IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I a 111^ 11^ ' IIIIU i^ ' i^ 12.0 1.8 1-25 I 1.4 i 1.6 V] <^ /}. e. ei c*J /: y/j y /A Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. MS80 (716) 872-4503 •^ \ ^q^^ % .V 4^ •\ \\ «> Cv ^ o^ ,<'"' rv % ^^^ fp Lfi \ CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions Institut Canadian de microreproductions historiques 1980 Technical and Bibliographic Notes/Notes techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. 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Les cartes, planches, tableaux, etc., peuvent dtre film^s d des taux de reduction diff6rents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est film6 A partir de Tangle sup6rieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images nicessaire. Les diagrammes suivants illustrent la mdthode. errata to pelure, }n d 1 2 3 1 n 32X 4 / . t \ / r, 7 TABLE -FOR- FINDING THE HOUR ANGLE WITHOUT LOGARITHMS. Entered according to Act of the Parliament of Canada in the vear .898. bv P. J. Lekch at the Department of Agriculture. ■ . r. j. LthtH. Copyrigrht applied for in the L'nited States. , PREFACE. This Table was prepared for the use of Surveyors in Canada, to enable them to find the Hour Angle from a morning or afternoon altitude of the sun without the use of Logarithms, with sufficient accur;icy to determine the Azimuth of Polaris at any time without waiting for an elongation (a Table for which is in preparation). This Table, however, gives the Hour Angle so close that it is available for Navigators, the error varying from o to 4 seconds, the greatest error occuring where the Declination is o, the Latitude 58 and the Altitude 28° 45'. It can be used in the Northern or Southern Hemisphere between the Latitudes 40° and 6o\ EXPLANATION OF THE TABLE. The column headed Alt. contains the altitudes of the sun's centre corrected for Parallax and Refraction. The column headed H. A. contains the Hour Angle corres- ponding to the Altitude which is on the same line, and to the Latitude and Declination which is above it. The column headed D. gives the variation of the H Angle for one minute of Altitude. our The Table is computed to the nearest second for every Degree of Declination from o to 24 N., for every degree of Latitude from 40 to 59 N., and for every 30 minutes of Altitude within limits of four degrees. Bessels' Refractions from Altitude 24° to 44° will be found on page METHOD OF USING THE TABLE. (1.) On the day of observation the observer shall note the Declination of the sun. and consultinj,^ the Table, shall time his observation, so that it shall fall within the limits of the Altitudes for that degree of Declination and those of the one following'. Having: taken his Altitude and corrected it for Refraction. Parallax and Semidiameter. he shall take from the Table the Hour Angle due to the next lower Altitude, next lower Latitude and next lower Declination. Multiply the minutes and seconds of the corrected observed Altitude by the number under D. and apply it to the Hour Angle with the sign minus. Multiply the difference between the Hour Angles due to the two successive degrees of Latitude between which lies the Latitude of the place, by the minutes and seconds in the latter and apply to the Hour Angle with the sign minus. Call the result A. Proceed in the same manner, but using the next higher Declination, and call the result B. Subtract A from B. multiply the ditrerence by the minutes and seconds of the Declination, add the product to A. The result will be the Hour Angle. N.B.-The result of each of those multiplications is seconds of time. The following examples will illustrate the method : (3) EXAMPLE 1, Corrirlid Alliliidc 41 4S 20 ..r 41 4^.}^ F,iitilu(le of placi' 46 27 10 " 46 27.17 I )f(,'n correct I'd for 1,011 u) 23 j.S " 19 2{.()} ll. 111. MV. Tahiiliir Hour .\nt,'lc, F)cc. 19" j 17 y M'l:. 18.33x6 =io. and the minutes of the Latitude and Declination are each ^rreater than 30. or if any two of those three quantities fulfil these conditions, take out the Hour Anjfle due to the next hi^Wier Declination. Latitude and Altitude. Proceed as in ( 1 ) but usinj. the si^ni plus where minus is mentioned, and subtracting from instead of addinj^Mhe final result to A. The following example will illustrate the method: EXAMPLE. Corrected Altitude ^. ,, Lalitiule , 5" J4 40 I )ec'n corrected ("or Loll . ^ HourAnyle, Dec. 6, Lu,. 57, Alt. 26. . . 3 ,x 36 12 40 '.r i2.7.S.X=nI;8 = ^ i 51.X 25 2oor 25.3.5.4=Hj.8 .,= ,. , ^^ ^^ 3 22 21. 6^ A n..ur Anyle, Dec. 5, Lat. 57, Alt. 26. , . 3 10 44 "•'^^^•'^■^ = ^ . 54-3 25.3x4.9 .24.0 ^ ^ ^ ^^ 3 14 42.3 H r 39 3 A n 7.6x23.8 180.9- 3 0.9 A ^-=3 22 21.6 Hour Annie. ... 