IMAGE EVALUATION
TEST TARGET (MT-3)
//
//A
V
/
>'■ c?.
/
s
<^ Mi
&"<
Cp,
y
1.0
I.I
1.25
;f iiM iiM
'^ IM III 2.2
It 1^ III 2.0
1.8
14 i 1.6
v]
<^
/a
OM
^;.
<^
//
y
/a
Photographjc
Sciences
Corporation
23 'Nlif MAIN STREET
WEBSTER, N.Y. 14SB0
(716) 872-4503
iV
^\-^
fd
:\
\
f^'
cv
<g^ «>
^^% ^i>
<S^'
%
^^
'^'^^\^"'«^'»
■r^
CIHM/ICMH
Microfiche
Series.
CIHM/ICMH
Collection de
microfiches.
Canadian Institute for Historical Microreproductions / Institut canadien de microreproductions historiques
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.
n
□
Coloured covers/
Couverture de couleur
Covers Hamaged/
Couvert.jre endommagee
Covers restored and/or laminated/
Couverture restaur6e et/ou pellicul^e
Cover title missing/
Le titre dc couverture manque
Coloured maps/
Cartes geographiques en couleur
Coloured ink (i.e. other than blue or black)/
Encre de couleur (i.e. autre que bleue ou noire)
Coloured plates and/or illustrations/
Planches et/ou illustrations en couleur
Bound with other material/
Relie avec d'autres documents
Tight binding may cause shadows or distortion
along interior margin/
La reliure serree peut causer de I'ombre ou de la
distortion le long de la marge int^rieure
Blank leaves added during restoration may
appear within the text. Whenever possible, these
have been omitted from filming/
II se peut que certaines pages blanches ajout6es
tors dune restauration apparaissent dans le texte,
mais, lorsque cela etait possible, ces pages n'ont
pas ete filmees.
Additional comments:/
Commentaires supplementaires.
L'institut a microfilm^ le meilleur exemplaire
qu'il lui a 6t6 possible de se procurer. Les details
de cet exemplaire qui sont peut-etre uniques du
point de vue bibliographique, qui peuvent modifier
une image reproduite, ou qui peuvent exiger une
modification dans la m^thode normale de filmage
sont indiqu^s ci-dessous.
D
D
D
D
n
V
D
D
□
□
Coloured pages/
Pages de couleur
Pages damaged/
Pages endommagees
Pages restored and/or laminated/
Pages restaurees et/ou pelliculees
Pages discoloured, stained or foxed/
Pages d^colorees. tachetees ou piquees
Pages detached/
Pages detachees
Showthrough/
Transparence
Quality of print varies/
Qualite inegale de I'impression
Includes supplementary material/
Comprend du materiel supplementaire
Only edition available/
Seule Edition disponible
Pages wholly or partially obscured by errata
slips, tissues, etc., have been refilmed to
ensure the best possible image/
Les pages totalement ou partiellement
obscurcies par un feuillet d'errata, une pelure,
etc., ont 6t6 filmees i nouveau de facon ^
obtenir la meilfeure image possible.
This item is filmed at the reduction ratio checked below/
Ce document est film^ au taux de reduction indiqu^ ci-dessous.
10X 14X 18X 22X
26X
30X
^
12X
16X
20X
24X
28X
32X
itails
s du
lodifier
' une
mage
The copy filmed here has been reproduced thanks
to the generosity of:
University of British Columbia Library
The images appearing here are the best quality
possible considering the condition and legibility
of the original copy and in keeping with the
filming contract specifications.
Original copies in printed paper covers are filmed
beginning with the front cover and ending on
the last page with a printed or illustrated impres-
sion, or the back cover when appropriate. All
other original copies are filmed beginning on the
first nage witi'i a printed or illustrated impres-
sion, and ending on the last page with a printed
or illustrated impression.
The last recorded frame on each microfiche
shall contain the symbol — »• (meaning "CON-
TINUED"), or the symbol V (meaning "END"),
whichever applies.
L'exemplaire filmd fut reproduit grdce d la
g6n6rosit6 de:
University of British Columbia Library
Ljs images suivantas ont 6t6 reproduites avec le
plus grand soin, compte tenu de la condition et
de la nettetd de Texemplaire film6, et en
conformity avec les conditions du contrat de
filmage.
Les exemplaires originaux dont la couverture en
papier est imprimde sont film^s en commenpant
par le premier plat et en term<nant soit par la
dernidre page qui comporte une empreinte
d'impression ou d'illustration, soit par le second
plat, selon le cas. Tous les autres exemplaires
originaux sont film^s en commenpant par la
premiere page qui comporte une empreinte
d'impression ou d'illustration et en terminant par
la dernidre page qui comporte une telle
empreinte.
Un des symboles suivants apparaitra sur la
dernidre image de cheque microfiche, selon le
cas: le symbole —^ signifie "A SUIVRE", le
symbole V signifie "FIN".
Maps, plates, charts, etc., may be filmed at
different reduction ratios. Those too large to be
entirely included in one exposure are filmed
beginning in the upper left hand corner, left to
right and top to bottom, as many frames as
required. The following diagrams illustrate the
method:
Les cartes, planches, tableaux, etc., peuvent dtre
filmifts d des taux de reduction diff^rents.
Lorsque le document est trop grand pour dtre
reproduit en un seul cliche, il est filmd d partir
de Tangle supdrieur gauche, de gauche d droits,
et de haut en bas, en prenant le nombre
d'images n^cessaire. Les diagrammes suivants
illustrent la mdthode.
irrata
to
pelure,
n a
□
32X
1
2
3
1
2
3
:. 4
8
6
IHh UNIVERSITY OI
BRITISH COLUMBIA
'fl';^ rt v^'- ]'V-'-r"''',
"v ^'.'//n '■■'' -':■,".*<'■'-' ^s "J
'■- if>ij-'.'--- :.-:'«j-;^-^-.;«<|K(c^t<
J^^7
"^-^ '*«•-►.<»
Read before the Royal Society of Canada. Section II.
At Halifax. ISI. S June 18 97.
BY MR. BAILLAIRGE FELLOW OF THE SOCIETY.
T)-l£ AB.STRACTy\ND CONCRETE E\ EDUCy\TIOX
Till'; \V()i;i). TiiK i.M.\(ii:. ti!k i;i;Ai,rrv.
Il is roiiiin^:' to 111' wi'li known, now n il;i\~. tli:it to cnsnri'
|iliU'tic;il .'ind >|i('rily l'csull> in tin' iici|ui-.il inii of 11 srii'nr.', ii- it,
'■vi'n lli.'il ol' l:ii,'U;i;i;i% t lis' c. inci-cli" niii>t 'i'o li.iml in li;ini| wilh tli-
iilisl I'iM't : I Ih' ri'iilil y oi' an iinau'f t Ilt^oI' wi i Ii i I|.' wor i cvin^'-s-.i vi-
ol' till' lliiii'i I I't'i'ii'il !■).
Till' wril'Ts lirst |i":-ri'^itio!i of ili ■ Imtli of this, was, wlii'ii.
a 1m)\' a! srliool, ho i ii t iii I i vi'ly so in say. innl- liiins'll' a sut of
.s)lii| roriiis. lip' siiiipliT oni' of wooil. ill.' olInT^ of |ia|ii'i' cut ont,
anii sliii'k or si'Wcd t.o;^('i hor ,il iIh' i'iIm-.'s. to i-naliN' iiiiii, the i|iiii'ki'r
ami iiioi'i' surely to tal\i.' in llo' I iMi'li I ii'.:'s of oiciiii'iilary '^coiiii'i ry
.■iimI inal liriiiat h's : ill" woril or naiin.'-a coin', a |iy r.iiiiiil, a spliri'i',
a cy lini|i-r — con vi'viii;.;' lln/ alistr.icl iilr.il of tli',' form alimli'il to,
wliili' till- inoilt'l itsi'll' was lli.i foncri'tion ol' liiat iilfa, ils finlio'li-
iijc'iit. il^ ri'.aliiy.
TIn-rr arc in;my il^'li ;i il ions of ih' two wor.ls; ili,. ,,\\ ' ^\n■^
\n nils', ii/ir,' to si'pai'atc, t') draw t'r.cn ; tli' ali-itr.U'ti'in of a i(iia-
litv inherent in anytliiiri i'r)ni iIp' lliiii'j; or entity ils.df; as of a,
man. a tree, a line, an anii'le. a liL;':ire -ihe tail, ill ■ I' iiliid, ill •■
si|ilal'e, till.' sti'oiiL;. ihe ri:lil. the rurx'.'d. th".iciP', ihe h-autiful
ill ueii, I'al ; or, witlioiii relV-rcMce to any mm or thiiiij, or t j any
|ie|-,-on Ol- (ilijcci, illnsi ra: i \ e of the i|iMlity si'll'orlh — in fact as
said II 'fore ; the mere name or a ppi'l l.a I ion of the lliinj' alluded
to; whih- the concrete {■'indm/ e/-/.s.j,-' |iii:roW toLTether) is the
thiic: itself; ilial man, that tree, tin- line \ 1!, the iiiaii'^le A I'. < '•
— tile ahslraci |ii'o|io~ilion a III! its ciiiicrete ;i|i|dical ion lo a part icular
ca-e; the word wind, rain, heat, cold as dist iiiei i \ i' iVoin the pin-no-
mi'iioii it-elf or from some taiiirihle, realistic idi'.il of the ihiiej-. as
a -en.-;ii ion. a ma nifeslat ion ilieieof ; or a piclnre wh ch renders ihe
ihiii'j \i-ili|e: lor insi.'ince. an inllaled sail, an nmiirel la. ;i mnllled
siiiinkiiri li'.:nre m' a persui i-iir^ man or auiiii.il. 'I'll iicr^t iiii;- of
an oliierwisi' jilistract day ofihe week ami year as •• .\sli Wednesday
"(lood Fiidav" " Kaster ."»iinday,' I )omi nioii. arh ir, t liaii k' -ii'i \iii'_'
da\'— a \i'ar; the year I'.IDIl, the year of siicli and siicli and eveni
— aiiioiilh: the inoiil h ol' may ■ a sea-oii : aul n iin. winter. spriiiL:',
Slimmer a million : a million doll.ars, :^ ihoiisand men —a iiiiliioii-
nail'e : a (loiilil. a N'anderhilt — a minisirr of ihe ijospel : ,a l!>' Mel.
,'i lieecher. a I'arkhiirst ci- a TaliiLiL:'!' — a, sciciitisl: a i)awson. a
.">tiipart. a Lallamme — a planet ; Saturn, X '|iiune, .Mercury— a star :
A Ideharoii. .Sirius, (iamma ('assiopea — .a lo\ely woiii in : you and
Mill and sou and all ol' yoii— an n^dy woman ; no, e\'.'ry ihinii' (lod
mad ' is lieaiil il'nl of its kind.
P?
.^i
i iil
('(im|iarc lljr \miv in which ;i chihl h'nrns tli( naiiic (il'a liall,
a [ihitt'. lu'caiiSL- hi' liamllrs it. and has ii paiiilcil in his ry^^ : whilr,
ndl sii till' la v< III' 1 hi' vvi'cl;.. licransc thi'V raniml hi'srcn, h"i Iclt,
niir a lurMil'i' hr inaih' nl' ihrni ; ami (inl\ niini' lo hi' iilcn! i fu'il, cni-
bmlii'i! in ihi'chihis' niiinl as Sniiihiy ; ihrilay we i^n to church ; Sa-
lunlax. the ihi\ piTci'di nu Sunday, ircniTaily a iudiihiy at scl.K.nl ;
Wfducsihu' will l>t' ihi' ih.ii'd day alter Sunday; or, more sul'-
I'l'stivi' in till' 'j,i'l'uiau ; til" iiiiddh' of tin' wck. Thi' (Juccn'- IJirth
dav will !>'' n'uii'Uili 'icd on acciinl of it- parades and lii'e works,
Cliristui IS hi 'CI use ol' Santa ( 'laus. Arhor day hfings itself iitu'k to one's
renu'uihfanee as the word sn'^iicsts. and otlii f dius to olln-rs lur
'.heir e|ad Ol sail le i einlii'ance-.
The ditlicnliy III' illiisti ation consists more in hnni.;inu the
mode of doiiiLi so or t h" simile to mi nil, than in apply in u it . l""or ins-
tance when ioidviiiL: at ilic iris en or drixiii'j' snow or sleet or rain,
you immedialely see in it an excdient modi' of oicl iiriim- the wind
if not of actually I'eelim;- it ; while, wilh r'"j,aid to the heat of the
sun, a stove, a lire, w hei'e there is no apparent motion, it nin.--l he
felt to render it seiisihle, or pii'lure to one's self what it is, in' its
action mnsi he noticed as excinpdlied in I he >,ofteliiii:;- of certain
sulisiances. in the lii|Uefy iiii; of ice or r'dueinL;- it to water.
I'mvideiice is full of modes or means co nip(uisator\- of missin'j'
or iiliseiit faculties, a- with the hriiid. the ihaf. the diiinh. who ;ire
;i"iiei'allv endowed with other senses, made more sen.-it i \e as t hat
of touch : the dwarf or hunchhaek is often tines more spiaLilit I v
hoth of ininii and hilly ; theii^Iy and defoi-med more in telli'.;en t ,
(plickiT ''f pel'-eption. .\nd if 1 he coinpi iisai ion he not coex ist.i n t .
it comes in time ■!< when-, th lU-h woman is the fairer, the prettier,
or more handsicaie while yoniii;-. the man whai old has the advaiil-
a'ji' nf les> oliliterated features.
