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(1)[Science Reports. On. Growth. the. NationalUniversity,. Yokohama. of the. See.. Flake. o壬Snow. i No.. 2, 1953]. Grallpel. and. By. Ch6ji班agorLO Abstract Ⅰt is considered the. and pal. Some t:ham. flakes,. and. of. for. do. has not. grow. but. that. by. the. by. the. rrlutual. of. for the. Considerations. drop. rain. the. Recently,. formation. crystals. or. process. is likely. alone,. ･of. Dr.甘ougbton1). two. processes,. the. collision. to. is required.. .accretion. of ice crystals.. the. growth. for. snow且akes, some. is two. ln. a. fall the. as. not a. so. flake. data. the. and. climate,. effect: of. called. temperature. a. Sapporo. on. the. and. it was. flake.. Some. Snow. the. Crystals not. as. form. snow. a. as. made. fall. velocity. and. Mt.. of. snow. The. shape. Tokacbi,. of and. Observatory,. used.. begin. individual. as. quantitatively process.. are. the. of. accretion. arld. form. to. crystal been. acting. combination snow 丘ake. the. also. flakes. format:ion. size,. of unlike but some. Meteorological. were. snow. which. Rake,. snow. a. as. Bergeron･Findeisen. has. University. university,. severely. cluster,. the. as. by. at. a. by. graupel. such. Temperatt)re cold. with. investigate,. to. paper. obtained from. snow. a. to. crystals. investigation. Hokkaido. at. obtained. size,. ice. Of. computations,. kilometers. 壱2.. to. the. were. meteorological. wbicb. that. of. of. systematic. of this snow. particles. optimum. clolld particles. no. pnrpose. requisite. possible, data. main. But. that. for. made,. the. neither. of cloud. clumplng. of super･cooled. BrauPeln. It is the. the. as. such. by. or. made.. that. out. drops. rain. snow. Introduction. collision. produce. were. that. estimations were. from. produced. of -graupel. pointed. the. nor. be. snow. snowーcrystals. with. process. the. as. cr･ystals. Quantitative. collision. may. i 1.. ice. fall.. of. snow. princi･. observed 且akes is. It appears. sizes.. fhkes. snow. type. crystal. between. collision. collision. same. their. relationwith. velocities by of snow且akes. sizeable. a. of the. the. custoITlarily of large snow. fall velocity. the. crystals. different. of growth. found. that. of the. Bakes. SnOW. are. graupeln. with. drops. for皿. to. cr如tals. particles. of rain. show. any. snow. of. cloud. snow. scarecely. of their. result. the. of sirlgle. 凸akes,. snow. rate. that. clumping. cooled formation. measurements. larger. Bakes. the. of super. collision. mecbanisms. size.. that. to. very. grow. often. crystals. flakes. observed It appears. is remarkable..

(2) 1 is. Fig. 凸akes. a. plot. were. On. the. of the. size. In畠g.. observation.. 1,. Snow. Flake. one. by. the. that. sees. Graupel. and. for. at. ground. is_re'presented. of snowflakes. of. of snowflakes. the. on. observed. Growth. 19. temperature. air. Sapporo. which 1950. The. December. in. determined. diameter. maximum. at. of largest. snow且akes. size. snow. size. by. were. eye. observed. S U. 5. I i. 雷雲. ○ L. iL/｡墨室三 ⊂ユ. ￠. L3-. 萱薫;ij >く q. +. 三. ⊂〕. o#｡. l. 1. 0. 0 0. 十2. AIR Fig. at. 1. which. the. ON. TEMPERATURE. Relation. between. snow丑akes. -4. -2. the were. -8. -6. THE. IN. GROUND. size of snow丘akes. -1O. oC. air temperature. and. observed.. 3000. 2500. ct;ヨ芸…荒ま苦言吾デc9i;oき孟,9rOW. ∽ ⊂ヒ lJJ. L-tJ. 2000. :≡. ≡. 1500. しJ. ⊂⊃. tc?. ヒ1000. tO. be9',”. Cr9Stdls. =⊃. form. Clurnp. snowデl屯kes･. ト _+. i. 500. 十2. 0. ,. -10. 15 A]R. Fig.. 2. observed.. Vertical. distribution. -15. TEMPERATURE of air. temperature. IN on. -25. -20. 9. Dec.. oC when. snow. 点akes. were.

