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| 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 

 | 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 Loga- 

 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 



