Measuring is a sort of counting, and weighing a form of measuring. We may count disparate things whether like or unlike. When we measure or weigh we apply a standard and count the times that the unit--cubit, pound, hour--is found to repeat itself. We apply our measure to uniform extension, meting out the waters by fathoms or space by the sun's diameter, and even subject time to arbitrary divisions. The human mind has been developed through contact with the multiplicity of physical objects, and we find it impossible to think clearly and scientifically about our environment without dividing, weighing, measuring, counting. In measuring time we cannot rely on our inward impressions; we even criticize these impressions and speak of time as going slowly or quickly. We are compelled in the interests of accuracy to provide an objective standard in the clock, or the revolving earth, or some other measurable thing. Similarly with weight and heat; we cannot rely on the subjective impression, but must devise apparatus to record by a measurable movement the amount of the pressure or the degree of temperature. "God ordered all things by measure, number, and weight." The scientific mind does not rest satisfied till it is able to see phenomena in their number relationships. Scientific thought is in this sense Pythagorean, that it inquires in reference to quantity and proportion. As implied in a previous chapter, number relations are not clearly grasped by primitive races. Many primitive languages have no words for numerals higher than five. That fact does not imply that these races do not know the difference between large and small numbers, but precision grows with civilization, with commercial pursuits, and other activities, such as the practice of medicine, to which the use of weights and measures is essential. Scientific accuracy is dependent on words and other means of numerical expression. From the use of fingers and toes, a rude score or tally, knots on a string, or a simple abacus, the race advances to greater refinement of numerical expression and the employment of more and more accurate apparatus. One of the greatest contributors to this advance was the celebrated Danish astronomer, Tycho Brahe (1546-1601). Before 1597 he had completed his great mural quadrant at the observatory of Uraniborg. He called it with characteristic vanity the Tichonic quadrant. It consisted of a graduated arc of solid polished brass five inches broad, two inches thick, and with a radius of about six and three quarters feet. Each degree was divided into minutes, and each minute into six parts. Each of these parts was then subdivided into ten seconds, which were indicated by dots arranged in transverse oblique lines on the width of brass. [Illustration: THE TICHONIC QUADRANT]