The flexure term and a correction to the atmospheric refraction constant calculated from meteorological data may be determined from the zenith distances of FK5 stars observed each night on a meridian circle. All such determinations on meridian circles and vertical circles have been corrupted-and in fact dominated-byinternal refraction which is often larger than 1" and quite variable. After removing internal refraction by a simple equipment at the CAMC on La Palma, it became apparent that the true flexure and the true correction to the calculated refraction constant vary by less than 0."09 (rms) from night to night. This is a reduction of the estimated uncertainty of these quantities by a factor of about four. This improvement is expected at any meridian circle which is equipped with sufficiently precise (photoelectric) micrometers if internal refraction were removed. Alternative forms of the observation equation for declinations are discussed. Observations over a period of two months may be solved in oneglobal least-squares solution keeping the refraction and the flexure terms constant. Furthermore, one ∆δ per star is obtained, instead of a different ∆δ each night for each star.