THE INVENTION OF LOGARITHMS 201 



was the great collection of manuscript tables of logarithms and 

 trigonometrical functions calculated by Dr. Edward Sang. 

 These were some years ago gifted by Dr. Sang's daughters to 

 the nation and were consigned to the care of the Royal Society 

 of Edinburgh. It was the existence of this remarkable and truly 

 monumental work which suggested to the Council of the Royal 

 Society of Edinburgh the idea of celebrating in some appropriate 

 way the three hundredth anniversary of the publication of the 

 first book of logarithms. 



In Edinburgh the first table of logarithms was calculated and 

 published ; and in Edinburgh there now lie thirty-seven large 

 manuscript volumes full of tabulated numbers and logarithms. 

 Can these great tables be placed at the service of mankind ? 



It is true that during the last few years calculating machines 

 have come widely into use for arithmetical operations which 

 were previously done by means of logarithms. The thought 

 has even been expressed that the logarithm has had its day. 

 The modern mechanical representatives of Napier's " bones" or 

 calculating rods are believed in some quarters to have ousted the 

 logarithm entirely. However this may be for certain of the 

 simpler kinds of calculation, there still remain many calculations 

 which are beyond the power of arithmometers and comptometers, 

 and these need for their successful working the use of logarithmic 

 tables. 



This at least is the opinion of Prof. Andoyer, the well- 

 known head of the Paris Observatory. As a member of the 

 Tercentenary Congress he read an account of his recently 

 published logarithmic cosines, tabulated to fourteen significant 

 figures. The paper, which is one of the most valuable contri- 

 butions to the Memorial Volume, discusses also this very 

 question of the need for more extensive and absolutely accurate 

 logarithmic tables. Now we have in Sang's manuscript volumes 

 all that is necessary for providing the mathematical world with 

 logarithms of all numbers from 100,000 to 370,000, calculated to 

 fifteen figures. The ordinary calculator is generally content 

 with logarithms to five places ; and for specially accurate work 

 in actuarial and geodesic problems seven-place logarithms are 

 usually sufficient. Nevertheless there are problems in which a 

 greater number of places would be a gain ; and in any case it 

 would be of advantage to the world of computers if they were 

 able at a moment's notice to turn to a table of logarithms 



