

-0.4

+0.06

290

-2.1

+0.39

+5.7

+0.16

-0.4

+0.14

+ 1.1

+0.06

-0.4

+0.06

+0.4

+0.06

300

+2.2

+0.44

+5.9

-0.13

+0.9

+0.08

+0.7

-0. 12

+0.4

+0. 05

+0.4

-0.06

310

+6.0

+0.28

+3.1

-0.43

+0.8

-0. 10

-0.7

-0. 10

+0.4

-0.05

-0.3

-0.06

320

+6.9

-0.12

-2.2

-0.56

-0.5

-0.10

-0.7

+0.08

-0.3

-0.06

-0.4

+0. 05

330

+3.4

-0.55

-6.9

-0.32

-0.6

+0.09

+0.5

+0.10

-0.4

+0.04

+0.3

+0.06

340

-3.0

-0.65

-7.5

+0.23

+0.6

+0.10

+0.5

-0.09

+0.2

+0.06

+0.4

-0.04

350

-7.9

-0.25

-2.7

+0.69

+0.7

-0.11

-0.9

-0.13

+0.4

-0.03

-0.2

-0.06

360

-7.2

+0.40

+4.5

+0. 65

-1.0

-0.19

-1.2

+0.11

-0.1

-0.04

-0.3

+0.02

[niz, 3 log r, and.S/?are to be computed in the Jorm ZA<ii+(dbi)t\sm n+I$bi+(,Abi)il cos ie+(Jbo)t.]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

369

Tables of (93) Minerva — Continued.

TABLE IV.— 8$.

PERIODIC TERMS. I'ml of a and 6=0.00001.

Arg.

a2

Diff.forl"

b.

Di IT. fori"

o

0

-23.0

-2.42

-23. 1

+0.70

5

-34. 5

-2.09

-16.9

+1. 77

10

-43. 1

-1.33

- 5.8

+2.62

15

-47. 1

-0.24

+ 8.8

+3.11

20

-45.3

+0.98

+ 24.6

+3.13

25

-37. 5

• 2 L3

+39.3

+2.66

30

-24.5

+3.00

+50. 5

+ 1.77

35

- 8.0

+3.49

+56. 5

+0.59

40

+ 9.6

+3.48

+56 3

-0. 68

45

+26.0

+2.98

+49.8

-1.86

50

+38.8

+2.07

+38.1

2. 75

55

+46.4

+0.91

+23.0

-3.21

60

+47.9

-0.31

+ 6.8

-3. 15

65

+43.6

-1.37

- 8.0

-2.67

70

+34. 7

2. 10

-19.3

-1.81

75

+23.3

-2.39

-25. 8

-0.77

80

+ 11.6

2. 22

-27. 2

+0.21

85

+ 1.9

-1.64

-24. 1

+0.97

90

- 4. 4

-0.84

-18.2

+1.33

95

- 6.5

-0.02

-11.6

+1.26

100

-4.9

+0.61

-6.3

+0.79

105

- 1.0

+0.90

- 4.0

+0.10

110

+ 3.3

+0.76

-5.4

-0. 65

115

+ 6.0

+0. 25

-10.2

-1.22

120

+ 5.4

-0. 52

-17.0

-1.47

125

+ 0.7

-1.37

-24.0

-1.28

130

- 8. 1

-2.08

-29. 1

-0.69

135

-19.6

-2.49

-30.4

+0.23

140

-32. 1

-2. 45

-26. 6

+1.28

145

-43.3

-1.96

-17. 7

+2.28

150

-51.0

-1.06

-4.3

+3.03

155

-53.5

+0.10

+ 12.0

+3.38

160

-49.9

+ 1.34

+28.7

+3.24

165

-40.3

+2.45

+43.6

+2.64

170

-25.8

+3. 27

+54. 4

+ 1.63

175

- 8.4

: :: 61

+59.5

+0.38

180

+ 9.7

+3. 50

+58. 1

-0.92

185

+25. 8

+2.87

+50.6

-2.06

190

+37.8

+1.87

+38.1

-2. 85

195

+44.2

+0. 66

+22.8

-3.19

200

+44.3

-0. 56

+ 7.1

-3.02

205

+38.8

-1.59

-6.6

-2. 39

210

+29.0

-2.24

-16.3

-1.43

215

+ 17.1

-2. 45

-20.0

-0.30

220

+ 5.4

-2. 15

-19.4

+0.73

225

-3.8

-1.46

-13.4

+1.58

230

-8.7

-0.49

-4.2

+2.02

235

-8.6

+0. 56

+ 6.0

+ 1.99

240

-3.3

+1.49

+15. 0

+1.51

245

+ 5.9

+2.17

+20.6

+0.59

250

+ 17.3

+2.35

+21.5

-0.36

255

+28.6

+2.11

+ 17.0

-1.41

260

+37.6

+1.44

+ 7.7

-2.27

265

+42. 5

+0.45

-5.2

-2.82

270

+41.9

-0. 67

-19.6

-2.87

275

+35. S

-1.75

-33.1

-2.47

280

+24.8

-2.58

-43.6

-1.68

285

+10.6

-3.03

-49.4

-0.62

290

- 4. 7

-3.01

-49.6

+0. 54

295

-18.8

-2.53

-44.2

+ 1.57

300

-29.5

-1.70

-34.3

+2.32

305

-35.4

-0.65

-21.6

+2.67

310

-35. 9

+0.43

-8.4

+ 2. 54

315

-31.4

+ 1.33

+ 3.1

+2.00

320

-23. 1

+ 1.91

+ 11.0

+1. 14

325

-12.9

+2.07

+ 14. 2

+0.13

330

- 3.1

+ 1.77

+ 12.4

-0.72

335

+ 4.2

+ 1.09

+ 6.4

-1.54

340

+ 7.4

+0. 16

-2.4

-1.89

345

+ 5.6

-0.84

-11.8

-1.80

350

- 0.9

-1.72

-19.7

-1.26

355

-11.0

-2.28

-23.8

-0.38

360

-23.0

-2.42

-23. 1

+0.70

[nSz, Jlog r, and Spare to be computed in the form Jtfaf + (J&t)r]sin U+2(bi+Abt)i[ cos U+(ibi)tA

