THANSACTIONS OF SECTION A. 5/3 



insulators, and currents in solids of different conductivity fixed together in 

 contact. 



4. If the subject is heat, as in Fourier's original development of the theory of 

 diffusion, the ' quality' is temperature. 



5. If the subject is diffusion of matter, the ' quality ' is density of the matter dif- 

 fused, or deviation of density from some mean or standard density considered. It is to 

 Fick, thirty-three years ago demonstrator of anatomy, and now professor of physiology 

 in the University of Zurich, that we owe this application of Fourier's diffusional 

 theory, so vitally important in physiological chemistry and physics, and so valuable 

 in natural philosophy generally. When the substance through which the diffusion 

 takes place is fluid, a very complicated but practically important subject is pre- 

 sented if the fluid be stirred. The exceedingly rapid progress of the diffusion pro- 

 duced by vigorous up-and-down stirring, causing to be doue m half a minute the diffu- 

 sional work which would require years or centuries if the fluid were quiescent. is easily 

 explained ; and the explanation is illustrated by the diagram of curves, § 7 below, 

 with the time-values given for sugar and common salt. Look at curve No. 1 , and 

 think of the corresponding curve with vertical ordinates diminished in the ratio of 

 J to 40. The corresponding diffusion would take place for sugar in 11 seconds, and 

 for salt in 3i seconds. The case so represented would quite correspond to a streaky 

 distribution of brine and water or of syrup and water, in which portions of greatest 

 and least salinity or saccharinity are within half a millimetre of one another. This 

 is just the condition which we see, in virtue of the difference of optic refractivity 

 produced by difference of salinity or of saccharinity, when we stir a tumbler of 

 water with a quantity of undissolved sugar or salt on its bottom. If water be 

 poured very gently on a quantity of sugar or salt in the bottom of a tumbler with 

 violent stirring up guarded against by a spoon, the now almost extinct Scottish 

 species called ' toddy ladle ' being the best form, or better still a little wooden disc 

 which will float up with the water ; and if the tumbler be left to itself undisturbed 

 for two or three weeks, the condition at the end of 17 x 10' seconds (20 days) for 

 the case of sugar, or 5-4 >c 10' seconds (6 days) for salt, will be that represented by 

 No. 10 curve in the diagram. 



6. If the subject be electricity in a submarine cable, the ' quality ' is electric 

 potential at any point of the insulated conductor. It is only if the cable were a 

 straight line that x would be (as defined above) distance from a fixed plane : but 

 the cable need not be laid along a straight line ; and the proper definition of ,r for 

 the application of Fourier's formula to a submarine cable is the distance along the 

 cable from any point of reference (one end of the cable, for example) to any point 

 of the cable. For this case the diffusivity is equal to the conductivity of its con- 

 ductor, reckoned in electrostatic units, divided by the electrostatic capacity of the 

 conductor per unit length insulated as it is in gutta-percha, with its outer surface 

 wet with sea water, which, in the circumstances, is to be regarded as a perfect con- 

 ductor. For demonstration of this proposition see vol. ii., art. Ixxiii. (1856) of mj 

 collected papers. 



7. Explanation of Diageam shoaving Progress of Laminae Diffusion. 



In each curve — 



1 9 r "',<■ 



to"'-- J. '"-■■■'• 



where .r denotes the number of centimetres in ON, and i the ' curve-number.' The- 

 curves are drawn directly from the values of the integral given in Table III. 

 appended to De Morgan's article ' On the Theory of ProbabiUties,' * Encyclopaedia 

 Metropolitana,' vol. ii. pp. 483-84. 



'at distance = OiV from initial surface or 



iVP denotes the ' quality ' (defined 

 below) 



interface, 

 and at time equal in seconds to [' curve- 

 number']- divided by sixteen times 

 the diffusivity in square centimetres 

 per second. 



