UNIVERSITY OF PITTSBURGH
Darli„^,oM Memor.al L;lua,v
^;o':^'TA■:■J camp - m~ whitne^"
[from a SKFTCH 9V t moh-^n 1
\M(MN!TY OF
MOUNT WHITNEY. California
With Plan of proposed
MILITARY RESERVATION,
^/rtlSIr ^ 'r,;S
s
^
V _r»
Prep*
RED UNDER
DIRECTION
CHIEF
SIGNAL
Julyl6«3
OFFICER
Soxirces of Informidion.
Xarid Office Flats -
Scale. JmiZe- to -i an inch .
3 1735 Oei'^iV'S
UNrPEl) STATES OF AMKKICA,
WAi; 1)i:i>ai;t.mi;xt.
PROFESSIOXAL PAPERS OF THE SKiXAT, SERVICE.
RESEARCHES (JN SOLAR HEAT
;s .\i;s(jiiPTio\ r,Y the EAirnrs at31osi>iiehk
A REI'oliT OF THE MoL.NT WHITM'IV EXI'KIHTIoN.
ri:i:i'Ai;i;i> rNiici; Tin-; mkixiuln df
BRIG. AND HVT. MA-T. OEN. W. B. HAZEN,
CIIIKF SIiJXAl. OFFICKll IIF THE AHMY.
BY
S. p. EANOEEY,
lURECTOR (IF THE ALLEGHENY 0BSEI:Y ATORT, WITH THE AI'PRIIVAL OF ITS TRUSTEES
PUBLISHED liV ArTIIilRITY (IF THE .SECRETARY "F \VA1!.
WASHINGTON:
GOVERNMENT FEINTING tiFFIf'E.
18 8 4.
12535 No. XT
The luiblieation oftliis Professiouiil Paper is (o be considered merely as a means of bringing-
it before the attention of the seientitie world, and not in an^ way as an indorsement of the views
or theories therein set forth.
P R E P^ ^V C E
All apuldiiV for placiiij; tliis work lu-luiv the M-iciititic- convspoiKU'iits nl rliis dllicc so Idiig
after tlie dati-of the (ibservatidiis Wdiild be due if the j;reat laluir iiivulveil in the tiual ]ireiiaiati"n
of the iiiamisoript for the jpriiiter were not ajppareiit to all.
Professor Langley is not only too well known to ir(|niie intio(ln(ti<iii. luit this work contains
within itself siillieient evidence cil' his worth, of his skill in original in\ csti^^al inns, ami (if his
perseveraiiee in overeomin.i; ol.staeles. It shnidil !»• sai.l tliat the aid ,:;iv(n him, whirh he .so
graeefully acknowledges in the text, was necessarily limited. A large pari of th.' e\|iense of
the outfit was generously lu)rne liy a friend of the Alleghmy Obser\atory.
The snitability (jf the site cho.seii lor these in\ cstigations led Piofes.sdi' Laiigle\ \<> icci.ninicnd
that it be declareil a (bncrnment lesci \ alimi. and the I'lesideiit ha\ iiig l'a\ anably cdnsidcacd this
rcco lendalioii, it is ndw a\ailable for rescarclies in lliis and simil.ir fields of inquiry.
The subject herein treated is oi f great impdilancc and value td the inilc(a(>ldgical work
of the Signal Office, and it is esteemed a iiri\ih>ge td publish it in cdnneetion with tin- rrdfcssidiial
Tapers of this Service.
W. Li. H.
T A B L "K OF C^ O TnT '[' E N T S .
LHtev of
Introduct
Chapter
transmittal
I.— Preliniiiiaiy ,il.-i,Tv ;.l i.ms on s.Ir.l iv .■il.snii,ti.>n, at AUegbony. itnrinK' l«l and Issi
II.— Journey to Monnt Wl.ifnry. I -I
III.— Actinomctry, liistori.al iiitr..ilmli.in
IV.— Pyrheliometr l.M-rvati.M.s
v.— Use of glolie aitinmrieter
VI.— Determination of n-ater-eqnival.-nfs of th.rnionieti-r bulbs
VII.— Table of results of arlinouu't.r obs. rv.itions
VIII.— Act inometer corrections
IX. — Summary of results
X.— The determination of tbc sol.ir constant by tlie study of honmgcneous rays
XI.— The spectro-liolometer
XII. -Bolometer observations on tlie solar-dilVraction spectrum, made dnrins tin- Jlonnt Wliiinc
expedition
XIII.— Spectro-bolometer obMivali.ms tak.n at Allegbeny, in l.^S-2. with Hilgei' Hint-glass prism.. .
XIV.— The transmissibility of our atiuospbcic for lioht '.
XV. — Sky radiation
XVI. — Nocturnal radiation
XVII.— "Hot-box" and solar-radi.it ion tbcruionicliTs
XVIII. — Hygrometric iibser vat ions
XIX. — Barometric hypsometry
XX.— Report of W. C. Day on carbonic- acid in locality visiteil by expedition
XXI. — General summary of results
I.
-Discussi,
in of the ni
II.
— Experim
ental deter
in.
— Experim
eutal det.-i
often
iperature b
A P 1' K X T) I C E
itbod employed il
n the reduction of psychrometer observations
-lengths in the invisible prismatic spectrum
indin-nci' of convection currents upon the loss or
bulb
1. 1 s r o I- I T. T. IT ,S T i; A T I O X s .
Frontispiece. View of mountain camp.
Map. — Map of country aroumi Mount Whitney.
Plate I.— Curves showing the relative euergy for high and hiw sun
II.— Imperfect and irregular actinometer curves
III.— Actinometer curves for August 4, 18^1, Lone Piue ; Actinometer No. 1
IV. — Actiuometer curves for August 4, l-SHl, Lone Fine ; Actinometer No. 2
V. — Actiuometer curves for August 4, 1^81, Lone Piue ; Actinometer No. 3
VI. — Actiuometer curves ,
1. Summit of Mount Whitney.
2. Mountain Camp.
3. Lone Piue.
VII.— Comparator curves
1. Lone Pine.
2. Mount AVbitney.
i. Allegheny.
liKSEAKCUKS OX SOLAU UKAT.
Page.
n-io VIII. — Spectro-bolomuter (side view) - KiO
IX.— Spectro-bolometer (in plan), as used for mapping prismatic Bpcctinm l:JO
X. — Spectro-bolonieter (in plan), as used for mapping iioruial spectrum i;W
XI. — Prismatic spectnuii chart (energy curves) 130
XII. — Normal spectrnni chart (energy curves) 130
XIII.— Plau of tent and arrangement of apparatus V.V2
XIV.— Lone Pine aud Mount Whitney bolometer curves 1311
XV.— Energy curves outside the atmosphere 144
XVI.— Hygrometer curves for Lone Pine and Mouiil Whitiu-y tsi
XVII. — Aqueous vapor in the atmosphere ls3
XVIII. —Diurnal variation of the barometer, Lone Pine and Mountnln Camp 193
XIX.— Curve n=^f{X) for the Hilgerpiism "J-JG
XX.— Curverf=/(A) for the Hilger prism 220
XXI. — Schemes for the distribution of energy 2M
',. 1. — Length of path of rays of heat in the atmosphere 14
2. — Arrangement of the apparatus for the measurement oT the angular deviation of a ray of heat 19
3. — Coefficients of transmission for the respective wave-lengths at Allegheny 26
4.— Mount Whitney Range. Out iiii<- from Lone Pine 37
5. — Small aetinometer, esterior 70
6. — Small actiuometer, interior 71
7. — Determination of mercury in thermometer, Green, Xo. 4571 S2
8. — Arrangement of the apparatus used in the determination of the correction for nadir sun 10.">
" 9. — Solar comparator 110
-Aetinometer readings as a function of the "air mass" 120
-Aetinometer readiugs as a function of the hour angle 121
12. — Bolonteter curve for Mntiut Whitney as extended by means of supplementary obscivations at Alh--
ixhvm- 140
-I)i;mr;iiii ilhistratiii- atnin,s|.h.-rir absorption UC
-S.'.'tiuii (,f hot box. 100
-Diurnal variation of relative humidity isl
-l)iiirnal variation of tension of aqueous v:tpt>r 1^2
-Course of rays through the apparatus in the determination of wave-lengths of obscure heat 223
-Spectrum formed by prism in determination of wave-lengths 225
19. — Curve illustrating the principle of transformation from the prismatic to the normal spectrum 231
-Diagrnm illustrating the principle of transformation from the prismatic to the normal spei-trnm 232
RElNlirr OF THE MOlM WHITNEY EXIl^DriTOiX.
s. p. l.AXC^T.i:^'.
jiii;k( iDi; ov the aij.kc^iikni ni'.sKijxAToia.
L K T T K T? ( ) ^^ T r? A isT H> ]SI I T T A I.
Ai.i.F.r.iiENY Observatory,
AIUyhiH!/, P(i., Pceemhcr 21, ISS;;.
(1k>-|',i;aL: 111 traiisniittiin; the folldwiiio- irimrt on flio cxpeditidii tn Moiiiit Wliitiu'V, it
appoiu's proiier that some ai'.'omil ol' tlic iiic'c|itioii of ils |ilaii slioiild lie incsiMitcil to tlic pulilU'.
luvesti.yations carried on liriv lor soiiie yciiis liad. in l.Ssii, led to (■onclnsions of interest to
astronoiiiy and nietoorolo<;y, wliieli it was found desiralde to verify liy exiieriineiits on a very
elevated iiioiintain.
The considerable expenditure needed for the special instrumental <iutllt of an expedition for
that purpose had been provided by the liberality of a citizen of Pittsburg, and otln'r preparations
commenced at that time. Tlie liearinj;-s of its objects on nieteoroloj;i<'al knowledge becoming;
known to you, the expedition then receiveil material assistance from the Signal Service, and pro-
ceeded under your otticial direction, in July, 18S1, to Mount Whitney, in Southern California. Its
results are so intimately connected with the previous investigations referred to at the AUeglieiiy
Observatory, and with others undertaken there since on its own account in elucidation of tlieiii,
that they are hardly separable.
The donor of the priiieijial means for the expedition, desiring only that its results shall appear
in the form likely to be of widest use, without reference to any private interest, and the trustees
of this (Jliservatory concurring. 1 have the Iionor to now address to you the report of the expedi-
tion, and with it an account of whatever in this (Jliservatory's own researches is needed in eluei-
datioH of it.
Leaving- it to Capt. O. E. Michaelis, of the Ordnance Department, to malic such a report as
he may think necessary upon the faithful performance of their military duties liy the escort and
Signal Service observers, I desire to acknowledge the obligations of the expedition to liim, not only
in his official capacity, but for his valued voluntary services as an observer, wliicli I Iiave else-
where spoken of.
I had every reason to be satisfied with Sergeants Dobbins and Nanry of tlie Signal Service,
and I should add that Corporal Lauouette, of the Eighth Infantry, rendered very intelligent and
acceptable help beyond his iuiinediate line of duty.
I have elsewhere acknowledged the important aid received tlirough Mr. I'lank Thomson, \'ice-
I'rcsident of the Pennsylvania liailroad Company, and also the assistance rendered liy Professor
Pickering, of the Harvard College Observatory.
Permit me to take tliis opportunity of expressing my ]iersonal thanks for the aid wliicli the
object I have had so much at heart, has received from ycni in e\cry way.
I have the honor to be, very respectfully, yours,
s. P. l.\x(;ley,
Din-ctor (i/thf Mligliciii/ Oltwrratimj.
C.eiu^al W. P.. Hazen, U. S. A.,
Chief Siyiinl OjVccr, Woshiiintoii. I>. C.
125;;.l— No. XV 1' 0
1N1^]U:)DU(JT [UN.
11 the (il>siT\;ili(>ii (if llic ;iiii(miit (iT Ileal till.' sun sends tlie .■iirtli is :nii<iiii; llie iiiosf iiiipiir-
t;iHl anil dillieiilt ill aslioi lieal pliysies, it iiia\ also lie ten 1 tlie I' laiiieiitai |iidl>le f
niete(iinl<i,;;v, nearly all mIhisc iilieiKiiiielia Wduld lieccniie piedietalile, if we knew Imtli llie <iii,-inal
i|iiaMtity and kind of this lieat; liou it alleets tlie ediistilneiits iif the atiniis]ilieie mi its passa-e
earthward; huw inueh of it readies the sciil; Ikiw, tlii<ui,i;li the aiil (if the atiiKisphere, it niaintaiiis
the siirfaee temperature (if this planet: and Ikiw, in diminished iinantity and altered kind, it is
linally returned tn (inter s|iaee.
MeteiM'.h.i-ists have till lately (ieiai|iied themselves more with the secondary ell'eets of this
solar radiation than with the eonsiderations Just referred to, though this primary study will at least
enable us to survey suliordiiiate and familiar phenomena from a more general point of view, and
w ill eorreet some errors. The knowledge that the solar heat; finds its way in more easily than out,
;iii(l the inference that our atiiiosplieic acts like the ;;lass of a hot-bed ill raisiiifi the temperature
of the soil — e\eii this knowledge, iniperfei-t ami misleading as it may be when thus stated, has
been most useful ill -i\ in- us a key to siilisidiaiy pliei leiia. It seems doiililful, liowe\ cr, whether
even the me.lliiiig of lliis has ahvays been clearly apprehended, when we find Sir dolili llelscliel (a
distinguished meteorologist as well as an (Miiiiient astr(jnoiiier) sayiux' "* * * the climate of the
11 nil II I must be very extramdiiiaiy ; the altcniatioii biMui;- that of uumiti^'iitoil and buniiiin- siinsUiue
liercer than an eipiatorial i n. ciintiiiniiiu Ibr a whole fortnight, and the keenest severity of trust
far exceeding that of our polar wiutcis, for an e(|nal time. * * * The surface of the full iimoii
exposed to us must ncecs-,arily be xcry much heated, possilily to a degree iniicli exceeding that of
boiling' water."'
It i.s here evidently implied that a planet at the earth's (or moon's) distance from the snii
would merely Slitter great \ieissitndcs of lemperalure, if deprixed of its at sphere, while yet
that the mean temiieratiire of the c\clc ol day and night would not be greatl,\ altered; and
though the lalKjrs of Tyndall and others lia\c given us some idea of the way in which ■ own
atmosphere may act, not merely as a conservator against the \ ieissitudes of radiation in d.iy or
night, but in raising this mean temperature itself, we lia\e had till very recenlly scarcely any pist
eonccption of the processes by which it does so, or of tln^ surprising extent to which we are
indebted to its action.
According to the results of expei iinciits made in llie years ISSII and ISSl al the .\lleglicny
()bscr\at(ir\, all the thermal pliclioiiiciia we ha\c been alluding to, and on which llic existence of
(iiganic lilc dc|iends, depend in turn on a lillle regarded property of our at sphere («/((7//t
(thsorjilioii), without which, thoilgli it retained .ill its pivsenl constitnenls and 1 1 .insinil led all the
heat it does now, the teinpcratiire of the soil, e\cii in the tropics at mid day under a vertical sun,
would fall to some hundreds of degrees below zero.
()bsci\ali(iiis made later coiiliniicd the oiiinion that, so far from the tciii|ieral lire of I he sinl
being chielly due to the direct solar ra,\ s, I liese ia\s alone arc far too feeble to melt the iiKaviiiy
in onr tlici iieter Inillis,* and that this direct solar radiation is aclually iiisignilicant, c pared
wilh the temiieratiire which the at mosplierc tliKHigh this selective absorption educes IVom it.
According- to the present view of jihysicisls, the solar energy is conveyed to us in vibrations
varying' from ii wiivedeiigtb of less than .(Mid. ; mm. to one indelinitely greater (the longest measured in
Uiu- ^t;kUiiiLut liua bfcu iiiailt by Mr. Erj
11
12 KESEAROIIES ON SOLAR HEAT.
the present invcsti.nntiou being about .003 inin.), some of which viliratioiis (those only who.se wave-
lengths are fnini 0.0004 nun. to .0007 mm., or violet to red) atleot the eye with the sen.sation of
light; all of wliicli, so far as is known, produce chemical action ; all of which, without exception,
convey heat.
"Light," "clieniical action," "heat," then, arc not qualities inherent in tlu^ ray, but names
given to the ditferent manifestations of one and the same radiant energy, wlii<'li is intcr|irctcd to
us in terms depending upon the wavelengths of the raj', stkI on the niciliiim through which it
passes or on which it falLs.
Let us, to gain clearer conceptions, supjiose one of these rays isolated* from the rest, and, as
au example, let it be one who.se wave-length is about 0.000-1 mm., which, when it falls on (Iji^
retina, gives the .sensation of "violet light," which, falling on certain salts of silver, darkens them
("chemical" action), and which falling on a sufficiently sensitive thermometer covered with lamp-
black would be absorbed by the latter and cause "beat."
Considering now the particular ray instanced, in reference to its heating power alone, we
observe, in view of what has just been said, that everything we know about it we know through
some particular medium on which it acts, and that what we learn about it is generally true only
of this ray and not of another. Our thermometer, for instance, according as its bulb is covered
with white lead or lampblack, gives a wholly diftereut account of the amount of heat in it; and
if we could measure the heat in this ray above the earth's absorbing atmosphere, and again at
the earth's surl'ace, we should find a notable difference, showing that only the smaller part of it
is transmitted. (In this particular case we find that if the sun's heat were all of this quality the
soil would receive only about 40 per cent, of it.)
If, now, we consider some other ray, for instance one at the other extremity of the sjiectrum,
who.se wave-length is over .0020 mm. ("dark heat"), we lind its visual, chemical, and heating
eftects altogether ditferent. Though quite as energetic as the first, it is invisible (i. c, to us, though
it may affect some other than the human retina); it has no chemical action on the previous suli
stances (though it has on certain others); and, as regards its heat, it will very po,s.sibly be insen-
sible to the surface which absorbed the first, while the same instrument, if its bulb be coated with
some other substance, may reveal its presence. Finally, we observe, by methods to be descrilicd,
that more than nine tentlis of the heat in this last case is transmitted by (Uir atnios]iheiv: so that
if the sun's heat were all of this quality, the soil would recci\e (normally) o\er W per cent, of it.
Like facts could be learned of an unlimited number of heat rays. Each dilfers from the others,
not only in amount but in kin<l. We know the heat of the ray only through its action on media;
and everything wo know of those media through which the rays collectively pass {c. (j., the atmos-
phere), or on which they collectively fall [e. //., tlie surface of the soil or the thermomeler bulb),
.shows that these distinguish between different kinds of heat with au actually infinite minuteness
of discrimination, letting one kind pass and holding back another, as though by an intelligent
choice. It is to this action that the name of '■'■ seleetive uhsorptlon^'' has been given.
The foregoing general considerations lead at once to others of practical import ; for instance,
to the conclusion that the thermometer must be a very imp<'rfect measurer of radiant iieat ; and
we are led also to ask how far all our present conclusions as to such heat (derived as they chieliy
are through the thermometer) may require revisal. Probalily most of tliosr who use it, while
aware that there are varieties of heat which it canuot discriminate, suppose that it still gives the
total amount correctly. It will appear, however, more fully later that it not only gives an niade-
quate amount for the heat which actually falls on it, but that in estiumting the amount of heat
emitted, as in the case of the sun, its use leads to gross errors, in a matter of fundamental imjior-
tance.
From what has preceded, we are by no means to coui'lnde that the tlu'rmometer can be dis-
peTised w ith, but that its indications need here to be iuteriireted through observations nmde by
*A.s tbcj wavo-lcngtli clian;;e3 coutiiuioiisly, not .-ilirnptly, wo cannot by .any pliysical nK-a\i.s actually isolate iin
absolutely lioiiiogcneous ray, sucli as our iliffurontial formulae consUlor; anil what is \w\'- said is to lio unilerstood as
true, with a more and more close approximation, as the width of onr actual hoat-piinil is lu.idi' less. As all our
actual observation must be on licat-i>oncils of sensible width, this restriction is imporlaut :nid should not be forgotten.
INTUODICTIOX. 13
some iustnimeiit which can (liscriiuiiiatr lutwccn the ilillciviit kimls <il' licat. Ami tliis is, almvc
iiU, necessary when we arc tryiii.u to estimate the a nut (.fsohir licat liclore alis.uiiliim (llic .^iiliir
constnnt).
Couhl we ;isceiiil above the atm()si)licie, tliis heat lui.uht lie diivctly measuied. i;\ idiiitly,
since this is impossilile. ami since we can tjnly nhserve the ]Mirtion wliicli filters ihiwn to lis alter
absorption, we niirst aiM to tins oliscr\e(l remnanr a unaiitity ei|iial to that wliicli tJLc atmosphere
lias taken ont, in onler to reproduce llic original ammiiit.
To liiid what it has taUcii out, we must study tlic action in detail, ami, iVom the knowlcil-c,
thus sained, frame a rule or lormiila which shall enable us to infer the loss, since we cauiiot directly
(letemiiiie it.
It is because the exact determimitioii ot'tlic solar constant thus jiiv sh/z/hmcv ii iiiiiuilr Lumrlcliic
of the iniij in irhicli the sini's hint is ii(lni<il hi/ tin- nirth's (it)iu,spl(,r,' ; and because every cIiaiiMC in
our atmosphere comes from this same heat, tliat the solution of the iiroblem interests meteorology
as well as astronomical physics.
We have just seen that notliin,^- less than a .■omplctc knowledge of the laws under which the
atmosphere is governed by .solar heat, would enable iis to frame the exact rule for liiidiii- flic lat-
ter, but tliongh such knowledge iiall\ exceeds human [lowers, most observers lia\c' coiifciitcd
tliemsehes with a simple anil primiti\e liypotln-sis, in using which they ically ignoic the infinite
complexity of the problem here iiresnitcd us. and assiiining that it is as simple as wc could wish
it to be, proceed to compute the solution by such a formula as it would be most I'ouvcnicnt to us
if nature would follow. Thus, owing to the temptation to accept as still siiflicicnt any time honored
scientitic dogma, which has res|icctablc siionsois, the simple formula establislicd over a century
ago by Couguer and consecrated by the use of a llerscliel and a roitillet, to whom it cmliodird all
the knowledge of their time, is commonly used to-day liy oliservcrs. who lia\c only to look aliout
them to see that it has long ceased to express the facts known to our own.
To justify this langnage, let us consider what the problem appears to be at a first glance, and
what the first suggestion is for solving it. [f a beam of sunlight enters through a crevice in a
(lark room, the light is partly intciiuptcd liy the dust particles in the air, the aiiartment is \ isibly
illuminated by the light relh'ctcd IVom them, and tlie direct beam having lost somcfliing liy this
proce.s,s, is not so bright after if lias crossed the room as before it entered it. If a i|Uaiter of the
light was thus scattered, the beam after it crossed tlic room would be but fhrce fourths as luight
as when it entered it. and if we were to tr.ice tlic now diminished beam through a second apart-
ment altogetlier like the other, it seems at first reasonable to suppose that the same iiroportion, or
three fourths of the vemainder, would be traiismitteil, and so on, and that the light would be the
same kind of light as before, and cuily diiiiinished in amount. The assnmption originally made by
Bougui'r* and followed liy llerscliel and ronillct was that it was in this manner tliaf the solar heat
was interrupted liy our atmosphere, and tliat by using such a simple progression the original heat
couhl be calculated. +
Now, it is no doubt true that a \ery scnsilile portion of light ami heat are scattered by an
analogous process in our atmosphere ; but w c ha\c in our present knowledge to consider f liat licat
is not a simple emanation, but a compound of an infinite number of radiations, and that these are
affected in an infinite diversify i>f wa\s by the different atmospln-ric agiMits, flic giosscr dust par-
ticles affecting them nearly all alike, or with a general absorption: flie minuter ones beginning to
act selectively, or, on the whole, more at one end of the spectrum than anolhcr; smaller particles,
• Hmlgiicr, Triiit(' di- la liiiui.io. I'aiis, ITCH.
H.rt iisaiviil..' in iiuagiiKiti.iii afiy li(,ii,n;;,-i„ .mis al.sorl.iii- uirduiiii i„t<. siuT.-ssiv slral;i "I mI
llii.kii. sN Mii.l .■lu-iiiiL-al c(iHHtit.ili..ii.
L.-t .\ 1..- a sn.ircc of rudiaiit lirat «li"s.- imO-timIj i- ivdil.rd l.y pass.,-,. tli,„u-li tli.> lil-.l slial
jiDSi;) } ((II- 11.7.')) of the first. Thi-ll, .sillL-c tlic s.ri.iid >tratiini i^ i.l.liti.al in ini-^l itiili.,11 and aiim
.audimi.st (it iuassimii'd) bavo an identical cllicl. it « il I al.-n I. , .if «l,at .iil. i-. 11. and A : , ■ , )
will emcrgi- from the .second, i of this =,;■ A m A n.:.'. 1 , «ill riii. i-.- I' i tin tfiiid. and so on. tin-
mitted Iiy tlie unit of thickness (tlie •■,-,.,.(;;. ,Viil .1/ /,.ni«mi,.v...: "1 h. in.4 evidently tie- e Iiion rati.
prosres.sioii, so that if the original h.at I..- A ami llie . ...•miiint of traiisinissioii ;i, tin- .inioiinl of 1
through f strata wifl lie Aj(«.
Toaiiply this iirineiide to til.' estimate, if I fi.- h.at oiitsid.- 11,.' atiMos|diere ( i. < ., h.f.ir.- al.soriitio
14 RESEAECHES ON SOLAK DEAT.
whetlier of dust or mist, anil siiialler still, forniing a probably continuous sequence of more and
more selective action <lo\vu almost to the actual molecule, whose action is felt in the purely select-
ive absorption of some single ray.
The effect of the action of the grosser ])article5 then is to produce a general and comparatively
indifferent absorption of all rays, so that the spectrum after such an absorption would simply seem
less bright or less hot. The effect of the smaller ones is, as has just been said, to act more at one
end of the spectrum than another, with a progressive absorption, so that the quality of the radia-
tion is sensibly affected as well as its quantity. The effect of the molecular absorption is to lill
the spectrum with evidences of the selective action in the form of the dark telluric lines, taking
out some kinds of light and heat and not others, so that after absorption what remains is not only
less in amount but quite altered in kind. Between these three examples of absorption, we repeat,
an niilimited number of others must exist; but we shall need here for simplicity to treat the whole
as coming under one or the other of these three ty]ies, a procedure already more accurate than
the primitive one followed by Ilersohel and Pouillet, but which we recognize to be still but a coii-
veiition, which is imposed on us provisionally by the actual complexity of nature.
It will lie seen now more clearly that the whole process, still in almost universal use, is
foiuided on a pure assuiiiiition, for no one has actually been without our atmosphere to see what
tlie alisoiption is, and it is simply taken for granted that the same proportion of heat will be
alisorlied liy line like stratum as by another. On actually trying the experiment, however, with
media in the laboratory, Melloni long since observed that like proportions were not absorlied by
like strata; and the reason was found in the fact that radiant heat is not a simple emanation, liut
the sum of an inlinity of diverse ones, each with its own separate rate of absorption. It follows
tliat thr cocriieieiit (if transmission is truly constant only in the case of the absolutely homogeue-
ous ray, wliicli the thermometer cannot in the least discriminate, and hence, that the original heat
of the sun, and the amount absorbed, cannot be ascertained correctly by this instrument and this
rule. I'hysicists have been slow, however, as we say, in making this application of Mellcini's
liriiici]ile to the ]iresent case, but have continued to deduce the solar constant from thermometric
(iliscivatidHs, in which tlie heat is either treated as absolutely homogeneous, or in which its non-
hi igcneity is scaiccly recognized as a factor of importance.* This neglect to make what seems
so iH'rtinenr an a|iiilic;iliiin of Melloni's observation, even after it had been explained and extended
(liy r.i(il), will siMin riHue explicable, when it is remembered that no direct means of measuring
portiuii nl' llir »';ii Ill's siirr;icc ;nnl Elv tlio iippur surfuec uf ttio iitmuHiiluai', whicli is boru alipjiosed, for aiuiiilicity, t
1)0 of Ullir.iri.i a.iisity a.1.1 lonsfitu. j^- j^
turn. (Tl iVr.-ls ,.f Ihr :iclii;illy _j.^ p g jc
L-.m. it IS jssiiiii.-,), li,- .■.il.'i.hilc.l i ~~-, ,,''' \ ,.-'■'' \_. ,---''' \
aiulall..«..l f.ir. ) L, t A I..- 1 li.- .ili- | ^\^ ,--'' ,,>'' ,,---'''■ '•
server's slnli tli.u ES ».,uia !"■ I %;'' ..-■'' ,.!i- — "' ', 1
thediivclM.ii "I a i;i.v Hire Ihr sun i .,-'' >--''.'.---'''' \ ; i
iu tllc /niitli wli.r, Ih.- al.s(.i|iti..ii ; ,-''',--','.'--V-" ' ', 1 '•
is le.ist, /'N. f/N. AN. 111.' i.i,oii,s ; ,_-/;i-'-'-''' ' ; 1 I
of tliC paths uf till- lavs as llic siiii ~s^
siuks lower (li'Ugl lis easily e.iiii|.iit Path of Raya iu thu Atmosphoro.
.ible); iiiid, to lis our i.l. as, l,t I'.s
= -i ES, r,S = :\ /i'.s, KK- 1 l:s, ,l,-. TI,,- oiiyinal lieat A would, if llie siui were, in tin' zenith, beeoliie Aj) after
passiiii; Ilii.Hi.^l e sliatmii I /■> i : ami, aeeording to wliiit lias lieen iLssiiined, it would l.eeoiiie (if tlic suu's zenith
ilislaiiic w.iv /•>/') Aji- after a lis.. i|, I ion l.y the two strata Ijelween /''and .S, Aj/' after absorption by the three strata
b.lue.n (, and .s\ ele. A. the original heat, and/), the cooliicient of traiisinissi are, nnkiiown; but if we niakB an ob-
s.i vali ' Ihr he.il arlii.illy i.a.h.iif; H along fA'Clet us call this heat h) and again bit.'r iu the day along /f.s' (ealling
tit is sec (Mid obsri ved iiiiaiit it \ (), We liavc lu tlio particular case supposed
Aj)"= h
whrn.-r ,\ aiid;> bnlli been liiHiwii, and it is evidently easy to extend the solution lothe genieral ease (d' any nnniber
of strata. ,s. A;i' -- /, then, in the exi.onelitiai formula of I'ouillet, and of later investigators, whose fniidaineiil.al
{and en aisi assiiiii|.l i.,ii is, tli.it the eoeftieieut of trausiuis.siou (;i) is a emistanl. If it be uut a eonstaul (and I
shall prove that it is ik.I), llie whole siiperstrueture falls to the ground.
" Exeejitions to this renuuk, however, arc to be made iu favor of the worU of Tnueipal Forbes aud M. Crova.
INTRODUCTION. 15
tlie absoriition in oven apiiroximatoly hninoseneous rays till very recently existed, ;niil lliiit
departure IVoin the old t'orniula wliich ignores the dilliculties, involves their reco.^iiitinn. ;iinl llic
devisal of new processes to meet them.
The writer has demonstrated that in neulecting to observe approximately homducncdiis lays
we not only commit an error, but an error wliieh always has the same sign, and that thr alismp
tion thus found is always too small. He accordinsly devoted mnch time to tin- ((iristructiou nf an
instrument (the bolometer, which will bo described in its place) for the special study of sucli heat
rays, and, with this, observations were carried on in the years ISSO and IS.sl at AllejAlieny, with llic
ccmclnsions which have just been stated. With this instrument the heat in some apitroximatdy
homoj;encous ray (that is in some separate pencil of rays of nearly the same wavelenstli) is
measured in the pure and normal spectrum at successive hours of the day, and the calculation of
the absorption on ISouguer's principle (justly applicable to strictly homogeneous wa\cs) gives tljc
heat outside the atmosphere in this approximately homogeneous portion with a ilesree of a]iin-<ixi-
mation, depending on the actual minuteness of the part examined. The process is tlien reiieateil
on ain>ther limited .set of r.ays, and another, until the .separate percentage and the seiiarntc original
heat is found for each heat pencil directly or by interpolation, and then finally tin- wlioU' lical, by
the summing of its parts, the result being tljat the solar constant is much greater than it was
belii'ved to be. and the absorption of the atmosphere much greater.
With whatever pains we measure, however, we remain at the mercy of the lliictuatious of <iur
lower air, and are compelled to make assumptions which we would gla<lly avoid. Thus, we ari'
comiielled to assume that the absorjitive powers of the air are the same throughout the <lay,
though this is at least doubtful, even in the case of the most absolutely pure sky. We are obIigc<l
to assume that like masses of air produce like absoqjtions, which is doubtful, even when the ray
ab.sorbed is sensibly homogeneous, and we must assume that tlie air above us is dis[ioscd in
concentric strata, while onr observations tell us little of its true disposition. On these ami nniny
other points, we know just enough to distrust our own enforced assumi)tions, without being able to
positively verify or di.sprove them. Besides such difficulties as these arising from our ignorance, we
are met with almost insuperable physical ones coming from the incessant clouds, mist, and <'hanges
of onr lower atmo-sphere, which the ob.server knows only too well, and which make it literally true
that not one day of unexceptionable conditions is to be found in an average year, while \el daily
observations must be commenced with e\cry clear ruing, since wc never know which is the day
which may prove fair to its close.
These remarks must be borne in mind in reading the account of the preliniiiiary oliserv ations
at Allegheny, on the absorption of the heat in the spectrum, given in tljc following chapter —
ob.servations which it is necessary to supply here, as they were the immediate cause <if the
expedition and are intimately connected with its work.
The meteorological reader is asked to bear in mind throughout, that (in the ojiinion at least
of the present writer) the master-key to .some of the most important ])roblems of his science is to
be fonml in the hitherto unrecognized study of the xclectirc absorption of our atiuosiihere for heat.
KKSKAKCllKS ON SOLAK IIKAT AM) ITS AIISOKITION
liY THE KAUTirS AT^loSlTlEUK
oil A I'TK i; I.
I'KEI.IMINAUV OUSlOKVATKlNS t»N «1:LI;( Tl \ K AllSOKl'TION AT ALLi;( I II ION Y
DL'KINd IMSd AND l.ssi.
Till' heat ill rile .sin-c-truin t'oiiiictl by a piisiii is nut uiily diiiiiiii.sla'il in an uncertain ili-.nicc liy
alisiiiiiticiii in its sulistaiici.', liut is (iisiicrscd in a iiianiiiT ililleriiig witli oxery ]iiisiii ami cxai-tlx
I'Xincssililo l>y no known I'orii.ula. The siicctniin tbiiiieil liy ;i retiectin^' ^ratiiitr. mi tlir (■diitrary,
is nearly free from absoriition, ami may lie strictly noriiuil, so that ineasiireiiienfs with the uratiiif?
possess tlie inestimable advantage of enabling; us to lix the wave-length of every ray measured;
but, while tlie average heat in tlie ;;ratinj; sijeetrnm is. at liest, less tlian one teiitli that in the
piismatic, the latter is itself, when taken in portions so naiiow as to be appidximately hoiiioj;ene-
ous, almost insensible.
As the best thermo-pile was foiiml incapable of nieasiirin;; lieat in such narrow iiortion.s of tlie
fi'ratiug spectrum, I was led to tlie in\cntion of an instrument for this purjiose, the bolometer
(/inXf/, fierpni'), whose eoustructioii will lie found descrilu'd in the Proceedings of the .\mcrican
Academy of Art.s and Sciences, \'oI. X\'l (ISSl). With this apparatus the e\|iciimcnts on the
diffraction spectrum were resumed; the first eutircl.v nniiiiestionable evidence of ineasni able heat,
in a width .so small as to be properly described as linear, having been obtained on t )ctober 7, issu.
Nearly the whole year 18S0 passed in modifications of the instrnment, or in the makiiii; of these
measures which gave promise from the first of bringing results of value.
When \ve have first with this measured tlie heat directly iu the normal s]iectrnm formed by a
grating, wc can return with advantagi' to the iirism. whose indications now become intelligible.
In these first measures, which were carried to a wave-length of .001 mm.,* I employed two of
the admiralile gratings of Mr. llutherfnid. one containing 17,1".IG lines to the inch, or iisi to
the millimeter, and the other one-half that number, both ruled upon siieculum metal, and I used
a slit at a ilistani-e of 5 m. without any collimator, keeping the grating normal to the o|Jtical axis.
It will be seen, then, that the rays passed through no absorbing iiiediiim whatsoever, excejit the
sun's atmosphere and our own.
The rays from the grating fell u| a e 'ave speculum (\xhose principal local distance was
about one meter), and fiom this were conccnlialed upon the mouth of the bolomcti-r, forming a.
uarnriv spcetrnm, which passed ilown the case of the ilistrumiMit and fell upon the bolometer
thread. As this thread moves aloiii; the spectrum iiarallel to the Frauenhofer lines, its coincidence
with one of them is notified by a loHcriiig of its temperature and a deflection of the galvanometer.
The instniment Is. of course. e(|iially scnsiti\c to the iinisible radiation as to the visible. It is
imiiiutaiit to observe that no screen is interposed between the bolometer and the ;;ratin.i;, for the
temperature of tin- screen itself, as it is reijlaced lu- withdrawn, will certainly affect such measure-
■ Tluini.;!. tlii-su nu■asm■.■^ tin- luut nl « :iv,--l.-]jt;i ii will 1„- ihr uniTnii (//) = , ;.,., inm., oi- ln.iiiiii tiim-s tin- unit
ulWiiL^Btr .111. Tim.-, tli,' wav..'-k-ii;;tli uf Fnuu-nh.. fur's ■■,\" is L.tu %vrittfii ii(».76.
iiijoj — No. XV a 17
18 ItESEARCHKS ON SOLAR IlKAT.
meuts as tlR'Sc. Tlirouyli tlie whole course of tlie oxiicrinieiit tlie bolometer is uiiiutciTiiiiteilly
exposed to radintioiis from the grating, whether rellected by it, or enianating; from its own sub-
stance. The iiiterruiiliou of the solar radiation is affected at the other cud of tlic train, 5 meters
beyond the uratiug itself. In the gratings employed, one of the second spectra is very feeble, or
almost lacking. The rays of the second spectrum are necessarily superposed on tho.se of double
tlie wave-length in the first; and as all evidence of solar radiation in the most .sensitive apparatus
at the sea level dies out near A = O-'.S in the ultra violet, it follows that we can measure down in the
first spectrum as far as A = Of'-C, or in fact further, without any fear wliatever of our results being
atlected by tlie underlying second spectrum, even if that were a strong one. AVe have, therefore,
knowing the amount of heat in the second spectrum at Om.,">, and Unowiug that our ultinuite point
of measurement at 1''.0 in the first spectrum overlies 0^.5 in the second, the means of asserting
with confidence that no considerable error cau bo introduced from this cause, after an allowance
Las been made here for the minute efiect of this actually weak second spectrum. Au allowance is
also made to reduce the effect to that which would have been observed with a grating so coarsely
ruled as to cause no considerable deviation from the slit of any portion of the spectrum measured.
The bolometer (iu a constant position relative to the concave mirror, such that the optical axis of
the latter bisected the angle between its central thread and the center of the grating), was moved,
together witli the mirror, by a tangent screw in arc, so that the siiectrum appeared to traverse its
fa.ce.
The actual angular deviation of any ray under examination was obtained from a divided circle,
on which the arm carrying both mirror and bolometer moved. A particular description is not
given, as the whole apparatus was replaced by a more i)erl'cct one later. That actually used will
be intelligible by the sketch (Fig 2), where S is the slit, (i the grating, M the concave mirror, l;
the bolometer, and C the divided circle.
The light came from the silvered mirror of a heliostat, passing through the slit, at a distance
of about 5 m. from the grating, which was bolted immovably above the center of the circle of a
massive dividing engine, with the grating's plane always perpendicular to the line joining its
center and the slit. The mirror and the bolometer, with tlieir attachments, were fastened to tliis
movable circle.
An allowance has been made for the absorption of speculum metal and silver, but the
absorption of the iron strips of the bolometer has only been indirectly allowed for. This has been
done by comparison with the action of a bolometer, with lampblacked surface. The wa\e lengths
are derived from the measured angles by the use of the formula
nsi = sin i + sin c.
where n is the order of the spectrum, s the space betwi'cn the lines of the grating, ;. = the wave-
length of the ray, i the angle of incidence (iu the present instance 0^), and r the angle of diffraction.
In the early observations it appeared from the examination of the diffraction siiectrum up to
-I = li^.O, that the energy iu the invisible part as far as this was much less than in the visilile.
Nothing definite is, even at this time, known to physicists as to the e.xteut of the normal solar
spectrum ; but the prismatic spectrum is still very commonly supposed to be limited by theoretical
considerations to an extent little greater than this; and one of those most conversant witli the
subject has treated this wave-length (i. e., 1.".0) as marking the limit of everything known to exist.t
t Draper, "Ou the Pliosphorograiili of a Solar Spectrum, and ou the Liue.i in the Infra-red Eegiou," Proceedings
of the American Academy, Vol. XVI, p. 233, December, ISwO. He asks: "Do we not encounter the objection that this
wave-length, 10,750"'-'" (the limit of Captain Abney's map), is altogether beyond the theoretical limit of the pris-
matic spectrnm!" Previous nieasnrcnients of heat had, it will bo remembered, been made by comparing its total
amounts, in the visible and invisildo prismatic spectrum, which gives lis no knowledge as to wave-lengths in any
case, and wave-lengths iu the dark-heat region had been estimated, by hazardous extrapolations, from contradictory
formuhe— formuhe which profess a theoretical basis, but contradict each other. Thus Miiller finds, by Redlcntiaclicr's
formula, a wavelength of nearly 5f.O for the extreme solar heat rays ; Draper (as we have just seen), a wa\e-lciigth
of but l/'.O for the same rays, &c. All these formuhe (Briot's, Canehy's, &c.) agree well with the observations in
the visible spectrnm, which they have in fact been originally deduced from. They contradict each other thus grossly
when used for extrapolating the pl.ace of the extreme infra-red rays, whose real place we give hater from actual
measures.
PRKI.nUNAItY (H5SEUVATIOXS.
19
It seemed at first, tlieii, imi)iolirtble tluit tlic licat below tlie red slioulil materially exceed, or
even eciual, tliat'above it; for tlii.s would demand (since the heat shown by the last ordinate at
/ =1'*.0 is very small) an extension of the curve of heat, as obtained from the grating, to a dis-
tance enormously beyon<l the furthest limit then assigned to the normal s|ieetrnm by experiment.
The writer's fiirtlier investigations, however, led him to believe that this immense and unverilied
extension really existed, and to thus eonlirm liy imh-iiendent means the statements (if Tyndall and
others as to the great heat in this region, lie was unable to determine its exact limit with t]u>
/■•«/.-'.
grating as then used, on account of the overlapiiing .spectra, but was some two years since led,
from I'xpcriments not here detailed, to suspect the existence of solar heat at a distance of lu'arly
four times the wave length of the lowest visible line A (A = 0^7G), or at i. = 3''.0.»
' See Comptes Hemhis de riiislilul dc France, .Inly 1.S, 1881.
20 RESEAROnES ON SOLAH HEAT.
We. rcroivc all tlie solnr radiations tlii-ouKh an alisdiliiny atniosplicic, ami it was tlio special
objoet of tliese investigations to dotennine, not only tlie amount ot' lii-at in each ray, l)at the sejia-
rate absorbent a<'ti()ii of the atmosphere on each.
The great ditliculty in this investigation, after tlic iiroxision of a snitieienlly delicate heat-
measurer, lies in the varying amount of radiant energy which (iiir atmosphere transmits, even for
equal air-inasses. The solar radiation is itself si^nsibly couslant, Imt the variations in the radiant
heat actually transmitted aic notable, even from one minute to another under an apparently clear
sky. The bolometer, in fact, eonstantly sees (if I may use tlie expression) clouds which the eye
does not. That these incessant variations are in fact due to extraneous causes and not to the instru-
ment itself has been abundantly demon.strated by measurements on a constant source of heat.
Those taken, for instance, on a petroleum lamp, so placed as to give nearly the same galvanometer
deflection as the sun did, were found to indicate a probable error, for a single observation, of less
than one per cent. The variations from minute to minute (under a visually clear .sky) amount,
frequenth', to t<'n \\\ws the probable instrumental error, ami they can only be partly eliminated
by rejieating the ob.servations a great number of times on many different days. It is probable,
too. that there is a systematic change in the absorbent power even of a given air-mass as the sun
approaches the horizon, lint this point may be considered later. Actually, twenty-nine such days'
oUservations have licen made (as appears below) in the preliminary series, but it would be an error
to suppose that this nundier was obtained without the sacrifice of a still larger uumber on which
the ai)paiatn8 was prepared, and the day spent without results, owing to the still more considera-
ble atmospheric changes between morning and afternoon. Even of the twenty-nine days cited, and
which may be considered exceptionally fair, it will be seen that in only ten cases did the sky con-
tinue sulli<aently constant in the morning and afternoon to allow complete series to be taken.
It will be understood that we aim to make at least two sets of measures throughout the spec-
trum daily, mie when the rays have been little absorlied (at noim), the other when they have been
greatly aliscubed (in the morning or afternoon). It will be understood, from what has preceded
that the exponential formula of Pouillet, founded on the assumption that like masses ab.sorb like
proportions (though misleading as applieil to the complex radiations noted by the thermometer,
and rigorously applicable only to strictly homogeneous rays), is yet more nearly applicable to those
which form the subject of these experiments, for though these cannot be absolutely homogeneous,
we may consid<'r them as nearly so, asthey are phy.sically measurable by the most delicate means
known. The mass of air, through which the rays pass, is taken ]n-oporlional to secant 1', for zenith
distances less than »;.". , ami for tho.sc greater to
0.0174 X tabular refraction
co.sine apparent altitude
The unit mass of air is that lor which secant : = 1. or that vertii'ally above an observer at the
sea-level, and who.se weight is reiiresented by the mean barcunetric pressure of 7<i0 mm., or 7.1! dm.
The coellicient of transmis.sion of heat for this unit atmosi>h<rc is here called n, so that heat,
which was 1-J before absorption, becomes Ea after absorjilion by om" such unit stratum, and Ea"
after absorption by » strata.
It is ccuivenient d emjiloy in the jircparatoiy comimtations, as the unit of mass of nu^rcury
in the barometer, one decimeter. If we choose to employ as our unit for the barometer, the whole
height of the column at .sea levi^l, we must then divide tlie value of tlic liaromctric prestsure here
given by 7.0. The mass of air through which the lays )>;,ss then being proportion.al to the
actual baidiiielrii' |iTvssure may be exjiressed in units, each ol' which is reiiresented by the press-
ure of one dcciiiicler of mercury at tlie sea-level. Since we mux take any unit we jilease, we may,
if \re wish to do so lor any spi'cial purpose, treat this as the unit of air-mass, and call its coefficient
ot transmission by some sjiecial name. Thus if/ were the coellicient of transmission for an air
mass, represented iiy one decimeter of mercury, f'= a. and cither (for a homogeneous ray) gives
the transmission for an cnlire atmosphere. The coellici.^nt of transmission for one atmosphere (o)
is then the iiio|iortion ol I lie radiation transmitted by a siiii in the zciiilh to an observer at the
sea level i w here the liaiomelric incssnrc is 7.0 dm.), and Ihis is here shown to be (under constant
r'i!i'.LniiXAi;v or.si;i!\"ATi<>xs. 21
■atmosplieiic comlitioiis) constiUit for any .uivni r;iv, hut to vary greatly tVoia imc U> aiiotlicr.
Thus by refVrcnce to TaUle <>, we iiiid of tliree scilar lays, wliose wa\-e lengths arc- O'- ..;::.. (i- .(iiio.
l^.tHK) that of t lie ray whose waveleii.u'th is (I c .:;:."', (in the ultra violet), (il jier eeut. <il' the ciri,:;iiial
energy would l>e alisorUed and '■•'.> transmitted; ol' wavr length Oc.tJOd (in tlu' orange) M) per cent,
wonhi be absoibed and fit transmitted; of wavelength l^.tllMI (in the infra reil) LMI [ler cent, is
absorbed and Ml transmitted, ive.
The following list sliows the dates at wliieh bolometer observations were made at Alleglieny
uj) to Jnne, ISSl, for the measurement of heal in Ihe siieetriim and the detei ininalion of atiiios-
idieric transmission, by the < jiarison of noon and afteri n measures. Those da,\son which
noon measurements were taken, which were rendered useless for this jiiiriiose b\ ,sulisc(|iieiit
changes in the condition of the sky or by other causes, are indicated by an asterisk. It will be
seen tliat of twenty nine days of observati nly ten could be fully ulilized, and that all of the
year ISSO maybe e(nKsidered to have jiasscd in the experiment .ind prai'lice which made the
observations of bS.Sl elfeetive.
Date.s: ISSd, November iL',* December 11.* Dccemlu'r IS:* bS.sl, January iL',* .lannaiy is,*
January 28, February 2, February .'i.* Fcbniaiy .">,' fdnuary 17, February 1!!,* Felniiaiy l'l;.*
February 2G,* IMareli 2,* March Id,* March 11.* March L'.".," March 2.S,* April 7,* Aiuil lO,' .\piil
22, April 2.;, Ajiril 2S,* April 2!). Ajuil .'.O. .May 1.' :\lay 2(;.* .May 27." .May 2S,
We will select as an e.\am]ilc of an actual da\\ oliscrvalions those ol .\|)iil 2!l, ISSl. The
record is maile in a book prepared for the |)nipose. Ironi which a co]iy of tl iigiiial eiili\ is jicre
given.
1. Station: Alleglieny.
2. Date: April 29, ISSl.
.3. Wet bulb, U^.n C. }
4. Dry bulb, 12^.(i7 C. I
r,. Black bulb, 24o.aC. ■ at !l h. 1.". m., a. m.
0. ]?aronieter, 7.'',") mm. I
7. Temperature aiijiaratiis, 1(1 .(!('. 'i
5. State of sky, milli/ hliic, ti-Uh finpinil rloinls.
0. Aperture of slit, (•.004 in.
10. Slit to grating, 4.8") ni.
11. (Iratiug to mirror, 1.004 ni.
12. ]\Iirror to bolometer, I.IT) m.
l;i. (iratiug u.sed, No. 2, large.
14. Weak .secoinl speetruiu thrown ircsl.
15. Galvanometer used, " Filliott No. '■''•."
10. Bolometer n.sed. " No. 1, old" (iron).
17. Rheostat used, '• Jlenairy " and resistance lio\.
IS. Setting on I), (.south vernier). 12.". .'ir.
m. Delleetiou battery galvanometer, div. iT.d.
20. Coii.stant of battery galvanometer, d.ddll.-.l.
21. Current <if battery, 0.230 Ampere.
22. Eeader ami recorder at siiectrodioloineter, F. W. V.
23. IJeader at galvanometer, W. A. K.
24. E,stiinated weight, all of equal raliie.
2.J. Kemarics. — Tlif fiiilrdnomclrr ijrift trrts moihriilt iinil toltriihli/ iiiii/orni. Jlx (imoiint nt
the time tif eodi dilhrliiui has hern (himiiini il, ami Ihe iicrcv.svir.i/ eaerecllmi f„y il is iinliiiled in eiirli
reei'rihd remlliiii.
The comlitions of oliscrvation which liav<' clian;;cd during the day are the following. (When
the original readings wer<' on the Fahrenheit scale, llicy ha\c been reduced lo ( 'cut ii;rade.)
22
IlESEAROHES ON SOLAR HEAT.
Table 1.
Time.
<)>■ IS™ a. m.
11* 30- a. 111.
1' 35"' p. ni.
5' 45" p. m.
11°. 11 C.
120.67 C.
1°. 5C C.
8"'". 02
81. S
240. 44 C.
no. 78 0.
1C".0 C.
12°. 22 C.
14».S9 C.
2°. 07 C.
8'»». 00
71.4
31°. 11 C.
10°. 22 C.
180.5 C.
110. 07 c.
15°. 00 C.
3°. 33 C.
8"". 20
64.7
31'. 11 C.
16°. 11 C.
2°. W C.
8""». 92
s 1
. 1 -I.VnOi
19°. 17 C.
4°. 72 C.
The sky rciiiaiiicil of aiiitainitly tbo same cliaiacU'i' iliiriiiK tlie ilay, namely, ''milky blue
with frequent clouils."
Table 3.
.=
0". 375
0^40
0^.45
0". 50
O^CO
0^70
0''.80
O^OO
l^OO
Setting soutlivcrnior
134° 21'
4
15
133° 21'
15
29
131° 18'
45
85
120° 15"
117
J25°02.
143
120° 41'
105
lOS
110° 08'
132
138
111° 21'
94
92
100° 14'
90
135 109
82
10
15
15
1
19
22
C5
126 , 150
197
135
93
86
1 1 1' lO- ;i. 111. t <> l-J' 0-2™ p. Ill
12" (12"' to 12" 34"' pill
31
26
133
92
140 2.52
101 1 218
243
226
152
120
103
90
88
90
„
13
29
113
151 235
235
139
100
89
rV' 07'" to 5'' 20"' p. m
li" 20"' to r>i' :{0"' p. Ill
—15
32
— 1
10
3
12
40
49
65 1 04
.50 I 119
119
112
71
72
70
46
59
73
5
8
49
110
72
58
66
Tlic arrows iiulicato tlio order in which tlio measuremouts wuro madu.
The miit.s are the arbitrary divisions of tlio scale of the galvanoraotcr.
The state of the sky in these observations is the primary consitleration. An absolute deep
blue over the whole sky, except the horizon, such as may be seen in Colorado or in some parts of
California, is almost unknown in Allegheny. The liest days for our purpose are those where the
blue of the sky is seen between passing clouds at times when these seem to sweep the sky nearly
clean of all traces of mist or haze between them. Yet even here the blue is not, to a critical eye,
the blue of the sky of the Colorado table-lauds or the African desert. The word "milky," above
employed, must be understood as used in comparison with the recollection of a nearly perfect sky.
The grating used, described as "No. 2, large," was the second of two large gratings ruled on
Mr. Rntherfurd's engine by Chapman, giving If inches square of ruled surface. The galvaiiome
ter, " No. 3," was a very sensitive Thompson's reflecting galvanometer, by Elliott Bros., of the most
recent construction.
When the astatic galvainimeter is in a condition of great sensitiveness, it is in a condition of
partial instability; and under these circumstances, minute changes in the temperature of the room
aud of the instrninents will alter its directive force .slowly frmn himr to hour, so that the image
has a motion upon the scaie due to this canse, quite independently of the diurnal variation, a
motion which is observed whether the thermopile or bolometer bo useil, and to which extraneous
causes in either of the last instruments contribute. This motion is here called "the drift." (It
has been greatly diminished, by various improvements siuce the observations here described.)
The bolometer used, described as "No. 1," was composed of ttfteen central strijis ol
iron, exposing (10 scjuare millimeters of surface. (Appendix No. I.) The setting ou D, is that
given by an eye piece mounted in a cylinder like that in which the bolometer is incased, and
interclian;;cablc with it, so that the optical axis of the one and the thermal axis of the other may
rUKLI.MINAl.'Y OIlSKltVATlOXS. 2o
be in;uk- to Cdiiici.le with i>icci.si(ii]. Tin- buttery i;;ilv;iiiimietcr (leteriiiiiii'S the .strength (if the cur
rent, which is kept cuiistiiut (hiriiin' the tliiy. The cdiistiiiit nl' tlie lottery f;alv;ui(iiaetci- is tlie
miiiiber by which tlic dclleetiuii must lie iruilti|ilieil to i;ive tlie curiciit iu Auipeies. The readiu-s
are taken by exposing successively lu the poilioiis (iIIIh' siiectniiu i-hciscii, b(•-illuin,^ iu tlir vinlct
end and going down to the iutraiecl at 1 ''.d, and then ivluiiiiug to the violet so that two readiniis
are taken on every point. It is the uieau of these two sets of readiuf^s which is gi\en abo\c, and
which constitutes a series.
The heat corres]iouding to A = (l''.o7.''» is very feeble at the ■•^eadevel, even with a hi^^li sini.aud
almost disajipears at the low sun observation. It is only, tlicn, on days of unusual cleaiiiess tliat
the heat in this ray, and others of shorter wa\c lcu';th, can be well observed, evccpt at n.
The ri'ader will i.bserxe that the mean time of the moniiu;: observations was at .S'' Hi'" a. in., when
the sun's distance from the meridian was .;" 11", and that those of the afternoon were taken at the
mi'au time 5'' L'O'", p. m., when the sun's distance from the meridian was .">'' L':5'". During' the
morning ob.servatious, then, the sun's rays had a smaller air mass to traverse than in the after ,
and the result is shown in the larger galva eter dcHeetion. It will be observed that the
absorption for any given ray depends, in theory, upnu the mass of air traversed, and not on the
length of the path ; but that this mass, for zeuitli distances of h-ss than (i.j , being almost exactly
proportioual to the length of the path — that is, to sec ; — we may use this expression in tinding the
mass. Evidently if the air be heavier, as shown by the barometer, the mass will be gri^ater, and
sensibly so in proportion to the increased weight, « heuee the mass of air traversed (in the case of
the actual example, and others where the zenith distance is less than 05^) will be Mfi = sec " x /i,
where .1/ is the length of the ray's path through the atmosphere, that from a zenith sun being
unity, and /i is the barometric reading (here expressed iu decimeters). For zenith distances
greater than (Jo'^, we use the f(jrmula, derived fr<ini that of La I'lace, where
,^_ 0.017 i X tabular refraction
cos. app. altitude '
which gives the mass willi moi'e than suHicient coricctness for (Uir purpose, even when (lie sun is
approaching the horizon. l'"rom tin' ob.serxed tiiues, then, we liud respectix cly liu the ipKirnin;;
and afternoon observations
Sun's hour angle = 3'' 11'", O'' Ot!"', 5'' 23'",
Sun's zenith distance = -IS''' W, 2.5^ 50', 13"^ 30' ;
the corresponding values of j1/ being 1..j17, 1.111, 3.."i01, the value of the barometer above gixcii
being unchanged through the day, /J = 7.3.5 dm., and the consequent air masses being as folhiw s :
in the morning 11.15, at noon 8.17, and in the afternoon 25.73.
The heat iu any ray from the ceuter of the sun may be treated for our present purpose as
being constant. The heat in this ray, as it would be observed before absorjition at the upiier
surface of the earth's atmosphere and at the sun's mean distance, would be ccuistaut also, but
would sensibly vary with the earth's distance frcuu tlie sun, being greatest in winter, when the
earth is in perihelion, and least in summer at aphelion. Let-/' = the radius vector, unity being its
value at the earth's mean distance, whence, to reduce any observation to what it would have been
if taken when the earth was at its mean distance from the sun, we have only to divide it by /f.
"We observe, however, that the present ob.servatious being for the jniriiose of cimiparing the heat in
one ray with another and of determining their coeflicients of absorption in the earth's atmo.siihere,
changes of their relative heat, introduced by the variation of the earth's distance from the sun,
are (piantities of the second order, and all of them negligible. It is not necessary, then, to apply
the correction just given to the present bolomctric oli.servations, though it cannot be omitted from
any determination of the absolute aiuount of heat. Our data above obtained, then, are snllicient
for determining the heat in this ray, and the coefncient of transmission; for, calling J-J thf original
rate of emi.ssion of solar energy, a the coetticient* of transmission of a ray froru a zenith sun
through the entire terrestrial atmosphere at sea level (whose pressure is eipiivalent to that of 7.(1
dm. of mercury), and d, the galvanometer deflection produced by this heat at nocui, (/,, that in the
* It Las ln'un f(MiiHl ilrsiralilc to mudify tlif original nut;.! i. .11 ..f I'ouillct, wlierc J is tlio solar loiisfaiit, jj the
coofticieut of transuiisBi e tW air-mass travoisoil by tin- ray, ami ( the tciiii.erature for this imtation iiiiliuclies ideas
whicli have heeu so greatly chaugeit that uew syiubols are more approipriate.
24
KESEAROITES ON SOI.AK HEAT.
iirtciiKHMi, ;iiiil olisi'iviiij; lliat M, ,i, is tile iiuiiibw of units of iiir-muss interposed at noon (= 8.17,)
unci .^t,, ,i,, thv. niiiiilierof uiiitsdf ;iir uiiiss intei'iiosed in the iifternoou = (25.73), we have evidently
since llic, lieiit emitted IVoni llie sun is sensibly tlie snme at all times of the day, whence
, _(loK(7„-loK,/,) X T.ti
" ~ "" " J/„ ,}„ - .1/, ,5,
Snlistilntinn in the above ei|nation the nnineiieal values jnsl given, we lind, from a couipai'isun
(if Udon and al'tei nciuii values on Ajnil L'tt,
, , _(1<'K''„- Io},'rf,)^7.(i
'" ' ~ 17.5(r ' '
and iKim the moiiiin^ ami noon eompaiisiin
lo" a =
(log d„ - log (?,) X 7.G
2.'JS
Hence we obtain the following results for this day's observations, remarking that in such a
elinuite a.s that of Allegheny considerable differences in the coefdcieuts of the most refrangible
rays will be fonml on different days, because these rays, as has been oV)served, almost wholly dis-
ajiiiear in the early morning or late afternoon, and the tirobable error of their value is very great.
Tahlk ;i
^ =
.375 1 .40
.45
.50
.60
.70
.80
.90
1.00
April liU.
Fr.im :
A\
f8h
Iteii
li;; and not
oun ana ni
valun ,if 0
n obaerval
m ulfHerv.n
ons, a = . .
tious, n=..
. 51-2 . 495
. 063 . 573
. 58S . 534
.244
.C97
.471
.631
.082
.657
. 3,52
.712
.532
.637
.738
.688
.927
.753
.840
.831
.791
.811
.916
.898 '
AVe now give in the ibllowing fable a snmmary of all the early observations at Allegheny,
« liich can be utilized for a determination of atmosiiherie transmission. The examjile just given
in fall, will serve as a tvpe of tlie rest.
Tablk -1.
TIk' observed galvaiKuneter deflections are reduced to a scale on w hich the readings aie pro-
Iioitional to the cnneiit iiassing through the galvanometer.
'/, = galvanometer deflection with high sun.
di,= galvanometer deflection w itli low snn.
.=
0^. 375
.400
.450
.500
.000
.700
.800
.000
1.000
j 1881.
Janiiai.T2K
J,
101
43
215
61
374
167
280
104
383
268
307
141
320
215
293
195
221
175
91
144
lie
102
78
47
d,
34
3
M'O'i'H- 17
d,
d„
23
(12
20
120
232
110
200
133
227
151
188
SO
71
39
d,
d„
19
CO
43.5
17
154
63
230
119.5
202
171.5
239. 5
160.5
177. 5
123. 5
89.5
84
April 23, am
d'
d„
09
41
1.52
124
200
189
203
258
227
257
191
187
121
122
94
90
Apnl23,p,,M
d,
d„
32
103
200
124
203
18B
277
198
191
140
121
60
94
00
Alilil29,a n,
d,
13
1(1
29
113
05
151
120
235
156
235
197
139
135
100
93
69
86
Aj.nl 2'J,l..ni
d,
d„
13
5
'"i
113
49
151
02
To)
235
116
130
100
58
89
06
April 3tl
d,
d„
21
18
33
121
180
148
245
2.59
175
160
119
97
90
80
d,
8
34
99
109
144
134
00
89
61
64
33
39
The ue.xt table gi\es tlie sun's position and the corresponding air-mass for each series in the
previous table.
PREWMIXAltY or.SEKA'ATIONS.
Table 5.
lliilU s
lei(/3,). (1I,^„|.
Low sii
Sim's
25
14.25
P.M.
2 57
71 28
7. 45
13.0^
12. 311
P. 11.
r. 11.
3 00
2 50
7(1 45
00 on
7.39
7.42
P.M.
4 30
06 22
7.3C
t* ;i7
.\. 11.
H lil
p. M
4 "'0
03 57
7.40
R. 17
A. 11.
3 11
4.-i 40
7 35
8-1?
P.M.
5 '^3
73 30
7 35
S. 21
A. M.
3 M
.50 31
7.41
PI!.
5 33
71 14
7.32
I'.v coniliiiiiii^ tlic lii;;li iiiiil low sun (ili.scrv;iti(ins of ciifli day scpiiratcly, tlii' loUowiiii;' ooelii-
.Mit.s ol'atiiiosplicric- tiaii.smi.ssioii are obtaiiifil h\ imimii.s of tin- t'orjiiiila
lo.U-
wIr'IV dr.. is the coi^ffici'.'iit of Vertical tran.siiiissiou by air at a liaroiiictiic pri
•Table C.
sure of one (Icciuiclci'
Jannarv 2R .
FeliriiaVv2.
FfbniarV 17
April 22
April 23. a. i
Aplil 23. ,,. ,
April 20. a.!
Api il 20, p. ,
Apiil30 ...
Mav2S
Adoptcil a' '■-
Transmisaioii
.esSi.008 . 903 i. oil .928 i. 006 .&42i.008
.003 .903 .-.008 .971 i. 004 . 97(
It -I1..11I.I I., niid. i,,i 1 lli.it ..wins 1« lliO ioivssant .-lianKM ofmir atniosplievp. n ear.s ori)li.<crvatiim niislit l.i- s|.,-iil \vitli..nt ^iviim to
11.1^ t.l.l. ;,11 1 x.1,11.. .. ul,„ I. IS tiuallv attaiti.il.U-. Latr.r ol.servatiunn, tarried oii througli the .lian.jiiiu' seaa.jus ..r a wli..!.- y.-ar. atiil
nirl |.l,.^..l :.|.iMi:,li., ;.|.|..ai h. ,Ilo»- tl.at .all tli.-s.- coera.jioiita »l[..iiia 1» a.iiiicwliat moditiwl. Tbt-y an- licrf L'ivcii a.i .•\aiiipl.-.s ..r tliB
i.M.ll, lii,t :.tl,.in..l
Tlif 110011 oli.sfivatiou.s on like lii.v.s, where iiiaile on sueri.'ssive ilay.'^, tluoiiiili like air masses
should .ui\e nearly like results, if the transinissiliility of the atiiiosiiliere for heat were idways the
.same for the same ma.ss of air and the same ray. A eomiiaiisoii of this willi the preeedinu tables
shows, liowever, that the heat transmissibility must often ehaus'e consideralily fm ■ day to
anolher. even when the sky is clear on lioth. We are forced. (;d least in tln-se iirelimiiiary
researches.) to make the ordinary iissumiplion tliat the transmissibility is coiistaur between nooii
and aflermion: but we recoyiiizi' that the transmissibility thies proliably ehaiisc e\-eii in lliese few
hours, and that tliis aMsiiinption. tlioii<;h it is usual and here necessary, cannot be considered exact.
If we take the probable errors ol'tliese eoelli(.ieiits, we shall, in accorihince with what has just
been obseiveil. timl the largest i.inbable eii,,r iittached to the sliortesi wave leni;lh. The probable
errors dcrivcil from each colnnin by thr' ordinary process are i^iveii ii^ainst thc\alui's marked
■'mean '/"." If these values lie made the ordiiiiitcs, and the wave leii-ths ihc aliscissa' a smooth
taiive i!i;i\ lie drawn throui;li the poinls. .\ line drawn between the points rcliresent iiii; the oriuinal
and entirely iincoi rectcil obsei vatioiis ol' ,i yives the s th tauwe in Imi;'. .!. 'I'he very slightly
2(1
RBSE ARCHES ON SOLAR HEAT.
illttcniit vnlni's oiveii by tlie sniootli curve are adopted as tliose of n, and a consideration of the
iiminicr in wliicli tlicsc values have been obtained, of the probable errors, and of the illustration,
will put flic n-adei' ill fall ]iossession of all the means of forming a judgment on the trustworthi-
ness (if the icNiilts wliich thewriter himself possesses. If he bear in mind that being- obtained on
only ;i|iprii\liiKitely honiogeueous rays, there is reason wiiy they should in theory (as is denioiistra-
Ird later) indirate rather too large flMii too small a transmission. One remark may, however, be
made in relation to the prolialile errors of the numbers eorresponding to (l''.iMI and I".(IO. There is
here a very great interruption of tlie speetral energy (see A M on the cliart of the normal speetrum).
Ill these early observations with a wide bolometer, the neighborhood of this '• crevasse" iu the curve
was a source of slight irregularities, which appear in regard to these wave lengths.
Fiff
--■
^^
OS
^
^
/
^
/
/
03
OZ'
.
out Oto iHtO o-o (luo
Coefficients of Transmission for the Respective Wave Lengths '
J. IK I
\ Allegheny. )
I.JO X
I'p to the time of observation, it Iiad been almost universally admitted by idiysicists that the
iiilia-icil hiat was iu general more absorbed by our atmosiihere than the lumiuons. This is the
festi ny of many, and even at tlie date of writing these lines (October ISS;^.) it may be consid-
ered 1(1 lie still the generally received opiniou, so far as the most recent and approved treatises on
l>li\sics can be recognized as the exponents of scientific opiniou on this ]ioint. As soon as accu-
rate means had been devised for comparing the ab.sorption in the infra-red with that in the lumin-
ous part of the spectrum, evidence began to accumulate that the latter was really the least,
tiansiiiissible. Considering the weight of authority again.st his own couclusion (that the infra-red
heat within the range of his researches was more transmissible than the luminous), the writer felt
liduiid to re|ieat his experiments in every manner and with every precaution. The reader's special
attention is called to the nature and weight of the evidence given in the preceding fable to the
l'lii:LI."MINAKV (HiSKiiVATIONS.
27
lact of the yi'oiitly iiUTcasod tiaiisiiiission ol lirat rays of as yuMt a w a\ i- Iciiutli as (t .(idl n\ri
those ill the huaiiious |iart of tiie sjiectium. Iinleeil, it is here seen that exi-i'pi in llic rase ol
absoi'iitioii bands each \vave-leiif;tli is, broaill.v speakiiiy', iiioie tiansiiiissilile as It is loiiiid lailher
and farther in tlie infia red.
We may add, tliat. besides tlie above (hiys of exeeiitionally anhbrni atmosjiherii- c'ondilicins, a
.yreat number were partially utilized when the series were so interrupted by the i;ailieriuy of mist
or ehuuls that they have uot been eited heie at all ; but that in all eases the obseivatioiis have
been found to lead to the same result here .yiven. and to warrant us in statuii; that, spealiiiiK
without reyard to loeal absoriitions lil>e those ol the telluru' lines, tlie coeliieients of transmission
iHvrmsc with the wavelen<;th from within tl iiscrvcd ran^e of A = Of .375, in the ultra violet, lo
A = l-'.OOof the infra-red.
On many days, wliieh do not aiqiear above, w lien both morninj: and afternoon series eiuild nol
be obtained, {;<iod noon seru's were observed. Those on whieli .uood noon s<'ries only were
obtained eannot be used for finding eoeliieieuts of transmission, but may still be useful, if we liUr
to eoinpare the relative transmission of these rays in sprini; and in winter. For this purposi-, all
i;iiod noon observations have been reduced to a unilbrm battery eiirrent of O.'J."! amperes, and the
results, arranged in two sets, the lirst for winter and the second I'oi spline measures, are as tollows,
the values !;i\cn beinj; detleetions of the iialvanometer in di\ isions of its arbitrary si'ale:
Tahle 7.
WINTER.
..
1
.375
.400
.450
.500
.600
.700
.800
.000
1.000
ISSO.
h.m. h.m.
I).. cnlMT IS ...
l.OII- 1.35
05
307
314
303
177
110
87
IKKl.
.I:iiiiiiirv 28
...11.55-12.33
flS
350
f'07
135
05
K.>l.uiary2 ....
....11.5U-12.23
a?
75
■.>fl1
271
2K7
274
104
87
I'Vl.liiiirv.'i --.
... 11.15-11,55
53
14S
343
4.5li
502
311
IM
130
l-'i-liriLtry 5 .. .
-.,-12.0(1-12.35
21
52
Iffi
206
300
207
137
67
....11.11-^ 1.10
no
225
220
182
31
88
100
204
328
2.™
172
111
L
STATE OF SKY DUEINfJ THE ABOVE EXl'EIiniENT.S.
Dicrmlnr is.— tSky cleared une.\lieetedly to a ^ood blue.
■Iminary I'S. — fair milky blue sky, continuiny very fair to close of day.
Fihniiiii/ L!. — Sky hazy, iiii[iidvin,!.; towards noon ; p. m. very thickly milky.
Fthnidfi/ :'>. — Sky unusually clear and free limu haze, e-\ce]it in measures on .7bb, ..S(Mi, and
1.(100 when tliin cirrus had ecuiimeiiced to form.
Fchriuiri/ '>. — Sky hazy.
Fchrudiij 17. — Sky hazy, irrcj;ular, but beciauiiiK more uniform alter noon, thicker at the last
observatiiuis, p. m.
Februiinj 'I'l. — Sky hazy, halo around the suu, occasional wisps of cirru.s.
Taijle .s.
spiiiMc;-
ISSl. h.m. h.m. >
MareL 10 11.31-12.18 |
Milll'll 25 12.00-12.45
JIalrli 28 12.03-12.20
.\inil 14 .... U1..V.-11 -111
•M'ol22 11„-.(1-12.35
, ,11, .'■.5-12,23
II .40-12 34
ll-;.3-12.li0
J
21S 281 ' 271
. .soo
. 000
1.000
lao
00
07
lao
148
!)3
182
150
2211
104
ISO
130
103
145
105
03
182
05
01
04
188
121
28 RESEARCHES ON SOLAR HEAT.
STATE OF 'JTIE SKY IJUKING TUB AlldVB EXl'lOKIMENTS.
March 1(1. — Sky a tliickly iiiilUy blue, iieurlj- iiiiitoMii.
jMiircli l-T). — Sky liiir bliie, with i>assing cloinls.
March L'S.—Sky i'air, milky liluo.
Ajnil li. — Excellent blue sky; light clouds iiassing.
April 22. — Milky bine sky, uniform, but increasing .slightly in thickness tlnough (lie (hiy.
.1/)/ // 2.1. — Sky rather thickly milky, only nioderatcl.x good, but (|uite regular.
April -'.). — Sl;y milky l)luc, with tKMjuent clouds; apparently of about the same intrinsic value
all day.
A/iril .111. — ."sky milky blue: nearly the same as on Ajiril 2I>; milkiness slightly increasing.
Mai/ 12. — Sky milky blue, witli oceasioiuil clouds.
The last line of each table gives a snimnary, that lor Ihe winter detlectionN being tin- me: f
seven series, and lor the spring the mean of nine seiies. Tlie absolute gahanometer delleeiidiis
interest us little. What is most important is a comjiarison of their relative, amounts.
'J'lic bolometer, like the thermo-iiile, is au instrument intended primarily for dilfereutial work.
Even ]\' the absd'ute amounts of heat measured by it were opeu to (]uestion, this would be a mattei'
of secondaiy importance were the rdatiri results trustworthy. As a matter of fact, however,
the alisiibite amounts of heat indicated by the bolometer, when the same instrument is used
under the same conditions, are found to be much more exact than the writer (who did not have
this end luimarily in view in its construction) anticipated. It may therefore be interesting at
this stage to apply tlie corrections for the selective ab.sor|ition of the materials of the apparatus,
so far as they are known, which will tend to give the values of the.se measures in terms whence
the absolute amount of energy in each ray can be cahailated with a certain approximation. We
repeat, however, that it is the relative amounts of energy which the instrument is primarily desigued
to fnruisli. We will observe here that, in accordance with the general considerations already
introduced (see \). 5 of introduction), we admit that what the sun sends us is, properly speaking,
eiicrij!/, conveyed in vibrations of certain wave-lengths, and that this energy, after falling on the
mirr(U'of our siderostat, the surface of our grating, and that of <mr bolometer strip or thermometer
bulb, causes finally eeitaiii mechauical effects in onp j^ah anometer or thermometer, which we take
td be prcipditidiial to the lieat in the lay, '-heat'' being the name we give to the solar energy, as
interprele(l td us by the above nientioued media, I'ach ol' which exercises some minute degree Ot
■sclei'tivc absdiptidn dl' its own. Tims, even if we su]))iose that (Uir apjiaratus were placed at the
iiiiper limit of the a tiiidsiiliere. receiving there the unmddilied solar energy, the silver of the siderostat
mirror W(aild, for instance, of two rays of equal energy, (Uie in the blue, the other in the infra-red,
aiisorb, in the act of retlectidn, more of the former than of the latter, so that the two woiihl be
une<pial alter relleetion from the siderdstat, though e(inal before; and the heat in each, when it fell
(Ui (lie boldinefer or thernidiiieter, Wdiild nut be piippoitional to tlu' original energies. Aiiodier
selective action takes ])lace through the metal of the retteeting grating, and still another through
the glass and meniiry of the thermometer, or through the iron or platinum of the bolometer, or
through the lampblack with which these are covered. If all the solar energy, of whatever wave-
length, were treated indifferently by each of these substances (even if each absorbed some of it),
the htial result, in the reading of the thermometer or galvanometer, would evidently be jiropor-
tional (d the energy nf the original ray, and the relative lieats in any tv.o rays wciuhl be strictly
a ineasiire df the relative energies originally sent in them eartliward from the sun. Thougli the
selective reflection which the ray has suffered in our catoptric ajiparatus be much less important
than that whiidi would take place with a lens and iirism, yet every part has exercised some
absorption of its own. We conclude, then, that if we could. determine the selective absorption of
each ageut and make a correction for it, we should restore the exact proportions of the original
energy existent in different wave-lengths. We cannot do this with ab.solute exactness, but in i)ro-
piuti(;n as we siu'i^ecil in doing so, will our final and corrected results be proixutioual to the
original energy itself.
PUELLMINAKV OliSEUVATK )XS.
29
We, liavc. iilso to make (■<iMvc.ti()iis, ihst, for tlic overhipiiiiif; jioitioii of the weal; .si'i'imil siicc.
Iniiii. which is toMiid iVoiii (_-xiK-riiiiciit to liavc an iiitoii.sit.v ot ,'„ tlial of the liisl s|ic(lnnii: sec. mi,
lor tin' (liiiiiriutioii of hrat in th<' ililfrai-tioii spiM/tniin, witli ini-ruasc of llir aii.ulc ol' difliactioii,
wliicli is hfiv talirri as |iiii|ini tioiial to srcaiil )■.
'I'liosc last two <-orici'tioiis aiv iiistniiiiciilal and in(h'iJrndfnt of the sclfctivc absoi |.lion. On
applxin- Ihoni lo tlic hisl tal>h' we yet the following lestilts :
Table 0.
.=
.375
.40
.45
.50
.CO
.70
...0
.00
1.00
rniT
i-ti,.i, I (.Hiil.lnirl
».■!
0
0.
u
IJ
jl
-■'■ ■ ''
'•>■''
.'» '' ,„
.■li..n 11 (lM,t..i)
2. oc;
Mine
1 44K
1.3111
1 227
Mil"
1. llili
1. ».'.
Win
lor land ID ..
OX 2
IKi U
•MT,. 0
4'J5. 7
41!i;. 7
317. K
2111- 5
122. 5
02.7
Sliiili
K, 1S81 (cmT.-,t..l
lor lan.l lll-
54. 1
117. a
■J2:i. s
31.'., 7
311.). G
332. 5
221.7
135. 3
00.0
We are now |ireiiared (n ajiiilN the correetioiis for seleetn c alisoi |pt ion. The third i-oneetion
is for the absorption I ly three snrlaees of siher deduced Iruiii independent e\ pciiniciils a( Allc
glieny not here given.
The fourth correction is for the alisorption liv the surface ol' specnhini metal. There remains
the iio.ssilile .selective alisorption dne to the liolometcr strip itself, or to the lamp lilacU with which
it i.s covered. It is nsiial to neglect the selective alisoriilion ot lamp lilack npoii the tlici mo pile,
and, indeed, there is so iiimcIi doiilit as to what this selecti\c alisoiiition is, ami how it is exercised,
that it isditiiiadt to talic it into acconiit. Our own in\ estigations ii]iiin it aic not .\et completed.
We are led liy them to think it prolialile that lamplilack is almost transparent to certain infra-
red rays, which, however, lie lieyond the limits of the jiart of the spectrnm we arc now study.
iiig. IJetweeii X = Ui'.375 and /! = 1''(I00, it exercises a certain selective alisorption which is how
ever, treated here as negligilile, since, on repeating our exiierimeiits, Initli with lainji lilack and
without, we do not tiiid within the iircseiit limits any dilfcrenccs dcsci ving Kiiiaik. We must
admit, howcx-ei-, that the ignorance wliicli « c, in common with all physicists, lalioi' under coiiccrii-
iiig the schctivi' alisorption of this snlistauce in tlie infra-reil, is iiincii to lii- regivtted. liigorously
spi'akiug, then, we ought perhaps to describe our present results as giving the energy (to use ilv.
Lockyer's expression) "in terms of lamp. black absor[itiou." Ap[ilying these eurrectioiis, we now
lia\e the following results:
Table Id.
1
.=
.375
.40
1. 02:t
1. 1130
3113. 4
235.4
.45
Lll.'.i
.570. 3
423.7
..50 .60 .70
I.ri05 L.ViO 1. 11111
I.OOI l.lioi, I.13S
,5G0!lj 1 02L0 r..02^5
.SO
1. 4118
1. 103
■.as. 3
.00
l! 21111
il.5. 4
38.0
1.00
(■ 1
Ill ll.l
|S>| l.oll
[.■iSl (. om
lor
1 i. 034
1 192. C
111.0
w'li.l.'
S„l.|„.
,'i',.,l loi
■tf.l for
I.li
1,11
iiV
III,
■I'n.VlVl""
mil IV)..
1.306
173. 0
234. 0
We repeat that, in the degree in which we have above eliminated the selective absorption of
the iiieilia. of the ajiparatiis, we are entitled to sjieak of the resultant \alues as proportional to the
.solar energy it.self. A\'c do not siippo.se onr.selves to have ai'eomiilished so untried and ditlicull a.
task with exaetness, but regard these curves as useful as a tirst approximation to the absolute
energy curve.
30
RESEAltOHBS ON SOL AH HEAT.
Till' ■.lir-uiiisscs on the (l;iys iiK-liiik'il in tliis sMMiisuiry were as follows
Table 11.
n|;le. distance.
0.110
0.09
0.39
Miircli 28 .
13.62 April 14...
13.78 Aiiril'ii...
April 2.T..-
April29--.
April 30. ..
i Miiyl2 ...
13, 88 I Srean air-n
13.37
12.33
11.51
Sun's
ZfuitL
distance.
0.14
0.18
0.07
0.53
0.12
0.11
0.00
0.04
0.64
25 50
25 31
25 00
i for sprii
M. p.
10. 22
9.33
9.18
13.98
8.35
8.37
8.17
8.21
8.15
9.33
If wo, take tlicse same winter oKscrviitioMS ;uiil select s]ieeial oliscrvatioiis made at tlie same
altitude in sprini;, we olitaiii, by a jirocess readily iimleistddd Irum wliat lias iireeeiled, the follow-
ill}; residts, in whieli we siipiiose tliv sioiic (oiiniint of heat in s|iiiiig and in winter, leinesented in
eaeb ca.se by lOtIO, to fall upon onr bolometer, the mean altitnde of the .sun at the time of observa
tiou being the same.
Table 12.
i;sEi;VATioxs at the same altitude of the sun.
.=
Winter.
ill
S,„.in„
Ecduced to sum = 1000.
"Winter. Spring.
192.6
363. 4
579.3
767.9
71.5
119.8
275. C
369.1
439.0
433.9
298.5
191. 4
160.4
49.0
9.3.7
149.2
197.7
ISO. 6
135.9
87.1
30.2
50.0
116.5
156.1
165.7
1S3.4
120.2
.40
338.3
215.4
173.6
44. 7 j 70, 4
1000. 0 1 1000, 0
1 1
It will be .seen from tables 10 and 1 1 that, althongh the ab.sorbiug air -mass was durinj; the winter
nearly half its large again as in the .spring, the heat received from the .shorter wave-lengths was
aetnally greater in the winter. (See also columns "Winter" and "Spring" of the table Just
given (11,'), where it is seen that for equal air-inasses the actual infra-red deflections were not
greatly different at the two seasons, within the limit of these observations.*) It appears probable,
then, that the transmissibility of the atmosphere for the light-producing radiations is relatively
greater in winter than in spring. As this etlect may be couuected in some way with the unequal
jirevah'iiee of atmospheric moisture at the two seasons, it may be well to state that the tension of
aqueous vapor during the winter observations was in the neighborhood of L' millimeters, in the
the spring of 8 millimeters.
We now proceeil to the ealeulatioii of the energy outside the atmosphere, for homogeneous
rays, with the data which have been given. For this purpose we have used the formula —
7.0 ■
Log E = log rf,
log a.
early oltsurvatioiis.
obtaiu till) same ail
■we have already n
Tile wide absorptinu bauds subsequently discovered in the infra-red lie below
licli cover but a small part of the great iul'ra-red region. It would be prem.i-
ioiis .as to the etfect of water-va|>or uiiou the invisible lieat region, in these
il. in regard to the whole subject of winter and spring comparisons, that to
li;i\ r In observe systematically at a ditierent time of day than in siiring, and
is probably a systematic change in the quality of the absorption as the sun
It may be i. !.,.,.•
■mass in wiiilir
marked that tin
approadies the hori/.on. It is with the latter fact iu view that I liai
■with the unciiual prevalence of atmosi>hcric moisture," &c.
iritton above : "As this effect may be conucctcd
PRELIMIXAKY < )r.SKRVATIONS.
31
WIht(> Fj is the eiiersy in niiy niy oiitsiilo tlir ;it?iiosi)Iior(^ (i. c, In-fore relliuic nbsorptidii), d,,
till' :nci;ii;(> fialviiiionieter ilcHeffioii :if iiniiii fur the sniiu' ray, /)|, tli<' barometer iircssiirc in units
<j|' one cliM-iiiicti'r, or tlic mass of air in lln- \i-rliral colnmn : .1/, /),. Ilic i'orrcs|ion(lliij; air-mass for
tlic sun's ziMiitli distance at noon, anil -( the ailopled <-.iellieicnt of ti ansmission for tlje ia.\ in
iinesdorj liy an air mass of anit\, re|ir<'sci]ted liy T.Odm.in tlie liaronjelcr.
Table 13.
WISTEK.
Ml Pi - 13. fit.
Mi/J, ^
^
LoSHjc
Log a fli
Logrfi,
LogE.
E.
10C5
.375
— . 0.-)3a
-. 742G
2. 2S47
3. 0273
.400
.4S(i
-
11491!
0414
-. 6.SH5
— . ,1746
2. 51104
2. 7(129
3. 24S9
3. 3375
1774
2175
.500
— . 4830
2. K«53
3 3f,S3
.000
0259
— . 3595
3 2UW
10.59
.700
0200
■>77lj
2 7''"'R
3. O0O2
1000
.800
0155
— . 2151
2. 5293
2.7444
.900
_
0132
— . 1832
2. 3333
2. 5105
329
1.000
—
012S
-. 1777
2. 2394
2.4171
201
SPRINR,
Ml ^1=9.33.
— . 0535
— . 0496
— . 0414
— . 0348
— . 0200
— . 01.55
— . 0132
—.0128
—.3803
— . 3247
—.2416
— . 1866
—.1440
—.1232
-.1194
2. 0480
2.3718
2. 6271
2. 7.5.55
Table 15.
.MEAN OF WIXTEl; -Wn SPKINC
Lose.
E.
2. .5478
353
2. 8340
683
3. 0134
1031
3. 0802
1203
3. 0.347
1U83
2. 9289
849
2.71.55
519
2. 4998
316
2. 4898
309
. 400
49
_
■>4
"43 301
11
.4.50
414
—
"00 3 1 04
1515
.500
-
348
—
3
"8 1 3 J
I 4
. 600
:
-
4
3 14
7 1 9j4
1 44
. 800
r 04
38
.900
_
_
1
" o«r
3 3
1.000
*
0 8 " 4 83
"8
e following talilc lias l.eiai |>rcpared witli tlie valin-s oliserved in tin- sprini; of Issl.
oeffiiMiaits of liaiismission. to show \\u- rc-lation lietwi-eii ciieriAy outside llie al s|iliia-i
I liii;li and low sini at .\de,-ln'ny. llie vaiions actnal ahsorhllie air-m.isses at tlie lo\
ilions lieini; reduced to a nniforrn \aliie, doiililc lliat at lii^li sini.
isnii;
' and
32
RESEAEOITBS ON SOLAR HE AT.
Table 10.
irny after ubs
■i-KT .iftcr ilbs
.iteil liislismi).
j.375
.400
.450
..■iOO
.600
.700
.800
.900
1.000
353
CS3
1031
1203
1083
849
.519
316
309
11-J
235
424
570
021
.553
372
238
235
j 27
C3
140
311
324
240
167'
167 1
E can be coniputod from d, and (J,, liy tlio fdriniila alicail3' given, ami witli tliese values the
curves in I'late I have been plotted.
Tlie nii<l<lle enrve (I) i.s that .showing tlie di.stributiou of the energy in the uornuil .speotruiu
at high .sun. Exeei)t for the heat below wave-length If.O, the area of the curve may be con.sidered
111 ri'pii'seiit tlie heat actually observed by the actinometers at noon, as presently given. Its maxi-
iiiuni ordinate is near (li'.GD in the orange-yellow.
Tlu' lower curve (II) is tliat at low sun. Its area is proportional to tlie lieat received when tlie
sun shone tlirough double the absorliing airnia.ss that it did at noon, and it will be seen that the
maxiiuuiii cu'dinate is near wave-leiigtii (•".TO, or near the extreme red.
The upper dotted curve is "the enrve outside the atmosphere." Its area will give the heat,
u liicli would be observed if our apparatus were taken wholly above the absorbing air, and the
distriliution of this heat (energy) before absorption. Its maximum ordinate is near 0''..50 to OcSS
in the green.
If we know the values in calories corresponding to the middle curve, we can now obtain the
absolute heat before absorption, /. e., the solar constant.
1 1 should be noticed that if we had attempted to deduce this latter value, by applying our loga-
ritliuiic formula', directly to ordinary actinometric observations (*. c, to observations where only the
indiscriminate etfect of all heat rays is noted by the thermometer) made at high and low suu, we
should have obtained a quite different result. This has been the usual process, but it can never be
a correct one; for, we repeat, these exponential formula; are in theory only ajiplicable to homo-
geneous rays.
■ The above values (in Table 10) are relative only. To obtain ab.solute ones we have now to
combine this result with the actual measurements of solar radiation in calories, or other units fur-
nished by actinoiiicters under approximately the same conditions. We shall at the same time
thus obtain a preliminary value for the solar constant. Taking the mean of our observations with
the Violle and Crova actinometers on clearest days, we have 1.81 calories* observed at Allegheny
in March, ISSl. This is the alisolute amount of heat represented by the area of a completed "high
sun" curve.
To this result, the energy distributed through the whole spectrum Ijas contributed, while our
lidloiiictcr iiieasuic'iiieiits in the diiiraction spectrum end at wave-length IcOO. Nevertheless, since
we ilo ill lai't know froiii subsequent measures (to be given later) where the efl'ective spectrum ends,
we can by the aid of these later measures prolong the curves and obtain their relative areas with
close approximation. In this way we determine, by measuring the charted areas, and making
allowance for the (here) uncharted area below A = Im.O:
.\ivir ..iilsi,!,. .■nrvi- alj.iye A = Ifi.OOO 47.17
.\iv;i , ml si, I.- . inv L.lowA = Im.OOU ai;,4'.1
Tntiil T.UK
lii.nli
lii-h
:itiovc ,\ = U.llnil -JI'lIIi;
[u-]nw ,1 " IM.INIU 20.11(1
'( Ar
= 40.'.I(J
■^ Tiicsc vntues in tlie cn.sc of M. Crova'.s .ictiiiomeler are somewhat liiglier than tliose found uinler favorable circum-
stanci'S by M. Crovii hiiiisc-.If. Ouv.s iiwiilt fmm the iutriicUiction of some small coii'i^ctioiis (not special to this iustru-
m.-nll nhi.li NliL^lilly in.reas,' llir y:ilii.> of 111,- ivailiiig.
Tli,-.^,' l,.-l ,al,iii,'s iv|.i,-.s.nl 111,' \,-ry iiiaMiiiiim ,.lis,a \ al.l,- at .Vll,-j;h,aiy. Ill ,iiii ri-invsi-iitation of the Alle-
ylHU\ ,111V,- ,il .li^liil.iili r,M,-v;;y in tli,- sii,-ili inn «,- liaye ailuple,! 1.7 as the ii.snal railiation for cle.ir blue sky.
PLATE I.
Relative Energy for High and Low Sun.
riJICMMIXARY or.SEltVATIONS. 33
We luivo, tlion, ii(UT])tin,n l.sl cul. :is tlic s<il;n' Kidiutiiui at Alli--li('iiy willi clcai- sky. l.si cal.
X l..""i7 = 2.84* oalorifs ((■.(". i-aloiics piT laiaiiti^ yei s(|iiaii' ci-iiliniclfr) as an a|>|ii(.\inialc value
(if tlK' sdhir constant.
Ill all tlicsc olisiTvat Mills, tlic ulijcrl has lirrii to aviiid tlic rci^istcnii.i; nl' small \ .inal i.iiis aiial-
o-(iMs ti> flic Fraillilinlvr lines, and In yive (Hil\ the };iMieral distiilnil inn nl the eiHn-\. The iiia|i
jiiiij;- (irilie interMilitiinisnltlieeiier-> caused liy \ isilile nr inxisilile lines or hands tnriiis a dislinct
l-eseai-eh. anil the results are t;i\en later in the present vnlnnie.
We lind I'roiii these iiridiiiiinary iiliservatinns that the inaxiniiini eiierjiv in Ihe niniiial s]iee-
triiin nia lii-li snii at the earth's siirtaee is near the yellow, and that tlu' |Hisition nl the iiiaxininin
lit heat does not ill tact (litter widely tniin llial olllie iiiaxi in otliyhl. It has lieeii Ion- known
that certain ultra-violet and \ iolet rays were iniieli alisorlied, lint it lias liecii siiii|.oscd that the
alisoriition increased also in llie intra red, so that the liiininous part of the spcctriini was, on the
whole, the most traiisiiiissilile.
I'.nt we see here, not only how (•nornions the alisorption at the violet end really is. lint lliat //»'
//(//(/ rrf^.s- iKtre .siifmil n luri/n- ahsorpliini hrf„i-r lliri/ rnirh lis lliini flic ■'/((.(/" nn/s (I. c, I hall
the extreme red and infra red rays), a eoiicliision ojiposed to the present ordinary oinnion, and, if
true, of far -reaching iin|iortaiice. For if this "dark" heat cscaiies by radiation through (inr atmos-
phere more easily than the liiiiiiiious heat enters, our view of the heat stoiiii^i action of this aliiios-
|ili( re. and of the conditions of life on our planet, iiinst be ehaiij;ed. Within the limits of the present
eharis, the "dark" heat apparently diws so escajic.
We can, from the data now gathered as to the rate of alisorption for each ray, coinpnle the
value of the heat or energy before absorption (the solar constant) by anew process which is in strict
accordance with tlieory. This preliminary \alnc indicates that the true solar conslani is lar,L;i'i than
that com nly yiven.
The ratio of the dark to liiminoiis heat has been so wholly (■liaiii;C(l by selective absorption that
we must j;reatly modify our usual estimates, not only of the sun's heat radiation, but of his ellect-
i\e temperature. Wo infer also, that llir sini, In an i-i/r irithont oiir iitiiiiisiilirrr, innihl iijiimii- of ii
hliiish tint.
According, then, to the observations which have been detailed, the actual value of the solar
heat is greater than has been supposed. Tlu^ aclion of this heat on our atmosphere is also \ cry
dilfereiit from that cu.stomarily asserted, and the extent of our misapprehcnsioii of the real
eiriaiinstances wiiieli nature presents to ns, may be s;iid to be ]ireseiiteil to ns face to face, in our
nnixcrsal belief that the sun is white, while its real color may be unknown. Our presiail condilioiis
of observation are. however, in maii\ respects most delieieiit. They all rest on the assiinipl ion
that the transmission of heat by like air masses irmains the sa tlir(aii;honl llicday. There is
too much reason to believe that it not only varies casually, but also chan.ycs .systemalically, both
with the time of the day ami with the .seasons of the year. It will be .seen, on consideration of the
method by which the tiansmissibility for the lii^li and low sun has been obtained, that we learn
only the mean transinissibility of onr atiiios|ilierc, and never its composition in other respects.
