"method and apparatus" is correct and commonly used in written English.
Example: The new method and apparatus for detecting cancer has shown promising results in clinical trials.
Krupenkin, T. Method and apparatus for energy harvesting using microfluidics.
Method and apparatus for determining fold difference significance.
Adamson, A. W. Method and apparatus for generating three-dimensional patterns.
Worthington, J. D. L. & Adelman, A. H. Method and apparatus for generating three-dimensional patterns.
C. M. Dobson, F. Chiti, J. Zurdo, K. H. DuBay, and M. Vendruscolo Method and apparatus for assessing polypeptide aggregation.
M. H. Graham and H. W. Johnson, "Method and apparatus for power line communications," U.S. Patent 5,257,006.
M. H. Graham, "Method and apparatus for transmission of digital data over a line," U.S. Patent 4,752,940.
J. S. Maltz and T. F. Budinger, "Arterial endothelial function measurement method and apparatus," U.S. Patent Application.
"Method and apparatus for power reduction during lane divergence". U.S. Patent Application 13/605,460, filed September 6 , 2012
Last month, Mr. Pearman received patent 6,296,808 for a "method and apparatus for protecting building personnel during chemical or biological attack".