370 MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X. NO. 7.

Tables of (93) Minerva — Continued.

PERIODIC TERMS.

Table IV.— 8p— Continued.

1'nit old and 6 = 0.00001.

Arg.

K

Diff. fori"

«i

Diff. fori"

6,

Diff. fori"

«3

Diff. fori"

O

0

-20.6

-0.62

+ 83. 6

+0.44

+ 69.8

-2.28

-1.0

-0. 18

10

-26. 1

-0.48

+ 81. 6

-0.85

+ 46.1

-2. 31

-4.2

+0. 10

20

-30. 0

-0.29

+ 67.2

-1.96

+ 25. 8

-1.64

- 8. 1

+0.49

30

-32. ()

-0.09

+ 44. 1

-2.56

+ 14.9

-0.47

-8.6

+0.61

40

-31. 9

+0. 11

+ 18.3

-2.48

+ 16.8

+0.85

-4.3

4 0.53

50

-29. 8

+0. 29

- 3. 1

-1.72

+ 31.3

+ 1.96

+ 1.8

+0.56

60

-26.0

+0. 4.",

- 14.4

-0. 50

+ 54. 5

+2.57

+ 5.8

+0.23

70

-21. 1

+0.52

- 12.9

+0.79

+ 80.5

+2. 55

+ 6.8

0.00

80

-15.9

+0. 50

+ 0.6

+ 1.86

+ 103. 8

+2.04

+ 6.3

-0.08

90

-11.6

+0.34

+ 22.8

+2. 51

+ 120.5

+ 1.28

+ 5.0

-0.19

100

-9.4

+0.08

+ 49.7

+2. 80

+ 129.0

+0. 45

+ 2.4

-0.31

110

- 9.9

-0. 19

+ 77.9

+2.77

+ 128.8

-0. 48

- 0.6

-0.23

120

-12.9

-0.40

+103. 8

+2. 35

+ 119. 4

-1.36

- 1.6

+0.02

130

-17.6

-0.53

+123. 4

+1.49

+ 101.2

-2.20

- 0.7

+0.08

140

-23.0

-0. 53

+132. 4

+0.27

+ 76.7

-2.61

- 1. 1

-0.19

150

-27.8

-0.43

+128.5

-1.06

+ 51. 1

-2.39

-4.4

-0.41

160

-31.5

-0.29

+112. 1

-2.12

+ 30.9

-1.55

- 8.0

-0.22

170

-33.5

-0.10

SS. II

-2. 60

+ 21.4

-0.31

-7.9

+0.27

180

-33.5

+0. 11

f 62.6

-2.37

+ 24.8

+0.99

-3.2

+0.60

190

-31.4

+0.31

+ 42.8

1.50

+ 40.0

+ 1.96

+ 2.7

+0.52

200

-27.4

+0. 50

+ 33. 8

-0.27

+ 61.9

+2.32

+ 6.4

+0.21

210

-21.8

+0. 62

+ 37.6

+0.98

+ 83.9

+ 1.96

+ 7.4

+0.02

220

-15.0

+0.72

+ 52. 1

+ 1.82

+ 99.1

+0.99

+ 7.4

0.00

230

-7.5

+0.76

+ 71. 8

+2. 01

+ 102. 9

-0.25

+ 7.1

-0.09

240

0.0

+0. 73

+ 90.0

+ 1.50

+ 94.4

-1.39

+ 4.7

-0.45

250

+ 6.9

+0.65

+100. 2

+0.48

+ 76.5

-2.09

-2.2

-0.87

260

+ 12.6

+0. 50

+ 98.8

-0. 75

+ 54.9

-2.11

-11.2

-0.81

270

+ 16.8

+0.32

+ 85.6

-1.81

+ 36. 5

-1.46

-16.0

-0.09

280

+ 19.0

+0.12

+ 64.4

-2.33

+ 27.2

-0.36

-12.0

+0.84

290

+ 19. 1

-0.10

+ 41.3

-2.16

+ 29.9

+0.87

- 1.0

+ 1.21

300

+17.1

-0.30

+ 23. 3

-1.35

+ 43.6

+ 1.80

+ 9. 6

+0. 77

310

+ 13.2

-0.48

+ 15. 6

-0. 16

+ 63.9

+2.14

+13.0

-0.10

320

+ 7.5

-0.63

+ 20. 1

+ 1.03

+ 84. 1

+ 1.78

+ 8.9

-0.63

330

+ 0.8

-0.72

+ 35.1

+ 1.85

+ 97. 6

+0. 85

+ 2.6

-0. 53

340

-6.6

-0.74

+ 55. 1

+2.04

+ 99. S

-0.41

- 0.6

-0.11

350

-13.9

-0.73

+ 73.5

+1. 52

+ 89.6

-1.58

- 0.6

+0.04

360

-20.6

-0.62

+ 83.6

+0.44

+ 69. 8

-2.28

-1.0

-0.18

[nSz, a log r, and If are to be computed in the lorm Z$ai+(Ab()i\sm it + Ji|i)i+J6i)i]cosit+(J6o)(.]

-MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

Tables of (93) Minerva — ( !< mtinued.

371

PERIODIC TERMS.

Tabh IV.— Sp— Continued.

Unit of a and 6=0.00001.

Arg.

b3

Dili', fori"

",

lh If, furl"

h

Diff. fori0

«5

Diff. fori"

h

Diff. for 1°

O

0

-4.6

-0. 14

-3. 1

+ 0. 00

+5.5

+0.22

-0. 1

-0. 10

-0.8

-0.01

10

- 5.2

+0. 10

+2.3

+0.37

+4.6

-0.33

-1.0

-0.02

-0.1

+0. 14

20

- 2.1

+0. 4!l

+ 3.7

-0.07

+0.8

-0.32

-0.2

+0.14

+ 1.0

+0.04

30

+ 3.8

+0. 61

+2.5

-0. 1(»

-1.0

-0.08

+1.0

+0.05

+0.4

-0.14

40

+ 8.6

+0. 29

+1.9

-0.04

-1.9

-0. 13

+0.5

-0. 13

-0.9

-0.07

50

+ 9.0

-0. 19

+0.6

-0.26

-3.6

-0.16

-0.8

-0.08

-0.6

+0.12

60

+ 5.7

-0.41

-3.2

-0.43

-3.7

+0.21

-0.6

+0.10

+0.6

+0.08

70

+ 1.8

-0. 34

-6.0

;

+0.7

+0.61

+0.4

+0.07

+0.6

-0.07

80

- 1. 1

-0.27

-2.9

+0.61

+6.2

+0.37

+0 5

-0. 05

-0.3

-0.06

90

-3.6

-0.23

+4.3

+0.67

+6.1

-0.42

-0.1

-0.06

-0.4

+0. 02

100

-5.3

-0.07

+ 7.7

o 06

-0.8

-0.81

-0. 4

-0.01

0.0

+0. 05

110

-4.8

+0. 10

+3.1

-0.76

-7. 1

-0.33

-0.2

+0.04

+0.4

+0.02

120

-2.8

+0. 18

-4. 5

0. 61

-6.0

+ 0. 51

+0.3

+0.05

+0.3

-O.n:;

130

— 2. 2

-0.08

-6.9

+0.16

+0.9

+0.71

+0.5

-0.02

-0.3

-0.08

140

- 3.9

-0. 18

-2.4

+0.60

+5.6

+0. 15

-0.2

-0.10

-0.7

+0.02

150

- 4.5

+0. 11

+2.7

+0.33

+4.2

-0. 35

-0.9

-0.01

+0.1

+0.12

160

- 1. 1

+0. 53

+3.6

-0.09

+0.5

-0. 29

-0.1

+0.15

+ 1.0

+0.03

170

+ 4.8

+0. 57

+2.4

-0.10

-1.2

-0.07

+ 1.0

+0.04

+0.3

-0. 14

180

+ 9.0

+0.21

+ 1.8

-0.04

-2.1

-0. 14

+0.4

-0. 14

-1.0

-0.06

190

+ 8.7

-0. 23

+0.3

-0.29

-3.8

-0. 15

-0.9

-0.07

-0.6

+0. 14

200

+ 5.2

-0.40

-3. 7

-0.42

-3.5

+0.27

-0.6

+0.12

+0.7

+0.08

210

+ 1.5

-0. 32

-6.0

+0.07

+1.4

+0.62

+0.5

+0.06

+0.5

-0. 10

220

- 1.4

-0. 2!)

-2. 1

+0.66

+6.4

+0. 25

+0.4

-0.08

-0.4

-0.04

230

-4.8

-0.42

+ 4. (i

+0. 53

+5.1

-0.49

-0.3

-0.02

-0.2

+0.06

240

-9.5

-0.47

+6.3

-0.16

-1.3

-0.64

0.0

+0.04

+0.2

0.00

250

-12.6

-0.07

+ 1.8

-0.57

-5.2

-0. 08

+0.2

-0.03

-0.2

-0. 05

260

-9.6

+0.68

-2.6

-0.24

-3.4

+0.35

-0.4

-0.06

-0.3

+0.04

270

+ 0.2

+ 1.18

-2. S

+0.12

-0.2

+0.21

-0.3

+0.06

+0.4

+0.06

280

+11.4

+0.91

-1.7

+0.04

+0.6

0.00

+0.4

+0.06

+0.4

-0.06

290

+ 16.2

0.00

-2.0

-0.03

+1.1

+0. 15

+0.4

-0.06

-0.4

-0.06

300

+ 11.6

-0.83

-1. 4

+0. 23

+3.4

+0.26

-0.2

-0.05

-0.4

+0.04

310

+ 1.8

-0.99

+2.8

+0. 50

+4.3

-0. 17

-0.3

+0.02

+0.1

+0.04

320

-5.8

-0.46

+6.3

+0.09

-0.1

-0. 65

0.0

+0.01

+0.2

-0.01

330

-7.2

+0.18

+3.4

-0.64

-6.2

-0.41

-0.1

0.00

+0.1

+0.02

340

-4.9

+0. 25

-3.8

-0.67

-6.3

+0.40

+0.2

+0.05

+0.3

0.00

350

-3.6

0.00

-7. 1

+0.08

+0.2

+0. 74

+0.6

0.00

-0.2

-0.09

360

-4.6

-0. 14

-3. 1

+0.60

+5. 5

+0. 22

-0.1

-0. 10

-0.8

-0.01

[niz, 3 log r, and ,3(3 are to be computed in the form Ii[<u+(Jbi)i] sin u+Ii[bt+Jbi)t] cos ie+(4bt)t.]

