DETERMINATION OF THE AXES OF ELASTICITY. 331 



is only a question here of applying the fundamental laws. We 

 therefore confine ourselves to a few remarks. 



(1.) If the polariser and analyser are applied to the Microscope 

 in such a manner that they cross at right angles, it is well known 

 that the field of view is dark. A double-refracting object therefore 

 appears dark also, if the axes of the ellipse of elasticity lie in 

 the polarising planes of the Nicols ; in every other position, how- 

 ever as when a circular section of the ellipsoid is not parallel 

 to the surface of the field of view it appears more or less 

 illuminated, most intensely when they deviate by 45 from those 

 planes. We will hereafter denote this latter position as diagonal, 

 and the former, in which the object appears dark, as orthogonal. 

 It is evident that each of these positions determines the axial direc- 

 tions of the ellipse of elasticity. Since, however, the greatest dark- 

 ness is always more certainly perceived than the greatest light, 

 the orthogonal position is preferable in angular measurements. 



(2.) In order to decide whether an object, which remains dark 

 on rotation round a perpendicular axis, belongs to the single- 

 refracting substances, or whether possibly a circular section of the 

 ellipsoid of elasticity may be effective, it is only necessary to 

 repeat the observation with different directions of the object, such 

 as we get by revolution round horizontal axes. Double refraction 

 would then be exhibited that is, if it takes place, and of course 

 always on the supposition that the effective layer is powerful 

 enough to produce a visible effect. 



(3.) If the object is double-refracting, and the axial direction of 

 the effective ellipse of elasticity known, it may be further questioned 

 whether perhaps the one of its axes or both at the same time are 

 axes of the ellipsoid. In order to discover this, the object is brought 

 to a diagonal position, and then turned, by means of the contrivance 

 we have described (p. 326), round the axis to be tested towards the 

 opposite directions successively. If the same changes take place 

 here whether we turn it in one direction or the opposite i.e., if we 

 observe in both cases the same change of colour with equal angles 

 of revolution the direction vertical to the axis of rotation is an 

 axis of the ellipsoid. We arrive at this inference through the 

 converse of the statement that two sectional surfaces which form 

 equal angles with an axis of the ellipsoid are equivalent. In the 

 orthogonal position the same rule holds good in all cases where 

 revolution produces increased illumination; and if the field of 