The air, for instance, a little way above our heads, might have a dilTcrent cheiiiical conslitiition
and (litl'erent transinissibility from lliat in the lower stratum, without such means as the ]iicsent
giving ns any hiut of tlie fact. All these circnmstances have an immediate bearing on the deter-
mination of the .solar constant and tlie above value of 2.S4 has never been regarded liy me as more
than a first approximation. Even as such, however, it shows the constant to be miich largia' than
hcreloforc supposed, and the absorption of onr atmosphere to be greater than has been imagined.
It must be constantly borne in mind that we assert that the formula ol I'onillcl has but a
limited application, and is, as generally used, erroneous. We pro\i', later, by actual demonslialiou,
that it always gives too small a value for the absoriition, and hence the less absorption there is
aboV(^ us, the less important (bies the error of this formula become. Accordingly, other things
■■i'lw ■TMlori.-" Il.-iv is tl s II (■:,:, ,rir" „t I'ouill.i :iii,l later iiivrsi i-ators. II is 111,- :i mil ..lli.-;il i-.-.iinrc.l
to heat 1 Hnniiiiie nf wat. r IVoiii n ('. to 1 ('., and In l',-IVrr.-.l t.. tl..- iiiiinit,- and si|naiv .■.nliini-h-r. 1 c-alinii- =
«,'2UI1,I1(I0 ergs = lliS ••artincs" .li llnsrliel = II .las i,-,. in.dtiil per s.|nar.;' .■(■ntiln.-l.l |..r niniille,
1U53.-;— No. X\' .!
34 ' RESEARCHES ON SOLAR HEAT.
hvu\ii i-i|iiiil. tli<' (iliscrvations in;i(lc even l\v the ])reseiit process, if repeated on higli moiTiitaiiis,
may lu- cxiuM'tcd to i;iv(' more iicrfect \alues tliaii tliose made at tlie sea-level. We have, it is true,
(iIiscia'imI 111! aiiproximately liomogeiieous rays, in olitaiiiiiis' onr coefficients of transmission, yet
\Yc iiiiisl remember that thonyh we may allowably s])eak in common terms of the bolometer's hair-
lilcc stri|> as "linear,'" it is not absolutely so, and the tine coelUcients of transmission are, inferen-
tially, smalh-r tliaii thuso obtained even by its means. In iitlicr words, the amount absoibed by
onr atmosplicrc is not improbably greater even tlian the pi'<'si'nt (il)si'rvations make it.
We liavc icachcd in these prelimiimry inrostiffations some conclusions quite at variance with
accepted beliefs. We liave found that the absorption of tlie heat, on the whole, diniinislies as we
f;o into tlie dark lieat region, and that the "light" is more absoiiied than the "heat," while it has
been generally understood that the contrary is tlie ease. It would appear from this that within
the limits of tln^ picsent observations (Oc-i to 1 ''.(I) flic "dark" heat escapes more easily through
our ail- than it enters as "light" heat, so that tlii' familiar comparison of our atmosphere to the
ciiver (if a hot lied does not here seem to be just, aii<l so far as these preliminarv observations extend,
we do not lind at all what the ordinary belief leads ns to expect.
The construction of onr ordinates for the curves outside the atmosphere, has shown ns that
the inasiniuiii point continnally advances toward the blue; in other words, that the sun must
really be of a bluish tint, so that we have never seen it as it is, and what we are accustome<l to
speak of as white light and "the snm of all radiations" is merely that remainder of rays, whether
of "light" or "he. it." which has filtered down to ns. Our view of the isolar light and heat, and of
their ellect on (iiir atiiiiisplicre must be mcidified if such results are true, and it would be most
desirable to jnove their truth by some independent iniide of observation, since we have nearly
exhausted the capacity of our preseiit means of research.
There does remain an entirely difl'erent method of observation, but one presenting peculiar
ditlieiillies. It is to ascend a very high miiniitaiii, and toc(ini]iare iibserx ations made at its summit
with olhers carried on at its base, so that we can licit only esfimate, but directly measure, the
absiirptioiis which the rays have actually iindergoue. The preiiaratiinis Ibf this form the subject
of the next eha|iter.
(jiiAP'i'Ki; II
.lOUKNKV TO MOTNT WUITNKV, issi.
Toward the (.•Nise ol' ISSll it liad alrcadv licci.ine clcai tliat tlir ,L;aiii in our I^ikiw U-(l,;;i- li.v
IcliiMtiiij; the olrscivatlulis then in i)ii..i;ie,-.s a( the Alleglieiiv (Jlisel \ atc.n , al thi- liase and al the
.smiinnt of a hit'ty niouutain, would JaslilX the lalior and expen.se ot suc'h an nmhi lakinu. There
wordd have been little |);obability. however, olsiieh a idaii being earried out by the Observatory,
were it nut for the generosity of a citizen of l'ittsl>urg, who plaeed at its disijosal the eoiisidera-
ble means demanded for the outtit ol' an i-\|ieditioii fur this purpose.
By his own wish his name is not mentioned in this eoniieetion, but it is [iroper to aeknow ledge
here, and llrst of all, the timely and indispensable aid whieh made the project ii reality.
The expedition was, as at fir.st designed, to be made wholly on the accinint of the Allegheny
Observatory, whose trustees autlHJrizcd me to use any of its api>aiatns Ibr the imrpose. it being
understood that the special exiiendilnres involved would be met from the source menticuii'd.
Upon the objects of the expedition and their bearings upon meteorology lieeomiug known to
the Chief Signal Ollicer of the United States Army, he coii.seuted to give it the advantages of his
otlieial direction and the aid of Signal Service observers, and upon the reasons which made the
choice of its objective point in a remote part of tin' I nited States territoiy being apiiroved by him,
he contributed further material aid in traiis|)oi tation. The considerable expenses ol rcdn<'tii.in
have been chiefly met from the private source just mentioned.
The principal conditions desiral)le in the mountain cho.sen should iie —
(1) Clear air.
(2) Great altitude.
(.'5) Very abrupt rise, .so that two i.-ontiguons stations may be found with ver.\ diirerenl alti
tudes.
(4) Sontliern latitude,
(."i) A dry climate.
(1) The hrst and lifth conditions are almost inseparable. Such summits as Tike's real;, and
the neighboring summits in tlie KocUies, are rarely free fr<im mist and cloud duiing the sunnuer,
anil both from the uatnre of the oliscrvations and the fact that ihe stay must be- brief, an almost
absolutely pure and cloudless sky is iiiilis]icusable.
(2) We ought if possible to Icaxc at least a third ot the atniosijhere below us, which im|)lies a
height of at least li,000 feet.
(.■;) An elevated plateau is unsidtable, i\,i it is almost indispensable to ha\e a relatively low
station (|uite near the high one. and. il jjossible, in sight from it.
(4) We must, other things being equal, luefer a southern latituile which will enable us to view
the sun nearly in the zenith. xVs no point east of the Koeky Jlouutains unites these reipiisites,
inquiries were made at all .sources, particularly of ojliccrs in various dc[iartmcuts of the Covern-
iiielit familiar with the Wi'stcrn Territories. I ,iin specially indebted to .Alaj. .1. W. I'ouell. the
present head of the United States (ieological Survey, and to the late Su]ierinlendent ol' the Coast
Surve,\, to Capt. C. E. Dutton, of the L^uited States Aimy, and to Mr. Clarence King (late in
36 RESEARC;ilKS ( »N SOLAK HEAT.
cliinuc of tlie Gciilo^ical SiiiV(,'v), for vahuilile iiirnniiatiuii. Aiiicmu tlie poiiits caivl'iilly coii.siil-
ITCcI wi'ic —
T,.iiii;ilihlr, LmIiImiIv
M I Sr\,„ Ill-- -15' -.yy 50'
S:ili 11. iii;i,lilli. 117 34'^ 05'
I'iii,- \:inr.v Jlniinlaiiis 111! .15' »-" 25'
'r..y:ilH' KaiiKi' UT' 05' :i!l yo'
liiiMii's Uea.l n-> 45' 1)7 20'
sites IVdiii 11.(10(1 to iL'.dliii tret ill beigUt, each of wliicli had its .several advautage.s, luit none of
wiiieji met all the eonilit ions. Finally, u|ion tlie ailvice <if Mr. Clarence King, and witli llie concnr-
reiitly fa\di'alile opinion of olliceis of the Coast iSiiivey anil others familiar with that region, !\I<iiint
AVhitney, in the Hierra Nevada Range of Southern California — aiiproxiniate longitude, ll.S'3 30'
(7 h. .")t m.); latitiiile, .'i(! ' ;!.">' — was found to lie, on the whole, most desirable. Its height was
known to lie lic>tu<'en 14,0(10 and l,"i,000 feet. Its eastern .slope.s are , so preciintoiis that two stations
can lie round within IL! miles, visilile froni each other, and whose difl'erence of elevation is 1 1,000
feet, and it rises from and o\eilooks one of the most desert region.sof the continent, while it.s sninmit
is almost perpetually clear during June. .Inly, August, and September. It is, it is true, far from
any railroad, in a wild region, and it had been ascended so rarely, and with .such difticulty, that it
was not certain that heavy instruments could be transported to the extreme summit. As there
were neigliboring mountains both in the Sierra Xevadas and Panamint Ranges, offering not greatly
inferior aihantnges, to fall back on, and as if was certain that a veiy considerable altitude, at any
rate, ought to be reached on \\'hitiK'y, in spite of the imperfect ncss of our knowledge of the extreme
siinimit, the site was submitted to the Chief Signal (Jthcer and approved by him. Capt. O. E.
Michaelis, of the Ordnance, temporarily on Signal Service duty, was ordered to establish a Signal
Scrxice station there, and Sergeants Dobbins and Xaury, observers of the Service, were detailed
to Join the expe<litiou in San Francisco.
It was most desirable that we should reach the scene of operations so as to commence our
observations in July, but delays occurred, in sjiilc of our wishes, which, as it will be seen, liiislrated
this iini|i(ise. The liisl |iiirtioii of the party, consisting of Captaiu Michaelis, Messrs. J. !■;. Kei^lcr,
of the Allegheuy Uliseivatory, \V. ( '. Day, of the Johns Hopkins University, aud the writer, left
Allegheny, I'a., on tlie Till of July, is.si. Tlie iiistrinnents, weighing in their outer cases about
"1,000 |ioniiils, were to ace l>:iii.\ us all tlie wa\ : and 1 have to express the very great obligation
of I he whole expedition to. Mr. Frank Tlioiiison. vice picsidcnt of the Fenn.syhaniaRailroad.by whose
kindness tiaiis]Hii tatioii was furnished toClneayo for a jirivate car. which was oocuiiied by ns,witli
our instruments, and which, through his introduction to jMessrs. S. 11. U. Clark, general manager
of the Uniou Pacific Railroad, Omaha, and A. N. Towne, general luauager of the Central Pacific
Railroad, San Francisco, was, by the courtesy of these gentlemen, continued in our use till we
reachi'd the Iilyo Desert.
we reached San Francise the L'l'd. It was considered advisable, in the possible. tiiigeiic.\
of our being forced to choose our station in some point in the ilesert legion east of the Sierra
Ne\ ada Uaiige, that an escort should ac'company us, and through this need an unforeseen delay of
nine days occurred in San Francisco, a time wliich was shortened to us by the courtes\ of (ieiieral
McDowell, I'ommanding the department, and of Prof. George Da\ idsoii, of the Coast Snr\i'y, but
wliii'h we could not but regret. On the 22d w<' left on the Southern Pacific road, the parly haxiiig
been joined by Mr. ( ieoii;e F. I )a\idson, who accomiianicd it as a volnnteer, by Sergeants 1 )obbins
anil Naiiiy of the Signal Service, by .Mr. Frost, a cariieuter, engaged in Sau Francisco toai'company
us, and by the escort of ( 'oipoial Laiiouettc. olCoiiii.any IJ, Eighth Fufantry, and five enlisted men,
who joined us at lienicia 1 liiiracks. \\"e reached Calieiite, where the writer, Mr. Keelcr, ami a
part (it the escort lelt the railroad, while Captain .Michaelis and the rest of the party iirocecdcd in
the same train to .Moja\e, about 40 miles farther, where the iustrniueiits anil ijrovisions were to
be taken across the desert by wagons. l!y riding day and night, 1 reached our station at the
moiiiilain biot (Lone Fine) on the evening of the L'tth. The road lay along the Iii.mi \'alley, a
shaileless, waterless desert, on the west side ol' « liicli (on our left) the Sierra Xe\ ailas rose in con-
stantly higher sum in its as we went northward, till we found oiuselveslookiiigiip through the desert air.
JOlTRyEV TO .AKirXT WIHTNKV.
37
wlicic tlir sliiidc tciiiiiiM-atiirc was uxcr KMI' F.. to the patrlit's of snow (in tlicir siiiiiiiii(s. wliicli tcild
(il the real altitiiilr of the almost iinkiLnuii up|M'i' ici; s tii wliicli uc were liiially liouiid. I'lir
iiiitaius on the li.ulit. at lirst low and distant, drew closer and .yiew hij;licr, niaUiuii I In- \al!i\
rliaiai'tcr nioii' and nioiv distinct as it nanoWiMl, whik' the desert over whieh we traxilrd eon
stantlv ascended, without losinj; its as|iect ol' a nariow extended plain, shnt in closer li\ niounlains
as we went northward. Near the njiper cxtreniily ol' Owen's Lake (a small dead sea), we :.;(il oni'
liist siijht ol' Whitney, and in a I'ew miles more reached the little handet of Lone I'inc, Imill on a
snjall patch of yrecn, due to the istnrc of ,i snow fed .stream from the niounlains which Ihrcads
the valley, here about H miles « ide. l.cl w ecu ihc loot hills, and almost perfectly Hat. .\s we rode
in, we noticed cellars helonyin,i;- to Ikhiscs shaken down in the last eartlnpiakc, which destroyed a
larj;c part of tlie inhabitants of the little place. l'(n- we were now in Ilk' call lupia kc conulr.\.
The outline of Whitney and the nei,i;hUorinL; peaks seen from Lone I'nu' is \ i'i.\ cMiaordimii \ ,
Ihe serrated edj;e and tlie snow, justifyin.u the name of the "Sierra Xe\ada." 'J'lie air is so clear
Ouilin > of IVIt. ■Whitney Railg-e,— A.^ S33n trom Lone Pine.
that the appearance of nearness is most dcUnsive. The mountains look like lai^e meks close by,
coxered with moss, on which ]ialclies of white arc .ulisteuin.i;, but only (Ui lookiiii; thioiij^h the
telesi-ope, which resolves the apparent niipss into lai^c forests ot uieat tiees, and the white [lalclii's
into snow lields, can we realize the actual distance to the summits, which is about iL.' miles, the
interval,— "the foot-bilks"— beinn' an elevateil desert taldc hind, broken into lo« liills. cMciidin.u
back with a gradual rise to rather more than half this distance, where the eastern wall bci^ins and
attains most of its tinal altitude of over M.(KI0 feet in about 5 miles, reekoncil on the level. 1 i^ivi-
in the form of a diary the events of each following; working day, as tar as the statement seems
necessary.
./»/_(/ L'.I^A.— With the aid of Mr. W. L. llnuter, of Lone Piue. to whom we were indebted for this
and other kindnesses, we made a pn-limiuary survey of the place and selccteil a siti' for our cam|i
on the grounds of Mr. Be.unle. We passed in our reconnaissanees a j;ravc where .-,c\ cutceii
l)ersons, victims of the earthquake, are buried together. They were killcil by the falling in on
tliem of their " adobe"' hou.ses, and we felt our tents a safer shelter. Sergeants Dobbins and
N'aiiry arrived.
'1^'ith. — Set iqi piers for the ex]ieeteil instrnmeiits.
Tith. — Cajitain Miehaelis arrived. .Mr. W. Crapo, of Cerro Gordo, was engaged as guide, and
arrangements were made for first miiletrains.
li.s^//.— Lrivatc Naiiry, two soldiers of the escort, and the carpenter were sent ii|i the moiinfain
with the guide, muleteers, and a small miilc train, carrying tent. pro\ isimis, and hcliol ropes.
Their iiistnictions were to establish a caiii]i at the highest point, within reach of u 1 and Hater
(a point on the other side of the ridge, to which .Mr. Crapo undertook to guide th.nii. Alter this
the peak of Whitney was to be ascendcil from their camp, and hidiotropc signals exchanged with
ouroun statnni. fniiii which, as I lia\c said, the peak was \isiblc.
l''roiii the L'.Sth to the 1st was jiasscd in enforced idleness, waiting for the iiist riiiiieiits which
were still on their slow w ay aiaoss the desert. Clouds hung ovei thi' mountains i for the onlv
tiine during our wiiole stay), but no rain fell. One or two Hashes came one moining ticnn the peak
of Whitney, showing that it had been reached by tlie iiarty witli the heliotroiies. but no answer
38 llESEAECnES ON SOLAlt HEAT.
to our sigiuils was I'cturiiL'd. It may here be stated that owiug to the difficulties of iiiakiiii;' any
stay upon the peak witlmut fire or shelter (which we had ourselves to experieuce later), and to the
lack <it men ex[)erieneed in heliotrope signaling, communicatiou with the camp ou the other side
of the ridge was kept up only by special 7uessengcr; although the conditions for heliotrope
signaling between Lone I'ine and the peak (were a sat ion once established there) are excellent,
the two i)laces being fall in view of each other, with almost constant sunshine.
'2'JlJi. — Tlie fciiciug in of a piece of ground in the village, CO by 150 feet, was conipletrd.
Aiijjunt 1. — The wagons arrived at noon. The instruments were at once unpacked, when it
was found that the desert dust had penetrated every crevice aud settled ou every instrument, how-
ever carefully lioxed. They were cleaned aud obser\'ations begnu immediately.
To Mr. W. O. Day was assigned the large actiuometer.
To Mr. J. E. Keeler the spectro-bolometer.
To Mr. (i. F. Davidson the comparator aud the preliminary observations for time and latitude.*
Sergeant Dobl)ins was directed to make observations with the pyrlielionu/tcr and (subse-
quently) with the snudl actiuometer, and to take tlie readings of the liaromctei' and wet aud dry
bulb thermometers usual in the Signal Service.
The writer observed with each of these instruments ami observers in turn, till it was certain
that each understood what was novel in his mn-k and had acquired fair exi)ertness at it, but his
chief time, whenever other duties admitted, was gi\ en, with the aid of Mr. Keeler, to the spectro
bolometer.
2/1. — A small tent was set up for this instrument and the reflecting galvauoiuetei', with a black
cloth inner lining. In form a dark room for the latter. The lirat was excessive without, and within
it rose to a point beyond linnum eudurauee, while the light proved not to have b<en sliiil out even
at the co.st of the cpiite intolerable heat. After a day's trial this plan was then abandoned.
3(1. — Set up a larger or '-hospital" tent (about 11 feet square) aud attem[ited, unsiiceessfally, to
construct a separate dark room within. In the adjacent hot box a thermometer iii air, but under
glass, rose to L'.'!.'!'^ F. At the same time packing for the mountain went on, and a mule train started
for Moiint Whitney this evening, carrying apparatus and quartermaster's stores. It was guided
by Mr. Ciapo, and accompanied by two soldiers of the escort.
-Uli. — Thi' dark cliaiiilier was, through Mr. Keeler's ingenuity, comjileted so as to get the light
excbiib-d, wilhonl a heal sueli as to make observation impossible.
[>tli. — Tlie systematic reading of the barometer and wet and dry bnlb tlierniometers commenced
to-day. Sergeant Doliliins was, however, directed by me to omit readings at those hours which
interfered with his observations with the pyrheliometer or actiuometer, it being impossible to spare
a second obsei'\er for these latter.
(itit. — Jlaiiy clouds over the valley (for the tirst time) aud a few drops of rain. The wind was
violent all day; the tent was shaken so as to make it doubtful whether it could stand, and all the
instruments in it were covered with sand and dust, while the lights for the galvanometer were
extiuguished by the penetrating gusts so as to make its use inqiossible.
7th {SundKy). — Still cloudy.
Sth. — A slight earthquake shock at night. Commenced bolometer observations.
nth. — After two days' struggle with difficulties incident to the novel conditions, the first com-
plete series of inorning, noon, and evening bolometer observations was obtained. The very consid-
erable changes of temperature in the tent thnaigh the day caused a troublesome drift of the gal-
vanometer needle, but otlu'rwise the result was satisfactiuy. On this as ou iirevions days the
other obser\ations were sueeessfully pursued in the jirescribed manuerand call for uo remark here.
Kaiiiig all the picviiius da.\ s hiring of mule iliixcis and animals and the arrangement for
llie tiansiioitalion of the somewhat elab(U'ate apparal iis, to the distaut summit, had been a constant
picoeeiqiatioii, for llie season was already far advanced, aud we had originally hojied to have com-
[ileted onr chief observations iu the valley and been at work by the first of August at the mountain
station, which rose above us iu constant view, apparently so near and really so distant. Every
* The ijlisurv.n.t.i<>n,s toi l:tl it mtf li:id uot Tjeen oommoncod wheu Mr. Davidsou left for tlie mouutain. We liud fioiii
the Ariiiy iiiaii, (Liciili-n:iiil Wli.clii's expoditiou), lonaitude, Limo riiic, im-' U:j' 47" ; hititudc, 30° :ili'.
JOUUNKV TO .MOUNT WHITNEY. 39
i-llort wu.s iiiadL' to luivo tlic iiacUiii.u dniii' so that the parts ofoa<'h iiistriiiiinit slionhl In- ki'lit to-
i;i'fl]er as iicail.v as ]Missilili'. anil In any case whcir thrsi- ni'ccssaiily .icciipird two oi nani' lioxcs,
thcv wi-ic |ilacc(l on tl)i' same iiinh'. « ilh sliict ordi'is ihat thi' airanycnirnl slionhl mil lic^ ilistnilicil
liv tlic ninl<'tccis in the asciait. It w as nrcc-ssar.\ , howvcr. to send olV srpai ate tiains. as fhi- nMil<-s
could l)e i;athci\Ml tor them, ami In-ncc the iiiidrtecrs could only lu- in pari o\ .■rlookcl.
Captain Mi(diac]is, witli Ml. Daviilson. Scr-caut Nanry. and two soldiers, left toila\ loilhc
-Mountain Camp with a train cari\ in;; |iai I of rhe intrnnnaits and (piartermaslei's sloics. inlendiuu
to make the ascent thron.^h Cottimw 1 Cihou. The muleteers lu'oniised Ihat thislrain si Id
reach the .M(Uintain Cainii on tlii> 1 Hh and lie back in Lone Tine liy llic ITlli. I reniaineil (hopin-
I imiilete the lower .station lioloim'ter oliservations) w itli Jlr. Keeler. .Mr. I lay, Sei-eaiit lloliliins.
Corporal Lnmiuettc, and I'l'ixate Kelly r<'maiiieil also in the camp.
i;;//,._My anxiety to know |iersoiially of the arrival of the instruments at the Mountain
Cam]! imliu-ed nu' to leave to (la.\. though another day's oliservatious was ilesiralile. This I left
to .Mr. ICeeler, with <lireetions to pack as soon as it was umde and to Ibllow with .Mr. Day on the
ITtli, or a.s soon as the ex]ieeted mule train had retuiiie(l. I left myself in the afternoon with Mi.
Crapo, reaehiiio- "Kidgei-s," an ele\ated ranch in the foot-hills, about eiylit in the c\eiiiiii:.
]4^;,._Aftcr a nij;lit pas.sed in the opiMi air, I started .southward with llie ;;nide ■ obiect
being- to reach a cafion which would lead iis o\er " the Great Divide" ami thence to the mountain
camp already e.stabli.shed at the western ba.se of Whitney Peak (on tl Iher si.le ol' the ran-e as
seen from Lone I'ine) where it was exiicclcd Ihat tlu' instruiueiits already tbrwarded iiy Ihe other
route wdiild be ready lor work.
Our cour.se tirst lay across a .sloping tableland already elevate<l .SdO or I, (Mill feet above tlie
valley, dotteil with sage-brush, but still below the lowest edge of tlie timber-belt. After three
hours" riding the trail began to ascend rapidly and the air to giow cooler, while we jiasscd oeca
sional dark stunted pines, which rose li the white grav(d. like ]iosts iilanted in il, lliere lieing
no grass under them anywhere, nor any verdure, even when we had fairly ciileicd Ihe tiiiilier.
The large dark trunks were so far apait. and formed such a contrast with the white ground
beneath them, that the eye followed the color of the latter through the distant linvsls. uhicli
looked as though a fire had passed through them, and presented a most de.solate as|iect fi the
absence of moisture and consequent verdure. The frail made sliar[i turns, plunged down into
ravines into which descent on the saddle seemeil at first impossible: and wdrmeil ils way liclwceii
bowlders, and cliinbed over rocks and fallen liinlu-r. in such a manner as to given forniidalile
iiiipression of the dangers our apparatus must have iniairred in the a.scent, though it had taken a
somewhat easier and longer route than oiiis. All trace of the trail itself finally I'cascd in the bed
of a water-course, seemingly barred to all passage by large bowlders and trees which had liimMcd
from above into the channel, up which, however, with the occasional aid of the a\. wi- slowly
forced a road, reaching at nightfall a small meadow whose altitude must have been s.iioii or '.i.odii
feet, wateie<l by the stream whose beil we had been following. Ihe femiieralnre had now fallen
greatly, and ice formed thickly dniiiig the night, which we ]iasseil like the preceding one. under
an nnid<iuded sky, whose stars seemed ]ier<'i'plilily brighter than we see them in the clearest night
from lower stations.
\'itli. — In the morning there could be no (piestii f the change in the blue of the heavens,
which was darker and more violetcolorecl than that at Lone I'ine: itsidf ]iurer llinu thai seen
cxcciif at very lare intervals at Allegheny. We hail now parted from any signs ol a tiail, and a
long and tedious a.scent was followed by a sharp descent, during which we lost nearly all Ihe
elevation gained since sunrise, and this brought us into " Diaz meadows." up tiom w liicli, alter
another forniidalile climb, we got over the " Divide." Then came a descent of aboni l'.oiki feel,
and then another iiiouiitain to lie climbed whose slojie. was so stee|i that occasionally Ihe insecurely
poised bowlders which covered it, as we step]ied lioiii one to anotlier. rolled lioiii under our feet,
and went leaping downward. The lost labor consumed in this incessant alternalion of ascent and
descent is enormous, and (as I found latcri, by the coiistruction of a miile-iiath along anolher and
direct route (which we took in finally desceiiding again to Lone I'ine), may be almost wholly
avoided.
40 RBSEARCIIES ON SOLAR HEAT.
The tlistrtiit .sct'iiciy had lieen much more monotonous tbau might Lave been expected from
tliis areount uf the iciiilc, Imt now one more ileseeut brought us into a great canon running west-
waril. with a iiiaiiniliciait \ jew ot the vast amphitheater of i)recipiees, behind Shce]i Mountain.
I noticed now. tlial, though long taniied by tlie hot sun of the vallej' before starting, tlie sliin
ol both njy face and hands was beginning for the first time to burn badly; a striking cttcet in this
cold air, and which ccudd not be attrilmtcMl, as it has be<'n in the case of some Alpine and other
climbers, to rclleclion from snow, for we had, as yet, seen none but at a distance.
latli. — After another night like the last, we clindjed, with .some hoars' work, several thousand
feet up the canon sides over the roughest country we had found yet. From tlii.s, as from other
eminences, we could see tlie smoke of forest fires at one or two very distant ]ioints, fires which the
guide .said would grow more numerous later iu the season; a sight which ad<led to my anxiety to
get to the monntaiii worli. We now came down into "Whitney Cauou by a descent which was actu-
ally worse than anything that had preceded, but which finally brought us in view of Whitney Peak,
for the first time .since leaving Lone Pine. It was still high above us, but looking most delusively
near. It was ditlicult. indeed, even wiih all one's experience of the decei)tion as to distances com-
mon here, to believe llial tlu' peak was even a mile away, or that the little patch of white on its
flank was more than a lew yards in diameter. The summit was really, however, six or eight hours
further, aud tlic w liite patch was a snow field w liich fed the considerable mountain toneiit now fall-
ing past us.
The rest was easy. We ascended liy the stream past little meadows and small lakes filled
with the clearest ice-cold water.
A little further we found the woods burning over many acres, the fire having been apparently
wantonly set by sonu' sheep-herders, who are the great destroyers of the tindier in this njiper region
where the few spots of herbage are found. Sluntly, we finally rose above the entire tindier belt,
and at five o'clock we ri'ached earn]) at an elevation of about li'.OdO feet, for which an excellent .site
had been chosen by Mr. ("rapo. It was bcautilully jilaced on a nearly circular and well-watered
meadow about I'dO yards iu diameter, while an amphitheater of very precipitous cliffs from 1,000 to
1,000 feet, fornnng the base and flank of Whitney Peak, rose immediately from its northern and
eastern .sides aud was continued by others more remote on tlie south,* the only distant view from
the camp being toward the \v<'st through the long valley along which we had ascended, and look-
ing back through wlii( h we saw a horizon of mountain .sumndts. Here I learned the dismal news,
that the mule train, which was to have delivered the freight here on the 14th, and which we had
been looking to meet ou its return,'had not yet arrived at the camp, and that only a single instru-
ment (an aetinomelei) had arrived in condition for work, of those sent by the ]ir('ceding train; not
that the others were biokcn. but that the niulcdrivcrs had left the boxes and par<'els along the
route, .so that nothing was comjdete.
Captain IMiehaelis had, 1 learned, ascended tin- peak that day with Sergeant Nanry, and lioth
returned soon after I entered camp. Captain Michaelis reported the ascent very trying. The ser-
geant, indeed, was sick iu eonsecpu^nce.
I pass over days spent iu anxious waiting. We weri- cat off completely from communication
with Lone Pine except by special messenger, liy scaling the mountain wall on the east of us, it is
possible, it seems, to descend ou foot through Lone I'inc (arion, direct to Lone Pine it.self (as we
proved by our own subsequoit experience), iu aday. .\n Indian guide, sent by this nearly unknown
route to Lone Pine, ri'lurne<l the next day, bringing letters, but no news of the mule train, which
was as completely lost lo the knowledge of those to whom it was coming, as a shi|i at sea cotdil be.
Most of us, while waiting for the instruments, had occasion to note, without their help, that
the solar radiation was wholly altered in character from that in the valley. I, for instance, have
albidcil already to thi' fact that my hands and face were considerably more burned on the way nji,
through the cool air, than in the hotter descit lichiw. ()n the day following my ariival in cam]),
in\ hands jucscntcil the appearance of as severe burns as though they had been held in an actual
lire, and my lace was hardly recognizable. Others suffered less, but all of us, with skins thor-
oughly fanned an<l indurated by weeks iu the desert, were more or less burned.
* See view in I'l.Mil Isihc-.t ,.] Ilic Moniit;iiii V:m]> nt I In- Utsv ,.f AMiitm-y roal<. Loiij^iliul.' ..f.':nn|i, rn.ni Army
m.ap, 118" 18' ;ia" : :i|.|.idxiiiKnr iMlitmlr l.y scxl.-iiil (Havi.lsnn), :'.i; :i.|'.
.TOIJL'NKY TO MOI'NT WIIITXEY, 41
lOf/i.— The sky to-day, as always, is of tlic most ilccp violt-f liliir. siicli as «!■ never, under an\
eirc.uinstaiiees, see near the sea lexel. It is alisululi'lx clcmdles^. and there is onlx a slii;hl iir;nii;e
tint about the horizon at sunset. C'arryinj; a sereen m the hand between the eye and tin' sun. till
thee,\eis shaded from the direct rays, it ean t'ollow this blue up to the edye of the solar disk
withiait lindmy in it any loss of this deeji \i(]let (U- any jnilkiness as it aiiiiroaehes the lindi. It is
an irie(JUiliarably beautiful sky for the observer's iiurposes. such as I have not seen eiiualed in llie
Koehy Mountains, iu Eyyid, or on .Mount Etna. It had been part of ujy olijeet to uKike an elforl
to .see the solar corona by directly euttinj; olf the sun's light by a very distant elilf, thou.uli I was
aware that Bond had tried a similar experiment inisucecssfully in the Alps, and though I had
myself been foded iu a similar attempt on Mount Etna. On the south of the camii was a range of
clitls, rnuniug nearly east and west, and whose almost perpendicular wall rose from l,bl)(i In l.L'OO
feet. They appeared to be within a pistol shot of the camp. 1 left it for them at aliout ele\ en o'cloeh,
but reached them at nearly half past twelve, after an hour and a half of hard s<Tanililiug. 1 Ibund
that I could choose a position on the math of the clilt, along whose edge the sun was mci\ing nearly
hiuizoutally; so that the shadow was ti.xed as regards the observer, and so sharji tliat, tluaigh I
nnist have been over oue-quarter of a mile from the portion of the clitf easting it, I could, without
moving from my place, and by only a slight motion of the head, put the eye in or out of view of
the sun's north limb. The rocks were, iu these eircumstauces, liued with a brilliant siUcr edge.
due to diflraction. This I had anticipated, but now I saw what could not be seen by screening
the sun with a near object, that the sky really did not uniintain the same violet blue up to the siiu,
but that a fiue coma was seen about it of about 4^ diameter, nearly uniform, though it was seusibl.v
brighter through the diameter of 1.}". Uiinn bringing to Ijear upon it an excellent portiible
telescope, magnifying about thirty times. I Ibund it was composed of motes in the sunbeam,
between the diffracting edge and the observer's eye. This result, if disappointing, is al.so inter-
esting in another point of view, as showing that the dust-sliell, which, as I have elsewhere statecl,
encircles our planet, exists at an altitude of at least l.'.l,Ollb feet, and under favorable eonditions
for the ])urity of the atmosphere. The result is not without importance in its bearing u]io]i our
conclusions as to atmospheric absorption.'
'2Wli. — A portion of the mule train came iu about noon.
21.VA. — Captain Michaelis started at 5 a. m. for Lone Pine, to engage more mules and to arrange
the trains. Actiiiometer readings and routine observations with the tlieriiionieter were all that
we e(Hild do as yet.
l'L'(/. — I had been ill since my arrival in eain]!, and on this day first a.seeiided the mountain. 1
started at 'J a. ui., and, being .somewhat weak, occupied over four hours in the a.seent, while it
might be made by an active person in le.ss than three hours, though not without dillieulty, the
actual height above the camp being something like .'3.0(10 feet, while the dillereiice between
exertion at this altitude and at the sea level is exlreme. The Peak would be wholly inaccessible
(from the precipices on its side, which rise in steps of several hundred feet) were it not that the
earthquakes have rent these into lissnres, and that thriuigh these narrow cracks bowlders and
rotdis from above have poured down in past times, in a rocky river, forming a ^Uviihiir," as it is
called in the Al|)s, the rocks being still ])oi.sed so that the surface oues ean easily be started
downward. Through the nearest of these couloirs, called by the guide "The Devil's Ladder,"
I commenced the ascent, the stones occasionally rolling away aud bounding down hundreds of
feet below me. After oue-half or three-quarters of mi Inmr iu this interminable <'(ailoir, I got (Ui
to the mountaiu slope, still extremely steep, the surface presenting au appearance as tluMigh
stones, from the size of a foot-ball to that of a grand iiiauo, had been hailed down on it and
covered it to an unknown depth. xVfter nearly three hours' time I came to the snow-tield, which
I have mentioned as having been seen from a distance. It was about one-quarter id' a mile in
length. .\t the summit were s c Indian and Mexii'an lalxuers, who hail been brought ii]i to
imiirovc the jiath up the ■•Devil's Ladder." lying and smoking in the sun. The view Irom the
summit was of a horizon of tumbled mountains on the north, west, aud south, not continuously
■ I'rof. Clarence Kiuj;, late li. :i.l nl the (1. ,.lc.,L;ical .Survey, iv liuje tamiliaritv witli tbe.^^e reeiuiis ail, I ulii.M'
eimilietcuce a.s a ,ncolu-i.st are well kllcXMl. inlmillMlie licit lie believ.- tins , Ins.! aliove tlle Siena ^•evalla^ lla^ 1.. en
iKil-iie across tlie I'acitic and uwes its ,,ii-iii tu llie ■ I...ess" ..f China,
lw'53.5— So. XV r,
42 KESEAECHES ON SOLAR HEAT.
wliilc as ill llic Alps, fov tlioimli ;it a more tbaii Aliiiiiii lieigbt, I saw only scattereil siiowticldis here
and llinc. I'lic nir was cold, but not \ery cliill.v, and the sky of a deeper violet overhead (liaii in
tlic caiiiiJ hcldw. On tlie east side, tlie inonntains descended in ii series of preeipiees between
;_;,(l(l(l and J,(i("l Icet to a little lake snrronnded liy a snow-liebl. The eye could follow the course
of the sticani running fioin it a little way dow n a canon, with tremendous vertical walls, which
lead in the diiection of Lone Pine. Lone Pine itself, was descried as a little spot of green on the
brown tioor of the desert. Opposite, on the other side of the Liyo Valley, was a range of
mountains nearly 10,000 feet in height, and beyond, to the .south, the Pananiiut and other ranges.
Betw een us and them was a reddish sea of desert dust, 4,000 or .5,000 feet above the valley floor,
and almost covering the lower summits of the mountains. Through this dust ocean, we at Lone
Pine must have been observing; yet the sky even there is, as I liave said, of unaccustomed purity,
and ]irobably \ve observe under still worse comlitions haliitually when at borne.
The to]) of WIiit7iey is an area of [lerhaps three to four acres, nearly level, or with a slight
downwaid slope toward the west. Stone for the erection of permanent buildings is here in unlirn
ited quantity. W'c look immediately down on one of the driest regions of the globe, from an
altitude of nearly three miles, in a sky of ex(|nisite purity, and this station, once reached, is ever,\ -
thing that 1 <'ould have lioiied to liiid it, and more; but existence is only jjos.sible on the summit
with permanent shelter, for though at the moment I viewed it it was calm, yet the wind and cold
would be fatal to life at other times, without house and tire. The nearest wood is over 3,000 feet
below it. It became evident to me that we must forego, at this late season, further hope of making
regular obscrvaticms on tlie Peak, and confine ourselves to those at Mountain Camp, for it was
e\ idcnt that w ithoiit mules to carry up wood and shelter no continued observations can be possible.
In descending I noticed here and there parts of great tree-trunks, some 8 or 10 feet long, e.vidently
\ciy old, I.\ iiig on the nakcil bowlders, without the slightest trace of vegetation withiu a mile or
any sign to show how they came there. I afterward found these isolated truuks eksewhere, and
it seems clear that they are relics of a remote day, when the forest grew 2,WW feet liigher than it
does at present, the pitch, saturating the wood, and the excessive dryness of the region, having
preserved tluni here for an almost indetinite i)eriod. They are a most striking and curious evi-
dence of a condition of things which once existed, aud which exists no longer, the change being
evidently due to a coires|i(Miding climatic alteration. W'liat lias caused this change it does not,
perhaps, lie within my pni\ ince to imiuire, but I caniiMl doubt that the changes in those conditions
of the atinos|ilieie's transmissibility for heat, whicJi we have climbed into this altitude to study,
are connected with the answer to the riddle. I staid but a few minutes at the summit, took a
tinal look at the snow-lields about us, and down into the torrid regions of the desert, far below ;
and llu'ii descended to the camp, wliicli 1 reached at about four in the afternoon.
-'illi. — ('ajitain Michaclis, Jlcssrs. Kceler and Day, accompanied by a train of twenty mules,
arrived bringing the long looked-for instruments. By evening the siderostat was mounted.
Through the kind assistance of Captain .'Michaclis the hospital tent "as set up aud two piers com-
pleted by the end of the next day.
Mr. Davidson left us on the 27th. Sergeant Nanry was instructed in the use of the Ivegnault
hygrometer, which was placed in his cliarge, together with the pyrheiiometer. A considerable
jiortion of our apiiaiatus had been constriU'te<l with a s|iecial \ icw of observing the solar corona
here, if]iossil)lc, without an ccli|jsc. W'c were engaged for tlic following three days with this, and
Just as a jMissibility ot success seemed near, a most disheartening ai'cident robbed ns of further
hope in this direction. As the attianiit was unsnccessl'iil, I will not enlarge uiion it, nor describe
the intended means.
W'e turned to the spectro-bolometer, which, however, in sjiite of all (Uir exertions, was not
got to work until the .■ilst.
On the lid of September Captain Michaclis went up the mountain, with Sergeant Nanry, and
Coles and Johirson as guides, canying a tent aud intending to stay three days for observations.
Early the next ni(U-ning, all the party made tlieir appearani-e in camp, rejiortiug that they had
jiasscd a sleeidess night, without shelter or warmth, the wind being so high that they could not
liitch ilic tent, while the cpiarter-cord of wood, carried up with great difficulty, had been all burned
in a \ain elfort to keep warm.
.TOUKNT'iY TO MOUNT WHITNEY. 43
Siptcmber 4.— Sky, fm- the liist time siiKiky, ;ipi)arciitly fniiii forest liics. .Messrs. Kn-lcr ;iiiil
.Idliiisnii a.scemled tlie iiumiitMiii with the haioiiieter.
r,tl,. — I ascemleil the peak a secDiicl time. Keeler and .Idlinsmi liail siie(<MMleil in passing; a
nifflit there, though not a pleasant one, and had secnred valual.le oliser\ at i(nis, lli(in,;;h it was
evidi'nt that the tri-hourly series, lieini;- <'ondneted at Lone I'ine, would not lia\c a eoiinlerpait on
the sunnnit. The afternoon was elear, thonfjh forest lires were iinnierons alioni the hoiizon.
Ijookint;- nortli, tlie great masses (j| Mount Tyiulall and ,M(uint \Villiams(ui wcic piounuenl objei'ls.
Sheep Mountain (whieli has somelinies lieen called :\lounl Whitney) is t., Ilie south ol' us, and an
almost nnmherless multitude of maj<'slic, l)ul still nameless, summits tills llu' «eslei n hoi izon.
With a little Casella theodolite tlu' lolhiwiii- hearin-s w.ue takiui hy Mr. Iseehu close to the nule
pile of stone (the •• nuunimeul "l which is cm the cxtrcMue summit at the easleiumosi \cr,i;eol'
Whitney Peak.
The bearing of Williamson by e(un]iass, L'.'. f.' W., was made 0 o' by Iheodolite, and the
Ibllowing others taken by Mr. Keeler and the w ritcr:
■Williamsou " '«'
Tyndnll, eastern iicali ■'■■'1 ' ''
Tynilall, western pcik aill IC.
Kawkab, liiglicst or sontlieni \H-.ik -.'ti- It
Ocanclio Peak li>T >'■<
Point of Sheep Poek 1'.- "1
Telescope Pealc l-'- 1"
"The Monnment" (Wliitii. y I'.aki 'M »>'
(!//(. — A few cirrus clouds in the air, the first seen.
lilt. — Our bolometer measureuHUds had been made with the grating, and llu' glass and ipiaitz
prisms, and now Laving made the discovery of the great band "£i" in the extreme red speclrunj,
we commenced to explore that interestitig region with the rock salt prism also. It \\as thouuld
safe in this dry air to leave the rock salt prism on the apparatus over night lalhei llian disturb the
adjustnu-nt by putting it away. The night proved to be pbenomenally damp l(U that locality, and
the ]nisui was so injured tliat we could not do m\H-\i with it the ne-xt da.\ , a most unfortunale
accident, as it i)re veil ted exploration of regie uis in the possilily existent solar lieal spectrum, lieuuid
those Just discovered witli the ulass prism. The 5 iiicli eipiatorial, loaned us liy I'rofessoi I'icker-
ing of Harvard College Observatory, hail heeii installed largely through the aid of Mr. ('rajio, the
guide (who by profession is a surveyor), lint when we came to take it out from its boxes upon the
nxiuntain, for the lirst time, it was not possible to use it to advantage, owing to the fact thai none
ol' the eye-pieces fitted the provisi 1 tube (which had been maile to carry the spcclidsco]ie). Hy
holding the eye-pieces in the hand, we could at least determine what the (luality of the atmos|iliere
as shown by the easier usual star tests was, and the result was very satisfactory.
By the 8tli, forest fires had midtiplied in frequency, and the air was e\ idently not so |uire as a
week ago. We bad, by hard struggling, and in sjiite of adverse circumstances, secured, however,
what .seemed most essential to our puriiose, and though we had not done all we liad ho]icd to do,
we liad done more than at one time .seemed possible. In view of the fact that the sky, tor our juir-
pose, had commenced to deteriorate, I decided to descend. We worked till the afternoon of Sep
temberlHli and then by hard labor at night, and all the next da.\' into the evening, uc got our iuslrii
ments pae.ked. Upon Sunday, Cai)tain Michaelis, Mr. Keeler, Mr. Day, and iiiysi'lf, « itli .lohiison
as guide, started early in the morning on foot, to reach Lone Pine by the diicct dcsiM'iil do\\ n Lone
Pine Canon — an almost unknown route. This day will alwa.vs live in my memoir , tliouj.;li 1 cannot
describe the grandeur of the sceuery uor its extraordinary character, here. .Much ol the roiilc, we
found, could only be followed by frc<inent actual climbing ibiw nward. We tiist aseemlcd lor mcr
two hours, past snow-clitt's and along the frozen lakes in the northern shadow of Whit ue.\ Leak,
and theu passing through a didile in the rocks, .so narrow that only one person could tra\ crse it at
a time, we su<hlenly found our.selves on the other side of the ridge, which had hidden I lie easleru
vii'w from us for weeks — so sucbleidy that we wi-re startled as we looked do« ii as tliroii;;li a'win-
dow I'rom our wintry Iieight, to the desert, ami the bright giceu of its oases far below, iii a climate
where it was still summer. We <'linibed ilow n, until alter many thiuisand feet, we reached the tiist
44 RBSBAKOIIES ON SOLAK IIBAT.
of tlie little deeply bine lakes we had seen from the jieaU, and tlien, following the ice-stream which
flowed froui this, we jiassed tliroiinh a deep gorjje, to other lakes and snow-helds below, and so on
down all day, until we left snow behind us, and, till looking up the long distance through which
we had (■(ime, we conkl see only the top of Whitney at the end of the vista. In the latter part of
the clay we traveled for over two hours through burnt or burning forests, always keeping on or
near the lied of the stream, and amidst scenery which I remember nothing to equal.
( 'aptain Michaelis and Johnson had pressed on to Lone Pine, while I, with Messrs. Keeler and
Day, was walking more leisurely. As it grew ilark we reached the desert. Shortly after night,
^Ir. Day, who had sprained an ankle in the descent, found him.self unable to proceed further. The
m'ght air was that of the desert, cool but not chilly. We were still some hours from our destiim-
tion. (living our coats to Mr. Day, we left him tor a night in the ojicn air, which at this season
in\(il\cd no special liardshiii, and pusljcd on to Lone I'ine, promising to send out for him in the
morning. We reached there just at midnight, after seventeen hours of steady and violent exer-
tion, and ;\[r. Day, to our agreeable surprise, got in on his own feet before sunrise.
There is little to add. AVe iiacked the remaiinng instruments at Lone Pine and made our way
back across the desert; the (uigiiial party leaving San Francisco on the 'S2(\ of September and arriv
ing in Pittsburg on the L'Stli.
I hope I have unide iilaiu my nwn belief that Mount Whitney is au excellent station for the
piiriiiise for which it was cIk.iscii. The great drawback in onr ca.se was the inability to remain
at tlie very summit, for to do tliis requires a iiermanent shelter, but a railroad will shortly run
through Inyo Valley, and irom this, by the aid of an easily constructed mule-])ath, the ascent of
the very highest peak can be made in a day, while the telegiaph will put it in direct communica-
tion with AVashiugton. I do not tliink tlie Waliaii ( iovernment, in its ob.servatory on Etna, the
French, in that of the I'liy de Dome, iir any other iiatiiui at any other occupied station, has a finer
site for such a imrpiise than the United States jkisscss in Whitney and its neighboring peaks, and
it is must canicslly to be hiipcil lliat sometliing iiioic llian a mere ordinary meteorological station
will be liiially ercM-tcil heiv, and that the almost iiMc(|ii;ded advantages of this site will be developed
by llii- ('.oNcniiiiciit.
CllAl'TKli 111
ACTlNOMKTltY.
ITISTdKICAI. IXTl;(JllI TTKlX.
1 liavc alivady ifinailiccl tliat. while tli<' ilcti-niiinatioii of the aniiiiiiit cil' lical lla-siiii scikIs
the cailli is (•(|ually iiiiiMiitaiit to Astic iiilcal I'liy.sics ami to :Mct(Mii(iI(n;\ , tin' prolili-m is one
whose cxart solution is not, at ini'sciit, in om- iiower. Fifty years aL;o. Ileischel and roiiillet lie-
lieveil that they had tixed this value with luceisioii. J>ater oliservers ha\c sneecssively employed
im])rov('cl methods of olisorvation and inference, with a tendency in their ri'sulls to |]ii;lier and
hishiT values; yet we are apt to look on tin- latest found as tliou.i;h they were final ones, mil duly
notinj;, perhaps, the warninj; f;iven liy these constant and pio<;ressi\ c increnients. that no deter
niination that has ever been made is ]iiohalily to lie considered as more than an ap]iro\iiiiation lo
the truth, which may, if we Judye from the amount of these discrepancies, lie very dillereiit from
any.
The .solution of the prohleni invohes two chief dillicidties. the lirst formidalile, the second
perhaps insuiiierable.
"We have lirst to determine the amount of solai heat wliicli the earth actually receives at llie
seadevel by observing the rtmouiit which falls in a ui\-en time on a .uiven surface. This, at least,
miplit .seem to be easily a.sautainalile by direct ex|ieiiinent; but the (blliculties, even here, are so
ureat that the most competent ob.servers ditfcr liy nearly a third of the whole amount in i|iiestioii,
even as to what is directly measureil. The \;irintions in the heat-transmitting powerof oiii atinos-
])liere, even on clear days, are so snrprisint; and anomalous that we can hardly ailopt such assuin|)-
tions in reducing our ob.servations as niaki' the method of least S(|uares useful in other branches
of physics; for when it may happen (as in the case of Forbes, cited later) that a single day's ob-
servation so outweighs years of jucn ions woik that the.\ are to be set aside as of coinparalix ely no
value, our ordinary methods evidently lad us. No one. who has not liersmially carried on a lonj;
series of these observations, can have any idea of the dilliculty of the conditions or their variety .
We are as though at the bottom of a tnrliid and agitated sea, and trying thence to obtain an idea
of what goes on in an upper region of li^ht and calm. Were we iudeed at the bottom of sindi a
sea, it isolivious that if it grew iiionientai il,\ clear above us, we should get in that iiioiiient a higher
idea of the light (UitsiiU- than by aii.\ aiiioiiiit of previous direct observation, ami liirtliei. thai thus
knowing that the best moments foi obsci vatimi were coincident with the highest oliservcd values,
we should .justly deem these highest values oiii most trustworthy ones.
Here, then, is another respect in which uc iiiiist dejiarr widely from ordinaiy usage, which in
almost every other branch of physics ami astronomy obliges us t" consider the mean of a large
number of oliservations as the most probable \aliic. In solar ai-timimctiy, the mean of all mir
ob.servations is iicrrc really the most jirolialile. and the triU' \aliie is always, ami nccessaril.x , higher
than this mean. This statement may apiicar strange, evtai paradoxical, to the reader unfamiliar
with this particular class of observations. It is one of griMt imiKutanee, and whose meaning
slnudd lie fully understood. We infer from it that if it were po.ssible to make an actinomeler free
from iiurel.\ instrumental error, that the highest ob.servation of .solar heat by it would always In-
the most trustworthy, and would in tiu-t outweigh (in our imaginary easi') an unlimited number ol'
46 KESEAllOnES ON SOLAR HEAT.
lower ones. Coniioctefl with this same iippareiit iiaradox is the liict that when we begin to imjirove
(inr actual instrument, and to aHow for minnte errors in its registration of some iletiiiite anionnt of
radiant heat, we llnd tliat these ei'rors tend to lie all in one direction. In other w<irds, the eoirec-
(ions wliicli xve inticiilnce lor tliem will not liave, on the whole, the negative sign as often as the
positive, linl however fai' we may laish our investigations, the corrections tend to assume the posi-
tive sign.
In most physical observations, while we know that we cannot reach absolute exactness, and
that the comitlexity of nature would oblige us to introduce minute corrections, and miiniter,
w illiiiul end, ere we could reach to absolute truth, we yet know that we can, after having ])ushed
)ii'c(isi<iri to its practically attainable linnt, rest assured that these neglected minutest corrections
\\\U on the whole lialauce each other. In saJar actiuometry this is not the case. Wnien we have
pushed ]irecisioH fo its practically attainable limit, where corrections become so minute that they
arc no longer individually manageable, we have reason to believe that the sum of those whose
individual consideration we nnist forego is not negligible, for these corrections represent the loss
and gain of heat in these nn-asurenieuts; of heat which is lost in nnmnnbered undetected ways,
an<l gained in alnmst none.
lint secondly the oliserved amount, even if its true value were foniul within near limits (as it
yet conceivably may be), only represents that residual heat which has come down to the observer
after a very large absorption by our atmosphere. He canuot ilirectly observe the heat before this
atnnispheric absorption, and the absolute necessity of adopting some hypothesis as to its action
iiilioduces the second dillicnlty I have nu'Utiom'd as ]icrhaps insuperable. To our i>redecessors,
llcischcl ami I'oniUet, this dilli(adty scarcely lu-escnted itself as being one at all. They had
iiilierited a fonnula reiuesentiug a primitive hypothesis, a kind of scientific dogma, which was
accepted on trust and used without (piestion ; and their successors down to the present day have'
with less jnstilic'ation, employed nearly the same rule, which is, it must be admitted, so easily
followed that it would be most convenient to us if nature would but follow it also; but, as the
writer has already endea\ored to show, the actual processes by which the solar heat is absorbed
are almost infinitely nmre complex than this hypothesis makes them. What is novel in the
present investigations is the attempt to accept, as far as our still imperfect knowledge admits, the
dillicnlt con(liti<ins nature actually imposes, and to discard what is called the exponential formula
III' I'duiUci, even in the modified shajie in which it has been employed by recent investigators of
re])ute. We shall thus reach results which cannot ]iossibly ha\'e the exactness which previiuis
obs(^rvers have attributed to their own, but which will lie between limits of error which seem
determinable. Tlii' width of these limits is but a statement in other terms of the great extent of
our ignorance on a niatt<'r where we have supposed ourselves, till of lat(^ to know nearly all that
tlici-e was to be learned. The most probable result between these limits, then, will be found to
be nniterially greater than that of previous observers; bnt, though our estimate of the actual
amount of heat which the sun semis the earth is thus increased, our conclusions will be that the
eflcct of its direct radiation is far smaller than has been supposed. In other words, though our
esliniate <if the heat received by direct solar radiation is increased, we also fiml that the acjtual
Icmiicral lire of th(^ earth's surface on which organic life depends, i.s iniiin1< lined in vcri/ slifilit ihi/rcc
III/ llif (liiii'l sdhn- nnjs. and in very large degree by some ]U'ocesses in our atmosi>herc intimately
con?H'cleil w itli tlial com|ilcx absorption which the old fmiunla ignores.
I do not propose to give a full history of solar actinonictry, or to give any complete list even
of the notable contributors to it, bnt some brief mention of the following names (which I place in
chronological order) is necessary to my purpose:*
1760.- — Date of the completed posthumous edition of Houguer's works, and the first enunciation
■ The rrnilcr do-sirin^;; to lf;ini inorc of the history of the suh.jcct is referred to the excellent little treatise by M.
Ill r;illeil " Aet inoiiietrie " ; he iiui.v iilso consult "La chaleiir solaire," by M. Mouchot, and the uunierous
oils 1. lei led to in Honzean's •' liibliofjiaphie de 1' astrononiie," as well as the theoretical investigations of Cl.an-
,1'..-U. Aiiiial., V..1. .Axix.,].. iniUV.sr.,.), otLunl Kiivhi^l, (London, t^.liiil.iii-li A Dublin Phil. Jla.;,, Feb., 1N71,
. ) 'l-he «.-ll-lvll..«ll vrse;in-hcsor ■|'yii,lall on till- bill. lor of III.- sl,.\ ll.ixe :ili I liipol I liner 111 I ll is ■■oniieetioil, as
llir rail ol K.lreliM- ivlleelion or ilillii.sion ue limy iiil.T llial e.,n es|,oii,l i n;; |,arls hiivi- disa|iliearecl from the
t beam In a v,7,r/,r, looeess ot «liieli Poniilel's formiibi tahes no aecniiit.
ACTOOMETKY. 47
(if till' I'liniiiila ailoptt'il liy IIimscIicI, riiuillct. ami llieir siKxe.ssor.s. This is stated li\ IJiiimncr iii
tl]i-sc Wdiils:
■■ WIkmi tlir tliickiicsscs" (dltlic alisdiliiiit;- iii(Mliiiiii) '• iucieasc liy cciiial i|iiaiilitics, li^lil
iliiiiiiiislics accoidiii;;- to tlii' ti'iiiis i>\' a jicciiiii'tiic iiriij;ivssi(ii)."
laiii.i^iicr points (lilt tliat tin- (liiiiiiHilinii can he .uialihicall.v i«-|iri'scnlcil li\ Ihr li>uai itliiiiic
I'niAc, wlicic tin- alisrissa' arc ]iic.|ioi iJDnal to llic lliiclincss of tin' alisorliiiiu ni.iliiini ami iIm-
onliinitcs to the anninnt of li-lil oi lii-al received, so tlnil on tli<- otliei' lianil, knouniL: llic aim I
of Ileal icceixeil and the anionnt of the alisoiliiiii; niediilMi, we can ilelerniiiic « lial I he heal \vas
iK'fore aliS(ir|ilion.*
This coiH'lusion was reiiiaikalil.v in advance of tlic physical assiiiii]ilioiis made liclore Koiiiiiiei.
It eiiilMMlied all the facts known at the time lie wrote, and it is to his (acdil Ihal he peicened as
much as he did. A stndy of Ins ori.ninal in\-esli.nations enhances oiii opinion of him as a skillful
and conscientious olisciver.
17(111. _In the same year with the poslhiniioiis imlilicatioii of IJoiinnei a|ipeai(d Ihe-'I'liolo
iiietria"of Lamlieit, a book which I have not lieeii aide to consult direclly. ImiI uliich is under,
stood to lie a work of merit, based in many ii'S[iccls upon Hiai^iiei's |iii\iniis iii\ (NimMtioiis.
J.aniberfs work is remarkable for the clear desiaiplioii of several nielhods or resiills uliich ha\e,
in later tiine.s, been rediscovered m leapidied by olhers. He was aware that llii' line measnre o|
radiant heat was the initial veloeily of heatiiii; resiiliinu tVoni it. lie ai.plieil ihis metliod lo ihe
delcrmination of the ]ieriiieability of succcssixc .ylass plates to the solar rays, with a resiill which
remarkably anticipates tlie law insually attributed to 1 )c la lloclie or to .Melloiii) Ihal the ■•lacilily
ol transinissioir' tlironyh sneccssixe jilatc's is variable, and ■■conliinially increases with the
nunibi'r already passed through. "t (Ijunyin-r's fornnila wnuld make the "facilily of liaiisniisslon,"'
i.r. the c moll ratio of the ueometrie ])ro,i;ression, a vmistant.)
isl'.l. — Ijcslie also points out ''that the iiiiliid (diaiiKc of the therniometer is, in e\ery case. Hie
only certain and accurate iiieasiire of heat."
ISL'o. — Sir Jolm Uer.schel devises his actinometer and introduces the inclhod of exposing;
alternately in sun and shade.
l,s:{S.— Date of the appearance in the "Comptes Kendiis" of I'oiiillcfs celebrated •■Miinoire
siir la chaleur solairo, sur les pouvoirs rayonneiils et absorbents de I'air et siii hi Icinpeiatiiic
(h- la s)iaee." I'ouillet reaches the followiiiit eoncliisious, which liaxi' obtained aliiiosi uiincisal
cm reiicy, and are even yet found in our textbooks. Adoptinj;' as his nuil the ipianlily of heal
which, tlic siiu scalds normally upon the siiil'ace of one S(|iiaie cm. exposed al llic sin fai-e of the
earth's aliiios|ihere during one minute (■•the small calorie"), he finds (1) that the obsiuM-d heal at the
seadevel from a vertical sun is about l.t calories, (2) that the aimauit of heat traiismilleil \ ertically
by our atmosiihere at the sea level is not (luite ', of the whole, and hence (.I) that ; of i.l = 1 ,'
calories, or. to .yive his exact value, tlial l.Tli.l:; calories is the solar constant, or llic : iiiiil
of heat at the upper limit of the atmosphere. This value eorrespomls to an aiuoiint of heal
which would melt a stratum of lee .">1 meters tlii(dc over the whole earth aiiiiiially. He then ^oes
on to imiuire whether the eartli receives heat from any considerable source besides ihe siiu. and
concludes that InTaimc the amoiiiit of sohir Jiiat just i/iren (hies not aeaiunt fur tin: mi Ill's nvlinil snr-
fticc tfm}ienitiire it must receive from siuue oilier souri'i; almost as much heat as finiu I he sun ilsell.
reachinj; the remarkable result that this olher source is radiation from the stars, whose nnilcd
action may lie represented by the radialion of an en\ ido|)iii.n shell whose niciin tciiipeial iiie is
— 1 IL' ' O. This —1 12- C.tlicn is, accordiu- lo I'ouillet. the "temperature of space," which seems
to him nearly as important in wariiiiii.i; the earth as the radialions of the sun.
As very few who (piote rouillet's value of the " temperature of siiace" ha\ c any kiiowlcd;;e
of the way he (leri\ed it (his celebrated memoir beiiii.; more often referred to tli.m read), 1 mav
explain here that he determiues by a most oii,i;iiial. iiii^eiiious. and plausible. lliou;:li uol abso
lutely satisfactory train of reasiuiinj;, that the ainoiiut of heat ri'ipmeil to maiulain the sinfai'c id
the eartli at its known mean teniperatiire, is that which wonld melt a stratum of ice e(]ual to ."i?
• Bouguer, ■'Trail.- ifui.li.im- »m In i;niilatii.n .li- hi luiiiitTe." Paris, 1760.
t Quoted by Forlies.
48 KESEAKCnES ON SOLAR HEAT.
iiictfi-.^ thiok aiiaiuilly, ((«.(/ Iiecaiisv Iw litis <(lyvadi/ found thiif, 31 iiuicr.s of thin oiili/ is reprcmjiifcil by
the sun, be is compelled to look for some other cause for Leat to melt the reiimiiiing L'« meters, ami
he finds it by assiguiug, as \vc have just seen, to ''space" the temperature of — 14:2-' C. I'ouillet
then did not determine the temperature of s])aee by any direct experiment, as be is often supposed
lo lia\e done. His so-called cxperimeuts on the temperature of space were inquiries to see what
(eiiiperatnre should be assiKued to it to meet the supposed necessity of melting 30 meters of ice
annually liy the heat of the stars in addition to that of the sun, since Sl + i-'ti, in all 57 meters,
was the amount, according to him, to be accounted for. If his methods of measurement of the
direct solar licat had been correct, it will be seeu from the Mount Whitney experiments that he
would have found a (juantity nearly representing his whole 57 meters from the sun alone, and in
this case the temperature of space assigned by his theory would apparently have been the absolute
zero. It is a legitimate iuferenec from Pouillet's own theory, theu, that in proportion as our meas-
urements of heat from the sun give larger values does the necessity for assigning any sensible value
to the "temperature of space" disappear.
Because we have pointed out cbanges which the progress of science has introduced in Pouillet's
conclusions, we must not be understood to speak otherwise than with admiration of the work of
this celeltrated physicist. The memoir cited contains, in a highly condensed form, the result of
great and conscientious labor. Owing to this condensation, the author's meauiug is not, in all
cases, as ileal as might be desirable, but this ariises from the great extent and painstaking char
acter of his researches, and his limited sjiacc for the presentation of them.
1S35-1S38. — At about this time Melloni observed that in the case of glass plates or like media
like proportions were not transmitted by like strata, ana the cause of this was pointed out by
lliot. All analogous observatiou had been (as we have mentioned) made in the last ceidury by
Lamlicrt, but was forgotten; and even the observation of Melloni, important as it is in its appli-
cation to our subject, has been slighted or altogether overlooked by nearly all subse(iucnf investi-
gators. A notable exception, however, is the work of Trincipal Forbes, who, even before I'ouillet
(in 18.32), with the aid of Professor Kiiintz, and using Herschers actinometer, made a .series of
oliscrvations at lirientz and on the Fanlhorn. It is signihcant of the iieculiar difficulties of such
work as we now consider that lie was led lo tlirow away \ery liumerous antecedent observations
in favor of tliose of a single <lay, the 25th of .Scjitembcr, 1832, and that he aiipears to have been
occupied during a considerable part of ten years in reducing these observations of oue day, which
with a few confirmatory ones made on the 13th and 14th of August, 1841, were published in 1842
in the Philo.sopliical Transactions.
This memoir is a model in many respects to lie followed even at the present time. One of its
most novel features is the application of Melloni's observatiou and Biot's conclusion to the
determination of the solar constant, for Forbes .sees clearly that if like masses do not ab.sorb like
proportions the old rule is useless. He therefore discards the exponential formula, and prqiecting
his oli-servations graphically, shows that, as a matter of fact, the absorptions cannot be represented
by a simple geometric progression, and draws an emjiirical interpolating curve, by the aid of which
he determines that the solar constant is 388.4 actines, or, iu our notation, 2.85 calories, the heat at
the sea-level being given by him as 1.52 calories, so that it will be seen that Forb&s's observation of
the heat received at the sea-level is only slightly in excess of Pouillet's. The great ditiereuce in the
value of the solar constant comes in jjart from his conclusion that all eipial air-masses have like
absorptions, and in part from his discarding Pouillet's formula. He also finds by photometric re-
.searches that the amount of light retiected from the atmosphere is equal to that directly received
from the sun. Forbes points out that the mass of air traversed ceases to be sensibly pro|iortional
lo the secant ol the sun's zenith distance as we approach the horizon, and lie gives the correct
\alue derived fnim La I'lace's, which we have ourselves employed. He found that the absorption
for a like mass of air was the same whether that mass was of the iiuality of Pliat upon the mount-
ain or in till' valley, an observatiou which mir great contidence in Forbes as an observer leads us
lo admit may have been noted by him in some exceptional case, but whitOi does not agree with
our observations or with tlio.se of others.
1847. — Sir John Herschel publishes, in the (Jape of tlood Hope Observations, his experiments,
ACTINOMETEY. 49
made in 1836, to (leteriuiin; tlic solai- coiistaiil l)y the beating of water, whence lie obtained l!(1.4
aetines (1.39 calories) for radiation at sea lexel, and for the heat outside the atnmsiihere, -.09
calories.
1872. — ]\r. Soret, of (uMieva.* leiiiarks lliat methods for measiirinfr the solar intensity nniy be
classed as static or dynainii'. "In tlie static, two liodies are placed in identical conditions,
except that one receives the solar lays and the other does not. 'flie final diHcrciic-e of temperature
taken up by these two bodies will j;ive a measure of the intensity of the radiation." He ijives his
reasons for )ireferriiij; the static metlioil.
M. Soret concludes that in winter, wlieii the air is dry, the radiation is more intense for the
same air-mass than in summer, ami that in j^cneral, other thinjis bein;;' e<iual, we ulilain a lii^;licr
value when the air is drier than wlic'U it is hiiiiiiil, e\en when it may appear more transparent to
the eye. He further iibserves thai the dust, };ernis, or wafer vapor iiarticles, in flic air, wliile
partly interceptiiif; all radiations, must iiaificularly aft'e<'t the most refianjiihle ones. He confirms
this result by iuterposiun' a definite thicUness of water between the sun and his thernnuneter bulb.
He very Justly observes that under such eoiiditi(Uis Pouillet's foriunla {t = Apr) cannot be abso-
lutely e.xact ; nevertheless, lie deems it juactically sntlicient for observations made in the conr.se
of a day at one station under like atmospheric condition?!. By observations on Mont Pdanc, lie
determines that the uiijier strata of the atmosphere are less absorbent than the lower for like
masses, and concludes that the formula, which may be tolerated in the case of olisei vatious at the
same station, proves r|uite iiisnllicient where those at two different stations are to be idiiipared.
He proposes for observations at tun ditferent stations to write Ponillet's formula
t = Ap-+r"
thus introducing' the barometric )U'essnre under the second power. The observations of M. Soret
are most instructive to the student, tlmiigli it is not easy to -express their result with certainty
in our notation, since he does not give us the amount of the solar radiation, but only one of its
efl'ects, which is to raise the thermometer emjiloyed by him at the maximum about Ifi'^ above its
surroundings at the sea-level, or about ]9:J'^ on the summit of Mont Jilanc. That we do not have
the heat outside the atmosphere gixtn us in set terms by M. Soret apjiears to be due to his
perception of the fact that there possibly may be certain kinds of lays quite ab.sorbed, even before
thej' reach the summit of the highest mountain, and hence his distrust of the best formula he can
frame, which must rest on the results of observation of only such rays as have actually reached
the observer. This wise reserve enhances our opinion of the value of the nieuioir.
1874-1879. — M. VioUe, in various communications to the "Coiuptes liendus," and especially
in two in the " Annales de Cliimic et <lc Pliysi(|ue" lor 1877 and 187!', has given a new value of
the solar constant, tie believes that the relation between the heat before and after absorption is
exactly expressible b_v the formula
7 = L'..J4 X 0.94G ■«"
which is a moditication of Pouillet's, I here being the amount of heat which reaches the soil, li..l4,
the solar cmistant, /?, the barometer, {% — ;)/„ a quantity proportional to the vapor mass traversed.
Although j\[. Violle alludes to the fact that the radiations of the sun are not homogeneous, he
gives, as it will be seen, little weight to this consideration in the above formula, of whose suffi-
ciency lie feels certain, remarUing of it, inileed, that the true law of abs(U'iition is always one and
the same, and always reju'esented by it without any doubt. In his observations he emiiloys a
moditication of the globe actinomcter, his use of it being to see how uuicli the thermcuiieter will
ri.se above the temperature of the surronuding inclosure. In such a use tliis iiistrumciit belongs
then to the .static method, but from this observed static excess M. Violle piiqiosc's to calculate by
a very ingenious method the initial rate of heating of his thermometer luilb. This initial rate,
then, on which everything depends, is not obtained by direct observation, but by a ]irocess of de-
duction from an observation of the static kind.
Knowing the initial rate of heating, we next require to know the exact mass of the thing
* Association Fran<^.iist» ponr I'avancement de science, t'ongri-s de Bordeaux.
12,535— Xo. XV 7
50 UESExiKCnES ON SOLAR DKAT.
Li-ated ill (iiiler to iletcruiino tin- sun's effect. Tlie tiling lieiitcd bere is not a large mass wbosc
■\vciglit is readily determinable, but the niinnte amount of mercury contained in a very small tlier-
mometer bull). It is easy to maUe a relatively considerable error in this minute determination,
and as liere again th'.' whole value of the solar constant depends upon its accuracy, this is a difM-
cnlty special to this instrument, and fuller e\ idciice would be desirable of the means by which the
very large value of this imiiortant constant "as obtained, and of the validity of the method for
finding the initial rate, which the data given do not enable us to verify. M. Violle's methods are
very noteworthy, the labor be has spent in observation (in the course of which he ascended Mont
Blanc), has given general cuiicncy to liis results.
1876.— We cannot omit MHiition even in this brief sketch of the extremely original methods
and very assiduous observation of ^Ir. .1. luicssoii, of Xew York. His observations, made by
methods entirely his own. give results for the heal recei\ed at the sea-level not very different from
tho.se of Pouillet. Mr. Ericsson laliors. as far as jiossible, to take nothing on trust, but to give us
in every respect the results of oliservatioii only. Since it is impossible, however, for him to
actually ob.seive aliove the atmos])here, he is obliged to eniiiloy some hypothesis to find the heat
before absorption. In this case the assumption is tliat a certain law of progression in the diminu-
tion of the absor[)tion, <ibser\ed at the eartirs surface as we approach the zenith (where the
atmospheric depth is unity), would also hold if we could rise above the earth's surface. Mr.
Ericsson's most interesting investigations may be found in the volume published by him for pri-
vate circulation in 1S78 ("Contributions to tin- Centennial Exhiliition"), and the reader who has
not access to this will also fiml the more iiiiiioi lant ones in the early volumes of Nature, where he
is advised to consult them.
;M. ('ro\'a, of Montpellier, has dealt with our subject in many most valuable memoirs. In one
pulilished in 1S70* we have an example of excellent observations, of great care in the conclusion,
and of a reserve of judgment which recognizes the really great difiiculties of the problem and the
really wide limits of probable error. M. Crova recognizes the importance of the effect of the
complex character of the solar radiation and the iusutiiciency of Pouillet's formula, but as he is
unable to discriminate between these radiations, he resorts to a method of allowing for their com-
])lexity, which is a further improvement on that of Forbes. He also shows that our value of the
solar constant is, as a matter of observation, greater, as the air-mas.ses by which we determine it
are less. He points out some very useful precautious to take in preparing a thermometer bulb,
and he devises a very convenient and rapid acting actinometer for his observations. (We are,
ourselves, under the impression that his own rating of the constant of this actinometer would be
raised with advantage if account were taken of .some of the corrections which we have pointed
out in a separate chapter.) M. Crova's observations appear to us to be among the most trust-
worthy made in recent times. He selects two days as especially good, January 8, 187,5, when he
obtains as the solar constant l.SOS, and January 1, 1876, when he obtains the solar constant 2.323,
or nearly 2."> jicr cent, more than in the other case; and I may remark that I have myself met
similar discrepancies under similarly favorable conditions. Eemembering M. Crova's high quali-
ties as an ob.server, we see that these discrepancies must be chiefly due to the different ab.sori)tive
powers of the atmosi^here on the two clearest and most similar days which he could find, and they
present the reader an idea of the real difficulties of our task. In what other kind of observation
than this could so great differences be expected as the final results of the greatest skill and the
most favorable conditions! They are peculiar to our subject, and they should teach us all caution
as to forming too absolute conclusions.
*JI<siina.' r inteusitr liiLiriliiiuc des radi.-itioiis solaires.
0 II A P T E R IV.
I'YKirELIOM KTTilC OliSEKVATIONS.
Perliaps the best liiiuwii inslrmiiciit lor iiicasuiiny sdlar licaf is (Jiic wliicli (iuj;lit to lir rdii.siil-
eri'd, among tbose .still in use, the wmst in iiiinci]ile. and in practii'i- onr (if the Micjst nntnist-
wortliy. I lefei- to tlie pyrheliometer of I'ouillet, which wa.s the best attaiitabh' tilfy years at;o,
and which is to be found descri1)ed in every text-book on the subject. While considering the nse
of tljis instrument as in our present knowh'dge full of olijecti<uis, I have, however, employed it us
an aiijnnct to others, in order to connect the.se late ofiservatioiis with the earlier ones made by its
inventor, and because the pyrheliometer is so generally known. I mention it first in the order of
observaticui, bnt the reader who desires to see its historical place is referred to the chajitcr on
actinometry.
The instrument, in the form in which it was used on the Mount AVhitiiey expedition, is e.s.sen-
tially that described by Pouillet. It consists of a sliallow, cylindrical box of thin cojiper, electro-
plated with silver, and Idaekened on its front surface, having a diameter of 113 millimeters, and
exposing to the .sun a surface of 100 square centimeters. It is 11.2 millimeters thick and ludds
when filled, after the thermometer is in and plugged, 104.2 grammes of water. (On Mount
Whitney, after August 31, ISSl, it was temporarily titteil with a I'ork and held nearly lOS grammes
of water.) It has a stem, insulated from heat conduction by wood. Deducting the weight of the
wood, which is here treated as absoibing no heat, we have —
Oranmu'a.
Wfi-lit iif l.c.x, IT-'.'J -raiiiiii.s; » al,-i .■,|iii\ .il.-nl li;.4
W.iglit of brass piecu holding' tli.Tiii..iiHt..r, s..l i^nninii.a; wati-r iM|iiivaI™t U.S
Theniiometcr bulb and i
Total ivat<TC.|iiivaI.'nt of v.-ssci .•ii.d iiiiiii.Ts..d i.nrtion ,.r tb.
The vessel can be rotated around the axis of the cylinder, liy wliicli motion the w ater is mixed
and kept at a nearly niuform teiui)erature.
"Tlie observation is nnide in tin' following manner: Tlir tcafi-r in the rcs.iel being nciirlij of tlie
svrroiinding temperature,* the pyrheliometer is held in the shade, but very near the ]ilace wheie it
is to receive the sun; it is placed so that it looks towards the same extent of sky, anil there, for
four minutes, its warming or its cooling is noted from minute to minute; during the following
minute it is placed behind a .screen, and then adjusted .so that on removing the screen at the end
of the minute, which will be the fifth, the solar rays strike it perpendicularly. Then, during five
minutes, under the action of the sun, its warming, which becomes very rapid, is observed from
minute to minute, and caie is taken to keep the water incessantly agitated ; at the end of the fifth
minute the screen is replaced, the apparatus withdrawn into its first position, and for five minutes
more its cooling is observed."
According to Pouillet ("Comptes Reuilus," .Inly 0, is.ls) let I! he the warming which the pyrhe-
liometer undergoes during the five minutes of the solar action, r and r' the coolings <lnring the
" A consideration of importance.
52
llESEAKOHES ON SOLAR HEAT.
tive-uiiuute intervals preceding aud following. The elevation of temperature t, wliioh would take
place if there were uo radiation, is ap])roxiniatel.v (when the loss of heat by convection is slight)
« = «+-+'■'•*
Let (7 be the diameter of the vessel expressed in centimeters, p the weiglit of llie water which
it contains expressed in grammes, p' the weight of the vessel and the immersed portion of the
thermometer reduced to a specific heat of unity. The elevation of temperature t corresponds,
then, to an amount of heat t {p + p').
This heat having fallen in live minutes on a surface . , each unit of surface has received
i(p±p')t
during the five minutes,
1
and in
(/-'
In the pyrheliometer used , = 100 square centimeters, hence
Calories per minute per square centimeter = .,,.. {p + p') t.
If I'ouilht's expression (which we Lave just stated) were correct, it would be quite immaterial
whether tlie day was calm or whether a strong wind blew on the instrument, provided that it
blew nniformly. Pouillet himself, however, has devised a special form of the instrument, covered
with a lens to meet the case of the wind, but has to correct this special instrument by one of the
l)rimitive form we are discussing. Now, tlie above formula, simijle as it seems, is theoretically
wrong (as I will not stop to demonstrate), and the instrument is untrustworthy even in a uniform
wind, as may be inferred from the following experiments. It is because we can so rarely command
the condition of a perfect calm that the error becomes of so large importance, though even in a
perfect calm the above equations seem to me to be still untrustworthy.
A second practical defect has been pointed out by others, and is, indeed, very apparent, even
to casual observation. When we take the instrnmeut out of the Sun and place it in the shade,
instead of falling, the temperature continues to rise for a perceptible fraction of a minute; and
when we take it out of the shade and ])ut it in the sun the temperature continues to fall for a
fraction of a minute. If the water be most thoroughly agitated, as in our own experiments, it is
certain that this effect will be much reduced; but it will be still apparent if the readings are taken
at short intervals, as the reader may see on examining the illustrative observation in the footnote.t
A portion of the water, in fact, clings to the copper, and is not removed by agitation, however
violent. It forms a non-conducting film against the cop])er .'surface, so that the actual comluctivity
is totally different from what we might expect, and ncjtiiing less than a .system of internal brushes,
which sliouid scrai)e away this persistent film, would suffice to remove it. A very great improve-
ment, therefore, has been made by Professor Tyndall in tlie siilistitution of mercury, a liquid which
11 +
' + >
* Puulllet aays, " it is easy to see that the elevatiou of temperature t produced liy tbe su
It seems to me tbat it is not easy to see, and tbat this lonuula does uot, in fact, represout auy accepted law of cooling.
\{March 28, lt:81 ; Staiiuit, AUvglienii.) — Tlie water in the ]iyrheliometer was incessantly agitated during tlie fol-
lowing espcriuient. In spite of tliis tlie result was somewhat as thougli the water were a poorly couductiiig solid,
the temperature remaining constant, or even rising, during a cniisidrrahle [lait of a minute, after file sun's rays were
cut oti; and usually falling for a cou,sideraljle time .ifter its exposiuv to the sun, as will he .m-.-ii clearly from these
figures taken from direct observation;
Table 17.
Transferred from aliade Trausferred from ami to
to sun .It l" 55"' 1)0: 1 shade at 2' 00'" OO'.
Trau.sferrfd from sliiidc Transferred fioiu son to
to sun at 2'' 05'" 00*. shade at 2'' 10'" oo-.
Time. Temp.
Time.
Temp.
Time.
Temp. Time.
Temp.
h. m. s. o C.
I 55 00 18. 98
1 55 15 1 18. 88
1 55 30 18. 82
h. m. ».
2 00 00
2 00 15
2 00 30
20.08
20.09
20.08
h. m. «.
2 05 00
2 05 15
2 05 30
3 05 45
O C. h. 111. s.
17. 70 2 10 00
17. 40 2 10 15
17. 2» 2 10 30
OC. '
19. CIO
19.05
19.01
ulinyM are typical of u great nuuiber oli.served and uot here |
PYRnELIOMETRIO OBSERVATK NS. 53
does not wet- the ssurface, and I desired to take a nierciu-y iiyiiieliometer of his pattern with nie,
but could not obtain one till the return of the expedition. I have used, then, Pouillet's apparatus
in its original form, for the reasons stated, although it has other errors besiiles those mentioned,
and have compared its indications subsequently with those of a mercury pyrbeliometer, and intro
duced a correction for the ditterence; but our "corrected calories" are corrected to this extent
only. While in deference to the long-established repute of Pouillet's instrument, we give a full
.series of observation-s made by it, we do not attach great weight to these values as absolute
determinations, although they may often be found convenient as relative ones. We have accord-
ingly omitted oliservations reiiresenting much labor, where the series were not so complete as was
desirable, for, even in this clear sky, wind or other causes fre(iuently sjioils a series, and perhaps
a whole day's work, as if both morning and evening series be complete, they are useless without
the noon one. We give an example of but a single series in full (that for noon of August 14, made
at Lone Pine), though the values here given for other series are reduced from similar complete
minute readings.
In our own reductions of the pyrheliometer wi' have (for the altitudes actually observed)
treated the length of the ])ath of the ray (.1/) as proportional to the secant of the zenith distance,
and taking the barometer exjiressed in decimeters as (/:;), M/i represents the ab.sorbing air-mass.
According to Pouillet's symliols, ,1 represents the heat outside the atmosphere (i.e., before absorp-
tion), p the coetlicient of transmission (the proportinn t transmitted liy his unit stratum, the z< nitli
depth), t the number of unit strata traversed; an<l it is (eri(iiieousl\ ) assumed by Pouillet that the
same />ni/)(((7iV>H is transmitted by one stratunj as by aiKilhei, or that [i is a ecmstant, so that if /
be the oliserved temperature t = Ap'.
Our unit stratum is that which wtuild suppiut cleeian'ter nt niereury. We designate the
heat outside the atmosphere by -B. The coellicieiit (if transmission fiua unit stratum, which Pouillet
writes;), we call a, where unity is the ab.sorbing mass oveihead at .sea-level or that supporting 7.C
decimeters mercury. "Wlierejt is expressed in terms of strata -- 1 deeimeti-r meicury, this becomes
a". We use Ponillcl's lonmila of reductiim, then, under a sli^htlv dillerent form, and writintr c
for the observed heat \\\ calories, we ha\-e C — Ea-'-, a forniiil.i wljieh we have given our rea-
sons elsewhere for In lieving incomplete.
COMPARISON OF VVA lEH Wnil IlKIiCTR Y I'VIIHEI.K ITMEl ER BY .snir LTANEOf.'^ OBSEliVATION.S.
The instruments \\>i-t\ in this conqiinison were, the uatei- iiyiheliometer (No. 1). used on the
exi>edition an<l abcadx desciiliecl, and a mereiny p,\ rlielioiiieler (No. li) made of cast-iron, nickel
jilated, and coated with lam|i l.liick on its IVont suilaee. It exposed a snrlace of L'O.L'C.S .sq. cm. to
the sun. It was niiMnili'd as au alla/.imntli, the theraiometei- stem projecting from the horizontal
axis. Both inslrunients Were piotecled Irom wind and variation of radiation from suri(aindiiig
objects by eylindri<'al screens.
The water eiiui\alent of p\ rlieliomeler No. 1 <iii tliis occasion was }> + p' = !t7 + 17.7= 114.7
grammes, and the ninulier of calories per minute jier scpian ntimctei' was . (/'+/'') t = .l.'l'!t4 t.
which is the formula used in rcMlnction of series A and 15.
I-,., ,.V,Ih
Grauiu
h.- w:,t.-i ...i-iisal.'Mt .,r thr iron ll;,,l< y.H4
he watiTpqiiv^drutuf tlir iiiHnsf.l part „t tli.Ti, t.T U.4U
In series A' :
In series B' :
The fornnila becomes:
i. = h).-u
j, + // = '.(.84 + 1().L'4 = I'll.u.S gramme.-
p + p' = (;.4."> + l(i.L'4 = 10. (lit gramme>
Series A', Xo. of calories = ., X (l-'b.OS) t = .]9Sl-' t.
.Series B', Xo. of cahnies = ^ , x (U\.r,'J) t = .1047 i.
54
EBSEAROnES UN SOLAR HEAT.
Table 18.
[Datfl, October 22, 16S1. St.ltioii, Allegheny. Sky, very milky with haze anrt cloudB near horizon. Wind.
jientlo breeze. Instrument, w.^ter jiyrheliometer (No. 1). Protected from iviud by a tin-plate cylinder open
at both ends and covered with cotton. Its condition is therefore similar to th.at of the mercury pyi heliome-
ter. Charge of waler=97 c. c. Observer. F. W. V. Observations synchronous with series A'.]
SERIES A.
No.
Interval.
IHn.
2
5
4
5
6
7
8
9
5
5
5
5
Fall.
11' 50" to 11' 55" fall i
11 55 to 12 00 rise
12 00 to 12 05 fall i
12 05 to 12 10 rise :
12 10 to 12 15 falli
12 15 to 12 20 rise
12 20 to 13 25 fall i
12 25 to 12 30 rise
12 30 to 12 35 fall i
30. 28
2 .85
2 .85
2 .52
No. •2: t — 3.'>f< + — ;,-
.4ri +
: :).(•.•;. C.alorif.s jjer
= 3'.;!r.. (.':lloiie,s |,er
= 3 .46. C.'llnrie.s per
iuule per i^qiiare i.m
liiiuti- iwr s,|ii.aro cm
limits per sqiiaro em
; :^
Calcfrie.s per niiimte ]ieT Hiniarc
0.830
0.768
0. 7i)4
Table 1!).
lUctober 22, l;>81 (continued). Sky. very milky with jiaze and clouds near horizon. Wind, geutle breeze. lu-
alniinent, case of mercury pyrholionieter (No. 2) fitted ivitti iralei: Protected fioni wind by pasteboard cyl-
inder open at both ends and covered with cotton. Charge of water=9.84 c. c. tibserver, J. E. K. Observa-
tions synchronons with series A.]
SERIES A'.
No.
Interval. 1 Noon.
FaU.
Rise.
1
3
4
5
C
7
8
9
Min. 1 After aboat 15 minutes' exposure to sun—
2°. 62
1°. 37
2 .12
2 .32
n .56
"1 .79
2 .42
1 .74
2 .97
.m No. i : ( =
.111 No. 4 : / :
.111 No. n : / =
nil No. .■^ : r =
Mean ...
1.37+ ■ -^-—=3-. 74. Calorii-K 1
:2.3'-'+- J- -=4".l6. Calorics 1
1.56+2.42
1.7'.l + -■ — ,;— = 3^\78. C'alor:
2.42+2.'.17
iiMto per.s.iuaivcm.
tiutf per square cm.
note Iter square cm.
per miiinle }ier square cm.
i per
PYimELIOMETRIC OBSEliVATIONS.
55
NO.
Interval.
1
3
4
5
6
J/ii..
5
5
5
5
5
5
■ to 1» 05" fall in shade
lo 1 10 rise iu sun .
to I 15 fall in shad.
1 20 to I 25 fall in shade
1 25 to 1 30 rise in ,sim .
1 30 to 1 33 fall in sliade
00.54
0 .48
0 .58
0 .03
rrom N... ■>: t = 2.7.^
From No. 4: (^2,H|| +
From No. li : ( = l.;i:l +
Mean
4rt + .5?
:!°.3:l. falo
■2 .tv. f.il..
ami the case dried by ho.
water the temper.itiirc at t
TAIiLE 21.
r. vt-rv milky but soniewliat eleare
ter (No. 2) lillcd Willi mercnrv ari-oi
er, J. E. K. Tlle water used in prev
before it was filled with mere ury.
et was considerably above the shade
.SEKIES B'.
AViud. jtentle bret
t3 bad been emptied out
nj; been hi-ate.l to expel
No.
Interval.
P. M.
Fall.
4"'. 47
Rise.
1
2
3
4
?
7
2Iin.
5
5
5
5
5
IHiO" tol* 5" falli
1 0.-. t.. 1 10 rise
1 111 to 1 15 fan i
1 15 tol 20 rise
1 20 to 1 25 fall i
1 25 to 1 30 rise
1 30 to 1 35 fall i
n shade.
1". 26
n shade.
3 .m
2 .98
1 .so"
a eh ado.
2.75
n shade -
2 .85
No. 2: ( = 1. 2fi+i::'"+''^'=.-. .4!). Calorii-s [i.t luiiiiitc per sqiinr
,+ 3. ,+..75^
i: I-
1^ i.;iii+'
Calo
Mite 1..
iiilf pi
0. !ICI4
1. "46
Mfuii
From tlic abdVL' siiiiiiltaiiedii.s iib.sfrvatiiiiis wu liaNc tlic i-ffii-iciify iif iiyrliclioiijott'r N(
terms of Nii. 1.
No. 2 tilled with w
ter. Series A and A'.
'S0.-2 filled with mercury. Series B
and B'.
--Nf
„ . No. 2
«-°N°;-i
Mean efficiency of No.
2 filled with water = 1.01.
--iJ:?='-7^--37
Mean eflieieney of No. 2 filled with merci
rv=1.27.
Accordingly we adopt the multiplying ructor I.l'T lor tlio ri'diictioii nf a rrsult olitaiiitMl with
a water pyrlieliometer to what it would have been if obtained with an instrnnieiit eniphiyiiig
mercury as its liquid.
5G
KESEARCHKS ON SOLAK HKAT.
EXAMPLE (IB- A rYllllELK ISIETEE SERIES IN FULL.
Station, Lone-Pinr. Observer, A. C. TJ. Sky, clear. Wind, fresli to gentle
istTiinu'Dt, pyrlieliometer No. 1. Cliarge of water, 85.26 grammes.]
Time.
Readins of
tliermonieter.
Change per
minute.
Exposure.
Time.
ReadinfT of
thermometer.
Chan so per
E.\posure.
11.30 A. M.
29, 211
Sliaile.
12.01 P. M.
39.82
^
h .62
Sun.
31
30. 20
+1.06
Sun.
02
40.58
.
- .76
Do.
32
31. 52
+1.26
Do.
03
41.60
-
•1.02
Do.
33
32. 90
+ 1.38
Do.
04
42,23
-
- .63
Do,
34
33. 9.';
+ 1.05
Do.
05
43,10
.
■ .87
Do.
35
35. 00
+1.05
Do.
06
42 50
— .60
Shade.
36
34. 80
— .20
.Shade.
07
41.90
- .60
Do.
37
34. 62
— .18
Do.
08
41.49
— .41
Do.
38
34.40
— .22
Do.
09
40.99
— .50
Do.
33
34. 3K
— .02
Do.
10
40.50
— .49
Do.
40
34.22
— .16
Do.
11
41.32
+ .82
Sun.
41
35. 30
+ 1.08
Sun.
12
42.00
+ .68
Do.
42
30. 21
+ .91
Do.
13
42.49
+ .49
Do.
43
37. 02
+ .81
Do.
14
43. 00
+ .51
Do.
44
38. 03
+1.01
Do.
15
43.74
+ .74
Do,
45
+ ,97
Do.
16
43.30
— .44
Shade.
46
38. 52
— ,48
Sliade.
17
42.80
— .50
Do.
47
38.18
- .34
Do.
18
42.43
— .37
Do.
48
37. 90
- .28
Do,
10
42.10
- .33
Do.
49
37. 58
— .32
Do,
20
41.70
-.40
Do.
50
37. 20
- .38
Do,
21
42.12
+ .42
+ .68
51
37.99
+ .79
Sou.
22
43.00
Do.
38. 85
+ .86
Do.
23
43.82
+ .82
Do.
53
39. 70
+ .85
Do.
24
44.40
+ .58
Do.
54
40. ,58
+ ,88
Do.
45.00
+ .00
Do.
55
41. .311
+ .72
Do.
26
44.24
— .76
Shade.
56
40.83
Sliade.
27
43.59
— .65
Do.
57
40.32
— .51
Do.
28
43.20
— .39
Do.
58
39. 98
— .34
Do.
29
42.64
— .56
Do.
59
39. ,59
- .39
Do.
30
42.00
— .64
Do, j
12. 00 M.
39,20
— .39
Do.
IFoi reduction of these otaervatious see Table 33,]
observations with the ptrheliometer made at lone pine,
Table 24.
[Date, August 11, 1881, Station, Lone Pine, Observer, A, C, D, Sky. clear. "Wind, gentle. Charge of i
S3,6c.c. Barometer (|5„) =6. 64 Length of piitb of ray (Jf„)=2. 281. Jf„ ^,, = 15. 15.)
No.
Interval.
A. M.
Fall.
Rise.
2
3
4
5
6
7
8
9
le
Min.
5
5
5
1". 54
30.31
1 .55
3 .34
1 .68
3 ,13
5
5
5
5
1 .73
3 ,40
7 45 to7 50 fall in shade
1 .60
3 .18
NOTE._V,
Nil. '.': I = :!.:!1 _).'•— -r '■■■" _ 40^1;. Calo
1..55 + l.ti,S
sky and no irind. The abo'
1..54 + 1,51)
nil Nil, 4 : / = 3,34 +
nil No, Ci: (=3.1:5 +
1111 No. 8: /= 3,40 +
nil No. 10: t= 3.18 +
1.68 + 1.-3
1.73 + l.Git
l.fiO + 1.07
odered by the observer an excellent one.
ler iiiinut,- per si|uarB cm 0.1(85
= 4 .'.m.' Calorics per niiiiuti- per sfiuan- cm 1.005
— 40.84. Calorics per minute per square cm 0.980
= 5 .07. Calories per minute per sijuare cm 1. 027
= 4'^.'J7. Calorics per minute per sciuare cm 1.007
Mean
Reduced to standard 1
cnry pyrlieliometer (1.001 X 1,27)
1,001
1.271
pykhp:liometeic obsiuivations.
Table l'5.
;l(v. AiiKllst 11. 18S1. St;
1:1.6 ,-..■. liml mat 10 a. 111.
.eiuUng the mercury abov
temppiatiirr nf tlic ail put a stiip tit tin ii .«ii
lifter (i3,)^t;.n-(. Ia'ii;;Hi of patbofra.y (J/,) 1 itT!
If 111.
