65 365 2 66

0- /ii- Man ziehe B'a' parallel BC, dann ist

Ca' C B ' - 88' Ca' -=-

Nun ist CB' die Resultirende von Ca' und a ' 2 ' und die Richtungen CB', Ca', A I' I

6'2' stimmen beziiglich iiberein mit der wahren Richtung des Lichtstrahles , der Richtung der Geschwindigkeit der Erde in ihrer Bahn um die Soone und der scheinbaren Richtuog des Lichtstrahls. Folglich ist das Verhaltniss Co' : C 2 dem VerhHltniss der Geschwindigkeiten der Erde in ihrer Bahn und des Lichtes gleich. Nimmt man fur die Bahngeschwindigkeit der Erde ihren mittleren Werth an und bezeichnet mit k die Aberrationsconstante, so wird

-- 'O'' - ksin 1" = x . C 8'

Substituirt man diesen Werth in die obige Formel und setzt CB' = C8, so wird

C B 2 8' 23A C A -- -

folglich, wenn zur Abkiirzung dx statt x' - x und dy statt y' - y geschrieben wird,

Um den durch die Annahme CB' = C B begangenen Fehler zu ermitteln, wird wie unter 2. verfahren. Es ist

CB' - C B = x dx +y dy . Substituirt man die vorigen Werthe von dx und dy,

so erhiilt man

x X + y Y X - - CB' - C B

CA I +xa+ Ya somit

22' - C B x x + y Y ~ - x - + x a B A CA I +P+ Y2 '

Folglich wird I +xz+ya x X + y Y

dx = x ( X - x ) I / + xax 1 + x2 + Ya I +xa+ Y2

Bezeichnet man die fur den Mittelpunkt der Platte gtiltigen Werthe von d x und dy mit und (dy),,, und setzt dx - (dx)o = Ax, dy - (dy)o = dy, so stellen Ax und dy die Corectionen dar, welche an die gemessenen und auf den Mittelpunkt der Platte bezogenen Coordinaten an- zubriogen sind, um die von der Aberration befreiten Co- ordinaten zu erhalten. Es ergiebt sich

- x+ (X - X)c>1/1 + xa + y2 x x + y Y 1/I + xa + Y2 I + P + Ya

- Y + ( Y - y ) 1 / 1 + s 2 + y 2 x X + y Y 1/1 +x2+ Y2

AX = x + x2 x

dy = x + x2 Y I + xa + Y2

Bei der Anwendung dieser Formeln wird man die Coefficienten von x io Reihen entwickeln.

Wien, 1900 Juni 19. L. de Ball.

Positions of (433) Eros in 1893, 1894, and 1896. (Harvard College Observatory Circular No. 5 I).

Approximate positions of (433) Eros during the oppo- sitions of 1894 and 1896 will be found in Circulars, Nos. 36 and 37 (A. N. 3540 and 3545). Since then, the photographs from which these positions were derived have been measured by the method described in the Harvard Annals, Vol. XXVI, p. 237, and reduced by the method of Turner. The mea- surements have been made by Miss E. F. Leland, and the reductions by Miss A. Winlock aided by Miss I. E. Woods. These photographs wefe taken with the Bruce, Bache, and Draper photographic doublets, whose apertures are 60, 20, and 20 cm, and the focal lengths such that I mm equals 60", I 79", and 163", respectively. Photographs taken with these instruments are designated by the letters A, B, and I, re- spectively. The smaller instruments photograph a field I oo square, and as some of the images fall near the corners

of the plate it was not supposed that positions cou i be determined from them with a high degree of accuracy. In some cases, the images are more than so from the centre of the plates and are consequently much distorted, the greatest diameter exceeding a minute of arc; yet, as will be seen below, the accuracy of the places does not greatly differ from that ordinarily obtained with meridian circles. The most remarkable conclusion to be derived from these observations is that if, in the future, any other object like Eros should be discovered, we have at this Observatory the means of tracing its path since 1890, during the time in which it was moderately bright, with nearly as great accuracy as if a series of observations had been taken of it with a meridian circle.

In the following table the designation of the original negative is given in the first column. The date, the Green-

6%

67 365 2 68

wich Mean Time of the middle of the exposure, and the duration of the exposure, are given in the next three columns. Two enlargements, on a scale of 0.1 cm = 10", were made from each of these negatives, and their designations are given in the fifth column. The number of catalogue stars on these enlargements used to determine the constants of the plates, such as errors of scale, orientation,,etc. is given in the sixth column. The standard coordinates of Eros are given in the seventh and eighth columns, and the resulting right ascension and declination for 1875, in the ninth and tenth columns. The two measures of each plate are inde-

Plate

I 9801

1 9832

I 9862

1 10095

I 10215

I 10280

I 10321

I 10469

1 '0559

A 2 2 2

A 246

I 10685

B 10909

B 10951

B 11174

€3 15531

B 16108

B 16157

B 16165

B 16518

A 1876

Date

1893 Oct. 28

> Y. 30

R P 31

P Nov. 26

P Dec. 19

D 23

3 2 1

1894 Jan. 19

B P 2 5

n Febr. 5

n B 16

W n 16

R April 16

P n 18

B May 19

1896 April 6

a June 4

, " 5

, ' 5

3 P 2 9

B R 30

- >. M. T

2 I h 5 s n

2 0 18

2 1 2 1

2 0 26

18 21

'9 49

'1 32

16 5 1

16 16

1 5 26

'4 49

'4 59

'4 '3

I 4 29

14 16

2 0 52

16 40

'9 54

2 2 4

'9 1 1

'3 46

- :xp

I 4n

-

I 0

' 5

' 1

14

'3

1 0

I0

'3

6 0

I 2

'3

1 0

1 0

I 0

60

7 0

I 0

I1

'5

60

- Enl.

