We have, therefore,
F = 1·4 + 0·253 R.
This is practically the same formula as
F = 1·44 + 0·252 R,
from which the table has been constructed. In fact, the column of calculated values of the friction might have been computed from the former, without appreciably differing from what is found in the table.
[THE METHOD OF LEAST SQUARES.]
[Table III].
Let k be the coefficient of friction. It is impossible to find any value for k which will satisfy the equation,
F - k R = 0,
for all the observed pairs of values of F and R. We have then to find the value for k which, upon the whole, best represents the experiments. F - k R is to be as near zero as possible for each pair of values of F and R.