546 Mr. W. H. Walenn on Unitation. 



laved. It should be searched for more especially as associated 

 with arsenic and with titanium. 



Note by the Translator. 

 Since the publication of M. McndelejefF's paper the disco- 

 verer of gallium has made known the results of further re- 

 searches upon the properties of this metal and of its compound. 

 He finds that the salts of gallium have most probably the 

 general formula Ga X 3 , that the oxide is best represented by 

 the formula Ga 2 3 , that ammonia precipitates solutions of the 

 chloride and sulphate of gallium probably with formation of a 

 hydrate, that this precipitate is soluble in acid and in alkali, 

 that gallic ammonio-alum is a crystalline salt almost certainly 

 isomorphous with ordinary alum. M. Lecoq de Boisbaudran 

 also finds that metallic gallium may be readily obtained by the 

 electrolysis of an ammoniacal solution of the sulphate, that 

 the metal is not oxidized in air at 200°, and that it readily 

 decomposes acidulated water, especially at high temperature 

 In these respects gallium appears to correspond with the hy- 

 pothetical eka aluminium of M. MendelejefF. Determinations 

 of the atomic weight and of the specific heat of the new metal 

 will be awaited with great interest. 



LXIV. On Unitation. — VI. Some of the Applications and De- 

 velopments of the General Formula (continued). By W. H. 

 Walenn, Mem. Phys. Soc. 



[Continued from S. 4. vol. 1. p. 527.] 



18. npHE decimal equivalents of all reciprocals of the form 



in _.. have the terminal figure of their period equal 



to 1. This is manifest from the fact that 1 must be the re- 

 mainder when the period recommences ; for the condition of 

 recurrence is that the dividend is the same as that which, in 

 the operation of division, commences the work, and this is uni- 

 formly, in the case of reciprocals, 10 or some power of 10. In 



the case of reciprocals of the form ^ r-, the product of the 



figure in the quotient which is the terminal figure of the period 

 must have its function U 10 / (/ being the product) equal to 9, 

 because this product has always to be subtracted from a num- 

 ber which has its unitate to the base 10 equal to 10. But the 

 denominator itself of the reciprocal is the only multiple which 

 has its unitate to the base 10 equal to 9 ; therefore the said 

 terminal figure is 1. 



19. To put a portion of the theorem illustrated in art. 17 * 

 * Phil. Mag. [IV.] vol.?. p. 526. 



