146 THE WORLD MACHINE 



that the present-day hierophant, lacking somewhat the sense 

 of historical perspective, draws a little the frowning brow as 

 he contemplates the rather lighter-hearted science of that 

 lighter-hearted time. 



Is it possible to effect a just adjudication ? Let us consider 

 with Kant that the extent of knowledge in any given field is 

 measured by the amount of mathematics which it'contains, and 

 make the attempt. We might think of the matter in this 

 light : 



. The century that saw the end of the Roman Republic and 

 the beginning of the Empire may be accounted the apogee of 

 Roman culture. The glory of Alexandria was on the wane. 

 There were richer prizes in the new world-capital. It was the 

 time of Caesar and of Augustus, of Cicero and of Pompey, of 

 Lucretius and of Virgil. It was an age of freedom and en- 

 lightenment. The study of Greek philosophy and ideas was 

 widespread. Greek physical investigation had practically 

 reached its term ; its fruits had been gathered. They were 

 then among the common possessions of mankind, and doubt- 

 less taught to children as are the teachings of Newton and 

 Darwin now. In what regard, let us ask, would a highly en- 

 lightened Alexandrian, or his compeer at Rome, heritor of 

 the Greek tradition and fully abreast of the knowledge of his 

 time, differ, in his larger world ideas, from a man of the same 

 temper and standing now ? 



It is evident enough from the pages of Lucretius, of Cicero, 

 of Pliny, of Strabo, and of Cleomedes, that in many ways the 

 difference was slight. The youth of that time were taught the 

 geometry of Euclid. It is taught to the youth of our time with 

 little addition and little change. The trigonometry of the 

 Greeks was but slightly developed, their algebra scarce at all. 

 Their system of notation was not decimal. It follows that 

 they had no logarithms. The calculus was quite unknown. 

 Their processes of computation were clumsy. There are some 

 problems which the modern mind has solved by means of the 

 higher mathematics. But in a large view it is doubtful if there 

 was any fact of deep import which was beyond the powers of 

 Greek methods of analysis. 



In their application of mathematics to the mensuration of 

 space, time, and mass, alike their methods and their instru- 

 ments were crude ; yet the accuracy attained in the construe- 