(3) 20. at. C. Magono. temperature. air. 免akes no. shrank. about:. to partialmeltirlg,. owing. snow鮎kes. were. _below -10oC. On 9 December ゴalling ざSnOW. snow. were. his. dendritic. tothe have. form. is supposed. air. begun. to. Tbe were. measurements carried. chie丑y. Fall. velocity. It is di用cult 8.akes. snow. neously drical. box,. flakes. are. shapes. when. illuminated by. produced is. snow丑ake. by. in丘g. of. snow. snow. their. employed. Several 4. stroboscopic. and丘g.. 5.. crystals. or. crystals. in丘g. plotted neously black marks represent proportionally be. seen. that. to the. the. the. paper. this. and 8.akes. the. the. auther. a. cylin･. Falling. snow. diffused. by. illumination,. images,. we. can. calculate. irregular,. were. a. 6f the. magni丘cation. intervals. small. simulta･. observed fall into. of dark丘eld the. or. crystals reason,. cylindrical box. successive. one. falling. a. snow且akes. practical. snow. of. pictures, in. observed 6. 'Ⅳbite. dependency. have. the. value.. In these. or且akes. while. would. interval.. 1From. When. photographs. nlakes. the. means. photographed. between two. mean. snow. time. a. within. By. the interval and photograph the fail velocit:y of the snowflakes. author. sec･. 3,. Snow. in. opened. O･01. per. stlCCeSSively. grown. in. It. 2.. snow且akes.. small. in丘g.. shown. as. discharge.. electric. alld. of sillgle For observation.. eye. is. once. distri･. in丘g.. used. to. grow. flakes. fall velocities.. camera. fbkes. snow. and. vertical. 月.akes. snow. cloud. Nakaya. have. 甲ould. fall velocity. their. with. the. is represented. the. needle. higher,. The. day. the. of. crystals. -18oC.. snow. of. crystals. camera. stroboscopic. their. svow. state. snow. 也, and. the. Prof.. and. observed,. velocity. the. measure. types,. -loo°, form. day.. Fall. of single. falling. a. the. employed. light. in. to. on. crystals. this. on. out. 壱3.. a). h. -14oC this. 15. Most. became. that. not. to. 8akes.. numerous.. to 1800m, and of 2400m he)'ght of about 1300m. for the fall velocity of. a. at. 12. 9 h. from. temperature. between at. can. spatialdendritic. became. snow. than. snow丑akes. snow. ascertained. dendritic. the. grow. the. experimentally. height. a. or. air. snow丑akes. temperature. that. fal1ir)蛋 from. As. temperatures. at. the. of. plane. that. form. to. dendritic. temperature,. temperatures. fall continued. snow. all clumped. rearely.. attached. colleagues2). bution. the. were. observed. particles. heavy. a. were. crystals. Crystals. type. 1950,. lower. at. and. is supposed ･It. observed.. freezing. the. above. and. -1oC,. by. in detail,. sees,. The. state.. this method. marks. The. dimension. represent. of fall velocities of. on. the shape. are. shown. and. motion. fall velocity and in March 1951, are single. dimension snow. 且akes. and. crystals. of. the. crystals. the. snow. sizes. is. of. simulta･. crystals,. marks or. shape. is. 且akes. extroadinary. and. plotted It. may at.

(4) On. the Growth. FLAKE. SNOW. FALLING. of. Snow. Flake. Graupel. and. 21. IN. STATE. ￣丁＼㌔＼. C?,. ////. ｢/,,n＼＼:､ i JAプ. 20CM. /. /. /. /. ＼､. //. <､. -ー〝 0.01 SEC. + ＼＼＼＼∪/// ＼. ＼. ＼. ＼. ＼. N[ED止. ＼ /. GAP. メ. DARK BACKGROUND ∫. I. O｢. ∫. A. V枯W. 72x48xlO. ∫. I. 也. A. ｢忙しD. I. 〟. ∫ ∫ ∫ ∫ ∫. ＼. MM3. CAMERA. Fi,gi 3 Appar,at畔モo Lower:触ure曲ovs. the. Ofミsingle, ran野く′. marks. o∇era､.wide. the. sno町CryStals･ range_. 耳alこ声S an′d partially. snow. photograph. state.. may･ミbe. iJn crystal. or. snow凸akes･. small. duf!. form.. tO. particles,L五ir1Other. the. of･ rimeトOn. the. Fall. The. よs. velocity. large. large. relatively. Was. ollt. from. flakes. 10. h. to. in. the. crystals･. and. wereⅥ. rimed.,,. fallh琴. of. the. scatter､ shape. flakes The. snow. of were､. all. in飢1enCe. Of. alrso remarkabl'e.. snowflakes. of large snowぬkes The reported.3) relation snow. snpw. vords,. is easily. fall velocity. <previously. carried. of. fall velocityL. The. variety. These. vith_ cloud. b). the. in. and触kes. s芦Ction.. assp,ciated grade. crystals､. hqriJzontal. between in. is shown. 14 h 9 December. by measured fall velocity. 卓g. 7.. These 1950.. The. a. stop and. lneaSurementS. black. dots. show. watch size Were. rimed. of.

(5) C. Magono. 22. 4-A Snow type,. fa11ing. ingly, lng. of. plane 且utter-. their 'planes. kept. be･. hori2:Ontally.. A. O･OI snow. s一iding.. sec･. in falling. crystals. 4-C. x2 crystal, at the rate 90O. rotating right. snow. snow. small. per. of. views. 4-B. x3. crystals. Side. 4. Fig.. Lower. Rake. is. A. snoⅥr. spatial. type.. state. 4-D. x3. crystal. of. A tbick. snow. plate. x2. crystal type.. of.

(6) On. Fig.. 5-A A. verted 1ng. x. cone. its top. type,. Side. 5. 2. flake. snow. 5-ち of. in-. keep･. downwards.. A. x. cone. its. downwards.. of. and. in. snow且akes. 2. type,. heavier. Flake. of′Snow. views. 丘ake. snow. verted ing. Growth. the. 5-C of. in･. keep･ part. A late. snow且ake type.. Graupel. falling. 23. state.. 5-D. x3. of tabu･. Snow perimeters ln.. x2. 且akes are. whose. turned.

(7) 24. C. Magono. Z20. I･. 句 200. J,tJ Q. 琵. 守. O.I. 琶180. I'′･卓ぜ. ≡ ⊂). ≡. y△●†4･サ. †60. +J. <t11√V QdbI. ゝ亡. くて. 亡140. 丘も. I. 汀Y. ⊂⊃. ,■′. J(. ≡ く‡. ≠⊥Y. ○. 貞12O トー. qし. pc[ dry. ○つ. 'ト.. >⊂ヒ:. ;. O[tク. 100. Iy/ て:T/. ⊂> Z く′つ. ○. LZ>0片. 80. し_. 亀. O. 井. ⊂). >. WHITEMARK-SINGL昏二畠中vJCRYSTAL. (I. トー. Q. 二ご〒_. 60. 8. BLAC. _.+. KMARK. sNOW￣FLAt(ど. +J. >. 40. ゴ ≡. i).}､. さ. 20. 4. 2. DIM【NSION. MAXIMUM CRISTAL Fig. やarious. 6. Shape. and. sizes ob岳erved. FLAKE. AND. fail velocity by. 6. of. snow. photographing.. crystals. 10. 8 0F. SNOW. IN. MM. and. small. sr)ow. 12. 且akes. of.

