T. F. Brownell

“ Even the sixteenth of a unit is more commonly used in trade than the tenth. In the stock-exchange, shares change in price by eighths of a dollar, and not by tenths. Even with our decimal system of money, we require coins for half and quarter of a dollar for practical use in trading. Almost the entire price-list of our stores advances and recedes by these fractions of a unit formed by successive bisections. ”

“ The sensation may be divided into three distinct acts. In the example supposed there is, first, the reception of the image of the star upon the retina; second, the transmission of the stimulus through the nerve from the eye to the brain; and, third, the mental perception of the existence of the star. The voluntary movement which causes the signal may also be divided into three acts. There is, first, the act of the will by which it is determined to press the button; second, the transmission of the impulse through the nerves from the brain to the hand ”

“ The octonary system, founded upon the number eight, most completely presents the qualities which are desired in a system of notation. Eight is without doubt theoretically the best number of all to be used. It is a cube, and admits of indefinite subdivisions by halving. The system appears to have all the merits of the sixteen scale, while it avoids the disadvantages of a large radix. It is much easier to use than the decimal scale. It requires only seven digits. The figures 8 and 9 do not appear, and its tables of addition and multiplication are much simpler than those now in use. ”

“ Of the personal equation, in its widest sense, there are many examples even more suggestive and worthy of extended treatment than these which have received mathematical measurement. These examples are to be found in all human action, and in the result of all human work. Noticeably is this true in all acts and occupations which have their basis and lowest forms in acts of imitation. ”

“ The French language shows the vicinary scale in parts of its notation, and the use of this scale is much more common than is usually supposed. The Greenlanders give to twenty a name which means "a man." Our word "score" is probably a vestige of this scale. Its use was at one time very common for numbers between sixty and one hundred, where a similar counting now obtains in French. There can be little doubt that our Teutonic ancestors formerly used the vicinary scale for a portion of their counting. There are other instances where the vicinary has preceded the decimal system ”

“ Upon the simplest kind of a perception, and that expected, the patient is required to exercise his volition in the simplest way. There is no necessity of making comparison between two or more sensations, or of deciding between two or more courses of action.
But in the following experiment the mental acts required were more complex. The patient, upon receiving a slight shock given to the right foot, was to give the signal by moving the right hand, and upon receiving the shock in his left foot he was to give the signal with his left hand. ”

“ A mosquito which selects our ankle as the field of his operations has nearly a sixth of a second in which to make his escape, for it requires at least one twelfth of a second for us to find out that the mosquito is there, and another twelfth of a second for us to make up our mind to declare war upon him and to initiate hostile action. ”

“ It will be observed that the rate of nervous transmission is comparatively slow. Electricity travels at the fate of many thousand miles a second, or, more accurately, 16,000,000 times as fast as nervous action. Light moves about two-thirds as fast as electricity. If we examine movements which are comparatively sluggish, we find that a cannon-ball, when fired, moves about 900 feet a second, or nearly ten times as fast as nervous energy. ”

“ The additional mental labor required to compute in this scale is not very great, while the manual labor is somewhat less than in using the decimal system. The scale has always been a favorite one with those who object to the decimal notation. ”

“ It requires a multiplication-table for all numbers from one to sixteen. The mental labor of calculating would, therefore, be increased. The number of symbols required would not be quite so large, but the advantage from this source would be slight. It may be noted, in passing, that in the Hindoo notation, the smaller the radix the greater is the number of symbols required to express any number, but the easier the mental work of calculating. ”

“ A railroad-train speeding along at sixty miles an hour would be moving at about the same rate as an ordinary nervous stimulus, though in a contest the stimulus would probably win.
By further experiment it has been determined that the time required for the excitation of the muscular fibres for such acts as the supposed pressing of the button, this being the factor last in order of the entire six, is about one-hundredth of a second. ”

“ The rudest savages manage to count to some extent. The attempts of many of them, however, do not succeed with numbers greater than three or four. With increasing knowledge, they learn to count larger numbers, but the process is a slow and troublesome one. It is performed in all cases by the use of the device of grouping. All systems of numeration that are known consist of this device. In the first stages, the groups are all of the first and lowest order. The savage, counting from one to five upon his fingers, closes his hand to express five ”

“ The sexagenary system, founded upon the number sixty, deserves a passing mention on account of its historical interest. It was used for a long time by the Greeks in astronomical and other calculations. ”

“ The Hindoo notation now in use, which superseded the Roman, differs from those which preceded it in many respects, all of which are to its advantage. It requires only nine symbols, together with the dot or zero. Its chief excellence, however, arises from its principle of "local values." Each symbol has two values: one intrinsic, and the other local. The intrinsic value is that which the symbol has when it occupies the unit place. Thus, the nine significant digits express the numbers from one to nine. ”

“ Such being the methods, an astronomer connected with another observatory selected at random from the reports of the Greenwich Observatory a large number of records, and caused the number of times each fraction of a second occurred to be counted. Theoretically, there is no reason why one fraction should appear more often than another. ”

“ The time required to observe and record the happening of a sudden and unexpected spark, for instance, is always greater than that required in the case of the expected appearance of a letter or figure thrown upon a screen. ”

“ It appears to be admitted by all who have considered the matter that ten is far from being the best number for the purpose. It would be remarkable if it were. It came into use not on account of any intrinsic excellence, but because the number of the fingers is ten. ”

“ The first record was made at the time of the observations by dots or punctures made in a tape running over a drum, the spaces between the dots representing corresponding lengths of time. The tape was prepared for use by being marked off by printed dots, about a third of an inch apart, into spaces representing seconds. The permanent record was prepared subsequently by reading off the results noted upon the tape. To read off the whole seconds was of course a simple matter of enumeration of spaces representing seconds. ”

“ At the present day astronomers, with better knowledge of the degree to which the personal element enters into all work, and especially into a class of labor so difficult as that of recording fractions of a second or hundredths of an inch, are accustomed to place as much reliance upon the observations of Mr. ”