522 SCIENCE PROGRESS 



important in practical nomography when / and m are simple 

 numbers, such as 2 or 5 or ^. 



Suppose now we introduce another scale, y, and so graduate 

 :*; and y that the two nomograms 



2x = a -\- b ) 33/ = a + 26 



are represented. 



To solve the equations 



a + b = 7, a -{- 2b = 12 



we have only to take x — 7/2 and y = 12/3, and read off the 

 values of a and b registered by the line joining these two points. 

 Immediate generalisations follow which enable us to solve, 

 e.g., the equations 



2,a -{- 2b = X, a + 6b = y 



(in which the graduations used are xfs and yjy), when x and y 

 are the unknowns and a and b have all suitable values. Finally, 

 we can make an elaborate chart to solve the equations la -\- mb 

 = X, l^a -f m^b — y (/, /^, m, m\ being whole numbers), obtaining 

 it merely by drawing in the various x and y scales required for 

 the various values of /, w, /^ m^ 



This discussion of the question of solving simultaneous 

 equations should give a general impression of the methods used 

 in nomography. The algebraic significance of the coUinearity 

 of points on variously placed scales is the essence of the matter, 

 and nomograms as a whole may be defined as being the various 

 classes of relations which result when variously placed scales 

 are variously graduated. 



Scales used are not always in the form of straight lines. 

 The nomogram for x^ -\- ax -\- b — o consists of two parallel 

 straight line scales, and a symmetrically placed parabola with 

 its vertex between the two. Another nomogram for the same 

 type of equation consists of two similarly graduated scales and 

 one branch of a hyperbola. 



The general theory of nomograms with two parallel scales 

 is worked out in Dr. Brodetsky's book. For the more general 

 theory, reference should be made to the classic of the subject. 



APPLIED MATHEMATICS. By S. Brodetsky, M.A., Ph.D., 

 F.Inst.P., A.F.R.Ae.S., University, Leeds. 



Profound modifications of our view of space, time, and force 

 are called for by Einstein's Theory of Relativity, and, whether 

 we accept the theory in its complete form or not, we must in 

 any case review carefully the basis on which our physical 

 science is built. It should, therefore, be of interest to the 

 applied mathematician to realise in what way the theory affects 



