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question cuts the line of motion in 2, and intersects the mirror in e. The wave-front reflected from D at $t=0$ will have reached the point f₁, and the tangent ef₁ establishes the reflected wave-front. At the times 2τ, 3τ, &c., this particular disturbance will be found at f₂, f₃, f₄, &c.

When D is at a position 2, a new disturbance will have been established at g, which, at the time $t=5\tau$, will be found at g₅. In the same way, h₅, i₅, k₅ will have arranged themselves in the line f₅ k₅. At the time $t=10\tau$ the six wave-fronts will have been reflected from I, and will be placed along the line o₁₀ f₁₀. The angle f₁₀ O I o is equal to the aberration of the wave-fronts after reflexion from D. As, at this azimuth, the angles of incidence and of reflexion at I are equal, this angle is also the aberration of the emergent rays.

Part of the wave-front f, indicated by f', will be transmitted through the mirror D. It will overtake the mirror II at the time $t=8\tau$,
Fig. 7.when II will have position marked II₈, fig. 7. Returning after reflexion, it will take the position noted for the times $t=9\tau$, $t=10\tau$; and meeting the mirror D at $t=10{\tfrac {2}{3}}\tau$, it will be reflected as shown f'₁₁, at an angle whose tangent is given by the formula below. The following wave-front g' will be reflected one period later, at II₉, and it is shown in several positions. The wave-front f, belonging to the other system, having passed through the mirror, and having reached the line, Sd, at $t=10\tau$, is shown at f₁₁.

Fig. 8.In fig. 8 is shown the position of the wave-fronts below the mirror D for the time $t=15\tau$. f₁₅, and f'₁₅ have moved along the paths indicated, while the other wave-fronts have moved in a corresponding manner, their position at the time $t=15\tau$ being as shown in the figure. The wave-fronts of the unaccented system are placed on the line op; the aberration of the system is equal to the angle δ. The wave-fronts of the accented system are placed on the line qr; the corresponding aberration is the angle δ'; the line T₁₅q being the position of the axis of the observing telescope at the time $t=15\tau$. Produce the planes of the wave-fronts, draw line l, l', parallel to qT₁₅, the axis of the telescope, each terminated by the planes of consecutive wave-fronts. Their lengths are $l={\frac {\lambda }{\cos \delta }},\ l'={\frac {\lambda '}{\cos \delta '}}$. It is to be proved that $l=l'$.

Putting φ for the angle of incidence and φ' for the angle of reflexion, we have for both reflexions at D, φ=45°. For this azimuth there is no change of angles at I and II. The