n6 PETER GUTHRIE TAIT 



Lussac, Dulong, etc., but first deduced from dynamical statistical considerations by 

 H?. The Hamiltonsche Princip, the while, soars along in a region unvexed by 



statistical considerations, while the German Icari flap their waxen wings in nephelo- 



coccygia amid those cloudy forms which the ignorance and finitude of human science 



have invested with the incommunicable attributes of the invisible Queen of Heaven.... 



General [quaternion] exercise. Interpret every 4nion expression in literary geo- 



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metrical language, e.g., express in neat set terms the result of - . 7. 



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There is a close association between these remarks by Maxwell in 1873 

 and some of Tail's own comments in his Kinetic Theory papers published 

 thirteen years later. 



In 1896, in a note on Clerk Maxwell's Law of Distribution of Velocity 

 in a Group of equal colliding Spheres (Proc. R. S. E. Vol. xxi), Tait published 

 his last views on the subject. He repelled certain criticisms of Maxwell's 

 solution brought forward by Bertrand in the Comptes Rendus of that year. 

 Bertrand's enunciation of what he conceived to be the problem attacked 

 by Maxwell, and the enunciation of the problem really attacked, were set side 

 by side ; and Bertrand was condemned out of his own mouth. At the same 

 time Tait strengthened the experimental foundations of the argument that 

 the solution of the problem is unique and cannot be destroyed by collisions, 

 by an application of Doppler's principle to the radiations of a gas. 



The results of Tait's investigations into the flight of a golf ball have 

 already been detailed (Chap, i, p. 27). A brief sketch of the mathematical 

 method by which he deduced his results is appropriately given here. Tait 

 published two papers on the Path of a Rotating Spherical Projectile, the 

 first in 1893, the second in 1896 (Trans. R. S. E. Vols. xxxvn, xxxix). The 

 foundation of the theory was the assumption that, in virtue of the combination 

 of a linear speed v and a rotation &) about a given axis, the ball is acted 

 on by a force proportional to the product of the speed and the rotation, and 

 perpendicular both to the line of flight and to the axis of rotation. This 

 transverse force acts in addition to the retarding force due to the resistance 

 of the air ; and the first problem solved by Tait was the case in which no 

 other than these two forces act. It is easy to show that under the influence 

 of such forces the sphere will move in a spiral whose curvature will be 

 inversely as the speed of translation and whose tangent will rotate with a 

 constant angular velocity. The projection on the horizontal plane of the 



