Mr. J. C. Glashan on Fractional Distillation. 273 



Now, if the coil be small and consequently the wire to be 

 used for filling it is thin/ the value ^ = 2500 wants a correction 

 to make allowance for the thickness of the insulating material, 

 by which g becomes somewhat smaller*. 



Before concluding, I may remark that the question of the best 

 resistance of the coil, when the resistance to be measured varies 

 between two fixed or variable limits, can be solved mathemati- 

 cally by the application of the variation calculus. 



XXXV. On Fractional Distillation. 

 By J. C. Glashan, Stratkroy, Ontario^. 



IN the current Number of the Philosophical Magazine Mr. 

 J. A. Wanklyn states that up to the present there is no 

 theory of fractional distillation, and thereupon proceeds to de- 

 duce one. The following I believe to be the mathematical 

 representation of the law of the rate of separation of the liquids, 

 and indirectly involving the 'theory of the process. The evolu- 

 tion of this theory is an inverse operation, giving a result invol- 

 ving "an arbitrary function;" but it may be noted in passing 

 that Mr. Wanklyn' s theory satisfies the equations — that, in fact, 

 they are very easily deduced by it. If the experiments are cor- 

 rectly made and the observations of p and q, formula (XI.) as 

 calculated directly from (VII.) and indirectly through (X.) 

 affords a test of the truth of the mathematical theory ; or, to 

 test the truth of the theory, calculate r from examination of two 

 portions of a continuously formed distillate. 



Let a + b represent a homogeneous mixture of a units of a 



* These expressions for g and g' must be corrected if the thickness of 

 the insulating covering of the wire cannot be neglected against its dia- 

 meter. The formula by which this correction can be made was given by 

 me in the Philosophical Magazine, January 186/— namely, 



corrected g = cg(l — \/gm 2 ), 

 where g= the resistance to be corrected and expressed in Siemens's units, 

 and 



AB 



b = radial thickness of the insulating covering expressed in millimetres. 



c= a coefficient expressing the arrangement adopted for filling the avail- 

 able space uniformly with wire ; namely, if we suppose that the cross sec- 

 tion of the coil, by filling it up with wire, is divided into squares, we have 

 c = 4 ; if in hexagons, c = 3 . 4 . &c. 



X =s absolute conductivity of the wire-material (Ilg=l at freezing-point). 



A=half the section of the coil in question when cut normal to the direc- 

 tion of the convolutions, and always expressed in square millimetres. 



B = length of an average convolution in the coil, and expressed in metres. 



•f Communicated by the Author. 

 Phil. Mag. S. 4. Vol. 45. No. 300. April 1873. T 



