WEIR S AZIMUTH DIAGRAM. 



297 



CAPTAIN WEIR'S AZIMUTH DIAGRAM. 



A List of rroblfms which can be Solved by its use. 



£y G. 



10.— ON STOKES' THEOREM. 



FLEUIil, LicvHcic es-scicitccs Mathcinatlques and Licencie 

 h-scie/iccs Phi/.siques, Sifdiieij, New South TFales. 



Plate VIII. 



One of the most interesting questions in mechanics and mathe- 

 matical physics is the study of the integral 



fXdx + Ydi/ + Zdz 

 where X, Y, and Z are functions of three independent variables 

 x, y, and ;:, and this study becomes of capital imjiortance when the 

 ■well-known necessary and sufficient conditions of integrability, i.e., 

 9Y _9X aZ_aX 9Y_ £Z 

 9x dy dx dz 9z dy 



of function under sign / are fulfilled. 



The first step in connection with that study is to show that the 

 integral round a closed curve is equal to zero, provided that the 

 functions Y, Y, and Z satisf}' certain conditions of continuity. 



