454 Brooke on the Measurements of the Angles of Crystals, [Dec. 



of ascertaining with precision the angles of the primary forms 

 of crystals,' hi order to determine their secondary forms with the 

 requisite degree of accuracy. Some remarks in Mr. Phillips's 

 paper, on the comparative value of the reflective and common 

 goniometers in affording accurate measurements of the angles of 

 crystals, appear to have excited a degree of anxiety in the 

 mind of the Abbe lest his theory, which had availed itself only of 

 the common goniometer, should suffer from any disrepute attach- 

 ing to that instrument. And in the memoir alluded to, he 

 endeavours to show, that in connection with his theory, the 

 instrument he uses is sufficiently precise in its results, although 

 it does not determine the value of an angle within one-half or 

 one-third of a degree, and is hence greatly inferior in accuracy 

 "to the reflective goniometer. 



It is true that the application of his original and ingenious 

 theory to the measurements afforded by the comparatively imper- 

 fect instrument he has used, has, in many instances, led to a 

 nearly accurate determination of the angles of the crystals he 

 has examined : but it contains, nevertheless, a principle which 

 in other instances has conduced to error, and which may 

 affect its worth as a theory more than any consideration of the 

 comparative merit of his goniometer. 



This principle is an imaginary simplicity which he supposes to 

 exist naturally in the ratios of certain lines either upon or 

 traversing a crystal, and which in his view assumes the character 

 of a limit to its natural dimensions ; and he is disposed to regard 

 generally the disagreement of an observed measurement with 

 this character rather as an error of the observation than a cor- 

 rection of his theoretic determination. 



The well-known error to which an adherence to his principle 

 of ideal simplicity has led this philosopher in his determination 

 of the primary form of carbonate of lime amounts to 37 minutes 

 of a degree ; and as he has assigned to the magnesian and ferri- 

 ferous carbonates the same angle as to the simple carbonate, 

 the error with regard to these is still greater, as will appear from 

 a statement of the respective measurements of each, of which 

 the two lower ones were first given by Dr. Wollaston. 



Indeed his application of this principle of simplicity seems 



limited rather by the quantity of error that may be admitted 



with tolerable safety into the calculation than by that attempt 



at absolute precision which appeared to Mr. Phillips so essential 



*to the accurate determination of secondary forms. 



* 1040 28' 40" it the precise angle given in the Tableau Comparatif. 



