ジャンプ力測定器における検出端の改良
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(2) B 22^ ^2^- (^2^ A) R^p47^1^. y + y -7°tim^Ki5^ S^?S®efc& ft . M ^ •^ TG. Improvement in Primary Means of Measuring Meter for Jumping Force Shigeo HAYASHI* and Ryosuke OKUNO** *The Department of Physics and **the Department of Mlechanical Engineering, Iwamizawa Branch, Hokkaido University of Education. Summary The primary means of the dynamic strain measuring meter for the jumping force in athletic sports consists of three parts ; frame, footboard and strain beam pasted together as strain gauges. We report here the theoretical analysis on the mechanical operation of such primary means.. Firstly, we found the following mechanical relations between the footboard and the deflection of the strain beam : 1) Even though only the normal force loads on the footboard, the bending moment, twisting moment and normal force act on the strain beam. 2) The bending moment, twisting moment, normal force and tangential force act on the strain beam, even when both normal and tangential forces load on the footboard. Secondary, the following relations between the combination of the strain gauges and the deflection of the strain beam were obtained : 1) Using the method of a single guage, the twisting moment is eliminable, but the bending moment is not eliminated. 2) Using the mothod of two guages or four guages, the bending and twisting moments are eliminable under a suitable combination of guages ; if wanted, even the tensile and compressive forces may be eliminable. According to these theoretical bases, we have improved the primary means of the measuring meter for the jumping force in athletic sports.. I.. ^. -K. ^, ^^-'y^^W^W\n]^(oSmbt^^^^<D^W^^, ^:/H^? 5 ^-@/WJ O?BIJ%, ITi^^^^ft^/h^J; 5^^^^^-^. jo^gl^^^^-f Y^^^^ij^^-^^&rm&^j+^J^i^i^^. -eo^M^ rs^'(9 (strain beam)J 0^^^^, ^^^ ^^V-^OM^^^^H^^^^^J^ L < ]|?^f L^ 4 0^ (07).
(3) Journal of Hokkaido University of Education (Section II A). Vol. 22, No. 2. January 1972. t^\ ^^-^^^-^ ^7°^aij^^^i^^g^XflL^^^^^^^^^'^^?, :f^Wr^? ^'t^OJ;^Bl? (sensor probe) 0^g+-^^^^^^lEa^B (5 ffi-^ %^^'-^-^M-^^^. ^-o^-C^L^.. II. L?§§0d^^ A^<7^t, mmcDj: $rjs^-^^-3^^o(;, ^+ >/7°~t/6<i:t?®. W-^W®6^^, i^ls+L-a^^L, ty-c, ^o^®^—. i^^rctffi^ffL-m^^. LA^, tua^ffio?aiT^+'-/7°^i. (Om^t, m^t]b^^(02^W^-f^(0^, ?§i?0^<hL •^, ^oeg<3^^-x-6H%.. (D 2^i^f?r?gij5Tet^^. (2) ^M'-e»ci?^O^IIt)^IEB^tB^t-6 ^ ^.. (3) ^OjA^J^fl^^C/^^.. (4) /SMn;b^M^'p^N$rct % ^ ^.. UJh^4^^^ ^<^t^W^r^.^-C^, TW$H-Cl^S? ^^sk.:^?. IT-6. C^^-^P ^"7-7-^^!±i^^^^^^^j:i\ ^oW^JMS^, ^%1g<7^'JW^W^. \&^WW\~t^ ^ h ^ffll-T, ^ (T)^M^^~? i^H^y- ':>^3l<7)?/6 ^t'; J ts: ^^. :$^wt^ot, r^';j ^^c^:^^%MSi'!Lfit©^<k^^^:L-c^ i;^T^<75^~^)^. L^ -5-c, 7 y ^o^xu^Ly-c^^isa^i^^, r^(?jos, sp-^,. K. WbWffW^^^^, ^ojjCS^J: ^MaJ$£-?:'t%. L/^L, —te-7 y ^o^XU^L^^$$5Hl*)-C~^^^^^^owf:', y'- >^-b < - h ^ h - -y 7" i; y '^^atfAs T - ^U4^1U%M^L ^M. ^^^%^i ^rj:^"c^<bf^^J; < L^I^. 2 00 J; $ ^< - h ^ h - y 7"'; '^ ^^<i±, ^S^fit ^ ^, /, K r-^^-r, (i) ^^-^^-^^^'^-^-M ^^M-NLA'^^^^. ^211. FJ=HK. (1). ^^x, y--'^ F, H, J, K ff^^Wxm^WW^^, FJ>HK ^, FJ<HK r/£ ;h^'J^\ L/^L, F, H, J, K ff^h^h^^^i>, FJ=HK ^;h^'f^;?^o-e, O^IN ^!r- ^ OfM 'S^^:^^ ^ o-^ < ^.. III. 1^^^^^^^T^ffi^oJSI+ .$^t^%®)^t+^:^^[tit7^-70^^i?, ;:o7>/7^;5Mo:a^mL'ri^^ ff-W^&^. ^o^ffiito ?^9J ^W^^^(}, ^^ r^t>j o±r^^'-~^^j(Ai9<t i^-C^/6.. ^i^^^oSJ^^^-^ r^^'^j o^®^J:^'?®^-^<}:/{S%L, ^b^. -ISr^^o^ f^it^r^^°7 v ^br.fcb-0'ULfca?^!:, v-^^lEa^^MT';6^, %^co^-^^'^,. -^^^a^^.^o^^j:-?^^, ^(om^^^^^t^^, ^^LT, ^^fit^a^^iit^ /£^o-e, U~Fot+^:^'^te%-t%.. i. >m r^yj &^jfflL^^ffl^ ;^i|I^^^L-mt|t312|cDJ; 5^0-C', ^0{AM(D^J:^^T^t^^f"lt^ff$^ 98).
