The careful measurements of Kayser and Runge of the carbon bands show that the successive differences in the frequencies do (1900), I, p. 399.
- Visual observation is limited to the range of frequencies to which our eyes are sensitive.
Wolfer's frequencies with data obtained by other observers for areas of sun-spots, and his figures show unquestionably that the unit in one or other set of data must have varied appreciably from time to time.
The frequencies are nearly in the ratios 1: 6.25:17.5.
The difference between the frequencies of the roots (s = co) is given by This is the first law.
If we wish to be more general, while still adhering to Deslandres' law as a correct representation of the frequencies when s is small, we may write n - A (s+ 1 1) 2 - - a Po+Pi(s + c) -F +pr(s+ c)r' where s as before represents the integer numbers and the other quantities involved are constants.
The method of counting frequencies was fairly alike, at least in the case of A and B, but in comparing the different stations the data should be regarded as relative rather than absolute.
In another party line system a harmonic principle is employed: the ringing machines deliver alternating currents of four frequencies, while each bell is constructed to operate at a particular frequency only.
In many experiments, however, different inductions and frequencies are employed, and the hysteresis-loss is often expressed as ergs per cubic centimetre per cycle and sometimes as horse-power per ton.
The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..
Then, since the frequencies are the same, U/2L = U3 /2l or L/l = U/U8.
Spectroscopic Measurements and Standards of Wave-Length.- All spectroscopic measurement should be reduced to wavelengths or wave-frequencies, by a process of interpolation between lines the wave-lengths of which are known with sufficient accuracy.
Distribution of Frequencies in Line Spectra.
Deslandres,s who found that the successive differences in the frequencies formed an arithmetical progression.
A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.
The Scandinavian data, from the wealth of observations, are probably the most representative, and even in the most northern district of Scandinavia the smallness of the excess of the frequencies in December and January over those in March and October suggests that some influence tending to create maxima at the equinoxes has largely counterbalanced the influence of sunlight and twilight in reducing the frequency at these seasons.
It is also necessary to notice that shunt instruments cannot be used for high frequencies, as then the relative inductance of the shunt and wire becomes important and affects the ratio in which the current is divided, whereas for low frequency currents the inductance is unimportant.
If, in this latter case, the proportion of cases in which b is B to cases in which b is not-B is the same for the group of pN individuals in which a is A as for the group of (I-p)N in which a is not-A, then the frequencies of A and of B are said to be independent; if this is not the case they are said to be correlated.
Experiments, which will be described most conveniently when we discuss methods of determining the frequencies of sources, prove conclusively that for a given note the frequency is the same whatever the source of that note, and that the ratio of the frequencies of two notes forming a given musical interval is the same in whatever part of the musical range the two notes are situated.
Here it is sufficient to say that the frequencies of a note, its major third, its fifth and its octave, are in the ratios of 4: 5: 6: 8.
A mode of exhibiting the ratio of the frequencies of two forks was devised by Jules Antoine Lissajous (1822-1880).
If the forks are not of exactly the same frequency the ellipse will slowly revolve, and from its rate of revolution the ratio of the frequencies may be determined (Rayleigh, Sound, i.
1, and so on, then the frequencies are n, n+m i, n+m l +m 21 ..., n+m1+m2+..
If two such flames are placed one under the other they may be excited by different sources, and the ratio of the frequencies may be approximately determined by counting the number of teeth in each in the same space.
All experiments in frequency show that two notes, forming a definite musical interval, have their frequencies always in the same ratio wherever in the musical scale the two notes are situated.
Using the term " note " for the sound produced by a periodic disturbance, there is no doubt that a well-trained ear can resolve a note into pure tones of frequencies equal to those of the fundamental and its harmonics.
Mag., 1907, 1 4, p. 59 6) found that the least energy stream required to excite sensation did not vary greatly between frequencies of 512 and 256, FIG.
But keeping r/X small we may as before form stationary waves, and it is evident that the series of fundamental and overtones will be just as with the air in pipes, and we shall have the same three types - fixed at one end, free at both ends, fixed at both ends - with fundamental frequencies respectively 41, p ' 21 V p, and I velocity in rod =velocity in air X distance between dust heaps.
The frequencies are nearly in the ratios 3 2 :5 2 :7 2 ....
The formation of beats may be illustrated by considering the disturbance at any point due to two trains of waves of equal amplitude a and of nearly equal frequencies n, n2.
Thus the interval b'c" with frequencies 495 and 528, giving 33 beats in a second, is very dissonant.
Thus, take the major seventh with frequencies 256 and 480.
He found that if two tones of frequencies p and q are sounded, and if q lies between Np and (N-Fop, then a tone of frequency either (N + I) p - q, or of frequency q - Np, is heard.
It can be shown mathematically that the velocity of propagation will be greatly increased if the frequency of the light-wave is slightly greater, and greatly diminished if it is slightly less than the natural frequency of the molecules; also that these effects become less and less marked as the difference in the two frequencies increases.
The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power."
Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies n1 and n, are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other.
We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the resolving power.
Some corroboration of the simple law was apparently found by Johnstone Stoney, who first noted that the frequencies of three out of the four visible hydrogen lines are in the ratios 20: 27: 32.
The roots of the three series have frequencies which diminish as the atomic weight increases, but not according to any simple law.
Distribution of Frequencies in Band Spectra.
A systematic study of the distribution of frequencies in these bands was first made by H.
Halm,' to whom we owe a careful comparison of the above equation with the observed frequencies in a great number of spectra, attached perhaps too much weight to the fact that it is capable of representing both line and band spectra.
Arcs, bands and, generally speaking, the more regular and persistent forms, show their greatest frequencies earlier in the night than rays or patches.
All are observed frequencies, derived after Wolf's method; maxima and minima are in heavy type.
„ 55.8 „ I12.2 The mean sun-spot frequencies in the two periods differ by only I %, but the auroral frequency in the later period is 45% in excess of that in the earlier.
Oliver Heaviside showed mathematically that uniformly-distributed inductance in a telephone line would diminish both attenuation and distortion, and that if the inductance were great enough and the insulation resistance not too high the circuit would be distortionless, while currents of all frequencies would be equally attenuated.
We must now however introduce a new criterion the " purity " and distinguish it from the resolving power: the purity is defined by n l /(n l n2), where n 1 and n, are the frequencies of two lines such that they would just be resolved with the width of slit used.
- It is natural to consider the frequencies of vibrations of radiating molecules as analogous to the different notes sent out by an acoustical vibrator.
The method ensures that the two frequencies shall be exactly the same.
The above figures would be almost conclusive if it were not for the conspicuous differences that exist between the mean sun-spot frequencies for different II-year periods.
Schuster, who has considered the matter very fully, has found evidence of the existence of other periods-notably 8.4 and 4.8 years-in addition to the recognized period of 11.125 years, and he regards the difference between the maxima in successive II-year periods as due at least partly to an overlapping of maxima from the several periodic terms. This cannot, however, account for all the fluctuations observed in sun-spot frequencies, unless other considerably longer periods exist.
Comparing it with the two adjacent periods of thirty-three years, we obtain the following for the mean annual frequencies: 12.
The association of high auroral and sun-spot frequencies shown in Table V.
A formula, similar to (5), may be given for the frequencies of vibration of a spherical mass of liquid under capillary force.
When the rings are coloured symmetrically with respect to two perpendicular lines the acute bisectrix and the plane of the optic axes are the same for all frequencies, and the colour for which the separation of the axes is the least is that on the concave side of the summit of the hyperbolic brushes.