242 A SHORT HISTORY OF SCIENCE 



must so often be the case with the ordinary marine charts and so much 

 the more the higher the latitude/ 



Mercator's geometrical method amounts to projecting the 

 spherical surface of the earth on a cylinder tangent to the earth 

 along the equator and having the same axis with the earth. 

 Under this method of projection, angles are preserved in magni- 

 tude, but areas remote from the equator are disproportionately 

 expanded. A straight line on the chart corresponds with the 

 course of a ship steering a constant course. 



THE GREGORIAN CALENDAR. Until 1582 the Julian calendar 

 (p. 143) remained in force with 365 J days each year and a gradually 

 increasing error amounting at this time to ten days. Under the 

 auspices of Pope Gregory the days from October 5 to 15, 1572, 

 were dropped and the number of leap-years in 400 reduced from 

 100 to 97. Religious jealousies prevented the adoption of this 

 reform in Protestant Germany for a century, while England 

 postponed it until 1752. 



A NEW INVENTION FOR COMPUTATION. The invention of 

 logarithms would appear to have been a natural sequel of any 

 adequate theory and notation for exponents. Thus Stifel in his 

 arithmetic (1544) had tabulated small integral powers of 2 from 

 J to 64 and shown the correspondence between multiplication 

 of these powers and addition of the indices or exponents, but his 

 use of exponents was too limited, he lacked the apparatus of deci- 

 mal fractions necessary for the practical application of the method 

 and probably had no conception of the vast labor-saving possi- 

 bilities so near at hand. 



In 1614 John Napier published at Edinburgh his Mirifici Logcb- 

 rithmorum Canonis Descriptio, for which the time was so fully ripe 

 that an enthusiastic reception was at once assured. Napier as a 

 devout Protestant, stimulated by fear of an impending Spanish 

 invasion, busied himself with inventions " proffitabill & necessary 

 in theis dayes for the defence of this Hand & withstanding of 

 strangers enemies of God's truth & relegion." Among these were 

 a mirror for burning distant ships, and a sort of armored chariot. 

 Impressed by the tremendous calculations then in progress by 



