Annus MirabilisEinstein in 1905
Reading preferences

Reading preferences

Keep every explanation and worked example on the page. Nothing moves or plays by itself, and the larger instruments load only when you ask.

Line length
Type size
Contrast
Paragraph spacing

brownian motion

The equation explained

J=J′.J = J'.
In wordsThe two factors are equal.OverviewThe bookkeeping said the two factors stand in the ratio of the two parts of the integral; the physics said those parts are equal. So the factor is the same wherever the regions are put, and the sentence after the display adds that it does not depend on the size of the volume either.Full explanationThe paper says that from this and from the equation last found it follows that J=J′J = J'. The two statements are of different kinds and that is the point of the section. One is a matter of definition, dB/dB′=J/J′d B / d B' = J / J', and holds whatever the particles do. The other, dB/B=dB′/Bd B / B = d B' / B, is where the molecular-kinetic theory of heat is used. Put together: the probabilities being equal makes dB=dB′d B = d B', and then the ratio J/J′J / J' is 1. The sentence after the display draws the conclusion the section was working towards, that JJ depends neither on V∗V^* nor on x1,y1…znx_1, y_1 \ldots z_n, and the next display integrates on that ground.Every stepdBB=dB′B\frac{d B}{B} = \frac{d B'}{B}The equality of the probabilities, from the display before.dB=dB′d B = d B'Multiply both sides by BB, the whole integral, which is one and the same number on both sides.dBdB′=1\frac{d B}{d B'} = 1Two equal quantities in a quotient.J=J′J = J'With dB/dB′=J/J′d B / d B' = J / J' from the bookkeeping, the ratio of the factors is 1 as well. The printed form.Also

Read it in the paper