Subtracting columns in a dataframe (or matrix)

I am trying to do less in Excel and more in R, but get stuck on a simple calculation. I have a dataframe with meter readings over a number of weeks. I need to calculate the consumption in each week, i.e. subtracting a column from the previous column. For instance, in the example below I need to subtract Reading1 from Reading2 and Reading2 from Reading3. My actual data set contains hundreds of readings, so I need to find an easy way to do this.

SerialNo = c(1,2,3,4,5)
Reading1 = c(100, 102, 119, 99, 200)
Reading2 = c(102, 105, 120, 115, 207)
Reading3 = c(107, 109, 129, 118, 209)
df <- data.frame(SerialNo, Reading1, Reading2, Reading3)
df
  SerialNo Reading1 Reading2 Reading3
1      1        100      102      107
2      2        102      105      109
3      3        119      120      129
4      4         99      115      118
5      5        200      207      209