A system of taxonomy of the cryptogams, the Smith system was published in:
Smith, G.M. (1938). Cryptogamic Botany, vol. 1. Algae and fungi. McGraw-Hill, New York.
Smith, G.M. (1955). Cryptogamic Botany, vol. 2. Bryophytes and pteridophytes. 2nd ed. McGraw-Hill, New York.
Division Chlorophyta
:*Order 1. Volvocales
:::*Family 1. Chlamydomonadaceae
:::*Family 2. Volvocaceae
:*Order 2. Tetrasporales
:*Order 3. Ulotrichales
:::*Family 1. Ulotrichaceae
:::*Family 2. Microsporaceae
:::*Family 3. Cylindrocapsaceae
:::*Family 4. Chaetophoraceae
:::*Family 5. Protococcaceae
:::*Family 6. Coleochaetaceae
:::*Family 7. Trentepohliaceae
:*Order 4. Ulvales
:::*Family 1. Ulvaceae
:::*Family 2 Schizomeridaceae
:*Order 5. Schizogoniales
:::*Family Schizogoniaceae
:*Order 6. Cladophorales
:::*Family 1. Cladophoraceae
:::*Family 2. Sphaeropleaceae
:*Order 7. Oedogoniales
:::*Family Oedogoniaceae
:*Order 8. Zygnematales
:::*Family 1. Zygnemataceae
:::*Family 2. Mesotaeniaceae
:::*Family 3. Desmidiaceae
:*Order 9. Chlorococcales
:::*Family 1. Chlorococcaceae
:::*Family 2. Endosphaeraceae
:::*Family 3. Characiaceae
:::*Family 4. Protosiphonaceae
:::*Family 5. Hydrodictyaceae
:::*Family 6. Oöcystaceae
:::*Family 7. Scenedesmaceae
:*Order 10. Siphonales
:::*Family 1. Bryopsidaceae
:::*Family 2. Caulerpaceae
:::*Family 3. Halicystaceae
:::*Family 4. Codiaceae
:::*Family 5. Derbesiaceae
:::*Family 6. Vaucheriaceae
:::*Family 7. Phyllosiphonaceae
:*Order 11. Siphonocladiales
:::*Family 1. Valoniaceae
:::*Family 2. Dasycladaceae
:*Order Charales
:::*Family Characeae
Division Euglenophyta
:*Order 1. Euglenales
:*Order 2. Colaciales (Euglenocapsales)
Division Pyrrophyta
:*Order 1. Gymnodiniales
:*Order 2. Peridiniales
:*Order 3. Dinophysidales
:*Order 4. Rhyzodiniales
:*Order 5. Dinocapsales
:*Order 6. Dinotrichales
:*Order 7. Dinococcales
Division Chrysophyta
:*Order 1. Heterochloridales
:*Order 2. Rhizochloridales
:*Order 3. Heterocapsales
:*Order 4. Heterotrichales
:*Order 5. Heterococcales
:*Order 6. Heterosiphonales
:*Order 1. Chrysomonadales
::*Suborder 1. Cromulinae
::*Suborder 2. Isochrysidineae
::*Suborder 3. Ochromonadineae
:*Order 2. Rhizochrysidales
:*Order 3. Chrysocapsales
:*Order 4. Chrysotrichales
:*Order 5. Chrysosphaerales
:*Order 1. Centrales
:*Order 2. Pennales
Division Phaeophyta
:*Order 1. Ectocarpales
:*Order 2. Sphacelariales
:*Order 3. Tilopteridales
:*Order 4. Cutleriales
:*Order 5. Dictyotales
*Subclass 1. Haplostichineae
:*Order 1. Chordariales
:*Order 2. Sporochnales
:*Order 3. Desmarestiales
*Subclass 2. Polystichineae
:*Order 1. Punctariales
:*Order 2. Dictyosiphonales
:*Order 3. Laminariales
:*Order Fucales
Division Cyanophyta
:*Order 1. Chroococcales
:*Order 2. Chamaesiphonales
:*Order 3. Hormogonales
Division Rhodophyta
*Subclass 1. Bangioideae
:*Order Bangiales
*Subclass 2. Florideae
:*Order 1. Nemalionales
:*Order 2. Gelidiales
:*Order 3. Cryptonemiales
:*Order 4. Gigartinales
:*Order 5. Rhodymeniales
:*Order 6. Ceramiales
Division Myxothallophyta
*Subclass 1. Endosporeae
*Subclass 2. Exosporeae
Division Eumycetae
:*Order 1. Chytridiales
:::*Family 1. Rhizidiaceae