1
■:'
11
■•1,';"
■J
5
11
4.1
X... 2:1 = 4.60 +
■,I In.staiiihiia iiiiT
■ fall in.sliaile
f.i'll 111 .^lia.li'l
I + I.-'.-, _
.V ,1,V,I,.-I,i
0^. so
57
. AllKU.st 11. ISSl.
L.-n^'tli of patli .
x.l.
lut.ival.
P.M.
Fall.
i;i»e.
.Will.
5
5
4b o.iji.
t 10
4 15
4 20
4 25
4 45
4 50
4 55
to
15
20
) 25
30
50
55
5 OU
fall in .ihailc .
1 .00
'
fall ill shiuie.
'I
i
fallin.sliaile.
fall iu Rliade.
■J ,,5
fall ill shade.
2.24
( = :!.sfi+
i.oo + i.-ji;
:l'J. falo
N... 4: ( = :i.ir.+ "'"Z," " = 4 .71. Ci.lo
Kr.iiii No. 7 : ! = a.05+ ^■■'■' + -•-■* = 4 .811. Calo
l.--'t;+l.
niiiit.MK-rsiiniirf
linute prrsiiiKuv
iiiiite per sqiutro
1.111
1.1148
Jliini
Ki'cliiced t.i staiiilaril iiitT.iii.v iiTrli.liniiii-t.r ...
Tabli: 27
[Date, AuKust 12. ISSl. Station, Lone Pine, oliseivei , A. C.
Wiud, gentle. Charge of water, 91.3 c. e. (Put in August
of p.ith of ray (J/„) =2.184. (J/,,?,,,) = 14.51.]
No. ' luterval. ' A. M.
T' 15™ to 7» 20" fall in .shade..
7 20 to 7 25 rise in sun ...
7 25 to 7 30 tail in shade. .
7 30 to 7 35 rise in sun ...
7 35 to 7 40 fall in shade-.
7 40 to 7 45 rise in sun ...
7 4i to 7 50 fall in shade .
7 50 to 7 55 rise in sun ..,
7 55 to J 60 fall iu shade .
1 .21
i'.'io"
1 .53
3' . 60
3 .41
3 .41
"" 3'.'2r"'
Frimi Nil. ■>: t = 3.(i0 + i!!ljhl*'A = 4-\46. Calories ]
From Xo. 1; ( = 3.41 +•'"' + '■-' = 4 .4-2. Caliirit-s )
FioiiiNo.i;: (^;;.4i+'-"-'+'-^"=i .72. c lu-si
Fn.ii, No. - : , = 3.21 +>-^f'+l-^ = 4M3S. Calories ,
iimite. jier si|U:ire i
liunte per square e
iiiiute per sriiiarcc
luiute per s.iiiare i
Mean
Ke.lUe.-il to st
l.n-Jii
fi.'.i'.ifi
i.laril mere
58
RESKARCnES ON SoLAK HEAT.
.oDi' Pine. ObscrviT, A.C D. Skv.liiii. Wiuil, lush lu Inisk. Ch.irae of
•lei (|3,) = C.M. LenKth ..l|.alli ..fray (.1/,1_1.II78. (Jf, (S,) ^7.11!.]
tlomis DO observations ni re lak.ii fr..iii 11, na to 12.]
No.
Inlerval,
Koon.
Fall.
Rise.
1
3
4
5
Min.
5
5
0°.67
12 15 to 12 20 fallinsbade
1 .80
2 .22
No. 'J: / = 3.KG+ - — -^-^ — = 5'-.10. Calories per minute jier si|uare i
N... 1 : ( = :i.:!,^ + —^ = .5-.y;l. C:il..ri.s p.T ininiit.- per »(,,inre <
Mean ....-
l;..iliieeil to.sraii.Uad iiiereuiy pyrlielionieter
1.112
1. 17.5
Table 2!).
Lnne Pine. Observer. A. C. D. Sk.v. fair. Wiu.l, fresb breeze. Charff
eter (/3„l = 6.62. I.entrtb of path of ray (.U„)=2.;)02. (J/„ P„l = l5.2,i.l
[Clou.Is prevented further observation.]
No.
Interval.
V. 11.
Fall.
Bise.
1
2
Min.
5
4'' 30" to 4» 35" fall i
4 35 to 4 40 risei
4 40 to 4 45 fall i
f.OS
^
Q sh.ade- ..
1 .55
nlei..T.s.,nareet,i 1.022
ry i>yrhelioiueter 1. 298
ie<]-\yitli a 20 e. e. i.ipette it), to aii.l in.lu.linj,. AugiLst 12, 1881. After tllis date
Table 30.
(Date, Aiiaust i:i, ISSl. Station. Lone Pine. Observer, A, C. 11. sky. .lear. Wind, very gentle. Ch.ar
water, 88.(1 grammes. Barometer (3„) = 6.62. Length of path of ray (J/„) = 2.302. (Jl„ 3„) = I5,25.]
No. Interval.
*05"'to7»10 fallinsbade-
10 to 7 15 rise in sun ..
1.-. t.. 7 20 fallinsbade.
1^.19
i .50
7 -J,^ U,7 -.W iHllinsbade
'" i'.'45""
1 -■16
^
,,
1 .09
1 .80
N'o. 4 : ( = :i.:iO + •• ~, • — = 4^.78. Cal.
1.1.". 4- 1.4(1
( --= :!.:!i +
l.(;9 + 1.80
4°.77. Calo
Cal.j
4<^.84. Calo
iiiiiteii.r s.iitar
N... 1(1: (-= :i.O!l +
MlMU
Ueddeed to standanl iiierctiry [.yrbelioinct
., .. 1.016
.... 1.014
.... 1.0.-.9
1.02; I
1.032
i.yu
i'Vi;iiELio.Mi:Tur(' op.seuaations.
59
[Date, August 13, lesl. Station, Lone Pit
rcifliius :i gale. Cliart^f of \v;vUt, stt.C gr;
(M,tf,)=7.!4.]
Table :".1.
niwervcr. A. C. 1). Skv
vatious takeu iu rear of liuit Jiuj;, to shit-Id tbc iostru
No.
Interval.
1
2tin.
5
5
4
5
6
8
5
5
jmrIi as possible.]
F.all. Kisc.
■ to If 50'" fall in shade 0^.60
toll 55 risein.suu '
1155 to 12 00 fall in shade 1.44
12 00 to 12 05 rise in sun
12 05 tol2 10 falliushade 1 . !IS
12 25 tol2 30 fallinshade 1.70
12 30 to 12 35 riseinsun ,
13 35 tol2 40 fallinshade 1.74
.,. __ .., ■*'" + !■•" _ .,, .- , , ,
1.41 + l.SW
l.TIl + 1.74
Nci. 7: (= 4.15 + Z - = r,'3.H7. Calori.-s |..-r miiiiit.- p.-r s.iuaiv I'll!
R.ilii.fil li. stall. lanl i
(Ni. I'V.-iiiiij; ,,l,s.•l^.lll
IDali-, Aiisusl 14. l.^tKl.
:i..l nil llii.s.lay.)
Table 32.
No.
Interval.
A. M.
Kail.
llisc.
1
3
?
8
10
11
Mui.
5
5
7 10
7 15
7 ii)
7 35
7 40
7 45
7 .50
7 55
to 7' 10'
to 7 15
to 7 20
to 7 25
to 7 30
to 7 35
to 7 45
to 7 50
to 7 .55
to 8 00
fall in shad.'
1 ■, 00
fall in shade
1 .46
fallinsh.atl.'.
1 ..50
fall in shade
1 .80
tall in shade.
1 .m
fallinshade
2 .27
)iii N.i. •-': (:=r;i,..11 +'•""+ '•"' - .-, .14. Cal.iri.'.s p.-i iiiiniile 11.
.niX...4:, = :i.s.+ l-">+'-^'' = n.:,:,. Cai.ni.'s ...t i i,,- ,„■
1.11 N.i. ('.; / = :l.i;4 + '■■''' + '■"■" =- ,-. .:w. ('al.iri.'s p.-r niiiiut., p,
1,11 N.i. H: / = :;.r,l + '■'"' + '-''^ =^ ^o.;,,,. ,',u„vi.'s p-r iiniiut.- p.
nil N... Ill: ( = ;!.:!- + ^■■'^' + ---' =;-. .4S. Cal..ri.'sp.'i-ii,iiiiit.' p.
M.-
'.1 t'l stall. lar.l i
p,Mli.'li.illl.-t.-r(1.0!l.-i X l.v'T)
60
UKSEAECIIES ON SOLAlt IfKAT.
I 14. ISSl. Sta
.A. CD. Sk.v
Lt-ngtb „fi,alli
No.
iDterval.
5
5
5
2foon.
Pall.
05. 78
Ei.ie.
1
ll'.W to 11'' 40" Ml in sliailp
11 40 toll 45 riseinsun
4 '.78
1145 toll on fallmsliade
I .SO
4
4 .10
115.-. Mil iin iMImshack.
2 .10
3 .90
12 05 l.ilJ in hill iu .^hailo
2 .60
8
3 .24
9
12 15 to 12 2(1 tallinshaile
2 .04
10
3 .30
u
12 25 to 12 30 fallinsbaile
3 .00
iN.>. 2: i = 4.7S + —
1 No. 4: ? = 4.10+-'
'8+1.1
( = :!.;)ii +
2.10+2.60.
fall!
Call,
fall.
f = .i.24+ J =5°.;il>. Calories per
, .,..„, 2.04+3.00 .,, J,, ,, , .
/ = ^!..!0+ ^1 =o-.b2. Calories per
per iiiiuntc per square (
per minute per. siiiiare I
per liiinute per sqilaie (
niite per square (
nntei.ersqn.ire.
. ... i.2r.o
.... 1.246
.... 1.14.-,
.... i.r.i'.i
.... 1.22.-.
p.vrlieli..in..te
: 14, 1881. station. Lone Pine. Obs.rviT. A. (.'. D. Sk.v, clear. Wiii.l, gentle t.. iiesli. C'l.arpe
S5.:) grammes, llarometer 0„) = C.C1. Lengtii of patli olfay (lf„) = 2.I48. ill,, p„l = 14.20.I
No.
1
4
8
li)
11
Interval.
P. M.
Fall.
Rise.
Min.
5
5
5
5
4' 0.5'
4 10
4 15
4 20
4 25
4 30
4 35
4 40
4 45
4 51!
4 55
to 4' 10"
to 4 15
to 4 20
to 4 25
to 4 30
to 4 35
to 4 40
to 4 45
to 4 50
to 4 55
to 5 00
fall in shade.
1°.42
fall in ahaile.
1 .00
fall in shade.
1 .92
fall in shade,
li.ieinsun...
2 .55
fall in shade.
2 .40
fall in shade-
2 .42
1
/ = :i.46+ '
Calt.ries per uiiiiiite per sqiia
.4: / = ;
6 : / = ;
,^1^0+1.112^,,,.,
. 2.47 + --"''+-••"' = 4-\94. Calori.-s per
.2.2S + -■'**'+'■■*' = J--69- L'al...i.-.-. p.r i
Ue.luie.l to ..(tMiiilaril i
r.v pyrheli.
I . o:i8
1.318
rVUIIKlJOMKTlMU ()l!SKi;\ ATIONS.
CI
]HSEl:\ ATKINS WITH TIIK rVKIl KLIi iMK ITCIi SIAIU; Al llnl \ 1 A I N CAMIV Mi'I'Nl WIlllNKV
Table .'.."i.
[Date August l:'.i. 18S1.
(Tmrge of water, 90 ;;!;
Al'ttT ]5 minutes' espnsii
SI' W' to 8^ or.'" fall in sbade .
S »:■ to 8 10 rise in sun - .
8 Hi t" j 1.-. fall ill shade-
Frniii Xo. -J: (^■,'.-,7+ Z = 4 .-".>. ( ';ilori...s jnT
Kc.lii.-.-.l t.i ^taiiilal.l iii,-r.iilvi.ylli.-li..iii't.-r
Table :iC,.
[Date. Aut'iist '.'a. 1881. Station, iloiintain Cai.ip. Ol'server, J, J, X. Sky. 'l.-.j. fine. Wiu.l li-lii I
Cliaige of water. 91.3 siamiuea. Barometer ((J,i = 4. 98. I.enj;tli of path of ray iJ/ i-l.li:5. I. If (9,1 =o
No. Interval.
Fall. Kis.
Alter 13 minutes" espo.mi
11" 411'" to UM.i'" fall in sliado.
11 4.'. to 11 .ill rile in sun .
11 .-'II to 11 ■'. I. .11 lit "I'.i.i.'
1:: no to IL' "". Lill III -ii.i.l.
12 10 to TJ 1.". fall in slia
Fy N.I. J: /=^:',.4s+ ;, =7 .11. (
V , , -l-"4+:i-"-
Ui. ('nl..ri.-s|or,iininl.. |..r,s.,,i
1 . ."..-■ I
l..'..'.ll
IJe.lll.'.-.l t.. >t:lM.l;l
I. mill
Xo. Jutenal.
.I]', lll'-.n.-i..f..l N Sky, rle.-p Mil.-. Wiiiil. light liiee/,.-,
1=4™, Liniilh ..r i.iitli .jKiy iJ; )— U,791, I Jf , /3,, |r= l:i,93, |
Fall, Risi
After 13 niiunti,s' expos
I' 23." t.i 4' 30"' fall in shaile
33 t.. 4 411 fall in shaile
I.. 4 ,30 fall insha.le
to 5 OO fall in slia.le
\:m^
FmmXo. U: / =:i,;,ll + --''^ + -''' =il .-M. r;,l,„i,.s ,„.r ininiit.- ii..r8.|naio
In.inX.i. I: / ^ :l,:a +'-'''' + -■"''= i; ,1111, l;,l,.fi,-s |„r miniil.. |,..r>,|u;ii,-,„, I,-.".i,;
rruiii Xo, I-.: l = :'..-M+'-'^~j^'-'-^'-=i: .17. Cnl.in.s lo-r nni.iiti- |..r s.,.kii.' ,iii l,:r.:;
Mean
l;.-.liu-...l I., stai'.laid I
l.yrh.li.
I,:i-'i;
i.i;-i
Ihe same houi.
62
KESEAHCllK.S ON SOLAU JIEAT.
Table 38.
Lciii; I
I. .1. X. SUv.clf.li bill
limll, .ilroy (l/„) = -L7
No. luterval.
A.M.
F.lll.
liiae.
1
Mill.
All
8k 0.-." I
S 10 1
8 IS t
8 '20 t
8 '-Ti I
8 lia t
, s LID fall
> e 35 riscj
1 8 40 fall
':!"""
:•':-■;■-
1=.77
1
3°.fi7 1
~i 1 '
[ 1 .60
r -
u shade.
2.02
(■ '■
■i t>i^
r.' r
n shade.
, N.,.4: l = X'!i\+^'^*' + ~^ = rfi'l). Cnlori
:',.■>!< + '
lit,' !.<•
i.itc p.
1.19.5
1.241
M.-
a-i-vev. J.,I. K. Sliv. .leeji Idii
Leuiilh nf i>;itli of lay (-V,)-
No. Ictt-rviil. i Noon-
Fall.
Kise.
2[i,i. ' After If. niiuuti's' exposiiii- to suu—
«2=.40
"'i^ls' '
3 fi 11 50 toll '-5 fall in sbaile 2 .78
1 ''I
2.05
2 .30
N».'.>: / = 1.;!S+"
No. 4: ; = ;i.-2l+-
.\„.r,: ( = :;.iii;+-
>'■! IIIUIUI.' 1
)Ie
|,y,lH.|ii
l..')04
l.-J.HO
Olwc.fviT. .J. .1 X. Skv
3.01. Length of inith of
Winil. lii.'ht breeze.
m. (j/„p„i =15.21.]
j No.
Interv.al.
P.M.
Fall.
Else.
Mh,.
5
5
After 15 niinntes' exposure to sun—
4'' 25'" to 4'' :»)'" fall in .shade
: i».7i
I
3».84
4 .15 to4 40 fall in .shade
' 2 .73
ij
2 .93
4 45 to 4 50 fall iu shade
2 . 24
j!
3 .22
7
FrouiXo.2; > = 3.84+^''^"j"'"''^:=6°.0fi. C.ilorics per i
I'i..ui\n.4: /=J.i«+'-'''' + '--'^'*=r, .42. (_'Ml,iii,s p.-i-
Km,,, N... i;: /=:!.22+-
, a.24 + 2.41_
1.301
1. ir,3
l.l'.ll
1.21!^
j;e',i,u','a lusi,.
„l:inl I
■ pyrlirli,
i>yi;iieli()Mi;tri('. ()r..si;i;\ATU)Xs.
63
[Date. Aiii;iivl :il. IP"
Cliargoiif ».il.r h«i
No. lutcvval.
Mill.
Fall. Ki
.^h;jde
Fn.iii \... ■-': I =--'.;i; +
■j.j-.' + i.;i-_
i.;is + -
.M. C'al..ii.-M"-i i.iim.l..p,-i M|,i
Fr.iHi X... I: /=vl.7.". + '■■" Z^""- = ■> ■"-■ (':ii"n. s l"i- iiiiniil.- per v.]ii
l-r.n„ N,.. 11: ( ^ i.-:l + -■''"' ^ "■'" = :i .VJH. C;.I.>| i.-^ |.ri ihmi.,I.M"-i- ..,"
M.M.I _
I.-JIT
i.-.'ii;i
i.-.'iii
invlH-lM.ln.-ti-l
T.vr.LE 4:^
Mill. After ISiniuutr.-! espoamc. tosliu-
lJ M la IL- 1
:;^ + :;.;i;
X... 1: / = :!.:,;)+■
Fr..iii No. r, : / = -J.-7
K.iM. Ki^
Fn.i.i No. -i: ( = :l..-.ll + - - + ■'■•'■' ^ U' .:!?. C'alo, irs por imn.ito ,,.■,■ >,,„
(■:,lo,„-M"-ii"in,it.- p.TM|„
C':,lo,,e..prr,n,uu..M"Ts,|U
1 . r.i.-
IJ.'.lilro.l tostJIl.hinl I
lip. (ll.srIV.V, .T. .1 >
s,.-:...ii. i.,,i^tii..ip.,
Xo. Ililprval.
Ji'l I. If /< l-ll
Fall. His
ixin'" toV'' i"Ta!"i"sl".r'!
i :i.'. li. 4 lit lall 111 Mia.lr'
F No. I : / ^ -,'.11 + .', - = I ..-,-. Calorie, por miiiiito por ...pun
Floiu N.i. li: ( - -J.-Jl + '■'"' ^ '■'- = 1 .3-1. (■ai.il-i.'.s pi-r iiiiiiulo p.T .sipiai
Ml. Ill
i;..lii.;.d toMaii.lar.l iii.rtiiiy iiNrlii-lioiiii'lLT
1.117
1.11^7
1. i.m;
i.4i;.-
64
ltESEARCIIi:S OX SOLAlt llJiAT.
JInmitaiii Camp. Observer. .T. .T. X. Sly, (l.rp l.liir. 'n'iii.l, li^litbrcezc.
r,arran,-t(ir (/3„) = 5.U0. I.c-ustli uf path of ray (,lf„l = 1.836. iA[„ (5,,) = !). 18.1
No. IiiLervnl.
4'. 60
3 .69
FldiM Nu. '2 : t^-i.m +
Fr..ui N.J. 1 ; ( =- ;!..S^. +
^3 + l.;J.\
1.-:^ + l.HT
= .'■)•. G4. Calories pi
= .-|\1G, Caluri.-.v |ie
utL'per.s.|"
.!.■ i.rrs,,n
iitc-p.r.s.|U
KwliKc'd 1(1 Btaiiihml i
l.yrl.Wioiiietor....
Tahle 4:.>
l.:W4
l.ia-l
, M..iMi(aiii Camp.
lervi-r. J. .1. N. Sky, dn-\: Mm;. Wiml. IV.sli breeze.
Leiifjth orpath of ray (J/,) = 1.132. I.H, ^,) = D.67.|
No.
Interval.
5
Noon.
Fall,
Rise.
After 15 minrites' exposure to sun —
'"jo.'es"'"
1150 to 11 sr, fall ill shade
1 .71
3 93
12 00 to 12 05 fall ill shaile
2.74
3 .23
12 10 In 12 15 fallinshade
2.28
= .^.40. Call.
= 6.111 <'.il..
liniitf per .-..ina
mH.leper,s,iua
linutepersqua
1. lilK
l..'i)ti
i.4:ir>
1.447
to Ntaiiilar.l me
No. Interval.
pyrlieliometer....
Table 46.
ouiitaiii Csiiup. Observer. J.J.N. Sky. dccji blue. AViiid. I'resh lireezt".
ivometer (j3„)=4.99. LeiigtU of path of r.iy {.l/,J=2.0.Mt. ( Jf„ 3„) = 14.77.]
1 5 ■
4' 25" to 4' 30'
4 30 to 4 35
4 35 to 4 40
4 40 to 4 45
4 45 to 4 50
4 50 to 4 55
4 55 to 5 00
fall in shade
1-\S0
rj
fall in .'.hade
1 .90
4 5
0 5
fall in sliade
2 .33
on, X„. 4 : / = -.'.ll.-, +
on. No. li; / = -.'.C.;i +
1+ I.(
+ ■>:.
= 4-.70. L'alo
= 4 .l.U. C'aloi
linnte per ,s,ina
innleper,s,|na
■a to .standard i
e.iry pyrlieln
i'Vi;ni;i.i()Mi:Ti;i(' oi'.sioitvATioNs.
CiS
WIIITNKY ri;Aiv.
Taiu.i: 17.
\Vli,i,i,.\ (llj.„'i
(j;,l ;; l-lll-'. iJ/fil
Nc.
Ilili-iv:,],
1
Min All.'.
S 1-JI'4.V" 1.. 1
S 12 •... 1.. 1
F..11. i;..
Fi.,i,i\...i;:t_:!.:ii; + -
Ml. C;,!.,,!,-. ,„.,„. ii. 1,1,. |„, s.|U
<>'■ (■;ll"rirs|,.-l'l,,, ■ |„', s.,,1
-■1 C. ■i,.M|,..|„.,l,lll.. |..TS.|M
l;.'.lll..-(l to M;il.,l,',
1. i:;i;
L.^.IW
1. in;
1. iiy
1. .-'r.T
|...;.k..l' Wl.il.i.'V. lll.s.rv.T, (), E- M. Sk\ , vl V 1. .Jy WiiJ.l, '. Tl...
r..l.i.-k..' (S,l ^4 40. I..>M L-lll ..f pill, i.r .■;i,v ll/.l :- 1 'illl. I.U, ^,1 - .'...'.!.]
Fall. Kit
121. .nl.' 111)1. to 121. r.ll". 30- fall ill .-.LiicU-
12 nS 311 to 1 01 30 vi.sc ill son ..
I 111 30 to 1 0(1 311 full III .-lia.k-
1 06 30 to 1 11 30 lis.- ill sun ..
1 11 30 to 1 in 30 fall ill .sl.ail.'
1 16 30 to 1 L'l 3.1 ris.- in s.ra .
I 21 3U to 1 26 30 tall ill .-li.l.l.-
1 20 .10 to 1 31 30 risr ii. -m. .
1 31 30 Iji 1 30 30 fall in sl.arli-
I .36 30 to 1 41 30 l.».. ill -son -
1 41 30 to 1 46 30 li.ll 111 sLa.l.-
""■i--
'23"'
■■'
so
3 . 70
I'r.iiii No.--'
F 1 N... 1 : t :i.>ii +
V N... <;m :'."ii +
I'r N... f-M :i.7ii +
Fi..i,i\... HI: t --:i.li-J +
1,1,-,+ 1.
l.;iii + (i.-
ii,;ii-l-i.,
1 .-,11+ 1.'
' -:, .11:1. (■:il..ll..i-|"l- liiill.it.- |"-fs.|.l
-4 .1111. l',il..iu-s|, ., ,„,„„l,. |,us,,„
'^4 .,-.11. l'i.l,„„-s,„T,ini,,it.-|,rrs.|,i
■---4 ..V. ('iil..ii,-s,.,., miiiiit,. |„.rs.|ii
11,011
K.-illlioil t.i stliu.liil.l
i.m.-,
1.-J4.-.
1. |,~^
1. li'.l
1.111
1.41:.
y i.v.ii.ii"ii»-t.f
iiisrrs..<irix nv tvriii'.i.iioif/i r.i; iiiis7^in',\l'l(i\s.
W .■ iilisrixr ,uii,siilii;ilili. viiiiiili.iiis ill till- liii'iisiurd he It lictwrrii iiiir day anil i IliiT, infll
wlini llic,--k\ aii|irai.s iM|iiall> rlrar. In lai'l. with this iiistiiiiiiciit mily a i|iiitc ali.siiliitf i-ailii i.s
siiitalilr fill' iili,->rr\;itiiiii, anil a,s wi- a|i|iiiiacli tlii.s iari'l\ allainnl r.inilili.in llir irailinu's w ill ri.sf, s .
llial llirsr lna\ In- ,-.ill,-.lili-M.il :1s 11,^11:1 1 1.\ to. 1 l.i« , ou illi; to I his r:t llsr :l h illr. We IniVfJllst olitaillill
by 0111 coiiiiiaii.s.in with llii- nn-iviiiy jiMlirli ■ttf tlir iiiiill i|il.\ in- l.irt.n l.JT, «liirli iii:i\ lie
ciinsiiU'U'd to intioilncc an a|i|iiii.\iiii:itf iinircliiin l.n tlif iion roiiiliirti\ il \ of tlir watt-r, alrraily
Il..-,,_i.-,_Xo. XV !t
ac^
KESEAUCriES OX SOLAK HEAT.
lelcricil tii: hut tlinr :iii' srviTal small eoiTCetiiiiis wiiicli I'diiillct omits, anil wliicli, tlioiijili not
pidlK'ily iic,uli;;ililc, we niiiil also liere, tlioii^li they aie f;iv('ii in full in (.■onnei'tion with the acti.
nomi'tcr. Il is. in fad. a waste ol' lalior to attempt the seiions task of determining' these s]ieeial
valnes for tlie pyi heli(jiiu'tei-, and for the ]inipose of improvinL; so nnsatisfaetory an instinment ;
Imt we lemaik lliat llii' oniilti d ronvctions aic in ueiicial of the positi\c sign, so that the valne
of the solar eonslant, w hieh we now ]>roeeed to deduce li\ I'onillel's method, wonhl be still greater
if these were iiitroihned. The values we use aic tai^iMi lium the |ireeeding' tables, where they ai'u
expressed in calories, (um' calorie being the amnuni ol' lieal reipiired to warm one gramme of water
tVom (T to 1 Cenligiade. and ihe solar <'oiistant being expii'^si'd by the number of calories i)er
minnte given by the sun's ra\s beibre absorption falling uoimally on 1 sij cm. Thus, on August
Utb,we obtained 1 .■'.'.il calories as tin/ loMting etfect olthe sun pel minute in the morning at Lone
Pine, where its rays fall noiinally on a surface I cm. sipnire, a \alue wliieh we consider as below
the truth.
Let M, ,1, re]iresent the absorbing air umss at the noon oliseivatiou, J/,,,;,, that at the miu'ning
or evening olisci\ aliens, (U' their ukmii. Let r, demile Ihe eiirr<'eted value iu calories found by
the noon observation and (',, that by the morning (u <'\ening observatiims, or their mean.
Then /,' being llie heat before absor]ition. i.e.. the solar constant, a the coefticieut of transmis-
si(ui through the entire ainiosiihere (such as woulil suiip(Ul T.li dm. of mereury), «'" is the eoelli-
eient of transmission.
•I -[(^' J-"""" ■"■"■ ^—^Xih
' l.n
Tlius, on August 14 —
Mi,i, = 7.1.S .l/„ ,i,, (morn.) = L'i.L'o -l^,,/?,, (eve.) = 14.1.'(i
<" = I..MS C„ (morn.) = ].:;!lt r„ (eve.) = 1.318
and if wedetennine n from noon and nnirniii.g obser\ali(Uis, we ha\e
II = (l.tl(lor> A'= 1.7St)
If from noon and exi'iiing obserxatious —
II = o.s,34L' E = l.Ts;;
We should, by l'<millet's theory, tind the same \alues lor ii and J'! under either eiriaimstanei.
Tabi.k 411.
llahulioii of Lone Pine pi/rheUniiiihi nli^,
fComputation of o. Ciniiii
> l„i roiiiUi-rH formula.
Morning and noon. Evening and noon.
August 12. August 13. ' August 14. August 11. ' August 12. August 14.
Lug. 7.6
.1/„S„
2lfi,
iL,ti„—il,fi,
Log. (.lr„^„-j;,;3,) .
Logic
V,,
u,i.c.,..^.l''^.'.'.'.
LoIr',-L."ig. (•,'!..■
Logo _
Tall. Logo
11. 8S0S
0. PS08
0. 88118
0, 8808 I
0. 8808
0. 8608
14. .il
15,25
15.25
14. 33
15.25
14.20
7.16
7.14
7.18
7.16
7.16
7.18
7.35
8. U
8.07 1
7.17
8.00
7.02
0. Sfifi3
11. £1000
0.9069
0. 8555
0, 9079
0. 8403
0 0145
9 9718
9 9739
0. 0253
9. 9729
0. 0345
1.034
0, 937
0. 942
1. OCO
0.940
1.083
1. 205
1,311
1.394
1.375
1. 298
1.318
1.453
1..'.43
1 .5!>8
1,591
1.4.53
1. 5.58
0. 11121
0. 1176
0, 144.1
0.1383
0 1133
0.1199
0. 1623
0, 1884
0. 1926
0. 2017
0.1623
0. 1926
— 0. 0602
-0.0708
-O. 0483
-0.0.-34
-0. 0022
- 0,0663
-0. 0455
-0. 0672
-0 0461
- 0. 0787
9. 937S
9. 9337
9. 9545
9. 0328
0. 9539
9,9213
0. S605
0. 8384
0. 9005
0. 8565
0. 8993
0. 8342
•'=if:.f>,
7,6
rvRiiiciJoMKTiii;.
(j7
Taule ."ill.
lCc„.,,„U.,tUi„ .,r i', CmiiMK,.,; A.B. S,]
August 11. j August 12. I Augu
Mr
Xii
Log
Lug
Log
C
m
76
Jff
J//J
'■"
"fi
Log
Log
J'";;- ;;;;;;;
0. nS3 0.2017 0. lu
l.l."iii2 0.8349 1,17;
0. 8«08 0. ►'S98 0. SSI
-11 1 -U 1
MeauoC Meauof
023 0 1170 0, IfiSI n. 1.12:i 0 1920
i.U9 ' 1. 1833 0, S537 1. 1(i82 0, 8301
iS(l8 0. 8808 0 8808 0. 8808 0. 8808
('iiiii|iariiii; llic- Miciiiiiii.;; ;niil ikkiii iiiiil cviMiiii;; anil iiu Ii.^frvatioii.s af Lciiic I'iiii'. we |j
tlii'li the IcilldwiiiK lalilc:
Taulk .■)!.
LdNE riXE.
0.8.367 1.841
0. SC0.3 0.8993 1.034
0.6.384 1.781
Till' iiiraii traiisMii,8siliilit,v at Liuii' I'ilir is tlii'li licrr foiliiil \>y Poiiillrt's iiirtliml tii lir aliout
ST ]HT ri-Mt. Tliat ili'tilliiilioil li.\ hi 'ai- llii- .sral li'Vrl was aliuiit sn prr rriit. Tlir liiiiilnl linn-
at (iiir ilisposal fur (ili.si-i\ afimi m-iuK-in rniirlii.^iiuis Imni mii ini'snit snir.s Irss triislwoi lliy lliau
IViiiii his fiilk'i' oues. It sci'iiis rh-ai, hii\\i-\ la-. tliat a I an aim iidc of aliiiust l.HHO inrtcis, w licii' uiir
oli.servations were tal.eii. the air. n-H<iht Jnr iniijhl. is innrli tnni; tniiisiniiciil tn tin- limt nii/s
(tliatlieriiiaiiiiiis) tluia at the sea-hrrl.
Even with this iiislrmneiit. then, u e sre that the iiimlili/ i,f tlie alisniliinu iinilnini as well as its
ilelisity eliaii,i;es as we asrenil. 'I'lie mean Aalne of tlie solar eonstant tioni i iiliseivations
(ealories 1.70(1) is reniaikalily near I'ouillet's (1.7(;4). Tin' only smniHianee of Ibis appears to be
that like llietlioils hiiii.i; about like results. The results thenisehes are, as we lielieve, in liolli
cii.se.s widely \vion<;.
Taiii.E '>-J.
I!,,hKl:ou nf M„i,„lain (•«/;.;. iihsnnilin,,^ { iiiirlH-limniln-).
I
Date.
Augu
Moruiiig
■n.
Evening
a noon.
Se|,t,.ii
licr 1. AngoiifJO.
A
igust 30.
A
ugustSI.
ptt-nilicr 1.
14.77
5.07
9.10
0.83
1.519
1. 838
0.1816
0.2643
-0 0827
— 0 0686
9 9314
1.3.21
.3. 67
9.54
r.347
1.084
0. 1895
0. 2203
-0. 0308
-0 iei4
0. 9343
14. 65
8 99
0. 83
1.408
1.800
0. 1667
0. 2553
-o.osfi;
S. 9247
iI,S,
-^.»,
S. 33
0. 91
f, ..
Log
Log.
Log
Tall.
vi,V'''^^.V/.'.'.'/.... '.'.'.
V,
f,-L"g.C,
,;:;j:;;';;;'
'.".'.'. -o'ooiil
(J
0 838^
0. 6409
0. 8539
■'■"1
08
KESEAKCIIICS ON .SOLAK HEAT.
Table 53.
[Computation of£.]
.Iff - 13.93
7.6
Loff.C
Aiigi
St 29.
Allgu
St 30.
Allgu
St 31.
SL'ptcn
jber 1.
Kvcniog.
13.93
Xoon. I
vening.
Jfoon.
EvouiDg
Noon.
5.66
Evening.
Ifoon,
5.00
15. 21
5.67
14. 05
14.77
5.07
1,830
0.737
2. 010
0. 740
1.930
0.745
1.910
0.740
0. 2263
-0.0661
0. 29«9
—0.0601
0.1 R95
-0. 0294
0. 22li3
-0. 0294
0. 1667
-0.07.53
0. 25,53
0. I.RIO
-0. 00.^6
0, 2643
-0. 06S6
-0. 12111
0. 3473
-0. 04R7
0.3476
2. 220
-0 0591
11. 24S0
-0,0219
0, 24S2
1 771
-0, 1453
0 3120
2 051
-0 0.561
U. 3114
2 049
-0. 1331
0, 3147
2 064
-0.0512
0.3155
2. 0C«
Taiii.k ."')4.
Wc now yivc :i .similar tabk' l(ir I lie uIlsim \ ntioiis at llic .Aldiiiitaiii Caiiip,
4K54
0 e'88
2. 226
7995
0. 9345
1. 772
6543
fl. 8409
2. 049
8375
0, 8539
2. 06S
\Vi' liavc niiiailvcl lit-ldic lliat uwiiij; ti, llic liij;li clitt^ im tl u.st »Iiu-li i.-(iiic(.-alc(l tlic sun
till its altitude was liij;li, men iiiiij; ulisin \ alicms tliere. are in i;eiieial, less li iistwoitliy than the
eNciiiiii; ones, and iliis is siieeially seen in the picsi'iit aiiomaloii.s values (if « Iroiii the niiiniing
si'iies. Tlie laKiii and e\eiiin,L: mies j^i ve (f = ..S7l' or \ ci y near that fiiiind at Lone Pine. Oiiiit-
tln.y the inoiniiif^ \aliies, we ha\etlie mean Solar (.'(instant L'.dl".!. a ureater \alne than that at
•Lone I'iiie.
In aeeoiclunee « illi the icsnils (if iiie\ ions olisevveis, then, and of onr (iwn with (itlier instrn-
melits, ire find a linujrr rain,- ,•/ tlir .S„l,ir CinifitKir k.s- ircdnliirr it finiH ohsn-nitiinis llirdiiiih ,i siiidUn-
Onr (iliser\ati(iiis (111 the untain and at Lime I'iiie imt lieini; s\ nchniiHins. we can liest coin-
(laic summaries of the results at the lii,i;liei station with those at the lower.
Taijle o.").
Siimiiiarij of piirheVwmettr rt'SiiUa.
AT LOSE PISE.
Date.
August 11
August 12
Augu.st 13
August 14
Mean Alp
lir-masa.
Date.
P.M.
tJucoireetetl calories.
A.M.
15. 15
14. 51
15. 25
M.
7.16
7.16
7,14
A.M.
M. P.M.
14.33 August 11
15,25 August 12
August 13
1.001
.996
1. 032
1. 098
1, 2,53 1. 083
1.144 1.022
1.215 1
15.04
1
7.16
14. ,59 Means
1. 032
em rected calories
1.311
1. 535 1. 331
A 4
MULMAIN CAMP.
-1
August 30 . . .
August 31 ...
September 1 .
1. 053 1 567 ' 1. 326
1.204 1,320 1.218
1.222 1.417 1.150
1. 3,t4 1,447 1.190
1.204 1,439 1.224
1.529 1.828 l7554~
PYiaiEI.IOMETK!;.
69
Applyiii.i; I'duillct's tonimla to these results, we li;ive. cciiiiiiarilii; like luiuis of obseix atioii on
the liioiiiitaoi ami at Loiii- Pine:
r;il.
JIouiitaiiit'aiiiiMi-.oiiiiiiu: e=l.oL".l i ^^i,,,,,,,,. „^ si',;: i;=l.'.l--l.
Lone I'ine, inornini; : r=l..lll '
.Alonntain ('ain]i, noon: r=l..SL.'S |
Lone I'lni'. nonn: . = 1 .VIo •
Alonntain Canip, <'venin,u: i=].o.'"it (
x\heiie,. ,( = .4i:i: /•;=i.'.)9:;.
■'■'. whence (( = L{;:;ilx It)': A'=.(l(il.
Lone I'ine. evening;: r=l :i.;i '
These i-esiilts si^ein to ns most instrnelive in ic-aid to t he defects of Poniliet's foiinnla foicnir
pli'sent ]ini|iose. Its use here imle|ien<leiil 1> ot its other erjors tacitly :issiinies that a t;i\en air-
m:iss ahva.\s exeieises the s:inie alisor|itlon \\hate\er thi' eoustil uents of the :iir may lie. The
results of this err. an s assumpti lo mit appiMr notaUle when we compare hi;;h and low sun
oliser\aliiuis at the sa stall. m. as I'.aiill.-t hinisell ilal. lor 111.' .-iLir atli-cts .■a.-h in turn; liut
v.lieii we c.mi]iar.- an air mass lal;.-ii on the m.innlain with an ..iual aii-iuass taken in the valli'V,
the conse.jneiii .'s of th.' eii.n^ nia\ lie.-.ain- sali.lil. riiiis. in llie e\enin,L: ohs, r\ ati.nis w .■ ha\ .■
the air massi-s at L.m.' I'ine an. I at M.iniilain < amp alaaist i.l.Miti.-al. th.'V lH-in:4 in tin- .in.' .-asi'
such as w.Mihl supp..it .111). It. oil of iiMl.aux. aii.l in ih.- ..tin 14. (i I. \\"e shouhl then hav,- the
alisorpti.ujs als.i almost iil.mti.-al if the assiimplioii were .■..ir.et. Imt n.ithinu of th.- kiml happ.ms.
and we yet, in fact, the monstrous lesnlts ^i\.-ii in the last iiislan..-. Il il.i.-s not seem liei'essary
to f;ive here further illustration of the null iisf w ..i i liiii. ss .if th.' t.ii miila in ..thi'i ways (see discus-
sion ill article ini s]iectro-boIoiiieter) t.i il.'t.-rmiii.' ns to depi'iiil as little as possilile on lesnlts
olitain.'il with this iiistr eiit ami in this mann.-i Wi- ai.' l..ii-eil L. .- lu.li' that tin- instruni.-nt
eiv.-s th.' 1. suits, i-xeii ..f dii.i-t ..Ii.mm \ atioii. iiiii.-li to.i small, ami, as \u- ileinoiistrate hit. 'f, the
toniiiila itseltwill inlallilily d. .111. .■ t.i.. small Miliii'S tor th.' Solar C.mstant ex.'ii Ikuii .-.iiivi't
oliser\ati.>iis. \\"e will pass on, tli.ai. to the .■.uisiili-rat mil ..f iiioiv trustw.uthy iiisti iimeiits ami
lueth.i.ls.
CMTAI'TER V.
TTSIO OF GLOBE ACTI>JOMETER.
W'liini it bcoaiiR' iii'cessary Id ilcti'niiiiK' dii llic use of siiiiic form of actinoineter in coiijiiiictioii
with tli(i siiei'tro-boloiiictiT. tlic iiistriiiiieiits ol' M. X'ioIIc, M. <'iova, and tlie conjiisate bulbs of M.
Marie Davy wore selected. 1 take tins (i|ipiatinnfy of aclcno\vled},'inf;' the kindness of all these
.Ceiitlenien, who weiv ;i 1 enough to nM(l<Mtake to see that I liad snitable eopies made of their
resjKM'tixc instriimenls: lint that of Jl. Maiie l)a\y was broken in transit, and that of M.
Crova, most unfortunately, diil not arrive in tinu' for the e.xpediticui. Oidy that of M. Violle
eatne befoii' the exjiedition started. I therefore ordered the eonstruetion of two small fjii^l't'
aetiiMimelers in I'if tslmi ;;■.
The use of the .ulolie aetinometcr jaesuiiposes the knowledge of the I'aet that the sun's temjiera-
tare, whalexci it may lie, is at any late so lar hi;;her than that of the inelosed shell of water or iee
to which the sun theiuiometer ladialcs. that the excess of the latter under solar radiation is sensibly
Iliesauie under all ((Uiditions of actual oliserv aticui. Accoidini; to Jlr. Ericsson's most earel'nl
delei-miuatious, t lie <'xeess of such a tlieiinomelcj' is thi' same whether it be radiatiuM' to an inclosed
IT8E OF (iLor.K .\( tin()Mi;ti:i;
71
slicll (.r incllili.y ire (ir tii (ilic (if red Iml iidii; -.nu] iIm.u^Ii :iII ;irc IK.I :ii;rc((l lli.ii tlic excess is so
alisciliitely iiidcpciHleiil el' tlie snri(iiiii(liims. tlicre is iie .liiiihl llinl li.e leiiii.i'i :il me i.lCxeess iii;i\
be liere triMfed ;is iiiile|MMi(leiil ..I' llie l,'in|,ei ;il in v nl' tlie \\;ilei ii-ed in (Mii ;ielii;il e\|.iTiineiil .
1 li;i(l expenineiiled ill :ill tile lime iit iii.\ iniii iii:i ml Willi tlie ]:ir-e i; I, ,1 le ml iiioinetei i.t M.
Violle, Il Itsiile or whieli 1 liml a -m, ll |.l.iee(l s,, tlllll itnili^llt he :ieel|] lltel.v illlceleil to
till' SUM witllllUt I>relllllili;l|-,\ ex | insure. ;iliil :il'ler ll X|ie,llti.Jli si ,irleil lud llie two slii:iller;letimiiii
eters inoilliteil altaziiniillil.\ (.in ei|ii:itni ial m.iiiiiliiiu w.nilil lie pnilialily helleri in an iin|jre\ iseil
Wdoilcii siipiiort. wliieli inn veil iii.iie manauealile t liaii t lie i in^. The lar,:;e aeti iietei nl' .M , Nnille
may hi' I'oiiinl ileserilieil in the Ai les de ( 'Inline et de riiysii|iie I'nr IsTil, Mil. 10. |,aues l.". an I 1(1,
and in nninerinis ntliei' plaees. sn Unit it is nut iieeessary tn redesenlie it here. The t u u smallei-
aetilinliletei's wliieli I eiii|dijyed uitli it are i-eiiiesented in Im-s. ."i aiel d, where I ) is the iliu|ilirai;iii
plate adniittin.e tlie solar ia,\s: S' the inlet t'of ilie water lietweeii the i;lolies: S llie exit: T' the
tlicniioiia'ter whieh re^;isteis the water teiniiei atare: 'I' Ihe tlieiinomeler w hieli reuisters the i^xeess
cail.sed by the snn o\er the siiiionndines: (" a eoiintei imise: C a \ciy sli-litly ;;ronnd ylass plate
whicli prevents the enlranee of air eiii rents Ironi below and ieeei\cs the shadow e.ist by the inilb
of tlie central theriiioineter: A is the leinpoiaiy inoiinliiii; ariaiiued on the expidilioii. Witli
either one oftlie.se two loniis of the ejobe aelii leter we have no -lass or abs.nbine material as a
cover, and eonseipienlly do not attempt to observe in \ aeiio but. liy a means to be diieitly explained,
oljtain in theory the saini' results as tlioii;;li we dill so. We may use them in various ways.
Aecordilif;- to Jl. \'iolle"s melliod the instriilnelit is exposed to the siin's radiation lor a I'ertain lime,
usually fifteen or tweiit.\ iniiiiiles. The inleriial thermometei T rises at llrst iapidl.\ . t hen more
slowly, till it sensibly attains its lemperatnie of eipiilibiinm. where it is radiatiii- as iiineli to the
surrounding gliAw as it is reeei\iii^ fiom the snn. ,\s ihe Ihennoineter rises, the teinpeiatiiie is
to be read from ininnle to miiinte until il beeomes stationary, then the solar i.idiation is eiit otf
and the therino ter allowed to eool diiiiii- a like time till it has sensibly regained the tempera-
ture of the .ylobe around it. When the excess ol' leinperal lire of the snn I liei mometer o\im' that
of its iiielosure is e\tlviii(d.\ small, the loss of heat is sensibly propoi lional to tin- teiiiperatiii e. so
that at the first instant of its healing (when the lempiaatiire ol excess is Oi I here is |iii tlieoiw ) all
gain and no loss, whether from ladialion or coii\ ection. and if tlii^ ////((e/ rale of heatin,:; could
be (letennined we should have the same result whether oar thermometer was in air or in vacuo.
KKSKAlailKS ON .SOLAi; IllCAT.
Tlic excess wliicli tin- llin iiKunrlcr \ liii;ill\ iviicli is, in Ibis )i(iiiit (if view, iiiiiii:it('lial, tor
wlu'iiwr kiioH Ihc ;iiv:i (iiir I iM'niKJiiictiT liiilli cxikiscs tn llic siiii(c;ill this S) ami tin' spcci tic
liiMl or wiitci' ri|iii\-,ili'iit of lis liiilli (M). «(■ nrid .,ii]> lii,. iiijiijl iiiti' ( \' ) to (IctiTiiiiiic the sohir
ladiiilion 111 cnloiios |ii'i' iiiiiinlc. loi ihis = ; . 'Iliis iiiiiial lalc. Iioucvci'. is < vaiicscciil, and
cMiiiiot he (liivrlly olisia\C(l. liul il nia> lir (IcIiTaiincil williiii \r\\ narrow limits liy actual oli-
scr\ali( f the rale ilnnnu I lie liisl (|iiarha' or lialf mil 1 1 in in- winch the iiu'aii ial<' can he
liilt very little inrcrioi- 1(1 Ihc niilial one. anil li\ also expci imciitallv (Ictcrmininji' anol liei' value,
Hliich iiiiist necessarily lie a \-ci y lili le in excess of it (« liicli is easily iloiie). ami lictHccii these
closely com il^mills values the line one liinsi lie. These liiclhoils ale t hose of ilii ect ex | iclilllen t.
The lollouiim ingenious iiielhoil. due to M. \"iolle, may lie -atlicr saiij to lie I hat of a mat lieiiiaticiaM.
If «e re|ires,uil the rise of I lie ilicriiionietcr ,L;ra|iliicall\ , ami if we ml in if the siip]ii)silion that,
iimler the \ arieil cireniustaiiccs w liich affect it, ils i isc is re|iresciileil riuorously li\ some siinphMUirve
(r. (/., a logarithmic lairvc;, it is cMileiit that. Ii\ uatcliiii- the thermometer loiii; enoii.^h, we coiihl
olitain the eiinalion of this can ve. ami then liy ilillei eiiliatiii u this ci|iialioii olilaiii the initial r.ite.
Il woiihl seem, however, that any lawwlneh iiiiilese\cr> paitof a know n curve to every other
in a simple ami li-oroiis -coincli ical iclalion. is one which n.itnre raii'ly exactly follows. The
reading; of the I liermoiiicter. for instama', at the eml of the lifth or tenth minute (lepeiids upon the
clomls that lia\c passed, or the luecze that has lilown. since it lic-aii to rise; and. so ion- as it is'
true that e\'eli nmlei the most la\ or.ihle comlil ions the Icadini; is allectcil from moment to inoinent
li\ niimliciless niinnte ami casual circnmstanccs. it is evident that this leading can lie exactly eon-
iiccled «itli the initial rate li\ no know n law. ,M. \' mile's form ii he. Iiowcm r. viitnally assume tluit
the lairve represent iiij;- this is aetnally such a louarilhmic one. or, at any rate, a lairve all whose
jioints are iiiterde]iemlent and eonnected li\ s ■ simple law. lie ealciihitcs the initial rates on
this assiiinption, and in doiiiLf so apjieais to iis to reason coriectly and elegantly as a matheinati-
eiaii, lint on premises whicli the pli\sicist may perhaps he jierinitteil to ipiestion.
Careful exiiiaimeiit at Alh-licny. which the reader will timl later in detail, has shown thaf
the initial rate detiainincd liy this piocess is always somewhat lua suhill. We take [out of nearly
a hundred examjiles we mi-ht cale) the oliser\ations with the small actii 'ter under the most
favorable condilions from 1 1 '■:'.()"' lo Il'i'on .\ii-iist LTi, l.SSl. tiie olisei vatioiis themsehes beini; .uiveii
in talilc ."iS. We draw . in our ow n in\ (■stij;atioiis, iijioii as laiyc a scale as iiraeticable (c. //., 1 in =
1 or 1 minntci. the c in \ c rcpicscnl in- the actual olisei \ ations. In the heatiii.i; (airve the ahseissa-
may he propoitional to times and t he ordi nates toll liseiM-d tcinperatiiics of excess, and we liiuc
then a (air\e lieai iii.^ most icsemiilanee to the hi- a nth mii- one. Taking in this laii \ e of oliscrxatioii
three snitalile ]ioiiils with eipiidistant alisiassa- llliose correspondin.i.;. for instance, to the excesses of
the tliiu' ctel^ at ilie lieminnili;;, iniildlc, and eml of the I ■), we next pass a lo-arithmie lanwe
Ihroii-h these poinls. and dctermnie ils axis of X. If the course of ohserxation is indeed repre-
sented hy a lo-arilhinic curve, the siilitan-eiils of the actual (anvc of olisia vatic n this axis of
X will lie sensibly constant. .\s a iiiattci' of tact they .v.(/^/( "("/'c,i/;i/ decirase toward the iiiitia!
point, so that the acliial rate ol rise is -reatcr than the rate deii\ed Iroiii the formula.
All the obseiA-cis were cxeiriscd at e\cry oppoi t iiiiitx . for some weeks before theai'tnal ivcorils
bc,i;aii. ill aeipiirin;.; exiicrtncss in I he use of the iiisi rnnicnt and accuracy in the icadin.y' of the ther-
meters. Nu less than ISd miiiiitc reailllii.:s. eai li taken on a I hennomelei. reading- direct to (1.1^
('.and by estimation toO.DF ('.. were made daily on eaidi iiisliiiment imlciiemleiit ly of the readin-s
of the water Ihermomeler. The results of this direct observation, whet hiu' made by the instru-
ment and tliermomeUus used by :\I . \' lolle or t he instrnmeiils made here, wit h tlierino ters by
other makers, in the clearest days ami in one of the driest cliiiiat-s in the world, were never
as l.ir-e as M. \i(ille has found. tlion,L:li. trom the fav Iilc comlitioiis. we slionhl exi>ect that
Ihcywould have been lar-ci'. I i-aiiiioi iindm take to. at pii sent, explain I his. I have, however,
f.iiind what apjicars to be a possible cause of i he discrep; y. On I hi' return from the expedition
our ow II thciii 'tm-s yaxc a less w ater cipin alciit in proportion lo their size than AI. Violle finds
tbr his. and this leil me to search critically in his urilin.us for si in le statcinciit as to the size of his
liiilbs ami the mass of menairy and .ylass in tliciii. lie says in a footnote : •• .1/, the water eqniv-
aleiit, was carefully (h'terinined. Il was measured iudiiectly by ex|ieriineiit.s on coolin.i;-, and di-
rsF, OK (ii.oiu-: Aci'iNoMiirKi;.
lectly liy ;i tlicrriioiiicti'r in i-\imv way rcsi'ijililiiiK lliaf \vlii<-h had Immmi used, Incikt'ii at tlic stem
In bnlli i/ascs .1/ was foninl (m|U;iI to ii.l.'1'l: yrai <'s." ami In- tdiind (I.-K;,"..
We jjive M. ^'i(lll(■■s own rcinarlis:
IMTMli....: .11,
Mtlirnnnn.rtlvl — rr,
rv.TM.I M .■■■ liMMH- .-sr.^ Osi I',,, I i 11 1 r I V , ■ ] , l ;, 1 1 r.,,11 ].■ l;i
.r.ili;n,llrMi.-iil .Im 111. nnonirli, .-.n i i;;.^.- .1 ii i .1 1 ,,i.l i^mii
.I..11. I'll. I1..11 .■.instil llll S.il.ll ll."!!",',' ,|.s .11. l,s .111 1
rlavit.'ssi- .Ifn-IVni-
liiMi.. f+l-T.-yU^rUU-
>l I ^'' 1^' ■""■"- t.-ui-
t, I'm .■.,iiM-.|ii,.„t, si
:.lil.s:n.iii.,l,sr,x.' I..ii.l;i,.t .,11, l,|.i.-, 1,1111111. ■- I',., Iiaiillini.i.l .1,1 lli.-iii,..n
l-.-pt.' .■.-It,. l;i,ll;il ,■! ,|.r .I.s.n.. ;il.,,, I., r.-r I.ss.ih.i,!, ,,|i tl..il.rl:i
nil,' 111,' v:il,-ii|- ,-..iisliilll.' .!.■ /"+/', .|ii 1.' s.i.il.nii.nil r rt r .■|,;ii,.j
i',Misliiiii,' |.ai- I:, Mil, 111 .11 .-an 1/ .1.' I.i |i.,i 1 1., i .In i I,, i i li.. .,111 s'.,!,:,,
Iiiilll.'. ,111 lima la .plan 111.' .!.' . Iial.'iii s.>laili' .,111 I. .111 1..' .11 111,.' luniul.' siii I 1 i-ii I iin.a 1 ,' . all.' .1.' s.iil
rav..lis. .'•I'st-a ,lii'.' la ,„,..„r, „l,.,.l„r ,!. la .] iia .1 1 1 1 .• .1, . Iial.iir l',',.'ii.' par l.i.li.' ^I.,l.,' ail p. nut .1 a I'm
V„i.i. pat .x.'iiipl,'. 1,N,.U,'M at Mills lail.s.lan- la ma 1 1 n.'.' .1 11 li.i I I-;:, an s,,|i,„.'t .iiiMi.iit-l
pns, a lala.llall.ais.
1.11. I, ..'ha.,.,.' ^al.
','». Kn innllipliaiil
11 la.l.MsanI pa, la s.
E.lmuBo K.-flui.li!
La siiliiiii,' » + (>' ,'sl ,',iiistalit,-i-t,';;ill,-:i«.,: r,-i'lniiili,Mm-iil ,'t 1.- l.'IVi.i.liss.'m.iit s,' s,,iil tails;
L,'s t,'iiip,;iatiirisir.',liaiiH,--iii,iit s.iiit ,l,,iin,M-s par la Inniink.
ct les ti-liip,'i'atnr,'s ,!,• i'.'IV..i.liss,'in,'iit jni- la tniinul.'
Li'S vit.-ssi-siV,
il ,'t .1.' i'cli..i.liss,',n,'iit Mint il.iiii- i',-sp,'i'li
,r,..i il siiit ,|n.'. p. Ill' n,.' II.- t.'nip.'ialiir,' 'j = 'j- . .,1. aula
r+ r= iii'i..
I'll a^allt.lL;,■ pi,', 1,11X ,1,' la m.^lll,.,!,- ,'st r,'lll]ll,.i ,1,' tnlltis 1,
i-"iili"l,' liL' ii.\ ,l,.iil riiiip..ll; n.'saiiialt .-. liapii.T.
al.'iil il.'la qilaiitit.: < li.Tcli,'
,11. an t/.l.'lap..rli In tin
La M.lnln,- I + rr,'pi,'s,. ra,t,.ni ,ln S,.l.-il : In pi i., pal la Mil, ill ,11.1111 t/.l.'la
,s-.','liaiill.. ill.'t .liMs.'.' pai la snila.'.'.i-niii;iaii.i.,'i.l.^.-ll.',,.i,str,n la ii-x pi ,'sM..„ ,iiiiii,'n.|ii,- ,1,. la .|iiaiilit.' al.s..lii
il.' .'Iial.'iir / i.'.,ii.' a In" -.'J'" .In inalm. 1.- \<: a. .,11 1-7:., an s int .In M..iit- Ulan.-, / = -.'MHI-J I'liiiit.- ,1,' ,'lial,'iii' ,'tali
la ipialitil.: ,1,- ,'lial,-iil' n.'.'.'ssair.' p. nil' .l.'V.'i .1.' 1 .I.';;.,' la l.'i.ip.i a 1 ill'r .1,' 1 - la liilii,' .r.'all.
I 1.1/ UN ail .1.' s,„'_.|i..i,s.' 1,1 . 1. 1.1 11,111.'.': -avail 1,1, s, 11,,' in,ln,','l, i„,.|,t pat' ,1,'s ,'Np,'ii,'i.,','s ,1,- ,.l,„i.liss,
111, -lit, ,'t ,ln',','l,'lii,'lit siir nil lln-i iin.iintl',' t.nit s.liil.la l.l.- a i.'llii ipii iiMlit s.-ni, rninpii a la liaiss ,• ,1,' la 'I;;,': ,,1 ,,
,lans l,'s,l,'iix,'as .1/ = li- .-.'■J-J .'t 1'..
.1/
Till- aliiivi'. j;ivcii as a finitiiiite (I ). (■unttiins all tlir inliniiiation lie allcuds iis alnmi tlir (li-lcr-
IMiiiatiiui lit the fitlidamrnttil \aliif mi w liirli liis snlar rmisttiiif n-sts. N (flu. ana nt a ;;iimI rinlr
(if Ills tliciiiHimclcl' litllli) \M' SIC "T (MKiS, w lirm-f \\ c liiid tlic (liamrlci iil his hiilli
il'.t;.-.— Nil. x\- 11)
74 liKSKAUClIKS OX SULAi; IlKAT.
tlio volume of such a spljeic. liciug
((•.SS)'X TT
(I
U..'ir)7 f. cm
If the IhiII. na> siilirioiil il latliiT tli m s|i'H-nc:il tin- r.'siilt i-; sciisiMv tin- s.imc. auil we sec ou
what a \ (ay aiiiiute c|uautity (aliiul oiu' Ihinl of a (ailiic eeiitimetei ) the liiial (h'teiniiuation reiioses,
auil ho V iMsily a rehitUely lar-i' eri.ji' uii-hl lie made \\\ I lie (leteiiiiiiialuiu of so sui ill a i|Uaiitity.
(I..;."!: culiic ceiitimcfer. tliiai. is the \iilume of M. \iollc's Imlli. an.l lie- water e(|uivaleiit of such
a siihciv, wciv it composeil eiilirel>(it iiienairy at a s|.e(alie ;4ia\il> ol l;;.(i ami speialie heat (if
.();«3, asdelermiued li,\ Ke.miaillt. would he hut .ILL' iiislead of ..'L'-'. The i;lass in these thermome-
ter hiilhs is of the thinnest desia i|iI]oii. hut \Mav the I luamometia' laillKd solid ylass with a specihc
.gravity of.", and of a hi.ulier specalie heal tli; iiy whadi we v.w liml as>i^iied to .ylass li\ Duhm^'
and I'elil (U^ li.\ l;ei;nanlt, the water iipii\ahait would slill he less than the .■JL'L' assij^ued to it hy
M. Violle. which appaicntl) can he U'pi csiaited l.\ no comhinat loll of ,i;lass and UKavury. It would
appear, since M. \i(ille's \ahie ol the s,.hii lonslalil (L'ol) is jiropiu ticmal to this S(aaniu,L:ly
jiiiiduiissilih' water cipiix alcnl. thai it is to he desiied that we should i,a\c an e.\plaiialioii ol these
iilipareiit dis(aTiiaucies.
Had it heeu known wlnai we ciuumeuced our oliseiAalious thai the init ial rale was smallei'
than thai j^iviai hy M. X'iolh's hirmiihi, we slnuild have saved oursidves -reat lalmr and attained
yreatcr accuiac\ h\ dm ct ohsi i \ al ions ol this mil ial lalc As w e m ipiiied I his know led i;c (Uil\ by
experience, when it w as t<io late lo altei l he melliod > f ohsei \ alicai aliead,\ e(Uiiiiii need, w e <-oli-
ti luted takiui; iniuulc leadini^s on all thicc ael iuomehas. and liaxe siihsicpacail ly applied corrections
to tliciii h\ means of caret ill deica iniiiathiiis liimui lua valtia'. The til lee actinomeleis arc thus <li.S-
caiminatcd. 'fliehiii;e acl inomeUa' w illi .■;(l.r, can. .i;lohc is calhdXo. 1. ll is supplied with two
thcni.ometcis h.\ Ihindiii ol I'aiis. dniihal to llfths of dc-rees, and read h\ estiinalion lo liftietlis.
The othei lluai ■leisaic divided totcuiths of dc;.;iees and read liy eslliuatiou to hiiudredllis.
"Baildili .sT:;!I," the wap l llici inmieler, has a liiilli (l.!)!ll cm. ill diainetei. The hiilli of ■• IhllHlili
ST::?."" the sun tlua uaei, is (I.IM;:; (un. m diaiiietei. The water ccpiivaliail of lliis thiainomcli'r
will he .u'xcai later.
Actinometci No. L', lia\ iii.i; a ,i;loh.' 1.", cau. in diamelel. is mouiiled so as to have an allazimril h
luolioi id i-. supplied w ilh a water tlier im'ter li\ ( ; iiinow , t iie diamctiu' of w lios,. Inilli s <l ,s:!(i cm.
ami with a siiii lluaiui ua hy (ire.ai. No, 4."i71, havin.u a liiilh di imelcr of l.L'tT laii.
The third ael ii.i unci ci is ol tie- .same size ami inouiil ili.u as No. 1'. In ll lia\c heeu used a wa! el'
I hen i-tcr li\ (liiiiiow.similar to I h. it for No. L', and .i sun I lici iiioiiiel er h\ (Ireeii, No -1."i7l', whose
Imlh had a diameter of l.L'l)7 laii. In all .mr olisei v.itions the wali-r has heeu (-onslaiitl> a^itale'd.
\Vc at lir.st did this hy torciu- the w.itcriii at om-lulieand out at the ol In-r, so as to k(-ep U|i a
uniform tiow and tempia at me, hut siilist it iilcd fiU' this auolliei method of a^iiitatin.i; tlu- water in
the acliiiomctia itsell.
Ill the lollowiu- tallies we h.i\e Used the same ,s> iiiliol.^ as M. \'iolle, lor 1 he la-adei's <'oii-
vciiielice. Thus, ii„ indicates the liiial* tempera I lire of I lie sun I licniiomctia' in excess of its sur
rouudiii.ns, in is a coiisi aut c-.u lesj.ondiii;; lo the icciproi-al ol the sulilaiiueut of 31. \iolIe's a.Ssuilil'd
loi^arithiuic ciine; aecoi.liii,ul\ m n., is the inili.il r.ite of waiiiiiii.i; ot the iiaitiiadar tliia niometer in
(luestiou when Ihe sun's ia\s lull upon it. If we suppose this rale to he e\ael and tocontinue
Ulichaiii;cil hir a luinule, w e cMdeiil l.\ lia\ c the clf-ct ol | he soj.ir r.idi it ion lor niinnlc, on tlii'
supposition thai all the heat Ins hee.i retailir 1 liy oar iimlnMu-ul, ;iinl muie of it dissi paled through
radiation, tIiront;li an i-iii lelits, lu III aii> oilier wa.\ . To this latter pai t ol I he ass ptioii we ma>
salely a{;iec. I'limi Ihis rate ]i(a' ininiUc, the ar.-a of the exposed siiilace in cciitimeters and Ihe
water ('(piivaleul of ihe healed hiilh in uiaiuiiu-s, we can cxichailly oldaiii the .solar laduilion ill
caliirii's, icterred lo the i;raiiiine, ci'iitimclcr and miiinte. We yive in tables o(j mid .">7 un exaiii|ile
of an ordinaiN ohseiN at ion iii detail.
•/. ,., 11, r liiLiI
:ih><l liMlii III.. Ihi
-.t ll.llll 111.- .Sllll Willi licit
USE OF (iLor.r; ac'tin():\ik:\ii:];.
75
Table 5(1.
„,,, 5r..„„l Wlnln.y, r-,],l.,u.i^. .\,-tU m.yU-r y.- 3. ;,i,t
iiijinv 1 ul sin.i,.T. J. N J..HM1 til, ,. ns.',l loii.liU.,
,Uv>lc^ii \Vi
Ii.sIl «ii,.I, v.iu.il.lf
Wirnl lislil 1
M :;i 111 ... ill.
■A i;s ... iln
11.1.-
I,i-1
Eeuiail*
at.il vvatf
f wiml.
-
llll
ill!.:;;.:;;:;...
r.
iln
llll
li. 4!)
-. llll
Sb.iili.
1. :ij
'" llll ".'.'.'" I'll
Fii-li niTiil.raniible,
Afti-r
gi\t'ii by 11
irrei'tiii
iiiiooth
i till- V.
lUVf, Wl
ry niiiiiite iiri-iilnital irr<';;iil.u itirs ot llic irnlfr
olltllill thi' lollowiil.u ralilo. wlll-lli till- tiMliprlMtl
tlirrni
IV.S llf
aluivi
if tUt
KlCSEAncilKS ON SOLAK HEAT.
.iKii tliiTindiiictcr lire lliosc ilircctly rt'liresclitinj;' the ilifl'cnMici' between tlie la'tei- iiiid tlie temper-
ature of tlie iiicldseil water-shell, to wliDse laiiii)-lilael;e(l e(i|iper surface the sohir thernioiiieter
radiates.
TAliLJi .58.
II 32
n s;i
11 34
11 3.T
11 30
11 .S7
11 3S
11 3!)
11 40
11 41
11 42
11 4S
11 49
11 .'iO
11 .il
11 52
11 53
U 54
11 55
41 50
11 57
Adtipteil Ex
. of
lUKiist 25
1881.
P. II.
Adopted , Excess of
12 00
12 (17
12 OS
1" 10
12 11
12 12
12 13
12 10
12 17
12 IS
12 21
12 22
12 23
7.01
11.04
12.43
13. J9
14. IB
14.80
15.25
15.03
15.87
16.03
10.22
1(133
16. 45
13. 28
10.46
8,33
6.66
.5.30
M. Viiille's luMiHila may lie written, nif lut;' p = lo.y ii„ — ]n!x ii'. where ii,. is the sum of the
eiiii-esp.indiii- ordiiiates iii^he heatiaL;- and ennliii;; (airves (whirh he assaiiies to lie ideiilieal curves,
th(ini;li rcfeiTcd t(i difha'ciit axes); f^,,. then, shun Id lie a ciinsfani and pr(i]i(iilHiaal tn the limil e.\ees.s.
\\'e dii licit lind it to lie s(i in (Uir (iwn |iiactice; and as the best we can dn. we always determine it
fnini the mean (if ciLjht ulisei valinns taken mi biiir cdriesiiniidins- pdiiits (it the heatiiij;- and eiKiIin^
curves; III is the reciprocal (it the siilitaiiL:eiH, ini the assnmptinii thai llie cairvc is a logjari'hmit.:
(inc. (is the Najiierian base. ]| is ( air iinildrm experience that m, whicli sin mid be (in thi.s assiiinii-
tiiin a eiinstant. varies, and v.iries systematic illy. acciMiliim' as it is detciniincd by the cdmiiarisdii
(it ii„ with an iirdinate which represents I lie excess near IIk iimemaaiieiit (if e.xpdsare (ir latei'.
We ha\c scarcel\ met an execpliiiii in semes of examples, df wliudi the fulhiwiiii;, cited at raiidiim,
may be cdiisidered typical. We ha\c Jiisl <;i\cii the dii;;iiial (liiscrx atinns. with readiiii,'s taken,
like all tlidse (in Ihe expeditidii, ttum minute Id miniile (tlidiii;li Id yivc all the ciliservatidiis in such
detail here wmild lie impossible in the s|iai-e al eommand).
We now imjueed to give the icdiiclidii by M. N'mlle'.s mellidd, applied sm^ce.ssively td the fifth,
the tenth, and the tifteeiitL minute (if heatiiii; er cddlinu.
Tahle ."I'J.
(Transcript from original reduction-book.)
i.ii.t.-rX" ■■■■■ s
ation, Mountain Camp. Apertu
re. medium. State uf skv. clea
. Sim th
Vni.l, lit;l,l. W
itt.itliermometer, ■•Grunowl.
Barometer, 5'*'
02. Obsi-lvir,
J.J.N.].
Time.
Water
tbei-mometer.
Suii
tbennometer.
Ditference.
Exposure.
h. m.
11 30 ii.ni.
20. 10
20.15
0.05
Shade.
11 35 a.m.
20. 10
32. 5U
12.40
Sun.
11 40 a.m.
20. 09
35. 72
15.03
Sun.
11 45 a.m.
30.50
16.42
Sun.
11 50 a.m.
20.08
25.38
5.30
Sliade.
U 55 a.m.
20.07
22. 00
1.93
Shade.
13 00 m.
20.01)
20.78
0.72
Sliade.
I"SE OF (i[,()l!K ACriNOMICTi:!;.
( loir .-=108 9„-l.)s 8'
log H„=1.i!C0
lo:; |V+C1=0. r.X24
1„." =1.00.^0
Wliiit we sec of ni m tliis particular cxiuiiplr we sec in cvoiy <illicr. tliat iimlcr tli,- rii'cnm-
Btaiiees of actual obscrvatiiin it is not a constant cither in tlic licatiii^dr tlic nidlin;; i-iii \ c ami tliat
ajiait from little irrejiularitii's of observation, it is lai-;^est w Iicn tal^en near tlic liist inoinent ol' licat-
iiij;^ or of cool in. i;-. 'I'lie mean of tlie three valnes Just j;i\en is i« = .I'L'J ; lienee t he initial rate il(aive(l
in this pailiiailar instance lia /// ('„ = .L'L'L'x 1 T.L'L' = .!.si.', a vahie which ninsi lie too small. We
have, fr the fact tliat the oliseivations hiic oii,yina]l\ tal>en liy Al. Violle's methoil. been l.-d to
reduce them by his formula, ami to afleiwanl ititroibiee a coireetion. Wholly imle|ienilent olisei-
vations taken by sncli means as to show by iljicet c\|ieriiniMit the initial rate within veiy naiiow
limits, liivi' a conlirmatoiy result, ami (hese will lie tbnml moiv |iaitiiailai ly mcntioni'd iimler the
head of ■• ( 'oi reelion A."
When the i;lobe is entirely closed to extraneous r.nliations fr the sun oi aii.\ <itlier source,
and the thermometer is heated only by ladialion Itiim the walls dl its inclosiiie, ni is much more
nearly constant, as we see by the c\|ici i incuts detailed in the .\|i|iendix.
(• II Ai'^r i; i; \-
DUTKKMIXA'riOX Oh' WATHi; I':(,>IM VALKNTS OK Til KKMOM lOTKli I'.l'I.l'.S.
Sinn- III! iiic:iMiiciiiriils (ifsolai' ladiatinii liy tin' ;;lolic ai'tiiuiiiictci s ilcpiaid upon llic llicniiii-
(•a|.aci;v 111- watci- cM|ni valciit ><i llic Imlli (il' llir t licinionicfi'r cmii|i1ii\ cd (a i-oiistant cm wliirli tlir
value (if tlic «>/'()■ <'<)H,vMHMiiiiiirilialcly (IcimmkIs), it b('<'(iia<-s iicccssai y to dctcMiiilH' tliis witli all
jKLSsible iiiccisioii. Tiic lialiility to iclati\cly lar^^c cnnr in tin- (Ictcaniinatidii of micIi niiriiilr
quantities is i;ieat. ami this liability must lie ailiiiitted to be a seiions iibjeetion to an ollieiwise
excellent insti'iinient. If the iletei niination is made by ordinaiycaliiiiiiietr ical pi'oeesses ( which
are nsnally ill adaptc.l lo this sp-ci il I'lsc), w/ oiiuiil to clieck them by soaie wholly iiide|iemlenl
means.
Two Mieh incfliods have been de\ised I •) llie writer Ibr tindiiii; llie .-eiiarale water e(|ili\ alents
uf the nieiiaii.\ and ,;;lass in the theriiiometer Imlli wiihont (lestiii\ in,u tlie insli-iimciit.
In each ol' these two mellioils the «ci;4hts of meicnry and of ,^lass in llii' tliermomeler bulb
are iiidirectl\ detiainined li> balaiii'ini; lli<- enliic tiieii 'ter upon a Inlcinm applied al selecleil
points on the stem. We ha\e Mse.l these results only as a clu-ek on the ad(ipl( d \alile. which is
that derived fioin the lliiril melliod. «hele tile Joint sp,M-ilic heal of meiciir\ and ,;;hiss in the bulb
has biMMi direcll) measured in a small .Mlorimeter. In view of tin- ,i;reat impurtanee of this eon-
staiit. we ,ui\e a des,-ri|itioii of the aiiplieation of each of these methods in detail.
i-ii!s'r :\i]yiii(iii.
Ihtiriitiniitiini of Ihc iriifcr i'(iiiinilriit uf tlir hiilh of UirniKiiiirt, r {'' lliiiiillil S7;;7") l,i/ iniiisiiriiiii its
,limn,sio„K ,111,1 h.il.iiirir.i it „i, ,i /„lrni,„ in nir.
The external dimensions of the stem are lirst measured, and by these and ils ealilii itioii* tli(^
center of ,i;ra\il\ of the slein alone is determined. If this iio'int be now made the fiilcnim, it is
obvious lliat the ulass sleiii in no way atlects the lialanciii,i;- of the Imlb and the mercury in the
stem, whicli may be ilone b\ a know n weicht at a Ullowii distance.
Then let the loUowin- data be obtained:
() = total wei.iiht of thermometer.
J=extenial v<ilnine of thermometer.
(7=exteriial volume of bnlb.
)H = siit'eilic gra\it.\ of merenrx.
/.■=aistanee from center of bulb to fnlcrnm.
?=distance from center ol' menairy in stem to fiilcinm.
H = ]irodnct of known balancin;; \veii;lit by its distance from fitlcrnm.
,r = total wei.iiht of mercury.
e.i' = voliiine (if mci'iaiiy in stem (determined from coetlii-ient of ex[iansion of mereiir.v).
(/.!-=\dUiine id' enipt.\ part (d'stein (determined from coellieient of ex|iansion of menairy).
(■»).'■ = weight of inenauv in stem.
'Jts .-.•ilil.i
(..i,iy)<iftlu-,|,i
t ;n<nviir> tnr lln^- |.ur|M,s,.. |.its.i|.|..im.s a |,icliii,inar,v .•ipi.r.isiiiKitc kiiuwlcly
^ Ihr wlin:,- niti-nial cai.antv . it llic stem is cMcssivcly Niiiall. We I'ali iii.tecil .s
en Willi this apiircMinafc kiic« I. ■(!-,'.
DETKRMIXATIOX Ol' WATKK i:(,)I'l \' A LKM'S ()!■' Til I'.UAfONnCTI';!; llHI.IiS, 79
FdrlnvviiN I 't—
III III
The vcliiiiif uf 111! the iiicrciirv liriiiu ' . tlic v,,| ,• ,,l' iiiciriiry in tin' lHilh='' -rr = f.i: thf
\vi'i};lit (iriiK-iriiiy in tin- liiilli = i 1 — )/a-) /■. ihr \..lnnic uf ,:;Ia-~s in tin- I ml 1 1 = ;/—/>. tin' l.ilal \(ilmne
of -lass in tin- wlinlr tln-i -ti-i =/,_'' -,/,,=/,-/,,,■.
Tln-n.siin-.- tin- tctal «cji;l]t (.rail tin- ^l;,s.. = „-., , tin- w.-mlit nf ula-<s in I In- lnilli = '"~''* ^ !'''~'''-'
(irtlifs|M-rith-mavitv (iftln-.^lass in tin- linlli li.- assann-il l.i l»- tin- same as that ui tin- >lrnii, and lln-
mcnih-nt nf tin- wlml .-IniH, iW. ' ''" ~''''^ '"-'■'^ + i\ - „ir)r J : a No tin- nninn-lit nl tin- nn-rrnryin tln-
st(-ni = /r«M. and tin- s il lln-si- Iwn valni-s = /, .- wln-m-i-. Iiy solvjii:;- tin- (|na(Irati(- tni- ,r, I In- \V(-iM|it
or all the IMi-li-niy is d(-t(-l ninn-d ; an.l In-n.r, a^siiniin- a \ ahn- Ini tin- >|H-,-ilJ(- ma\ ity nf tin- ,i;lass
ill the lilllli. tin- sni.arat.- wc-i.uhts nl' nn-irniy an<l ,i;lass in tin- Imll. nia\ 1h- nlitainrd. Tin- s|i,-,-ili,-
licat nf Mn-ii-iir\ is alr.-ad.x kiniwn with ;;i.-at ai-.-m a- > . a ml that cil tin- ulass ran la- i-itln-r tak(-n
IVoni talil(-s (II- di-t(-raiin(-d uitli (■l.is(- a|i|.|(i\iniat n>n Ikhii tin- lUslinnn-ni itsclt. '1 In- ]n(i(ln(-l nf
fin- W(-ii;ht (if the iin-iviir\ li,\ its -.|ic(-ili(- In-at. plus tin- ] ln(-t of tin- «(-i,L:ht of tin- -lass liy its
s|((-(-iti(- In-at. iniisl la- \ ,-i-\ n(-ai!\ (-(pial t(( tin- (-fl(-cl i \ (- ival(-i (-(piiv ah-iit nl' I In- luill.. It wcnid l.(-
n\a(-tl\ (-(|nal to tins \\(-ic it not Inr a (-i-rtain ainoniil ot In-at ti'aiisli-i ivd to or tf- tin- biiHi li,\-
( lin-tioii alon- tin- sti-iii, wliii-li i-anin.l la- .-asily d.-ti-ianiin-d. It is small, lint iiol in-,-li^ili|(-.
I willnmt it (Mil- n-siilts imist la- ia-lnw tin- Iriilh. It is iii-n-al lirst ln-;;li-(-t(-(|. A liiiiii(-rn-al
i-\aiiiol.-, showiiii; tin- n-Milts ai-tnall\ olitaiin-d. is now ui\(-ii. (Tin- iin-asui-ns wa-n- fak(-li with a
\ (-rnlii (-alli|ii-r,)
Ilnii,„si„iis „f ll,,rm.,m,hr -■ l:a„,Iii, sT 17.-
M.-aii .liai,.,-tri .,( s|.lirii,-Ml liaP. li- "-. lit;:-,
Sti-ai .^radnan-a hi ' CIn.iii -Jll ti)+74 C. : U is lilAI ciii. iVma imicti f sti-iii
aiul l.all..
I.rii;;tl, „t ,->li,,,liiral j.ail .if ^l.-iH -i;!-"'.:,!!!
Av.-ia;;.- .llaiiii-n-|- .if .■yliialni-al [.art .if st.-ia IK'". Irn
L.-ugili ..f 1; ii-'-.-j-ji;
V.iliniio iif 1- .if tini.- (i-'.diliil..-,
^ V.iUniK- .if 1- (if stem L--.(i:i>;i
V,.liiiii.- .if t.iii. mm |i-.iii ■ si. Ill ;n l.all. .-ii.l n- . iiil-.".i
Vdlinui-df ta|i.-nia; |..iiti.iii ..f -l.-i.i .it nia; .-a. I 11". HUM
V..linii.-.a iiiii; (l--.n-ls
S|„-,ni.-;;l:,MIV„l tl,.-:;l,,s>..,|ii.oiMMI.,l.-, -.-;;
The .^1 tii(.-al ri-iitcrof ti-iin- of tin- stnin (i-.\(-liisi\a- of liiilli) was found li\ (-ah-iilatinn fnmi
thnsn lui-.isiiK-m.-nts t.i fall at +|n .1 on tin- st(-in. Tin- I ln-iinoiU(-t(-|- w .is ai-.-.inli iiuly Iial.iin-(-(l
(111 a fill. -1 inn at tins |i.iiiit liy a wi-mlit «lios(- iiniiin-nt 11 i(-(|nal to that ot tin- iiicicuiy and liiilli)
was 1 1 to 111- so. 1,-1 1 ^i-,i ,- (-i-iitiai(-l(-i-s. Tin- v.ila.-s nf all fin- syinliols nmiil.iyi-d in tin- cmii
|inlali.iii an- as f.illnws:
" = '^-"" !' = ■'-'■' '•=5.^;inx i:!.ti = -' ''"' '' = oa^ii x i:;.ii = ' ■'^''
1 I
y = j.,|. -(- = .(i.L',:i;i ,/ = n.i,(;, /, = j.. ^. + </ = .(i7i.-,i.-, /, = i.-,..ss-i
/ = ,s..-,ll III = !.;.(; II =.sn. |.-,l (li-iiiia-iatuii- dm in;; (-\|i(-riiii(-nl = + - C^.
From tin- (-(lual ion
;, ^ i^_i^^, + ii-iii,)., ^ + 1,1,1,-11
80 UESEAKOHES ox SOLAl; HKAT.
we ol)taiii. I)y siiliitioii nf tin- (|Ua(lratif for x,
~ \chhn-hl+'fk-i-hlm i' 2
wliL'iv lor liicvity
helm + hii + hk — { hchm + ((/k+i/k)
-■'-= rhUl, + fk-{rhlm + hk]
SuIistitiitiD.u iiiiiiilicrs for NViubols. we olifaiii tlic total 'Vfi/'it of iiu-riairy ill the tlicriiioiiu'ti'r,
.r = 4.7() j;raiiniics.
With this value llii' a|i|ir(i\iniati' water iMniivalciit of llic luilli may be found thus:
At .'lO^ 0. tlie \veii;lit of iiierriiiy ill .steal =l).()(i ,i;raiiiii!es, lea\ iiif; weight of mercury in bulb =
4.(U j;iainines.
As tlie density of niereury at .'id O. is about !.'>.. "if, tlie vobiiiie of 4.04 Kraninie.s of mereury =
4.04
,o-F. = 0..:i4i:i ee. Ihe exteiiial vobmie of bulb (assiiiiiiiiy it to be a sphere of (l.4.Slo e. in. radius)
i.s :'f - x(.4Sl."))' = (l.fO.s.s ,.,■.
The difference of tliesi^ Ncliiiiies i;ives the VdliiMie of j^lass in biill> = .40.S.S - .3427 = O.lL'Ol c.
c.: wlieliee weij^lil nf .i^iass in bulb = . lUOl x L'.s:', ^, l).:j.-)0;i -lainiiies.
Takiii.i; the s|MM'ilie heat of nieieuiy =.0:i:'.:;. and tlie sperilie lieat (d'ghi.ss =.198, we have:
WiO.i ..|inv.il,.i.t ,.l iH.iviiiy 4.0)4 X .0333 = 0. 154.5
W;iiiTi'.iiiiv:ii..iit ..r uUiNs II. nr.osx.iiw =0.0707
Tr.tiil «:lli-l .niiiviil.-nl of Lull. II. affii
Tiy a similar apiilieatioii of inethod I to thermometer "(ireeii l.'iTl", the following result.s were
obtained;
\Vci,;;lil ..I in.'iviiiy in I ml I. 9.80
\Vili;lll ..r u|;iss in hiilh 0.8190
Water ci"! viilent u! bull. 0. 488.''i
SECOXB METnOli.
IMifmhidtUin nf the irdtrr ((iiiindciit (if the hull) of tlirniiiniii-ti'r •• (liirii 4.571,'' hy h(dancin<j at sev-
ii-iil !ini)its <„i thf slviii. hoth ill nil- mill in iriitn:*
In this method we seek to diseriiiiimue between tlie weiyhls of mereury and jjhiss in the ther-
mometer by the difli'ienee in the liuoyant elfeet of water on them. 'Ihe piiiieiple of the method
may be illustrated by the follow iiij; e.Kainple : Suppose that we knew the exact center of gravity of
the glass in the thermometer, and made this point the fuleriim; suppose, also, that we balanced
the mercury in the bulb and stem by a rider, of the same density as mercury, jilaced at a suitable
di.stauce tiom the fuleiiiiii upon llie part of the stem opposite to the bulb. Under these circum-
stances the whole appaialns iiii;;lit be iiiiineiseil in water and the balance would remain undis-
turbed. Xexl. siipjiose the liileniiii situated between the cenler of gravity of the glass and the
bulb of Ihe tiler iiieler. Ill this jiositioii the iiieieiiry would be balanced by the combined weight
of the rider and a poll ion of the glass stem at the extieiiiity opposite to the bulb. (This last is
only aii|iioxiiiialely deiei iiiiiiale.) If now the ap]iaialiis were iiiiiiiersed ill water, the counter-
balancing poilioii of the stem, being of siiinlirr speeilir g|-a\ ity Ihaii the rider, would suffer a
grealei- proporl innate diiiiiniilioii of weight than the rider or iiieKairy ; the distance of the comi-
teipoise would theiel'oie ha\ c to be iiieieased ill oiilef to reslore the ei|ailibrium ; and hence if we
were to neiih'ct Ihe aiiioii ol the balancing part of the stem, the calculated weight of mercury
would appear lo be iinntrr fioiii the water exiierimeut than from that in air. On the other hand,
if the tiileiiim were placed ton near the ring end of the theriiioineter, the ap|iarent weight of mer-
cni\' would be /(■-«• from Ihe water ex|ieiimeiit than liom thai in ail. The mode of ]irocedure sug-
gvste.t by these eoiisiiler.il ions is to shift the fiilciniii and deleiiiiine expel iiiieiitally the point at
■ TIm- will, r ].in|„,Mil Ihis Ml. III. .a, il. Ill 111! 111.' i.i.Mi.l .1. l.iilN ..r ils a|.|.lic,iri.,n al.- .In.' to Mr. F. W. Very.
DErEimi NATION OF WATKR E(,)UIVALKXTS OK TIIinniOMETl'.i; IM'LliS. SI
wliii'h tho iiicrcmy is halaiict'd li\ tin- siiinc wcir;lit iu water as in aii. The iiKJiiH'iit oltliis wfight
is theu equal to the iiKiineut of the iiiiTciin . In what uocs lirloic \M' have siiiiposeil the counter-
lioise to l)e of tlie same cleusity as the nieiiinv ; luit this is nut neressaiy, luoviih'il its density 1)e
known. It is (h'siialih% liowevei-. to use a dense metal lidef, since tiie Kicatci the diir.'rence
between tlie s|iecitic i:iavity of llie counterpois,. and tlie ^jass, tin/ .mvaler wdl l>e the diriiavace
between the water aiel tlie ail vahies lor the same dis|dace id «\' the Inhaiim.
Let U' =tolal weight of meicuiy.
((•i = weif;ht of menaii'v in the bulb.
;r. = weiyht id' ineiciiry in the stem.
»-;, = \vei}iht id' rider.
/i = le\'er arm of mercury in tlie bulb.
/. = le\"er arm of mcKiiry in the stem.
/;=lever arm at' rider m air.
/,T=le\i'r arm of rider iii water.
?.-.=lever arm of emi)ty and uneoiinteibalaiic'cil |iai t of bore.
(' =volume of empty and iini-imnliubalaiiccd part of bore.
e =apparent expaiisiun of mcKaiiy Ibr 1 centijiiade de,i;rce.
(( =leiii;'th of mercury column in centiy'rade dei;rees.
.S' =specilic gravity of mercury.
\ =specitic ijravity of rider.
Theu if the expeiimeni be ]iei formed in air we have
(1) ir, 1, + irj ^ = «•,; /,
and
{!') ,n = (w W
whence
If the weiyliini;- be made under water,
T. /,x(l \) rh
When the fulcrum is properly jilaccd (.'i) is eipial to (4).
lu the actual perforimince of the esperimeut, the stem of the thcrimuiieter, placed iKU'izon-
tally, was tirmly attai'hed by tine co]iper wire to the beam of a balance from which llu' scale pans
had been ivihommI. An\ de-ivc of the stem could be brought opposite to the index id' the beam,
and the ei|iiilibriiim could lie restored by a metal rider slidiuji- along the graduated thermometer
stem, wliiise dn i--iiiiis scr\ed to measure its distance from the fulcrnin.
As any mai ked inequality in the ilfiisili/ of the balance arms, though of very little iiiipnrtance
in weighings conducted in air, wuuld have seriuusly alfecteil those made under w.iler, the beam
was tested for such inequality, which was found to be altogether negligible.
Dimensions ut' thermometer -Mireen i.JTl":
The bulb and l.'l mm. of the stem of this thiuinometer are bhiekened. The diameter of the
stem is but slightly diminished where it joins the bulb.
M.-nii.liaiu.tir..f s|iliericul Imlb 1"".-.M7.
Sfi'in i;r:iilii;iti-il hi-,!,; C. from + In t.. + i;ii ('.
Ill is ;.« ■ "'. fniiii iuiu-tiiiii of steni an. I l.ulli.
Li-ii-th nfi-vliii.li-i.-:il iiart <.f stem :;;:■-. lid.
Avefnj;r .liriiiirtiT .it i-vliii.lric'al jwii of slnu .Ml).
Lenmli oft ,4so.
Volui f 1 of l.oic l.'MNiOl-J.
Volmiu' of 1 of stem : ii". l;;-i::i;.
SiK'iitic gravity of the sl:is.s (aiiproxiraati'lj) •_'. T-
Tlie weight of the rider used was ((■3=i;i.(io grammes, ami its density. .s='.t.dO,"). The density
of merciiiT at 10-' V. was taken to be .s'=i;3..57. Ileiice 1— . -O.SSDCi), and 1— ^,=0.!tL'(;;U.
The following are the results of e\)ieriineuts with various |iositions of the fulcruin. IV is calcu-
lated from formuhe (;>) and (4), in which the inllueiice of the glass is iieglected. The apparent ex-
12535— So. XV 11
82
RESEARCHES ON SOLAR HEAT.
pansion of mercury is taken to be e^gi'^jo. The correction (vJ;,) for buoyancy in water of the
empty and uubalanceil part of bore is here negligible.
Table 60.
jv^r.
/
■Jtaijr
/
/
/
/
/
/
'Air
/
/
/
/
/
/
'/
//
/
j
/
/
-"«' Sa" M" J7 32" 33''jFahrenhmt.
Determination of Mercury in Thermometer, Green, No. 4571.
U.sing the numbers in the tiflli and eighth colnniiis for graphical construction, we obtain two
slightly cnrvod lines (see Fig. 7), which intersect at the point whose ordinate is 10.45 grammes,
falling opposite the point on the stem registering 20°. 42, which is the true center of gravity of the
DETERMINATION OF WATICK E<.>mVALENTS OF Til ICK'MOMFTFIt I1ULI;«. 83
frluss portiiiii of tbf tlicMiiomoter: ami l(M.""i j;iaiiiiiics (wliii-li is tli<' wi'iylit whirli wmild liavc bi'cii
obtained eitlier in air or in water iftlic fiilcruai lia 1 licen |ilaceil at L'!):.lL') is tlierefore tlie trne
weiylit (if the mereury.
From this we calculati' tlie water ei|ni\a lent iif tli<' linlli. At .1(1- ('. tlie weij^lit nl' iiieiiairy in
stem = 0.00 grammes; leaving; tlie wei.:;lit of aierenry in lialb = llt..'!'.l j;raiiiMies, iieeuiiyinj;- at jO ( '.
a volume of O.T(!72 ee.
The external volume of the bulli (assuming- it to be a sphere of o.(ii:.!5 cm. raduis) is ', n x
(.()l':!r))'= I.(H.S4 cc. Tlie ditfereuue of tliese volumes fiives tlie volume of .ulass iu the bulb =
1.(I1S4_.7(;7:.' = (|.-J.-)12 ec., and its weiyiit = .i'll-Ix-'.T.S =().(i;is;! gratumes, wheuee:
WmI.i i'.|in\;il.iil Dl'ni.-iciiiv l".:i'.i X .lOM^n. :i4i;n
\V;.UT,Miinva:.'llt of -lass..' O.r.HSiix .1'>=II. !>:!
Ti>tal wall 1 .iiuival.nt nt l.alli 0. 4-j:!
li.v a similar apiilieation of method II to theriuometer " I'.audin .S737 " the following- results were
obtained: crauiin.s
Wii^bt. oliii.ivinv in Imll, 4. -T
WeiyhtuCi^lass iu IhiII> 0. :i;!14
WiiteriMinixaldit i.f hull, 0. 'J-JTS
THIRD :»[ETIIIlD.
Ih'hrminatUin of the icutir iijiiifdlvnls af the biilhx (if thiriiKiiiickr-s ^•lUiialin .S7.:17"' and •' (Irecii 4571"
ht/ilirevt mtanuiviiunt.i of spccijic heat.
A eylindrical cup, slightly larger lliau the bulb of the thermometer, was made of veiy thin,
highly pollsheil steel and attached by a line stem to an elMinite base, tlie whole being inclosed iu a
eyliudrieal ease of retleeting metal. This cup, containing either mercury or water, constituted the
calorimeter.
The thermometer was lirst heated to about GO- C. Its bulb was then held directly over the
calorimeter, into which it was plunged at the instant it had cooled to a certain recorded degree.
Under these conditions the temiierature of the theruiometer tabs, at first raiudly, l)ecoiniiig nearly
statiouary iu about one half minute. This stationary point was assumed to be the temperature of
the mixture.
Calling ir=weight of the thermometer bulb and small part of stem.
.(•=:speciHc heat of thermometer bulb and small part of stem.
Gj = weight of steel cup.
V = specific heat of steel cup.
jr = weight of liquid in cup.
2/ = siiecitic heat of liquid in cup.
r=origiual temperature of thermometer at immersion.
w = maximum temperature of mixture after immersion.
( = temperature of liipiid and cup before immersion.
the thermometer bulb, cooling through (T—H)^, loses H> x (T—H) calories, and the ciiii and con-
tents gain {cor-\-icy) X (H—t) calories. Neglecting provisionally all losses or gains by radiation or
couvection, we may eipiate these expressions:
Wi-(T-ti) = {u„:+icy) {H-t)
The water equivalent of the thernnimeter bulb is then
_(an_^Kii){H-t)
"•'- T-H
We give an actual experiment in full:
Thermometer "Baudiu 8737"; 19.05 grammes of mercury being used in a steel cup weighing
2.51 grammes, the thermometer fell upon immersion from 5S°.0 0. to 2S^.S, and the cup rose from
20''.85 to 2S°.S; whence the water equivalent of bulb=
[(2.51 x.ll7) + (19.05x .033)1x7.95 ^(, ogj^j^
The following results were obtained ; using mercur}' (mean of.! experiments), water equivaleut=-
.2546, using water (mean of 2 experiments), water equivaleut = .2522. From all experiments with
calorimeter TFj=.253G.
84
liESEAllCIIES ON SOLAK HEAT.
Tlie experiiiH'iits weri' viiiIimI in several ways, beside the substitution of mereury for water.
