590 



REPORT 1893. 



Join O D, and draw a perpendicular to it through D, cutting A pro- 

 duced in E. 

 Then 0D=3/0E. 



In this way points on a curve can be found. Having obtained the curve, 

 any cube root (say of I) can be found by setting off a length 



OE=l. 



Upon O E describe a semicircle intersecting the curve in D. 



Then OD=^I 



Culmann treats the subject of roots, and shows how to obtain the 

 value of 



that is of 



3_ -"/b c 

 I \/ a a 



Cremona treats fully the use of the logarithmic curve in the extraction 

 of roots, and shows how to find by its use 



i/piXpoXpsX . . . p,. 



Probably the most important of all graphical constructions in relation 

 to mechanical science is that which gives the sum of a series of products. 

 Suppose the values required to be 



5(0A.K)=0A, .K,+OA,.K2 + OA3.K3+ . . . 



Fig. 12. 



^, 



^il- 



•^ 



^M- 



P> 



'O^ 



\0' 