372

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7,
Tables of (93) Minerva — Continued.

TABLE V.— TERMS TO BE MULTIPLIED BY T=(t— 10) IN JULIAN YEARS.

tut:

8 log r

t
3/3

Uni

Unit-0.00001

Unit=0.00001

Year

(J &0)l

,J,V,

<M>,

(Ja2)t

U b2)t

(i6b)i

(J v,

iJ/v,

UK),

J a,),

<-"+>,

1864. 0

+2.7

-8.4

+ 45.3

+0.3

-1.6

+0.5

+ 17.2

+ 3.2

+ 2.9

-136.5

- 20.7

6

+2.7

-6.9

+ 37.5

+0.2

-1.3

+0.4

+14.1

+ 2. 6

+ 2.4

-111.7

- 16.9

8

+2.8

-5.3

+ 28.8

+0.2

—1.0

+0.3

+10.9

f 2. 0

+ 1.9

- 86.9

- 13.2

1870

+2.8

-3.8

+ 20.6

+0.1

-0.7

+0.2

+ 7.8

+ 1.5

+ 1.3

- 62.1

- 9.4

2

+2.9

- 2.3

+ 12.4

+0.1

-0.4

+0.1

+ 4.7

+ 0. 9

+ 0.8

- 37.2

5.6

4

+2.9

- 0.8

+ 4.1

0.0

-0.1

0.0

+ 1.6

+ 0.3

+ 0.3

- 12.4

- 1.9

6

+3.0

+ 0.8

— 4. 1

0.0

+0.1

0.0

- 1.6

- 0.3

- 0.3

+ 12.4

+ 1.9

8

+3.0

+ 2.3

- 12.4

-0.1

+0.4

-0.1

-4.7

- 0.9

- 0.8

+ 37.3

+ 5.6

1880

+3.1

+ 3.8

- 20. 6

-0.1

+0.7

-0.2

- 7.8

- 1.5

-1.3

+ 62.1

+ 9.4

2

+3.1

+ 5.3

- 28.9

-0.2

+1.0

-0.3

-10.9

- 2.0 - 1.9

+ 86.9

+ 13.2

4

+3.1

+ 6.9

- 37.1

-0.2

+1.3

-0.4

-14.1

-2.6- - 2.4

+111.8

+ 17.0

6

+3. 2

+ 8.4

- 45.3

-0.3

+1.6

-0.5

-17.2

- 3.2

-2.9

+136. 6

+ 20.7

8

+3.2

+ 9.9

- 53.6

-0.3

+1.9

-0.5

-20.3

-3.8

-3.4

+161.4

+ 24.5

1890

+3.2

+11.4

- 61.8

-0.4

+2.2

-0.6

-23.4

-4.4

- 4.0

+186. 2

+ 28. 2

2

+3.2

+ 13.0

- 70.1

-0.5

+2.5

-0.7

-26.6

- 5.0

-4.5

+211. 1

+ 32.0

4

+3.2

+14.5

- 78.3

-0.5

+2.8

-0.8

-29.7

- 5.6

- 5.0

+235. 9

+ 35.8

6

+3.3

+16.0

- 86.6

—0.6

+3.0

-0.9

-32.8

- 6. 1

-5.6

+260. 7

+ 39.5

8

+3.3

+ 17.6

- 94.8

-0.6

+3.3

-0.9

-35.9

-6.7

- 6.1

+285. 6

+ 43.3

1900

+3.3

+ 19.1

-103.0

-0.7

+3.6

-1.0

-39.1

-7.3

-6.6

+310. 4

+ 47.1

2

+3.3

+20.6

-111.3

-0.7

+3.9

-1. 1

—42. 2

-7.9

- 7.1

+335. 2

+ 50. 8

4

+3.3

+22.1

-119.5

-0.8

+4.2

-1.2

-45.3

- 8.5

-7.7

+360. 0

+ 54.6

6

+3.3

+23.7

-127. S

-0. s

1 +4.5

-1.3

-48.4

- 9.1

-8.2

+384. 8

+ 58.4

8

+3.3

+25.2

-136.0

-0.9

+4.8

-1.4

-51.6

-9.6

-8.7

+409. 7

+ 62.1

1910

+3.2

+26.7

-144.3

-0.9

+5.1

-1.4

-54.7

-10.2

-9.3

+434. 5

+ 65. 9

2

+3.2

+28. 2

-152. 5

-1.0

+5.4

-1.5

-57.8

-10.8

- 9.8

+459. 3

+ 69. 7

4

+3.2

+29. S

-160. 8

-1.1

+5.7

-1.6

-60.9

—11.4

-10.3

+484. 2

+ 73.4

6

+3.2

+31.3

-169.0

-1.1

+5.9

—1.7

-64.1

-12.0

-10.9

+509. 0

+ 77.2

8

+3.2

+32. 8

-177.2

-1.2

+6.2

—1.8

. -67. 2

-12.6

-11.4

+533. 8

+ 81.0

1920

+3.1

+34.3

-185. 5

-1.2

+6.5

-1.8

-70.3

-13.1

-11.9

+558. 7

+ 84.7

' 2

+3.1

+35.9

-193. 7

—1.3

+6.8

-1.9

-73.4

-13.7

-12.4

+583. 5

+ 88.5

4

+3.1

+37.4

-202. 0

-1.3

+7.1

-2.0

-76.6

-14.3

-13.0

+608. 3

+ 92.3

6

+3.0

+3S. 9

-210. 2

—1.4

+7.4

-2.1

-79.7

-14.9

-13.5

+633. 1

+ 96. 0