(4) m 47 ^ i ^. (^2^ A). 2-^. 22:. ^ ^, ?^''? J ®^ ^^ ^ ^~ y' - i>®^. wti^^x- ^ (o^mww^^ts:. ^. ^-h^tlW^-^-r'^^^^^^^. 7^ <}, G^jcy->>^?i9^^%o-c',. a (D G ^(D^^^^tc^^b^^i.^^. Pi ?. ^•N^^)^'^^^)/5.. -b-|. _Mi_Px_ £=£Z=EZ L, e. ?3 ^^). E; -y y^ Z; r^ t)j<7). P; W^-to^M GPi, ^. d^ (^. fff 1r Ii. M; ^-^< V Y-^ Px. ^ OS b^^^^^^^^-t (2) ^', p=p, ^ p=p, ^^, ^^w\ i^ (3). (D &. ®w. ® ma^w. U' H?4g|. II. x; ^f21^fAfi£;^6/r->>(7)+'L>. ^ G ^'CD^gl. /. i If I) 7 V—L.. ^b (4) ^c.^;6. \l-g-aY,. (3). _(l-g+b),. (4). EZ. '-p.. 83=- EZ 'rz. <,L, P,=PS^, ^/c^LX^, si^ss <h^^, NU-^M^^x.-C^. -T G Ajc:W;5^:H^^c^. ^l-O^^L-T:^^to$^^<,. <9, 7XTO^L ^^lW-oM'CT;^e^;S). 2. HfUJ ^IJfflL^ffl^. -eote%{M^j;-3. ^L-rw^-e^. ^ R^J o^^^^^^{/F^~t^^o^, it5|Hoj; $^N)^li;. r^j ^IJ^L^HJ. ^-e^/5. ^^W?^^^^^h^Q?ts:t), ^-eiW@^l. [^E^^m, ?-^j. (3)<i:TO^fo]r^^M -Pi, -P2, -Ps ^, ^^^^ ^n:^^i"]^^^^i. p,, p,, p, ^^,. ^ztbo^r^-^N^iiTO^^W/h^ fW^ftl^^r^W^M^^^, ^-^ ^^^M^^:^±o5f@o^rM7c$^%^&^rpim^^^.. ^M6Hl^fW^Ly-cM7(?^'C^%^, 0, A ^&^y~-i>^^ G 0^ £1 b A, B ^0 G ^O^g £2 ^^0 (5), (6) ^r.^%. P< Pi . PS. ^em 5g] (99).
