The Slip-Curves of an Amsler Planimeter. 643 



The existence of absorption bands and fluorescence maxima 

 with constant frequency differences, and the results of the 

 above calculations, seem to show fairly conclusively that 

 the application of the quantum theory to absorption spectra 

 observations is thoroughly justified. Many interesting de- 

 ductions may be made from this application. Thus, since it 

 would seem that phosphorescence and fluorescence only differ 

 in the relative velocity and absorption of the energy, and 

 since the emission of infra-red radiation appears to be 

 intimately connected with absorption in the ultra-violet, it is 

 to be expected that the converse would be true. This may 

 indeed give an explanation of the well-known fact that the 

 phosphorescence of a substance after exposure to an exciting 

 cause is at once destroyed on exposure to infra-red radiation. 



Finally, since refractivity and magnetic rotation are bound 

 up with chemical structure, it should be found possible on 

 the above grounds to connect these properties with absorption 

 and constitution more intimately than has hitherto been 

 found possible. 



Inorganic Chemistry Laboratory, 

 The University, Liverpool. 



LXXII. The Slip-Curves of an Amsler Planimeter. 

 By A. 0. Allen, M.A* 



IT was shown by Lang in the Allgemeine Vermessungs- 

 Nachrkhten for 1894, in an article on the Amsler Plani- 

 meter, that when the pivot of the instrument has been fixed 

 on the paper, a family of curves may be drawn round it 

 having the property that while the tracing-point moves 

 along any one of them the reading of the wheel is constant, 

 since it slips without rolling. The importance of these 

 curves is that the instrument works least accurately when 

 the tracer travels nearly along any of them ; consequently, 

 in measuring an area the pole should be so chosen that at 

 all points of the perimeter the tracer may as far as possible 

 cut the slip-curves orthogonally. It is sometimes advisable 

 to divide the area into portions and use a different pole for 

 each portion so as to attain this end. Lang recommends 

 that a template should be cut out in stiff paper, having the 

 form of one of the slip-curves as found empirically ; by 

 revolving this about the pole as centre it is then easy to see 

 which portions of the perimeter are inconvenient] v situated 

 (Henrici, B.A. Report, 1894). 



* Communicated by the Author. 



