Ma HOPKINS, ON KESEARCHES IN PHYSICAL GEOLOGY. 63 



.neasure the hades), the angle DCB (Fig. 1.) between their intersections 

 wuh the horizontal surface, and the length of the line CC, which ev 

 dently measures the throw of the unbroken vein AB, produced by the 

 supposed movement. - To express the horizontal displacement oi the 

 vem m terms of these quantities, suppose a sphere described with ente 

 C m the previous diagram (2), {or in the following one in which the 

 same letters denote the same points as in (2)}, anJ any radius so as to 



form the spherical triangle ahc, by its intersections with the planes of 

 the veins and the horizontal plane. Let 



c = angle bac, the inclination of the plane DCC of the broken 

 vein to the horizon. 



/3 = abc, the inclination of the unbroken vein to the horizon. 



^ = «* = DCB the angle between the intersections of the veins with 

 the horizon. 



be = angle BCC", 



h = CC\ the throw of the unbroken vein. 

 Then shall we have 



cote = cota.sin/3cosec.^ + cos /i. cot ^; 

 and the apparent horizontal displacement CC" 

 = h . cot Q 

 = h {cot a . sin /3 cosec . ^ + cos /3 cot ^f . 



The quantities CC, a, (i and o^ can generally be obtained with very 

 considerable accuracy, as may h also, when the mass in which the veins 



