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This paper is a brief survey of the vast amount of work on magnetic shielding of instruments against steady stray fields, and allied problems, by several authors during the last fifty years. It contains, first, a simplified presentation of the method of zonal harmonic analysis, by way of introduction to the mathematical theory of shielding as presented by those authors, and second, a brief summary of their theoretical inferences and experimental findings. In a paper of this kind no ``conclusion'' is necessary; the following table of contents explains the plan of presentation followed herein. 1. Introduction 2. Designed and incidental shielding 3. Problem of shield design 4. Theory of shielding, methods of analysis 5. Method of magnetic images (geometric) 6. Harmonic analysis; conception of harmonic magnets and harmonic images 7. Zonal harmonics 8. DuBois' formula for shield factor 9. Material for shield 10. Importance of differential permeability for shielding 11. Failure of magnetic shield 12. Incidental shielding 13. Dynamic shielding 14. Differential shielding Appendix Mathematical theory of Zonal Harmonics 15. Zonal Harmonic coefficients 16. Geometric and harmonic images 17. Analysis of any magnetic field in general into component spherical or zonal harmonics.