I 8 3 433' 184

representant une tache, que j'ai observee le 23 aoiit 1908 A 9h 25" du matin et B ah 30" de I'apres-midi et le 2 5 aoat A gh30" du matin.

On peut observer aussi, que de la penoinbre s'avance dans le noyau une saillie ou une langue, qui etait aupara- vant t r b Claire et qui devient ensuite plus sombre que la penombre voisine, mais beaucoup plus Claire que le noyau. Ces saillies et ces langues deviennent le plus souvent, apres quelque temps, de nouveau aussi claires que les autres langues, qui pendent de la penombre dans le noyau. Les figures 5 et 6 en donnent un bon exemple.

Kichineff, Russie, le 7 / 2 0 avril 1909.

Ces phenomenes interessants peuvent &re facilement expliques, si I'on admet, que le noyau de la tache est beau- coup plus chaud, que la photosphere, et que dans les noyaux des taches ont lieu des courants chauds ascendants, qui font rechauffer et volatiliser les particules, les flocons et les langues de la penombre, qui se plongent dans l'interieur du noyau et qui se condensent de nouveau en gouttes liquides et re- deviennent clairs apres le passage de ces courants.

I1 n'y a pas de motifs, me semble-t-ill qui empechent de croire, que ces courants ascendants ne sont pas les pro- tuberances.

A. Amaftounskv.

On the flexure of the tubes of Zenith telescopes. By K. Hiiq~ania.

Immediately after my note on the discordance 0-W'- W-0 was published in A. N. 4207, Prof. Turner criticised it in his ,Oxford Note-Bookt (the ,Observatory((, Vol. 30, p. 43 I ) .

He suggested, against my opinion, that the error noticed by me and having the peculiar relation to the zenith distance would be similar in nature to the BR-D discordance< of the observations made with a meridian circle, which he had investigated some time ago and ascertained to be an error arising from ,some gradual change of position in the in- strument<. I found, however, soon after having read his note, that his hypothesis is not applicable to my own case, because such an error, if it exists in the latitude observations must be contained as an odd function of in O-W+\V-O, but not in 0-W--W-0. Notwithstanding this, I have taken his idea as a valuable suggestion, for, if the error really does exist in the mean latitude, it is more important than that in 0-W-W-0, which does not affect the mean value. Since then my attention has been turned to that point of view and at length the effects of a gradual change of the flexure, I believe, have been found in the results of the lati- tude observations, being greater in amount than was expected.

I shall first discuss what effects on the mean latitude and also on 0 - W - W - 0 should be produced by such a

change of the flexure. If we denote by 5' the zenith di- stance as read by the graduated vertical circle and by t the time after the telescope is fixed, then the error of 2, due to the flexure, may be, in the most general form

&' = P (2, t) . 'Thus, if .dry be the error of latitude and to and t, be the times, corresponding to the observations at the east and west po- sitions respectively, then we must have

4 = '/. [P(5', to) - -F(5', t,(Jl I

in which it is assumed that the graduation of the circle coincides with the zenith distance for the east position of the telescope. Denoting, now, by tl and t2 the times, cor- responding to the first and second star of a pair, and by cl the zenith distance of the first star, we have for O-\V observation

and for W-0 Observation to = tl , t,/ = t.?. , 5' = 51

to = tl , tlU = tl , 5' = - 51 . Hence, the error of the mean latitude AyVr may be ex- pressed as

from which we see that, whatever may be the functional form of P(c , t) , Aspnz is always an odd function of and 0 - W - W - 0 is an even function of the same quantity.

Now, in the actual case, if the difference of the right ascensions of the two stars of a pair be denoted by An and the time t be expressed by the sidereal unit, we have accurately

tz - tl = da . The time interval tl or t2 is not definite. But, in many cases, when the observations are made by a regular scheme, it also may become a definite quantity, except the first pair in each group, because the observer would direct his telescope to- ward the first star of a pilir soon after he has finished the readings for the second star of the preceding pair. Thus,

if the difference of the right ascensions of these two stars be denoted by d'a, then

where c is a constant. The expressions for Ary7,z and 0 - W - W - 0 may, therefore, be written

tl = d 'cc - c

dryVJ = li, (LA'% da) 0 - W - W-0 = da E; (el, l a , A x ) ,

in which Ps and Pc are odd and even functions of jl re- spectively.

