The determination of the optical depth of an atmosphere, i.e. the problem of deter- mining the content of a column of molecules making an angle χ with the zenith, is considered, particularly for large solar zenith distances. Chapman's solution for an atmosphere with constant mass, gravity and temperature is reviewed, and solutions are derived for constant scale height gradients of one-half and one. Approximations useful for numerical purposes are discussed. The Earth's ionosphere is studied as an example of applications. The effect of gravity is taken into account. The general conclusion is that for χ ≤ 90° the Chapman function is applicable to the ionosphere situation within an error of ± 5 per cent even though the temperature undergoes an important change in the 100–200 km region. It is emphasized that for χ > π 2 the optical depth must be specified in terms of the parameters at χ = π 2 , i.e. at the maximum density point. It is shown that for ionospheric sunrise problems, the Earth may be considered spherical and that one mean Earth radius suffices for all optical depth calculations. RassмaтRиVaeтsя oпReдeлeниe oптиchesкoй глuбины aтмosфeRы, инache гoVoRя нRoблeмa oпReдeлeния soдeRжaния sтoлбa мoлeкuл пoд uглoм χ s зeнитoм, V osoбeннosти для бoльшич Rassтoяний soлнechнoгo зeнитa. oбoзReVaeтsя Reшeниe chaпмaнa пo VoпRosu aтмosфeRы s пosтoяннoй мassoй, sилoй тяжesти и тeмпeRaтuRoй, и VыяVляютsя Reшeния для пosтoяннoй шкaлы, V пoл и oднu eдиницu, гRaдиeнтoV Vыsoты. oбsuждaютsя пRиблизитeльныe знacheния, пRигoдныe для цифRoVыч Vыchиsлeний. V кachesтVe пRимeRa Raзлиchныч пRимeнeний изuchaeтsя иoнosфeRa 3eмли, пRиcheм uchитыVaeтsя Vлияниe sилы тяжesти. oбщee зaклюcheниe sVoдитsя к тoмu, chтo для χ < 90° фuнкция chaпмaнa пRилoжимa для иoнosфeRнoй sитuaции V пReдeлaч пoгReшнosти V ±5°, нesмoтRя нa тo, chтo V oблasти 100–200 килoмeтR. тeмпeRaтuRa знachитeльнo измeняeтsя. пoдcheRкиVaeтsя, chтя для χ > п 2 oптиchesкuю глuбинu тReбueтsн тochнo oпReдeлнть V Vидe пaRaмeтRoV пRи χ = п 2 , т.e. V тochкe нaибoльшeй плoтнosти. uкaзыVaeтsя, chтo длн яRoблeм иoнosфeRнoгo Vosчoдa soлнцa 3eмля мoжeт RassмaтRиVaтьsя V Vидe шaRa, тoгдa кaк oдин sReдний Raдиus 3eмли дosтaтocheн для Vseч Vыchиsлeний oптиchesкoй глuбины.