Then the numbers in column 3 may be represented by the expression

Σ (e2 + e2 + p2).

(3)

Column 4 contains quantities similar to those in column. 3, except that the refraction pairs (pages 143 to 151) have been used instead of those near the zenith. Representing by ← the mean error of the mean of the four refraction pairs, and remembering that at 60° zenith-distance the effect of anomalous refraction is four times that at the zenith, the numbers in column 4 are the equivalents of

obtained by taking the differences between the refraction pairs for the same night, squaring and adding.

By adding corresponding items in columns 3 and 4, subtracting those in column 5, and dividing by 8n, we evidently obtain

the values of which are given in column 6.

(6)

The data in Table II do not permit us to separate these two errors, but from other considerations1 it is known that e is about 0".02. Whether we assume this value of € or a smaller one, we should get practically the same values of P, as is shown by the following:

Adopting the former as definitive, and substituting in expression (3) above, we get these values for the mean

1 See the residuals on pages 163 to 166 of ALBRECHT'S memoir.

errors of the latitude as determined from one night's ob

The conclusion that we may draw from these computations is that observers have little to fear from anomalous refraction. Its mean effect, at a properly chosen station, appears to be considerably less than the accidental errors of observation in the best work that can be done at the present time. Accordingly, this explanation for inconsistencies in meridian work should be advanced with caution. The present paper also throws light upon the nature of KIMURA's phenomenon; this, it will be remembered, is a small term in the latitude variation and is independent of the longitude. Our computations indicate, if they do not indeed prove, that this term is real, and is not due (as has been suggested) to anomalous refraction.

ALLEGHENY OBSERVATORY, December 22, 1905.

VARIABLE STAR NOTES.

BY ROSE O'HALLORAN.

U Cassiopeia.

On September 17, 24, and October 15, 1905, this variable was invisible in a four-inch telescope. The maximum predicted for November 3d was looked for, and according to the following observations occurred somewhat later.

1905. October 23, 26-Of 12th magnitude. November 3About 11.7; dimmer than g.1 November 13-Between g and

1 For comparison-stars, see chart, Publications A S. P. No. 98, p. 209.

e.

November 18-Brighter than g or f; equal to e. November 20-Brighter than e or d; iess than c.

V Cassiopeia.

This variable having risen to maximum in the middle of August, 1904, declined gradually, and on October 19th was only equal to the star of 10.5 magnitude about half a minute of arc preceding. On November 15th of the same year it had sunk to invisibility. September 17, 1905, it was of about 10th magnitude, being distinctly brighter than the above-mentioned star closely preceding, and on the 24th was still brighter, though about half a magnitude less than e in the star chart.1

1905. October 10-Equals d. October 15-Between d and b. October 23-Equals b. November 3, 13, 20-Equals b.

R Pegasi.

1904. September 12-Brighter than g; equals d; less than c. September 29-Between d and c. October 30-Nearer to the light of g than of d. November 6, 8-About two tenths brighter than g. November 27, December 2-Equals g; brighter than h. December 4-Between g and h. December 17-Equals h; less than g.

1905. January 2-Between h and m; nearer to m. September 17, 24, 26, October 15-Equal to d; less than c. October 25-Brighter than h; equals g. November 18, 20, 24Between h and g. December 3-About midway between h and g. December 21-Less than h; scarcely brighter than m. December 28-Fainter than m (night very clear).

The period is about 380 days, and maxima were predicted for September, 1904 and 1905.

U Herculis.

1904. May 8, 10, 14, 16-Equal to f. June 2, 10-Three tenths dimmer than f.

1905. May 5, 9, 19, 21-Equal to c; brighter than d. May 29-The same (night clear and dark). June 5, 10-Between c and d. June 17-Equals d; brighter than f. June. 22, 27-Less than d; equals e; brighter than f. July 1— Between e and f. July 5-Scarcely brighter than f.

The accompanying chart shows the position of this variable. with regard to Gamma in the arm of Hercules. The scarcity of telescopic stars in the field of view makes identification easy, and the range from about 7 to 12 magnitude places each phase within the reach of small instruments. Its long period of thirteen months is subject to periodic inequality.

I Ursa Majoris.

1905. January 27-Brighter than h; less than f. February 22-Equals c; brighter than e. March 26-Equals e; brighter

than for g. April 4-Between e and f. April 21-Between f and k; nearer to f.

S Boötis.

1904. May 2, 16-Invisible.

1905. April 4-Equal to g; brighter than h. April 27Brighter than for g; equals e; less than c. May 4, 9-The same (May 7 was the date of predicted maximum). May 19— Between e and c. May 21-It seems nearer to the luster of c than of e. July 1-It has sunk to about 11.5 magnitude.

S Ursa Majoris.

The comparison-stars used for this variable and also for I Ursa Majoris and S Boötis are those of the charts published by the Harvard Observatory in 1891.

1904. February 16-Invisible. April 4-Equals f. April 17-Equals g.

1905. January 9-Very close to the brightness of d, perhaps two tenths less; brighter than g; less than c (night clear). January 24, 27-The same. February 22-Two tenths brighter than f. March 26-Equals h. April 4-Less than h or 1; of about II magnitude. April 21-Not discernible (night hazy).

A four-inch refractor was used for these observations.
SAN FRANCISCO, December 30, 1905.

TOTAL SOLAR ECLIPSES.

SKETCH OF AN APPARATUS FOR INVESTIGATING THE POSITION OF THE PRODUCING ELEMENTS OF THE SHADOW

BANDS IN SPACE.

By M. RosO DE LUNA.

It is known that some moments before and after the total phase of an eclipse we can see sinuous bands sliding along the ground, which alternately are bright and dark. The orientation, direction of movement, speed, etc., of these bands have been studied by means of a white piece of linen laid horizontally on the ground and placed from north to south. From