Since Ps and Fc are periodic functions of 51, they may be developped by Fourier's theorem in the following series :

I 85 4332

Y u n error of

N-S-SN

fol118 I 3 5 I28 I31 137 137 62 53 41

119 88 91

104 I08 123

f0.135 '43

I 86

Instr.

Z.T. ' ' '

P.T. Z.T. '

U.T.

Z.T. ' ' ' ' 3

'

Z.T. ' '3*

We see that, if 5, is not great and the higher terms of the series can be neglected, then 0-W-W-0 may be assumed as a constant with respect to 5,. Thus, the constant term in the expression of 0-W-\W-0 in my preceding note, may possibly be explained as the effect of the change of flexure.

Let us now consider other kinds of errors, viz. the systematic error of the adopted declinations and the error of bisection depending on the declination, which was dis- cussed in my preceding note regarding 0-W-W-0. With regard to these errors, it may be easily shown that the first does not affect the difference 0-W-Ww-0 and the second does not affect the mean latitude. Thus, combining their effects with those produced by the flexure, we obtain the following general expressions :

N-S-SN

+o?186 + 208 + 345 + 380 + 59 + 360 + 167 + I42 + 85 + 289 + 3' + 31 - '43 + 84 + 5 2 5

-0.147 - 163

where f, and f, are even and odd functions of C1 respec- tively. We see from the first expression, that if the results of the latitude observations have really been affected by the change of flexure according to our supposition, then Aynt should not be a simple even function of L1 but also involves an odd function of the same quantity. This may be actually shown by the existence of a systematic difference between the lati- tudes obtained from the pairs N-S and S-N, viz. the pairs with negative and positive values of C1 .

As to the materials for this purpose, I take those ob- servations which were made for determining the variation of latitude and the results of which have already been published definitively. Those of Tokyo, by myself, although

Nu1 Of 1 -

N-S

14 I4

5 5

14 18 15 32 32 29 14

I 7 30

9 16 16

21

- No.

- - I

2

3 4 5 6 7 8 9

10

I 1 I 2

13 14 ' 5

I 2

<6*0 ' ' 8

e7.0 <8.0 q9.0 - - - - - - -

<5.0

>6.0 ' -

Observations

+0?041 + 5 0 + 488

+ 15'1 + 133

, + 89 + 62 + 29

79 + 33

5 2 + 42 + 206

-0.062 10

+ 510

0 -

Intern. (I) ' (111

Intern. Ref. (I) ' ' ' (11)

Prague Leyden Potsdam Berlin M.

B B. Honolulu M. New York Philadelphi8 S. Bethlehem Tokyo Intern. (II) Intern. (I) ' (11)

not quite definitive, are added as an exception. The error of the mean latitude, in each case, excluding those specially referred to below, is calculated by

./yrtr = - (mean reduction to the group mean

Here, it must be remarked, that the resulting value JyVL includes the accidental errors of the adopted declinations, more or less important according to the sources of the de- clinations. The errors Aym of the observations at Berlin and at Potsdam, for example, are based on declinations all specially determined with the utmost accuracy, so that they are generally small in amount compared with those at other places.

The values of J y f I z , except that of the first pair in each group, are at first divided into two classes according as the pairs are either N-S or S-N. In a few cases, it may be noticed immediately that the values in one class are generally positive while in the other, they are generally negative. In most cases, however, this peculiarity is not appreciable. The values in each class are now arranged by the amount of Y c t . We see then, in general, that when J ' c t is relatively small, our peculiarity is most remarkable and when J ' c t is great, it becomes almost insignificant. In- deed, in some cases, it seems to be reversed in sign when '/'a is greater than a particular value which differs for each series of observations. In such cases, the values in each class are divided according as M a is greater or less than its limiting value, approximately determined by inspection. The mean values N-S, S-N and their differences are tabulated as follows:

+ final correction to the group).

