Studies in sex physiology, No. 16. Surface area in the foetus of the Merino sheep

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0 nderstepoort .1 ournal of F eterinary Science and Animal Industry, Tlolwne 7, Xumber 1, July, 1936.

Studies In Sex P hysiology, No. 16.

Surface Area in the Foetus o f the M e rino Sheep.

By A. P. ":\IALA::\" :ttl(l H. H. C'"GHSU::\", Sections of Stntisti('~ awl Anatomy. OmlerstPpoort.

lX'J'I{OTlCCTIOX.

ll\ reality thi~ ~huly is a <·ontinuation of Stu<l.\- 1a (l'urson awl Malan) "·here the eff<eet of age wa~ sttHliP<l in relation to (11) general hoc1y form,

cz,)

body \Yeight, and (1') C.R. leng·th. "\~ the foetuses in <tnestion \Yere requirecl for the huther itl\-eiitig:dion of the external O(l(l,Y fonn, :uwtlw1· se1·ip,; of foetnses has hePn ohtainer1 tln·ough thP kindness -of Dr. L. L. Houx, ~\I.Sc., o£ Ermelo, for this obsen:1tion.

~eithPr Xeeclham (1881) nm· HammmHl (HJT2) ha~ an_\· infonna- iiou beariug directl,v ou the subject.

As the ordinan· metho<1 of 1·emoYing the skin and calcnlating its area on a measuring table ,,-a,., ob1·iously Ullsatisfactcn·~-. >Ye a<lopte<1 the suggestion of 2\Ir. F. K H. Appleton of Onrlerstepoort. This consisted iu dipping the foetus in a celloidin :solution, allm1·inp: the Hlaterial to dry, 1·emo\·al of the ('elloidin coat aurl then measuring this. In this way "·as olwiatecl the shetching of the skin which would nullify the results obtai ned.

In Foetuses 32969 (107 clayR) aml !'\697G (122 days) and Lamb 450GO (two <lays plus gestation perio{l 147 <lays), since the hairy coat was well established, no attempt \\·as made to remove separately the adhering celloiclin coat, "·hich in any cast>. prel't>ntt><l sh·etrhing of the skin during remoYaL

251

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S1TDIES I::Y SEX PHYSIOLOGY, NO. 16.

The data ohtni ned from the ten foetuses are ta hula te<l thus :-

'fAilLE I.

2 3 4 5 6

Lamb.

I ^(w) ^(l) ^, ^(a)⁽²⁾ ⁽²⁾

Age.

I ^Weight. C.R. Length. Surface Area.

I

Surface Area.

(Days.) (gm.) (em.) (sq. em.) (sq. em.)

I

^(Observed.⁾ (Expected.)

: 1

... ± ²⁸ - ^- I :1·1 -

... 31 1

I

1·9 3 ·:i 3 6

... 55 40 9 8 58 i\8 ·3

... 61 70·6 llO 90 90 9

... 64 82 12 9 98 101·6

... 9:2 617 ^I 2:i 0 I ⁴⁴⁰ ^48!\

Ko number .. ..

35712 ........ . 38510 ........ . 35659 ........ . 35592 ........ . 33131 ........ .

39004 ........ . ... 94 680 25·0 522 524

32969 ........ . ... 107 1,320 29·5 854 87f)

35976 ........ . ... 122 2,230 32·0 1,275 1,314

45060 ........ . ... 147

+

2 2,97ii 40 0 (1) 1,920 1,644 45023 ........ . ...

I ± ¹⁴⁹ ^3,750 ⁴⁵^·0 ^2,100 ^1,902

(l) Height :1t "·ithers on second day "·as 34·3 em.

(2) The legs hclo"· the carpus and tarsus "·ere not taken into consideration.

DISCUSSIOX.

vVe shall rleal IlO\Y "·ilh the effPct of age on (n) the increase in :>urfacP area .:uul (b) thP relation heh,·eeu surface area and borly

"·eight.

(a) The l~'ffcct of Aqe on the increase in Surface Area.

