Why do we get different f-statistics for the ANOVA of two models in R if we add third model

Question

For example, using the mtcars built-in dataset.

A two-model ANOVA:

anova(
  lm(mpg ~ 1, data = mtcars),
  lm(mpg ~ drat, data = mtcars)
)

Model 1: mpg ~ 1
Model 2: mpg ~ drat
  Res.Df     RSS Df Sum of Sq     F    Pr(>F)    
1     31 1126.05                                 
2     30  603.57  1    522.48 25.97 1.776e-05 ***

A three-model ANOVA:

anova(
  lm(mpg ~ 1, data = mtcars),
  lm(mpg ~ drat, data = mtcars),
  lm(mpg ~ drat + wt, data = mtcars)
)

Model 1: mpg ~ 1
Model 2: mpg ~ drat
Model 3: mpg ~ drat + wt
  Res.Df     RSS Df Sum of Sq      F    Pr(>F)    
1     31 1126.05                                  
2     30  603.57  1    522.48 56.276 2.871e-08 ***
3     29  269.24  1    334.33 36.010 1.589e-06 ***

Now, looking at row 2 of each table, you will notice that sum of squares and degrees of freedom are the same as each other, but the $f$ statistic is 25.97 in the first test and 56.276 in the second. Why is this? How is $f$ calculated in both cases?

My understanding of the $f$ statistic is that it's the ratio of two chi-squared RVs, ie $f = \frac{ESS(\gamma_j \mid \gamma_{j-1})/r}{RSS_j/(n-p)}$ (where $r$ is the difference in number of parameters between the two models). However all of these components are the same between the two tests, so I don't understand why $f$ would differ.