6441 6442 6317 6318 6391 6392 6390 6389 6375 6376 6416 6411

6382 6408

6383

6409 6393 6394 6410 6411 6414 6415 6436 643 1 6311 6374

63 7 0 6365

6344 6346

6350 635' 6355

6353 6354 6348 6349 6413

6360 636 I

6357

6412

- k* -

9 9 9 9 I 7 7 f 4 4 4 4 7 7 I 7 9 9 7 7 8 8

I 1

I 1

I 7 9 9 I 7 1 7 5 5 5 5 4 4 9 9 6 6

pedent, except for errors in the original negatives and in the method of reduction. The differences in the two results for the right ascension, and for the declination, are given in the last two columns.

On I 9832, the image is irregular. The position of the brightest part is given. The centre precedes it oS66, and is 81'6 south. On A 2 2 2 and A 1876, the images are much elongated, owing to the motion of Eros. The means of the measures of the ends are given. The discordance in the positions derived from I 10685 and B 16108 is pro- bably due to the poor quality of the images.

P o s i t i o n s of Eros.

X

- 96271'2

-__

- 9626.9 + 9760.3

- 10903.8

-15368.2 - I 5370.6 + '0544.4 + 10546.8 -10591.8

+10j80.3 + 10580.7

+ 9160-1

- 10900. I

-10593.1

- 654.1 - 656.7 - 3564.4 - 3564.6 - 4630.1 - 4630.8 + 1059.4 + 1058.2 +10991.4 +10992.6 + 2201.3

+ 2200.9

+ 8488.5 + 7 I f O . I

+ 7171.6 - 7958.9 - 1958.6 - 10686.4 -10677.8 + 15242.6 + I52454 + 1306.6

1301.4 - 9732.1 - 9733.9

+ 8489.9

+ 5864.8 + 5864.8

Y

- 15941!'0 - 15941.2 - 14440.0 - 14441.3 + 3653.4 + 3655.3 + 4066.2 + 4065.5 + 5340.3 + 5340.5 - 642.9 - 644.5 + 10362.3 + 1036 1 . 7 -15161.6 - I 5760.7 +11541.9 4- I 1541.0 + 5011.8 + 5013.1 - 9589.6 - 9589.0 - 13093 8 - 13091.4 +13823.8 +13825.6 + I 2 761.3 +12762.6 - 10985.5 - I 098 1.9 - 3771.5 - 3170.5 - 9103.3 - 9102.7 + 8861.3 + 8861.9 - 8891.1 - 8887.7 + 4124.9 + 4126.3 + 4119.0 + 4119.4

5h 5grn48?1 I 5 58 48.14 6 4 33.13 6 4 33.16 6 7 37.42 6 7 31.82 7 I f 31.35 7 17 31.06 7 45 56.41 1 45 56.69 7 45 57.59 7 45 57.40 7 44 43.11 7 44 43.20 7 26 28.40 7 26 2 8 . 2 0

7 23 33.46 7 23 3 3 4 5 7 23 11.83 7 23 17-78 7 29 58.55 7 29 58.47 7 29 59.0' 7 29 58.69 9 1 7 0.62 9 I t 0.59 9 2 1 47.01 9 2 1 46.91

10 38 1.88 10 38 1.98 18 36 59.92 18 36 59.95

I8 27 51.27

18 2 1 39.55

18 30 6.81 18 30 7.56

18 2 7 51 .51

18 2 7 39.62 ' 1 31 43.9' 'I 37 43-82 17 36 22 .23

1 7 36 22.23

+ 5 3 " 39' 46Y8

+54 6 25.8 +54 6 24.5 +54 2 0 11.2

f 5 4 2 0 '3.4 + 5 7 49 34.0 + 5 1 49 33.0

+53 39 46.7

+54 38 39.2 +54 38 39.3 +52 58 16.4 -1-52 58 '4.1 +50 55 0.2

+50 54 59.6 + a 8 45 48.4 + a 8 45 49.3 + 2 1 14 58.0 + 2 1 1 4 5 7 . 0 + 8 45 22.8 + 8 45 24.7 - o 2 1 42.7 - o 2 1 42.1 - 0 2 1 54.4 - o 2 1 58.0 -13 33 54.0 -13 33 52.2 -13 38 5 2 . 1 -13 38 5 1 . 4 -14 51 21.9 -14 57 18.3 -38 32 48.8 -38 32 47.8 -40 2 45.2 -40 2 45.0 -39 58 33.0 -39 58 32.3 -39 58 2.1

