542 M. D. Mendelejeff on the Discovery of Gallium* 



used. But this question, although of practical importance, 

 has nothing to do with the Theory of Duplex Telegraphy. 

 This settles the solution of the first problem of the compensa- 

 tion method. 



Other methods. — There have been suggested from time to 

 time many other methods of duplex working. On a closer 

 examination it will, however, be found that, as a general rule, 

 they do not differ essentially from the three fundamental me- 

 thods treated of. I shall therefore dispense with the labour of 

 investigating these derived methods. 



In case it should be thought necessary to investigate them, 

 no difficulties ought to be met with, if only the general plan 

 of attacking duplex problems be remembered, viz. : — draw the 

 diagram of the method in its most general form ; develop the 

 forces p, P, and Q; from these three forces determine the 

 functions S and D ; find the relations which must hold between 

 the different variables (resistances and electromotive forces) 

 of which the system consists, in order to make S and D simul- 

 taneous minima ; consider the question of immmediate balance 

 which determines also the best mode of adjusting balance ; 

 consider that the movement of the key must not alter the com- 

 plex resistance of the station to which the key belongs, i. e. 

 that the working of the key must not affect the balance of the 

 distant station ; determine the absolute values of the different 

 variables when balance is rigidly fulfilled by considering the 

 question of economy, i. e. establish the relations for maxima 

 currents and maxima magnetic moments. Any variables which 

 should then be left indeterminate must be fixed by secondary 

 considerations and by certain practical conditions. 



Before comparing quantitatively the efficiency of the three 

 fundamental methods treated of, it is required to solve two 

 questions, viz. the electromotive force required for each duplex 

 method, and the absolute size of the increments of the adjust- 

 able resistance. 



[To be continued.] 



LXIII. Remarks on the Discovery of Gallium. 

 By D. Mendelejeff*. 



IN 1869 I announced the following periodic law : — " The 

 properties of the simple bodies, as also the properties and 

 constitution of their combinations, are periodic functions of 

 the atomic weights of the elements." 



Among the different applications of that law I shall cite only 

 the following : — 



1. This law constitutes the basis of a complete systematic 

 classification of the elements. 



* Translated from the Comptes Rendus by M, M. Pattison Muir. 