(5) Journal of Hokkaido University of Education (Section II A). Vol. 22, No. 2. January 1972. _(l-xV(2gx+lg-lx)^. (5). _x^3lg-2gx-l2+lx). (6). '1-J3EZ~ 62=. ¥EZ. p. -^H^O^J: (5 ei^Ss ^/];^£^05g^—^r^?t$^, ^=^,2 o^t^ ei=£2 ^^-e. fc&oSA^L<, ^(DS^^^^l^ft^A.t^ Rtt)j o^iN^MSIUoj; 5^^^, 1214' ^lEtB^-^M-^PO^J: ^ R-^J (7)^®^<E|i^7c^O^^^L, ^^m^^^lN^^^Lt 1^.. ^Ot$^, m^j CD^®HIE^^X, ^^^, X^^6IE^.<i:^/fbL^i^o^~, -eoroi^^ ffl^^L, _b^®, T^So^^—^-t^o^', ^o^J^r/r'-^^Xi{i-3^^;t^^^i\ -:e ^{M^OJ; •y^L^^bh^. M7121^^ol^, A'I ^^oH/5^:^^A^ y h-tW, r^. ^J (Ot^-^^± (7) ^r/£;6.. g=-^(M,-^,). (7). {ML, I; Elf® 2^-^ ^ h Mo; O^jr.^ott^^-^ >/ h I?o; 0 ^r/W%gttX;tJ ^-C, (7) ^O^a^'P ^-t^^'^ffl^^^^^H, -^-(7)^^:^ ^1=^/4 ^^%0-C', 0^^' J:U? B ^fb43?^]-3f //4 0^^/5^V~-^^?%^ <1:^M^^'^^\ he-a:. °1. r? l-II-^l. 3B. ^iom (i) ^^itL-r, '^Qm^k^^m^^^^-v ^v-'y-7}) ^ ^^m.isb, ^oHt9|g]oj;. $^;5, FJ>HK ts:(0^^-^-^mW^mW-^-^^. BL, ^M^^'P^^t^lSM jS.m^^L< F=f=H=K^^^. fc, ^6|g]0 Pi t^l^Ps O^M^^^) r^^'^J o^^^x--6^^^, ^ogl^T^Hb ^^k^iQm^m^ts:^, m^ojA^ 2ff^%-^L-r<^. A ^^i^-^m^w^^^^b, Pi ? A ^jCta^p^%o^^]^^-^%^^[|t]jgo|3p^^^1-%^, ^o^-?, -Uzrtx.-C EM a, h ff^^tc^b, A^r^^<D-&-^ 'y h/SMlt, ?^' ^J ^M 11 00 J: 5 ^y-c^tj(OT, ijl^-e-y '^ h^J;^^^^.^!/^). L/^L, ^(D^-^ 'y h^-J;-6/^^W^7^0-f:-,fef5, ^(^^S^N^^^^i^^l-J: 5 ^~t^t^'^%. i^-c, ^8 m^^ iiBo^^^-j: ^, ^'~^r^^%^a^^N-t/5^^^ &^.. m^^W^^^/r~-i>i'W^U±, ^03®?;^^^, ^-Sr^L^il ^->>'S^ <-) 2y~- i>^ff^ 2 f^jt^ j; < , 2 y'-^^J; i; 4 ^-- ^•%^it) 2 ?j^ J; I \. (i) iv->% ^\\^i, Msm^^i^ ^ w^^~~^^:?{}, ft!l<7)3{@^^g^M^^t. ^t^mm?^^^.. (2) 2T-y^ m^, F, H tW^T-^^^, ftJ1^2^?^g^L^L^. (3) 4^--^ m^t, F, H, K, 7^^^-^^^^, m^?^^-t^\ <K^, i^-'^^^^-x., ^-^^x>ii-6fi:fi^ ^ <]i-r%<^, ^8[2]rj;t), S[t^firj;^wt. (100).
(6) 22-. T - ^ ® |a. 1 2 3 4 5 6. TO 47 ^ 1 ^. (^ 2 ^ A). 2^-. ^^. F-H,. R-R. F-L. K-R. F'K,. R-R. F-R,. H-R. .F-R,. J-.R. tS ^ J; % ^c -h ^. + + + + + +. K-R. F-R,. / / /. +. /. / /. +. -e'. / /. ^ H<IJ;%?^. + + + + + +. /. / / /. +. / / /. / /. / / / / / /. / +. ^o^ogu^r^, M 11 ^1^^-e-^ vhrj: ^tc^^t,. ^h^^cts:^. •teof^fi^v'-^^M^^^^^^Ii^M^^^ 7-c;b^^L< ,£?^0-0, N^fit^: L^^'^^^^l3:^^-^. ht^^-r:-, ^o^d^-m l ^-^^•{^•t^^^Tj: ^\ ^C, 2 T - >%^^ -6 ^, H 8 ft] ^ ? (9 om^te ^ ^^, ^ ~ '^fel. :oa^^i?H' i. |03Jg^:fx-?, ^M^f504]?^T^;60^', lt8^1<h^ll 0o^ofM^a§^ 1^04^'IEX^ ^X7r.L^&^. -^ o ^^'yJHJ^oT^^ 4)0^1 S:^ 3. ia^^ti^l2til^J: 5^;6. FJ-RR= {R+AR+AR'} (7?