PROFESSOR IIENFRY A. MIERS : AN ENQUIRY INTO 
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PAIIT 1. 
(1.) The Variations of Angle Previously Observed. 
All who have lieen practicallv engaged in goniometric nieasuremeuts are well aware 
that ill crystals of (')iie and the same substance small variations ol angle are usually 
encountered even when the crystals are taken at the same time from the same 
solution. The differences are sometimes so small that they are only appreciable by a 
goniometer which will read accurately to 1 minute or less, and very oiten the cia stal 
faces themselves are too irregular or too Imperfect to yield sharp images of the 
collimator slit such that they can be adjusted within, say, half a minute. 
But even if account he taken oidy ol those faces which are truly plane and yield 
a perfectly sharp reflection ol the collimator slit, the indiviciual variations may amount 
to 5 or 10 minutes, and the measurements of the same angle made upon, say, 20 good 
crystals of the same substance, may differ to this extent. I have studied'^ an 
example from the mineral kingdom in the case of the very heautilully crystallised 
Proustite, where tlie angle between perfectly smooth and plane rhombohedron faces 
varied between 42° 39' 50" and 42° 48' 27", even ivpon the same crystal 
It is customary to eliminate these vaiiations, as well as errors of reading due lo 
the imperfection of the faces, hj measuring a considerable number of crystals and 
taking the mean of corresponding measurements. This process appears to lead to 
very satisfactory results, for angles may sometimes he obtained which are consistent 
even within half a minute of arc ; that is to say, the lengths and mutual inclinations 
of the crystal axes having been calculated from some of these angles, the remaining 
angles are calculated on the assiniiption that they belong to planes whose intercepts 
are certain rational sub-multiples of the axes, and they are then found to agree very 
closely with the means of the observations. 
Two assumptions are here made : (1) that the individual variations are jnst as 
likely to give angles which are too large as angles which are too small, and (2) that 
the faces do obey the law ot‘ simple rational indices. 
Even when the calculations are made by the method of least squares, these 
assumptions still underlie the process. 
T'lie small individual variations are, in fact, regarded as irregular and of secondary 
importance, and are practically ignored ; if they be thus left out of account, it cannot 
be denied that within narrow limits the angles of most crystals do approximate veiy 
closely to those required by the law of simple rational indices. Occasionally, hove^er, 
the deviation is too great to be treated in this wav, and the direction of the face can 
* ‘ Mineralogical Magazine,’ vol. 8, 1888, p. 49. 
