﻿534 Prof. Cayley on the Geodesic Lines on an Ellipsoid. 



Table T.— Ethylic Ethers. 







Specific 

 gravity. 



Calculated 



Observed 





Name. 



Formula. 



boiling- 

 point. 



boiling- 

 point. 



Observer. 



Ethyl formiate . . . 



C 3 H 6 O 2 



37 



40 







53 



f Pierre and 

 1 Delffs 



„ acetate 



C 4 h 8 O 2 44 



68 



74 



Kopp. 



„ propionate . 



C 5 H 10 O 2 



41 



95 



96 



Kopp. 



„ butyrate . . . 



C 6 H 12 2 



58 



118 



119 



Pierre. 



,, valerate ... 



C 7 H i4 2 



65 



142 



134 



Berthelot. 



,, caproate ... 



C 8 H 16 2 



72 



164 



162 



Fehling. 



„ pelargonate. 



C 11 H 22 Q2 



93 



224 



224 



Delffs. 





Table V.— 



Other Ethers. 





Propyl acetate ... 



C 5 H 10 O 2 



51 



■ 95 



90 



Berthelot. 



Propyl butyrate... 



C 7 H 14 2 



65 



142 



130 



Berthelot. 



Butyl formiate ... 



C 5 H 10 O 2 



51 



95 



100 



Wurtz. 



Butyl acetate 



C 6 H 12 Q2 



58 



119 



114 



Wurtz. 



Octvl acetate 



C 10 H 20 Q2 



86 



204 



193 



Bouis. 



Ethyl laurate 



C 14 H 28 2 



114 



277 



269 



Delffs. 



Table W.— Compound Ethers. 



Amyl formiate ... 



C 6 H 12 O 2 



60 



126 



116 



Kopp. 



„ acetate 



C 7 H 14 2 



67 



149 



137 



Kopp. 



,, propionate 



C 8 H 16 2 



74 



170 



about 155 



"Wrightson. 



„ valerate ... 



C 10 H 20 Q2 



88 



210 



189 



Kopp. 



,, caproate ... 



C u H 22 2 



95 



229 



211 



Brazier. 



LXVII. Note on the Geodesic Lines on an Ellipsoid. 

 By Professor Cayley, F.R.S.* 



THE general configuration of the geodesic lines on an ellip- 

 soid is established by means of the known theorem) an 

 immediate consequence of Jacobi's fundamental formulae, but 

 which was first given by Mr. Michael Roberts, Comptes Rendus, 

 vol. xxi. p. 1470, Dec. 1845) that every geodesic line touches 

 a curve of curvature ; that is, attending to the two opposite ovals 

 which constitute the curve of curvature, the geodesic line is in 

 general an infinite curve undulating between these opposite ovals, 

 and so touching each of them an infinite number of times (but 

 possibly in particular cases it is a reentrant curve touching each 

 oval a finite number of times) . The geodesic lines thus divide 

 themselves into two kinds, accordingly as they touch a curve of 

 curvature of the one or the other kind ; and there is besides a 



* Communicated by the Author. 



