i88 PETER GUTHRIE TAIT 



Once, in conversation with Kelvin, I learned incidentally that these sections 

 had been inspired by Bolzani, professor of Mathematics in Kasan. Writing 

 subsequently for fuller information, I received from him the following letter 

 of date February u, 1904: 



"I learned a good deal from Bolzani in the course of a few days that he stayed 

 with us in Arran, some time about i860 1 . He gave me a very clear statement 

 regarding Gauss' curvatura Integra in relation to a normal through the boundary, 

 which I had never before seen in print or learned otherwise. He did not give the 

 name Horograph, but with the aid of my colleague Lushington I devised it and 

 put it into T and 1". I have never seen it elsewhere since that time." 



The discussion of the curvature of surfaces leads naturally to the 

 question of flexibility and developability of surfaces ; and then follows an 

 important series of paragraphs on strain or change of configuration. A 

 comparison of the sections in "T and T"' with the corresponding sections 

 in Tait's Quaternions, which was published in the same year, is very 

 instructive in the light of what has just been said regarding Thomson's 

 attitude to Quaternions. In a few lines the quaternion author gives what 

 in the larger book requires paragraphs and even pages. Tait had a great 

 liking for the theory of strains, and usually discussed it in considerable 

 detail in his Advanced Class lectures. 



The last sections of the first chapter deal with degrees of freedom, 

 and conditions of restraint a subject for which Kelvin had a particular 

 fondness. Probably no instrument of any importance was ever constructed 

 by him which did not contain some neat example of geometrical constraint. 

 The illustrations given in the Treatise are fundamental and far-reaching. 



True to their general plan the authors finish the chapter on Kinematics 

 with a brief discussion of generalised components of position, velocity, and 

 acceleration, preparing the way for the great dynamical developments of 

 the next chapter. 



In an important appendix, Thomson and Tait give (a) an Extension 

 of Green's Theorem, (b) Spherical Harmonic Analysis. In the latter of 

 these, which covers 20 pages in the first edition (extended to 48 pages in 



1 The date was probably 1862 ; for among Tait's correspondence is a letter from Bolzani 

 of date November a of that year, written from Hull on board the "Volga" as he was 

 leaving for home. In this letter he thanked Tait for various kindnesses and for a copy of a 

 quaternion paper. He also asked Tait to get for him as early as possible a copy of 

 Hamilton's new work on quaternions. 



