One might say in general that dead reckoning on the polar ice is the personal estimate of approximate distance, always checked and corrected from time to time by astronomical observations.
Three members of the expedition had had sufficient experience in traveling over arctic ice to enable them to estimate a day's journey very closely.

These three were Bartlett, Marvin, and myself.

When we checked up our dead reckoning by astronomical observations, the mean of our three estimates was found to be a satisfactory approximation to the results of the observations.
It goes without saying that mere dead reckoning, entirely unchecked by astronomical observations, would be insufficient for scientific purposes.

During the earlier stages of our journey there was no sun by which to take observations.

Later, when we had sunlight, we took what observations were necessary to check our dead reckonings--but no more, since I did not wish to waste the energies or strain the eyes of Marvin, Bartlett, or myself.
As a matter of fact observations were taken every five marches, as soon as it was possible to take them at all..