536 Intelligence and Miscellaneous Articles. 



The present instalment is but a portion of Part I. of the whole 

 work, and the succeding portions will be eagerly awaited by those 

 interested in the distinct contribution to a fascinating subject 

 which is being made by this distinguished scientist. E. H. B. 



L. Intelligence and Miscellaneous Articles. 



DR. LINDEMANN'S CONSTRUCTION FOR RECTIFYING ANY 

 ARC OF A CIRCLE. 



To the Editors of the Philosophical Magazine. 



Gentlemen,- 6 A £ dis0 " »°«d, W. 4. 



Dec. 8th, 1918. 



l\/f AT I be allowed to point out that the construction given by 



^*J- Dr. Lindeinann in the current number of the Philosophical 



Magazine (vol. xxxvi. Dec. 1918, p. 472) follows the lines of a note 



entitled "A Geometrical Construction for ir" in the Mathematical 



Gazette for 1910 (vol. v. p. 188). 



The demonstration given with Dr. Lindemann's construction is 



analytical in character, and does not bring out the important fact 



that the lengths A-E, AH in his figure are the sums of the lengths 



of the chords joining the points which divide the arc AB into two 



and four equal parts respectively, whilst the length of AI is the 



sum of the lengths of the tangents at A and B and at the middle 



point of AB. The construction is calculated to give the length of 



the arc as the common limit of the sums of the sides of the inscribed 



and circumscribed polygons. Dr. Lindemann's last step, the tri- 



section of the interval KI, makes the approximation to the limit 



more rapid (theoretically), but sacrifices symmetry, and necessitates 



the introduction of trigonometrical analysis ; otherwise the Third 



Book of Euclid suffices for the proof. 



I am, Gentlemen, 



Tours faithfully, 



F. J. W. Whipple. 



