499 



The paper concludes with observations on some real and alleged 

 differences between the laws of solid elasticity and those of the 

 lummiferous force, on some hypotheses in connexion with the 

 wave- theory of light, and on the refraction of light in crystals as 

 connected with the symmetry of their Enthytatic axes. 



"Report of a Committee appointed by the Council to examine 

 the Calculating Machine of M. SCHEUTZ." Inserted for 

 the information of the Fellows by order of the President 

 and Council*. 



The various applications of mathematics to physical questions, or 

 to the transactions of common life, continually require the compu- 

 tation of numerical results. At one time isolated results have to 

 be calculated from particular formulae ; at another it is required to 

 calculate a series of values of the same analytical formula ; in other 

 words, to tabulate a function. It is only in the latter case that 

 different instances have so much in common as to permit of the 

 application of general methods irrespective of the particular function 

 to be calculated. But even in the tabulating of functions one or 

 other of two objects may be kept in .view. At one time a result 

 may be arrived at expressed in a complicated, perhaps transcen- 

 dental, formula, and the mathematician may desire to know merely 

 the general progress of the function. In such a case it will be 

 sufficient to calculate values at rather wide intervals, and the mode 

 of calculation must depend upon the peculiar function. But at 

 other times functions present themselves which are of such common 

 occurrence, or of such practical importance, that it is desirable to 

 tabulate them for values of the variable increasing by small steps. 

 In these cases general methods of interpolation come into use : it is 

 sufficient to perform the calculations directly for comparatively wide 

 intervals of the variable, and the intervening values of the function 

 can be supplied by the mere addition of differences. 



* The Committee consisted of Prof. Stokes, Sec. R.S., Prqf. W. II. Miller, Prof. 

 Wheatstone, and the Kev. Prof. Willis. 



