IV. — On the Errors in the Methods of Measuring the Rotary 

 Polarisation of Absorbing Substances 



BY FRED J. BATES 



In the half-shade polariscope the settings are made with the two 

 halves of the field of equal intensity. Let A^O and MO, fig. i, 

 represent the directions of the vibrations of the wave-lengths in the 

 three similar beams as they emerge from a transparent substance in 

 a magnetic field. Let A be the amplitude and Xi to X„ the wave- 

 lengths, A„ being the shorter. Let B£^ be the direction of vibra- 

 tion after passing into the analyzing nicol, and a„ to ai the angles 

 which the vibrations in each half of the field make with the normal 

 01/. We then have as the condition for equal illumination of the 

 two halves of the field: 



(Ai sin ai)2+(^2 sin ao)^-! \-{An-i sin a„_-^y^(An sin a„)-= 



{Ais\x\an )-+(^2sin a„_i)-^H h(^«-isin a2)2+(.4„sin ai)^, (I) 



where each term is the intensity of the wave-length as it reaches 

 the eye. 



Consider any two wave-lengths, \s and \,., fig. i , and let them 

 have amplitudes As and A,. 

 Then 



{As sin aj)2-)-(^,. sin a^)-=(^^ sin a^ y^-\-{Ar sin ai)^, (II) 



Let^,2=/r.4/ (III) 



then 



sin-a^ . sin'-^a,. . ., 



j^ + sm^a,= ^^ -f sm- a^, (IV) 



since, by transposing, (IV) gives 



Y^'Csin'^aj — sin^a,.)=(sin^ai — sin^a,), (V) 



255 



