The effect of surface texture and other factors on the specular gloss of flatted lacquer films

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\

PURDUE UNIVERSITY

I i J

! |

T H IS IS TO C E R T IF Y T H A T T H E T H E S IS P R E P A R E D U N D E R MY S U P E R V IS IO N

js by

Sarah Margaret Claypool Willoughby____________________

ENTOTr.vn

THE EFFECT OF SURFACE TEXTURE AND OTHER FACTORS ON THE

____________SPECULAR GLOSS OF FLATTED LACQUER r'XLMS_____________

C O M P L IE S W IT H T H E U N IV E R S IT Y R E G U L A T IO N S O N G R A D U A T IO N T H E S E S

A N D IS A P P R O V E D BY M E A S F U L F IL L IN G T H IS P A R T O F T H E R E Q U IR E M E N T S

FO R THE DEGREE OF

Doctor of Philosophy

'FESBon i n CnAROE o f T n n s is

H ea d o f S c h o o l oh D e p a r t m e n t

June

10 $0

T O T H E L IB R A R IA N !---T H IS T H E S IS IS N O T T O B E R E G A R D E D A S C O N F ID E N T IA L .

IF B S S O S

CHARGE

GRAD. SCH O O L FORM 0 -3 -4 0 -1 M

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TIE EFFECT OF SURFACE TEXTURE AND OTHER FACTORS ON THE SPECULAR GLOSS OF FLATTED LA0Q,UER FILLS

A T hesis j S

S ubm itted to the

Faculty

f

I

of Purdue U n i v e r s i t y

by

S a r a h M a rg a re t C la y p o o l V/illoughhy In P a r tia l F u lfillm en t R equirem ents f o r th e

of th e Degree

of D octor of P h ilo so p h y June,

1950

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

U M I Num ber: D P 1 2 5 1 4

®

UMI UMI Microform D P 1 2 5 1 4 C opyright 2 0 0 5 by P ro Q u e st Information an d Learning C o m p a n y , j |

I

All rights r e se r v e d . T h is microform edition is p ro tected a g a in st u n au th orized co p y in g under Title 1 7, U nited S ta te s C o d e .

T

P r o Q u e st Information and L earning C o m p an y 3 0 0 North Z e e b R oad P .O . B o x 1 3 4 6 Ann Arbor, Ml 4 8 1 0 6 - 1 3 4 6

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ACKNOWLEDGMENT | t

The w r i t e r w is h e s t o

express h e r a p p r e c ia tio n to Pro-

f e s s o r R. N o r r i s S h r e v e , Head, o f t h e S c h o o l o f C h e m i c a l E n g in e e rin g , Purdue U n iv e r s ity , throughout t h i s In d ian ap o lis,

p ro je ct,

In d ia n a, I.

f o r h i s h e lp and g u id an ce

t o t h e L i l l y V a r n i s h Company o f

f o r t h e i r s p o n s o r s h i p , a n d t o Mr.

i i

C. H. S p r i n g e r , D r .

W. B u r r , a n d P r o f e s s o r C. F . K o s s a c k

|

o f t h e S t a l s t i c a l L a b o r a to r y , M athem atics D e p a rtm e n t, Purdue

j

U n iv ersity ,

fo r t h e i r in v alu ab le h elp in th e

ev alu atio n of th e r e s u lts also expressed to th e

of th is

research.

sta tistical A p p reciatio n is

f o llo w in g com panies f o r m a t e r i a l s

f u r n is h e d and f o r c o o p e r a tio n i n t h i s

work t h r o u g h o u t :

The

i i

M a l l i n c k r o d t C h e m i c a l W o r k s , The M o n s a n t o C h e m i c a l Company, a n d t h e L i n d e A i r P r o d u c t s Company. i i t

Ii s i

i

Ii ! i i{

f ii I i

j

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T A u L a, O j?

i U S x ’i U O i 1 .............................* .................................................................................................. D E F I U I Y I O iv 3 OF

OF IA T H E IL & T IC a L

i

T E A L S U SED A c I) E X tL A l'U iT IO U

S Y iL B O L S • • • . • . . • • • • « • • . • • « . . - » • • . • • • • • • • • • •

I F T A O L u 0 'jl'I OF AL'jj) BUnV jc*X

OF

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FORK. • * • • • • • • » . • • « • • • « . . . • . . . .

1

11:10 BRU SH C O L P A E Y 3 u~Ai>A'JE A 1A1 Y Z E A . . . . . . . . . . . . . . . . . . . . . . .

1 51 > 5 2 ) was

w orkers t o d is c o v e r t h a t th e w ater o f a g e l m ight be r e p l a c e d p r o g r e s s i v e l y w ith p e tro le u m e t h e r , and propane

( a t low t e m p e r ­

rem oving th e l a s t by h e a t i n g u n d e r p r e s s u r e .

■White, i n a d i s c u s s i o n o f t h e d r y i n g o f s i l i c a

aero g els

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i

19

F IG .

h -

THE

PHOTOVOLT

GLOSSMET3R

!

) I i i

R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.

!

20

i < i j

(93,

99, 100),

s t a t e s t h a t rem oval o f t h e l i q u i d

is ac­

c o m p lis h e d by h e a t i n g above t h e c r i t i c a l p r e s s u r e . of a g a s-liq u id th e g e l is

in terface

v rithin th e g e l i s

com pletely f i l l e d

tem p eratu re

is

reached.

p revented sin ce

w ith l i q u i d u n t i l

'.vhen t h i s

po in t is

lik e

stru ctu re

w hich c o n t r i b u t e s

It

the c r i t i c a l

reached,

a n i n s t a n t a n e o u s ch an g e from l i q u i d t o v a p o r , o r ig i n a l porous s tr u c tu r e u n c o lla p se d .

C reatio n

th ere

is

leaving th e

is th is

sponge­

m a te ria lly to th e e f fe c tiv e ­

ness of s i l i c a g e l as a f l a t t i n g

agent.

Many o t h e r r e f e r e n c e s t o t h e p r e p a r a t i o n a n d u s e o f s il i c a g e l are a v a ila b le 40,

52,

53,

69, 31,

Inorg an ic

in th e l i t e r a t u r e

(4,

19, 23,

101).

silic a te

compounds, e . g . ,

cium , a s w e l l a s o r g a n i c are a lso used as f l a t t i n g

silicates, agents.

m agnesium and c a l ­

e .g .,

ethy l s ilic a te ,

M agnesium s i l i c a t e

o b tain ed as a f ib r o u s , h ig h o i l a b s o rp tio n type T alc")

may b e

("W estern

( 3 ) ’o r a " m e d i u m o i l a b s o r p t i o n E a s t e r n m a g n e s i u m

silic a te ".

A h y a r a te d calcium s i l i c a t e

i s u n d e r one m ic ro n i s silic a te

is

v arnishes

w hiting

w hos e p a r t i c l e

a l s o on th e m arket

good when u s e d a s a f l a t t i n g

(97)• agent

size

E thyl in alkya

(18).

A b ib lio g ra p h y covering chalk (calcium c a rb o n a te ),

(barium s u l f a t e ) , head

39,

(calcium c a rb o n a te ),

calcium s u l f a t e ,

in a d d itio n to

(102) and c o n ta in s t h i r t y

silic a s,

and b a r y te s

i s g i v e n b y vfood-

r e f e r e n c e s t o th e use of th e s e

m ateria ls. D iatom aceous e a r t h ,

a l s o known a s k i e s e l g u h r ,

d iato m ite,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

or i n f u s o r i a l e a r t h , has been used i n p a in ts It is

f o r many y e a r s .

composed o f t h e i n o r g a n i c r e m a in s o f d ia to m s

u l a r p l a n t s w hich l i v e

i n f r e s h o r so.lt w a t e r ) .

sk e le to n s are n e a r ly pure various th ic k n e sse s.

silic a

(u n ic e ll­

These

and a r e found i n beds o f

Most o f t h e d e p o s i t s now b e i n g u s e d

w e r e l a i d down i n t h e M i o c e n e E r a a n d a r e now o n d r y l a n d , th o u g h t h e y were form ed u n d e r w a te r p u rest d ep o sit

is

lo cated

(72).

T he l a r g e s t a n d

i n S an ta B arb ara C ounty, C a l i f o r ­

nia. T he p a r t i c l e s

com posing d ia to m a c e o u s e a r t h ,

since th ey

a r e g e o l o g i c a l i n o r i g i n , h a v e many v a r i e d s t r u c t u r a l f o r m s . The y may b e d i s c s , h o l l o w n e e d l e s , In o rd e r to processed,

sta rs,

o b ta in sta n d a rd iz e d g ra d e s, i n g e n e r a l by c a l c i n a t i o n ,

and a i r c l a s s i f i c a t i o n .

cy lin d ers,

etc.

t h e m a t e r i a l must be

chem ical t r e a t m e n t ,

The p r o d u c t i s

an amorphous pow der,

ranging in s i l i c a

c o n t e n t f r o m 8 0 - 9 5 :^ S i O p .

n atu ral p o ro sity ,

i t h a s e n o r m o u s s u r f a c e ar e: :-, a n d t h i s

p ro p erty , v alu e,

Because o f i t s

t o g e t h e r w ith i t s h ig h o i l a b s o r p t i o n and b u l k i n g

m ak es i t

M eta llic

a valuable

fla ttin g

agent

(15> 5 6 ) .

s o a p s a r e w e l l known f l a t t i n g

ag en ts, th e ir

use d e p e n d in g i n l a r g e d e g re e on p h y s i c a l c h a r a c t e r i s t i c s

(27)*

Since a la r g e

number o f m e ta ls form s o a p s ,

organic acid s

may b e u s e d i n c o m b i n a t i o n w i t h t h e s e m e t a l s ,

th e number o f p o s s i b i l i t i e s th e norm al so a p s,

a n d s i n c e many

is very la rg e .

In a d d itio n to

s o a p s c o n t a i n i n g v a r y i n g am ounts o f f r e e

a c i d c a n be made, and o f t e n even b e s i c

soaps

P ro b a b ly t h e most u s e f u l soaps f o r f l a t t i n g

c a n be fo rm e d . purposes are th e

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

22

alum inum ,

zin c,

stro n tiu m ,

tita n iu m soap i s

and c a l c i u m compounds.

