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XLIV.— NOTE ON A GEAPHICAL METHOD OF SOLVING 

 CEETAIN OPTICAL PEOBLEMS. By HOWAED 

 GEUBB, F.E.S. 



[Read February 16, 1887.] 



In the calculation of curves of optical lenses it is frequently re- 

 quired to add and subtract reciprocals ; and formulae of the form 



JL i. -1 



a ~ |3 x 



are of constant recurrence. 



In the study, where a logarithm book is available, the arith- 

 metic of this is generally very simple ; but in the workshop or 

 laboratory a graphical method of solving the problem is often 

 more convenient, particularly in the hands of workmen who have 

 not had a mathematical training. 



In the working out of some optical diagrams on logarithmic 

 paper I accidently arrived at the following graphical solution, 

 which I have found very useful, and on the principle of which I 

 am constructing a calculating machine suitable for solving these 

 particular problems : — 



Draw a horizontal line = the a of above formula, and erect at one 

 extremity a vertical = j3. Join the extremities of these two lines. 

 Bisect the right angle, and produce the bisecting line till it reaches 

 the line joining the extremities of the lines a and /3. From the 



