188 On the Adjustment of Crystals for Measurement. 



But h z = fia and C = — nearly. Therefore, .by integration, 



*'=^cos{<l- 3 -f)}' 



which is the true approximation. As both approximations com- 

 menced from a fixed ellipse, it thus appears that the failure of 

 the first is u-holly due to the mode of integration. The occurrence 

 of a like failure in the lunar theory is to be explained in the 

 same manner. 



This reasoning shows that the truth of my theorem respecting 

 the eccentricity of the moon's orbit will be tested only by pro- 

 ceeding to the third approximation, which takes account of the 

 effect of the tangential force on the motion of the apses. 



Cambridge Observatory, 

 January 22, 1855. 



XVII. On the Adjustment of Crystals for Measurement with the 

 Reflective Goniometer. By W. H. M. 



THE Philosophical Magazine for December last contains a 

 description of a contrivance for adjusting a crystal for 

 measurement on Wollaston's goniometer. Any observer who has 

 taken the trouble to read the very clear directions for using the 

 reflective goniometer, given more than thirty years ago by the late 

 W. Phillips in his 'Mineralogy/ and by Mr. Brooke in his treatise 

 on Crystallography, will find in this instrument, as usually con- 

 structed, ample provision for making the intersection of any two 

 faces parallel to the axis of the graduated circle. The descrip- 

 tions of the use of this instrument, to which reference has been 

 made, are accompanied by figures. In these figures it will be 

 seen that the pin which carries the , late to which the crystal is 

 cemented, is represented in a position nearly parallel to the plane 

 of the graduated circle. In this position, the rotation of the pin 

 round its own axis, and the angular motion of that part of the 

 branch into which the pin is inserted, are sufficient and neces- 

 sary for the adjustment of the crystal. But when the branch is 

 turned so that the axis of the pin coincides with that of the gra- 

 duated circle, as represented in the figure in the Philosophical 

 Magazine, that part of the power of adjusting the crystal which 

 depends upon the rotation of the pin round its own axis is en- 

 tirely lost. In addition to this inconvenience, the branch inter- 

 cepts the vision of one of the signals, and thus renders an obser- 

 vation impossible, through no less than about 75° out of 360°. 

 When the instrument is properly handled, the vision of the sig- 

 nals is uninterrupted through an entire revolution of the circle. 