In some of tlie triiils the Imlb alone was dipped; in others, a portion of the slender glass stem
(about 3 mm.) was also iaebided. Losses or gains by radiation and convection were confined
within known limits by insiiriufr that the initial temiiei'atnre of the calorimeter was in some cases
that of tlie. place of experiment ; in others, that it was ciioler, S(j that the hnal temperature should
be that (it the nmm. Thus the calorimeter and its contents weii> in some instances radiating heat
to the im-losure. while in othi'rs they were recci\in;; heal IVoul the inclosure; or, in other words,
part of the results Just cited were designedly too small, and others too large. Hence we may be
sure that the true result lies between certain uarrow Hunts. What these limits are may be seen
from the following table, which shows the variations produced by these changes :
Table 01.
Liqiiiil usGd
in calorimeter.
Stem near bnlb.
(Whether included or not.)
Belativo te
mper.aturo
of inclosure.
"Water
eqnivaleut.
Mci-ciir.v
Watfi
>H.'Ml r... st.m
bl™l :. I ~l.-...
(lK...tu...nMllM.i„»tM,i
i Heat U..I re.jL-ived li.jm stem
W.lllll H^,l.,
W.Lriii (t.ilo
Cool (ealohii
Cal.
0.25U
0. 2515
(1.2611
0. 2440
0. 25'J7
Qeiei'rad'ia
miJi heat) ...
iugheat)
The value 0.253G cjal. (mean of the above 5) has been adopted as the water equivalent of the
bulbof '-Baudin 87;i7."
By similar calorimetrical experiments the water eiiuivalent of "(i-reeu 4.571" has been found
to l)e 0.4971 cal. This value is also adopted.
DETEtlillN.VTKiN OF THE WATER EtjUIVALEXT OF TnEUMOMETER "GREEN 4.571'."
This thermometer, which was one of those n.sed in aitinometric measurements on Mount
Whitney, was, after the return of the expedition, broken in transit to New Haven, where it was
being sent for rating Three methods, however, remained open for determiuiug its constants.
First. The bulb having fortunately remained, its dimensions were carefully measured and its
mercury contents weighed at the Yale Horological Bureau, so that this determination of its weight
may be considered at least as accurate as any, though it was obtained at the saciilicc of the in-
strument.
Second. The eijuatorial diameter of the bnlb of '■Green 4.571" as measured by a. vernier caliper
at Allegheny was ].1'17 cm., and that of "Green 4.57L"' was 1.207 cm. The.se thermometers,
made at the saim- time by the same maker as near alike as possible, may be safely assumed to
have their water eijuivalents nearly in the ratio of the volumes of the bulbs, and if we multiply
(1.207
0.4'.I71 (the adopted water eipiivalent of "Green 4571'') by
(1.247
; we get .4508 for the approximate
water equivalent of "(!reen 4572." We prefer to treat the.se two values, however, thus obtained
as check values, and to rely for the adopted oue on the reduction to the calorimetric stahdard.
Third. A considerable number of simultaneous actinometer readings having been taken with
the thermometer "Green 4572," and with the very similar "Green 4571," it was possible to redui^e the
measures made with the broken thermometer to the standard of those made with the unbroken oue.
The diameter of the bull) of "Green 4572" was 1.207 cm., and the weight of mercury contained
in it was 10.(10 grammes; whence we calculate:
cc.
Voinin.. ..n.iiii. o.a208
Ti.tal ■
.8 x.iii4=u. ai)r>u
. f;)8 x.3U5',i=o. ors4
. o:a:jxfo.(jo=o. :i."iHO
For the comparison of the thermometers "Green 4571" and "Green 1572
actinometers No. 2 and No. 3 respectively, we have the following initial rate
synchronous readings of the instruments:
II. 4:;i4
which were used in
determined during
DETKKM I NATION OK WATER E<H'IVALKNT.S OF TIIKKMOMIOTKK BUM!^. 85
Diili'. ! Local tinu.-.
luitial latv
of be;i
.-...
Ailiiioiuit.r Xo, 2 .
Act!
IOmeter No 3 ;
1
""■'■'""""■'"'■"''■'■■''■"
tlicnoi
Tllutcr "G.4572."
1881. 1 h. m. h. m.
o '
Aus. a 11 ;io to 12 05
3. 031 C.
3.717C.
■i' VI or, to VI -iT,
3. 041
3.734
:) 1 4 00 to 1 :io
2. 045
3.048
3 I i 30 to 5 00
2. 034
3.018
4 7 00 to T 3U
3. 071
3. 127
4 7 30 to S 0()
3.273
3. 400
4 11 30 to IJ 00"
3. .361
3.474
4 12 00 to 12 30
3.427
3.434
4 4 00 to 4 30
2.073
3. IIU
4 4 30 to 5 00
2.941
2. 889
ii , 7 00 to 7 30
3. 120
2. 956
5 7 30 to 8 00
3. 375
3. 332
5 11 30 to 12 00
3.573
3.797
5 12 00 to 12 30
3. 6511
3. 599
5 1 4 00 to 4 30
2. 572
2. 587
5 . 4 30 to 5 00
Average iuitiMl rate —
2. 47,S
2, 5SU
3. isi;
3.239
Reduction of " (Ircrii 4."i7L"' io cahiriimii-ic utitnihird.
Calliiif; ("( ''o); tlif iiiitinl latr of li<>atiii,n' t>f <'.\in).se(l thfiiiHmiftff in Xo. L',
(III «„);; the iiiitiul ratf of lifatiii<; ul' expo.scd tlifniiuiiu'tfi- in No. .'i,
71/.., the wattT eqiiivak'nt of Inilb of fxposfd tlifriiioint'tcr in No. li,
31; tlie water t'<|uivaleiit of liulb of exposeil tlieriiionieter in Ko. 3,
S. tlic avoa of ini'diiun section of bulb i]i No. "J,
,S'; the area of niedinni .seetion of Inilb in Xo. ;;,
/I'j the .solar ra(bation in cahnies in Xo. 2,
1\, tlie .solar radiation in calories in Xo. :!,
have
ill which, lor syuelnuiiou.s exposiue.s,
whence
{m H„l .S
In the iire.seut ease, (m H^). = 3-'.l.S(;.
(Ill H„), = 3'-'.l.':','.»,
H, = 1.1'L'l .s(i. cm.,
S, = f.llt ,s(i. em.,
,1/, = ().4!I71, and
M. = water equivalent of bulb of "Ureen 4.571',''
= O.l.'jSO, which is the \aliie finally adoiited.
It will be seen tiiat the water ei|iiivalents of thermometer liiilbs, (hdermlned hy direct eahiri-
uietrieal observations, are in e\cry case ure. iter than those inferred from weiyhinns. The dilfer-
eiiee may perhaiis be taken as a roii.^h measnic of tin- amoiiiil of heat conducted by tlie stem,
which will vary, owinj;- to the dilference.s in the form and blaekenin;;- of the stem, already alluded to.
Our direct ealorimetrie method lias taken a partial account of this eonduetion in the stem, while
our cheek methods ha\e not taken any. and some small c.irrection should lie added to the latter
to make them a,i;ree with the foriuei'. 'f here is some doubt, lio\\e\cr. as to how lar this eorrei-tioii
should be inehuled iu the direct value: for. while tliis is taken in theory to depend oiil\ on the
initial rate, which is .su[iposed to be the siaiie whether the heat is lost by radiation or conduetiou,
B, = (111 H„)
^ s'.
U, = (III H„)
/.'i = A';,,
■ ^'^ .'/.
86 RESEAliUllBS ON SOLAR UEAT.
it is hard to a.<liiiit Hiiit in practice it is a matter iif entire iiKlillereiice wlietlier tlie bulb is insulated
or attached to a. coiiiliictiii.u' suiiport.
The amount of lieat conducted by the stem was determined by the following experiment,
which, however, strictly applies only to the Green thermometers, which have not so small a neck
as the Bandin. The stem of thennonieter, "Green 4571," was passed transversely through a piece
of rubber tubiny, so that the bulb and 1.5 cm. of the stem projected beneath the tube and were
protected from radiation liy multiple card-board sci'eens. A stream of hot water was then made
to tlow through the tube, lieatin"- the included portiiui of the stem. When the thermometer was
inverted at intervals, so as to distribute the heated mercury in the bulb (an essential jirecantion),
it was found tliat the tlow of heat from an excess of 15^ 0. in the temperature of the stem, along
a distance = 1.5 cm. of the stem, by its conduction caused the bulb to attain a stationarj' tem-
perature of 5'^. 75 in excess of that of the sun'ouudinj;' air at the end of 12 minutes. Now, sup-
posing (what is but ajiproximately true) the rise to have followed the logarithmic law, we have to
inquire, in order to tind what the radiation was at the end of 12 minutes, what is the initial rate
of cooling of this thermometer for an excess of temperature of 5°. 75 above its surroundings. This
rate is about 1°.25. We conclude, then, that, when the eciuilibrinm was established, the tlow was
sufficient to lieat the bulb 1°.25 per minute in the above experiments.
If, now, we ask what the flow would be the other way — that is, if the bulb were 15^ hotter
than tlie stem — it does not seem probable that it would be materially ditt'erent; for, though the
stem is a poorer conductor than the bulb, it is still able to cumlnct heat so as to produce this result
through 1.5 cm. of glass, and it radiates freely. We conclude, then, that the bulb, which Icses
heat by immediat<' cnntact with the glass, will lose its heat by this comluction at the rate of 1^.25
per minute when its temperature of excess is 15-, or that the loss of heat by conduction along the
stem is S'g per cent.
I'lNAL VALCES.
IValer eqiuriihiil of •■Ituuiliii S7:l7
■ Mean
By woiHliiiiK (Mc'tlioil I), 0.2251! )
(Methoil II), 0.2278S
Correction for conduction along stem, 8 por cent OlSl
Check vahic 0. 244li
Ailoiited value by direct calorimetrical measurement 0.2536
(The check value is illi per cut of the .adopted v.alue.)
Water equiraUiit of •' Gmn J.571."
By weighing (Method I), 0. 4885 (
(Method II), 0.4843 j ^^I'^™ "■ ■1'^'"'^
Correction for conduction along stem, 8 per cent 0.0389
^ Check vahn' 0.52.53
Adopted value l>y direct calorimetrical mcasuri'uients 0.4971
(The check value is ItKi per cent, of the adopted v.alue.)
Water erjiiii'aleiit of •■Greiii 4572."
By direct weighing 0. 4314
Correction for conduction along stem, 8 per cent •.... 0.0345
0. 4G59
By ratio of hull, v.dume 0.4508
Mean eluck value 0.4584
.\ih)|>ted v.ilue l)y reduction to calorimetrical standard : 0.4580
We have adopted, then, these values for what may be called the effective water equivalents,
namely: "Baudin 87.37," 0.2,530; "Green ■1571," 0.4971; "Green 4572," 0.4580; with the admission
that, owing to difficulties inherent in the method, there can be little confidence in the figures be.
yond the second decimal place (and some uncertainty, perhaps, even in regard to these), while yet
it must, we hope, l)e clear that no noteworthy error in the solar constant can bo due to this cause.
CIIxVl'TE i; V I I
TABLES OF RESULTS OF ACTINOiMETER OBSERVATIONS.
A full exiuiiiile of the iictual rise aiiil fall of the tberinoiiieter from iniuute to iiiiiiute in I lie
heating aud cooling carves has already lic<'n yhen for Augnst 25 (Monutain Caniji). Every one
of the observations which follow, jyas taken with snrh minute readings, though tin- results are
only here given for every fifth minute, reduced l>y M. Violle's method. Wherever the custoniary
mode of reduction has been departed from in any way, tlie resulting nnuibers have been distin-
guished by enclosing them in jiarentheses. The changes are in all eases triHiiig, and do not re-
quire detailed explanation. We have, using his notation :
Wo=Temperature of final excess.
?B=A quantity, which he assumes to be a cdnstant, and tin' reci]iro<'id of the sul>tangent of
a logarithnuc curve.
m «ii=Tlie initial rate of heating.
»(, as actually (U4i'rniiiie<l here, however (see Chapter \'lll), will lecpiire subse(|Ucnl concctidu.
Table l!.:i.
[Lone PiDO, Aiigtist IS. lisS:. Olis
'^'""^- mmuLVc'r' nioml'ter Uill^Mco.
E.xposnre.
Time.
71' 30" A.M.
Water ther- Sun Ihei-
inomotcr njometcr.
Ditterence.
Exposure.
7'0()»A.M. 1 17;. M 17". SO
0°. 16
Shade.
li'.m
19=. 48
0 .50
Shade.
li.i 17 . «0 i'G . 93
9 .07
Sun.
35 19.211
28 .89
9 .69
Snn.
111 , IS .(IS , 29 .70
11 .62
Sun.
40 19 . 42
31 .70
12 .28
Snn.
l.'. 1 18.31
30 .80
12 .49
Snn
45 19 ..69
32 .51
12 .82
20 IK . 53
22 .60
4 .07
Shade.
50 19.95
24 .15
4 .20
Shade.
25 1 IS . 76
20 .19
1 .43
Sliade.
55 "0 . 20
21 .60
1 .40
Shade.
30 1 18. 9S
19 . 48
0 .50
Sliadx.
8 00
e„-i3';.
20 . 48
20 . 90
0 .42
Shade.
9«=12°.06; »» = .223; me,=2\S!>.
8; )n-(.227); )n9„-3o08
Sky, clear, very gooil. Wind, calm.
Sky, clear. Wind. calm.
lli'SlI" A.M. 30°.48 1 30S.50 0^.02
Shade.
U'Oll-M. 303.77 31=. 50
0\73
Sliade.
35 1 30 .M 1 41 .20 10 .66
Sim.
12 05 P.M. 30 .80 41 .70
10 . 90
Snn.
40
30 .60 44 . 20 13 . 60
Sun.
10 30 .83 44 . 40
13 . 57
4.1
30 . 66 1 44 . 96 14 . 30
Sun.
15 30 .86 45 . 12
14 . 20
.50
30.70 , 35.31 4.01
Shade.
20 30 . 88 35 . 40
4 .52
55
30 . 74 32 . 48 1 . 74
Sliade.
25 30 . 90 32 . 69
1 .79
Shade.
12 00 M.
30 . 77 1 31 . 50 0 . 73
Shade,. ,
30 30 . 92 31 . 70
0 .78
Shade.
9c]=14».99i m=.218^ m6»-30.27.
«»-15'.20i 111-. 218; m9o-3u.31.
Sky. very clear. Wind, nlmoat calm.
Sky, cle.lr. Wind, .llmost calm.
4»00»r. M. , 31". 62 32^05 ! 0". 43
Shade.
41'30-P.M. 1 3P.35 1 32'. 20
0'. 85
Shade.
05 1 31 .57 41 .20 1 9 . 63
Sun.
35
31 . 30 40 . 70
9 .40
Snn.
10 31 ..53 43 .63 12 .15
Sun.
40
31 .24 1 42 .90
11 .06
Snn.
15 1 31 .4S 44 .15 12 .67
Sun.
45
31 .18 43 .29
12 .11
Sun.
20 31 . 44 35 .65 4 . 21
Sliade.
50
31 .12 35 .12
4 .00
Shade.
25 31 . 39 33 . 09 1 . 70
Sh.ade.
55
31 .06 32 .70
1 .«
Shade.
30 31 .35 32 .20 1 0 . 85
1 , 1
Shade.
5 00 30 . 99 , 31 . SO
0 .81
Shade.
9„=13".58-. m = .209; me«=2=. 84.
9„-13». 15 i m-. 202 ; »i9o-2'. 66.
Sky. very clear. Wind lijllt.
.Sky, very clear. Wind, lijiht, d
ininlsliing.
88
RESEAKCnES ON SOLAR HEAT.
AuRiist I'.l, 1881. Obs
eter No. 2. Jlrdii
Tint. .W.^tcr tbor- SiiD ther-
luoiiioter. luometer.
Ditlerence.
Exposure.
Time.
Water ther-
mometer.
Sun ther-
mometer.
Diflercnce.
E.\po.sure.
TMIO'" A. M. 1 10^.32
10°. 32
0". 00
Shade.
71' SO" A.M.
170. 62
ISO. 20
00.58
Sbade.
05
10 .49
25 .48
8
99
Sun.
35
17 ,87
27 .09
9 .82
11)
10 . 00
28 .44
11
78
Snu.
40
18 .13
30 . 59
12 .40
15
10 . 87
29 . 48
12
01
Sun.
45
IS .40
31 .51
13 .11
Snu.
20
17 .11
21 .28
4
17
Shade.
50
IS . 68
22 . 90
4 .22
Sli.ide.
25 ; 17 . M
18 .67
1
51
Sliado.
55
18 .98
20 .48
1 .50
Shade.
30 i 17 .02
IS .20
0
58
.Shade.
8 00
19 .30
19 . 72 ] 0 . 42
Shade.
911=130.00; m = (.217); m9o-20.83
60-130.81; m-(.222); m 9«-3o.07.
Sky, very light haze. Wind, ca
m to gentle.
Sky, very light haze. Wind, gentle to calm
lli'30»A.M. 31". 80
31°. 08
00.18
Shade.
121' 00" M. 320.5S 330.41 0^ 83
Shade.
35 31 .%
43 .12
11 .10
Snu.
Od p. M. 33 . 69 43 . 90 11 . 21
Sun.
40 32 . 10
4.1 . 94
13 .84
Sun.
10 32 .80 40 . 01 I 13 . 81
Sun.
45 32.25
46 .73
14 .48
Sun.
15 ; 32 . 90 47 . 40 14 . .50
Sun.
50 32 . 37
37 . O.s
4 .71
SIi.ade.
20 ! 33 . 00 37 . 80 ' 4 . 80
Shade.
55 32 . 48
34 .29
1 .81
Shade.
25 1 33 . 0!) 34 . 90 1 . 81
Shade.
12 00 M. 32 . 58
33 .41
0 .83
Sh.ade.
30 33.18 ' 34.01 1 0.83
Shade.
eu-15».37; iu = .215: m 9o=30.31.
80-150.57; m-.215; 7» 80=30.35.
Sky, very clear. "Wind, calm.
Sky, clear, Wind, calm.
4'' 00"' P.M. S.io. 82
34'. 30
0°. 4S
Shade.
4''30'"P. M. 330.20
340. 23
00.97
Sliade.
05 33 . 73
43 .80
10 .07
Sun.
35 1 33 . 10
42 .80
9 .70
Sun.
10 33 . 63
40 .20
12 .57
Sun.
40 33.0c
44 .90
11 .84
Sun. ■
15
33 .54
40 .08
13 . 14
Sun.
45
32 .97
45 .30
12 .33
Sun.
20
33 .44
37 . 90
4 .40
Shade.
50
32 .88
30 .97
4 .09
Shade.
25
33 . 35
35 .20
1 .85
Shade.
55
32 .78
34 .49
1 .71
Shade.
30
33 .20
34 .23
0 .07
Shade.
5 00
32 .08
33 . 00
0 .92
Shade.
e„ = 14=.17i m = .205; III 8i,=2°.ni.
9«-13o.47; m-.208; 7>ie«-2o.80.
Sky, clear. Wind, very sUght b
oczo.
Sky, clear. Wind, very slight breeze.
Table 0.5.
[Lone Pine, August 20, 1881. Observer, A. C. D. Acl
fter No. 2. Medium aperture.]
Time.
Water ther-
mometer.
Sun ther-
mometer.
Difference-
Exposure.
Time.
Water ther-
mometer.
Sun ther-
mometer.
Difference.
Exposure.
71' 00'" A. M. 1 160. 10
I60. 16
00.06
Sh.ade.
7"30"' A. M.
170. 33
170. 80
00.47
05
16 . 24
25 . 58
9 .34
Sun.
35
17 .63
27 .05
10 .02
10
10 .39
28 .53
12 .13
Sun.
40
17 .94
30 .70
12 .82
15
16 .59
29 .50
12 .91
Sun.
45
18 .27
31 .90
13 .03
20
10 .83
20 . 94
4 .11
Shade.
50
18 .71
22 .91
4 .20
Shade.
17 .09
IS .51
1 .42
Shade.
55
19 .10
20 .47
1 .,37
Shade.
30
17 .33
17 .80
0 .47
Shade.
,9 00
19 .50
19 .70
0 .20
Shade.
8o=13o.34; m=.227; m 8«=3o.03.
8«-140.09; 111- (233); M 9o-3o.2t
Sky, clear,little haze about luyo mountains. Tl
rind, gentle.
Sky, clear. Wind, gentle.
11'30"' A.M.
330. 00
330. 35
00. 29
Shade.
121' 00"' M.
330. 53
340. 50
00.97
Shad".
35
33 .14
44 .30
11 .10
Sun.
05 P.M.
,33 . 61
44 .90
11 .29
Sun.
40
33 .22
47 .11
13 . 89
Sun.
10
33 .69
47 .53
13 .84
45
33 .30
47 .97
14 .07
Sun.
15
33 .77
48 .30
14 .53
Sun.
50
33 .37
38 . 05
4 .68
Shade.
20
33 .84
38 .41
4 .57
Shade.
55
33 .45
35 -39
1 .94
Shade.
25
33 .92
35 .80
1 .88
Shade.
12 00 M.
33 . 53 1 34 . 50
0 .97
Shade.
30
34 .00
34 .91
0 .91
Shade.
60=150.57; 7ll = .211; m 60=30.29.
9n-15o.63; 7)l-.210; 711 9o-3o.38.
Sky, slight haze. Wind, gentle to fresh.
Sky, lig
it haze. Wind, geutle t
fresh.
4'00"'P. M. 330.53 340.03
00.50
Shade.
4'' 30'" P. M.
330. 30 340. 30
10.00
Shade.
05 1 33 . 51 43 . 00
10 .15
.Sun.
35
33 .24 42 . 90
9 .66
Sun.
10
33 .48 40 . 00
12 . .52
Sun.
40
33 .17 45 . 12
11 .95
Sun.
15
33 . 44 40 . 34
12 .90
Sun.
4o
33 .10 45 . 30
12 .26
20
33 . 40 ,37 . 71
4 .31
Shade.
50
33 .02 37 . 14
4.12
Shade.
25
33 . 30 ; 35 . 19
1 .83
Sliade.
55
32 . 94 1 34 . 70
1 .70
Shade.
30
33 . 30 34 .-30
1 .00
Shade.
5 00
32 . 84 33 . 81
0 .97
Shade.
60=140.03; ;u=.205; m6o=2o.8S.
80-I30.5O; 7II-.200; 7n 60-20,78.
Sky, light haze. Wind, brisk, vari.able.
Sky, light hazo. Wind, gentle tc
fresh.
TABLES OP HK-SULTS OF ACTINO.MKTEK or.SKKVATION.S.
89
[Loilf I'iii,.. AllKHsl 21. IKSl. 01>a
Table GO.
vtT, A. r. U. Actiiionietcr No. 2. Medium aperture.]
Water tliiM- Siiu the
05
no
61
13
4
nil
0
18
■JO" A. M.
32^. 71
35
32 . 75
40
32 .80
45
32 . 90
50
33 .00
5i>
33 .10
10 .75
13 .71
14 .30
Sun.
Sun.
Sliaile.
Sbaile.
SUaile.
:.224: in«i = 3'5.41.
'.04
00.74
Shade.
.20
11 .04
Sun.
05
13 .75
Sun.
.80
14 .38
Sun.
.42
4 .89
Sliade.
.50
1 .80
Shade.
.59
0 .83
Shade.
Sky, very light ha
aiiioke. 'V^'illd, fresb, steady.
Shade.
Simile.
Shade.
Shade.
Shade,
iioke. Wind, fresh to brisk.
r .smoke. "Wind. IVoili to brisk, dii
Table 67.
[Lone Pine, Augu.st 22, 1881. Observer, A. C. D. Aetiuouioler No. 2. M.'.lium aii.-rture.]
Time Water ther-
mometer.
Sun ther-
mometer.
DiHerenec.
Exposure
Time Water tluT.
Sun ther-
iiometer.
Differenee.
Exposure.
7''nO"A.M. ; IS'. 80
18». 80
O'.OO
Shade.
, 7i'3ll'»A.M. 19'. 98
20'. 32
0'.34
Shade.
05 18 . 97
27 .84
Snn.
! 35 20 .20
29 .71
9 .51
Sun.
10 19 . 14
30 ,70
11 .56
Sun.
40 20 . 45
32 . .59
12 .14
Sun.
15 , 19.34
31 ..5S
12 .24
Sun.
,: 45 211.70
33 . 05
12 .89
Snn.
20 ' 19 . 54
23 .41
3 .87
Sliade.
' 50 21 . 08
25 . 13
4 .05
Shade.
2.-. 19 . 70
21 .00
1 ..30
Sh.adc.
.55 21 .40
22 . 70
1 . 30
Shad.'.
30 19 . 98
20 .32
0 .34
Shade.
8 00 21 .73
22 . 119
0 .36
Shade.
9«-12».61; m-(.227)
me«-2">.86
1 9o-13'.37; 7n=(.233):
Sk.v. light, smoke. Wind, gentle
j Sk.v. light smoke. Wind, gentle.
11' 30" A.M. 33'. 00
33'. 01
O'.Ol
Shade.
12i'00"M. 32'. 85 1
33'. 67
0'.82
Shade.
35 32 . 97
44 .00
11 .03
Sun.
1 05 P.M. 32 .87
43 .90
11 .09
Sun.
40 32 . 90
46 -62
13 . 72
Sun.
|l 10 1 32.90
40 .69
13 .79
Sun.
45 3" . 85
47 - 45
14 .60
Sun.
15 32 . 88
47 .27
14 .39
Sun,
50 32 . 80
37 .43
4 .63
Shade.
1 20 32.88
37 . 48
4 , lill
Shade.
55 32 . 83
34 . 62
1 .79
Sliade.
25 32 . 88
34 .62
1 74
Shade.
12 00 , 32 . 85
33 .67
0.62
Shade.
30 32 . 88
33 .72
" ■^"'
Sliiide.
».-(15'53); m-.218
m9o-3'39.
1 e.=15'.42; ni=.218: »
9,, = 3'.36.
Sliy, light haze. "Wind, fresh to
.gentle.
Sky, light haze. Wind, fresh.
4''00»'I'. M. 33". 92
34'. .50
0' 58
Shade.
4i'30»r. M. 33'. IS
34 '. 20
1' 08
Shade.
9 .58
1 .15 1 33 .07
42 . 40
9 33
Sun.
10 33.54
45 . 65
12 .01
Sun.
1 40 32.97
44 .38
11 41
Sun.
15 33 . 52
46 . 20
12 .74
Sun
' 45 1 32.87
44 . 80
11 93
Sun
20 33 . 40
37 .73
4 . 33
Shade.
50 ! 32 .78
36 . 85
4 07
Shad.'.
25 33 . 29
35 . 18
I .89
Sliade.
.55 i 32 . 69
1 81
Shaile.
30 33 . 18
34 . 20
1 .08
Shade.
5 00 i 32 . 50
I
33 . 00
1 01
Shade
9.-1.3074: 111- 200;
ifiu— 2^.75.
e«=13'.14: ?n = .201 ; )
»o=2'.64.
Sky, light .smoke. Wind, gentle to fresh.
Sky, light smoke. W
nd, light t
gentle.
ll.'.-.3.5— No. XV-
90
EESEAECHES 0:N^ SOLAK HEAT.
|L(rac Pint-, August 23, ISSl. Oils
Table OS.
■CT, A. C. D. Aclii
r No. 2. Medium aiiertiire.]
Time. ^I;',;;;V,';,;;'-
>,'m„Ser: Difterence.
Exposure.
Time.
"Water thcr- Sun ther-
mometer, mometer.
Ditieronee.
00,33
Exposure.
Shade.
7' 00" A.M.! I7». 55
170.40 :— 00.15
Shade.
7' .30'" A.M.
190. 27 19°. 60
05 1 17 . 84
20 .59 , + 8 . 75
Sun.
35
19.66 29.23
9 ,67
Sun,
10 1 18 . 12
2!l .70 ' 11 . 58
Sun.
40
19 . 86 1 31 . 65
11 ,79
Sun.
15 IS . 41
30 .80 12 . 39
Snn.
45
20 . IS 1 32 . 90
12 ,72
Sun.
20 IS . CO
22 . 58 3 . 89
Shade.
50
20 . 50 24 . 50
4 .00
Sliade.
25 18 . 98
20 .26 1 . 28
Shade.
55
20 . 62 22 . 10
1 .28
Shade.
30 19 . 27
19 . CO 0 . 33
Shade.
8 00
21 .16 21 .45
0 .29
Sluuli'.
e,=12o.62: m = l.229); m««=2°.89.
eci-130.20: )ii-(.233): )ll9,i=3=.08.
Sky, light smolic, a few dri'i and cirrocumnli.
Wind, light.
Sk,v. light haze, passing cirri. TViiid, light.
11'30"A. M. 31='. ,10
31". 30 OO. 00
Shade.
12>'00"'M. 310. 98 ; 32°. 66
00.68
Shade.
35 31 .40
42 . 32 1 10 . 92
05 P. M. 32 . 00 1 43 . 23
11 .23
Snn,
40
31 ,50
45 . 25 1 13 . 75
Sun.
10 32.10
45 .98
13 .88
Sun.
45
31 ,65
16 . 09 14 . 44
Siin.
15 32 . 25
46 .68
14 .43
Snu.
60
31 .75
36 .19 4 .44
Shade.
20 -32.40
36 .00
4 .50
Shade.
55
31 .85
33 . 50 1 . C5
Sliartc.
25 32 . 50
34 . 15
1 .65
Shade.
12 00 M.
31 .98
32 . 06 0 . 68
Sliade.
30 32 . CO
33 .31
0 .71
Shade.
9o=(150.29)i ni=.22l); m,eii=,1o,45.
, 9,1=150 38^ m— .235; ™eo— ,3°.46.
Sky, clear. Wind, j;eutle to fresh.
Sky, clear, WiDd, gentle to fresh, increasin
41' 00"' P. M. ' Sir: SO
34' 62 0'. 76
Sliade.
4''30"'P, M, 330.03 340.03
10.00
Shade.
05 :a . 72
43 . 95
10 . 23
Sun.
35 32 . 88 , 42 . 55
9 .67
Sun.
10 :h , 58
46 . 29
12 .71
Sun.
40
32 . 74 1 44 . 60
12 .06
Sun.
15 1 33 . 44
46 .64
13 .20
Sun.
45
32 . 60 1 45 , 03
12 .43
Sun.
20 33 , 30
37 . 72
4 .42
Sliade.
50
32 , 46 1 36 . 70
4 .24
Shade.
25 1 33.10
35 .06
1 .90
Shade.
55
32 . 32 34 . 12
1 .80
Shade.
30 33 . 03
34 .03
1 .00
Shade.
5 00
32 . 18 1 33 . 18
1 .00
Shade.
8,i = 14».3e; m = .205; mSi, — 2°.94.
9»— I306C; l;|— .204; l?l9«-2o,79.
Sky, clear. Trind, Iresli to brisk, decreasing
Sky, clear. Wind, fresh to gentle.
Table G9.
[Louo Piuo, August' 24, ISSI. Observer, A. C. D. Actinometev !No. 2. Medium aperture.]
Time.
Wafer flier- Sun ther-
Diliercnee.
Exposure.
l''"""- Kmrnetei-"" Immeier: Difierence.
Exposure.
First set of observations not taken.
7" 30'" A.M. 210.46 220.30 00. 84
35 21 . SO 31 . 72 9 . 92
40 22 . 14 34 .43 ; 12 .29
45 22 . 50 1 35 . 40 I 12 . 90
50 22 . 84 ! 26 . 90 1 4 . 06
55 23 . 20 , 24 . 60 1 1 . 40
8 00 23 . 56 1 23 , 90 : 0 , 34
Shade.
Sun.
Sun.
Sun.
Shade.
Shade.
Shade.
e»-13o.66; 7)7 = (.228) ; m9o = 3o.ll.
Sky. clear, light smoke on mountains. TT
gOULlC.
ml, light to
Ill' 30'" A.M. 310.00
310.16
00.16
Shade.
12i'00'"M. 1 310.27 320.09
0°. 82
Shade,
35 ,11 .00
42 .09
11 .00
Sun.
05 P. M. 1 31 . 37 ) 42 . 60
11 .13
Sun,
40 31 .00
44 .79
13 .79
Sun.
10 1 31.43
45 . 26
13 .83
45 31 .00
45 . 51
14 . 51
15 31 . 50
46 .00
14 .50
Sun,
50 31 .10
35 . 75
4 .65
Shade.
20 ' 31 .55
36 .20
4 .65
Shade,
55 31.18
32 !IK
1 .80
Shade.
25 ! 31 . 60
33 .42
1 .82
Shade,
12 00 M. 31 .27 32 . 09
0 .82
Shade.
30 i 31 . 06 ' 32 . 56 0 . 90
Shade,
9«=(15o.52); m = .217; >n8„ = 3o.
37.
On — 15°53; 7n = .215; )nfl„ = 3o.34.
Sky, slightly smoky. Wind, ge
otle to fresh
Sky. slightly smoky. Wind, geutle.
4i'00'"P, M, .320,80 330.25
00. 45
Shade.
41' .30" P. M. 32°. 25 ' 330. 30 1°. 05
Shade,
05 32 . 71 42 . 81
10 . 10
Sun.
35 32.15 1 42.05 1 9.90
Sun.
10 32 . 62 ! 45 . 13
12 .51
Sun.
40 ' 32.06 1 44.15 1 12.09
Sun.
15 32 .,52
45 . 77
13 . 25
Sun.
45
31 . 97 1 44 , 49
12 .52
Snn.
20 :<2 . 43
30 .88
4 .45
Shade.
50
31 .88 36 . 07
4 .19
Shade.
2.1 :12 . 34
34 . 25
1 .91
Shade.
55
31 .79 33 .60
1 .81
Shade.
30 : 32 . 25
33 . 30
1 .05
Shade.
5 00
31 .70 32 . 70
1 .00
Shade.
9o=14o.24; ))i = .203; m9« = 2o.s
9,1-^130.77; -m — .205; 11160 — 2°.S2.
Sky, light haze or smoke. Wiiu
, brisk, van
iblo.
Sky, light haze. Wind, brisk.
TABLES OF RESULTS OF ArTIXO:\lETEI! Or.SEKVATIOXS.
91
[Lmn- Piijc-. Aujiist -2:,, 18K1.
TAliLE 70.
■vci. A,C. D. Ac
MfiUmii :ipeltiir.-.l
Tim
\ T\r
W.i
r-rtlii-r-
1
n ther-
DiQVi
'iiix'. ExiiQsuie.
IB Sluiile.
Ti
,e.
Wat
cr ther
Son tlicr.
luonieCcr.
IS'. ."lO
Hill.
-'™-
Ejpiisure.
71' IW"
,
:■. :!-,
7>':i(i'
A
JI,
MO
1
■.40
Slia.Io.
Siiu.
111
1
11
ir. Sun
In
.SO
.ni .-.'0
12
.40
Sun.
.](!
32 . 4:1
1:1
4
Mil Sliad.'.
fil)
.51
-1
.10
Slia.U..
Ml
1
1
:;:. sii.i.U'.
fij
.-G
51 .211
1
.34
Slia.le.
■M
1
.10
]
- . -M
"
ill >Ii:nl>-.
S.JO
L'
■-'-'
20 , 52
0
.30
Slia.lf.
40 . 32
11 .42
Smu.
43 .04
14 .04
Siiu.
43 . ^3
14 .7K
Sou.
33 . ••^.i
4 .60
Slia.le,
31 .12
Sliaile.
30 .20
0 .80
Slia.U-.
Sli.v, il.-ar. Wiii.l.
''.M'»r. M. 3P.01
'inil, gmllu to I'resli.
0'. 39 Sliade.
41 ..1I
41 .10
0". 80
11 !o«
12 . 2<
4 .13
1 .74
0 . 93
n-iail, geutk- to fiosb.
10, Aii;ii«t 27. 1S81
Son thcr- r,i.r....
Table 7L
rn-.A. CD. Actii
Stfdiiiiii apertuve.l
■''00"' A.M. 10.44
«"=12;'
Sk.v. cl
ear: '.I.-.,
lilisk.
." ha/.
.";,n=
-.81.
1.1. Wind. KMtlc
"
Sha.le.
7"'30"
A. it.
10. 90
Sun.
35
17 . no
Sun.
40
17 .11
17 .23
Shall.-.
.5.1
17 .30
Sliaile.
55
17 .51
Shaili'.
8 on
17 .70
9
=i3;.so-
1,1= (.223)
o:.53 ; Shaile.
Wind, i;.-ntki
40
20 , 03
40 ' 77
14
14
Sun
45
41 .58
14
Sun
50
-7 ■ "i
31 .OS
28 . SO
4
1
68
Shall.-.
Sha.le.
12 00 11.
27 .40
28 .08
0
OS
Shad,',
fl -15"
|-
Sk.v, li
ih
ha/.,-. W
u.l. light.
4i'nn«' I'. M
10
30 = . «7
30 .70
30 . 05
31'. 17
40 .70
4:1 . 10
12
. 30
04
. 15
Shad.-.
15
20
30 . 54
30 .41
30 . 33
43 .43
12
1
Sllaili-.
Shad,-.
30
30 .22
31 .20
"
.OS
Shadu.
e» = 13':
84
. ,„=..,„s-
m«n = -ia..S8
Sky, 11
liaz.-. W
mil, lijjht.
brisk.
"
12'nn»' jr. 2
5. 40 "SJ, OS
„,;
08
Shade.
05 P. 51. 2
. 50 3S . 93
11
34
S.tii
10 2
20 2
. ,0 41 .93
. 02 42 . S3
14
14
( 4
17
91
25 2
. 19 20 . 93
1
74
Shade,
30 2
. 30 20 . 03
"
'■'
Shade,
«',-15-.77; II
-■'-4 ,»ft.-3--53
Sk.v, lisht In
Zf. Wind, lisht.
■ 4''3n'»P. M. 3
'.22 31". 20
. 10 30 . 65
0'
9
98
Shade,
i H
,9'J 41 ,74
11
lie
Shade.
55 "
, 50 ' 31 , 28
7S
Shade.
5 00 2
1 . 2S 30 . 29
01
Shade,
en-13=4l : I
-.204; m(l"-2",74.
Skj-, light h
Zf. Wind, Imht,
92
KESEAECHES ON SOLAE HEAT.
Aii,:;ust I'S, ISSl. Ol)si
Miiliuiu aperture]
Time.
7*0(1" A.M.
Water ther-
mometer.
Sno tber-
DiHerence.
E.-ipo.sure.
Time.
Water tlier-
monieter.
Sun ther-
mometer.
DifTerence.
Exposure.
1 3'^. 60
13°. OS
0°. 06
Shade.
71' 30" A.M.
150.00
150.49
00.49
Shade.
Of)
13 .S4
22 . 75
6
91
Sun,
35
15 .26
25 22
9 .90
Sun.
111
14 .07
25 . HK
11
81
Sun.
40
15 .51
28 .00
12 . 49
Sun.
1,1
14 .31
26 . BO
12
49
Sun.
45
15 . 76
29 .10
13 .34
Sun.
20
14 .54
18 .02
O.S
Shade.
50
16 .01
20 .21
4 .20
Shade.
25
14 .76
16 . 19
1
41
.Shade.
55
16 . 26
17 .76
1 -50
Sliade.
30
15 .00
15 . 49
0
49
Shade.
6 00
16 . 51
17 .00
0 .49
Shade.
e»-12°.94; m=.224i
TO 9«=2'.90.
flB=130.ff7; m. = (,223)
: )/i 811=30.1
Sky. clear. Laze on m
oumains, Wiuil, calm to light.
Sky, clejir, haxe on lu
onntaius. Wind, calm
0 light
11' 30" A. M,
29=. 03
280. 85
- OO.IS
Shade.
la^oo" M.
290. 08
290. 92
00. 64
Shade.
3,^
29 . 04
39 .86
+ 10
82
Sun.
05 P.M.
29 .10
40 .00
10 .90
Sun.
40
29 .04
42 .77
13
73
Sun.
10
29 .12
42 .54
13 .42
Sun.
45
29 . 05
4.1 .50
14
45
Sun.
15
29 .15
43 .11
13 . 96
Sun.
50
29 .06
33 . 64
4
58
Shade.
20
29 .18
33 .54
4 .36
Sliade.
29 .07
30 ,81
1
74
Sha<le.
25
29 .21
30 .88
Sliade.
12 00 M,
29 .08
29 .92
0
84
Shade.
30
29 .25
29 .92
0 .67
Shade.
()«-15°.ll; m-.216i
m e„=3f .20.
e.= 14o.93; m = .224;
VI 9n=3o.35.
Sky, clear, light haze
on horizon.
Wind. Ken
h- to fresli.
Sky. clear, light haz
on liorizon
Wind, ligl
1 to fie.sli.
[Lone Pine. Au;iiist '.
Tajslk 73.
1, I8SI. Ohserver, A. C. D. Actinometer No. 2.
130. 70
14 .07
14 .44
25 .85
27 .03
19 .05
Shade.
Shade.
Shade.
Wind, calm to 1
280. 00
28 .61
28 .62
26 .61
43 .00
33 .25
30 .45
29 .47
Shade.
Shade.
Shade.
150. 95
16 .34
16 .74
17 .15
17 .55
17 . 95
18 ..35
30 .01
21 .55
19 .20
IS ,59
00. 35
9 .47
12 .03
Shade.
Sun.
Sun.
Sun.
Shade.
Shade.
Shade.
12' 00"
M
05
1-
M
10
15
25
30
290. 47
39 .45
42 .12
42 .74
Shade.
Shade.
Shade.
Sky, clear. Wind, fresh.
4i'00"
P.M.
290. 70
0.5
29
69
10
•^9
68
15
29
07
20
29
64
25
29
60
30
29
57
10 . 62
10 .85
3 .67
Sun.
Shade.
Shade.
Shade.
9o = 110.67; m,
Sky. smoke fro
to brisk, vari
29 .50
29 .50
29 . 50
80 = 100.67; Iil=.204
Sky, .smoke from tire
to brisk, variable.
39 .30
32 .82
30 .90
Shade.
Sun.
Sun.
Sun.
Shade.
Shade.
Shade.
ng. Wind, fresh
TABLES OF RESULTS OF At'TINO.METEl! OliSERVATIONS.
93
Table 74.
(Lone Pine, August 30, IS.*!. Observer, A. C. D. Actinonieter No. 2. Meilii
THIll"'
\ V
IIP
!)?.
JT.OO
II-
OS
Sli^dc.
17
23 . 42
8
■XI
Siiii
10
Ij
17
28
28 .40
20 . :i6
11
11
12
Sun.
20
17
GK
■n .41
;)
7;{
Sliiule.
■*5
17
S8
19 .10
1
"2
Shade.
30
IS
CS
IS .50
0
42
Sliade.
IMO'
A
M.
2-3.
40
28 .
50
28.
2 00
M
2S .
..59
20".
30 . SO
28.44 I 40.16
28 . 37 32 . 42
28 . 30 i 30 . 00
28 . 23 29 . 14
7*30"
\.M.
18 .0.<
JO
IS .40
32 .83
30 . 18
29 . 40
4 .40
1 .58
0 .00
Sli.iile.
Shade.
Shade.
huom
M.
"8 ■ 74 '"J
111
I'. M.
28 '. 80 42
15
28 , 80 43
28 . SO 33
28 . SO 30
30
28 . 80 20
[Lone Pine, Aupist 31,
Tatile
vei. .V.C. D.
Water ther. Sun tber-
14 .38
14 .M
14 .90
26 .45
18 .30
16 ,10
DitTerenee, Exposure.
Shade.
Sh.ade.
:ini)rueter Xo. 2. ili-.liuiu aiuutu
Water ther- Sun ther- „
"■■"
et*r.
140
90
!.■)
19
15
84
10
4S
eo=13='.80 ; m=(.227) ; ra9»=3i'.13.
Sky, light amoiie. Wiud, ealm or
28'. 65
39 , 65
42 .41
0». 15
11 .10
13 .80
Shaile.
Shade.
Shaile.
Shade.
Shade.
Shade.
8,=15^.39: M=.214;
m«n=33.29.
9o-15:.CS: m— .216;
m»»-3'.39.
Sky, slightly smoky
Wind, gentle t
0 I'resh
Sky, sliHhtly smoky
4»30'"P. M. 20'. 37
Winil, ger
30'. 30
tie to IVesl
4' 00" P.M.; 29", 85
3U0. 11 0
'.20
Shade.
Sliade.
05 29 , 70
39 . 27 !
.51
Sun.
35 29 . 31
38 . 33
10 1 29 . 68
41 . .52 1 1
Sun.
40 -ll . ■•(;
40 .41
11 .15
Sun
15 1 29 . 60
41 , 90 1 1-.
.30
•Sun.
45 29 . 20
40 .76
11 ..50
Sun.
20 1 29 . 52
33 .56
.114
Sliade.
50 29 . 10
Shade.
25 t 29 .44
31 .10 1
.72
Shade.
55 29.11
30 . 76
1 .05
30 1 -" • 3'
30 . 30 0
.93
Shade.
29 , 91
0 .84
Sh.ldc.
80=13^.23; )»=.206;
)ll»o=2'',73.
ei,=12'-65 ; m=.207
l/i()„=2; 62.
Sky. alightjy sraoky
Wind, fresh.
Sky, slightly smoky
Wind, lig
it to I'resli.
94
EESEAECHES OX SOLAR HEAT.
Table 7G.
[Loim Pin
e, .Ss;.toii
bor 5, IS^l. C
iK.rv.r
A.
:.D. ;\..iiu.„n
•ter No. 2.
M8,liani ape
•ture.l
xin,e. ^i;;;:;;;:.;;:;:'-
Sun tlie
20-. 10
" DiffiTonco.
;' (>". 00
Expnaure.
Sliaile.
Time.
pVaterthor-
Sim ther-
DilibreDco.
E.tposure.
7''0U'-A.M. i;uf, 10 1
7ii30'" A.M.
21=. 92
220, 26
S .9S
Sim.
35
10 -M .aa
32 . 27
11 .,5S
Siiu. -
40
■'2 50
34 .70
12 .20
Sou.
12 .30
Siui.
45
2.T . J4
■l.li
Sljaile.
23 .06
27 .18
4 .12
Sliade.
23 .32
24 .SO
22... I,
0 .34
Shade.
« 00
23 . 56
24 . 02
0 40
Shade.
»„=12M1S, „, = ,.-lh
,«(). = 2-
11,
ft,— 13-
brisk.
nt^iins. Will
1. sen 111
to
Skv, ek
freah.
ir, liiihlsmo
aiu.s. Wiui
, seutle to
ni'30»A. M. 35". 10
3,^.:'. 19
0°. 03
Sliade.
12H«I". M.
34°. 86
35°. 90
4C .12
11 .00
Sim.
05 P. M.
34 . S2
40 . 22
Sun.
10
34 .79
48 .90
Sun
15
,34 . 77
49 .60
Sliaile.
20
311 .SS
1 .97
Shade.
25
1 .04
Shade.
30
34 . 7,3
35 .00
0 .88
Shade,
^.1 = 15=. 75; 7JJ, ^.210
1/19„=3
'.31.
ft,— 1.5'=
.Sky, clear. Wiud, li
.:lit.
Sk.v, cle
ar. Wind, I
ght.
4»00»P.M. 34". 90
3,io. 50
0". 60
Shade.
4«30"'r. M.
340. on
35= "O
I=.]4
Shade.
9 ,90
.Sim.
,35
33 . 92
42 . 55
8 .93
Sun.
4() . S2
12 . 20
Sim.
40
33 . 7S
45 .10
11 .32
Suu.
45
33 .04
3S . ,2
4 .38
Shade.
33 . 50
37 . 62
4 .IJ
Sliade.
.ill 20
2 -00
55
33 . 30
33 . -'0
1 .14
Shade.
5 00
33 . 22
34 .22
1 ,00
Shade.
8ii = 13c-.03i 7)1 =.197
™e,=25
75
8.1 — 12^.
Sky, clear. A\ iml, calm.
Sky, cle
XV. Wind, calm.
Table 77.
Siniiinnry of Lone Pine acHnomcUr ohscrvation
d( diii-iiiL: the corrected from the imcelTe :ted obserrations i
[Instruraeut. small actiiionietcr, Xo. 2.]
Diiialion of Diiiati..!,
experiment. experiiii.-
l' 30" to S'' 00'". Il'30»'tol2
■ 121' 30". 4ii00"to4''30"'
1881.
Aug
IS
15
f^
£■=
C^
Cul.
fill.
1.177
1-44S
1. 153
1-233
1-193
1- 1115
1-41S
1.517
1.407
1.433
ii
t i
~ -
^ "
E £
; ;
2'-
-^
Cal.
C'ui-
1.551
1-330
1.541
1.345
1. C51
1 338
1.019
1. 390
1. .507
1..54-i
1.378
1- -too
1 371
1,349 1.087 , 1.15
1.703
1.1S2
1.717
1.170
1.(772
1. 110
1.712
1.119
1.762
1.199
1.700
1.177
1.438 1.799 1-172
1.214
1.271
1.382
1. 4S1
1.4.54
(1.423,
1.447
(1.423) -
(1. 423) .
(1.423).
1. .371
1.381
1.423
Cat.
1. OS!
1,141
Cal.
1. 329
1. 403
1.001
l!305
1.134
l.HO
1. 304
1.414
1.114
llS,
i.'oiiii'
1.010
(i:!.5.5)
1.312
1. 2SS
7i'00i»to
-'SO"
7'' SO"' to
1, oo'i'
1'' 30'" to 1
21 00'"
12» 00" to 121' 30'"
4' 00" to 41" 30'"
4i'30»to5'00"'
Mcim till
Air
e of exposure to mm..
in hour aiiKle
till /.enitih distance
7k OS'"
4'' 54'"
70" 33'
a.m.
i 71' 38'"
41, 24'"
04=33'
.,,n. 1
111' .38'"
01. 24'"
20" 38'
r.,n.
121' 08'" p. m.
0'' 00'"
20° 1)7'
4'' 08" 1). m.
41' 06'"
00» 58'
4l'3S'"p.m.
41. SO"
06" 50'
19.70 15. 3S 1 7.42 1 7.39
13-00
16-84
TABLES OF liKSULTS OF ACTlXOiJETEU OliSEEVATK )>'S.
95
Taf.le 7s.
[Mouiilam C;iiiiii, August 'Jl, IKSl. Ol.s.TV.-r, J. J. >\iiir
Time.
Water tlier-
nlunSe"
Dim.
enee
Kxposiirp.
Time.
■Walir th.r
m!™!';;:;. Di'^rence.
Espoanio.
'sL'.illl.'l ^
l.i.l l,.v liisli
elifls on til
until
7' 42"' A
8 112
12
M. 15.00
15 .00
15 . 00
14 .;i<i
14 . til)
14 .04
14 . tlS
(10 ' 9)
(15 .9)
(0\ !l)
11 .7)
14 . .■<)
1.5 .51
Shade.
slin!
Shall.'.
Sliado.
Sliade.
»« =
IC'.aS; )n = .213
mO.=3:'.67.
Sky
elcar. Wind.
aim.
111' 3 a.m.
Iiistniineut uut aJiu.Me
1 01
.rvvn
ti..ll~»oi(li.
l-.'lUi.. p
M. 21 .00
22'. 32
0:'.42
Sliade.
k-sa.
1.-.
21 .98
34 . 23
12 .25
Sun.
37 .^X
15 .48
Sun.
'1'^ o->
38 .11;
Hi .14
Sun.
30
22 .04
27 . 12
23 .71
i !(i!l
Shade.
Shade.
■ 40
22 . 00
(22 . 03)
(0 . 63)
Shade.
ft,-
lli=.9f1: ,n— .231
l»ft, = 3:-92.
I
Sky
cleai-i Wind, i
aim.
4k|l(l"P. M.
210. 22
2P. 20
04
Sliaile.
41" 30'" P
M. 20.31
21-.1.<
u--: 87
Shade.
(15
21 .02
31 .53
IN
;.l
Sun
20 .11
30 . 13
111 . 02
Sun.
10
Li
211
20 . .<H
20 . 74
2u . 50
20 .44
34 . 22
34 . S4
22 '.in
13
14
4
1
.10
.no
ill!
silade.
Sliaile.
m
10 . :•.•<
lil . HI
111 . 60
10 . 53
32 . 71
33 . 24
21 iiil'i
12 . 73
13 .43
4 ..50
1 .83
Shade.
Shade.
30
20 .31
21 .IS
0
.S7
Sliaile.
5 00
19 . 37
20 .31
0 .94
Shade.
fti-14=
IT: in— .205 i
„i(!.-35.0-
ft.-
14:45: m— .207
; )/ie„=2».90.
Sky, clL
ar. -Wind.fi
BSll.
Sky
clear. 'Wind, Iresb, variable
Table 7ii.
[Mountain Camli, Angnst 22, 1S^1. Ohseiyer, J. J. X. Ac
r Xn. 3. ITedinui apeltn
Titue. ^f,;;;,Vt';^f-
nrm'et": "'"■•■
enee.
E.i,„.,„re.
Time.
Water ther
^z"^z:
Hide
enee.
Exiiosiire.
71'a. ni. Sun hidden by
■litis.
less.
121' 00"' M,
05 P.M.
10
15
20
311
Instrument not adjusted
Ob
eivat
ons worth-
111' 30'" A.M. 21':'. SO
35 21 .90
40 21 .95
45 22 . 00
55 21 !tl9
12 00 M. 21 .95
23':'. 98
33 .98
36 .03
37 . 31
20 . 78
23 .63
12
14
15
4
1
IS
OS
cs
31
64
Shade,
Snn.
Shade.
Shade.
Shade.
21 loli
21 .97
21 .97
21 . 00
21 . 94
30 !49
37 . 12
; liiOii^S'^.OS
resh, variiibl
213. OG
,30 .31
32 . 50
32 . 85
24 . 10
21 .16
20 . 04
00
11
14
15
4
1
I
Shade.
Shade.
Shade.
«.= (160.35): ;n = ,2
Sky, clear. Wind,
3: ml>„ = 3^.81.
resb. variable.
s'kj, i'l
4''30"'r. M.
45
50
98; „i = .-2.'10
ar. Wind,
20M3
19 .97
19 .82
19 .00
19 ,.50
10 ,34
10 . IS
4Mlll"'P. M. 21.07
^ 5o:?o
20 20 .'44
25 20 .28
30 ' 20 . 13
31 :.52
34 ,13
34 .70
21 !00
10
13
14
1
01
11
93
Shade.
.Shade.
Shade.
Shade,
111
12
13
1
0
34
8(1
Shade,
Suu,
Sun.
Sun.
Shade,
Shade,
Shade,
Sky, de.ar.' Wind.
)n8B^3M3.
lesh. variable.
9,. = 14:'
Sky. eU
40; ■m-.208
ar. Wiud. t
»lA, = 3='.00.
•esh, variiibl
96
RESEARCHES ON SOLAR EEAT.
IStrnmlain (^ai.i],, A„
Table SO.
23, ISSl. Observer, J. J. N. Actinometer No. 3. Meilium ii|it
Table 81.
[Mountain Cimp, Aiignst 24, 1881. Oli.^erver, J. J. N. Ai^iiiotueter No. 3. Medium aperture.]
Time, ^y;",',;;;,,',!'.;:"' '^'"i!!'iZ-. nin-eicuce.
Exposure.
Time.
Water ther
luonieter.
Sun ther-
Difference.
Exposure.
71' a.m. Riiu lii.l.l.-n l„ , lin.«.
7M2»A.M.
180. 77
190. 66
00.89
.Shade.
47
IS . .54
30 .47
11 .93
Sun.
52
18 .31
33 . .iO
14 .99
Sun.
57
18 .09
34 .48
16 .39
Sun.
8 02
18 .00
23 .55
5 .49
Shade.
07 1 18 . 15
20 .13
1 .98
Shade.
12 ' 18 . 23
1
18 .96
0 .74
Shade.
ei,= 17o.20; m=.218
M«o — 30.75.
-
Sky, slightly cloudy
Wind, light
11' .30" A.M.
210.00
21". 7S
00.18
Shade.
12i'00"' M. : 210. 78
220. 49
00.71
Shade.
35
21 .70
33 . 88
1^
18
Sun.
05 V. M. 21 . 71
34 . 18
12 .47
Sun.
40
21 .74
37 .47
15
73
Sun.
10
21 .65
37 . 45
15 .80
Sun.
45
21 .75
38 . 35
in
60
Sun.
15
21 .62
38 . 23
16 .60
Sun.
50
21 .70
27 . 05
h
29
Shade.
20
21 .60
27 . 00
5 .40
Shade.
55
23 . 70 I
1
93
Shade.
25
21 . 63
23 . 53
1 .90
Shade.
12 00 M.
22 . 49
U
Shade.
30
21 .66
22 . 37
0 .71
Shade.
eo = (17o.48); M=.224: TOe.-3.o91
So -170. .55; 1)1— .224
m 80—30.93.
Sliy, cloar. Wind, fresh, variable.
Siiy, clear. Wind,
resh, v.ariable
4''00"'P. M. 20^^32 20-'. 47
00.15
Sliade.
41' 30" P.M. 190.60
200. 50 ■
00.84
Sluade.
05 , 2(1 . 22 31 . 51
11
29
Sun.
35
19 . 5t
30 . 52
10
98
Sun.
10 1 2(J . 12 34 . 70
14
.S8
Sun.
40
19 .42
33 . 04
13
62
Sun.
15 ' 2(1 . 0(1 1 35 . .52
I.I
52
Sun
45
19 .30
33 .90
14
0(1
Suu.
20 19.90 25.14
24
Shade.
50
19 .17
34 .14
4
97
Shade. .
25 19 .79 21 .78
1
90
Shade.
55
19 .04
30 . 97
1
93
Shade.
30 10 . 6(! 2(1 . 50
0
84
Shade.
5 00
18 .90
10 .70
0
K3
Sliadc.
9,i = lCt>.2S: m = .212; m6a=3°.45.
««— 150.59; Jii — .212
m9„=3'>.31.
Sliy, clear. Wind, liglit, variable.
Sky, clear. Wind, 1
ght, variable.
1
Time '^^alerthe
^"""^ iiiometer
-' Sun ther.
Difference.
Exposure.
J, , W.iter ther- Sim ther-
luouieter. ! nionieter.
Difference.
Exposure.
7' A.M. Suu hidden by
elids.
7M2" A.M
47 190. 14 300. 65
52 19 .06 33 . 66
57 19 . 00 .34 . 77
8 02 1 19 .00 34 .00
07 1 19 . 08 30 . SO
12 1 19.12 19.77
(OO. 00)
11 .51
14 .60
15 .77
5 .06
1 .78
0 .65
Shade.
Suu.
Sun.
Sun.
Shade.
Shade.
Shade.
9„ — 160.29; m — .323; 11180 = 30.
3.
Sky, clear. Wind, calm.
HI- ,30" A.M.
200, 18
200. 23
00. 05
Sh.lde.
12' 00" M.
200.54
210. 24
00. 70
Shade.
35
20 . 54
32 . 55
12 .01
Sun.
05
20 .51
32 .88
12 . 37
Sun.
40
20 . 51
35 .90
15 .39
Sun.
10
30 .43
35 .87
15 .44
Sun.
45
20 .50
36 . S3
16 .33
Sun.
15
30 .33
36 .52
16 .19
50
20 .50
25 . 72
5 .22
Shade.
20
20 .20
25 .44
5 .24
Shade.
55
20 .51
22 .40
1 .89
Shade.
25
20 .16
21 .93
1 .77
Shade.
12 00 M. 30 . 54
21.24
0 .70
Shade.
30
20 . 15
20 .80
0 .05
Shade.
e.i=17:'.I8i in=.224i 7ne«=3o.S
5.
8,1-170.14: m = .227; )ii9o = 3o.i
9.
Sky, clear. Wind
light.
Sky. clear. Wind, light.
4l'00"P. M. 1 200.30
O.50
0'. 20
Shade.
4l'30"P. M, 190.70 200.44
00.74
Sluade.
05
20 .IS
31 .32
11 .14
Sun.
35 19.59 30.34
10 .75
.Suu. 1
10
20 . 07
34 . 17
14 .10
40 in . 43 ' 33 . 10
13 .67
Sun. 1
15
19 . 93
34 . 89
14 .96
Sun.
45 19 . 25 1 33 . 88
14 .63
Sun.
20
19 .SO
24 . 73
4 .87
Shade.
50 ; 19 . 12 : 33 . 97
4 .85
Shade.
25
19 .70
21 .55
1 .79
Shade.
55 19 . 01 , 20 . 80
1 .79
Shade.
30
19 .71
20 .44
0 .73
Shade.
5 00 18 . 90 19 . 02
0 .72
Shade.
90—150.09; m — .2
4.
9,, — 150.45; m— .217; ™9„ = 3o.3
5.
Sky, clear. Wind
brisk, variab
0.
Sk.y, clear. Wind, tresh. variab
c.
TABLES OF EESULTS OF ACTIKOMETER ORSEliVATIOX.S.
97
Table 8:i.
(MoiiDtaiD Camp, AiiLiiiat 25, ISfl. Observer, .T. J. N. Ai-tinometer Xo. :i Mv.lium ap.-
Table S3.
[Mountain Camp, August 26, 1S81. Obsii v,r, J. J. X. Ar
r No. 3. ilfdiuni apt'
Time.
^"ometef' mome'tM DiiTeience.
Exposure
Tin
ae.
Water ther-
Sun ther- „,„
niometir. ^ '"'
.^
Exposure.
T'A. M. ,';ui
bijil.-n by .liffs.
57
8 02
12
A
il. 26». 05
25.24
24 . 59
24 . 45
24 '.m
23 .79
■.■IF.7S 0'
.■i7.U0 11
.•)9 . 68 15
39 .70 15
29.11 4
2.-1 . 90 1
24 . 60 0
76
09
31
89
90
83
Shade.
Sun.
Sun!
Shade.
Khlde.
Shade.
8
^
103.46; m=.219
T7l8u = 3 = . 00.
1
Sky
clear. Wind, light.
11»30'" A.M,
20°. 10 1 20''. 15 0'>. 05
Shade.
12i'00'»
M
20-'. 06
203.78 0"
-,
Shade.
35
20 .10 32 .50 12 .40
Sun.
05
F'
11. 20 . 05
32.49 12
44
Snn.
40
20 . 09 35 . 72 • 1 15 . 63
Sun.
10
20 .05
35 . 68 15
63
Sun.
20 . 08 36 . 50 1 16 . 42
Sun.
15
20 .04
36 .49 16
43
Sun.
50
20 . 08 25 .38 5 . 30
Shade.
20
20 .03
40
Shade.
20 . 07 22 .00 1 . 93
Shade.
25
20 .03
21 .93 1
90
Shade.
12 00 M.
20 . 06 20 . 78 1 0 . 72
Shade.
30
20 . 02
20 . 75 0
73
Shade.
8.-17°.
22- m= "22 »,9.-3"8'
8
_
17».43; m— .223
m9,-.- 30. 89.
Sky, cle
ar. Wind, light.
Sky
clear. Wind, li
{ht.
4HI0'" P.M.
19^.42 (20°. 1) 1 (0». 7)
Shade.
41,30m
V
M. , 180.73
190.46 90
73
Sliade.
05
19
22 (30.5) (11.31
35
18 .U
29 . 66 11
.02
Sua.
10
19
117 1 (33 .5) (14 .4)
Sun.
40
18 .57
32 .73 14
.16
Sun.
15
18
96 1 .34.55 15.59
Sun.
46
18 .41
33 . 10 . 14
Sun.
■JO
18
87 23 . 92 5 . 05
Shade.
18 .32
23 . 35 ' 5
03
Shade.
18
SO 20 . 70 1 . 90
Shade.
55
18 -18
20 . OS ' 1
.90
Shade.
30
18
73 19 .40 0 .73
Shade.
5 00
IS .10
18.86 0
.76
Shade.
60=16=.
23-m = .219.,„«. = 3^57.
8
_
15°. 90; OT=.215
m8„ = 3'.42.
Sky. cle
ar . Wind, fresh, variable.
*
ky
clear. Wind, fresh, vanable.
ry,. , 'Waterther-, Sun ther- t»!h-
T"'"'- mometer. 1 mometer. \ ^''^'
cure.
Exposure.
Time. ■"j^;;;'/tl^'r^
- Sun ther-
DilTerence.
Exposure.
7' A. M. Son hidden by cliffs.
7' 4.5"' A.M. 193.3a
50 IS .40
203. 7ii
30 .CO
1 .38
12 .20
Shade.
55 1 17 . 93
1 32 . 45
14 . 52
Sun.
00 ' 17 .77
33 .14
15 .36
Sun.
(15 17 . 69
22 . 90
5 .21
Shade.
10 17.64
15 17 . 59
19.72
18 .02
2 .08
1 .03
Shade.
Sliade.
ft,- 163.79: III ^.210
m«„-33.53.
Sky. clear. Wind.
light.
11'' 30" A.M. 153.97 16'. 10
00
13
Shade.
12''00»M. 1 163.15
173. 04
03. S9
Shade.
35 16.02 28.011
11
98
Sun.
05 P. M. 16 . 14
28 .39
12 ,25
Sun
40 16 .09 .'11 .25
l,i
16
Sun.
10 16.12
31 ,60
15 .48
Sun.
45 16.11 32 . 23
IB
12
Sun
15 ' 10.09
16 .27
.50 16 .12 21 .38
26
Shade.
20 1 16 . OS
21 .43
5 .35
Shade.
.55 16.16 18.18
2
0-3
Shade.
25 10 . 10
IS .13
2 .03
Shade.
12 00 M. 16.14 17.04
0
90
Shade.
30 16 . 15
10 .95
0 .80
Shade.
8„=I6o.92; ?n~.214; m9o-3o.62.
80-173.34 ; m-.21S
11180=30.-8.
Sky. clear. Wind, brisk, vari.ahle
Sky, clear. Wind.
fresh, variab
6.
4' 00" P.M. 173.48 173.76 '
03
28
Shade.
4''30"P. M. 163.59
170. .55
03.96
Shade. '
05 , 17 . 36 1 28 . .52
11
16
Sun.
35 16.37
27 .14
10 . 77
Sun.
10 17 .23 ; 31 .,33
14
10
Snu.
40 16 . 19
29 .69
13 .50
Sun.
15 ; 17.06 32.08
In
02
Snn.
45 16 . 03
' 30 . 28
14 .25
Sun,
20 > 16 . 93 21 . 97
04
Shade.
50 15 . SS
, 20 . 75
4 .87
Shade.
25 10.79 18. SO
2
Shade.
55 15.73
1 17.76
2 .03
Shade.
30 16 . 58 ' 17 . 55
0
97
Shade.
5 00 15 . 56
16.52
0 .96
Shade.
811— 15°.90; m— .208; m9B=3'>.31.
80—153.40 : ni— .206
: Jli8„=33.17.
Sky, clear. Wind, fresh, variable
Sky. clear. Wiud,
fre.sh, variab
e.
12535— Xo. XV-
98
RESEARCHES ON S(3LAR HEAT.
Table 84.
lll(.iii]t:iiii Camp, Spiili'iiibcr 6. 18S1. Olisfi vji-, I. J. N. Ac
!■ >'o. 1. Largest aportii
Time ."Water tber-
Sun ther-
mometer.
Diil'erence.
Exposure.
Time "Water tber-! Sun ther-
mometer. [ mometer.
DiU'cl'OUce. Exposure.
7b 42u,. xiK- earlier observations wer
rendered TV
ortbless bv
8' IS"' A.M. 150.92
150. 18
00.16 ' Shade.
an accident to the instnimeut.
20 15 . 20
27 .06
11 . 68 Sun.
25 15 . 33
(28 . 88)
(13 . 55)
Sun.
30 15 , 44
(30 .36)
(14 . 92)
Sun.
35 1 IS . 53
IS .78
3 .25
Shade.
40 1 l.>) . 61
16 .41
0 .80
Shade.
45 15 . 04
15 .94
0 .30
Shade.
90=150.34 : m=.288 : TO»,(=4o.42.
Sky, deep blue. Wind, calm.
Ill' 30" A.M.
10°. 34 19". 34
Oo.OO
Shade.
12''0I"'P. M. 190.77
(I90. 88)
(Oo.ll)
Shade.
3.5
19.43 32.10
12 .68
Snu.
06 1 19 . 80
32 .84
12 .98
Sun.
40
19 .48 34 .38
14 .90
Siin.
H 19.93
35 .18
15 .25
Sun.
45
19 .50 34 . 94
15 . 3B
Sun.
16 1 20 . 00
(35 . 44)
(15 .44)
Sun.
.W
19 .63 22 . 90
3 .27
Sbade.
21 20 . 05
(23 . 38)
(3 .33)
Shade.
55
19 .70 20 .40
0 .76
Sliade.
20 1 20 . 12 (20 . 86)
(0 . 74) 1 Sbade.
12 00 M.
19.77 19.88
0 .11
Sbade.
31 20 . 20 1 (20 . 30)
(0 - 16) Sbade.
ei,=150.62: OT=.302; m(),^4».72.
90=1.50.861 ■nl— .308; to9^4.o89.
Sky, deep bhie. Wintl, calm.
Sky, deep blue. Wind, calm.
41' 00"' P.M. 21°. 47 210.04
00.17
Sbade.
Note.— The obserrations of this da
y made Tvitb the large
05 21 . 45 ] (30 . 82)
(9 .37)
Son.
actiiiometer (Jso. 1) are not directly comparable with the I
10 21 .43 (33 .m
(12 .43)
Sun.
rest.
15 21 , 40 (33 . 97)
(12 . 57)
Sun.
The first and last series are not includi d m Ihe final sum- 1
20 21 . 35 (24 . 14)
(2 .79)
Sliaile.
niarv. the instrument havinj: been disturbed. Tbey are.
25 21 .29 (21 .95)
(0 .66)
Shade.
however, not altocetber valueless.
30 21 .22 (51 .40)
(0 .18)
Sliade.
8,,=I30-36; »n— .293i m9o=3o.91.
Sky, partly cloudy. Wind, frew
1.
iKirji of acfiiioiiirlt.
iig the corrected froa
[Instrument,
:is „l Mountain '
ctcd observations
ncter Sn. 3.]
xi'lained in the next chapter.)
Date.
Dura
exper
7b iL. t
ion of Duration of
ment. experiment,
OS' 12"'. lI'SO^tol^HO-
Duration of
experiment,
12li00"'tol2i'30».
Duration of
experiment,
4I' uij. to 4' 30».
Durat
exper
4' 30- t
ion of
ment.
S' 00».
II
1
1=^
Corrected ob-
servations.
Uncorrected
observations.
Corrected ob-
servations.
|l
11
H
p 0
jl
0 "
11
6"
1881.
Cal.
1.428
Cal.
1.729
(1. 752)
1.819
1.760
1.746
1.709
(1.752)
1.752
Cal.
"i.'sss
1.568
1.540
1. 531
1. 450
•1.560
1.529
Cal.
(1. 882)
1. S7S
1.930
1.895
1.884
1.784
1.920
Cal. ! Cal.
1..569 ' 1.931
1.472 1.811
1. 573 1. 935
1.558 1.918
Co;.
1.229
1.255
1. 381
1 370
Cal.
1.493
1.625
1.677
1.666
1.736
Cal.
1.198
1. 199
1. 323
1. 343
1.369
Cal.
1. 451
1.452
1.601
1.625
1.058
1.538
(1. 554)
1.554
23
24
1. 602
1.454
1.443
1.412
8. 962
8 864
(1.617)
Mean
1.551
1.448
1.S82
1.909
1.332 1.617 1.284
7I' 42'" to 8' 12'".
11»30"
to,12l' 00"'.
12'00"'tol2l'30"
4'' 00" to 4' 30"'.
4' 30- t
D 51- OO".
M an time of x >osure to un
7,
50'. a. m.
111
260
38'" a. m.
12' OS'" p.m.
O'OO""
2CO07'
4' OS" p.m.
jb 00'"
6O05S'
4k 3
41'3t
06O5G
2 ''■ "'■
Suli's mean hour 'in"le "
Sun's mean zenith distance
Air-mass
.-, 020 09'
. . 1 10. 72
5.61 1 5. 58 10.32
12. 73 1
standard of No. 3.
20
__
\
A^
\
/
/
1
\
0'
V
\
/
\
/
\.
^^
f,i Xrm.Iniu.AK, II.
Showing ArreNTUN or Ob^ervfr DiSruHeco
/J 20
J J 40 I, J ji' Ji Y
J« :To i, _z;«„,p,„i, jtu, ^
-^
^
\
s^
\
\
^^
/
/
""
20 25 Ja JJ
Act %: I LoncT.m, AuiJ
PLATE II
Imperfect and Irregular agtinometer curves.
J\ \
^_
'
^
/
\ \
/
/
\
' 1 i.
^u
1
—
sc S5- x'm
1 1 1
/
1 '1
_]
y"^
\
i\
/
\
/
\
/
/
\
1
[
,
\ 1 '
K
/
\
\ 1
\ !
/
\
1
\i
/
\
W 5!'
iVCNINC-.
PLATt III
ACTINOMETER CURVES FOR AUGUST 4TH, 1881
LONE PlNL— ACTINOMETER Nol
,7J ^0
ss ^(\\l
!
1
1
! :
i i
1 1
j
i^^T"^!
1
{
\
/i
! \
1 \
/
\
\
/ i
i
I
^^^_/'
1
1
^n
,S 20
ijS J<. W V
actinometer curves for august 4th.
Lone Pine-Actinumeter No.2.
t
1 1
! 1
1 i
1 ! !
1 1 1
\ i 1
1
r^
y
\
/
'
\
/ i
>\
_______
/
^
N
15 JO 31 «e 1i Ju
Morning
io" JJ fe i,s JO 35 ill
Noon
20 IS
20 2J 50 55
Ev€m N6.
PLATE V.
actinometer curves for august 4th. ie
Lone Pine-Actinometelr No.3.
JS 1-0 ij JO JJ SE
Ac! K J Sept S
■W" JS
Act ,Y«J Au.zi
Summit or Mt Whitney
20 IJ JO
\
\
/
^
\
' /
\
/
\
1
U/
1
1
-^_
JC' JS 1)0 i/J So J J
Act X< 2 .luy.'J
Lone Pine
jj 10 25 JO
PLATE VI
ACTiNOMEieR Curves or Mt. Whitney.
TABLES OF RESULTS OF ArTIXo:\rETER ORSEKVATIOXS.
OhscriiUioa^ irilli tlir iirHiioiiiiler on thr Pnik „/ Mount Wliitiii-ij.
09
[PL.,k
:.f Muimt Wl.ilufv. .Sc'i
trTiilicr ,■,, ISf
1. ,.bs,.r>
er, .J. E.
ii/cl.i-. Actiu.miet
■r N... 3, Medium aper
ule.J
Time.
^Viitertlier- Sun tlier.
nuuueter. momefer.
Difleieuce
Expostut
Ti„,. AViitertlier-
■ 1 ^'""- mom..ter.
Sun tlier- v,ift-,.ivii,e
luometer. l^'luenee.
Exposure.
!
1 8' 00'
05
10
15
20
25
30
A. M. 18=. 20
17 :bb
16.40
15 . 87
15 . 38
15.00
IS". 90 1 0'. 70
29 ,40 11 .85
32.00 15.00
32 .51 10 .11
21 .08 .1 .21
17 . 20 1 . 82
15 . OS 0 . 6S
Slirtde,
Sun,
Sun.
Sun.
Sliade.
Sliade.
Sliiule.
I
e»=16=.87; m = .224i iBft, = 3".78.
Sky. tleeii violet. Wind, very lisht.
11'3U»A.M. 145.90 15 = . 90
35 14 .81 27 .SI
40 14 .7L 31 .00
4,1 14.61 32.06
50 14 . 4.S 20 . 4,1
55 14 . Il.'i 16 . 71)
12 00 M. 1 14. . 29 , 15 . 30
l-.OO
13 . 00
16 . 35
17 .45
1 !oi
SLiidf.
Sh;ide.
Sh.iile.
Slimle.
I2i'00"
10
!' 20
25
1 30
M. 14'. 29
P. M. 14 . 22
14 . 15
14 .09
,' 14 . 04
13 . 99
! 13 . 94
155.30 I'.Ol
27 .05 12 . 83
30 . 50 16 . 3.5
31 .32 17 .23
19 . 94 5 . 90
18 .12 2 . 13
14 .80 0 . 86
Sliade.
Sun.
Sliitde-
Sliade.
Sliade.
eu=lS=.e4: m = .210; M8o=3t>
Sky, deep violet. VTinil, ve
91.
ry light breez
li
fc=lS0.39; m=.2
Sky. deep violet.
0; Ol0„=3'.97.
Wind, very li^bt bree
"■
From the above we have for Stiptember
At— 1 8* 08" A.M. Ilk 37" A.M.
12' 07" P.M.
j Cat Cal.
TTneotiected ob.seivations 1.513 1. 567
Corn cte.l obaervatiODs ' 1.843 1.926
Oil
1. .591
1. 954
Tlie ]iioci'(liiig observations have all been examined, and re]iresented by means of i^raiihical
eonstructiciiis, aeciiiii[iaiiyiiii;' the miuinal rediictiiins ami ser\ iiii;' as a cheek iiliiiu tlieni.
Wlieie the uliseivatious were iiitemiptetl i>r sensibly alfeeted liy lia/.e, cliMids. cir other cause,
the enrve exliiliits tlie defeet in kind and dej;ree in a NtiilciiiL; inaiini'r. A\'e lia\ e (imilted a jiPeat
number thus defective, but give one or two examph/s (if detective carves in iiiustr.ition. (See
Plate Xo. II, '• Jmiierfeet and irre.milar aetiuoineter enives.'")
AVe ,i;ive, as examiilcs taiily typical of a j;i'eat number, three plates, ,slLnwin,i; the readinj;s
of actiniimeters Xos. 1, 1', and .•. on August J, at Lone Fine (Plates III, IV, and \'), and alsii a
plate (Nil, \'l) showini;' curves of observations at tlie Peak of AVliitni'y Septenilier ."i, Jbiuiitaiii
(Jainp on Aii<;ust 23, and Lone Pine on August '2:'>.
It is t(i be observed that the smoothness and nniformity of these curves in ueiieral is due not
only to the cX(|uisit(dy clear sky and abseiii'c nf all ordinary disturbing causes, but to the skill of
the (ibservers, wIki were very thuidiinhly drilled and practiced before these were taken.
Niitliing has licen dune tn smiKith the curves, which as now engraved faithfully represent the
accuracy of tlie uriginal observer.
CHAPTER V 1 1 I .
ACTIXOMETER COltRBCTlONS.
ConHECTKtX TO THE RESFLTS OF JCTIXOMETlilC ItEDUCTIONi^.
A great (leul of ImIkii- liiul been already sjieiit in reiliiciug the actiuometric observations by
the method proposed l)y M. Violle, ^vhen it became clear that the actual initial rise of the ther-
mometer was ill every case greater than this method made it. It was then necessary to apply a
correction to the results thus obtained. It is here called "correction A." The necessity of cor-
rection A, it will be seen, would not arise with direct observation by the method which was finally
adopted. It is, tliercfoic, spei'ial to the observations made and reduced by M. Violle's method.
A secniid iiirrcction arisi's fniui the imperfect conductivity of mercnry. It is called here
' correction 1!.'"
A third cin rciiidii must lie made for the iniiierfect absoriition of heat by the thermometer
bulb. It is here called ■■(■<iiTccti<in C."
A fourth c(iMc<'ti(in ("conection D ") is dne to the fact that Violle's method demauds in theory
an unlimitedly long fx|Hisure. and that in practice, when we limit this exiwsure to 15 minutes,
the results are too small, 'fliis correction, then, is special to the observations made by this
method.
All the above corrections are instrumental ones, and all are additive.
A fifth correction (''correction E") is due to the fact that the portion of the thermometer's
heat lost by convection an<l conduction varies as the air is rarer or deu.ser. This correction is
instrumental and is negative.
The necessity of the sixth correction (" coirection F ") is indicated by M. Violle. It arises
from the fact that the actinometer registers radiations from the portion of sky immediately around
the sun with those from the sun itself. It is insignificant in amount as compared with the others,
and is subtractive. It is the only one of the preceding list which M. Violle applies. * ♦ *
Though most of the above corrections are here applied for the first time, they affect the value of
the solar constant most materially. Their method of determiiuitiou as well as their value is there-
fore given in detail.
r>cter)iii)iiitiiiii i>f the first cnirrclion (A), irhose iijipliciilinn xJudl rrrhice the initinl ratrn, hifcyred
I'll .V. l'/»//(\ iiiiilnxl, to tin- inn initial riitix irliicli icinilil lie ijieeii hij ilirevt nhsernitiini.
Since the losses of temperature by radiation, convection, and conduction are more consider-
able as the diflerence between the temperature of the thermometer and of its iuclosure increases,
the eriors produced by neglect or erroneous estimation of these losses will be least if we nnike our
experiments of short duration and allow the temperature of the exposed bulb to vary only slightly
from that of the iuclosure.
Two methods of ]irocedure suggest themselves.
ACTIXOMETER CORRECTIONS. 101
DETEEJIINATIliN liF COKKF.CIIO^ A, BY FIRST METHOD.
Take tlio reii(liiig.s oftbe first three miiintes of an exposiue. II' tlie sliv reinaiiis elear we may
conqiare the initial rate of lieatiiig. ealcuhiteil from tliese tliree minutes, with that of the coiniilcte
.series.
Let n = tlie greate.st attainable exeess of temperatare. ami ^i, «., ^i, the exi-es.ses at the end
of I, 2, and 3 minntes. Sinee, under the eondition.s of the whole ex[)eriment. radiation is aiiiu'oxi-
luately pruiiortional to Ihe exee.ss of leniperature: for a brief time we may treat it as exactly pro-
portional, without scnsil>le erna-: that is, we njay i;raphieally repre.sent these excesses by the
ordinate.? of a logarithmic curve : and (since the lengths of tliree equidistant oidinatcs luust be in
geometrical progre.s.siou) to deterunue the axes of such a curve to be jiasscd througli tlicse points,
in case ^,, ft, W, are not already in geometric iirogression, they must be made so liy tlie addition
of a constant, n. The common ratio is
I, _ rt, » _ H,
" = n- «, = /, - h]
whence
H-, — ft, H.
«=2ft-(«, +'h;)
and since n = ;'". where ; is the Xa]iierian base,
log ti log a
'" = Iog . = 0.434:1
and the initial rate of healing: pel minute is veiirescnted by the iirodiu-t m x n, if the sun ther-
moiueter starts exactl.x at tlie tcni]ieratiire (p| its eiivinuimciit at tlii' instant of exjiosure, or by
II X {II— I-'), if there is ;im excess ot' temperature, ". For examiile, tala' the lollowing observation
made on Mount Whitney, iVom 11'' .'.ii"' to 1-'' (Ml"', August 1'.;. issl:
f„ = (»■■"". H = (P. IS = excess of temperature at the instant of exposure.
/, = 1""". «i= -.y.v.ii ] \ II - II, = iL'. x:. log III - f/|) = 1. (nio!i>i'
f, = 2""", w,= OMid I- n = i.-,.!i:; j „ _ h. = it. .",:!, hig (h - »..) = 0. 05!I9 D
t-j = ,3"'"', ftj= S-..S7 \ \ n - ft,= :. 00, log (II - Hj) = 0. 8488
From (1) and (2) ;
From (2) and (3) :
and
log (( = 0.1210
log ,( = 0.1211
0.1211
0.4343 '
m X {n — H) = 0.27S8 x 1.1
The entire series, including l."> luiniitcs' exjiosure to tlie solar radiation and an cijnal time for
cooling, gave, when reduced by \ i.ille's iiietiiod, an initial rate of 3 .014 pi-r minute.
Tlie lollowing table gives the results of both luethods of computation for a considerable
number of oliscrx atious.
102
EESEAEOHES OX SOLAR HEAT.
Table SO.
Initial rate
Irom first,
Initial rate
station.
Date.
Hour.
second, ant
by Violle'8
tliiril min-
utes.
metliod.
18SI.
;M.,.iiit;iiii Camp (WMtney)
Aug. 21
12k 10"-I2ii 40"'
4. 20S
3.918
Auk. 23
11 30 -12 00
4.391
3.914
Auk- 23
12 00 -12 30
4.895
3.930
An;:. 24
11 30 -12 00
4.743
3.848
Aug. 24
12 OO -12 30
4.730
3.890
Aug. 25
U 31) -12 00
P.M.
4.020
3.823
Mountain Camr (Wliitney)
Aug. 21
4 30 - 5 00
3. 031
2.991
Aug. 22
4 30 - 5 00
3.558
2,995
Aug. 23
4 30 - 5 00
3. 306
3.305
Aug, 24
4 30 - 5 00
3.205
3,353
Aug. 2.i
4 30 - 5 00
3.824
3.418
Aug. 26
4 30 - 5 00
3.737
3.173
Loiio Pine
Au" 21
Aug! 23
11 30 -12 00
a 970
3! 454
Aug. 23
12 00 -12 30
3.687
3.460
Aug. 24
11 30 -12 00
4.782
3.368
Aug. 24
13 00 -12 30
P.M.
3.879
3.338
Aug. 25
11 30 -12 00
3.901
3.420
LoiioPino
Aug. 21
4 30 - 5 00
3.286
2.607
Aug. 22
4 30 - 5 00
3.156
2.641
Aug. 23
4 30 - 5 00
3.225
2.719
Aug 24
4 30 - 5 00
3. 050
2. 823
Aug. 2,i
4 30 - 5 00
3,058
2,751
Aug. 27
4 30 - 5 00
3.403
2.735
Mountain Canip
11 30 —12 00
Sept. 5
12 00 -12 30
41787
4!l9S
Sept. G
11 30 -12 00
5.720
4.718
Sept. G
12 01 -12 31
5.424
4.887
1SS2.
Allc-ulitny
Mar. 4
U 30* -12 004
4.854
4.061
Mar. 4
12 OoJ-12 30S
4. 582
4.101
Mran
Mar. 4
12 32* - 1 02i
5.095
4.260
4.0S3
3.566
The dvei-age iiiiti:il rate from 31 observations is by the fir.st method i^.OS.'?, and by Violle's
method 3'^. 5(30, and tlie ratio of these numbers is 1.145, whence a correction of 14..") per cent, ought
to be added to a result deduced by Violle's method of comjiutation, according- to this compari.son.
DETEK.MIXATION OF COKRECTIOX A, BY SECOND METHOD.
By the second plan we obtain direct observations of the initial rate of heating for short
periods of exposure (l."i or .'lO second.s), exactly deteriuincil li\ an audible signal from a standard
clock, or better still, aiitoinafically regulated by an electro luagnetic mecliaiiisni, controlled by the
clock.
This method reijuiiespiel'erably twoactinomctcrs and tuoobservers— onetociirryon tlieordinai-y
routine, alternately expo.sing and siiailing his instiiinicril for l.'i niiiiutes— the otlicr to make simul-
taneous direct observations of tin- initial rate cjI' the ,scc(.nil instinmcnt for short exposures. The
mode of procedure in the second instance is ns follows: The san-thermometer is taken out of the
case and cooled as much below the temperature of the water as it is expected to rise above it in the
course of the exi)eriment. We thus insure that, during the lirst part of the exposure, the bulb of
the sun-thermometer shall be receiving heat from the iuclosure as well as from the sun, while,
during the second pii rt, it receives heat from the snn but radiates it to the iuclosure. The amounts
of heat received from or radiated to the surrounding water-jacket by the thermometer are nearly
equal, though not exactly so, because the middle temi)erature is attained in less than half the
time of exposure, whence the cooling agencies are slightly more effective than the heating, and the
initial rate thus measured will tlimiurc stiU be hch>u- the truth, although, as will be seen, it is in all
cases larger than that inferred by the usual process. Uaviiig cooled the thermometer, the observer
trau.sfers it to the ca.se, centers it, reads its temperatare, as well as that of the well-mixed water
in the snrrounding jacket, and exposes it at the beat of a loud sounding relay, which repeats the
ticking of the clock. Then, having counted the seconds from 0 to 30, he closes the shutter at the
instant of the .3(HIi beiit and proceeds to read the temi)erature attained, which may be done in a
comparatively leisurely manner, since, though the reading rises rapidly-, it scarcely falls percep-
tibly for several seconds. This observation is therefore far more accurate than that obtained by
a hasty glance while the mercury column is still moving rapidly up, and thus, although the total
AOTIXOMETEi: COUKECTIONS.
103
change is small, the degree of accuracy is idiiiiiaralilc witli that olitaiiied iu the orilinary way.
Moreover, a coiisideralile. number of Dbseivatiiiiis can lie made in a sliort time. Tlie operations,
however, need to be ])errorunMl with care, and the tVc(|n('nl liandlini; of the tliermometer is, of
course, attended with increased danger nl' bicaka.ue.
The following special (.lisiavations Inivi- been made bv lliis second nu'lhod Ibr the jniiiiosc of
comparing the method of re(bietiiin useil l)y M. N'ioIIe with tlic residts (d' direct (iliservation :
[Allcali<.i].v. Marcli 29. 1SS2. Olis
Taule ST.
. F. W. Very. Me;
ActiuometiT Ko. 1 (largt-)-
Aetiuometer No. 2 (small).
Excessfof tempemtiire.
IDte^T.^lof
IntiTvalof
time. t.
Mi,,
10
15
Excess of temperature.
time. t. 1 1
iroatiiiE, 8. Cooling, «'.
Slim, e+8'.
Heating, 9.
00. 19
a .25
12 .50
13 .80
Cooling, 9'. .Sum, 9 + 9'.
130. SO 13". 90
4 . 00 , 13 . .15
2 . 00 1 14 . 50
1.15 14 . 95
Min. 1
0 1 — oo. IS -1 1« 15
5 1 8 . 7.5 1 2 . .W
ID 1 11 . 2.'> ' (1 . .'iS
15 1 12 . 15 0 . 05
11 .;i7
11 .2.-.
11 ..■■0
12 .20
From tlic. eqiianon 7H ( lofje^log flu — log u';
For (=5. );i = .210^ for (:^ 10. Jn = .307; for
(=15. 1(1 = . see.
Aver.igc 7« = .294; eo = e + e' = n°M.
j«9„ = 3=,47.
From tlie equation „i f log e = log 8n — logfl':
For * = 5, m = .227 ; for ( = ] 0. 7« = .137 : for
(=15, m = .]liS.
Average m = .197; 8. = 9 + 8' = 14 = .32.
Initial rate obtained from direct measurements,
30.85.
Eatio=^'™l»W™J.? = 3^j
observed rate 3.47
Initial rate obtained from direct measureniouts,
30.35.
Eatio -f iilcoliited rate_3. Z^_ ^ ^^g
observed rate 2^ 82
' The comparisona ol" MarcL 29, having been made hy only one obstrver.
lutely ayDchronous. The sky however remained uniform, and the results ar
Table SS.
[AUegben.v,
Dotober 20. 1862. Obscrv
■r, J. E. Kei
er. Sk.v.n
illi.v blue ivith oeeasional tliin smoke.]
Actinomet
-r Xo. 2 (small), measurements made
Aclinoim
tei Xo. 2 (small), measiirenient.s made
fi.im 111130"' to 121' 00™.
I'rom 12'' 00- to 12" 30-.
Excess of temperature.
1 E.veess of temperature.
Interval of
Interval 0
'
time, (.
time (
Heating. 9. Cooling, 9'.
Sum, S+e'.
1 Heating, 9. Cooling, 9'. Sum, e+SK
Ifin.
iriii.
0
OO. 70 1 130. 30
140. 00
0
10.22 ]3'O.40 1 140. 02
5
10 . 03 4 . 07
14 . 70
5
10.39 4.00 14.99
10
12 . 50 1 2 . 08
14 . .58
10
13 .00 2 .00 15 .00
15
13 . 30 1 . 22
14.52
15
13 .40 1 1 .12 1 14 .52
From the
equation i,t ( log d = log 9d — log 9' ;
From tbe
For ( = 0
7rt = .'22C: for ( = 10. m— .1941 for
For t -
(=1.5. w
= .ir.5.
t - 15. ,
Average m
= .195; 8u = 8 + 9' = 140.)5.
Average
1 = .202 ; 9,1 = «+9' = 140.7s.
)n 9,,— . 20.99.
„, e„
J'=2 82..40.70..,14Seal.
«(»
u • -^ — 2.99 . .4070 — 1.217 cal.
Table .S9.
15 seconds
exposure
30 secon
Is
xposure.
60 secoi
40.051
dses)
.sure.
Keiimks.
10.001
10.951
1 . 05
1 . 95
3 . 95
Time from 11'' 1
2'" to
in = 10.02
2 .00 ^1
lea
a = 10.99
3 .95 >(
nean —
30.98
12'' 35'". Obsc
1 .05
2 . 05 1
4 .05 1
F. W. Very.
2 .00)
3 .90J
Mean < 4
= 40.08.
Mean
.2
= 30.98.
Me.an
vl = 3
.98.
Mean of all=4<'.01 (15 observations), 4.01 x. 3484= 1.397 caloriea.
104
EESEAECHES OX SOLAR HEAT.
Table 90.
lAllcglifiiv, OctolierSO. 16S5. Observer. J. E. Kteler. Liglit breeze. Sky. good bine. A little smoke
ess of temperaturi
Cooling, «'. Sun
s of temperatnr
! Interval of |
time, (.1
e + e'.] I He.iting. «. Cooling.*'. Snm.e+f
oo. 1.5 I 120.10 I 1TO.2R
10 . 53 1 2 . 67 I 13 . 20
11 .97 i 0 .69 I 12 .66
12 .10 0 .22 12 .32
12°. 41
12 . 41
12 .40
12 .40
m9,,= 3o.6l
=3.66x.3JS4=
nie»=3°.G2.
=3.62X-348J=1.2C1 calories.
r S-o. 2 (small), dii
Table 91.
t observaliiin of inii
i-sl.v ^"ith above. J
15 seco
nds exposure.
30 seconds
6-vposure.
60 seconds e
\posnre.
1=30.33
Eeniai-lis.
0°. 89 1
0 .S3
0.71 J
mean=0".82
lo. 73 1
1 .75 [me
1 .551
n = l'>.68
30.451
3 .35} mea
3 .20 J
Time from 12"^ 55'." to
1' 51". Observer,
F. W. Yer.v. •
Mea
[1X4 = 30.28
ilean> 2
= 30.36
Meanxl=
30.33
Mean of all = 3o.32 (9 observations), 3.32 y .4070=1.352 calorii
TIio (ili.sfrvatioijs of October 20, 1SS2, may betlius summarized.
AVitli iK'fiiKiiiU'ter Xo. 1 :
) .•io.OG (
(1). — Initial rale liy Violle'.s iiietliod j 30 (jo )
(2).— Initial rate liy direct uietliod
With ai'tiiKiiiieter Xo. 2:
Mean
4°. 01 (^Mean of 15 ob.servatious
( 2o.,^2 )
Jle
;P'..">2 (-Alean of 0 observation;
20.91
(3).— Initial rate liy Violle's metliod
(i). — Initial rate by direct method .
(1) is synebrouous with (4), and (2) with (3).
In order to compare tbe radiations measured syncLrononsIy, but by diflerent iustrnments, tbe
measurements made -nitb actinometer Xo. 2 bave been reduced to the standard of Xo. 1 by multi-
plying- the results, expressed in calories, by the factor 1.054, whose determination is described
further on. AVe tlieii have —
(1).— Actinometer Xo. 1. Calories by Violle's method 1. 2:(i and 1. 2(;i
(2).— Actinometer Xo. 2. Calories by direct observation •. 1. 424 and 1. 424
1. 117 and 1. 129
1. 210 and 1. 2S;j
1.3:17 and 1.397
1. 154 and 1. 08S
And tlicir ratios arc
(3).— Actinometer Xo. 2. Calories by Yiolle's method 1- 7^1.' ""'J }■ ^''~J5
(2). — Actinometer Xo. 1. Calories by direct observation "
And their rat ids are
Fr(jTii Ihe observations of March 29 and October 20, 1882,
the first <'orrccti<iii .should be.
+ 11.3
+ IS. 8
1+11.7
+ 12.9
+ 1.5.4
(_+ S.S
+ 13.2
ACTiN( »,M i-yr Ki; < ( )i; im;( tk txf^.
