2 3 2 D O C . 2 8 0 J A N U A R Y 1 9 2 0 Instead of concluding from this that Δt and are different measures of the same time interval, and consequently that clock runs slower than clock U, one intro- duces the periods, or their reciprocal values, the frequencies, and writes:[6] (2) , so clock only apparently runs slower than U. Now I shall prove that this point of view cannot be maintained. We take light rays as clocks. We may set additionally, we have, as is commonly known, . If we now set , we get , hence, (3) , which relation is incompatible with (2), whereas it is in full agreement with (1) if one considers Δt and therein as different measures of the same timespan. In or- der to retain (2), one must set , hence , i.e., observe perpendicular to the path of the light source, which was already known. In your article “The Foundations of General Relativity,” page 62, you write:[7] “Here we have for a clock period: , , and infer from this that the clock runs slower when it is set up in the proximity of ponderable masses. From the above consideration it follows, however, that and ds necessarily must be regarded as a different unit for the same timespan dt. In my notation, I then obtain the relation , Δt′ U′ ν ν′ 1 α2 –= U′ Δu c0Δt = Δu′ c0Δt′ = Δx Δucosϕ = Δx′ Δu′cosϕ′ = ν ν′β( 1 α cosϕ′) + = cosϕ α cosϕ′ + 1 α cosϕ′ + --------------------------- = Δx′ 0= ϕ′ cos 0, ϕ′ π 2 -- - = = ν βν′ ν′ 1 α2 – ------------------ - = = Δt′ Δx 0= ϕ cos 0 ϕ, π 2 -- - = = ds 1= dx1 dx2 dx3 0 = = = dx4 1 g44 ----------- ds = g44 1 α r --- –= dx4 c c0 1 α r --- – ---------------- -=