In th' s me way. m 'ii not endowed with the ■neiital
facilitio for the ac.|uisilion of the hi'^iier iiial lieinat ics : liuxions
11.11(1 the like, enahliii^' them to de d w,lh and follow up or (dose upon
the \-ar\in,e p.nli and velocity of motion of a Jet of water, a stone
tJii-oWn from a sliii'.^ or from the hand, a hiillei. hall or --hcil from a.
rille. t:un or mortar, the motion ol' a planet or a. comet — such ineu
are sometimes endowed hy iiatnr' Wit h i n 1 lii i ve pi-oc'esses of eon
ci'ption of the pli 'iiomeiion and of itsinode of ex posi t ion. and with a
llicilitv of illustration which if ies- .-at isfactory to the truly scien-
tiCic. is the more so to humanity in i.;i'neral.
And to proof. a'.:ain. that the hrineiii'i of a thiiii;- t.> mind is
sometimes more .lilliciilt. than the dealiiiL;- with it. when ihomiiit of,
i.s the fact that so Ioiili' as. in readii:'..!' of the proposed Chicii,ti;ii dru-c.
Canal, the writer did not look at the map, he saw iiothini;' of a.ii
.'darmin.ii nalme in it, knowiiiL;' ('hicatio to he soiiie llDI) miles in-
hiiid or away from onr (.'iiiiadiaii frontier line aloiiLi' ihe Lakes; hut.
so soon as, he oiiv da\ diaiu-u'd to Innlv hehiiid him at a map of the
I ii
I'liilliniil'l :ll|il I'llilril Stilli.'S. il ,-tl'llrk him lll;ll liV ill • |>l'(l|li)SI'il t:l|i-
liilli: n|' l;ikc MlrhiMiiM III ill" rxlrllt i>\' 111 IU,I II H I Cllliic I'l . cil' WaUT
|H'r iiiiiiiili' ainl niiiiiiiij i t (ill' I nv ii'iis I li ■ ( iill' of Mi'xir i I liniiiLili
llir Drs .Mdiiir-. Illiiidis ami .M issi.--i |ii |-i\-ci's : ihi' llnw (iscr ill"
NiaLiara. woilil lie u'-^si'in'il liv .^u iiini'li ami liy su wiiirji i In' i'('>|i"i'i i vr
(i"|illi- nf I lie (iTiMt Lak •> I) 'low Si 1 |i ■ I'i i iT, ami (if I III' M. i,awrcnci',
lii'li.w ( (ntariu; tlm I'ili I In' lak"s may li ■ ila ii u al ii|i In I Inir rnriiiiT
li'\rl. wliilc llii' ilr.nulil (if ill" Si. l,a \vi\Miia_' raa mil li,' imaaaisail
This iiiiTc ai-riili'ii lal uiaiio' of his al \\i>' ma|i. ami wliidi iial
him to lie I he lirsl. in Drr sii') •!■ 1^.' I. ill r illlll'i' lIp' a 1 i fli I ii ill (if iiill-
fiiiVcni lllfll t In I hi' s|iiil ia I iiiii. iiiiihl hav- nccarrcd Id aiiul Iht, hut
iliil mil iiml is lu'iMil' (if wliai is IhTi' ailvaiici-il llial llu' hriiiiiiiii^' (if
a ihiiiu' In miml is iiiur.' illli aill lliaii ill ■ il 'iiiu' nl' it, when tlmii^^'ht
di'; and as a iinTi' id 'a is or has h 'I'li >i iVaill'ul in citiirr casrs ;
it't llif here ai'ml.' to tll ■ a;i|iar.'li t y cnmiiliral rd 'i iicst inii i,r riii--
I'l'iits and ire dril'ts alidiil I h • ! olrs (if I In' I'liilh a ml smli'^' 'Sl In such
us an- slniUiiiL'' I he siili'p ct nl' |Milar travel ami dlscdVcry. to lake
in '• cent rit'ii^al " liirri' or action, which im mitj as yt'\ seems in
ha\i' lildii'jht df ddiiiL;'. as ( iic iirilic im|iirtaiit lai'ldTs lint td lie
ncjih'ctial ill diailiiii; \\ i t h tin.' snl.jicl i.f al'clic ami ai.larclic di>-
CdVt'iy .
Aiiaiii in ihc -tiid\' dl'iimtidU in c.i him los li(|niil~. mi man
can iimlcrslaml ill' lliiii:'. ai ica Ic^ r'ld.'i'it I'vM'nt t i dlli.'i-s,
until llic idea dcciirs Id him (if Cdhirinir the 1 ipiids nr diic dl" tln'iii,
xshcrelix' il> nidi iun may h- -.■en and rnliiiw.-d n|i and s ilcni 1 t>.'d to
caciilaiidii, as when, with the (ihlT Slicam. ad\a:ilai:i' can he taken
df its dill'cia'iict' df ti'nipi ralni c Id sliidy it as what il ri'aly i~, a
li \ cr i n I 111' derail .
()t' |iriit'essd|- '1"\ iidall, Ileili'i't S|H'iieer says: "he was eml-
dwed with cdiist riieti \ e i imi u i II a I idii in a liiuh deLii'ee. in cdiiimdii
with sncce-rnl in\ e-tijatdf . in ■.;■ 'ii Tay li'ilis:ilayel il in ldiMiin'.i-
true (■diice|itidns nl' iihysieal |iiMcesses previnnsly iiiisi ii t er|irek'd nr
iinintei'|ireteil : amiaiiain in cmicei \ i n;_:' imides hy which iheacUial
relaliniis df the jiheiidmeiia cdiild li' ilcnidiist ra 1 1 d. ami aLiaiii in
dt'\isiu<i lit a|i|iliances tn lli > end. lie wa- an eMa'Ueiit expd.-i Im-
ami u'l'dd e\|iii.-ii inn inqdies in icli e imsmmicI i ve iiiciLii nat inn .
A |iri'|-eiinisile IS ilie t'drmiii'j: ni' tni ■ ideas nf the mental
sl.ates df tlids,. whil arc In he lac;:lit. and a fiii'lhcr |iren'i|i,i-itc is,
the imaeiniiii; nf iiictin ds ly which. In ,i;i iini iiix with < dncc|i! imis
lhe\- iKissess, there may helmili up in there mimls. the ( ceptidns
ill 'N- (Id mil p.isse.-s. Of c iiistriiclise iiiia-iiiaMdii as displayed in llii.s
sphere, nieii ,at lar,:ii — says Spencer — ajipear td he almust devdid ;
as willies- the alisiird sysleiiis nl tcaidiiii'.;' which in past limes,
ami hiruclv tn lliisdav, have sliipelied and still si iipefy children , hy
]ircsentiiii; alislraci ideas liefurc they have any Cdiicri'tc cnicepl inns
iVdiii which they can he drawn. Whether as a led nrer or writer,
profosjsnr Tymlall carefully avuided th,-. vieidn- practice.
i
— \
lllixlcv ill his lii(i.jr;i|iiri,'i|l ..kctcl. nf 'l'\ ii(l;iil lllsii alllldcs t(|.
Iliis wciillli iil'('\()t.'riniriit;il illiisi ral iun, ami of Lis inakiiii,' his wav
'" :i piisitioii ill s f vos|u'cts iiiii((iie l)_v sliciir Inrcc; of cliiiractiT
and inlcliccf, uilliuiil a(l\ iiiitaut's (if iMliicatiim or I'xti'aiiooiis aiil,
'" :' |'l:i''i' ill till' lii'st rank imi u;i|y of sciciitilii' wnrlci'rs I) it of
\\'iit('rs ami sprakcfs.
Now, while a siirictv like ihf prosi-iit is not to iKv-cciid (o tip-
roll »)!" impaitiiiL' knowledge direct lo the million, it hidmves It,
thoiio-h, to put olhci's ill the way ofdoim: so, \,y hriiii^ ^iiirir,.. stive to
th-m ol'the ways or at least of some of the modes of so doiiiL' in a
quick ami iiileHiL;-ihK' niaiiner. Siadi siin-u'esi ions n ay l<e fruitful and
always are in conjuriiiLr up in (he iiiimi like way- or amilo'joiis ones of
illnstnilion a,pplical.le to tlie deiiioii-t ra tioii of other phenoinena.
I'er adventure we may not have a [■'aradav. a Iliixlcx,
a rymlall, in tlie ranks of ihe soei,.|y. I'ivi'ry I hiiii: is dime here
hy purely malhenialiral processes, in no way siiitahle to popiilari/.e
scieiH'c of any kind, 'I'he writer himself is i),'rliaps the onlv (.ne
wliocan claim to iieofkin to the.-e inslrmt(ns of t he p,'o|,ie hv his
similarity of treatmeiii of what he handles, hy the anahmv of his
modes of illiistralioii, lmpal■lin,^ kiiowled-c and siig^estinj; toolher.s
how to do it.
Many have wondered and l,(.rd Aherdeeii mnsi have heen
amoiijisi thelii-sl to put the iph-.t ion as !,> why i he writer's paprr
on •• 'Irrlnii'-dl Kilii'iilinii ill l'i,t,Tliinr,tl iiiniihiij,:" ,if which Ills lv\-
fidlei, cy said that it was" Aihiiirnl,!, ,uiJ iims/ ii,h ri.s/im/ " and(]fwhi(di
llie Lurd r.ishop of t.Miehec, .M i; r He-iii ami th' t eeliiiolo:rists of i he
I'fpartnieni o| l'nhli<' liistriiclioii have i'\press,.d iliems<dves in smdi
^■lowin,!;- terms, should have failed to ser;ir.- a phu'e in o ir vol. of
Transaction 'or IS'.il, while so much oih.'r material of more donl,t-
fnll utility has heen put under cover.
ll there w-as no one there to judLT • of the im'i'its or iitilit v o|'
(he ])aper. why was it not snl.mitled to an outsider, or even I > I, ,ul
A herdeen iiimseif as patron of the sociiU v.
Amuheri'ase, in p.iint, is when some ye.irs ajro, the writer
suhiuitted a pajier (m " ll'mis In ( ;, ,,,nrl, rs h,r 'i )i>'ir r litim, of l-:,i,-l i,l "
a most important suhject for consith-ral ion and discussion hv the
world at hir,-u and whi(di if c;ii-ried oiil wonid ere this have" hen
fruitful of a yearly economy of millions of d,, liars .saved to parents in
tiif tuition nf tiieir (diildren l>y tlie ciiri.ailinn- ,,f | Ju,. time iiece.s.sarv
for the piirpo.se. This paper, it will hardly he credited, was referred
for their repoi-l to niemh'rs of the ,S,,ciety, '|iioiid,i;u lu'ofes-iors at
tiie Seminary of (>iieliec. totally niiacq nain led with Kiiclid. whi.di
nover crossed the threshold of that I nsiitntion ami a more .synopsis
of tlie contents ,,f the paper was triven hy th ■ ivport iuu^ coiiimi t tee.
instead n\- leavin- that for the author to ,lo if the whole p„per could
not he |iilhlished. thon^^h I ludeivc, of only someei-ht to ten paL'es.
The writer iherefore aftei- til' |ire>.nl s.-ssi ,n had mav h.j
I
m
I
''■■"'■I' l"<'iil'' 'III Iciivinu tlic r,iiik-i of she S(icir|\-, as il cdmics
t ' ill'' ^.i.iir lliiii'i wiii-llirr lii> iisi'l'iiliicss lias (h'|iai'lci| >iv llicri' Ik?
I'll line ill ihf Siirictv to a|i|ii'cciah> il. Ami yt tlpTi> is nn nnc to
lilaliic Inr ihis, CNci'pl may lie ill.' fart |li,-,t in aiMilioii to lli.' luiir
sfclidlis— Frcncli 1111(1 KiiL'lish l,;liTa!i||c. (mmiIuu'V, i'liv.-ir--. Clic-
illi^l^_v ai;(l .Mailiciiialic.--, lli;'rc sIhmiIiI df m i- li I lir a lil'lli >riiiiiii
i-niii|Mi>(>.| nf >iirii iii.Mi a- jlnxlry. r'aiadav, 'I'yiidall aiiil lln' like
NVlii'li al llic iricc'|i|i,.|i (,r llh' SiMidy, ih,. wiitiT Was iiiaiji'
liv I-di'il l;niaic aihl his ( 'naiocllors f ii- lumi'ia I Imh iiirnili.T.-. it
iiiiisl have lircn fur mpiiic Mipimsial sijcciality — iircMiiiiaMy dii ac
f'liihl (if hi,- 1 laliictiiin ill his liTaii>r of | sCit'i in ilir iMrnch laii^riiau.'
t't' Kiu'lid'.s 1 .ii'nrciii.s 1(1 hall' liicii' ii iiiiihir, while sacriliciiii;- imne
111' llu' ciiiiclii- Miis lilllif (Irci'is (liMiini'hT. -it (ui acniiiiit iif his
a]i|iliraliiiii cifllic |)risiii(iii |a I rorinnla In llii' cnliiiiL;- of allnnsl csci'V
kliiiun (ir cniiiTi \ alilr rlciin'liIal'V \'i>rii\ ii[' spai'c-i licdsi li l;' li'^iiri' —
with liir t'.\cc|itiiiii Hilly (it .-|iilii|Kvs. thri'- I'riista ami nl' iliii;-iilar ;
1 hill I ^h r\cii I'or I hrsc t III' antlliir's sysliMii hi'i ni^s (nit a cIdsit a|i irii\-
iiiKili'iii III ra-k L'liaiiaiiu- I'm' i nslaiicc. than a ly ii'iiaii'iiiL; rml I'a ii ihi :
■-iiiri' till- mil hilt iiirasiiri's tin' ilislaiin' Ih't wtimi ill' hiiiii:- ami lieail
with. nil any ii'l'iTcnci' tn t he ciii-val un' hetwi'eii ilu'iii. whih' tin-
|iris iilal I'lriiiula takes in as a fartMr tli" hall' w i \' il\a']i,'lei- h't-
wei-ii the Iiiiiil:' ami heail ami reiliices r he '.', tn i |i t e'lit nrerrnr h\'
the I'l'il to a 111 Te I'lMrl ina ,i;' ,i ,,• p n' (''ill In I 'i ■ aill il ir's pi'.iivss.
