As the subject of the reduction of astronomical observations in the air had been the subject of several conversations with the late Squadron Leader Johnston, who was one of our best exponents of aerial navigation, Mr. A. J. Hughes, O.B.E., suggested to the writer that a short note based on Squadron Leader Johnston's methods would be useful in order that his valuable experience should not be entirely lost, and that some systematic survey of the methods available would be useful in connection with a subject that is becoming of increasing importance now that the range and reliability of aircraft have been so largely extended.