The information aYailable concerning skin uren at rlifferent ngec;

i~ contained in columns G anrl 2 respedi,·Ply i.n Table I. These particula1·::; are diagranJ:lticalh· sho"·n in Chart A, "·herP surfflce area is plotted agninc;t age anrl t hP Yariou::; JJoinh; joinerl by a spnes of straight lines.

As in other featnres of prenatal growth, e.g. body 1night and C.R. length. the incrPase in sudace aren "·iih age is exceerlingly slm1· <luring ear-]:\· ]H'Pg'Ilanr·~~. huL increa;-;ed rapidly with alhancing age. This acceleration in the gTOIYth rate has its maximum in the beginning o£ the gestatio11 periorl and r1ecreases to a negligible Yalue to11·anls the enrl.

The aYerage rate of innense m ~urfaee area for !he "·hole prenatal periorl was aiJproximatel.'; 1:~ sq. em. [Jer diem. Hmv this rate of increase, ho1vever, YariPs

'"ii

h age is sho11·n in Chart A, anrl also if one arbitrarily cliYides the gestation period into three stages of about :fift_y da.n; each. 'l'he gr011'th rates in surface area during these successive interYals are approximately 1 sr1. em. pel' die111, 15 sq. em. per diem, anrl 20 S<J. em. z1er rlirnn respectiYely. It is also obvious that the total illcrease duriug the first half of pregnancy 1s very little in comparison "·ith that dmiug the seconrl halL

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A. P. ::.IALAN A~D H. H. CURSO~.

CHART A.

The Increase of the Skin Area of the MeTino Focht.<.

2000

~ ~

^.-~-^.;

I f.-~-

I

_"^'"·

I I ^'C

1500 ^N

I '

I

i

I

f

I I

~

I

i I

I _-_- _{- -}_{1 - - -}

I

I I ^I

1000 ' I

I

I J

^I

I ^I

I

I ⁱÎ Î ÎⁱÎ I

f

i

I

!

I

I I

/

^I

I

^I

i ^I I

500 I _-- I

I I ^I

i I i

I

i

-+·

₁

~I

I

I /_ I

I

100 i

£_

Ll--+4

0 10 20 30 40 50 60 70 80 90 I 00 110 120 130 140 Age (days}.

The surfaee area is found to tlouLle itself during the last forty days of the gestation period, and the skin area of the mature }[erino sheep (Lines and Pierce) is approximately five and a half times that of the ne11· bom lamb. (The body "·eight also doubles itself during the last forty clays of the gestation period, bnt the mature weight is approximately tweh e tintes the birth weight.)

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STUJ>TES IK SEX PHYSIOLOGY, XO. 16.

CIIAltT B.

'J'he GT01ufh ·in IJod!f Weight of the Merino Foetus.

J700

.1000

I I

^I^I

I

lSOO

I

I I I I

1000

I

1 /

I

1500

I

I I

^I

I

··-

I

1000

v

I

,... _..., I

>00

I

100

I

^..

~

Days.

" ³¹ ⁵⁵

.. . .

_" _" ¹⁰⁷ _'" ^14'1

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A. P. :MALAN AKD II. H. CURSON.

(u) The Effect of Age on the Relation uet1ceen Surface Area awl Body W eight.

For the sake of compatisou 11·ith Chad A (IYhich illustrates the increase of surface area \\·ith n<hanciug age), Chart B has been prepared to sho"· the gTO\dh in bocl_,. "·eig·ht for the smne series of foetuses. Then' is a remarkable resemhlam·c behn~en the bYo graphs ex c;e~pt for a les~ Hwrkecl in ere a se of bod:;· \Yeight during the fi r.-.;t half of pregnancy and a more pronounced grcn1th in 11eight (luri11g the second half. This indicates the relntiYe1)· greater acceleration of the gr01dh in borly weight.

A. better pidurr. ho\\-:.;YPr, of the actmd rrlaiion.,hip i,;; furni:;hed by Chart C \\·here log. (11·eight) is plotted against loge \Surface area) as tabulate(l brlo'L

CHAin C.

