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velocity of light = 186600 English miles per second, according to the latest determination of Cornu. Then, by Doppler's theory,

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If now, in any group or spectrum lines of small extent, I is put for the difference of wave length of the extreme lines of the group; Afor the interval between the extreme lines measured in micrometer units, and 6 for the displacement as indicated by the difference between the micrometer readings on a given line when the slit is placed on the eastern and western limbs of the sun's image respectively, we shall have

δ

d=Ix and U=186600 ×

A,

λ A'

(2)

where A of course is to be taken as the mean wave length of the group.

Taking Angström's wave lengths, we find for the D group

δ

δ

U=1903 and for the 1474 group U=361·1 1o; which amounts

Δ

to saying that a velocity of 190-3 English miles would displace one of the D lines by a space equal to the distance between them, and for the other group a velocity of 3611 miles would be required.

From the sun's known dimensions and period of rotation, adopting Faye's numbers, the equatorial velocity of its surface is easily found to be 1248 English miles per second; U, of course, ought to come out double this, or 2:496.

66

The tables need little explanation; the expression "grating right," means that the grating was so inclined as to throw the reflected image of the slit to that side of the collimator which was remote from the eye-telescope. In this position the spectra were more dispersed, but less satisfactorily defined than those of the same order obtained by turning the grating "left," i. e., toward the eye-telescope. The first column contains the designation of the line observed; the second, headed west," gives the reading of the micrometer obtained at this limb; the fourth, headed "east," gives the reading of the eastern limb; the third, headed "mean," contains the mean of the numbers in the second and fourth columns, expressed in divisions of the micrometer head; the difference between these, given at the bottom of the column is a. The fifth column contains the differences between the numbers in the second and fourth columns, and their mean, given at the bottom of the column, is d.

In the earlier observations of the D group several other lines were observed besides the three given, but they were so faint that the readings were very discrepant, sometimes to the extent

of two or three divisions, and they are therefore omitted. The readings of the nickel line are retained, though far less reliable than those of the two Ds.

(1.) July 10, 1876; 9.30 to 10.15 A.M. (civil time); grating right; spectrum of 6th order; definition poor.

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(2.) July 10; 10.30 to 11.10 A.M. D lines; grating right; spectrum of 6th order; definition medium.

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(4.) July 15; 10.15 to 10.40 A.M. Observation interrupted by clouds when half completed. D lines; grating right; spectrum 6th order; definition poor.

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(5.) August 10; 9.30 to 10.40 a. M.

Twice the usual num

ber of readings taken. D lines; grating left; spectrum 7th

order; definition excellent.

6=0.65

This observation is entitled to little weight.

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(6.) August 10; 11.10 to 11.50 A. M. D lines; grating right; spectrum 6th order; definition poor.

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Ꮄ'

Δ

D2

0 32.05

Rejecting the nickel line, d'=1·60, =0·0151 U'=2·87.

(7.) August 12; 9.30 to 10.10 A. M.

1474 group; grating

left; 8th order; definition fine;* instrument inverted.

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(8.) August 12; 10.35 to 11.10 A. M. left; spectrum 8th order; instrument erect;

1474 group; grating definition fine.

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(9.) August 12; 11.30 A. M. to 12.20 P. M.

1474 group;

grating left; spectrum 8th order; slit radial; definition ine.

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* The definition was such that 1474 constantly showed double, and on moving the slit to the base of the chromosphere, the bright line which appeared was clearly seen to coincide with the more refrangible of the two components.

Since the points observed were not situated upon the solar equator it is necessary to correct each result by multiplying it by a factor depending upon the heliographic latitude, p, of the point. If the sun's surface rotated as a coherent mass the factor would be simply, sec. p. Since this is not the case however, the expression becomes more complicated. Adopting Faye's constants and formula of solar rotation, we find the factor,

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On July 10, q=2°, f=1·001; on July 15, p=3°, f=1·002; on Aug. 10, p=14°, f=1·044; on Aug. 12, q=15°, f=1·051.

Applying the corrections we have the following, in which the column headed Us, gives the results without discrimination, while the column U'e contains the results obtained by throwing out the nickel line in observations (1), (2) and (6), and rejecting entirely (4), while (5) is counted twice, as having double weight for the reasons assigned.

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The two results do not differ materially, but the second is much more reliable. It makes the velocity of the sun's rotation 142 miles per second, while direct observation gives 1-25; perhaps the difference is no more than might be expected; still the difference of 0:34 between the values of U as determined spectroscopically and directly is so many times larger than the probable error of the spectroscopic result, that I am much inclined, especially considering the agreement with Vogel's result, to think it indicates a physical fact, and that the solar atmosphere really sweeps forward over the underlying surface, in the same way that the equatorial regions outstrip the other parts of the sun's surface. If the equatorial acceleration is produced by external causes such an effect would be likely.

It may be interesting to add, that on Aug. 10, a careful series of readings was made on a principal line of the B group, in the spectrum of the 6th order, with entirely negative results; as was to be expected, since the line is atmospheric. The mean of ten readings at the west limb was 56d-22, at the east limb 56d-23. Hanover, N. H., Sept. 12, 1876.

ART. XXXIX.-Researches in Acoustics; by ALFRED M. MAYER. Paper No. 8, containing:

1. On the obliteration of the sensation of one sound by the simultaneous action on the ear of another more intense and lower sound.

2. On the discovery of the fact that a sound even when intense cannot obliterate the sensation of another sound lower than it in pitch.

3. On a proposed change in the usual method of conducting orchestral music, indicated by the above discoveries.

4. Applications of the interferences of sonorous sensations to determinations of the relative intensities of sounds.

THIS Communication is preliminary to an elaborate paper on the above subjects. For conciseness and clearness, I present the few facts I have now to offer in the form of notes of experi

ments:

1. On the obliteration of the sensation of one sound by the simultaneous action on the ear of another more intense and lower sound.

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Experimental Observations on the Obliteration of one Sound by another. Several feet from the ear I placed one of those loudticking spring-balance American clocks, which make four beats in a second. Then I brought quite close to my ear a watch (made by Lange, of Dresden) ticking five times in the second. In this position I heard all the ticks of the watch, even those which coincided with every fourth tick of the clock. Let us call the fifth tick of the watch which coincided with one of the ticks of the clock, its fifth tick. I now gradually removed the watch from the ear, and perceived that the fifth tick became fainter and fainter, till at a certain distance it entirely vanished, and was, so to speak, "stamped out" of the watch.*

Similar and more striking experiments were made with an old silver watch, beating four times to the second, by causing this watch to gain about thirty seconds an hour on the clock, so that at every two minutes the ticks of the watch and clock exactly coincided. When the watch was held near the ear, every one of its ticks was heard distinctly; but on gradually removing it from the ear, the ticks of the watch became fainter

* In the publication of this paper in Nature, Aug. 10, 1876, my friend Mr. Alexander J. Ellis, F.R.S., appends the following note to the above experiment :— "The precise number of ticks in a second here mentioned are not necessary for roughly observing and understanding these phenomena. I observed them by a common American pendulum clock placed on a table, which increased the power of its half-second ticks, and a watch beating five times in two seconds. Rev. Mr. Haweis informs me that he has often noticed a similar effect at night with ordinary watches. The sensation produced by the obliteration of the tick, when the proper distance of the watch from the ear has been attained, and the consequent sudden division of the ticks into periods separated by silences, is very peculiar. It is difficult not to believe that some accident has not suddenly interfered with the action of the watch, instead of merely with our own sensations."-A. J. E.

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