3 J9 20.7 (5) z o h < z Zj o u o ■Ji ft d d o IT, J5: "1 a ?, #-• - - ,, 5 ^ ' ^ ■* •*■ g f^ <^ » r>. Ml 00 "1 =», f 1/% »- o- _ ") >/^ •^ ^ k*M 30 ■yj X X vd & d- d d- ^ X^" --SO" 'S> S, ^ »> t>. M N - !>. ") >3 t •o '■0 ^ £ -t "> "1 ri ') n r>. a •r. °: «« N ^ iri ^ hN rx so 00 SO 00 00 00 00 d **| f, ^O % s; N 8 <♦ u^ M M vo •t ■o ri r-«, ''I X . A 1^ t "1 "> ") N P| ,, *? vO t>> QC m. N 'f "^ t^ tA r4 ri so W9 00 00 00 i •£> Pt X ^n On ■*• S "^ •f- t 'o "1 r^ N pj 1 ^ "? 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ON o - - -^ "> c M — _ — I "i - - t «^ >D a »0 : « fl — -. ^ t-. ao (0 »<5 — ; "5 c r o so !?> o so o iQ _: "> <^ _ - _; "> c ao 'O z _; '■o ■r. "^ vO vO ir. O C >f5 — ri — •o U5 ON — ; "1 o S V/^ iri ri M O - « _ ON ■r. lo 11-1 •^ '"' - r^ SZ5 ^ ON ri ri C-. C^ - -t n ~ - ( 19) , -4 _ ri "1 '^ t m «^ *. d ' r'. i'~ i'- 1^ t^ t'. i'- »4 r4 J^ • ■g, - ^ ^ ir, in o 1 ^ "1 in " in ir, '1 iV, pi in , «r a q q - fi '^ vC t^ 1^ 1^ in 1^ PI 1 - in p| 1 ^ "1 1 fn 1^ '1 t^ -f 2 V5 I-. 'PI 1^ ■jO a. C^ -A Q 1 "^ vd vb vd ^6 ■■6 m m 5 i4 p) ^ 1 .,. v£_ '1 •va" "if" t 9, yi pi "ZL 1 S'' M 1 ^ t ■' t 96 1 sd in 1 ^ in « •^ vd sd r> >^ in pi ' '" !» 'I '1 "* ^ . S 1 "^ 1 ="> n f^ -r - 1^ t -. l" '^ ^r •t -t -t m ir. o -O - 1 "-^ o o ^0 •c 'C '■=' -t z x" 1 ./, in -.0 1^ ^ Ft ■■ 1 ^ m r* i. 1 "^ "1 1 = "■■ 0-- 'n n '- rr- - 1 ^ z 0i- i -^ t\ '1 "1 vd "5 ^^, t •t ECLINATIO • /-I "■I "•1 PI in -t ^/*, *<^ 1 •/. C-- 1 _ ri o ri ~i>r" , 1 q ■M .. PI PI PI — 1 -^^ >o o ^ vd vd vd O '6 1 ^ ■; - ! >-- -1- 'n in -r in PI ^1 PI PI P|' i-n Q • n o O c ^6 << "' ^ ' '"^ in 1^ in - M t ir, in •t -■ 1 "■• = r^ r'l ") p^ ri in PI PI PI - o 1 r^ r^ t^ v: v; ■y. V, C^ C^ ^ 1 - .n in in in in in in m in CI - ^ 1 '-"'^ "1 — Ov in PI n 'I 'n = 1 -r^, _ 1 S-^ 'n ^n rn O 1^ PI pi PI I >« vC M3 t->. I^ 1^ r^ t^ 00 ^\ 1 -.>. in in in in in in in in 1 ^ ■' Tr, o t r- ^^ "i ■^ in 1 1 "^ tr^ 1 s-^ ^n in PI v2 PI PI PI O 1 ''^ in in in in O >q . ^- in in in in in in in in -* - 1 ■'■■ - i-r ■^ in PI ^- m in - Tr. o 1^ 'n O "•n t "■n in "•n N ' o !^ 1 - : i "° ?n o o '■n " "o O rn 1 < i ° '-^ o "5 "1 ^ p) PI rn pn en 'n ^n -t (20j •c 3 ifi fle 9' & - I "> 'O -J "> I- 1^ "> ~ ^ c- '' c o ~ o I, t- C V, c X - >: ? j a c-' 3- f ^ ^ — 'I tr* ^ 'I — _ >5 r o •c — t^ >r) in "*, -*. 'M O - _ _ '- •- I- .; '- t^ I, - 'r, ,r, 10 li^ fl M •^ - J f^ t^ ,/; '■O C 'C c - iJ >Ci C O ^O f- X t^ ; H n >n c N M O On PI M (21) -■ — PI t-^ 1^ t-^ PI t". O »0 S PI 1^ o Pl o Pl 'f - -t O ^0 'I M - « OS so ■n -t Pl •* N M VO ;: 'n pi ON PI 'I q q - - r^ 1^ 1^ CO o c PI - 2 9, a- so O so so sO ^O s t^ M 'O 1/^ •t PI ''-I P| ;^, o ;_; ro Pl PI ■■ X •* 'I- LO SO ■o o t^ t>. 00 iO iO so so so sO sO l/^ >ri 'O O sO -t PI 'O 'I C> o "> C' PI — ■^ "^ ■~6 »j I fi in >: Pl 1^ PI so so PI so so P| C^ O PI PI "H « "" PI vO Cs >o sO Os Pl o 00 z o h < z o o Pl •o "1 zz c -^ ") Os PI - >; "1 PI o - - " sO o " G sD O O PI i- p| sd Os in ■o X X i-H ■/: .-" ^ _! "~i "*" - O OS o 1/1 m ■o -t •o vs PI c- o o ■o o 1/1 1-^ PI ON "5 Pl - v: PI - ON "1 c Pl JC X X OS 1/1 1/1 11 11 ■r ::^ <* c sO ul t-H *-< r • p/1 "•o NN X m C 't Tf- ") fO PI o "1 'I /■I "■I Pl PI >0 11 Pl Pl Pl 'I 'O o o o sO Pl 11 O *^ *^ f^ 1^ O O so O 'O PI — o o Pl li OS PI PI li 11 1-1 11 PI 3C PO X CO n •5- c ^0 o Pl PI 11 11 11 >i 11 sO so n n 11 n >i 11 n 11 o (22) z 00 z O < z Zj o LU o ii — I, 'O 1/-) 5 "^1 "1 - rt v: ~ „ r-y JC y. c ~ ~ ■o "4 c - -f 5 '■' ">! n — - . t 'C o r^ y. 'jC v: >: >: X „ ^- '^ "1 Q i; ") _ "-, ri' - o >: >:' f. '-^ c "-, y. ^ — , '•o '^ >; 1/^ « >0 f. q c o 1^ 1-^ • O >0 n^j o - y. n 1^ I"! y o M "5 o o >X >o '/~l t l/^ o 1^ c C'. C". X (■I iTri ^ "1 "1 o 'n ,2 ri — _ ''I 1^ vi y y. y; q to ^ i^ — I - ■>^ '-W '.C vO •sO "■I — ~ i^ '■^ -^ OS C^ -t - — c t^ y o X - I X c- C » >. ri PI ! o - - t^ I^ i» 1^ I- 1^ ■/. 1^ - 'O -t "i n ?n 1 f-n _ M "> ^■1 ~i - "o "■I y. -t r. >/". 1/". 1^ 1 ^ y. y. - ■c ~ i S ~ - - r^ 1^ r. '1 ->: >X - z -t X '1 '1 — "•I -yi »o "■ y. ■o >o »/"» •0 ■O 1^ 1^ i>* o w — r^ ~ ''■' _ ^ r. - O 1^ "1 -y PI ri n _ ». « — n pi d o d i-i _ — f"! t^i in - - - n _' y. Pl i-i 1^ ^• ,^_ ,^_ ^rv 'O C - - 3 p| PI Pl "1 0) 2 g < Z _1 o Q ^^, p^ -i- CC _; "-; >: PI c 1^ y: >: O - - - Pl — — I*". c — y. Pl o Pl "5 Pl Pl 10 I-I ir, 1/", I/", 1^ 11-1 -t 1- >/". >/"; 1/^, "/~. X ^f. ^4 I A I r-, 525 c - - (^4) ^ 1 '^ "t I') u^ t^ t^ ^ J k-« '■ i'-. i-^ i^ l-L t~^ 1^ r^ y; ■/. ^ ^ / C" rf^^ o "•I o X 'I t M ~\ -t o "i C^ lO ^^ ,^ PI — IM 1 5 '^ o >n -t -r -t "1 ri ^' - "1 u-l ■c r^ ■"" '■ r^ li 1^ r^ t~^ t^ t^ 1^ t^ ■j: ■+ -..