52 Mr. F. W. Lanchester on the Radial Cursor : 



The toluene had been used in some of Prof. Ramsay's 

 previous work ; it was distilled once and showed a constant 

 boiling-point. 



The metaxylene was fractionated three times, and the 

 portion distilling between 138' 1 and 138*7 was used; it was 

 probably not quite pure. 



The alcohol was obtained from Messrs. Baird and Tatlock, 

 and distilled from quicklime, and finally with a little sodium, 

 until its boiling-point remained constant. 



The acetic acid was bought from Messrs. Kahlbaum ; it was 

 fractionated by freezing, and the portion melting at 16°*2 

 was separated and used. 



The esters were prepared by Prof. S. Young, E.K.S., and 

 all details may be found in his paper (J. C. S. lxiii. p. 1191). 



III. The Radial Cursor : a new addition to the Slide-Rule. 

 By F. W. Lanchester*. 



THE slide-rule in its ordinary form is chiefly useful in 

 working simple problems involving multiplication and 

 division, also involution and evolution where the indices 

 occurring are integers. When an expression involves frac- 

 tional indices its solution is only possible, on a slide-rule of 

 ordinary construction, by employing the scale of logarithms 

 on the back of the slide in the same manner as a table of 

 logarithms, when the process becomes so clumsy as to prac- 

 tically destroy its utility. 



The object of the present improvement is to enable the 

 operator to solve problems of the latter class with the same 

 ease and degree of accuracy as that only previously attainable 

 in connexion with the simpler cases. 



In thermodynamic problems such as arise in dealing theo- 

 retically with gas- and other heat-engines, the need of some 

 method of computation more rapid than that of ordinary 

 arithmetic involving many references to tables becomes 

 evident, and it was in connexion with work of this description 

 that the author was led to devise the instrument which is the 

 subject of the present paper. 



In the case of the isothermal curve of a perfect gas, the 

 ordinary slide-rule is all that can be required, for the curve is 

 represented by the simple expression 



pv = constant. 

 * Communicated by the Physical Society : read October 25, 1895. 