105
I mi'tlioil
CfUt. to 1
s that till
i|ual till' 1
Tbe couclusioii fioiu tin' iiioaii of six comiiarisoTis lis tin- si'coiii
method j;ives a. result which is to I)e increased l>y at least l.'J.l' per
direct observation (which is itself too
small). Although the number of com-
parisous by the secou<l method is very
much smaller than by the lirst, they
are so much more relial)le tliat c(inal
weights will be yiven to the mean of
each set, and the finally ado]ited value
of correction A is + 13.8 per cent.
DetcniiiiiKtioH of the acnind cDfi-cctimi
{cdrreciion B) fur impf)fcct amdiic-
tirily of the iiiereur!) in the bulb of the
thermometer used for metifnuiug the
intensity of solar riKlintioii.
The communication of heat to the
mercury within the bulb of a tiier-
nioMieter takes place ])artly by con-
duction and i)artly by convection cur-
rents in the lic|uid. If the heat is ap-
plied from below, the ccmvection eui-
rents attain their maximiiin eneri;y ;
but if the source of heat is aliove the
thermometer, the eoniinunieatioii of
heat nuist be larRely due to conduc-
tion, which, on account of the nnper-
fect conductivity of the mercury, is
slow. If the heat is received from tiie
side, con\c<-tiou ciurents will be free
to act, lint in their uiiwanl course they
meet a surface already heated,
must lie tar less etiicient than when
they rise iVoui a lower heated hemis-
phere into a cool uppei' one.
It follows tliat the altitude of the
sun aflects the accuracy of the indica-
tions of the solar thermometer, as has
been well iiointed out by Mr. Erics-
,soii ("Contriluitnins t<i tlu' (A-nteu-
nial Exhibition," Chap. XVII), and
that the most reliable use of tlu' ther-
mometer as a measurer of radiation
reipiires that its lower surface should
be exposed to the source of heat.
This being imiiractii'able in ordinary
actiuouietric measurements, a correc-
tion must be ajiplied to all observa-
tiims to redu.'e them t,i what ,l,^.y -^■■r»nK<-™,torarp.anm,.a» n.,,l „■ tin d, l^mMMOon n, ,l,,c..n.,lin„ r,,, ,,:,,!,, .,,,,
would have lieeu with a miilii- sun. This correctiou has been determined as follows by Mr. V. \V.
^'ery : A beam of su}ilii;ht, lieiui; kept tixed in a horizontal direction by a heliostat, was recei\ ed upon
a .second mirror, which retlected it either uiiwards, downwards, or horizontally, the actinometer beinj;
correspondingly and successively placed above, below, and at the side. (See Fig. S.) The rise of the
li;53o— Xo. XV U
100
UESEAKOIJES ON SOLAll IJKAT.
siiii tliciiJjdiiit'tcr ill one iniiiutc Wfi.s noted in eiicli case, and tin- oliscrvations wcri' repcati'd often
enons'li to eliminate error from atmospheric, changes.
An e.xamiile is here given in full. The eomiioneiit.s of a pair were taken in as rapid succession
as possible. The exiiosures could be timed with great precision by listening to the beats of n loud-
sounding relay, which repeated the ticks of the observatory clock by the observer's side.
Table 'M.
(Station, Allr]::lnn,v. olja.rvcr, F. W. Very.]
1 .30
1 .20
2 .70
2 .30
2 .GO
2 .40
1 .35
2 .10
2 .40
I I N.iilir.
( I Zmitli.
( Nadir.
\ Ztuill..
^ Kadii.
i Ztnitli.
^ ' Nadir.
(, Zenith.
f Zenith,
i Nadiv.
^ Nadir.
( Zenith.
The following is a suniinary of all the results obtained in two days of e.xpeiinieiit, nich result
here given being usually the mean of 5 determiiiiitioiis like those Just I'ileil. Tlicjse ul' lljc llandiii
thermometer (obtained on a favorable day) are entitled to special weight.
Table 93.
IStation, Alkgbeiiy. Ohservor, F. W. Veiy.l
Thennoniutor.
Direction from ' «_,,„!,, ;_ .
which radiation "-f^'Stg '
1
Ilatio.
Baudin8737...
(Zenith 2a.28(
)Nadir 2.47)
( Horizon 2 .43 ?
Green 4571....
(Zenith 1 .291
) Horizon 1 1 . 85 1
An inspection of these tigures shows that the correction for imperfect conduetivity of mercury
is not only an appreciable one, but is of considerable importance, where the radiation is received
from points above the horizou, which is the condition occurriug iu ordinary actinometric work.
For a constant amount of heat received, then, the reading of a thermometer progressively increases
as the sun approaches the horizon. To determine the exact law of increase still more experiments
are required, but the present ones show that for the thermometers actually employed this incre-
ment is approximately proportional to 1 — cos .J : (: being the zenith distance). AVe have, in fact,
upon expressing the above observations in terms of the radiation from nadir sun (after giving the
Baiuliu thermometer results double weight) —
A( TIX( )MKTFj; COltRRCTIONS.
Taiii.k 114.
01)s
(ill filiation fro
107
\\'c shall use. tliMi, ill lliu Icilldwiiii; rccliK'tHiiis till' i'iiiiiiri(.-al loiiiiula—
T = t + b cos A :
where
/) = tlie ciirrectioii {always additive) to the reading of either thermometer reeeiviiiy ]ieat
tVoni a zciiitli sun, to ie(hiee it to what the thermometer woidd record it' receiviiij;- the
xiiiiic licat riiiiii a nadir sun; 7' = tlie corrected reading: t = tin- (>l)scrve<l reading'.
II may he (.LscivimI that, if tliis cdirectidii he neglected, net only will the <liiect cilis<'rvati(ni
lie 1(1(1 small, lull as i n oliscrx aliim in lliis case is small rclatixcly to an allcr n olisci \ atioii,
the icsnlting heal luitsidc the atniiis|ilicrc (as determined from tlii' two) will lie smaller in an
enhanced degree.
I'd- cent.
Taking the high sun's mean n zenith distance at T;(ine Pine, 2(i" I'i" /; x cos .1 : = S. (IS
Taking the lew snii"s mean zenilli distance at I.one rine, (i."i^ 4.7 /; x cos i : = O.'.l?
Taking- the lii,i;li sun's mean zenith distance at Wcuiiitaiii ('amp, -li^ 1'13'. . ..bx cos ^X = S.i)^
Taking the low snii's mean zenith distance at Moiiiitaiii Camp, (i3" 21' h x cos .t ' = 7. IMi
riiiid luiiiKiiiidir (■(inriiioii ((■(iiicctidii C)—lh1ermimition iif the ifiiKiiinf of Jicnl hixt thi-oiujh its im-
jicilirt iitisoiptidil 1)1/ tlicnixiiiiftci- bill!/.
This im]ieife<'t alisdrjilidii is due to various causes, and tirsfly to the fact tliat lamii-lilack,
thougli the liest heat alisorlier kmiwn, is yet partial in its action, selecting the short wave-lengths
more than the long, so that an ordinary lilackened tliermometer luilli is jirolialily less .sensilive to
a gi\ ell amiinnt of heat of great wave-length, (extreme invisible or dark heat rays,) than to the same
anKiniil of visihle heat, as Tymlall has iminled nut.
We kiKiw little aliiiut the matter. ]iliysieists being accustomed, save in exceptional instanees,
1(1 Ileal the laiii|i black with wliicli tlieir theiino-piles or thernioiueter.s axe covered, as a ]ierfect
absdibeiit. in at least as an inditfereiit niie. Sdi ■xperimeiit.s of our own, however, indicate that
its absdiptidii 111 ciilaiii radiations is selective in a high degree, but as these are not yet complete
we can only concliide tliat the correction will be additive and that were it applied, the general re-
sult wintid be to increase in some small but ]ierceptible degree the value of the .solar constant.
Beside the effect of selective absoi'iition we have that of reflection (al.so to some extent .select-
ive), as the spherical fiirin nl' the bulb causes the rays which fall nearly taiigentially to the sphere to
be more retlected than those which strike its surface iidrmally. To determine the amount of this
latter effect a .sjiecial thermometer with a hemisplierical lamp-blacked bulb, (1.H42 cm. in diameter
("Green O.'IU") graduated to one-tenth degree Centigrade, was designed fur use in the large \idlle
actiuometer. It was at tiist th(in;;lit that by reversing the biilb. so as In expdsc alternately the
Hat and rdiinded snifaees. when the maximiim excess of temperature was attained, a dilference iif
reading might be detected, iiwiiig to the diminished loss by retlection with a flat surface. Upon
trial it was found that the highest temperature attained with full exiiosiire to the sun (averaging
14.^ C. above that of the inclosure) the gain by the use of the flat side of the bulb iiver the hemi-
spherical siufice was diily (I .02. This is pmlialily owing tii the Hat side of the bulb being neces-
sarily (IVdin the miide (if ciinstriiclion ) thicker than the dtlier, whence a greater anidiinl (it heat is
retained by the glass df the flat side and shiwly \ ielded t(i the meicniy li,\ cdnductidii and ediivec
tioii when the flat side is liiiiied ilnwii. thus cdiiipeiisating in a great measiiic fur llie diininished
abs(ir|iti(iii of the hemispherical surface.
10«
RESEARCHES OX SOLAR HEAT.
T1](.T<' rfiiiaiiicd diic iillici- method, iiaiiii'ly, the ilirrct nuMsurcinciits of initial rates with alter-
nate Niirliu'es.
On June lit), ISSL', nieasiiicinents of lliis cliaracler were made at in, tlie sl;y lieini; a. sxood
bine, with oeeasional <auiiulns clouds.
I Initial I'ate jier miniile fV liieet measui-ement. TheiuKunetei' "(Iroen ."p314" in larye acti-
nometer ease. Staiion. AlleylH^ny. Observer, F. W. Very:|
Fl.it siilo up.
RoQDd side up.
70.4
7 .8
7 .0
7 .05
7 '.h
7 .'15
7 '.3
7 .1
7 .8
■7'^ AS
73. 29
From six jiairs <if nu'asmement.s, the exiiosure.s being separated by an inter\al of only a few
minutes and the sl>y apiiarently coutimiiui;' uniform, it was found that the initial rate, being 7°.2il
with the round side u]>. a gain of 0^.19, or 2.0 per eent., was obtained by using the tlat side. This
value +().0i;(! is therelbre adopted as the factor for the ascertained part of " eorreclion 0."
]>etermiinit'i(in of tlic iictinomcti
viionjiir iiiijiiiinlicil r.rjidsiirc {corrccthn T>).
The actiuometer thermouietei', when used in the present method, slionld be one with a Indb
sulUciently small to rapidly attain its temperature of equilibrium. The I'.audin thermometer, u.sed
ill the large actinomcter Xo. 1, nearly fultill.s this requirement when the exposure i.s prolonged to
fifteen minutes, as ha.s u.sually been done ; but the Green thermometers, used in No. 2 and No. 3, are
.so large that fifteen minutes are not euougii to wholly establish eipiilibi inm. P.oth the heating and
cooling curves are therefore incomplete; and, as will be seen by an inspection of any good set of
curves, the value of W„, obtained by taking the sum of a pair of iiicom[ilete heating and cooling
curves, will be slightly smaller than that from the same curves completed.
Hence an additive conection must be made to the results of all observations with actinometers
Nos. 2 and ■'!, whenever the time of exposure does not exceed fifteen minutes.
c(urectioii has been determined from siuniltaueous observations carried on at the
actinometers Nos. 1 and 2.
Table 9.5.
The value of this
same station witli
Synchronous comparimus of
tctinomders.
'
Station.
D.ate. , Hour. Actiuometer Actmomfl,.!
1 ■ ■ j
Lone I'ini- ...
L.Hh rill.
Lmi' I'liii ..
I,„ii,- Mil.- ..
LoDO Pine
Lono Pine
Alli'^li-iiv
1861.
Auiinst 3
Aii;iist4
\ ,;ij',t4 .....
Aii^ustb
Augusts
August 5
Augusts
1S82.
M.mb 17
M:n.h21
M ii.li 23
Min.li 29
Ii.m. h.vi.
7, 30 to 8. 00
7.00 to 7.30
7.30 to 8.00
4.00 to 4.30
4.30 to 5.00
11. 30 to 12 00
12. 00 to 12. 30
4.00 to 4.30
4.30 to 5.00
1.10 to 1.42
10. 25 to 10. 57
11.21 toll. 53
11.48 to 12.20
Cal.
1.353
1.333
1.423
1.24S
1.233
1.555
1 494
0.942
0.995
0.662
1.105
1.081
1.267
Val.
1.32S
1.250
1.332
1.21U
1.198
1.451
1.48S
1.047
1. 009
0. ,563
1. 054
0.940
1. 007
""" 1 1
I'^dm the above comparisons, it is found that to reduce observations from incomplete series
with actiuometer No. 2 or No. ."> to the effect whiclj would have been observed with the fullest ex-
liosnrc. a correction of + "i.l jier cent, must be added. The actual value of "correction D," lierc-
after used, is but 3 per cent.; accordingly, so far as this is concerned, our resulting values of the
solar constant will be too small.
It will be observed that all our corrections ha\c thus far been adilitive. that is, they have in
every case iiicicascd the linal result, anil not diminished it. A reason (or this predominance of ad-
ditive coricclions is to be fi 111 ml ill the uni\cisal lendency to the dissipation of thermal energy.
A("nx():\rETEi! cokiiectioxs. 109
We take siifU precaiitioiis a.^s we can In ]iic\t'iit tlic loss ot' lical, and iiexci'tlii'li'ss at i-vcry step (pf
the indccss. lu'at is lost, lor the |iui|h>sc nf lair iiirasiiri'inciil, williout any (■oiiipi'iisatiiift .uaiii.
Usually i I] an in vest i,ya linn. I he iici;Iim|i-iI niiiiutc iiistni mental ernirs tciiil to eon i pen sale eaeli olliei'.
Here and for tin' alio\c reason, all. or nearly all. the inslriiniciilal errois have the same si^n. We
have considered oiliers too minute or loo dillieiilt to <leterniine (piaiililalivel\ « ilh Ihe same result.
There is another class ot errors, ho\ve\ei, I o wliich this remark does not apply, and which we miw
investigate.
Jk'tciminiitinii <ij' til, (■iin-(rti<iii Itir rdriittimi ul' iitiiiospliirif pirxxun {r(inrcti(i)i A,').
A lilth correction (correction K) ai ises I'nim Uw f.ict thai lieside th.' eooliny ot tlje thernnaiicter
from radiation, it loses heat by ccmlaci with the air, and iiKn'e rapidly as the air is denser.
Aecordinjily, other thin;;s lieiii.y e(puil. the rate ot loss of heal for a jjiveii excess of temperatnie
will be less on tlie mountain (where the li.iromi'lric inessiire is less) than al the sea level.
To clcterniine this correction, the lailli of the tlieiii Ii'r was sealed within a small copper
gloVie two inches in diameter. lilaekeiiiHl within, and ttom uhicli the air could lii' cxhausled liy a
Sprengel's pump.
First, the j;lolie lieiiii; tilled with air at a Uaronietric jiressnre ol 7.11 mm. (that |ire\ailine al
the time of the e\|ierimcnt at the station. Allcuhenx ). was cooled diirinu 1."> minutes from a han-
perature of excess of 17 to an excess of little more lliaii <l . and Iheii the best vm iiiini attainable
by the use of the 8inenj;ers i>uni]i haxin^; been iiia<le in the copper j;lobe, Ihe same expeiimenl
was repeated. The exiierimeiils were so condncli'd that llii- rate ol Coolinj; for each dei^rei' of
excess eould be determined with acciiiacy. A niori' |iaillciilar acconnl of them will be fonml
under another head. (See Appendix.)
The (airves by which they were lui.^iually represented are not here .si\ en. I'.y measurements
taken on the lar.:;er oiij^iiial sheets, we find — , \ for various lempeialnres of excess (/. c, llie rate
of tlie tlK'rmometer's cooling accordiiio- to its excess over the temperature of Ihe j^lolie) in vacuo
and in air, at a pressure of 731 nini. From a comparison of these results, we obtain the loss l)y
convection in air at this pressure, for various teni]>eratures of excess. Thus with an excess of 10",
the convection amounts to 27 jier cent, of the total loss; i'or b''. Ill ])er cent.: for L'i" (which may
be taken as the a\erai:c excess of the sun thcrmiain'ter duriiifi its lirst minnle of heatinj;). 1.'! per
cent., which is very nearly the value of "corrcciion A." "(.'orrection A," then, reiire.seiils nearly
that part of the loss, due to correction. We shall a.ssume it to do so exactly. It is not certain that
the diminution of convection is directly iiroiiortional to tlie jiressure, but ex]ieriineiils rather indicate
that for moderate pres.sures the diuiinntiou is less than for very .small <Mies. Jf we treat, then,
the diminution as proportional to Ihe inessiire within the ran^je of these exiierimeiits, we may con-
clude that we have rather over than under estimated the aimaiut of the e(a'reclion itsidf
The mean reading of the liaromeler at noon al the Moniilain Camp was ."")(I2, whii-li is L'.i;; mm.
bolow 735, the average pressnn- of the air at Allegheny. We have, then, the iuii|i(Ution
7::!o : 2;i3 :: A : E
whence E = 4.4 per cent.
This value of E is probably too large, hence since its sign is lu'gative, we rather under than
over estimate the resulting value of the solar constant.
This c(urecliou has been taken account of by M. .Soret, but, like all the lu-eceding, has lieen
omitted by M. Violle. II is the only considerable correction whose sign is negative.
Taking into account that the etteet of this is to diminish correction A, we tiiitl that, if we
express it here as an independent correction {K}, we have
For L .' I'iiie, E = - .014
For Mountain Caiu|i, = — .OH
Bdcrm'iHiitUin nf Hie (U'tiiimnetcr corn'ctidii fnv sky radiiitinti (cityrcctiiiH /•').
This correction must be snbtraclive, since the actiinmieter has included a ]iarl of Ihe radiation
from llie sky about the sun with thai from Ihe sun itself
In connectifui with the acliuometric obser\ alions, pholomelric measures of the intensily of the
110
RESEAROHES OX SOLAR HEAT.
light retlcctcil IVoiii the ]i(ijtioiis of the .sky in tlie iiiuiiediate vicinity of the suu were made both
iit Lone Pine, and Mount A\ liitncy, in order to cletermiue the correction to be applied to the acti-
iionieter readings on aeeonnt of the retlected radiation.
The.se nieasureuients were eft'erted by means of an apparatus designed
for the purpose, and which we will heie najiie -'the comparator." It con-
sists of a wooden box (Fig. 9) 100 cm. long,10 cm. wide, and 10 cm. deep,
blackened on the inside, and provided at the ends with small astronomical
telescopes, S L, S' L', whose common optical axis is parallel to the central
line of the box. M and ,1/' are plane glass mirrors, silvered on the front
face, each capable of rotation in two directions about axes, one axis being
peipendicidar to, and the other coinciding with, the longitudinal axis of the
box. J/' is provided with a tangent screw, with graduated head, so that
it may be nnived through any desired angle, in order to bring into view the
[larl of the sky which is to lie compared with the sun. B is the screen of a
IJnnsen photometer, both sides of which, by means of two mirrors inclined
at a suitable angle and placed below the screen, may be viewed by an eye at
]•]. This screen is attached to a sliding piece, so that it, together with the
viewing; aperture E, maybe placed iu any position between X' and L, its place
being read by an index and centimeter scale on the outside of the box.
\)\ means of this arrangement, the intensities of light from two In
mincins olijei-ts, retleeted by means of the mirrors ]\[ and .1/' into the box,
may lie(lirectly c<>Mii)ared. The len.ses L and // should be focused so that
an image of the object is formed on either side of the screen when placed
midway between them. The screen is next to be moved until the two sides
apjK'ar equally bright. Then, as.snming that the lights from 7/ and L are
ecjnal when the telescoiies are directed on the same object by means of the
mirrors, light from TJ : light from L :: LB- : L' 11--
When the light from the sky is compared with direct sunlight, the
latter must be greatly diminished in oi'der to nnikc an observation ]iossiljle.
The original a|i]iaiatns was ]iro\idt;d with a system of nnsilxered retlectors,
to be placed lietween N and L, for this purpo.se; l)ut on trial this was found
to efl'ect too great a diminution of light, and a cap, i)ierced with a snndl
circular aperture to cover the objective »S', was substituted for it.
Let ni = the ratio of the intensity of light from the solar lens to that
from the sky-lens, when both are directed on the sun, and a — tlie ratio of
the amount of light from the solar lens with diai)hragm to the amount with
lidl a]ieiture. If, then, tlie intensity of solar liglit from the sky-lens be
taken as unity, that from the solar lens will l>i' w <i. Let
7y = the intensity of light fiom any part of the sky, relali\-ely to
that from the sun :
7' = distance from focus of sky-teleseope to point of e(|ual illnmina-
tion:
from focus of solar-telescope to point of ei|nal ilhimina-
<J= di.stanc
tion.
Tin
tional t^
;n, since the lichts which have come through the lenses are propor-
the .s<pmrt
)f th.
distant
L = a III
(.>'
In order to determine th
a ]iiece allached lo the l.o\, .'
ri<-ntlv enfeebled by distance
abi(
of
', tl
that
sill
ligl
hi'
din
ctly
sky-telescope ami mirror were titted on the end of
IVoiii the sky lens, with full aperture, became suffi-
uiipaicd with the light from the sun-lens with the
ACTINOMETKi; OOKKIXITIONS.
small iipertuie. In tliis way it was Itiaml that k = (I.(M>5(I. It was also luiiinl li\ din
tiou that III = 1. Tluiclniv, loi' tlir coiniiaratdr iisimI,
k'jiiiiiiiU >if Ihi rnliirlmu „f r,i/i/;i«/,i/..r nh'.i rniliiiiix
[Station, Lone Pino. Oliservtir, Mr. (i F.
l>;itv, August .-I, ISKl. (Ill tins
Una. 2.r. till.; r+Q— r.l.a cm.J
Dist.iucc from a
1 (liaui.
2 ilium.
2^ diam
16.2
12.0
11.6
13.7
9.5
9.1
38.2
42.4
42.8
167.7
90.25
82.81
1459
1798
1832
- 000642
. 000250
. 000225
19.5 I 17.2
17.0 14.7
34, 9 I 37. 2
. 000203
(.\llKllst .".)
■t, llllt sll.
cry iiiipcrri
lire nf liazc anmiiil tlir siiii.
lisei'xatiiiii ami iciliictidii tor i.-acli i\:
lot conwti'il lor ililliiscd li-lit (/. ,., I,
ruh
•rcat
y.
OH .^
Til.
pec
r 11
Ill'C
iitl>
(k-
Tl
is is
The af'teruoou observations of tliis date
increase in the sky illuiniiiation, caused liy tlic pics
The above example will indicate tlie mode of
results are given iu the following table. They are
iilar relleetion) in the mirror.
The silver of tlie mirrors, however highly iiolislicd. docs not possess alisoliitc s|iei
tioii, but its surface, with the help of tlie nearly invisilile dnst |iarticles, wliicli are iiicess
liosited everywhere, ditViiscs a certain aimmiit of li^ilit, wliicli is added to llie slv\ lij;lit.
negligible until we appioacli witliiii a solar diameter of tlie solar limb. We ha\c, from tliis jioint
up to tlie edge, an increasing amount of liglit entering tlie instrument, along with that from the
sky, but which has been directly received from the sun. The conse(iueiice is that the residts here
given lor sky radiation within half a <legree of the sun are too large; but, owing to the ditiicnity
of determining quantitatively the amount of this exces.s, no correctiou for it has yet been applied.
It may be observed, however, that it is probably owing to the absence of snch a eorreetion that the
observations appear to show much the same sky radiation immediately around the siiii on the
luouutain as in the valley. The absolute ditierence is very small, but the relative one is large,
and becomes most mauifest very close to the snn, for the ditfiision has ailded a c-onstant i|iiaiititv
to the sky heat close to the sun on mountain or in valley, and has thus made the ratio of these
values approach unity.
T'rom the following photometiic observations, there appears to be in the clear air of our sta-
tions no very great ditierence in the intensity of sky illumination at ui from that at the time of
morning and afternoon observation. In determining the correction to be apjilicd to the actinom-
eter readings for the heat rellected from the regions immediately suiroumling the sun, therelbre,
the mean of all the photometric measures will be taken.
112
EESEAU(JHES ON SOLAR HEAT.
Tadle !IG.
Siimmari/ of vomparaior ohm
TiniL'.
BistiiuL
0 from Buu
s limb.
i diam.
1 diam.
2 diam.
2i diam.
3 diclm.
. 00102s
. 000C4-J
. 0007711
. 000342
. 000454
is-s
■■i-
".'oooio5'
. oooiyo
liinllSO
a:;;::::;:::::;;:
!!, ".'001162'
Mi'au values of L
.. .001173
. 000801
.00027,'.
. 000190
Table 97.
Mount Wiiitnky. — Sumiuttri/ of fonqmrator ohs(
Tim
^
Diatano
.,V„m.su„
a limb.
S diam.
1 tUaui.
2 iliam.
Augu.st 2
Mi-a
0, m...
1, a. m
1. p. m
n valu
sofL
. 00124S
. 001123
. 001204
.001162
.OOOtiSl j
.OUOIiHl
. 000250
.OOOlliG
. 000201
.0011S4
.O00GS5
. 0002 ;i'i
Fidiii tlicsc iiicaii values curves have beeu plotted, as given on Plate VII, where the unit of
leuf^th on the alisei.ssa' is a solar diameter, and the ordiuates denote intensities of sky illuniiuatioii
exi)resse(l in units, each of which is Yjfuo of the mean solar Inminosity. The central column, if
prolonged to a height of 1,0011 uuits, would represent the direct ladiatioii from the solar disk, and
the curves show the dimiiuitioii of sky radiatiou at various distances IVcmii the sun's limt).
DctcniiiiKilion (</' thf iicHniiiiictcr con-cctiou from the itlmrv viiri'cn for Lone I'hii- tmd Mount Wliitnvi/
'olwrnitions.
If tlic curves all- idtati'd abiint tljc axis of Y. the amount of li.yht emitted hy the sun will he
represented hy tlic xdhime of the cylinder descrilied liy the two lines representing the boiindaiies
of the sun's dis]<. wlmse eqiuitions are i/=i and (/= —.\, or calling the height 1000, -] ttX 1000; while
the volume ol I he .solid, included between the plane of the axis ol .V and the surface described by
the curve, will represent the amouut of light received fronj adincent iioitimis of the sky.
The curve of ob.servation (uncorrected for diffused light) coineides (|uite closely with an equi-
lateral hyperbola whose asymjitotes are the lines ,(■=—], //= — ',. Tlie eijiiation of the equilateral
hyiieibola I'el'ell'ed to its a.symptotes is
a-
■*'.'/=.,
l>y measurement (i=1.9, whence the equation referred to the lines x=—\, //= — i (the dotted
lines of the liguiv), is .r .(/=l..S0-5.
Transferring to the origin O, who.se co-ordinates are x=+ \, //= + ],
(.'■+1) (//+1) = 1.S0.-.
or
1.S05 ,
y=
■c+i
LDNE PINE
MT.WHITNEY
ALLCCHCNY
plate vii
Comparator Curves.
actix()mii;ti-:i; coiMtKd'ioNS.
113
The ilultcil line shows tbr locus iif 111 is iM|iial loll. Tlic voIuiik' ,i;.'iici\ilril liy I Ins iMir\X' lii:iy lie
Olisiilcicil to lie iiiailc ii[i oT clriiiciilary c.vliiiillii'.iil riiius \vlios<' ciKMIiiilciciU'c is L' ,t .c, xvliosc tliick-
ifss IS il X, aiul whose height is //. Theieloiv
V = -J 7
-/■
» ,1 .
Takiii.u the limits of the ei|natic)ii, .V=V and -V=l, the Miliiiiie lieeome,-
V = 3.(11. J' 'i;^''; -: f ,,-/,,=[ :;..;i r [.,-1 loj;,, (r+ DJ -
./• = 4, V,= 1(I.4I r-.!MIL',-, - lou, 1,1'.">
.i = i, V|= 1.74 r — .'.IOLTj r lo;;, (1.75
V = V,-Vi=.'<.7(t --.tldL'.j T (lo.u, l.L'.j-loj:,, .7.">)
-S.70 --.wi:, - :
l.L'."
(1.7."',
'=s.7() r-.!i(ii;,"> - loii, r,.(;(;7=L'i.Mi.
The volume of the eyliiiiler is l-'-'.O - = 7S.-,.i'; heiiee siiiili-lit : .skyli-ht -- 7s.-,.2 : L'i:.ll = l : .Ol'.s.-).
The eiiive of sUy illiiiiiiiiatioii on Alouiit Whitney does not differ .greatly from that at I. one
Pine. I'efened to ax<'s who.se equiitioii.s are .r = — ], )/= — ',, it is nearly represi'iited liy the eqmi-
tioii a7/ = 1.8(r>, the same that has been used to repiesent the Lone I'ine curxe. The only no-
ticeable (litten-iiee is that it a]>iij'oaelies closer to the axis of .V at a distance from the origin. The
vohinie of the (airve generated by its rexi'liilion is therefore somewhat less, and eoiise(|iieiitly the
derived actinouieter correction, ex|iressed as a iinantity to be subtracted, will also be smaller. If
the total light received from sun and so nmeh ol' the adjacent skv as radiates to the theriiiometer
1(1,(1(1(1
lll,'J.s,-i
the fraction of this total amount due to the sun aloiii'. This is the actiiiometric corrcctixe factor
F as detennined from the IjOIic Pine and Jloiuit Wliifney obserx atioiis. We next give the results
of similar <leteriiiiiiations at Allegheny, a hazy sky being chosen to determiiio an extreme, value for
tlio correction.
('(iiitpaitito)- ohsffratiiins- of October o, 1S81!, iikkJv itt AUeijheni/.
iiml th.- sun ; ,sliy vc-ry li,i?,.\ and -moty. Siuiiiltimcous ol).s,>iT.-itions mailr- by Mr. F. W. Very witb
V(* tliL- luUowiii^ rfsiilt,s ; tlu- iu.slnimi'nt.il iictiuometef corrections havo been aiii'lad.]
Espoanro to siiu from 11". I(i"' a. iii.
Exposure to sun frimi 1- .1:1 p. in.
Exiiosuro to sun fn>.n I'J .11 p. ni.
idi.Ttic
i(li:iti<
Klnitii
Cal.
= 0.al.".
The observations w itli the comparator, made at dilfereiit times, .seem to indicate no similar pro-
gressive change in the sky ilhimiuatiou, and therefore the means of observatious made at tlie same
distauce will be taken.
Distance from tlio p
V iliam. 1 tliani. 2 di:
Koilnctiou of observations of October 3, 1882.
25 U
20.1
14.0
9.9
27.2
32.1
37.3
42.3
625
404.0
98.01
7:19. S
1U30
1391
1789
.0U42H
. 0018".0
. 000796
. 000273
li'D.:i5_Nu. XV 15
73.96
llJOf
. 000194
114
keseak(;hes on solai;- heat.
Obscinitiuiis wilh comparalor ill AJIcijImiij Uclohcr 1, lf82.
|Sky, dense imil'miu linjc, mainly proJiacil by suiuku. Observer, J. E. Kteler.]
27.9
2S.5
28.4
Distances from £
i diam. ^ diam. 1 diar
33.0
31.0
32.0
24.5
23.8
22.0
lieduction of obscrrationa iif October 4, 1882.
30.4
28.6
21.8
21.8
23. C
30.4
924.2
818.0
475.2
475.3
557.0
924 2
. 00970
. 00732
. 00250
17.0
35.2
289. 0
1230
.00110
Acthiomcier correct km fur AUcijJuiiii ohsirrtitinnn.
Ill lU'tci-Miiiiiiig tlio actiiionieter correction for Allcgliciiy, the curve of tsky illuiiiiiiation from
tlic oliscrvatioiisi of October 3, 1882, i.s used. It is sufliciciitly nearly rein'c.seiiteil by a liyperliola
wliose a.syiiiiitotes are .r= + (t. 4, ,)/= — "•-. and whose transverse a.\is is 2.12. Its ciiuatioii, releircd
to these asymiitotes (dotted lines in figure 3, Plato VII), is os y=2:iil.
If in this equatiou .r=0.1, ^=22.-i7. The hyperbola therefore cuts the line, •(■=■1, at a consider-
ably higher point than the curve of observation; but ou the other hau<l it lies nearer to the line
than the latter. Keferred to the axes drawn in the figure, the ciinatiim lieconies i/=~'" — . 2, (he
locus of which is represented by the dotted curve. If revolved about the axis of 1', it describes a
solid w hose volume between Xi and .r, is
\ =2 7T r.r II il .1-
U llic hyperliola .r//^„ be transferred to a new origin .v=p, il = ij^ its ei|iiation liccouies
(^I'+J') (!l+'l)=Z
^=2(.r+,)-^^
and if rotated around llie axis of Y, the ])ortion included between the axis of A' and the curve and
the two ordinates at .ci, .c.. will describe the volume, —
V=:3 Ttjxy d ,r= 7t a? £' ' '^-^ rr y J_' ' x d .t;=[;r ir(\r~p log, [.v+p\^~7r q .c^]^^
= [^LI'MttI.i+A log, f.i--.4]^-.2 ;r.i-'1
where « = 2.]2, p= -0.1, and (/=0.2. Taking the limits ,i'|=0.5 and ,i-'=5.0
\'.,= 17.17 ,T + l.T'.KS n- log, i.(> l"i=2.2(l tt +1.798 tt log„ 0.1
V,-V, = V = 15.27 7r + 1.7'J8 n-log.4.(i
whence
y= 09.55
ACTIXO.METEIl CORRECTIONS.
115
The volume oftlie cylinder lieiiii; a.s before, 785.2
,siiiili-lit: skyIi';-lit=7S.J.2: fi0..55=l : 0.0880
1
The aiij;iihir apertures ui' both lar.i;e and inedinin iliaphraiiins, used on the small aelinometer,
are so yreat iis to iiielmle all ol the |i(Ull(Ui of the sky witliin tlie limits of the integration — that is,
the correction is the same for lioth apertures. ( )\\ ini;' to dilfu.sed lij^ht from the sl;y-lens, mirror,
•and telescope-tube, these factors, namely. .'.iTl-'o from tlie Lone Pine observations and .018.^ from
those at Allegheny, an- prolialily someuhat too small; that is, they should be nearer unity.
The followinj; subtractive I'lu rcctlcuis lor sky radiation were linally adopted after c(uuparis(uis
of all available observations, liotli fr(Uu thosi^ made with actinometcr and comparatiu- at Ijoue I'ine
and Mt. AVhitney, and also from those obtained with the same iiistru nis at Allegheny, after
applying- suitable corrections lor the Allegheny sky.
COKUECTION F.
For Lone I'ine at noon = — 1 jier cent., with low sun = — L' per cent.; for Mount Whitney at noon
= 0, «ith low sun = —1 per ceid.
Snmimirizing the preceding stat<'nieiits, we havi^ the following adopted values, expressed as
mulliplying fa<'tors, where c is the etfeet of the solar heat, as directly determined by the globe acti-
nometcr through the method proposed by M. \'iolle. As .some of the factors chaugv with the alti-
tude of the snii, the linal corici-tiiui will ditter .slightly acc(udiiig as the ob.seivation is taken at
high or low sun, and at Lone Fine or Mountain Camp,
Table 98.
Loco Pino observations.
Moiint;iin Camp (ibst-rvatioiis.
HisU snu. Low sun.
1
IlisU .suu.
Low sun.
-f.lSSo
+.081
+ , U2G
+. o:io
+. 138 0
+. 070
+. 02G
-f.030
-.1)14
1
— 014
+ .138 0
+.081
+ . 026
+. o;io
-.044
— . 000
+. 138 c
+.071
+ .0211
+. 030
-.044
-.010
Corr. 0
Corr. I)
Con-. F
+ .275
-.024
+.204
-.034
+.275
-.044
+.265
-.054
= +.251 c
+.=230c
=+.231c.
= +.211c.
We have then a mean additi\c I'orrection of about 2." per cent, as the result of all the lire-
ceding iux'csligations, as the least we can assign. In ]iassing, however, fnmi the " nucorrected "
to the •'corrected" obsci\ations, «c use the I'.xact xalni's above. The limd values in the"siiMi-
I ics (it aclinomcler observations" are obtained liy appl\ing llic alio\e coi icclioirs In the \alnes
in calorii's detcrnjine<l from tin' initial lale (iiiH,,) iii each day, and the water e(plivalcut of the
thermometer used.
CHAPTER IX.
SUMMARY (»K KIvSULTS.
Ill this suiiiiiiiiry we liiivo selected tlie tAvn cleiirest iiiiil best ilays of syiicliroiums olisevvation,
viz, August 2.". :iiiil August 25, for separate ie<lnctioii. The iiieaiiin,a; of the syiiilmls is M,,;,, tlie
aii-iiiass traversed at noon ; M_, ,;.., tlie aifiiiass traversed at iiioriiiiig or evening, obtained from the
n.rmiih. M= see. r, Ibr zenith distances less than GoO, and Iron, M = .MIl><..ta^"''^"' ivIVartion
Cos. Aiipt. Alt.
for those greater than (i5°; ,5 the barometer in deciiiielers; where », for brevity, is put equal to
7 0
'- — =rr^ ; C, and C, the values in calories at hii;h and low sun respectively ; «• the coefiicient
M,„3„ — U„i, ' ' '" 1 .' J
of tran.'-niis.sion for an entire atmosphere of 7. (!''"' ; B the solar constant expressed in calories. Be-
sides these two days all the noou observations at Lone Pine have been united for comparison with
all the miiniing and cxeiiing observatinns. In like manner the ciliserxaticms at ^rountain Cam[)
are reduced, and the noon observations eompared with the mean of morning and evening.
TAtiLE '.Ml.
I!i(h(rtion of Loin Vine (uliimmelcr uMerratioim.
UOMl'UTATION OF a.
D.nla.
Mo
rniug anil ii
on.
Ev
Dning nm\ n(
on.
From ol>-
aer\ atians
oIAiisnat
23.
From t)b.
serrations
of Anmi.st
25.
From mean
of all ob-
a^rvation.s.
From Ob.
aorvatioua
o( August
23.
From oil-
of Aui^iist
257
From mean
of all ob-
servations.
M„I3„
M,0,
M„fi„-M,li,
.i 15.71!
7.117
S.39
(1. 900
1.4M
1.760
0. 1749
0. 24.'..i
. - 0. U7(J0
. -0.0040
9. 935S
. 1 0. SG26
lG..-iS
7.39
8.99
0. 845
1. .543
1-749
0. 1.SK4
0. i;4'JS
-0. 0.'i44
-0.0400
9. 9539
0. S993
17.57
7.40
10.17
0.745
1. 508
1.707
(1. 17S4
0. 2322
-0. 0,538
-0. 0401
9. !I599
0. 9120
15 99
7.37
8.62
0.882
1.437
1. 7C0
0. 1.575
0. 2455
-0.0880
-0. 0770
9. 9224
0. 8304
10.03
.7.39
0.24
0.822
1.410
1.749
0. 1492
0. 2428
- 0. 0930
-0. 0709
9.9231
0. 8378
15. 25
7.40
7.85
0. 90S
1. 397
1. 707
0. 1452
-o! 0870
-0. 0842
9. 9158
0. 82.38
f
LaiiC
UiiC --.-
Los t'„-U)gC,..
Lnu a
Tab losm
Tablk 1(10.
computation of e.
Data..
Angr
St 23.
Angi
at 25.
Mean of all observa-
tions.
Fr..iii Til. 'an
i'iii;MbH..i-
From mean
I'lniii II 1 III iiioiiiin^ From noon
15. 87
2.09
0. 1002
^0. 0708
-0. 1480
0. 2142
2. 1101
7.37
.97
-ojmis
-0. 00.87
0.3142
2.001
10. 50
2.17
0.1 CR8
-0. 0014
-0.1332
0.3110
2. 040
7. .19
0. 2428
-0.OG14
-0.0.196
0. .3024
2. 000
10.41 ' 7.40
2. 10 . 98
0.1018 0.2322
-0. 0021 -0. 0021
-0.1341 1 -0.0009
0. 29.59 0. 2931
1. 970 1. 904
??
Logl.'
Li,!ia
Lo«„'^f^
je;.".
Computer, A. B. S.
Sr.^tMAUV OP UESHLTS.
117
Taele 101.
n,'^„ll^„f I.iwr I'illi nrtiilniiu
. ;
£
Diiti'S,
jrimilii;;
mill iiiHiii.
Eveiiiiia
.'iiiil iiiiuii.
(1. s;iri4
0. 8.-I7S
From me.a
ins "'■•"■I
1
Fro
oil
i'.;™"
Ai
Ai
Sliial
?n . .,
'ill ..liV,.iA"ut
II, I.I 11 ~lllls
0 ,SSli:i
■.:. oci
2. 04S
1. !I70
.001
i!)»4
U.-S!I13
0. S.1'.>7
2. 0?S
mil
l.;,l„rli„i, uf Mmnilun, Cliup urlinnmrtcr „\,s
ruMl'l'TATIliN llL' „
M„fi., 9.S2
il,li S.5I1
J/„p„— M,)5, 4.20
« 1.73
r'„ 1.S19
r', ],ii:i2
Lo2 a, I), 2.V.)S
I..1U. r, ii.2siio
I-oi; f„-l"i; C, .- -(1,112112
I.ii.-n —II 114(111
Till. Ins; <i... .. '.I. ll.'.:il
a U.sy77
10. 25
10. 72
12.34
13.4(1
.■5.59
-1. m
5. 50
5. 59
4.00
a.n
6. 7S
7.K1
l.r.3
1.49
1.12
0.97
1.746
1 7.'>2
1.639
1. 097
I.IIOC
1. S95
1.032
1. 9(16
n. 2420
0. 2435
(I.214C
0. 2297
II. 2S0I
0. 27711
0. 2W10
0. 2S01
—0. U021
— I).0:i41
— 0. (1714
— (I.ll,.04
9. 9492
9 92(11
'.U.l.-.ll
II. fllC7
11. m\i-,
0. k:;2ii
0. .S93I1
Table 103.
I'llMlTTATIllX UF i'
Aiisi
»t 23
Ausii
,t 23. ' ™
liiiln.
Fri.iii III. Ml
vTitiiiii,...
r
50
n.s2
I'l
.1/3
11. (IS
5. 59
.Wd
1,40
73
1 55
11,7,
l.OL'
L.ii; .
'.'.'. — iii I'liiH
J
I'li'l'l'l
-.11 is.
J'l iiv!.5
Los (
jIf/3
7.C
... -9.II92I1
0403
-(,,(i,.ili,
-11.0111
t: ...
.., 2,137
■-
149
2. 09.1
2,095
—
—
.5. 93
1. 29
1. 585
1.895
0. 200(1
0. 2776
—0. 0770
—0. 1001
9. 8999
Mciaii of .ill ol.si.iva-
('■illl|iUtrr, .\. P.. S.
118
RESEARCHES ON SOLAR HEAT.
Table 104.
7,'fsn;(s of Moiiittaiii Ctimp nctiiiomilii- mhidinns.
DiltPa.
..
JS.
Moniins
and noon.
Evonins
anil noon.
From mean
of morning From noon
and oven- ob.serva-
iug obser- tions.
vatious.
Alls
AllL-
1st 23
1st 2".
1 of Jill observations. .
Means of resnlta
0. 8977
0. 8C07
0. 8897
0. 8320
0. 89311
0. 7912
2. 137 2. 149
2. 098 2. 095
2, 151 2. 155
0.8847
0. 8390
2. 128 2. 133
The simultaneous observatious of August 23 iiud August 25, aud the means of all observations
at Lone Piue and Mountain Camp, were reduced by the same method as the high and low sun
observations at each station, noon beiuf;' couipared with noon and evening' with evcTiing. Since
the process has been illustrated by the tables already given, we omit the lengthy c.omiiutations,
and simply give the results, as follows:
Taisle 105.
reiliictk
■n, Loiii
iipiioii ilinl ahiiiwphr,
[Compntor, A. B. S. |
Dates.
a. 1 E.
Noon.
Evening. Noon.
Evening.
2.56
3. ec
2.34
AiieHst2.')
Moan of all observations...
Moans of results
0. C954
0. 6445
0. C469 2. 49
0. 7731 2. C2
0. C719
0.72eC 4 2.56 | 2.85
Final means- (1=0.6992; i? = 2. 705.
In deducing a value of the solar constant by a comparison of Mountain Camp and Lone Pine
observations tliroiigh ronillct"s formula, just employed, we have taken account only of the air-
masses, and have tacilly assumed that for the same air-ma.ss we shall always have the same
absorption. If it were true that we had one absorjition for the air-mass between the top and
bottom of the monntain and another and <litt'erent absorption for au identical mass taken from air
above it, our formula would not hold good, had it no other defect than this aloue. Let us, then,
compare observations taken in the valley and on the mountain, when the mass of air was the
same in each. At some time — late or early in the day — on the mouutain, in spite of the greater
altitude, the mass of air traversed must have been the same as at noon in the valley; and though,
as observatious wn-e not incessant through the day on the mountain, none may have aetiiall.x been
made at this instant, we can, nevertheless, liy interpolation between neighboring values, olitaiu
nearly as trnstwmtliy a result. Thus, if we represent the observations of August 23d graphically,
we Hud that at Lone riiie, noon, the air-mass was 7..'!7''"' and the observed calories 1.700c. On the
same day, on the monnhiin, onr interpolation between contiguous values shows that eipial .air-mass
would have been obser\<'d tlinuigli at 9'' 30'" in the foreiioon and at 2'' 30'" in the afternoon, with
a value of 1..SSJ <•. in the lirst im.sc and I.S.j.S e. in the .second. It appears, then, from this day's
observations that like ma.s.ses of air on the mountain traiismil, more heat th.au those in the valley.
ST'MMAUY OF KKSULTH. 119
In (.itlier wiirds, williiiiit iv^anl In iUv ixn-A\vv raiit.v of the air mi tlic uiilaiii. Imt roiii|iar-
iiig a given weight of it witli an eipial one tal>en in tlie valley, the luriinr is, in a seiisilile ilej;ree,
more iliatherraiUKius. If we reiieat the exiieriineiil with the oliservatiniis of Angnst L'.j, we have
the following values :
il. HI. 1-.
At Lone Pine, noon air-mass = 7.o'J; calories, 1.74!t
At .Alouiitain Cani]!, 0.3(1 a. ni air-niass=7.;;'J ; calories, l.,S:_!0
At JIdiintain Oamii, L'..">(l p. ni air-ina.ss = 7.3'.l ; calories, ]..s.j(t
Finallj-, if we re]ieat it for the means of all observations, we liud the values —
Lone Pine, uoon air-mass = 7.-t( I : eahiries, 1.7'.t7
Mouutaiu Camp, 9.30 a. m air-niass=7.4(> : calories, l.sii^
Mouutaiu Camp, 2.30 p. m air-mas.s=7.40: eahiries, 1.784
So that the evidence from the actiiiometer alone appears to lie conclusive as to the fact that
■some ingredient pre.seut in the lower air, is comparatively aliseut in the upper,* an inference
already drawn from our p\ rheliometer results.
Comliining the oliservatiims just cited, and giving to the mean of all doulile weight, \\v have
the fiillowing, taliing the mean of morning and afternoon values (for the rcadei' will imt have
failed to remark that the.se values on the mountain systematically dilfer for an eipial altitude of
the sun, the same nuiss of air being found always more diatheriiiainuis in tlie morning than in the
afternoon).
For same air-mass (7..'i'.l''"') at Lone Pine and .Miuuitaiu Cam]i, we lia\e ;it Lone I'ine, L7.'ilc;
at Mountain Camp, LS.".3e. The results tor various air-masses are re|iresented graphically in Pig. 10.
It ap]iears that in the valley as well as on the mountain, with the same air mass, we have
greater diathermancy in the morning than in the alternoon. (See Fig. U.)
AVe have just found from the mean of all our comparisons between observations on the mountain
and at Lone Pine, noon being compared with noon aud evening with evening, the aetiuoiueter value,
2.70.JC, for the solar constant, but this was on the usual assumption as to the uniformity of the
absoriition of eijual air-mas.ses, an assum]ition whose fallacy we have just exposed. Ueserving a
fuller discus.sion of this point for the cluipter on the spectro-bolometer, we may jioint out here a
method of approximately correcting for the efl'ect of this ditferent constitution of like air-masses,
with the least possible dependence on hypothesis.
Knowing that the air-mass above Mountain Camp was of the same ([iiallli/ as that piution of
it included witli the part between the stations in a Lone Pine olj.servation, and knowing the com-
parative transmi.ssibility of two eipial air-masses at Lone Pine and Mountain Camp, since the
barometer gives us the air-mass above and below, we have sullicient data for introducing two
coefficients of transmission.
(In view of the large error which Pouillet's forunda involves, irrespective of the one we are
now discussing, it does not seem expedient to do more than approximately correct the last \alue
of E, found by comi)aring observations at ^lountain Camp with synchronous ones at Lone Pine.
Let c'l be the coellicient of transmission tor the mass of air above Mountain ( 'amp, ii. that tor
the mass of air between Lone Pine and Mountain Camp.
From the ob.served values of C given above we find the actual ratio of trausmissibilify at
Mouutaiu Camp to that at Loue I'ine for the same air-mass,
1.833 , .
J7733 = l-W' (nearly).
I!y tlie eom])ari.son of the two stations, the coetheient of transmissinn for the mass ol air
between them was found to be (r_,=0.70; l)ut r(, is obviously larger than this in at least the above
ratio.
In order, then, to (ix a value of the coeHieient for the ma.ss of air abo\e .Mountain (_'anip, (i^
may be multiplied by the ratio of traiLspareucy, 1.06, giving (ri=0.70 x l.(NJ=0.74. With this and
" Sco Journoj to Mouut Wliituey, pago -I'J.
120
KESEARCnES ON SOLAK HEAT.
Ficf.M
3.00
cat.
' .^ \
\..
-.^
raX
^~*
'"---..
----,..
ca7.
25 30 3J 10
Actinometer Reading as a Function of the "Air Mass.'
SUI\rMAKY OF IMO.SL'LTS.
121
•? a -:
■Sunrise.
C"-
^^^
^,
\''
\
>■
s
\
\
\
\
|-
c
^
\
/
f
/
/■
/
/,
/
/ /
y 1 ,''
y
I
-.w..
!
iL'Joo— No. XV 10
122 UESEAIMMIKS OK. SOLxVK HEAT.
the mean actinoiiicirr ivadiiij; at Mountain Oanip in calorids, C=1.'J, as arj^uinents the valnu ot E
m;iT HOW be deteiinined.
By actual coiii|mtati(iii we tind £='J.3S'2, a value wliicli is perlnqis as near the truth as \vc
can reach by these methods, but uecessarily nuieh inl'erior to that wliicli would lie attained eoukl
we consider the effect of selective absorption.
A very imiiortant piece of evidence which these oliservations at elevated and low contit;uous
stations have furnished is that the solar constant, as determined liy observations of hif;h and h>w
sun at one station, is too small. We say ci^Uhncc, for, however we may have felt assured that
this must be the case from indirect observation and inference, we could never, with a single station,
have tested this conclusion as we can uow; for it will be observed that, with the values of the
observed heat at Lone Pine, and the transmissibility determined there, wo can calculate the heat
received at a certain considerable altitude — that of Slonutain Camp — aud that by direct experiment
we fiud it too small.
Beyond this (with an exception to be immediately noted) the chief use of the elaborate deter
minatiou we have just made will, so far as the .solar constant is coucerned, be found in the ensuing
chai)ters in connection with the work on the spectrobolometer.
One most important conclusion remaius, however, to be drawn, which must rest directly on
the evidence of this globe aetinometer. We have pointed out at the commencenieut of this chajiter
that, owing to the eiiorinons difterence between the temperature of the .sun and that which is
familiar to us at the surface of this planet, the amount to which a body exposed to the direct
solar rays will rise above tlu- temperature of its surroundings is, though rigorously speaking, de-
pendent on the temperature of tho.se surroundings, yet sensibly indepeudent of them within the
range of our experimeuts. This very important remark appears to have been tirst made by Water-
stou, and has been confirmed by most careful experiment at the hands of others. According to
Mr. Ericsson's experiments, a difterence of temperature of nearly a thousand degrees Centigrade
made no sensil)le difterence whatever in the excess, while M. Violle (who argues for an extremely
low temperature of the sun) admits that but a niiniit* difterence is observaltle within a range of
100'-' C. We conclude, then, that if the temperature of our aetinometer globe was that of the ab-
solute zero, or — 273^ Centigrade, the thermometer in it would either give sensibly the same excess
that it does now, or one but slightly greater.
If our thermometer bulb were rejilaced by tlic glolie of the earth ils<'ll', and if the walls of its
chandler were represented by empty inter-])lanetary space, returning no radiation, (and in this re-
spect ciinesiMinding to the aetinometer walls at a temperature of — -73°), the temperature to
which the sunward surface of the earth would rise, would be sensibly the same as that to which
our thermometer would rise in vacuo, unless we suppose some source of heat for the earth's surface
other than that contemplated in what has just preceded. Such other sources as we can suggest,
namely, the internal heat of the earth, the friction of the tides, the dynamical ett'ect of the fall of
meteorites, the radiation from stars or dark bodies in space, &c., are absolutely insignificant in
compari.son with the solar heat, and the old idea of a " temperature of sijace" is founded, as we
have endeavored to sliow in the case ol Pouillet's celebrated value, on a snpiio.sed necessity which
no longer exists.* It may be stated contidently that we have no rea.sou to believe, from any ex-
* I have made experiments where possible, ami ealeiilatious fouiuted ou autlientic data, which satisfy me of the
trntli of tliis statement. I feel eontident that the nnited lieat of all tlie stars aud planets cannot be represented by
the ten thousandth part of our small ealorie, or anytliiuH ]uar as ^reat. The dyiinuiic elfect of meteorites may pcr-
liaps be admitted to !■.■ Ibe luosi luiportant of those above .il.d, but this is demonstrably ne{;li};ible in the present
connection.
I •annot here enter npon the results of the measurements of the heat of the heavenly bodies other than the sun-
but as Pouillet concludes that the heating elfect of the stars
per square centiuieter, i( may be well to jmiut <Hit some eoiisi
doctrine that liulil and lirni .■nv lull dillVniit uiaiiin-shitious (
any statement I itmld (iKn.
The most recent aiul (riislwoitliy iH.lupalisous of 1 he li^lit of Sirius with the I mill of I hi
proxiiiialely 4x10'", that of .Sinus lu^iii^^ unity, while lliat of the whide heavens visible lotlie
alone it
i considerably over one sin.all calo
rie pc]
: minute
deratioi
if a, cum
IS which, to the reader who accep
ts the
i coiicl
modern
SITMMAIiY OF RICSULTS. 123
Iieriiiifiital ovidi^iice, tliiit IIk^ licat dcrivcil fVoni :iH sources liesidcs iIk; sun is otlicr thiiii ciitiri'ly
iic;;lij;ililc at this staj;(' (iT tlir iii(|iiir\. Tlicri' is one iin|Miitaiit I'inainislanri- wliicli causes tlie
tlicriiHiinetei- witliiii tlic actin <'ler t(i attain a lower excess tiian tl arfli would in space, for our
tlieriiHJiiu'ter is losiiij; Ileal li.\ tlie couductiou aud e(Uivectioii of air about it.aud space, outside the
oarth's atiaosjihere, we must here e(Uisi(lcr as a void. I have uuide careful cxpi^riuientson the heatiu};
and cooliu};- of the theriu<MiH/tcrs used on Mount Whitney, by inclosiufr tlieni in a xacaiurn chamber
and detiTiniuing the rates of heatinj; and coolini; corresiiondiufi' to a K'^'cn excess. These experi-
ments will be found detailed in the appemlix. The result, so far as it atlecls our present purpose
is that the rate of heatiuj;' or coolinj;' in vacuo i.s ajiproximately propcu-tional to the excess (as we
might anticipate that it would be from the approximate truth of Newton's law of radiation), and
that the ratio of this rate to the excess is, though not strictly constant, yet approximately .so; so
tliat if, for instance, the exce.ss is «°, the rate of its radiation at that instant in vacuo is O.ISW'^ per
niinuto; whence it follows that if the initial rate be the highest admissible initial rate observe<l, as
IS shown, ."i'. 7, the final temperature of exces.s on Mount Whitiu'y in vacuo woidd be .'!1^.7. A not
dissimilar conclusion was reached by JM. Violle, who fouiul that the linal temperature of excess of
his thernionieter lui Jfount Blanc would have been, if in vacuo, 1'9^.8. If we ado]it, as we shall see
reason to do later, a value for the solar constant nearly onedialf greater than the highest oliser\-ed
heat on Jlount AVhitney, we shall conclude that the temperature of timU excess would be increased
in like ]>roportioii, and be not far from 48° C.
We have seen, in the chapter on the ascension of Mount Whitney, that as the air grew rarer
the temperature fell, though the sun's direct radiation increased. Wo might infer, then, from this
primitive and comnuui experience, that if the air grew rarer still, the temperature would fall .still
more, and that irhcn nir iras ultoi/itlicr ah.irnt, the teinpiriiturf of flu- enrth ididfy dirccl siiiishiiic
irinild he excesnivili/ lor. We now draw further conclusions from the experiments with the globe
actinometer, which we have Just detailed, and which show that a small sphere in full sunshine would,
in the ab.sence of any atmosphere whatever, attain a final excess of •18'^ above its surroundings ;
that the surfaee of the earth, were there no enveloping and heat-storing atmosphere, would (imt
off, as it is, from heat within, and owing its temperature to the .same conditions as hold in the case
of our small sphere) reaeli only a e(U-rcspcuiding excess above the temiieratnre of its surroundings —
in this case — 'J7.'!-'. Iil other words, I believe that if the atmosphere were wholly removed, the tem-
perature of the earth, under the direct solar rays, would not be greatly more than — 225° C, and
that the same result wduld follow if the earth, while still retaining that atmosphere, were deprived
of the power of selective absor].tion which it now i)osses,ses. In my view, then, these experiments
.show that, after making every allowance for other .sources than solar heat, the temperature of this
planet, and the existence of our own and all organized life upon it, is maintained in but slight de-
gree by the direct .solar rays, which of themselves are far too feelile to render fluid a planet of frozen
mercury, but that the life of the globe is rendered possible by to this little regarded juoiierty of
selective abscu'ption in our atmos|ilierc.
1 expect to take an opp(utunity elsewheri^ of eidargiug ujion the present remarks. I will at
present only repeat that I I'onsider that llie teiiijierdiiirr nf flie earth under ilireef sini.shine, ereu
though our ntmo.iphere were 2're.sent ((.s' iimr, iniiihl jiriilidlilii /all to — L'dll ■ V. if that (itiiio.yihere did
not possess the quality of selective absorption.
times tliut of Siriua. AccniiliiiHly. a lifjljt yK^atcr tli.'oi that of all tlio stars ilowii to t.lin sevoutli maf,niitiiae is less than
4X1U- "'■" "'' *'"■ *""• ^'^'•' ''■'"■ "" '■'■''' '■''"""" "•''■•'♦"•"'. ■" "»■ li^l't "'■ ""I- ■""'Ion. ki)..wl,.,l;;.-, to SI, s,. that
the ratici uf star liylit tn sini li^lit ililVcrs iiiat.-rially tVoui that of star li.-at to sun heat. If we a.lniil that the h.^at of the
sun i.s hnt three ealories, tlnn the united heat of the star.s will he lepivsente.l hy ^^'j^, cal., =ll.(in000tlllll7r.. or nnieli
less than oni- er;;. It will not materially help the e.ise of those wh. iiten.l for a sensiljle heat of the stars, if any
sncli persons there be, to assert lliat it iies from those lieyoml the range of the eye of IS'leseopio vision, unless thov
are prepared to assert that thiue is nol only :i seu^ilii,. lii;lLt, hut a lari;e degree of it, more than comparable to that of
all naked-eye stars, from this smire,-. f,u 1 h:ne lonud that Ihe s.nsitiveness of the eye is ,it least 10.000,11(1(1 times that
of our most sensitive heat I usl ni iii.'ii I , wli,-lher Ihermopile or hoi. .meter. .\i;ainst the cev. si, ■,.,■,■ .if hyp..l h.^l .. a! .larli
bo.lies in spa.-e rail.atii.K h.'al si.lliei.'Ut m .|iiai.lil\ lo lie .■.lusiileivd here, it w.iuld s i to Is- i|riil.' siiperll.io.is to
CHAPTER X.
THE deti:i;mixation of the solar constant by the study of homo
GENEOUS RAY^S.
I luivi' ii'pcatrdly called iUtontidii t<i the tact that tlie exponential tbrimila of Koii};uer and
I'ouillet still in nso (J=yijj ) is only applicable to an absolutely bouiogeneous ray, such as we
cannot physically isolate, and I have added that if we apply this fornuila to actual observations
with the thernionR'ter on highly composite radiations, we get in every case, so far as the formula
is concerned, too small a value. If we admit that the solar radiation is of different wave-lengths,
passing from one to another by steps which we cannot consider individually (or at least can only
consider as infinitely minute gradations), these statements are susceptible of rigorous demonstra-
tion. To show this let us take up the demonstration I have given elsewhere* for a particular
case, and let us first suppo.se, in accordance with what has just preceded, that the original intensity
of the sun or a star before absorption is represented by A, and that i) represents the fraction of the
energy transmitted from the sun or star in the zenith, the mass of air above the sea-level being
here taken as the unit of mass, and it being supposed that this air is everywhere of the same
cojistitution, according to the ordinary theory. When the energy is transmitted through one such
stratum, what was A has become A}); when it is transmitted through two .such strata, A])-;
through n such strata, ^4/)", and so on — a formula whose fundamental error lies in assujning this
coefticieut of transmission p to Vie a constant, for the energy of the sun or star, A is in fact not
homogeneous, l)ut composed of an infinite number of radiations, each of which has its own coefti-
cient of transmission. To commence with an iileally simple case, let us suppose the energy to be
really coiniiosed before absorption of two portions, A and B. Let A have a special coefficient of
transmission, a ; and B another special to itself, b. Then if we assume (still for considerations of
convenience only) that each of these portions is, .sejiaratelj' considered, homogeneous, we may write
(hiwri the results in the form of two geometrical iirogressions, thus :
Table 100.
Original
liKht^
Coefficient
111-
LiRht niter .ibsolption. 1
1 j 1
By one stnitiim. Ry two .strain. ' By three strata.
.1
b
Aa
Bb
Aaf
Bb'
Aa'
Bb'
Snm..^l ^B
Aa+Bb> .-In'-l-BV' > j AaHBh'
The fractions here are the coellicients of transmission, as deduced from observations at ditfer-
it zenith distances. They evidently ditfiT, ami (as will lie shown) each is larger than the pre-
■ding.
Li the above table Aii + Bh is the sum of the twi> kinds of energy as observed, after alisorp-
■ Sci- t'liiiii.tos Ri>iiilns, lonif iW. it. 701 (Miirs, 1881).
THE DETEKMINATION OF TIIK SOI.Ai; CONSTANT. 12;")
tioii by one unit stnitiiiii (sec. C = l) l\v the tlieniioiiieter or iilidtoineter ; Aa'-\-l!li' is llie sum of
the euerjjies observed after absniiiticni liy two strata (sec .' = l'), \-i'. ; ami we aie lien- suiiimscd to
know the really dual constitution ot tlie enerf^y, wliieli tlie Ihernicnneter (U- pjiotonjeter (bics not
discern. According to tlie usual hypothesis, the coeliicient of transMiission, which is tlii' (|Uiitient
obtauied by dividing the value after n absorptions by that alter ii — 1 abscjiiMions, (U-, aioic f^eiici
ally, that from the expression
/ Value after n absorjitions X J-^
V Value after m absorptionsy
is a constant. It is, in fact, not a constant, as we shall jirove later; but we shall lirst show that
if we proceed upon the ordinary a.ssuinptiiui that it is such, the value obtained for the orij;inal
energy of the sun before ab.sorption will always be too small. For if we observe by a iriethod
which discriminates between the two radiations, we shall have, if we sejiaiately deduce the original
energies from our observations of what remains after one and two absorptions,
A= ^,,,, ; and7, = *^.^.i
whence the true sum
'' + ■"- Aa' + I'.h-
while if we ob.serve by the ordinary nii'thod, which niaUes no discriiimjatinii, wc ^hall haxe the
erroneous erjuation
(Aa + r.hy
Ad- + llh-
A + B:
which is algebraicallv less than the lirst or correct vabu'
.1 + /; =
(.1,0
All'
^ Jill'
An' + III,'
>
(Aa + Uh)'
An' + Ilh'
For the expression
readily reduces to the known form
n' + /,-■ > -1 ah
.^lorcoMM- since a' + h' — 'lah = (a — h)', tin- ermr incnusix with tin' iliffi reiicc hdirnii thccihfficiftilx.
Now, in the gcniaal ea.se, if we siippusc tiic (iri;:iiial radiation /, to be ccimpuscd liefore ab.sorp-
tion, of any iiiiinbcr of part.s v!,, ylj, /I;,, + . . . Inning respectively the cocl'licicnls of abso]]ition
„i, II,. ',;,+ ... the true \alnc of L is given by a series of IVactions which may be written in the
form
Aa-
whereas the value of the <n'igiiial energy by the customary tbrmnla would be
L,
^ (Aji)'
:^Aai
so that all the (luantities being positive, by a Uiiown theorem Ly L,. and for the same values of
.•li. .1.,, .-1 ;, . . . Ibis iniMpnility is gn^ater, the greater thi' dirteri'iice in the values of the coetii-
cients a,, a,, ,(„ . . . J!ut this is stating, in other words, that the true value found liy observing
separate coetiicients of transmission are nliraiis (ji-entcr than those foiiml w ben we do not distinguish
between the radiations of which the energy of the sun (u- star is composed.
126 RESEAliOIIES CN SOLAli HEAT.
We li;ivc stnli'il iilnivc. tliat tlie usual Iiy|iiilliosis iii;il;i'S tlic coplUcient of tniiisiiiissidii a
i'(iirst;iiit. It w ill lie seen IViiiii the :ilin\c lalilf. lio\vc\('i-, tli:it it \iiries tVdiii one stniliiiii to tlio
next; tli;it it is least « lieu olitaiiied liy olisi-rvatioiis made near tlie zeiiitli, and lluit it inrrcaxi'H
jirof/n'ssirrli/ as ire iijiiinnicli thr hor'r.on.
I'or since (( and /) aiv less tliaii unity, each of the sums ,1 + B, A(t + /;/», iS:c., in the aliovo,
tahle. is h'ss than the ]iicc-cdin.u.
II is also i'\idcnl that their rate of diniiuntioH ilfiTciisea as we approach the horizon, since
A(,r — Ai(' > Aa?—Ait^ JUr — Blr > llb' — Bb"
Deuce
( Atf + P''r) — {Ao+ nh') > ( .1 a ■■+ TUr) - ( .1 a' + HI,')
i-onse(|ncntl> the ililfcrence lic.Uveon the nuiueralors of two successive ratios, such ;xs
Aa'+Hh- Afi'+P,b'
Aa- + Bly' ^ AaP+nir
is less than that of their <lenonunators. Fn other words, althou^ll liotli nunu'rator ami denonii-
, nat(U- decrease in sncccssi\-c ratios, the ratnis thfiiisrh-rs iiirrnisf iinHjirxsirrly.
Further, a simple iusi)ectiou of the form of the cxpivssion
.l,r — .!« >.l-r — .!<(' I'.lr — I',h'> Bh' — Bb''
shows that whal is there demonstrateil for two nnmhers, and two eoelli<;ieuts yl, f(, aud /.', /), is true
for any unndicr, <'\en inlinite; wliicli is the ease we deal with in actual observation.
In <ither words, it is uuiN'ersally true that when the nuTid)ers are positive, aud ((, /*, c, </, &.C..,
pro|)er fractions,
.1
A
„,"+'+ /*■^'+ rV'+'+ 7<-?"+^+^ . ^. . . . .l»"+^+ l'.h''^'+ ('<■"*'+ I>d"+'+.
even if the uumlx-r of eorrespoudiug terms be inhnite ; aud hence universally true, that when the
separate enefticients of transmissiou are positive aud less than unit.\ , as is the case in uature, the
H'eneral co<'Hicient id' traTisnnssiiui in the custoinary exiionential formula, is (1) uot a constant, (U)
always too lar-e under any circumstances, (li) always lai-.U' r and lar-cr as we aiiprouch the hori-
zon, aud (1) that the orujiiuil I'Hii-ijn i>f the sun er ^■^(|■ injhi-e (itisiirptioii, usthuiii! liij the theniinmetric
and phiitometi-ir prarcxxes and formnia' in nnirei-niil i/sr, ix nliiKt/s tun smalt, a couclusiou which we
have just reached here hy another method.
It seems to be incumbent, tlieu, on those who still use I'ouillet's formula, to at least show that
though it may i;ivc too small a value, the errorisa negligililc one in iiractice, but this has uot Deeu
atti mpteii so far as I know, aud the result of actual observation detailed already, shows conclu-
sivelv that the error is not ])racticably negligiWe, but induces a wide departure from truth, aud
tliat it is a jirim'ipal cause that the vaUies of tlie sobir constant already found are too small. I
have already observed that dust and the gros.ser paiticles in our atmosphere, by scattering a part
of the liuht and heat, exercise a uearly uou-selective absorption on that part to which separately
the foruuda of I'ouillet would api)ly with little error, but that there is every degree of fineness iu
these particles, fiom the grosser dust to to ihc water vesicle, and that on the whole the absorption
5>Tows more ami more si'li'eti\ e, even down to th(> purely seleeti\c absorption caused by the mole-
cule itself, r.nt tlion-h there may be such a continuous gradation iu nature, we cannot follow it
in our i)resent fdrniuhe, which would become unmanageably complex at the outset. I accordingly
jiresent a nnmeiical diustration iu the following table of the way iu which we may makea first ap-
proximaticui to a considcratiim of the actnal ( iplc\iiy of tbe atuuisphere's actiou. I have here
supposed theoriL;im\l heat of the sun before alisor|itiou (corresponding to our symbol, Ponillet's
A) to bedivide<l iido 1(1 jiarts. aud that these are of such a imture as to be acted on with as many
Tui'j j)1':tki;minati<»n of tiii-: solai; roNsxANT. ]:.'7
(k'.^rccs of .si'li'i'linii, (';u-li liaxiiii; a se]iai:it<.' ciicllieieiil (if tiinisiiiissHJii, sn that tfii ih-.i^riM'S ol
absuriitioii arc rcincscntcil. raiiuiii.i; lidiJi cxtiiictioii to m'arly tctal traiiMiiissicjii. And lliu.v we
may fjrossly tyiiity the far iiKirc roiii|ili'x arlioii wliicli artaally jidcsoii iii iiatiiii'.
Till' lir.st coliiuni represents the aiiMiiiiit and ediiiiiiisitinii of the uri^iiial eiieruy. The xcoiid
cohiniii represents tlie intensity in each ease nnder imr sni)positi(ins when the ra> has icached a
hci^lit of about one-third of the iHuno.^eneons atnnis|]here. The tliird eolnnm represent^ the mien
sity attained in <-aeli ease when the radiati<ni has rea.'lied llie sim level after a vertical I ransniissiini.
Tlic fourth column that which W(]iild he olisei-ved al an,\ la;e niornin.u or i-arl.\ aflcrnoon ol,sei\:i-
tions when sec. ;=li. T'lie lillh column that lor an oliser\atnin when the sun is sldl lowei-, or when
a (11
0. m
(i! lb
(Ullll
(MI'JT
0. (1(14
(1. 1-jr.
o! 411
(1.21(1
0. :!4:i
0.04
O.Sl
0..il2
4.0
= ^'■=5.451,
= (t.S-_'4
1 = (i.."ii;(i
) 7^/- = .-,.4.-.!i
1 /■,> = 4..-.
Jl = d.."p(id
E = S.(I4
= '' = 4.5
= (i.t;;;;;
, J-Jp = 4..-,
) hy = 2.SO
p = o.<;.j.j
i;= 7.11
L'.dL'."'!
= ''"= 4..-,
P
= d.l.'lK
= O.tiTl
, J-p = 4..-.
1 J'Jp: = LMIL'.")
;/ = ().i;71
IJ = 11.71
Aa + /;/; + Cc + etc.
Aa.+ r.b:. + (V.+ etc.
Aa- + r.h- + Cc- + etc.
,1(1 + 7.7* + (V + etc.
.lir + />7/'+ Cc- + etc.
Ail + Bb + Vc + etc.
We have u.sed the .syiiiUols of our prccedinn' foiinuhe, tli.m-h here .4 = 7.' = (', etc.
(Tnder the above hypothetical c(uiditions an actual observer on the suinniit of Mount Whitney
pidvi(h'd Willi an acflmmieter or iiyrheliometer (whose thernioincter bulb cannot dis(a-imiiiiito
betweiui radiations) would lind an amount of lieat re[)re.sented by 5.4(i, and c(Hnp,irinj.;- this by
i'onillefs tbrniula with the lieat at sea level (4.5) he would find the eoetUcieut of transiui.ssiou O.ofi
and for the heat outside the atmosphere J. =8, .so that under these ideally favorable circumstances
his value of the solar constant would be but four til'ths of what it .should lie. We say "ideally
favorable" because the construction of our table tacitly assumes that all strata of like density
have like transiiiissibilities, an assumption which in no way represents the comjilexity of the
actual state of things. If our obser\-er is at tlie sea Ie\-el, wliere he linds a heat represented
by 4.."i at noon under a vertical sun, and a heat of I'.S.") when the sun's zenith distance is sucli tliat
the mass of air traver.sed is doubled, he will, by a combination of these two tlirough I'ouillet's
tbrniula, lind the values ((=0.63 ; .4 = 7 nearly. Now, since we are supposed to know hero that the
actual heat outside the atmosphere was 10, wo see that the real coelticieut of trausmissioii is reprc-
seiiteil by " or that </ is actually 4."i per (tent, iii.stead of <I.(J.'!, so that this determination yives a
much larger value than the truth for the transmissibility, and a iiiii(4i smaller value than tlie truth
for the solar constant. Finally, if wc suiijiose the oliserver to compare his noon \aliie «ith that
after the ray had sutl'ered three times its noon absorption, yi viiin an obser\ i;(l heat only a lit tie over
13, wo lind 0.07 for tlio transmissiljility and (i.7 for the solar constant, so that the error in each case
is increased still further.
128 IIESEAKCUES ON SOLAU HEAT.
It may, iierbap.s, be asked liow it is that if the trausmissibility, as determined by the ther-
mometer or by ordiuary photometric measurements, is really as erroneous as we assert, that
we obtain values for it on the whole so harniouions when wo observe through very different
depths of atmosphere. Our jjreseut table shows quite clearly how there may be such a coinci-
deuce of results by the ordinary method, for we know that the low snu or star observation can
seldom be taken with advantage much nearer the zenith than we have here represented it, where
sec. C = 2, or seldom much farther from it with advantage than where sec. C = 3. Now the entire
range of values for the trausmissibility to be obtained under these conditions is, as we have
seen, only from 0.63 to 0.07. No one who knows anything of the difficulty of such observations
will affirm, I think, that the difference from the mean of 0.05 could be determined with any cer-
tainty even by years of observation. A lifetime of observations at a single station, under ordi-
nary (• litions, would probably only confirm the oliserver in the belief that the true coefficient of
transmission in our hypothetical case was about 0.05 per ceut., whereas it is, as we see in our
imagined instance, but 45 per cent. The same considerations will help us to observe how it is that
the method of Forbes and M. Crova, of deducing the solar constant from an empirical curve which
strictly represents the facts of observation, though sound in theory and the best the acfinometer
observer at one station possesses, must fail to give a proper result, owing to the insufficiency of the
data at the command of the most skillful and assiduous observer by the old method. The results
thus olttained at a single statiou must always be too small then, even under the ideally favorable
conditions we have here imagined; but there is every reason to believe that apart from the diffi-
culties we have just mentioned, nature presents many others, and that among these is the fact
that there is a systematic difi'erence between the condition of the air observed through, at high
and low sun, even on the clearest day. It results from all we have stated, that a great step toward
accuracy will be made by measuring on pencils as homogeneous as possible, which we proceed to
do with the spectro-bolometer, but that also the same considerations which prevent us from
regarding the use of the thermometer as trustworthy, apply, though in a greatly lessened degree,
to those with the spectro-bolometer, since the pencils on which this operates cannot be absolutely
homogeneous, and their coefficient of transmission can not be absolutely a constant, so that even
its observation will in theory tend to give somewhat too small a result.
To prevent misapprehension, it may be remarked that our theoretical conclusions here rest on
the algebraic demonstration, and that the munerical table is only presented in illustration.
CHAPTER XI,
THE SPECTRO r.OLOM ETEi;.
Bi'fore (It'scribing the use of the spectinbohiiiieter it will lie cinivenieiit to recall the nature of
the iiiiahiyoiis processes already eini)loyed at Allegheny and the tirst results.
Thus we found, as in Table 10, that the heat in a certain narrow jiencil of rays near A=(t.''(iO
was Ulil (on some arbitrary scale), and that the mean coeflicieut of transmission for this pencil
(Table <i) was O.O.'ifi ; so that '" = 'JTii reiiresents the energy which would have lieen observed in
this ray, could we have ascended from the sca-hvel to the upper limit of the atmosjdiere. We have
here been obliged to make the provisional assumption tlnit this narrow pencil of rays is homogen-
eous, and that its rate of transmission is a constant. When we examine our iiencil, however, with
the spectroscope visually, we find that, irrespective of the solar lines, there are in it a large number
of alternations from complete transQiission to absolute absorption, familiaT to us as the telluric lines,
and due wholly to absorption in our atmosphere. If we ascend a loi'ty mountain with our spectro-
scope, we tiud that some of these lines are sensibly as black (and as cold) there as at the sea-level.
To flx our ideas, let us consider the familiar I> lines. The space between these is (on the scale
of ordinary observation) far narrower than the narrowest linear thermopile, or even bolometer
strip, yet within these narrow limits we have at least four conspicuous lines, which we know to be
cold spaces where telluric absorption has already done its comiilete work. These particular Hues
are visible at great altitudes, and hence at the highest point we can observe in our atmosphere we
find that some of the rays are alieady totally extinguished by it, and never reach us. In other
words, their coefticient of transmission is so small that fur our pur[)oses it may be treated as zero.
But the intermediate spaces between the J) lines we know to be crowded with other lines at sun-
rise and suu.set, and each must be there in fainter degree even at our high sun observation ; con-
tributing to diminish the aggregate brightness and warmth, although it may not be separately
perceptible. In such a narrow space, then, which we have treated as homogeneous fr.im necessity,
we have no real homogeneity. Our bolometer strip or our linear thermopile thus used in oift'erenti-
ating different ])orti<ins of the s])ectrum is diuibtless a great advance ujion the thernionu'ter. which
does not discriminate at all, but we .should need an inlinite minuteness of discriininatinn to bring
all our conclusions to the test of direct experiment.
Still considering the telluric lines between the D's as an example, let us suppose them divided
into two typical groups, the first of which is ab.solutely extinguished before it comes in any way
under observation. It is the second ahme of these, including all that is relatively bright, then,
which has furnished us the coellicicnt .Ii3ii whicli we have ju.st found, and if we suppose (merely for
illnstration) that Diie-tliird the energy in this narrow group was extinguished before we could ob-
serve at all, it wiMihl fcdliiw that the heat outside the atmosphere in this iiencil was certainly <iver
one-half moie tlian our fm lanla g:i\ e it. i ri ii irlivii ice (ipphj that formula tii ob-serrations ichieli dix-
eriminatc betircen different liimis uf tmit. It is not, it is true, probable that in this particular region
which we now consider, so iiiiieh as (ine third of the heat has disappeared before its descent to the
highest mountain top, but the crowds of telluric lines which, as we have Just remarked, spring ont
at sunrise and sunset, blotting out the light between the sodium lines, make us believe that, if we
could take the separate action of all into account, there would be little exaggi'iation in our esti-
mate. I have elsewheie piiiiite(l out that the grosser dust particles with which our alnidsphere is
tilled, must, in scattering all rays indiscriminately, exercise a kind uf noii-selecti\ e aUsdiption, and
that between this and that of the mcilecules whose vibration gives us the telluric lines, every kind
1253.J— No. XV 17 ' li'J '
130 RESEAECHES ON SOLAR HEAT.
aiul degree of iiVisorptioii iiuist go on iu tlie narrowest pencil that we can ever hope to physically
isolate.
It is most plain, however, tliat we must operate on pencils as narrow as we can, anil our appa-
ratus for (loint; tliis (the s]iectro-bolometer*) is shown in elevation in Plate VIII, and in plan in
Plate IX.
Two long arms, A A', turn independently about the vertical axis, the angle between them
being measured by a graduated circle with two verniers reading to Ul". One of these arms is
directed toward the slit, and the other toward the spectrum formed by the light on leaving the
pi ism which we here suppose to be used. (When the grating is employed the arms are brought as
nearly as possible together in the position shown in Plate X.) This latter arm carries at its
extremity a concave mirror M, of 98 centimeters focus, and bears on either side of the prism an
accurately planed track directed toward the center of the mirror. On either of these tracks slides
a carriage with /s. Into these j/'s, at B, drojis either of two like ebonite cylinders, one containing
the bolometer, and the other the ordinary reticule and eyei)iece. The bolometer used in the meas-
urements of the cold bands on the charts (see Plates XI and XII) exposes to the spectrum a single
vertical stri]) of platinum, ^ mm. wide, covered with lampblack, and placed accurately in the axis
of the ebonite cylinder by reversal under a compound microscopet. The eyejiiece also has its cross-
wires centered in the axis of the second cylinder, and serves to examine optically the place which
will be occu|iied by the bolometer strip when the bolometer cylinder is in the i/'s. A simple inter-
change of the cylinders places the bolometer strip with precision in the part of the spectrum optically
I)ointed on, a moment before. The optical axis of the mirror ]\I exactly bisects the angle lictween
the direction of the arm '^' and the central line of the track, so that a ray falling on the center
of the mirror from the centerof the instrument atP, after reflection falls upon the iMjlometer strips.
C, C are counterpoises to offset the weight of the arms A, A'.
To adjust the apparatus for observation, the screws at P are loosened, the iirism removed,
and the arm A' brought around in line with the long tube. The eyepiece being placed in the )/'s
at B, the image of the distant slit is brought upon the central wire, when the reading of the divided
circle should be 0^ 00' 00", indicating a deviation of zero. The arm is then moved to one side as
iu Plate IX, until tlie mirror intercepts the rays from the prism, which has first been replaced
upon its tal)lc anil adjusfi'd by the screws below. The prism is now carefully set to minimum
deviation (usually tVu- the /', line), and is then automatically kept in minimum deviation for all other
lays by the tail piiTc and attachment at I). When the cross-wires of the eyepiece are set iijion the
/*, line ilic liirlc slioiild indicate a deviation of 47° iV 15", for the particular prismt in iiuestion.
A bright and pure image of the spectrum about Cmm. wide and 610 mm. long between the A and
// lines is now formed in the principal focus of il/ near the prism, and the bolometer case being
substituted for the eyepiece, the carriage is slid along the track until the central strip, placed verti-
cally and parallel to the Fraunhofer lines, comes exactly into focus. The heat of the solar rays in
any iiart of the siiectrum may now be measured by the bolometer (the galvanometer giving a marked
detiection as it ]iasses over the leading Fraunhofer lines), and the deviation for that part is indi-
cated by the divided ciri-le to 10".
"DIRECTIONS FOR AD.TUSTI.Xi; THE SPECTKOMETER FOR COMPARATIVE MERIDIAN AND AFTER-
NOON MEASUREMENTS WITH THE liOLOMETER, OR FOR MAPPING THE SPECTRUM OF THE
PRISM. §
'■^Arrangement of (qqxirdtiix. — In the present (June, 1883) arrangement the light comes from the
north, and in this case the bolometer carriage slides on the west track, the spectrum is thrown
"^ Made t'ruiii tlie writer's designs by W. Gruuow, of New York, and first used on tliis ex]iedition.
+ Wlii-u studying tlie extended grating infra-red spectrum a wider liolometer is used.
t Tlie prism used was one of a glass specially diathermanons to infra-red rays. It was made Ity A. Hilger, of
London, and its oi)ticaI properties are excellent. Its principal constants are: Size of two polislied faces, 53 inin. X
49 mm.; specitto gravity, 3.25; refracting angle, G^o 34' 43"; index of refraction for /), line, 1.5798; index of refrac-
tion for H line, I.6U70.
A rock-salt jirism of nearly equ,al size and great purity, liy A. Clark & Sons, li.-is .also been used. It is capable of
dividing tbe D line wbea fresbly polisbed. Prisms of qn.artz and si)ar have also been used, .and tbe selective ab-
sorption of tbe glass for ditiereut parts of the spectrum determined by comparison.
^ Taken from iustructious iu Observatory Record Book for tbe use of tbe observer.
PLATe !X.
SpECTRO— BOLOMETER -
As USED fOR MAPPiNG PRISMATIC SPECTRUM
PLATE X
SpECTRO — BOLOMETER (PlAN)
As USED FOR MAPPING NORMAL SPECTRUM.
50
_L_
4^
^
v:
D
C B a A
> y
PLATE XI.
Prismatic Spectpum.
(Energy Curve)
4" 50 ^f ZIP ip 2jl ;5C 260 IJO 2i
Si liiil!
l«illiill!'ili!'^ii'iiJfcli. .'...'..■:. i
H G F b D
!li!lllilllllllllllllilli!il
llillililiiilillllllllliliiiliiiillll
HGFb D CBaA
a a 1
plate xii ,
Normal Spectrum.
(Energy Curve)
THE SPECTKOBOLOMETEIJ. 131
toward the cast, and tlie reading' of tbe circle bv the E. vernier, wiien the image of the slit is
thrown on the bolometer, is 0^. Tlie figures on the circle run in sncli a direction that under
these conditions the reading of the circle for any position of the arm on tlie east side of the instru
meat is c(inal to the deviation.
".lf//)/,s/)»r»^— The spectrometer nuist first lie adiasted b.v the three fodt screws until tlu' plane
containing the centers ol the prism, mirror, and bolometer jiasses tlirougli the slit in the cud of
the l(uig tulic. It is iirefcralilc. though not necessary, in making this adjust uieiit. that the axis of
the spectnuiietcr sluaild be vertical, and the slit and central plane 1 mctci' alieve tin/ 11 , wlii<'h
is suppo.sed to be level.
"The collimating lens having lieu placed in th.' tube at itsuwu focal length liiuu the slit, tlu'
end (if the tulie should ui'Xt be so placed, by iru'ans of the ail|ustalile stand, thai the ciiclc of light
prejei'ted from the lens falls fair upon the face of the luisai |jlaccd over llic ccntei' of llie iiistru-
ment, normal to the incident rays. The prism being tln-n remoxed, the circle of light wdl also fall
centrally np(Ui the mirror when the two arms of tin- instrument are in line. lieuiove the prism
and screw the snuill sight into the central lade of the iirism table, and move the short arm which
cariics tlu' niiiror. piclci-alily by the hand, until the shadow (jf the si^lit faIN as nearly as possible
U]ion the <'entcr of the aiirror. The slant arai shcaild then be I'lamped finuly by the lower clamp-
ing-scrcw.
"The reading on the slit .should now be made 0'-'. As it is exceedingly ilillicult, iu this
liosition of the arm, to get the eye down to tl bserving eyci.iece ni order to do tins, the
lollowing aielhoil has b,-eu hilheito used and tbuud to i.c ei|ually accurate and niui-h more
convcuicnt. TIh' shadow of the sight falling centially upon llu- minor', the light liiuii the miiror
should lie diri'cted liy the two-slow motion screws until it is reficcted down into the ailjusting eye-
pii'ce and the iiua.ue of the slit formed uiion the cioss-wiies, when, upon properly bieussing the
eye|iiccc, a sharp image of both slit and cross-wires will be projected upon tlie ninth wall of the
daiU room on the west side of the .slit itself and at tbe same height above the tioor The wires
should be made to bisect the slit by means of the two slow motion screws of the mirror mount.
l!y this adjustment the optical axis of the mirror has been made to bisect the angle between the
slit and tbe eyepiece.
"The long arm of the spectrometer should now be moved by baud until the reading of the
east vernier i.s 0^, which is therefore the reading on the slit. The tripod having lieeii iTliiued
nearly in its true ]iosition at the beginning, the change in i)osition will be small. Tlie long colli-
mator liciiig, tor ihc present purpose, disconnected from tbe long arm, the position of the slit "ill
not ha>e been changed by.tliis maiiiiailation. Now unclasp the short aim and move it to the
east, the long arm reinainiiig iiudisturbed throughout all the subseipient o|ici-.i(ioiis. attach the
arms ot the miuimum deviation apparatus to the tail-jiiece of the prism tabic, and set the circle liy
a jiositivc rotation of the tangent screw to a devi.itioii of 47'^ 41' 15". Place the prism on its table
with its refracting angle over one of the small leveling screws, its back surface at right angles to
the tail piece, and at a distance from tbe center of tbe table such that the rays leaving the prism
appear to ]iriiceed from the center of the instrumeur.
■'Tin n tin' piism table to adjust lor minimum deviation. The siieetruni, aflcr leaving tlie in'isin,
should strike the center of the ndrror and be retlected back upon tbe cross-wires. If the s]iectruni
(\icwed iu the manner desiaibed below) is not bisected by the horizontal wire, it must be made to
do so by means of the leveling screw nuder tbe refracting angle of the prism — tbe mirror must not
be disturbed. Note if, on rotatiug the prism table in both directions past the position for minimum
deviation, the spectrum returns on tbe same path. If not, tbe screws under the other two angles
on tbe prism required adjustment. Tbe spectrum must then be brought on the Inuizontal cross-
wire again by tbe first screw, and so on until the spectrum remains bisected by the horizontal
wire while the prism table is rotated, when the refracting angle of the prism will be vcitical. The
slit should now be closed up and an image of tbe spectrum, together with the cross-wires, projected
from the eyepiece upon a piece of white paper held about .a foot distant. I'.y jiroper focussing
both the wires and the /' lines may be sharply seen. The prism sliouhl now be \cry carefully set
to mininiiim deviation by rotating its table, when the image of />, should fall exactly u|ion the
vertical cross-wire. If it does not, but comes within a distance of only about twice that separating
132 RESBAECHES ON SOLATt HEAT.
the D lines (say), the difference is iirobalaly due to springing of the long arm in moving by the
band, and possibly to change of temperature, and i>i may be brought upon the cross-wire by slightly
moving the horizontal tangent screw of the small mirror.
"Note the <listauce of the cross-wires from the mirror ou the graduated scale of the bolometer
track, take out the eyepiece, and put in the bolometer case holding the recjuired bolometer, and
set mark whicli indicates the position of its strips to tiie distance just noted. Set the bolometer
slit or strip vertical and at right angles to the spectrum, which nmy be done by means of a small
reflector held in front of the aperture of the case. Secure in position by rubber bands, open the
slit to the recjuired width (usually two millimeters), and the apjiaratus, so far as the optical
arrangements are concerned, is ready for work. The .settings should all be nmde by a positive
rotation of the tangent screw. It is, of course, assumed that the cross-wires of the eyepiece and
the bolometer aperture have been previously truly centered."
Plate XIII shows the arrangements adopted in the observations made on the expedition; the
solar rays were directed into the instrument by a heliostat, H (made by W. Grun(iW), having two
mirrors both (i inches in diameter, and silvered by Foucault's jirocess on an optically plane surface.
One of these mirrors revoh-ed by clock-work on a polar axis, the other was fixed, and the heliostat as
thus used was about ."i meters to the south of the spectre-bolometer, B, which was placed upon a solid
jiier and covered liy tlic ''hospital" teut described in the general account of the expedition. The gal-
vanometer used, ( i, was an extremely sensitive reflecting one of Sir William Thom.son's pattern, and
of the most riM'c-nt coustruclioii, by Elliott. A current of (!.()( I000l)l)(l."i2 ampere caused a deflection
of one division iiiion its scales. iilace<l at a distance of one meter.
It will lie rciiiciulicicd that most of the observations upon the mountain were made directly
in the diffract inn s|icctium and only carried as far as A = l^'.l'. This wave-length (If .2) to which
we measured « ith the grating is beyond the limits of the invisible spectrum as those limits were,
until very recently known,* but below this lies a great region whose extent was first discovered in
the course of the very observations now in (luestion.
Towards the clo.se of our stay upon Mount Whitney, w Iicii using the prism, a hitherto unknown
extension of the infra-red region was observed, and once found, we have been able to coutinue its
observation at Allegheny, and have thus obtained data in continuation of those obtained upou tlie
mountain. Those on the mountain extend, as we have said, only to l''.^. Those at Allegheny
have been contiiiiied in tiie folhiwing year, 1882, to more than double the length on th noinuil
scale, of the ]irevioiisly know a spectrum, or to wavt-leugtli of rather more than 2f.1, where the
solar spectrum sensilily tcriniiiates (at the sea-level). Since these latter observations were taken
both for a high and Icjw altituile of the sun daily, we have obtained, with their hrlp, a knowledge
not only of the heat in each ray, but of its transmissibility, a knowledge, that is, of the coefficient
of transmission throiigliout the whole of the invisible .spectrum which reaches ns; and we are able to
supplement our determinations on .Mount Whitney by tlieni. Immediately after the bolometric
observ tious on Jlount Whitney, in 1881, with the grating, we give accordingly those taken at Alle-
gheny, ill 1SS2. with till- same apparatus, except that in lieu of the grating the special prism of glass
already descrilicd as transparent to the lowest infra-red rays, was employed.
All the observations quoted in the following tables are made without reference to local absorp-
tions like the Frauuhofer lines, and give only the general distribution of the solar energy ou the
normal scale, the grating being employed on the expeiiitiou for this purpose. But on the 9th of
September, 1881, at Mountain Camp, a hasty review of the sjiectrum was made by a prism of rock
salt, and also with a glass one; and with this the great cold band which we have marked on our
charts as ,( ', was discovered. It was, at first, su'piiosed that this would not be discernible uear the
sea-level, but on the return to Allegheny it was found to lie entirely within the reach of the linear
boljineter. Two minute cold lines of even greater wave length were indeed observed and an
investigation of the whole spectrum below \=>\f.7 at Allegheny, extended our knowledge to the
limit 2''.7; betv een two and three times that previously known.
* Dr. J. W. Draiii-r, .so l.ito .is ISSl (Procceilings AniLiicau Acacluniy), rogarils tliis wave-leugtli as prolial)!)' es-
cec.liii.' tlie limits iif tile .xtioim-st iiifra-iv.l.
platc xiii.
Plan o^ Tent
AND
Arrangement of Apparatus,
THE SPECTKO-BOLOMETER. 133
Tbi're is no more iiiipi)itaiit tlnifiire of these bolometer obseixiitions than their contradiction of
the common, imleeil tlie universal, belief, prevalent at the present time amonu sc'ientitic men, that our
atmosphere is least transmissilile to the son's dark heat. It is constantly asserted that the "heat"
ray has found easy admission to imi atiii(is|iliere as "light,"' tliat it Inis fallen npcjn the surface of the
earth and been returned toward spare as dark heat, which because of its nontransmissibility can-
not readily escape ajjain; ami the n]etcoroloj;ist has seen in this beat storing action a preservative
of the surface temperature of our planet. In a certain sense this is true, but the jihysicist, bia.sed,
l>erhaps, by the meteorolo;;ieul evidence, has asserted far too hastily that all the dark solar heat is
comparatively non-transmissible by the atuiosiihere. The contrail/ is tlic casr. It is dillicidt to say
how far physics has here leaned in the past on in<'teorolof,'y, and meteoroloi;y on ]iliysies, but if the
present observations ai<' ciniect, it seems clear that the present view of both must be moditieil.
