Chase.] "^^^ [June 17, 



61. Photo -thermal Unit. 

 Since temperature varies as the square of the velocity, we have, 

 v^ : Vj^^ : : 100° : x. 



.565582 . 185,751.62 : : lOQO : 10786240000000O. 

 The corresponding projectile abscissa may be found, in terms of Sun's 

 semi-diameter, by multiplying by 1389.6 and dividing by r^, (Note 56); 

 1389.6 X 10,786,240,000,000 -- (431,206 X 5280) = 6583265 ; log. 6583265 

 = 6.8184413. This agrees, witiiin less than i- of one per cent., with the 

 pliotodynamic determination of the third centripetal abscissa in the stellar- 

 solar paraboloid, (log. A37 = 6.8190131, Note 46). 



62. Thermo-gravic Paraboloid. 



By talking \ r^, f L, and A37 as the paraboloidal elements, we substitute 

 the thermal for the photic aspect of the sethereal waves and are enabled to 

 compare gravitating actions with thermal reactions. "We thus find, 

 Log. :,;=— .001788316 

 Log. ^ = .0055973414 

 The closeness of agreement between the photic and thermal abscissas is 

 shown by the following comparisons : 



Tlie greatest difference is, therefore, less than | of one per cent. The 

 photo-thermal unit (Agg = L M, see Note 46), is intermediate between 

 the photo-gravic unit (A,,), and the stellar locus (A39). We have thus 

 five elementary loci where only three are required. By equations of con- 

 dition we ought to be able to determine all the values which are involved, 

 with much greater accuracy than will ever be possible by astronomical 

 observations. 



63. Unity of Force. 



The belief that all forms of force are modifications of one fundamental 

 energy, is as old as the oldest Greek philosophy, but no approximation 

 towards a demonstration of the belief seems to have been made until Rum- 

 ford performed his experiments at Munich, in 1798. During the present 

 century, the undulatory theory of light has commanded a general accept- 

 ance, the science of thermodynamics has been largely developed, and Tyn- 

 dall's works have made the reading world familiar with the proofs that 

 heat is a mode of motion. Stephenson taught that the energies of sunlight 

 were stored in vegetable growths and in coal-beds; Herschel called attention 

 to the enormous elasticity of luminiferous aether and to the Sun's rays as 

 "the ultimate source of almost every motion which takes place on the sur- 

 face of the earth ; " Titius, Bode, Alexander and Kirkwood, presented evi- 

 dences of law in planetary arrangement ; Peirce and Hill found similar 



