We can hardly doubt that mankind first obtained empirically the art of weighing, and that it was only at a later period that mathematics were called in to fix scientifically the standards obtained by the older and cruder method. Such is the function of mathematics still. Thus Professor Cayley observed (in his address at Stockport), “I said I would speak to you not of the utility of mathematics in any of the questions of common life or of physical science, but rather of the obligations of mathematics to these different subjects. The consideration which thus presents itself is in a great measure that of the history of the development of the different branches of mathematical science in connection with the older physical sciences, Astronomy and Mechanics. The mathematical theory is in the first instance suggested by some question of common life or of physical science, is pursued and studied quite independently thereof, and perhaps after a long interval comes in contact with it or with quite a different question[291].” If such then is the part played by mathematics in an age when even the mathematician has come to the aid of the hangman, and the wretch meets a well-deserved doom in strict accordance with a mathematical formula, _a fortiori_ must empirical discovery have preceded mathematical theory in the second millennium before the Christian era. Just as countless malefactors were successfully executed by empirical Jack Ketches before ever the mathematician turned executioner, so we may be certain that untold sums of gold had been weighed by means of natural seeds and according to a standard empirically obtained before ever the sages of Thebes or Chaldaea had dreamed of applying to metrology the results of their first gropings in Geometry or Astronomy. PART II. CHAPTER X. THE SYSTEMS OF EGYPT, BABYLON, AND PALESTINE. We are now in a position to approach the last stage in our task, that which deals with the growth and development of various weight-standards, all of which start from a common unit. Of necessity Egypt, Babylon, Greece and Italy will claim a chief share of our attention. The question now is, Shall we deal with these regions according to the priority of their civilization, that is, in the order in which I have just named them, or shall we rather adhere to the principle which has hitherto guided us, of working back from that which is better known to that which is less known?