The

r e p o r t e d t o be t h e b e s t one y e t fo u n d , b u t

h&s b e e n u s e d o n l y e x p e r i m e n t a l l y b e c a u s e o f m a n u f a c t u r i n g d ifficu lties

(27)*

The f a t t y

a c i d p a r e n t r a d i c a l may b e ,

s te a ra te , p a lm ite te , o leate, or o i t i d e a t e .

lin o leate,

f o r exam ple, th e

naphthenate,

T he n a p h t h e n a t e s o f c o b a l t ,

resin ate,

l e a d , a n d man­

g a n e s e a r e w e l l known a s d r i e r s o r o i l o x i d a t i o n , c a t a l y s t s , w hile th e

ste a ra te s

a r e t h e most u s e d f l a t t i n g

A d isa d v a n ta g e of the th e ir th ix o tro p ic

n atu re,

use o f t h e m e ta l s t e a r a t e s w hich r e q u i r e s t h a t

i n c o r p o r a t i n g th em be o f low s o l i d s ate,

w hile an e x c e lle n t

which o f t e n makes i t

tem peratures or sto n e

co n ten t.

is

form ulations Alu min um s t e a r ­

fla ttin g ; a g e n t, has a h eat s e n s i t i v i t y

d i f f i c u l t to g rin d .

an d c a l c i u m s t e a r a t e s

compounds.

Z inc,

m agnesium ,

can be s u b j e c t e d t o h i g h e r g r in d i n g

s o t h a t t h e y may b e g r o u n d , w i t h c e r e , o n r o l l

m ills

'w ith o u t g e l l i n g

(27).

They a r e , h o w e v e r,

less

w a t e r p r o o f a n d more o p a q u e t h a n a l u m i n u m s t e a r a t e . Th e p r e p a r a t i o n a n d u s e o f t h e m e t a l s o a p s a r e d e s c r i b e d in d e t a i l

in the l i t e r a t u r e

22,

25, 2 6 , 28,

29,

31,

70,

79, 8 0 , 8 2 , 35, 86,

48,

(5, 6, 7, 49,

55,

88, 39,

90,

12, 13,

16, 17,

20,

6 0 , 6 1 , 6 3 , 64, 6 5 , 6f , 68, 9 6 , 103,

104).

W axes, R e s i n s , a n d G-uras I n a d d i t i o n t o th e pigm ent

ty p es,

r e s i n s have long been used as f l a t t i n g c a r n a u b a wax,

f o r exam ple,

is

w ax es, gums, and agents.

Th e

use o f

co v ered by p a t e n t f o r use i n

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

m

23

lacq u ers and th e

(ll).

L e s s t h a n o n e p e r c e n t o f t h e wax i s

fin ish

is

used,

a p p lie d a t te m p e ra tu re s betw een 55-120°0.

F o r t h e m o s t p a r t , h o w e v e r , w axes a n d gums p r o d u c e s o f t , cloudy f i l m s ,

w hich p r o p e r t y l i m i t s

th e ir use.

R e s i n s u s e d may h e n a t u r a l o r s y n t h e t i c . tu re of a f la t

s p ir i t v arn ish ,

The m a n u f a c ­

c o v e re d by p a t e n t

(92),

d e sc rib e s th e use of th e n a tu ra l r e s in batu d isso lv e d in to lu o l,

m o d i f i e d w ith s m a ll am ounts o f c h l o r i n a t e d r u b b e r ,

an d p l a s t i c i z e d

w ith d ry in g o i l s .

S y n th e tic a lly prepared

c a r b a m i d e - a l d e h y d e r e s i n s may be u s e d a s f l a t t i n g but o fte n produce u n d e sira b le h ard s e t t l i n g p aten t of th e of co atin g

in th e can.

In te rc h e m ic a l C orp o ratio n d e s c rib e s

such r e s i n s w ith a p o la r l i q u i d

to avoid t h i s

ag en ts,

pro p erty

A

a method

such as g ly c e r in e

(32).

R e s in s o b t a i n e d by t h e p o l y m e r i z a t i o n o f h y d r o a b i e t i n o l vin y l e th e rs ,

usin g boron t r i f l u o r i d e

a lso advocated f o r use in f i s t

as a c a t a l y s t,

v arn ish form ulations

are (30).

S o lv e n t Im balance An i n t e r e s t i n g illu strated (21,

m ethod o f p r o d u c i n g f l a t

by p a t e n t s h e l d by th e

is

In te rc h e m ic a l C o rp o ratio n

59) > a n d b y t h e D u n l o p R u b b e r C o . , L t d .

form er d e s c r ib e s a d e l i b e r a t e

fin ish es

(84).

flo c c u la tio n of the

Th e film -

fo rm in g c o n s t i t u e n t s t h e m s e l v e s by u s e o f a n im m i s c i b l e so lv en t.

I n one c a s e ,

lose d e riv a tiv e s

f o r e x a m p l e , a m i x t u r e o f tw o c e l l u ­

i s u s e d , t o g e t h e r w ith a s o l v e n t which i s

b a l a n c e d f o r one and u n b a la n c e d f o r t h e o t h e r . I

I

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

The D u n l o p

p aten t

covers a f l a t t i n g

p rep aratio n co n sistin g

of a sus­

p e n s io n o b t a i n e d by form ing a s o l u t i o n o f a r e s i n o u s S --'a

1

stan ce

in a v o la tile

}g| f u r t h e r s o l v e n t

so lv en t,

i n which t h e r e s i n o u s

s o l u b l e , b u t w hich i s Examples g i v e n a r e : ! I-'? f:s

the

and a d d in g t o t h e

l)

sub-

so lu tio n a

subste.nce i s

less

m isc ib le w ith th e o r i g i n a l s o lv e n t. a v in y l r e s in disso lv ed in bensene,

s o l u t i o n b e i n g t h e n mixed w i t h e t h a n o l ,

o r colophony i n a l c o h o l ,

a n d 2)

sh ellac

s u b s e q u e n t l y mixed w i t h w a t e r .

PREPARATION OF TEST SAMPLES ft Th e p r e l i m i n a r y w o r k f o r t h i s p aratio n of f l a t l.g

stu d y ,

involving; th e p r e ­

l a c q u e r s , was p e r f o r m e d b y J .

K. H. E d m o n d s o n i n t h e s e l a b o r a t o r i e s , a n d t h e i r w o r k i s co n sid ered to

c o n s titu te th e f i r s t

present over a l l invo lved in th e

ste p s lead in g to th e

e v a lu a tio n of th e q u e s tio n o f fundam entsla e v a lu a tio n of sp ecu lar g lo ss.

p ro je ct,

then,

in teg ra te s

in t h e i r

(u n p u b lish ed )

covered,

T he e n t i r e

t h e w o r k o f 3 e h r l e a n d E dm onds on

M asters th e s e s

(10,

24), but i t

a d v i s a b l e h e r e t o g iv e a b r i e f resum e o f t h e

$

M. B e h r l e a n d

s eem s

im p o rtan t p o in ts

s in c e th e p r e p a r a t i o n o f th e la c q u e r s and f i n i s h e d

panels

is

c o n s i d e r e d t o b e o f much i m p o r t a n c e f o r t h e e v a l u ­

atio n s

s u b s e q u e n t l y t o b e made.

G iven below i n T able 1 a r e t h e v a r io u s

fla ttin g

agents

which were s u b j e c t e d t o t e s t .

E d m o n d s o n ' s w o r k was c o n c e r n e d

w ith th e s i l i c a

w hile S e h rle p rep ared th e

agents l i s t e d ,

ste a ra te s:

R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.

25

I

hM

T a b le 1 . Product

T r a d e Name

S o u rce o f Supply

S ilic a aerogel

"S antocel"

M o n s a n t o C h e m i c a l Co.

S ilic a hydrogel

"S i-O -L ite"

M allinckrodt forks

S ilica

"L inde S i l i c a "

Linde A ir P ro d u c ts Co.

D iatom aceous E arth

"C elite"

J o h n s - K a n v i l l e Corp.

A lumin um S t e a r a t e

" T e c h D"

M a l l i n c k r o d t Che in. ■forks

Alum inum S t e a r a t e

" T e c h M"

M a l l i n c k r o d t Chem. Works

Alu m inum S t e a r a t e

"Tech F, F lu f f y "

M a l l i n c k r o d t Chem. Works

Zinc S t e a r a t e

"USP X I I "

M a l l i n c k r o d t Chem. Works

Zinc S t e a r a t e

"USP X I I I , G r a d e A" M a l l i n c k r o d t Chem. Works

Chem.

M a g n e s iu m S t e a r a t e

M a l l i n c k r o d t Chem. Works

S trontium S te a r a te

M a l l i n c k r o d t Chem. ’Works

Calcium S t e a r a t e

M a l l i n c k r o d t Chem. Works

m r •A>1

Th e r a w m a t e r i a l , so lu tio n ,

;;at i;-|I {H PS pi ‘Afl L3

I n d e x o f A g e n t s Used

m ills

fla ttin g

agent,

n itro ce llu lo se

and l a c q y e r s o l v e n t were g ro u n d t o g e t h e r i n b a l l

co n sistin g

of quart size

a charge of s t e e l b a lls th ese b a lls diam eter.

i.e .,

For th e

s ilic a p aste s,

50% o f t h e m i l l v o l u m e was u s e d ,

b eing th r e e - e ig h ts The s t e a r a t e

jars.

in c h ana o n e - h a l f inch in

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of th re e -s ix te e n th s

inch r e j e c t

all

o f m otor' d r i v e n r o l l s

cases,

a series

tu rn in g the m ills .

These r o l l s

s te e l b a ll bearin g s.

b rin d s

o f 200 r .p .r n .

was u s e d f o r

were d r i v e n by a l / 4 h o r s e ­

power m otor th r o u g h a p u l l e y and b e l t t h e m at. a r a t e

In

s y s te m which t u r n e d

S e e F i g u r e 5«

o f o n e h o u r ' s t i m e w e r e made i n a l l

causes.

T his

i n t e r v a l was d e c i d e d u p o n a f t e r p r e l i m i n a r y w ork h a d i n d i ­ cated t h a t

in c re a se d len g th of g rin d a c tu a lly

glo ss reading o f th e

f in a l lacqu er.

These f in d in g s a r e in

a g re e m e n t w i t h t h e work o f su ch a u t h o r i t i e s Beakes, ing i s

who s t a t e s

a s H e n r y L.

t h a t th e t r e a tm e n t o f a pigm ent i n g r i n d ­

of utm ost im portance

to him ,

in c r e a s e d the

"For f l a t s ,

th e

in th e f i n a l p ro d u ct.

fin e p a r tic le

not a d isp e rs io n . . . . F la ttin g

size

A ccording

is d esired , but

i s p ro d u c e d by t h e u n d isp ersed ,

p ig m en t f i n e s . . . . Sub-wave l e n g t h p a r t i c l e s

a r e no b a r e q u i r e ­

men t o f , f l a t t i n g . " ( 8 , 7 3 ) * In the

case

of the s i l i c a s ,

f o r m u l a t i o n s w e r e made

each a g e n t u s in g

5%, 1 0 6 , a n d 15>» b y w e i g h t o f a g e n t ( w e t

b asis).

p a s t e s w e r e made f o r t h e

O nly 5p

T y p ica l form ulae T a b le 2.

100.0 g.

stea rates.

f o r 5 r p a s t e s a r e g i v e n i n T a b l e 2.

