and the following explanations will be sufficiently intelligible, without a figure, to those familiar with the subject.

Mr. Hill finds the desired projection, on the plane of the instrument, of any point above that plane, as the extremity of a steel rod, by means of a silk thread stretched on a brass bow, set on a triangular base, and made normal to the chart or plane of the instrument, by screws in the base. I effect the same end very simply and readily by the following expedient, based on the optical principle that an incident ray and the corresponding reflected one coincide when they are normal to the reflecting surface. A bit of a good glass mirror with parallel surfaces, and a few inches square, having two lines traced on it with a writing diamond perpendicular to each other, is placed on the plane of projection, and moved under the given point, representing the place of observation, until by the eye placed above that point and close to it its image is seen to coincide with the intersection of the lines on the glass. Evidently, this intersection is then the projection required on the plane of the mirror, and the corresponding point on the plane of the instrument is easily determined, if desired, by the use of the intersecting lines as lines of reference. In my instrument there is no necessity for determining this point on the plane of the instrument, as the time of disappearance is found by moving the point representing the place of observation, and the disc representing the moon, to successive corresponding positions belonging to successive minutes of time, until the image of the point is occulted by the disc; the time of reappearance is determined in like manner. Instead of the pointed extremity of the rod, may be used a minute perforation in a thin sheet of metal or of pasteboard, through which may be viewed its image in the mirrors. If instead of either of these, were used a polished bead of glass or metal, smaller than the pupil of the eye, the light reflected from it would be seen in the mirror as a star-like point, which by the principles of the projection employed, would be the representatives of the star to be occulted, and by the interposition of the disc representing the moon, would actually disappear, and again reappear, as in an occultation. The use of the minute perforation gives the best results, as the eye cannot then fail to be in the proper position above the point indicating the place of observation.

I use the same method for adjusting in position a plane which in my instrument represents the plane of the parallel of latitude of the place of observation; this revolves about an axis, to which ought to be parallel the plane of the instrument or the chart, and this parallelism I test by finding, by reflection, the projections of a certain point in three or more widely distant inclined positions of the plane; these projections ought to

lie in a right line. This plane ought also to form with the plane of the instrument, or plane of projection, an angle equal to the complement of the declination of the star, and any line in it, perpendicular to the axis of rotation, being taken as radius, will have its projection equal to the sine of the declination. Having a scale of equal parts, for sines, drawn on the plane of the instrument, corresponding to a certain line in the movable plane as radius, I take from a table of natural sines the proper length for the given declination, and placing the intersection of the cross lines on the mirror, to coincide with the proper point in the scale for sines, I rotate the plane about its axis, until the image of the extremity of the radius adopted coincides with the center of the cross; the plane will then have the proper angle, without requiring an arc divided into degrees and parts as in Mr. Hill's instrument.

Mr. Hill mentions several methods of adjusting the varying relation between the moon's hourly motion and semi-diameter, and decides finally upon a fixed permanent scale, in inches and parts, for hourly motion, and calculates the corresponding values of semi-diameter and parallax, in order to avoid the labor of dividing in every case the moon's hourly motion along its path into minutes of time. I adopt a permanent scale of ten inches for the earth's radius, (which fixes moon's semi-diameter also) compute the value on this scale for the hourly motion of moon in her orbit, from the horizontal parallax and hourly motions in R. A. and Dec., for each occultation, and adjust the instrument for this varying quantity, by using a scale of equal parts for minutes of time, laid down on an extensible sheet. This sheet is of caoutchouc, and the scale is made variable by extending the sheet, until sixty minutes or one hour on the scale corresponds in length with the computed value of the hourly motion of the moon. Two such scales might be used if the uniformity of the rate of extension of the sheet could not be trusted throughout the required extent of the variation of hourly motion in different parts of the orbit. These scales, made of the vulcanized caoutchouc obtainable at the date of the construction of the instrument, have now lost their elasticity and must be replaced before I can again use the instrument.

These expedients are simple, and I make them known, as the adoption of one or both may add to the efficiency of Mr. Hill's instrument, or similar instruments. I am not aware that any one had proposed them at the time I applied them to my instrument. I have heard that Mr. Adie of Edinburgh has proposed something similar to the last to thermometer scales I believe, but I do not know the date of his proposal, nor whether it has been adopted in the scales of any instruments. College of Charleston, Charleston, S. C., 19th Dec., 1868.