^' •■I >: % O "C^ "5 t ^ Ti t^ -+ o 1^ 'O o ^ *** yl "** ^ 'O "~. lo -r -r t "1 ri -i-S 1 "" >: 1 ' ^ -y. c~. q » t^ '■'5 1 ^-1 d o 1-^ r^ t-^ l~^ t^ ri ^ ' _ '■ ^T "< o o^ O 1- iC tr-i '1 — f-i ^ '"^'' — "" ■y. -t — t^ -r ^ * ") 1 j ■"*" = i/^ '/■l >ri t -r t 'O ") ^ C r^ r^ iO Cn C^ ^ 1 •" d d d d d d ri r-L 2 ' 1 <& ^ 1 < ") -t ■r. >0 PI M t rr^^ 05 ^ "^ _ -r ./: •+ „ 1^ -t ^ t^ *** = LO LTl lo t t t- ""j 2 't >o >o 'O ■5 t^ 1^ >: >o -+ /, w -i^ -r in >: cr. -*. 1 -^ < *-^ "^ _ t^ '^ >: f) >: ^ -t r-X 1^1 ^e-, >o U-) ^ ? ■^ 2 ri 'O -r.. -r 1/-1 i'". • /". Ij ' -^ ~ -^ ~_'- ;? y. „ r; '/■! ^ ~ r^ d o -^ -t *• '"- -T LJ 1 '^' O " — — i-i r • "", "■. ") ^ 1 — c c c ^ -■ ~ -." 1 / >: y: "~, r/-. ~ -r i^ ^ ^ ^ _ "^' ir, l/"i ""- ^1 -1- n n _: '^, rj 3^ -C fr^ O ' t^ -t _^ \r. ■" = ~ li-l U-) I'', •r j" ^ ■r. • O c^ o q q ~ _ ^ ti «■! _: 'o y. v: -y. v, ~ "^. 10 iri ir, I A, O r-, xr-t in _ '- -t - >; c in ' ~i~, >n "n in >n 'n y >n ■y. C^ *n ri "■; - ■■I S ~ s, -t "~ y. • n Q "V, "~* «0 3> "1 'n ^n ■y. "5 ^ i^. (25) 0) z O h < Z 3 o Q ON O ^ PI p<^ -* m NO r^ M '^ cc 0^ On C^ c^ On dv ON On OS — ~ x "-I o 1^ 00 M P| c- -r in -^ ^ '•') ") PI ") in PI ^ "1 'O >; -t CN >n O NO ■*" M PI •^ ■^ in l>^ ^ iri vO r>. 00 On o M N PPi X -"o<> CO X cc X c^ ON C^ On /, "1 X o o I^ M PI On M < ^ t 'o 'f PI in -t ri r^ ri X! t CN in O NO M £ "> "1 P) PI »-t ■■ 1-^ 1^ , n 00 "1 in X ON NO 00 -t X NO X X 'O ON 00 f. r> X o PI -- 'f '■'> ••I PI m 'n in .. t '^ o so pj 00 ■* ON in M NO ■M S '^ rn p') PI PI ^1 •^ ■^ . cr o o ^ ^^ PI "■, •1- in i-H i^ iO 00 00 o X X X i~ X X r. ^ ON o X "* r^ in --" r- ■■ in t •■n ^ -■O -r o PI X •t ~ in ^ "*" 2 -T t 'O '■1 Pl PI "■ ^ *^ ^ t^ t^ X X ON O - - lO - t^ r^ 1^ I^ r^ r- X X X ■/. ■" '■I p^ PI X 'O ini NO -+ -^ ^ ri PO ^ -t u-i in in in ") r^ "5 -K lo _^ r^ 'n c in 1 — _ s ^ t 'O ") PI PI PI 1 ^ >/-) r^ NO 1^ NO X A 'I 1^1 ^ ^ HH -»- in t p| -»' ^ fs T in — PI '■'1 t in J ' rr o o PI X 'n H 1^ '■n ON I - £ "^ "* 1- '1 ""' '"-J PI PI "• .rt M PI 'O i-n -r -1- in ■ n 1 H^ t^ r^ 1^ t^ r^ r^ t^ r-^ t^ r. ("I iO ro vO X On X in O ^ ^ 'J- PP) uo NN PO in rr^t •-n 1^1 ~ irN »M X -f c t-» 'O -^ ■z in T -1- •+ r^ 'n PI PI Q On O o o Nl n PI PI PI "•o 1^ r^ r^ r-^ r^ r^ t^ r^ 1 ■/; O PI 'I PI M O in CN PI ^ , ^ t — t — rr^ PI in •■o lO _ v; •t „ t^ -i- NO — 1 1 iri •i- T X -r ■■O 'O "5 PI 30 00 Cv ON O o o 1 -'■SO >o '~ o NO nO t^ t^ I^ >0 t ■r. O n- M 1^ PI in X r^ CN ^ ^ ri -r — in p| in PI in s=5 ! ■- CT3 >-3 o ^o o ?p> O o pn o o -■n O nO PI nD PI PI Pl X PI X PI PI On n ?. (26; z o z o p < 2 o UJ Q f^ ^;• iO X! c> "O o >o v,d sd O -- - M ^^ t^ t^ O "~i tr~, O 'ri "1 -.'I ^ "? 'O ^ O r^ t^ ""I ■ ^ o ^ ^ vo vd CO , _ -; __ t n ~ ,r; rr^ r, 'O u-i iri ^ ^ OS '1 "1 ro ro •A o SO ~ ' "1 - M M ■O o o" "1 ly^ -)- O O • I T; 00 l/-) CI "^ 'r-, I/-) ■J- -> -t 1/-, 1/-, ^ I"! "^ <■' c- C "■, o l/^ LT) LT) LO CO o- o o ■A >o o q ►- - n o : ^ "1 "". lo 1/1 u^ "+ — >: ir-, ir-, 1/1 '^ -r. \r. \r >-. lO ir-j irj lA^ ,^ X 1 5 '"' 11-1 IT' - t^ t ^ •n o >A •A lA •A — "r^ "■I S- 4 in >n CO —3 o '■I o o O o o o o (2/) z o 2 g < Z -J o ui >(7 »0 >17 X ! 1^ X X c o — "-, -r >o JC >: X X ^ c~ :7 ^ 3^ ■/. '^ ■C n - X X — i/^i ri *-; ^ ^ "1 1^ '1 X -t ^ 1- /. .^, -t >/". ,3 r^ X ~ c « y: X X X X X X c w"' ■/. rr-^ - "4 n X 'l' -t in '■^ ^ -t 5, -^ 1 ^ '1 X -f ry^ » _ ri '■n "-, -t- "". ^ t^ •; X X X X X X X X /, -t ^■ X rr-^ X - '1 o O _. -t •t '••l >/". -^ 1^ (■I l-l' X •^ /. X X o- - c Q - l-l I"! 1^ 1^ 1^ 1^ X X X X X /. >/"( t^ »/". - -1- -t "■, iV, 1/1 ""' = o 1^. '=1- -1- ~n >o r/^ I"! X y. 1-^ r^ 1^ 1^ X ,"; r-^ X /. '1 1^ - rr-^ '^: =t- 1/", -t 4 "' = ^ "^ -t X -t -, n "-. 'O -t -t ""( i'^. ^ o 1^ 1^ t^ 1^ t^ t^ 1^ 1^ l~. r^ — 'O X ~, X f. l"l •+ o _ 1- t -t "' " (2S 1^ (^ o r O t -t ir, C 1^ y. c^ I ^ 1 ^ J^ in 1^ r^ t-. iri '■1 -t r^ O M in tr, 1 ^ t -t o "1 "5 05 !- ■r - I ^ I - '' "■! "". -* tr, in '- 1- 1^ I- i', i^. ■I- in y. 1/", in in »+ 2 O < Z o o •- --^ >■- :7 o C •^ -6 \6 yd t4. t-^ '•I ri 1^ t-^ r '^ in y. ""' ''I y: in — in in in r^ >n c / '1 I- I ^- I 2 H T -" in ''"; 'I ""■ 'I y. in — y "•. in in -f "t in m vc o 1^ "1" — ] , A, I,-, ,^ '~i <•! ri ■A '^ — in y; in -^ — in 'O v, • n in in y -t 1- -r »n m - ~ - o z - 1 ^ ,^ "" in y. in „ in in in . ■-? 9 t ■" - o vd vd so c -+ in in in 'I I"! ^1 — — _ - "1 :: t^ ~t - y -^ "" in in -- I 1^ in 'r ^. ^ ■^■ in in ir, ir-, Ol '■I '■I - J _ f-- X y; in in w fi ri — _ _ in in in m ;: M '■I I"! — — _' - - O (29) >o in ^ ■■A) "5 •/: a o rO - >o •1- ri "*. — ^ iri ir, "1 r»^ o - - ri y; -c ■/. >; y. "■ "5 ") t a- cK •^■> C' ~1«""" 1^ ^'*j y. 