(8) On. u. Growth. the. of Snow. Flake. 25. Graupe1. and. 2.5. e魯e. +lJ. (ノ). ＼ = _I-一一一一--. ≡. I-----一. ?.0. ■-. I //ー. /. 丘A. J■. ++. l//. 二ヒ亡. /. J +. >. 享ご二. /. < ′ ′ ′. 7･5. o喜∴d_ /"-/忘o享 _′. ⊂) = くノ). ′ ′. l/. 旨1.0. T. l∠. 一. -. U ⊂) J u+. >. 千. ･く声. i･-守. >. ■-. ーむ一一T_____ 好糊EDSNOWFL. J■. 0.5. AKEO｢. O臥ATETYPE･. p伸一---一別MEDSNOWFLAKEOFTABULATETYPE･. .J J. ′邑/6p--NON剛M【DSNOW｢[凸KEOrOB[AT[TY?i:I. /. i.L<. 〆一--NONRIM【DSNOW'FLAKEOFTABULATETYPEllJIJJl. 0.5. 1. 1.5 DIMENS10N. MAXIMUM. 7. Fig.. and. snow丑akes nakes. snow. the. of. relation. Fall. tabulate. type. facts. :. that. of their sizes. Sawada4). only to. to. the. the sum. vohlme. receives,. while. cross. section,. of. non. type,. and. the. in. but. resistances. size. and. to. are. the. an. cm,. like. body. State･. The. author. which. volume; individual. one. sees. four. regular; almost. receives. snow. other. those. the. and. the. a. resistance that. proportional words. crystals. two. the types,. independent. supposes. resistance in. represent. represent. into. are. feather. aerodynamic. the. 7,. comparatively 2. dots. dots. classi丘ed. Ⅰarger than. fal1irlg. falling,. 8.at. In丘g.. thus. are. s]'zes. sizes.. The. ones.. type.. cone. that. out. of various. 4.5. CM. IN. tor)gitudinally long. snow且akes. of. snow丑akes. 4. 3.5. FLAKE. rimen. inverted. if the. pointed. proportionaltothe snow且ake. show. snow丑akes. has. SNOW. of large. fall velocity. betweenthe. fall velocitiesノOf. the. or. 3. 2.5. OF. velocity. dots. white. of the. oblate. following. 2. the not. proportional in. the. snow.

(9) 26. C. MagollO. flake,. TYPE. OF'SP舵劉CAL. s悶O樹FL鮒E. the. tbrougb. C,琵YST乱. is. /. the. tance. the. ㌔. i #. which. by. 班. R. we.re. is. namic to. ち. i. ii. i. 8. flake.. Schematic The. a. as. resistance. some. receive. crystals. constant. the. radius. for. snow･. of. section. the. of. A. air,. to. coe氏cient:. 凸ake. has. a receives and individロal. is. γ. non. If. the. permeable the. ordinary. the. its terminal. reached. drag. air. flake.. to. β. volume,. When. 0.5.. related. 且ake,. the. snow. equal. of air, aerody-. snow. is. is. drag. which. constanl:. of. related. of fall, its weigtht. flake. whole,. the. (1). ∫)〝2the. 1/2 the. :. ,. resl:stance. sphericalsrlOW丑ake. aspect. snow. the. cross. receives,. p the density. A. pressure,. resis･. Bake. total. fall valocity,. the. 〟. is. followll唱formula. the. receives,. snowflake. fhke. mentioned. srlOW. the. aspect 8.. snow. (A汀r2･Bwr3) ㌔ R-÷pu2 #. *,. Fig.. above the. is described. a. of. passes. which This. in丘g.. shown. shape. spherica一,. ㌔. t:heair. snow且ake.. schematically If. /. from. receive. snow. velocity. by. balanced. the. force,. from. resistance. air, too.. 1. where formula. is the. o･. (2),. density. we. the. r. 8･-P_ p. the. non. permeable. percent. snowflake.. be. 瓦i面g that. seen. (3). in. ･. the. rarlge. r, ” root of r, and for larger on fall velocities observed 9 December formula (3). Because of theoretical. propriety. 20. From. acceleration.. gravitational. r, ” is proportional Of small independent of r.. is almost. the. I:he value. it may. (3),. square. For. (2). a. get. 〟-ノ to. a the. of snowflake.. 8 3. In formula. (q-p) ÷-r3. u2(Awr2･Bqr3)-. すP. spherical. of A. is Oho. of theair Further,. body. is. the. case. in. which q. was. of. collided estimated. non. the at. drag. snow. rimed. with. the. the. alユthor. snow瓜ake,. 0.Ol g. cm-3.. flakes;. assumed in. passed This. examined. coe氏cient. be 0.5, the author. to. considered. 1950,. other. a. of. that words,. throughthe estimation,. the.

