xvi.J THE METHOD OF MEANS. 369 



surface and the direct ray from the star. Hence the 

 horizontal or zero point is the mean between the apparent 

 place of any star or other very distant object and its 

 reflection in mercury. 



A plumb-line is perpendicular, or a liquid surface is 

 horizontal only in an approximate sense ; for any irregu- 

 larity of the surface of the earth, a mountain, or even a 

 house must cause some deviation by its attracting power. 

 To detect such deviation might seem very difficult, because 

 every other plumb-line or liquid surface would be equally 

 affected by 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 of 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 applied to the mountain Schiehal- 

 lion 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 probable estimate of the earth's density. 



In some cases it is actually better to determine the zero 

 point by the average of equally diverging quantities than 

 by direct observation. 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 ob- 

 struct 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 position 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 ob- 

 servations we may determine this retardation and allow 

 for it. Thus if a, 6, c be the readings of the terminal 



