576 



SCIENCE 



[N. S. Vol. XLni. No. 1113 



The second chapter deals with damping 

 and how it is obtained in meters. Permanent 

 magnet instruments, iron core instruments, 

 electrostatic meters, hot-wire meters and 

 dynamometer meters each receive one chapter. 



Watt-hour meters are discussed at some 

 length; the errors in reading due to friction, 

 short circuits, etc., are illustrated by erperi- 

 mental results. Magnetic testing apparatus is 

 described and typical results given. The last 

 chapter deals with the Wheatstone bridge, the 

 Kelvin double bridge, and the potentiometer, 

 for both continuous and alternating current 

 circuits. 



The writer knows of no book on electrical 

 measuring instruments which is its equal in 

 value to the advanced engineering student. A 

 companion volmne dealing with oscillographs, 

 ondographs and other special devices is prom- 

 ised by the authors for the near future; it 

 should receive a hearty welcome. 



J. H. M. 



axis, at the rate of B units per centimeter, B 

 being so taken that the values of F{_x) likely 

 to be met will fall within the limits of the 

 chart. 



SPECIAL ARTICLES 



A NEW METHOD FOR THE GRAPHICAL SOLU- 

 TION OF ALGEBRAIC EQUATIONS 



The writer recently devised a graphical 

 method for the solution of algebraic equations 

 that seems to be of such general interest and 

 importance as to be worthy of publication in 

 this journal. 



Let us consider first an equation of the type 

 /(«) -/W +/(«) -Fix) +/(2,)=0, 



where /(«), /(■«), /(a;) and /(j/) are the same 

 or different functions of u, v, x and y. Con- 

 struct a chart (shown in outline in Fig. 1) 

 consisting of three vertical axes, P, Q and B, 

 any convenient distance apart, intersected by 

 a horizontal axis H. Along the right side of 

 the axis P plot the calculated values of /(a;), 

 positive values being laid off upward and 

 negative values downward from the horizontal 

 axis at a rate of A units per centimeter, A 

 being so taken that the values of f(x) likely 

 to be met will fall within the limits of chart. 



In a similar way lay off values of F(x) 

 along the left side of the axis iJ, positive 

 values being measured off upward and nega- 

 tive values downward from the horizontal 



Fig. 1. 



Along the horizontal axis lay off values of 

 f{y) at the rate of C units per centimeter, 

 positive values of f{y) being laid off to the leji 

 of the middle axis Q, and negative values of 

 f{,y) to the rigM of that axis; C, being so 

 taken that the values of f{y) likely to be met 

 will not lie too far to the right or to the left 

 of the middle axis Q. Label the points thus 

 located with the values of y used in calcu- 

 lating those of i{y). 



Values of /(v) are to be laid off along the 

 axis P in a way similar to that employed in 

 laying off values of j{x), positive values being 

 measured downward and negative values up- 

 ward from the horizontal axis 3, at the rate 

 of C/mB units per centimeter, where m is the 

 perpendicular distance in centimeters between 

 the outside axes P and B. Label the points 

 thus located with the values of v to which they 

 correspond. 



In the same way, calculated values of f(u) 

 are to be laid off along the axis B, positive 

 values being measured upward, and negative 

 values downward, at the rate of 0/mA imits 