:::*Family 2. Olpidiaceae
:::*Family 3. Synchytriaceae
:::*Family 4. Cladochytriaceae
:::*Family 5. Woroninaceae
:*Order 2. Blastocladiales
:*Order 3. Monoblepharidales
:*Order 4. Ancylistales
:*Order 5. Saprolegniales
:::*Family 1. Saprolegniaceae
:::*Family 2. Leptomitaceae
:::*Family 3. Pythiaceae
:*Order 6. Peronosporales
:*Order 7. Mucorales
:*Order 8. Entomophthorales
*Subclass 1. Protoascomycetae
*Subclass 2. Euascomycetae
:*Order 1. Aspergillales
:*Order 2. Erysiphales
:*Order 3. Hysteriales
:*Order 4. Phacidiales
:*Order 5. Pezizales
:*Order 6. Tuberales
:*Order 7. Helvellales
:*Order 8. Exoascales
:*Order 9. Hypocreales
:*Order 10. Sphaeriales
:*Order 11. Dothidiales
:*Order 12. Laboulbeniales
*Subclass 1. Eubasidii
:*Order 1. Agaricales (Hymenomyceatae)
:*Order 2. Lycoperdales (Gasteromycetae)
:*Order 3. Dacryomycetales
:*Order 4. Tremellales
:*Order 5. Auriculariales
*Subclass 2. Hemibasidii
:*Order 1. Urediniales
:*Order 2. Ustilaginales
:::*Family 1. Ustilaginaceae
:::*Family 2. Tilletiaceae
*Subclass 1. Ascholichenes
*Subclass 2. Basidiolichenes
Division Bryophyta
:*Order 1. Sphaerocarpales
:::*Family 1. Sphaerocarpaceae
:::*Family 2. Riellaceae
:*Order 2. Marchantiales
:::*Family 1. Ricciaceae
:::*Family 2. Corsiniaceae
:::*Family 3. Targioniaceae
:::*Family 4. Monocleaceae
:::*Family 5. Marchantiaceae
:*Order 3. Jungermanniales
::*Suborder 1. Metzgerineae
::*Suborder 2. Jungermannineae
:*Order 4. Calobryales
:*Order 1. Anthocerotales
*Subclass 1. Sphagnobrya
*Subclass 2. Andreaeobrya
*Subclass 3. Eubrya
Division Psilophyta
:*Order 1. Psilophytales
:::*Family 1. Rhyniaceae
:::*Family 2. Psilophytaceae
:::*Family 3. Pseudosporochnaceae
:::*Family 4. Zosterophyllaceae
:::*Family 5. Asteroxylaceae
:*Order 2. Psilotales
Division Lepidophyta
:*Order 1. Lycopodiales
:::*Family 1. Protolepidodendraceae
:::*Family 2. Lycopodiaceae
:*Order 2. Selaginellales
:::*Family 1. Selaginellaceae
:::*Family 2. Miadesmiaceae
:*Order 3. Lepidodendrales
:::*Family 1. Lepidodendraceae
:::*Family 2. Lepidocarpaceae
:::*Family 3. Bothrodendraceae
:::*Family 4. Sigillariaceae
:*Order 4. Isoetales
:::*Family 1. Pleuromeiaceae
:::*Family 2. Isoetaceae
Division Calamophyta
:*Order 1. Hyeniales
:*Order 2. Sphenophyllales
:*Order 3. Equisetales
:::*Family 1. Calamitaceae
:::*Family 2. Equisetaceae
Division Pterophyta
*Subclass 1. Primofilices (or Inversicatenales, Coenopterideae, Palaeopteridales)
:*Order 1. Protopteridales
:::*Family 1. Protopteridaceae
:::*Family 2. Cladoxylaceae
:*Order 2. Coenopteridales
:::*Family 1. Zygopteridaceae
:::*Family 2. Botryopteridaceae
:::*Family 3. Anachoropteridaceae
:*Order 3. Archaeopteridales
*Subclass 2. Eusporangitae
:*Order 1. Ophioglossales
:*Order 2. Marattiales
*Subclass 3. Leptosporangiatae
:*Order 1. Filicales
:::*Family 1. Osmundaceae
:::*Family 2. Schizaeaceae
:::*Family 3. Gleicheniaceae
:::*Family 4. Matoniaceae
:::*Family 5. Dipteridaceae
:::*Family 6. Hymenophyllaceae
:::*Family 7. Cyatheaceae
:::*Family 8. Dicksoniaceae
:::*Family 9. Polypodiaceae
:::*Family 10. Parkeriaceae
:*Order 2. Marsileales
:*Order 3. Salviniales