+JJ?-J7?/) -R^'ZRAR FR-KR=R{R^AR+AR') -R{R-AR+AR') =2RAR. :^'^ ^ , 7" I; '-^ >>0. (8) (9). ^ ^ ^%M®M{itota^-^<^o J; ^ r^^T. ^R; ^ ^^m^t^i ot^;b^yc;&^I:L/c'®M®^ILfjto^<b;ft AR'; ^ (; ^ - ^ y H;: J: ^ ^^^^^/-c&^^ C^'SMS^Lfito^fU R; y-'^-^. ^V^^oMMS^fit. U$E?a-? i^z-r^ /5 @l^®in;fit^^ L^) t^4^-^^0^-T:^-;tX^^,. fr - i> cr> ^. H. /. K. ^ ^ £ % -^ ^ ^. ^^Mijt 9 |Uo j; $ ^ 1 ?B ^ OM^.^^. ^:L^^<, ^oa^^r^Stffig^^ v h^j;^^^^r^^r;t^x^%^,. ^- ^V \~^l^tc^h^. 2^0 J; $ r /£ ^. ^, ^, /, ^ ^-^^^'^L. F= {R+AR+AR'), H= {R-AR-AR'}, J= ^R+AR-AR'}, K= {R-AR^-AR'-) b^it1-^<D^,. !-hb^ (1) ^i-^A-t^b, (10) ^^;6. FJ-HK= {R+AR+AR'} {R+AR-AR') - {R-AR-AR') {R-AR+AR') =^RAR. (10) ^o^o^S^, ^-^ y v^^^^-W^ht^^ ^^-c^. ?Sr J; ^MMS^fig ^. ^L^o^U%"]'tB^^. 7j<TOr^i^^o 1c < m^iNWTO 0"MX ?3 Uj-t ^ ^ ^^' ^ /6.. <^? b ts. ^<^^, M 13 00 J: $ r^tf o ^. ^130. ig^^r^M Pi (it 5 m, n 6 [g) ^|^o ^;jn ^UEI ^~^h, ^-£'(9r^Stg^<):^l:^-&"^ -Y h T^;JB^t), S^^^^^^offii^^u.^^^T. ^. ^-(Dmww^-t^^^mwt^< ?2 ^riij< ^^^^^^^^^Msin^^jgr^-t %.. (.101).
(7) Journal of Hokkaido University of Education (Section II A). Vol. 22, No. 2. January 1972. ?fi;j ^—^r^ll^i^^:^, ^o^^-o^CH^^^^^oRil^^^:^^, ^^z^A ^w^^&^^wts:ms^&^, ^r^^^L<w%Lfcw^^ • -7"-^>/2^-^, -:e o^l1, ^^mMi4@oj: 5^^^-t--6. J:-^^, ^'-^^^^^^X^^^o+^rXi'i^^^. TO', ^-^'-^O^A^^L< ^ (5^fi?aiJ^J^O^@^^C^L\ ^±.<D^h^m^^h, ^+>/7^^?JU%-t%^^^S/J^J+^^^^.^^0^!±i^^L-f^,. ^o^^^-^.. (l) ?-^J ^, W^- r^'^J -r:^^x^^t^\ (2) ?-^j ^, N^@]^ r^'??j ^, L^^, —-ft^tf®, ^-M^^-3^^0.. (3) ?-£ ^ j ±rXiii%^"^^N—?t^^~^ ^, £CT^o?-^oiEX^:f^<1:^™ ^x^\ (4) ?^J rt;b%^? .(S[t^5, 7j^^, ES^-^-^^h, BL, ?±-m^"e^-r. <>j;<, ^5 mo(3)oto ^mj^<o^b) <t±, r^^j o41^-c'^^^^'i^^i\ (5) y'-^&^4 y~':>^:t^j:i^, 2v--^'B^^t^, ^-^^jlt'i^^^r^'^f;-!^.. ^(D5^ J; i?, ^5(30 Pg (DfAg^S ^^J O^U^< ^J: $^^{/FL^^O^, i>^ 'y. ^W^^^h L-m^fW^^.. iv. -eo?oa? 1. g§CTO®m&l£< Ltc^ )?^M^JA < L^c^, rs^' ^ J ^ 1 ;? ^^~-& - ^ '^ H^ J; /6 r^^' ^ j o^^^^^-. <^%o^, ^-<DW^^^<-t^t^^ rag^j ^^: <-tH^'^jt^® < ^%^^ rs^'(?j ^2M^-t^^h^^hh, -eo:s<>w^f±i)^m'i5H]^, lu^z^o r^^'^j ^ {^L-ri^.. ^o^, ^+^7°^^luf^iJ^^^iI±S^-^^, -CoN^M-t^^^^WS^, iitr^Hj-t^^^^^/6. ^<^ij^^y:sT^??, 2^:0 r^^-^j ^%^^^^, 2y'^<^4v-^^T^;i^~J;i\ ^-eFnTOc^am, ^M^^?^Ao^^^, ^H^?^J L7-cS^N^^C%^l^ ^ <i:'^-^-6^, ^ 16 00 J: 5^m^^:^^-^l{@^?(5 b^yL &. ^. ± a. Ac p. ^-. I \ T p ® ® m Stf 0. 3. i. ^ 16-1 D 16-212]. © % S tf '). ^ ® M^-W a is m (102).