8

+3.0

+40.4

-218. 5

-1.4

+7.7

-2.2

-82.8

—15. 5

-14.0

+657. 9

+ 99.8

1930

+3.0

+42.0

-226. 7

-1.5

+8.0

-2.3

-85.9

-16.1

-14.6

+682. S

+103. 6

ndz

3 loe r

sp

Uj

iit=0°00

L

Unit=6.00001

Unit =0.00001

Month

(Jo,),

(-1 6x)i

(J &i)i

(-(«,)<

(4&i)i

(J fc,i, ' (Jo,),

(-1 &i)i

Jan. 0.0

+0.0

-0.0

0.0

0.0

0.0

0.0

0.0

0.0

Feb. 0.0

+0.1

-0.4

0.0

-0. 1

0.0

0.0

+ 1.1

+0.2

Mar. 0.0

+0.1

-0.7

0.0

-0.3

0.0

0.0

+ 2.0

+0.3

Apr. 0.0

+0.2

-1.0

0.0

-0.4

-0.1

-0.1

+ 3.1

+0.5

May 0.0

+0.2

—1.4

0.0

-0.5

-0.1

-0.1

+ 4.1

+0.6

June 0.0

+0.3

-1.7

+0.1

-0.6

-0.1

-0.1

+ 5.1

+0.8

July 0.0

+0.4

-2.0

+0.1

-0.8

-0.1

-0.1

+ 6.2

+0.9

Aug;. 0.0

+0.4

-2.4

+0.1

-0.9

-0.2

-0.2

+ 7.2

+1.1

Sept. 0.0

+0.5

-2.7

+0.1

-1.0

-0.2

-0.2

+ 8.3

+1.3

Oct. 0.0

+0.6

-3.1

+0.1

-1.2

-0.2

-0.2

+ 9.3

+1.4

Nov. 0.0

+0.6

-3.4

+0.1

-1.3

-0.2

-0.2

+10.3

+1.6

Dee. 0.0

+0.7

-3.8

+0.1

-1.4

-0.3

-0.2

+ 11.4

+1.7

[ndz, 3 log r, and J/3 are to be computed in the form ^i[oi + (J4()i)sin t'e+J<[6( + (J))i)i]cos j'j-HJ&o)!-]

MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNER.

373

Tables of (93) Minerva — Continued.

TABLE VI.— CONSTANTS FOR THE EQUATOR.

Year

A'

B

C

log sin a

log sin b

log sin c

1865. 0

O

4. 6662

O

275. 1318

O

273. 4766

9. 99996

9. 92830

9. 72466

6

. 6800

.1469

.4870

6

0

65

7

.6938

.1619

. 4975

6

0

65

8

.7070

.1770

. 5180

6

0

65

9

.7214

. 1921

.5185

6

0

65

1870

4. 7352

275. 2072

273. 5290

9. 99996

9. 92830

9. 72465

1

. 7490

.2223

. 5395

6

0

65

2

. 7628

.2374

. 5500

6

0

64

3

.7766

. 2525

. 5605

6

0

64

4

.7904

.2676

. 5710

6

64

1875

4. 8042

275. 2827

273. 5815

9. 99996

9. 92831

9. 72464

6

.8180

.2! ITS

. 5920

6

64

7

.8318

. 3129

. 6025

6

64

8

. 8456

. 3279

.6130

6

63

9

. 8594

.3430

.6235

6

63

1880

4. 8732

275. 3581

273. 6340

9. 99996

9. 92831

9. 72463

1

.8870

.3732

. 6445

6

63

2

. 9008

.3883

. 6550

6

63

3

.'il Id

.4034

. 6655

6

63

4

.9284

. 4185

.6760

6

2

62

18S5

4. 9422

275. 4336

273. 6865

9. 99996

9. 92832

9. 72462

6

.9560

.4487

.6970

6

2

62

7

. !I6!IS

.4638

. 7075

6

2

62

8

. 9S37

.4789

.7180

6

2

62

9

.9975

.4940

. 7285

6

2

61

1890

5. 0113

275. 5090

273. 7390

9. 99996

9. 92832

9. 72461

1

. 0251

. 5241

. 7495

6

2

61

2

.0389

.5392

.7600

6

2

61

3

.0527

. 5543

. 7705

6

2

61

4

. 0665

.5694

.7810

6

3

61

IS! 15

5. 0803

275.5845

273. 7915

9. 99996

9. 92833

9. 72460

6

.0941

.5996

. 8020

6

3

60

7

. 1079

.6147

. 8125

6

3

60

8

. 1217

. 629S

.8229

6

3

60

9

. 1355

.6449

.8334

6

3

60

1900

5. 1493

275. 6600

273. 8439

9. 99996

9. 92833

9. 72460

1

. 1631

. 6751

. 8544

6

3

59

O

. 176!)

