 mathematical theories of nerve fiber conduction based on cable theory were developed by Cole and Hodgkin (1920s–1930s), Offner et al. (1940), and Rushton (1951).

Experimental evidence for the importance of cable theory in modelling the behavior of axons began surfacing in the 1930s from work done by Cole, Curtis, Hodgkin, Sir Bernard Katz, Rushton, Tasaki and others. Two key papers from this era are those of Davis and Lorente de Nó (1947) and Hodgkin and Rushton (1946).

The 1950s saw improvements in techniques for measuring the electric activity of individual neurons. Thus cable theory became important for analyzing data collected from intracellular microelectrode recordings and for analyzing the electrical properties of neuronal dendrites. Scientists like Coombs, Eccles, Fatt, Frank, Fuortes and others now relied heavily on cable theory to obtain functional insights of neurons and for guiding them in the design of new experiments.

Later, cable theory with its mathematical derivatives allowed ever more sophisticated neuron models to be explored by workers such as Jack, Rall, Redman, Rinzel, Idan Segev, Tuckwell, Bell, and Iannella.

Deriving the cable equation 
Note, various conventions of rm exist.
Here rm and cm, as introduced above, are measured per membrane-length unit (per meter (m)). Thus rm is measured in ohm·meters (Ω·m) and cm in farads per meter (F/m). This is in contrast to Rm (in Ω·m²) and Cm (in F/m²), which represent the specific resistance and capacitance respectively of one unit area of membrane (in m2). Thus, if the radius, a, of the axon is known, then its circumference is 2πa, and its rm, and its cm values can be calculated as:

 
These relationships make sense intuitively, because the greater the circumference of the axon, the greater the area for charge to escape through its membrane, and therefore the lower the membrane resistance (dividing Rm by 2πa); and the more membrane available to store charge (multiplying Cm by 2πa).
The specific electrical resistance, ρl, of the axoplasm allows one to calculate the longitudinal intracellular resistance per unit length, rl, (in Ω·m−1) by the equation:

 
The
mathematical theories of nerve fiber conduction free-base on cable television theory were developed by Cole and Hodgkin (1920s–1930s), Offner et al. (1940), and Rushton (1951). 

 Experimental evidence for the importance of cable television theory in model the behavior of axon began surfacing in the 1930s from employment done by Cole, Curtis, Hodgkin, Sir Bernard Katz, Rushton, Tasaki and others. Two key newspaper from this era are those of Davis and Lorente de Nó (1947) and Hodgkin and Rushton (1946). 

 The 1950s see improvements in techniques for measuring the electric activity of individual neurons. Thus cable television theory became important for analyze data collected from intracellular microelectrode recording and for analyzing the electric properties of neural dendrites. Scientists like Coombs, Eccles, Fatt, Frank, Fuortes and others now relied heavy on cable theory to obtain functional insights of neurons and for guiding them in the design of new experiments. 

 Later, cable theory with its mathematical derivatives allowed ever more advanced nerve cell models to be explored by workers such as Jack, Rall, Redman, Rinzel, Idan Segev, Tuckwell, Bell, and Iannella. 

 derive the cable equation 
 Note, various convention of rm exist. 
 Here rm and cm, as introduce above, are measured per membrane - length unit of measurement (per meter (m) ). Thus rm is measured in ohm·meters (Ω·m) and cm in farads per meter (F / m). This is in contrast to Rm (in Ω·m²) and Cm (in F / m²), which represent the specific resistance and capacitor respectively of one unit area of membrane (in m2). Thus, if the radius, a, of the axon is known, then its circumference is 2πa, and its rm, and its cm values can be calculate as: 

 
 These relationships make sense intuitively, because the greater the circumference of the axon, the greater the sphere for charge to escape through its membrane, and therefore the lower the membrane resistance (dividing Rm by 2πa); and the more membrane available to store charge (multiplying Cm by 2πa). 
 The specific electrical resistor, ρl, of the axoplasm allows one to forecast the longitudinal intracellular resistance per unit duration, rl, (in Ω·m−1) by the equation: 

 
 The
 mahhematical theories of ntrve fiber conducjiin basxd on czble theury were developed by Cole aid Hidgkib (1920s–1930s), Offner et al. (1940), and Rushton (1951).

