# Physics307L F09:Schedule/Week 13 agenda/Error

### From OpenWetWare

## General question

- Recall when q = f(x) and we know x_best and sigma_x
- How about when q = f(x,y, ...) and uncertainties in more than one x, y are important?
- Let's derive

## Key points after our derivation

- General formula is an approximation (small relative uncertainties)
- Usually written down to ignore covariance

## General formula, uncorrelated uncertainties (From wikipedia)

Given

### example formulas

## Specific example, Millikan oil drop

Formulae for droplet charge (from John Callow):

*V*_{f} = fall velocity

*V*_{r} = rise velocity. These (along with others) can have comparable effects on q.