'O 1^ ./: - o >; X y C^' c y. -t Tr, 1^ ". y _; "> o 1 vO 1^ ■r HN 1^ I-. ^' / -f '■1 "/* fr- », „ f, *n ■' . •+ -t f "" 1^ 1^ »o lO ^ r. -t ' • "■O ~. • - HI r ^ in 'A . . . '^ t^ x »/~, I/-, o f- y 1^ y >o •■I ri PI — t^ r^ X o^ — t^ l/-i -i 1^ I^ 1^ o m in m 1^1 X PI u-i O '-2 to •o X ~ I "^ o o O o O vT) -o O ri CI ri X tr, ^ -t p| "1 -f CI in "-1 — ■+ i-i X -1- HM I^ ■* », iri U-) u^ t •* t ri ri 1/1 1/-J 1/1 m o O O .0 o kO 0~> ^ MX ro r) »" W1 ro — — : "I- li-l lO 1/1 »o O -O t^ X o P) N M M M M M CI r<1 ro m (30) I z 01 z o h < Z 13 o bJ o «5 1 M= iC 1^ ' * -f "^. c t>, t -• 1 ^ '^ 1^ 1^ 1^ 1^ t4 1^ '^, '1 o "■I t t t I'", "1 o ^ '1 -r ~ q O - '1 •1 ,^, 'n *" t^ r>. (■L (^ li li 1** ''1 ~i PI ri 1^ 'i' 1 , ON t O 1^ 'V, -t r->. 1^ r. >: ~ -. ^ O* ~ ■^ ■^' -2 1^ r^ (^ lo "*j I") -I- '1 i"^. - - " 1^ 'f-i T 1 ^ '"'^ 1^ ""i 1^ iC rs n - -t ^1 ( ^ t^- "^ "~. I ri T' -^ -^ -t - O c c 'r, "1 •o 1 ~ O ■o ' PI >o i r 1 O 1^ f1 r. r. ~ - P| PI - "■- "/: C PI 6 '■^ '''^, '■^; rr-. -t -r o "1 1^ 1- pi 00 (M l/", "', '/~, >/", 1/ O c -1 '1 •^1 ^ 1^ -t ^ 1 -^ 1^ 1 ^ v: A, "". "". 'O tr 5 p| PI p| rj _ _• ""' i/"i tr-, PI p| n O 1^ 1^ 'I "1 '1 (JI) '1 ro « 1^ r^ !(-, O ~ o 1^ -Vi — I^ 1^ 1^ t^ r^ I ^ I » I ^ I - i/~, « C I ^ I >. I ^ »/-, iri vO ^O ^o l/~l f^> >-" ■I- o c o o ^ >o w ^ '■^ •« — "O c^ ir-, 1/1 •+ f, rO 52) 0^ - ■2 I- r; ,; "1 'I >f» ^ "IOC "1 r o '- r. "1 c o f^ c _1~ -coo t N >; O -J ' ") ©\ iri ,n I- '1 - ir, 'I — _ I >: ir, 'I 'I -I / - >/■, CO ("1 ft — - _ m n y o o - - _ "I 'I — vz 1 /-, •5 "10 1^ ">. - N M N « _' - I , -* o UJ -h = "I i-i ^, ^ - _■ - ' - -t t^ '^ >: >5 >: — ""i ri — >: 1^, ri ri _ : ""■ "". : y- "-) "; r^ ,^ ,^ ") 1- (33) CO o UJ •«: ' "> t 1/-, t^. y. y. A ^1 - 1 ^ ?r, ^ t I- »o •c 0t '1 'I y, o ~ 1 , A >5 ^ w ? ^ c 1^ 1^ 1 » 1 ^ 1 , '1 »v _^' N '1 ^S t >rt sO V. A y. Pr. jr.^ i-i' ^J_ '1 '■I — '1 ri VO r. x. .^ I •«•_ )/"> — 1^. tr, iTj t^ 1^ !>. !>. r^ f- ir, — -J '^ -t ^ - ^ "■I to — 'I t ir, ~ - "■I r. -t -t •I- -t "' s 9 9 a q - _ »i '1 ■o' 1^ i> <\ ri I'^'m (^ 'I ''i *fi 1^ '1 ._> tr. t I r. ,r, _ "■, ir. ir, • i A 'I 1 » 1 . y. /•, ii ■6 ■6 ^p* -t "■, A tr, - A tr tr. ir, •5 'O 'r, 2 2 O h < z Z! o Q - •i -2 C c 'I -I - _ - 'I 'I ", 'I -, -, IT' r^ i4 1 ^ A t A • r, »r, r , 1^ - d '1 A 6 I - -t - "5 I I _ -A. •r, '■I '1 '1 - iri q q q ' -T ~i t ^ 'I 1 ^ '1 ^ = '>, 1 , 'J t '1 y A f. A. ~ ~ >r, tr, <^. >r, ir , A. ^' n "1 1 '1 <■! n 'l '1 N 1^ I » 1 ^ >: -y. ir, tr. "^. "", ir -r tr, 'r — . •I tr. o >: y- A A. t r, ^ rr rr r\ tr, r 1 ■q o -J ir ir, ,r f>\ 'r, tr, tr ~t tr, tr, 'I 'I 'I _ "-, ,r. ,r. - A tr. r, A -t 'o c — '■'" ^^, 'r. — A. tr f^X ri n 'r, I/-, ,,-, tr, tr. T T "^ > r. tr, tr. "". ir, ir, 1^ tr, ri .0 o . O O I -, :- :r - -A -X r, ,| O C o I 1—3 ' ^ A. y; j3 z z o h < Z Ij o LU Q — 1^ v5 yj OS o o >^ N ' t^ 00 CO 50 00 A -*• ■o so in "! '^ _ -1- o in in m "•1 >3 1-^ t^ 1^ r^ >: 1^ so o 'n v6 Q. >o m ■M PI "1 in o t O 'O 'n .^ 'I X -1- ^ 1-^ -■n Cs ^ o in yr, m -}■ "i- -t -■I rn PI PI i o » » t-* Pl N "\ rn pn •+ ■t 1- 1 '^' '"^ t^ i^ t^ t^ 1^' PI r^ X t^ o r^ / X r^ •^ r*-; Q 1^ -I- — ■T — ''\ p| 1- 1-1 in •i- PI X m „ X -*- „ 1^ 'n -. ,.^ PI ^ m in in 't -t T 'O PO PI i -^ o c- c- -> O O _ ^ PI Pl PI o ■o o •o 1^ r^ t^ I-. -r 1^ t^ 1^ i^ \ r. -f C\ i-n r-^ n PI ro -f « o in O m PI ro 't -t •* PI , r" r<^ -+ -n '~^ t^ "■n o •^ '■n CN v^ P| c in PI ■"* in in -r -1- -t "■' "-, '"■ 1 t-» 1^ 1^ t^ X ao X Cs Cs o Cs c- ! ''^ so so so so so so so so sO so SO 1^ •o 1 -r M PI PI ^ X in » _ -t X 1 ' ri 't PI '/~ — in ■•1 "■n rr> -r in »1 X in PI X in _ X in _ X •+ in in sC ^ • n in m -t -r -t "■• ^^ 1 -^ c r^ t^ t-^ t^ 1 --^ so X so 1^ ■o "~l ■O r^ ■o so X X o -o ■r PI r^ t -r ^J •— in -t PI -t •^1 -1- Pl "1 T O 'O o O '■n C) 1^ "1 n r-. "") ^ r^ i s - •^ in in in -1- in "" -t fr* 1 "^ "* "^ >+ Tt "+ >* m in sO o o ■'sd so so so so so so so SO sC SO sC so / -^ -- 1 r- -t T-^ _ X I'"! _ ,- ^ -t 1^ -r fr\ r\ H. -t 'n rj \r . -n •+ r- -r — X in Pl y ir, PI ^ in Pl C* 1 = - — •- in in in -t t 1- rr^ fi^ rr- o - - (3t>: © ,^ ■■^. "-^ --^ >: ?' ^ O O "- '- - c o o o t^ 1-:. ■''^' - ,7. '.r ^' ^r^^~-vr~'- ^1 ►) >0 O ' '-^ >o ^C ' - o ,^" '- y X 3 ^ X t^ O I/", '/^ -< - tn -)- ,,~ — ; '"'^ 0^ ui i>i - "« S M PI rj Z t^ / !!! ^i ''i '? 'p '■'> ''^ " -t '■^ -c c o vd ^d -o o A O - ir, ^1 'I r 'I - i/~, *l - - J z 10 7'^ ^ -1- M r-i i-i x". y. n ^1 n' r"| i^ IT Z "'"' z h < z Ij o Ll] Q 1 r. 1 o ir-; 0-- ^ ^ "O C t -t -r -+ i ^ ' - rJ ^ "iS >0 fl c^ ,- I — I g '^' "5 PI r, fj X ^ ^ y-c y: r. •f' I'"' lo in ir •/■/ O 1^ -i- 0^ C^ O^ ""■ ""' "1 lO vr, ^r -T n -^ L"' ::: y: ^ '"^ '" 'r '^ '-^ >5 :0 CC '^' ^'^ '■-■ "^ "^ '^ .n ., .A "> "-■ "■■ n ci ., K, L- H" i<-, 1/- .^ .^ ,., "^ "o I/-1 in ,^ ,^ "" 1 r, IT) •n _ ^, '^' '". "; "1 tM pT f! i "£ -f "■■ "". ir, ,n ,n ,n ,n" \^ '^' '^' ""■ ""■ "^. ^o ,r, ,n ,o C \r, — - , "^ - 2. i- -1- •" 5 T rn 'n >n \r, in ■"I P| ri •t '^". — -t -f in in in m in. ,, - >0 1 n . O O O O O M P| ^1 ~ 2. o '■') 'O fO '"n ''o '^ '■O ri ^ J/ 05 ir, — ! '■/: >: i/~, — »o ir, — I^ '•^. 