T y p i c a l F l a t t i n g P a s t e Form ulae

S ilicas, 5 .0 g. 59.2 g. 35*8 g .

for

5/o p a s t e

S tearates,

5$ p a s t e

f la ttin g agent 7 * 5 £• f l a t t i n g , a g e n t la c q u e r so lv en t 8 7 . 5 6* l a c q u e r s o l v e n t n itro c e llu lo se n itro ce llu lo se 55-0 s o l u t i o n (26.8/s s o l i d s ) s o lu tio n (26.86 s o lid s ) T otal 150.0 g . T o ta l

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F I G . 5 - THE LABORATORY ROLL HILL

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

28

A fter the p re p a ra tio n of the l a c q u e r s were p r e p a r e d by t h e

sam ple p a s t e s ,

of th e p a ste

!

sim ple m ixing.

■I

s i l i c a p ig m e n ts were a d j u s t e d

1

fla ttin g

;

to determ ine th e a t t r i t i o n and s o lv a tio n e f f e c t s

agent

Th e 5 $ ,

fin a l s ilic a -fla tte d

•1 1

10$.

t

c o n t e n t , by

1 0 $ , a n d 15$ p a s t e s made

from t h e

so t h a t t h e f i n a l am ounts of th is

b e i n g done o f varying

th e o e r c e n ta g e o f s o l i d oigm ent i n th e o r i g i n a l p a s t e grinds.

agent in the d rie d

laco uers

f i l m r a n g i n g f r o m a p p r o x i m a t e l y 2 . 50$ to was made f o r t h e

s a m p l e s was done i n

u s i n g a D e V i l b i s s T y p e OM-501 s p r a y g u n w ith S heed.

stearate

lacquers.

S p ray in g o f th e t e s t

:

c o n t a i n e d am ounts o f f l a t t i n g

T h i s same p e r c e n t a g e s e r i e s

fla tte d |

l a c q u e r o f 21$ s o l i d s

i n t h e l a c q u e r w ere c o n s ta n t,

1 ■] .1 'I ii

fla t

i n c o r p o r a t i o n o f v a r y i n g am ounts

i

in to g lo ss

the

a s p r a y chamber* a No. 3 9 , Model

A i r p r e s s u r e was m a i n t a i n e d a t 5 0 - 5 5 p . s . i .

manual s p r a y i n g .

Th e p a n e l s

u s e d were 3 x 5

g la s s , h a l f of each p an el b ein g

during

inch p la te

s p r a y e d i m m e d i a t e l y upon

r: ■ ■ ; ■-

; 1:

m ixing t h e p a s t e

w ith t h e l a c q u e r , t h e o th e r h a l f being

s p ra y e d a week l a t e r w it h t h e tem pt to f i n d t h e e f f e c t

K-

same l a c q u e r i n

o f c a n a g i n g on g l o s s .

p a n e l s were s e l e c t e d b e c a u s e o f t h e exh ib it a p e rfe c tly so t h a t a l l

o r d e r to a t ­

smooth " p r o f i l e "

f a c t that, such panels o n th e S u r f a c e A n a l y z e r ,

su b se q u e n t r e a d in g s on co ated p a n e l s

th e c o a tin g and not t o t h e g l a s s

P l a t e glass

surface.

T his

w e r e due t o c h o i c e , how­

e v e r , h a s c e r t a i n i n h e r e n t d r a w b a c k s , c h i e f a m o n g th e m b e in g th e

fact th a t,

wh en t e s t e d o n t h e g l o s s m e t e r ,

two u n w an ted r e f l e c t i o n s

are obtain ed ,

i.e . ,

one o r p o s s i b l y some p a r t o f t h e

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29

lig h t passes

th ro u g h t h e la c q u e r and s t r i k e s

betw een l a c q u e r and g l a s s , and, differen ce g lass,

i f th ere

betw een th e r e f r a c t i v e

s p e c u l a r l y and w i l l p a s s

through th e tr a n s p a r e n t la c q u e r a g a in , even though i t

by t h e l a c q u e r i t s e l f .

in d ices

T h is e r r o r i s assumed to be n e g l i ­

is

sm all d i f f e r e n c e s betw een th e

o f l a c q u e r and g l a s s .

th at of tra n sm itted lig h t g la s s and a i r ,

r e g i s t e r i n g on th e

does not r e p r e s e n t l i g h t r e f l e c t e d

g ib le , how ever, because o f th e refractiv e

an a p p reciab le

i n d i c e s o f t h e l a c q u e r and

some l i g h t w i l l b e r e f l e c t e d

glossm eter,

is

th e in te rfa c e

strik in g

The l a r g e r e r r o r ,

th e i n t e r f a c e betw een

a p p re c ia b le , and, unless

would g i v e a b n o r m a l g l o s s r e a d i n g s .

B ehrle

corrected

for,

(10) worked o u t

a m ethod o f c o a t i n g t h e b a c k s o f a number o f t h e t e s t p a n e l s w i t h b l a c k l a c q u e r a n d f o u n d , b y so d o i n g ,

a f a c t o r which

may b e u s e d f o r c a l i b r a t i o n a n d c o r r e c t i o n o f g l o s s r e a d i n g s ta k e n on p a n e l s curve i s

w ithout th e b la c k backing.

This c a l i b r a t i o n

r e p r o d u c e d i n F i g u r e 6.

T hickness o f th e

sprayed film i s

im portance i n a stu d y of t h i s

so rt,

r e c o g n i z e d t o be o f

and u n i f o r m i t y o f sp ra y in g

t e c h n i q u e w as o b s e r v e d a s c l o s e l y a s p o s s i b l e . fl I'M

on t h i s

facto r,

a test

procedure

r e p r o d u c i b i l i t y was i n a u g u r a t e d ,

As a c h e c k

f o r f i l m t h i c k n e s s and th is

being d e s c rib e d in the

fo llo w in g s e c tio n . B e h r l e 1s a n d E d m o n d s o n ' s w ork i l l u s t r a t e d t h e v a r y i n g effectiv en ess of d iffe re n t

fla ttin g

agents as a fu n c tio n of

t h e q u a n t i t y o f a g e n t u s e d , a n d t h e s e r e s u l t s h a v e b e e n com­ p i l e d a n d a r e p r e s e n t e d h e r e i n a s F i g u r e 7*

B e c a u s e some o f

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Fig.

6-

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io o

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35

average thickness

f o r t w e l v e p a n e l s was a p p r o x i m a t e l y 0 . 7

m ils. COLLECTION AND TABULATION 0 ? DATA The c o l l e c t i o n o f d a t a from t h e B ru s h A n a l y z e r p r o f i l e j

ch arts

was d o n e i n s u c h a m a n n e r a s t o g i v e a m e a s u r e o f

th e d e s ire d q u a lity

ch ara c te ristic ,

the p a r tic u la r t e s t

sam ple b e in g

pose,

i.e .,

co n sid ered .

a r e f e r e n c e p o i n t was a r b i t r a r i l y

g rap h ic p r o file ,

th is

th e roughness of For t h is p u r­

s e l e c t e d on t h e

p o in t being c a lle d

"one", and fiv e

r e a d i n g s w i t h i n t h e r e c o r d e d c y c l e w ere t h e n t a k e n by t h e random s e l e c t i o n m ethod o f F i s h e r and Y a te s sele cted

These

s a m p l e s o f f i v e we r e t a k e n f o r e e c h o f f i f t e e n

d ifferen t g iv in g

(3^)*

cycles o r p o in ts

fifte e n

sub-groups,

on each p a n e l u n d e r t e s t , and a t o t a l

th u s

of sev en ty -fiv e

m easurem ents f o r each p a n e l. T h e o b s e r v e d d a t a was t e s t e d of

sta tistic a l

f o r c o n s i s t e n c y b y t h e vise

c o n t r o l c h a r t s w hich a r e composed o f a c e n t r a l

lin e

to

in d icate

a v e r a g e p e r f o r m a n c e a n d tw o s o - c a l l e d c o n ­

tro l

l i m i t s banding th e

cen tral lin e .

below th e s e c o n tr o l l i m i t s

in d icate

V a r i a t i o n s aoove o r

th a t th e p ro cess cannot

r e a s o n a b l y be s u p p o s e d t o be a c h a n c e c a u s e s y s t e m ( i n w hich case th e process

would b e s a i d t o be " o u t o f c o n t r o l " ) .

i

T he o b s e r v e d v a r i a t i q n may b e d u e t o is,

"random c a u s e s " , t h a t

c a u s e s o v e r w h i c h o n e h a s no c o n t r o l a n d w h i c h a r e i n ­

herent correct

in the p r o c e s s ,

or to assig n ab le

causes such as i n ­

experim ented p ro c e d u re s o r d e f e c ts

in th e instrum ent.

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1

36

If,

how ever,

a l l th e experim ental p o in ts l i e

co n tro l lim its ,

th ere

assignable causes, are re p ro d u c ib le ,

is

not s u ffic ie n t

betw een th e

e v id e n c e o f any

and t h e c h a r t s g iv e n by t h e

instrum ent

in d ic a tin g th a t the p ro cess is

a relia b le

one. S tatistical w. A. S h e w n a r t

co n tro l c h a rts,

(38),

and sam p lin g t h e o r y .

such as t h o s e d e v e lo p e d by

a r e based upon th e Th e c h a r t s

law s o f p r o b a b i l i t y

s e l e c t e d f o r u s e were t h e

c h a r t f o r sam p le mean X an d t h a t f o r t h e sa m p le r a n g e R (R = Xmax - Xm^ n ) . used re p re s e n ts

The h o r i z o n t a l a x i s o f t h e c o n t r o l c h a r t s

t h e number o f c y c l e s ,

one t h r o u g h f i f t e e n ;

the v e r t i c a l a x is r e p r e s e n ts th e c a lc u la te d ( e i t h e r X o r R) f o r e a c h o f t h e f i f t e e n in g o f f i v e m easurem ent X 's . chart is fiv e it

sub-group v alu e

sub-groups c o n s is t ­

The c e n t r a l l i n e

l o c a t e d a t t h e g r a n d mean ( a r i t h m e t i c )

o b serv atio n s,

fo r th e X of a ll

seventy-

a v a l u e d e n o t e d b y t h e s y m b o l X, s i n c e

i s t h e mean o f t h e

s u b - g r o u p mea.ns.

The t o t a l o f t h e

R* s d i v i d e d by t h e n u m b e r o f s u b - g r o u p s g i v e s t h e o o s i t i o n of the sin ce

cen ter lin e it

is the

F in ally ,

fo r th e R -ch art,

mean o f t h e

the

a v a l u e d e n o t e d b y R,

sub-group ran g es.

co n tro l lim its

fo r th e X -chart are lo c a te d

b y m eans o f f o r m u l a e d e v e l o p e d f o r t h i s

purpose

( 1 , 3 8 ):

Upper C o n t r o l L im i t_ X

=

X + (Ap)R

(l)

Lower C o n t r o l L i m l t _ X

=

X -

(2 )

w h e r e Ap i s

a co n stan t p e c u lia r to th e

(A? )R sub-group siz e

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

"n".

