fdarationa! fleparltnent SSII fE. E. Quim..c.;, . S.. WILT, , CM/Mittel - REV.' D. Ciuirr., , . 0 H G. !IV. R 1 AN, 411soricrts Editori t I I 2 ,A' , E,EN ET, • romimmirationi may ,be sent to either of the stn'.• editor.. as may be pieferred, and •or 111 appeal In the b.sue of which be has charge. •- • • W. RT.N., Editor present 'week. RULES Fos MENSURATION The old edithins of Robinson's 'Higher Arithmetic and latest -edition,, contain mensuration, but most of the .editions of this book .contain duthing.of-these 'import ant rillet and even,ifin 'eWy book but ft 4 teacifers make pupils use them, er cept an occasional scholar ;who may•com plete the book. Many oftthese rules'can, be easily explajned--by arithmetic, but if, t aibitr.i.rily men iorizJl.; the task is , not yery onerous, as there . , are only 20 of .1s soon as pupils•taidershuld decimals these rules 511011111 Lc gradually• given hi '.-addition to daily lessons, tut(' fixed -in mind b; abundant practice.. - Tim re is iiu reason why these shOuld be deferred to the very last ofan arithmetic iiid as x. result many scholars •choul. without kUowing percentage and allegation and - progression, in- no way-assist in titesefrules; square.and cube re ry, and can and should be ed when needed in using or learning hese rules. * Many of the land masses (State& conti tine n s) are're4ati,gles, triangles, etc., or tuibi nal ions of sucli:figure, and the area It.l~ht be easily- rwiiintfed *arty 'correct by pupils, if familiar wits! these rules. Thus,!. artied. such fits would be easily ret6',,Plhered„ This exerco;e would necessitate on &he . Ftt t ..f pupils, to find length, width, etc., the :t ale iC miles 4tached to all maps. do pot Ipow what the scale is, and it is'gcnetally ignored; hence lit- know little or the;silitnensions . and area of the porOng of I .. ttd and ,water on .lur earth: 7 • 'nit \ oliameter, 7 - 1)14;;„, multiplied by: :1.1117..12 c circumference (a• process 1,11;1! any pupil can earlY• learn): The ;aunference divided by 360 - --49.16 nearly. A.,pnpil taught the length of 'a degree at th e!,mitor in this manner,learus it with interk:,t and never forgets it. Pr, qn lack of a good knowledge of these tales, a boy is oftenobliged to, go a mile . to I%errow some measure,, when a nio 11:4;nt's application of these_ rides would ender s!,lller pail at home 'equally accu rate and g.:l4ieeablc. will learn thesC-it'iles and anilithe !rti,rl le on besides, and hr.c Le it•tial lesson better than without : 0,11 -Id! • All, of the - tales of mensuration are, 41.1•1n0!1-t rat ed our geometries except t rile for a. scalene triangle, which is fronetwarly -Mr. 1: 13: Craw 'f!!r.l. the Tow:lnd:a Graded School, be , in a 7 ked byhis-Pupils for anexplanatioti of he yule,' developed the following dem : I the,thrpo ~ides of a triangle to Cilia t he •orea Let A B C be a triangle, paving,its ides . repre' settled by a bandy. *• * Frpm C let A 7 7 -;!. lt r B fall C D per kinbeolti- fo 11; thenbyyrop. 34, Cot. 11. : 1, LoO!inis'llnometry, or Art. 4fl, Dtv. S'iL;;" Plane ,TrigOttometr2, - , we tied that, if ;in any tt:ianght, a line be drawn ve'rfeti of the vertical angle per •in wl:.••nlar' i to the base, divi4ing it intrt it -el:1-eelltS, the sum of the ta o'seg mein s, (4, the whole base, is to the sum tin- two other sides - as the difference of s,aes is b, the difference of the seg7 mein ! • / ~ r:‘l a-b :DA-A -AVIR.:I I) 11-i 1) thL•II 1) 11 (C' r -• c C U 132, C 1) But as f_' Tr 2. , 1. 2--(,/2-h . ...-r.2)2 or l 4',11 (202 f-- ME tiiY,rt fl.te area of any triangle is found b) ,me-half the base by-the tole. We find the area .of A II C.= it t v 4,,i2e20;24,2±r7.) = r'2)(?a — e—(a2 ME 4 1•;at e e . 2) (ft-i-b+c)(a—bi-e e) = 2 . if we vat x a the half 81.11T13 ( . ..f , tli.± three .shie.s, • . r—a•lbsif*--,(.• lielice the al -e 1 - 1.11.. rule :" From the half sun. 