Mr. IJnvic'S Gillln-I nn Ihr Vilmtirim i,f Haay Umlm: 



"^ ^«'—i'- 24.V"' — •■' S4.,^<i!_.r' 4stV>'-*° 3946 V «'-■■■' 



/' - ^' = the circulnr Arc to rn-lius imitv & cos. 1. 



r - £!^'!= _L X r "'"-^"'^ - "" = ± j-;s^rTT - /- "•"' 



II 



ff! X r -" -ci- A ' 



r - 3j*.r _ 3 ^ / ^ 3q*j-V>' — 4^^I• _ 3Q«r»,r _ 1 -^ _ p 3ra'j'j 



II ... 



^ _ 15 I'j ' '" 15 rsa'-x"! — oj"r _ 5<i«x''j _ _1_ -^ ■ _ f 5a'j«..' 



/^_ 105.r8i' _ 105 / *7D'.r".r— S-C'SJ _ 7a«J>^i __ _ 1 _ / * 7a»j' \r 



J 3"^I7^rT7?Sf"3s.ti« J S^A-.. -X.. sVaV-x"""?'^ "'■'"''"■'" J8,/l?JTTi:^ 



-pi ^_: .".■;." _ ; " 



And 



T = 2^ 2 X circular Arc to radius Unity and cos. ~ 



X±X (±xx^;?371 + i.„.xcir.Arct„c„s.i.) 



"l^r X ii'-- V>^-H-|»-xxx^^:^. + i.„. xcirArctocos.^) 



" ^ ^ (I- X ^~^ + A"- X ^^ - H..xxxV^* + H„o xcir. Arc tocos. ^) 



X -^ X ( i- X' X ^^^^r^i + ^ „' X x= X v"^^"' + -^ o'x' X ^~^^r:? + -l^«<x X v'^^^" + -i 





•t) 



T = 2s/2 X circular .\rc to radius Unity and cos, -^ 



t) 



'^ 486» '' 1. -T ■'' 



' +- 



X s/o- - X" + 



4S 





105 



V 8 4S 192 



&c. &c- 8tc. Soc. 



AVhen i = all the terms vanish. 



ring the whole seminbration) all the terms vanish except the last in each rank. 



\nd T 



X s/a' - j' + -i::r. flB X cir. Art 

 &c. &c. . Sec. 



= 2v^3 X (1 + -LV..^ + ±V.^ + liV°.^ + i£i^ ".^ &c. Sic. kc.) X Quadrantial Arc to radius uuity. 



AVhen it may be observed that the different numerical coefficients are the sqtiares of these arising from the expansioa of a binomial to the 

 _ 1 