The Relation /,ehccen the Relotire Grmcths in 1T'eight and Skin 1lrca for the Jlerino Foettts.

(Dotted line: ::r=l·284y- l i530.)

8

i

r

7

/ +--

^r----

6

5

4

~

3

v

2 ^I

1 /l

I 2 3 4 5 6 7 8

Loge [Skin Area (sq. ern.).]= y

255

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STUDIES IN SEX PHYSIOLOGY, KO. 16.

TABLE II (Logarith1nic ralues).

I

Log. (C.R. Length).! Loge

(~"eight).

^Log.

(Sl~:n

^Area)^.

- - -- · - -- - - - ' - - - · -- - ' - -- - - - -___c-- ----"--- - Lamb.

No number ......... . 35721 .................. . 38510 ............ . 35659 ........... . 35592 ............. . 33131 ...•. 39904 ....... ..

3:Z960 ........... . 35976 ....... . 45060 ............... . 45023 .............. .

0 6419 2·2824 2·3979 2·5649 3·2189 3·2189 3·384a 3·4657 3·6888

:~ ·8067

3·6888 4·2627 4·4067 6·+249 6 ·5221

7 ·1854 7·7008 7 !)!)80 8. 2:205

1·1314 1·2528 4·0604 4·4427 4·5850 6·0868 6 ·2558 6 7499 7 ·li>07

7 ·.)ii96 7·(i.J.()7

The strong linear relationsb i p between the log a rit bmi(' Yah1es is clearly shOII'll by Chart C. 'l'hi,; apparent linear·ity suggests a constant ratio bet,,·flen the relati.Ye iuneases in sm·face area a]l(1 those

. . { d 1 dw cl 1 da

m ho<h· we1ght. -d (log,.w) = - -d , and -

1- (log/t) = - dt

" t w t ct a .

Therefore for a constant relationship bei11·eeJL these relati1·e increases.

a straight line is to follm1· IYhen the natural logarithms of the \H'ight are plotted against the natural logarithms of the corresz10nding skin areas. )· The be,;t fitting straight line to these logarithmic Yalues was obtainN1 by the metho<l of le<:~st squares and is sho\\·n on Chart C l1y the dotte<l lin<-', its equation being:-

.'l;= l·284.1J- l ·:j30 or v=0·778.r+1·200 . . . . (1)

\There :v =loge (lcet:.l)ht) and

y= loy,. (Mea) as shown in Table II.

vVhen in the ahoYe equations the logarithmic Yalues are transformed into units of actual obenation the following parabolic relationships are obtained:-

tv=0·217a'·²⁸'1 or a.=J·3201r⁰· "8

•

where w=uody tceigltt i11 gm. and a=surface area in sq. em.

. . . (2)

This relationship is sholl'll h.,- the (lotted line ou Chart D. The points joined by a series of c·outiiluous straight line;; 1·epresent the ohsen-ed Yalues ±or body weight :md surface area, as giYen in

column~ 3 ana £) of Table I, \Yhile the expeded surface arPas for the cones pond ing o hsened weights are call'ulated hom (he ahoYe relationship (2) all(l giYeu in column (j of Table I. These " expeeted "

Yalues are in fair agreement "·ith those ohserYecl. Although the obYious (1iserepancy of the second last point in chart D is, when expressed as a percentage, not unduly great, some explanation may be given. Lamb 45060 was measured hYo days after birth and the fact that it was rather thin explains the relatiYely lo1Y ,~·eight in comparison with skin area.

256

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1 ' 3 -

A. L'. 1\IALAl'\ Al'\D H. H. C"CRSOX.

CH,\HT D.

'L'he llelation uehreen Body-1ceiold ond 8urface-oreu o.f the Jlerino-foetus.

(w)

3,500 1--- - - 1 1 - - - + - - -- ---+-- - - - ---l---1-- --1

3,000 f---- - - l c - - - - -- - -- - - J . - - - + -- ,0

2,500 1--- - - - -- - - - l - - - - -- - + - - - -

2,000

1,500

I I

!

i

I

!