37

F o r n = 5>

in th is

s t u d y , Ao a 0 . 5 7 7 *

For th e range c h a r t , Upper C o n tr o l L im it Lower C o n t r o l L i m i t

=

R

(I>4 )R

(3)

(D? )R

(4)

F o r n s 5 , D3 = 0 a n d D4 - 2 . 1 1 4 . One o f t h e b a s i c a s s u m p t i o n s u n d e r l y i n g t h e

co n tro l

c h a r t s u s e d i s t h a t t h e p a r e n t p o p u l a t i o n from which t h e sam ples were draw n i s a norm al p o p u l a t i o n , parent un iv erse G aussian) v a lid ity

is

d i s t r i b u t e d according to

p ro b ab ility of t h i s

i.e .,

fu n ctio n .

th e norm al (o r c h e c k 011 t h e

In order to

a s s u m p t i o n , a s a m p l e p a n e l was r u n u n t i l a

t o t a l o f two h u n d r e d i n d i v i d u a l m e a s u re m e n ts corded.

th a t the

(X 's )

were r e ­

T hese were t h e n t a b u l a t e d f o r a f r e q u e n c y d i s t r i ­

b u t i o n and a norm al curve f i t t e d of grad u atio n

(44).

t o t h e d a t a by t h e method

A C hi-square t e s t

( 4 7 ) was t h e n u s e d

to d eterm in e w hether or not th e observed d i s t r i b u t i o n of X 's d i f f e r e d

sig n ific a n tly

from t h e n o rm a l c u r v e .

gave C h i-sq u a re = 8 .2 4 f o r 8 d eg rees o f freedom , it

can be concluded t h a t

th at

is,

t i o n of n o rm ality of th e p aren t p o p u la tio n is stated ,

is

in co n tro l;

th is

t h e assump­ ju stified .

t h e X and R c h a r t s d e t e r m i n e , by

th e p o s it i o n of th e p o in ts p lo tte d th e re o n , process

from w hich

ch a n c e a l o n e would p r o d u c e

g r e a t a d i s c r e p a n c y 42v£ o f t h e t i m e ;

As e a r l i e r

T his t e s t

th at is ,

if a ll

w hether th e

points

f a l l betw een

t h e u p p e r and lo w e r c o n t r o l l i m i t s and a r e random ly d i s -

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

tr ib u te d about th e

cen ter lin e ,

th ere

any a s s i g n a b l e c a u s e s i n t h e p r o c e s s . th e c e n te r l i n e s p o in t,

the

range,

sin ce ,

zero,

it

for a ll

if

in equations

seen th a t

n u m erical v a lu e ,

( l ) , (2),

equal to

a fu n c tio n of R

( 3 ) > a nd (4-).

o f a c y c le ru n on th e

con­

is a p ic to r ia l

rep resen tatio n

Brush A n a ly z e r

in stru m en t.A

corresponding to a s ty lu s tr a v e l of l/8

mm. p e r " s e c o n d )

p a rtia lly

single

o f f i f t y v e r t i c a l d i v i s i o n s on th e

in c h fo rw a rd and l / l o

T able 5 i s

This

f o r e v a l u a t i o n and co m p ariso n o f

in c h backward)

inch

on t h e t e s t p a n e l ,

and r e q u i r e s a te n - s e c o n d p e r io d o f o p e r a t i o n a t 5

zero

on th e Brush A n a ly z e r i n s t r u m e n t .

com plete c y c le c o n s i s t s

(l/l6

and (2) X i s

o b ta in a b le f o r each p an el under t e s t ,

F ig u r e 8 , w hich f o l l o w s ,

ch art,

(l)

the roughness i s

a sim p lified b asis

surface te x tu re

p ro file

inasm uch as

on th e X -c h a rts a re v e ry n e a r ly a t th e

four equations,

of part

F u rth er,

m a i n c r i t e r i o n o f r o u g h n e s s i s R, t h e a v e r a g e

is

stitu te s

i s no e v i d e n c e o f

slow s p e e d

to com plete th e c y c le .

an in d iv id u a l

data sheet fo r

rep ro d u ced in F ig u re 8.

th e

chart

The t e s t p a n e l i n v o l v e d

was s p r a y e d w i t h a l a c q u e r c o n t a i n i n g 7*3S > d i a t o m a c e o u s earth

( p e r c e n t a g e b a s e d on d r i e d f i l m c o n t e n t ) . T a b l e s 6 , 7> 8 , 9> s.nd 10 a r e c o m p o s i t e d a t a s h e e t s

f o r each f l a t t i n g

agent,

i n d i c a t i n g t h e R 1s p r e v i o u s l y

d e te rm in e d from i n d i v i d u a l d a ta s h e e ts

such as t h a t g iv e n in

T a b l e 5* I t w i l l b e n o t i c e d i n t h e t a b l e s t h a t tw o a d d i t i o n a l f a c to r s have been c o lle c te d ,

i.e .,

" P e a k - to - V a lle y " and

with permission of the copyright owner. Further reproduction prohibited without permission.

oy

F ig . &

T y p i c a l B r u s h A n a l y z e d Ch a r t Tr a c e , A c t u a l J / z e , a n d M e t h o d o f K e e p i n g Da t a -

3

S fe

I C? 1

*

5 peci m en No K~52E— //2.5pec. Gl o ss VERTICAL MAI3VIFICATI0N ATTENUETOf? Imm. DIV. SETTING EQUALS 1 I 0 .0 0 1 iH o .o i 10 ” 1OO ” 1 0.1 m

1.0 R e m a rk s'.

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“ A n a l y s i s No. n 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

40

I n d i v i d u a l D;a t a S h e e t :

T a b l e 5-

D iatom aceous E a rth

S a m p l e No.

116

( 15% P a s t e )

S p e c u l a r G-loss = 1 6 , R = 6 9 . 4 X1

x2

1

*•55

2

P ositio n Number

R

X

R-

X3

x4

X5

4. 3

-40

-20

-10

- 2

95

95

-30

0

4.45

4-25

4-10

4-10

75

170

3

1-10

-15

0

4-15

-10

0

30

200

4

4-30

-30

-40

-10

t20

-14

70

270

5

0

4-10

-15

*•30

-25

0

55

325

6

4-40

4-10

-25

4-30

0

4-11

65

390

7

0

0

-30

_

4-8O

4- 9

110

500

8

*• 5

4-40

-55

4-40

-35

- 3

105

605

9

0

-20

-10

0

-30

-12

30

635

10

0

-25

-15

4-60

4-35

4-11

85

720

11

r 5

i-50

4-10

-30

0

4- 7

80

800

12

• 4-10

4-10

4-35

4-45

4-15

4-23

35

835

13

+70

-25

-20

4-45

-50

4- 4

120

955

14

4-25

-20

4-15

*• 5

-40

- 3

65

1020

15

-10

+ 5

4-10

- 5

-10

- 2

20

1040

+39

1040

R

T o tals

x

= 4- 2 .6

R = • 6 9 .4

L0L£ = +2

UCL^ = 1 4 7

40., 0 8 4.42.6 1 -FO

• o\

UCL£ = +2 .6

. 0 a -• 3 7 . 4

ALL

in

a ONTROL

(See page 3 6 )

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

41

Table 6. A.

C om posite Data S h e e t:

5 f0 F l a t t i n g A g e n t I n G r i n d i n g Mix

Panel No.

When Snrayed

46 47 44 45 42 43 40 41 38 3.9.

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. 3

% Agent i n F in a l Lacquer 1.5 0 1 .50 1.25 1.25 1.00 1.0 0 0.75 0.75 0.5 0 0 .50

60° G loss

Max. P-V

Freq.

R

a 11 13-5 15-5 19.5 22.5 27-5 30.5 40 42

95 107 8 6.7 71.4 9 6.4 99.6 63 55 63 37.7

255 280 190 105 245 255 215 210 150 150

70 68 64 33 70 77 68 64 70 67

Max. P-V

Freq.

220 250 210 255 135 315 220 170 125 130

75 71 65 61 75 63 68 59 78 76

Max. P-V

Freq.

R 97-4 38 SQ 9 2.3 75-3 62 55-3 54.6 33-3 35

255 310 265 240 265 215 170 145 155 150

71 63 68 62 69 64 32 74 53 71

10% F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

When Sorayed

18 19 20 21 22 23 24 25 26 27

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. G

Santocel

% Agent in F in a l Lacquer 1.5 0 1.5 0 1.25 1.25 1 .0 0 1 .00 0.75 0.75 0.5 0 0.5 0

60° G loss

7 10 12 16 17 19 25 90 40 43.5

R 80.4 104.7 76.4 7 4 .6 69 .4 62 58 59 48 45

15% F l a / t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

When Snrayed

28 20 30 31 32 33 34 35 36 37

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

% Agent in F in a l Lacauer

.

1 .5 0 1 .5 0 1.25 1.25 1. 00 1 .0 0 0.75 0.75 0 . 50 C. 5 0

60° G loss 10 12 12.5 14 20 22 26

20 47 46.5

I

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

T able

7.

C om posite D ata S h e e t:

S3 - 0 - L i t e

A . 5;6 F l a t t i n g A g e n t i n G r i n d i n g Mix Panel No.

then Sorayed

76 77 74 75 72 73 70 71 68 69

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. 3.

10.6 P l a t i n g

Panel No.

Vv’h e n Sorayed

66 67 64 65 62 63 60 61 53 59

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. G

/o A g e n t i n F in a l Lscouer 1.50 1. 50 1.25 1 . 25 1.00 1.00 0-75 0.75 0 .5 0 0.5 0

60° G loss

11 11 16 17 23 23 31 32.5 41.5 45.5

R 101 12 4 76 50 51.6 55.3 54. 3 47. 6 56 55 .4

Max. P-V

Freq.

Dat a Not C ollected

A g e n t i n G r i n d i n g Mix

% Agent i n F in a l Lacouer 1.50 1 . 50 1.25 1 . 25 1.00 1.00 0.75 0.75 0 . 50 0 .50

600 G loss

R

15.5 18 21 24 28 30.5 41 44 52 55-5

04 .7 67 .4 79.4 5 0.6 76 5 5.4 43 .6 45.4 2 8.6 31

Max. P-V

Freq.

D ata Not C ollected

15/6 F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

When Sorayed

56 57 54 55 52 53 50 51 48 49

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

% Agent in F in a l Lacquer

•

1.50 1.50 1.25 1.25 1.00 1.00 0.75 0 .7 5 0 .5 0 0 .50

60° G loss

Max. P-V

Freq.

R

14.5 29 20.5 26.5 28 3 8 .5 37 55 57 53.5

84 28.3 69.7 50. 6 80 41.4 35.3 21. 6 33 23.2

245 190 290 165 180 155 130 100 110 225

68 93 68 74 68 76 69 67 61 59

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

43

j Table 8 . A.