ALiaiii. may he the aiilhnr's simplilieil trealmeiil nl' sph.'rics
Was mil lA'erlii 'ki'il hy the ni'iuinal hnacil aiel I'.niiiiiii t lee, iinr hii new
ami ciii'la, ieil pnieess nl' ai I'l \ I iii:' at spherical areas. I)\- the sn eilleil
sphiTleai excess, lahillati'il I'nr ih':^ri'es. iiiiiiiltes. sccunds ami ilji In a
1 liiiu>aiii| I h nf a ■ecu ml nr le--. i h a \va \ In render il pn-i-i Me li\' mere
addilinii In allive al the area reiplireil nl'ailV pnl'linii nl' a sphere,
nl' nl' a le>>'l' pnrliiill nl a >j'hernid ill le^s ihaii ^> miiiutes.
liiii likely, the Siiciely since that, ahsiirli 'd in tie' iii ire inter
est iiiu' .-I ndy nl' (lei lunly, .Xaliiral lli-lory, Uinl i-y , IMi \'sic-;. I'liem-
isiry and I'dcci .m iiy . aid llm wi'il'-r ii'ini nii!' ni' ,'~^ir i'iliirind
Head's, ■• inl'erinr rac'.' " Ids Wiuk wa-^ iicxcr theri.'al'ter In, iked al nr
e\ I'll dreaine I nl'
.\nd ihiiiiLih the anllidi's .Mma .Mater, t he ,<eiiii ;.ar\ nr(^ielii'c.
In cnvcr ajipeai'i'iices. made him an .M . .-V. mi lie- slrenuhl dI' it. this
institnlinii ;.,:a\e the treatise the cnid -hnnlder liecanse the a itllnr was
iiii|irii(lcnt emiiiLih In hint at the pns.sihily n!', willi such a Imnk,
lea riiiii'j,' mathematics withn.ii a mister.
'I'lie dillicnliy (if illn-trat inn, as already set rnrtli, cniisisis not
in the dnin l;' nr linw tndii. liiii in ciinci.'i v.ii'i', in fad, nf hriii'^inn' 'In'
thiiej In mind as in illiisi rat i ii l;' the rntalinii ul' tin.' earlli upon its
a.xi-, when a im nnted ,-ph -re is mil at hand.
{•'nr this, an (iraiiL;e nr a;i apple nr a well made pntalo with a
liddkin nr a kniltin,!;- ne die nr a slin pen handle ihrii.st liirni'ih il
t l ililHWPWtl l lWW^^
1 L
llnni sfi'lli rn,-lc'lil iir jMili' III jMili.' ni;iy (In jjiinl (|llt\-; ;| |;|iii|i (i|-
li^lit : till- sun - ;i lin'k .-^tiick in t li" oraiiLT. a |iiiiiil dii llio ciii'iIi'm
Mii-riicc : aiul Imldint: thi' ends 111' 111'- axi.s irivoiir llnjiurs nr ratlirr
lifluTi'u iliiiiiili ami lini; ■!• ami idcliiiin'i il to tin' hnrizon, while
|iiiinlinL' a|i)ini\imalfl_v in I he (lii'cci i(in <>{' the nuitli star nr |hiIi' nl'
tiu' licavtMis, walk aroiin I llic imaginary >nn. irvolsini; llir oiMmrc
ax yoii go, n|Hin its axis, tliiis ilhist ratin-' day juil niu'lit. and the
wcascins and the year, sliowini;- the while Imw the (ililii|ue ravs
spreadiiiu over a laruer surl'aee temper t||c at imis|ihiM'e. renderinj: it
void or ('Old or rather not so hoi ; while when they stiike more |iei'-
]i 'ndicularly as at the ai|Matoi- and the trn|des, the heal is more!
intense. (>!■ the doiiMe rotation may h- pi'tiiri'd hv a vehide or
bicyele around a rill^^ a jet d'eau or th' like -ihi. forward motion
of the wheel, the yearly —that around i Is hnhor eenire, t hu diurnal ;
while the smaller or sleerinir wheel may re|ir.'seiit t lie moon, sine •.
thoi:i,'h it does not appear to eireiilal" aroiiid the uartii, it die-i so
ill reality hy, on aeeoimt of the d life re nee in \ elm'ii v of its rol at ion,
lireseiiting itself sueecssividy toevery portion of the ei(uallv roiaiimf
Eartii.
And in another must striking inaiiner can the rot.alion of the'
earth iipou itsidf he made visilde. to wit : ,i ttdieai'sal of Koiieanlt's
fXlierimeiit in the i'aris i'aiitlieon hiit on a smaller scale— suspend
ftii iron or otle-r heavy hall to aswivelhil hook in the eeiliiiLi' over
yoiir dining room or olllee tahh'. .Srt it (,-eillating in a direction
parallel in one >idc ,,{' the room, to a join t of I he II lor tn' lahle and in
less than an hour you will find it oscillaliiu' in a plane i|uite dill'er-
ent lV(Mn that in which you started it. .Andlhatthe ml il ion of I he
siispendinir sh im'. with the house and earih. has had no (dl'ect in chang-
ing the |daiie of o.seillatiim, you can see loi- yours(df hv holding' out
your waUdi ,at arm's length, it.s chain hel ween your thumli.anil linger,
and after starling it to oscillate, ivvcdve the (dialii which will al.so-
revidve the watch hut have not the least (df^cl in altering its |)lane of
oscillat iim.
Now I he writer does not propose to repent here his pap.-r on
" 'I'echnical eificai KMi of llie pciiph'. in u n I eidinica I lain;'uatie " as
read hy him in .May lMi| hefcjre sect imi II of I he .Societ v at Olta wa ;
hnt merely to give yici an idea of how to cimcei \ c a mode of i llust rat imi
(d' that wliii h you dc-ire to learn cu' to impart. In the-*; ideel ric ila vs of
va.st vcdocilies of pulsati(ms or v ihi'at ions, hv the mill imi mi llions in a
siiiirie second of time, (if tiny and e\i'ii microicipic niicrohes ; we are
at a loss to sec or to helieve ; liut wleoi the ^dld heater swcdis out
his i " ciilie of the precious metal to ,a n .irca of 20 ft. Iiv 211 or ll)(>
t"t. in aiea. the calciilal ion i.s (de.m'ii tary that its thickness is
reduced to the four mi llion I h of all inch or that it takes or would
reipiire 'Jolt.nno such thickness, 's th ■ o.ie upon tin; other to make an
inch ; and if there he IDU leivcs in an iu(di liouk, von then are
forced to the ( 'lusi.i-i that, ihiu as is a sheet of paper, the •tOOtli.
of an imdi in t hick iiess, yet is- e.ndi such leaf CilMI times the thickness.
^iini
mmmt
I L_
"I till' Ic.'iC III' j^olil ; and tliiil is mhiicI liiiiu vmi can lake lM'tW(.'i'ii \i)iir
liii'icr.M ami Icrl,
N'lnv as 111 an a|i|ifi'ciat inn nt'tlic iVactiun nf a sitihhI ; vmi
<'iiii call all niinil In ini in hall' a sit I nr tn Iwicr ten liftwcon two
sncccssivr lirats nt' a s.-cn.nls |n'Millllinn. I iln mil S:i v In iwt'iily hilt to
iNvirr ten. ihiis a\iiiiliiii;' ihi- I \vn sy I la lih-'il wnnis i hi rlri'ii, rniii-ti'cn ,
Iwcnly uliicli wniiiii he lnn;:i'i' in the sayiiiL;. irmilhc (.,>nt'iii's IJirtli
ilay Villi slaiul al iinr rinl nf a lanj;- • nl' nill) ini'ii I'lrin;,' a \iil!('V iiliil
as ihi' sniiiiils will reach ymii- cai' succcssi \ el \' - siiinnl travcllili;;
say llMlll fl |iiT siTdnd—lhcn ii» the nilll men at sa v '2 ft. centres, will
<'tiV('i' that distance theii' liiaiiL; will In \'nii|- ear ili\ide tin? secnml
inti) •"illll di>;iiiclly sepaiale inlervals. Nnw I'n a -tep rnrlhcr. takt;
lip a linnk III' say nlHI shei t > nr lea \es In I he i ncji, ymi can lillL'er it
and teel each sii(M'e<si \e le il' rush ]i 1-.I yn ir thiimh nail in I he ten I ii
part of a second — 1 hen ha\ e ymi the second di viiled into olM)!) parts.
ASi'aiii let there he a wheel divided into lOIII) parts, each part an
imdi nr sn. I he circinnrerence iherej'dre say ^'li I'l . and tin: diam lili.*
nr thereahniit — this is niily an ordinary si/.ed wheel, rind iiiav
re\nl ve once ill a s cniid, siippiSL' now t h ■ I U)l| t 'eth or cog ^ or y.iy s
are made up each nl' IdlMI thickliL'Sses nl' paper, iheii would Von have
the second divideil hy this process into a niiilinii parts, as eaidi
ciimpniient leaf wmdd pass yniir eye or ah iltiii^' tliiimh ur Hiit:(.'r in
I he million t h of a sk'cnml.
Nor need yon he at a hiss In nil ierstami how llie \elocit\' of
shot i- iniMsiired a\- as ■ertaiiied. lhnML!'h invisiMe hy tlie ver\- taet
of such Ireineiidniis s .ecd nil its way. i'llect rici ly .ikiii tn HljIiI. Ilies
arniind the w nrld at iieai'ly ■JMD.UIO mi les a s -c. iiid, nr I'nr our pur-
poses we may say i nslaii la iienusly . Then let a scM'cen n|' tins wire
lie put lip al say IHi) j'l . frnm ihe i^iin and aiinlher at anniher
hnmlreil t't. rnrlhcr (dV. mi ihc hill will piss t liro.iiih and st rike them
Illll h, thus hreakiiiii' the wir • and t h,,' idectric circuit : the interval of
of time hut ween I lii/se suc'-c-si \e lireaks tri Ves t he vidoci t v nf I he lia 1 1
which is as much as "JIKHI fi per second mure nr less accordiiiu- I,,
calihre and (diari;e ui' powder.
This ii luiniiLi'h to Lrnide ynii and h:i\e ynii under-tand hnw the
niniinii 111' a Imrse for instance, 011 the race, may h ■ phnln'd "JH times
a secmid, nr in HI I dill'erenl pn^itiniis nl'oiie nr a sin;:- ,e leap i'rom cart h
tn earth ajiain, and this same prncess can he pursued with an allileu'
snmei siuiltinji', with a circus man re\'nl ving a hall in midair nn
his feet, wilh a jngLT cr thrnwiim- and in succession catching halls nr
knives, etc , and if these plintns, or paiiitinfj;s made thereof he placed
snccessisidy arnuiid the inside nt' a hnllnw cy li nder, with slits in the
cvliiider ahn\e the line nl' picture^, and il' t his cy liinlei' he revolved
sa\' S times in a second, and as the hum in eye retains the impression
of any tliini; it sees diiriiii;' the Sth part n\' a second, then thus iU'e
yon made to see any ohject in 11; ition you may desire, such iis of ii
man sawini;' wood, a horse 0,1 the ;^'alnp, an acroliat's coiitnrtious and
the liki'.
i
'I'lif kinrlilatnL'l;i|ili uliii'li li;iNlifc|l tlh' ilrlkllil ami \Vii|i,|rl
111' X. 111,111 v. M III ill' iiiV-tiTliMis ih III tins : il is I lilt I In; a |ililica t inll
111' till' tact iliai till' I'Vi' retains iln' iiii|ir('ssiiiii ulam' iliiiii; it s.m'H
ilni'iiii;- a rra^'lnui of a s-tiiiiiI. I'lmln- arr lakrii. — sa \' 'iltll iimri' of
Ics-i (It'll III till' scriiiiil I'll." iii-laiii'i'i il carh i \ li ilij I imi is In last '\t\
>L'i'iiii(is nr a IlilllUli' il aiiv iiliirct i.f srfio ii|' (iliirc|> in Inntiiin
'I'lii'so arc rcilnrcil m h\/.v ami [laiiit '.I mi a st ri|i (if suinr I raiis|ian'ii I
ami [iliiilil'' HI' i'la--lii- ^iililai a^ ri'l In I niil . rapaMr iif li.nnu' wminil
iiinl iiiiiviiunil at |i!i'asiiro. Well it iiiei'ih' fiM|niri's that llic nn
wimlillir III' at lIlc fate nf at least S In 111 |ier s eoinl ( til.' imire. the
llinrt' lierfeel I he i 11 ii -ii 'U ) a llil li\ a li I i if I li e m ra Hi 'd ' ' liia;^ ie la II I iTli "
priijecteil (HI I'l a >r|-eeii with thai veli,,'jtv 1 n |ire\ en I | he t I'a lisi I inn
riiiiii the uiie III llie iheV rvnlii lieiiii: liiitiie'.l, and cause the ini-
iii'e>siiin nf I'Kiit i II mms ninl inn.
lietnni \\ e niiw !u mir iheine nl' the al'slract ami ennerete in
eiliiratiiiii. An exhiliil s.ivs ihe •■ .V'/V, ,/////' A >ii' rii'iii " w hieli in the
edncat innal depa rl men t iimie;' llie head nf e\|i.)S|| inn i|e:iis ('liii'aL:n
atlfaeted nineh alteiilinn fl'nni leaeh.'i's. i> tin' mellinil nl' leachili'i-
mat heiiiaties as ex|diiiti'd in the Wa^hi mjtnii |iiililie srlimd at llacken-
^aek. New .lersev, hv |Hiil'esMir Nelsnii llaa->. The General |ii'im'i ph'S
of this .svsteln were >linwi.' in the New Jers.'v edncatiniial exhihit.
the fnlimlalinli idea lieliiL'' In enmliine the alisliM.'l with, ihe en/ierele
sn that the |in|iil can eniii|ir.'hend in a |iraelical w.iv what he i i Ii'\iiim-
tn dn. In the pll nia r V m'ades w heir ch i Idl'eii fmni .>-i\ lnei'.^hl \('ar,^
nid are taii'^lil I In- iildinieii n nf mat heina I ics, ihe [iii|iil adds In m-
wilhilraws iVnm a Inl ti\' a|i|i|es. hall.^ nr marhles. mils. eii'.. ih,'
niinihei' In h.- add"i| nr sniilraeleil . sn that he ha^ liefnre him a nrac-
tic.al deiiiniisl rat inn nf the prnlde.n. In ihe luni'e advanced urailes.
|in|iils are a-ked In liml Imw manv vards nf e.i rjii'i i n.,.- of ,ji vcn width
ivniild he ri'i[niri'd In cnver a llnnr, nr hnw inncli jdasteriiiLi' In cnver
the walls, ul' nl' paint fnr the ceiliii;: and siinilai' praelical prnhlenis.