Table I.

S N

-0.145 - a 5 8 + I43 + 130 + 98 - 2 2 7

- 78 80

- 56 -

2 I 0 - + 2

3' + 91

42 - 319 +0.085 + 93

- -

Rr irs

I N

16 r6 6 6

- =

I1 I1 I 0

30 30 26

I 4 I9 24

16 16

10

I 0

'87

NO.

- 3 4 5 6 7

4332

Obsemtior~ /a N-S S N N-S-SN 5;: [t;lii; N-SISN N-S-SN

1ntem.Ref. (I) >6mo -001085 +or041 -of126 4 7 fo?301 Z.T.

pwPe >1.0 - 15 - 62 - 13 18 18 106 P.T. Leyden >8.0 , - 33 + 16 - 49 2 0 2 0 122 Z.T. Potsdam ~ 9 . 0 I - 76 + 33 - 109 9 16

. .' (11) . - 92 + 33 - 125 4 I

I 8 8

No. 1-4. International observations with the latitude- pairs and with the refraction-pair< in Bd. I and I1 of the ,Resultate<. 10 latitude-pairs and 2 refraction-pairs which are the first pairs in the groups, are excluded. The values of */'P~,z for (I) are taken from Bd- I P. 129 and for (11) the values (11)-(I), taken from Bd. I1 p. 138-139, are added to (I). Since all these values given in the ,Resultate< are cor- rections, their signs are changed to convert them to errors.

No. 6. LeYClen 1899. Besides the first Pairs, the Pair

No. 7. Potsdam 1894-99. Mean reductions to the VII 7 consisting of 4 stars, is excluded.

group mean are taken from the 'On Potsdanlc, 111. Heft, p. 26-27.

No. 12-13. Philadelphia 1896-1903 and South Beth- lehem 1903. On these observations, important remarks are given in the latter part of the present note.

The pairs F 2 and F 3, in which the first star of F 3 precedes the second of F 2, are escluded. The values are calculated according to my )>I)e- clinations and proper motions of 246 stars<.

No. I 5 . International observations of the pairs with ,/'a less than 5", appended to show an extraordinary value

In the column *Instr.<, are given the instruments used

scope, by P. T., the portable transit and by U. T., the uni-

No. 14. Tokyo 1901-05.

of X-S - S-N.

for the observations, designating by Z. T., the zenith tele-

We see in the first division that the values N-S-SS-N are generally greater than their mean errors. We also notice in the Same division, that the signs of N-S-values are gene- rally positive and those of S-N negative, so that those of N-S-S-N are also generally positire. This peculiarity, which is quite unexpected, seems to show that the error arising from the flexure, if it may be accepted, is common to all the observations

The value of N-S-SS-N amounts to 0716 in its general average, the largest exceeding 0:s. This, being certainly greater than the corrections either for the differential re- fraction or for the curvature of the star's motion, can hardly be overlooked in any way on determining the latitude.

by the Horrebow-Talcott method.

Intern. (I) ' (n)

prasue Leyden POtdlUIl Berlin M.