C o m p o s i t e D ata S h e e t :

5p F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

When Sprayed

106 107 104 103 102 103 100 101 98 99

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. 3

Panel 96 97 94 95 Q? 93 90 91 88 89

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. C

Panel No. 36 87 84 35 32 83 80 81 73 79

% Agent i n F in a l Laccuer 1 .5 0 1.5 0 1.25 1.25 1 .0 0 1 . 00 0.75 0.75 0.5 0 0.50

60° G loss

53.5 54 61 59* 5 00

63.5 71.5 6 0 .5 75 74.5

R

4 7.4 37-7 23.7 23. 3 25.3 25.4 23.4 24 9-7 2 2 .6

Max. P-V

Freq.

D ata Not C ollected

10% F l a t t i n g A g e n t i n G r i n d i n g Mix When Sprayed

No.

Linde S i l i c a

% Agent i n F in al Laccuer 1 .5 0 1.50 1.25 1.25 1 .00 1 .0 0 0.75 0.75 0.50 0 . 50

60° G loss

R

58 54.5 62 59 64 62.5 7 0 .5 6 9.5 74 72...

35.7 38 23.4 25-3 23 18 20 19.7 17.7 20.7

Max. P-V

Freq.

D ata Not C o llected

1 5 $ F l a t t i n g A g e n t i n G r i n d i n g Mix When Sprayed Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

$ Agent i n F in a l Lacauer 1.50 1.50 1.25 1.25 1.00 1 . 00 0.7 5 0.7 5 0 .50 0 .5 0

60° G loss

R

46 57 53 54.5 53.5 60 66.5 66.5 70 69.5

91 47.4 51 4 4.3 33-7 33.3 19.7 15-7 16.7 17

Max. P-V

Freq.

D ata Not C o llected

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

I

T a b l e 9* A.

C om posite D ata S h e e t:

5b F l a t t i n g A g e n t i n G r i n d i n s Mix

Panel No.

When Sorayed

132 133 13 0 131 123 129 125 127

I mined l a t e l y A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. 3.

fa A g e n t i n F in a l Lacauer 1.23 1.25 1 . CO 1.00 0.75 0.75 0 .50 0.50

60° G loss

R

17 19.5 25 30.5 35 33.5 49 53* 5

72 .4 59 • 6 51. 6 4Q. 4 42.6 41 20.5 27*7

Max. P-V

Freq

D ata Not C ollected

10/» F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

V/hen Sorayed

124 125 122 123 12 0 121 113 119

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. rt O

D iatom aceous E a rth

b Agent in F in al Lacauer 2.00 2 . 00 1 .5 0 1 . 50 1 .00 1.00 0 .50 0 . 50

60° G loss

R

3.5 3.5 14.5 14.5 27 29.5 51 54

63. 6 87 *6 64.4 73 .6 54.4 56 24 18.7

Max. P-V

Freq.

D ata Not C ollected

15.$ F l a t t i n g A g e n t i n Gr:' . n d i n g I lix

Panel No.

When Sorayed

116 117 114 115 112 11 3 110 111 108 109

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

% Agent in F in a l Lacauer

•

1 .50 1.5 0 1.25 1 . 25 1.00 1 . 00 0.75 0.75 0.50 0.5 0

50° G loss

Max. P-V

Freq.

R

15 17 21.5 24 30 32 41.5 42.5 55 56.5

69.4 66.4 57 55*6 47.5 50.3 34.7 32.3 2 7 *6 21

240 210 240 135 215 150 170 115 110 13 0

36 83 72 73 62 72 72 75 50 52

i

)i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

T a b l e 1C. A.

C om posite D ata S h e e t:

The S t e a r a t e s

panel No.

ALUMINUM 3T EAriiii'E D, 5 /a 7 l a t t i n g A g e n t i n G r i n d i n g Mix Max. Freq. % Agent in 60° When P-V G l o s s R F i n a l L a c q u e r Snrayed

17 0 171 163 169 157 133 134

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately B.

'When Snrayed

17 2 173 l4 l 142

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

% Agent i n F in a l Lacquer 2.00 2.00 1.00 1.00

ALUMINUM ST’EARATE F , Mix

Panel No.

When Snrayed

13 9 140

Im m ediately A f t e r 1 wk. D.

11 13 24 13 30 30.5 59

7 5.7 4 4.6 53 72 34.6 34 25.6

200 150 152 150 125 215 85

63 80 74 6Q 79 60 49

ALUMINUM STEARATE M, 5 6 P l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

r\ U1

2.00 2.00 1.50 1 . 50 1.00 1.00 0.30

Panel No.

When Sorayed

149 150

Im m ediately A f t e r 1 wk.

Max. P-V

Freq.

R

17 17 42 31

30.6 50.4 25 30.3

175 155 115 110

76 58 78 62

5% I[’l a t t i n g A.gent i n G - r i n d i n g

% Agent in F i n a l L a .c q u e r 1.00 1.00

CALCIUM ST IURATE,

60° G loss

60° G loss 43.5 41

Frea.

R

Max. P-V

16.7 25

95 115

85 78

5% F l a t t i n g Ag e n t i n G r i n d i n g Mix

1o A g e n t i n F in al Lacauer 1.00 1.00

60° G loss

R

48 53.5

13.3 1 1.3

Max. P -V 80 45

Freq. 39 109

(C ontinued n ex t page)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

T able

10 ( C o n t i n u e d ) E.

STRONTIUM STEARATE,

Fanel Wo.

When Sprayed

132 183 130 131 14 7 143 184

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately F.

When Sorayed

174 175 143 14 4

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

When Sprayed

145 146

Im m ediately A f t e r 1 wk.

A g e n t i n G r i n d i n g Mix

60° G loss

R

23 25 34 36 59 59 73

33.3 11.3 31 19-1 10 28. 3 10.3

Max. P-V 105 2Q P0 56 36 85 36

Freq. 81 58 91 71 74 85 58

% Agent i n F in al Lacauer 2.00 2.00 1.00 1.00

60° G loss

R

Max. P-V

30 30 63 64

13.3 22.8 12.Q 12.5

42 60 33 40

5% F l a t . t i n g

% Agent i n F in al Lacauer 1.00 1.00

Freq. 114 90 86 73

Agent i n G r i n d i n g Mix

60° G loss

Max. P-V

Fre q .

R

59 56.5

11.5 10

40 36

70 74

MAGNESIUM STEARATE, 5 $ F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel When . Sorayed No. 166 167 173 17 P 135 13 6 17 6 177

2.00 2.0C 1.50 1.50 1.00 1.00 0.50

ZINC STEARATE X I I ,

Panel No.

H.

6? A g e n t i n F in al Lacauer

ttin g

ZINC STEARATE X I I I , GRADE A; 5% F l a t t i n g A g e n t i n G r i n d i n g Mix

Panel No.

G.

$?o Fla

Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk. Im m ediately A f t e r 1 wk.

% Agent i n F in a l Lacquer 2.00 2 . 00 1.50 1.50 1.00 1.00 C. 50 0.50

600 G loss

R

31 36 48 53-5 65. 5 71 31.5 dO u . 5nr

5 9.3 19 .7 16 .5 14.2 °-3 P r0 . a 3. 3 16.5

Max. P-V 159 62 43 41 2P 29 21 48

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Freo. 62 37 86 37 81 31 42 36

47

" F r e q u e n c y " , f o r some o f t h e p a n e l s . d e sig n a tio n is the fifty -cy cle

run,

The " P e a k - t o - V a l l e y "

maximum h e i g h t a n d d e p t h d e t e r m i n e d i n a

w hile th e

of tim es th e p r o f i l e

lin e

frequency

i s a c o u n t o f t h e number

crosses the

These d a t a w i l l be t r e a t e d

chart cen ter lin e .

in a sep arate

sectio n .

ANALYSIS OF THE DATA In tro d u ctio n The i n t e r p r e t a t i o n in a study o f t h i s

o f t h e e f f e c t o f a n y r .lv s n v a r i a b l e

k i n d w o u l d bec o m e i d e a l l y a c c u r a t e

were p o s s i b l e t o h o l d a l l

o ther fa c to rs

P r a c t i c a l l y , how ever, t h i s m ental e r r o r s , selv e s,

a b so lu te ly co n sta n t.

of the

in s tr u m e n ts them ­

and unknown o r i n s i g n i f i c a n t v a r i a b l e s .

are av ailab le

of c o n tro l'd u rin g th e ex plained.

a n aly sis

w ith w hich i t

y ie ld valu ab le

of the d a ta ,

is p o ssib le to

H erein l i e s and m ethods

show t h e d e g r e e

c o lle c tio n of the d a ta ,

F u rth e r, the

it

i s an i m p o s s i b i l i t y due t o e x p e r i ­

m echanical f a u l t s

th e need f o r s t a t i s t i c a l

if

as fo rm erly

c o l l e c t e d d a t a c a n o f t e n b e made t o

i n f o r m a t i o n , by s t a t i s t i c a l

m e th o d s , which

w ould o t h e r w i s e be u n s u s p e c t e d b y mere p e r u s a l o f a g i v e n set of fig u res. resu lts b asis

To t h i s

end,

I n te r p r e ta tio n of th e ta b u la te d

was u n d e r t a k e n , a n d t h e c o n c l u s i o n s d r a w n h a v e t h e i r

i n m a t h e m a t i c a l l a v / s a s w e l l a s i n t h e more p r a c t i c a l ,

observed r e s u l t s

of

the ex p erim en t.

