200 PETER GUTHRIE TAIT 



treatise. They constituted a careful logical setting forth of what might be 

 called the analytical geometry of forces and couples, necessary perhaps 

 for solving problems, but not demanding much thought on the part 

 of the man familiar with elementary Cartesian methods. This Glasgow 

 pamphlet then may be considered to be Thomson's earliest attempt to 

 contribute his share to the elementary book as originally planned. Its 

 first, second and third paragraphs are identical in language with the corre- 

 sponding parts of the Edinburgh Sketch; paragraph 16 on the formula for 

 gravity is the same as paragraph 222 in the Treatise; and paragraphs 17 

 to 21 (the last being on Kater's pendulum measurements) correspond with 

 57 and 58 in the Edinburgh Sketch, and 223 and 226 in the Treatise. 

 With the exception of these few paragraphs the Glasgow pamphlet forms 

 no essential part of the Treatise on Natural Philosophy. The fact that 

 the Edinburgh Sketch, though bearing the names of both authors, was quite 

 unknown among Glasgow students, and is not mentioned in Professor 

 Sylvanus Thompson's bibliography at the end of Lord Kelvin's Life, proves 

 that it was practically the work of Tail. 



It is this Edinburgh Sketch, accordingly, which must be considered to 

 be the earliest published form of the real " Thomson and Tait." I can best 

 exhibit this by comparing in tabular form (see page 198) the corresponding parts 

 of the three distinct publications, the Sketch, the Treatise, and the Elements 

 of Natural Philosophy. In many cases the original paragraphs of the 

 Sketch are simply reproduced ; in other cases they are expanded, but in 

 the expanded form the original sentences exist practically unchanged. Of 

 course in the Treatise the expansion takes in addition an analytical form. 



Thus we see that with the exception of the part on Kinetics and the 

 last two paragraphs on Hydrokinetics, which lay quite outside the scope of 

 Volume i, the Edinburgh Sketch passed bodily into the Treatise, forming 

 indeed the nucleus about which the first and second chapters of the work 

 crystallised. The great work having been completed, the large type parts 

 of the first four chapters, along with the Kinetic and Hydrodynamic parts 

 of the Edinburgh Sketch of 1863, were pieced together so as to form a 

 pamphlet of 120 pages. This was issued in 1867 by the Clarendon Press 

 for the use of the students both in Edinburgh and Glasgow, and was followed 

 in 1868 by a second edition ("not published") of 138 pages. The Glasgow 

 pamphlet was then partly incorporated in the way already indicated ; and 

 with the addition of large type parts from Division n of the Treatise, the 