(10) On. thinks,. author fallen For for. reasons. to. similar. determined. by. fall ve王ocit圭es. mean. lcm;. ones,. ”. -. estimates,. Values. in. is, for. the. 185cm. see-1.. rimed Using. above. B. -. 0.63. for. non. B. =. 0.6つ. for. rimed. gCm-3. Non. rimed. Riユled. β wbicb. snow且akes.. 1. 185. 0.60. For. fTa!f of. r:. the. ri血ed,. non. and. curves. oblate. (4) 7.. for. (5). are. lt is considered after. the. one. non as. to. snow且ake. rimed. Formula. expected.. r. (4). (5). types. that. are. estimates. 壱4.. Growth. the. formation. cloud of. the. that. and. lie in. the. snow. particles snow. for the snow. Ⅰtmay. 9.. of those. middle. these. mentioned. above. type. same. single. of. on丘g.. Considerirlg. of. the. on. fall velocities. entered. rarlge.. and. 9. of. types,. (4), (5). awide. theory. in丘g.. represented four curves. comparison.. over. the. rimed. a. a. ”-194J. spherical. types. of. ノ師'. -132. and oblate of tabulate Nakaya's observations,5). justi丘ed that. collected. 〟. volume. r. and. For. of the that for. than. dimension.. maximum. effect. forrimed,. the. sec-1′. 0.0013. follows.. obtained. cm. 0.03. rewritten. by. 〟. r*cm. gcm-3. 0.45. (3). used. p. 1.. 0.63. larger. snow且akes. folloⅥ7S.. 130. is. for丘g.. mentioned. 1. as. formu王ae. rimed. 0.00i3. represents. The. above. 0.01. its fall velocity, is. radii. for. and. 0.40. *. The. whose. sec￣1,. 凸akes. snow. as. Table. a. the. employed. types. the. Of β. vallle. author. values,. 0.03gcm-3. at. The. oblate. newly. 0.007gcm13.. a.. ones.. -130cm. in. obtain. rimed. tabulated. are. mentioned,. we. and. the. and ”. observed. (3),. 0.45. at rimed. snow月.akes, those. is observed. of density. case,. of tabulate. theoreticalformula. and. A. 27. snow. snow丘ake. of non In this. measurements.. non. light. estimated case. Graupe. and. a. a. observed. author. of snowflakes. that. Flake. Such. smalI.. author. those. Snow. of. too. the. flakes,. snow. rimed. may. are. I.ater･, the. snow.. be. be. not. may. Growth. the. results, wereal1. of. plot. observed crystals. be for it. that. seen. tabulate be. may. suitable.. flake observed. 丘ake;. in. the. therefore,. snow. only. 且ake non. were. rimed.

(11) 28. C. Magono. 2.5. S.争. /oB. U 一▲+. く′つ. LC.e'･. /cA. ■■■一一一-I----. ＼. ---一一■一-. _d-1一--I. :∑. ●-一一一･--A-..I-. _----￣ ■一一一一一一●一一一●. 2.0. _一■4J. ,dd7. i. 一一一一一●I-. ≡. 〆一〆r. /OBS･J. オー一一一一一一一一一■. //_-････-''. JJ 3<. /oBS･0. q i-i. cALc.o書 ,,if9:･'/-ヒニ工････････-I-L:i.f9yて/･･･レー･･････ i i. 7.5. ≧ C〉 Z U'). %. F::････9''''z. メ//. _.p--■dFdPP. l. 〆′. i. 7.0. .-o8S･F 1'spATIAしDE”DR17-CCRYS`TAL. o-. >. ♂.チ. トー U. ⊂〉. 己 o.5. ｡Ill;/./占L&ANE･DENDPi7C-CRYSTAL. >. ■b■仙d_V. J J. ≡ I. 0.5. 1. 1.5 B糊ENS10N. 村A¥糊U醐 Fig.. 9. ments. theory. and. also. proposes snow. in. the. to. explain. crystals. same. the. the by. small. growth. of. with 凸akes. mutual collisions of If the snow crystals. which. by. the. with the. snowぬke, for. crystals crystal,. IN. 4.5. CM. flakes. snow. of. sizes. then the. is shown. of. fall by. be. witha that. of. The. case,. that the show form dendritic of facts,. the. author. of collisionswith a Llakeand between. collisions as. measure･. result. velocities. with. pointed. out. clolld by. particles. Masons),. effect. from. the. and. the. negligible. snow. the且ake. which. these the. as. crysl:als. also. collide volume. of drop. foregoing. may. relative distance follows, as. 凸ake. snow. the. crystals. snow. Considering. snow. rain. collisions. compared. a. of. a. Single. size.. fig. 9).. difference. the. muttlal as. (see. growth. to. snow. the. and. 4. 3.5. FLAKE. SNOW. fall velocities. of the. cases). owing. crystals, The growth be. between. is independent. like. may. OF. 3. concerned withthe growth of the srlOWflake. for the fall velocity of large snow且akes. are. crystals. fall velocity are. Relstions. ?.5. types.. various. snow. 2. the. flake,. are. increased 丘ake. always collected by the collision. traveles. compared. to.

(12) OLl the. Growth. of SrlOW. Flake. Graupe1. and. 29. dV-αnvsdl V=. where. volume -. α n. If. tall. we. collectir)g. e氏ciency. density. -space. v. flake. snow. of. snow. of. (number. of. increase. of volume. -. snow. crystal,. in. a. 凸ake.. snow. s. -. cross. l. -. relative. section. crystal in. crystals. centimeter. cubic due. volume. words,. of. one. of snowflake. other. of air). to collisionwith. by. o9Cupied. a. a. snow. crystalwithin. snowflake.. distance. tha七the. assufYle. (6). snow鮎ke. travels. is spherical,. then. which Rake. snow. s=kVi,. we. crys･. get. 盲宗一. (了訂'. k=. where. to. compared. and dV-anvkV!dZ. The. author. the. cross. that. supposed section. a. of. 触ke･. Integrating. obtain･. assuming. is unity;. α. sr10Wflake. (7) from that. ”. in. are. by. all collected of the height,. invariantwith. are. ls呼ept by. crystals. formation. origin of the. V. snow. words,. other. falling,. while. the. and. (7). the. snow. snow且ake,. we. 5yv暑dV-nvkS三､グl 3Vo V3dV=nvk58､グI れvo is the. Vo. where. volume. 13. initial. an. of. (-Pi3Vi)3. -. flake. snow. l. accretion. for. V. two. of in this. i compared. snow. to. of different. crystals. the volume. case, sriow. of. a. on. 9. follo∇ing. 1951.. a) / Space. density. The. space. watei'content. mean. expressed. density. of the. is calculated. The. is the. December. in. water;. of. snow. of. snow. space. fromthe intensity. practical. as. crystals. to. snow. in other. the. by. the. be neglected distance. relative. (9). (9) for. the. fall. snow. ”. is calculated. mass. of the fall of words,. travels. of formula. example. crystals:. ratio. of. which follows,. a. born. (竿)3･. v-. Tbe. types･. be may which Because Vo may. snowflake. is shown. crystals. (8). ,. of. intensity that. a. from And. crystal.. of time. snow was. the. fall 3･7mm. 1.01×1014gcm-2see-1.. ice to. of the. ratio Water. COntent. fall. the. p改hour The. ice. volocity. being mean. fall.