The s t a t i s t i c a l m e t h o d c h o s e n f o r a n a l y t i c a l u s e i s k nown a s t h e A n a l y s i s o f V a r i a n c e

(35> 9 3 ) •

c e p t upon w hich t h e t e c h n i q u e s o f t h i s

The b a s i c

method a r e

con­

founded

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

4S

d e s e rv e s m ention h e r e . In c o n n e c tio n w ith any c l a s s i f i c a t i o n o f th e v a lu e s of a v ariab le

i n t o tw o o r more f a m i l i e s ,

f o r w h i c h t h e members

o f e a c h f a m i l y a r e r a n d o m l y c h o s e n f r o m some p a r e n t p o p u l a t i o n corresponding to th a t th ere

fam ily , th e re a r is e s

the q u estio n ,

e v id e n c e t h a t th e v a r i a b l e b ein g m easured v a r i e s

n ific a n tly

from fa m ily t o

fam ily?"

does th e r e

sig ­

That i s , h av in g o b ta in e d

some s e t o f mean v a l u e s o f t h e v a r i a b l e s , fam ilies,

"is

one f o r e ach o f t h e

seem t o be any i n d i c a t i o n t h a t t h e s e

m e a n s a r e r e a l l y d i f f e i - ' e n t among t h e m s e l v e s a n d t h a t t h e p a re n t p opulations

from which t h e s e v a l u e s

a c t u a l l y be c o n s id e r e d t o be d i f f e r e n t It

were draw n s h o u ld

from one a n o t h e r ?

must be r e a l i z e d t h a t t h i s t y p e o f q u e s t i o n c a n n o t be

answ ered e x a c t l y , as e s t i m a t i o n of th e n a tu r e o f a p a r e n t p o p u l a t i o n from a sam ple o f i t and can n e v e r be p r e c i s e u n l e s s l a t i o n as th e

sam ple.

in terp retatio n s

is

alw ays s u b j e c t t o

error

one h a s t a k e n t h e whole popu­

Because o f t h i s ,

it

o f such d a t a be q u a l i f i e d

is

necessary th a t

i n some m a n n e r

which w i l l i n d i c a t e t h e d e g r e e o f a s s u r a n c e w ith w hich con­ c l u s i o n s a r e drawn. a fa c to r in to

F or exam ple,

several fam ilies,

m i g h t show t h a t t h e p r o b a b i l i t y by chance a lo n e i s

c l a s s i f ic a t io n of

the r e s u lts

of th e a n aly sis

of such a r e s u l t ' s happening

l e s s t h a n one i n one h u n d r e d ,

assum ption t h a t th e re

is

no d i f f e r e n c e

f r o m w h i c h t h e d a t a was d r a w n . resu lt at th is

in th e

under the

in th e p opulations

I f , how ever, th e observed

low l e v e l o f p r o b a b i l i t y

is

n o t a c c e p te d as

being a chance o c c u rre n c e , th e h y p o th e sis o f a s in g le p aren t

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

49

p o p u l a t i o n must be r e j e c t e d and t h e c o n c l u s i o n r e a c h e d t h a t there

really

is

a s i g n i f i c a n t d if f e r e n c e betw een th e

classi­

fic a tio n s . The t e c h n i q u e o f t h e A n a l y s i s o f V a r i a n c e l e a d s co n clu sio n s of ju s t

i

w hich i s

th is

attrib u tab le

nature.

to

3y a n a l y z i n g t h e v a r i a t i o n

to th e v ario u s c l a s s i f i c a t i o n s ,

to

th e d i f f e r e n t i a l r e a c t i o n s betw een t h e s e c l a s s i f i c a t i o n s , and t o t h e

inherent

experim ental e r r o r ,

it

is

p o ssib le to

t

sta tistically

t e s t th e h y p o th esis th a t a g iven e f f e c t

p resen t in the d ata.

T his t e s t ,

makes u s e o f t h e r a t i o m ates o f t h e

c a lle d F is h e r 's

F-Test

(3 6 ),

o f tw o i n d e p e n d e n t a n d u n b i a s e d e s t i ­

experim ental e rro r.

From t h i s

u n itless

may b e e s t i m a t e d t h e p r o b a b i l i t y t h a t t h e h y p o t h e s i s The p r o b a b i l i t y d i s t r i b u t i o n d eterm ined,

is not

of th e s t a t i s t i c

and from t a b l e s t h e r e

number is tru e.

F has been

c a n be o b t a i n e d v a l u e s o f

F f o r a g i v e n s i t u a t i o n w hich w i l l be e x c e e d e d by chance a l o n e 5% a n d

ifa

o f th e tim e i n th e long ru n (9 4 ).

p a rin g an observed F w ith th e ta b u l a r v a lu e s , to

judge w h eth er a c l a s s i f i c a t i o n d i f f e r e n c e

ably supposed to

ex ist,

it

By com­ is p o ssib le

can be r e a s o n ­

o r w h eth er such o b s e rv e d d i f f e r e n c e s

c o u l d be e x p e c t e d t o h a v e a r i s e n by c h a n c e a l o n e . I n e a c h o f t h e tw o m a i n a n a l y s e s c a r r i e d silic a

fla ttin g

ag ents,

and one f o r th e g l o s s used.

out fo r the

one f o r t h e r o u g h n e s s f a c t o r

(R)

(Gr) , a f o u r way c l a s s i f i c a t i o n was

E a c h m e a s u r e m e n t was c l a s s i f i e d u n d e r t h e

fo llow ing

h ead in g s: i

!

i

I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

50

1) T ype o f f l a t t i n g a g e n t 2) Tim e i n t e r v a l b e f o r e s p r a y i n g 3) P e r c e n t a g e o f f l a t t i n g a g e n t i n t h e l a c q u e r , b a s e d on t o t a l w e ig h t o f t h e f l a t t e d l a c q u e r 4) P e r c e n t a g e o f f l a t t i n g a g e n t i n t h e g r i n d ­ i n g m i x , b a s e d o n t o t a l w e i g h t o f t h e mix T he r e s u l t s

o f t h e s e a n a l y s e s a r e g i v e n on t h e

p a g e s, w ith th e o bserved F - r a t i o s sig n ifican ce.

In a l l

fo r the 5 %

in terp retatio n s

follo w in g

and T i

le v e l of

of th ese r e s u lts ,

e f f e c t was c o n s i d e r e d t o b e s i g n i f i c a n t

an

i f th e observed F

1% F - r a t i o , n o t s i g n i f i c a n t i f t h e o b s e r v e d F

exceeded th e

d id not exceed the

5% F - r a t i o , a n d d o u b t f u l l y s i g n i f i c a n t

f o r c a s e s i n w h i c h t h e o b s e r v e d F was i n t h e r a n g e b e t w e e n t h e 5r> a n d t h e 1% F - r e . t l o s ,

interm ediate

i n ac c o rd a n c e w ith

common p r a c t i c e . I t s h o u ld be collected for

t h e a g e n t D i a t o m a c e o u s E a r t h f o r 0 . '7 5 b f l a t t i n g

agent in the

o r f o r 1.50;^ f l a t t i n g g r i n d i n g m ix. th is

agent in the

fin ish e d lacq u er in a

T h e s e p a n e l s w er e n o t a v a i l a b l e Because o f t h i s ,

f o r u s e when

f i c t i t i o u s d a t a was

i n t o t h e a n a l y s e s a t t h e s e p o i n t s by t h e

method f o r f i l l i n g

m issing blocks

(95)>

stan d ard

i n s u c h a way t h a t

t h e a d d e d v a l u e s w o u l d b e o n l y dum m ies a n d n o t a f f e c t co n clu sio n s

f o r 1 . 25%

f i n i s h e d l a c q u e r i n a 10/a g r i n d i n g m i x ,

s t u d y was b e g u n .

in serted

p o i n t t h a t 110 d a t a was

f i n i s h e d l a c q u e r i n a 10% g r i n d i n g m i x ,

agent in th e fla ttin g

m entioned a t t h i s

i n a n y way.

the

T h i s i n s e r t i o n was e s s e n t i a l t o t h e

s y s te m a tic and sym m etric te c h n iq u e s o f c a l c u l a t i o n u sed in th e A n a ly sis of V ariance.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

51

A n aly sis

of V ariance:

S ilico

(F or G loss D ata) The v a r i a b l e b e i n g c o n s i d e r e d , i n t h i s of th e g lo ss read in g s on th e

a n aly sis

is

that

(G) made w i t h t h e P h o t o v o l t G l o s s m e t e r

in d iv id u a l panels under t e s t .

The a n a l y s i s was c a r ­

r ie d th ro u g h com pletely u sin g the t h i r d

o rd er in te r a c tio n of:

F l a t t i n g A g e n t s x Tim e I n t e r v a l s b e f o r e S p r a y i n g x P e r c e n ta g e o f A gents i n L acquers x P e r c e n ta g e o f A g e n t s i n G r i n d i n g Mix. T h e s e w i l l h e n c e f o r t h b e a b b r e v i a t e d .a s " A g e n t s x T i m e s x P e r Cent x P a s te s " . T his i n t e r a c t i o n is v arian ce,

c o n s id e r e d t h e m easure o f e r r o r

and t h e r e s u l t s

of th is

com putation a re g iv en in

T a b le 11. As c a n b e s e e n f r o m t h e F v a l u e s a s s o c i a t e d w i t h t h e t e r m s A g e n ts x Times x P e r C e n ts x P a s t e s ,

th ere

s tro n g evidence t h a t th e ag en ts as in d iv id u a ls d i f f e r e n t l y 'i n producing o f a g e n t seems t o

a given r e s u l t .

in flu en ce

the d a ta

in d ic a te th a t each r e a c ts d i f f e r e n t l y any o f th e o t h e r t h r e e raw d a t a ,

facto rs.

is extrem ely

are re a c tin g

That i s ,

th e type

i n s u c h a way a s t o t o t h e sam e c h a n g e i n

As may b e n o t e d f r o m t h e

and from t h e p i c t o r i a l r e p r e s e n t a t i o n o f e f f e c t i v e ­

ness of f l a t t i n g

a g e n t s , g i v e n i n F i g u r e 7 , t h e a g e n t Linde

S ilic a d id not give r e s u lts o f th e o th e r ag en ts low f l a t t i n g .

in .the sen se t h a t

Th e r e s u l t s

are con sid ered to

w hich w ere c o m p a ra b le t o t h o s e it

g iv e n by t h i s

produced abnorm ally ag en t,

give an erro n eo u s p i c t u r e

th erefo re,

of th e o vere.ll

effect.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Reproduced

• 1 —1 i—!

with permission

Table

Summary Ta b l e ;

A nalysis

S i - O - L i t e , Di a to m a c e o u s

of the copyright owner. Further reproduction prohibited without p erm ission .

of

Source

V ariation

T y p e s o f 1> ,L g e n t s ( A ) • T i m e Ba f o r a S p r a y i n g ( T ) /o A g e n t i n L a c q u e r Ob L ) /b A g e n t i n_ G r i n d (% G r ) (A) (A) (A)

X X

(T) (T_)

X

( '/o L )

(A) (A) (A) (T)

(T)

L)

"V

Gr) ( f o L)

X X X X X X

Gr) {■ % i G r )

x (,i L) x (A G r ) Gr) ( y t L) x ( A L ) x (;b G r ) (T) (T)

R esidual

(E rro r)

Total1

NOTE:

of

V ariance

E a r t rh,

w ith

and L inde

Respect S ilica

to

Gloss

for

Santocel,

( Compos i t e )

F

F( 5 /o )

F ( l/o )

(4)

(5)

(6)

3070.63 44.14 1232.60 17.96

3.16 4.41 2.93 3.55

5.09 3.28 4.58 6.01

15.54 23.67 46.53 1.61 4.35 3.88

3.16 2.34 2 . 66 5.84 0,00 2.51

5.09 3.37 4.01 14.15

•vHf -'Hr j /j /

2 8

46.96 71.50 139.98 1.S7 14.65 11.73

6.01

■;>

19.17 99.64 111.66 33.53

12 6 24 o (J

1.60 16.61 4 , 65 4.19

1,89 5. 50 1. 54 1.39

2.57 2.15 2.66 2.51

3.92 3.00 4.01 3.71

54.28

18

3 . 02

45,255.45

113

400.49

Sums o f Squares■

Degrees Freedom

(1)

(2)

27,330.49 133.35 1 4,395.48 108.51

3 1 4 2

9,276.83 133.35 3 .723.87 54.26

140.88 857.94 S39.88 7.47 29.30 95.87

3 12 6 4

Lie a n Sum Squares

(3)

Numbers i n p a r e n t h e s i s r e f e r t o E x p l a n a t i o n T a b l e H e a d i n g s on f o l l o w i n g p a g e .

