we have seen assignable to oxygen, in seventeen the coincidences are absolute; in four the difference is only five onehundredths of a wave length; in twenty-two, ten one-hundredths of a wave length; in four, fifteen one-hundredths of a wave length; in eleven, twenty-one one-hundredths of a wave length, and in the remainder the greatest difference is only thirty-five onehundredths of a wave length, or about that which Angström has made in different measurements of the same line in the solar spectrum.

The small figure attached as a power to each wave length of the electric and solar spectra in the table, is a proximate expression of the photographic strength of that particular line in each spectrum, and an examination of these upholds the statement made in a preceding paragraph that the oxygen lines of the solar spectrum are very weak when no other element furnishes a line which falls on the same wave length. Of course photographic must not be compared with visual intensities, for as the one diminishes in the less refrangible regions of the prismatic spectrum the other increases. An example of coinci dence in the lines of different elements, and consequent increment in strength, occurs in the line 4118, and probably in the line 4303 also, though it is supposed to be free.

In conclusion, I give a list of certain lines in Ångström's chart which have not as yet been assigned to any element, together with the wave lengths of the same lines in my solar and electric spectra. From this table it will be seen that Ångström himself observed a number of lines, the relations of which to elementary bodies no one has as yet demonstrated, and which I believe represent the oxygen in the solar envelopes. Table of free lines in Ångström's solar spectrum which may be attributed to oxygen.

The subjects presented in this communication may be briefly summed up as follows:

1. The resort to the process of reflection in producing and

photographing solar spectra, and thereby avoiding certain errors, and the employment of the silvered surface itself of a glass grating.

2. The extension of the measurement of oxygen lines into the ultra-violet region.

3. The measurement in the region of less refrangibility than H, of lines of oxygen not heretofore recorded, and the use of projection as a method of measurement.

4. The establishment of a close relationship in position between certain lines in the solar spectrum and the lines of oxygen; the slight differences that exist being assignable to the experimental difficulties in the way of making accurate measures of the oxygen lines, and falling within the limits of error of experiment.

5. The evolution of the fact that the lines of the solar spectrum which appear to correspond to the lines of oxygen are weak, or faint, and show that that gas possesses a feeble absorb. ent power when compared with metallic vapors or gases like H, Fe, Ca.

6. The demonstration that in Ångström's chart there are many lines not assignable to any elementary body, and that these lines occupy very closely the positions of certain oxygen lines.

7. The suggestion that the proof of the presence in the solar envelopes of oxygen, and other substances giving faint lines, is a problem not to be solved by the comparison of two spectra of small dispersion. The solar spectrum in certain parts is so crowded with lines presenting all kinds of details, that the only satisfactory way is to make measures of the positions of these lines on a large scale, and as truly as possible, and then compare with these the most accurate measures of oxygen lines that can be made.

ART. XXIX.-Correction for Vacuum in Chemical Analysis; by G. F. BECKER.

TURNER, in his atomic weight determinations (1829) was, so far as my information goes, the first to correct the apparent weight of solid bodies in chemical analysis for the air displaced. Berzelius at first accepted this correction but afterward rejected it as insignificant. Erdmann and Marchand adopted the somewhat illogical practice of reducing the body weighed to vacuum while neglecting the correction for the weights. Nor has the practice of living chemists in accurate investigations been less contradictory. Some of them have entirely ignored the buoy

ancy of the atmosphere while others have laid the greatest stress upon

it.

Consistency among chemists in the treatment of this source of error is certainly desirable. The subject is a simple one and the cases in which the correction is of importance are so readily distinguished from those in which it is insignificant as to repay the small amount of thought necessary to discriminate them. the apparent weight of a body;

If

the true weight;

y= its specific gravity;

d

the specific gravity of the weights, and

c = the weight of one cubic centimeter of air; then

If c and d are regarded as constants, this equation represents an hyperbola referred to axes parallel to its asymptotes.

