forms of the backstaff. Continental European navigators called it the English Quadrant. A later modification of the Davis quadrant was to use a Flamsteed glass in place of the shadow vane; this was suggested by John Flamsteed. This placed a lens on the vane that projected an image of the sun on the horizon vane instead of a shadow. It was useful under conditions where the sky was hazy or lightly overcast; the dim image of the sun was shown more brightly on the horizon vane where a shadow could not be seen. Usage In order to use the instrument, the navigator would place the shadow vane at a location anticipating the altitude of the sun. Holding the instrument in front of him, with the sun at his back, he holds the instrument so that the shadow cast by the shadow vane falls on the horizon vane at the side of the slit. He then moves the sight vane so that he observes the horizon in a line from the sight vane through the horizon vane's slit while simultaneously maintaining the position of the shadow. This permits him to measure the angle between the horizon and the sun as the sum of the angle read from the two arcs. Since the shadow's edge represents the limb of the sun, he must correct the value for the semidiameter of the sun. Instruments that derived from the Davis quadrant The Elton's quadrant derived from the Davis quadrant. It added an index arm with spirit levels to provide an artificial horizon. Demi-cross The demi-cross was an instrument that was contemporary with the Davis quadrant. It was popular outside England. The vertical transom was like a half-transom on a cross-staff, hence the name demi-cross. It supported a shadow vane (A in Figure 4) that could be set to one of several heights (three according to May, four according to de Hilster). By setting the shadow vane height, the range of angles that could be measured was set. The transom could be slid along the staff and the angle read from one of the graduated scales on the staff. The sight vane (C) and horizon vane (B) were aligned visually with the horizon. With the shadow vane's shadow cast on the horizon vane and aligned with the horizon, the angle was determined. In practice, the instrument was accurate but more unwieldy than the Davis quadrant.