(8) : 22:. TO 47 ^ 1 ^. (^2^ A). •2^-. ~^b, -^0?^<7)N^^N r^l^^J 0^^6^@%$^-Cl^O-G'^%^^'?5 ^^%^, ^^W ^ ?-^j ^^L-c^i^^', m^ A, B ^^^)%@Jt|f:S^^II&t-6©^, A, B ^-m^0^. ^^p^'^^^/h-^^^f^ ^^^-C^^^^^l^^V), A, B ^:?%gigM^m, ^==6,^ P, RB=afl-P bts:1}, A, B^/5 ?f^J ^^^tr^, ^ 16 |gloT[U<7) j; $ ^, A, B re-f. 10} (Dt^^-h^i:)^W-W^-^± dx Wt^^, W\^^-, ;fe?^T%^ ^-C^%. dx<DR^ (11) ^'^;b$;^%.. (11). dx=L-^/L2-x2=^. ^-, L ^JtL ^ ^^4^ (^J 1/1000 UT) 7^0^, ^ dW^^S^/S. /?-5?r-3^-m±tBoJ; 5^^--^ ^^(5lli@<7)i+t^n^[^^-c^%o^'[3R^^^l\ tV-c, <^M^. ?^W^'?^-fht^^^, ^ - ^ v h ^ J; ^ ^^^^ ^-f^ff\ 2^:0 ?^j ^%A^M^-r^%^^', ±tao. 1 M^) bW, ^9 lil^Ml2 IUOJ: 5^^-^^M^^^ ^, ^h^h^ r^j ^^i^^aij%"Tt^^'^>^. ^^^'^ MT^) ^ <}i^, ^M^^ 16 [gl<7) A, B ^U^^^)^) ^^-(t,. ^-^ rggu^j 0^^^,^;^^^%^^, ^f^^^^^figo IEX^^tt/5 &^ff^ ^. <^r., N r^^'^J ^^-f-'^^^^^^-^t^'BMS^LO^ <bt^'SM6f)^-7°7^^-ti:-c^^t-5^^^^^^-^t^-T ,5 ^, .'KD^t^-^^^^^ja^-^^oj; ^c^^-r.. R; v'-^sg^^^MMfeKfit (N^f^a^&i;. 17-1 ^g^l;J:&ni)Stfl)(7)^^^. ^T ^-5 H^g^fif ^ ^ LI-). 17-2 -6-^ >- H^J: & ". 17-3 ^ia^t;j:s^sifi)o^^A. AR; w ?^J ^Slt^J; <3'C^^^^^:^^^C^'®. 17-4 ^-/'> H^J; i ". mw^m (17-1 m\. nm. ^R'; m ?-^J ^^-^ v v^^^ft^A.tdk^^. ctcm^w^m^ (17-2 no.. dR; ^ ?~^J ^Slt^rJ; ^•^tc.^A.f^&^Ct^ dR';. ^^{ito^<La. (17-3^1).. ?f??j ff^-^ >-^rJ;-)X^^^^^^^^C^'SMS^{ito^{b£ (17-40).. ^-^Hlisgioj; $r^M -P ^An-b;6^, rsg^'^j ^Hi7[gioj; $r^^^>. ^;h^2v ->>fe^M5 ^S*^)^^^-^oa^.^^^M3^0J; $^435(9 ,1:^^. ^(0^, 2^4 r^^J; 5^^.,^, ^-T - h^ \--^-f}) y ^(7)M^^^^18|U^'^L'r^^.. Ff-RR= (R+^R+^R') (R+dR-dR') -R2= ^R+dR)R+ {AR'-dR')R. (12) FR-K'R-={R^AR^ARI)R-{R-dR+dRI}R={AR+dR)R+{AR'-dRI)R. (13) y-^o 1 2 3 4. M^^r. F-F' R-R F-J' R-R F-R H'-R F-R K'-R. L;^J;;£>fcb^ + + + +. + +. / /. /. /. / / / /. -&-. + + + +. ^v }>ii .^^t •-^^. +. / / (103). / / +. / / / /. ^ (R+4RJrdRI){R+dR+dR1), RR (,R+AR+ARI){R+dR-dR1), RR (^R+JR+JR')R, (^R-dR-dR')R {.R+AR+AR')R, <iR-dR+dR')R.
