540 Royal Society : — 



In the case supposed by Professor Sylvester, i. e. v = 1200 

 feet, and the height BP = 300 feet, the line BH, if we suppose 

 g=S2, will be 300 times BP, in M'hich case the point B will lie 

 so near the circumference that the line BT will practically make 

 equal angles with the plane and the vertical. So that, in general, 

 the fact of the ball being fired from a height above a plane should 

 make no diflference as to pointing the gun for a maximum range 

 on that plane. 



LXX. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 4770 

 June 21 , 1855. — The Lord Wrottesley, President, in the Chair. 



THE following communication was read : — 

 " Report of a Committee appointed by the Council to examine 

 the Calculating machine of M. Scheutz*." 



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. 



It is well known that Mr. Babbage was the first person who con- 

 ceived the idea of performing all these systems of additions mechani- 

 cally, and thereby saving both the mental labour and the risk of 

 error attending their calculation in the ordinary way. This idea was 

 actually carried out, and resulted in the invention of his Difference 

 Engine. The engine, so far as it has yet been executed, was constructed 

 at the public expense, and is now deposited in the Museum of King's 



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

 Wheatstone, and the Rev. Prof. Willis. 