10 to I /-, >: X I- 1^ i^ 1^ IZ-j I/-, 1^ 1^ 1^ 3 - - I ^ I ^ t^ o LU r^ -^ M~, ir-, to o o o in ri >; ri lo ^J « Cn r^ i^ .^«t r t-^ '-L; ■z (M — - - — ^c »o ^ •/-J H^ -t 1^ 'o ^" - >ri VO >> r •O O \ •-^ - lO ^ _ / -t ■■I ^ -t S >: lO >o iri vO ^O O I^ -C O 'C c' o M >0 LO Lri in -+ ■r •1- .r- N "" h VO ' "u- <; ^ O in •t 'O "" •ri 't vO "•O o 1^ -t S C^ C\ O O O O PK i ^ o - - o o (3>S o z £ z o h < z 13 o UJ Q 'N^ ■^ (39) 2 CO »o c^ h < 2 -J -f, O 1 UJ Q 1 l~l ''I rr\ t -t in in o r^ X CT' "- -y y. ■X. ■K. X X JC X 30 X '■n '1 X "J -t ON '■1 iri ^O m "5 a- 'I in ►O ^, 1/", O 1^ -t o 1^1 y. 'n 'n in PI 1^ m PI X c o N M 1--. 1^ X CO ao 00 X oo 00 X PI X o X in in X "1 in tn in -t "> "■ 1^ 'O 1/~* •i- in -t 1^ 'n 'n r| in PI PI O N '-C 1^ 1 -^ •jC -yi - :> o o - PI PI PI '" O -r I ^ '" 1^ -t M m 'n ■yi '■n in ri y. X PI m X PI X X PI X -r T r\ PI X -t '■1 u-i ^ ^ 1^ -r 'n in Q r^ X - ON '-^ I-. 1^ 1^ 1^ 1^ 1^ t^ 1^ 1 ^ 1^ I^ 1^ - d' % in ON PI in in t m, m M X ""l U-1 - n y. in m 1^ -t -r ^n in 'n PI X rl PI PI M M "1 "•n 'n 1- ^ in m >o >o vO 1^ 1^ 1^ '- i^ i^ i^ 1^ 1^ t^ t^ t^ r>. in - in in ■^ •^ -t '■I •1- ih 'n PI ^t t^ •t O 'n in -r i"i I"! y ri 'n "■n '■'^ 1 ^ PI -r P) r\ C C rt I ^ 1^ 1^ ^n r^ m 1^ t t^ r^ 1^ t^ >^. in irt ^ - n >n m m m 't 1^ rr; ^n PI + „ q 1^ to in — \Z _: -r - ^ q 1^ pn 1^ ^6^ ON p) in PI sO NO 1^ t^ 1^ o o c Z X 1^ PI -t 'n r| CN in in in • O in in u-1 \0 O in PI O X o X 'n in -1- >o C-' C-. ON c -: o PI — C 1^ C I- — in "1 X - -t ^^ '^ — ir. in in »< 1^ in 'n vO j I 'n CN PI t -r -t m "". m in in m ~ x" in - •^ PI o i-i in O o c 3; 1^ ^n N 1 PI X in -n in C ^ PI 'n O o c w ^ S-. O '■n 'n — PI ■■n "•n in i-O (40) c^ >n o O O l^ '~d o o c c" v: — • ir, — "5 O O ~ ~ "-, -t l-l I/-, r^ _ 'j' ^ '^ to lA, ir. ir-, ^ ^^ o o vd o o -c o c c /. -T "1 1^1 -' -t 11-1 CN lO n o = ") o 1^ PI r^ -t a .1 T. c« M >0 0-. O f-l y; \o o -o — '■'> "1 C O 0^ O 'n I/-) o I , O O OS I"! n o O — v. ir, ri ~ — ^ >: -A ; "'' S ^ rn i-o — ■ -t- o tu c^ = t > O » r-, cc (Tl = I "~, I /-, t(~, — 1 /", 1 /~, ; X >: >; X X X ■Ti X / o ■"Ti n- 'n "1 '■1 >: ^ ^ PI o c 5 "^ in -r I-- n PI o Pl o o O - f\ ri 'O "1 t •t '■-x ./3 -I- o -t v; >: 'n PI y; A. '^ -1- fO •* ri t -r pT % I^ ^ O _ « ' 1^ 1^ 1^ 1^ 1^ -jC ^ pi" " >: ■r, " o ^ o in m t -1- o "> ■ n <-n 'O 1^ PI v: 'n PI •n m o o o t^ I^ x ' t^ r^ r^ i->, 1^ t^ t^ t^ ■';? in t^ o M 'O ^ ^ lin 1^ lO ^ o 'n -t "■n c. pi ^rj ") fO ■+ ^ vn in in '■ I. t^ X -t i^ 1- -t t^ ' ;? in - PI in in ■z in in in O in -t "■n pi "•n 'n PI O o 'n t^ 1^ 1^ r^ t^ 1^ 1^ t^ in O in q 1^ "1 o P) pn 1^ >n x; X in 1^ ■6 X o -t PI in O X in O in X X in M 'O - X o o X PI 1^ lo O CCS •-3 in m ^n X •1- p'l 'n o ,o in r^ t^ r © *— ) 1 ~ d '- ■d d to *rj 1-'^ -r - "1 -t n ^ ""i - _j fO _ 0^ •o ") - ^^ ^ ^ "*" S "^ r^ r/v ~i 'T n Z ^- ■ — ! X ! '-'^ -t -^ -^ -t t >/-! »r, 1/ C5 i ! o o ■6 c d d d d O -f „ ■'■ ^' o "■I -■ IV, -1- "'. '1 '•1 y. -1 » "1 - >: »^ « JC \r\ ^i ^, ""* E "^ ' "-, '^ ri ^\ i-i - ^ 1 •'^' <-! f-i M "^ 'O 'n "1 X "" 1 o O ■d d d O d O d ■* -^ /. "^ i^j -1- y: f\' -t -t ' ~h "5 ^ -^ ^^ ^ _ = t o r. ^. -, ""' 1-1 t '1 y: ^ ^ t^ -^ - c - -' - d o •6 >* -^ ^ ' ^ n' ri y: Z "1 y; -t ,^ ''■- -t H vt ir-. ^1 ^ _^ » = -t •+ "^ ") "5 ri n pi' o ^ 1 r. *". C^ c- ~. O q "" i-ri lo >^. 'n d \C ■sC O ^ ; ^ *-^ •^ '^. lo i~i 1^ ■ n 1 ^ "^, 1/-) E "•■ '"o "1 c "5 "^1 PI ^• v. ■f. iO X >; >: >: •y: ^ ^^ 1— ■ i/^ >A ^r-, 'A "^ 'o >Ai ><-i >o •o •* < 1 ^ ' '-^ O r^ —' y: m' y, "■1 •^1 1 h"-i E "*■ -t •t "5 ri fi ~i Pl /— >* ■f. 1^ r^ t^ 1^ ,^ t^ r>. !>, ; "^ 1 LT) 'O ij-i ■A lA lA in "~t \r\ -f< 1 -H 1 H ' ^ " '"^ ■A v: >: "1 1^ ^ -t P| mJ. ") t^ -t r-i -» ^ ,^ ^ — ^ 1- -1- -t "'■; ^^ "~! ^ 1^ T^ I '"'^ , '^ S5 i ^ "1 rn PI ~ 'I' 1^ t^ y; •c _: -t If I -c y, '"S Cr> iri 'A X ■>;■ X o - in iri -t I r, I r, -I- O I- "5 - 1^ X X 1^ x '!» z z o h < z Zj o •IT If: lO X X C^ C' 1^ 1^ 1^ I^ ■" ""I 'I "-, 1^ "■, °. 9 - XXX — ''I X X X 'n O m 'O 'O "*; 1/-) lO in -}• Tf 1^ I ^ X / O "i 'n 1^ 1^ o "■; ^ — ri "^ -t in — — _ ''^ — ; I 't ~- i-n — t-, 'n o o «-N g in in m -t 'n X 1^ o 'I in »« in X "1 C^ in — C 1^ 1^ 1^ O X in in in 1^ i4 1^ 1-^ 1^ in n 1^ 'n in in in "■I X in -t — 1^ 1-^ "■I 1^ N M N i-n r^ r^ t-^ r^ n X o in X in »n in 1^ X o_ 0_ >^ '^ i-^ 1^ 1^ r^ X X X o in in m "I- in 1^ X X X / X o in C 1^1 C in o ■+ rn -• •+ PI "I ~ X 't - X -^ i-i in in 0~' ^^ X « q "1 X PI o X o 1^ o PI o 'n PI O in '-C vO \C o \d -c — P| M — in 1^ in in in in in in o o o vo \d o ■6 o o in 'n X Pl in m in o PI '■1 X q C 1- X in "I X in >-< ^ ~ in 'n Pl — m -t "■. o 1^ -r o 1^ ■- - in rn rn 'n i-n rn tj- rf >o ^o vo o o \d o in PI C^ •n in t in in r^ t -a- t t ■* * MD o O o ■r X "~, ' O ~\m' Pl r) _ — "-, — — ^— -^ 1 in t t "-i PI '— •n ") fc-H 1 ^ _ '"^ -t "" X in PI Cn in PI a> vo -o o - - 44 o ^ 1 "^^ lA ^ «i C y. -t _^ •<; ^ t '1 ■«** "! 