In each case tji" rnnm n\- r.ilher siilijeel nf the |iiM!dein is mil-
lined ill a. di' I wini:. Sn as in |i it he fnr.' I h ■ "V-'S i)\' the I Ml 1 1: 1 a iial lira 1
deinniistrati"!! nf what is w. unci. Tii,' s\-s! mi ii a|i|ie.irs li.is |MMceil
SI) elllcieiit that I lie cadet shi |i,< i n t li.' di^l rid nf \'.' w .lerse v, hilh f.ir
Annapnlis and W'.'.^i-I'. .in t areiik.'ii hv si mli'ii t s iv lin wer.' ediicaled
amler tins s\s|ein. 'Ihe same ]iriiici|i|es are carried niil in the
hi'ili 'I- 111 itli. 'Ilia ic^ nn a similar |d,iii. si that ]iiiiii Is fr i;ii I 1 in |S
years nfa;;'e seem In ha ve a clear c eii|irehcji-<iini nf |irnhK'ius inak't.'-
hra. ti'iL::onninetr_v a'ld even dilfcrein iai c.ilcnlns; the iimdels clearU-
and easily exem|ili ly in;.'- ilu' di 11' 'reui i 1 1< ,if liie several nrders in-
(jiiired intn.
And ih'T" are menial liindes nf prncednre in he resorted Id.
fnr .-iich a thijiLi', i'^'V ('.\ain|ile, as cnmini.i i nii,- the wei^idit nf har irnii
of any .s<'aiitliii.;:' ; there ar rtain uiiiis tn he reniemhered ami
they had hel ler he as few as |ins-.ihle. sn ma n \- I liiiiL!S I here ai'" linw
adavs In sinrc ill' mimi with in tie- .-a-nc wa\' as w (■ must
m ^,1
W'!..i»*w,'iwi?ww,JW---Ji?.R-^iT WT-n'v«.-rr-T'P*iTCT-*jm«p«WW(P»''«!i':iTW-r=^t Wfwr.i«»TT<i'VTi.. rv .■^■.^iMW»sW«cffPf«^nj»l>i.lHl#i-7^k 'ClI ^' .y^ 1*h^J!/*«C^ f«a
!l
:
know, \\>v \-vv\ iiiiiny |ir.ilili'iiis in livilniulics that :i ciiluc luoi cif
wiitcr \vci;:lis frJ* His. jukI tlint tlicidiin' an iiii|ii'rijil t^alldn islOlhs
ii-- I liii'c an' ti I iiallnns td I lie foot, iiiid that a hnrsc |i()\vit is i'<|iii-
\alc'nt to ly.'A) |I)S. I'aiscd td a hri^jit ol' jDII I'l. in r.iic iniiiiilr itv In .'):;,-
(iilll Ihs raiscil In ihi' hiM'.:iit oldiif Imit in him- minute nl' liinc. ami
thil thus wr can (Mnipiilc the water imiksct \\,y instance dl' i hi' falls
i>r .Miintnini'enev. i>v Niagara, nr u!' the llamilinn nf iialirailnr. Ii\' mul-
ti|il_vin;^- the al'ea in I'ei'l ut'eiciss si'etion nl' the river alin\c the rail-,
Uy the mean velneiiv dl' sti.'am. thus ^ri t ini;' the nuinlier n|' enhie
I'l- pi'i' minute (^thc Niauaia eurn'ul hein^;- I S,()(}ll,lli)l) euhie ft. in thai
inter\al nl' lime) ami as this niimhei' nl' euiiic I't. mulii|ilie(i intn
02* Ihs, the wei.uhl nl' water, ami the result intn the hei-ht nf fall
iiivcs what we call I'nnt pnunds; ami asa II. !'. is ;;;!,IIIIU ft. ||,s., it js
ihel'el'nre evident that diviilin;: ihe tela! I'nnt |inu; (Is li\- ih' .\(i. nf
them in a 11. I'. We ir 't th.' tnlal [inwer nf the stream.
Well then a cnli.e f i . n'' ;.•,,., j.s .|,s(| 11,^. reiuemhei' that and
nnthiuL'- t'l-t' nf what I am li'idnj i- tell ynu. I'ni' as \n i shall see, it
will take von less time In n , i ihinu:^!i the process nn'ntailv than In
cnnjnre n|) vonr rem lu'auccs of other i|ua:itities, J.MI ihs. divid-
ed into twelve slici:S to I'.e culiie fi. Lnvesvon 1(1 11, . to ihi. ineh
tliick and a It. si|nafe. Then. J an inch is HII |hv. |=|(i|hs. i .">
ihs., I „,■ -JMhs. ' ,_, I J Ihs., '„,'ihii'k -ives'Jh. an<l so ,.n. .'^av
now \-nn have a hii' '■) - % and since i =-■') Ihs., I ] .") 11,,^, ;||,|| ;] •
Ijeinu ihe (|uarter nf a I'n it ynu u'et ilr' } of I -"i Ihs. lU' .".',' Ih^. Airain
say yon have a 4 s|iiare har— spread it out nn'nlall\- into n
sheet ' ; thick. It will h" 7 limes 7 nr '\ in wnlih ^n- ll inches plus
" 'd' an inch., and the Wei-ht will li • •i\ |lis.. p|us',,,if 10 ,,/. ,ir
iH'arly another o/.. Iniieter sa v '1 Ihs. ',' o/..
In tin,' All ml, r Mn^iilhii fni- M.irch IS'.M there is a feniarkahle
article liy Xieh ilas .Muiu-ay iSatlernn ■•'{'he I'efnrm nf si'<'ondar\- edu-
c'inn in the Unit. 'd .-Stales " It has c nne tn he distinctiv nnder-
slnnd says Butler iliit any fir reaching- natinnal refnrm nnist hei^'in
with the secondary scIm ds .'-^ecindary sell )ols h,i\e inn nften saeri-
llced the necessities nf sound traiiuni:- In the Incal dennind fnr an
am hi I inns prni.'rannne cnnlainiiiL' I wn scoi'e or nn ire nf sclmnl suhiects
nn nne u\' which is pursued far ennuijh (u' lon,i; enou,i;h fnr the pupil
In del i\i' frnm il the edueatinnal Value i| possesses. Or rhev ha\e
erred nn llie nther side and in their de\'olinn to a past ideal, excluded
from the cnrriciiluin whole fields nl' kimwl 'il'ie that hive '.irnwn up
within a century or less.
'•The cniisei|uenee is as presid 'iil Kli.it u\' the Xatinmil Kdn-
caliniial .Vssoi'ialinn, shewed very clea rly. se\-eral vears a-n, that the
Aiiii.'rican hoy nf lifteen or sixteen, nn whit inferior In iiis French,
or (terman fellnw in native a hil ily. is trmn t wn to three scars ludii ml
him in a('i|uirc'd knowledir .,
"For s.'cniid.iry educitimi aiil tlireu'i it ^~n- I'ducatiniial
orii-ani-^atinn, a Inn-' ■■'^lep Ins been taken in this directiini hv the
in
.i.u ' i.J.i^.i,..i...a. i .
i
.... l,t
(i| .H'l'filili;;- lli.it I'Ml lip h' llii' ;i|i|Mililin<'lit III ■ llu' ( 'iiiiilnil Ice
of Toil." Ivv ilii' N:iti(in;i! l'Miir;iti(uial As^iH'iatit'ii. ami nv (Im' cncimmI •
ii:irly viiliialih' rc|iiii t w lii'-li lliit (•i>-;muill('i.' lias recent Iv laid liefuru-
till' jiiiMie.
Tlii.v repiirt is |i,ihli,-iieii i>\ I lie U'i I't'iiii (if I'lilileiM ioli , W aslii n^-
tuii. i).(j HI 1(1 Id Iteolilaiiied ,)ii re,^!i 'st. I'li' ini.'iul>ers of l\: • e, (imnil lee
were: prosiilenl I '. W . VAlni nl' I larv arW l' nlvei'sity . eliaiiinan ; l>r.\\'
T. Ilal'ris, ecinilllis-iiiiiiT ^ r ( ilicat inn ; ]>l''sii|eiit ,1 aaili'.-' I>. Aiiuell, nl
tiie l.'inve!v-il_\ t>i' Mieliinali ; |U'<'siileii 1 ,1. W. Tavlni. nl' \a>s;ir('ii|-
ie'Ze . Mr. .Iclill Letliiw, 111' iKe ...m'Is' liiuii scllnol, llistdli Mass.; Mr.
I). I). Itivhi s.'ii, Mf (111. .VIImiiv .\. V 111::!' .SvIiimiI; ivresideiii .lalili'S
II. I'ml-ier, ot' the Uiiiver-ity ol' i '.'Iium,i|.> : iiresiiient 1!. 11. ,Ies-e. i>l
'.lu' L'lli ver>ir '. Ill' .\Iiss(( ii'i : .Nlr .'. < . Melven/ie, (iriln- I.awrenee-
\;lle X. .r. .-seiiiiiii ; and ] • n i|'.' -s, ir Henry C Kini:, of ( )lierlin ('<iUcm,u
Ni lie rnii|'e\'en','.'s Were a]ij ••'in ted u'.'teli nn.'lulK'rs e:u'li ; one.
I :\r[' 'III Ijatiu. (iri>id\. I']ii>;li~li ; one mi "ther inudei'ii laii iniajie.- ; .i
r.itii'erenee nn I'liy,-:''-. .\ ■! i' einau' a: i d ' 'lieiiiisl ry ; one uii Natiiial
(listnry, i iielndi III;' liiiii(':jy, ll'tiny. Zi;ilo:;-y and I'll \>ii >lri.;y ; au-
"tlier Mil !Iis;i)!y. (iiil ( inv (■niniini t and I'ldilied Keonniiiy ; ihe
uillth lei ( l.'ii'i'M j.'iy. I'!iy-.ie;il ( le. ';j r.i piiv, (MMloiV, Mi.'t eiiroliljy .
Aniniij:- tile ni!ie;_\ n.mie- will Ke riniii.l in my t'.ial st ind in tlie
('■reniiist ran k^ nf .Vnieri.ean ^clinlai '-hiii. and iin nin' nt liie ninety was
vvitliniit valii.aMi ■■ lue.iti.nial e.\|vertenee of smne kind. 'L'kis I'a't
lit" Itself e'ives ereat W'eiM|i| tn t llei r reeinnm.Mld 1 1 i. m < and lkeire.\-
l'..insti ve rejiiirl - w kiidi are a|>|iended (,) the re pin t nl' t li' ( 'nmniit tee
e!'Ten..ire a iiuii' .4' edaea.t iiii!.i.l inl'.irai.;i | inn and -iiL!'i:e>t imi "f the
nlllMist V.lllle.
