Properties of Radium in Minute Quantities. 183 



from which we get : — 



U'4-V'=--058 

 U'-V' = -0302 

 tan 20' = 8*11 

 or 



U'=--0139 (u = -72 cms.) 



V' = — -0441 (v'=— 23 cms.) 



^= 41i°. 



This method of power resolutions, as also the associated 

 u generalized " parallelogram, can only be applied to astig- 

 matic problems in which the wave-fronts after refraction are 

 paraboloidal, or are ellipsoidal and can be assumed para- 

 boloidal in the neighbourhood of some point. 



Sturm appears to have been the first to show that all the 

 normals to a paraboloid in the neighbourhood of a point 

 converge to or diverge from two lines at right angles to 

 one another. 



XX J I. The Properties of Radium in Minute Quantities. 



r lo the Editors of the Philosophical Magazine. 

 Gentlemen, — 



IN connexion with Mr. Eve's paper on the above subject, 

 the following fact may be of interest. 

 In December 1903 I prepared a solution b^y dissolving 

 1 milligram of a preparation of radium — stated to contain 

 To L 00 of its weight of radium barium bromide — in a few 

 c.c. of water. Some of the solution was poured upon 

 a glass plate about 60 sq. cms. in area and the water 

 evaporated. A film was left behind which gradually increased 

 in activity, and at the present time, seventeen months after 

 preparation, is qnite as active as it was a week after prepa- 

 ration, and will still excite luminescence on a screen. No 

 sort of care has been taken of the plate. A piece of glass 

 •25 sq. cm. in area was cut from the plate today and its radio- 

 active power tested and compared with that of 25 grams of 

 fairly good pitchblende. The quantity of active salt upon 



this area could never have been more than * nnn milligram, 



J o u > u u u i 



and yet after seventeen months this small amount is at least 

 20 times as active as the 25 grams of pitchblende. 



Yours faithfully, 



W. A. Douglas Rudge. 



Woodbridge School, Suffolk, 

 May 17, 1905. 



