Meldon authored medical papers on cholera, diseases of the skin and gout.

[1] He was a member of the British Medical Association and attended the annual meeting in Dublin in 1887.

[2] Meldon rejected the uric acid theory as a full explanatory for gout.

He promoted his own "neuro-humoral theory" which held that gout and rheumatism were caused by a depressed condition of the nervous system.

[1] Meldon was a double gold medallist in surgery and midwifery and first prizeman in anatomy at the Catholic University Medical School.