222 PROCEEDINGS OF THE AMERICAN ACADEMY 



XI. 



APPLICATIONS OF THE GRAPHICAL METHOD. 

 Br Prof. Edward C. Pickering. 



Kead, May 12, 1ST4. 



To establish any physical law, or the relation between two quantities 

 so connected that a change in one produced a corresponding variation 

 in the other, the following method is commonly adopted. A great 

 many corresponding values of the two variables are detei'mined with 

 the greatest possible care, and corrected for all the errors to which 

 they are known to be subject. Other errors known as accidental 

 errors, however, still remain, whose minuteness depends on the excel- 

 lence of the method of measurement and the care exercised. If now 

 an equation can be found to satisfy all these values, its expression in 

 common language will be the required law. Two methods are in com- 

 mon use to determine this equation. First, analytically, the form of 

 the equation is assumed, and the values of the constants in it are found, 

 by assuming certain of the observations to be correct ; or, better, by 

 the theory of probabilities employing all the observations, and com- 

 puting from them the most probable values of these constants. The 

 principal objection to this method is that it furnishes no means of dis- 

 criminating between the accidental errors and the real variations from 

 the law. In the second or Graphical Method, the two variables are 

 taken as co-ordinates, and points are constructed corresponding to each 

 observation. A curve is then drawn, coinciding with them as nearly 

 as possible, and its equation determined by trial. The form of the 

 curve shows very clearly the accidental errors or other causes of devia- 

 tion ; and the want of accuracy of this method, when the acciden al errors 

 are only small, may be completely overcome by the method of residual 

 curves (Journal Franklin Instit., April, 1871). 



There still remains, though in a less degree than in the Analytical 

 Method, the difficulty of deciding whether a valuation is due to errors, 

 or to incorrect value of some of the constants taken. And it is to meet 

 this difficulty that the following method is proposed. 



