1881.] ^^'' [Chase, 



mensions and formulas which can be readily converted into standard kin- 

 etic units ; gravitating formulas can be similarly converted through the 



i. 

 m I — /in \ 2 

 correlations, ^r cc -n oc ~j-, i/grcc \~r ) ; thermal formulas, through the 



P 

 correlations, w oc [m] 7ioc [m] «^ oc [m] -^. 



74. Complex Variability. 



Any variable unit may be dependent upon some other variable unit, 

 and different values of m, I and t may thus be involved in the same ex- 

 pression. It is necessary, therefore, that the significance of every variable 

 symbol should be fully understood before undertaking to convert it into 

 terms of the corresponding standard unit. For example, in the thermal and 

 electric formulas, [;»] refers to the mass which is lifted against the constant 

 pull of gravity, while in thermal formulas v, I and t also introduce con- 

 siderations which are dependent upon the centripetal energy of Earth's 

 mass, m^, at a constant distance. The conversion of thermal into standard 

 formulas, therefore, requires due attention to the ratios both of [to] and 

 vi^, to Mq. In such cases it may often be well to introduce a second nat- 

 ural unit, which can be simply derived from the standard unit, as in the 

 deduction (Note 56) of the terrestrial thermal unit of velocity from the 



m^ _ _ 



solar unit of luminous velocity, i\ = ^ Vo := ^3 Mo ^ L^ To ^ . 



75. Notation and Approximate Values. 



Let r„ = Sun's apparent semi-diameter =* 961. "83 2.9830990 



11 =r-i-r^ = 214.45 2.3313261 



r„ = Sun's semi-diameter = 431,208 miles 5.6346866 



^3 = »?■„ = Earth's semi-axis major ==92, 472, 500 miles. .7.9660127 

 ^3 = Earth's semi-diameter = 3962.8 miles 3.5980023 



p^ — Sun's parallax = ll^ = 8. "8392 9464146 



«!„ = 2 TT (''o G^o~')^ = 1 year --- n^ ^ 10049 seconds. . .4.0021223 



i53 = 2 TT (rs 5r3~i)i == 5073^6 3.7053158 



d^, d^ = density of Sun, Earth 



^ = (^^y = .25491 T. 4063870 



/2 T \l 

 ?„ = Laplace's limit = ^( r^) " ^6.3658 r„ 1.5606934 



Vo = ?jr° = ^3 H- 497.827 = .4307721 r„=velocity of light.T. 6342476 

 1)^ —2 7ti\-^t^^ .0006252556 r„ 4 .7960576 



v^ r= (2 (73 X 180 J -- 1 Ib.)^ = .56558 miles T. 7524940 



^Nearly equal. The right hand column contains the approximate logaritlims. 