(13) C. Magono. 30. at. estimated the. on. 160cm abovt 0.64gm-3･. was. velocity. and. ground, the. which. This. According,to. .･important.. of the. plane. ･estimated. at. 0.C43mg. and. IAeStimated. at. 1.49xlO-2. spatialtype. of the :. crystal. weight. in. a. of. an. same. For. the. So. type. and. forthe. volume. t:hat. plane. a. of. is equal. ”. @akedue. snow. individual that. snow. dendritic. snow. ”. to. type. space. density. the. not. OA4x10-2. were was. for. cm-3. a. of. dendritic. to the. the. a. of. accretion. in. crystal. of. is. calculated. the. density. from. the. snow. 3, density. type. snow. I:he. of It. is. On. observed.. was. the. and. a. 且ake.. directly. not. by ratio. snow. a. of. was. paragraph plane. is occupied. which. volume. 且akes. snow. of. described. as. reasoning. the. crystal. density. the. to. Therefore,. 丑ake.. snow. unfortunate the. respectively.. is. weights. mean. spatial. in. space. uncertainty. the. the. and. the. of. v. It is considered crystal. 0.146mg. cm-3. this. observed. respectively.. Incresae. b). type. data. the. that. thinks,. author. measurements5),. dendritic. crystal. ･snow. Btlt, the. from. was. content. water. from. different. Nakaya's. ice. the. estimated. somewhat. grew.. snow凸akes. was. value. be. may. So. (see丘g. 7).. sec￣1,. 0.01 gcm￣3.. at. one,. spatial. we. get. respectively I.46×10-3cm3.. v-4.3×10-3cm3, Relative. c) The froml 2,. distance. fall. mean. 8akes. of. non. rimed. crystal spatial dendritic distance The relative elapsed vas. therefore calculate. 990m, the. and. _to. the. snow. Bake,. a. of. 凸ake. snow. are. Table. g cm-3. of. crystal. plane. Dendritic. crystal. of spatial. using the. the snow. type. type. dendritic. plane 31,. 57cm. tothe. sec-1. in. tabulated. calculated paragraph and. crystal･ I. (see丘g･. dendritic. plane. Tわe. values. the and. 9)I is. crystal. to. requisite. 2･. table. 2.. ㌘……;s;ail. Icce.諾r Dendritic. is in. 1300m,. was. space,. 730m.. type. spatial. the. 130,. respectively. of snow且akes. growth. traveled. to. ∫. crystal:. to snow crystal of snow瓜ake As described their fall velocities.. snow. which. velocity. to. compared. distance. between. difference. travels. snow且ake. wbicb. relativ弓elapsed. the. the. distance. ”. mg. cm-3. v. ￠gcm￣3. cm3. Jm. 0.e4,. 0.043. 1.49× 10-2. 0.01. 4.3× 10-3. 990. 0.64. 0,146. 0.44. 0.01. 14.6x. 730. in table values Bakes observed. 2 and ,on. formula. 9 December. (9), the 1951よre. ×. 10-2. mean. volume. calculated. as. 10-3. and weight follows.. of.

(14) On. the Growth. Snow. of. Flake. Table. V. Dendritic of. plane. Dendrilic of. 3.2. 172. crystal. 6.8. 2.3. 68. D:. diameter. ”:. weight. a:. diameter. observed form, and. of. snow. flakes. of sleet. very. our. climate,. similar. to. formed. by. origin. large. of. before. known.. graupel. is, a a. deposit. solid. of. ice. In. the. the. anyⅣay,. the. 且akes. snow. separate. once. fan solid. Small. observed,. they. and. that. accepted cloud. are. a一most. the. graupel but. particles,. や. on J′. origin. ノ. ＼J. to. ). ＼-. fog. particles. the opposite. type,. side. section. cross as. object. shown is. a. con-. edge. grows. of wind･. of the. small. ー′. i) ). tT<:J. rime. in丘g.. ノ. 10.. point,. in. graupel. -一l. a. to. drops.. that. it. comparing. spherical. equivalent. whether. phenomenon.. frozen. ward,. If. non. not. particles the. a. or. smaller 丑ake of. snow. that. rime,. considered. accretioI】,. on. is of the. of. a. be. ＼-. frequently and. of. of. super-cooled. is. noticed. fog. graupel,. by. structed. piece. frozen. accretion ice. numerous. grallpel. author a. object,and. of co･ne､･1ike the. The looks. rain. It is generally. with. cone･1ike. of. frequently. form･. diameter are,. to. appears. separations,. Formation are. snowflake. of. the. problem. without. a. diameter. maximum. fnrtber. size. graupeln cone. is. centimeters. a. in. here,. calculated. formation. the. drop. contained. former. several. it is. collisions. the. of. clearly the. the. 2･3cm. the. of. but. the. crysta)s. or. i 5･ ln. 465. form. spherical. water. ユatter is the. the. drops. equlVqlent snow. of. 4.5cm,. rain. state. 400 0,. 6.9. snow且ake of. 3･2cm. to. change the. of. number. drops;. of. of snow且ake. size. rain. sizeable. 〟. mm. _5.1. the. spherical form･ Such. a. 17.2. AItbough that. Wmg. cm. spatialtype. 31. 3.. crystal type. N:. than. D. cm3. Graupel. and. Fig.. 10. Rime. on. thin. pole.. all is the.