1- » y. 'A M4 = -^ -r ''> ■■" ~ 'O o / y: a M <; r- ir) m "5 ^ '■'^, — ") "> -t z 2 z o h < z I] o Q 1^ Q 1 1 / O ■■6 >o I"! PI I Y r>. ~ -_^ - ■ ^ , ^ *-* ^ n i-i (-1 - - ■w l-l r>. 't „ \r. "** 1 fc * •r o -t "> r** ^' 1 r. o o ^™' 1 o o o o o o , 'X, C^ <^ -t t . , ' "1 •; \r, ri ,-» — • Z -r t -t "1 - -^— X - ^ C^ o> o^ "^ in iz-i in I/~, in r^^ I^ 1^1 ^ "". ^ T t 'O 1/". in m ^0 •O o O vO >o VO "1 »t >n 1*1 in 1^1 ■j: -t -t t '^ ^ •o >c "•I o o ''1 -1- c'l n CI M M o O ^0 O CI O O m ri ri On 30 vo " 'n o On ON O^ O^ ■n in in in in in -t _: "1 c in in -JTj in O vc O in i-n in /. — rn m »n >3 ^ uS in in ij-i ■n in >o in in in C'- o '1 O r>. fn ro ro ro PI in in m 1^ in - y. "1 ri in in in in pi in • n ■O ^0 >o ^ in in m in in 'n 1^ P| ^ in i/"i -1- ■y: in p| Q 1- in in m in n in ir-. ir, m '■1 in O in C in in I/-, "1 "1 ;: in o in O fi in ty. On — in M "1 _ in in PI in PI ^ir~, in, I- 'n in ri ") 'n in i-n 'y -Z: c. PI in t in PI in "5 fO PP) rp) 45) w I'.l i , ^ t-> r>. r>. X X On On o ''■^ ^ -X> VO NO NO NO NO *<" " n ■" o -t 1^ -t in P| in "1 - i s - tort oc in X in in in . 1 >n iri in o O r>, r^ !>. 5 N^ 1 •'■■o ^ o o c >o •o o -t- ■ n t PI "•n t P 'n m m t m , "1 "> ^ * * m in m 2? ^ 1 '•o \0 vO vd NO NO NO NO *<< ^ t>. NO in On PI m *^^ "1 _ CN o 'O nC ^rj C ^^ PI o >d 'd Nd "1 NO *«* 1 '^. •t r^^ 1^ in P| t X o U-) PI O' vO PI On in z 2 o •* ^^ 1 o O d o .5 ■d NO "^ ! x: 5 "' On O ri -t ■o X in 1^ in z : 00 a> On On On On O O 1—4 j ' uS iri m in in in NO NO -# fi ■'^ in in in in On m o ECLINAT --C >D in PI CN O -t tn so in SO in 00 in X in o in D. j H.A. ■r. N O PI 1^ T o_ NO t X m in Q NO in in in in 1^ in in ^ = « > x: " O •in PI in 00 rn NO "•n "■n PI o l-t PI pn iri in in NO NO NO ' .A, in >n •n in •I- PI m X in in % in in O in t 1 . o PI 1^ ■^ - CN in in in in in in in in • in ^ r. f -* *^ Cn 1^ "5 •I- in 1.^ '' X PI PI X in "> o 1 w^ r^ r^ rn m PI ■* '*• ^ 1 ^'- ^h vn in in m in in m 1 ■f. -n PI PI t PI PI PI 5- E 1 "^O O in PI O •* - » r- -O o O o o o o -■n o .^ O ^ ^ PI PI "■n 1- ■■n -t (46) o - _ ") >o lO :• r a; 30 o-> C q -. -. -C >3 00 -^ , -r _ ") c. c >»^ lo in o '^ I- 1^ /■ t — , "t _ "^ - I- O C G o -O ■O -C o' 'C' •o t - t^ — "I- O 'O o vO '■o C-. c /" - - ^ ■sO '/. N-^ fM - . - 'O -^ -C r. '^ ^_, t l~* l-« P <"! "" ^^ ■r t O ,_^ •<■ »o ^.•:!; -1- ^ 1 E ^* ■c O O O t^ I^ ,^ ■C M5 •* U-, "^ >n i/-i "^ -O c .c „ "^ '^ 'I ro ' ^ \d o o L/^ PI PI PI PP5 "1 LTl 1/-) p| o^ vO vO 'O ^D 00 '^ C O PI PI — "^ >n ir, ir,~ !Z5 ! c 1^ t w "1 U-) IT) ''O ro r'^ 'O 'o :47) A in sO '« se t>. I-. >5 X -jO J^ ~" >« >o ^d sd sd sd t >0 •I- C| ^ ^ g '1 'I lo % C| ^ ?i ix "^ 1^ ") •" ~ " "* in ' d •'.■ •t 3 in d in •6 in o '6 4«b -*< ^ '■ id :r '1 3- ir, M in ^ ^ *«j ■=. fi *• m -r "1 in r, -^ ^ ") in '1 c ir '1 — ^ C| a- "" S ^1 M ■™ ■■ "" in . 'I ft "1 "1 '? f t -r "-" ^d vC •6 '6 ^ >o o 'O <{ / J^ "■I >/"l "At -r ^ ?n £ !» 1 = 1 t fl i^ -t "" >: in ci ^1 M M ^ ^ ^ C| '1 CI CI • '■o O 'C o >o 'O ^d •d X >/~. '1 2' o 'n D t>. •t - S <"' n CI ■* 1 ^ I ■'• ."ri ?' o „ _ 2 ' .. ' taM 1 i>i 'd. '~ vd o O 'O O O ■^ , **j ; /. O X' CI -1 C( C| re- "1 ci C) CI ci I , * 1 "^ 1^ t ^ y. to C| ~, vO CM 1 p-4 1 = 'O CI CI CI M Z -^ >0 in \'r\ in in m in -t- --^ "1 '"o O in in t 1^ o LjJ (48; CM >4 >6 o - - I c , ' 5 f O f) *" s "" ac lO ?i £ :* wi in in in 1^ r>. N. in m r^ 1^ f>. , fn •t _ "■I 'I - f, y; c 4-9) 1 . u^ ir^ in o O NO r«. t^ - Il o »-H "''O^d'xiovdvdvd O vC X "^ o in o PI in o o in •o **- '•'< M "t 'n ■" in 'O ■" . •^ >0 in PI 00 in PI 00 in N £ <■< PI PI " •-H . (^ "> Tf- ■* "I- t in in in ^ ^" " "'vO O O •O NO o o o o X "^ t PI On in o -f m t m PI in '1- 1^ 'I n r^ -t „ r^ •t ' •■N S "^ PI PI PI ■^ ■^ r. PI PI PI m 'O PO ^O m QC u 1 -^ >o vO so NO NO NO NO NO •y. ^ M o o t NO ON M ^ t t "■n CI PI in (^ « 00 in PI ON NO ") o NO S '■'> p) PI PI ^ , 1 o O M « M l>H l-l Nrt -4 1 -^ o vO ^ NO NO NO NO NO ■r. f^ t^ vO in '■n O r^ rn ON ^ 1 fO "1 in in Tf X o 1^ •t M >3 -t M 00 1 £"> (^ PI PI On PI On •^ Q 1 .=^ Cn c^ O O O o CO 1 ■'- U-, in in in NO NO NO o z X O "t t^ M ■* m NO NO -Tl PI PI 'O ro PO m ro m i_ 00 in PI On NO r'1 O ^^ ■ Lm ? CI rO PI PI PI M CM ■■ 1 00 00 ce OD «3 X 00 ON ON Z i— i I '■- v>) in in in in in in in "■ >n 1 -J? rn ^ PI un 00 in •a- ON ^^ j ^ H * 1 fO lO PI CN ^ "■n O >: in PI P-M 1 £ ""^ "•I PI PI PI PI < 1 • Z d 1 , 'T t^ r^ i^ 1^ t^ t^ t^ t>. 1 -^ u^ m m m u-i m m in in ■■M ^ "* ' J 1 r. 'O f-n 't Tf ■* rf i-n PI O ^ 1 M •■n t in PI rn ■* o 1 '■I O rr. o i^ in PI On o r^ in 1 £ ^-^ ro rn PI PI PI IM •^ >-t Q ' r^ 1 "^ lO in o NO o NO NO NO CO f^ 1 -^ in in m in in m in in 1 lA '■'^ t^ 1-4 in 00 M 't o 00 ^ 1 - PI •* in PI '■'*, 1- m 1 -c K 1 ro t^ 1- t^ X NO ro O r^ ■>t £ <^ (^ m PI N PI PI *^ 1 -^ "I- •+ ^ in in in in in j ^ .