n

Figs. 5-8 show the curves of variation of with R2/L2 for different values of the coupling in the neighbourhood of the limiting value 0 889. Fig. 5 is the curve for k2=07. At this coupling the frequency diminishes, but not uniformly so, as R2/L2 increases. At k2=0·85 (fig. 6) the curve shows a

minimum frequency at R2/L2 nearly equal to 2400. The bend in the curve at this point develops into a double point in the curve for k2=0-889, the limiting value, as shown in fig. 7. For values of k above this limiting value, the curve breaks up into two distinct portions as shown in fig. 8, the curve for 2=0.95.

Comparison with the equation for a single circuit.

For a single circuit, the frequency of the oscillations is given by

When R/L is very large, the values of n given in the Tables should approximate to the values given by the formula. Table VIII. shows how this approximation becomes closer the higher the value of R2/L2, 2 in this case being 0.95.

It appears therefore that the simple expression (8), which is strictly applicable to a single oscillatory circuit possessing resistance, cannot generally be used when the damping arises from the resistance of a closed secondary coupled with the circuit. As already remarked, the above results are applicable only to the case in which the capacity of the secondary coil is negligible. In certain actual cases, when the secondary

resistance is varied by means of a rheostat across the secondary terminals and the secondary capacity is not a negligible quantity, the system will possess two oscillations if the resistance of the rheostat is greater than a certain value.

LIV. Light Absorption and Fluorescence.-V. The so-called Molecular Rotational Frequencies of Water. By E. C. C. BALY, C.B.E., M.Sc., F.R.S., Grant Professor of Inorganic Chemistry in the University of Liverpool *.

Na recent paper † the absorption system of sulphur

the

of the absorption-bands shown by this gas can be expressed in terms of three fundamental frequencies: 2·4531 × 1011, 819 × 1011, and 1·296 × 1012. It was also shown that the frequency 2:4531 × 10" is characteristic of the atom of oxygen, and that the two frequencies 8·19 × 1011 and 1.296 × 1012 are characteristic of the atom of sulphur, since the infra-red absorption-bands of oxygen can be expressed in terms of the first and those of sulphur and hydrogen sulphide. can be expressed in terms of the last two constants.

The combination of these three constants to give the frequencies characteristic of sulphur dioxide would seem * Communicated by the Author.

† E. C. C. Baly and C. S. Garrett, Phil. Mag. vol. xxxi. p. 512 (1916).

to be of great importance, for it affords a very complete example of the least common multiple principle which forms the basis of the frequencies of absorption-bands, as has been pointed out in the earlier papers of this series. The least common multiple of the three frequencies of oxygen and sulphur given above is 2.89299 × 1012, and this number multiplied by 10, 12, 14, 18, 26, and 33 gives the exact central frequencies of all the absorptionbands which have been observed for sulphur dioxide in the infra-red region between the wave-lengths 12 and 3 μ. Then, again, of these absorption-bands the one with the central frequency 2-89299 x 14 x 1012 has the greatest intensity, and this central frequency multiplied by 25 gives the exact central frequency of the less refrangible band in the ultra-violet, the central frequency of the more refrangible band not having been observed.

It is well known that the effect of cooling is to decrease the width of absorption-bands and that at very low temperatures only the central frequency remains, this persisting at the lowest temperature yet reached. It is evident therefore that the central frequency is the only one which is truly characteristic of the molecules, the subsidiary frequencies to which the breadth of the bands is due being connected in some way with the temperature of the molecules. These central frequencies are thus true molecular frequencies, and therefore it may be concluded that the fundamental molecular frequency of sulphur dioxide is the least common multiple of the frequencies characteristic of the sulphur and oxygen atoms it contains.

It was also shown that the subsidiary frequencies of sulphur dioxide to which the breadth of the absorptionbands is due are also derived from the three atomic frequencies of sulphur and oxygen. In the less refrangible absorption-band there are a number of sub-groups symme trically distributed with respect to a central sub-group, and, further, each sub-group contains a central line of maximum absorptive power with a series of lines symmetrically arranged on either side of it. In the less refrangible absorption-band of sulphur dioxide the central lines of the sub-groups form a series with a constant frequency difference of 6·69696 × 1012 which is the least common multiple of two of the atomic frequencies, namely 8.19 x 1011 and 24531x 10". Again, in the more refrangible band there exist sub-groups the central frequencies of which form a series with the constant frequency difference of