(15) 32. Magono ､■C. Fig.. ll. Side. views. of graupel【l.. 11-B 111A Side. view. photographed. 11-C Side. Views. of graupeln. x a. of. 0.3. piece. Side of. x. views. of. 5. graupeln.. ri血e. Ogucbi.. by. x. 5. replicated. 11-D by. Sugaya.. Side. views. of. graupeln. x. 5. vitbout. to￣p of. cone..

(16) On. Growth. the. Fig･. 12. of. Snow. Falling. Flake. state. of. Graupel. and. 33. graupel.. づ. G. ＋. &. ＋C?. 12-A A graupel by. a. snow. x. 2. accompanied crystal.. 12-ち A. snow. downside rimed.. x. 且ake is. 2. 12-C whose. somewhat. Graupeln, keptロpWards liquely.. 2. x. the top but. 12-D being ob･. Graupeln are. x. whose. rotating.. 3 axes.

(17) 34. C. Magono. the. One. n.. graupel snow. the. the. off from. torn. the. to. grows. rime. was. a. similarity. (see丘g.. the. is. graupel top. out. in. of the a. the. of. it is falling.. while. the. 4-A), and. is,. See丘g.. flake. consists which falls pointing graupel is. state. From. seen. larger. cloud. packed. newly,. becomes. the. larity. of. the. as. the. the. dendritic. spow. that. such. author. the. as. type. cone. as. but. layer. of. snow. crystds. from. The. rotation in. is rarely. observed. 14.. the. in. cone. fig.. have. grapeln. is,. The. more. com･. grow?. which than. top,. the. that. heavy. the. and. be due. the. strongly. understood. to. bot声 irregtl-. the. as. of the. irregular. many. a. the -･top, occurs. wbicb paperlO). ,. small. not cones. and the. at. spiral1ine. would. to. be. as. only. which. the mark bottom. observed. believed. The crystals. front delldritic. snow. n.ot. passed. ,througha. direction. ll-D･. ･tinfig･. of rotatipg of. on. as. for the. be. a. motion. cone,. condition. words. other. it is fallir】g may. a. fal1･. of. I,copstant. shown. vbile. gtaupeln. It､is not. thi疎こplates一; ､in. a'necessary are. small. observed.. crystals. turn. crystal of dendritic spatial. very. resuit. gav争. snow. gave. dendritic. type. cone. typ3wi11. graupel. a. from. g･rown. particles,セeeping. plan与. Czermak's. frequently. are. the. however･. lmaill). and. from. celleag.ues9). country,. 13,. ･typeLWithout. of. his. our. Barkow8). separated. and. perhaps. cloud. rotation. for. In. source･. small,. of the. gratlpeln. type,. it is. would. follows.. stage.. early. part. upwards. type,. which. Nakaya. and. seen. that. of the. But. top. the Thi虫. as. more. dense. ∴more. facts,. state. cone. of. braTICbes. super-cooled. described. is. these. falling. the. result,. snow. hand,. therefore, the. a. graupel. in the. stage, the. light. the. in. graupel. graupelp. small. proposes. crystals,. the. rimed. form,. crystals. of the. grown. heavier. of. be. to. the. are,. top. obliquely.. collides. than. stage. Considering pointing. larger. pointed the. of. other. axis. graupel. early stage. The bottom of graupel. rotat:ion. origin of. source,. plane. a. As. the. -the. that. as. view. of and. that. side. a. top. observed. cone,. is considered. the. grown. is. consists. On. keeping. So,. is.. is. keeping. the. form.. cone. About. 12-A. crystal.. but. largely. Reynolds.7). The. downwards.. tom. a. it. flake,. The.reason. 12-p.. the. falls obliquely. graupel. Fig.. falls. long. snow且ake. of the It is considered. snow. measllrement.5). in. in the. by. the. upwards. of graupel in the largely. heavier.. out. pointed. and. and. colliding than. pactly. as. Terada's. particles. graupel top. and. particles. cloud. the. 12-C. fall velocity. the. with. of. in丘gs.. Nakaya. 12-B.. a. 12-A,. the. by. its. whether. of. of that. horizontally. type. snowflake,. 5-B.. views. keeping. type,. problem. wbicb. considered. downside. and of. side. plane. cone. of. rime. of. is. -It. downside. the. 5-A. are. its. dake. simple. on. view. need一e. of the. downside. 5-B,figs.. a. case. or丘gs.. the. the. or. i? situated. paper3),. cone,that. the. and. Side. ll-C. them.. snow. upperside. In. snowぬke. previous. crystals.. the. on. situated. ll-B. falls keeping. type. the graupel … -while of is, Tt however, not obliqtlely.. cone. a. sbbwS. b･etween. horizontally. its a‡is. cone. 1トA. figs.. and. plane. regular. force. aerodyna血ic. axis. as. the. see. of. Fig.. body,. solid. may. crystal. type.. cone. same. of graupel. shown､. the. cause,. in. ･fig･ to. growth plane. of. an.