It will readily be seen that the form of the curve is independent of d, or the material of which the weights are made, this constant simply determining the position of the axis of y, for

Sx=0
y=d

The curve is plotted (figure, page 269,) for d = 21.5, the specific gravity of platinum, and c = 0.001225761, the weight of one cubic centimeter of dry air with the normal carbonic acid contents, at 45° of latitude, the normal pressure, and a temperature of 15°. The abscissæ in the diagram represent the correction for atmospheric displacement necessary per gram in tenths of milligrams. The ordinates represent the corresponding specific gravities. A glance shows that for high specific gravities the correction is small and changes but slowly, while for specific gravities but little in excess of 1, the correction is comparatively large and increases with great rapidity as the specific gravity sinks. This is expressed algebraically by the formula

which indicates that the error decreases in proportion to the increase of the square of the specific gravity, or that the intervals through which the specific gravity may be regarded as constant decrease as the square of the specific gravity decreases.

Ordinates have been drawn to the curve at equal intervals corresponding, for reasons which will presently appear, to 0.0000667 grams, or two-thirds of one-tenth of a milligram. The abscissa of each of these ordinates represents the mean correction necessary between certain limits of specific gravity. These limits are indicated by the points on the axis of y cut by lines parallel to the axis of x and passing the ends of the arcs the mean abscissa of which is cut by the ordinates. Thus a correction of two-thirds of one-tenth of a milligram per gram corresponds to all the specific gravities between 78 and 13.6. The maximum error in this correction will plainly be only onethirtieth milligram. The figure might evidently be employed to form a table of corrections for vacuum for platinum weights; but while the principle is more readily apprehended geometrically, calculation possesses the advantage in accuracy. An entirely similar figure might be drawn representing the correction for weights of brass or any other substance. The curve would be identical, but the axis of y would cross the curve at y=d, for brass y = 8.5.

The attempt is rarely made, as is well known, to push the accuracy of chemical analysis even in the most refined investigations beyond one-hundredth of one per cent or one-tenth of a milligram per gram. If the error made in correcting the weighings for the displacement of air is kept within this limit, the requirements of the case will therefore be fully met. Substances the specific gravity of which approximates within certain limits to that of the metal of which the weights are made, consequently need no correction. As may be seen from the figure, if platinum weights are employed, no substance the specific gravity of which exceeds 78 requires correction, if one-tenth of a milligram be regarded as an insignificant error. For brass weights the error is less than one-tenth milligram for all known specific gravities above 5·02.

Bodies are usually weighed with both platinum and brass, the integral gram weights being made of the latter metal and the fractions of the former; corrections must therefore commonly be made for each. As the absolute error in neglecting the correction for small fractions of a gram is very slight, while it is as much trouble to ascertain the correction for a milligram as for ten grams, it is convenient to omit small quantities from calculation. Three errors in the correction for vacuum have, then, to be taken into account, viz., that incurred by want of absolute accuracy in correcting for the whole grams weighed with brass weights; a second similarly incurred in weighing parts of a gram with platinum weights, and the error caused by neglecting the correction for small fractions of a gram. The sum of these errors must not exceed one-tenth of a milligram,

a condition which will be fulfilled if none of the three is over one-thirtieth milligram.

The following tables answer these conditions, for all specific gravities above 1, in the fewest possible numbers.

The fraction which may be neglected without an error of more than one-thirtieth milligram will of course vary with the specific gravity and will in any case be

x

0.0000333'

x being the correction. Uniform rules, however, are desirable in the application of such corrections as the one under discussion. It is therefore sufficient to state, that for specific gravities above 1 no quantity less than twenty-five milligrams needs correction, while for specific gravities above 3 nothing less than one decigram requires to be corrected or, in other words, only the first decimal place.

In discussing analyses recorded in the literature of chemistry it is, in a majority of cases, impossible to discover with certainty whether the gram weights were of platinum or brass; though the latter is the rule and an exception to it is apt to be stated. The difference between the corrections per gram for brass and platinum weights is