_The Methods of Observation of Quantity in general are_, Numeration, _which is precise by the nature of Number; the_ Measurement of Space _and_ of Time, _which are easily made precise; the_ Conversion of Space and Time, _by which each aids the measurement of the other; the_ Method of Repetition; _the_ Method of Coincidences _or_ Interferences. _The measurement of Weight is made precise by the_ Method of Double-weighing. _Secondary Qualities are measured by means of_ Scales of Degrees; _but in order to apply these Scales, the student requires the_ Education of the Senses. _The Education of the Senses is forwarded by the practical study of_ Descriptive Natural History, Chemical Manipulation, _and_ Astronomical Observation. 1. I SHALL speak, in this chapter, of Methods of exact and systematic observation, by which such facts are collected as form the materials of precise scientific propositions. These Methods are very various, according to the nature of the subject inquired into, and other circumstances: but a great portion of them agree in being processes of measurement. These I shall peculiarly consider: and in the first place those referring to Number, Space, and Time, which are at the same time objects and instruments of measurement. 2. But though we have to explain how observations may be made as perfect as possible, we must not forget that in most cases complete perfection is unattainable. _Observations are never perfect._ For we {146} observe phenomena by our senses, and measure their relations in time and space; but our senses and our measures are all, from various causes, inaccurate. If we have to observe the exact place of the moon among the stars, how much of instrumental apparatus is necessary! This apparatus has been improved by many successive generations of astronomers, yet it is still far from being perfect. And the senses of man, as well as his implements, are limited in their exactness. Two different observers do not obtain precisely the same measures of the time and place of a phenomenon; as, for instance, of the moment at which the moon occults a star, and the point of her _limb_ at which the occultation takes place. Here, then, is a source of inaccuracy and errour, even in astronomy, where the means of exact observation are incomparably more complete than they are in any other department of human research. In other cases, the task of obtaining accurate measures is far more difficult. If we have to observe the tides of the ocean when rippled with waves, we can see the average level of the water first rise and then fall; but how hard is it to select the exact moment when it is at its greatest height, or the exact highest point which it reaches! It is very easy, in such a case, to err by many minutes in time, and by several inches in space. Still, in many cases, good Methods can remove very much of this inaccuracy, and to these we now proceed.