'or 11“. three slaw, subtract each side sep --a...iteir: tdultiply to i g j ether the half Aurn retnainders,•and extraci the •sylii i •e rout of the ircxlucty- - N N ' we give' the programme for he next session . of the Towanda District 'l . 4 !lwtiers . Institute, Saturday, Nov. 17, S it. to I'2-M., at Graded School These sessions are held regu i.niy every tWoweeks, and are .attended teacher:: of (he Graded Selax.d, and a few Herons _front adjacent , Ali'sc tr a ils. Onc.pbject in making this notice is'to : %we a C , iVillakinVithtitYli to all teachers; di ; en!Ors„and: friends of education to at ;i,-atlierings,—to encourage by svii presence, or to aid in instrtting. \Y,. feel that 'this gathering its entitled to at least visits or aid from edocAtors:livi.lz within stone's throw of Co! of 0t!...--;:ng.. Why callow ;Chore be at one . or the ~t h er O f tl i .s;-1 1 .0 hulldings in.Towaoila rc;gular nircting, of an orpnization of that shall hi; generoMsly attimul cd ami — rendi•ted exceedinzly profitable. 103 nn` bear from tho , ;e Nvorable: . Tc.tchcrs,havinz the c9oportanity to tcnd , and aid such an institutes, yet never 11•cre, - could not conscientiously expect commontations or assistance: in procur- situations to S:10, Singing, Rol aid Minutes read. s;io Dis .;S:7‘7, to 9:40; .I{ending,, or Penmanship 9:10 to 9:45 Singing. - - . 9:15 to 10:30 Arithmetic. I 1'll:30 to 11:13, Grammar 1 11:15 to 11:20, Singing. ' c11:20 to 12, 4.lciigrapliy.. AT SEEMS to us that. the people of Rome, are fortutiate, inseeuring.sOWell'qualille4 and cilleient teaeli!iT- as Mr. Brown for , the fall and winter' sehoOl. • As a ,mathenia .ticiad he has few equals - 1p the ,county. I'Ve hope to. hear from him in the tduci t Iona! colninn. pvivo:coiocowtivlvri A person has a tin - pail - 10 inches diam eter at the top, 6- inches diameter at 90 bot . tom, and 9 inches deep, which he wish es to us 73 for .measuring milk. ,Required the number of inches from the' bottom 'and on the side of the pail that marks be placed to show when the pail contains pint and when a quart. Being upon the bank of ir river. and wishing to know the distance to an object some distance beyond the opposite, shore, I placed on the .bank a six-fOot vertical staff, and walking back from the bank 60 feet; found that the top of a Of foot verti cal staff placed at that 'point, the top of the 0 foot staff and the distant object were just in line. Required_mi distance from the object. /4, 42 , A teacher sukgeats that the length of a degree of longitude on any pirallel of latitude; may be found by simple4propor tiou; i. e., as the meridians appiorich each other69i. ruitei in , 909, or from equator to the pole, On the fortieth parallel•10-90ths ..of 694 miles .niiust eqbal . a degree. This is. not correct, as ,the strAceiN tweeit two meridians and the- part of A parillel of latitude intercepted \ by them is a ,:plieri&ti triangle instead of a plane one, and requires-for its solutioh spherical trig onometry. We know arithmetical solution. Teachers mayfa - scertarn \ very nearly the length of a degive of longitude on any parallel Ity measuring on mair s of hemisphere or globe : the space , letween any two meridians on say, 40th parallel; \ and applying the dista.7e to the equator on .arne map or globes It will be noticed that 10 degrees on the fortieth Male lea than 10 degrees at the eqUator. Now multiply the number of degrees on the equator thus_ found by 69.16 and divide by 10. The majority of the teacheris at an ed ucatiorifil gathering 'solved the folloWing . problerj incorrectly and as it may profit some we insert it: :3:xai-9 - x.l--S - 2=how many? The answer is 59. In this case, `ni3 vinculum or..parenthesis is used, the sign of multiplication, or the sign of division, affects only the numbers between which it stands. SoolOtime since a leading educator of our .!minty claimed that it is incorrect to . say 3 per cent.; that the correct expres sion is one per cent. Robinson's arithifittick contain / many similar expres sion's, and we 'de not hesitate to say ei .Per cent.;-wl4lMt per cent.? OUnmon School '-Grammar is somewhat 'like the reputation of hotel hash : it contains plenti,of m but would gtrAtiortinu nd classifi4tiog. . We fail l tolinti in his grammar as com plete and concise instruction is the fol- loWin CiIEAP r.ARE. pETwEEs TOW-AIN DA AIN .1) I'll( F ,Tho 111:17.!x P , I.