Let me state, to prexcnt misapprehension, that I do not at all deny that dark heat iivJiated
from tJic soil is arresteil by our atniosjiherc, or that the surface temperature of the earth may be
elevated by such a heat-storinj; action as has been jiointed out as jiossible by Tyndall and by
others, but I asseit that out to the utmost limit known, at '2''.'! of the invisible infra red solar heat
siieetrnm. the rays grow progressively more trausmis.sible as their wave h-ngth ineieases, (always
exei]]ting e.f course the regions of special absorption known as telluric lines ov cold hands).
At the present time (1883) it is almost universally understood, on thi> contrary, that the light
rays are most transmissible, and these dark heat rays least transmissibh'. so that the traiismissibility
declines on either side whether toward the infra-red or the violet.
I Ix'gan these bolometric investigations three years ago, and when I had lirst perfected appa-
ratus which enabled me to measure with a novel degree of precision in I lie invisible heat region,
nothing surprised, and iicrliaps I should say disconcerted, me more than to liiid that the lower in-
visible heat rays were iiiorr t'reely transniitle(l by our atmosphere than any oilier; for this was
directly the opposite of what I had been taught to believe. The ai)parent conseciucnce which the
reader may jieihaps remark I also saw, and asked myself how, if this were so, the atiiiosjihere
could play toward the earth the part of the glass cover to the hotbed, to which it is so usually com-
pared. I need hardly say that it seemed to me unlikely, also, that jirevious observations by others
could be so wrong as to a matter of fact, wliere that fact was so important; and with all these
doubts ill mind I resumed my work, and tested in every way my first ob.servations. All observa-
tions that I was able to make in this respect agreed, however, and all checks I could applv veri-
fied this tirst result. Within the extremest range of the then known invisible spectrum, though
the heat itself diminished, the proportion of that heat transmitted grew greater ami greater as the
wave-length increased, instead of less and less. When no further pains could be apidied at
Allegheny, it was largely \sitli this point in view that I rcsolveil to rciicat the observations at the
base ami sunimit of a hjfly mountain, and to actually (lemonstrate there, either that tlie heat
waves were less transmissible than the light waves, as is usually thought, or were more so, as I
had cause to belie\-e. Direct observation, as will be seen by tliese tables, couiiiaring the absorp-
tion between the mountain and \alley, demonstrated that the heat was more transmissible.
On Mount WIntiiev was (liseo\ cred, as 1 haxe said, a great extension of the infra-red spectrum.
On m\ return to Allegheny in fs.SL', this extension of the spectrum was studied with reference to
the same question.
1 have now given over two years of most assiduous observation to this jioint, and if the truth
has been missed it is not for want of careful cxiieriment; but I believe that 1 have not been misleil
in this resi)ect, and I desire the reader's attention to the nature and amount of_ the evidence that,
within the entire region open to our observation, the solar heat uniformly (with the exception of
the telluric lines and cold bands) becomes more mid iiiorr troii.smisnil/lc as i7.s- inirc IciK/lh hceoiiics
(irnitrr.
"How, then," it may be asked, "can the heat-stonng action of the atmosphere be maintained,
if the 'dark' heat escapes more easily than it enters as 'light' heat ?'" 1 might answer that it was
suiiicient tor me to have demonstrated the fact of this increasing transmissibility, and that the
fact was not to lie disiJidved by the coiitingency that inferences from it might conflict with pre-
conceived oiiinioii. I desire, however, to re-iterate here that I do not say that nil dark heat escapes
more easily than it enters as "light" heat, but only that throughout the solar spectrum, an far as
134 BESEAKCHES ON SOLAE HEAT.
we Mow it, even iu the extremest iufra-red heat, these heat rays are more absorbed thau the light
ones, r believe that "dark" heat of the wave-length of that which must be re radiated from the
surface of our planet could only be found in the unabsorbed solar beam before it enters our atmos-
phere, and that such heat as this has never reached us in the actual sunbeam, and has never been
analyzed by the prism. I do not at all question tlie experiments of Tyndall and others on the non-
transiiiissihility of such heat as that from the Leslie cube, an<l I do not myself tind any contlict
l)etwcen them and my own, but as far as I have been able to learn myself by direct experiment,
the wave-length of the heat absorbed and re-radiated by the soil, or that from a source much be-
low the boiling point of water, is such as to preclude the forming of any spectrum of it which we
can yet analyze with the grating or the prism.
At present, the great cold band discovered on Blount Whitney is far larger than any previously
known in the upper part of the spectrum. Experiments made shortly after the return of the
exiiedition were indecisive as to the nature of these cold bamls, but our later ones render it
probable that all of them are telluric. While within the whole known infra-red spectral region,
then, I Hnil the heat growing more and more transmissible, excepting in the cold bands, I find these
cold bands (*. e., the regions of non-transmissibility) growing wider and wider until they obliterate
the spectrum beyond 2". 8, for we may look, I think, on what remains as an uidimitedly extended
cold band, |iossibly varied by one or two traces of spectral energy. It is below tliis ultimii tliidc
of tliese latest irivestigations that I believe is yet to be found the wave-lengtli corresiioiiding lo
the niaximuni ordinate in the beat spectrum of the surface of imr planet.
1 may make my meaiiing plainer, if I say that if the mean surface temperature of th-^ globe be
taken at 15'^ or 1(1° ('., unless we could form an energy spectrum from heat of some such degree as
this, and determine the maximum ordinate "fits curve, we should, in my view, be unable to deter-
mine the approximate wave-length of the heat in question, to which I believe our atmosphere is
sensibly impermeable; yet it is on the retaining of this extremely low kind of heat that the organic
life of our globe, it seems to me, largely depends.
On the return" to Allegheny, with the linear bolometers, and especially the one whose single
strip was + of a millimeter in width and less than j-^o of a millimeter in thickness, a distinct
special exploration of the invisible spectrum went on, as I have said, with particular reference to
the mapping of tliese unknown cold bands. The imlilicatiou of these results will be found in part
in a ii;cmi)ir iji the American Journal of .Science for March, 1S83, in which, by the jiermission of
the Chief Signal Oilicer, I'crtain of the laesent results are Micorporated. I will in turn borrow
from that memoir* tlie chait »' hicli includes the great liand .'( discovered (ju Jlount Whitney,
which the reader will hnd in the lower curve of j-hitcs XI and XU. He will tind. also, in the
Appendix Ko. 2 an account of the method of determining the wave lengths in these charts, from a
memoir comnuinicate<l to the X^ational Academy of Sciences in Ai)ril, 1883, which may perhai)S
receive a separate imblication elsewhere later.
Tim iiiMxiiuuiii
1 ordinate on the normal curvfi, as ikidn
ccd froi
n the iirismatic
line, sir
mild fall in the same place
IS th;i
t ol.strv.-a ilirf
'ctly in tbi- lu'ilt spectrum of a grating,
and act
;nally does so in
onr cln
irts with gratifying exact-
hr |.r
In th.- illtistrs
.•pai-itiuii (if tl
ition first given in tlie American Jonrn
le drawing for the engraver, tlie maxin
al of Sei
mm uidi
ence and other ji
iiafe of the nnn
inrnals,
iial ciir
, owing to a slight error in
V.I til
;ni il uliculilbf
■, and the descent of tlie curve tenard l
lie viole
t SOllleuliat h'SS
almipt
CHAPTER XII.
liOLOMKTEK OBSERVATIONS OX TllK SOLAR DIFFH ACTION SPEfTIUM MADE
DIKINO THE .MOL'NT WLUTNEY EXPEDITION.
With till' siJiTtro-lKiIiMiictt'i-, ciiiiildyiiiy tlif laigo Kutlierl'uril {;ratiiif;- of (iSl lim^s to tlu' iii illi
iiii-tcr. and iitliin- siilisi,liar\ apiiaratiis already fully described, Iiigli and low sun oliservations were
made in tlie diftracticni >]icrtruni at Lone Pine on August 11, 1'J, and 14, and at the .Mountain Camp
on Mount Whitney on Sei.tcnilier 1, L'. and .".. Owing to the i ifiieulties incident to sucli an expedi-
tion, these days were tlie (inly cines on whieh observations of any value were secured with the
bolometer.
Among the diHicnllies encountered at the lnwer station, one of the must serious arose from the
derangement ol' tlie api.aratus by lii};h winds, the instniments lieing inclosed and protected by a
tent oidy. wln're llie hot wind lunnd lice cnlraiicc, everj part of the instruuients being covered by
the deseit sand and oust, wliile the heat of the darkened tent was often very near the limit of
hnniaii eiuluram-c. Amither dillicnlty arose tnuu the rajiid rise and fall of temperature iu the
morning and evening, which produced a galvanometer drift.
In s]iite of all care, the ap|iaratus was too elaliorate not to have suffered somewhat during
trans]iortation, and the nundier of dther impediments to successful work was enough at the time
to call out all the resources of dur ingenuity and patience. In order to eliminate the eii'ect of these
changes, the coinlitions were assumed to remain constant only for the time reijuired to comi)lete a
single series. The detlections were then approxiu)ately corrected for the cflect of galvanometer
drift, a lurther correction being made graphically by drawing smooth curves through the tirst
irregular ones, and the numbers were so reduced that their sums should equal 1,000 for each series
(thus representing one and the same sum of heat whetber the previous absorption had been great
or snmll). As the labor of separate reductions and couiparisons of each day's observations would
have been very great, and as the ob.servatious themselves were not such as to make such a course
desirable, they were divided into groups, according to the lu>ur-angle at which they were niade-
Eor the Lone Pine obscrvati(Uis these groups are:
ii. III.
Lone I'ine I, including 8 series, average hour-angle 0 2:2
Lone I'ine 1 1, including 10 series, average hour-angle 4 L'.'i
Lone Pine III, im-Iuding 4 series, average hour-angle 5 21
And for .Moiuitani (_'anip observations:
ii. III.
jMountaiu C;imi) 1, including 0 series, average hour-angle 0 17
Jlountain Caiuji b(, including 4 series, average hour-angle 1' 48
Mountain Camp II, including 7 series, average hour-angle 4 U
Mountain Camp III, including 3 series, average houi-angle ■"> lil
We gi.'e first the original observations, desigmiting each series by a letter of the al|>habet.
WImt the re:uler has before him here iu Talile 108 is the observation as taken from the smooth
curve. The wave-length is ;it :hc head of each ci.ilumu, and it is very obvious from the first that
the higher the sun the greater is the proportionate heat in the short wave-lengths. Table lO'.l is
elucidatory of Table los, and needs no exiilanatiou.
136
RESEARCHES ON SOLAR HEAT.
Table lOS.
Lone Fine ohservalious with spvetro-hoJo
Date.
A=''.350 , A=''. 375
/=''. 400
A=''. 450
X = ''. 500
A =''.600
A=''. 700
i=''. 800 ^=1^000
A=l''.290
Sums.
Ang. 11,
^
0
5
15
55
90
133
145
120
72
37
072
11,
h
2
y
15
78
123
140
120
70
37
640
11.
r
3
9
23
65
99
133
110
119 ,
78
50
719
11.
d
5
10
30
64
96
145
US
r'O
76
34
734
11,
r
2
7
14
50
91
125
128
111
68
37
633
11.
t
3
7
22
57
95
147
135
101
60
45
672
11.
4
7
20
95
145
145
120
66
25
682
11.
0
0
62
114
157
102
130
68
■ 35
733
11.
I
0
0
0
35
67
107
109
84
42
19
463
Aug. 12,
a
2
7
20
82
132
177
172
140
81
42
855
12.
h < 3
8
24
65
110
180
194
170
98
45
897
12,
c 1 2
6
20
75
122
170
160
131
86
51
823
12,
d , 0
0
5
45
80
122
130
no
79
56
633
12.
0
0
4
41
74
126
75
49
635
An". U,
a
2
11
34
86
126
1K2
194
145
68
26
874
l>
3
7
20
82
128
197
197
147
75
25
880
I*,
r
3
9
20
92
120
200
187
127
60
39
857
14,
.(
4
3
25
64
100
100
102
120
60
40
743
u.
c
2
6
20
70
120
151
150
14C
94
57
822
14,
t
0
2
5
56
99
140
147
130
80
40
699
14,
0
0
5
36
59
104
90
52
17
4.58
14.
h
0
0
4
27
60
101
109
96
60
30
487
Table 100.
Lone Pine conditions during ohserration.
uilh spcctfo-boJometer.
Auk. 11, a
61' 53"
to 7' 17"
7 20
to 7 55
a
TU.
11, c
11 20
to 11 33
n
in.
11, d
11 40
to 11 58
n
ni.
11, e.
12 05
to 12 19
01.
11,/
12 19
to 12 37
TU.
iU.
3 65
to 4 18
TU
4 45
to 5 21
ni.
11, i
5 40
to 0 03
01
Aug. 12, a
7 06
to 7 45
TU.
rz.b
7 45
to S 14
ni
12, c
12 00
to 12 27
TTl.
12, li
4 15
to 4 40
ni.
12, e
4 30
to 4 40
Ul.
Aug. 14. a
7 07
to 7 35
m.
14, h
7 40
to 8 02
14, c
11 13
to 11 40
i\
TU
14, d
12 09
to 12 31
P
m.
14, e
12 35
to 12 56
14, f
4 00
to 4 19
ni
14,3
4 30
to 4 50
TU
14, /i
5 05
to 5 22
P
Ul
and D. Gal
and D
and D. Very littlo drift.
eter drift +, luoderate.
ft +, greater tban at noon,
peratureof galvamiueter 105^ F.
siuall elouds, drift +. luodi
I diift +, slighl.
T iiioderatel.v rapid.
; iiix-venttd cib.servation.
D ' Temper.iture of galvauoi
D i Veiv little drift.
D ' Slow drift.
D I Variable drift.
D I Packed up apparatus.
Table 110.
Monniain Camp observations with spcctro-hoJonuler,
Date. A=''.350
A=''.375
A=^ 400
A = ''.450
*=". 500
A = ''.6O0
A=^700
A=''. 300
A = l''.000
A=1^20o's^nlS.
Sept. 1, a
1
0
1
5
3
26
14
44
25
62
37
01
35
47
28
24
IS
14
10
286*
171*1
1. c
1
2
6
23
34
44
37
26
17
10
200'
l.d
1
2
4
15
25
33
31
27
10
10
164«
1, e
0
1
3
26
41
56
60
50
30
15
282*
I../'
0
7
50
85
118
108
80
44
20
514
Sept. 2, a
3
5
27
100
135
1.15
142
114
62
30
773
2,6
5
28
105
145
105
148
108
58
30
794
2, c
7
''2
55
200
263
2sa
263
193
109
60
1,460
2,d
9
27
75
189
270
290
268
200
111
55
1,500
2, e
5
14
30
144
2.59
228
158
92
49
1,200
2./
2
10
34
1,50
225
250
221
165
90
42
1,189
1
4
25
no
160
200
200
150
85
40
975
2!).
0
4
o.i
. 90
140
200
209
171
92
42
970
Sept. 3. a
3
14
65
170
256
347
349
280
157
79
1, 720
3
15
68
192
275
305
285
190
90
56
1,479
3. c
13
21
50
184
280
333
305
209
113
64
1,572
3. d
8 20
53
176
277
360
317
228
130
74
1,643
3. e
4 10
30
142
224
248
183
100
50
1, 201
3./
3 1 10
27
160
258
305
2S9
215
115
60
1,442
Table 110, above, shows the correspomtiug Mouutaiu Camp ob.servatious. It will be reiuem-
* Observations made in weak lirst spectrum.
MOUNT WIIITXEY BOLOMETER OBSEEYATIOXS.
137
bered that tlii' f;iatiiis' has one of it.s tir.st specti-ii stroiif;', tlie either weak, ami that ineasincs are
customarily made in the former. The low readiiiss on September 1 are due tn an inadvertent
rever.'^al of the fiiatins', eansiiiK the mea.sure.s to be taken in the weak tir.st .spfctiiuii.
The aiiparatu.s on September L' and :.; was m all n^spects, save tempeialnre, in the same eun-
ditiiin as at Lone Pine, nor ronld tlie liiwer ti-mperatuif nf tlie iMilometei and i;alvaiionieter possi-
bly aeeoiiMt for tlie great inerea.se nf the readiii,i;s as shown in the talile of snms. It is observable,
too, that this increase lia.s been made eliiedy by the liain in the shorter wave-lengths, the wave-
length.s lM.(K)(t, li'.LJOO (Table ll(l) not showing, for instance, tlie same jiroportionate increase over
tbo.se in Table KtS that wavedengths (l^.-'idO, Of.GUO do. Tliese last eonsiderations show clearly that
the change is not due to instrumental causes, but that tlie biil eter registers a very great incre-
ment of radiant heat in tlie \ i.sibh' part of the spectrum when mi the muuntain, while showing no
corresponding gain in most iufia icd radiations. It ma> r\cu, it sceiiis. indiratc for some of these
wavelengths greater radiant heat bidow in the vallry than ab.Ac mi the mountain. This la.st
effect is so slight that we must admit the pinbabilitx nf its lieiiig due to instrumental causes.*
There is, however, a cause theoreticaIl\ acting tn prndiicc suih .1 n-siilt, ami one not ditticult to
explain. In fact the column nf air lietwceii tin- iiistnimciit and the- sun wliirli has alismbi-d heat
of .short wave length mn.Nt necessaiily lose this heat in ]iart by raili.itimi toward the observer, and
it will by the ordinary course (the degradation of heat) part with this by radiations of a greater
wave lengtli than those it first absorbed, and it is not iierhaps absolutely imiiossible that this muti
be sutKcient in the case of some infra red rays to mask Ihe effect of the very slight atmospheric
absorption of these rays tbemselvrs. It is to be obsi-rxcd also more generally, that whenever we
measure the atmos]ilieric absorption nfany lay whalsiK'\ cr, wr should, according to what has just
been said, strictly s]ieaking make a emrectimi fm- tin- hisit nf the wave-length under discussion
radiated by the air culumn between the instrument and tin- sun, ami tliat if we have not done so
throughout this researcli it is imt through any oversight but tlie occasion for correction, but be-
cau.se the whole amount of this correction is so small that its value is not determinable.
It may be remarked also that the mountain observations indicate an even greater facility
of transmission fur" dark lieat" rays than has been inferred from the [irevious observations at
Allegheny.
Table 111.
iluitnUlin Camp i-nndUiwis diu-'iiiij ohsi rr
[L. iipi.^.-iit^ S. P. Laodcv; K.. J. K.
<m.t iriili ^pcctro-holomctc:
.rl, !■ 1)., W. C. Ilay.l
Date. Local time.
Son's
iioiir
angle.
Zenith
di9-
State of
skj-.
Wind.
Observers.
Keniarks.
Sept. 1. a
1, '■
1. c
1. i(
1. e
1,/
Sept. 2. a
2. h
Zd
Sep..3,„
3. c
■d.d
3. e
d.f
S" 15" to S> 36" a. m.
9 15 to 9 35 a. m.
12 07 to 12 28 p. ni.
12 28 to 12 43 p. m.
3 38 to 3 58 p. 111.
4 34 to 4 50 p. m.
8 19 to 8 50 a. m.
8 50 to 9 16 a. in.
11 44 to 12 09 p. ID.
12 09 10 12 28 p. m.
4 10 to 4 27 p. m.
4 27 to 4 46 p. m.
5 05 to 5 25 p. m.
5 31 to 5 46 p. in.
R 3.1 to 8 M a. III.
9 25 to 9 42 a. ni.
11 55 to 12 13 p. m.
12 13 to 12 30 p. ill.
4 38 to 4 58 p. m.
4 58 to 0 16 p. m.
;i. m.
3 34
2 35
0 18
0 36
3 48
4 42
3 25
2 56
0 03
0 19
4 19
4 37
5 16
:i 15
2 26
0 05
0 22
4 49
5 08
56
45
26.t
29'
6«»
69i
%'
68
I?
f
29
Deep blue.
'.'.'.'.i\o '.'.'.'-
....do ..--
... do
...do
.. do ....
...lie ...
....do ....
... do ....
...do
.--.do
.-. do ....
.-- do ....
...do ...
... do ....
-- do
... do ....
.--.do
---do
Li^lit lireeze
K.D.
.. L, K..D.
} Observations made in weak 1st .spec-
i tnim.
.--.do
Gentle
do
LiStt
Hi-1. wind'
.. do
... d..
. . L.. K., D.
K..D.
K..D.
.. L.K.D.
.. L..K.,D.
.- L..]i.,D.
.. L..K.,D.
.. L.K.D.
Do.
Do.
Grating turned, strong 1st spectrum.
Strong -1- drift. Changed bolometer.
Strong - drift.
Bntlittle.il lit.
Do.
Moder.ife drift.
- do
Fr.-.sli
Hi-_di
.- do
...do
....do
... do
. . do
.. L.Iv.D.
-. L.K.D,
. L. IC.,11,
.. L. li.D.
.. L.K.D.
.. L., K.,D.
.. L„K..D.
.. L..K..D.
Do.
Sky slightly milky about setting sun.
) A tew cirrus clouds, the first seen on
) tlie monntaiu.
- Ill lait, otiservations of the li.lttery
tlie ciiireiit t-iiiplojed on the nioiiiitaiii was
niaile for tliis chaiigc and tbi' Mountain f;
this discrepancy disappears, as will be slio'
12535 -No. XV 18
galvanometer sbo
soniewliat small
1 the cluqite
ived that, ow
■r than that
[ to some internal change in the battery,
d at Lone Pine. When an .allowance "is
M.oiid with those ohtained at Lone Pine,
138
KESEARCIIES OX SOLAR HEAT.
The followii]!;- tablfs (113 and 113) exhibit all the bolometric iib.servatioiis made on the expe-
dition, reduced so that the sum of all the deflections for each series equals 1,(100, and divi<led into
groups so as to show the distribution of energy in the spectrum at four different times of day,
when the sun had the folldwiui;' Iidur-augles:
I, meridian observations, oi- hoiir-anyle zero;
Iti, hour-angle of about -i liours;
II, liour-angle of 4+ liours :
III, hour-angle of 5+ liours.
Table 112.
LONE riNE (l]iSKI(\ATIi_iN!S.
Il.Hrcliuiix n-diiird In rcpnuinl u miislunl laiVutiit lunt.
41,27., 3
12
4 02 6
10
4 39 2
y
4 05 1 3
(|
4 23 0
0
4 33 0
0
4 43 2
13
4 13 2
8
O^.TOO
0"*. SCO
1%
105
203
171
203
19.-,
175
150
ii;o
1000
1000
1000
1000
1000
1000
1000
1000
4 23
1.8, 6. 3 19. 5
SO. 6
134. 0
204. 8
210. 4
ISl. 2
104.3
51.1
1000 I
ni.
.5' 00™
0 7 22
82
134
198
210
179
107
55
4 58
0 0,7
S4
155
215
221
177
93
48
5 47
0 .0 1 0
70
145
231
235
ISl
91
41
1000
5 10
0 0 ] s
55
123
20s
224
197
123
62
1000
5 14
0 1.8 i 9.3
74.2
139.2
213.0
224.0
183. 5
103. 5
51.5
1000
Table 113.
OBSERVATIONS AT MOUNTAIN OAMr.
Dejlections reduced to represent a coifslant railiaiit htat.
1
i
11
/J
%
1
|l
I/I
//I
III
m
7/
1
/■■/
§
0/
■'■' 1
I
'n
\
K^-::.,
""^
%.„
"••■"■"^■.:
1
) i
■ M
; 'i
i i;
m
m
m
M
' ^7 ^^
l\\\
Iw
j li
/
' ■ '
llj.
/
.7/
-■■■'/'.
/ / '
1
\ u.
^^^%feis
■-.-^_
■■•••"^':i
MOUNT WHITNEY ROLOMETEH OBSERVATIONS. 139
(IBSERVATIIJXS AT MilUXT CAMI'— Continued.
0^800
I^OOI)
l*". 260
s,„„».
16.-.
lur,
59
luoo
io:j
45
1(101)
10(10
:t«:
« 1
5 4
i; IS !ii 1.-,? i'ls
:i 11 iPL' 114 -Jill
:i 14 !P7 ir.:. ■■■M
VJ Tr. l-JO 1K4 -Jlj
s -jii iL'd ls:i '.■111
77 41
1(1(10
«4. 1 4'i. :i
1000
r,» ic» 1
s an
r, on
1
0
2
4
4
26
23
19
113
93
111
161
144
20.5
212
205
201
131
170
149
9.5
41
lOOIt
1000
1000
1.0
5.0
22 7
10.-. 7
1G1.7
207 G
2(17 3
150. 7
87. .'1
42.0
1000
The p;iit (if the spfciMiiii tliiis t-ir cdiLsidciM^d fxtt-iids as fur towaids tlie lower limit as the
gratiii};' wliicli wa.s used jum iiiitted, witli due regard to tlie overlapping spectra, but a eousiderable
part of tlie total beat, iiainelN , that of the infra-red below wave-leii.i;tli, 1 .1', is not represented iu
these tirst tables, while tlie actnionieters, with whieli they are later to be compared, represent
ill the readings of their tliermometer.s the aggregate eti'eet of all heat ol' all wave-length.s. The
curves (Plate XIV) have therefore been completed by extending them through the aid of .sub.se-
quent measures at Allegheny to l. = 2'^A (the heat beyond this point being neglected), making the
intermediate ordinates bear tlie same proportion to each other as in the Allegheny normal curve,
determined after the return of the expeditiiui.
Tills is shown in Fig. 12, where the dotted line represents the part of the curve supplied fnun
the Allegheny observations.
Corrections having been applied for the angle of ditfraction and for tlie selective absorption
of the metallic reflecting surfaces employed, the curves were extended in the way just now
explained, and the area of each curve was detei'inined. For this purpose an Amsler's jiolar phi-
nimeter was used, to get by direct measurement the area aliove i = 1''.L'00. The section-]iaper on
which the curves were drawn is divided into square inches and hundredths of sijuare indies. (.)n
the axis of abscissiv j;. - Oc.l ^=t 1 inch, ami on tlie axis of ordinates a dellcction of ."io scale divis-
ions = li:ich. One sipiare inch tlicivl'orc . L'..".!!!) in units of the tables. 1 '.clow A ^ P' .L'OII, the
areas of the curves were detcriiiinc(l liy means ot' u formula for aiiproximale areas,
A=,,(^U!, + !,,+ 'V')
,'/(, .'/-', .'/.I, •■^^■•i being tlie heights of ordinates separated by distances each e(|ual to /(.
140
KESEAECHES ON SOLAK HEAT.
^:i
o a
MOU^n^ AVHITXEY ROLOMETER OliSERVATIONS.
141
Table 114.
Mr, III irsidls of Tiihlis WJanil U:! conirl.il for mrtnllir ulim-iilinii and aiujli ../ iliirnirlinn, cileiiilrd
1,1 inivi-hliiltli •-'''..I, mid uijiiln ndiind lu njircseut iiiie and llic same amount a/ li,,il fur ia,l, Kiriin.
EXTENDED BY SUBSEQUENT MllASDRES.
Sums from '^.35 U
Asl'.MO
1 .6(10
1 .800
2 . 000
2 .-200
2 .400
Are.aabovel'^.li..
Area below 1*^.2..
Total area .
l''.?0
1092. 3
1080. 9
1048.7
1211.8
1185. 2
1190.2
11S8.0
.W. 0
42. 5
29. 0
18. 9
10.1
3-2
51.4 51.1
37. 9 37. 7
2C. 5 26. 4
17. 11 16. 9
9. 2 9. 1
2. 9 2. 9
,50. 1
27! 5
IS. 2
10.2
3.4
46.9
3.5.1
25.5
17.4
9,8
3.3
44.3
33.5
24.0
16.0
9.1
3.3
40.5
14.2
8.2
3,2
.1.i, 125
19,875
.57, 3110
17, 700
57, 375
17, 625
57, 200
17, 800
58,150
16, 850
.59. 100
15, 900
75, 000
75, 000
75, 000
75, 000
75, 000
Having now obtained the areas of the cnrves, we are prepared to still t'lirtlier iiiiiirove tlie
results directly obtainable from the observations made with the speetro-boliimeter by ronibiniug
the latter with the still more numerous results of aetinometer observations. For this piir|)ose we
have merely to reduce the total areas of all the spectrum curves until the relation between them
is the same as that of the solar radiation measured under like conditions liy the aetinometer.
We therefore deteriniue reduction factors which, niulti[ilied into the ordinates of the curves
in Table IH, shall reduce the areas of the curves to eiiries|iiiiid to the aetinometer readiuys.
Table ll."i.
I'ttctors for ndncimj bolomtliic lo (At staiiditrd nf intinomt'tr
Bolometer obseiTatiL
Kertuction fac
iries by tors; ratio
oineteis.* of calories to
Lone Piue I.
Lone Pine I
Lon-rinell
Lsuurinein
Moiujlain Camp I
MmiutaiuCampIa
Mountain Camp II
Mouutain CampIII
• Tbcse values ditfer so slii;htlT fp
ut considered necessary to n-iicat tbt
alues there given.
The iie.xt table gives the tiually atlopted ordinates of liolometrie curves, the areas ol' wliich
correspond to the readings of the aetinometer at the same time. It was obtained tVnm T.ilile 111
by applying the above reduction factors.
142
EESEARCHES ON SOLAR HEAT.
.iih>jil>''f rahu's of hoJometric energy in the spectrum at high and loir i
tcith corresponding actinomefer rtadinys.
nfs reduced to agree
Lone Pine.
Mountain Camp.
I.
II.
rrr.
I.
la. II.
in.
25.1
10.0
0
39,9
14. 8 , 16. 3
,5.4
.375
26.4
15.7
4.0
43.8
23. 2 20. 3
12.8
50.1
29.6
12.4
71. 5
68. 0 42. 1
35.3
110. G
88.3
71,1
174.2
162. 5 149. 3
118.5 ■
153.9
129.5
117.0
229. 0
214. 4 . 203. 2
160.0
.600
201.0
177.0
160.7
249.7
240. 4 228. 1
183.5
.700
191.1
180. 7
162. 5
214.8
218.3 204.6
176 1
155.5
100.2
70. 4
151.7
94.6 1
58.5
134. 3
82.1
.51.4
159. 4
100.4
72 1
165. 3 157. 9
100. 4 94. 7
69. 1 1 60. 0
136.9
81.1
49.1
1.200
5e.O
44.4
38.8
56.1
,50. 5 ' 43. 8
32.7
n.600
42.5
32.7
28.6
42.7
37. 8 ! 33. 1
24.1
29.6
22. 9
20.0
30. 8
27. 5 1 23. S
17.2
IS. 9
14.7
12. n
20. 4
18. 7 1 15. S
11.4
10. 1
7.9
6.9
11.4
10.5 ! 9.0
6.6
2.400
3.2
2.5
2.2
3.8
3. 6 ' 3. 2
2.6
55,125
49, 550
43^^580
63. !I30
62, 540 , 58, 450
48, 720
19, 875
1.5, 300
13, 380
19, 920
18, 130 15, 700
11, 790
Total area
75, 000
61, 850
56, 960
83, 850
80, 670 74, 150
60, 510
All observations at Lone Piue are supiiosed to be made with a declination of +14<^ 30', and all
at Mountain (Jaiiij) with a declination of + 7^ 30'. The actual declinations of the sun were: For
Au"'ust 11, a. in., I'P 0(1' : for August 14. p. in., 14- 0(1' : for Seiitcinber 1, a. m., S° 04' ; for Sep-
tember 3, p. in,, 7^ 00'.
The zenith distances in the following table were comiiiitcd by the formula —
cos r = cos ("
*) — 2 cos '/' cos
siir i h
where r = sun's zenith distance, » = sun's declination, '/' = latitude =30° 35' (for both stations),
]f — hour-angle. The barometric readings (,5) were obtained from the average of the corrected
readings on the days of observation. .1/ was determined froiu the formula,
.0174 X tabular refraction
cos apparent altitude
.1/:
Table 117
nasses Iraver-sed hit the soJar r<
t njrh ohscr
ation.
M,
Barometer.
"u^r'
1,083
d.m.
6.62
7.17
14.14
21.52
,5,72
7.46
11.28
23.00
i. 147
4.99
We now know (and largely from the present observation.s) that as we ascend in the atmos-
phere we find in general that the coelHcient of transmission for any ray grows larger and larger
for like n!r-mas.sex. so that even for any given homogeneous ray there is a different coetlicent for
every stratum in the atmosphere and we could only represent the actual state of affairs by nsing as
our coclticient of transmission the result of an inte,gration of all these "differential" coefficients,
an integration wliicli we have no .sufficient data for making. The more of these independent coeffi-
cients wc can actually determine the more accurate will be the result, and as we employ fewer our
result will increase, being lar.gest when we employ but one (which is the usual practice). Since
we have succeeded in determining but two independent coefficients for any given ray, the assump-
tion (which we arc forced lo make by our limited observation) that these represent accurately the
result that such an integration would give us, must obviously give a result somewhat too large.
MO('^'T WITITXKY T.OLOMKTER O^.SK^VAT^()^'S. 143
though, as olivimisly. we i^ct ;i il.isci- a|iiiio\iiiiatioii U> the tiiitl] tliau if tliis assiniiptii>ri had not
l)eeii Iiiiule. So far as depeinls dii Ihese euiisiihMatiolis, then, the value cif llie I'eiistaiil thus
obtained is too sreat.
In the ol>sei\-atioiis wliich we n.iw proceed to discuss, we i;o on to deal witii separate rays,
eaeh ot whieh, we may infer hy aualo,i;,\. will have a sandier eoi-llieicMit of transmission deteiniined
by the eomparison of tlie nioiintain ami l.onc> I'ine ohsc-rvatious than that (h-teiinined by obseiva-
tioli throiiirh the uir-iiniss al)nve the' inoinilain. The aetital determination, however, of two distinct
coetiieients for eaeh speetral ray is ]iraetieally impossible, and even if we lunit onr study to a
.small luimlierof tyiiieal r.i,\ s taken lu the iidra -red, ihe .\cllow. ami the \ iolet or ultra vioh-t |iaits
of the .speetrum. we shall lind that \\ilh many of these it is impossible to do more than slate
certain general results. In regard to the iidrared lays, for instance, whose coeliicieiits of trans-
mission are in every ease, save tli;it of a<'tual absorption bands, very near unit\, minute eirois of
ob-servation, such as are .sure to present themselves, will be. ivlatively, .meat emuij;h to iire\eiit
us fnuii distinguishing between the eoellieieiit above and the eoetiicieiit below. Hut we may
expect to find a sensible ditferenee, if anywhere, in those rays belonging to the sluu-ter wave
lengths, whose eoetiieieiits are small, and here we may hope that the ililfereuees between the
upper ami lower transmissibilities will not be iiroportionally atfeeted by the errcus o[' obser\ation
to be expected in eireunistauees of such dilliculty.
Thi' task, in tact, is a wholly nidiieil om-, and such results as we may obtain are to be regarded
only as useful approximations.
^\^i proceed as follows: We lia\e abeady tWiiiid tliat at '.I'-W a. in. ami al L'..:il p. m.. (Ui the
mountain, the air-masses were, a[>|irci.\iinately. the same as at noon m the valley. \\r select a
number of typical points in the speetruiu whose wave-lengths are O".'.)'). ()"..17."i. (•■ .1. iVc. W'l' lind
for each one of these rays, by the use of the formula, I nA" = f? the eoetficietits ot' transmission for the
air-mass above the mountain by cninparisoii of high and low sun : and again, by direct eomparison
of simultaneous observations at Lone Pine and Mountain Camp, we deiive a second set of coetii-
eients special to tlie air-mass between the two stations. We follow, in other words, in the ease of
each of the above iiii-nticuied rays the same inethoil of procedure, whieh we ha\ e already explained
in the " summaiy of actiuometer ri'sults."
The results are given in the following table, whose data are, we believe, new:
T A ISLE 11 .s.
Coefficientfl
or
CoetBcients of
transmissi
tra
lunmissiou
afor.'inenti
ire
bti
>rau entire
1
atmo.splie
re
all
niospUere
oftlH-iiualitv
of tlic- quality
or tliat abo ■
of
that be-
Mount a
in
tvr
een tlie
Camp.
sta
,tiona.
A = 0.373
0.33
0.10
0. 400
0.18
0.15
0. 4.io
0.81
0. 8.'i
0.09
0.12
11: ?i;ii
0. 88
0 94
0.32
0.54
0, sou
0.99
0.88
I. 000
0. 92
0.99
1.200
0.97
0.96 1
The diSerence between the results of the luiler theory and of direct observation are Iiorc pre-
•seuted, and the discrepancy is most n-markable. Theory bids us deterinine with confidence the
coetiieients of transmission from the eom]iarison of high anil low sun at any single station, and this
we have done at Allegheny, at L(Uie Pine, and the inounttiin with, on the whole, fairly concordant
results. Put an actual a.seent above much of the tibsorbing mass of the atmosphere gives tlie coeffi-
cients just exhibited, which, as far as l.l'OO, represent the transmissibility of the atmosphere be-
tween the mountain and valley tor each r.iv of the spectrum from immediate ob.servation, aud have
nothing hypothetical about them. This remark applies to the coefficient b, special to the air-mass
between Mountain Canij) and Lone Pine, and if we calculate the value of the heat before ab.sorp-
tlon in each ray by these coefticients alone, we shall obtain enormous v.ahies for those in the green
144 RESE ARCHES ON SOIjAR HEAT.
and blue, and a ivsulting- value of the solar constant between 4 anil 5 calories. (See column (>,
Table iL'd.)
Our observed values here appear to us to bring novel and important data, but they are still
not complete enough to enable us to determine the rate at which the trausmissibility for each ray
increases for like air-masses as we ascend in the atmosphere, though they show here how enor-
mously this trausmissibility dimiuishes between one ray and another as we pass from red to violet.
We may expect, then, that the use of these double coetiicients, wliile giving us a smaller valne
than that obtained with a single coefficient by the customary formula, will give us an E^, or energy
outside the atmosphere for each ray, which, so far as it depends on this process, will be rather in
excess of the truth than within it, and we shall represent our results thus obtained by a curve
whose area shows the energy before absorption, as obtained in this way. (See upper curve, Plate
XV.) The value of a unit of area in this curve in calories is determined by a comparison with
the like curves for the mountain and Lone Pine, where the value of this unit is known from simul-
taneous observations with tlie actinometcr. We have, however, in what has preceded, neglected
flic consideration of the portion of the curve below Ic.O, where the coefficients, as obtained by the
com])arisiiii of mountain and valley observations, are sensibly eijual to unity.
With tlir.se values the column 7, in Table ll'O, is prepared, the value (E^) being the energy in
each ray luitsiilc the atmosphere as thus determined.
With these values of A'a as ordinates, we proceed to cimstrurt ii|ii>n the normal scale the curve
of energy outside the atmosphere shown in Plate XV by the upper line. (Xo. IV.) The lower
(No. I) curve in the same plate is that of the normal spectrum already given, originally drawn to
represent the distribution of energy in the spectrum of the high sun at Allegheny, and the area of
w liich within the continued sinuous line closely represents 1.7 calories. The area of the curve (No.
n') outside the atmosphere, obtained by the process just described, is 3.505 calories, and 3.5 calories
we regard, then, as a maximum value of the solar constant.
We now proceed to determine from our bolometer observations a value which we may believe,
from considerations analogous to those just presented, to be a minimum of the .solar constant, and
one within the probable truth. All the evidence we possess shows, as we have already stated, that
the atmosphere grows more transmissible as v/e ascend, or that for equal weights of air the traus-
missibility increases (and probably continuously) as we go up higher. In finding our minimum
value we iirocecd as follows: still dealing with rays which are as approximately homogeneous as
we can experimentally obtain them. Let us take one of these rays as an example, and let it be the
one whose wave-length is 0.(3 and which caused" a deflection at Lone Pine of 201. (See table of
adopted values, &c.) The coefficient of transmission for this ray, as determined by high and low
sun at Lone Pine and referred to the vertical air-mass between Lone Pine and Mountain Camp, is
.976. Prom the observations at Lone Pine, then, the heat of this ray upon the mountain should
have been
,„, 1000
201 X cyjQ = 200.(1
but the heat in tliis ray actually observed on the mountain was 249.7. Therefore, multiplying the
value for the energy of this raj- outside the atmosphere calculated from Mountain Camp high and
2497
low sun observations (2i.">) by the ratio ,,.|...^ we have 333.3, where 333.3 represents the energy in this
ray outside the atmosiihere as determined by this second ju'ocess. In like manner we proceed
to deal with the rays already used, thus forming column S in table 120.
With the values thus obtained as ordinates, we again construct a curve on the normal scale,
whose area represents the solar constant on this hypothesis, so that the area of this curve gives a
minimum value. The area thus obtained is found to be equal to 2.03 calories, the curve itself (No. II)
being given by the line with the contour ( — . — . — . — . — . — . — . — .) on plate.
Finally we draw the curve indicated by the line ( ), whose ordinates
are intermediate between these two. (See Table 120, column 9.) The area of this last curve is 3.07
calories.
We have, then, upon Plate XV four curves. The lower curve (I) represents the actual obser-
vation of the solar spectrum, including its principal absorjition bands on the normal scale near
144 RESEARCnBS ON SOLAR HEAT.
and IiUif, uud a rcsiiltiiii;- value of the solar constant between 4 and ."i calories. (See column ti,
Table llio.)
Our observed values here appear to us to bring novel and inqiortant data, but they are still
not complete enough to enable us to determine the rate at which the transmis.sibility for each ray
increases for like air-masses as we ascend in the atmosphere, though they show here how enor-
mously this transmissibility diminishes between one ray and another as we pass from red to violet.
We may expect, then, that the use of these double eoetticicnfs, while giving us a smaller value
than that obtaine<l with a single coefficient by the customary Ibrmnla, will give us an E^, or energy
outside the atmosphere for each ray, which, so far as it depends on this proces.s, will be rather in
excess of the truth than within it, aud we shall represeut our results thus obtained by a curve
whose area shows the energy before absorption, as obtained in this way. (See upper curve, Plate
XV.) The value of a unit of area in this cnrve in calories is determined by a comparison with
tlie like curves for the mountain aud Lone Pine, where the value of this unit is known from simul-
taneous observations with the actinometer. We have, however, in what has preceded, neglected
the consideration of the portion of the curve below l^.O, where the coefficients, as obtained by the
comparison of mountain and valley observations, are sensibly eipial to unity.
\\ itli thrsc values the column 7, iu Table lliO, is prepared, the value (E^) being the eneigy in
eacli ray outside the atmosphere as thus determined.
With these values of E^ as ordinates, we proceed to construet uiJoii the normal scale the curve
of energy outside the atmosphere shown in Plate XV by the niii)er line. (Xo. IV.) The lower
(No. I) curve iu the same plate is that of the normal spectrum already given, originally drawn to
represent the distribution of energy in the spectrum of the high sun at Allegheny, and the area of
which within the continued sinuous line closely represents 1.7 calories. The area of the curve (No.
IV) outside the atmosi>here, obtained by the process just described, is 3.505 calories, aud 3.5 calories
we regard, then, as a maximum value of the solar constant.
We now ]>roceed to determine from our bolometer observations a value which we may believe,
from considerations analogous to those just presented, to be a minimum of the solar constant, and
one within the probable truth. All the evidence we possess shows, as we have already stated, that
the atmosphere grows more transmissible as we ascend, or that for equal weights of air the trans-
missibility increases (and probably continuously) as we go up higher. In finding our minimum
value we proceed as follows : still dealing with rays which are as approximately homogeneous as
we can experimentally obtaiu them. Let us take one of these rays as an example, and let it be the
one whose wave-length is O.t! and which caused' a deflection at Lone Pine of 201. (See table of
adopted values, &c.) The coefficient of transmission for this ray, as determined by high and low
sun at Lone Pine and referred to the vertical air-mass between Lone Pine and Mountain Camp, is
.976. From the observations at Lone Pine, then, the heat of this ray upon the mountain should
have been
1000
201 X g^g = 206.0
but the heat in this ray actually observed on the mountain was 249.7. Therefore, multiplying the
value for the energy of this ray outside the atmosphere calculated from Mountain Camp high aud
24:',>7
low sun observations (2i.)) by the ratio .,,.,.,. we have 333.3, where 333.3 represents the energy in this
ray outside the atmos]ihere as determined by this second jirocess. In like manner we proceed
to deal with the rays already used, thus forming column 8 in table 120.
With the values thus obtained as ordinates, we again construct a curve on the normal scale,
whose area represeuts the solar constant on this hypothesis, so that the area of this curve gives a
minimum value. The area thus obtained is found to be equal to 2.63 calories, the curve itself (No. II)
being given by the line with the contour ( — . — . — . — . — . — . — . — .) on i)late.
Finally we draw the cnrve indicated by the line ( ), whose ordinates
are intermediate between these two. (See Table 120, column 0.) The area of this last curve is 3.07
calories.
We have, then, upon Plate XV four curves. The lower curve (I) represents the actual obser-
vation of the solar spectrum, iucludiug its principal absorption bands on the normal scale near
o 3o
270
PLATt XV
Energy Curves Outside the Atmosphere.
JIOUNT ■WHITNEY BOLOMETER OBSI^RVATIONS. 145
sea-level, as determiiuMl at Alle^jlieiij-, its area within t lie iires'iilar line con-esponding to an actually
observed valne of 1.7 calories. We have, by onr subseiinent lony-continued observations at Alle-
gheny, determined at leisure, and with all the accuracy we can at present coinniand, the coefficients
of transmission in this extreme infra-red portion, where we tind them, in general, slightly less than
unity. They are given in Table IL'.l. It is by the use of these subseiiuent Allegheny observations,
below A = l*'.2 (to which point the measures mi the expedition were limited), that we have extended
the upper curves (II, III, I\') shown in I'late W to L'i'.T near the exlreniest limit of our latest
observations. The calculated ordinatcs for curves II, III, IV from near (1"..^ to I".!.' coincide very
nearly with the Allegheny ordinates in the .same region. In other words, we obtain in this part of
the infra-red nearly the same heat at Allegheny as outside the atmosphere, these rays being trans-
mitted almost uuabsorbed (always with the exception of tlie cold b;inds).
We shall take, when necessary, a meaiL of lliese values and of those determined for the same
rays by comparison of Lone Pine and Mountain Camp, and employ this single ini'aii coefficient for
each ray, slightly modifying the contour of curves II, III, I\" near \ =1'' so that they may not be
discontinnons with the curve showing the results in this regiiui as derived from Allegheny. This
modification, it will be understood, is maile only to prevent a confusion of lines which tlie eye could
not follow in the plate, the four lines liere lilending m'arly inlu oiu'. The measures of the areas
have been made before this is d(Uie. The actual areas and tlie eiuves as presented, however, will
be found to be almost exactly in the ratios already given.
In examining these curves, the reailer's attention is direetecl to the fact that since the large
depressions in the lower curve corresponding to A=0".!I4, Ic.l.;, lu.od to 1^.37, and li'.Sl to 1''.87,
are deemed by ns to be most probably due to telluric absoiption, these depressions disappear in
the cnrve representing i-iiergy before absorption. Altlioiigli the coeflicients of transmission for
this extreme infra-red heat, ilerived from oliservations on the intervals between the cold bands,
are very nearly unity, the undeteriniiied coeltieieiits of transmission in the cold bands themselves
are much nearer zero. Acconliiigly, if we measure the aica of the lower curve below (l'".7ri (('. e., the
whole dark-heat curve) following the sinuosities, we obtain an area for this part alone, which is le.s.s
in proportion to the corrcspoiidii'g area in cuive three; so thai, roughly speaking, the coefficient
of transmission of the dark-heat, considereil as a whole, is less than might be inferred from a hasty
consideration of the coefficients of transmission olitaim il from tin- littlealisorbcd iiortions, as given
in our preceding tables.
It will have been seen from what has preceded that there are at least four modes of combining
the observations.
I. We may coiii]iare high and low sun observations at a gi\eii plai'e. In so doing we assume
that the diatliernianeity of the air has sulVeivd no change in the inter\al between the observations,
a snpiiositioii which is veiy iiiiproliable : Init apart from this we know by direi't comparison of the
values thus deduced for tiie heat on Whitney from l.one Pine oliservations, or the heat at Lone
Pine from Whitney observations, that this method gives results so erroneous that no dependence
should be placed on if, when we have better at command.
II. We may combine the simiiltaiieous observations at to|i and bottom of the mountain, as-
suming the transmission by the air aboxc the mountain to be the same as that of the intermediate
stratum between top and bott and this method is better than the preceding, but we know it to
bo incorrect by ilirect observation, and it gives so large a value that we cannot make u.se of it witlr
safety.*
III. We may endeavor to use our knowledge that the atmosphere is made up of strata having
difl'erent coefficients of transniission by the following process:
Consider the atmosphere divided into two strata having coefficients of transmission, which wc
will call 0 for the upper ami // for the lower layer. I'iist, using the customary exponential formnla
applied seiiarately to onr apiiroximately homogeneous rays, determine the coefficient of transmis-
sion h,, for the atmospheric stratum between top and bottom of the mountain by comparison of
Mount Wliitney and Lone Pine noon observations. These values we may accept with considerable
" Tliis was the melliod of Forbes, anil be fouud tbe trausiuissibility of the upper air tbe same as tbat of tbe lower.
OwlliK to bis use of it, more tban to auyotlier eause, be olitaineil tlie result bo did, wliieli was far larger tlian he would
have found I>y tbe legitimate u.se of bis actiuuineter alone.
12035— >o. XV 19
146
RESEARCHES ON SOLAR HEAT.
confidence, since they are quite iuilependeut of any liypotlieses as to the manner in wliieli tlie in-
termediate atniospbere exercises its absorption. Second, let the coefficients of transmission of the
upper air, ir\ be determined by comparison of Mount Wliitney high and low sun observations.
Tliird. multiiilv the nunibrrs denutin"' outside energy, obtained from method II, bv the factor '.
An examph' will make tlie subject clearer. Fig. l.'B represents the homogeneous atmosphere
divided into two strata of eijual thickness, but having different coefficients of transmission, namely,
a for the upper and /) lor the lower .stratum. The slanting lines represent rays from the sun, whose
zenith distance is 60^, ,so that sec "=2. Then if .4 = true solar energy outside the atmosphere and
ji;=relative air-mass traversed = sec ; = 1 and 1' in the above cases, the quantities written on the
left of the upright line, or rays fur zenith sun, are the energies of the ray from zenith sun, found at
the points where written. Those on the right of the lino are the energies found there when C=60°.
The following are modilications of the forniuhi^ used in computing the energy of a ray before
entering the atmosphere iu reduction of bolometric observations :
) ^'h
(1)
(-')
E
Their trntli is apparent if the law of transmission of a homogeneous atmosphere is that as-
sumed above. In these forniuhe
(Ij = registered energy of a ray Avhen air-mass = .1/...
Ji = registered energy of a ray when air-mass = ,1/",.
t = coefficient of transmission for zenith depth of atiuosphere.
E = energy outside the atmosphere, computed by the Inrmula (2).
jV. = is taken greater than Mi, and eonse(]uently (/.. is less than tli.
luj.n.
,1
A -1,/^^ ^^
~-
— / / Oxffii'umi €^
-—
— ^ y^ Tr'fznsmz^^u^n^^^ar—
— ^ — — - — y^— — - — — ^_ — n
^.Va~ ^
^ -
^^<
—
- - ^— f^yif.fY\fHff,fyf-y,f
-
~~~~ ^~~-^ ~~~ lr~aish]~ ' li ' ~ ^~ —
^i:
^ — -^y-^ ^=— —
—
^ . -ZIL ^
^Uil,
>^3V7^- ^^ — ^^ ^
lUustrating- Atmo3ph3ric Aboorpbion.
For measurements taken at the npper and lower limits of the lower stratum the following
examples are typical of the hrst three methods :
Taule 119.
Co.npa:
Sulisfitutius i
Substitiitiiig i
1 observ.i- Compa
1 r,.ii„,il.T (-)-
Silbstitutin;
Substitiitiu!
iro have—
di = A<t>}fl J/j-jr, -1
in loijMula (D-
ill foimiila (2)-
In this cas
SuUsliliUiii
MOUNT WHITNEY liOLOMETEK OBSERVATIONS. 147
The nicaning to ho drawn from the first two of the above examples is that, //' tin' ithsiu-pthin
ircic iiirariahlc at all hours of the tjay iin<l fur all parts of the earth sitiuiteiJ at the saiiw lirhjhl nlmn the
sea and snhjeetcd to the same alr-pressiire, the eoiiiparison of high and low sim oliservatious wouhl j;ive
ustbetriieeiier<ryoatsi(Ie tlie air, whether t lie absorbent material wcreilistribnteilniiiforiiily thi'ouyh-
out the atmosphere or were gathered into horizontal layers suiierposed aeconling to any law what-
ever. Theeharacter of the atinosplicre inler|ioscd iietwecn us and the snn, however, is constantly
varyiiiff through the day, and even if it wit.' at rest, a vrrliral si-ction wnuld ji.ive a different
composition from that made at a wvy great imlination, whicli wonld necessarily i)ass over ]iortions
of the earth's siirfae*' snbji'i-teil to cunditions \ ny ditferent from those existing at the [ilaee of
observation. lint bcsiiles tliese unavoidable \ariationsof the atmosphere, we have to consider
the effect of tlie actual non iKunogeiicity of the pencils obser\-cil on. and othrr objections aln^ady
referred to, piirticalarly that tliere seems to lie a progressive change in the atmosplieric Iransmis-
sion for the same air-iiuiss dependent on the altitnde of the sun, whose ray.s are (•ontinnally affecting
the. condition and distributiini of at least one of its constituents, atmos])herie moisture. That these
variatious exist is conclusively shown by the want of agreement between the results for outside
energy from the combination of different series, and notably liy the ililfcrcut results from high and
low sun observations at the summit and at the base of the nionutain. Tin- lirst two uu-thods, then,
while theoretically correct, are so only in the case of theoretical atmospheric cinulitions which
nature never really presents us.'
In the third case, however, the formula gives a value tor the eum-gy outside the atmosphi're
which is certaiidy iucorri'ct. or one which is only true when ((=://. If <(>/(, as in the case in olisiu'-
vations made on :\Iount Whitney. /;>-l .■ but since from the last ei|Uition .l = /v'', wi uld find
A, or the true value re(|uired, if h and a were known. .\s. howe\er, we cau only determine a by a
method already shown to be olijcctionahle, the determination by method 111 is still doi.btless theo-
retically imperfect, though less so than that by method II. For reas(Uis giviui later we may expect
that the value found by it is nn.ire likely to be in excess than in defect.
There remains the fourth method which we have ilescribed as I'uruislnug the rmist trustworthy
miuimum value; i. e., from the Lone Pine high and low sun observatiiuis of each ray, compute what
should have beeu observed at Mountain ('amii. and tluui mu!ti[ily the \alue representing the con-
stant for the ray obtained from high and low sun observations cui the mouidain li,\ the fraction
Value actually observed (Ui monutaiu
\alne c(Uiiiinted ttom L(Uie I'me ubservalu>iis
We thus obtain the \alues iu column S. The following are the combinations which have been
made :
No. 1. U>\w Pine I ami Lone Puic 11.
^To. -i. Lone Pine 1 ami Lone Pine III.
No. 3. Mountain Camp I and Mountain Camp II.
No. 4. Mountain Cam]) I and Mountain Camp 111.
No. 5. Miuuitain Camp In and Mcuintaiu < 'am[i 111.
No. (j. Lone Pine I and .Mountain Camp I.
No. 7. Lone Pine I and .Mountain Camp I (using - <'oeflicients of transnussion).
No. S. Jlountain Camp I and II mulliiilied by factor from Lone Pine obs(.'r\ ati(Uis.
No. 9. The mean of S and 7.
The results follow in the next table. Ncjs. 1 to 5 are obtained by method I, No. <i liy method
II, No. 7 by method III, and No. 8 liy juethod l\', while No. '■> is the mean of ."i and 7.
148
RESEARCHES ON SOLAR HEAT.
Table Il'O.
E\ER(iY OUTSIDE THE ATMOsrilEltE.
No. 6.
No. 7.
No. 8.
No. 9.
248.2
203,0
122, 5
163.2
242 1
106. 0
110.0
153.3
200. 7
242,2
139.1
190,7
1046. 0
783 2
105.5
544.4
1O09. 0
S52.9
374.1
613.5
5H7. 8
514,7
333.0
423.8
340. 6
317.7
255. 4
286.5
175,7
173,9
167. 3
170.6
101. 2
102. 3
105. 0
103. 7
57.3
61.3
78.2
09.8
40,3
62.2
05.1
68.7
43,5
45.0
48.0
46.5
30,0
30.4
39.2
37.8
IS, 4
17.5
19! (
18.5
J.0
'■"
AREi. OF OUTSIDE CURVE.
AbrivoA = l;..2
Bulon A = 1^.2
Tolal area
SOL.lIi CO-XSTAN
T (calories) . .
GI,900 63,075 70.625 | 70, .500
26, 030 1 24, 240 25. 490 , 23, 700
-0, 530
22.320
152, 950
20.T10
127,830 ' 69,088
21, 230 1 26, 245
98, 759
2.3, 738
67.930 1 S3. 315 , 90. 115 94,260
)2. 850
173, 660
149,000 95,933
122, 497
2. 007 1 2, 053 1 2. 360 j 2. 217 j
2.183 ,
4.0S1
3. 505 2. 630
3. 008
The fir.st live Viilues ;nr tliose obtaineil li.v cniiibiniiji;
station. They arc iiio.sciitcd \n-i\- only fur tlii-ir use in
as sliowlnn' the errors from this iiioik- of o!isfr\ atioii, sii
sixth value is tliat obtaineil by the hy[i(ithesis of Forlio,-
concern oiinselves oulv with the value.s given in eohlllln^
liiuli and low sun observations at a single
lelerHiiiiing the seventli and eighth, and
ICC I hey are dciiicnstralily too small. The
. It is deniiiiisiialily too hirge. We need
7 and 8. Colnnin !l is the mean of the last
two, and represents a value nearly aooordaut with that hiially ado|)ted by us. The values below
X = 1/1.2 are of comparatively small importance in their effect on the sun. They are obtained by
aid of the AUeglienv observations. '
C H A P T E R XIII.
SI'ECTIIO BOLOMETKl! OliSICltVATIOXS TAKKX AT ALLEdllKXY, IX l.SSi', WITH
FLINTGLASS I'KISM.
The foUoxviiifj arc the diites on wliicli iiieiisiireiiieutf* of atiiiosplierie transmissioii were
attempted. Those whieh hail to be rejected for the present purpose are indieated by an asterisk.
1S,SL' : February 15, llarcli 3,* Mareh -t,* Jlareh 23, March 2'J, JIarcli 31, April 3,* April 4,» April 17,'
April 24, May 1, May 2, May 3,* .May 10,* .May 24.'' May 2!t, .Tune 22, Septenilier 4,* September 12,
September 15, November 25.
The following table contains a rcM'onl of liigli and low sun oliservations availabli' for determi-
nations of .atmospheric transmission.
The same notation is used as in tlie previous arti<'1e, except tliat on sonu' days there are
several sets of low-sun observatinns, whicli are ilistin^uishcd by subscript tiiiurcs. The noun
detleetion is, in all cases, denoted by <?,, and tlie afternoon njcasures by d., </;,, \-c., in tlie order in
wliicU they were taken.
Table 121.
52" 00' 51=00' 50' 00' W 30' 49=00' 48" 00' 47' 30' 46' 45' I 46» 30' 1 40° 12' ! 45= 53' 45=28' 44=30'
300
233
288
165
415
337
335
212
203
428
300
337
212
170
Mar. 31
Apr. 24
May 1
2.20
1.33
2. 20
0.61
10.80
7.15
10.80
3.92
18.3
13.23 ,
18.3
7^1
28
21.71
28
l.i. 20
74
33
110 , 2
62 ; 1
^3 226
73 : 207
247
225
209
192
136
124
17
21
150
RESEARCHES ON SOLAR HEAT.
Table 121 — Continued.
MO 00'
51" 00'
50^ 00'
2.6
0. 53
2.6
9.0
1.70
9 0
0.80
, -
490 00'
48= 00'
470 30'
40° 45'
23.5
78
33.5
120
61
218
222
ISO
23. 5
5
7S ^
60 12' 450 53' 45= 28'
The next table };ives the sun's po.sition, anil the eorrespondiiig air-mass for each series in the
previous table.
Dale of
obaerva-
Highs
„.
Low sun.
Sun's hour
aijgle.
Sun's zenith
distance.
Barnm.
eter OJ.
mT
Sun's hour
angle.
Sun's zenith
distance.
Baronj.
eter 0„).
Air mass
(Jf„S„).
1882.
Feb. 15
Mar. 23
23
23
23
23
Mar. 29
29
Mar. 31
Apr. 24
24
May 1
May 2
2
.2
May 29
29
Jnne 22
Sept. 12
12
Sept. 15
15
15
Nov. 25
Ob 21.,
1 45
53»30'
45 56
d. m.
7.36
7.38
,1. m.
12.37
10.61
4k4S,
5 46
4 45
5 26
5 48
6 16
4' 53'"
3 31
5 06
5 33
5 43
5 .50
4 51
5 34
4 51
to 5 26
lo6 01
5 15
to 5 01
to 5 39
5 50
toC 02
to 6 26
6 23
4 37
5 22
4 38
5 09
5 33
4 00
85048'
61 43
79 00
84 04
86 00
87 20
74 34
82 42
73 55
67=55' to 74 46
78 33 to 81 44
71 46
65 52 to 68 53
73 37 to 76 05
78 28
73 57 to 76 31
79 01 to 80 49
79 OS
71 40
80 10
72 28
77 30
83 00
82 50
<l.m.
7. .36
7.37
7.36
7.36
7.35
7.33
7.35
7.35
7.37
7.37
7.37
7.36
7.40
7.40
7.40
7.34
7.34
7.39
7.37
7.37
7.36
7.36
7.36
7.37
rf.m.
83.78
15. ,57
37.76
04.11
86.66
111.72
27.34
54.10 '
26.52
19. 53 to 28. 42 '
37. 54 to 48. 64 i
23. 39
18. 06 to 20. 51
26. 07 to 30. 23
36.10
26. 22 to 31. 01
37. 95 to 44. 76
38.27
23.29
42.01
24. 36
33.41
55.20
.54. 83
0 30
38 34
7.35
9.27
0 26
0hl2„tol 32
36 38
27°35' to 33 65
7.37
7.37
9.18
8. 36 to 8. 89
1 .34
0 37
32 32
26 15
7.36
7.40
8.73
8.25
oVrVoiio"
2i'42Vo23'54
7.34
"'7.'96VoS.63
0 13
0 22
17 10
36 46
7.39
7.37
7.74
9.21
1 02
40 07
7.36
9.62
0 58
62 46
7.37
16.07
From these data tlie coefficients of transmission through
porting I''"'- of mercury, liave been deduced.
stratum of air, capable of sup-
ALLEGRENY P.OLOMETER OBSERVATIONS.
151
Table 123.
Corjhinils of I run mi
Deviation | 52»00'
51^00'
50=10'
J9::iO'
49:'U0'
48=00'
O". 550
47=30'
o''.015
40=15'
o''. 7,vl
46O30'
0». 870
46=12'
l^.Ol
15=53'
1". 20
15028'
l^.SO
4403O'
2". 29
*= 0",356
u". .-iss
O^ 41C
III'. HO
0''. 4r.8
Feb. 15
Mat. 23
.940
.903
.971
.985
""."998'
.994
.994
.992
.991
,990
.9,55
.999
23
.946
.960
.982
.987
.992
.992
.987
23
23
.9.18
.901
.967
.961
.975
.981
.979
.984
.981
.985
.990
.991
.984
.990
23
.967
.968
. 982
.985
.990
.990
Har 29
.945
.915
.955
.961
963
.967
.907
.907
29
.906
.9 9
.975
.970
.979
.977
.985
.985
Mar.31
. 900
.930
.955
.959
.908
.974
.985
.981
.903
.950
Maj-1
.!I13
.91.S
.945
.953
.901
.972
.975
.983
.980
.987
.987
May2 | .001
.ntio
.967
.971
.990
.911
.9U0
.939
.929
.940
.933
.9-.8
.954
Mav28
95K
.973
.999
.998
.997
.997
.994
.984
2!) -
.9117
. 9.W
.946
. 9,-.9
.971
.976
.993
.995 •
.995
.995
.996
.998
Jmii!22 '
. 02.5
. 923
.9,53
.900
.979
.988
.980
.984
.986
.986
Si-pt.12
.879
.902
.923
.943
.958
.971
.977
.983
12 ,
.929
. 9.50
. 9.59
.975
.980
.985
.985
.989
.992
Sfpl.l.i
.933
.930
.9.57
.973
.978
. 965
.986
.988
.991
.992
.997
.949
.907
.9K0
.990
.992
.990
.994
.994
Nov. 25
.907
.934
. 9.,2
.067
.977
.977
.981
.981
.991
.996
Adoptwl <i"« .!«I0
.9-11
,,.,-
912
■r.o
'too
. 90,4
,,„
.982
. 985
.987
.989
.990
" •■'■'■'
. (,llll
.fi,;ij
.0,7
.734
.781
.844
.871
.891
. 905
.919
.926
By a coniiiai-i.soii of tlie above table with Table (5, p. l'."i, it will be .seen that the values of the
coefficieiit.s of traiisiiii.ssioii rtetemiiued in 1.S.SL', after the retiii-ii of the e.^peditioii, are somewhat
greater than those found in ISSI. This may be due iu part to the different seasons in which they
were obtained, but the last values are entitled to more weight, because they rest on observations
covering an entire year, and made with matured e.xiierience and improved apjiaratus.
In all, whether in l.S.sl or 1.s,sl.', ime fact is salient within the range of onr experiments, that if we
excejit tlie cold bands— ^/ic traiismissihilit!/ iiin-f /.■if.t irith the inirelciiplli, no that tl,r ■^daii;" hciit Is
iiKii-f ti-diixmissililc than tJie •'Jiijht" a I'oncliisidu directly opposed to the at present ai^cepted belief.
The follnwiiig iKiou oliscrvatiiius. obtained on the clearest days diirini;- the year 1882, have
been selected to give an average high sun curve The battery current was not measured. The
prism and lenses enii>liiycil n-eie of a s|iecially diathermanous glass. As it was nut absolutely so,
a correctiou sliould If, in ihi, but tills h n u il yet been ajiiilied. Its ettV-ct would lie to relatively
increase the values iMrrcsp ludiiig t^i the greater wave-leiigtlis.
T..U!LE 12J1.
Dcvialion.
53=00'
.52=00'
51=„0.
50=00'
49=30'
49=00'
48=00'
47=3<'
46=45'
46=30'
40=12'
4:.053'
45=28'
44"30'
-
i =
0-339
O". 358
0.70
O''. 383
2.71
o^4lo
11.07
0''.140
0". 408
O».550
O". 015
0''. 781
0^.870
1*01
1". 20
1^50
2''. 29
April 24
23.0
.38
100
140
292
266
177
Ma.vl
0.57
2.20
11.50
38
102
1,58
320
348
369
2-23
2.50
247
304
209
268
136
17
M;iv3
::.... ..
0. 52
1.94
9. 96
16,6
30
281
0.44
1.27
0.90
12, 5
2;i
09
115
2,53
302
253
178
193
199
173
. . i 0. uu
0. 73
9, 00
10. 0
21
78
120
'2*2
202
Sopt.4
Sc'i.t.l2
.. , 0.29
2.20
il 70
139
124
328
343
279
302
"11
24
2. 22
.»i '.IS
59
96
223
''00
133
"0
Moan (Icllbct
6.41
1.89
"Too"
7 110
11.14
15,8
— J-
50
81
185
244
290
214
136
24
81
124
'244 208
-.90
236
Tlie correclien
the above values.
L'leetive ab.so]|i|i
it silver and glass have not lieeu introduced
152
EESEAROHRS ON SOLAR HEAT,
The conditiou of the sky during tliese observations was as follows : April 24, excellent; May
1, fair blue, occasional clouds ; May 3, blue, with passing clouds ; May 3, faint haze, in irregular
wisps ; May 19, very thiclily milky, with some clouds ; May 21, rather irregular milky blue, with
clouds; May 29, good blue ; September 4, milky blue, with cumulus clouds; September 12, milky
blue; September 1.), milky blue, with fracto cumuli; November 2o, blue, with clouds.
The air-masses at the time of observation are given in the next table.
Table 12.j.
Date ot observation.
Sun's liour Snn'fl zenith
angle. , tlistaneo.
Barometer. Air-mass.
w 1 (Mm
1 34
0 37
0 -18
0 38
0 07
1 01
0 59
0 -a
30 10
32 32
26 15
26 45
22 07
19 41
22 48
35 55
36 46
d.m.
7.37
7.30
7.40
7.38
7.38
7.37
7.34
7.37
7.37
d.m.
8.51
8.73
8.25
8.27
7.90
7.83
7.98
9.10
9.21
9.62
May 1 ;;:::
May 3
CHAPTER XIV.
THE TKAXSMISSIBILITV OF GUI; AT.MOSl'HKKK FOK LKillT.
The absorption by onr atuiosiiliere of the heat in any ray must always be pro|)ortional to that
of tlie light iu the same ray, since light and heat are but names given to different manifestations
of tlie same energy. It was of evident interest, tlien, to determine tlie transmissiliility of the
atmosphere at Jlouiit Whitney for liglit; but as this was njerely an ailjunet to tlie study of the
heat, no sjieeial photometers had been provided.
There is, however, one method of determination which requires none.
In 1877, Prof. E. 0. Piekering suggested to the writi-r, who was then al'out to visit Jbiunt
Etna, that an estimate of the transparency of the atmosphere there might be made without any
photometric apparatus, by comparing the light of two stars, one near the zenith, the otlier near
the horizon, at the moment when they appear equally bright; for the absolute brightness being
known from the magnitudes in the Star Catalogue, and the mas.ses of air traversed by the rays
being computable subsequently from the times of observation, we have all the data demanded by
the usual formula. This method was therefore used on Mount Whitney in the following observa-
tions, made under my instruction by Mr. J. E. Keeler, assisted by Mr. W. C Bay.
Let it be understood that for our present purpose we use the word "liglit" as syiioiiymons with
the expression "light between the wave lengths i)^A and (»'\7," and let this light of the sun or a
star before ab.sorption by our earth's atmosphere be denoted by L. If the celestial body be viewed
in the zenith, a portion of the light will have been absorbed and a portion transmitted when it
reaches an observer at the sea-level. The fraction expressing the percentage transmitted to the
sea-level is called the coefficient of transmission, and denoted by I, so that the original liglit L
becomes TA after absorption by one such stratum, and would, if the light were homogeneous, become
LI" after absorption by n such strata. The light is not really homogeneous, but we shall first (in
accordance with custom) here consider it as such, and shall afterward jioint out the consequences
of this incorrect assumption. The ab.sorption depends not upon the length of the path, but on
the mass of air traversed,* and we may choose as the unit of mass anything we please. Since the
weight of the mass of air iu a vertical column above us equals at the sea-level that of 700 mm.
of mercury, l'^ will represent the transmission by a mass ^ as great, or to that of the mass cor-
responding to one decimeter of mercury (always on the assumption that the light is homogeneous,
and the law of extinction such that the percentage traiismitte<l by any one unit stratum is the
same as by another, or that I is a constant). When the words "coefficient of transmission" are
used without qualification, the transmission for the entire atmosphere (/) is referred to.
I arranged the subjoined form for the few observations made on Mount Etna,t which gave a
transmission of 90 per cent, at that station, where the barometer was 660 mm. (r'=90), whence by
reduction to the sea-level, 1=0.88. The early observations by Bouguerf give, when expressed in the
same terms as ours, !=0.81L!; those by Seidell give ^=.794; the recent ones by Professor Pritch-
''This statemont is usually treated as axiomatic, aud we do not here discuss it; but plausible reasons may be
offered for tbiukiug that the same mass may not exert the same absorption under ditierent densities.
tSee American Journ.il of Science, July, 1880, page 3.
tBouguer, "Trait(5 d'opticpie," Paris, 1760.
^> " Uutersucbungao iiber die Extinction des Lichtes.'' Potsdam 01>s. Rep., Vol. IU, No. IV.
1253.5— No. X\' 20 153
154 RESEAKCHES ON SOLAK HEAT.
ard, at Cairo,* give a higher value (?=.S4.3); those at Oxford give l=.191; the still more recent
observations by Miillert give ;=0.S2o. Other values might be cited, giving abundant testimony
that the absorption of light at the sea-level, in the opinion of the most trusted observers, is about
20 per cent, for a zeuith star. In nearly all these observations, so far as is known, the same formula
that we here employ jirovisionally, and under caution, has been used without reserve.
In all of them but the first, the determination has been made by photometric apparatus, but it
is the peculiarity of the present that none is absolutely demanded; for let Z be the original light:
if I = the coefficient of transmission of light for a zenith depth of atmosphere, assuming no
selective absorption of light, the light from this star in the zenith would become LI.
If m = the mass of air traversed by the rays from the star at the zenith distance, r, the light
reaching the observer, is l'"L.
If we select two stars at ditferent altitudes, which appear equally bright to the eye, we have
a means for determining /, provided the altitudes and magnitudes of the stars are known; for,
since the ai)pareut amount of light from each is the same,
l'"'Li=l'"''Jj2 nil log l+hg Li=m2 log l+log £2
from which
Ion i->"fl Lj-logLi
nil— mi
We shall here assume that the magnitudes of stars bear a relation to their light e-xjiressible
by the formula log Z= — .4 M, where L is the light and M the magnitude of the star.
The observations (which can be made by one person) have in this case, in order to eliminate
personal ijeculiarities, been made by two observers, each of whom independently selects two stars,
one not far from the zenith, and one only so far from the horizon as not to involve any sensible
error in taking the airmass 2iroportional to sec. J. The two stars so selected must be of apparently
equal magnitudes; and since the lower star, whose light has suiiered greater absorption, must
really be the brighter, the amount of this absorption is determined by the formula just given,
which is that used implicitly or explicitly by all the observers just cited. Having selected the
stars, the two observers then confer with each other and unite on what they deem the most i^erfect
match, a search and comparison usually occupying some time, during which many comparison
pairs are observed and rejected before one entirely satisfactory is found. When this is found, the
time is noted to the nearest minute, and from this and the latitude, the secant of the zenith distance
is obtained bj' subsequent computation. The tables which follow will be intelligible without
further explanation.
The magnitudes of the stars used for the following comparisons have been furnished by the
kindness of Prof. E. C. Pickering, director of the Harvard College Observatory.
* Memoirs of tlie Royal Astronomical Society, vol. XL\'II. p. 416.
t Publications of Potsdam Observatory, 1883.
TRAIS'SMISSIBILITT OF ()TTR ATMOSPHERE FOR LIGHT.
155
Table 12C.
[Station, Mountain Camp. ObstrTSis, J. E. K. and W. C. D.|
Date. ! Mf,^" i Stars matclied.
1881.
AUR. 2
(SHcrcnlis 23= 3.28)
10 1
31 10 34
31 10 34
9 7 30
0 7 41
i(.'Cj-sni.-.
i /SScorpii..
;!;H.r.nli».
!(/5Cv!nii...
).,Bootis ..
(vA'inite..
(,l'.ooti,...
< V Dilphiiii
)<Booti8...
(iBLyraH...-
( ^l Sei-pentis
) a tJrsa- m:
J ^ Lyrie . . .
I ^ Scorpii .
( t Herculis
I o Can. Tenat .
j ^HcrciUis
2. 35 — 0. 04 ,
+ 2.34
-1.39 I
-1.19 ! -1-6.18
-1.02
-l!lfi
11 J ' 2. 99 ;— 1
76 , 3.84 —1.53 I
22* , 3. 57 I — 1. 42
78' I 3. 48 ' — 1. 39
29 3.81 —1.52
84 3. 48 — I. 39 1
27 I 4.13 —1.64
84 I 3.48 ' — 1..19 I
12 I 2.31 —0.92 I
82 2. 71 'i — 1
7 I 3.48 I —1
82 * 2. 71 ! - 1
iaTJrsasmaj
(SCj-sni-..
i t," Ojiliiuchi
73
2. sr,
— 1.02
I-'
2.31
— 0.92
v:-:*
1.96
— 0.78
11
3.57
— 1.42
"<H
2,91
— 1.16
■'4*
•> 3.5
— 0.94
731
1.96
U 7S
3.92
— 1. 56 1
77t
3.00
— 1.19
3.09
— 1.23
79+
2.89
— 1 15
4+
2.31
— 0.92
1.96
— 0.78
13
2.99
— 1.19
70»
2.84
— 1.13
-1-4.39
"-fi'si
'+'i.'.5i'
't2.41
4-3.05
' + 3.'73
+2.:
-hi. 99
-hi. 50
■H.'2.'3i
-12.41
+ 2.30
+ 3.19
+ 2.37
+ 2.80
" + i.'97'
-0.11
+o."i7
+ 0.15
-0.034
+ 0.071
+ 0.064
-0.20 -0.0.32
' + 6.'i5 '+0.034
-c.'ie' -o.iin
-6.59 ■ -6.3ui
-6.61 -0.239
'-6.07 -0.029
—0.04 -0. 007
+6.65 +0.009
—h'.ih -0.043
'-6.63' '-6.068
-6.13 -0.615
'-6."25 '-0.636
+ 6.16 I +6.028
"-o.'si j'-'6.'656
+6.69 I +0.646
"-6.'i4 !'-o.676
+0.1
+ 0.040 I
-0.09 I -0.039 1
+ 0.08 I +6.036
-6.'i9 -6.679
-6.14 I -0.061
— 6.28 -6. 082
-6. 16 I —6. 068
-0.37
1.109
-0.08 I -0.020
"-6.'i4'['-'6.'649'
I '
-0.06 ; -0.030
0.93
"i.'isl
During tlie.-se observations the slcy was con.stantly clear. On one occasion, Sejiteinber '.t, the
horizon \va,s rather bright, owing to the .snuset on one siile and tlie ri.sing nioon cm the ntlic-r.
The mean from these thirt.y pairs of liigh and low .-^tars at tlie Mountain ('anj]i gives lor the
value of atmospheric transmission of stellar light J^' =0.93 rb .02, whence /=.8S. A series of ob
servatious (not here given) made as the party was returning across the Inyo De.sert, at a mean alti-
tude of less than 4,000 feet, gave a smaller value for / than those on the mountain. I do not, regard-
ing the considerable probable error, attach great weight to the value .88 above given, or to its
coincidence with that obtained ou Etna. It is certain that to obtain an entirely trustworthy value
the exclusive time of the whole party <lnring our stay on the mountain would have been insuflicient ;
and it is doubtful whether there might not, even then, remain some systematic error tending to
affect the results, as the conditions favoring systematic error are all present.
156 KESEARCHES ON SOLAR HEAT.
Professor Pickering, whom I consulted with reference to his own experience as to the vahie of
high and h)w star comnarison, writes rae as follows:
Hahvaku College Observatory,
Cambridge, U. S., Uctoher 15, 1883.
" " • We liave fiiiind liere tliat the couiparisons of liigli ami liiw stars give a result appareutly affected by a
eyetematic error, according to which the lower star seeins too bright, and the resulting coefficient of transuiiBsion will
he made too large. The coefficient of trausmission resulting from the observations of this kind made here baa not
been determined, but the obaervations give residuals from SeideFs tables of absorptions, ranging from one-tenth of a
magnitude at a zenith distance of 65° to eight or nine-tenths close to the horizon. Seidel'e table for extreme zenith
distances does not agree precisely with that for ordinary zenith distances at the junction of the two, arid at about
86° the comparisons between high and low stars made here give results exceeding those of Seidel for difference of
absorption; but the general result is the reverse of this, as already stated. * * • It may be a general rule among
observers that the lower of two stars seems comparatively bright. • » *
Very truly, yours, EDWARD C. PICKERING.
We may observe that, whether there bo a systematic error or not, we may be confident of our
ability to draw the entirely legitimate conclusion that, at any rate, the air at such a site as Jlount
Whitney is not only clearer than at the sea-level, owing to its rarity, but intrinsically clearer, and
in a very marked degree — clearer, that is, when equal masses of air from the mountain and sea-level
are compared.
I have already remarked that, since we cannot actuallj' observe the radiation of either sun or
star before absorption, we cannot determiue the coefficient of transmission except by employing
some hypothesis; and that the ordinary assumption made implicitly by all the oljservers cited (the
assumption that the original brightness and the coefficient can both be determined from the simple
exponential formula used here) is erroneous, and not only theoretically' so, but that it leads to sensi-
ble error in prai'tice when we neglect, as we do in using this formula, the effects of selective ab.sorp-
tion. I have alluded elsewhere to this fact in this same connection (see American Journal of Science,
July, 1880, p. 37), and more recently I have demonstrated,* though not with the greatest generality
possible, that when we neglect the effects of selective absorption the exponential formula not only
gives erroneous results, but results which always err in one direction only, and under all circum-
stances make the calculated value of the original energy, light, or heat too small. 1 have also
stated that the absolute value of the error introduced may be very considerable indeed, and that
in the case of previous investigators the use of this formula by them has given a value for the
solar heat essentially smaller than my subsequent determinations, in which the selective absorp-
tion is taken into account. These general views have already been developed in this volume in
the chapter on the theory of the spectro-bolometer. I repeat them here with special application
to photometric determinations.
Let us now consider whether they may not enalde us to account in part for the fact suspected
by us, and confirmed by Profe.ssor Pickering, that "the comparison of high and low stars gives a
result apparently affected by a systematic error, according to which * » • tlie resulting
coefficient of transmission will be made too large."
Having found that the actual energy (whether shown as heat or light) of the sun, as deter-
mined by the ordinary method, is, so far as it depends upon this method, always too small, and
that the error is always (when referred to the same unit air-mass) greater when the absorption is
greater, or when the sun is nearer the horizon, let us now apply these considerations, which belong
equally to the stars, to the case of two stars, one of which, near the zenith, has suffered but slight
absorption, the other, near the horizon, has suffered a greater oi\e, and let us suppose that the
real light before absorption in the two stars is approximately known. It appears, then, since what
has already been demonstrated (loc. cit.) as regards heat applies equally to light, that the coefficient
of transmission, which would be found by separate photometric observations, is larger (as reduced
to the same unit stratum) when obtained from the lower star than from the other; and as the
coefficient derived by the exponential formula from the direct comparison of the two stars will be
intermediate between these two values, of which the least is Itself too large, the coefficient of
transmission obtained from the comparison of high and low stars will always be too great.
The above demonstration does not tell us in hoic great a degree this coefficient is too large,
and, for aught we have here demonstrated, the error may be practically negligible. We have
' Comptes Reudus, tome 9*2, p. 701.
TRANSMISSIBILITY OF OUR ATMOSPHERE FOR LIGHT. 157
already stated that as a matter of fact, however, it is not negligible; and we are i)repared to
assert that the error is fiir greater than has been supposed. For it way be observed, in general
terms, that since the rays with large coefficients are represented by diminishing geometric progres-
sions, whose common ratio is near unity, these rays will persist, while others with small coeffi-
cients are very early extinguished; and something like this was shown by Biot, at the time when
Melloni's first observations on the transmission of heat through successive strata attracted atten-
tion. But what we desire now further to point out is, that according as the ditterence of these
coefficients of trausmissiou for tlie ditferent portions of the light of tlie same star is greater, so will
the error of the result in tieating them as e(iual be larger, a conscciuence ho obvious that it is only
necessary to make the statement in onler to have its truth recognized.
Since it has now been demonstrated that the formula ordinarily employed leads to too small
results, it might properly be left to those who still eni|)loy it to show that their error is negli-
gible; but this has never been done. There is possibl.y an imjjression that if there were any con-
siderable error its results would become apparent in such numerous observations as have been
made all over the world in stellar photometry during this century. But it is, in my opinion, a
fallacy to think so; and I Iielieve, as I have elsewhere tried to show, that the error mii/lit be enor-
mous— that the actual absorption* mifiht be twice what it is customarily taken, or 4(1 jjer cent,
instead of L'O per cent., without the errors being detected by suc'li observations as arc now made.
It is true that this error aflects all magnitudes iieaily alike, and conse(|uently is not of the great
importance in stellar photometry (which deals chielly with relative magnitudes) that it is in solar
work. All of those who, wliile ailuiitting the sufficiency of the foregoing demonstration that error
of a detiuite kind exists, continue to use the erroneous formula, may, however, be invited to con-
sider whether the burden of proof does not properly lie with them, and asked to demonstrate that
the continued use of methods and formulne certainly in some unknown degree erroneous does not
involve an error equal to the entire amount of the absori)tion* in question.
Nothing in what has i)receded is calculated to disprove the observations made both by Pro-
fessor Pickering and the writer, to the effect that in the special method of high an<l low stars there
is also a systematic error calculated to give too large a coefficient of transmission, as comiiare<l
with the ordinary method. What I have demoustrated is that both this and the ordinary method
necessarily give too small a result for the absorption.
"The word "ahsorptinn" iw used, it will 1k_* reniPinliered, in agciu'ral si^nse bcro fore very prnce,s9 in our atninspher
(liich the lifht is prevented from reaching ns, aiieh as its scattering hy dust i>articlen, d-e.
CHAPTER XV.
SKY RADIATION.
The heat sent in all iliroctious from the sky is diffused or reflected or radiated suu heat, and
the original intensity of the sun's radiation has evideutlj" been diminished by this amouut.
If we consider the aualogy of light in the simple case of a single white cloud in an otherwise
clear sky, we observe a greater amount of light from the cloud than from the adjacent parts of the
heavens; but in this case we gain the added light at the expense of that portion of the earth in
the cloud's shadow. If the sky is absolutely cloudless, however, it is clear that every point in our
horizon is receiving sensibly the same amount of light which we do at our own station, and in this
case we must admit that if we could rise to the upper limit of our atmosphere we should find the
sun brighter (1) by the amount which the whole sky sent us at our station, and (2) by the amount
which the sky <litt'nses, reflects, and radiates airai/ from that station. If we add to the direct solar
radiation only that directly observed from the clear skj-, we obtain, then, an amount certainly less
than that representing the radiation before absorption, a statement which seems to me incontro-
vertible, though advantage does not seem to have before been taken of this fact to determine a
minimum value for the solar constant by a method perhaps the most trustworthy of all in our
possession.
It is very desirable, then, to get the relation between sunlight and skylight in a clear sky;
but I shall have to dejiend here largely upon evidence from other sources than our own direct
observation on Mount "Whitney, as the apparatus fitted for this end (such as the Marie-Davy
thermometers) either failed to reach us in tune for use, or was, as in the case of the solar com-
parator, not well adapted to the purpose, and as the already overburdened observers had no
time to organize other experiments during the brief stay of the expedition.
It may be well to remark that, besides observation, we are not without the aid of theory upon
this subject, which has been treated by the distinguished physicist, E. Clausius, * with great thor-
oughness from a theoretical standpoint.
It may be premised as almost self-evident that as the direct sunbeam is diminished in trav-
ersing a greater depth of atmosphere, the relative sky radiation will be greater. We tirst present
a part of the result of the investigations of M. Ckiusius on this point in the following table, where
the ratio of sky radiation to sun radiation for different altitudes of the sun is given first from the
theory of M. Clausius, and second from direct ol.iservation at various statious.t
Tabu-: 127.
•See Poggendorf, Aimalen, Vol. 129, p. 230, 1866.
t See also Eadau's " Radiations chimiqncs du soleil.'
SKY RADIATIO^r.
159
We have here, for instance, for a height of the sun of 00-', the statement that at Heidelberg
the direct radiation of the sun was 1.0 that from a clear sky.
It is to be observed that the radiation considered in these experiments is not the total radia-
tion of the entire spectrnm, bnt of a sun emitting energy of a certain wave-length and transmissi-
bility. This wave-length can only be obtained infcrentially. It is that probably not far from
0''.;i5 to Oi'A, or that near the border of the invisible "actinic" spectrnni, where the radiations
appear to have been most efiicieut on the whole for the various chemical means here employed in
noting it, and it corresponds in the theory of JI. Clausius to the ray wliose coeHicieiit of transmis-
sion is about 0.50.
The following table has been calculated by Clansins on the assumption that tlie coefficient of
atmospheric transmission (/))=0.75 by the formula
C=Zcosr(l-p»)
where
C'=Iight reflected and dittused by tht sky,
/=intensity of sunlight upon a surface exposed normally to its rays,
(S'=intensity of sunlight upon a h(uiziintal surface,
~ =zenith distance of sun,
e =secant of zenith distance of sun,
cose {l—p' )=the loss undergone by the direct light of the sun,
Z=ratio of portion lost to that reflected and diffused by the sky, as determined by
Clausius's theory of the ditiusion of light.
Table 12S.
0.19
0.33
0,43
0. 03
0.07
0.10
0.09
0.09
0.18 (
0.15
0.11
0.26
0.21
0.13
0.34
I 0.2S
0.14
0.42
0.35
0.15
0.50
0.41
0.16
0.57
0. .i3
0.17
0.69
0.02
0.18
0.80
0.69
0.18
0.87
0. 74
0.18
0.92
o.'.i
0.19
0.94 '
According to tliis table it will be seen that when the sun is at an altitude of 40- the light
given by the entire sky is l'5 per cent, of that received upon a surface expo.sed normally to the
sun's rays.
Photometric comparisons of sunlight and sky-light can seldom be made at Allegheny, on account
of the rarity of a satisfactory blue sk3'. A single day's exjierimeut* there (October 30, 1.S8.3), on
an exceptionally fine day, gave the ratio of total sky-light to sunlight -p;/^, the altitude of the sun
being 3S° and thelight coming from the central part of the. ■solar disk, and being therefore richer in blue
rays than the average solar light. The com[)arison was made by a Bunsen photometer disk. The
sunlight was reflected Ijy the siderostat mirror through a hole 0.035 mm. in diameter (area 0.314 inm.),
placed at a distance of 25. L' in. from the disk, forming there an image of the sun 0.24 m. in diameter.
The sky-light was reflected by a similar mirror through an aperture 5cn]. square, situated at the
other extremity of a long darkened passage, and distant 3.3 ni. from the liunsen disk when equality
of lights was produced. For equal areas the ratio of intensities of sunlight {central part of solar
disk) to zenith sky-light was consequently
2,500 X (25.2)
and the ratio of areas of the solar disk to the entire sky being 0.00001107, the ratio of total .sky-
light to sunlight would Ik
_=0.10, if the average light of the solar disk were the same as that
'The experiiueiit was couducted by Mr. F. W. Very.
160
RESEARCHES ON SOLAR HEAT.
at the ceuter. From measurements made at Allegheny, but not given here, we have found that
the average brightness of the solar disk is O.S of that at the center, whence the ratio of total sky-
19
light to average solar light would be ^=0.24, which is in close agreement with the calculations
of Clausius, based on the assumption that the average coeiHcient of transmission for the luminous
rays between A and H is 0.76.
Professor Tyndall attributes, as is well known,* the blue color of the sky to selective reflection
from fine ijarticles of dimensions com;iarable with the wave-lengths of the more refrangible rays,
a conclusion which we need hardly say we accept, since our whole theory of selective absorption t
in the present work rests u]ion the belief that the heat is reflected and diffused by particles of
various sizes, the grosser ones exercising a general absorption, the finer ones a partially selective
one, the finest a purely selective one. (See pji. l-'i and 14.)
Messrs. Bunsen and Roscoe have measured the direct effect of sunlight and sky-light npon a
mixture of equal volumes of chlorine and hydrogen, in which, when exposed to a moderate radia-
tion, chlohydric acid is generally formed.
We quote the table which they give, the effect being stated in "photo-chemical degrees."!
Table 129.
Direc
rays.
Hfifbt
Sk.y. a
Total light.
Total ligLt.
Jformal
Verticil
C+H.
O+I.
effect, /.
effect, S.
0"
0.0
0.0
3.1
3.1
3.1
10
2.6
0.5
15.1
15.6
17.7
20
27.9
9.5
24.7
34.2
52.6
30
60.2
30.1
31.7
61.8
91.9
40
S6.7
56.0
36.1
92.1
122.8
50
107.4
82.2
38.1
120.3
145.5
60
121.6
105.4
39.1
144.5
160.7
70
131.2
123. 3
39.6
162.9
170.8
80
136.7
134.6
39.7
174.3
176.4
90
138.4
13S. 4
39.7
178.1
178.1
If in i)lace of the mixture of chlorine and hydrogen, which is sensitive to the violet and idtra-
violet rays, we choose a substance which is more jiowerlully acted npon by still shorter waves, the
effect of sky-light will appear relatively greater. Thus it will be seen hy reference to the table just
given that the etfect of normal radiation from the sun is e(]ual to that from the entire sky when
the altitude of the sun is about 1S°; but when photographic paper is useil in place of the hydrogen
and chlorine mixture, the effect of normally received .solar radiation does not equal that of sky-light
until an altitude of 40° is attained by the sun. It is evident, then, that the extreme ultra-violet
rays, which chiefly affect the photographic plate, are reflected by the sky in still greater proportion
than the violet and bine rays, whose predominance gives the characteristic skj' color, a conclusion
which confirms our ob.servatiou of the enormous absorption of these ultra-violet rays.
We need further experiments, but with our present knowledge we may say, in reference to
what has preceded, that under an exceptionally pure l)lne sky, when the sun's altitude is not far
from 60° (which is about that in the mean of the Mount Whitney noon observations), the light
(meaning by "light" all radiations between 0''.4 and Oc.7) from the sky is about ^ that from the
sun. If there is the slightest perceptible haze or milkiness in the blue, this value becomes greater.
The amount sent upward and in other directions than towaril us is, according to the estimates of
M. Pouillet and il. Clausius, from 7 to 10 per cent.
We conclude, then, that if we added to the ell'ect of the observed light [i. e., total light) of the
sun not more than one-half its amount, we should get, accoriling to our own observations, very
nearly the liyht of the sun outside the atmosphere. The mean of the total "heat" radiation is,
* Proceedings of tlie Royal Society, No. lOS, 180'.!.
tMr. Koyl (.Joliiis Hopkins University circular, Angust, 1883) Nuyyests that the e
miwleading, and that \vc Hliould rather epealv altogether td" "[>cloctivo rcdcction."
{Quoted I'roiii Kadaii'H " Radiations chimiques du Holeil."
elective ahsorption"
SKY i;ai>iation. Kjl
aci-orilinj; ti) dill' (iliscrvaliciii, sdiiHiwiial iikhv transiiijssililc than that of tlic part ln'twccii \va\c
lengths O^.-t ami O^.T. WC ha\c Idiiiid that Ihr lower s[iocaral nuliatiori, as far at h'ast as (,mt
2.1' .(I, is, except in tliu actual case of alismption liaiids, more transnii.ssil>h' than the himuioiis.
Oonsiileriiig this ratio of total traiismissibility to that of " liifht transniissibilit.v" to lie appioxi
mately as 8(1 to 75, and that the ratios of sky-lif;ht and sky heat are nearly in the same iiroiNirtnin.
we draw the tinal inference, from all that has ]>receded, that in tlie case of onr highest actnal
observations of heat, taken in the purest sky, at an altitude of the sun ol a little over 00^, the
total skybeat reflected, diffused, or radiated both toward and away ticiin tljc observer is somewhat
over .'i the <lirectly observed solar ladiation.
li>5o5— >{o. XV IJI
CHAP T E R X ^' I
NOCTDKNAIi KAIJIATIOX.
Tbe experiments of numy jiliysicists, notably AVells and Melloni/jMove that diiiins' calm and
cloudless nights bodies exjiosed freely in tbe opeu air lose a portion of tbeir lieat by radiation,
tlie amount radiated varying with tbe nature of tbe surface and with the atmospheric permeability.
That tills frausf<>r of beat takes place between the body at the earth's surface and tbe highest
rciiioiis of tb<' air oi' llie celestial spaces beyond is rendered certain by the fact that the effect is
obliterated by ihc intcr|iositi(in of a cloud. Some experiments in this direction were jnade im the
ex])editiou. tlic disposition of tlie thermometers employed being altogether similar to tliat used l)y
.■\lelloni.*
hi Ills memoir on nocturnal cooling, Melloui, studying the subject with a view of improving on
the worK ot INiuillet and Wells, employs three thermometers. His object is to find bow much a
tbermoi'iiter, radiating freely toward .s])ace, falls below the temperature of tbe surrounding air.