.6902

.8649

6

3

59

3

.1908

. 7053

. 8754

6

3

59

4

.2046

. 7201

.8859

6

4

59

1905

5. 2184

275. 7354

273. 8964

9. 99995

9. 92834

9. 72459

6

.2322

. 7505

.9069

5

4

58

7

.2460

. 7656

.9174

5

4

58

8

.2598

. 7807

.9279

5

4

58

9

.2736

. 7958

!i:;s|

5

4

58

1910

5. 2874

275. 8109

273. 9489

9. 99995

9. 92834

9. 72458

1

.3012

.8260

. 9594

5

4

58

2

. 3150

.sill

.9699

5

4

57

3

. 3288

. S562

.9804

5

4

57

4

. 3426

.8713

.9909

5

5

57

1915

5. 356 1

275. 8864

274. 0014

9. 99995

9. 92835

9. 72457

6

.3702

. 9015

.0119

5

5

57

7

. 3840

.9165

.0224

5

5

56

8

.3978

.9317

.0329

5

5

56

9

.4116

.9467

.0434

5

5

56

1920

5. 4254

275. 9619

274. 0539

9. 99995

9. 92835

9. 72456

1

.4392

.9770

.0644

5

5

56

2

. 4531

. 9920

.0749

5

5

55

3

1669

276. 0071

. 0854

5

6

55

4

.4807

. 0222

. 0959

5

6

55

1925

5. 4945

276. 0373

274. 1064

9. 99995

9. 92836

9. 72455

6

.5083

. 0524

.1169

5

6

55

7

. 5221

. 0675

.1274

5

6

54

8

. 5359

.IIS26

.1378

5

6

54

9

. 5497

.0977

. 1483

5

6

54

1930

. 5635

.1128

. 1588

9. 99995

9. 92836

9. 72454

Year

log cos a

log cos b

log cos c

1865. 0
1930. 0

8.114
8.180

9. 725 n
9. 724 n

9.928

9.928

374

MEMOIRS NATIONAL ACADEMY OF SCIENCES, VOL. X, NO. 7.

TABLE VII.-

Tables of (.93) Minerva — Continued.

REDUCTION OF MEAN TO ECCENTRIC ANOMALY (£-g), AND CORRECTION
J(g-g'l TO BE APPLIED TO (g-g') TO FORM ARGUMENT N.

Arg. g

■%-?')

£~9

Arg.jr

Arg.?

■1(9-9')

'-9

Arg. g

Arg.?

■1(9-9')

e-0

Arg.?

0

0

0.000

0.000

O

360

O

60

4. 571

7. 438

O

300

O

120

3.980

6.477

O

240

1

0.100

0. 164

359

61

4.605

7.494

299

121

3. 932

6. 399

239

2

0.201

0. 327

358

62

4.638

7. 547

298

122

3.883

6.320

238

3

0.301

0.490

357

63

4.669

7. 597

297

123

3.834

6.238

237

4

0.401

0. 653

356

64

4.698

7.(;ir,

296

124

3.783

6. 156

236

5

0. 501

0.816

355

65

4. 725

7. 690

295

L25

3.731

6.072

235

6

0.601

0.978

354

66

4. 751

7.732

294

126

3.679

5. 987

234

7

0.701

1.140

353

67

4.776

7.772

293

127

3.626

5.900

233

8

0.800

1.302

352

68

4.799

7.809

292

128

3.572

5.812

232

9

0.899

!. 463

351

69

4.820

7.844

291

129

3. 517

5. 72:;

231

10

0.997

1.623

350

70

4.839

7.875

290

130

3. 461

5. 632

230

11

1. 095

1. 782

349

71

4.857

7.904

289

131

3.405

5.540

229

12

1.192

1.940

348

72

4. 873

7.931

288

132

3.347

5.447

228

13

1.289

2. 098

347

73

4.888

7. 955

2S7

133

3.289

5. 353

227

V

1. 385

2.255

346

74

4.901

7.976

286

134

3.230

5.257

226

15

1.481

2.410

345

75

4.913

7. 995

285

135

3.171

5. 160

225

16

1.576

2.564

344

76

4. 923

8.011

284

136

3.111

5. 062

224

17

1.670

2. 71S

343

77

4.931

8.024

283

137

3 050

4.963

223

IS

1.763

2.869

342

78

4.938

8.036

282

138

2.988

4.863

222

19

1.856

3. 020

341

79

4.943

8.044

281

139

2.926

4. 762

221

20

1.947

3. 169

340

80

4.947

8.050

280

140

2. 863

4. 659

220

21

2.038

3.317

339

81

4. 949

8. 054

279

141

2.799

4. 556

219

22

2.128

3.463

338

82

4. 950

8. 055

278

142

2. 735

4. 451

218

23

2.217

3.608

337

83

4.949

8. 053

277

143

2.671

4.346

217

24

2. 305

3.750

336

84

4.946

8. 050

276

144

2.605

4.240

216

25

2. 3!l|

3. S!I2

335

85

4.943

8.04!