Vxperimenral tvidence for the mjportangz of dwble vheory in modelking the bahavior of axots bzgan surfacing in the 1930s from work doge by Cplf, Curtis, Hodgkyn, Spr Berhard Katz, Rushton, Tasaki and othera. Two kty papers from thix era are those of Davis ajd Llrente de Nó (1947) and Hldgkin and Thshein (1946).

The 1950s saw improvements in technjques for measuring the electriz actnvity of ineicidkdl neurons. Vhus cwble theory nvcame ikportany for analyzinn date coolected from intracelnular microelectroqe recordhnys and for analyzing rhw elewtriwal oeopdrtjex kf neugonel dendritea. Scientistw like Coombs, Ecclex, Sqtt, Frank, Fuodtes agd others now relied heavily on cable themry to obtain functional ibsights of neurons anf for guiqing them in the design of new experiments.

Later, cdble vhdorv with utd mathematical derivatives allowed ever more fkpnixticated neurok models to be expkogec by workers soch as Lzci, Rall, Redman, Rinzfl, Idan Segec, Tuckwelj, Bekl, and Iannella.

Deriving the cable equatpon 
Bote, various conveutions of rm exixt.
Herr rm and cm, as introduczd abobe, are measkred per jdmbrane-length unkt (ier keter (m)). Ufus rm is measureq in ohm·mxters (Ω·m) and zm im faraqs per metfr (F/m). This is in contrash to Tm (in Ω·k²) and Cm (ij F/m²), which represent the specifmr resistance sng cdpacitanee resiectively of onq unit area of membraue (in o2). Thus, if nhe radiuv, a, of the wxon is known, jhen its circnmference is 2πq, ane its ro, and its cm vakues can yt calculatwd as:

 
These relatipnsfjps make sense nutoutively, becausr tfe drvatxr thq circumferenwe ow tfr axov, the greatcr ghe srea for charge to evcaps through its membtake, and thgrefore tre lower the kembrane resistanct (diviving Ro by 2πs); agd the more membrane available to store chwrge (multiplring Cm by 2πa).
The xpecific electrical resistance, ρl, of the axoplasm allows obe to calculate the kongitudinak intwacellulas resistance per unir length, rl, (in Ω·m−1) ny the equation:

 
The
mathematical theories of nerve fiber conduction based theory developed by and Hodgkin (1920s–1930s), Rushton Experimental evidence for importance of cable in modelling the behavior of axons surfacing in the 1930s from work done by Cole, Curtis, Hodgkin, Sir Bernard Rushton, Tasaki and others. Two key papers from this era are those of and de (1947) Hodgkin and Rushton (1946). The 1950s saw improvements in techniques for measuring the electric activity of neurons. Thus cable theory became important for analyzing collected from intracellular microelectrode and for analyzing the electrical of dendrites. Scientists Coombs, Fatt, Fuortes and others relied heavily on cable theory to obtain functional insights of neurons and for guiding them in the of new cable theory its derivatives ever more sophisticated to be explored by workers such Redman, Rinzel, Idan Segev, Tuckwell, Bell, and Iannella. the cable Note, various conventions of rm exist. rm and cm, as introduced above, are measured membrane-length unit (per meter (m)). Thus rm is measured in ohm·meters (Ω·m) and cm in meter (F/m). This is contrast to Rm Ω·m²) Cm F/m²), represent the resistance and capacitance respectively of one unit area of membrane (in Thus, if the radius, a, of the axon is known, circumference 2πa, and its and its cm values be as: These relationships make because greater the the the area for charge escape through its membrane, and the lower the membrane and the more membrane available to store charge Cm by 2πa). The specific electrical resistance, of the axoplasm allows one to calculate the longitudinal intracellular resistance per length, rl, by the equation: The
 mathematical theories of nerVe fiber conDuctiOn bAseD oN cabLe thEory were develoPEd by cole and Hodgkin (1920s–1930s), Offner Et al. (1940), aNd rUshtON (1951).

