Eczema

A comparative study into the topical anti-inflammatory activity of cannabinoids (on croton oil-inflamed skin in mice) showed that Δ8THC, Δ9THC and THCV are about half as effective in reducing inflammation as Indometacin (a commonly used Non-steroid anti-inflammatory drug), but approximately 5 times more effective than CBCV and CBD. CBC and CBDV had no appreciable anti-inflammatory activity (Tubaro et al., 2010).

epilepsy

In a mouse model of epilepsy (Maximal Electro Shock), the following cannabinoids were found to be anti-convulsive (ED50)(referenced within: Devinsky et al., 2014): CBD 120 mg/kg Δ9THC 100 mg/kg 11-OH-Δ9THC 14 mg/kg 8β-OH-Δ9THC 100 mg/kg Δ9THCA 200-400 mg/kg Δ8THC 80 mg/kg CBN 230 mg/kg Δ9α/β-OH-hexahydro-CBN 100 mg/kg Apart from that the doses reported above are incredibly high, it does provide a proof of principle that many cannabinoids exert anti-convulsive effects.  

References:

Devinsky, O., Cilio, M.R., Cross, H., Fernandez-Ruiz, J., French, J., Hill, C., Katz, R., Di Marzo, V., Jutras-Aswad, D., Notcutt, W.G., et al. (2014). Cannabidiol: pharmacology and potential therapeutic role in epilepsy and other neuropsychiatric disorders. Epilepsia 55, 791–802.

Tubaro, A., Giangaspero, A., Sosa, S., Negri, R., Grassi, G., Casano, S., Della Loggia, R., and Appendino, G. (2010). Comparative topical anti-inflammatory activity of cannabinoids and cannabivarins. Fitoterapia 81, 816–819.