Rental Society. 355 



cal aberration by the concave lens 13 proportionably greater for the 

 rays that are remote from the centre, than for the central rays. The 

 degree of confusion in the image hence arising, is, in similar glasses, 

 inversely as the square of their focal lengths. It increases very ra- 

 pidly with a small enlargement of the aperture, but may be rendered 

 much less considerable by distributing the refractions equally among 

 a greater number of lenses of smaller curvature. Hence the advan- 

 tage obtained by certain combinations. The experiments made by the 

 author have established the fact, that in general an achromatic object- 

 glass, of which the inner surfaces are in contact, will have on one 

 side of it two aplanatic foci in its axis, for the rays proceeding from 

 which, it will be truly corrected, with a moderate operation ; that for 

 those proceeding from any part of the interval between these two 

 points, the spherical aberration will be over-corrected ; and that for 

 rays beyond these limits it will be under-corrected. Methods are 

 pointed out for ascertaining the situation of these aplanatic foci. The 

 principle liere explained furnishes the means of destroying both kinds 

 of aberration in a large focal pencil, and of thus surmounting what 

 has hitherto been a chief obstacle to the perfection of the microscope. 



Experiments on the Influence of the Aurora Borealis on the Mag- 

 netic Needle. This paper is extracted from letters from the Rev. 

 James Farquharson to Captain Sabine, Sec. R.S., by whom it was 

 communicated.. 



In the first letter, dated from Alford, 15th December, 1829, the 

 author gives a description of the instrument which was furnished to 

 him by the Royal Society for measuring the variation of the mag- 

 netic needle, and also the magnetic intensity ; and of his mode of 

 using it. The needle was so delicately suspended as to render very 

 sensible, changes in the declination as small as 10". In his experi- 

 ments on the magnetic intensity, the intervals of time occupied in the 

 needle's performing 50 oscillations, commencing with an arc of 12°, 

 were noted by a stop-watch, in which the stop, being applied on the 

 balance, is instantaneous in its operation. The watch is again released 

 from the stop at the commencement of a new observation ; thus com- 

 pensating, on the principle of the repeating circle, for any inaccuracy 

 in the reading oft', or any inequality in the divisions of the dial-plate. 



The observations made on an Aurora Borealis which appeared on 

 the night of the 14th of December, are particularly detailed. On 

 that occasion the disturbance of the magnetic declination was so 

 great, and so frequently changing from east to west, and the reverse, 

 as to leave no doubt in the mind of the author of the reality of this 

 influence. The needle, however, was affected at those times only when 

 the fringes of the aurora were in a position such as to include the 

 needle in their planes. It appeared to him also, that the side towards 

 which the needle declined was the greater, where the aurora gave out 

 the most vivid light. 



Ilis experimetjts on the oscillations of the needle have not yet 

 enabled him to determine satisfactorily whether any change of mag- 

 netic intensity accompanied these changes of direction. 



In a second letter, dated 2Gth December, he gives the results of 

 2 Z 2 later 



