422 Prof. Tyndall on the Absorption and 



hollow is the double of the quantity mentioned in Proposi- 

 tion IV.* 



The hydrostatic pressure at each individual particle during the 

 wave-motion is the same as if the liquid were still. 



Friction between a Wave and a Wave-shaped Solid. 



In an Appendix to the paper is given the investigation of the 

 problem, to find approximately the amount of the pressure 

 required to overcome the friction between a trochoidal wave- 

 surface and a wave-shaped solid in contact with it. The appli- 

 cation of the result of this investigation to the resistance of ships 

 was explained in a paper read to the British Association in 1861, 

 and published in various engineering journals in October of that 

 year. The following is the most convenient of the formulae 

 arrived at. Let w be the heaviness of the liquid; /the coeffi- 

 cient of friction; g gravity; v the velocity of advance of the 

 solid ; L its length, being that of a wave ; z the breadth of sur- 

 face of contact of the solid and liquid ; /3 the greatest angle of 

 obliquity of that surface to the direction of advance of the solid ; 

 P the force required to overcome the friction ; then 



P = ^ Ls(l + 4 sin 2 /3 + sin 4 /3) . 



In ordinary cases, the value of/ for water sliding over painted 

 iron is -0036. The quantity Ls(l + 4 sin 2 /9 + sin 4 /3) is what has 

 been called the " augmented surface." In practice, sin 4 j3 may 

 in general be neglected, as being so small as to be unimportant. 



Glasgow, September 30, 1862. 



LVIII. On the Absorption and Radiation of Heat by Gaseous 

 Matter. — Second Memoir. By John Tyndall, F.R.S., 

 Professor of Natural Philosophy in the Royal Institution. 



[Concluded from p. 350.] 



§ 12. O INCE these researches were commenced, an eminent 

 ^-J experimenter has been led by his own inquiries in 

 another field to enter upon the investigation of gaseous diatherm- 

 ancy. On the 7th of February of the present year (1861), Prof. 

 Magnus communicated to the Academy of Sciences in Berlin a 



* Mr. Stokes's investigation of the motion of waves in deep water, which 

 is carried to the third approximation, leads to the same result with Prop. IV. 

 as regards the difference hetween the elevation of the crests and the de- 

 pression of the hollows. According to that investigation, however, the 

 revolving motion of the particles is combined with a translation having a 

 velocity that diminishes rapidly as the depth increases. JXo such transla- 

 tion is indicated by the investigation in the present paper. 