(9) Journal of Hokkaido University of Education (Section II A). Vol. 22, No. 2. (12), (13) ^^, AR'=dR' f^b. MIJ^"T^ ^ ^ ^ ^^ LTl ^. fc, 4 y'-^ro^-c^x-'c. January 1972. m'&'l.. +AR. +AR'. ^^b, W ?f»9j <D^)^ F, H. ^•fr±. ^ffll^^ ?^'(9J ^^, ^/,. +SR. BiJ-£'T. J'. H"'-AR'. -dR'. H' b Ff, ]' b F', K' 03® ^. is m. ff^i}, ^(D!Lb^h~Si~^^tSi/r~. -AR'. m i^m -^oa^^:^ 3x3 0 9 M ^ ^^-t-6^, AR'=dR' ^^^L-CN^"Tt^^&^^^^ 1. ^-e. ^)(9, ^W (14) ^'i^b^;h^. FJ'-HK'= {R+AR^AR') {R+dR-dR') - {R-AR-AR'} ^R-dR+dR'). (14). =2{AR+dR)R+2{AR'-dR')R ^^^^j^-t/6 -7 D y ^O^^^^M 19 ISl^^L^. t tc., W ?t t> j r^T'^) -& - ^ '^ h ^ j; ^ ^^^ ^ ^ r^^'. \ V. (^J r^irf^-e-^ >/ho^^^n, ^^^S;^^^^:HU/?^^>^. ^L< AR'^dR' ^^^ff., W^WM^ ?^J 0{A|. A, B o41'U>^$N;^-^-^-^ ^ h^^i/t'x:^C^^%U^H-&-. ^ v h^i^^fM^: r^tf^j t^o^lr^bfUL-r, -^^z WO r3&^' t) J ^c:b t T ^ ^ ^ ^ ^ , -B^^ ^' ^ dR' ^~. ^9, w, ^ r^^~(?j o^^^^77^o^^^^-r%^ ^^^. ~^m^&^. L^oT, ?k?^.WW ?^J OfAi. (D ims.m (D? +S ©BiJSli'') (D%./^ ©^S (f). O^^^-O^^^^^^J; $r^!±!^5^?^^'^^\ L/^L, ^X. ^^^Ml- k, ^ 20-1 ^0 ^ $ rmw^^wo^-t-^-r^ ^'t-r, ^^^^20-2^015 r-&-^ y h m ^^^-CM^H,. 20-1 El. N ?-^J ^f^L-T:IEB^^MN^'^"T^r^'5L, 7J^^?. 20-2 [sg. ^^^^WWUot^wm^bt^^o^, ^^^{±!^o^f/F^^^-3'r^, Mtt^± i^'^HW^, ?^W^X^r?-<-c^<-r^^j; ^, |u, ^ r^^'^J 07j^^^J: %. ^;b^^L< T-5^^/6. 2. JS.O^;?M;I?0^. ^oN^^^-a-, ^.^^m-t^^wi, -eH-e'^o^^diT^ $^T;M~J;^ ?^, ^wj^o{@-^ rsgi'-f^j ^i^T'^^ffl L, N?iil%L^o^fF;hXJ:i\ {QL, m^t^. —j I—:. t^ ?^J o4^^^< %J; 5r^t+t'%^^^^);6.. —_1 i__.. BiJ. I I. 21[UMB^2^L^(D-C, 2^0 r^^i?J ^. 8E. TV-. {^L, ?^%^LTl^o-Trtu^oag^t?^BJt. ~~! i~'. ^, ^22 0M^4^L^O^~, 4^:0 ^^'^J. SS2. ^^L^i^^, ^o^, r^tf^j o^'i^^'^ai^. ^x-^y-^^i^^-rt'S). m^, m^^^^^v. -AO—gR^,|3/N9^ 5H-T, r^^J Oflfi)^^^:^^. L^. ^<r>m^^ 4.^:0 r^i'^J ^^^^^-^--C, -^^. ^^^M^BtH-rs. (104). r. sss. L. ^. —^. 21 m. m \sk.