1,000

·-r--

I ' '

I ,. ~-- ;t---~ ----1-~

I

I / I I

i

^I

/ I ^I

I : , ,

: ! / I

500 l.OCO 1,500 2,000 (a)

SvrfJce Area (J.I.

~q em.

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S'LTDIES IX SEX PHYSIOLOGY, XO. lG.

In Yarim1,; puhlif'ntion,; ou b:hic JIJPta1Jolism of ~ltPP)J (e._r;. Line.~:

and Pirrcr, l!J31), cliffrrent ,·aluP:-: for the con~ta11t~ in the aooYe relatiow:hip (:2) are gil'ell .. ''' A fairlY r:-.:ltau~iiYP reYir"· ol thr lite1·ah1rr on the snbjrd i~ g-iw n h~ Jho<l_\ (l!JT±) in thr ..Jnnunl He-rie1c of lJiuclteiJiistty. 'l'he IJOII·er in<lP:-.: in iltr par:1holi<: rel:Jtion- shij1 behl·een .-md:1ce :n ea ancl ''"right is-~ :i(·cmdinp: to :Jirrh, ,,-ho~<'

Y::due i.~ mo~t frequently 8tlopte<1. Brod_'i·, h011·eyer, sug-gr~h: ()·I()

"IYhich i~ ,;till 1aflwr lm,·e1· than the Y:due for thP prrnat:ll st:1gr Cl"·

ShOII"ll :1 hoYe .

• -\.lthough tl1r Jllllllher of foetuses fm· '' hicl1 thta <·oucrrning·l;oth

"·eig-ht ancl .~kin area (':-.:ist i:-: oni1· tPn, ihe Yctlur for tlw indPx i,;

gin•n h~- tlH~ prec;ent 1ndhod of <·:1lcul:dio11 as O·i"iS±O·Ol0-:1-. Thi,;

Y:11ue lll:1y thc•reforr not hr c·:-.:pedt•d for 1 per <'<'Jit. pmhahility lron1 an :1dual nlue 11·hich lies oubidt• thl' limit,; O·Fl a1Hl O·SI. It i,.;, ho11-e1·rr, .-;uggrsted t-lwt thi~ Y:du<' ^HW\.Y<ll'.\' hoJJJ hJ·c•p.J io ln·rr<l :md ei-PJJ cliHN :-:light]_\· f01· cliftert>nt floc·ks of ihP s:IIIJP hn•c•cl.

.\.nothrr point for con,;i<lPJ':il ion 11·a.-< the rdat ion:<h i p l~Pt ,,·0e11 -~cnfnce :nr:1 :md ('.B. length and thl' rel:dion.-<hi11 lJl'hH'('li ~udn<·e

an-•:1 allll both \w ig-ht :11ul ('.H. length. Sinn·. ltollei·Pr, sudnr-P nrra \\':1' morP a<·t·lir:ltrl.\-e:-.:pn'~~-~l'd in trn11s of l1ncly ,,·eight t-li<lll i11 ten11,; of C.H. leJigth, :1nd fudhPI'IIIOn' silJ(·p the rem:1ining- ,-~ni:mce

in ,udal'e :nP:I "·11 il'h ,,-:ls 110t e:;:pressetl in tPrm;; of horh· IYl'ig·ht "-a~

of the s:1me onler ns the nt·t·nrn(·\· of obsrn·atiml, thr i]l(·h[;;ion of C.ll. length in the prl',ent <·nsr scorYrs no 11seh1l pcnpnse.

Scii.ILUn·.

The incrPn,;e in surbce :n·e:< of thr :Jierino foetn' is <li,;cussed. The re l:d ion.-; hip hrhYPP ¹¹ .~11rfac·e <HP:I a ¹¹r1 bo<l.1· 11·eighL as estimatecl hom thr pn•,ent serirs of foetu.~es i.~ expres.~rcl bY tlw ecp1 ^:1tion a = :)-:)20 u·⁰· ' " .