>. in L/^ in in in in in m 1 -y 1^ rj- H^ 00 m M t^ ■■n X <■ 1 iri 1 ^ r*^ t PI m in CI r^ in PI ON r^ •+ t-i >o NO - 1 £^'> rn "1 PI PI PI PI "■ ■^ 1 rn (^ ■n 3 ; 1 <^ 00 in rr. o r^ m PI On 1^ : 1 £ ^ m l-O ri PI PI PI ^^ ^^ . 1 r^ rn rn rn 'I rn -^ -^ o h- i 1 ■■"•>, in in in in in m in u-i •/■ 3C o -n in h^ ON -^ "1 ^ ^ i j= CO in 'n in PI ■* • ro On O m M oo >n 'n O X 1 a - £ '^ fO m PO PI PI PI PI " 1 , 1 - o o o o o o o O i »=i ^ 1 rn rl 'O '■'-} 1 ; : 1 o o ^ „ PI PI "•0 ": ^ cis 1 ' 1 w Tf "t t ^ f 't •t ■<}■ »-3 (5.0) 2 O h < 2 li o u Q 30 ?" K. o id O ^ r^ ly, „ ,^ •- £ M M « -I £ N 1^ IV. O 00 1^ CN o o - « ao 00 00 00 00 oo vO lO n M 0^ I") "^ "* U1 'J- r4 tv. PI O ^£) PI >-; ! ro 00 — i £ <^ M M r^ '■1 q ; 00 "5 r4 1- vo ■<}■ l~^ 00 00 N M t^ t^ t On 00 00 xOO >o ^' x Hi r. *>' PO C J^ vd ON ") Cn vd o o ON Pl ON ON On NO tv PI 1^ no' NO \0 00 '^"o" NO Pi --„'::; ro " NO NO NO NO NO PI -H -; „ NO O ' NO >0 NO vO >o NO NO NO \C, 0\ 00 NO PI -~ lO NO vo NO vo '2 ^ c> pT ^ NO O o -o 50 ?! S^ '£ o - - On \0 (51) Z o < Z 13 o o in cc 00 M N M u in 30 O !» 00 SO CO O vO — P) — — o *^ », N Q ■^00 00 00 00 .y-vO vO Tj- o < u-i in in • N a> in M t^ MM s ^-^ 'I ") M OO 'n 00 OO m 30 00 in 00 rn VO rn 0^ 'n "-i (->. N ►» 1-1 « 52) n ■x 1 M i^. m m m vo o o -■I "1 PI o PI rn o r^ Q t OS ^ o ^D •O vO vd sd vd ^ -*• 1 -i .^'- ^ "5 PI u-1 m Tt in PI O 'n -- — 1 - '■O >0 PI in P) PI PI Ov in PI PI a^ Q 1 PI PI PI PI PI 00 -* 1—1 1 o vO >d vd \6 o 'n o o in m 1- ^ PI = 1 £ "^ "5 o PI pn PI PI — t •^ X 1 o o o o o o t-^ ^ ^ - 1 ^ 50 sd ^ ^ ;3- vd 3C r>. o - t 'O PI m PI PI Os PI — « po a o ON O a. CN o 1— ' 1 U-) LO in in in in in sd o' 2 CO Hi 1^ rn in "5 iO — PI in (N ; - I = "^ ■■I PI PI PI PI PI r^ "1- CM i 1 -• ■>•. ^ r^ 1^ V3 x; 50 CC >: 50 2 »o H- 1 .n in in in in in in in in rj^ .1 T. "^ rj ? in in 1- O < 2 - '1 i-n O "•1 PI PI PI ON t^ i /^* x^ -o O o ^ ^ r^ H^ uri •n in in in in in in »A I 'f 13 -f .1 r o "^ "1 PI in in o m O m [ PI 1 o LU — '■I o 1 ■■n PI ■n "-n PI PI >4D t^ O PI t^ 1 Q d T.^. r-» 1-^ >n ■n in in in in in in in i CO 'n C in y; in PI P| c- "+ in in 'O S ' E 't >: "1 in "•n "5 O "•n 1^ -r PI PI PI PI ^ ■f. '"O "■, "-, -t -t 1— 1 •■^ lO in in in in in in in in rj" -< .■^- t in PI >n in in t PI -t -1- "1 PI ; E £ "1- "1 O 'n f^ 'X: in PI PI PI PI 'I PI "5 X ri PI PI PI ►— « u-l in in in in in in in in O ' -* . 1 -x '- < 1 -c O fn in sD 50 PO 1 o "1- >3 isE: E 1 £ ^ '■I -0 -1- '■I O ••n 'O 0« \0 PI PI 'n PI '■1 PI H . o "•I O o O O -•n 4-S 3 < c O o r?" •5- PI '1- PI <-n ? 53) •i: CM Z o < Z Zj o Q X , N N r^ rn t m VO r^ 1 OS u 1 ■^ 00 00 00 QO 00 CO 00 00 o6 X <^ vO a* o o r^ ") VO vO »o -< I j: " in in •+ N ■" in PO I f> rf o ir, ^ r^ r*^ ON 't o — — ^**, 'O M M •-4 pPl Ml O NN N PI •* X ti 1 ^ r;. t^ 00 00 00 00 00 00 00 •/: vO 0^ M •M o r^ PI vO 1^ >o ^ 1 ro i-l t -t 't i-O 'n PI " . 1 rO VO N 00 't o VO PI CO •* "" 1 £ ^ t fo rO 'O N PI »-^ o H^ 1 VO t^ r^ y: X ON ON o t- •^ r4 t^ tv. r^ t^ r^ 1^ X 00 •/; ^ t^ VO in PI 00 PI U-, vO »o *r^ iri "" M N PO PO PO x t M t^ -^ Ov in », r^ 2 f T •t ro m N PI N 1 •^ -t »ri in in vO "O r^ t^ '^ CD -^ 1 t-» r^ t^ r^ r^ r^ r^ r-^ r^ . 1 X N O r^ r^ 00 PI in vO vO »o < 1 •4- ri ■* PI PO m o r^ 'O ON in PI >s -t- o - 1 p iri ■* Tt- 'O f-n m PI PI PI N N M fn m fl pn Tt '^■ >^ ^ ^ r:. r^ t^ t^ 1-^ t4 N. 1-^ 1-^ 00 •y: ^^ M vO Cv 1,^ PI PI ^ >o -- N VX) ro rj -1- : rn N JC in H cc •+ n 1^ PO ! ^ £ "^ t -+ ■+ rn rn PI PI PI . O O O ^ ^ ^ PI PI ^ -- t~» t-» t^ t^ t>. r-» 1^ t^ J^ PI M M o oc 1- in --■ 'O 'O PI in PI -1- 1 ri -J- o t^ "1 o vO PI c> in 1 ^ in 11-1 C<3 ■<1- ■* ON r'1 pn PI PI • 00 00 00 Ov ON o O W " ■^■o ^ vO VO VO VO VO r^ r^ X. v» t-t 1^ o t^ »o rO '-' t P) m PI in N CC in t^ V3 Tt ^ r^ ~ >n lO t t -"I PO PO PI 00 \o ^ r^ r^ r^ 03 ■^•vd >o VO VO vO O vO vO VO (N X O M rO (^ rn fn PI o 1^ •O -^ X ^ M ^ M t PI in • ro ^O '■'1 O VO '■n o vO i-n o £ '^ i/^ in ■* 't 1- PO PO PI ■^ lO m in in o vO VO VO 1— t hH ■''vo vO VO VO VO >o in VO vO VO X ^ "■1 Ov •<1- n X) PI in »o ■^ rn m rn •* . ■* M 00 ■* M 00 in M X £ "^ ir\ m •t ■* •* PO PO PO '■'^ (^ ••o rri ■* ■. tv. VO vO Tf PI >o •< ro N »-< m •>«• PO N lO n ON VO P) Ov VO PO bx« p "-) u-l in "i- Tf "i- pn 'O PO > O O O o o O O o O ss; ;_^ f^ m rn PO 4—' _; vO O t^ t^ 00 00 Cv ON O C«3 < ro r^ m •^ i-n fn pn PO t- •-3 o vO in '■1 "1 00 O o M "^ ^ M >5 1/^ (S JZ. rn M •■n "5 o o ^ ■d ^d PI o PI vd \d 30 o t: '1- Pl _; "5 -o PI cr PI — \0 o PI IT) PI PI PI PI PI p-l o /. PI PI o "-1 PI o •d PI o PI PI rn O vd PI PI o PI PI o vd P4 PI o ^d PI o -d PI CO (N 00 /. PI f^ PI >0 'O -• PI 00 00 PI o ON PI p< CN Cn 1^ -« r^ oc t P4 -. 