ART. XV.-On the wave lengths of the Spectral Lines of the Elements; by WOLCOTT GIBBS, M.D., Rumford Professor in Harvard University. Read before the National Academy of Sciences, Aug. 16, 1867.

IN a memoir published in the Philosophical Transactions for 1864, Mr. Huggins has given for a particular scale the relative positions of a number of spectral lines. The scale selected was purely arbitrary. The number of elements examined was twenty-eight, and as the measurements were made with much accuracy it seemed to be desirable to extract from them all the information which they were capable of giving. For this purpose I have endeavored to determine the wave length of each line with as much precision as the present state of science permits, and in this manner to form tables which might enable me to determine whether the spectral lines are distributed according to definite laws, and if so, whether they can be considered as particular cases of the general principle of interfer

ences.

The materials at my disposal were as follows: First, measurements by Angström of the wave lengths of 37 lines identified with particular elements and expressed in ten-millionths of a Paris inch. These were reduced to millionths of a millimeter by multiplying them by the constant 27-07. Second, measurements by Ditscheiner of 107 wave lengths, those of Fraunhofer's lines A, B, H and H' not being available. The entire number of spectral lines measured upon his scale by Mr. Huggins is about 1000, distributed among the elements as follows:

With respect to Ditscheiner's measurements I may here state that I have reduced them as in my memoir on the construction of a normal map of the solar spectrum." That is, I have taken the wave length of the more refrangible line of D, as 589-43, as determined by Angström, instead of 588-8, which is the *This Journal, II, vol. xliii, p. 1, Jan., 1867.

value found by Fraunhofer. The reduced values as thus obtained correspond very closely with those of Angström, as I have shown in the paper referred to, excepting in the part of the spectrum between C and D.

With these materials it first became necessary to identify a sufficient number of lines upon Mr. Huggins's scale with lines the wave lengths of which had been measured. This proved to be a task of extraordinary difficulty and a severe tax upon my time and patience. Mr. Huggins's scale cannot in any part be superposed upon that of Kirchhoff. The identification of a few strongly marked lines, like those which Fraunhofer selected, is of course easy, but these do not suffice as data for interpolation. By very careful and laborious comparisons of the two scales; by observing the coincidences or close approximations of lines produced by different elements; by occasional graphical constructions, and by employing the numerical results obtained in my two papers on wave lengths already published, I at last succeeded in obtaining data covering all of Mr. Huggins's scale between 589-5, or C, and 4671, which lies about half way between G and H. Of the correctness of the identification of the lines I shall be able I think to furnish satisfactory proof.

In selecting the wave lengths to be used in interpolation, I have given the preference to the measurements of Angström. But in the part of the spectrum between C and D, these were not sufficiently numerous to be of service. For this portion I have employed exclusively the values given by Ditscheiner, reduced in the manner already pointed out. In other parts of the scale it has also been necessary occasionally to use Ditscheiner's measurements, but in all these portions the difference between the results of Angström and of Ditscheiner rarely amounts to a unit in the first decimal place.

The number of lines upon Mr. Huggins's scale identified with lines the wave lengths of which have been measured, amounts to forty-five. For the purpose of interpolation these were divided into nine groups. In table I, I have brought together for convenience both the data employed and the results obtained.

In this table the column H gives the scale-number of the line; the wave length as observed, the wave length as calculated by the formula obtained, ▲ the difference between the observed and calculated wave-lengths, and the probable error for each group of data. The wave-lengths marked † are those of Ditscheiner; the others are given by Angström.

The method of interpolation employed was that first given by Cauchy and afterward reduced to a practical form by M. Yvon Villarceau, in the Connaissance des Temps for 1852. As in my recent reductiont of Kirchhoff's scale, I employed only expressions of the form

λ= a+bh+cha+dh3 &c.

these being found to give an approximation within the limits of the probable errors of observation.

Table II, gives the values of the constants, a, b, c, and d, as deduced from the data given in Table I.

In this table H is the initial and H' the terminal point of Mr. Huggins's scale in each group of data employed for discussion. For easy use in calculation it is more convenient to transfer the initial and terminal points, so as to make each parabolic curve

*Moigno. Leçons de Calcul Differentiel et de Calcul Integral. Tome Ier, 513. This Journal, II, May, 1868, vol. xlv, p. 1.