275

145

2.539

4.132

215

26

2.477

4.031

334

86

4.937

8.035

274

146

2.473

4.024

214

27

2.562

4. 168

333

87

4.931

8.024

273

147

2.406

3.916

213

28

2.645

4. 305

332

88

4.922

8.011

272

148

2. 338

3.800

212

29

2.727

4.438

331

89

4.913

7. 995

271

149

2.270

3. 695

211

30

2.808

4.570

330

90

4.902

7.977

270

150

2.202

3.584

210

31

2.888

4.700

329

91

4.889

7.957

269

151

2.133

3.471

209

32

2.967

4. 828

328

92

4.875

7.934

268

152

2. 064

3.358

208

33

3.044

4. 954

327

93

4.860

7.909

267

153

1.994

3.245

207

34

3.120

5.078

326

94

4.844

7. 882

266

154

1. 924

3. 130

206

35

3.195

5. 199

325

95

4.826

7. 853

265

155

1.853

3. 015

205

36

3.268

5. 318

324

96

4.806

7.822

264

156

1.782

2.900

204

37

3.340

5. 435

323

97

4.786

7.788

263

157

1.710

2.784

203

38

3.410

5. 550

322

98

4.764

7.752

262

158

1.639

2.667

202

39

3.479

5. 662

321

99

4.741

7.715

261

159

1.567

2.549

201

40

3.547

5.772

320

100

4.716

7.675

260

160

1.494

2.431

200

41

3.613

5.879

319

101

4.690

7.633

259

161

1.421

2.313

199

42

3.677

5.984

318

102

4.663

7. 589

258

162

1.348

2. 194

198

43

3.740

6.087

317

103

4.635

7.543

257

163

1. 275

2.075

197

44

3.802

6.187

316

104

4.605

7. 495

256

164

1.201

1. 955

196

45

3.862

6. 285

315

105

4. 575

7.445

255

165

1. 127

1. 835

195

46

3.920

6.380

314

106

4.543

7.393

254

166

1. 053

1.714

194

47

3.977

6.473

313

107

4.510

7.339

253

167

0.979

1. 593

193

48

4.033

6. 563

312

108

4.475

7.283

252

168

0.904

1. 472

192

49

4.086

6.650

311

109

4.440

7.226

251

169

0.830

1. 350

191

50

4.139

6.735

310

110

4.404

7. 166

250

170

0.755

1.228

190

51

4.189

6.817

309

111

4.366

7.105

249

171

0.680

1. 106

189

52

4.238

6.897

308

112

4.327

7.042

248

172

0.605

0.984

188

53

4.285

6.974

307

113

4.287

6.977

247

173

0.529

0.861

187

54

4.331

7.048

306

114

4.246

6.911

246

174

0.454

0.739

186

55

4.375

7. 120

305

115

4.205

6.844

245

175

0.378

0.616

185

56

4.417

7.189

304

116

4.162

6.773

244

176

0.303

0.493

184

57

4.458

7. 255

303

117

4.118

6.701

243

177

0.227

0.370

183

58

4.497

7.319

302

118

4.073

6.628

242

178

0.152

0.246

182

59

4.535

7.380

301

119

4.027

6.553

241

179

0.076

0. 123

181

60

4.571

7.438

300

120

3.980

6.477

240

180

0.000

0.000

180

Note. — When the argument exceeds 180°, it is found to the right of the function and the function is negative.

INDEX.

Page.

Acimotrocha, bibliography of references to in

figured pls. 6-11 (pp. 126-136)

fully developed g5

internal organization of fully developed 87

metamorphosis of r 98

see also Phoronis architecta.

Alcohol, action of, upon the circulation, a memoir on the 39

conclusions as to action of, upon circulation 66

experiments to test action of, upon circulation outlined 44

facts in regard to action cf , upon circulation 64

AUinastrum, section of Claytonia, with included species 27

Althaea, explanation of tables of 208

tables of - 348

Aneilema nudi riorum R. Br., discussed 173

Artemis, explanation of tables of 204

tables of 236

Athor, explanation of tables of 204

tables of 291

Bache fund, grant to T. C. Mendenhall for experiments in determining absolute value of the acceleration of

gravity 3

Becker, E., computation of perturbations by 197

Brooks, W. K., Memoir on the affinities of the pelagic tunicates: On a new Pyrosoma 149

Brooks, W. K., and Cowles, R. P., Memoir on Phoronis architecta: its life history, anatomy, and breeding

habits . 71

Circulation, action of alcohol upon, a memoir on the 39

conclusions as to action of alcohol upon : 66

facts in regard to action of alcohol upon 64

Claytonia, anatomical structure of vegetative organs 32

as a genus 27

distinguished from Monlia 27-2S

inflorescence of 28

morphological structure of the shoot 29

morphological and anatomical study of, by Theodore Holm 25

chamissonis figured pi. 1 (p. '38) , rig. 7

diffusa figured pi. 1 (p. 38), Bg. 8

megarrhiza figured pi. 1 (p. 38), figs. 2-4, and pi. 2 (p. 38), fig. 9

parvifolia figured : pi. 1 (p. 38), fig. 1

sarmenlosa figured pi. 1 ( p. 38), figs. 5-6

Virginia), figured pi. 2 (p. 38), figs. 10-18

Oommelina, compared with Tradescantia and Weldenia 188

dianthifolia D. C, discussed 171

erecta L. , discussed 167

hirtella Vahl., discussed 168

figured pis. 5-7 (p. 1!il')

nudiflora L., discussed 161

figured pis. 1 and 3-6 i p. 192)

virginica L. , discussed 1 65

figured pis. 2 and 6 (p. 192)

Commelinacea?, memoir on morphological and anatomical studies of the vegetative organs, by Theodore Holm . 157

species examined by Holm listed 161

Cowles, R. P., see Brooks, W. K., and Cowles, R. P.

375

376 INDEX.

Page.