-39 5 1 58.7 -36 2 1 26.7 -36 a1 k 5 . 3 -36 11 20.9 -36 11 20.4

Aa

+ 0So 3

c0.03

t o 4 0

-0.29

+0.28

-0.19

+0.03

-0 .20

-0.01

-0.05

-0.08

-0.32

-0.03

-0.10

+ O . I O

+0.03

+Om15

+0.24

+0.07

-0.09

0.00

7

Ad

-0 l l

- 1.3

f 2 . 2

-

-1.0

+0.1

- 1.7

- 0.6

+0.9

- 1.0

+1.9

+0.6

- 3.6

+1.8

+ 1.3

+3.6

+ 1.0

+ 0 . 2

+o.7

+3*4

+1.4

+ O . $

69 365 2 7 0

A complete discussion of these measures, including the original settings and the results for each comparison

have been used. The average value of the 296 residuals for the catalogue stars is, for x, f 1103, for y, f 1106.

Star-Occultations observed at Windsor, N. S. Wales, in 1899. The observations on June 23 were made at the moon's

eclipsed limb and all the others at the dark limb. No. 60 and 78 were made with the equatorial of 41/, inches aperture

Merfield of Sydney kindly supplied me with a list of occul- tations of small stars for the total eclipse of June 23. The stars were taken chiefly from the Cape Photographic Durch-

Yarna 1 7 2 2

YarnQ 1 7 2 4 Yar% 1 7 1 5

9 D I D 1 7 8 6 29.2

7 I : 1 D 17 8 2 9 6.6 17 8 24 9.2

13 I Lalande 12932 '4 ' 5 16 1 7 18

'9 2 0

2 1

2 2

23 24 25 26 9 7 28 29 30 31 3 2

33 34 35 36 37 38 3 9

Lalande I 4 7 7 I

Lalande 14794

Lalande I 4803 Lalande I 7 5 2 3 BD. +15?1931 BD. +1401990 Lalande I 7 5 5 2

BD. +is01935 Lalande i 7 593 o Leonis Lalande 20142 BD. +5?2331 BD. +5?2332 Lalande 33386

BD. +14'1993

' 16 7 39 25.3

11 7 38 37.0 ' '7 7 42 4.6 ' ' 7 7 49 5 5 . 0

N 16 7 50 47.2

)) 17 8 14 19.6 D 1 7 8 2 0 41.4 u 1 7 8 49 16.6

May 16 7 14 36.7 16 7 18 54.8

a 16 7 38 11.4 n 16 7 54 20.9

' '7 8 49 '7.9

a 16 8 I 36.1 D 16 8 7 7.4

n 1 7 8 38 2 7 . 2

a 18 6 1 5 54.1 P 18 8 2 0 45.2 D 18 8 31 50.4 me 23 I I 1 7 8 . 2

* 2 3 I I 38 2.1

' 23 1 1 39 47.1 ' 23 11 43 35.5 s 23 1 2 4 36.7 )) 23 1 2 10 9.8 a 23 1 2 1 1 50.3 D 23 1 2 14 43.2

= 16 8 37 59.3

I

No. 1 star 1 Mag 1 Ph. 1 Windsor M. T. I

t8 19 50

5 1

5 2

53 54 55 56 5 7 58 59 6 0 6 1 6 2

63 64 65 66 67 68 69 70 7 1

1 2

73 74 75 76 7 1 78

85 Virginis Lalande 2 8 2 5 I Lalande 30690 Lalande 3 2 47 1

Lalande 31501 Cinc. 2. 3107 33 Sagittarii 6 1 Sagittarii Lalande 28444

d = - 2 2' 48' Lalande 30207 B. A. C. 6347

Lalande 36947

Lalande 37001

Lalande 37060 Lalande 3 7 o 7 9

B. A. C. 6710 B. A. C. 7063 Yarn3 9129

.40e, 20367

- -

-

-

-

23 '3 33 45.9 23 13 44 44.8

July 16 8 50 0.2

D 16 9 2 2 42 .2

2 18 7 2 0 49.3 Sept. 1 2 9 5 7 41.1

D 13 6 50 6.4 * 13 7 1 2 27.8 D 14 9 I 6.8 = 14 9 8 42.4 > 14 I I I I 34.0

Oct. 8 6 58 58.1 m 8 8 o 30.8

9 7 46 52.3 9 8 2 0 42.5

w I 1 I 0 10 9.4 B 1 2 6 5 1 43.5 B 1 2 7 30 57.1 ' 1 2 7 49 55.4 B 1 2 8 19 7.1

a 1 2 8 31 42.4 * 1 2 8 5 1 17.5 B 12 9 33 15.8 a 1 1 9 40 22.9 > 1 2 9 5 2 21.9 a 1 2 10 19 54.2 ' = 3 7 34 57.2 ' ' 3 7 59 19.2

Nov. 9 8 1 I 40.9 m 9 8 13 6.8

9 10 4 43.2