420 



Profs. John Perry and W. E. Ayrton. [May 27, 



velocity of the plates, and our students have obtained experimentally 

 some materials (not yet published) for the calculation of such forces 

 when the fluid is water. If the fluid is tar, o r a mixture of tar and pitch, 

 in any proportion, or even if it is the more solid substance pitch or 

 sealing-wax, we find that although the viscosity is almost infinitely 

 greater than in the case of water, still the phenomena exhibited are 

 exactly the same. And just as experiments on water enable us to exa- 

 mine best some phenomena exhibited by viscous substances, so experi- 

 ments on sealing-wax enable us to make the best examination of other 

 phenomena. 



When external forces suddenly act on a viscous fluid (and we know 

 that all substances, whether solid, liquid, or gaseous, come under the 

 head of " viscous fluids,"), tending to cause strains in the material, we 

 can calculate in the well-known way the strains and stresses. If the 

 forces do not alter, and if the shape of the body varies very little with 

 time, the stresses do not alter, but the strains increase according to 

 a law — 



v ds 

 dt 



where X is the stress at any interface, s the corresponding strain, 

 t the time, and r a constant. Of this strain, if the part which was 

 suddenly produced, and which is suddenly removable, is /, then — 



X=&/ 5 



h being the coefficient usually given in books to connect the corre- 

 sponding stress and strain. 



During the increase of strain, mechanical energy is being converted 

 into heat, through the agency of internal friction or viscosity at the 

 rate — 



dt 



per unit time. 



If the external forces are not kept constant, the stresses X alter, 

 and also the strains ; the second relation given above remains the same, 

 but the first becomes — 



x=4(,-/). 



Now the first and last relations constitute our hypothesis ; we have 

 arrived at it by analogy, and not yet by experiment. We know that 

 for the motions of pendulums, &c, in air, this law holds, and as the 



ds 



velocity or — is less and less, the law is found to be more and more 

 true. For the motion of steamships it is usual to assume the law — 



*='(£)• 



