NEWTON’S INTERPOLATING POLYNOMIAL
Calculation of deltas (examples):
To get the denominators for the deltas, move along the diagonal downwards to get the t value alongside the corresponding c value and subtract the t value found by moving along the diagonal upwards alongside the corresponding c value. The downward diagonal for ∆5 (row 6), for instance, takes you to c=10.355, corresponding to t=30; the upward diagonal takes you to c=5.02375, corresponding to t=5; so the divisor (denominator) is 30-5=25.
When t=32.5, c(t) from the polynomial=-5.7528125mg/m³. Because this is negative it is not meaningful. It seems to indicate that Newton’s polynomial is not helpful in this case.
The above graph shows a probably more realistic value of 7.2mg/m³ at t=32.5min by simple interpolation.