Taylor.] dio [Oct. 21, 



■which every zero multiplies all the value that precedes it, by the amount 

 of the radix, it results that the addition of a cipher to the figure 1, would 

 of course multiply it by two (instead of by ten as in our common sys- 

 tem) — the addition of two ciphers, by two times two, or four (instead of 

 by a hundred) — the addition of 3 ciphers, by eight ; of 4 ciphers, by six- 

 teen ; of 5 ciphers, by thirty-two, etc. The first fifteen numbers would 

 read thus : 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 

 1110, 1111.* The present year, 1887, would require eleven places of fig- 

 ures to express it; namely, 11101011111. Fifty places of figures (or 1 

 and 49 ciphers) in the binary system, would require but fifteen places of 

 figures in the decimal system. One hundred places of the binary (1 and 

 99 ciphers) would require thirty places of the decimal. So that the for- 

 mer system would involve, on an average, the constant employment of 

 about three and a third times more figures in all our arithmetical opera- 

 tions, than the latter system, or that in common use. This increased 

 expenditure of time and manual labor would evidently be a very serious 

 inconvenience. On the other hand it must be considered that the writing 

 down of any given mass of figures, in only two characters (always either 

 1, or a cipher), would be much more easy and expeditious than if the 

 mass consisted of ten different characters ; so that the actual increase of 

 trouble should be set down at probably not more than double that we 

 have at present. This much quantitatively. But in the quality of the 

 work done, the difference will be found immensely in favor of the binary 

 scheme. In the first place no tables would be required to be committed 

 to, and retained by, the memory ; either of addition, of subtraction, of 

 division or of multiplication ; not even the fundamental " twice two make 

 four." Every form of calculation would be resolved into simple numera- 

 tion and notation. In fact, calculation as an effort of mathematical 

 thought, might be said to be entirely dispensed with, and the labor of 

 the brain to be all transferred to the eye and the hand. A perfect 

 familiarity with the notation of the scale, and with the simple rules of 

 position, would enable the operator to determine in every case by mere 

 inspection whether the next figure should be a 1, or an 0. It follows 

 that the only errors possible in such a work would be the merely clerical 

 ones of the eye or hand ; and when we reflect that a large majority of the 

 arithmetical errors committed are usually those of the brain, fatigued or 

 bewildered by the constant strain upon the attention and memory, this 

 consideration of the increased accuracy of such a system is one of the 

 very first importance in estimating its value. To manj', the relief it 

 proffers in exchanging head-work for hand-work will appear no trifling 

 recommendation ; and it may well be doubled, whether in all important 

 and l&ngthy calculations, the binary system would not be found to afford 

 a real economy of labor, instead of an increase as has been generally 

 supposed. 

 It has been previously noticed, that the great Leibnitz, the rival of 

 * See note B, page 359. 