(10) ro 47 ^ i ^. (^2^ A). :2Ji. •22.. -fe-frA. .+AR. \. (+dAR. \,. ^^. I (D m. ©^. (3)BU-. -X.. &$(A'l). ^. -z-. ®^-^. ©/fe/&, hl^-fz^[o]ffl£(f1). © m • HW. (D a • ^. ©f^ • & ". © % +s $ ^ ^. It 25 @. (9)$t;P)^t.^. © m • -k ". -^. (D±T. Bu^^fflSl.P). ^22 gl. ®£(f1)^^^. U±^%gm^^'^i±i^^fF-t^i, ^ -f v 7^oau%^ "T t^ -e & -6.. 3. 4^7EW??^ ^^-r^^/6^.co?S-®)^, ^,H^^°. H%^oM^?, ±T, £^i, tut;. ^^(D^^wwh 4:?m^. ^1-^. ;IO:?NR^, L^<>, IE5t. ^.ta^'t, ^:L^{?^^5 ^. t^t^w^^\. ^, H 23 00 J; 5^-^ffi^^^-^^. ^^. ;:;?M5|ilo^i?o?^J O^fn]^ 90°-f C? L-C 2 ^^M^l^ ^ CD (D±T, ilUf^[o]fflS^'1) &/&, ,tal:<l^[o]^S^'l). hf^m^W^^^^, ^22|U(7)(D. ^L^m^^ r^j ^'^"T (^. L^I) ^[^Br^r"]^?N%L, (2) (D;CT7 l/-A±^^l^l^^^(9j. F-A ^f^7 1/-A. 'e^CT^o:^??N%LJ; 5 ^. +S5^W. i.$ ^(D-e^.. ;23E] H<Dm^, M 500 Pi ^ Ps 0^5^ ^tu^f"]OW{@^g!)< h, ^W®o ?^J ^^ol^^^L^^ffi^^, P, ^ P, <D ^r^^CT^M@^^N)^^m"e^;6. J;^-c, ^o^^l^^^^^^^'t^^^, H24|^ oj;5^, ^4:l'?iiT2^:o^(7)^rf^^, L^^, ^^%^^@l^^-^^^^^i ^Ll\ <>L, N^^lf§^^M^'%IJ%T%^'^, 2^:^^0ta]^4i^^^f3-^5/^^^^, ^^ ^r> ^??$-?^^\ ^(OJ: 5^^^-H, ^+ y-7°^om^.^ 1o ^~&M^, m'ite^^^ {105-).
(11) Vol. 22, No. 2. Journal of Hokkaido University of Education (Section II A). January 1972. ^^^>(0^, ^^<Dt^^±mm^^^ff\ ^T'^23[Uo(Do ?-£(;J ^^^^^t^-Lt ^-6.. ^<7)tHisrj; (9, ^o r^»;j (DnuiteA^^c^^^, tu^:^>^ ^^^L^|S(^^-^ ^ h^. l^t^^of^ (M ll MM) ^Mx^^w^-r^-^, (Do ^??J ^ttI^g^X ^/^J; 5^^-^^.. fc, ^o R^^J ^^M^]A^J^T^)^T^]^^NJ^^^. R. K. % ©-e, M 25 nio^ao j; 5 r^-^-^to '9, -^^r£^^. ff-M^b^ b, t^^±^ 25 IUtTWaoJ: $ ^<bL, £^i0 K. t^^tW^^^. ^o m^;j ^tt£^i^o^^r,n±. R H. at 26 is]. ;^j o4}^j: (9£{pjj^^?y?, -^o^^^ r^'9j offi^^fS. ^±^< L, -^m^ r^j ^^jEtg^^m, tl^., ^-L^!SlW:|S^J^< L-^^^ ^o Dt';j ^^Sia^rj:^S^cfito^<ba AR Oft&^-fiN^J^^-M: AH b, ffi SteJ:/6^<k:a dAR o3^-fbfl:^Ni^r^;£T^.. J;^T. ^So. :25mo^<b:B:^^'c^iEX^tBW. MMe^^^-t-^rmE, t^-r'-6^^^X^L X&^. <lh^2 ^-^^^^^bSW^^ JF, RR <Dim^^S.^^~L^ts:<, ^? (16) ^, -7 1; y i>(D^.^^ 26 |U£(0 J; 5 r^C (9 NCTt^'^) % . FJ-RR= {R+AR+AH-dAR) {R+AR-AH+dAR-) -RZ=2RAR (16) 4y~->^-e^, JF, HK oiM^H^-^-e^, -^/?z^ (17) ^^', 7';^^^&^.^^. • 26 TOO 15^^^ ?"TtB^ ^ . FJ- HK= {R + AR + AH- dAR~) {R + AR - AH'+ dAR) (7? -AR+JH+ dAR) {R-AR-AH- dAR~) = ^RAR. ®(D ?^~';J ?i|5:^£^;??T/5^^^;6^, !-(02tl^^ ?^'9J ^7j<TO±^-^/b^-t^O^%^^ ?f??J o_b~r^^±/r-^^:^^'&^it^^'\ SltSr. ^2@ix (mis^^^£^i^^) M-<'r?/6^'^^^^. ^o ?^' ;9 J (Dr&^^AMSA^, ^ 25 0o j; $ ^XTOii^c ;^"e, ^;h^.tfj^Wto-5^(?;b^^, ^25[g)r^ 7C $ H;5 <7)^R-$ ;h-0 ^ .. H^, M 27 [g]0±(DJ: $nall|5^^J; o-rlU^^C^^ ^C-c^;b ^'i^dDo R^J ^, ^ f^^lu^^^in^^M 27|UoT<7^^oj: $^»L^T/6. ^olU^tfiA^^ ^i^^^^^J;'6^<bAoiEX^ (16) ^[^ C^-^ ';, A ^l"l^^rj;-5lg^^^o^<bt, ^9' ^?^rj;%^<b [, dAs ^w^^l^ltfi-r:^^. ^o^o^'-^oa ^.i^m, 2 v-'^^i^^^i^at QM/, 7?7? 01% {9 L^ < , -^^^ (18) ^^, 7 '; y >>OM^^ttM 28 [U 0£^-^)%.. u. QW-RR={R+As+AH-dAs){R+A£-AH+dA£~)-R^2AeR itc, 4y-'^jS^^ 0^, 5£/Ol®i9oa^^^L^^^<, -kh^ (19) ^-,. M^^M 28 [g] 0^-^ ;6. QW-SU={R-^As+AH-dAe){R+As-AH^dAs). {106). (17).