The radiating thermometer either has a black bulb or has its ordinary bulb covered with a black-
<-ni(l tbimble. The temperature of the surrounding air is to be determined by a thermometer
wliicli itself radiates as little as possible. This second or air thermometer, then, has a metal-
coN'creii hulli, or has its bulb inclosed in a bright silver thimble. This silver it.self radiates in a
minute <legree. To allow for this MeUoiii takes a third thennometer, also covered with silver, and
compares tlie action of the two hitter when cue is free to radiate toward the sky aud the other is
sliielded. This tliird thermometer, then, is merely to obtain the correction for the sliglit radiating
]i(>wer (if silver, whose efleets we wish to eliminate.
Tbesi' exjieriinents are absolutely dependent for success on tbe calmness of tbe night; and
those undertaken (m tbe expedition conld so seldom be made under favorable conditions in this
respect that the results are of but moderate value. All the ob.servatious made at Lone Pine by
iSergeant Dobbins ]irove, from tliis or other causes, to be useless; and a series made under cir-
cumstances of great <lifticnlty at tlie peak of AVhitney, by Captain Michaelis, who volunteered this
trying service, are, though interesting, unfortunately prevented by tbe same cause from giving
the results whicb might be exiiceted under such otherwise uniquely favorable circumstances.
Here, then, only a few of the considerable series of observations will be given.
UEStilMl'TION (IF Al'l'AEATUS.
Three thermometers, di\ ided to (t.l° (_'-., wei'O j)rovideil. The tirst of these (Green, 45S1) had a
clear bulb, with black tbimble ior the radiation. Tbe second (Green, 4.^S,'>) was a clear-bnlli ther-
mometer, with silver tbimble for measuring the temperature of the snriounding air. A black Imlb
Ihermomi'tcr (( ireen, 4082) was also usrd as a radiation thermometer for comparison with the hrst,
but its Jesuits weie less satisfactory than where t'lc blackened tbimble was used, and they ai'e
here omitted. Our tallies, therefore, give the com]iai'ison of thermometers 4581 (radiation) and
-\'iX'J (air lempciatiiK). Each thermometer was passed through a small cylinder of cork near its
luilb. On this cork was fitted the tbimble, in tbe one case covered with lamp-black, in the other
of jiobshcd sil\ er; and each thermometer was placed horizontally about 4 inches from tb ' rock
siipjiort. witli its reservoir at the bottom of an inverted, truncated, tiu cone, whose upper diameter
(the ajiertuie <lirected to the zenith) was 14 cm., and whose altitude was 9 cm. Each cone bad a
uioval)le tiu cover. According to Jlelloui, tbe action of such a cone is to almost exactly double
* See Memoir nii NoetiliiKil L'ooliiij;, Ac. Auualcs dr Cbiraie p( d<- l'li,vsii|iie. Febni.ary, 184s.
16-2
NOCTUKXAL RADIATIOX.
163
the effect of tbe radiation. Tlie tbermonii'ter stems were tliemselves eovereil with tin eases,
except at the inonieiit (if reading'.
Ill general, the apparatus was broiiylit out an liour liefore it was to lie used, and after tliat
time was alternately covered and exposed for intervals varying fnim l.'i to 70 minutes, the thermom-
eters heiiii; read once at the end of each interval. On one occasion (.September 2. I.SSI) readings
were taUcn e\cry fliree minutes.
All tbe ipliservatiiins which ha\-e lieni thciii^lit worth prcserviu.u- I'.iUiiw. In these tables the
lirst cubiinn gives the date; the second, the time; the third, the readings of the black-tljimlile (/. '■.,
radiation) tbermometer; the fourth column (/',) gives the absolute fill of this thermomerer through
radiation; the fifth c'olumii gives the silver-thiailili" initial ami tiiial readings; the sivtli I'lihniiii.
the difference (if the silver thimble readings ( /»,). \\'ere the silver an absolute non r.uliator. ami
the lamp-black a perfect radiator, /*, — /'; would represent the etfect of r.idiation. .\ correct ion
has been introduced for the actual sliglit radiation from silver. This has been (letcrmiue(l by corn-
pa lug the readings of the silver thimiile c(ivere(l and iinco\e imI; mid. on its lieiiig applie(l. we
have in eoliiain 7 the fill due to the tempeiature of the air (l>:). CoMse(|ueiitly. !>:-!>. is the
ellect due to ladiafiou alone, al\v.i\s on the liy|iorliesis that the night is ((/;.<»/«/(•/,// ca I m, a condition
that was only approximately obtained even on the niglits of August .">U ami 31.
OnsERl ATIllXS ll\ \(li /TA'.VJ/. H.IKI Alius.
Table loO.
[Stution. ModutniuCiiniii. Mcrant Wliitney. Califiiniia. OlisorviT, Capt, (I. E- Mi. I.a. lis Ii.i,-,
elearskv. wiud li;rlit at si" l.'j™ p. iii. : no oligervations recorded al'ler tlii'* hour M< .Lti n-l.iii\ .
furct of vapor = ■_'.■.' mm. Tlip reliilivi- Inimiditv .-.nd fim-c of v»]i,.r iirr iiiv.-ii l,.r Um ,h.-..i-. i,
rectioos f..r instniiuontal rrrors have been applied. Instruuieut in. muted on \u,\ on talile I
Elaek Sdv.r
Date. I Time. tliimlje, D, tliiral.lo. Di
■ gWllil.'lp
l.i'Mat
10''08'»p.l
10 ;i:) p. I
11 "5 p.,
l:; 1.5 a.:
3 .40
I)i — Di Exposure.
;):. 3,1 l"iiei
'i'.'si" i;i,e,
'^■'is' Uuei
Table 131.
E. Miel.aelH II;
9' 00" p. 1
n ■>.i p. 1
10 00 p I
Corel ed.
. .-4 rile.u-ered.
.... Coveied.
. al Uneovered
Mean Doctaraal radiation =
Time.
Blaek
thimble
4581.
8» 50" p. m
9 10 p.m
9 30 p. m
10 00 p, m
3".S
—0 .0
-1 '4
111 -J:-, p.m
11 10 p.m
— i 's
4". 40 3.4
. ISRI. Weath.'r. .-le
Di D,-D] E.xi.c
4 .111 rneovereih
Covi-reir
3 . SI Uncovered.
*Kecorded with a mark of inti
164
EESBARCHES OX SOLAR HEAT.
[Station. Monnluin Camp. Mount Whitnev, California. ObserTri , rapt II F. Tllirlnplis. Date, Ausust 31, 1881. Weather, dear
sky. calm at , SI' 15'" p III.: sillisequently ■■very ealra nii^bt," Mean r.-lati\ '■ timt.i.lity ^40 per cent. ; mean force of vapor — 2.4
Date.
Time
1 Black
thimble,
4581.
V,
Silver
thimble.
4583. \
Di
Si
D1-C3
Exposure.
Ai
"iiat.'ll
:il
31
31
31
31
31
31
71' 55'" p. m
8 25 p, m
9 45 p. m
9 15 p. m
9 40 p. in
10 10 p. m
10 40 p.m
11 10 p.m
40.4
! 3 '. 7
-0 .0
4.0
-0 .5
3 .5
—0.4
"'40.' ao'
"4".'M
IJO.O
4 .1
4 .1
3 .8 1
4 .2
3 .5
Covered.
Uncovered.
Covered.
Uncovered.
Covered.
Uncovered.
Covered.
Uncovered.
0°.9O
0". 59
4". 31
0 .30
-0 .01
i .31
i .50
"'a'.'go'
0 ..50
0 .11
4 .39
0 .03
—0 .28
4 .18
1
4 .30
J
L
»n, peak of Mount Wliifuev. Observer, Capt. 0. E. Mich.iais. Date, September 2, IfiSl. TVeathe
"liisli wind." Mean relative humidity— 44 per cent.: mean force of vapor — 1.6 miu. Iusti
iited between two rocks and protected from wind a.s miicli as practicable. ]
Time.
Black thii
ble. 4581.
Silver
thimble,
4583,
constantly
covered.
4583—4581.
1
D,— D-,
1 Covered.
Uncovered.
1 -3^.0
-20.S
-2 .9
-2 .9
-2 .9
-2 .9
(-2 .7)*
(-2..'.)-
-3 '.a
-3 .1
-3 .15
-3 .3
-3 .8
-3 An
0O.2
2 .0
1 .1
0 .7
0 .5*
0 .4'
1 .7
2 .2
2 .5
2 .55
3 .53
2 .6
1 .7
0 .95
0 .6
0 .5
0 .4
1 .7
-5". 5
2o. 5 1 0". 1
2°. 4
' -4 .9
-4 .0
-3 . G
. 1 -3 . ."i
.1 -3 .4
-5 :6
-5 .7
-5 . V3
-5 .8
1
1
'
2 .4
0 . 2* 1 2.3
-4 .9
'_! -3!k
.' -3 .7
-3 .6
S 42 p.m
;;::::: 1::::::..
-4 .9
2 .3
0.1 2.2
Mean uoctnrnal radiation = .
libera in parentheses have been rejected in la
r ofthi- followii
[Station, in-ak of Mount Whitney. Observer, Capt. O. E. Mirhaelis- Date, September 3 and 4, 1881. Weather, clearsky.at
first <aliH but afterward " slijibt north wind." Silver thimble kept constantly shielded from sky radiatic- ^^
tioii is tli'Tofore required to 7>j, which indicates the change of temperature o"" " " - -i. n.
Consequently i)i — Z>i=nocturnal
Date.
Time.
Hlaek
thimble,
4581.
D,
Silver
1 thimble,
4583.
Bi
Bi-ft
Exposure
(black thimble).
Septt
Sept
Ifli'OO'" p. m.
10 15 p.m.
10 30 p.m.
10 45 p.m.
11110 p.m.
11 15 p.m.
1 1 30 p. ni.
11 45 p.m.
12 00 m.
12 15 a.m.
_ 0°. 9
_ 9 .0
-7.1
-10 .3
- 8 Is
-7.8
-111 .0
"WVo'
"3 ".2o"
"2 '.'30'
-60.7
-6 .9
-1! .6
-6 .6
-0.6
-6 .4
-fi .!1
-7 '.d
Covered.
Uncovered.
Coveied.
Uncovered.
Covered.
Uncovered.
Covered
Uncovered.
Coveied.
Uncovered.
0°.20
2=.50
0 .00
3 .20
.J
-0 . 20
2 .50
1 . nil
0 .20
10 . 80)«
0 .30
1 .90
2 .53
NOCTIK'NAL K'AIllA riOX.
165
(Station, p.:ik ..t M"
|.t. II, E Mu:liac-li3.
P.l:li>ktllimlil.',45lil.
Coveie.l. I'lR-iiT.-!.
tllimblo,
4jsn.
""-0 ,'15'"
—11 .4
—0 , !t
-0 !«
i'.w' 'o\i' 2',7n'
':i".g" "ij .".'.' '3 ,'i '
':i'.7" "0 -i 2 .li '
:) , i: 0.3 1; . 9
'
2,7 01 ■_' . s
■J . ;i — u . 3 n , 1!
■i ,0 11 .1" 2 .r.
The mean of fimr iletorniiiiatinii.'^ maile mi tlit? faliiicst iii;;lit. Attuii^t .".l. ;;ivc> iis Ihmv as tin'
nocturnal radiation from laaip-lilaclc 4^..'!0C'. (in a dry air ami at an altitude (if immiIv Ii.',(Iiiii IVfi);
and there is reason to Iielieve tlmt witli ali.solutc calin tlie ri'siilt wimiM ha\'r ln'i'ii j;icalrr. .M(d-
loni's result, ol)tained liy tlie stime mean,s Octolicr 'J. ISli;, in the ch'ar air of Simtiieni Italy, on a
very calm night, was .'{^.."iS C.
rouillet's vahu'S (see Comptes l.'endns, July il, IS.'.S) are netirly doiilih' this, tlioiiuli olitained
at Paris, near the setilevel. They tire prolialily exaK.i;erated by tlie delects (if his tictii leter, tiiid
throuyli his apparent linliit of ])laciiig his railiatioti thermometer near the earth and his tiir titer-
raometerat some distance almve it, it practice which usually insures too Iti^jh readings for the latter,
as Melloui has shown.
Pouillet uses his results on nocturiial radiation indirectly in olilaiiiiii.';' his celelirated Viiliie
( — 142'^ C.) for the " tein]ierature of space."'
All the present writer's observations jioint to the conclnsicm that this '■ teiii|ieratiire of s|iace"
is little ahove that of the absolute zero, or. in ..(her words, that all tlie hetit the etirth receives from
all external sources, exceptin,a' tlie sun. bill inclnding that raditited IVoai the sttirs, the dark heat
from invisible bodies in .space, tlie lietil coinMiniiicatcd dynamically by the contact of meteorites,
i^c, are collectivel.v negligible, or nearly so. The ground for this i-om-liision rannot lie given here,*
but an extension of these experiments on noc'tnrnal itidiation woiihl fninisli a method of testing
them, did we know the iiermeability of the dilfereiit stnitti of otir almos|iliere to lietit rays nf low
refrangibility. We sliotild in this ciisi- need to place the biilli of our rtidiatioii titer iieter in ti
snittible inclosure, so that il could rttdiatc to only a liiiiiled |Miilicin of the sky tit once, tind then
inclining it to successive iiortions from the zenith to llie lioiizon. and noting its iiidictitions, we
should obtain data for determining the amount of heat radiateil earthward by this atmosphere
idone, for the heat coining from the celestial sptices (if any) must be nearly constant at every
inclinatiou, while that from the atinosphi>rc must ordinarily increase as we aiiproach the horizon.
If. then, we know the law of this increase, we can determine whether a coiislaiit term is to be tiddeil
(to the expression tor atiiios|)lieric nidiation) for the ■' temiieratnre of space." tiiid if so, its a it.
The actual experiment, it m-cil htirdly be stiiil, would be ;i delicate one. Iml it docs not seem bi'Voinl
the reach of effort. An allcmiit to retdize it wtts tictittilly made on Mount Wliilney, but wtis
defeated by the presence of wind ami the imperfeclidii of lite apintratus.
].. 1-2-J.
CHAPTEi; XVII.
HOT r.UX" AXI) SOLAK-KADrATlON THERMOMETERS.
A Iiastily deviseil ;ni(l coiistnieteil apiianitiis was tali
temijerature whieli could be attained by the uHcdiicciitiatiM
A nest of shallow boxes, alternately of wood and of l)la
or by loose cotton packing, and covered by sheets of cuini
sort of "hot box" (shown in section in Fin. l-l). Within t
.cm. deej) and lliA cni. in diameter, was placed the bulb of
temiierature of tlic iMclosmc. This copjjcr vessel had a yl
vessel, wliich in turn icsti-d on the bottom of the lar!;i'i-
diameter, itself covered by a layer of glass and protected a>
an outer enveloiie of wood, with loose cotton iiaid^in;;. Tlic
sun's rays normally to its glass face.
At tlie IMountain ( 'amp the result of the best trial wa.-
at 1'' -lO'" p. m. a Icaipcrature of 113Jo 0. was attained, the
I40.S, and the excess in the inner compartment of hot liox I
The following table gives tlie details (,f tlie oliser\ atioi
en with the expedition to observe the
1 solar rays on the mountain.
•kened copper, separated by air spaces
nin American window-glass, formed a
he inner vessel of thin spun copper, i
a thermometer for registering the air
ass cover, and was placed in a wodden
copper one, 8 cm. deep and .'.L* cai. in
i niuidi as possible from loss of heat liy
whole w-,is inclined so as to receive the
1 on tlie '.ith of September, 1881, when
shade temperature at the time being
in the moiintain :
-P?y. J^.
O
%P^WMW&Ms^Wi¥M
Section of Hot 1
. 10. jr. ^DatL-, So|
iustuimeiHal elTii
■HOT BOX.'
167
I.i. 94
S8.06
IG. 61
89.33
1.'.. 67
91.40
SOLAR-rATtlATION TIIETnrt>JIETEKS.
Tlieir \v:i.s piii\ iilfd a jiair ol' " coujuijate tlicnuonu'feis." /. r., diic lia\ iiij; a lilackciicd liiilb, tin
itlier a 1iiij;lit oui.-, cacli in \a(.iio, not coiiiu'ctcil, Imt alwa,v.s placfd toi^ftlitT and read tuyL-tliiM'.
Tlio tullowinK cilisiTvaliim.s weix' made at l.iine Pine:
Taiu.e l:.!8.
■minliicti-is Aii^ii.iit and Sciiteiiilji-r, IS^I.
Fahiv.ilipit.
Brii-lit iMilli. r.hl.U Inilli. DHlVlviiif-
Statidi. Lciii.' riue. (Iliservt-r. A. C. D.]
Centi-iade.
Hiiul.t Lull.- Walk bulb. Diflt-rencc
90.33
3!l<=
28
48°. 61
39
■»2
56 .95
.Vi
44
79 .83
4'!
7S
53
-M
411
no
62
44
33
■2S
33
76
43
67
30
48
.■.li
37
33
61
ila
4K
61
73
17
44
72
18 .61
49
44
11 .Is3
3.i
S9
8 .83
4::
50
20 .00
4U
42
(lU
)7 !78
168
im:skai;('1IKS on solai; rioat.
Table 138 — Coutiimed.
„„nj of „l,«,-n-atU
of gale. t On uccoant of ,s:ale nni
Table 139.
«;,<.in-»j iifferawes of readings of bi-iijhl niiii bla
[In tleyrees Centijiradi-.]
Date.
4p.i
3S
170
IS
19
19
24
17
73
88
73
73
44
62
56
37"
28
22
23
26
24
20
39
61
30
80
30
56
39
16
10
10
15
18
83
120. 62
20 .07
80
72
34
44
11
61
67
00
78
72
78
73
78
28
44
6t
17
11 .12
4
11
8
8
3
S
6
8
6
6
44
26
26
25
25
23
06
73
61
72
-j^
24
24
25
25
21
20
67
06
62
44
11
45
17
61
6
S3
34
12
61
14
4
S
10
10
V,
23
16
12
28
M.>
I'"i(iiri a (■(iiii|i;n isoii or' fourteen iiliser\ atious of the solar-radiation thermometers at noon with
eorrespoiKliiiK reiHliii.ys n( llie sliade teiniieiature, it appears that ou the average the bright bulb
rei^istered H'PX) V. and tlie black bolb il'^.'ii) V. above the shade thermometer.
It will be iKitieed that the ladiatioii is always greater (tor the same altitude of the sun) in the
morning than in the aftefnoon, a fact deducible alsc. fidrn tlie aetinometer curves (see Fig. 11, p-H'-'),
which, however, present it in a less salient manner.
C H A 1' T E i; X ^■ I 1 I
irY(ii;(i:\iKTi;i(" oi;ski;\'ati()>;s.
Ill :niy iiivi'stii;atiiiii of ;itiiios|ilii'rir aliS()i|iti f radiation, the i;i'eat inipdiraDci' of «ati-r as
au ubsorhiii.L;' a.uclit is (_'\ i.Iriit. Ill spite .if iiilliicicms (■(iiitriiMTsies as to its iiKiili' iif acl ion at
(liffi-i'i-iit tciii|ii'ralmc-s and in dillcivnt plivsical states, tlinv is no donlit that water in sonic loriii
lias iiiucli lo do with the \ariatioiis in aliiios|iliriic |iciiiii'aliility to ladiation.
Ai-cordiii,^l.\ a lai',i;c iiiinilna' of olixa'vatimis wiili tlie ii^yriiroiiiclcr and oilier li,\j;roiiu-tricaI
iustruirielits were made on I lie expedition, wliieli are now to lie redneeil. It is lielie\ed that the
lonjl-coutilined tri lioiiii\ oliser\ alions at Lone I'liie Inrnisli a \aliialile reeoid nl' the peenliai ilies
of il desert elimate. It was intended to iiial>e similar ones on the iiioantaili, Imt the excessive
liiti.mie and dillKailly attendant mi the lattero lisei rations, made it impossihle lor Hie overworked
oliser\ers tin the iiionntaiii to aci'ompli.sli their share.
INSTllUMENTS USED Vn\l II VI : i;( JME I'lMI XVL i ICSF.K V.VTIuXS AMI ('llXDri'luN Ob' ION' V 1 l!l l-\:\Il;>; T.
At Lone I'iiie (elevation .".,7i;(l feet) the psy.diromelcr, in cliaree of Scryeaiit Doliliins, Uniti'd
States Sijjnal Service, was in one of ihe ^al\aiii/eil iron fr.iines ]iio\ideil liy the Signal Ser\ ice.
It consisted of dry hull) IheiiiKHiieter S. S. l(l.;7; wctlmlli tliennomi'ler S. S. l(U."i, covered with
thi(d^ wnddiij;' in.-fead of the oriliiiar\ st.iiiiiard thin niislin.i .' r
At the lower camp on .Mount Whitney (altilnde 1 I ,ii(lO f.'ct) the psyclirometer, in cliarj;e of
Serjeant Xaiiry, I'liited States SiL:iial Service, was Iiiiiil; in an e.xleiiipori/ed clianilier. formed oi
a box with lattice work o[ieiiiiig, lookiiij; towards the nortli.and a~ well slnddcd from aircnirents
as coilhl he olilained. It consisted of diw-lmlli theniioiiieter S. S. ; wctlnilh t lici iiiometer
S, S , co\cred with tliick wickinu,! .')"
On the moiintain it was imiiossililc In olilaiii any de[iosit of dew with Ke.uiiaiilt's Iiyurometer
or dew iMiint apparatus in its onlinaiy treatineiil, and Iheivfore no oliser\-alioii-, will lie found
recorded by Serjeant Xanry, who was in cliar.u'c at the upper stalion. Snbseipieiil ly, liowe\-er,
results w-eri.' ( btaiued on one day iSepfeiiilier '.Ij. Ii> (.'.iplain .Michaelis, by the use of a fri-orilic
mixture. These obsei\atioiis are uncn ami discussed turtlier on.
The i;ej;iiault dew-point readinus olilained by Siaueanl Dobbins .il Lom/ I'ine were taken in
the ordinary way, by blowiiijL; air Ihrough the ether in llii- ■■dew-pomt " Il.isk. These obseiw atioiis
are nivini and disi iissed on pa_i;es 171 and 171'.
KEDrOTIIlN or rSYCIIKOJlETEK OnJ.SKKVATlOXS.
The h'ahreiiheit tlierinometer readin,i;s are from the oii;;inal records kejit by Serj^eants Dobbiii.s
and Naiiry, The readings of the dry bulb, ^ and of the wet bulb, /', and ti'ieir dilVereiice, / — /', are
reduced to the centigrade .scale by Table .V iw ■■Smithsonian .Meteorolo.i;ical and I'liysical 'J'ables."
With these numbers cxiiressin- the \aliies of /' and I — I' in Cenl i.madc .le.urees used as
ar.unments, the value of ./, the toice ol" \apor, expressed in milliiiieteis of pic.vsnic of niercnry, is
ublained from the table i; ii. Tins lable is calciilaled by llc.unaiilt's loiinnla for Ihe p.>\ clirometer,
ll.tSI)
•'■■=./-(iui-/' ('-'')''
"Tliero is .somn lioiilit about the uatiuc of the uoveiiug ii.w.l. Thu iiue^tioii is fully .lisciKsscl in Apiieiiilix I.
IL'oSO— Xu, XV I'li "'■'
170
liESEAKCIIES ON SOLAl; HKAT.
in which h represents the height of the barometer, assuiiieil equal to 755 mm., and/ the force of
aqueous vapor in .saturated air at a temperature equal to V. (See Smithsonian Tables, B, page lli.)
At the end of tlie talile is a sliorter one givint;- the "correction for the barometrical height."
/'= \{y.M\
EXA:\[rLE.
liar. = ri(!(i mm.
In the table we lhi<l for (' = KP and t—V = s:m',
Force of vajinr = S.">."> mm.
For t — t' = 8*^.4,
Force of vapor = s.41 mm.
Whence, by interpolation, for t — t' = S.3i.»,
Force of vapor = 8.42 mm.
Correction for extra {)°.'>() in value of /' = +(».4.~) mm.
Correction for barometer (COG mm.) = +0.(i(l mm.
Concluded force of vapor = 0.47 mm.
The lluctuatiims of tin- barometer being very slight, and the ileviations in the barometer cor-
rection i)roduced by neglecting them causing at the most only a change of a few hundredths of a
millimeter in the resulting force of vapor, the following table was compiled from the Smithsonian
table, by interpolation and extension, for a mean barometer of 6C0 mm., the height at Lone Pine,
in order to expedite the cidcalation.
Table 14(i.
t-
('
0^0
oo.l
0°.3
0».3
0^4
0". 5
OO.O
0'.7
0t>.8
0°.9
2
3
.08
.15
.23
.09
.16
.24
.09
.17
.24
.lo'
.17
.ll'
.18
.26
!lii
.12
.20
.27
.13'
.21
.14
.21
.29
.14
129
4
.30
.31
.32
.32
.33
.34
.35
.36
.36
.37
5
.38
.39
.40
.40
.41
.42
.43
.44
.44
.45
G
.40
.47
.47
.48
.49
.50
.50
.51
.52
.53
.54
.55
.m
.,56
..57
.58
.59
.59
.60
8
.61
6:i
.62
.63
.61
05
.05
.66
.67
.67
0
.68
.69
.70
.70
.71
72
.73
.74
.74
.75
10
.76
.76
.78
.79
80
.81
.82
.•2
.83
11
.84
85
.85
.86
87
.88
.88
,89
.90
.90
VI
.91
9?
.93
.93
.94
.95
.90
.97
.97
.98
13
.99
1.00
1.00
1.01
1.02
1.03
1.03
1. Ii4
1.05
1.05
14
1.06
1.07
1.08
1.08
1.00
1.10
1. 11
1.12
1,12
1.13
15
1.14
1.11.
1.10
1.10
1.17
1.18
1.19
1.20
1,20
1.21
16
1.22
l.Ki
1.23
1.24
1.25
1.20
1.26
1.27
1,28
1.28
17
1.29
1.30
1.31
1.31
1.32
1.33
1.34
1.35
1,35
1.36
For the reduction of observations at the Mountain Camp, a mean barometric pressure of
500 mm. was adopted, and the following corrections were deduced :
Table 141.
1
t-t'
1 1°
.16
.08
.17
3<= 4°
1
. 2i' . ;i2
. 12 . 10
. 25 . 34
.61 ' .82
50
.40'
.20
.42
1.02
6»
mm.
.48
.24
.50
70
.56
.28
.59
1.43
8°
.64'
.32
.67
1.63
90
.72'
.36
.76
1.84
10'
.80'
.40
.84
2.04
11°
Correction for a diffi-ron
Correction for :i tlifl't-ren
Correction for 650 mm .
Correction for 500 u.
eof 1 dm..
voi h dm..
. ,08
, .04
-I .08
. .20
.88
.44
.92
2,24
Difference for 0°.1=
IIVCI.'O-METUIC ()I'.Si:i;\'ATlONS.
171
Wlii'ii till' tciii|MT;itmcortlii- wet l>iilliis licluw the iVecziiiu |iiiiiit, Kciiiiiinlfs Inriiiula liccoiiK'
o. ISII
with uliicli the tblhiwiiij; liafoiiietcr conrrtiDiis liavc lii-eii used, caluiihitecl fur the lowef eaiiip.
Mount Whitiiev:
Correction lor a ilifffiouei- of 1 (In
Correction for a ilitfercnce of A iln
Correction foresomni
On ai'c'duiit of tlie (IiTiiess .It tlie air a coiisidei.ililr iiiiiiilier.il' tli.' olisei vat ions fall outside
the limit of the Siiiithsoiiian talil.'S. wlii.-li lia\i- not lieeii eal.aihit.'.l for s.i low a ivlatix.- liiiiuidity,
and wliieh in .'onsi'iinen.'.- an- |ir.ilialily h-ss r.Iialile in tbesi' imrts. Ueiny foiind.'.l on iiistriinieiital
readiiij;s taken iimli-i .lilfeivnt .•on.litions. The \alnes that have lie.-n d.-iliu'i'.l liy e\ten.liiij; the
tables are ilistiiinuished in tin' following pa^.'s liy an asterisk.
(For a diseiission of th.' iii.-thod employed in th.' re.lu.'tion of the psy.dirometer oliserxatioiis
see Apiiendix No. I.)
T\i;i.f. IJ:;.
Tlim-I n,mi),n-is„ii of rr>illls bij thr psij.-liromilrr iiiul hii l:,;j,„uiU hij.iromilir or dr,r-pi)Uil npimratiis.
|Stfiti..ii. Lone fine. Obanver, A. 0. H ]
Date.
I...ialtime.
i
r
-" Cmt.
An-. 8
SM5
.a. ni.
28.94
9 ....
8 15
8 15
y..ni.
19. 89
29.33
10 ... .
8 15
23.50
11..-.
8 15
26. 89
l"-
8 lo
8 15
p. m.
27. 39
27. lil
13 ..
8 15
27.44
14 ....
8 15
11. in.
25. 56
14 ....
Mean ....
8 15
p. m.
25. 94
25, 68
Willil. iln.l elasi
= Ceil. I - Cent.
elear
Clo.i.l
V. Fnsb. B
1.1.89
8,87
63.1
51.4
Clear
10.05
11.70
55.0
38.6
Clear
Fresli. li
10.08
8. K7
40.9
41.2
Clear
Gentle. A
11.01
7. U8
44.0
26.8
Clear
Fresli. I!
0 52
5.84
?+ 1
21.5
Clear.
l-ienl.le. A
12,20
7.39
44.4
26.9
il.:a-
Fle^ll. B
12. 10
8.23
60.7
41 3
.'liMI
.Iriilje. A
):i. UO
7.49
47. R
27.6
. Iral
lain., A
9.98
8.08
41.0
33.2
; Fe'^hto-.entle.!'' -
5.04
5.51
20.3
22.2
11.30
8.07
45,6
33.1
The above .ibsei vatioDs w.-ie iiia.li' diiiiii.i;' a short p.Ti.i.l .if eoiiiparatively moist weather.
Siiliseiiiientl,\. h.ove\fr. til.- air Imm': so .-xc-ssi vely dry tli.i t th.- .liflieulties in the use of the
lieyiianlt liyj;ioiiieler b.'.ame almost insuperable with the limited ies.iiiii,'es at .•ommaii.l.
The iie.xt table (141) r.'peats th.' pivvi.ius results, elassili.-d a.-eordiiig to the vehieity of
the wind.
172
KKSEAKCHi:S OX SOLAi; MEAT.
T.V]!LE 144.
CLASS A_GKNTLE BKEEZE (IK CAL5I.
Echxtivc liumiilit
Kcsn
aiilt
li.VKru
1,-tlT.
''■"'""""'"■
ni
Firn;)i:
10. IS
.-.4. 7
ii; 05
11
70
r,:,. 0
11.01
I
■lil
44,4
18 S3
10.89
W.30
13.72
i:i. lil
0.17
14. S7
C.44
If. 36
7.00
11. '^n
8.11
lll'iUl.s..i:i. 27
CLASS B— FKESH BKEEZE.
10. so
8. 87 63. 1
51.4
12.02
9,50
+.3. 12
S. 87 ; 46. i)
41.2
11.44
9.50
+ 1.94
0. i>2
r.. X\ 24. 1
21. a
4. S3
3. 39
+ 1.54
a 39
+ .5. 86
... M
1. 28
2.50
-1.28
M,'an.s..s.U3
7.40 43.0
35.5
8.00
0.67
+ 2.24
As far ;is tliey yo, these iibsorvatidiis show a inarkt'd teiidenry tDwanl a diiiiiiiiitioii of tht
diffcreiiro betwi'i'ii Ihe indicalioiis of tlie two iiistniiMeiits as Hie •\viiid incicases.
Table 14.").
I uf2>siii_ln;i,ii,kr null EajiiuuU hiiyromcUr.—IU-nml of the results l,ij llie psijeltromeler
[Stiiliiiii, lliiumaiu Camp. Okserver. 0, E. M. Tate. SL-pteml.ev 9, ISKl.]
1
Eahn-ulicit
Eeilu
ccd to Cfn
[grade.
By Smithsonian tallies
(Regnault).
=
Div.
Wi-t.
Diflercnic.
Force of
Dew-
7H7n
0 C.
0' 1»3(
6 " -.
50°. 5
17^. 0
19°. 72
10'=. 28
93. 44
5.41
+2. 28
49 .1
1* . 7
19 .33
9 . 50
9 .83
4.84
+ 0.71
61 0
51 .8
17 . 2
20 . 56
11 .00
9 .56
6.01 ' +3.77
40 .5
IS .0
IS .06
8 . 06
10 . 00
4.0s 1 —1.00
6 1
46 .7
18 .4
IS .39
8 .17
10 .-12
4.03
-1.73
1 .1 30
64 0
40 .0
JS .0
17 . 78
7 .78
10 .00
3.91
-2.15
1 0 30
64 ^
40 .8
IS .0
18 . 22
8 .22
10 .00
4.17
-1. 30
1 i] ol
6 0
47 .6
IS .0
IS . 33
8 . 33
10 . 00
4.24
-1.09
1 36 3)
( ' 0
44 . 0
IS .C
10 , 07
6 67
10 .00
3.38
-4.03
1 41 30
04 0
45 . 8
IS .2
17.78
7 .67
10 .11
3. 80
-2.52
1 46 31
( s
4!) .8
18 .0
in .89
9 .89
10 .00
5 12
+ L50
1 51 30
05 . 0
IS .1
IS .67
S .01
10 .06
4.38
-0.48
ilnail ....
18 . 62
r.y the tallies for tension of aqueous vapor, the dew-iioiut, corresponding to a mean force of
vapor of 4.45 iiiiu., is— 0°.45 which is adopted as the dew-point given b3' the psychroiueter.
Oil the same diiy readings of tlie liegnault hygrometer were obtained liy Captain Jlichaeb's
Willi the fdllowiiig result:
•Tiieil Itcgmialt hygrometer. Xo success with ether, ^lade frigoritic mixture of snow and
sail. Olitaiiied Iciiipcratuie iit \:\- and I."i- F.. but no depusition nt miiisliire. l!y using the
hy.unimeter (.Signal) thimble a tcmpeiature of l'' was olitained with ice and salt, and the dew-point
WHS reacheil willi the fnll(i«iiig icmliiig:
b'c.mi.iiill IlKaiiiomctcrs— di\, (11- I'ahr.; wrt. T^' Falir. (shade): in the sun, copious dew at 7=i,
dry, liu: ; at 11' '. moi.stuie began slowly to ev:iporate; at V., . rapidly— ilrybulb, l.;f^..V
TivcKO-Ali'/ilMc ui',si:i;VATi()XS.
173
Till' result (iftlic (■(iiii]i;iiis.in is tlicivlc.iv
Di'W jioiiit I'.v l;c-ii:iult hv-nmu-tri- =7' to lU- V.
Mi-aii il('\v-]«Miit l.y Ui'^iiaiilt li,v;;niiiiclcv. . =-12^..") C
Mruii ilrw iiniiit In iisycliKiiiii'ter =-(l.4.". (.'.
I'Mclir..iiiclcr-l;c.miaiilt liy^rdiiictrr = + Il'\(r, ('.
This iin-rrcs with tlic iircvicms mcMsiiics. olitaiiicMl al Tanir I'liii- iliiiaiiu lii;lit cir jiciitlc wind, in
indicatiu.t;- that tin- |isyclii.iiiii-tri' uavc drw-iMiiiit^ >oiiicwliaI t(in lii,;;li.
(.)u several other (iccasKiiis attempts were made to reach the dew point, hut always « ithout
success.
Tabular statements now follow id' the ori.L;inaI oli<er\'atioiis with lln> psyidirometer (expressed
both in the Fahrenlieit and Ceiiti-rade scales). toj;ctlier with the results of their rednclnm.
TAliLE 14(i.
/.'(■</«. ■(Mill ufiirl ui„l ,l,!i ball, ll„rmum,l,r niuUiujs.
(atiou. Loin- I'int. Liititud.', 30 30". I.ousituili-, lis 03' 47". EU-v.itii
Ri-,hRV J lo Centisraili-. ]!,v Sniitlison
M7".i. 1
I? I.. I
17 a. 1
17 ],.,
17 a. !
17 p. ,
17 a. 1
17 p.i
8 17
9
S 17
a. 111.
84 .8
9
S 17
p.m.
83 .8
10
S 17
a.m.
84.3
11
S 17
p.m.
74 .3
SO .4
11
8 ir,
S 15
8 1.-.
IT
p.m.
81 .3
81 .7
73 .0
13
s 1.-.
p.m.
81 .9
U
S 1.1
a. Til,
78 .0
14
l->
8 ir.
8 13
ii; 3:,
8 i:>
p. m.
p. 111.
p. Ill
ji. Ill,
78 .7
78 .1)
80 .4
81 ,3
17
s ir.
8 ITi
rj 35
8 ir,
p. Ill
p.m.
p.m.
84 .0
U
8 15
7J .0
1.5°. I I 24^89 IG".
19 . ,-9 15 .
.015
.f^
. 17 13. 96
23 . 50 10 . 39 7 .
L?C . 89 18 .07 s .
27 .01 19 .33 8 .
-,50 17 .11 8
.91 13 .01 12
.22 15 .11 15 . 11
. 89 12 .78 12 . 1 1
.00 15 .44 13 .02
.44 13 .28 10 . 10
, 17 12 .00 11 . II
18 12 35 p.ni,
IS 8 15 p.m.
.3 14 .78 111 ,72
. 5 , 23 .17 14 . .50
- " "■'■ '
( CI.iiul.\
9 3 52. 5
9. 4 30, 0
i Cleni.
\ Fifsb
0, 5 40. 0
((iiiill.
) Ck-ar.
1, 4 40, 9
( Gcutl,
3. 0 44 0
( Calm.
4, 9 , 24, 1
4,4 44,4
) Cl.-ar.
( disk.
) l.-liar.
( Gnitl,
( Clear.
( Geutk
1. 3 40, 9
( Calm.
1. 3 SO. 3
5. 4 27. 5
( Fl-esli
(Ck-ar.
( Fresli
) Ck-ar.
( r.ri.sk.
8. 5
- 1,4
ri 7
1, 0.7
30,7
- 0.2
14,0
( Fr,-,Hli.
( nil^'li".
( cli-al,
( Kr.-,k
( Cl,,.,r
\ niisk,
, Cli-ai,
( l-'l.sli.
174
RKSEAKCriES OX SOLAR HEAT.
Tahle U(! — Coiitiiuied.
nahiL'liou iifin-l u)ld ilnj hiilli thrniwmrirr )TOrf/».(/»-^Ciilitiinli'il.
ectetl Falirenbeit.
Date. ' Local time.
CO .5
51 .9
61 .5
50 .0
50 .6
49 .6
Reduced to Centigrade.
J 30 .1
12 .5
31 . 56 15 . 83
14 .50 11 .00
23 .72 14 .44
33 . 06 10 . 3.3
-c '
13 .S3
25 .11 16 .39
32 . SU . 17
22 .3
20 . 83
14 . 44 !
14 .6
24 .17
IC . 00
27.5
31 .00
15 . 72
10 .6
17 .50
11 .67
15 .5
25 . 00
10 .39
29 .1
31 .50
15 .33
15.2
=2.00
13 . 01
20 . 28 ^ 14 . 72
30 . 33 I 10 . 11
24 . 89 I 13 . 00
22 . 61 14 . 83
15 . 73
3 .44
8 .28
10 .73
6 .95
S .72
12 . 39 i
8.11
S .45
11 .56
14 .23
II .83
7 .78
24 .7
28 .00
14.28
13 .72
10 .1
20 .39
11 .44
8 .95
14 .8
23 .44
15 . 22
28 .8
30 . 17
14 .17
10 .00
14 .6
IS .44
10 . 33
8 .11
15 .6
IS . 44
9 .78
8 .00
24 .67 ; 13 .06 11 .61
13 .01 I 13 .50 1
14 .1
17 .2
29 .3
11
44
15
00
11
11
13
01
12 .00
7 .83
*4. 79
8.02
5.02
9.22
*5. 07
6.30
■ 6. 00
53 .2
13 .3
19
17
11
73
7
39
6.43
59 .0
20 .5
20
39
15
00
11
39
0.03
53 .1
54 .2
7 .5
15 . 0
15
20
89
67
11
12
33
4
17
34
S.09
0.27
50 .4
23 .4
20
50
13
50
13
00
4.65
47 .0
12 .4
15
50
8
07
0
89
4.79
.-.3 . 6
14 .1
20 .3
19
83
44
12
14
00
17
11
83
0.30
6.00
48 .6
11 .1
15
39
9
22
6
17
5.46
' Cent. Per cent
ft. 9 14. 1
8. 0 I 65. 3
7. 6 ' 38. 0
21.5
41.0
39.3
12.4
35.8
24.8
41.1
17.0
30.0
39.7
11.1
32.3
23 .17
31 .00 14 . 72
30.3
30.7
44.3
33.5
23.8
35.2
30.8
11.5
i Clear.
( Gentle.
1 Clear.
; Freah.
[ Brisk'.
j Clear.
J Liglit.
i Clear.'
j Light.
I Clear.'
( Fr-esli.
( Freali.
i Clear.
( Brisk.
( Clear.
S Calm.
C Fresh.
i Clear.
( Fresh.
I Clear.
( Light.
( Fresh.
5 Brisk.
) Clear.
! Light.
i Clear.
J Light,
( Fresh.
) Clear.
( Gentle.
) Clear.
; Light.
) Cli-ar.
entlo.
i Clear.'
(Calm.
( Clear.
; Light.
: Fresh.
I Clear.
) Clear.
i Clear.
{ Fresh,
j Clear.
( Calm,
i Clear,
t Calm,
i Clear.
> Clear,
II VGKOJI ETEIC OBSERVATIONS.
Table 1 H! — Ooiitimu'd.
Itohivlion Iff ir,l Hint ihij hull, thrrin.nnrUr )T„.(;;,./»— Coll tilliu-.l.
175
Corrected Falireuheit.
Kcduccd to Ceiitijijrade.
Ey Sli
itlisoiiiaii tallies.
Wind and
weatlier.
Date.
Local tiiu
Dry 6. 9.
No. 1(137.
Wi't s. a.
So. 1045.
Differ.
Wet. 1 Dry. "j^"--
1
Force o
■ Pew- r„,lative
point, liiiniidity.
1881.
Si'iit, 2
S 15 p.
ni. 73 .3
52.1
22 .(14 11 . 17 11 ,77
3,69
Cent. I\r crnl.
- 2. 9 17. S
( lirisk.
( Clear.
3
S 15 a.
ni. 7(1.3
.52 . 9
23 . 4
24 .61 11 ,61 l;i .00
•3,30
-4.3J 14.4
( Hale.
, 1 'Icar.
3
12 35 p.
85.3
56 . 7
28 .6
29 .61 13 ,72 15 .89
■2.72
- 6, S 1 8. S
(Cale.
) Clear.
3
S 15 p.
m. ' CD ,7
49 .1
20 .0
29 .94 9 .59 11 .44
2, .■i5
-6.2 1.5,5
( llri.sk.
, Clear.
4
II, 1 C7 . 7
49 . 2 ■ 18 . 5
19 .83 9 .,56 10 .27
3,50
- 3. 6 , 20.4
S lllisk,
t cl.i.r
4
4
5
5
,1.7 p.
S 15 p.
8 15 „.
12 35 p.
11. , 77 . 0
11. .■il .0
.54 . 6 23 . U
51 .2 23 .0
54 . 5 17 . 7
59 . 5 21 . 5
25 . 33 12 .56 12 . 77
23 .44 10 .67 12 .77
22 . 33 12 . 50 9 . S3
27 .22 15 .28 11 .94
4.08
•2.89
5. 59
0, 55
— 1. 6 17. 0
- 0.0 1.3,5
5. 0 24, 4
( i-.u'^k.
s l;n'~k
1 Cleai,
< (ieiitle,
( Clear,
8 15 p.
ii.j 72.(1
52 . 6 1 20 . 3
22.72 11.44 11.28
4.14
- 1. 4 20, 2
( C.ale,
6
S 13 a.
ni. 65.7
.50 . 4 15 . 3
IS .72 10 .22 8 ..50
4, SI
0. C 30 0
( Brisk,
( Cl.'ar.
C
:12 35 p.
6
8 15 p.
11. ...^^..^..
47 .5
5 .2
11 .50 1 8 .61 2 .69
6.67
5. 7 67. 9
SiS
7
8 15 a.
m. , 67 .1
53 .6
13 . 5
19 .50 12 .00 7 .50
C.4S
4.9 36.4
U^^:
7
12 35 p.
■1. 70 . 8
56 .9
22.9
26.50 13.83 12.73
4. ns
1,1 19,2
( Kresli.
(Clear.
7
8
8 15 p.
8 15 a.
m. ' 52 .a
m. ij'J . 5
49.2
56 . 0
3 .7
13 . 5
11 .61 9 ..56 2 .05
20 . m 13 . 33 7 . 50
7. S4
7,7 77.0
7.7 42,9
(Calm
(Clear,
( Li^lit,
( Clear.
8
12 35 p.
HI. *i . 3
59 .5
24 .«
29.06 15.28 13. 7S
5.56
2,7 16.6
( Kresli.
8
§8 15 p.
ni.
" 1 1""
On ius tn tin
Omitteil on a
illness of
ccount of
the olis
Jlnc-ss 0
(Tver tile leadiniis at 12,
f Sergeaut Dolibius.
5 were d
elayed until 1.27.
J Statiou closed by Uiruutiou of ProtVesor Lan^^ley.
176
KKSEAKOHES ON .SOLAE HEAT.
Takle 117.
Itnhii'lioii (if ml mid dii/ liillh tlarmm
V.T. Latitu.l.', 30-- 34'. Li.li,:;itlia.-, llS ' IS'
llOUXTAIX CAMP.
ldi„u^.
Date.
Local tinw.
Conec
eil Fah
Ifulioit
1 Ked
iceil to Centigrade.
By Sinitlisoniai
tables.
Wind a
ud weather.
1
Dry s. .s.
Wets
s. 1 Dmei-' T.„
■\\'ct.
Differ-
Force of! Dew-
Kelative
No.' .
No. -
-. en
e.
enee.
vapor.
point.
humidity.
1881.
vim
^ Cent
Per ceil!
Ang. 22
12»35»i>.m.
or:'. 5
41=
20^
5 ( IOC
4 5« 0
11 4
2 04
— 10 2
14 7
Fiesli NW
steady clear
22
8 10 p.m.
4C .
37
9
7
8 2 S
. 0
3 06
— 1 0
40 1
I l^'lit NW
^teuU char
23
23
8 16 a. 111.
12 3.1 p.m.
51 .
59 .
li
19
15
0 3 9
10 6
11 1
0 4. — > 7
'1 60 —13 2
12 0
' "'* '' "
23
8 15 p. 11,.
42 .5
33
9
5 5
8 0 0
5 2
2 70 — 6 0
)0 1
1 1
24
8 15 a.m.
49 .
33
16
9
4 0 .6
-1 35 —15 3
15 4
21
21
25
12 35 p m.
S 15 p. m.
59 .
44 .
47 .
41
32
18
12
10
15
3 ■ 0 ! 0
10 0
8 !
2 ns — 7 4
1 08 —10 6
1 47 -14 3
20
26 1
17 0
1
h Ueu
25
12 35 pirn.'
58 .
40
18
14
4 4.4
10 0
2 il — 8 7
19 1
eleai
25
26
» 15 p.m.
8 15 a.m.
41 .
43 .
32
11
11
0
0 -1.1
1 1 0.0
0 1
6 1
2 11 — 9 8
2 34 1 — 8 0
31 .
1
K cl, II
20
12 35 p.m.
54 .
38
10
12
2 1 3.3
H 9
2 31 — V 7
21 >.
1
II
26
27
27
8 15 p.m.
S 15 a. 111.
12 35 p. m.
8 15 p.m.
36 .'
30
37
30
5 12
6
5 4
11
s j — i .1
2 —I'.l
6 9
3 9
S 3
3 i
1 39 —1.0
2 30 — 8 0
3 11 — 5 1
12 1
51 ,
57 8
,
28
8 15 a.m.
12 35 p. m.
41 .
52 .5
30
37
11
6 1 15
11
0,-1 1
4 .-1 . 1
1. 1
8 3
2 11 — 0 8
' 46 1 — 8 0
32 1
24 5
h clear
28
29
20
S 15 p. m.
8 15 a. m.
12 35 p.m.
30 .
44 .5
53 .
28
32
38
8
5 1 12
5 11
9 r~o ii
7 3.0
4 4
8 1
2 38 '— 8 4
2 11 _ 9 v
2 74 — 0 7
44
28 1
JO -
\\ cloir
ilear
l\ cleai
29
8 10 p.m.
36 .
31
5 4
5 2
2—0.3
2 5
d 01 — i 1
30
8 15 a.m.
32
13
7
2 0.0
7 2
1 70 — 11 9
2) b
1 cleai
30
12 35 p. m.
50 '.
39
17
13
3 3.0
9 4
2 36 1 — 8 5
20 '
h clear
30
8 15 p.m.
29
10
3
9 —1 .7
1 b
2 08 —10 0
34 3
1 I
lear
31
8 15 a.m.
37
7
6
7 2 . s
i 9
4 10 1- 1 5
55 s
1 \\
1 i.l\ cleai
31
12 35 p.m.
58 !
39
5 18
5 14
4 4 ..
10 J
2 10 ' - 9 5
17 7
III \ W
1 ih cleii
31
8 15 p. m.
39 .
30
9
3
9 —1.1
5 0
2 48 — 7 9
40 9
< T 1 1
Sopt. 1
8 15 a. 111.
47 . 5
32
15
5 8
6 0.0
8 0
■1 23 1 — 16 4
14 S
1 i_iit ^^^
sf, ^ll^ chai
1
1
'i^ i:::;
50 .5
38 .
40
5 10
13
5 3
0 4.7
3—1.0
S 9
2 87 1 - 6 1
2 17 9 5
24 7
37 3
llesli « s
Calm elt 11
c uly clear
2
8 15 a.m.
44 .
32
' !2
0
7 1 0.0
0 7
1 08 - 10 6
.0 9
Lulit NW
8te idi , cleai
'
tl2 33 p.m.
MOUNT WHITNEY PEAK.
Sept. 2
0 00 p. m.
30 .
9 . - 1 . 1 — 0 . 1 : 5.0 1. 30
-15.8
30-7
rill
,-, NW.,\
ii'iiilile, lair.
9 00 p.m.
Midiii-ht . . .
0 .0 l_ 2 .8 I — 6 .4 3 .0 1 1.03
— 12. 0
45.2
(;..
e. N\V..\
"
■*5 5
IS .
7.5-3.6—7.8 4.2 1.21
— 16.6
34,6
(i.i
.-. NW., \
ilialile clear.
3
3 00 a. m.
4.5,-5.3—7.8 2.5 1.74
— 12 2
56. 9
liii
e, X\\'„i
iiiable clear.
3
6 00 a, m.
22 .
19 .
3 . - 5 .0 —7 .2 ( 1.0 2.13
— 9.7
71.4
G.i
e, NW., \
arialile, cle.ar.
uts on the way to the summit.
HYGROilKTRIO OliSEETATIONS.
177
Unhulwn ofxpc-iiil tn-hourhl nbsi
IStalioii, LoDe I'lue.
rl and (lr;l hiiU, ll„r
I'. D. and ![, I..|
Date.
Local time.
Observer.
Correrted Falirenheit.
Reduced to Centigrade.
By Snii
tllsonian
tables.
".HI:
Wet a.
s. No.
Differ.
Dry.
Wet. »|,«;^-
Force
of va.
Dew-
point.
°C6nt.
Rela-
tive bu-
1881.
1037.
1015.
"JL
por.
mm
raidity.
Pr. ct.
Aug. 15
N0..1I ...
11. L.
80'. 3
61". 0
28°. 3
31". S3
160. 11 1.5^ 72
•5. 24
1.8
15.0
1,";
3 11.111 ...
A. c, n.
89 .8
60 .0
29 .8
32 .11
15 .56 , 16 ..55
-0.8
12.1
15
A. c. n.
82 .8
58 .3
24 .5
28 . 22
14.01 13.01
5. 15
1.6
18.1
15
9 p 111
A. C. 1).
74 .7
53 .4
21 .3
23 .72
11 .89 11 .83
415
-1.4
19.0
15
Miilnii-lit
A. C. D.
67 .7
49 . 6
18 .1
19 .83
9 . 78 10 . 05
3,75
-2.7
21.8
16
3». m ...
H. L,
58 .6
48 .1
10 .5
14 .78
8 . 94 . 5 . 84
5,74
3.1
45.8
l(i
6 a. m ...
A. C, D.
50 . 2
42 .7
7 .5
10 .11
5.91 4.17
4,83
0,7
52. 2
16
A. CD.
79 .3
61 .6
26 . 28 1 1(1 . 44 9 . 84
8.68
6,2
34.1
16
NOOQ
H. L.
84 .8
59 .0
25 is
29 . 33 15 .00 14 . 33
•5, 05
1.3
16.7
16
3i).m....
A. C. D.
88 .0
.59 .5
28 .5
31 . 11 1 15 .28 15 . S3
'4,47
-0.4
13.3
16
6p.m
A. CD.
79 .3
58 .5
20 .8
26 .28 14 .72 U ..i6
0 35
4.6
25.0
16
9p...i
A. C D.
69 .5
68 .5
11 .0
20 .83 1 14 .72 6 .11
9,24
10.1
60.5
10
Miilnight .
A. C D.
62 .1
49 .6
12 .5
10 .72 9 .76 0 .94
5.38
2.2
38.0
17
3a. m?....
A.(^ D.
50 .2
5 .5
10 . 1 1 ! 7 . (10 3 . 05
5.93
3.6
64.0
17
6a. m
A. C I).
49 .7
46 '.2
3 .5
9 . 83 7 , 89 1 . 94
0.92
5.8
76. S
17
9a. m...
A. C. D.
78 .2
58 . 0
20 .2
25 .67 ' 14 .44 11 .23
4.4
25.6
17
Nuon ....
H L.
84 .S
58 .2
26 .6
29 .33 14 .56 14 .77
*4:50
-0.3
14.9
17
Sp.rn ....
A. C. D,
88 .3
60 .1
28 .2
31 .28 15 .61 15 .(i7
•4.84
0.7
14 2
17
6p.m-..-
A.C D.
79 .8
58 .5
21 .3
26 ..50 i 14 .72 11 .84
0.20
4 2
23, 9
17
9p.m
iliduit^ht
A. C D.
62 .1
53 .6
8 .5
16 ,72 1 12 .00 4 .72
7.90
7.9
56.3
17
A. C. D.
57. S
47 .0
10 .8
14 , 33 8 . 33 6 . 110
5.13
1.5
43,3
18
A.C D.
54 .2
43 .7
10 .5
12 .33 ; 6 .50 , 5 .83
4.19
-1.2
39,3
18
6 a! ni . . . . '
A.C D.
52 .7
44 .7
e 0
11 . 50 . 7 . 00 1 4 , 44
5.19
1.7
51,3
18
9 a. m ....
A. C. D.
78 .0
59 .1
18 .9
25 .50 15 .06 ! 10 .50
7.16
6.3
29.4
18
Noou
A. C D.
86 .8
61 .7
25 .1
30 . 44 16 , 50 13 . 94
6.54
5.0
20.3
18
3p III
A.C. D.
89 .8
59 .5
30 .3
32 .11 1 15 .28 ' 16 .83
'3.94
-2.0
11.1
18
6p.m....
A. CD.
70 .8
61 .2
18 .6
26 .,56 10 .22 1 10 .34
8,21
8.4
31.7
18
9p.m ....
MitluigUt .
A. C D.
54 .7
51 .1
3 .0
12 ,61 10 .61 2 .00
8,48
8.8
78,0
18
A. C D.
56 .1
47 .6
8 .5
13 .39 i 8 .67 4 .72
5,94
.3.6
51.9
19
3 a, m..--
A.C D.
51 .7
44 .5
7 .2
10 .94 0 .94 4 .00
.5. 37
2.2
55.3
19
6a. m
A. C. D.
52 .2
44 .7
7 .5
11 .22 7 .06 4 .10
5.34
2.1
53.9
19
9 a. in
A. C. D.
79 .8
61 .1
18 .7
26 ..56 1 16 .17 10 .39
8.14
8.2
31.4
19
Noou
A.C. D.
91 .3
63 .5
27 .8
32 .94
17.50 15.44
•6.61
5.2
17.8
19
3p.TIl
A. C. D.
92 .3
62 .5
29 .8
33 .50
16 .94 16 . 56
•5.55
2.7
14.4
19
6p.m
A. CD.
82 .S
59 .5
23 .3
28 . 22
15.28 12.94
6.02
3.8
21.2
19
9 p. Ml - .
A, 1', 11,
57 .6
53 .6
5 .0
14 .22
11 .44 1 2 .78
8.63
9.1
71.6
19
5Ii.lNi-lil
.\ r 11,
.59 . 2
4S .1
11 .1
15 .11
8.94 6.17
5.34
2.1
41.8
:!0
,\ , 1 11
.50 .2
40 .7
9.5
10 .11
4 . 83 ' 5 . 28
3.67
-3.0
39.6
•Jll
tj a til -
\ I' 11
51 .7
44.7
7 .0
10 . 94
7 . 06 3 . 88
5.48
2.5
56.4
,\ I', I),
80 .0
61 .5
18 .5
26 .67
16 .39 10 . 28
8.39
8.7
32.2
'JO
>;„„ii
A, r, 11,
92 .5
63 .5
29 .0
33 .61
17.50 16.11
•6.26
4 4
16.2
29
3 p. Ill ...
6p.m...-
A, C. 1).
A. C D.
93 .7
82 .1
62 .0
60 .0
31 .7
22 .1
34 .28
27 .83
16.67 17.61
15 .56 1 12 ,27
•4. 75
6.01
0.5
5.2
11.8
23.8
211
9p.m.,..
A. C D.
72 .0
56 . 5
15 .5
22 .22
13.01 8.01
7.01
6 0
35.2
L'»
Midnigbt
A. C D.
67 .8
53 .1
14 .7
19 .89
11 .72 , 8 .17
5,97
3.7
34 6
21
3a. m?....
A. C. D.
58 .6
49 .9
8 .7
14 .78
9 . 94 1 4 . 84
6.58
,5.1
52.5
31
6a. ni
A. C. D.
58 .6
49 ,0
9 .0
14 .78
9 . 78 5 . 00
6.41
4 7
51.1
21
9 a. Ill
A. C D.
81 .8
63 .9
17 .9
27 .67
17 . 72 . 9 . 95
9.75
10.9
35.3
21
Nuim
H. L.
91 .8
63 .0
28 .8
33 .22
17.22 10.00
•6.07
3.9
16.0
21
3 p. Ill
A. 0. D.
91 .3
S3 .3
28 .0
32 . 94
17.39 15,55
•6.46
4 8
17.4
21
6p.m ....
A. CD.
85 .3
61 .5
23 .8
29 .61
16 ,39 13 ,22
0,82
5,6
22.1
21
9p.m
n. L.
72 .2
57 .5
14 .7
22 .33
14 . 17 8 . 16
7.70
7.4
38.4
21
llidniglitt
aVc. b.
'58 '.'6
Sl.'i
■■■„-i-
....
14 .78
■-■--
io'.'re' "i'.'iio'
"'^:i2
"m.'o"
22
6a. m
A. C D.
53 .7
46 .6
7 :;
12 .06
8.11 3.95
6 01
3.8
57.1
22
9 a. ill
A. C. D.
80 .8
63 .0
17 .8
27 .11
17 .22 9 .89
9 33
10,3
3.5.0
22
Noou
H. L.
90 .3
63 .0
27 .3
32 .30
17.22 15.17
•6. 52
5 0
18.1
22
3p.m ...
A. C D.
92 .3
61 .1
31 .2
33 . .50
16 .17 17 . 33
•4,43
-0,5
11.5
22
6p.m
A. C D.
81 .3
60 .0
21 .3
27 . 39
15.56 11.83
6,84
5,7
25.2
22
9p.ni
A. CD.
56 .7
51 .6
5 .1
10 . 89 1 2 . S3
8,19
8,3
70.1
22
Midniglit .
A. C. D.
58.2
51 .6
0 .6
14 !56
10 .89 1 3. 07
7.70
7,5
62.7
23
3 a. in
A. C D.
56 . 7
50 .1
6 .6
13 . 72
10 . 06 3 . 66
7.27
6,6
62.2
23
6 a. ni
A.C D.
55 .2
47 .6
7 .6
12 .89
8 . 67 ; 4 . 22
0.20
4 2
55.9
2S
9 a. m ....
A. C D.
80 .0
62 .5
17 .5
26 .67
16.94 9.73
9.19
10.0
35.3
23
Noon
H. L.
89 .0
62 .0
27 .6
32 .00
10 .67 15 .33
'.5. 95
3.6
16.8
23
3p.Ti
A. CD.
92 .2
60 .5
31 .7
33 .44
15 .83 ; 17 .01
■3. 97
-2.0
10.4
23
6p.m
A. C D.
80 .8
57 .0
23 .8
27 .11
13 .89 1 13 .22
4 70
0.5
17.9
23
9p.oi
A. C. D.
66 .7
53 .2
13 .5
19 .28
11 . .78 7 . 50
6 38
4.7
38.3
23
Midniglit
H. L.
59 .1
50 .9
8 .2
15 .06
10 .50 4 . 56
7.51
7.0
58.7
24
3 a m
H. L.
55 .7
48 .1
7 .6
13 . 17 8 . 94 4 . 23
6.35
4 6
56.1
6 a. ni
A. C D.
52 .6
48 .6
4 .0
11.44 9.22 2.22
7.54
7.1
75.0
24
9a. m.-..
A.C. D.
81 .5
59 .0
22.5
27 .50 15 . 00 12 . 50
6.04
3.9
22.1
24
noon
U. L.
88 .6
61 .0
27 .6
31 .44 16 .11 15 .33
•5.45
2.4
16.0
24
3p.m ....
H. L.
90 .6
61 .0
29.6
32 .56 10 .11 , 16 .45
•4.87
0.8
13.3
24
6p.m
A. C D.
81 .8
57 .0
24 .8
27 .67 13 .89 1 13 .78
4.47
-0.4
16.2
24
9p.m ....
A. C D.
67 . 2
51 .3
15 .9
19 . 56 10 . 72 8 . 84
4 93
1.0
29.0
24
Midniglit .
A.C D
53 .2
46 .0
6 .6
11 .78 8 .11 3 .67
6.16
41
59.7
25
3a.m....
A. C D.
M .2
44 .2
10 .0
12 . 33 : 6 . 78 5 . 55
4 49
-0.3
42.1
25
6a. m...
A. C. D.
52 .0
43 .6
8 .4
11 .11 1 6 .44 4 .67
4.78
0.5
48.3
25
9a.m....
A. CD.
79 .3
59 .3
20 .0
26 .28 1 15 .17 11 .11
6 92
5.8
27.2
25
Noon ....
H. L.
83 .6
58 .8
24 .8
28 . 67
14 .89 13 .78
5,29
2.0
18.1
25
3p.m....
U. L.
88 .2
59 .5
28 .7
31 .22
15.28 15.94
•4,42
-0.5
13.1
25
6p.m ...
A.C. D.
74 .2
64 .0
10 .2
23 .44
17. 7S 5.06
13.10
14 2
56.5;
25
9i,.m....
Midniglit
A. CD.
68 .2
52 .1
16 .1
20 .11
11 . 17 8 . 94
.5.16
1.7
29.6
25
A. C D.
63 .6
48 .1
15 .5
17 .56
8 . 94 8 . 02
4.04
— 1.7
27.0
26
3a. m-...
A. C D.
50 .7
44 .2
6 .5
10 .39
6.78 3.61
5.49
2.5
58.2
12535— No. XV-
-23
178
RESEARCHES ON SOLAR HEAT.
Table 148 — Continued.
Reduction of special in-hourly observations of wet and dry hitlb tlicrmometers
[Station, Lone Pinu. Oteervers, A. C. D. anil H.L.]
r LaDgley, dated September 3, 1661.
HYGROMETRIC OBSERVATIONS.
179
ry of sptciiil tri-hoiirftj '>l»i
Table 14i>.
rutimiH of force of aqueous vapor at Litue Fine, showing dim-
DfttL'.
3 a. m.
6 a. ni.
9a. n,.
Xoon.
3 p.m.
6 p.m.
9 p.m.
Mid.
ni,..
18S1.
mm.
mm.
mm.
mm.
mm.
mm.
mm
4.15
16
5.74
4.83
8.68
5.05
4.47
6.35
9.24
5,38
17
,1.93
6.92
6.28
4.50
4. 84
6.20
7.96
5,13
18
4.19
.5.19
7.16
0.54
3.94
8.21
8.48
5,94
19
5.37
5.34
8.14
6.61
5. 55
6.02
8.63
5, 34
20
5.48
8.39
6.26
4.75
6.61
7.01
5.97
21
6..i8
6.41
9.75
6,07
6.46
6.82
7.70
22
7.52
6.01
9.33
6. .52
4.43
6.84
8.19
7.76 i
23
7.27
6.20
9.19
5.95
3.97
4.76
6.38
7.51
24
r,. 35
7.54
6.04
5.45
■ 4.87
4.47
4.93
6.10
25
4.49
4.78
6.92
5.29
4.42
(12.10)*
5.18
4.04
26
5.49
4.92
8.28
3. 45
3.10
3.34
4.63
2.41
27
3.06
3.08
4.32
3.21
4.62
9.54
6.48
5,42
28
4.20
6.66
4.92
4. .33
5.76
0.49
4,14
29
5.06
4.41
6.54
4.14
S.32
(10.78)*
3.63
2,98
30
3.28
3.94
6.62
6.85
4.26
5.32
5.97
6,10
31
4.62
4.43
6.16
4.83
3.81
9.25
5.51
6,13
Sept. 1
4. 29
3.90
4.16
5.65
4.13
9.94
7.51
3.97
4.38
4.07
7.41
3.30
3.29
5.65
3.36
3
2.28
4.33
2.81
2.70
3.19
3.08
2,44
2.45 j
4
3.83
2.98
3.82
4.30
3.86
2.36
3,39
5
5.40
5.49
6.09
6.24
6.51
1
Me.in. .
4.94
4.98
6.80
5.14
4.34
6.09
6.06
4,94 [
<•!/ of Special tri-hotirJi/ i
* Rejected.
Table 149a.
rvations of relative humidity at Lone Pine showing diurna! i
D.lte.
3 a.m.
6 a, m.
9 a.m.
^'oon.
3 p.m.
6 p.m.
9p, ra.
Mid-
night.
1881.
Per ct.
Perct.
Per ct.
Per et.
Per ct.
Per ct.
Per ct.
Per ct.
16
45.8
52,2
34,1
16.7
13.3
25,0
50.5
38.0
17
64.0
76,8
25,6
14,9
14.2
23,9
56,3
42.3
18
39,3
51,3
29,4
20,3
11.1
31,7
78.0
51,9
19
55,3
53.9
31,4
17,8
14.4
21,2
71.5
41,8
20
39,6
56.4
32,2
16,2
11.8
23,8
35,2
34.6
21
52,5
51.1
35,3
16,0
17.4
2'* 1
38.4
22
60,0
57.1
35,0
18,1
11.5
25.2
70,1
62.7
23
62,2
55.9
35,3
16,8
10,4
17.9
38,3
58,7
24
56,1
75.0
22,1
16,0
13,3
16.2
29,0
59,7
25
42,1
48.3
27.2
18.1
13,1
•56.5
29,6
27,0
26
58,2
50 7
33.5
10.3
9,5
12,8
28,8
15,3
27
24,9
26,9
24,8
13.3
17,0
61,7
68,0
61.8
28
49.8
35,6
17,7
14,5
25,1
52,4
38,6
29
65,8
50.0
32,0
15,6
11.2
♦64.5
23,3
18,2
30
26,0
33.7
35,5
26,3
15.1
27.9
53,1
68,3
31
54.1
59.4
29,1
17,2
12.9
55.2
45.7
74.2
Sept. 1
48,9
4,5,6
19,7
19,5
12.9
59,3
56.6
27.5
46,9
48,4
32,0
9.9
9.3
30,3
17,0
17.5
3
4
12,4
25.9
27.0
21.1
11,4
20 5
8.7
17,8
10 6
14,6
15,0
10.1
13,5
16,6
17.3
5
Mean ...
49.7
46.5
42,4
49.2
28,0
29,0
22,0
lefe^
13.3
27,5
42.4
40.9
nury of psyrhromttrr detfi
* These observations are rejected.
Table 150.
litions of force of aqueou.^ vapor at Lone Pine .^hon-ine/ infln
of wind.
Calm.
Light.
Gentle.
Fresh.
Brisk. 1 Gale.
9.46
13.28
16. 05
11,61
9.98
7,32
8.39
5.-33
5, 46
.5.70
9, 20'
9,22
9,24
8,50
5,03
6,43
6.27
7.15
6.48
7.85
12. 38
10 89
13.96
10,06
13.00
4,99
7,96
7.43
7,72
4,89
8,01
7.80
8,02
8,09
4,79
8. 83' 7. 08
6. 52 6. 30
5. 04 6. 00
6. 71 4. 78
4. 59 5. 34
5. 76 5, 08
8, 28 6, 63
4. 58 4. 65
4. 52 6. 30
4, 79 6. 06
6. 11 , 4. 43
5. 07 6. 30
7. 12 ; 4. 08
4.27 1 4.98
5.58
12.20 3.30'
4.71 1 p. 72
5.94 1 4.14
4.13
5.62 1
4,89
4,48 1
3,83
3. 69
5.72 '
6.52
6.87 1
7,81
3, 50
2.89
5.59
4.81
4. 84 ; 3. 39
Mean, 8, 39 7. 54
8,54 ' 5,72
ceptiijlewind"; lijht inilicatea a velne
indicates a Telocity of more th lu 2t mil.
refers to velocity and not to direction.
180
RESEAKCHES ON SOLAR HEAT.
It is impossible to estimate how far the apparent reduction ot atmospheric moisture with in-
creasing wind, shown in Table 150, may be due to the influence of air currents about tlie instru-
ment, and how far it may lie owing to the coming of the ordinary winds from a very dry (jnarter,
since there was no record l;cpt of the direction of the wind at Lone Pine.
Table 151.
Suiiimniii of ohsm-atioiis of almusphcric muisliire maih at thr Moiinluin Camp.
Date.
Force of vapor.
KelatiTe Immulity.
SMS'-a.m. 1 12'35"p.m. 1 8»15" p. m.
845" a.m.
12'35"'p.m. , 8'15"p.ni.
1881.
Aug. 22
24
25
26
27
30
31
Sc-pt. 1
Me-ln...
3.60
2.75
1.98
2.11
1.39
3.11
2.38
3.63
2.08
2.48
2.17
Per cent.
Percent. Percent.
0. 42 ! 1. GO
1. 35 2. 5S
1. 47 2. 32
2.34 1 2.31
2. 88 2. 36
2.11 2.46
2. 11 2. 74
1. 79 ' 2. 36
4. 10 2. 16
1. 23 , 2. 87
4.4
15.4
17.9
33.2
51.3
32.3
28.3
23.6
55.8
14.8
12.6
20.3
19.0
21.8
23.8
24.5
26.7
20.7
17.7
24.7
39.9
26.9
32.3
22.1
57.8
44.3
67.5
34.3
40.9
37.3
1. 98 2. 35
2. 62 1 27. 6
20.6
40.9
Table 152.
Effect of tvin-d npou the force of vapor observed with the psychrotncter npo7i the ynouutaln.
[Station, Mount Whitney Camp. Date, from August 22 to September 2, 1881. Observer, J. J. N.]
Variation witli velocity of wind.
Variation with direction of wind.
Calm. j Light. ^ Gentle.
Fresh.
Gale,
N. KW. W. 1 SE.
E.
2. li
3.63
2.48
2.17
3.66
0.42
1.60"
3.75
1.35
1.93
1.47
2.34
1.39
2.88
3.11
2.11
2.38
1.79
2.08
4.10
2.16-
1.23
1.98
2. 46"
2.11
2. 04"
2.58"
2.32"
2.31"
2, 36"
2-36"
2,87"
2.32
2.11
2.03
mm.
2.04
3.66
2.58
1.98
1.47
2.34
2.31
1,39
2,88
2.36
3,11
2.46
2.38
2.74
1.79
2.36
4.10
2.16
1.23
1.98
2.87
0.42
1.60
2.75
1.35
2.11
Mean, 2. 60 ' 2. 15 2. 29
1
2,45
2.17
2.37
2.87
1.59
1.73
Though the psychrometer observations at Lone Pine were sutficieut, those on the mountain
which are grouped togetlier in Table 1.52, are too few, and the results too unequally distributed, to
base any conclusions upon tliem as to the influence of wind upon the psychrometer. The most
tliat can l)e said is this :
Tlie Jlount AVliitncy station was at the bottom of an immense amphitheater of rock, rising
to tlic lii'ight of l,i;(lii feet on the east, on the north, and on the south, and only open on the west.
A glance at the map and frontispiece will enable the reader to realize the influence which these
surroundings must have exerted upon the direction of the wind. At the mouutain camp, west of
the summit of Mount Whitney, during the latter part of August, 1881, northwest winds prevailed,
being generally light, of a force not exceeding " fresh," the strongest winds blowing always in the
middle of the day, as may be seen from the table, where the noon observations are marked with a
small n. It is probable that the large surface of I'ock, strongly heated by the sun, produced a
-^"3^ ^"S-' ''"9^ ^^S'' Aav7 ^ua,.IS Augl'j Auj20 Aaj 2
,
--
.4
1 ^
]
AA
A
/
11
1 1
\7\
\ I.^f 7,,,
Uij.ll Auj.12 /\u^2i Au^.l4
Sijii i Sept 4. iiepi.5 iapt fe Stpt- 7
ITYGROMRTRIC OBSERVATIONS.
181
powerful indraught towanls the summit of the mountain at miil-day. On the few occasions when
southeast winds blew they seem to have been drier than those from tlie nortliwest.
It will be seen by an inspection of tlie tables and of the corresponding curves (Plate XV'I),
that the force of water vapor on the mountain usually increases during the day. Apparentlv
after sundown it begins to decrease, and has ordinarily fallen somewhat by the time of the eveniu"
observation at 8.1."> ]i. m.
The relative humidity is lowest at the noon observation ;inil liigliest in the evening. Xo
observations were made before sunrise at tlie mountain camp, but the tri-hourly readings durino-
a single night at the peak showed the highest relative humidity in the early morning. The curves
of relative humidity (Fig. 15) at the upper and lower stations are in toleral>ly close agreement
both as to form and numerical vahie : but tht> dhsnliite humidity, or fence of vapor, is totally
different in amount and in the law of its variatidu at the two stations.
D.ui-nal Variation of Relative Humidity.
A
^'.\.
^ .1
o" If
Auj.7 Au^S. Aujl Au^ 10. AutjII Au^ It Auij.lJ Auij I'r Au^'S Aulcj lb Aiuf n , Au<j. I S Au(jlf Au.ij.lO Au
A«jZI _Au.<^U' /Iwj 23 Aiuj.li, Aaj.ZJ
Sift k Si.pt J
plate xvi.
Hygrometer Curves for Lone Pine, and Mt. Whitney.
n yCtROMEtric observation s.
181
powerful indraugbt towards the summit of the mountain at mid-day. On the few occasions when
southeast winds blow they seem to have been drier than those from tlie nortliwest.
It will be seen by an inspection of the tables and of the coiTespondiiifr curves (Plate XVI),
that the force of water vapor on the mountain usually increases during the day. Apparently,
after sundown it begins to decrease, and has ordinarily fallen somewhat by the time of the evening
observation at 8.15 ]■. m.
The relative humidity isi lowest at tlie noon observation and higliest in tlie evening. No
observations were made before sunrise at tlie mountain camp, but the tri-iiourly readings during
a single night at the pealc showed the highest relative humidity in the early morning. Tlie curvi's
of relative humidity (Fig. 15) at the iqiper and lower stations are in tolerably close agreement,
both as to form and numerical value ; lint the tthsnlute humidity, or force of vapor, is totally
different in amount and in the law of its variation at the two station.s.
/
/'
\
n
^
\
j
\
\\
X
1
1
1
1
1
1/1.
Diurnal Variation of Relative Humidity.
182
EESEAEOHES ON SOLAE HEAT.
Attention is particularly called to the curve showing diurnal variation of moisture at Lone
Pine (Fig. 16). It is the result of tri-hourly ob.servations which, individually considered, are fairly
concordaut, and which extend over a period of three weeks, sattieient, it is imagined, to eliminate
all abnormal variations. The curve should also be compared with that for each day (Plate XVI).
It will be seen that during the night, from midnight to sunrise, the force of vapor remains nearly
constant. Vpon the rising of the sun it rapidly increases, usually attaining its greatest develop-
ment about '.> a. m., after which it diminishes until the middle of the afternoon, becoming smallest
at the hottest hour of the day. The moisture after this time progressively increases, reaching a
second maximum after sundown, and then decreases again until midnight.
The curve, which is entirely different from the diurnal variation ob-served at sea or in moist
climates, is confirmatory of the results obtained by other observers in hot and dry climates, and
may be considered characteristic of such.*
Quite different is the curve of absolute humidity at the mountain station, which exhibits a
continual rise during the hours of sunshine, if we may be permitted to draw conclusions from
J--i^. 16
/
r-\
]
Zone .
"irve.l
\
■
y^ Ml
Camp.
-
N^
"
noon:
Dal Variation of Tension of Aqa
'Compare Blanford, " Indian Meteorologist's Vade-Mecum," page 110, where a very prob.able explanation of
this effect is given. Quoted in this report, page_186.
! ^ri
1
//
//
///
/
7//|
// /
/ /
/ /
^
-/-/
/ /
^^..^
^ /
/
^___,---
^^^---''^
r %y
^
/^^ _
" ''
^^
^^-^
^/
s,,e . s^^s.iiy
nYGKOMETRIO OBSERVATIONS. 183
tbe comparatively small number of observations at our disposal. This result is probably to be
explaiuetl by the transference of water vapoi' from the lower regions of the atmosphere to the
higher by difiusiou and convection — motions which are largely produced by the heating eft'ect of
the solar rays. If the relative humidity of the upper air does not also increase, it is because the
source of supply at the surface of the desert plains is too limited to counteract the very great
increment in the capacity of the air for retaining moisture, produced by its rapid rise of tempera-
ture. It will be noticed that the ranye of variation of relative humidity is smaller at the upper
station than at the lower. In a moister climate this midday decrement of relative humidity at
high altitudes tends to disappear, and may even be changed to an increment. The tendency to
increased cloudforniation and rainfall in the afternoon has been noted by many meteorologists.
It, no doubt, indicates a corresponding law of diurnal variation in the relative humidity of the
cloud-bearing layers of the atmosphere. That no such law was observed on Jlount Whitney is
again to be attributed to the extraordinary dryness of the climate. The transference of moisture
from the lower layers of the atmosphere to the higher by diffusion and convection, which, in a
nearly saturated atmospLiere, might produce cloud and i)recipitatiou, is here powerless to effect
more than a slight lessening of the desiccation produced by the midday suu. It is worthy of
note that, during the latter part of August and early in September, no such thing as a cloud-
bearing stratum of air appears to have existed at any altitude. With the exception of smoke from
forest fires, not the slightest visual obscuration of the sky could be detected. This tact is of
importance in any estimation of the probable (piantity of water existing as vapor in the atmos-
phere above Mount Whitney; for, since the air-layer between Lone Pine and Mount Whitney is
but one-fourth of the entire air-mass above the lower station, we remain in comparative ignorance
of the hygrometric CDuditiou of the larger part of the atmosphere. It is couceivable, therefore,
that a layer of moist air might exist, unknown to us, superposed on the dry one; but when we
know that for weeks not even the faintest streak of cirrus was visible, such .an assumption appears
most improbable, and we are justified in expecting a comparatively regular decrease of moisture
with the increa.se of altitude. I have endeavored, on this hypothesis, to obtain an approximate
notion of the amount of water contained in the air above Lone Pine and Mount Whitney at the
time when observations of atmospheric transmission were being made with the spectro-bolometer.
It will be .seen by reference to Plate XVI that the atmospheric conditions were quite dift'erent at
these two ejiochs. From August 5 to 14 a moist atmosphere prevailed. Clouds, and even a few
drops of rain, were formed at Lone Pine, where, from the average of observations at noon on
August 11, 12, and 14, the weight of vapor per cubic meter of air may be assumed equal to 10. 4S
gramuies.
The greatest dryue.ss occurred from .Septembi'r 2 to 1. During the bolometric observations
on Mount Whitney of Sejitember 2 and .'! the average weight of vapor jier cubic meter at noon
was 2.0."> grammes. Synchronous midday comparisons from August 22 to September 1 showed
that the force of vapor at Lone Pine was usually about 2.2 times as great as at the lower camp,
Mount Whitney. With these data the curves in Plate XVII were drawn, in which abscissa; repre-
sent altitudes, and the ordiuates give the probable weight of vapor in grams per cubic meter at
each altitude up to the height where the curves coincide with the axis (at about 20 kilometers) for
the two epochs.* The areas included between the curves and the ordiuates at any two altitudes
are, then, proportional to the total moisture in the included atmospheric layers.
The uiost common way of expressing the amount of water vapor in the atmosphere is to state
the pressure which it wcuild exert upon a barometric column. As thus determined at a particular
point in the atmosiihere, it is independent of the quantity present in higher or lower strata. If,
therefore, we would know the total quantity of water vapor in the atmosphere, it is necessary to
* It is believed th.at the allo\T.aiiee made for water vapor in the hi<:;lier atmosphere is not excessive, as a very
nmeb slower decrement has been observed on sever.al oceasions by Glaisher in his balloon ascents. For example, in
that of .July 17, 186'i, Glaisher found a dew-j>oint of 24^ Fahr., corresponding to a force of vapor of 3.'.i7 mm. at a
height of 11 kilometers, the dew-point at the surface of the ground being 'a" Fahr. and the force of vapor 11.00 mm.
In this instance, a current of warm moist air was superposed over a cold one, and for a short space the usual decre-
ment was reversed, but there is reason to believe that this condition is not very unusual. The distribution of moist-
ure during the Mount Whitney observations, however, was probably more nearly like that found by Glaisher in his
third ascent September 5, 1862. (.See "Report of the British Association for the Advancement of Science'' for 1862,
pages 463 and 468.)
184
RBSEAECHES ON SOLAR HEAT.
make some assmnptiou as to its distribution, which has been done iu the altove instances by
assuming all moisture to cease at a height of UO kilometers, and drawing smooth curves through
the points of observation. The quantity of water present in the form of vapor in a layer of air of
a given thickness can be best expressed by stating the depth of liquid water which would result
from its condensation; and since a stratum of air 1 kilometer thick, containing, on an average, 1
gramme of water vapor per cubic meter, would give a liquid layer 1 mm. deep, if the water were all
condensed, we may conveniently take this quantity as our unit.
Calling /('" the height above sea-level at which water vapor practically ceases (say, 20 kilometers),
h" the height above sea-level of the upper station (Mountain Camp),
h' the height above sea-level of the lower station ( Loue Pine),
w the average weight, in grammes, of water vapor per cubic meter = millimeters of water
capable of being precipitated from a layer 1 kilometer thick,
we haxe, approximately,
Liquid layer from atmosphere above Lone Pine = »■' (h'" — h')
Liquid layer from atmosphere above Jlountain Camp = «•" (/('" — k")
These quantities, as graphically determined by the method just described, are as follows:
Above Lone Pine, August 11 to 14 w' (h'" — h' ) = 30.G mm. precipitable water.
Above Mount Whitnej* Camp, September 2 to 3, w" {h'" — li") = 0.0 mm. pi-ecipitable water.
THE CONNECTION BETWEEN ATMOSPHERIC MOISTUKE AND GENERAL SELECTIVE ABSORPTION.*
We are led to believe that water vapor is an etMcient agent in modifying the solar radiation
by three classes of observation :
First, by comparisons of observations at different seasons.
Second, by comparisons of observations at dift'erent hours of the day.
Third, by comparisons of observations at dilferent altitudes above the sea-level.
As an instance of the first, we take observations already made at Allegheny.
When we compare observations made in the winter with those of the spring, the sun being at
the same altitude and the air-masses the same, we find certain rays most absorbed when the
moisture is greatest. Apparently, therefore, these rays are especially cut off by the absorption
of water vapor or by the action of some substance whose amount varies synchronously with the
atmospheric moisture and in nearly the same proportion ; or, what is exceedingly improbable, the
composition of the solar radiation which we receive is itself variable within notable limits. The
last hypothesis may be dismissed without further consideration, and we shall, for the sake of illus-
tration and in this pi-eliminm-ii consideration mercli/, assume that this part of the atmospheric
absorption, which exhibits a seasonal variation, is directly produced by water vapor, and that the
law of extinction for this substance is the same as that deducible from Melloni's experiments on
the transmission of lamp-radiation by liquid water. (See " La Thermochrose," Table IV, pp. 200,
207.) By applying to Melloni's figures a modification of Bouguer's formula for transmission,
y = 2''i '" which p still denotes the transmission by a layer having a thickness of unit}-, but in
which X, instead tif representing the number of such layers, is some function of the thickness, the
following values of the exponents are obtained:
Table 153.
Thickness
1
2
3 j 4 1 5
6 j 7
8 j 9 10
50
100
ExponeDta
1.00
I.IG
1. 26 1, 34
1.40
1.46 1.51
1. 56 1. 60 1. 63
2.27
2.64
' We here use tlie word absorption in its most general sense, ami intend it, in the absence of a better word, to
cover every process of retlection, ditfusion, or other interruption, by which the ray is hindered on its passage to us.
Messrs. Lecher & Pernter assert tliat absorption of heat by our atmosphere is chiefly due to carbonic acid associated
■with the vapor of water, and not to the pure vapor itself. For our present purpose, we are not called on to aifirm or
deny their statement ; for, by vapor of water, in atmospheric moisture, we here mean, it will be noticed, that whatever
is at all times and places .associated in nature with water vapor and varies synchronously with it (if there be such
association), shall be held to be water vapor in our present sense.
HYGEOMETRIC OBSERVATIONS.
185
A very similar law of extiuctiou is (leiliu'ible from Melloni's oliservations on tlic trausiuissioii
of lamp-radiation by rocU-crystal, glass, and otlier substances: ami altl](m^;li it would be desirable
to repeat his experiments with homooeiiiMius and solar radiations, and tnl)es Hlled with water
vapor, these numliers will, nevertheless, serve to illustrate the mi-tliod. whieh is now merely a
tentative one.
Let the eoetlieient of transmissiini ot homogeneous rays, of wa\e len;;th /,, by 1 kilometer of
water vapor at an a\cra;;e density su<'h that 1 eubio meter shall contain I ,:;raiiiiiie of water, be
denoted by TI'a ; /( bein^' the height of statiim above sea level in kiloaieters ; /('" the height above
sea-level (in kilometers) at which water vapor practically ceases; ir„ the depth of water (in milli-
meters) ca[)able of being precipitated from a layer one kilometer thick, at the avera.ij
the air-columu between h and h'" in wintiT; ir,, the cnrresponding depth in spring:
sun's zenith distances at these seasons
bv the ratio of galvanometer detlection
Then the seasonal change of tiansimssidn
spring {d;)
humidity ot
ind :, :„ the
represented
winter [di)
if due to uneipial prevalence of water vapor, may be expressed b.v
Ij- ,|.H[ic, I*" --M.sec!(;„]-(*.[ii',(A'"-'i)aeCil
or ( U\), raised tn a piiwer whosi- exponent is the ditlereiice lietween ct
titles in brackets, which are here taken from the above table (iyA>.
eft'ects produced by other atmospheric absorbents, which vary as tie
combine measures made at nearly the same zenith distance, or fur « liii
possible identical. Hence we select spring observations, made when tli
the meridian, for comparison with winter ones taken at niMin. Also, mi
rtain functions of the ipiaii-
lii order to eliminate the
■ air mass, it is desirabh- to
h :, and ;„ ale as nearly as
e sun was ;it a distance from
ice till' earth's distance from
the sun has changed considerably in the interval, a correction must be aiiplied to eliminate the
etlect of this variation, which is here accomplished by reduction to the earth's mean distance {ij=l).
We have the following data : Winter of 1881, average ^, = .57° Ol" ; sec :, = 1.84. Spring of
1881, average ;„=56° 13'; sec r„ = 1.8(). Average force of vapor (winter) = L' mm.; spring=8 mm.
Average weight of vapor per cubic meter (winter) = L'.liO grammes: sjning = S.l'.'i grammes.
Average depth of precipitable water (winter) = 7.3 mm. ; spring = -(i.3 mm.
The dejiths of [irecipitable water have been obtained by measuring the areas of the curves in
I'late XVII, which involve assumidions as to the distribution of moisture in the upper air, which
have already been alluded to.
The formula by which coefficients of transmission have been calculated, are
ir, "" (by Table l.-i.i)
= ir -'^(by Table 1.13)
aud
(ir,)""* ^ ^, n,M ^ (/..(spring)
(ir )' '" * //, (winter)
Winter of 1881, ( 11',
Spring of 1881, ( W,
■!■) (-je 3 .
Table I'A.
■ pr„hahl!i ,
cird
ilh ulmosphf'
Winter re-
Sprin" re-
A
Winter ii.
Spring dt.
duced to
P = l-
diu-ed to
P=l.
.375
1U2. G
71.5
187.5
72 5
.17
.400
.363. 4
119.8
353. 9
121.4
.14
.450
579.3
275.6
564-1
279. 6
.27
.500
767.9
369.1
747.8
374.3
.28
.600
724.9
439.0
705. 8
445.2
■43
.700
527.9
433.9
514.0
440.0
.75
.800
338.3
298.5
329.5
302.7
.85
.900
21.1. 4
191.4
209.7
194.2
.87
1.000
173.6
166.4
169.0
168.9
1.00
I table is giTeii iu onioi
on of solar radiation.
13535— No. XV-
■ide for himself how far atu
186 RESEARCHES ON SOLAR HEAT.
The al»i\(' valiiL's of an atmospheric absorption, (lt!))eiRleiit in some way upon water vapor,
iMiiiKit lie 11 i^ardc'd as possessing au absolute signiflcauee; but there seems hardlj' room to doulit
(if I he I'xlsinici' of such an absorption, or of the fact that it increases progressively from wave-
leu.ytli l."(t to (I." 1.
SiM'diidly, we liiid (in c(im[iariMg- actinometer ol)servati(nis maile in the morning and afternoon
with ecjual altitudes of tlu' sun, and hence witli nearly iMiual air-masses, that the measured radi-
ation is greatest when there is least moisture.
The very numerous Allegheny observations taken with the same altitude of sun (morning and
afternodu) are incdnclusive on this sjiecial point, owing tn the great irregularities of its sky. The
independent (ines in the clear atiiLOSphere of Lone I'ine and Monnt Whitney agree in showing
that, for the same altitude of the sun and the same air-mass traversed, the total heat absorption,
as indicated liy the actiuometer, increases with the amount of water vapor in the atr. (The ex-
tremely minute barometrical change between morning and afternoon evidently cannot account for
the efiect.)
The low relati\e humidity of the desert elinmte ami the almost complete absence of haze or
cloudiness ai all hours of the day render these observations uncommonly well fitted to decide the
((uestion as Id the iiitluenee of the absolute humidity upon atmospheric absorption, siuce they are
freed from all eoiii|ilications which the capricious skies of nniister climates introduce. It must,
howe\ er, lie reiiicmliered that we are here concerned with the entire ipiantity of nxiisture con-
tained in the atmosidiere above the place of observation.
Both at I.due I'ine and Mount Whitney the morning readings with the actinometer sui'i)assed
tliiise taken in the afternoon with the same altitude of the sun (see Fig. 11). The di.screpauey
was, hdwever, relatively greater for the mouutain observations. The same thing has been noticed
by other observers, and it is presumed that the effect is due td the increase of the absolute
([uantity (if moisture ii] the upper atmosi)here, produced by evajioration at the earth's surface
with subse(|ueiit ascension of the water vapor by diifusidii or convection currents, an increase
which goes on as long as the sun shines.
At the earth's surface the law of diurnal variation of atmospheric moisture is dift'erent for
land and sea, and is atfeeted by various local causes. Thus on the arid desert around Loue Pine
the vapor tension rises for the tirst hours of the forenoon, attaining a maximum at about 9 a. m. It
then decreases until the liottest part of the afieruoon (about 3 p. m.), after which it again increases
until sundown. 1 )uring the night the water vapor decreases until midnight, after which it remains
constant until the rising of the sun again .sets in action the process of distillation and difl'usiou.
This diurnal variation is characteristic of au arid climate on the ])lains, and, according to Blauford
("The Indian Metcdnilogist's Yade-Mecum," p. 110), "it probably depends on the ratio between
the rate of p odiictini of vapor on the one hand and its rate of removal on the other; the rate ot
diffusion \aries as the square of the ab.solute temperature, ami therefore by dift'usion alone the
removal ni vapor will be accelerated, at least in that proportion as the temperature rises; while
from a dry land surface, with little vegetation, the iiroduction of vapor may not increase even
directly as the tem|ier.ittire: nay, nmy even fall alter the nnire superficial moisture has been dissi-
pated."
In the upper atmosphere, on the other hand, there is usually a gradual increase of moisture
during the day, as is evident from Table 151 and an insiiectiou of the lower curve, Fig. 10, showing
force of vapor on Mount Whitney. "That the humidity of the cloud-forming strata of the atmos-
phere and in all probability the ten,sion of vapor at comparatively moderate heights do not follow
the same law of diurnal variation as in that stratum which rests immediately on the earth's
surface, may lie inferred conclusively from the ob.served diurnal variation of the cloud projiortion
and of the IVe(ineiicy of rainfall." (Ibid, p. 110.)
At Calciilta rainfall is most freiiuent from 1 to ^i p. m. Loomis "found a decided diurnal
ine((iiality in the rainfall at I'hiladelphia. showing a uuixnnnm about t! p. m." (American Journal
of Science, vol. CX I, p. 7.) He (|Uotes from Kreil the results of ten yeans' observations at Prague,
showing a maximum about 4 p. m.
The psychionieter ob.servations on Mount Whitney were not sufficiently numerous to gi>'e any
very reliable inforuuition concerning the diurnal variation of moisture at that high altitude; but,
so far as they go, they indicate an increase of water vapor throughout the day.
nYOKO:V[ETRI(' OBSERVATIOyS. 187
If tlie want of syuunetry lictwcm tbi- twn halves ul' a liiiiriial ciirxe ol' ladiafion is fbiis diir
to the increase of moistiiic in the iipiicr air willi the hour of the day, it should nearly disaiiprar
in the cold winter weather when tin- alisdlute i|iiantity of Tuoistiire heeoiues minute, and the e\ ap
orating power of the sun is diminished. This is what M. Crova has found. He says:
'•Dnring tin/ winter beautiful days may lie encountered at Monlpellier. in whiidi a series ol
o!)ser\'ations can lie eontinued under u^xnl eoudilions from nioruiuu' toeveninu: " * " in these
eases the horary curves of calories may piesenl a symaielrx so neaily eimiplete that we may, with-
out sensible error, consider it as peifeet."
On the other hand, thi' al st constant character for summer da\s. he says, is a want ..f s\ni-
metry. The cairvi's are '■ hardly ever symnudrieal witli relation to tin' <udinate which passes
through true solar noon; they are ,i:enerally more regular after noon than in the iLnnniui;; the
nm.ximum is attaiiu'd bef(Me midday, and the tangent at true solar noon inclines Inward the after-
noon." ("Mesure lie I'intensitc' caloritii|ne des radiatioirs .solaires." |i. ."ill.)
