14 SEC. 1. ARITHMETIC. 



49. Apparatus affording Physical Illustration of the 

 action of the Law of Error or of Dispersion. 



Francis Galton, F.R.S. 



Shot are caused to run through a narrow opening among pins fixed in the 

 face of an inclined plane, like teeth in a harrow, so that each time a shot passes 

 between any two pins it is compelled to roll against another pin in the row 

 immediately below, to one side or other of which it must pass, and, as the 

 arrangement is strictly symmetrical, there is an equal chance of either event. 

 The effect of subjecting each shot to this succession of alternative courses is, 

 to disperse the stream of shot during its downward course under conditions 

 identical with those supposed by the hypothesis on which the binomial law 

 of error is founded. Consequently, when the shot have reached the bottom of 

 the tray, where long narrow compartments are arranged to receive them, the 

 general outline of the mass of shot there collected is always found to assimi- 

 late to the well-known bell-shaped curve, by which the law of error or of 

 dispersion is mathematically expressed. (This arrangement was devised, by 

 the exhibitor, to illustrate a lecture before the Royal Institution on Friday 

 evening, February 27, 1874.) When using the machine, tilt it backwards 

 and all the shot will be returned to the receptacle at the top ; then set it in 

 its proper position, and the shot will run to the opening whence they distribute 

 themselves. It is now necessary to press to and fro a button at the top of 

 the frame, which sets a small rake in action, which prevents the shot from 

 getting jammed at the mouth of the opening. 



50. Practical Approximation to the value of the circum- 

 ference in terms of the diameter, by means of a right angled 

 triangle having one acute angle =27 35' 49-636". 



Edward Bing, Riga. 



For the purpose of effecting this object, as well as for answering 

 kindred questions, use is made of a triangle, specimens of which are 

 here exhibited, and of which one angle is a right angle and another 

 is defined by an equation. 



