Beaconpole. Whence [M1 = 71° 14′ 55".2] or about 2" away from the tabulated figure. The application of (4) with this value of M1 will give [147] and [14Z"] within 1". The precise longitude of the intersection may be then obtained by solving (18). We thus obtain [M1 = 71° 14′ 57′′.83] subject to the correction [-0".44], giving [57".39]. The latitude of the intersection would then be calculated by applying (152) to the McSparran line; and the position thus found would be taken as the origin when the other lines are to be calculated and plotted.

Let us return to the use of (14), (15), and (16). For longitude computation, after the origin has been fixed upon, (16) has the advantage of giving the distance to be taken on the scale in plotting, but (14) or (15,) may be used to calculate a longitude which is to be assumed as that of the origin. Of these (14) is the less dependent upon accuracy in 4Z; but (15,) has the advantage when the errors of observation are liable to be larger than the uncertainty in 42, since the result may be made to conform to an amended latitude by merely changing the logarithm of [L — L1]. In this manner the use of (18), (19), or (20) may be avoided. Thus, suppose that a map has furnished the estimates [L1=41° 34′ 58′′ and M1 = 71° 14′ 55′′], differing several seconds from the fact, and suppose that the observations are hardly good to single seconds. The estimates being therefore good enough for obtaining [142] by (4), the value [M1 = 71° 14′ 56′′.99], obtained by applying (151) to the Great Meadow line, will be sufficiently accurate for the longitude of the point (on that line) whose latitude is [41° 34′ 58′′.00] ; but this latitude will be beyond the convenient limits of a plot. With this value of M, we should then solve (15) for the Spencer line, obtaining [L1 = 41° 34′ 55′′.02 = L1']; i. e. it is taken as the latitude of the origin. We may now quickly amend the result of (15) for the Great Meadow line in accordance with the new value of L1, obtaining [M1 = 71° 14' 57".67 = M']; i. e. it is taken as the longitude of the origin. The point on the Great Meadow line will then lie upon the origin, while the point on the Spencer line will have an ordinate zero and an abscissa

=

[56.99—57.67=-0.68] in seconds, or [-0.68 (B1 cosL''÷A1) -0.51] in units of the plot. It will always be found convenient to arrange that every point shall lie upon one or other of the co-ordinate axes.

Enough has been written to show that the method can be planned to easily deal with any case which may arise. In conclusion it may be remarked that the length of the discussion has been caused by this adaptability, rather than by any complexity in dealing with a case in hand. The method is possibly less fitted in general for routine calculations, done according to specific directions issued from the headquarters of a large survey, than it is for the use of persons who have their own computations to make in extending the results of the larger survey. But where a routine is made of constructing the azimuths and measuring the resulting positions on a chart, the dependence upon the judgment of the computer reduces to a minimum, and the operation, except the final selection of the position on the plot, becomes a simple routine. In comparing the aggregate work with that by the old process, it must be remembered that the whole work of computing the triangle sides is saved.

HARVARD COLLEGE OBSERVATORY,

CAMBRIDGE, MASS., U. S.

J

A PLAN FOR SECURING OBSERVATIONS

OF THE VARIABLE STARS.

FOR several reasons the investigations here proposed are especially suited to observers under very various conditions. The work is capable of indefinite sub-division. Small as well as large telescopes may be employed and many observations are needed which can best be made with an opera-glass or field-glass, or even with the naked eye. No attachment is needed to an ordinary telescope, so that no additional expense on this account is required. Useful observations may be made by an unskilled observer provided that he is capable of identifying a star with certainty. The work is quantitative, and the observer has, therefore, a continual test of the increased accuracy he has acquired by practice. As a portion of the investigation will probably lead to the discovery of interesting objects, the observations will possess an interest often wanting in quantitative research. The aid of the professional astronomer is earnestly requested for this scheme. Suggestions by which it may be modified and improved will be gratefully received. The professional astronomer, in consequence of his greater skill, instrumental appliances, and command of his own time, could fill gaps in the work, and thus greatly increase its value as a whole. Such observations could often be made in the intervals of other work or at times unsuitable for the observations to which he was especially devoting himself. It should be added that especial