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10. 11. 12. 13. 14. Eddy, J. , Gilman, P. , and Trotter, D. , Science, 198, 824, 1977. , and LaBonte, B. , Astrophys. J. Letters, 239, L33, 1980. Gilman, P. , Astrophys. , 283, 385, 1984. , Astron. , 155, 87, 1986. Hathaway, D. , and Wilson, R. , Astrophys. , 357, 271, 1990. , and Kambry, M. , Astron. , p. 21. There is a wide literature on the vexing problem of meridional motions on the solar surface. The following papers may be noted: 15. Kambry, M. , 132, 41, 1991. 16. , Astron. , 254, 381, 1992.

Stauffer, J. , Hartmann, L. , Prosser, C. , Patten, B. , Astrophys. , 479, 776, 1997. 4. Early-type binaries have been considered by: 43. , Astrophys. , 203, 680, 1976. 44. , Bull. Astron. Soc. India, 9, 309, 1981. 45. , Astron. , 135, 393, 1984. 46. , Astron. Astrophys. Suppl. , 59, 37, 1985. 47. Hall, D. , Astrophys. J. Letters, 309, L83, 1986. See also: 48. , in Wolf-Rayet Stars: Observations, Physics, Evolution (de Loore, C. W. , and Willis, A. U. Symposium No 99, p. 251, Dordrecht: Reidel, 1982.

47) thus implying that the vector with components dxi is also tangent to an absolute-vorticity line. This concludes the proof. By virtue of Eqs. 47), we also note that the ratio ω/ρ is proportional to the length of a line element along an absolute-vorticity line. This is known as vortex line stretching or shrinking. In summary, we have shown that the absolute-vorticity lines move with the fluid in the absence of baroclinicity and friction. However, although one can also construct lines of relative vorticity, it is only the absolute-vorticity lines that may remain coincident with material lines.

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