668 



DR WALLACE ON A FUNCTIONAL EQUATION. 



Table of Corresponding Values of x, the Abcissa, or Amplitude, f {x) ; the Ordinate ; 

 F {x), the Arc of a Catenary ; and <p, the Angle which a tangent to the curve 

 at the top of the ordinate makes with the horizontal axis : The Parameter 

 being the unit of the numbers by which they are expressed. 



Table I. — The Amplitude between ^ = 0, and cz; =^ •.01. 



Amp. 



Ordinate 



Arc 





Angl 



B 



X 



/w 



F(*) 





<p 





.0000 



1.00000 00000 



0.00000 00000 



0° 



0' 



0" 



.0001 



1.00000 00050 



0.00010 00000 











21 



.0002 



1.00000 00200 



0.00020 00000 











41 



.0003 



1.00000 00450 



0.00030 00000 







1 



2 



.0004 



1.00000 00800 



0.00040 00000 







1 



23 



.0005 



1.00000 01250 



0.00050 00000 







1 



43 



.0006 



1.00000 01800 



0.00060 00000 







2 



4 



.0007 



1.00000 02450 



0.00070 00001 







2 



24 



.0008 



1.00000 03200 



0.00080 00001 







2 



45 



.0009 



1.00000 04050 



0.00090 00001 







3 



6 



.0010 



1.00000 05000 



0.00100 00002 







3 



26 



.0011 



1.00000 0G050 



0.00110 00002 







3 



47 



.0012 



1.00000 07200 



0.00120 00003 







4 



8 



.0013 



1.00000 08450 



0.00130 00004 







4 



28 



.0014 



1.00000 09800 



0.00140 00005 







4 



49 



.0015 



1.00000 11250 



0.00150 00006 







5 



9 



.0016 



LOOOOO 12800 



0.00160 00007 







6 



30 



.0017 



1.00000 14450 



0.00170 00008 







5 



51 



.0018 



1.00000 16200 



0.00180 00010 







6 



11 



.0019 



1.00000 18050 



0.00190 00011 







6 



32 



.0020 



1.00000 20000 



0.00200 00013 







6 



53 



.0021 



1.00000 22050 



0.00210 00015 







7 



13 



.0022 



1.00000 24200 



• 0.00220 00018 







7 



34 



.0023 



1.00000 26450 



0.00230 00020 







7 



54 



.0024 



1.00000 28800 



0.00240 00023 







8 



15 



.0025 



1.00000 31250 



0.00250 00026 







8 



36 



.0026 



1.00000 33800 



0.00260 00029 







8 



56 



.0027 



1.00000 36450 



0.00270 00033 







9 



17 



.0028 



1.00000 39200 



0.00280 00037 







9 



38 



.0029 



1.00000 42050 



0.00290 00041 







9 



58 



.0030 



1.00000 45000 



0.00300 00045 







10 



19 



.0031 



1.00000 48050 



0.00310 00050 







10 



39 



.0032 



1.00000 51200 



0.00320 00055 







11 







.0033 



1.00000 54450 



0.00330 00060 







11 



21 



.0034 



1.00000 57800 



0.00340 00066 







11 



41 



.0035 



1.00000 61250 



0.00350 00071 







12 



2 



.0036 



1.00000 64800 



0.00360 00078 







12 



23 



.0037 



1.00000 68450 



0.00370 00084 







12 



43 



.0038 



1 .00000 72200 



0.00380 00091 







13 



4 



.0039 



1.00000 76050 



0.00390 00099 







13 



25 



.0040 



1.00000 80000 



0.00400 00107 







13 



45 



.0041 



1.00000 84050 



0.00410 00115 







14 



6 



.0042 



1.00000 88200 



0.00420 00123 







14 



26 



.0043 



1.00000 92450 



0.00430 00133 







U 



47 



.0044 



1.00000 96800 



0.00440 00142 







15 



8 



