1893.] Lord Kelvin on Isoperimetrical Problems. Ill 



WEEKLY EVENING MEETING, 

 Friday, May 12, 1893. 



Sir Douglas Galton, K.C.B. D.C.L. LL.D. F.R.S. 



Vice-President, in the Chair. 



The Right Hon. Lord Kelvin, D.C.L. LL.D. Pres.R.S. M.B.I. 



Isoperimetrical Problems. 



Dido, b.c. 800 or 900. 



Horatius Codes, b.c. 508. 



Pappus, Book V., a.d. 390. 



John Bernoulli, a.d. 1700. 



Euler, a.d. 1744. 



Maupertuis (Least Action), b. 1698, d. 1759. 



Lagrange (Calculus of Variations), 1759. 



Hamilton (Actional Equations of Dynamics), 1834. 



Liouville, 1840 to 1860. 



The first isoperimetrical problem known in history was practically 

 solved by Dido, a clever Phoenician princess, who left her Tyrian 

 home and emigrated to North Africa, with all her property and a 

 large retinue, because her brother Pygmalion murdered her rich 

 uncle and husband Acerbas, and plotted to defraud her of the money 

 which he left. On landing in a bay about the middle of the north 

 coast of Africa she obtained a grant from Hiarbas, the native chief 

 of the district, of as much land as she could enclose with an ox-hide. 

 She cut the ox-hide into an exceedingly long strip, and succeeded in 

 enclosing between it and the sea a very valuable territory* on which 

 she built Carthage. 



The next isoperimetrical problem on record was three or four 

 hundred years later, when Horatius Codes, after saving his country 

 by defending the bridge until it was destroyed by the .Romans behind 

 him, saved his own life and got back into Rome by swimming the 

 Tiber under the broken bridge, and was rewarded by his grateful 

 countrymen with a grant of as much land as he could plough round 

 in a day. 



In Dido's problem the greatest value of land was to be enclosed 

 by a line of given length. If the land is all of equal value the 

 general solution of the problem shows that her line of ox-hide should 



* Called Byrsa, from /3up<ra, the hide of a bull. [Smith's ' Dictionary of 

 Greek and Roman Biography and Mythology/ article " Dido. "J 