Siiiii ■ of the eiMiel.i-i.ee, ;ir;(\el at liiav h • s iinaia ri/,ed as :
-liiiiteii in;:' whil" i-nrielii ii'.' ik.e seli'iid i II iiifii 1 11 111 : the aetnal aiirid-
-inu "t" tli>' till-' iHv.v d.'\ >;,. i 1.1 aril 11 ii't ie. al,uel>r.i, I'.enmetry. w kieli
r.lli he dune Uy inelirillLl llUlliy | 'Vi>|h isi t iull s ilitn die, lli.lkillL;' eii-
rii!larii'< u| niliers, making u.^ • of instead (vl' di-e.irdini.' the nierhan-
i.eil iih'a nrniiiiiiei a.s in ih" sii]K'r|i.i>it inn ul" lejin-.s [\u- nne iinon
'.he nth''!- I 1 pi'ix e (' inalil les iitid nther pruperlies set I'lil'th ill the
ennneialioii.- ; tiiil tii'tin' ii,,w -p-nl mi i^edMraphv in thesehuid-
'■- nnl of .all priv|) iftini; te the \aliii' nl' tin.' fe-nh .■"eelireil.
dne ti> I ml iinin d lately I'nner.' I i nu or einhnilv j lej; t In' iiirni'in.il inn nh-
'■ i!'i"'l ;i;id r.'ndi'riiiL; it peiaiau'iil or lastiin.'' hy the siiinilla neons
lindmi: or li.\inji on the .napev»i\ leealitv, lake, sin. river, inniiiit-
iln chain or oi Imr r,!ature alliid d to in the text, and only toihe
exi.nit re(|nired, or ,-o iniu h .a- ineiuniy can taki.' hold, ol'aiid store lor
'•line IIS' ; and ninh'r this li,;id | u,,iild advi-e thai an alias,
he always at h.ind ami tiii't v\ iienev er re.idiiie- hisio; \ , a, liierar\-
■vnrk, a iiewsp iper ai Mele, nri'Ven a r.Mii.inee. \<in -honld pas> h\
uol :t siimh' iialii'^ of a pi; , or T'li'i;".' of ih • I'lar ill's sni lae ■, with-
out st,,p|ij||n I,, |,,,.]^ jt |||, 1,11 ii,,. ,||.|p .||^,| |,ic;|te it ill y.iiir mind in
its r ■i;r.ti\(' po-iiion lo niher places kimwii to ymi. (.'hildr.-ii kick a.l
L-.
- li -
''''■' ■!> i!lt''rni|lti\r ,,tlllr s,M|,l;,| n,'|l!V:|ll uf 1 1 , , ■ si .„• \ aV ;,r,irl..
''"'.'•■ '"'" ■" ; '"'I- il "I"-! I"' iil-i-tr,l ,„| l,v til.. kMrll, ■!■.-, ,,'r ll,,. |,:,,,,,ll
••'-^ 111.- nlily u.l.v ..l','.Mlciv;ill- 111,. iiir.r:,i:,tioii .,iv,. • nr., !li i v j l,\-
' I''''""-'' "I' lli>' nrth'l,' ill (|:i..sli ,:i ; ,ii,,| ,h. not I, ■ alV; i.l h, ■!;,-. to
'"''■'■''"I" }'"•>■ iVii'liii- cvrii .,(■;, !,-.|,, A l,'.|.. l,.tu-,-i, I u,, lov. ■!■..; |1„,
'•"■'''■■' ^^''" -"ill '" '1' •'■'• \^ii ■" yo.i iviiini IVo;n your a!l,-,s, aiiYvo:.
^'' '11 "'il> 'll'' iiiori' a|.i.riTiatf llie -.ili.ilHiii.
A,L'aiii i!ir .-.|,cllin- !)ook i> <li-roiiiii,.|,ai I \<y ili,. ivp ,ri of ih..
'■""""'''•" '""1 '■'"■■"•ll ^iM iiniar is r..!a;atr,l to I lio' s,,!, ,r,li nalr plac ■
•!i;'i ii <.lrs.TVL'>. For f,vo L;..,i.MMii„iis, says |{i,|..r. tl,.- s, tuIKmI
•ii-anuniir sHiooi. !i ... ,; ,„s|,iiv,l will, tli.. j .u- t ,„• iM-iii,arv ..Tal.s to
"•'•"■'1 'Ik' iiiK'li-'iMil |,ro-n-- ,ft!i,. p i|,;| ii, (I,,, int."r,..-t nfil, ,.
'■""-''"■■-■■^- '''I"- i^'l^nn 'li.' ol iua:,y iMi//.|,.,. ih>. toriiial ■.•/a naia r
;".'l fh- spdiiii- l,.ol. will, it. Ion- lists of <'!iiM-rn-lil,Mii,i- wor.ls
liavo l„on its woajioi.s. >iov\;y ami u i i i, a st im-.;!,. tlo.-.,. aiviii,,-
>vn;.r,.,l iVon. ,t. ,\,.u- k •,ow..-.lj-o i> l,..i,i^ i.itro.lar.,| to .11 aai, nat."
"!'l. liiid iii-licr [),„...-,•. to ,.x|,laiii ill.. I ,u-,.T.
'i'lio ,.,Hit\.i-,.|ir,.> ,,ii laii-iia,-.. ai>. a unit in ilr.-i, in-- roa.lin.^-
'';'""' '" ll"' i.-iii^nii.-... 1 , I,. MihlirJ aii.l III., wriirr wo.,l,| a.M : sto.,"-
I"'"-- '■" ''■■"■!' ■' "1 "■'•'■y ^^■'"■'!- 1--I 'in;,- it. t,. Innilra;.. its |,r .|,..|. aii',1
''""■""-!' i':"^'iioci: lion a. Ill to ,..N|,laiii it-, nn-an ni;..-. as of all tin., mi-
nu'n.iis ahoivviaiioi.s u-:,i,.|, aro in..; wiiii i,, ij,. iva-lin- ot' a n<^^^■s.
l'.i!"T ai'tii'le tor ii,.-iaiir,.. aii.l liosi.of u-.r-h u-;,i,.|i tli,. ], i|,il |,,,s
in'V.T s,....n l>,.caiis.. tii-y s..l,lo:,, or novrr ocnir i n lii,.ratar.. of anv
kind: acon<,T..tion of th. woi-.l to I h,. ,.ar a. i t. ■Aiattoi, r..|nv.„.n tat ion
1^ !■> tlio <.y,.. lIiMor\ i.al.iral. |ir..fanr or sarr-.l. ->.o_:fa|,|, v. cat,.-
''I'i'^'i' "1' in a noV(.| or iia ir.i I i v.- ol' w iiatr vrr iiaiur,-.
'I'liHl lal.ofat..r\ l.-ai!iin- i< ii-tli-r i|i;:i trx; i,:„,k t,.ac!iiii^-
uhicli iiionns .i.^aii, that i li-. ...nin n,- niiiM u.ilian.i in iiaml v.ill, tlio
■|''-'''"'f •■ ''^ if in disc --in- ol tlir invssnr.. of i ],,. at lii.,s|,i, .f,., tli'
'■"'' "'"'d.! not ll . iMor,. (.a.-i!y in, I ..idrkiy civdit -,1 and !i.ti,.r r..-
'""'"'"■'•'•'I l'"i''dl tiin,. V, iili lliaii will,,,,, i li-. ..\ i„.ri ;,,.,, i,,] i,,-., ,f ,,t'
ill'' |iln nonii'iion rnunfiat.'d .
'I'll,. (•onf,.r..|H\. on History \vidi to Ini \ i. t hat s dij,.,'! aUvaV-
='■•^-'"■••""'1 ^^''li tin. st.idy of ,;■, o.;|-a|,liy. a.,d tli.. f.ivnc,. ontji,.
'■'"'''■ ■^"''i'' ! 'II''' "T III.!' niiiion : a Ii.'r iiImt of tip. ,.,,:,,.|.,,, ,.
"I'l' 'I"' :di-tract and a i,io-| in!|i.irlan! oiio \, iiiili any on,, ran |Mit
to til,. ;..sl l.y rndnaxonria- to I, 'all, or t..a..|| tli,. liistor>- ,il' a |, .,, ,|,.
v\ i til ami wil hoiit til). nia|i.
What uoni,; ill, lii-i,ir\ of a r:\\ Ul>' London. I'aii.. IJ.inii. or
cviMi Halifax- animiiit to in lli. ali-vm... .,f a iiiaii or rallmr niii-s
"I'll Hi 'll" sn((.i.sd\,. |i>.|iods of i;s .'xislt.m.,., virv.s ,,fi;s i,i|!,|i,.
'"'ddiii'^- and oiliiT c iilic.s wli, I-,. 111,. |iis!,,r\ unfolds its,.|r L,„,k
•'I' 111" \V'dlii "I" illusliati..n now a days: ..vcii t lie coininon ,.v,.rvdav
n.'Ws;>a|H.r, t,.niii-^ wiili |i,iri ra its ot ..vi-ry ind i vidua 1 ,if noir alindnij
to. dill-rams, .N|,lanalory of ,.v,m y li,.|,| ofacli,Mi; and -.Twliat faith
^^■'' li'^''' i" ii'i'ildiii' illn-^iralio., of li, . kiml, ||,,w |.r,.dulons ,,f ih,.
1-J
ti'Mllifiiliu'ss tlu'l'fnr. ulii'M We il,i mil even st(i|i Id |i hhIit on tin' fart,
lliat ill the a ji|i:ii('nl 1 y r.Mlisii.' rc|>rf-iciiiatii>ii nf a lial t Ic ln'twern
the li'diuaiis and tin' ( irrcks. t Ii'M'c cdulcl liavc ln-i'ii no iiliiitn'.M'aphois
at Iiaiiil to Hri/,c it (III the iiisiaiit. as at tlie [H'oslmiI tiiiiL' \vc ciiii d".
Look at the wcalili nf illii.-t ra ! idii in all iMir ^tory books. aiiiU'Von
iiiilo till' cliiliis A r. ( ', every letter iias its jiirtiire. a jiictiire of wliicli
the sound ot' the letter is siiiit'esl i \ e as A ol' ajje and lieiiih and
liny. 1) the verli to lie ami hee and insert, ('of to see and sea the
oecan and so on of all the oiIht letti'r- of the aljihahet ami if tlie
letter be a eonsoiiant with no homonym, then it is the initial letter of
some name or word or ihiiiLi'. some [irettv and suir^estive (Miihodi-
iiient of the let t er or of t he word and siirh as to li\ it in the meiiiiiry
and cans., it to be (piiekly taken in -another e\am|ile of the holp
the eoiii'reie is to the abstract in almo-i e ver\t hiiiLi capable of beiii^'
illustrated.
Allot er princi|i!e 1^. that ea< h year of the School course,
lie MS I'ar as ]i(issibh co!ii|dete in it-elf. and sidt' siillicieiit. and not
Tiiade dejieiidanl on what i- to follow. 'I'liis. say the conference, is
essential because thousands of [iu|ii|s an.' obliired to leave the Hjirh
School after one or two yiMrs and durinu^ that time ling-iiisiic. Iiis-
torical, niMthematie.d and -ci,:n till' s nj 'cts shoild bj iiroseiited to
them in an adri|uate manm-'r. ainl nunc than one foreiu'ii lanirua,i;'e
-lionld not lie taunht at tlie<ame time
Now the writer mii-l t lioioiii;hly concur in iliis o|.iiii()ii and of
the iinjioitaiicc of its leachin.irs bavins.' been witness to the fact duriut!;
his (Mirnculiini of studies at the (..(iHdiec Seminary, where the full
course runs over eijidit yi'ars ; the number of students eiitei'inu on the
course each year -- 10(1 or more — beini:' lieiierally reduced to 'JO per
ciuit of the number before ihey reached the n-aol. Well ? while it is
iinderslood that the La\al course is especially adapted rather to pro-
I'es-ionnal men and the priesihooil. than to the sciiuitist, or prac-
tical mecdiaiiic : this does no! do away w 1 1 li t he fact t hat man v of those
destined ;ii advance by their preiiuit iois parents, to become iaw\-ers,
di ctois and ministers of the 'jospid, iie viu- — tor one reason or another •
want of means or ot lierw ise. — j^-ei be\ ond the third or fourth or lifih
_\ear. ami as mathematics are taiiLihl only diiriiie' the Ttli \ear of tlio
course, while e\-en elementary ijeoiiieiiy is not coinmiMiced till the
lib year, the coiise(|iuuice is that those leavim.; after the two or three
first years of tuition or even the louiih, j^o away with a lot of to
then) — useless hitin. a lit tie iireidv and a mere inkliiii,' ofljterarv
attaiiiliienis, in sullii leii t Cither for the Inn-, the pestle or the luilpii
and without even anylhiii'j in fact to fit them lo enter upon the
St III lies ot all e lie- nicer, iui arct . a laud surve\or. nor even to start in
the world as an ap[)rentice to a car[>emer or joiner m- intelli"-ent
imadianic.
This is due to the fact that ueoiir'try is not tauulit. as it
sliou'd be, diii'i'iM- (he ver_\ lirsi year- of th' coarse; it is put oil' i i
te y . u» J
rj i
^Tjr-^s!W-.'«'.T'r''i'''^-'^^"-'i^'ti»^^i'".~;.:-'t*»^"'5Js:.*i-'
^:-''i'^Tip(jr-i'f«»v-.-:'''7>::Ar'ji:5:?.i«rv'.f"^»5ii^Ji^-5«a
''"'■"''■'■'"' i"l"""ly "'■n M"i'"i''Hi,.- ,,„ il,. t;„„.,|, ,„. |ir,|, v..:,r„|-
"""""•'■"■"'""""' ^""'i'-- 'I'l'i-^ i-^ ^' ^1 scTinns, ,„ust important
■n.itr.rlorcn,.<„l..n.ion a,p| ,■, si,,,, .i„H,l.| l„. ,,„. .t unr. to sn..|, a
Y'";';'-.'"'" ^''"'" f""^i-l^""n. ,„. I),.,.:,,-,,,,,.,,! „ri>ul,lu. In.lnirlM,,,
''""'''' ""^■'■^"' ''int.TfVn. in ,|„. |„vn,is,.s ; ,l,„„d, it i. h.nl t„
''■'■ '"'"•^"'•1' "I liisMhiii,,,. .,,, sn l,li,„| ,„ ,|„. i„,,.r,..l. „r ,|„.
