﻿36 Mr. R. Hargreaves on Ellipsoidal 



diminishes, it is clear that a point will be reached beyond 

 which it will not be possible to measure it directly because 

 the telescope would come into contact with the collimator. 

 Indirect, though perfectly accurate, determinations may 

 be made by clamping the crystal-holder rigidly to the 

 graduated circle and noting the reading in any position 

 when the telescope is directly opposite to the collimator. 

 If a certain direct reading 6 has been found to correspond 

 to an angle of incidence i, then a reading 6 ± co (depending 

 on whether the angle of incidence diminishes or increases 

 with the reading) corresponds to an angle of incidence 

 i — ft). This is, indeed, the most convenient way of deter- 

 mining the angles of incidence. 



Obviously much labour may be avoided if previously the 

 orientation of the indicatrix has been determined either from 

 the crystallographical symmetry where possible, or from 

 observations under the polariscope. 



IV. Ellipsoidal Harmonics, JEolotropic and Isotropic, 

 By R. Harg reaves, M.A.* 



IT is the first object of the present paper to show that 

 Lame's functions are applicable to the seolotropic form 

 of the equation of Laplace, with some modification in the 

 meaning of the constants used, and practically no change in 

 the form of the results. It is also shown that in seolotropic 

 and in isotropic work, the parametral equations required to 

 determine Lame's functions in every case involve a single 

 constant of the ellipsoid. This point is obscured in Heine's 

 treatment of the functions by the use of the unsymmetrical 

 notation in which squares of semi-axes are represented by 

 A 2 , \ 2 — a 2 , A, 2 — b 2 . If a 2 -\-\ b 2 -{-\, c 2 + \ are used there is 

 exact correspondence between the classification of curvilinear 

 and Cartesian forms, i. e. distinctions depend on the presence 

 or absence of the radicals \/\ -fa 2 ,... in the one case, of the 

 linear factors x y z in the other. This follows from the con- 

 nexion between curvilinear parameters X fiv and Cartesians, 

 which for isotropy is given by 



/= i - °° 2 y 2 , z i- *-fl v-o y- e 



If R w is used for a product f\...f n in which the subscripts 

 correspond to different values 6i,...6 ny there are normal 



* Communicated by the Author. 