Crawford, R. T. , assistant in preparing seventh memoir 193

Cyrene, explanation of tables of 204

tables of 265

Dipleurosoma, new genus, diagnosed 154

Dipleurosoma elliptica, new species, described 154

figured pl- 1 (P- 156)

Dogs, experiments upon to test action of alcohol upon circulation 44-54

Eichelberger, W. S., tables of Minerva prepared by 197

Elements (TableC) 234

explanation of -0-

Euclaytonia, section of Claytonia, with included species 27

Frogs, action of alcohi >1 upi in isolated hearts of 54-62

Glancy, Estelle, assistant in preparing seventh memoir 193

Gravity, acceleration of, determination of absolute value by ring-pendulum method 1

Helena, explanation of tables of 208

tables of 327

11, ra, explanation of tables of - 208

tables of 338

Hobe, Adelaide M., assistant in preparing seventh memoir 193

Holm, Theodore, Memoir on Claytonia Gronov.: a morphological and anatomical study 25

Memoir on morphological and anatomical studies of the vegetative organs of the Commelinacese 157

Hoyt, D. M., see Wood, H. C, and Hoyt, D. M.

Juewa, explanation of tables of 204

tables of 278

Jupiter's mean anomaly (Table A ) - 217

explanation of 201

Klytaemnestra, explanation of tables of 204

tables of - 313

Kroneker's apparatus for measuring action of alcohol upon the isolated reptile heart, figured fig. 1 (p. 56)

Land tortoise, action of alcohol upon isolated heart of 62

Lawton, G. K., comparison between theory and observation by - - 200

Leuschner, A. O., Memoir on Tables of the minor planets discovered by James C. Watson, part 1 193

Limnia, section of Claytonia, with included species 27

Ludwig's stromuhr, result of experiments with pis. 1 and 2 (p. 70)

Man, action of alcohol upon size of arm 67

Mendenhall, C. E., Memoir on the determination of the absolute value of the acceleration of gravity by the

ring-pendulum method 1

Mendenhall, T. C, work upon determination of absolute value of acceleration of gravity by ring-pendulum

method 3

Minerva, explanation of tables of 210

tables of 359

Montiastrum, section of Claytonia, with included species 27

Montia, distinguished from CluyUmia - 27-28

Montia rivularis, figured pl- 2 (p. 38), fig. 19

Naiocrene, section of Claytonia; with included species 27

Nemesis, explanation of tables of 204

tables of 255

Newcomb, Simon, preface to seventh memoir by 197

Newkirk, B. L., assistant in preparing seventh memoir 193

Pelagic tunicates, memoir on the affinities of, by W. K. Brooks 149

Phaedra, explanation of tables of 204

tables of 301

Phoronis, bibliography of references to - HI

Phoronis architecta, adult form 1™

breeding habits '6

fertilization in 77

figured pis. 1-5 (pp. 116-124), pl. 11 (p. 136), and pis. 12-17 (pp. 138-148)

formation of Mesoderm in s0

gastrulatiou in 79

larval growth of 8"

laying of eggs by ' '

memoir on life history, anatomy, and breeding habits of, by Brooks and Cowles 71

INDEX. 377

Phoronw architecta — Continued. i-age.

method of study of 76

segmentation of 77

summary of study of 107

see also AcHnotrocha.

Pyrosoma, memoir on a new, by W. K. Brooks 149

King-pendulum, azimuth error calculated 12

conclusions drawn from use of, in determining acceleration i >f gravity 23

construction of the rings 13

described, theory of stated, desirability of discussed, etc 3

effect of flaws, etc., on the period of the ring calculated 6

effect of nonbomogeneity and errors of figure calculated 8

history of use in determining absolute value of acceleration of gravity 3

measurement of the period 17

measurement of the rings 15

value for acceleration of gravity determined by 23

vibration of a perfect ring calculated 4

Ring-pendulum method, determination of absolute value of acceleration of gravity by 1

Ritter, W. McK., tables and perturbations by 200

Ross, Frank, assistant in preparing seventh memoir 193

Snake, action of alcohi >1 upi in isolated heart of 62

Snapping turtle, action of alcohol upon isolated heart of 63

Thyra, explanation of tables of 204

tables of 246

77 Html Hi anomala (Torr.) Clarke, discussed 173

figured pi. s (p. \\rl)

Tradescanlia compared with Commelina and Weldenia 188

crassifolia Cavan, discussed 181

floridana Wats., discussed -. . . 182

micrantha Torr., discussed 183

pinetorum Greene, discussed 181

rosea Vent., discussed 1 75

figured pis. 2 and 7 ( p. 192)

seopulorum Rose, discussed 179

virginica L. , discussed 177

figured pis. 2 ami 7 (p. L92)

warszt wicziana Kunth and Bouche, discussed 183

figured _.-... pi. 8 (p. 192)

Traverse tables (Table B) 218

explanation of 21 11

Tunicates, pelagic, memoir on the affinities of, by W. K. Brooks 149

Watson asteroids, memoir on, by A. O. Leuschner 193

Weldenia Candida Schult. fil. , figured '. pi. 8 (p. 192)

Williams's apparatus for measuring action of alcohol upon the isolated reptile heart, figured lig. 2 (p. 57)

result of experiments with pi. 3 (p. 70)

Wood, H. C, and Hoyt, I •. M.: Memoir on the action of alcohol upon the circulation 39

Wood and Hoyt's apparatus for measuring action of alcohol upon the isolated reptile heart, figured fig. 3 ( p. 60)

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