Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. To the question about the use of mathematics we may reply by pointing out two obvious consequences of one of the applica tions of mathematics: mathematics prevents much loss of life at sea, and increases the commercial prosperity of nations. Only a few men — a few intelligent philosophers and more amateur philosophers who are not highly intelligent — would doubt if these two things were indeed benefits. Still, probably, all of us act as if we thought that they were. Now, I do not mean that mathematicians go about with life-belts or serve behind counters they do not usually do so. What I mean I will now try to explain.