Star # 242 fact page
0N THE ANNUAL PAEALLAX 0F P. Ill, 242.
I Have already given a brief sketch of this investigation, and of the results to which it has led, in the Monthly Notices of the Astronomical Society, Nov., 1880, p. 36. I shall here give the more detailed account, as well as the record of the Observations themselves.
In the Monthly Notices, Vol. XX., p. 8, is a Paper by 0. Struve, "On a Star which would be suitable for a Parallax Series." The star in question is P. III., 242, and its position for 1879.0 is a = 3h 59TM 30s, and 8 = + 370 45'.3Argelander, in his Catalogue of 560 Stars, had pointed out that P. III., 242, probably formed a wide binary system with the next following star of his Catalogue, 50 Persei, on account of the equality in direction and quantity of their proper motions.
Struve remarks, also, that P. III., 242 is a double star of Herschel's first class (No. 531 of 0. Struve's Catalogue), the components being of 67th and 89th magnitudes, respectively, and 3" or 4" distant. The physical correction of the two components of P. III., 242 appears to be established by their equal proper motions. A fourth star, Arg. Zone, + 370, No. 877 (mag. 78), is south, preceding P. III., 242 at a distance of nearly 4'. This star does not belong to the system formed by P. III., 242 and 50 Persei, for the changes in its position with respect to P. III., 242 correspond exactly to the proper motion of the latter. " This star, therefore," says Struve in conclusion, " would be a very qualified object of comparison for determining the relative parallax of P. III., 242, for which a considerable amount is indicated by the proper motion and by the probable physical connexion with 50 Persei at 15' distance." Great additional interest becomes attached to this object from Mr. Burnham's discovery that the comparison star here suggested is itself a first-class double. It is No. 545 in Mr. Burnham's Paper (if. A. S., Vol. XLIV,
P- 37)
So far as I know, no attempt has hitherto been made to test whether Struve's surmise as to the existence of a parallax for P. III., 242 could be substantiated. I therefore commenced a series of observations in January, 1879, of the distance and position of the comparison star, which Struve suggested, from the larger star of the pair, P. III., 242. The instrument employed was
the South equatorial at Dunsink Observatory, with the Pistor and Martin filar micrometer. The methods of observation and of reduction are the same as those employed by Dr. Briinnow and myself on previous investigations: see Parts I., II., and III. of the Dunsink Observations.
In an important feature, however, the observations now to be discussed are very different from those which had previously been made with our micrometer. The distance in the present case was no less than 237" ±, which is greatly in excess of the distances measured in the regular series of parallax observations contained in our previous publications. Had there been any suitable comparison star nearer to P. III., 242, I should certainly have preferred it, for the distance 237" is too great to be measured with our micrometer with the accuracy which may be expected when the distance is only about one or two minutes. From this cause the results of the observations are not so satisfactory as I would wish, though they are quite sufficient to show that P. III., 242 has no appreciable parallax.
The observations having first been reduced by the values of the micrometer screw with the temperature coefficient obtained by Dr. Briinnow, it became necessary to apply the corrections for refraction, as well as for the reduction to the mean places at 1879.0. The refractions were computed from the wellknown formulae, and were first tabulated for each half hour of sidereal time, as here shown:
REFEACTION COERECTION.
220
ON THE ANNUAL PARALLAX OF P. III., 242.
In a similar manner we have found it convenient to calculate the reductions, first of all, for stated intervals of twenty days, and the results are shown as under:
From these Tables the actual corrections to the observations have been deduced by interpolation, and they are then applied as shown in the measures appended hereto. For instance, on the nth January, 1879, the distance obtained from wire I. is i4o".951, from wire II. is 96".533. The correction for refraction is +o".090, and for reduction is o".o16, so that the final corrected distance to be used in the discussion is 237".558. In a similar manner, the position angle is 2070 17'. 2 5 before any correction has been applied. For refraction we apply + C/.33, and for reduction C/.23, so that the corrected position angle for nth January, 1879, is 207° i7'-35
The following Table contains the result of the observations, duly corrected, for the refraction and reduction. The first column contains a number for reference, the second is the date of observation, the third column gives the fraction of a year which has elapsed since the epoch, 1879.0, the fourth is the
222 ON THE ANNUAL PARALLAX OF P. III., 242.
According to 0. Struve (loe. tit), the annual proper motion in right ascension is +o8.o167, and in declination o".i52. It hence appears that the arc moved over in one year by P. III., 242 is o".2497 ; while the position angle of the star in the position it will occupy next year, measured from the present position, is i270.5. The correction to be applied to the observed distance, in order to reduce the observed distance to that between the places at the epoch, is + o".04407 per annum; while the corresponding correction to the observed position angle is 3'-565, or in arc o".2457.
There are altogether thirty observations of the distance which, corrected for refraction and reduction, but not for proper motion, have a mean value of 237".293 23. The mean date of the thirty observations is 0.60421, so that the proper motion from the epoch to the mean date is + o". 02 663. The adopted mean distance is therefore 237".29323 + o".02663 = 237".32o. The mean value of the thirty-one measures of position angle is 2070 15'.98, and the correction for proper motion is 2'. 12, so that the adopted mean position is 2070 i3'.86.
From the usual formulae, it is found that when © is the sun's longitude, R the sun's radius vector, and it the annual parallax of P. III., 242, the correction to be applied to the observed distance, to clear it from the effects of parallax, is (the figures in brackets denoting logarithms) :
- [9.82787] 7ri? cos (O-1740 56' o");
while the corresponding correction of the observed position angle is
-[9.90007] 77-i? cos (O 1420 8' 29").
Assuming that x is the correction to be applied to the assumed mean distance, while x' is the correction to the assumed value of the proper motion in distance, and K is a possible difference in the coefficients of aberration of the two stars, then the equations of condition can be determined. For instance, on the 9th January, 1880, the coefficient of a? must be 1.0219, the coefficient of parallax is 0.2699, and of aberration 0.6150. The observed distance on that day was 236".7i5, and the correction for proper motion being + o".045, the corrected distance was 236".760. The mean distance was, however, 237".32o, so that the absolute term of the equation is o".56o. In this way the following system of equations has been obtained:
