24 ANNUAL llECORD OF SCIENCE AND INDUSTRY. 



governuients in this geodesic congress, especially in view of 

 the fact that the geodesy of England needs to be united with 

 that of Europe across the Channel. 6 A, Jul^, 1873, 176. 



LOGAEITHMIC TABLES. 



Mr. Glaisher has contributed a number of interesting: arti- 

 cles on the history of the published tables of the logarithms, 

 from which we make a few extracts. 



The system of logarithms now most commonly used was 

 invented by Briggs, and differs somewhat from those pro- 

 posed by Napier, the original inventor of this ingenious de- 

 vice. Briggs published a small table of logarithms in 1617, 

 and a larger one in 1624, in which latter are given, to ten 

 places of tlecimals, the logarithms of all numbers from one 

 to ten thousand, and from seventy thousand to one hundred 

 thousand. In 1628,Vlacq published in Holland a similar 

 ten-place logarithmic table of all numbers from one to one 

 liundred thousand, in which the portion from ten thousand 

 to seventy thousand is given as computed by himself, the 

 remaining portion being taken from Briggs' table. These 

 great works of Briggs and Ylacq have now for two hundred 

 and fifty years been of daily use among mathematicians, as- 

 tronomers, navigators, surveyors, and all others who have oc- 

 casion-to use logarithmic tables; for it appears from Mr. 

 Glaisher's very careful bibliography that of all the innumera- 

 ble smaller logarithmic tables that have been published, not 

 a single one has been computed anew, all being merely ab- 

 breviations of the great works of Briggs and Vlacq. 



One of the most curious facts brouo'ht out in the course of 

 Mr. Glaisher's studies is the slow successive approach to ab- 

 solute accuracy. Taking the seven-figure logarithmic tables, 

 for instance, we find that in Vlacq one hundred and twenty- 

 three errors occur, affecting the first seven out of the ten 

 places of decimals given by him. Taylor's seven-figure ta- 

 bles, published in 1792, contain six errors; in 1794, the first 

 edition of Vega had twenty-three errors; the second edition, 

 in 1797, had five errors; the tables of Babbage, in 1827, one; 

 Hasler, in 1830, two ; Callet, in 1855, two ; Bremiker, in 1857, 

 none ; Schoon, in 1860, none ; Callet, in 1862, none.. 



Mr. Glaisher, with much force, urges the propriety of the 

 publication by some permanent society, or some other high 