2 O h < z I] o UJ Q 1^ ro PI r. PI O in O iri in 1^ u-1 in in - 00 1^ in PI PI in O. in -■n in O i-n CO PI in in On PI •■n m in '■'5 in oc 00 in PI in in in in PI in PI in u-l *" f^_ O PI in PI PI in m pi' m in PI in O PI m in in in PI PI (M Tji JZ in 1 "■n ' r^ *— t 1 '• m . 1 •y. 00 i *< J= t l-T-1 pn •* p **« £ ■* in On 1—* t 'X, PI >n P) in . 'O ■o *^ -r: PI M rr* in ri ^ c •t -t- '1- in - ON PI in O ON PO M in in "•n PI "■I in "J in O Ln — t PI in ^ >- O - - ■^ •^ -1- Pl in o in — O "-1 "■n in PI in 00 PI 'n in PI in in m ") in PI fn in — PI (N| "■I in — '"'■. PI PI PI in c in pi PI in PI M in 55 CO CM z o h < Z Ij o u o G I. t - PI M "1 'n -t t 11 X X X yj v: yi JC X M t-^ PI --0 j^ t^ 11 M4 **- tr, 1/1 t "1 P4 j: ,,„', m - 1^ Pt X t o v£> PI X ^ £ '^ t 't 'O 'O 'I PI N . '■^ 00 ON «r o o » >. PI c 1 r^ r^ 1-^ »3 CO c<5 CO c/i 1-^ o r4 , 1 •f. o ^ NN M fO t 1/1 -c ^T r'S Wi MN «^ "i ON 1/1 PI X -t *** E '^ LT •+ t <-n "^ rn PI PI 'I ^t. 't Tt "+ ui •r, NO NO y^ X ^ r^ 1^ t-^ r-^ t^ r-^ r4 r^ 1-^ »o V. ON O >: t^ t .. O « -t l-O LO ■- ri "1 M PI 1- n .£ * ro vO ri ON ui Nri >: -t o vO = £ "^ •t t PI PI "•n '1 PI 'I M Pt X •c H-t 1^ o r^ r^ 1^ 1-^ 1^ t4 >/i ON PI m CO PI 't i-i "•o 11 ^ -C • rl aic ■* l-N f^ "; o O^ PI ON - 1/1 q q 1- q q 'f 'I PI q ^ ^ >-C •/■ • -f* 1— 1 t^ 1-^ 1^ PI l~^ Ov NO o i-i PI lO <-] LO i-O i-n "■O 11 PI ' rn CT> "-> P) ON ir-, M X t NH ~ £ "^ U-, IT) t ON "1 Ov ON X c. t^ t^ Q •"vx: vd vd vd vd vd -d vd NO ^ -?;5 ""S' ■^ N " ~l" v£i PI 1-^ 1^ PI j: fi * ^ "^ CO >n kM >D 1/1 h- < X "1 — £ ui U1 "1 1- ^ •1- n PI , ., ^ -* •* ■ ui ■* '^ 't '1 PI 1 (^ ro '■D m ro '■O 'o n r1 j o /^ ■^^ ^ >d vd vd o o vd NO j X Cr ^OT 1^ M PO •* ~^^ n-~' t < >/1 ^ r<1 N i-i j: '■'1 • Tt ^ ro O t^ '■'5 o t^ -I- f^ X E LO 1/1 ui "4- ■* 'O . -O ' - o o"~ 0^ "o" , !SQ r- f^ f<1 f^ 1 «-: <5 c^ vO t^ t^ C(0 CO ON ON o ccl "ro f) 'O rn r'5 r^ /-! in o •o o '^ \0 1 t PI !>. PI "5 PI PI r^ "> "i l-o ro vO ^ o ^ "^ ;t ^ = "^ r<^ "1 PI in •n — PI p| » I r. "^ "— "^ pq vO sO O vd ^ ~pn ^ rn r/^ O O in On O PI PI PI Cn "5 PI PI PI 6 o PI » 'n M On in in in c. o in \o O o o o o PI ^« ~ -* **j 1 1 ^ ■f PI PI PI PI PI 'O pi 'n "it "5 m fn s 1 f) 1 s in <* PI fn o 'n 'n 75 "^1 -1- Pl PI r^ iO X >D ■Z\ C^ in in in in in in in in in CO < j= « '^~- "ST ■* 30 t C^ in PI in 'n O ^ NM PO s "■I 1- o -n PI in PI PI PI ^ ■r J^ 1^ t^ r^ t^ r^ t>. r^ r^ «o in in in in in in in m in '^ 3 1/^ — -r t '1 1^ "1 "> y; X "1 "■1 ^ PI in . r^ X X X c C-. o »— H 1^ t^ I^ 1^ t^ t^ X X X ^ -^ ^rr -t ""so in p'T >o l-x 1--. j: ^ * r^ C. in M 1^ r*-j w •■I X ^ S »^* lO l/"j T -f -t rr; PI U1 u^ vO sO »o !>. t>. h^ 1^ t-^ t4 t-^ rA. t-^ t^ o 1 / '- ri o n" _^._^_ in t PI ^ 1 '■ M 'O >o PI '0 -t , r" ") , * -1- ^ - !>. 'O c- ■o ''1 X -t o — ' lO >o •+ -i- t "5 "5 'O , ■/. o '? PI •i- -t "t »*■ in in CD ^^ '- PI I-^ t^ 1-^ ri r4 1^ 'O " PI taN '^C^ ■■>d"" p) ^ 'I m I—I "1 in ■« PI -t ^ "^ • t fl X ■ o »« 1^ ? o 'O Mi^ c ir> l/^ in 't t ro PI ^^ 1^ PI PI PI PI PI ^N A • . 1^ I^ '^ t^ i^ i^ '" '^ i'- x: " lO M. t ■^ 1 ^ T >-• 'O 'O in Pl t i J= •1 1 * ■*_'•') O o 'O C' in PI X in ."-._ £ c- "O in -t o q -t o PO o i CN o ^> 7". HH ^O o 'O o 1-^ 1-^ I^ r^ 1^ o X C^ o O 1 O 1 ^ ■r. «^ o "■n ^ _ 't N • o •■o >o ^ vO vO o o o -^ =^o X O O ^r'^ vd o ^d o / "^ X ~ ~c^' ~o ^ '''"> 1/-1 -t PI •i- PI f o -r „ o "■n C\ o "1 o O i-n c — irl in m in ^ 't rj- "I- ^ t t t ■+ in in in /-».' :a . ^H 1—* o ■y. <■' o ^ -o o •o O o x~~ o "^'4^" '6~' r^ ■^'^"" " cK~ >o ^ M HM in •* PI • ~^ 1- o 1^ t M r-» -+ M ^ - r^ >n in in t -1- t , N PO P*! PO PI pn pn PO PI O —1 (/5 • vd vd ^d ^ vd o vd vd ./. O Cv taN i-n" in t^ X ~cr" ■~o »o *rj __ -I- rn PI ^ in 't t • "^ - '^ t 1-4 X in PI X in M — >n in in 'J- t 't SB - ~l3~~ ^o"" "0 "o" ~"o "^O^" o ^ po m P'5 m , '■ J^ ."^ o I^ i>^ X X o CN CIS r*^ !■■> •"I rn '■'> •■') r1 'I •i- l-Q 5s: BESSEL'S REFRACTIONS. Alt. o 24. 25- 26 27. 28.. 30 32 34 Iv-'fu. Alt i> r 2 cS.9 .... ." ' " ^ j5 I 22.3 " '^ 36 , ,9.3 ' 57-8 ^,7 , ,65 ' 5^'^ 3S , ,3.8 • '*^- 39 , n.2 59-7 25-4 The Parall; IN "iny l)e taken as 7" throughout. ERRATA. I'lij^c 5, line i6, for 25.3 ■- 5.4 rmcI 25.3 •, 4.5 I ., » ' in s 111 s II, L;il. 5.S, Ah. 27 30 r,,r 21 5S mid 21 15 12, " 4', t ( 33 30 • '63- 6 30 14, " 50, ** 30 30 • ' 59 49 ' ' 59 39 •5, ' 50, t 4 27 30 ' ' 21 40 " 21 48 16, 6.7 5.7 ^•7 5-7 40, 32 10 34 f,,r 6.7 mid 5.7 6.S 5.8 6.8 5.8 111 ^ 111 s " 26 30 lor 54 16 read 56 16 " 28 30 •' 46 30 " 46 36 " 40 " 6 13 " 6 15 40, " 36 30 •• 38 8 " 38 28 31 30 Id 32 30 Inr 7.0 read 7.1 111 S 111 s " 3''^ 30 lor 35 ^^ read 35 S3 45, " 44, " 3^ jJ " 40 43 " 4« 43 " 26, " 50, " 30. " 53. " 35. " 45. " 57, " 40, ' 42, ' -54, ' 43, ' ' 42, J /p ■^