(18) On. Growth. the. of. Snov. Flake. Fig.. Sma11 Several. snow. graupeln. crystals. of of. and. 35. Graupel. 13. type,. cone. ×1.5. form. six.petalled. arealso. seen.. Fig.14. x4.5. View. of the. bottom. side. A. of. cone-like. spiral. graupel. li°e is. replicated. seen.. Fig.16. Rimes. pf. i:One. tyPe･. attached. ･to. a. Solid. body... by. Sugaya..

(19) C. Magono. 36. initially thick 12;'B (育. '#. '@. ■㌢. fig. 15.. in. in. seen. crystal. Stich. plane Fig. of. a. snow. of Smal1. 15. snow. that. of. crystal. cふゝ to. attached. cones. the. a. the. plane. type.. plane. is. of irregularity. result. of. 壱6. lt is i:onsidered. Id. 丘g. 17-A.. Angle. tnat. of fog. attachment. the. distributed. bomogeneously as. the. in. by. a. rime. particles. radius. =. m. fig. 17-B,. in. a3,. a. we. a. within. obtain tan-1. of. of. is. particle. shown. in. graupel. is. r,. are. graupel. cone. then. a3,. a. the. of. be. may. the. density. the. mass. p, con･. to. fro2:en. a. from. (10). individual at. particle. If. particles.. the. side. of. a. cloud as. graupel,. formul早(10). i-%-(i 4.. the. top. of. 0つ. graupel:. cone･1ike. 0三bs.. of. observed. p gcm￣3. (mean. OcOa).. value). 70 -80. F16gel. Nakaya. in. packed. graupeln. Wegene. the. grows. cone･iike. angle. Number Place. by. Bakes.. schematically. graupel. between. Table. Observer. the. 317,r3･. -interval. Atlgle. but. follows,. as. tangentiall吏. attaches. particle shown. in. mass. as. are. the. cone,. a. accretion. angle. Qf a,frozen. particle. ice. which. form,. cubic. of the. cause. graupel. rime. the. rime,. by. bottoi一1 0f. the. the. of. snow. of. of. of the. m-pa3t-0･9×. where. case. of cone･1ike. side as. If the. is expressed. α3. the. in. follows.. top. frozen. that. occupied. volume. tained. to. manner. Assuming. irithe. fan-shaped. the. same. As. the. of. particles. considered.. calculated. form. thinks. suggested. not. formation. cone. in. shown. author. line at. spiral. as. the. rotation. graupel. afe､ also. cones. ice acctetion. fig. 16. Ratheri. shown. as. about. r. etc.. Antbor. Mt.. Tokacbi. d.125. 4. Mt;. Tokachi. 0.125*. 28. 0.125*. Sappord. ll. Eamakura. I■. *: **. Density :. 7. 0.35. **. 16. 90. 6g. 64. 68. 65. 66. 65. 81. 83. is assulned.. Graupel由as. slightly. wet. when. dens二ty. was. ■observed･.

(20) On. e=the. where graupel. e. is the. function. It. difncult for. requisite density. are. are. computation is not. of graupel. Gra11pe1. and. be. It中ill. only. p. 37. no. values･ because. theory, exact. of the. observed. graupel. calculated. author'sforgoing too few, the and. angle. relationwith. of the Lcone･like. wi也tbe. the. seenthat. has. and. angles. compared the. Flake. cone.. 4, the. In table. discuss. to. of the. density. of. of the particle. radius by various investigators is yet. top. of the. angle. of Snow. Growth. the. data. the. meastlrement. Of. the. easy･. I. /. /I ＼＼＼. /. )ぺ. /Le. /訓gl` e /. of＼＼. c:One. /. ＼. /. / /. ′. i. ′o/z. According and. 6, the. particles the. to. is. of. to. of. volume. shown. Angle. を7.. Grovth. as. of top. the. of. どra.tLPel. with. been. have. the a. like graupel･. ccne. of. which. compute. in contact. come. which. 17-ち. considerations. tried. author. increase. particles,. the. 17-A,. ._⊥__. a. Zr_. Fig.. he;8hlof. size. attainable. graupel. to. owing. of. all collected. are. graupel. 5 paragraphs If cloud graupel･ in. stated. the. by. collisions. the graupel･ lwith. cloud. follows,. (12). dV=anvsdl, vhere. y= α n. of graupel. volume -. collecting space. -. particles v. =. increase with frozen. e氏ciency. de碑ity. one. in. of one. cloud cubic. of volume cloud particle. graupel. due. (volume. particle, a. of. cloud. of air)･. centimeter. of. within. (number. particles. graupel).. to. the. occupied. collision by. one.

(21) 琴. ′c. Ma酢nO S皇area. l. botto申Of. Of the. -■r軸tive ^distance to. cloud. which. bottom. the. 土hatthe. bottorn･. the. volume. a. of. s. in. (13). the. which. passed;. somewhat,. assuming top,is. of the. atlgle follows,. 65Q. (]3). in. as. 2.3. =. the. case. througha. passed. the thickness. graupel. the. as. k,. manner. which. compared. ･. k'Vi. =. same. graupel. dl. Vi. where. that. and. travels Z is. caLSe,. outward. (12) isaltered. dV-anvkl. Integrating. is curved. graupol. has a鮎t circular in table 4･ formula. cone. described. as. of the. this. through. cloud. graupel. gratipel. kl. ､pa,rticles.. of super甲01ed Although. cone･1圭ke. of. snowflakes,. cloud. we. obtaip. thickness. of. i. fol_. as. lows,. It is known. of the cloud Reynolds'number･. radius and. however･. the. that. no. V. (-. the. collecting. αnvk/ 3. particle. the. and. has. eBiciency. graupel. of. data･5). to. the. calculate. the. as. of. eBiciency. to. a. adopted. particle. the. upon. the. drop,. rain a. of in. graupel, this. drop,. the. case,. for. By. semisphere.. respectively. the. the. use. following. of graupel. collectirlg. e氏cierlCy,_. 15 Ih. -. of graupel. of graupel. density .and. collection. author. bottom. the. fall velocity. obtained. dopends. fall velocity. e瓜:iency,. of cloud. radius占f. drop. rain. is approximate. collecting. radius. a. of. The made･ author adopted, by Langmuir12) for a rain. computed. of the bottom of a Nakaya Teralda's and. (14). drop･. rain. the. been. form. values. enciency. Concerning. corr)putation. collecting. )313. 2. -. mm. s印-1. m. 0,125 g. -. 1.5. =. cロ1-3. ,. α±=0.72 According tl'on. ]'s. often. observed･. here･. author･. Takano's. to. the water. selected. in theair. paper,13) water. content. of. of O･5g. content. in. conditions. the. m-3. air. and. ,. is. carried. ice which 0.1-1gm-3. out. the. accre･. The. following. COmputation. water. 〝=. where particle. ” is. the. is equal. space t￠. conteIlt =. mass. density. of. a. cloud. Lo空 cloud. 4/3汀(0･0015)3g･. 32cm-3. particle particles, The. volume. arid. the. occupied. mass. by. of one. a. cloud. particle. is.

