i98 ADDITIONS. 



which the bearings of the work on Science are very fully discussed. 

 The Dialogue treats not only concerning the numerical laws of har- 

 monica! sounds, of visual appearances, and of the motions of planets 

 and stars, but also concerning heat, as well as light ; and concerning 

 water, ice, gold, gems, iron, rust, and other natural objects ; concern- 

 ing odors, tastes, hearing, sight, light, colors, and the powers of sense 

 in general : concerning the parts and organs of the body, as the 

 bones, the marrow, the brain, the flesh, muscles, tendons, ligaments, 

 nerves ; the skin, the hair, the nails ; the veins and arteries ; respira- 

 tion ; generation ; and in short, every obvious point of physiology. 



But the opinions delivered in the Timceus upon these latter subjects 

 have little to do with the progress of real knowledge. The doctrines, 

 on the other hand, which depend upon geometrical and arithmetical 

 relations, are portions or preludes of the sciences which, in the fulness 

 of time, assumed a mathematical form for the expression of truth. 



Among these may be mentioned the arithmetical relations of har- 

 monica! sounds, to which I have referred in the History. These occur 

 in various parts of Plato's writings. In the Timceus, .in which the 

 numbers are most fully given, the meaning of the numbers is, at first 

 sight, least obvious. The numbers are given as representing the pro- 

 portion of the parts of the Soul (Tim. pp. 35, 36), which does not im- 

 mediately refer us to the relations of Sounds. But in a subsequent 

 part of the Dialogue (47, D), we are told that music is a privilege of 

 the hearing given on account of Harmony ; and that Harmony has 

 Cycles corresponding to the movements of the Soul (referring plainly 

 to those already asserted). And the numbers which are thus given 

 by Plato as elements of harmony, are in a great measure the same as 

 those which express the musical relations of the tones of the musical 

 scale at this day in use, as M. Henri Martin shows (Et. sur le Timee, 

 note xxiii). The intervals C to D, C to F, C to G, C to C, are express- 

 ed by the fractions f , f , |, J, and are now called a Tone, a Fourth, a 

 Fifth, an Octave. They were expressed by the same fractions among 

 the Greeks, and were called Tone, Diatessaron, Diapente, Diapason. 

 The Major and Minor Third, and the Major and Minor Sixth, were 

 however wanting, it is conceived, in the musical scale of Plato. 



The Timceus contains also a kind of theory of vision by reflexion 

 from a plane, and in a concave mirror ; although the theory is in this 

 case less mathematical and less precise than that of Euclid, referred to 

 in chap. ii. of this Book. 



One of the most remarkable speculations in the Timceus is that in 