""'''"" '" "'iMM-li-iinr^aiwis,.,.!,,.-,!,;,! |Hn il. nt tliat „^,. tak. -.,
inurl, ,,,.„•.■ ,,nM.klv t„ anvil, in^i,, ||,. ,I,..,.ni,| , ^ ,. „, ..„n.| n„.n v,-
'"'"■"■'"■'■'■""> '■^"' l'-"'l,. ,■:■!,.,■. |,..nnl.,lui,|,.,-ss,.al..s i olh-r
in.slrniijfnts Im ilicii' oivat drljolir.
This is wi.v ,.,lM,.;:,i„„ i„ L„uvr Canada, ll, i,„-aii ,f,|„.
I^-'PK., .snnt rl,. |,rar,„.al,.,|n,.ali„n il„n^l,l I., I,, and .s,.:. na 1 1 v iu
*!"■':'■'• '"'''"'^■'^'^"'"^ I.Tit..inris,li..,i„M.an,| wl,i,.|, In nnn.rs
""""";" ''''^■" '" 'I'r-^'.Mid lillr.nlinn,. t„ lak- llnnr rin,. iVun.
""■'""""■'■ '"•^'■'""^"""l' li'" "I'l-H rai.itai. .^aininu• r.,r„fe.,
=" ""■ ''^'"<l-<"l'Sii' Iv i !I,.ad. c,;,..„r,,nr..-,s,.n,„r- ||,,
<tii:i-< 1 1 lias
iMiii'i-a-
nnnsa|,,,..|lat,v,.„r-,nl,n-i„r,a,...- i, ■ n,nr,:. |.,.,v i, ,„ , l,,,,,:;,^,.
''^■'^"' '"'■'""■ """''■'■" '■■'l'n.vnn.nts:an,|,.v,.nin m v I inn-, nuwlinV
■ V"";'^"- "'"'" ' ^^■-'-' |-,v,.ars,.ra„. an,l had n.n. ,.,.a,.h,.d
'''"" '-■''ll'"i-l^'--l-.-| ..i,ldn.„ sland.,anvl„n,..,-. llwa^ih,.,.
"""■''"•"'^■""■i"-i-n,ana:,|,r.nlia.sh,,,. uhid, I did. „f Ci vi] Fn„.i
"■'■"'^- A.vh,t,.,.in,a.. Land -nr.,.vin^ and hadinun-v in ..vnnral
^""'■"'"^ "1'^" "'^i" '"^ nnill, nnilic.s a,nl nn j,!,,,,,.; ,dnnni<irv'
l'h,l„.,,i,hv. inv i-hvl,„nVand 1,„„.. rarh in ils m,-, I, varv nialhT."
"'"' ""' l^'' ''"■'" '•■'•"">• '"unninnMns. an, I llnis .ain-l milv throe
•'■'■'"'■- ^■'""■^"■'•'' '" ^^1'^" I ^^""I'l. h::,| I r.dlnu.al in ih. ,d',| ,„l of
(■i,nsfi\ alisiii.
''"'■': ^''>- ' ^^i''' ''"• ^n,li„„,,v ,,f on.. ui,„kn,,u-s|Vo,n
'""-'■''"■'"■'''•"^ "^"1' n:alh,.nn>nr, or li,. ,|,.:n,.nN HnTrof IV,,.,,
""■ ^■'■'.^ '""-" ofih.. n,niM., a,ldi.,^ol,i,.,.; i,.ssons on .h,. kin,hn-
irniirn s.xsl,,n and ~- noi hn^Hlin^ as | m.v,. hini.] at hHoiv
"^^"'"' I''-'"-" l"-Hs,oi„. |,,„a„.d In n.adin^ al | uilh sonu^
""" ""■'"■'■'■'■' v • |,rononnnalion a; rarh wo.d. and ,.x|,lain ih,'
""•'"""■'■-• ''"■ ''^'y ■■'"" "i'"M-.nv of ih,. ihin. as for in.,,,,, ,■
""■":'"''■ "^'" ''"ll^l"-'l-"-'''".ii:nrtnHn„sorano,.,.anlinnr- u„rds
7'"'"' i'"''"-l —""V i', hn^nn.^s. in ,.v,.rv ,lav l,r.;uo,,|.
'"'. "■'■""^^■''"■"•^"•''■'■|^""^^-ll'"'" ("-inav In. nni) h,. n,.v,.rhas
"'■ "'"^ '1'^"-I.n,.lh,. nn.an,n.o|-|, , his xonnulVi.n.dsih.iH, nils -
^^■'"■''^"' •"■'■'■'"^ ""l'"i-i ^1- <h'hlor. ,,v,|,i ,.. I,ankn,|,u.v, tax-s o,-
.ss,.ssnnn,l. .■nsUnn- d, ti.s. ..^nM. - Un ..torial .iivisn.n; ami .vpiv-
'""";'""" '" ''-^'>^'""V. ra-liann.nt.S.n,al,. Con^n.ss. K.i..hs,.,.,-
7""""; "' '""■'l'--<'"y uanis and n,nniu|,al ,v,„v.,.n tat i .vs of
111.. |Ho|d. -tiR. n:nrii.nsaiid ,lnt„.s of , |i,. „|i ,.,_ ,,,,„. ,,,^.;|
.iii'l'''i:il. ''hTical -|ilainliir and d.d'i
'"''"' '■ii''iiii, sn|,rrior, ii|i|,nal,
""■'""I"';''"'"' ^"l""'""' '■'""■'■^ ^""1 piivv ,.onnnl. lh.„- riiMrtions
p.vro,al,v..s ami j nn.lir, ,on. as iIms,. of ih. srv,.,,.! ni,iiistri..s'
nniHTial, local, I'cdrral. rolonial |not,.cl ion. IV,.,. tra.l,. li,.,.ns.s ,|r'
A''Mi'
'/> ' <>♦■
'■, i.>M>\;:'iir '<i.^i'/-;;*<:v***W.>***'«-l«s«'
11
'I'lit' siili'n'ct is si)\:i>!. Si i-(i-iiiii|ii)lii;iri !li;M I iiiii u fitidi'riiii;:
I'll in iiiv t'lvini' •■|ln' ;ili,-li;irl :iii(l ci ii< ri'Ic in i-(|iic;il inii " llioiiurh
Id 111' sure ; I :Ull still ill line. I'liT I lir \ .TV i-x [illiliMt inn (if ;i Wnl'il, is ill 1
iiiiiig't'. ;i iiii'iMrc. II rdinr.'iion nl' ii.
It is sinunliir imIim-iI ih.il lliis iiiT<'.--il v dI' lilrinlini,' tlii!
riijii'rctc rciiliiv with tlii' iiific iiann nr jili-t i ;ii;l iiji'iil of a I lii n^ shiiiilil
lia\e hot'ii so liiiij^- in fakiiiir iimiI, in a'-'Ttin^i: its*-!!' iis a spccily
nuidi? ol" ti'Mciiiii Li. liarniii'i alinii-.i f\i'iv lliiiiu' I'lincri vaiilu. WliiTc
and liow did wt' all li'arn llial this is a laid"-, that a (diaif, a knitV, a
hail, a windnvv nv a dmir ; hut in the \fvy ,-aiiii- wav that wt; always
have and always will tcath idi Idrcii — nut In- a incre repetition of
till' won!, wdiii'li to thciu would he ni; aninuii.'n.s, hut hv as ortcn and as
coiiMtantly jiointini;' to till' t hiii^ alludi.'d to, in fart taUiiiiraml Iniiidl-
iiii;' it. a.H iihi -tfal i \ c id' the meaning ol' lii'; word, Ilcru then is
till' coin'rctc with thr ah~Iract t'roin nur vi-ry infaiicv. and what was
rssfiltial then, wdiy not in al'tfr lite.
Ill t iiiu's i:oiii' hy tliiTi' Wen- nu olh.-r schmhv's to toaidi or
h'arii than tdfiiiioi I ary liciiinri ry , nr <diani' - and ast roiiiini\" — no
jihysii's, no (dii-'inist ly, im aeiiistirs, no oidii;-!, no |>iKMiiiiat ies, no
idfftririty, no |diotun raph v, cm,, could tln-n airord the time to dwell
on siu'cnlali ve pioposit ions ; Imt life is |i)o .liiort I'or ihat ill lliis T'di
I'eiitnry of ours, aiid no liiiie eaii h'' ;;ivi-ii to a inrndy theoretical
jii'oposition, or t hat has imt hi nu idse lo I'-'oininend it I han the ainiise-
nient it atVonls. X.i iiKirc time i.- now uasl'-d on the ui.'omet rical
solution of the '^i|UariiiL:' of the circh-. ih" Iris'ction n\' an ani:ie or
I he duplicat mil nl I he ciilie, since i hci c ari' so many ot her and (|uii kcr
modes ut' arriviiic :ii tInTii \\ 1 1 h all lie- aci'iiracv re(|iiired.
It liecoines nhsiird or iiseles- now a ijav to -av that iiiire
ireoinetry repudialcs the lie ch.i meal idea of ii.otion, since Ivicliil
hiniselt" eniild nut L'^'t on willcml li. as 1/ vide need in one of the first
pro[iositioiis (if t lie fust h'lok 'A here In; pits oil" fiL'iire on iiiiotlier to
deinon^trate their c'luality, aid since lie di 1 it inice, «liv not ii;iain
and airaiii whiidi would iia \e en;; Med hnii tosinipiily his deinonslra-
lidiis and reduce the iium'ier n{ h - propositions. Sec for instance
the loiii; and ro:iii(l ah ml way of hi- diowin(r liow the aiiiides at ihi!
ha 'c of an isoscelo t lian ul.' are eip.id. \vhile, hv .•(Mpposiin.' the anule
at llie sum mi I lii-ected and fdid 1 iic mic' ii.alf of t he ti;.'uri,' over on I he
(illier a \i'ry lew w (ir is sullice Id show t||c I nil h of t he ennneiatioii.
Aiiiiin i'.iielid makes fnur sep irate pr.ipoii I ions of wdial can he
exprcssetl 111 one, to wit tliiit : |) 1 ra 1 hdou raui s and Irian^'les upon tlii;
same or eipial has'-s and hetwecii the nun: parallel hi'c ei|ui vhIlmi t
111 area; hy merely suppoiiiii^ th | nil hiise-s siiperiinposed and
reniemlnjrin,:,' : 'at t'Very Iriaiiiile heinu- ijn! hiilf of its eorrus| ondiim
parallelogram, and tliil wlial i^ true (d'llie wholes is triii' of the
halves, tlierefiire must the tiiilli nl' iln- four M'para te eniincial ions
becoiiio apparent . .Ami how mmdi more .ihor! and faeiie would 11, it
liiive heeii, Kiiclid s whole theory of paralli.ds and ot" alternate, j.xto-
■■""■•""I i'l'iTlnr ail-l.'S. l|;i,i I, Iv (mILmI atl-Mtiuli luth,. \\u-[ nv
in.iilu;! CMrullary of his (lrliiiiii,,ii.s |„ il,e fllVci tliat (jnuiil iiicliiialioii
"I :i line tu otiiris LL-ivcs or implii's t'i|ual m||;;I('s,
riii'i-c is nui. Ilii'ii. can imt Ijc tin^ saiii'; iiitcn-st iiiiuiit'e.Mtfd or
'■veil Crll l,\ aiiv uiir III (I . stiidv ufa iIumiivih wIhmi Ii.' docs not sea
jii-l (il'ulial use Mirli llicdiviu mav l,o, wliurc it can liavc iHappli-
witioii; I. Ill llic iiiumciil iIjc .^ildcnl sees llic trend of t In; siilpj.;ct under
consideration, lie iinincdiatel y I livcs t,, ii aiid iin.ro especially .so if it
■"'I' ' 'li'ii "II 'li'^ priilessional ui.rk. 'I'aUe fur instan<'i; the thenreiu
thai '-tlie taii^-ent is a mean jiropnrt iuiia I lietweeii (lie wind-' secant
and the portion thereof which lies uilhonl the circle. 'I'liis the
•Mir^'ineer would look iipoii as a uu're t;.\ercis(; in geoiiietrv niid likolv
not tr.Hihle hiinsidfahHit i ts deinoiistratinii, if not tohlliow itapplie.i
III 'lie .solution (;f the prohh'ni of riinnin-a rai I way curve lliroiiH-l)
lu-o pidiits .,1- cities in sieli a w.iy as to hecoine tanu'eiii to and c miiect
ivitii or hi-aiudi into an e.xisiin-- I'a i I w;iy . Here again then von sec
'lull \vliile the tlnM.ivm is tin- ahstract of the tliiiii; nf proposition, its
Mpplicalion to a case in praelie,.. is its ciniciv. ion, its eiiih.d imen t
into real life.
