'288 Mr. P. G. Tait on the History of Thcrmo-chjnamics. 



diagonally a new series of curves, which will be the stream-lines 

 required. 



24. The stream-lines thus drawn closely resemble those in two 

 dimensions, but arc somewhat fuller. For those at a distance 

 from the axis, the difference of form is scarcely perceptible; for 

 those near the axis, and especially for the primitive oval, the 

 greater fulness of form is conspicuous. 



25. The ratios of the component velocities of a particle on a 



stream-line surface of revolution to the velocity of a particle at 



an infinite distance from the disturbing solid are given by the 



expressions 



bdb bdb ,^ T N 



U-—J-; v= r (XL) 



ydy ydx 



26. By applying to those stream-lines of revolution the prin- 

 ciples of the second part of the investigation, it is found that the 

 radius (b) of the asymptotic cylinder of a lissoneo'id surface of 

 revolution bears the following relation to the greatest radius (y ) 

 of the surface itself, and to the excentricity (a) of the set of sur- 

 faces to which it belongs : 



^'^^•^ • • (XIL) 



111 order that this equation may be real, — must not be less 

 than \/ -j nor greater than l-j. The corresponding para- 

 meter is found by the general formula 



ys_ [iJo-Q*) v a-^Vv (XIII.) 



2a 



v 2 2 

 In the oval lissoneo'id of revolution, b' 2 = Q, ~ 2 = -—==1*1547; 



and ^ = VV3 ± 2 ==0 , 644< 



a 3 



September 1864. 



XXXIV. On the History of Thermo -dynamics. 

 By P. G. Tait, M.A., &c. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



IAYISH to make a few additional remarks on this subject : 

 especially as it appears to me, after a careful perusal of all 

 that Dr. Tyndall has written upon it, that he does not yet quite 

 understand the points which Prof. Thomson and I wished to esta- 