(7)

t *»**(/r

3,71

of O'. co

T a b 1 e 11 ( Co n t i n u e d ) E^LAKA'i’ICE 07 1'ASLE HEADIEST

(1)

" Sums o f S q u a r e s "

= Sums o f s q u a r e s o f t h e d e v i a t i o n s o f t h e c l & . s s i f i c e t i o n mean s f r o m t h e g r a n d mean o f a l l

(2)

individuals

" D e g r e e s o f F r e e d o m " « T h a t n u m b e r by w h i c h e a c h "Sum of Squares"

m u s t be d i v i d e d i n o r d e r

t o g i v e a n 'U n b i a s e d e s t i m a t e o f e r r o r variance (3)

" K e a n Sum o f S q u a r e s "

- q u o t i e n t o f "Sum o f S q u a r e s "

d i v i d e d by " D e g r e e s o f Freedom" (4)

"F " = T h a t F - r a t i o

a s s o c ia te d w ith each e f f e c t . t a i n e d by d i v i d i n g Sum o f S q u a r e s "

i n d i v i d u a l "Kean

f o r e a c h e f f e c t by

" K e a n Sum o f S q u a r e s " (or E rro r)"

Ob­

f o r "R esidual

term .

(5)

"F (5;0"

= F - v a l u e s o b t a i n e d from F i s h e r ' s F - T e s t T a b le s

(6 )

"F (l/0 "

= F -va.lues o b ta in e d from F i s h e r ' s

(7)

S ig n ifican t E ffects:

F -T est T ables

■k-* s S i g n i f i c a n t a t 1 % l e v e l * = S i g n i f i c a n t a t 5^ l e v e l

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

54

j

3e c a u s e t h i s

a more d e l i c a t e

f a c t was r e c o g n i z e d ,

an aly sis

on L inde S i l i c a ,

In th is i

would r e s u l t

was d e c i d e d t h a t

from o m i t t i n g t h e d a t a

a n d a new a n a l y s i s was made u s i n g o n l y t h e

| t h r e e am ents S a n t o c e l , These r e s u l t s

it

S i-O -L lte,

are tab u lated an aly sis,

the

and D iatom aceous E a r th .

i n T a b le 12. resid u al

(or e rro r)

estim ate of

v a r i a n c e was c o m p o s e d o f t h e p r e v i o u s l y m e n t i o n e d t h i r d order in te ra c tio n ,

p l u s t h e tw o s e c o n d o r d e r e f f e c t s :

A m e n ts x P e r G e n t s x P a s t e s Times x P e r G ents x P a s t e s These seco n d o r d e r i n t e r a c t i o n s

were n o t s i g n i f i c a n t , h a v in g

F v a l u e s o f n e a r l y u n i t y w hen c o m p a r e d t o t h e t h i r d

order

in te r a c tio n e stim a te of experim ental e r ro r . Before pro ceed in g to

a d iscu ssio n of th ese

effects

and

t h e a s s o c i a t e d mea n v a l u e s o f G- u s e d i n t h e c o m p a r i s o n s , j j a m e a s u r e o f t h e r e l i a b i l i t y o f t h e s e m ea ns w i l l b e n e c e s s a r y . | O b v i o u s l y , e a c h mean v a l u e t h a t i s g i v e n i s a s a m p l e v a l u e I drawn from t h e e x p e r i m e n t a l d a t a , a n d , a s s u c h , can be i n t e r [ p r e t e d t o b e o n l y t h e m o s t p r o b a b l e v a l u e o f t h e t r u e mean.

J

F o r e a c h m ean v a l u e l i s t e d , error,

i.e .,

th ere

can be a s s o c ia te d a sta n d a rd

a number t h a t a llo w s one t o a p p r o x im a te t h e

j p re c isio n of the estim ate.

If it

|

th a t the

for th is

w ell o rdered d a ta ,

is

assum ed, as i s

ju stified

i n d i v i d u a l sample v a l u e s

| were draw n from a norm al p o p u l a t i o n , t h e o r e t i c a l c o n s i d e r | i a t i o n s l e a d t o a method o f c o m p u t a t i o n f o r t h e s t a n d a r d e r r o r s o f t h e m ean s o f t h e a set1 of s o -c a lle d

sam ples

(45).

"co n fid en ce lim i t s "

Know ing t h i s

can be o b ta in e d ,

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

valu e,

ith permission

Table

1&

Summary

Table:

S i-O -L ite,

of the copyright owner. Further reproduction

Source

of

and

V ariation

T vX p e s o f A g e n t s (A) ' Time B e fo r e S p r a y i n g (T) 7 > A g e n t i . n L a c q u e r (>t L ) fo A g e n t 1n . G r i n d (% G r ) (A) (A) (A) (T) (T)

prohibited without perm ission.

l

(A) (A)

x (T) x ( 7 L) x u Gr) x ( 7 L) x (7 o G r ) ) X ( 7o O r ) x x

(T) (T)

Res idu a l

x X

( ,i Gr) (; o L )

(E rro r)

T otal

NOTE:

A nalysis

of

V ariance

w ith

Respect

to

G loss

D i a t ornaceous

E arth

Sums of Squares (1)

Degrees Freedom (2)

M e a n Sum Squares (3)

1,573.40 233.61 14,181.93 572.67

2 1 4 2

786.70 233.61 3,545.48 186.34

156.32 49.39 749.57 39.40

29.21 71.79 349.00 8 . o2 IS . 84 89.94

2 8 4 4 2 8

14.61 8.97 87.25 2.13 8.42 11.24

98.09 16. 83

4 8

24.52 2.10

160.79

34

4.73

17,202.62

33

207.26

for

3a n t o c e l ,

(C om posite)

F

F ( 5>a)

F ( l/o )

(4)

(5)

(6)

3.23 ^ . 1o 2 . 65 3.28

5,29 7.44 3.93 5.29

3.09 1.90 1 8 . 45 2.22 1. 78 2.38

3.28 2.23 2.55 5.73 5,23 2.23

5.29 5.03 5.93 13.79 5.29 \ j • i 'O

5.18 2.25

2.65 3.07

5.35 5.16

Numbers in p a r e n t h e s i s r e f e r to E x p la n a tio n T a b l e H e a d in g s on f o l l o w i n g p a g e .

(7)

of

Cl cn

55

Table 12 (0ontinued)

EXPLANATION 0 ? TA3L2 LEADINGS (1)

"Sums o f S q u a r e s "

= Sums o f s q u a r e s o f t h e d e v i a t i o n s o f t h e c l a s s i f i c a t i o n means from t h e g r a n d mean o f a l l

(2)

in d iv id u als

" D e g r e e s o f F r e e d o m " = T h a t n u m b e r b y w h i c h e a c h "Sum o f S q u a re s" m ust be d i v i d e d i n o r d e r to g iv e an u n b iase d e s tim a te of e rro r variance

(3)

"Mean Sum o f S q u a r e s "

a Q u o t i e n t o f "Sum o f S q u a r e s "

d i v i d e d b y " D e g r e e s o f Freedom" (4)

"F " = T h a t F - r a t i o

a s s o c ia te d w ith each e f f e c t . t a i n e d by d i v i d i n g Sum o f S q u a r e s "

Ob­

i n d i v i d u a l "Mean

f o r ea c h e f f e c t by

"Mean Sum o f S q u a r e s "

f o r "R esidual

(o r E r r o r) " term . (5)

"F (5 b )n = F -v alu es

o b ta in e d from F i s h e r ' s F - T e s t T a b le s

(6 )

MF ( l ; 5 ) "

(7)

S ig n ifican t E ffects:

= F - v a l u e s o b t a i n e d from F i s h e r ' s F - T e s t T a b le s

- S i g n i f i c a n t a t 1% l e v e l ^ = S ig n ifican t at

5% l e v e l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

!

57

w i t h i n w h i c h o n e may b e ?5'-o c e r t a i n t h a t t h e t r u e value l i e s . w hich i s

Th e r a n g e w i l l d e p e n d u p o n t h e s i z e

means.

T he s t a n d a r d e r r o r o f t h e

th u s th e

confidence l i m i t s ,

fic a tio n

f r o m w h i c h t h e mean i s c o m p u t e d .

p retatio n s,

the

ta k e n , giv in g

is th e

confidence lim its a t

l e a s t a s w ide a s t h e t r u e

standard' e r r o r of th e lin e

in d iv id u al

of T able 12,

sin ce

f o r t h e I-Iean Sum o f S q u a r e s f o r T o t a l V a r i a b i l i t y

square of th e

Taking t h e s q u a re 3 . S.

To u n i f y i n t e r ­

s ta n d a rd e r r o r of th e t o t a l d a ta has been

The e s t i m a t e o f t h e

fig u re

mean, and

w ill a ls o vary w ith th e c l a s s i ­

r e a d i n g s may b e t a k e n f r o m t h e l a s t th e

of "n ",

t h e n u m b e r o f i n d i v i d u a l v a l u e s u s e d i n t h e com­

p u ta tio n of the

ones.

mean

stan d ard e r r o r of the in d iv id u a ls .

r o o t o f t h e number ( 2 0 7 . 2 6 ) ,

= 14.4-0 a s t h e

one o b t a i n s

stan d ard e r ro r of th e in d iv id u a l v alu es.

The s t a n d a r d e r r o r o f a mea n i s t h e n d e t e r m i n e d b y d i v i d i n g th is

f ig u r e by

\j n - 1

, where "n"

i s t h e number o f i n ­

d i v i d u a l v a l u e s u s e d i n c o m p u t i n g t h e mean. numbers o f s a m p le s , b u tio n ta b le s t h e means

e .g .,

l e s s th a n 30, F i s h e r 's t - d i s t r i -

m ust be u s e d i n s e t t i n g

(37).

Th e v a l u e s o f " t "

t h e number o f s t a n d a r d e r r o r s sam ple s i z e

For sm all

confidence lim its

on

from t h e s e t a b l e s a r e

o n e i t h e r s i d e o f a mean o f a

" n " , w i t h i n w h i c h o n e c a n be 9 o% c e r t a i n t h a t

th e t r u e v alue l i e s .

F o r th e sam ple s i z e s u s e d i n t h e

fo llo w in g d i s c u s s i o n , .t h e

t-v alu es

are as fo llow s:

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

58

T able 1 3 .

E is h e r 's L im its

" t " - V ? l u e s U s ed i n S e t t i n g

for S ilic a

C. L.

t (956 l i m i t s )

S . E . K.

