Since L and R agree to the sixth place, p is correct to within a unit in the sixth place. A more precise value of p is p=1·579432+(L−R) Δρ =1.579432+00000032. =1.57943227. The complementary value is p=0·42056773. 5. Determination of the Coefficients. The coefficients will now be determined to six-place accuracy. Let e。=1, then y = cos 1.579432 x −0·206830 cos 3.579432 a +0.014744 cos 5.579432- -0.000542 cos 7.579432 x +0·000012 cos 9.579432 x +0.459527 cos 0·420568 x −0·351349 cos 2.420568 x +0.042752 cos 4·420568 x-0·002240 cos 6.420568 x +0.000066 cos 8.420568 -0.000001 cos 10:420568 x. The second solution is obtained by merely writing sine for cosine throughout. 6. Change of Sign of 0. Fig. 1 is symmetrical about the 7-axis, though it should be noted that in the negative half of the plane am+1 and bam+1 are interchanged. Consequently, if the number-pair (0, 1) gives stability, so also does the number-pair (−0, n). The Mathieu equation is unaltered if is replaced by -0 and x by π-x, so if y= A Σ e, cos (2r+p)x + B Σ e, sin (2r+p)æ 1x is the general solution of (1), then the general solution of y=Ae,cos (2r+p) (†π−x)+В Σ e, sin (2r+p) (π —x) -x = A1 Σ ( − )'e, cos (2r+p)x + B, Σ ( − )ˇe, sin (2r + p)æ, where -∞ A1A cos pπ+В sin pπ, B1 = A sin pπ-B cos ρπ. Thus in general the only change in the fundamental solutions is a change in sign of the coefficients of odd rank. As before, the only exceptions arise when p is an integer or zero, in which cases A or B, and consequently A, or B1, are zero. LIII. On the Zeeman Resolution of the Oxygen Spectral Line at X 5577 Å., the Auroral Green Line. By Prof. J. C. MCLENNAN, F.R.S., J. H. MCLEOD, M.A.*, and RICHARD RUEDY, Ph.D.† IN [Plate VI.] N previous publications (1) it has been shown that the green spectral line of the aurora and of the light of the night sky originates in oxygen in the atomic form in the upper atmosphere. A problem still outstanding is to determine just what electronic transition represented in the spectral scheme for oxygen is responsible for the production of this radiation at X 5577 Å. A careful search for other spectral lines that might be associated with the green line has up to the present failed to elucidate the problem. A powerful method of classifying spectral lines is found in the character of the resolution experienced by the lines when the radiation giving rise to them is emitted by atoms in the presence of a magnetic field. (2) In 1927 McLennan, McLeod, and McQuarrie reported some visual observations on the Zeeman resolution of the oxygen green line in which it was seen that, viewed longitudinally, the green line was resolved into a doublet, the amount of whose separation appeared to be the same as that of the two outer components of a normal triplet. * J. H. McLeod wishes to acknowledge his indebtedness to the Research Council of Canada for the grant of a Fellowship that enabled him to participate in this work. + Communicated by the Authors. The present paper deals with a more exact determination of the longitudinal Zeeman effect of the oxygen green line. The necessary magnetic field was provided by a watercooled solenoid shown diagrammatically in fig. 1. The coil was wound on a brass tube as shown, and consisted of ten layers of No. 16 B. & S. gauge enamelled single silk-covered copper wire. The layers were separated from each other by ebonite strips F each 3 inch in thickness by inch in width, laid parallel to the axis of the coil and about 1 cm. from each other. These strips provided a series of open spaces running longitudinally to the coil between each layer of wire. The ebonite end-pieces B were perforated with many small holes to provide openings at each end of the spaces between the layers of the coil. When the coil was in operation tap water was forced through the spaces from one end of the coil to the other, so that every wire was bathed by flowing water. This method of cooling made it possible to pass a current of 30 amperes through the windings continuously, with a rise in temperature of the cooling water of only 9 or 10 degrees. The length of the solenoid was 35 cm. and the total number of turns was 2390. The calculated field then for 30 amperes was 2620 gauss. Too much reliability should not be placed on this calculated value of the field for it could be that some current might leak through small cracks in the insulating enamel and so reduce the value of the field. A comparison of the strength of the magnetic field at different points throughout the coil was made by means of a small search coil and a ballistic galvanometer. Fig 2 shows the graph obtained when deflexions of the galvanometer (proportional to the field strength) were plotted against distance through the solenoid. It is seen that for a distance of nearly 25 cm. in the central portion of the coil the field was within a few per cent. of being uniform. It was light emitted in the central portion of the solenoid that was used in the determination of the magnetic resolution of the green line. The green line radiation was produced in a tube containing a mixture of argon and oxygen. A current of about 30 m.a. from a 2000-volt D.C. motor-generator set was used to excite the tube. A second tube containing neon gas was used to measure the strength of the magnetic field both before and after an exposure with the tube containing oxygen and argon was made. The yellow neon line at 5852 Å was used as the standard. |