262 Mr. W. S. Davis on a Method of Illustrating 



of material systems. For the free motion of heat in a conductor, 

 we obtain equations corresponding to those of material systems 

 which are supposed to be devoid of inertia. The functions F and 

 V may thus be reduced to sums of squares; and the effect of a 

 small variation in the system may be investigated by methods 

 parallel to those employed in the present paper. 



Terling Place, Witham, 

 September 11, 1874. 



XXXVIII. On a simple Method of Illustrating the chief Pheno- 

 mena of Wave-Motion by means of Flexible Cords. By the late 

 W. S. Davis, F.R.A.S., Derby*. 



[With a Plate.] 



THE simple methods about to be described, of exhibiting the 

 chief phenomena of wave-motion, were suggested during 

 some experiments lately made by the author on the refraction of 

 liquid waves f. These experiments consisted in the production 

 of waves on the surfaces of two liquids of different densities, 

 lying side by side : on agitating the surface of either liquid, 

 waves were produced which passed from one liquid to the other, 

 at the same time undergoing changes in amplitude, length., and 

 form of front. In preparing diagrams to represent these phe- 

 nomena it became necessary to make drawings of vertical sec- 

 tions through the two liquids, perpendicular to their line of 

 separation. 



The appearance presented by the sinuous lines on these dia- 

 grams immediately suggested that a similar appearance could be 

 exhibited by means of waves on flexible cords. India-rubber 

 tubes, variously suspended, and both empty and loaded, were 

 tried without satisfactory success ; the waves moved too quickly 

 to be well observed, and the reflected waves interfered with the 

 direct ones. Further experiments led the author to devise the 

 simple apparatus now exhibited, which, however, has been made 

 to serve for many other illustrations of wave-motion in addition 

 to those it was at first intended to show. 



The apparatus consists essentially of: — (1) a piece of stout 

 board about 20 feet long and 9 inches wide, which should be 

 painted black; and (2) three or four ropes, which must be both 

 heavy and flexible : the ropes used by builders for securing their 

 scaffolding have been found to answer very well, especially if 

 they have been in use some time. To enable the eye to readily 



* Read before the Physical Society, May 9, 1874. Communicated by 

 the Society, 

 f See Brit. Assoc. Report, 1873. 