SeYl'ral l'klrt,; are ginm in ill11Str:dr th<' fe:dures ,]e:-;n ihetl.

.\.Cl\.\0"·1,EDG'I E:\T.

\Vco wi:lh to t1J;IJJk :Jiess1·s. C. U. \Yal];pr and }'. D. JTon1·ell for their as:-;istani'P ::11111 intrrr,;t in tl1r oh:-;PJ'Y:lt iou.-<.

BHODY. ~- (UJ:l,!). l\utrition. Article> in .lnnuu/ Hn ieJt· of J!iotlrel!lisfry.

Yol. 3. 1-:)tanford l'ni,·ersit_,. Pn•ss. C'alifomia.

cr

ll

sox .

^H.^1-f.^' ^A^:'>ill^l\L\LA:\. A. p' (l(J:l.i). '1'110 Ch;lllgi ng 1:' roportions ol

the :Herino Lamh from tl1<• Second to tl1e Fifth l\lontl1 nl Pn•nabl Life.

OndenfrJ,uorf .fournu/ (Jj l·,,t_ Sr. ontl .lniu111l. }ndu.<fry. Yol. -L So. :2.

H.-\l\fl\10.\'D. J. (Un2). (.'rrncff, und tltr J>n·rlop111P11f uf Jluffon f,Junlilies ·in the Slter']J. Oli,·er and Boyd. J.onclon.

LJl\l~S. 1•:. \V., AND PIERCE, A.\\". (19:31). The Basal (Standard) :\[etaholism of tl1e >-\ustralian :\Jerino Sheep. Rut/. -55. ('ouncil for Sci,·ntifir und lnr!u.,triul Be-H'/1/'Ch. Comrnomnealth of ~\ustralia.

::'\EEDH.-\l\I. J. ^(1931). ^C'hPnl^icol^RmlJI'IJUIOrtl/. 3 Yols. Cambridge rniYersit,- l'ress.

- - - -- - - - - - - - - - -

*See Section "Heat-production nf :\lamrnalian Embr,,·os ", p. 71:2, Vol. lL Seed ham.

258

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A. I'. JVL\LAN Al'iD H. H. CL:RSOX.

ADDEXDUl\I.

In a rlcli hon to the o bsena tions presented and discussed in the preceding' article the following information is nmY anilable :-

TABLE.

(a)

Age of ("") ( 1) Surface area (sq. em.).

.Foetus of E\\'C. Foetus \\"eight C.H. length (days). ln gm. (em.).

Observed.

I

l~xpeetecl.

44803 ............ 3:3 ^J.25 2·4 4·4 4·6

44849 .......... 60 44·5 10·5 79 71

15337 ............ 90 ;i30 24 451 4/2

3582l. ..... ... 1:.!1 2l70 :{6 1353 t:{87

44307 ............ 146 3300 37 Hl30 1911

The data g1Yen in the aboYe table should be compared with 'raule I in the text. (The straight C.ll. length is included me1·el.Y for the su ke of completeness.)

The " expected " values for the surface area in the last column of the abo....-e h1ble are calculated hom the follmYing equations.

?J = 0 ·I ()6.1"

+

1 · 358 (:r = 1 · 30 7 y - 1 · 7 71),

\rhere .l}=log. (surface area), and .c =loge (hocly 'night).

'rhese equations a1·e obtained by fitting straight lines to the data in the third mHl 5th columns.

\Vhen these equations are transformed to units of actual obser- vation the following para holic equations are obtained :-

rz=;1·889 1c0.m (u·-0·170 a¹·3o;). where fl=.swfoce oren in sq. em.

1c = [,ody wei.l)ht in gm.

The agreement bebnen the obsen ecl and expected ....-alues is obvious.

The numerical coefficients in the aboYe equations are by no means significantly different from those given in the text. Therefore, in ordel' to obtain more reliable estimates of these coefficients all the relevant (lata giYen in both Table I (already referred to) and the above ta hle were taken together. The resulting parabolic equations are:-

269