This method consisted in the dexterous intertwining of knots on strings, so as to render them auxiliaries to the memory. The instrument was composed of one thick head or top string, to which, at certain distances, thinner ones were fastened. The top string was much thicker than these pendent strings and consisted of two doubly twisted threads, over which two single threads were wound. The branches, or pendent strings, were fastened to the top ones by a single loop; the knots were made in the pendent strings and were either single or manifold. The length of the strings was various. The transverse or top string often measures several yards, and sometimes only a foot; the branches are seldom more than 2 feet long, and in general they are much shorter. The strings were often of different colors, each having its own particular signification. The color for soldiers was red; for gold, yellow; for silver, white; for corn, green, etc. The quipu was especially employed for numerical and statistical tables; each single knot representing ten; each double knot stood for one hundred; each triple knot for one thousand, etc.; two single knots standing together made twenty; and two double knots, two hundred. In this manner the ancient Peruvians kept the accounts of their army. On one string were numbered the soldiers armed with slings; on another the spearmen; on a third, those who carried clubs, etc. In the same manner the military reports were prepared. In every town some expert men were appointed to tie the knots of the quipu and to explain them. These men were called _quipucamayocuna_ (literally, officers of the knots.) The appointed officers required great dexterity in unriddling the meaning of the knots. It, however, seldom happened that they had to read a quipu without some verbal commentary. Something was always required to be added if the quipu came from a distant province, to explain whether it related to the numbering of the population, to tributes, or to war, etc. This method of calculation is still practiced by the shepherds of Puna. On the first branch or string they usually place the number of the bulls; on the second, that of the cows, the latter being classed into those which were milked and those which were not milked; on the next string were numbered the calves according to their ages and sizes. Then came the sheep, in several subdivisions. Next followed the number of foxes killed, the quantity of salt consumed, and, finally, the cattle that had been slaughtered. Other quipus showed the produce of the herds in milk, cheese, wool, etc. Each list was distinguished by a particular color or by some peculiarity in the twisting of the string.