332 Mr. W. C. D. Whetham. Electric Conductivity of [Feb. 14, 



29 algebraically independent invariants ; while, if only a single function 

 4> occurs, all the invariants that occur up to the second order can be 

 expressed in terms of 20 algebraically independent invariants. 



The significance of these respective aggregates of 29 and of 20 

 invariants is obtained in connection with curves 



= 0, t = 0, 



drawn upon the surface. The investigation reveals new relations- 

 among the intrinsic geometric properties of a curve upon a surface. 

 In particular, up to the second order, four such relations exist for a 

 single curve ; and their explicit expressions have been constructed. 



" The Electrical Conductivity of Solutions at the Freezing-point 

 of Water." By W. C. D. Whetham, F.E.S., Fellow of Trinity 

 College, Cambridge. Eeceived February 14, — Eead March 5 r 

 1903. 



The following paper contains an account of experiments which 

 bring to greater concentrations the series of measurements on the 

 conductivities of dilute solutions at the freezing point, communicated 

 to the Royal Society in February, 1900.* The work has been carried 

 on at intervals during the last two years, and was made possible by 

 the kindness of Professor Ewing, who placed a room at the Cambridge 

 Engineering Laboratory at the disposal of the writer and his wife. 



The earlier experiments were originally planned in connection, with 

 the observations undertaken by Dr. E. H. Griffiths on the freezing 

 points of corresponding solutions ; they were therefore conducted in a 

 platinum cell of design similar to that used by Griffiths, with the 

 object of eliminating any solvent action of glass. Any such action 

 would be quite inappreciable at the concentrations used in the experi- 

 ments now to be described ; resistance cells of glass were consequently 

 used, and the labour of observation was much reduced. 



The structure of the cells is shown in figs. 1 and 2 ; that illustrated 

 in fig. 1 was made of Jena glass, and reserved for the more dilute 

 solutions. Each cell is so arranged that by applying a slight exhaus- 

 tion, the whole of the contents can be drawn up into a bulb ; by this 

 means, when water or stock solution is added, complete mixture can 

 be easily secured. The method of preparing the solutions was usually 

 the same as that formerly employed ; the pure solvent was placed in 

 the cell, and its weight and resistance determined ; weighed quantities 



* 'Phil. Trans.,' A, vol. 194 (1903), p. 321. 



