173 



by which the position of the needle with respect to the mag- 

 netic meridian, when at rest, is determined. In the case of 

 the astatic needle the preceding equation becomes 



-M' , . 

 tan Mo = ,r w> • sin 1 '. (6) 



From this we learn, 



1. That the tangent of the angle of deviation of the as- 

 tatic needle from the magnetic meridian varies, cceteris paiibus, 

 as the angle, S, contained by the magnetic axes of the two 

 component needles. 



2. That however small that angle be, provided it be of 

 finite magnitude, the tangent of the deviation may be ren- 

 dered as great as we please, and therefore the deviation be 

 made to approach to 90° as nearly as we please, by diminish- 

 ing the difference of the moments of the two needles. 



Sir W. R. Hamilton communicated the following double 

 mode of generation of an ellipsoid, which had been suggested 

 to him by his quaternion formulae. 



Conceive two equal spheres to slide within two cylinders, 

 in such a manner that the right line joining their centres may 

 remain parallel to a fixed line ; then the locus of the varying 

 circle in which the two spheres intersect each other will be an 

 ellipsoid, inscribed at once in both the cylinders, so as to 

 touch one cylinder along one ellipse of contact, and the other 

 cylinder of revolution along another such ellipse. 



And the same ellipsoid may also be generated as the locus 

 of another varying circle, which shall be the intersection q/* 

 another pair oj" equal spheres, sliding within the same pair of 

 cylinders, but having their line of centres constantly parallel 

 to another fixed line. Every ellipsoid can be generated by 

 the above double mode of generation. 



Professor Graves read the first part of a paper on the 

 Ogham Character. 



