98 M. A. F. Sundell on Absolute 



attraction— which is equal to the square of the so-called Gauss's 

 constant. The value of this constant is given by Gauss* as 



« ^. »^ semi- major axis of earth's orbit 2 



0-0172 =*- : ; ' 



mean day x sun s mass" 



Hence we have the attraction-constant 



, n M «^9 semi- major axis of earth's orbit 



= (0'0172) 2 r-^> ; 



v y day z x sun s mass 



_ (0-0172) 2 x (19,900,000) 3 geogr. mile 3 



~~ (86,400) 2 x 320,000 sec. 2 x earth's mass 



_ (0-0172) 2 x (19,900,000) 3 x ( 7420) 3 metre 3 



~(86,400) 2 x 320,000 x £ x 3-14 x (6,370,000) 3 x 6000 sec. 2 x kilof 



615 metre 3 



"~ 10 13 sec. 2 x kilogr. 



if we take the mean mass of 1 cubic metre of the earth as equal 



to 6000 kilogr. The force with which a mass of 1 kilogr. 



attracts an equal mass at a distance of 1 metre is then 



615 metre x kilogr. T „ 



=7vn s — — . It we transform the value of the con- 



10 ld sec. 



stant of attraction into the gravitation system, we obtain 



615 metre 3 615 metre 3 



10 13 sec. 2 x kilogr. 10 13 2 1 s ec. 2 x kilog r. (Paris) 



SeC * X 9-808 ~ metre - 



_ 615 x 9-808 / 604 \ metre 4 



"~ 10 13 ( 10 12 /sec.*x kilogr. (Paris)'' 



7. Of systems with four fundamental units, that with fun- 

 damental units of length, time, mass, and force is not without 

 interest. In order to obtain such a system we must retain 

 two constants in the fundamental equations (2), (3), (6), 

 * Theoria Motus Corporum Ccelestium, p. 2. 



f Wiillner (Lehrbuch der Experimental-Physik, vol. i. 1870, p. 145) 

 puts the mass of a cubic metre of the earth =U, and heuce tinds for the 



6128 

 attraction-constant the value -jqti , which value, if the unit of mass 



( = 9-808 kilogr.) employed in the same work (vol. i. p. 59) is to be 

 retained, is ■ times too great, and must be altered to 



9-808 6128 601 



1000 10 u W 2 



(very nearly the same as given above). The unit of mass, 



lS ec.'xkilogr.(Paris ) = 9 , 808 



metre 



therefore attracts an equal mass at a distance of 1 metre with the force 

 601 , ., 





