1883.] Crystallography of Miargyrite. 371 



following equation between the errors in the three observations. 

 Let the errors in xt, cos and cox be d<£, dyfr and da respectively ; 



Then 1-51 d<f> = 2'56 da + -6df, 



whence it is obvious that the best method of using the angles is to 

 calculate cox from xt and cos; and that the most disadvantageous 

 combination is to calculate cos from the other two. 



Again in crystal 3 a well developed plane (8) which gives a 

 good reflexion is present in one of the zones [dst], and which 

 is inclined to d at an angle of 1° 24'*5. The true plane d is itself 

 inclined to s at an angle considerably less than that usually found. 

 For the adjacent plane 8 no indices lower than (17 6 6) can 

 be found which at all fit with the results of observation. The 

 angle (d, 17 6 6) given by calculation is 1° 37''5. The angles in the 

 other zone [dst] are very near the normal angles obtained from the 

 elements. The angle dd t is, however, much below that common on 

 other crystals, and this will clearly be connected with the dislo- 

 cation in the zone [rfSs£]. The presence of this plane 8 in a well 

 defined zone shows how difficult it will be to obtain reliable 

 measurements where such variations are rendered less distinct by 

 stronger striation. 



The measurement of all the crystals was first made with a 

 small goniometer made by Cary and supplied with a mirror for 

 giving a faint-signal line. When the images were bright and 

 definite enough, the image from the face was brought accurately 

 on the faint signal when both were viewed through a small 

 Galilean telescope held in the hand. Good observations so obtained 

 would be underlined once, twice or thrice, according to the good- 

 ness of the readings. The better angles were then in most cases 

 measured with a large horizontal goniometer (200 m.m. in diameter), 

 to which a telescope (magnifying from 10 — 12 times) and collimator 

 had been fitted. It was found that the readings obtained from 

 this larger goniometer, which reads to 20", differed from those 

 given by the smaller instrument by only a fraction of a minute, 

 whenever the angle measured by this latter had been twice or 

 thrice underlined. Three or four of the angles on the best crystal 

 (that represented in Fig. 2) were also measured with a Fuess' 

 goniometer in the British Museum, when the extreme variation 

 from those previously obtained by me was 1''5. This difference 

 probably arose from the difference in the images as magnified by 

 the telescopes. The angles so compared were : 



Miller's Goniometer. Cary's Goniometer. Fuess' Goniometer. 



