7 1 2 D O C . 4 5 8 C A L C U L A T I O N S

458. Calculations

[Buenos Aires, 11 March–15 May

1925][1]

[2]

[3]

AD. [82 887.1]. On the verso is a list of professors at the Universities of Buenos Aires and Córdoba

in an unknown hand. A note is placed at the bottom of the page in an unknown hand: “Mandelstam

Padilla 453 Dept [10].”

[1]Dated by the fact that there is a list of South American professors on the verso.

[2]Here c represents the speed of light in the gravitational field of a mass m at a distance r. The full

form of this expression is , with the speed of light in a field-free region and

K the gravitational constant. Obviously, Einstein set and assumed .

In the following, Einstein proceeds to derive the angle of gravitational light deflection of a beam

of light passing in the y-direction at a distance Δ (δ in the diagram) from the center of gravitation. The

calculation proceeds along the lines taken in Einstein 1911h (Vol. 3, Doc. 23), §4. (Note that the result

derived there was only half the value obtained in the final theory of general relativity; see Einstein to

Carl Runge, 8 November 1920 [Vol. 10, Doc. 195]).

In the first expression below a factor of is missing but can be neglected for .

[3]Taking into account Einstein’s omission of factors of c and K, this expression would be .

c 1

2m

r

------- –=

∂x

∂c

yd

∞ –

∞ +

³

∂x

∂c

2m----

x

r3

=

y

Δ

tanψ

----------- - Δ tanψ = dy

Δ

2ψ cos

-------------- -dψ =

r

Δ

cosψ

------------ -=

2mΔ³--------------

Δ

2ψ cos

-dψ

3ψ cos

Δ3

--------------- ⋅

2m

Δ

------- cosψdψ

π

2

-- -–

π

2

-+--

³

4m

Δ

------- = =

c

c0©§

1

2Km-----------·

rc2

-–

¹

= c0

c0 K 1 = = c c0 ≈

1

c

-- -

2---

m

r

- 1 «

4Km

c2Δ

----------- -