•:: , "; carlylfig Wt • ,ll ..• Tt , s: I,l= plovid—t f.;l‘,;-;r, ,1;11 . i;• v: foct:ll.l.. sdag.• I.nri go. dlr.tutc, e3rlY-rd,scog,i...z.i.d , l' roust) Tin.i"nrEETS. tp: i 52.00. i•-___, • ..,„.-': i . N 11 . , :e1;111111.1:1:e 1."1 - - , i1 , :3.23 :lig' ! it• i:: , , trai , :tiit, I hal. e ciiiiviiiiled te ,•Al iiim 0 t:!1 I,,dt; tor A,2.liii. Tii li..t, rer f;ii - iiiir.dn Timid , irei e r , ..,...,‘,.3,.,,,, iiiiil Tioy ii 4, ' , ante rid f:lty .iiige i•:.: r,.. ; i i.. ride. TII ' h ET- -- fi•r,:sr:i , . t.qi .I.twi it Mit, *junta, and Anions 11.iiim.., i ll' i rti::. ~ Ist7 * O -1 1. 7 :ilATEIFANNA I Tllf. Fail Tenn of ltd., Itis , ittzte nIIF cow:A Aut;usT with a c~pot;3l . 1 .:,11:111 . 11.rrS. 1 .1 1;p 1 ..11 1 11 ; 1 1:ig1111 to di., %SI:41111g to 1 , 1 . 1•1.40• !or 1:4 , ;:( W.:1:b.:311d to (.I,talte r. 114.. i mint; of 1.:11.1ts of study. aria th.• • j r.r 11 , 11 S 11 1 ,1111! 1131v1:11 1111!1111111.er of TI - at h . in:! ; : il.a InNtiet• may he 110/1 1. each st L. , 0•11t. 't!o ISt, i.t•ta•, - wltt 11 a: liar r:ntpgn'nrrlu•l. 11; .• term_ I:,ji•Nlat zltit . tffl..ox W 11! I t j •,;;‘• j'Llurir.g th.• . - EN. - Vezises as rh, al; eau be r , r :st.t tietion list fir itralltc.:•! Q.' F.rc:xt:l l 4'grie. or I.:hor jar: itit.at - • Foti . : Tnietet.s 'FE E FAB ME II . tGUIT Nur (10.01 - F Is row isNue p.!rpetual iii, • -FA MI rnop.EßT`l" ONLY Each taen . klTr pace a Tee, at thellrne et'l rt.:lr to corer charter:tat , . nletztalrxpen,e.F...l tt:.• after rllttell lilt rtl":e n er raylllolll to meet aete3 r,1,3 I Cite amen g the neenll..r. piae of in - ,urance for VA In! 1 . 1:1..14 . ;!: . 1h rofe'..,g Into . .' c.v., or litsine, , .. SP RING II I Lt.. The Agent will . eanNa, 110 slap. or ;I .l '. rera, Wya:e,sing. and Standing Stone: and taz tn.et, In hhlpi wibhing lnsnranee or Infmniati , n, dress, . W. M. SI-I UM WA Y. - Pres. Qi EELE)."S ()YST R N, E BAY A 1.1151101•EAN few the M...5h51101i;4.. Board .the (Inv or '0.•••1' , rreasonable ternm.,Warm 84.Trell at all . Oysters at icholesale and 6-1,117 ' 9 4 4 ) , . KM. P.M. P.M., ~, ; 2 ... ... 442 • 2 41):„..„...: ',' •. 5 '35 ..... ~ 7 .:*, ! ,7 35 :.,.. 11 i.. , . 4 T...V x 3.; 'to 71, i 3 20 ; 9 IX/ 2 171ff.;,.j, 6.05 , 9 35',3 29'11 20 6 1,4-0 413 30 II 31,, 6 2.91 9 50;,3 36 13 ", 630: d..-.. •• 344 I 1 44 8 40 .... ', 3 7...!12. 'Po :,6 55,1025 4 15 1226 j - , 4 2412,?.; • - 1 '442 12 .40' , .. i - 4 59 12 V; :. .. •.5 ,#) 12 ,',. . 5 12 - I - 10 ....'11.23 53: 1 ..0 5 30 1 :..: LO 4fc a n. OZZIE It fAt• Z, 4 i I.? 1 7,9 7 3.4'+ 4-47 ..... . 7 t I • •11 13133 ' "S :10 9 9') P.M:. A.11..1.11 r• :to 4 :9 A•• 6 .• li) - 11 . . I 15 7 '2O s:, 1 V; 7 55, 4 4 '2 - 2: - • 1!1', . .. .... 1.5, ~ 4,-, ' /', . : .... , 9 1,1 3. '2. .-.. : • -4' t, .35 7 . •:- • : ~,', , ;3:, •/1 »h. .. ....1 ' . . • ,i 4 w If) ( . 4 -4 14. • if. /5 4 '":. .. 10294 a .. ...' .' . ~.•10 22 4 !.. ./ , '.. ~----- ... .. : ... 10 ,41 A0[,....7 31) 4 '0.",. • : : . 'OO )I.1:%?,--';, .... 11 1D 5 21 4 , T 2 1 1 2:1 5 .sr. 4 1 4 s 11 23- 5 24 s 4 4111 45 5 1.. s. 4: 1 1:42 411 .6 I !i 11 Tan ' 1, 4 , 11 .5." I 611 1 ~5 41...DZ1.. DEEM IMEINE ESEEISE IMO= IMIE =I B. I'. Tilt 'F X COLLE(“ATF: INSTITU'I 1:. E. 9t,1 N, . „ I _ _ : MEI A. B. N s_er. and A 7. Spring . 11111, Bradford Co_l%l. Mill