Memoirs of John Napier of Merchiston, 257 



long in hand, he courageously gave them that new form by which 

 they are adapted to the usage of logarithms. Upon what acci* 

 dents depends the progress of human knowledge ! The Ru- 

 dolphine Tables appeared in 1627, six years only before the 

 death of Kepler. Who can say that, without the unforeseen suc- 

 cour of logarithms, he would have had time to complete those 

 tables ; and yet they were destined to become the basis of all our 

 ulterior knowledge of the system of the world. For being es- 

 tablished, for each planet, on the conditions of elliptical motion, 

 and for the mutual ratios of the orbits in terms of the propor- 

 tionality of the squares of the periodic times to the cubes of the 

 mean distances, their invariable accordance with the actual state 

 of the heavens offers perpetually the essence, as well as the proof, 

 of those great astronomical laws justly called the laws of Kepler, 

 From these it was that Newton deduced, mechanically, his law 

 of the central force proportional to the masses, and reciprocal to 

 the square of the distance, which is purely a concentration 

 of the former. But if the general conditions of the plane- 

 tary movements had not been previously known and demon- 

 strated, Newton would not have been enabled to remount 

 to the law of gravitation. So that without the invention of 

 logarithms, which in some sense rendered the life of Kepler 

 long enough to achieve his task, perhaps universal gravitation 

 would have been yet to be discovered. That revolution, so 

 fortunate in Kepler's tables and calculations, has been described 

 and celebrated by himself in a letter to Napier, dated 28th 

 July 1619, which he placed at the commencement of his Ephe- 

 merides for the year 1620 ; but this important illustration of the 

 history of letters had become so rare that neither Montucla nor 

 Delambre were aware of its existence. Happily, however, the 

 Bodleian Library at Oxford possessed a copy, of which the 

 author of the present work obtained an accurate transcript, 

 which he has inserted in his text ; and from thai we have de- 

 rived the details given above. Napier never received this letter, 

 which would have overwhelmed him with joy. He had been 

 dead for two years, since 14th April 1617, and Kepler knew it 

 not ; so difficult and slow was the communication between 

 scientific men, in those times of wars and storms, occasioned by 

 the shock of political interests, and by the change of religion. 



