THE METHOD OF MEANS. 429 



affected by the very principles of gravity. Nevertheless 

 it can be detected ; for if we place one plumb-line to the 

 north of a mountain, and another to the south, they will 

 be about equally deflected in opposite directions, and if 

 by observations on the same star we can measure the angle 

 between the plumb-lines, half the inclination will be the 

 deviation of either, after allowance has been made for the 

 inclination due to the difference of latitude of the two 

 places of observation. By this mode of observation ap- 

 plied to the mountain Schehallien the deviation of the 

 plumb-line was accurately measured by Maskelyne, and 

 thus a comparison instituted between the attractive forces 

 of the mountain and the whole globe, which led to a very 

 probable estimate of the earth's average density. 



In some cases it is actually better to determine the zero 

 point by the average of equally diverging quantities than 

 by direct observations. Thus in delicate weighings by a 

 chemical balance it is requisite to ascertain exactly the 

 point at which the beam comes to rest, and when standard 

 weights are being compared the position of the beam is 

 ascertained by a carefully divided scale viewed through a 

 microscope. But when the beam is just coming to rest, 

 friction, small impediments or other accidental causes 

 may readily obstruct it, because it is near the point at 

 which the force of stability becomes infinitely small. 

 Hence it is found better to let the beam vibrate and 

 observe the terminal points of the vibrations. The mean 

 between two extreme points will nearly indicate the posi- 

 tion of rest. Friction and the resistance of air tend to 

 reduce the vibrations, so that this mean will be erroneous 

 by half the amount of this effect during a half vibration. 

 But by taking several observations we may determine 

 this retardation and allow for it. Thus if a, b, c be the 

 terminal points of three excursions of the beam from the 

 zero of the scale, then ^ (a + b) will be about as much 



