214 Dr. T. C. Charles's Analyses of Coal from 



above-considered variable has the value Z in the original motion 

 at the time t, and in the deviating motion the value Z* at the 

 time t*, Z and Z* are corresponding values of this quantity, and 

 the difference Z* — Z is their variation. This kind of variation, 

 in which cf> is taken for the measuring quantity, shall be de- 

 noted by SqZ. Therefore the difference t—t*, which according 

 to the two preceding equations has the value e/"](<£), has also to 

 be denoted by 8<pt. 



We have previously represented the time by an undetermined 

 function of <f>, which on the transition from the one motion to 

 the other undergoes an infinitely little variation. In the nearer 

 determination of this function we can be guided by the nature 

 of the subject of investigation. In the subsequent investiga- 

 tion a very simple form of the function is selected, which is 

 closely connected with the conception of the phase introduced 

 in my previous memoir. 



To elucidate the notion of the phase, let it be first assumed 

 that the variations which the quantity Z undergoes in the course 

 of the motion proceed periodically, and let the duration of a 

 period be denoted by i. For such a case I have formed the 

 equation f=ty, (10) 



and named the quantity thereby defined the phase of the varia- 

 tion. With the deviating motion the duration of the periods 

 may be denoted by i + Si, and then we may put 



i*=(i + 8i)4 (10a) 



If the phase <£ has one and the same value in both these 

 equations, t and are corresponding times, and we have 

 therefore ^t=0-t = ^Si (11) 



Just so for the quantity Z, those values are corresponding which 

 belong to like phases ; and consequently the variation a^Z has a 

 very plain meaning. 



Variations of this sort do not with the time take ever greater 

 values, but only change periodically, just as do the quantities 

 themselves of which they are the variations. 

 [To be continued.] 



XXVI. Analyses of Coal from the Coal-Measures in co. Tyrone, 

 and of a Lignite from Ballintoy, co. Antrim. By T. Cranstoun 

 Charles, M.D. fyc, Chemical Assistant, Queen's College, 

 Belfast f, 



THE following results were obtained in the analysis of two 

 specimens of coal from the Coal-measures in co. Tyrone, 

 and of a lignite from Ballintoy, co. Antrim. A series of analyses 



t Communicated by the Author. 