U'hy also is any interest nnnil'ested in lh^> deui.ni.«triuioii of
iln- fact Ih.it the parts of t wo secants wit lioiit llnj ciivle are reciproc-
ally jiroportional lo the entire s.'ca'its? Sinply h-cmseit is ins-
'I'l'iiiental ill the soliilioii of the case i:i t ri-'oiioMnt r V wlii?ro the
''"'''■ ■''ides ar.> f:iveii lo lind the an^iles S.-e llic interest that
cnitres ill what is called the s.piare of the liy pot lienns,.. th,- so called
I'"'" ■'■'' til" JTih of t!i' lirst, h-iMirse of iis appiic.itioii to
Ihe soinlion of so ina:iy ca-e-^iii pr;i.'< i.-i 1 en-i neeriii-. arcdii tect lire
and land siirveyin-, as in the ereclicni of mie line i>erpeiidiciihir to
another; liiidin-- lor instance what leii- li ofhidderit take.s to reach
I" .■! certain lieitrht on a h iiise or w.ill. with its to it .it a ^'iven dis-
lancc lli"r.'fr<in) ; how when in a s,nniciivle ii .-liowsth" p-rpeinli-
<-nlur to the diameter from its apex, to he a iilmii proportional
lii'lw.-en the seuMiieiits of the diameter or h.isi', .a hI how h\ ih^' use of
this lacl. it siillices. to -••■t at the railinsof a i;,ilr,,ad oroth-r I'nrve.
lo niea-nre any cord of it. and lli' vers.^d -in,, or distimc.e at the
'•■•ii'ii' li'twcii til.' cord aid ,irc. iIim s|invi.' hilf the cord,
lli vidiir.' hy the know II porliini ot' ih' di.am, to -et the nnknowii
.s.■^Mlellt wliiidi adiled ,ind the .nm h, lived hrinL' out the soiii;ht for
radins; lor I neeil hardly remind you mieaml all that, cnrvi's on
railw.iys are of such inaLrni:nde ofr.idiiis as to preclude the jiossi-
iiilily of layini: theai (mt. as a uard -iier w.nilij a llower plot hv
ineanH of a rope or chain altaidied to a picket at the centre; tlioinrh
lo pill it down ini pa|ier on a small sc,il,. iju' radins must he known.
.A'.'ain. what more than mere (airiosity would hj ma iiife.sted
at the fundamental principle ,,| .all ueomelry, lint tin' tiiri'c aiij.Hi.'.s
of a iri.aiiLde are loiietjier ei|iiai lotwo ri-iit allJ.'•le.■^, wert; it ;iot that
ill-' pra-lical appTuMtioii of ili,' kiiowlelj-e of this fact enahlesono
1
11
- k; -
iml •'nl\ Im (iiraMiiT iii:icrc-,<iMc (lisi;ii;i-cs (111 thr cailir- siiii'acc. but
iiImi the tli>t, ■111 CCS In I ho -^iiii ami hk.dh ^hmI [ilaiii'ts, niliiiinal i iiu' in (Hir
kiiciu-|f(l-c ^<\' hr.itii'Ics and |nn-ii-,i(lc< ami nf (he liLnirc ol' ihc carili
»iiul liiiw In liinl (Mir wav ali(aii il and I raci.' nil I llic I ra jccldrv ot a
I"""'' "II the ('(d.'^tial ciiiicavc. wiih 1 lie same facilitv the ciiLiinc'cr
nnikcs piddi' nf ill iiinniiiM a sti-aiLrlil nv cnrvcd I'oad aniiiUl llic
li'|-c>^ls and w atcis n\' l\\r cai |||,
And wiili (ii licr cniA I's I liaii llic ci i clc, as I lie |iaral)(>la : tlnTc
i> inilliiiiu s(i iK'anI ifnl a- tn ciitr; ical its iiutc a |i[icai-aiic(.!
nr nil iMiisidciiim- its |n(i]MTlic< in the alistract : hut linw all this
warms inin aihiiirat inn. uIi-mi wc lind that a stiidv (d' its loriii
|HTmiis us witli uiuM-rin,-- acnracv tn I iimw a sludl iiiln the Inrli-css
nl the ciiciny — to iMlciilalc li i\v lii.si, Il <\v far a jet nf waicr IVoiii
a rcsiivnir. iVn ii a lire hn-c will rca.di ; and when uindicd to a
speaking lrniii])cl will (■..nccii I rate the vnicc and allow it tn h"
|'i".i''*'li'd tn a distanr-. n:- ili ■ curve suiicd tn a rcllcclnr wiiiidi m
a li-ht iiniist! -athcr- tiic ra v-^ nf liiiit ami mmkI- ihciii idl' tn-'ctiicr
(Ui i licir errand nl huiuanit v.
And nil a -^indlcr scale, a iimre inndest and cleiie n tarv : if
V" «"iild int(u-c-t ihc |iu|ul in ihc dc>(U'il)iii '.:■ nl' a circle in a tfi-
iin.^le, tell hiiii iinw IJiis wil; n\- uwy li • sniiie da\ ulili/,cd li\- liiin
in his trade nf tin ni- cn|.| cr smiih nr |iliiiii her. in ciiitiii: t'rniii a
triaimillar piece nC metal ;lie hiL;.;csl hittnui nfaii n\sler can nr
water |iill. the piece my 1,.. sil^ceptihle nf ; nr a milliner ihe ci-nwii
"' 'I 'ill' '"■ hmiiie! frniii a ihr.-e cnviiered [iice nf paste heard. (U'
I lie hnllnm nf a hask -t.
^" iidcpiale i.iea can he fnrnied ( f the d i tl'eieiice in (he time
"'' '•■•'I'liilf^ II >li:il.^ I','. dniliLi II ,uic>,df instead nl Iileivly heiii- Inld
'"'^^ t'idnil, \n (huiht the lliere hckill- at the li eu r- nf W ha I is
'"'"''' as. tn descnh' a Illan-le n\' which iiie three sides a I'e
I'lveii, tn hi.cct an .iii-le. in erect (M' let fall a perpendicular, the
(nllnwm- up the psnc » ^K^]\\i ry lut-Ult is a step tnw.ard the full
uiuhu-siandm- nf ih • thiiiu tn he done ; hut Imw mindi re tlin
'""i~'''h\' i~^ 'Il ■ !hin^ lint under>ln(i(l. when ynii pill \(uir hands In
It, yniir nwn hamU ; a< had ynii in j iiiier\ to si match two hoai'ds as
In imiki' a perfect j(nnl, nn amnunt nf i.dliiiM-, nntliim; hut an nft re-
1"-"'''' 'I'lil II' '11'' 'liiii.i: «'ouid r, iider you siiccc^>fiil in ilsaccom
plishimuii.
'I hi.^ >ysl,mi the wi iler durinj- his Inn^' career in the ediicMtlnii
I'l' Ins f(dl(iw> has alwa\ s carried nut llavinn fnr year> liad as iiiaii\
IIS a dn/eii sliid.;,,i> in hi^nHice, ill prepar.itiou as 'I'l'ch mdo.; ists, in
Knc-incerine. A rcliile, l ure. I.and Survi^vinc-, ,,\t.,-y (Uie of I hem wa.s
'"■•"''■ '"'I" 'II'' llii'i- ic(piire,L li uid lint sutl'ice for one nf them to
lonk nil while aiiniher ledd the 1 11 1 ( r, a nni he r tiie dividers and a third
III'' poiicil ; no! each of llnun hid to p.Mlnrm the operatiou. In ihi- \va\-
three mmilhs silliced fnv Ihe uh,,h. ten, hint; (d' plane and spherical
ureniiietr} and 1 1 iiidnoniet ry , the ineii-uratii full areas and the
''
\
- 17 -
ii|)Iili(Mti()ii of tlif |irismciul;il lurriiulu Tor solid (•(intiMitH to ovltj
iin!i;ri!i!ililc t'lciiu'iiliirv solid us illiMtrMtcd on ii iio'ii'd of soiiii' two
liiiiidrcd iiiodids. ofuliiidi tin- writer, had tin' honor of i-;iti'rliuiiing
tiic liiti'i'iin' and IlistoriL-al Socii-'ty Qiioht-c in 1S72 or sonic 'J'j ytvir.s
iigo, nndcr the iiciidinf.' " (leoiiiL'try and the StereoiMetricon."
'riu- solid ll^rnn-s now used ovcrv whi'ix* and c )nsidt'red e^-
wcntial to a proniiit nnderstandin.n' n\' 1h)\v to nicaimo tlioir areus and
Holidities, and tiioiii;ii llii'v may theniselves lie lixiked ii[ion in the
abstract as similar ligures of any other size, have their concretions
or enibodiineiits : t he one, tiie middle IVnstuni of a sp'udle, as a ciisk
of any size or curvatui'e — tiie frnstiini of a cone on its larj^er base, a
salting t'.ib or when re\'ei-se(l a butter (irkin, a waste paper basket,
a tund)ler or drinking' s^oblet, a brewery vat, a bncket— its pi'isms,
tiie forms of solids of conslrnctiou —its pris;noids, roofs ot" everv kiiul,
bins and other vessels of capacity, railway ombinknients and exca-
vations. — cones, pyramids and their fiusla, the sphei'e and sdieroids
and their sections; illustrative for instance of the facility, with the
one (|narter of the heimsphere at hand and its tri rectaniridar triiin-
<l\c. of how one can see the way in which a splu-rical triaiitrle may
become so snntll as to be e(pii valeni in arOa to a i)lane triangle, and so
fjreat as to e(inal in its snrface one half of tint of the sphere itself,
with the sum ol" its annle-i t'ormed by th ■ three pairs of component
phnu'H, each pair spreadin.i: oi- jpeiiini^ till the contained angle reaches
the limit of two I'iglit aiij^les, tinally bec(jmes eijual to six liixht
angles, and illustrative of what in s|dierics is termed spherical excess
and of its use in workinjr out the true area of any extent of cauitrv
(Ui the surtace of the earth.
One cannot too stroiii;ly insist cm the fact that nothing to the
vouiig piijiil is so instrnclive because so amusing, as any solid form
he can lay his hands (ui and turn over on all sides and mani[inlate,
and asked nv tn\.\ what it is represi'iitati \'e of. according as it stands
or its broader or its b sscm- base or on its a[)ex ; as wh.-'n a hemi-sphere
suggcrt sa dome when lying on its base, while if reverseil it in-tantlv
bi'Ciinies a cauldron; a right angieil |)rism, not onlv the image of a
block of fmildings but of each and evei'y ol' its c imponent stones or
briiks, or other parts; an ebiiig:ite(l pi'isii'oid, a slick of sipuire or
waiov timber, a vessel of capacity — turned upside down, a roof, a
railway cutting — an enibankment when reversed ; an edougated
frustum of a cmie or may be i should rallier say the frustum of an
elongated cone, ih • ping of a sto[)co(;k. the shall of the Orecian Doric
coliim; the prolate or elongated s|uiidle, the weaver's shuttle, — its hall',
cut lengthwiise, a boat, a sliill'or caiio'.'— and with bottom cut away
and ends cut short, a scow or Hat ; — uv, the half spindle when cut
the other way or acro-s its long 'V axis, a tilteriiig bag if held as such,
a minaret if turiiod point upwards; the same spindle with both its
ends cut short, the windlass of a ship or the shaft ol the connecting
nul of a steam engine, or winui unet|ually cut, the shaft of a grecian
.^- IS -.
or a I'Diniin roliiiiiii lirtwci'ii li.i^c uml r;i|>ilal •, tli" acuti' tiii'^ula nl a
M.herc, llic iairiL'o (ifoin' nt ili.- cumiitiiu'ii t .-ii'ci imis (ir iMiinla' ut' tin'
niantl' wliirli w 1 11' 11 perl I'd nH' ii'\ i'al~ In I In' ast( ill i slircl a In I adaiii'iiiir
rvt' till' \t'i'\' jiiu'lrv (if 'Ui'oiiirl rical ruiiri'i'l imi.
V.'s I lie uraii^'c iM' ii-,u>k iiiclnn wii h ii.s lifiaitilull \ rililicii v\[v-
ii<ir iiiii.'^l 111' aiiiKiii:' till' iiiiiilfls (.'ithiT ill its rcalitv ur in iiiia^n as
siliru'i-S'i Vc III till' |ill|iil 111' l!lr llli'riiliali iiia'S W llirli nil tin' ;^liilii'S lie
.-Iiiilics lain'i'l luit tin- I'ailli anil ln'a\(n> iiitn ;j,riiil|iiiii:s i-i' land and
water luni lln. I'l'iistt'lliitiniis, and wln'n iiiln'r lines ai'o drawn acrn.-s
tlii'-e eiiiiidistaiit tVdin tlie iinii's and the ('niiatnv. ]iaral els nt" latitude
Ml railed, eireles iil' di'dii.iii inn, nii>>iiiLr 1 lie meridians at right angles
and the ill trrserliuii iil' tin.' twii, ii,iiieali\e III' the exact im^iliuii i,il'
anv point niioii the >nrrai'e.
Again there is the ijiiarl iT->]ihe re reinindt'ul nl' tlie vaulted
apsis (if a ehiinh, the head nl a nieh; prisiimids i llii>t rat i \e nt' a
sijiiare liased tiiiviT, riml' ur ul her st 1 iieliiie terminated li\ aiMietagou
at tii|i, iir hv a Hi|nari' turned angle-\vi>e In the oiln-r i r liy a circle;
the wedge illnstratn ■' ul'the iiii|dement id' that iiaine ur w lien ui'eet,
of a ridge-|aile-caliiliing tent or hut; the twisted [iiisiii or parallehi-
pipedmi to cut a hand rail froui for the well hole ol' a sla ii ease ; tin;
eiirveil cone a:.d twi>teil as ol' a horned animal or (lowder-llask or
eoinii-cii.pia. eti'.
'! hiTr al'.' also the eoiiU'ouiid solids or which iiia\ he dceoiii-
po.sed into a evliuder ami hemisphere or other t'rnstuni ot' a sphere
iiliist i'ati\ e of a murtar or engine ol' war for throw iiig shidis -ihe
heiiiisplnre and I'rustuiii of an e.oiigati'd coin' : a gun. a cone and
frustam of a sphere, .i lnio\ — or the gas hmn composed of tlu-
hest portion of a sphere or s[i|ieroid (that is more than half)
Mirinount''d liv a hollow or eon-a\'e cone or the fru>tiim of
one and ih ii.--l rat i ve agiiii of a tnrkish or a nioori-li dome
or hiiial i.r in. iiaiei ; hill t In"-!- I'l,' \v comp i and li^rnrcs are nu'relv sug-
Lfestive (if ho w ol hers Ilia y I )■ grouped or a pp lied the one to t he ot her ;
till' cone to tin' cy I inder or to the I'm -I nm of a cone as the iunnje of
a tower with \i'rtieal or haltered side- and a conical roof, or ol' a ha iv
-lack.