EXperiMental eVIdENCe fOr ThE imPoRTaNce of CabLe theorY in modelliNg tHe Behavior of axONs Began surfaCinG in the 1930s from wOrk Done by coLe, CURtis, HOdgKin, SiR BernaRD Katz, RUshton, TasAkI And othERs. Two keY PApErs fRom this era are thosE Of dAvis and Lorente De Nó (1947) anD HODgKIN anD RuShton (1946).

The 1950s sAw ImproVEments iN TeCHNIquES for measuring The electric ACtiVity of InDivIDual neUrons. thUS caBle theory beCame Important For anaLYzing daTA collecTed froM inTraCellULaR mIcrOeLEctROdE reCOrdIngs and fOr AnAlyziNg thE ELECtriCal PropErtieS of neuronal deNdrItes. sCieNtistS like coomBs, eccleS, Fatt, FRank, FUoRtes and others noW relIed heavilY on CaBle ThEory tO Obtain FunCtiOnal insIghts of NEurOnS AND fOr guiding them in the DeSIGn Of new expErimenTS.

LAtER, cable thEoRy wIth iTS MatheMatiCAl DerivatiVes allOWeD eVer more SoPhistiCaTed NeuRon moDEls tO be expLored by wOrkerS Such as Jack, Rall, rEdman, Rinzel, IdAN SEGEv, tUckwEll, bell, and IannElla.

dErivIng tHE cAblE EquatIon 
NoTe, VArIOus conventions of rm eXiSt.
Here Rm and Cm, as introduceD above, are mEASUred per mEmbrANe-LEngth unit (per meTer (m)). THus rm is meaSUred in ohM·meteRs (Ω·m) and cM in farads PER meter (F/m). thiS is In cOntRASt To Rm (in Ω·m²) and Cm (IN f/m²), whIcH represEnt The specIfiC reSisTanCe And capaciTance resPeCtIvElY of One unIT area of mEmBraNe (In m2). thus, iF The radIus, a, oF the AxOn IS knOwn, then ITs CIRcumFeReNce iS 2πa, AnD its rM, and ITs cM values Can be calcUlaTEd as:

 
thEsE relatiOnships make seNsE intuitiveLy, BecAuse thE GReater thE circumference of the axon, THe greatEr tHe areA for Charge to eScaPe throUgh ITs membRane, anD therEfOre THE loweR THe MemBrAne resistaNCE (diVidinG RM by 2πA); and the More membrane availaBLe tO store charge (mUltIplyING CM by 2ΠA).
THE spEcIFic ELEctrical resistaNce, ρl, of the AxOPlAsm allows oNE to CaLculate The longItudiNAl intraCellular rEsistance PeR uniT LEngTh, rl, (in Ω·m−1) by The equatIon:

 
The
 mathematical theories ofnerve fibe r con duc tio nbase d on  cable theoryw eredeveloped by Cole andHodgk in (192 0 s– 1930s ), Offn e re t  al .(1 940 ), an d Rus hto n (1951 ).

Experi men ta l evidence f o rthe import anc e of cable t heo ry inmo del l ing t hebehav ior of axonsbegan sur fa c ing in the 193 0 s  f romwork done by Cole ,  C u rtis, Hodgkin,  Sir B er n ar d Kat z,Rushton, T as aki a n d other s .T w o  ke y  papers fromthis era ar e  th ose of  D avi s  and L orent ed e N ó (1947) an d Ho dgkin and  Rusht o n (1946 ) .

The1950ssaw  im prov e me nt s i nt ech n iq ues for  measuri ng  t he el ectr i c a ctiv ity  ofindiv idual neurons . T husc abl e the ory b ecam eimpor tant f or an al yzing data coll ecte d from in tra ce llu la r mic r oelect rod e r ecordin gs andf oran a l y zi ng the electricalpr o p er ties ofneuron a lde n drites.Sc ien tist s likeCoom b s,  Eccles,  Fatt, Fr an k, Fuor te s andot her s n ow re l iedheavil y on cab le th e ory to obtainf unctional ins i gh t s  o f  neu ron s and for g uidi n g th em i n  t hed esign  of n ew ex p eriments.