6

2.57

6.44

16.55

10

2.26

4.80

10.85

18

2.13

3.49

7.4 3

1.96

Belov; e a c h t a b l e

o f m eans p r e s e n t e d d u r i n g t h e i n t e r ­

p r e t a t i o n o f th e A n aly sis

th ese

Com putations

n

more t h a n 30

size

C onfidence

of V ariance is n o ted th e

"n" f o r t h e means i n t h e t a b l e , m eans

(S.E.IT. ) ,

th e

sample

stan d a rd e r r o r of

a n d 95.6 c o n f i d e n c e l i m i t s

(C.L. ) f o r

t n e me s.ns . R e f e r rin g nou to T able 12, m ain e f f e c t s

it

is

seen th a t th e fo u r

are a l l h ig h ly s ig n ific a n t.

T he t h r e e d i f f e r e n t

a g e n t s p r o d u c e d a v e r a g e g l o s s e s t h a t were s i g n i f i c a n t l y d ifferen t,

according to th e

c o m p ila tio n g i v e n i n T able

l ¥ below : T a b le 14.

E f f e c t o f D i f f e r e n t S i l i c a A g e n t s 011 G l o s s Agent

Ave.

60° G lo s s

B antocel

22.95

Si-O -L i-te

31.55

D iatom aceous E a rth

32.07

n = 30;

3.S.M . < 2 .o 7 ;

C.L.
a n d i s

statistical

an aly sis

of the

da t a . The e f f e c t

of the

in te rv a l before n ific a n t.

"Tim es" f a c t o r ,

i.e .,

spraying th e la c q u e rs ,

t h e tim e

was a l s o h i g h l y

The a v e r a g e g l o s s e s o b t a i n e d

sig ­

fo r the v a r i a t io n in

t i m e a r e g i v e n i n T a b l e 15 b e l o w : T a b l e 15*

E f f e c t o f Time o f S p r a y i n g o f S i l i c a - F l a t t e d L a c q u e rs on G lo ss T im e o f S p r a y i n g

60° G loss

Im m ediately

27.24

A f t e r a g i n g 1 wk.

30.47

n = 45; T his ta b le

S.E .M . < 2 .1 7 ;

shows t h a t

w ere o b s e r v e d when t h e o n e w ee k b e f o r e in th e

Ave.

+ 4.25

s ig n if ic a n tly g r e a te r g lo ss values l a c q u e r s 'were a l l o w e d t o

spraying.

can aging o f f l a t t e d

" g l o s s i n g up"

C.L.
$1*jOst/tA/VlAA/lAXfoJtii ft's (Xhx- IaA m L*

R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

*5 7 5,

I I i j

65

The m ethod

type

used

variable is

w ith

panel

points ment

panel. the of

fifte e n

In

a ll,

gloss

of

the

011

the

previously

single of

roughness

series,

and

explained

in

analysis

four

agents,

ting

power

analysis

was

though

of

effects

being,

carried

it

Linde

was

studied.

can

be

of

A gents

seen

in

from

x Time

through

expected

S ilic a

is' sum m arized

As

on

each

used.

were

th at

w ould

bias

Six

vacant

The

re su lt

Table th is

of

because

were

herein

A nalysis

the

before

A gents

in

F inal

A gents

x

Gent

of

A gents

in

G rinding

of

three

Type

of

four

m ain

(t;*o

of

second

A gents,

were

effec ts

w hich the

were raw

biased

order

and

the

three

in

the

doubtful

because

reveals of

the

Linde

M ix,

f l a t ­

and

obscure

in teractio n s: Type

and as

in

f ir s t

range). these

Type

addition order

one

factor to

the

in teractio n s

A close

data

of

as

the

conclusions

S ilica

of

w ell

containing

high,

other

th at

three

Lacquer,

interactions

sig n ifican tly

data

low

prelim inary

Spraying,

of

Per

the

a ll

the

re su lts

of

using

20.

tab le,

in terv al

again

the

Gent

largely

data

com pletely,

x Per

of

in stru ­

V ariance

A gents

atio n

A nalyzer

mean v a l u e s the

is, fifte e n

were

c la ssific a tio n s

that

w hereas

factor

R values

readings

one,

Brush

the

c la ssific a tio n

reading,

the

w ith

readings.

The

the

id en tical gloss

instead

individual

in

was

each

gloss

te s t

possible

panels

as

to

1710

120

that

single

done

discussed

readings

a

co llec tio n

inserted

Type

exception

subjected

m issing

the

the

work

previously

exhibits

possible

for

the

of

were

for

an a ly tica l

for

composed

each

of

exam in­ are

included.

R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.

Reproduced with permission

T able

20.

Summary

T able:

of the copyright owner. Further reproduction prohibited without p erm ission .

S i-C -L ite,

Source

of

A nalysis

D iatom aceous

V ariation

Sums o f Squares (1)

of

V ariance

E arth

'

w ith

and L inde

D egrees Freedom (2)

Respect

to

R for

S a n t oc e l ,

S ilica

H e a n Sum Squares (3)

F

F ( 5 /o )

F ( l .j)

(4)

(5)

(6)

4 0 6 ,- 3 1 7 . 75 13,833.83 425,567.52 22,185.22

3 1 4 2

135,505.92 1 o , 3 3 o . oo 1 0 6 , 3 9 1 . 83 11,091.51

153.05 15.70 127.93 13.34

2.50 5.64 2.37 2.99

3.78 5. 64 3. 32 4.60

(A) x (T ) ( A ) X (;'b L-) ( A ) x C /o G r ) (T ) x (% L) ( T ) x (. c G r ) ( C o L ) x (.,= G r )

15,535,55 25,709.44 42,594.66 8,708.89 5 , 3 6 3 , OS 19,408.41

3 12 6 4 2 8

o , a4co. l o 2,142.45 7 099.11 2,’ 1 7 7 . 2 2 3,431.54 2,425.05

6 . 67 2 . 58 5.54 2 . 62 4.13 2.92

2.50 1.75 2.09 2.57 2.99 1.94

3.78 2.18 2.80 3.32 4.60 2 . 51

(A) (A) (A) (T)

x x x x

(-a

11,560.32 8,604,67 52,181.35 11,451.93

12 24 6 3

946,69 358.53 10,353.64 1,432.74

1.14 2 , o2 12.46 1.72

1.75 1.73 2.09 1.94

2.18 2.21 cO. OQOn 2.51

(A)

x

(T)

26,152.48

24

1,039.59

1.51

1 . 52

1.79

1,522,357.47

1590

331.58

2,430,505.13

1709

1,422.13

T y p e s o f A g e n t s (A) Time B e f o r e S p r a y i n g (T) ,i A g e n t i n ' L a c q u e r ( % L ) 'a A g e n t - i n G r i n d ( h G r )

(T) (T)

R esidual

x L) x (;c G r) L) x (u Gr) L ) x (.j G r) x

C /o

L)

x

(Error)

T otal ROTE:

(.)

Gr)

I T u mb e r s i n p a r e n t h e s i s r e f e r t o E x Xc l a n a t i o n i c l .L^ H e a d i n g s o n f o l l o w i n g : p a g e .

of

(7) j>• j g

ti"/ r

•

i

-T

67

T a b l e 20 ( C o n t i n u e d ) EXPLANATION

(1)

"Sums

of

Squares"

0?

the

the "D egrees

of

Freedom"

"Mean

Sum o f

= That

"F" = T h a t F - r a t i o

deviations means

of

a ll

number

by

which

Squares"

to

give

must

be

individuals each

divided

an' u n b ia se d

from

"Sum in

estim ate

= Q uotient by

of

"Sum

"Degrees

of

of

of

Squares" Freedom"

a s s o c ia te d w ith each e f f e c t . tained

by

Sum o f

Squares"

dividing

" M e a n Sum o f (or

order

variance

divided

(4)

the

mean

of

Squares"

of

c la ssific a tio n

grand

erro r (3)

HEADI NG' S

= Sums o f s q u a r e s of

(2)

TA3LE

Error)"

for

individual each

Squares"

Ob­ "Mean

effect

for

by

"R esidual

term .

(5)

"F(5/o)" = F - v a l u e s

obtained

from

F ish e r's

F-Test

Tables

(o)

"F(l$)"

obtained

from

F ish e r's

F-Test

T ables

(7)

S ignificant

& if

= F-values

E ffects:

= S ig n ifican t

at

1%

level

= S ig n ifican t

at

5$

level

=

S ignificance

low

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Because of t h i s ,

t h e a n a l y s i s was r e p e a t e d ,

d a t a and i n c l u d i n g th e o t h e r t h r e e : D iatom aceous E a rth o n ly .

The r e s u l t s

om itting t h i s

S antocel,

S i-O -L ite,

of t h i s

new a n a l y s i s

and

a r e g i v e n i n T a b le 21. I n t h e . same m a n n e r a s b e f o r e , have been se t cussion.

It

on a l l

mean v a l u e s u s e d i n t h e

must be rem em bered t h a t t h e s e

w idest p o s s ib le fid en ce l i m i t s

ones t h a t

T a b le 21.

value

is

lim its

An e s t i m a t e o f t h e s t a n d a r d

S ince a l l

and l a r g e

o b ta in th e As w i t h t h e

ings a re th e v a r i a b l e ,

lin e

14-75 • 9 1 > a n d t h e

of square

stan d ard e r ro r of

sam ple s i z e s a r e h e r e

s a m p l e t h e o r y may b e a p p l i e d ,

n u m b e r may now b e d i v i d e d b y t h e

sam ple.

are th e

ana th e a c tu a l con­

33.4-2, which i s t h e

in d iv id u al v alu es.

sam ple s i z e t o th at

fo llo w in g d i s ­

rang.es c a n be o b t a i n e d from t h e l a s t

g r e a t e r th a n 30, th is

cases.

Th e Meen Bum o f S q u a r e s i s

root of th is the

c o u l d be s e t ,

("O .L .")

f o r t h e m ea ns f o r a g i v e n c l a s s i f i c a t i o n w i l l

be much n a r r o w e r i n a l l e r ro r of th e

confidence l i m its

square ro o t of th e

stan d ard e r r o r of th e form er a n a l y s i s ,

the ta b le

fo llo w in g d is c u s s io n in c lu d e s th e

mean o f

where g l o s s r e a d ­

o f mean v a l u e s u s e d i n t h e sam ple s i z e

" n " , t h e max­

imum s t a n d a r d e r r o r o f t h e mean " S . E . K . " , a n d t h e 95% c o n ­ fid en ce lim its

" C .L ." corresponding to t h i s

based on a norm al curve " t" From T a b l e 2 1 ,

v alues

were o b t a i n e d

of 1.96.

i t -appears t h a t th e

Type o f A g e n ts i s h i g h l y

stan d ard e r r o r ,

sig n ifican t.

main e f f e c t due t o The f o l l o w i n g o v e r a g e

fo r R fo r th e th re e a g e n ts:

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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