MR. AIRY'S SUPPLEMENT TO A PAPER "ON THE THEORETICAL 

 Tableof(?^y-cos^(»-|). 



Values of w. 



-175 



- 165 



- 155 



- 145 



- 135 



- 125 



- 115 



- 105 



- 95 



- 85 



- 75 



- 65 



- 55 



- 45 



- 35 



- 25 

 _ 15 



- 5 

 + 5 

 + 15 

 + 25 

 + 35 

 + 45 

 + 55 

 + 65 

 + 75 

 + 85 

 + 95 

 + 105 

 + 115 

 + 125 

 + 135 

 + 145 

 + 155 

 + 165 

 + 175 



Values of R. 



25 

 229 

 610 

 1050 

 1372 

 1413 

 1109 

 567 

 84 

 104 

 1111 

 3473 

 7298 

 12346 

 18020 

 23474 

 27778 

 30154 

 30154 

 27778 

 23474 

 18020 

 12346 

 7298 

 3473 

 1111 

 104 

 84 

 567 

 1109 

 1413 

 1372 

 1050 

 610 

 229 

 25 



60° 



20 



230 



738 



1553 



2560 



3527 



4168 



4231 



3618 



2453 



1111 



148 



169 



1654 



4796 



9402 



14887 



20389 



24959 



27778 



28360 



26651 



23038 



18220 



13045 



8294 



4519 



1964 



567 



47 



33 



184 



279 



245 



123 



17 



120° 



8 



123 



499 



1286 



2560 



4261 



6164 



7896 



9032 



9216 



8294 



6396 



3962 



1654 



204 



217 



1994 



5427 



9996 



14887 



19175 



22060 



23038 



22013 



19294 



15475 



11282 



7378 



4231 



2043 



767 



184 



12 



6 



16 



4 



180° 







17 



133 



515 



1372 



2882 



5101 



7896 



10912 



13631 



15475 



15970 



14884 



12346 



8835 



5104 



1994 



231 



231 



1994 



5104 



8835 



12346 



14884 



15970 



15475 



13631 



10912 



7896 



6101 



2882 



1372 



515 



133 



17 







240° 



4 



17 



6 



12 



184 



767 



2043 



4231 



7378 



11282 



15475 



19294 



22013 



23038 



22060 



19175 



14886- 



9996 



5427 



1994 



217 



204 



1654 



3962 



6396 



8294 



9216 



9032 



7896 



6164 



4261 



2560 



1286 



499 



123 



8 



300° 



17 

 123 

 245 



280 



184 



33 



47 



567 



1964 



4519 



8294 



13046 



18221 



23038 



26652 



28360 



27778 



24959 



20388 



14887 



9402 



4794 



1654 



169 



148 



nil 



2453 



3618 



4231 



4168 



3527 



2560 



1553 



738 



230 



20 



It has been deemed unnecessary to continue the Table beyond the values o^ w — 1/5° 

 and + 175°, because the values of y~-) become very small. The greatest maxi- 

 mum of this quantity occurs when tv = 0; its value (expressing w in terms of the 



radius) is then = 1 ; the second maximum occurs when w = '-^ nearly; its value is 



/ 2 \2 1 



then y^J nearly = -^ nearly ; the amount of which will probably produce an in- 

 considerable influence on the expressions which we are now about to consider. 



The curves in the annexed figure represent, by their ordinates, the values of 

 /sinw\2 / R\ , 



\~i;r) ' ^^^ V^ ~ 2"/ 5 the values of R being continued as far as 720°, in order to 



exhibit more distinctly to the eye the successive displacements of the principal bows 