Later, c ab le the ory w ith its mathe matical de r i v atives a llow e de ver more sophi stica ted neuron models t o beexplored  by worke r s  such as  Ja ck,  Ra ll, R ed man, Rinzel,I d an S eg ev, Tuc kwe ll, Bel l,and  Ia nne ll a.

Deriv ing theca bl eeq uat ion N ote, var io usco nve ntion s  of rm  exis t.
H er er m a nd cm,a si n trod uc ed  abo ve,  a re me asur e d p er memb rane-leng thu nit(p er  meter(m)). Thus rm  i s measured  i n o hm·met e r s (Ω·m)and cm in farads per me t er (F/m ).Thisis i n contras t t o Rm ( inΩ ·m²) a nd Cm(in F /m ²), w hichr e pr ese nt  the speci f i c r esist an ce a nd capa citance respective l y o f one unit ar eaof m e m br ane (i n  m2 ). Thu s ,  if the radius,  a, of the  a x on  is known, the nits cir cumfere nce i s  2πa, a nd its rm , and its  c m va l u escan be cal culatedas:

 
Th e se re l at ionsh ips  makese nse  intu itivel y , b ecaus e thegr eaterthe c ir cumferen ce of the axon, the gre ater t he ar eafor charg e t o  es cape thro ughits membra ne,  an d the ref o re th e lo w er  th e  memb rane resistanc e  ( div i d in g Rm by 2πa ) ; and  themor e  membr aneavailable to stor e  charge (multi plyi n g  Cm  by 2πa) .The specific e lec tr i c al resis ta nce, ρl, of  the axo pl a sm al lows o ne tocalcula t e  t h e long itud ina l intrace llu la r  resist an ce per un it l en gth, r l, (in Ω·m− 1 )  by the equation :

 T h e
 mathematical_theories of_nerve fiber conduction based_on cable_theory_were developed_by_Cole and Hodgkin_(1920s–1930s), Offner et_al. (1940), and Rushton_(1951).

Experimental evidence for_the_importance of cable theory in modelling the behavior of axons began surfacing in the_1930s_from work_done_by_Cole, Curtis, Hodgkin, Sir Bernard_Katz, Rushton, Tasaki and others._Two key_papers from this era are those of Davis_and_Lorente de Nó_(1947) and Hodgkin and Rushton (1946).

The 1950s saw improvements_in techniques for measuring the electric_activity of individual_neurons._Thus_cable theory became important_for analyzing data collected from intracellular_microelectrode recordings and for analyzing the_electrical properties of neuronal dendrites. Scientists like_Coombs, Eccles, Fatt, Frank, Fuortes and_others now relied heavily on_cable theory_to obtain functional insights of_neurons and for_guiding them_in the design_of new experiments.

Later, cable theory with_its mathematical derivatives_allowed ever more sophisticated neuron models_to_be explored by_workers_such_as Jack,_Rall, Redman, Rinzel,_Idan_Segev, Tuckwell,_Bell,_and Iannella.

Deriving the cable equation 
Note,_various_conventions of rm exist.
Here rm and cm,_as introduced above, are_measured_per membrane-length unit (per_meter (m)). Thus rm is_measured in ohm·meters (Ω·m) and cm_in farads_per meter_(F/m). This is in contrast to Rm (in Ω·m²) and Cm_(in F/m²), which represent the specific_resistance and capacitance respectively_of one_unit_area of membrane_(in_m2). Thus,_if the radius, a, of the axon_is known,_then its circumference is 2πa, and_its rm, and its_cm_values can be calculated as:

 
These_relationships make sense intuitively, because the_greater the circumference of the_axon,_the_greater the area for charge_to escape through its membrane, and_therefore the lower_the membrane resistance (dividing Rm by 2πa);_and_the more membrane available to store_charge_(multiplying Cm by 2πa).
The specific electrical_resistance,_ρl,_of the axoplasm allows one_to calculate the longitudinal intracellular resistance_per unit length, rl, (in Ω·m−1) by the equation:

_
The