(22) On. from. obtained. Growth. the. formula. (10). of Sn6w. ×÷rr3. v=a3=. As. for. the. of the. m,. volume. the. lapserate. the. concerning. cm3. to. conformable. cloud. of写raup占1. growth. data. of. The. formula. and. I,. :. graupel. temperature.. of air. bylthose. computed. (14). are. 5.. in table. presented. a. of. 1000. adopted. author. result. thickness. 10-7. ×. =1.1. P. the. 39. Graupel. and. follows^,. as. o･9. Flake. Table5. Size. A/. v. ” cm-3. 2･3. ; 0･72. When. this. 1n water. graupel. will. this paper, content,. the. lx. elements. collecting. bllt it is not. are. su缶cient. toinvalidate. the. conclusion. are. not. based. thinks. that. the. investigation. author rain. drop. the. 凸ake. snow. and. believed. Acknowledgement.-The U.. Nakaya. graupel. to. wishes. dl'rected. who. complltation However,. foundations. the. words,. important. The between. state. problem.. his best. express. invariant. above･. experimental. fllture. a. the. presented. instance,. be. to in. 1.2mm. for. air,. assumed. uncertainties. on. is. of diameter. of the. are. conclusion. mm. graupel 2.6. drop. rain. of sleet, in other. author University. of Fokkaido. these. general. of. conditions. completely. or. a. e缶ciency,. that. Heigbt. cI℃3. 7.3× 10-3. 105. of physical. beigbt,. with. Volume of graupel. become. itwill. melt,. density,. space. graupel. ∫ crn. cm3. 1.1×10-7. 32. of. to. tharlks. Prof.. this work.. Reference$. 1) 2). HouGHTON,. H･. mechan)Isms. NAZくAYA, U･,. J. Meteor.,. Amer.. 3). 1950:. A. The. Soc.. 207-220.. C., 1951･.. Preliminary. γol. 7, No.. 1951:. Meteor.. MAGOhTo,. G･,. On. formation. the. quantitative. of. analysis. precipitation. 6, 363-ご69. of. fall velocity. ice. crysta一s.. of. Cornpenditlm. I. Meteor.,. snow丑akes.. Meteorology,. Of. γol. 8,. No.. 3,. 199-200.. 4). SAWADA.. T･,. Gakugei. 5). NAZ(AYA,. U･and form. velocity. Ser.. 6) 7). and 1Ⅰ,γol. 1, No.. MASON, Roy.. Meteor.. Soc. 1877:. or. investigation of a甲Odyr)amic Univ.) γol. 1, No. 1, 107-109.. Gakugei. TERADA,. T･, 1935:. of individual. snow. the. Simultaneous 【rysta)s･. Composita.. of. seed. observations of the S°i. Hckkaido J. Faculty. falling. mass,. Imp.. Univ.,. Centenary. Proc.. 7, 191-200.. J･ S･, 1950:. REYNOLD, 166,. The. 1949:. (J. Hokkaido. The. formation. of. ice crystals. formation. of rain. and. sr.ow鮎kes.. 51-58. On. the. drop. and. hail. stone.. Nature,. γol. XV..

(23) 0. C. Magono. A., 1928. WEGENER,. 8). BAREOW･. Zur. der. Entstehtlng. der. Atomsphaere.. Graupeln･. Zeit. γol. 25, 456.. Meteor.. 9). Thermodynamik. :. E･, 1908･. NAF'AYA,. U., SEEIDO,. ¥.. TADA,. and. M.,. 1935‥由oteson. Ser.. 1I,Lγol. 1, NQ.. irregularsnow. crystals. and. Snow. pellets. I. Faculty Sci., Hokkaido CzERMAK,. 10) Sitz. ll) 12). Wien,. 7., ]951･.. LAfJGMUIR, at. 13). Ber.. IMAI.. P., 1900. TAEANO,. On. above T., 1950 :. Eagaku. γol. 5, 9-20.. Zur. Strtlktur. γol. ⅠⅠ,a,. E., 1948:. temperature. Tfon. :. ∫mp. Univ.,. the. fall by. Studies. der. 7, 215-226.. tlagel始rner.. (in. Monsoon.. Japanese).. of rain bF a Chaitl Vol. 5, 175-192･ J. Meteor.. production. freezing.. (Magazine. Form. 185.. snow. The. und. on. ice formationwith. of lnstitute. of Low. awind Temperature. reaction. chanr[el. Science.. in ctlmtllus. ⅠⅠ(h. clouds. Japanese). Univ･). Hokkaido.

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