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SCIENCE PROGRESS 



where it cuts the axis of x, and write down the solutions. The 

 nomogram of this type of equation enables us to read off from 

 the diagram the roots of the equation for any suitable values 

 of a and b. Other nomograms enable us to read off solutions 

 of equations of types such as, for example, 



x^ -\- ax -\- b = o, 

 a tan x -]- b sec x + i 

 bx = a', a* = x^ 



= o, 



for various sets of values of a and b. It is evident that it is of 

 great utility, in applied mathematics, to be able to do this ; for 

 it means a very great deal of labour to solve even a simple 

 equation like a tan x -{- b sec x -\- i = o, when a and b have 

 special values, and to solve a set of equations of this type is 

 a considerable labour. It is by no means impossible that 

 diagram sheets should be made once and for ever which would 

 solve the various types of equation, and then they could be 

 printed and made available for all mathematicians who need 

 them. They would then be as much the stock-in-trade of an 

 applied mathematician as the tables of logarithms and sines 

 and cosines. 



The theory of nomography is merely certain parts of the 

 theory of ordinary co-ordinate geometry carefully manipulated. 



There is nothing essentially new in it beyond the application 

 of certain well-known results to accomplish certain graphical 

 ends. We begin, for instance, with the graphical representation 

 of a and b. Take three scales, a, b, x (Fig. i). Let a and b be 