B. Honolulu M. New York Tokyo

I shall now examine the influence of the zenith di- stance of the Preceding Pair, X'hichi for the sake of Sim- plicity, has not been considered in the above discussions. Since, by the ordinary mode Of observation, the first star of a pair is observed in the same position of the telescope as the second star of the preceding one, the effect of the flexure on the second pair, as far as our hypothesis is true, must be greater when the two stars are situated on different sides of the zenith, viz. when the zenith distance, c1 , of the pair has the Same sign as that of the preceding pair. The following table contains the results of comparison of N-S - S-N for the two kinds of pairs, ( I ) of those in which c, and the zenith distance of the preceding pair are of the Same sign and (2) of those with different signs:

(4

+of20 + 23

3 + 5 0 + 20 + 20

+ 15 + 41

+ 6

-

2 -

obaemtions N-S-S-N

/a (4

-to0114 + 16 + 22

+ I9 + I3 + 5

I + I2 + I + 6

-

8 8 6 8 8 8 6 8 9 1 5 4

1 0 6 8 5 1 0 3 5 1 19 19 13 X I rg 19 13 X I 20 14 9 12 8 2 6 8

15 10 15 14 Remarks. On account of the small number of pairs, the International observations with the refraction-pairs are

not taken into Table I1 and 111.

With 2 exceptions out of 10 cases, our supposition is affirmed. Here, with regard to the results of Philadelphia and of South Bethlehem, the following must be remarked. In these observations, following the method of Prof. Doolittle, the telescope is directed always toward the same side of the observer, either right or left, as long as the observations are carried on for a single group in each night, so that the position of the telescope is necessarily altered when the sign of c1 is the same as that of the preceding pair. Without doubt, this mode of observation must be better than the ordinary one in di.minishing the systematic difference. This

Winter Summer Winter Observations

htern. (I) (11)

Prague Leyden Potsdam Berlin M.

= B. Honolulu M. New York Philadelphia S. Bethlehem Tokyo

9 9 1.1

4

14

may actually be seen in Table I, that of Philadelphia being the smallest positive value and that of S. Bethlehem, a unique negative value.

Now the question whether the 'change of flexure is constant or not throughout the seasons, must be discussed. Two separate values of N-S - S-N are accordingly computed from the groups observed in the winter and from those in the summer. Here, the terms, winter and summer, are used in an extended meaning, in order to involve a sufficient number of pairs in both divisions. The values are com- pared in the following table :

j.; 11 1 1 16 16 4 18 9

4 3 6

4 2 4

16 10

Table 111.

-0153 - 56 + 10

+ 25 + 22

+ 3 4 + I 1

+ I

-

- + 46 + 24

6 6 5 8 7

I 2 12 I 1

3 3 5

, 5 I4

I 0

+ 8

I 111 + 1 0 111 2 I

I 111 + 19 A-D E-H + 19

v-VIII I-IV + 35 -

~ We see thus that N-S-sS-N slightly increases in the autumn and decreases in the spring. This contradicts the results in Table IV and agrees with the general tendency. Re-examinations of d y , will, therefore, be needed in the future when the declinations adopted for the International observations are determined with sufficient accuracy.

The Present note may be closed by announcing the existence Of a large error in the resdts Of the observations made with zenith telescopes, which may be explained as the

, Except the first two, our results show that the effect is generally greater in the winter than in the summer. It is curious that the effect is decisively negative only upon the International observations. To see whether this singular fact is real or merely apparent, arising from the accidental

effect Of a gradual change Of the flexure. In the case O f a meridian circle, the variability Of the flexure on account of the warmth of the observer's body Or of a hand-lantern, has already been noticed by Several ObSer~ers. In my own case, however, I am not aware whether the discordance N-S-S-N may be attributed entirely to the same source of error or not. Investigations must be carried out more in full, in order to ascertain how and in what part of the in- strument, it arises and further to know how it may be re- moved from the results of the observations.

Summer

+0?43 + 46 + I 0 + 26 + 3 + '3 + I2

+ 24 + 9 + I

- 2.1

5 -

Number of pairs Winter I Summer

errors of declination, the individual variations of latitude of the autumn- and spring-pairs are to be examined. Accor- dingly, the P. V. (proper variation), given in A. N. 4281 are taken and the values for N-S and S-N pairs are com- pared. The results are as follows:

Tab le IV.

(511) Davida. Correction de I'CphCmCride (A. N. 4322): 1909 Juin 14 - I I ~ +O!I Gr. 11.0. J? Chfar&f.