CHAKLES B ABB AGE. 167 



be used with the ]N"autical Ephemeris for finding latitude and longitude 

 at sea," computed, revised, and rerevised with the utmost care, under 

 direction of the British board of longitude, and pubUshed by the govern- 

 ment, was found to contain above a thousand errors. The tables of the 

 distances of the moon from certain fixed stars, published by the same board, 

 is followed by 1,100 erra to, and these themselves contained so many errors 

 as to mate errata upon errata necessary. For the special use of the 

 national survey of Ireland, the logarithmic tables, most carefully prepared, 

 were found to contaui six errors, and these, by comparison, were found to 

 exist not only in tables published during more than two hundred years in 

 Paris and Gouda, Avignon and Berlin, Florence and London, but also in a 

 set printed in China, in Chinese characters, and purporting to be original 

 calculations. In fact, absolute correctness in logarithmic tables has 

 never been attained. Year after year, through eight generations of 

 mathematicians, one set has followed another to correct its predecessor. 

 Even the last claims but approximate accuracy. Precautions, compari- 

 sons, revisions, and alterations from computers to computers, make ad- 

 vances only totcard an end that is never absolutely reached. And no 

 wondSr. We need but to consider the nature of a numerical table, where 

 a thousand pages are covered with figures alone, where neither note nor 

 comment, letters of the alphabet, nor rules of syntax, are permitted to 

 intrude, to understand that the law of chance is on the side of error, and 

 that for one mistake that may happen to be detected a score may escape 

 unnoticed. 



Besides the errors incidental to computation, there are those of trans- 

 scribing for the press, and of composition into print. Kor does the liability 

 to error stop even here, errors being often produced in the process of 

 printing. A remarkable instance of this occurs in one of the six errors 

 of the Irish Survey Tables, just mentioned. The last five figures of two 

 successive numbers of a logarithmic table were 



35875 

 10436 



Both were erroneous. The "8" in the upper line should be "4," and the- 

 "4" in the lower line should be "8." It is evident that the types, as- 

 first composed, were correct — that two of them, "4" and " 8," became 

 loose, adhered to the inking ball, and were drawn out— and that the 

 pressman in replacing transposed them. And this inadvertent error in. 

 Blacq's tables of 1628, traveled over three continents, and, with more- 

 or less of mischief, remained undetected for two hundred years. 



I^umerical correctness in logarithmic tables, is then, and has ever been,, 

 the great desideratum. This Mr. Babbage proposed to attain by ma- 

 chinery; to calculate the tables unerringly, as if by a law of nature, 

 and by the same law to reduce them as unerringly to type. Thus was. 

 the single purpose of the difference engine No. 1. 



The difference engine i^o. 1 was only partially competed. Confided' 

 to the care of King's College, it remained for twenty years in the mu- 