(12) •22:. TO 47 ^ 1 J!. (^ 2 ^ A). •2-^-. - (7?-Je+J^+rfJe) (,R-As-AH-dA€) =4Je7? (19). -H, ^ts. ^ 0^^^4{§^^^^l^^^J%^t^ ^ ^^^^/-c.. ^±.0^h^b,. ^. V.. j^±oaijra^s<^^, n 15 m. =4-. 5HB. |—90 ~f< 90-. b ^ 21 [gl^:W ^ ^ ^ y 7°t) m. \-^-l7Q >)< 170—>|. T". iL. ^ma^^fpL, -;eom±o. •290, HtSO^^tJ; 5^^^. LO. ^ 10kg O^S^±Tttl^^f^]. 1--. ^^ ^ ^ i/tt^', ^ - ^ - CD^^ 100. 29 in. m^Tr.-ti 5 ^»L^,^L^. 30 [K]. ^^1^4^^'^^. ^<7)^0£{|IJ^ 210^HJj^-, fu^2^0f. F^-^< NC^M-^, ^o^^^5F.^fiI^^;^/h.'c^. (9 , ^± 13^ 0|fi^^^®)T ^ ff\. ^r^^-l^rm 8% ^^j. ^o.S^oWrM^o^'M^^, ^(D^-V 'y-y^m :L^C^l\ ±tc, ±T^|o]r^M^x.^t, tu^^fo]. (Of) b L-^m^h^W^^m^ P ^^ i9 , T- ^0? f5 ^;?5n:0t^/? ^ IE%^^'5 ^ b ^. ^t) 1 -^(D ^+^7 ^IJ^ ^. ±T ^ 1 2 3 4 5 6 7 8 9. 100 100 100 93 91 94 87 90 91. BUf^^?X-. 0T^ 0 0 0 0 0 0 0 0 0. W ^ tl 93 93 106 100 105 97 93 95 93. £19 2^:®^^^7^1J% ±T^Ao 3r ^ 0 0 0 0 0 0 0 0 0. 3TS 1 (107). ±T ^ 88 100 118 100 120 115 125 115 91. BUf^X0'^ ^. 8 2 13 5 - 5. 15 5 - 6. w \^ 1} 107 108 105 85 100 100 98 98 98. _bT^ 0^^ -10 -12. -12. 0 - 5. 0 12 12 12.
(13) Vol. 22, No. 2. Journal of Hokkaido University of Education (Section II A). January 1972. t^c, it4^;&tijo^mtni5[gi©m *0 ?^J ^{^^ L^^ffi^O, L/^^, 1£M?7°7;^-^;5J; 5^-/r->>^l@^^ <> oo^:H:-^;6^, rp^^<, t^-c. ^^O^XU%^ L^jt^'t^. H^. -^^ -6. Uii^ 4 T- ^S^'N^^ 0 f- ^ -6. ^, 2 /r-^r^i^^^lL^-^. U±0 ^ b J; ^ , ^ ^ ^ 7°t>0?IIJ%^d 1. omrML^ 1^0 r^tf^j ^{^jE§-t^;. i^^^lt^J; <, L^,M?L^. ^. t-fo, mw^iww^^^& ^. ^S 3. zrefit^ ^•&^.. <>, ^-^ox^^^^^i^^^^/ta^-^t?. ^^ 'y^f >%b;h^o^-BM^t%.. ^X 3^1 ismo^yj^'^.. gri, 2^21^0^)^?^, ^®<^i. 1) ^EBX^ (1965) Wtl^, lU^lt, 87-89 2) ^?- (1963) m^, 28:. {108). -t.
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