Hartmann overcame these and many other difficulties by directly superposing the image of the spectrogram of a star, having iron comparison lines, upon the image of a spectrogram of the sun taken also with iron comparison lines.
The phenomenon of colour may, however, be obtained with thick plates by superposing two of them in a suitable manner, the combination acting as a thicker or a thinner plate according as the planes of polarization of the quicker waves within them are parallel or crossed.
The method for superposing the two spaces on one another was deduced by Sir David Brewster in 1856, but he does not appear to have dealt with the problem of range-finding.
He went on to deal with the case of projectiles, and was led to the conclusion that the motion in this case could be regarded as the result of superposing a horizontal motion with uniform velocity and a vertical motion with constant acceleration, the latter identical with that of a merely falling body; the inference being that the path of a projectile would be a parabola except for deviations attributed to contact with the air, and that in a vacuum this path would be accurately followed.
Instead of the operation of superposing accelerations, we may compound the several forces acting on a particle by the parallelogram law (see Mechanics) into what may be called the resultant force, the total acceleration of the particle being the same as if this alone acted.