The sections or I'ru-ta of I ho cones and conoids, straiiilit and
curved eive the iiiigula of ho if. the lunette Inaded opening intcr-
sectinir a curseii or \Mulled ceiling or a doiiie, while llie plane
>ecIioiis illustrate the lriaiii;le. ellip.-e. liicle, patiiliola, h\ perholu
Now, 1 here are compound .-olnls illustrative of the lines of
penetration or of iu let .-vciidn thei-cof ; or tin! frusta ol' cones and
cylinders and spheres can he |iiil logeier ur held hv the piiiiil in
ju.vta position in a way to show the projections of said li nes of peiie-
tialion as looked at iateralh or endwise or from ahove : as of t\\'o
('\liiiders representative of intersecting \aiil t s or sewers or drainage
pipe-i, water or other ooiiduits which wiieii ot' e (inal diaiiit ter, gi ve
■ I
- Ill -
.straight liih's ut' li iii/miliil \u\(\ (;;iiiii; and wlii'u ciii'Vi'il nmii'
or U'ss iiri' iii'irc 1)1' Ic-s iiii:'rp Mict rat i ir: a:^ tln' iliaiiu.'U'iN ari' more
or Ir.ss lliu'ijilal.
Milt ulnTc till' (iii'iosii V, ilic inliM'i'st. tlio ciiiMlalinii ut' tlic
|r,i|iil CDiiu's in, i.-i ill till' >lnil\' nl'ilii' (Irvclniiiiu'iit ut' -iiirrac-'-i ; anil
in verity iiolliiiiji can Im' iinii^ini.'d mi iiist rn<'l i \ r In tlu'iii as iliis, su
siiiTurst i VI!, Mil I'diirati vt' nl'ji is a|i|irrn I iri'slii ji III' fill iiri' t radi'siiia iislii |i,
t'iiluT ii-i till or i'(ii>iuM' Miiitli, iir jil muIkm', cuiiium', juiii-M', tai or, iiiiili-
ncr, dri'ss maker mid wiiut-not ; I'u:' as the tin ami eiiji|ier sniitli
and iiliiinlier. iiinst kimw what shape t.i eiit his lu'lal tn, tn I'uriii
an (dhow, sii in, 1st the arl isf eharu' 'd with roliini;- ih-'hiiinii loriii
»ii\ilie he aware ot'liij peeii iarlv doiihly eiir\-ed or eeiea vn-e in vev;
outline which a sh eve iim.-t h« iir to lit it to I he hody ai t he sliiHilder,
niid so of oilier coiiioiir^. and ihe niilliiier to iiiak ■ a hit, or hinnet,
iiiiist he all I' to descrili..' I he circu ar or (dliplic crown, as well the
more or less spla veil la ho'a 1 'Oi \' iroimieii I and liiially the rim which,
nil. Ill list lit the one the (it her ami should do ho il' artistically diaiiiNl,
without the help of scissors to liriii'^' 1 hem into c intact
r.et iIhwi till! liov or air! or [iiipil or aoprentii f tlm •• Kin-
der^^arten" lie taiulit to lak" a eoae fir inslaiic.'. ami a pply iiiL' :o i i a,
piece of paper in a wa\ lo have an edi;'e of it iiin slrai'^hl froin the
apex to the hase, eii\iron il. eiividope ii. iii\cst it, wra|i it ify in
like, (lose liltiiiiily and ill. '11 ciil <ilV I he snrpl lis pi p m' with a scissors
or sliar[t cnltiiifi knife. .\ow ,ei him rem iv. lli • envelope ami spread
il Mill on the talde or a plane I'lc^d h lard. and h ■ will have the imiie
(if the sector of a ciivl •. I'll Ml {•■ \t ailill h- pi! toj; -tiler or its
edijeH he midi'to meet a iid en v.dnjie, if allow inc.' has li'en therd'or
made in the cnltiim': and let the edii'' he >tilcli('d, or i;diied. or pasted,
and von have the iiiiai;!' of the eoiic. of liie e\ t i iiu'ii isler. of the
cornet, of ihe spire iif a lich :\ . '['he smi I h see- mid notes this and
makes unto himself a pallerii or patterns of ihit ih'velopeil shape
which when iis ed,--'s are m id ' lo ai •■■I, will repro lace th',' c m.'.
And now for ilo' developed lateral snrface of the IV istnm of
a cone. Wraii as h 'fore ami then Miiwnp the solid, and spread ont
the oi'.velope on a lahle ami yon will have a sia'tion or poi'tion of
the aniiiilns of a circle, wliudi when its straijith or lateral edges
aie ii'^ain hi'oiiellt tonelher will h.' s i!.;;i'e-t i \'e to yon of the lamp
shade, the lateral pirlion of a pail, a pie dish, or a L'-ohlet. of the
ordinarv milk lareen of onr farmers, of i he siirronndiiiij: of a hai or
lionnet, of a collar or spl ^- (1 sleeve, cull', etc.. and in the same wa,\
as. to draw the cnr\a'd portion or hase of the s"ctor to form a c me,
voii mnsi take for c.mtr.' of the curve or cirelf the sanimit or
apex of the com- wlii(di thus makes know the radius reiinired ;
in the sime wav, to draw tiie lateral envelope of the friisliim of a
cone, the splav hein,<;' iiiveii or as-iiiii d and the diameter : you
miisl proloim' or iirodiic • the sid 's t i ai.'ct in a p.iint wliiidi will In;
the apex of the cone of "hicli th' iVusiaiu f.irms a piiriioa. and the
ffav«rffl«rT?irff>riiWfw-'
^^t^'^fr'^'? i"i-i^'
I'iit'^^if'.Tt'-i'tiril.
— -Jd ■-
ciiiicfiitric ii|i|M'i' :iiii| liiwor or inin'i- .iinl (tiittfi' I'lii'scs diinvii iVoiii
tlii.-< |Miiiit. witli ciuiiigli to simn' for ov«rlii|) at Joint, will solve tlii;
[irolili'm.
Ami ifllu' IntiTtil portion of a Imlii'H hat, I uioan that lu'twiMMi
the oroNvn ami luini is, to liivo it a jaunty look, to he higher on the
one Hide than on I he other, tin; milliner will not l)e slow at seeing or
if she (Iocs not. inn St he tohl ol' it, that in such ease the n|)|ier ami lo\^•er
lines of tiie annulns heing non |i:irallcl and therefore noii concentric,
they ninst eaehoflheni b- descril>ed from dill'erent points, oi- c(;ntres
the further apart, thi? greater the dilVerence of the hight or breadth
of rim of one side us compared with the other.
P'lhows can of course \\ ■ also traced out and at what ever
nngie : right, acute iw obtuse. l)y simple rnle.s thongh too lengthy to
dwell on in a paper which does not pni|iorl to teach the mode of
doing, hut is merely suggestive. ilin>tralivc to the teacher of the
value of models for the purpose, and of the extent to which the con-
crete forms or realizations of the abstract ideas of certain shapew,
quicken and facilitate ihe intelligiuice thereof and tin- modus
o|ierandi.
lint the ]u-ettiest solution, most dillicult of conception had not
nature itself led the way by suggesting it in the orange and ribi)ed
structure of the Tuelou, most ditlicnlt of execution, and where the
concrete form is most lielpful to the alistract idea of how the tliiii"-
is to be done, is that of the deve!o|)ped •lurface of a s|)here or sphe-
roid n8 for tlie covering; of a liall to play with, or the formaticm of one
fur geographical or urauographical purposes, or the ii.ill of n (diurch
steeple, or of an observatory, etc., or of any portion thereof as for ii
dome or vanltid ceiling, and the only ami best model for this is the
Bkin or peel of lb' orange, wliicli can be divided along its e(|Uiitor
into eiputl parts tlie more the lietter. lor a more pert'ect develo])e-
ment of the double curiature— with lines drawn from the poles oi-
opposite emls of the stem or iuniginary axis. These lines beiipj: cut
through, except at the e(|uator. the skin or peel can with the help
oftbecnrved bowl (U' hand e of a tea spoon be reinovi"(l without ii (law
iuid the whole spread out upon a plane, and exactly illustrative of
how to proceed in shaping the semblance of a ball, a dome or a
balloon.
"N es.it may be averred, without the fear of contradiction that
this concreting of the abstract, reduces in a ten fold maimer the study
of geometry and trigonometry l)oth plain and spherical and thus re-
duces it to the mere endeavour of as many months, as without it
would reipiire years to nnister and even then mit understand so
thoroughly, ami not, s) p(!rni;iueutly ap|)rehond and easier or more
liki ly to forLiet.as would be the mere word-painting of a landsCiipe
or of a hunnin foiin in the absence of the thing itself or of its picture
paint or photo.
And just here is proof of wliat the writer has advanced as to
I'M'ii cliil.iiTii iii.iiiil'f-liiii; nil inlfit'-t III kiiiiuiiij; (.r Iriiniiii-- ii
tlilli;: llial liiis mi |iriictic;il ii|ilil|c;it inu ; AllMh' dun.: llt<T nl' 1111110
liuw live \cars uraiTi'. callU' tn lin' :!.■< !<lu' \\ a ^ wiml In ilo linii' uilil
a^'Ulli wlit'li 1 liinl ilrawii I'ur IuT a linn.-'i'. a tier, a (lurk, an iltnisil iil
any kiinl. 'I'lii^. ili' (iuld \va> always int.'rcsti'.l in. Idcikiiii;- nii ami
wiiitiiiH |iati(.'ntly till it was lone ami why : h 'imiim' it wiis the r<'-
liroHiiitati \ (• of ,-iinict 111 lit; in ri'al litV.
'I'liif tiiiif I -tarl'Ml at a siinai'f- wliu'li 1 was sululi vidiiiL;- iiU'>
siiuilliT M(|iiarcs. Not 1 hat , said slu-. siiiiiinsini: I was >tartiii'j, at a
tic-tnc til in whli'ii she had li.'cnim' tnuld alr^'ady tntaki- t'lirth'T iii-
torest. .Nut thai. sIm' -aid ; mi mmsi'iisr ; lull, wait a liil 1 said and
lK■^'an t(i t.dl her Imu tin' littlf .■.i|iiart's wvvv the iiattiTii ol'thfciil-
(dnth ill the passa-i' Oh y.'>. sli" said: ll'iW liiak'' t he ma! liii!
S'lnari's and tih's that Isiw in thfllnDi' iil'tln' lirwrhaii.d uftllti
liasilicii. an I 1 I'lit tlu- iMfm'is nl' tin' si|iiari's and tiirn.'d theiiiiiiti)
iicta^'iins and sniian-s and ntlirr |iattiTns, and nh h )W didigiiti'd sin"
was whfli I iiiadi' a lot dI' !i vv u' >ns, wliirh hi.ik'Ml sn jn-i-tty In hrr
ovc, and liuw iiiiirh |ir.'ttirr win-ii I shiiWfd her jiDititiii nf a liecs
m-.st Mild tnld hiT Iniw th^ h -.s hiiild thidr iitth- ci'lls in this shaji.',
iiiid Imw tiii'ir iiistiiirt and (ind nivm 1 nt idliLiTiiri' iiianit'i'sts itsidt' in
iisiiii;- this iiartir'ilar six sided ti-nr". tlie uiily mii' wdiiidi, while ae-
ciiinimidatili^' itself til the li,i ly , if the insect, lil.s the lUieiiitu the
other witliiiut loss nf -paee. as in the nelaLinn where there are iiitM'-
veiiiiifT Mqiiares, in the s.inare whei'e I here are use, ess eiirners, and 111
the eirele where there are also iisu ess spaees and ul' which imiremer
not oiilv is Ih" iieripliery u-reater than that nf the hexaL'nn, li:ll where
a whole circle would In' reiiuired for each li.'.^ and the reiiuireil i|naii-
titv of wax thereliy douMed. while, with ihe li-iire chosen each iMii-
nouelit side does doiiiile dill \ .
In eonclu.-iou the wr.ter w,iuld reiiiurk. that as already
stated, the I, aval Cour-e in his liim- was and is still in .ereal im asiiro
,„,,r,. conducive to clerical re,|uireineMts or to theolo-ical lore to
which may he added the h .eal and medical sciences. 1 han adaiitedfor
Kn^rineirs. Architects. >cient ists Surveyors ; nor have many of tlio-c
who received their education there l.eeo.iie hriliiant in the e.xercis-
,,r the lalter s|iecialit!es, and due as stall il to an ah-eiice or oiiiissiou
, if the concrete toi;ellier with the ahslract I heori.'s taii-ht ; while of
ihe fornior. where no iiiatliematics were riMiuirci, there liavO keen
manv tuK'iited professors and pra^ti t ioiier>.
It may also he said as a tiiial allusion to the colicietioii of a
snhjecl that in treatises on malheimitics. and as carried out hy the
author in hisl'hineand Spherical Ceom. and 'rrii;. piihlished in I.SIir,,
much valuable «pace is niine 1 hy, insti'ad of ^iiivinii- the eniineial i ve
of a proposition in the ali^trac! and iheii rej. eat 111,1; it in tlieuiiierete,
so writili.ii' the eliuneiation with the letters of re fereli ee id the te.xt,
hnt in darker or ditlVreiilly coloured or formed lype. that it may he
reail lirst witliout the let ters refe rring to the concrete example
"■iviii", and then will. 1 hem.