1878.] 



using the Balance with great delicacy, fyc. 



15 



The factor by which we must multiply the observed difference to 

 reduce it to the attraction of the mass on the weight in its in position 

 is therefore — 



,_ 1 CD 2 BF CD 3 _CD 2 BF 

 J ~~ BD 3 CE 3 BE 3 



= 1-0185 

 since CD= 22*13 centimetres. 



BD = 192-03 



BF=18770 



CE = 172-36 



BE=257*09 



The values of r and n being observed, the distance between the centres 

 of the mass and weight d is then measured by adding 17*362 centims. 

 to the sum of their radii, the distance from the top of the mass to the 

 bottom of the weight as measured by a cathetometer. 



It now remains to explain the calculation of the mean density A 

 from the observed values of r, n, and d. We have — 



fx increase in weight observed Attraction of mass on weight when "in" 



Weight of weight Attraction of earth on weight 



But the increase in weight is ^^^llf. mgms., since the distance be- 



r x 202716 



tween the notches is 6*654 millims., and the half beam 202*716 millims 

 The weight of the weight is 453*92 grammes. 

 The attraction of the mass in centimetres 



_ Volume X density 



(distance between centres of mass and weight r) 2 ' 

 _ Weight in grammes 

 d z ' 



_ 154220*6 

 &* 



The attraction of the earth is 



A X irR 1 1 +M- 1 (M- e) J COS 2 \, 



where A = mean density of the earth, 



R= earth's polar radius in centimetres, 

 centrifugal force at the equator 

 Equatorial gravity 

 e=ellipticity. 

 \= latitude. 



The logarithm of the coefficient of A when R is in inches is 9*0209985 

 ("Astronomical Soc. Mem.," xiv, p. 118), or if R is in centimetres it 

 is 9*4258322. 



