508 



Prof. J. Perry and Mr. H. F. Hunt on the 



The area of the curve is easily obtained by means of the 

 planimeter. Having found the 25 abscissae once for all, they 

 may be used for the development of any arbitrary function of 

 r of which 25 equidistant values are given. We now publish 

 four tables giving these abscissae, which we have carefully 

 calculated for the first four terms of any such development. 



In the column headed P we give the number of the point 

 in the curve of which %J 1 (a;) is the abscissa, there being 25 

 such points altogether. In Table I. the point 24 corresponds 

 to x = 2*40483. In Table II. the point named 24 corresponds 

 to # = 5*52008, and so on. 



In Table II. an additional abscissa is given corresponding 

 to some unknown point between numbers 10 and 11 ; this is 

 the extreme abscissa of the curve, and the corresponding 

 ordinate would be a tangent to the curve. In Table III. 

 there are two additional or bounding abscissas and in Table IV. 

 there are three of them. 



Table I. 



Table II. 



P. X . 



Ji(«0- 



o- 



0000 



1 



0050 



2 



0200 



3 



0450 



4 



0787 



5 



1216 



6 



1727 



7 



2312 



8 



2962 



9 



3667 



10 



4116 



11 



5197 



12 



5999 



13 



6807 



14 



7609 



15 



8392 



16 



9142 



17 



9845 



18 1 



0490 



19 1 



1062 



20 1 



1 552 



21 1 



•1949 



22 1 



2242 



23 1 



•2423 



24 1 



•2485 



P. 



x . J^x). 







00000 



1 



+ -0267 



2 



•1010 



3 



•2242 



4 



•3800 



5 



•5578 



6 



•7458 



1 



•9191 



8 



1-0706 



9 



11825 



10 



1 2417 



11 



1-2160 



12 



11141 



13 



•9418 



14 



•7052 



15 



•4132 



16 



' 4- -0791 



17 



- -2801 



18 



•6455 



19 



•9963 



20 



1-3118 



21 



1-5723 



22 



1-7605 



23 



1-8626 



24 



1-8783 



10 A 



1-2485 