Tlie diminution in the solar railiation penetrating our atmosplieie after midda,\ cannol be
accoiiuteil for by any assumption nf instrumental error: let ns then cunsidei it to be I he elfect of
incre;ised alisoiptioii liy the v;ipiir iif \s:iter. :ind, assuming that the mountain oliscrvatioiis give :i
fail a|ipro.\imalion to the \aiiali f moisiuie for the entire atmosphere, let ns caleid.itc the
absorption proilaced by \\ .iter alone. If this \alue should be foiiml Inamei' wilh ilial nbliiiued
by other iiroccsses, it wnuld lead conlii nmlioii to these, though in itself it c: I pretend to the
jicsscssion of great aecllrac^.
The following figures giving \ nines of solar radi:ilion and atmos|iheiic i stiire arc taken from
smooth cnr\cs representing average results at .Mouul Whitney.
8nn 1 hours t'roin meridian; © decln. = + HI : 0 zenith dist. = (iO ; sec ,' = L'.
A. M. i: M,
Solar ifidijition calories.. 1. Hli 1.72'
Force of vapor niillinieterbs 1.9S ■-'. ,i3
Precii.itablew.iter do 6.4 s. 1 j
from these
'*M'<-i--'1^1.7l'_ ,|.,.
anil detcrinined iis before the values of ( <//) (»■(/,'"_//) sec :J by table lo.:
log ( IV) '*! 111'.-'' -"Ci 'li- =_.ii,s:iit= w "■'•"■ log Tr=— .03.">'.i -H .()ris=_.4;is,-, Il=.:;i7-1.
Here If is the coellicient iif liansinissi..ii hu tin' entire or complex snhir ladiatinn.
Thirdly, .some agent present in the iiir between the top and bottom of the monnlain c;inses a
greater alisorptiou of heat, for a given air mass at the lower station, than is piMiluei'd liy the same
air mass ab.ivc the mountaiti (see Fig. lir. \\e know of no cinispienons agents which make the
ciinstitntiiin ol the hiwcr air diffiu- limn that of the upper except \v:iter v;ipor and dust, and we do
know that there is more of Imth in the same air-mass below than above. \\i- will cnnMiic our
present attention to the water vapor. ;ind proceed as if it were the only agent.
Considering for cxamiilc the difference in the radiation observed at Lone riiie ;i ml and Mount iiin
ramp with an air-mass of unity we have the following datii. Iladiation (a\eiage): Lone i'nie
r'--\.~'i calories: .Munutain ('am]i, /■'" -I.IU calories. Approximate depth of preci|iitalile water:
Lone Pine, iy.7 millimeters: .M(iiint;iin Camp, CO millimeters.
Determining the values of the exponents by talile l."i.'! we have —
(W) I*) 11:1.71^ (11') '*i [>■'■" =;::=.!»i(; log ( 11 )"-•'= — . (i;isi ir = .tiiiy;
We now proceed In the comparison of homogeneoiis rays in tlie spectrum as measured by the,
bolometer at Lone I'ine and Mountain Camp, in order to determine how these results are affected
188 RESBAECHES ON SOLAR HEAT.
by tlie agent in qiiestion. Here, on aecimnt of the limited number of measurements, we are obliged
to comjiare observations in which both the air-masses aud the transmission of the uuit of mass have
changed, since the meteorological conditions have altered in the interval, as described on page
183. We must therefore consider not only the air between the stations but also that above the
level of the higher. We may ex])ress the change in that portion of the transmission which is
aftected the aqueous components of the atmosphere by
( W^) (*) [«■' Ift'"-''') sw 4'l-(*) [■»" (V"-*"l sec. s"|
where, however, the transmission is that pertaining to the difference of water masses above the
stations aud not necessarily to the water included between the stations. Besides this, as we have
just said, there is a certain part of the absorptiou produced by atmospheric constituents, other
than water, whose mass has also changed. At present, we are unable to separate these effects,
aud shall here jirovisionally consider the second part negligible.
To compare mountain observations on certain days with hi/pnthetical valley results obtained by
reducing those of other days by an arbitrary rule, which does not take into account the variation
of the aqueous couipouent of the atmosphere in the interval, can only lead to imperlect results.
The /())■»( as well as the area of the energy curve has been changed by the new conditions of absorp-
tion, and both must be i)reserved for the present purpo."ie.
The determinations of the energy of homogeneous radiations made with the speetro bolometer
having only a relative value the energy curves, drawn with these tigures, must have their area
adjusted to corresp(Mid with the more reliable indications of actinometric instrumeuts, as is described
elsewhere. For the present purpose, the ratio of measurements, made with the pyrheliometer on or
near the dates of bolometric work, has been adopted as the criterion for bolometric reductions.
Below is given the solar radiation as determined by a water pyrheliometer, uncorrected for
non-conductivity or loss by convection or imperfect absorption. The application of these correc-
tions is here unnecessary, since we wish merely the ratio of measurenients made with one and the
same instrument.
At Lone Pine the radiation registered at noon, August 11, l.L'r).3 calories; August 1-, 1.144
calories; August 14, l.'Jl35 calories; mean, 1.207 calories.
. Xo pyrheliometer observations are recorded on September U or 3; but it is fair to assume that
those made on Se])teinber 1 and 5, under almost identical circumstances, furnish a close approxi-
mation to the results that might have been obtained on the former dates.
At the Mountain Cam]) the pyrheliometer gave at noon September 1, 1.447 calories; Septem
ber ."), 1.4C2 calories; mean, 1.455 calories.
The areas of the energv curves have therefore been made conformable to the ratio — *"' = I.2(lt),
1.207
and the resulting ordinates are given in the second and third colums of the accompanying Table 155.
The values of sec C were, for Lone Pine, 1.08; for Mount Whitney, 1.15. And the exponent
of Wm becomes:
(<p) [30.r>xi.0S]-(,p) fti.oxi.i5j
which IS equal to
2.05-1.51=0..54
by Table 153. The fourth (•olumn of Table 155 contains the coefficients of transmission, according
to the assumption that the entire absorption is a(ineous, computed for an amount of water vapor
which, if condensed, would produce a layer 1'"'" deep. In this result is included the effect pro-
duced by the layer of dry air between the stations, which is here provisionally assumed to be
negligible.
This table is inserted in order that the reader may compare the results with those furnished
by oliservations at different seasons and judge for himself how far atmosjiheric moisture may be
considered to have affected them.
n YflROMETRIO OBSERVATIONS.
189
„„ ,j,,>«iM,, ,„
Tahle 155.
I r.rf uilh aliiiosi>htric moi:
)fromnhs
<,ii.i nuuh ,il diffirrnl filliluilr.
Mount
Lone
w.
Whitney.
Pine.
.350
43.1
25.1
.37
.37,"i
47.3
28.4
.39
.400
50.1
.45
187! 8
110. 6
.37
. .iOO
246. 9
153.9
.42
.600
269.3
201.0
.58
.700
2.'il.6
191. 1
.70
.800
1,000
1 L'llO
172.0
108.2
77.8
155. 5
100.2
76.4
.83
.87
.97
AVe may SHCciuctl.v rcpciit lierc witli .special refV'rciice to onr tliinl and jircsi'iit ainiinifrit what
has been alreafly given in aiii>tlicr idnncclKni.
The observation.^ Jii.st I'iri'cl aic iiiaiii- liy tlie iiyilirliimirlcr mi flir lieat rays as a wlmle.
The observations with the s|iertin lidhinictiT ilisi rinnnati' Ix'twecii (lilVcrciit sp<M'tral rays, and
if tliey were luiinerniis enoiiKh would sliow, by the idiiipai ismi ot tlmsc taken al l.niic I'liic and
Mount Whitney camp, what pirliiailar rays the a<'tioii iit this water vapdi- has most atb-cied.
Unfortunately, the ob.servations with the spectro-bolonieter, uiuler the dilliculties ot the e.^iiedi-
tion, are too few to settle so didi<'ate a point as the mie iinuiediately in ipiestiou. The.\ do. Ikiw-
ever, bring indepeinb'nt testinionx to thc> tact that in pinportiuii to the presence nl' water vapor
the beat radiation as a uliole is iljniiiiislied : ami they i;ive some Imlii-alion, tl ,L:h mil a eoncln
sive one, as to the particular s])ectial rays which it lias most aHected.
We, draw, then the general <leiliiclioii from all oin preceding iir-iinicnts thai the pivMiais
conipan.sons, whether made between observations lakeii at lUllerent seasons ol llie year, at dilier
cut hours of the day, or at ditlerent altitudes above sea level, all point to the same conclusion,
namely, that there is a large absorption of solar radiation which depends upon and increases with
the prevalence of atmos]ilicric moisture (as we have defined the word), and that this cllcct is most
marked for the rays of slmrl waM' length.
We shall not attennit to deduce any absolnle values of aipieous transmission from the abo\e
measures.
CHArTEli XIX.
BAKOMBTHIC H VJ'S( )M ICTKY.
TXTRdDX'CTION
The iiistmiiiciits iiscil by the i-xpeditioii in tlir liiiroiiirtric work were the three Signal Servieo
lianiiiietcrs N(js. IsiMI. L'OIS, and 1!I35, the emirs of which liave been round to be +((.0(ll', -,-l).()OL'
and —(I. (HIS, respect i\-ely.
It was till' inieiilion, on leaving one of these iiislrunienls at Lone I'ine, to establish a series of
sinuiltaneoiis rcadini;s at Mountain Oamp and the I'eak of Wliitiiey with the other two. One of
the barometers (l!);)."!) being injured, however, in its transit to Mountain Caniii. synchronous observa-
tions between that point and the Peak were neoessai il.\ rendered impossible. Simultaneous oliser-
■vations were therefore obtained only between Lone I'nie and .Mountain Camp, and between Lone
Pine and the I'eak.
The persons eni;at;ed in barometric obser\ ations, with their initials as used for abbreviations
in the tables, were the following: Capt. O. E. Miehaelis, U. S. A. (O. E. M.); Sergeant d. .1.
Xanry, T. S. S. S. (.1. .1. N.); Sergeant A. C. Dobbins, I'. S. S. S. (A. C. D.); Corporal II. La
uouette, V. S. A. (11. J..); and Mr. J. E. Keeler, Allegheny ( .bservat(U-y (J. E. K.).
The very trying observations at the Peak are due to ('ajitain Miehaelis, and Mr. -I. E. Keeler.
who volunteered this service, as well as to Sergeant Nanry.
A series of special tri hourly ob.servations bad been organized for comparisou between Lone
Pine and tin' Peak, which was carried out eftieiently at the former station by Sergeant Dobbins
and Corporal Lanonette, who volunteered their .services for this extra duty. It was found imjios-
sible to continue tlie same tri liourly observations at the Peak without tire or shelter. From the
eighteen obseivations (djtained there, it will be seen, however, that if all are not absolutely .syn-
chronous wilh those at Lone Pine, all are so nearly so. that the\ nniy be treated as such, without
sensible error, when we have interpolated \alncs between Ihe closely contiguous actual obserxa,
tions.
In the tables following, the original readings ol' the baromcler are given for tlie three stations,
with a synopsis of each set, as well as of the temperature and relative humidity, since the latter
enters into the hy])sometric formula of Bessel, employed in the reduction.
The altitucle of Lone Pine above the sea level was first obtained by comparison with the stations
of Sau Diego, and San Francisco on the sea-coast. Subsequently, through the courtesy of Mr.
George Davidson, the value for Lone Pine was separately given from the levelings for the projio.sed
Carson and Colorado Railroad through Inyo Valley. The heights of Mountain Camp and Whitney
Peak are then severally referred to Lone Pine.
The general arrangement of the tables may be staled as follows: (1) Summaries of barometric,
thermometrio, and relative humidity readings at Sau Diego and Sau Francisco; (2) the same for
Lone Pine; (3) the same for Mountain Camp ; (4) the same for Peak of Whitney.
In the reductions the formula adopted is that of Be.s.sel, with Plautamour's moditications in
the values of the barometric constants, but others have been used for comparisou.
This formula, as adopted by Guyot (Smithsoniau Tables, D, p. 7.5), is as follows:
[log ji — log B'] X 39S^'.5 L (1 + KT)
(1-0.002G257 cos 9] X [3'JK2.5-/rr|^
1
E' — II.
^_(„ + „')X 0.34807
(397.25 — A'T)V5JS'
190
P,Al!OMETi;iC riYl'S( )mi-:tuy.
1<)1
H--
wliero the various qii;iiitities have tlie fidlowiiif; sii^nilicafiun :
A = till- elevation of tlie lower station, and
h'= the elevation of the iiiiper station.
/■ --- the lailiiis ofthi' earth.
/■/(
^ r + /(
B = at spheric pressure at lower station.
£'= atmospheric pressure at u|iper station.
/v = constant l)ar(MiU'trieal coetlieient dcpen iiiifi (Ui the relative <lensit\ (
ami the air.
Ar= the eoetlieient ot the expansion of I lie air.
T= the mean temperature of the lavei of air ln^twecn the two .-(tatimis,
a = relative huiniility at lower station.
<i'= relative huiuiilify at upper station.
ifj = mean latitude ol the two stations.
The formula was a|iplioi| li\ means nf riaiitamoiir's tables, as ^'iven liy (niMit.
if the meicairv
1.— LONIO I'IN'i:.
T.Vlil.l-, l.-iC.
Cimiimrimii uf mciiin hilirmi s, ii-l,'i;l uiiil /,,,,/c Pliii'.
I SleauM ..t till- V2^ 30"' iind ^i* l."!" p. iii. olis.TVjitii.iis f:u[ii Au;;itst 17 tn S.-
Appl.viiin- IJessefs formula to these data we olitain from iiu-an 11', .'i.") p. m.
.■i,!»LM..')ll feet: from mean S.l.", p. m. oliservations, 3,.H4;it;."i feet: ;;'eneral mean, a,S.Sl'..
iliservations
ll'...,n,„t.T, F. W.V I
12i':e"p.m.
» 15" p. I„
12' 35" p. 111.
8' 15- p. ID.
1881.
Fret.
Fret.
1881.
Fert.
Frrt.
AiiR. 17
3920
3905
Aii^, 30
3890
18
:i890
3800
31
19
8829
3719
Sept. 1
2U
3899
3820
39''0
3885
21
:iS80
3700
3
4020
22
.1845
37.50
4
3900
3835
3815
3800
3779
24
3940
3915
i;
3020
.25
3940
3899
7
3729
3625
26
4140
3830
4939
3769
S
3795
28
3905
3855
Sums
85725
3960
3905
Mpiiiis.
3896. 6 ± 15. 3
3829. 4 i 29. 5
;eueral iiieiiu =36i;y.ri=pa(i.O.
,il PaiHTs of (lie f<ij,'nal Scry
192
RESEARCHES ON SOLAR HEAT.
II.— MOUNTAIN CAMP.
Table 1.58.
IlemiUs hi/ ISesaer« formulii. — .UUIuth almir f.wie Pine
[Computer. A. B. S.|
Date.
Kesults from observations at—
8' 15" a. m. 12' 35" p. m.
8M5»p.m.
1881.
^23:::::
7935.3 ! 8022.0 7734.2
24
7904.0 1 8000.0 7781.7
25
7676.5 ' 7990.4 7733.0 1
26..:..
7830.7
7969. 0 7713. 9 1
27
7646,9
8088. 5
7712. 7
28
7907. 8
7998. 3
7670. 7
29
7910. 7
7994. 4
7679. 5
30
7959. 3
8052. 8
7732. 5
31
7925. 2
8028. 6
7681. 7
Sept. 1
7891. 4
7996. 2
7683. 8
2
Sams
Means
7866. 8
8645i.6 j 88177.9 j S4S52. 9
7859. 6 1 17. 1 1 8016. li- 0.4 7713. 9 ±6. 3
A.s tilt' leader will dli.seive, the great probable error in the general meaii arises from the com-
bination of olisei vatioii.s at diflerent lionrs, and which .separately considered have, relatively,
.small errors.
III.— THE PEAK OF WHITNEY.
Table 15!>.
Results hy BesseVs formula.— Alliluile above Lone Pii
[Computei. A. U.S.]
Date. ^"'[li'^'^"" Results. ' Date. [ ''°°,iij^""' ' Eesulta.
1881.
Sept. 2
3
4
5
e' 00" p.m.
9 00 p.m.
Miiluight.
3" 00" a, m,
6 00 a.m.
8 15 p.m.
8 30 a.m.
12 40 p.m.
5 07 p.m.
6 30 p.m.
8 20 p.m.
Feet.
10659. 37
10683. 85
10923. 00
106S3. 85
10673. 84
10739. 60
1U970. 80
11233. 80
10903. 00
10769. 90
10823. 40
1881.
Sept. 5
6
Feet.
10 22 p.m. 10654.00
Midnight. 10643. 40
1' 00" a. m. 10544. 90
3 00 a. m. 10549. 30
5 00 a.m. 1 10557.70
8 17 a.m. 10934 10
9 00 a.m. 11025.90
The special mean of the first five results (which meet all requirements, inasmuch as those
observations are exactly synchronous with the corresponding tri hourly ones at Lone Pine), with
its probable error, is 10724.7 ±29..S, and giving this last value double weight, we have: Final
mini). ]07(i2.
rtm
G(H
^
■
Lone Pine
»
/
"^
tt2
/
/
\
/
£C|
51)2
Mountain
Camp
,,'-''
.,'- '
- --— "
==—..
"^-
^^,
501
MIDU JAM
plate )<.viii.
Diurnal Variation of the Barometter.
nAi!():\ii:Ti![(' dyps(»i\ikti!V. • 193
Tahle 1G(I.
.S>r(«/ ivsijf.s- oUained bij l.wiinisH lahl.s for rumparhmi.^JUituilv of W hilnnj I'mk uhorr l.oiic r,n,.
[f;om|,„lvr, J. E. IC.)
Date. ^°'';!l.,"""" Kcsultainfert.
..^Sl.
9'' I'll'" p. III. UiUTao
i; nil :u 111. Kiau.v r.
.S :iO a. lu. 1070'J. ."i
12 w II. ui. was:;. II
Inorilerto uompare tin; ditleri'iit liyiisoiiiftiical foniiuUt' in use, tlie sniiic (liit:i, obt;iiiif<l by
iibservatidiis mi Hit- s.iiiic day and at tlic .same liimr, woiv reiblccil liy thr variims riictlidds.
Tin.' followiiii^- talilf (if ifsiilts (ibtaiiicd will sli.iw tlif vaiiatioii due U> the dideiont iiiaiiiu'is
ill treating; tlu- iiiatoiial:
T.\J1LE Kil.
l;,,l,ul,o„^ „rsi„,ll, uhsnroliou. Srplemli.r -J, L^.-l I'l J.. III. ).~Altilii,l,' of liluli,,,, I'uil. „/„„r /..,;„■ /■,;„.
l!,.Milt-. M.-lli.i.Is. I'.,ii,imf,-is.
10683.S Besscla formula A. ]i. Sclian/,.
1U674. 9 EngtaciTS Pvor. Pa].. Xo. 12 . . . Do.
10435.7 Delcrtiss talili'8 Do.
10.^0.4 Guvofs tables Do.
1(127(1.1) Looiui.ss tallies iPi. Astr.l J.E.Keeler.
10510. fi Loomias tables iSmilhs. Colli.. A. E. Scbanz.
10189.3 Dippe's tables Do.
UCiOS.O Bailey's tables Do.
A iiiiiiit wortliy iif iidtic-i^ is the fact that the result.s from observations made at different times
of the day by no means a.yree. If. for example, we take the leduetioii of Mountain Cainp observa-
timis liy l!e.ssel's formula, we have fur tlieS.l."i a. m. observation the mean altitude above seadevel
(11 results) ll,700il7 feet; for the ]l'..'l."i ji. m. observation, the mean (11 results) ll,S(in±(; feet :
for the 8.1.5 p. in. observatioii. the mean (11 results) ll,.^!.^^:!) feet (witli the assiimiition f.one Pine
altitnde=.i,So(» feet).
From our laldes ef relative humidify we see that liotli at Lone Pine and Jlonntain (.'amp tlie
percentage of satiiratiini is at a niiiiinuim at noun, while tlie luoriiinj; reading;' is lietween the imon
and evening readings. It might, therefore, be suggested that the relative humidity, besides its
primary etVeet on the results, had a secondary influence due to its diurnal variation. In order to
test this possibility, the means of the morning, noon, and evening observations at Lone Pine and
Mountain Camp were again reduced by another method, viz, Hazen'.s table extended (I'rofessional
Papers of the Signal Service, No. ^']).* The results came out : For 8.1.5 a. m., assuming the height
(if Lone Pine to lie '-^.^M feet, altitude (if Mduntain « 'amp ali(i\e sea-level = ll.<;2.'i feet ; for iL'-'ioji.
ill., 11.77.") feet: lur s.l.") [). m., ll,t.'i(l feet.
It becomes immediately apparent that these (piautities, though separately less than the corre-
sponding numbers above, bear almost exactly the same ratio to one another as the results by lles-
sefs formula, although Ilazeii's formula has no term depending on the humidit.v. It is therefore
very jjossible that the temperature and relative humidity, though they must be taken into a(.'count,
are not taken into account in the best way in our fornuihc. The investigatiou of this problem is
not, however, part of our jnirpose.
Another observation made in this case, as often before, is the small scope of tlie diurnal
variation of the barometer on the top of a uionntain in comiiarison with that at its base. This is
readily shown by examination of Plate XVIII.
* This table depeiid.s oil a furmiila developed by Professor .\ugot, but luoditied by ilazeii, from tlie results of
observations at high aud low stations.
22535— No. XV 25
194
RESEARCHES ON SOLAR HEAT.
Still iiiiotlier fact is brought out very promineutly when the parallel series of observations at
Lone I'iue anil Mountain Camp are plotted together, namely, that on the mountain the principal
maxima and minima of atmo.spheric pressure fiill from 0 to 10 hours behind the corresponding
lieriods at Lone Pine. lu general, the maxima appear to be less retarded than the minima, and
the mean of 15 comparisons indicates that the retardation for a maximum amounts to one hour for
an elevation of about 1,50(» feet, while the minima fall an hour behind when the elevation is but
800 feet. Loomis (American Journal of Science, CXVII, p. 11) concludes from his comparisons,
"that over the United States both maxima aud mininui of atmospheric in'essure generally occur
hrst near the surface of the earth, and thej' occur later as we lise above the surface, the retarda
tion amounting' to one hour for an elevation of from 000 to 1,.300 feet." Here, however, Professor
Loomis is referring to those larger maxima and minima which accompany storms. It is interest-
ing to note the similarity of the phenomenon in both the larger and the smaller atmospheric fluc-
tuations.
The followiug letter was sulisei|uently received, further couimeuts lieing superfluous:
DaVII>.SON OlifSKKVATOItY,
San Fmndsco, October 25, 1883.
My I)p:aii Sin: I'lillnwing ii] • trail .tihI auotlier, I am alile to answer your qnestion about tlie heiglit of
The top of tbe
111 CoL.rad.i Kailr
(iECIP.GE DAVIIKSON.
If, therefore, we take the altitude of Lone I'ine fnini barometric determiuatious, we have the
altitude of Mimut Whitney
l(l,7(;2 feet + 3,8S:3 feet=U,G45 feet
while, with the above value from recent railroad levelings furnished liy Mr. l)avids<in, of the Coast
Survey, we have the altitude of Whitney Peak
10,762 feet+3,760 feet =14,522 feet
The discrepancy between these two values is not at all surprising when we consider the
distance from the ocean anil the intervening elevations, but the latter value is probably the more
trustworthy.
The adopted results, then, arrived at by this departmeut of the reductions are
e, abo\e eea-le
utai
('a
-levi-l.
Wliitn.y r.ak. al.ovi- sca-hv.l .-
Former results ol)tained for the height of the Peak an
Whitniy
Captain Wlie.-l.-r
:!. 7(10
14,8118
1.1,448
Table 1(2,
)/ o/ haromeiric readhttjs at Sa)i Dhf/o ami Siui Frutu
\-leYel. Observers, Uniteil Stiitea Sii;nal Service. Cumpiiti
1
21' 35"' p. 11
S' 15" p. m
I
2' 35'" p. m.
Ki' 15'" p. ni
Lo
w PinJ M
T
Lone Pine M
T
U-ite
Lone Pine M T
Lone Pine M
T
Date
Sanrnn
Die, 3
Mian
ban Prin San
ilsto Diego
Mean
1881
San Tran
D^;."c Mian
sau Frill
San
Du„o
Mean.
188i
Au' 17
30 046
29 94"
29 99b
30 013 29 924
29 968
Auj 31
30 038
29 958 29 998
29 981
'9 898
29 9.39
18
30 004
29 908
29 956
29 900 29 980
29 973
Sept I
29 981
.9 858 29 91 1
29 931
29 817
29 874
19
29 Oil
9 M
1 14
2
29 954
ICO 1 81
9 931
"9 8J6
29 S84
20
30 11
'■
3
4
'9 9-3
■jg 75
'
I
29 824
29 706
P
29 1
T
'9 731
4
29 762
23
1
29 88
29 890
24
25
30 Ul
1 11
„
1 4j I
11
7
9 9-1
.9 9 1
1 SSI
1 8 9
29 870
1J 859
16
10 lb3
9 9b0
JO 081
30 1.0 29 923
30 0 1
17
30 100
29 t,t,o
a 192
30 033 '9 810
29 1 1
Sums
688 493
687 905
26
29 988
29 863
.9 925
.9 934 29 S75
.9 91)4
-
29
-J 941
29 909
_9 9..-1
. 1 928 "9 885
.9 906
Moms
.9 934
2J 909
30
30 010
29 971
-9 900
30 015 .9 960 1
-9 98
]!Ai;():\iETiur iiypsomf/i ry.
195
Table IC:').
fnmmani of h-mpniitiiri- niiil niatire hiiiiiiilitil at Sini DUyo and .'-'.in /Vriiirisr.., Cil.
[Observers, United States Signal Service. Cnraputer, A. B. S.)
12' 35- p.
Relative iuniiclity.
San Fran-
ISKl.
oF.
Aug. 17
62
61
19
62
20
01
21
.W
23
511
24
61
25
611
26
27
60
65
Siin Difi;... M
Sams ..
Means .
&> IS-" p. m.
Tfiiiperatiire. Kt-lativc humidity.
can. SanF,.an-s„„Diegd
61.7
7s
77.5
60.9
70
73
71.5
59. 6
f<3
78
80.5
60.5
S3
78
80.5
60.9
S6
78
82.0
60.5
90
84
87.0
62.0
HO
78
79.0
63.7
75
73
74.0
60.7
96
73
64 5
59.2
:i6
87.0
61.2
113
84,5
j 59.1
96
84
90.0
fBaronifter Xo. 1890. Si^
Drisinal.
Table 164.
nttric ohstrvations at Lone Pbie.
Corr6rtion^ + 0'".002. Obaerrer, A. C. D.
i
t
^ .
i
3
i -
F =
i. -
"
■<
^
-
26. ::.-'i
-'."'
!;■■,' •
;,. /
26^ :''■■■
26, ,;j;
20. :;7-
•■I :
■.: ::i
i:
51 Ang. 19 12 35 p. :
a
15
26. 150
8
15
26,212
»
1^
p. m
26, 073
8
15
26.119
IV
15
35
26. 2.50
20.210
8
15
26. IJT
8
12
lb
35
p m
211 ■::■
26. 109 663. 16
Probabl.v this reading slunibl Ua
-': \ :'.
■-. Ill ' ' ■■
-'. 113 ,—.082
26.031 1
:■! 'i; -'17 ' — llil
26 098 1
■y. 1.,: -1 " jii 169 L.130
26. 039
25.987 I
2ii. ;a3 76. .~
26. ;)15 —.113
20.202 !
662. S7
661. 18
662. 87
661. 38
660. 06
665.52
196
KESEAKCHES ON SOLAR HEAT.
Table 104.
lUiivmetric ohscrvation^ iil Lone I'liw — C'olitimied.
Origi
aa\.
Barometer.
Origi
oal.
Barometer.
_L
;
i .
g
K
^
J.
i .
i
i
.J.
g
i.
'" o
.£
£
?
'^ S
.£
S
Hat,-.
Li.i^il
mean
"
£s
|fc
£g
si
Date.
iieau
^
-S
£S
ai
£2
|.s'
ll
.2g
S p.
i.i
1.1
l~
1 i
si
i
o
Jill-;..
"Fnh
Inch.
pa
<
o "^
Inch.
1881.
1881.
Inch.
"Fall.
Jmcft.
Inch.
nun
Ang. 30
12 3.".
■_'(■., ;io:i
S3 0
20- 30,S
— 120
26. 1711
604. SO
Sept. <
; 1 27
20. 1144
70. 8
26. 046
—.lis
25. 927
658. 54
8 I.-.
8 15
"6. 015
—.103
25. 912
658.15
31
8 ].'.
- 1".
( 1 r, M
5
1 8 35
r I'l'
26. 102
—.126
25. 976
659. 78
31
31
12 3.'i
8 1.^
h "
, 1 '.
5
12 35
8 15
l> 111
'. r '
'j 1
26. 081
20. 114
—.138
—.107
25. 943
20. 007
658. 94
060. 57
Seiit. 1
1
8 1;-|
12 3r,
8 15
8 15
]., 1,1
p.m
26! 075
26. 194
SC. 5
63.0
62.7
26! 077
26. 196
— !oso
— . 120
:: ',■
1
S 15
•12 35
S 15
8 15
p.m.
26.270'
26. 430
55.5
80.5
20. 3.'.3
-.117
26. 2;io
000. 38
2
12 .35
26. r.2
00.6
—.145
7
12 35
26. 369
86.2
^1. 7
].:i,
1,110, 36
'2
8 15
.Ji; ^..f,
71 n
.-.,- ^...1
._ (ii'i
7
8 15
26. 252
56.0
211. 2.74
. Uli.l
21.. l.-'O
065. 19
3
3
S 15
12 35
-;;. ,",
:;■ ';,;
: 1'
8
8 15
12 35
26. 381
26. 311
86.0
87.7
26. 3S3
26. 313
—.135
-.139
20. 248
26. 174
660. 68
664. 81
3
8 15
■_'.'■ :■■'
i
18 15
p.m.
4
8 15
21. .•■-'
- 11,
iiiit of illness of observer. tStatiini closeil by ilii
Table 16.5.
1 of Professor Langley.
Siunmarii of Lone Pine haromctrir readings.
[Con-ected, reduced to freezing point and to miUiractc-rs. Obfjorver, A. C. D. Compater, I". W. V.J
Date.
1881.
Anff. 17
18
19
20
21
23
24
lie
27
28
29
30
Sii 15" a. m.
12' 35" p.m.
8' 15" p.m. 1 Date.
» 1.5» 3. m.
1211 35»p.m.
S" 15" p. m.
OOs! 26
665. 16
667. 04
666, 08
665. 62
065. 75
665. 95
664.84
666. 01
663. 52
664. 33
664. 74
662. 87
665. 52
66l! 43
664. 20
665. SO
664. 91
664.17
664. 96
664.74
663. 89
664.94
661. 48
663. 62
662. 87
661. 38
664.80
mm. ;| 1881.
662.57 , Aus.31
651.14 ,1 Sept. 1
665.36 , 2
663, 62 1 3
664. 79 I 4
664. 23 5
663.47 1 6
662, 72 1 7
663.79 ,i 8
660. 47
663.62 Smil8....
661.18 ,
660.06
604.55 Means.. -
666! 51
664. 71
662. 17
661. 35
660. 06
659. 78
606. 38
068. 24
066. 68
604! 94
602. 65
060. 62
61)9. 37
658. 54
058. 94
663! 49
660. 31
660. 98
658. OS
658. 15
660. 57
665. 67
665. 19
666. 36
664. 81
1.5289. 17
14592.48
14577. 01
664. 75
663. 29
662. 59
Table 166.
narti of Loin- Phie iliermomcirlcal and hi/grometrk-nl ohscfVdiioiis
[Observer, A. C. B. Computer. F. VT. Y.'
Date.
Drvliulb tbemiometer re-
duced to Centigrade.
Relative humidity by
Smithsonian tables.
Dry bulb thermometer re-
duced to C'-.utigrade.
Relative humidity by
Smithsonian tables.
8' 15"
't'j:
8' 15" 8' 15"
p.m. a.m.
1211 35m SI, l,!im
p.m. p.m.
1 gh ijm 12' 35"
1
8' 15" 1 S* 15"
p.m. 1 a.m.
121' 25"' , S* 15"
p.m. 1 p.m.
1881.
Aug. 17.
19.
21 !
23 !
24.
24.33
22.22
23.17
22.72
2.5.11
24.17
2.5. 00
26. 28
29. 22
29.61
31.56
33.06
32. 89
31.00
31. ,50
30. 33
28.00
30.17
24. 67
26,39
26.56
25.44
23.17
14.78
14.50
20.78
26. 83
17.66
22.06
24.89
Per c.
36.7
36.7
36.5
38.0
38.8
41.0
39.3
24.8
Pn c. Per c.
13.7 21.7
14.6 59.3
14.1 6.5.3
12.7 4.3.9
16.4 1 21.5
15.2 1 47.6
12. 4 , 35. 8
18. 7 1 20. 9
ISSl. loo
Aug.31 19.28 27.11
Sept. 1 19.72 27.00
2 23.17 31.00
3 '. 24.61 : 29.01
4 ' 19.83 ' 25.33
5 , 22 33 ' 27.22
6 18.72
7 1 19,50 1 26.66
16.17
18.94
22. 94
20.94
23.44
22.72
11.50
11.61
Pfl-C.
42.9
33.5
30.8
14.4
20.4
27.9
30.0
38.4
Pert: ' Per,:
16. 6 44. 3
23. 8 35, 2
11.5 17.8
S.S 1.7.5
17. 0 13. .5
24. 4 20. 2
in. 2' 77! b
18. 44 39. 7
11.78 28.4
15,89 1 38.8
11.1 1 32.3
21.7 .51.0
25. 9 1 60. 1
17. 9 .36. 3
25.1 41.9
28.
18,44
19. 17
20.67
19.83
Sums 505.15
633.29 ' 409.28
792.2 j 376.4 859.6
29.
30.
15.56
1.5. 39
34.5
36.7
Means 21.96
28.79 1 16.60 1 34.4 [ 17.1 j 39.1
BAKOiM ETHIC HYrSOM ETUY.
197
Tablk 107.
ii.-n,,! b-i-huui-Jil ohsrmitiaun „r Imrinuihr X,>. Is
Original.
, „ Attadivcl C.
L
c
c
n
A
iK..V/"'.V\..V.-
D
6a. n,
A. C. D
Noou
:!pm
1 A. C. D
A. C. I)
il.8
2r>. 1!()C
21). \m
■j;. 21K
18 Mi<liii"lit .
19 Slidnislit ... A. C 1).
20. JOS
20. 390
20. :iio
2ti. ;io.T
20 ■ Midiiiglit-
r
D
1'
l>
c
U
r.
T)
('
11
c
11
c
11
6p.ni
9n.m
Midnij
23 9l).m A. C. 11
•Z\ MiihiiKlit H.I
2t 3a.iii ... n. I
24 6a. m A.C. II
24 9a. m ( A.C.I)
2li. 3.iS
26. 274
20. 252
26. 244
20. 248
26. 2.'i2
26. 3;h
26. 340
26.240
2ih?;
H. L
A. 0. n.
A. C. D.
198
RESEARCHES O^ SOLAR HEAT.
TA3?le 167 — Continued.
Special In-Iiniirlii iihstrr<ilioiis onmrometer M. 1890— .5. S. .stntioii. Lorn- Fine—Cimtinued.
. CD.
. CD.
. O. D.
. U. D-
. CD.
. C. D-
. C D.
. C. D.
•_>8 Midnight I A. CD
29 MidnijiLt H. L.,
30 3p.m A.
Midnight H.
Midnight I A.
Midnight A.
r
('.
D
(•
D
<;
D
<•
D
T,
i:
D
D
r.
D
(;
D
(;
D
i:
D
i;
D
i:
D
r
D
r
D
c
D - :
r
D !
C'
D 1
r
D
1)
D
(;
D
(■
D
<!
D
i5
1'
D
c
D !
. C D.
. C. D-
. C. D.
Or
ginal.
Barometer.
Barometel
reading.
Attached
Corrected
Correction
Eeduced
Reduced
Ihermome.
for in.stru-
for tem-
to freezing
to millime-
ter.
raent error.
perature.
point.
ters.
Inches.
^ Fahr.
Indies.
Inehes.
Inches.
7/1 ?»
L'6. 166
51.6
26. 168
— ,054
26. 114
663. 28
26, 200
90.7
26. 262
,146
26. 116
663. 33
26. 208
94.0
20. 210
.153
26. 057
661.84
26. 186
85.8
26.188
.133
26. 055
661. 79
26.112
86.3
26. 114
.135
25. 979
659, 86
26. 088
67.0
26. 090
.089
26. 001
660. 42
26. 131
02,0
20. 133
.078
26. 055
661.79
26.141
57.0
26. 143
.067
26. 076
662. 32
26. 196
50.5
26. 198
.063
20. 135
663.62
26. 262
72.8
26. 264
.104
26. 160
664.45
26. 280
85.8
26. 282
. 135
26. 147
664.12
26.212
76.0
26. 214
.111
26. 103
663. 01
26. 198
69.0
26, 200
.094
26. 106
663. OS
26. 184
55 5
16, 186
.003
26. 123
663. 52
26. 204
52.5
26, 206
.056
26. 150
664. 20
26. 210
44.5
26,212
.037
26. 165
664.68
26. 299
80.8
26, 301
.123
26. 178
664.91
26. 200
90.2
26, 26R
. 145
26.123
663. 52
26. 160
80.8
26, 162
.122
26. 040
661. 40
26, 130
83.5
26, 138
.128
26. 010
660.64
26. 110
62.0
26,112
.078
26. 034
661. 25
26. 118
51.2
26, 120
.052
26. 068
662. 11
26. 124
46.0
26. 126
.041
26. 085
662. 55
26. 1.50
49.0
26, 152
.018
26. 104
663. 03
26. 224
84.2
26, 220
.127
26. 099
662.90
26. 192
86.8
20. 194
.1.36
26. 058
661. 86
26. 088
82.0
20, 090
.124
25. 960
659. 52
26, 060
72.0
26, 062
.101
25. 961
659. 40
26. 068
64.5
26. 070
.084
25. 986
660. 03
26. 128
63.8
26, 130
.082
26. 048
661. 60
26. l.W
57.3
26. 152
.066
26. 086
662. 57
26. 212
54.5
26. 214
.060
26.154
664. 30
26. 320
79.4
26, 322
.119
26. 203
665. 55
26. 326
69.2
26. 328
.142
26. 186
665. 11
26, 256
79.0
26. 258
.118
26. 140
663.94
26. 234
74.0
26. 236
.107
26. 129
663. 67
26. 235
01,0
26. 237
.076
26. 161
661.48
26. 276
51.8
26. 278
.055
26. 223
666. 06
26. 222
48.0
26. 224
.045
26. 179
664.94
26. 256
26. 258
.037
26. 221
666. 01
26. 368
82.2
20. 370
.126
26.244
666. 58
26. 340
90.3
26. 342
.145
26. 197
665. 39
26. 250
82.0
26. 252
.125
26. 127
663. 62
26. 223
73.2
26. 225
.105
26. 120
663.44
26. 200
60.7
26. 202
.075
26. 127
663. 62
26. 182
50.2
26.184
.051
26. 133
663. 77
26. 190
48.5
26. 192
.047
26. 145
664. 07
26. 194
46.5
26. 196
.043
26. 153
664. 2«
26. 299
85.0
26, 301
.133
26. 168
664. 65
26. 2.52
91.8
26.254
.148
26. 106
663. 08
26. 150
84.0
26. 152
.130
26. 022
660. 95
26. 094
73.0
26. 096
.103
25, 993
660. 21
26. 081
65.0
26. 083
.085
25, 998
660. 33
26. 073
58.5
26. 075
.070
26, 005
660. 52
26. 070
50.0
26. 072
.050
26, 022
660. 95
26. 094
47.0
26. 096
.043
26, 053
661. 74
26. 200
86.5
26. 202
, 130
26. 066
062. 06
"6. 162
93.6
20.164
. 1,52
■■fi. 012
660 69
26. 114
SO. 0
2S. 116
, IK;
20 (103
060, 47
26. 100
77.0
26, 102
,112
25, 990
060, 13
26. 128
72.0
26, 130
.101
20, 029
061,13
26. 110
69.0
20. 112
.094
26.018
660,84
26. 095
66.0
26, 097
.087
26.010
660.64
26. 120
65.0
26, 122
.085
26. 037
661. 33
26. 162
84.0
26,164
.130
26. 034
661. 25
26. 032
26. 000
26. 000
26. 115
26. 10(1
26. 032
81.0
20.114
89.0
26. 103
80.0
26. 005
77.3
75.0
2.5. 9,53
26. 035
54.5
26. 024
00.0
26. 031
87.0
26, 117
S3. 7
26, 102
82.5
26. 034
25. 992
2.5. 963
25. 881
657. 37
656. 35
656.54
6_'0hscrver failed to airaken. f Omitted; observer sick. ; Discontinued by directions of Professor Langley. Dated September 3, 1R81.
BAliOMETEIO IIYPSOMETRY.
199
Table 16s.
Siimmarii of sjiiriul tri-hourlii iih^,-n;ilioiis uf the hantiuetn- nl Lone Pine.
l',.-.liK-e.ll.. ri...v.iii;; i.,.jiit :ii[.l Ci njilli t.Ts. H:,i.,Tn,lri. Isuu, S. S. Olis.rviT.s, AC. 1 1, ^iml H. L, C |mt,-r. li. Jl WM
Dale. 3 a.m. | 6 a. ni. U a. m. K,.i>ii, 3 ji. m. 6 p. in. I 9 p.m. . Miilnisht.
i 6B2,25 660.31 li/.i i.- i.'.l :ii 661.60
661.74 I 663.4SI 064.20 66:1.52 661.96 'J. " ". 6C3. 41
663.54 664.60 665.29 6S4. 55 6C2. 96 " ' ■: im. .'.!l
663.62 I 664.63 665.29 664.43 663,23 i i.j , ...1 m 66.'.. 06
665.47 I 666. 6S 667.14 006.11 064. H9 oi.l..., oi... ;i4 60."...'.;
665.44 066.43 006.61 005.14 663.67 662. ti2 , 1103.74 063.97
004.02 604.91 665.50 064. 3S 662.70 662.06 I 002.70 ...:
663. 77 66.1. 19 665. 95 ' 00.5. 44 663. 79 663. 38 J 664. 43 004. 84
664.65 66.5.29 666.06 005.21 663.08 662 50 Oo::. 50 603.67
063. 62~1 604.45 664.91 664.17 662.52 0.,IT'. .:.,.:.. 603. .'.2
66.3.99 604.96 065.70 66,5.14 663.77 Oi " ' ■'. 603. S6
663.44 663 2S 663.33 661. S4 661.79 ' ' ' U 001.79
662.32 663. K2 664.45 664.12 663.01 i,' - ' . eU-JII
004.68 064.91 663. .52 661.40 0 i .i i j,-, 002.11
662. 55 : 003. 03 662. 90 661. 86 659. 52 6.'.9- 40 000. 03 ' 601. 60
662.57 064.30 665.60 665.11 663.94. 663.67 664.48 6*06.00
664.94 066.01 666. .58 665.39 663.62 063,44 66,3.62 663.77
004. 07 604. 28 664. 65 603. 08 660. 95 660. 21 660. 33 600. 52
060.95 061.74 662.06 060.69 660.47 660.13 001.13 660. S4
660.64 661.33 661.25 659.63 658.08 657.72 657.93 65s 99
659.20 060.08 660.18 6,59.45 6.57.37 656.35 058. .54
659.45 059.32 659.91 059.81 6.58.08
13259.99 13942.50 13952.47 14.594.84 14.501.11 13891.80 13909.48 12599.13
003.00 063.93 6frl. 40 003.40 06187 001.. 52 002.35 603.15
If in the above table the missing; readiiiiis be
."> a. 111. will be GO.'!. 10 and that fur iiiidMij^ht (iOL'.'.i."i.
For a snniiuary of the special triliourly oliserx atioii
the reader may consult the Table li'.ki.
We give here a .summary of the thermoiuetric measurement
upplied by iiiteriKilatioii. the ii
f the iclative hiiiiiidit\
It Lone I'ini
Siuiimari/ of ^pivial Iri-liourlii uhserrnlmiis iif tht Ih, niinmehr
(Dry bulb. Reiliice.l to Centigrade. Observer.^. A. C. D. ami U. L. Co
■il Lour Pint.
iputer. f. \V. v.]
Date.
■=
6 a. m.
9 a. m.
Noon.
3 p.m.
6 p. m.
9 p.m.
Midniglit.
1881.
o
Aug. 15
10
31.83
32. 11
28. 22
23.72
"ii'78'
"io.'ii"
'26.' -is'
29.33
31.11
26. 28
20.83
16;72
17
10.11
9. 83
2,5. 07
29.33
31. 28
26,56
16.72
14. 33
1*
12.33
11.50
25.56
30. 44
32. 11
26.56
12.61
13.39
19
10.94
11.22
26.50
32.94
33. .50 i
28.22
14. 22
15.11
. 20
10.11
10.94
20.67
33.61
34. 28
27.83
19. 89
21
14.78
14.78
27.67
33. 22
32.94
29.61
2-1 33
22
14.78
12.06
27.11
32.39
33.50
27.39
13.72
'"'ii.'so'
23
13.72
12.89
26.67
32.00
33.44
27.11
19.28
15.06
24
13.17
11.44
27. 50
31.44
32.56
27.07
19. 56
11.78
12.33
11.11
26.28
28.07
31.22
23.44
20.11
17.56
26
10. 39
10.94
25.83
31. 00
.30. 72
26. 72
18.72
18.44
27
14.50
13.44
20. 00
25. 44
27. 39
18.11
10. .56
9.44
28
9.00
21.22
27.83
29.06
24.61
14.61
12.44
7.44
9.83
22.61
27. 00
28.94
19.28
18. 33
19.00
30
14.94
13.07
21.06
20.07
26.06 ,
21.50
13.11
31
8.89
7.00
23.17
28.00
28.89
19.44
14. 22
s'.u
Sept. 1
9.28
9.00
23. 22
28.50
30.17
19.39
15.72
17.00
10.33
8.67
24.67
31.00
32. 00
21.06
22. 06
21. 17
3
20.94
18.72
25 7''
29. 07
29.17
20.61
16.72
4
17.39
12.61
16.67
15. 33
21.06
23.72
25. 44
28.22
20.89
29. 17
24! 89
22.61
Sums ..
253. 76
248.15
518. 25
"653.97^
078. 51
516.61
375. 87
290. 44
Means .
12.69
11. 82
24.68
29. 73
30.84
24.60
17.90
1,5. 29
200
RESEARCHES O'S SOLAR HEAT.
Table 170.
Barmnelric ohscrvaiioiiti at Miimitaiu Camp.
[liaioiii.-lei No. 2018 Signal Service. Correction + 0'". 002. Oljsorver, J. J. If. Computer, K. H. \V.|
Barometer.
Indies.
"Fn/i
Inches. Inches.
I-nches.
mm
11I.71G
40.0
19. 71S — 021
19. 697
500. 30
19. 7m
lU. 7KII
01. 0
19.765 — . 0!i9
19.706
.500. 52
500. 91
15 a.m.
19. 794
VS. i
19. 790 ~. 962
35 i).m.
19. S20
04. .'i
19. S22 — . 063
15 p.m.
19.771
41.1
19.773 —.02"
15 a.m.
19. 747
5;.. (
19.749 —.040
.ctioii=+0».002.
Table 171.
ri) Mountain Camp Iniro
ml 1935, S. S. Observer. J. J. K". Compi
Date.
SM.5™a.lil. 1
2" 3:.- p.m.
S" 15"' p, m.
Dale.
8i.l5..a.m.
2'' 35'» p.m.
498.42
500. 12
501. 10
499. 86
8'' 15"' p. 1.1.
1S81.
mm.
mm.
500. 30
501. 67
.503. 02
592, 69
591.74
502. 20
501. 97
502. 97
501.07
498. 77
499. 15
499. OS
1881.
Alls- 29
30
31
Sept, 1
Sinus
Meau.s...
498' .37
499. 25
500. 75
509, 35
499, 23 .
498.13
' 18
19
500. 52
.502. 20
}m2. 45
.502. 2S
502. 15
.591. K9
501. 23
500. 45
400. 09
498. 98
500. 91
502. 50
.503. 26
502, 53
502, 53
iiOl! 92
501. 87
499.84
497. 71
499. 30
500. 72
500. 88
499. 20
^■.
23
591. 82
502. 04
502. 18
8511.77
8016. 22
9017.50
28
500. 69
501. 01
590 98
P.AEOMKTRIC HYrSOMETUY.
201
Taui,]; 17i'.
•ip llirnnumrlric <iii(l InjijruinilrK'iil ,
.T J. X. C.iHl.iiti-T, F. W V I
.litv liy Tliv.l,nll.lli.-ini..i
ir." :]Ui':i>' 8' ir.™ '!
•2J.I
c-pt.l
13.1
14.1
34
40
37
■"■f SiiDm -. 7S.3 148.5 47.4 ,301.9 -"li 5 i 449. 4
'"■■' Mraiis...; 7.1 13,5 | 4. 3 j 27.6 ^ 20.6 j 40.9 |
Table 173.
hsirviilionxnl I'eak of Whihirii.
(■..rif.,'li„L, 0 DIE iii.li foMiiiut.-r, K. 11 TT.l
Ori
Baronu'tor.
.■.■ti..ii l:c.1i 1
.r .1 \ . .
.7. J N . .
.i..r. X ..
.l.J.N ..
J.J.N. .
J. B. K .
! J. E. K .
J. E. K .
J. E, K - .
(). E. 51 .
!''i' ('hi']",.
t.i llr, /III-
r„rhe.s.
Indus
- . (ju;{
17. nyS)
t". (1114
17 tm
■+ . OlJ.T
17. fuC)
+. 009
17. fiiO
+ .00!)
17. fiJ!)
-'. f-H
]^--;J;;
-. 0115
si:^S
Tahle 174.
Barometer rcadiug. , Temperature ° C. ' Relative luiniidity.
-
-
Whil
l,v
L.rac riiic.
447
00
o
21. 00
447
10
■>■!. 06
0.332
oiiJit
44.i. 88
in, i«i 1
M :io - (
I'll
0.107
0.1 Kll
ll! 310
447. 27
In
147. 27
0 043
447. 33
l.'i "0 — L
"0
0, .110
0, 312
448.47
14 111) r
10
448.09
10, 40 IL
40
0. 273
0.714
8M0.79
357. 05 +52
09
4. 106
6. 742
446. CS
19. 87 ; +2
89
0.228
0.486
CHAPTER XX.
REPORT OF W. (J. DAY OX CARBOXIC ACID IN LOCALITY VISITED BY EXPE-
DITION.
[When tlie services of Mr. Day were secured for tlie e.-Lpeditioii, it wa.s intended that tliey should bo chietiy yivcu
in his capacity aa a professional chemist, to the determination of the ainouut of carbonic acid in the air at the variitua
stations. The esij;encies of the service essentially modiiied this plan, and a larfre part of Mr. Day's (iuie was neces-
sarily diverted by me to the physical experiments, for which we were short-handed. Accordinj^ly, for the fact that
a larger number of chc-niiial deteruiinatious was not made I am resj siblc rather than Mr. Day. I present those
which were secure, 1, t,>,^,-tbrr with an interesting rAiimi- ol ..iir i.ievious liiK.wledge on the subject by him.— [S. P.
Laxgi.ky.]
REPORT ON WORK DONE IN DETERMINING THE A3I0UXT OF CARBONIC ACID
CONTAINED IX TEE ATMOSPHERE OF THE LOCALITY VISITED BY THE EX
PEDITION.
Hy Mr. W. C. D.tY, of J, .bus Hopkins University.
Before .suliiintliiij; ^m aceount of the work iierforiiied, it will perhaps be best to present a brief
statement of our knowledge lu reference to tlie following (juestions:
First, what is tbe proportion of carbonic acid in the air, and is this proportion constant?
Second, wbat is tbe action of atmospberic carbonic acid upon .solar radiation ?
The chief causes tending to increase the atniosiilieric carbonic acid are as follows:
(1.) Tbe respiration of animals.
{•I.) Combustion of carbonized material.
(3.) Exhalations of carbonic acid caused by volcanoes and other iiitVaterrestrial agencies.
Tbe causes of decrea.se in the amount of this gas are chictly —
(1.) The decomjwsition of carbonic acid by living vegetalilcs under the intluence of sunlight;
oxygen being thereby liberated, while carbon is assimilated by the idant.
(2.) Tbe formation of carbonate of lime by the absor|itii>n of atmo.spheric carbonic acid
through the agency of certain animals, giving rise to coral reels iind animals and the whole of the
vast limestone deiiosits.
(o.) The absorption or fixation of carbonic aciil by inoiganic chemical processes.
Owing to insutticient data, it cannot be said whether atumspheric carbonic acid is increasing
or decreasing; but certainly if any essentia! change is going on, siicli change must be very slow,
and years of the most accurate and .systematic analyses would be necessary to reveal it. From
such knowledge as we ha\e, however, the total amount ol' this ^as in the atmosphere seems to be
constant.
With regard to local variations and their causes there has been much discussion within the
past few years. As it is with the question of local variation that we are chiefly- concerned, let ns
consider, in a general way, the causes capable of producing alterations in the amount of carbonic
acid contained in the atmosphere of any given locality.
The large amounts of the gas emitted by volcanoes would naturally tend to rai.se the proportion
of carbonic acid contained in the surrounding atmosphere. Air in the vicinity of densely popu-
lated cities would also be expected to contain an excess of this gas. The atmosphere of one place
non-productive of carbonic acid, and separated by miles from another characterized by a large
consumi)tion of fuel, might, nevertheless, contain a large proportion of this product of combustion,
REPORT ON CARllONIC ACID. 203
tlu' excess beinu (hie to pi-evailin.i;' winds swrciiini:' fVum tlie Intter iilacf over tlic toniiei- anil ciiiry-
ing witli tlicni the contaniiiiated air.
>Sneli ai'e .simie ot'tlie canses feiulini; towanls Incal accaniiilatiiin.
What, uiiw. aie tljc eanses tcndilii; to oppose those Jast (■(Jiisiileied ?
The diHiision of L;ases is, of eouise, the iansi> of pi'iniai.v iinimitanee. The stiirins' up of the
air by winds also tends to eipializi- the jiropoitions <>( the atnM)sphei'ie constitneids. Tliese two
canscs may be eonsiilcred the chief om-s, wlneli aet in direct and iinmeiliate op]iosition to those of
local aocnninlatioii. Another cause, wliicli not only tends to prevent aoeuninlatiini, bat which
may even be th(> cause of a local deileiency, is tlic idtirnate consumption of carbonic acid by vcfie-
table life. We would naturally expect to lind less of this s'as in the atmo.spliere of a region charac-
terized by abundant vef^etatiini tlian in one more barreiL or one inhabited to a greater extent by
animals.
Other causes bearinj; u|ion the question of the uniform eom)iosition of the air have licen sup-
posed by individual investigators to exist. These causes, more or les.s generally accepted as such,
will be jncsented later, together with the facts which eitlier supiKU't or oppose tliem.
The tigures which in all i)roliability nmst nearly rein-escnt tlie actual average iiropiution of
carbonic acid in our atmosphere at sea level are: Three jiarts by volume of carbonic acid to 10,000
parts of air; the extreme limits of local variations nniy be considered to be L' and l.."i |)arts carbonic
acid to 10,(H»(l of air, altliongh some analyses on record would extend these limits in either
direction.
All interesting theory, bearing ui)on the constancy <if the ]iiii]iortion of atmospheric carbonic
acid, has lately been advanced by JM. n. Schloesing. (Coinptes liendus, tome 00, jiage Ulo.) This
investigator maintains that the variations of the atmospheric carbonic acid is contained between
very narrow limits, and in this connection expresses his firm confidence in the opinions of M.
Rei.set (to be referred to further on). Schloesing has found that pure water, ]daced in contact
with an earthy carbonate and snrronmled by an atnnisphere containing carbonic acid, becomes
charged with a quantity of bicarbointte, which increases, according to a imithematical law, with
the tension of the carbonic acid in this atmosphere. The bicarbonate is found as a result of the
absorption of carbonic acid by the earthy carbonate employed.
When a neutral salt of soda, lime, or magnesia in .solution is introduced into the water the
quantity of bicarbonate found ditlers from that found when pure water is u.sed; but it increases
with the amount of carbonic acid, and a state of equilibrium is produced between the amount
formed and the tension of the gas. As a result of a series of analyses of sea-water, Schloesing has
also found that the greater part of the carbonic acid contained in a given amount of water is
present in bicarboinites. The.se experiments have led the author to (he belief that the sea acts
as a reservoir and regulator of atmospheric carbonic acid.
Owing to the continual motions going on in the air and in the sea, the state of equilibrium
above referred to is not perfectly realized in nature. However, there is a tendenc^y toward that
condition.
If the variatiiui of the carlionic acid is i)ositive. the sea-water absorbs the excess with the
formation of bi- or aeiil carbijiiales ; it ncgati\f, carbonic acid is released to the air and neutral
carbonates are precipitated. The sea is regarded by the same investigator as a regulator also of
atnnispheric ammonia.
JI. Marie-Davy (Comptes Reiulus, tome 00, p. 3l') claims to have established a relation between
the carbonic acid of the atmosphere and the great general movements of the latter.
The above author has in his possession the results of four years of <laily determinations of
atmospheric carbonic acid. These determinations were made at Montsouris by M. Lc\y and his
assistant, M. Allaire. They show variations between the limits 1'2 and .'JO parts of carbiuiie acid
to 100,000 of air.
In atti'iiipting to account for these variaticms M. Jlaii('-l)avy first thought that they were due
to the influence, on the one hand, of Paris as a fruilful source of carbonic acid, on the other, of the
cultivated fields as agents of consumption. Hut, contrary to this belief, it was noticed that the
northern winds, which blow from Paris over Mcjiitsouris contain less carbonic acid than those
from the south, which come directly from the countrv.
204 RESEARCHES ON SOLAR HEAT.
The local influence is thus subordinated to another of a liigUer order. Generally the winds
from the south or southwest graze the surface of the soil, while those from the north or northwest
plunge down from the elevated atmospheric regions. If, then, it can be supposed that the latter
contain less carbonic acid than the former, the matter is explained.
If his views on tliis question are true, the great value of including among the ordinary mete-
orological observations systematic determinations of carbonic acid in the air, is at once apparent
The following views of M. Reiset (Oomptcs Reudus, tome 90, page 11J:4), upon the proportion
of carbonic acid in the air, introduce a controversy between the latter and M. i\Iari6-Davy, the
point of difference being the more or less wide limits of atmospheric carbonic acid variation.
In the month of June, 1879, M. Reiset commenced in the country a series of investigations
which was continued up to the first frost in November. The general mean deduced from ninety-
one determinations made during the day or night during this period is 29.78 volumes of carbonic
acid to 100,000 of air, dry at 0^ and 760 ™™. In a jireceding communication it had been announced
that from the Oth of Septemlier, 1S72, to the 20th of August, 1873, the mean was 29.42. These
latter determinations are therefore confirmed by those made six years later thus showing that the
limits of variation are much smaller than as revealed by the investigations of M. Mari6-Davy.
The conclusions arrived at by M. Reiset are as follows :
After an interval of six years the same i)roportion of carbonic acid is found, ;'. e., 29.78 vol-
umes carbonic acid to 100,000 of air.
The air analyzed during the night contains more carbonic acid than that during the day; 28.91
to 100,000 is the proportion found for the day between 9'' a. m. and I'' p. m.; 30.84 is the propor-
tion for the night; several foggy nights are included among the number for which this mean was
found. M. Reiset then refers to the results obtained by M. Mari^-Davy; he makes no comment
upon the value of the hypothesis advanced by the lattei', but says that the variations between the
limits 22 to 36 per 100,000 of air shown to exist by M. Marie Davy's determinations are in total
disagreement with the results of his own investigation. M. Rei.set further expresses doubt as to
the degree of precision attainable by the method employed by M. Marie Davy, and justifies this
doubt by a criticism of the lattcr's methods and apparatus.
The author concludes this paper by quoting some remarks of Gay-Lussac advocating the idea
that the proportion of carbonic acid in the air is constant, i. e., varies between very narrow limits,
this constancy being due to the state of incessant motion which, it is reasonable to suppose, exists
in the atmosi>here, thus tending to distribute uniformly its acci<lental coustituents.
M. Marii^-Davy rejilies to the remarks of M. Reiset, and reasserts his confidence in the results
arrived at by his collaborator, M. Levy, and he emphasizes the importance of continued investiga-
tions, in various places, with the aim of settling the question of the connection between the pro-
portion of atmospheric carbonic acid and the general movements of the atmosphere (Comptes
Rendus, tome 90, page 1287).
The principal point on which these eminent observers differ, is whether the extent of variation
in the amount of atmospheric carbonic acid is contained between the limits believed to exist by
Mari6-Davy or between less widely separated limits as those advocated by Reiset.
The recent investigations of MM. Miintz and Aubin (Comptes Rendus, tome 92, page 247), on the
pro])ortion of atmospheric carbonic acid, had for their object the solution of the following questions
For a given place are the variations in the ])roportion of carbonic acid considerable or merely
insignificant?
Is the carbonic acid uniformly distributed in tlie various layers of the atmosphere, or is there
an excess in the lower portions?
Miintz and Aubin first possessed themselves of a method which would give results upon which
entire dependence could be placed. Their method may briefly be described as follows : The prin-
ciple involved consists in fixing the carbonic acid by an absorbing body, from which it is subse-
quently disengaged and measured directly. The absorbing body is inimice stone, impregnated
w ith a solution of i)otassium hydrate. This is contained in a glass tube drawn out at both ends ;
the tube thus pre]iareil is scaled at both en<ls and opened on the spot when the determination is to
be made. Air to the amount of at least 200 liters is passed through the tube by means of an aspi-
rating gasometer. The tube, again sealed, may be preserved indefinitely. The remainder of the
KEPOET ON CARBO^^C ACID. 205
deteriiiinatioii is made in the lalinratory. Thus one end of the tnbe is eonneeted with a niereury
pump, tliroUKh tlie other end dilnte sulplinrie aeid is allowed to enter, the earbonic acid thus dis-
engaged is determined by direet measurement in a graduated receiver.
The evidences of accuracy given in the memoir are certainly satisfactory, at tin- sami' time the
method is simple throughout. Tlie operation of passing the air through is one which may be per-
formed by a person uiuiccustomed to delicate nmuipulation. The method is s[)ecially valuable in
its application to determinations iu places ditlicult of access. For accuracy and simjilicity this
method seems to be ecjualed by no other at present in use. All work connected with its applica-
tion involving delicacy and careful nuinipulation is performed iu the laboratory ; tlie remaining
operations may be perlbmied by an ordinarily intelligent person at the i)lace chosen for the deter-
minations.
In the ]n-esent state of meteorological science the indications are that the functions of atmos-
pheric carbonic acid are more important ami nuire complex than has been supposed until within
the last few years. Assuming tlie correctness of the views of Marie-Davy, a knowledge of the
variations in the amount of this atiiiospheric ciuistituent would lie of the greatest jiractical xalue.
But iu order to prove the correctness or tlie incorrectness of these views, it is necessary that simul-
taneous analyses should be systematically maile at a number ol dillereiit phices widely seiiarated
and so situated as to secure various conditions. The Signal Service system of this country seems
to embrace conditions most favorable for work of this nature. The men stationed at the various
observatories over our vast area of territorj* are amply well titted lor the portion of the work which
would fall to their lot. From a single laboratory tubes prejtared as above described might be sent
to the different stations, where the necessary volume of air could be simply jiassed through them,
the atmospheric conditions at the time noted, and the tubes returned to the laboratory, where the
operation would be completed.
Let us now consider some of the results which this method in the hands of its originators,
Miiutz anil Aubiu, has already developed (Comptes Kendus. tome !I2. jiage 1229). Two stations were
established, one at Paris, 6'" above the ground, the other at an ojieii place iu the country. The
atmosphere of a large city like Paris is incessantly contaminated by the products of combustion
and those of the respiration of its numerous inhabitants. The atmosphere of the country is with-
out these abundant sources of carbonic acid. At the Paris station a large number of determina-
tions were made during the interval between December, ISSO, and May, ISSl.
The differences in the proportion of acid arc notable. They varied Iietween the limits 2.S>i to
4.22 volumes carbonic acid to 10,000 of air.
The maxima correspond always with weather cloudy and calm, the air being disturlied by no
energetic agitation; also with a predominance of the local influence. The miiiiina, on the other
hand, are evident with an atmosphere pure and agitated.
The quantities of carbonic acid found during weather cloudy and calm vary Iietween the limits
3.22 and 4.22 volumes per 10,000 air. Those found for clear weather are comprised between the
limits 2.S0 and 3.1. These figures do not differ sensibly from those by I\I. Boussingault.
The largest quantities were observed during abundant falls of snow or during thick fogs, con-
ditions which fetter the movements of the atmosphere. The results obtained at the station in the
country contirm those of M. Eeiset. Daring the day the quantities are cuniiiriscd Iietween the
limits 2.70 and 2,09 volumes per lU.OOO air. During the night there is mi iiicieasi- and the mean
approaches 3.
The variations observed during a single day, the weather meanwhile undergoing change, are
given as follows:
VfihlnlPanflO.IIIJO.
April 1, 91' ii.
l'' 31
4'' 1..
Sky clear.
air
m. Skv ck
ilulv
Sky very
iIoiM
These variations, although contained between narrow limits, are nevertheless significant.
Miintz and Anbm (Comptes Reiidus, tome 03, page 797) have also applied their valuable method
o the analyses of air iu elevated regions. In these determinations the precaution of taking the air
206
RESEARCHES ON SOLAR HEAT.
through metallic tubes, about 30 feet from the observer, rendered any error due to respiration of
the oi)erator null. The point chosen for observation was the summit of the Pic dn Midi in the
Pyrenees Mountains, altitude, 2,877™. This peak is separated from other elevated mountains.
The air which circulates there is that of the upper currents; the rai)idity of the winds removes
any suspicion of local influence.
The following table shows the results:
00" SW., BtroDg.
11 18 ' SE.,
10 511 : SE..
40 SW., stroDff
237.3
206.7
237. 2
235. 4
236.8
236.2
233.5
235.3
234.3
221.5
243.1
234.6
3.01
2.95
2.91
2.76
2.67
2.85
2.79
For the sake of comparison analj'ses were made in two valleys at the base of the mouutains,
i. e., Pierrefitte, altitude SOT", and Lnz, altitude TSO™, as follows:
Pierrefitte, August S, 2'' to 5'' p. m., carbouic acid per 10,000 of air 2.79
Pierrefitte, Aujjust 6, Si" to 11'' a. m., carbonic iicid per 10,000 of air (foggy) 3.00
Luz, Augu.st 7, .^'^ to 11'' a. ni., carbonic acid per 10,000 air 2. 69
The last determination was made iii the midst of abundant vegetation.
MM. Miiutz and Aubin arrive at the following conclusions :
All these figures are very nearly iilcntical with these (niiiHl in the h>\viT portions of the atmosphere by ourselrea,
by M. Eeiset, and M. Schnltze.
We believe, then, that we are authorized in making the .statement that the carbonic acid is uniformly distributed
throughout the atmosphere, and we confirm thus the ideas of JI. Reiset upon this subject and those of M. Schloesing
on the circulation of caibonic acid at the surface of the glolte.
Our present knowledge as to the proportion of cinlMiiiic acid in the iiir and the limits of varia-
tion of this proportion may, so far as it is based on e.xiicrimcntal exidcnce, perhaps be stated as
follows:
(1) Carbonic ai-id jirodnced and consumed as shown in the beginning of this report is present
in our atmosplierc in tlie iiiiirli/ constant judportion of three volumes of carbonic acid to 10,000
of air.
(2) The variations of this proportion are contained between narrow limits, but are significant.
Maxima of these \ariations are caused by predominance of causes of jirodaction ; they are also
coincident with weather cloudy and calm, with falling rain or snow.
Minima are noticed simultaneously with an agitated atmosphere and clear sky. Minima have
also been attributed to the immediate proximity of abundant vegetation.
(3) The nature and direction of winds have been found to influence tlie proiiortion.
(4) The sea appears to exert a controlling influence upon the proportion of carbonic acid, act-
ing as a reservoir for the gas, absorbing or liberating it according as it varies, increa.sing or dimin-
ishing, within the narrow limits which have been determined.
(5) The influence of altitude is as yet not established beyond the possibility of doubt.
By some ex|)erimenters the proportion has lieen found to increa.se with the altitude; by a greater
number to diminish with the altitude; by still a third class of investigators the proportion has
been found to be constant or independent of altitude.
In order to secure the best possible result of analyses which have already been made by
various investigators, and by use of various methods, the latter should be compared by simul-
REPORT OX CARBONIC ACID. 207
taueous aiipliciition to the analyses of the same air, and under tlie same conditions, the standard
test for each method being its ability to determine the ammint of carbonic acid in a certain volnme
of air artificially prepared by introdncinfr into air lirst deprived of carbonic acid a known volume
of the latter.*
"We \\\\\ now present the results of observations and determinations made in connection with
the Mount Whitney Expedition.
rilNDITIO.NS LIABLE Tl) AFKEf'T THE QUANTITY OP CARBONIC ACID IN THE ATMOSPHERE
srR];oi-Ni)iN(; movnt wiiitney.
The territory l>ordrriiiL; ujion this jioition of the Sierra Nevada Range is, owing to the
scarcity of water, of a dtsdiate (•liara<'ter. The vegetation <if the Owens River ^'al^y is t-xcced-
ingly scanty, consisting of jilaiits capable of extracting tlie little water they need fniiii a consid-
erable depth.
The country is naturally sparsely inhabited, occasional oases having been selected for the
location of nnning cainjis. One of tli<' latter, known by the name of "Lone Pine," is situated on
an elliptically-shaped oasis whose dimensions may be stated as 3.J miles by about :.'.
The soil thronglK.nt tlic valley is fertile enough for abundant vegetation, and when suiijiljed
with water, as is the <ase in the oasis of Lone Pine, amply repays cultivation.
The mountains are, up to an elevation of ten thousand feet, covered by jiine tbrests. Some
of the individual trees are of large size.
The soil, naturally more sterile than in the valleys, is apiiareiitly the condition which imjioses
a limit upon the <leveloiinient of trees i>v other vegetation capable of withstanding extremes of
heat and cold.
Water among the mountains is abundant, accumulating in numerous little lakes and rushinn'
in streams down the steep sides to the thirst}' soil below, from which it is speedily removed by
evaporation to the still thirstier atnuisphere.
The sky at the time the determinations were made was, with one exception, beautifully clear.
Occasional forest tires in the mountains are a source of carbonic acid capable of producing
a temporary" local excess iu the amount of this gas in the atmosjihere.
We see, then, from the above considerations, that the causes both of iirodtu-ticjii and con-
sumption of carbonic acid are apparently somewhat less active than in territory less barren.
:Mr,TII(iIJ EJIPLOYEIl.
The method used was a nioditication of Pettenkofer's process, which consists in passing a
known volume of air through baryta water, the strength of which solution is determined before
and after the operation l)y means of a standard solution of oxalic acid. In the following deter-
minations standard hydrochloric acid was used instead of oxalic acid and litmus solution was
used for the color reaction.
*Au extremely important fiiiictiou of atmospheric carbonic acid iu tlie view of many investigators is its action
on radiant lieat, but tlie laboratory experiments upon the suliject have not yet broiiylit certainty, and we here can do
hardly more than to refer the reader to the best Icnowu orijiiual memoirs.
Tyndall ("Philosophical Transactions," ls.">u, ami •■ liivestifi;ations iu the domain of radiant heat") finds that
the absorptive p<iwer of carbonic-acid y:as is about I'n liiin-s that of oxygen, aud reaches well-lcuowu conclusions as
to the absorptive jiower of a([neoas vajtor.
Magnus {trausl.ated, "Philosophical Ma^jaziuc," vol. a,;, ii,„is absorptiie ertect of air the same whether dry or
saturated with aqueous vapor.
Lecher aud Perntcr ("Wiedemann's Aunalen," ISsl, l-J), after extreme precautious, tiud results not ijreatly
difl'ereut from Tyndall as regards gases, but reached wlndly opposite ones .as regards aqueous vapor, believing that the
absorptive power of the atmosphere for radiant heat is due mainly to carbonic acid, which is present with the water,
and to whose association with the water the effects attributed to aqueous vapor are really dui'.
Reiset and Miiutz aud Aubin (already cited) also hud a couuec tioii between the amount >•( aqueous vapor aud
that of carbonic acid in the atmosphere.
208
EESEARCHBS ON SOLAE HEAT.
Determination at Lone fine, August 9, 1881,
1 c. c. IR:1 Hcliiti ■diitainetl 0.003230 gramme CI.
1 c. c. Ba (Oil); soliitiou before operation = 0.663 c. c. HC'l.
1 c. c. Ba (OH)s solutiou after operation = 0.(jUO c. c. HCl.
0.063 c. c. HCl = .0002035 gramme CI., equivalent to t-arli
71 Clj : 44 COj : t .0002035 CI
60 0. c. Ba (OH)j solution were employed in tbe operation.
60 c. c. Ba (OH): = .007566 gramme CO: found:
Volume of air passed througli solution, 20.18 liters.
Barometer 669""". Meam temperature of air, 27*^ Centigrade.
Volume of air reduced to 760"'"' and 0^ Centigrade, 16.1(> liters.
Volume of CO: found .003838 liter.
0.003838-^16.16 = .0002377, L e. there were 23.77 parts b.v vcilu
and 0'=' Centigrade.
The skv during thi.s determination was clouded.
ic acid precipitated fron
,0ll012IJl CO:
of CO: to 100000 of i
Ba(OH):
Determinations at Mountain Camp. Aluunt Whitueij.
I. — September 7, 1881.
1 c. c. HCl = .003230 gramme CI.
Before operation added 4.69 c. c. HCl to neutralize 10 c. c. Ba (OH):.
After operation added 4.09 c. c. HCl to neutralize 10 c. c. Ba (OH):.
50 c. c. Ba (OH): stdution were employed in the operation.
Weight of CO: found = .006005 gramme.
Volumes of CO: found = .003046 liter.
Volume air passed through Ba (OH): = 30.24 liters.
Volume air corrected for temperature and pressure = 18.52 liters.
Volumes CO: per 100000 of air found =16.44 liters.
Sky ckar. B.arometer = 502"'™. Mean temperature = 21^ Centigrade.
II.
Weight of CO: found = .00729 grammo = .003099 liters CO:, at 0" and 760"'"'.
Barometer^ 502""". Mean temperature = 21.6° Centigrade.
Volume air passed through = 30.24 liters = 18.49 liters at 0"^ and 760'"'".
CO: per 10(1000 volumes of air = 20.00.
III.— September 8, 1881.
Weight of CO, found in 60.48 liters air = .0158838 gramme.
Volume CO: found at 0° Centigrade and 760""" = .008058 liters.
Barometer = 502""". Mean temperature ^ 20.4'^ Centigrade.
Volume air used = 60.48 liters; reduced to 0"^ Centigrade and "I'lO'"'" = 37.16 li
Volumes carbonic acid per 100000 of air= 21.68.
SUMMARY.
Place.
Date.
Volnmes car-
bonic acid
per lUOOOO air.
Aug. 9, 1881
St-pt. 7, 1881
Si-pL 7, 1881
Sept, 8, 1881
23. 77
16.44
20.00
21.68
19.37
Mouutaiu CaniD
^'
According, then, to these analyses there is a greater ainouut of carbonic acid at the lower than
at the higher altitude.
It is to be regretted that the method proposed by Miiutz and Aiibin had not appeared in the
journals in time to have been applied in the above work.
CHAPTER XXI.
GENERAL SOniAKV OF BESFLTS.
PRESENT CONDITION OF KXOWI.EIlliE ON TIIF. POINTS INVESTIGATED.
It i.s tlie ]ire.sent lieliff tbat we know with sdiin'tliiiii; like ucciiincy tin' aniuiiiit nf bi-at which
the sun sends llu- ciirtli. and also that \vi- Icnciw in ;;cnci:il Ijow the atnHis|ihrrc acts in keiiiing the
earth warm l),v hdlin;; the sohir rays ]>ass int(i it and kcciiin;^ liack citln-is IVnni tin' soil. It Inis been
usual to state that tlie extreme violet rays are not readily transmitted by our atmosphere; that of the
light rays about i are <absorbeil and ,; transmitted, while tlmt as we go on tlirougli the extreme red
to the dark heat ray.s w-e find the absorption growing greater and greater, the dark heat rays being
found in very small quantity beeau.se they are absorbed almost wholly. It is eoimnonly added
that it is owing to this cause that the heat, which freely enters as light, escapes w ith ditiieulty wheu
returned as dark heat iu the longer rays corresponding to the lowest portion of the solar heat
spectrum, and that thus the atmosphere acts to the earth a part somewhat like that of the gla.ss
cover of a hot-bed, materially aiding the solar radiation in maiutaiuing the temiierature of the
planet. The ordinary conception of this heat storing action then involves the conclusion that the
dark heat of the known solar spectrum is less transniissil)le than the light heat, and this presumed
necessity may possibly have in soiue degree biaseil jihysicists in their invest igatiims on this region,
where exi)eriments are difficult. However this may be, tliey have lieeii on this point provided
with little evidence, .so that it was rather taken for granted as a supiiosed necessity, than indubi-
tably demonstrated by suflBcient experiment, that the dark heat region of the solar spectrum
was comparatively non-transmissible by the terrestrial atmosphere. A conlirnuitory circumstance
to this belief was the fact that Tyndall, and after him others, had proved, by actual experiment,
that, to such kinds of heat as come from terrestrial .sources of very low" temperatures, vapors and
gases known to be imi)ortant constituents of our atnuisjihere were aimnst impermeable. Such
investigations, it will be remembered, had been ma<le almost solely by tln' prism, and there was no
way known of learning what the wavelengths of this dark heat really were, physicists depend-
ing for their knowledge of these wave lengths on certain formula- which had never been verified, as
they did also in a much more important matter, the determination of the amount of heat which
the earth's atmosphere diverled from the direct radiation of tlic sun: a iletermination which was
often made in a way wliich seemed to assume that nature had spared ns all the tronlile possible, by
here conducting the whole train of her ordinarily mysterious operations, in a way so sinqile that
the formula ex|)ressing them was itself as elementary as we could i)ossilily wish.
To know what kind of heat was radiated from the soil we slumld need to know the wave-
lengths of heat of this quality, of which even now we remain in ignorance. Draper, in ISSl, gives
the limit of the solar heat spectrum at a wave-length of about O.OOI of a millimeter. M. Eec(]iierel,
in a memoir in the Annales de Cliimie et de Physiipie, so late as August, iss.',, jdaces the ultimate
limit of the known spectrum at less than .(l(»l."» millimi'ters, and uKjst explically approves the
statement that these heat rays are less transmissible by the atmosphere than others. (.»urown meas-
ures, here given, add the very remarkable absor|)tion liand .(.', with others, and extend the directly
observed spectrum to a wave length of nearly .Uu:! millimeters, while making it ]irobable that the
•209
12535— No. XV L'5
210 KBSEARCHES OR SOLAR HEAT.
truusiiiissiliilitv (if llic atmosphere incri-'aKes up to nearly this point, wliere it snddeTily ceases, as if
all lievund were an unlimited cold body.
Having- been led by the study of selective absorption to think that the portion of the sun's
radiation reflected by particles of dust or mist, or other\vi.se dispersed in our atmosphere, is far
larger than is ciui.monly supposed, and that the little-known processes by which it is thus with-
held are nt' impcutance m their bearing on problems of the widest interest, we commenced iu
ISSO, at tlir Allc,L;lieny Observatory, the study of the solar heat by an instrument (the bolome-
ter) specially invented with tlie object of doing for this heat what the eye iu the visible pris-
matic spectrnm does for light, that is, of discriminating between one heat ray aud another, and we
have been able to nse it so as to determine, together with the hitherto unknown wavelength of
a great number of dark-heat rays, the hitherto unknow n amount of heat actually observed in
each of tlie.se near the sea-level, and to tell approxinuitely the hitherto equally unknown
amount of heat in each of these dark rays before It was absorbed by our atmosphere. The
results of these investigations went to show^ that the heat in most of the known dark-heat wave-
lengths, instead of being absorbed by this atmosphere, was most freely transmitted by it, a conclu-
sion directly (i])p(ised to the common belief, and, if true, of importance, for all the few known
observations of jiliysieists seemed to prove the contrary, and meteorologists had generally accepted
these supposed observations. Continuing the heat measnrements in the "light" region, 1 found
■ that the heat existed there indeed in greater quantity than in the ••dark-heat'' region, and yet that
it had been already greatly more absorbed, so that the original (juantity of heat here must have
been enormous as compared with that in the dark-heat region. All this was studied by narrow
pencils of heat of diflerent wave-lengths, each one of which was found to be acted on in a different
degree by the atmosphere, so that the law of its absorption was not simple, but extremely complex.
Taking such a partial acconut of this complexity as was possible, I found that the anjount absorbed
was much greater than had been suppo.sed, and that the nuUir constant* or heat outside the
atmosphere was much greater than had been commonly stated, aud the primary distribution of
the rays so totally different from what we see that it seemed that they had originally been heaped
together Inwards the blue eJid of the spectrum, or that the color of the sun, could we see it outside
the atmosphere, would bo bluish, so that media in our atmosphere, which we commonly think of
as transparent, had been '']ilaying a part analogous to that of a yellowish or reddish glass whose
impure color is not a monochromatic yellow or red, but a compound of many or even all the
spectral tints in unaccustomed proportions. Had we in all our lives had no light but the electric
light, .seen only through such a reddish glass shade, we should doubtless believe this reddishness
the 'natuial" cohir of the glowing, naked carbons, and tlie sum of all radiations. It would appa-
rently answer (to a race lirought up in ignorance of any cither light) to our notion of icliitcncss.
Its cohu- would then seem to be no 'color' at all, and the medium would, in this case questionless,
be deemed transparent (as we believe our air transparent): ami if this medium were removed, and
the electric light seen in its true whiteness, it could not but seem that it was strongly colored."!
•Let me he pii iiiitlfil, foi the use of .my reader uufamiliMr witli tin- subject, a very elementary illustration: Our
oljservatious at Alleglieny had appeared to sbow tliat the atiuuspliere had acted with sdectlve absorption to au
unanticipated degree, keeping back an immense proportion of the blue and green, so that what was originally the
strongest had when it got down to us become the weakest of all, and what wiis originally weak bad become relatively
strong, the action of the atmosphere having been just the converse of that of an ordinary sieve, or like that of oue
■ft'bich should keep hack small particles analogous to the short wave-lengths (the bine and green) and allow freely
to pass the large ones (the dark-heat rays). It seemed from these observations that the atmosphere had not merely
kept back a part of the solar radiation, but had totally changed its couipcsition in doing so, not by anything it had
put iu, lint by the selective way in which it had taken out, as if by a capricious intelligence. The residue that had
actually come down to us thus changed in proportion was what we know familiarly as "white" light, so that white
is not "the sum of all radiations," as used to be taught, but resembles the pure original sunlight less than the electric
beam which has come to us through reddish-colored glasses resembles the original brightness. With this visible heat
was included the large amount of invisible heat, and if there was any law observable in this "capricious" action of
the atniospliere, it was fuuud to be this, that, throughout the whole range of the known heat spectrum, what I have
compared to the atmcispheiic sieve acted in the opposite way to the couimou one, or that large wave-lengths passed
it with greater laeilily than the smaller ones.
tSee Young's ■■Tl"- Sun" (liist edition) for the views which had been reached oq this poiut at Allegheny before
the expedition started.
GENERAL SUMMARY OF RESULTS. 211
The siinpli' law wliii-li we sr.^m to have .•sfnl.lislicd is, then, that (with thi- t'xcc|iti(iii cif thr
coki bands anil intiTiiiiitiinis aiial(i;;(iiis to the lilack Iiurs of the. .spectiauii) thi- hiiyi-f the wave-
length the f^rcatei- is the tiaiisiiiissiliilit.\, (hiwii to the utmost limit of tlie snhii heat siieetiain
which has been obser\e(l, and that here tlie liaiisiiiissibility .■niddcnh/ eeased.
I was shiw to admit this myself at tirst, and mueh rather disposed to lielie\c that I liail made
some mislcake tlnin tlnit tliele eonld ha\e been so mueli iire\ i(ais error in tin- matter. ;\Iv eoii-
elusidiis were then tested in every iiossiliK' w a> without eiiaii-in.^ the reMilt. and the obJiTt ol' this
expedition was to test still otherwise and to put if jiossiMe be\oiid a ihuilit eoneliisions wliich if
true innst eonsiderably atl'eet our whole present view a. to the reijioii of the aetion to which we
owe the preservation of the organie life of the globe.
The following summary of the results of tlie expi'diticni. so far as tliey refer to the deterniination
of the solar constant alone, will direct the readca's attention to cei lain conclusions to be g;itlieied
from what ha.s already been stated, at large in ]ue\ ions jiagcs. Eiist. as regards mithoils of obsiava-
tion. It had si^emed to me most |irobable. after nearly two ycais id' obseixatiou on the tiansmis-
sibility of different hinds of heat tlironglj the eoniparison of high and low sun obscr\ ations, that
this method was afl'eeted with somi nstant error of a kind wliieh had never been determined, or,
in other win-ds, that there was a daily systematic change in the transmissibility id' the atmosjiliere
between the liigh and the low sun observations, calculated to affect tlieir results, and this ipiite
independently of any error which might liave been due to inaliibty to stmly tlie heal in separate
rays. At the goal of our expedition we tbund one of the most perfect ibimites of the ylobe Ibr lair
purpose, where the observations of high and low sun at either station conhl sometimes be made
in seemingly almost ideal conditions of tranquillity and constancy throughout the day. Ajipa-
reutly we have found that there is such a systematic error in high and low sun oliservations at one
station. This .seems to be demonstrated in a couviucing manner by calculating at the lower station,
from our high and low sun observations there, the heat which should be found at a certain height
in the atmosphere; then actually ascending to this heiglit. and Mnding the observed heat there
conspicuously and .systematically greater than the calculated one. (See page 144 and elsewhere.)
But we find also, by direct ascension in the atmosphere, that there is another imiiortaiit point
wliieh apparently can never be settled by observations at a single station. It is not the question
whether the upper air is thinner than tlie lower, but whether if we take equal weights or
equal masses as samples of tlie iqiper and the lower air, we shall find these equal masses
possessing equal transmissibilities. The exiierience of ]U-evious observers has rather tended to
give us a contrary opinion, and our own leaves this important ]ioint in no doubt. We tiiid, as we
ascend in the atmospliere. its transmissibility ((CCiV/Zi^ yiic ic(ii/lit) markeiUy changing, so that on
the whole, quite independent of its lessening density, the air becomes more and more transmissible
as we directly ascend in it. (See page 117, etc.) Our present observations further bring us infor-
mation about the way in which the atmosiihere here behaves, not only as a whole, but also as regards
each spectral ray. We liud the transmissibilities, as determined cudy by actual obscr\ ation, and
without the u.se of any formula, confirm in the most absolute manner the conclnsion tliat, with the
exception of the cold bands already noticed, the tra>t>imissihilitii increases tliroiii/liDiit the s/ieetriim
ichen the rcare-lenijth increases^ the violet being more tiansmi.ssible than the ultra violet, the blue
than the violet, the green than the blue, the yellow than the green, the red than the yellow, and
the border of the dark heat than the red, until when we have gone still farther down the .spectrum
the transmissibility will become almost complete, except for sudden great interruptions ol it —
the cold bands, the largest of wliicli was discovered on .'Mount Whitney, and will be louiid
delineated here in our spectral charts. (See page i:;:j and cha|itcrs on s|icctro-boloinctcr gen-
erally.) We find also, however carefully determined the transmissibilities are at any single
statiiui, tliat the ratio of these transmissibilities to each other may be very ditiereiit when
determined by direct comparison of the results aliove and below. We mean that, for instance,
the transmissibility of the red ray may be nearly the same whether determined at one station
or by the comparismi between two, but that the transmissibility id' the blue ray as determined at
anv single station, even an elevated one, is altogether greater than that determined by combi-
212 EESEAROHES OF SOLAR HEAT.
nation of observations made at an elevated station with those at a lower one. In other words,
when we have actnally ascended to the elevated station we tin 1 there a greater proportion of the
bine rays even than we had been prepared to expect from our observations at Allegheny, and it
seems jirolialile tliat all of onr previons conclusions as to the predominance of these and tlie com-
position of tile light outside the atmosphere have been rather within than without tlie truth.
\Vi- liiid. thi-ii. liDth that the ordinary metliod of liigli and low sun (■(uuparisiius, nnder excep-
tionally gcjiiil conditions, gives us too large coclUcii tits of transniissiuii, and that the error is
greater as the ray is more refrangilile, the error of the most assiduous observation at one station
on the more refrangible rays being very marked indeed, and always of a uatnre to give too small
a value to the solar constant. These remarks apply not only to heterogeiieons radiations such as
are noted by the thermometer, but even to pencils of rays almost physically linear. It is observed
at the same time as we ascend that the transmissiDn of each ray on the whole grows greater for
like air masses, but that the proportion in which it grows greater appears also to vary very much
lictwecii tlu' extremities of the spectrum. Tlie fact that like air masses grow more transmissible as
we ascend, and the fact that non-homogeneous rays as a whole are less transmissible than we cal-
culate from our present formuhe, are not isolateil from each other, but have a bond of union in a
third fact, tliat tiir sclcrtive absorption of onr atmosphere is largely due to distinct particles present
in the low<'r air in greater (|Manlity tlian in tlie, tipper.
From all (liat has lieeii observed, whetlier at Allegheny, Lone Pine, or jMountain Camp, we
couclude that the action of onr atmosphere is incomparably more complex than the ordinary theory
assumes it to be, and, even were we provided with a much better theory, we repeat that causes
not yet fnlly understood, introduce systematic errors into high and low .sun observations, tending
to impair the results of the best observer at one station, and on the whole to lead him to underrate
the amount of the absorption. It will not be surprising, then, to llnd that, while onr results for
the amount of tliis ab<(ii ption are much larger tlian those of most ]U'e\ious observers, we cannot
assert tlieir aeeiuaey within limits as narrow as might be wished. I'ouillet gives his resnlt in
terms of thousandths of a calorie, and so do some of his successors, though piobably the use of a
third ]ilace of decimals is not intended by them to represent the accuracy of their results, even in
their own opinion. Uowever this may be, it seems certain that the earlier results have been cliauged
by amounts significant even in the unit's place ; or if we suppose that only the second decimal is
significant in the o]iinion of these writers, we shall tiiid that their error is still fully one hundred
times as great as wliiit they tliemselves supposed it likely to be. Warned liy tliis, I shall not
ask for confidence in tlie new value of the solar constant beyond at most the tiist decimal jdace.
We have from the observations at Allegheny 2.S4 calories. Tliere seems to be very little doubt,
in view of subsec|uent experiences, that this value is larger than would have been obtained under
more perfect observing conditions. We believe, in other words, that during the low sun observa-
tions at Allegheny the atmosphere is systiMuatically less transmLssible as compared with the noon
observations than it ]iidved at !\Ioiiiit Whitney. The actnally observed heat at Mountain Camp we
have shown was about '2, calories. We have already remarked that an extremely useful check upou
onr observations is the value to be found by adding to the heat received directly from the sun that
received at the same time from an exceptionally pure sky. This {in view of the sun's altitude at
iMoniit Whitney) will give us a value of about li.6 calories. The result which we have deduced
as most jiiobable from our comparisons of the heat at the uiiper and lower station is 3 07. (See
jiage 1 IS.) These are the principal means for our final detcrinination, unless we include one other
of a wholly dilleient nature.
The earth's actual mean surface temperature being about 15'^ or 10° (Centigrade), and it being
admitted that the heat from the interior, from the stars, from the dynamic effect of meteorites, and in
general from all other sources, is negligible, it will follow that if we know the laws under which this
heat enters and e.sca|ies from our atmosphere, we can determine what amount must be supplied to
the earth from without to maintain tliis known annual temperature of 1.5 or 16 degrees. The time has
uot yet iiroliably come for doing this with certainty, but this method is so wholly independent of
the others t hat it may be interesting to us to know its results. Pouillet's data in this respect have
been modified somewhat liy recent observation. Accepting them, however, as approximately true,
we must admit, if we follow his ingenious course of reasoning (but reject his hypothesis of an euor-
GENERAL SUMMARY OF EESULTS. 213
iiious licnt racli;itinii tVoni tlie slais). tliut tlic solar radiatiou is reiiresenteil by 3.13 calories. We
have lixeil already. tViim the iiatare of the observations on Mount Whitney, a.s an upper limit to
tlie solar eonstant the value ','</< ealories, and as a lower limit the value U.C calorie.s. Betv\-een
these limits we have three independent deteninnations, witlnint iiieludinjj; the method of Poiiillet.
I have already given the reasons which maUe me deem it uuadvisable to attempt to assiyii weights
to these determinations and to rondiine them by any conventional rule.
The reader has liail lielure Idai in the preceding jiages a detailed statement of the observations
and methods which have led to these result.s, and my own inference from them is that in the
present condition of our knowledge it is impossible to Us. any value of the solar constant with the
precision which used to be assigned to it ere the diffieidt conditions of the actual i)roblem were
known, though I thiidi that it has been clearly shown in the jireceding pages that this solar constant
is greater than has ordinarily been believed.
I\Iy coni'liisioii is that in \irw of the large limits of error we can adojit '1'IIi;i;e i'.\l<iI!IES an
the must pnilidhlt niliw (./' //k S(iL AK cuNSTANT, by which I mean that at the eartli's mean distance,
in the absence of its absorbing atmosphere, the solar rays would raise one gramme of water three
degrees Centigrade per nduute ibr each normally exposed square r-entiiiieter of its surface.
This is aiiproxiniately li;ti,.'i.")(t, 000 ergs ]ier s(|nare centimeter per minute. Expressed in terms
of melting ice. it implies a solar radiation cap.ibic of melting an ici- shell ."il.4.'") meters deep an-
nually over the whole surface of the earth. S(jiiie\vliat less than two thuds of this amount reaches
us at the seah'Vel oriliiiarily tiuiii a zenith sun. but unless very great luecantions are exercised
we are apt to iiiidei\ .line this directly recei\ccl amount. It Ibllows. then, that the selective absor])-
tion of our atiiiosiihere is not only more diverse in kind, but that the total atmosiiheric absorption
is far greater in amonut than has been commonly supposed.*
On other important poiuts our conclusions are as follows: (1) That although the actual solar
radiation is thus largel\ increased, yet the temperature of the earth's surface is not due principally
to this direct radiation, but to the quality of selective absori)tion in our atmosphere, without which
the temjiirdtxn-c of tin- soil in the tropics iiinhr ii ruticdl sun iroiihi prohiihli) not rise above —200 C.
Nearly all the '2lo or more degrees of ditfcreiice bet ween this and the actual mean temperature of the
planet's surface is due to this selective absorption, which accumulates the heat, though in a manner
which has not been hitherto correctly understood. It should be understood that these researches
have here a practical bearing of great consequence. The temperature of this jilanet, and with it
the existenci', not only of the hiiinan race, but of all organized life on the globe, appears, in the
light of the ccuiclusiiiiis reached by the .Mount Whitney expedition, to depend far less on the direct
solar heat than on the hitherto too little regarded quality of sclcctire absorption in our atmosphere,
■which we are now studyiug. (2) Generally speaking, the radiation which we see enter we see
escape within the utmost limits of the known solar spectrum. The heat storing action, from
checked re-radiation, to which the surface temperature of this planet is due, apparently goes on
beyond these limits where no spectral measurements have yet been made. No such wave-lengths
as those bc}onijln(i to the heat radiated from the soil, we believe, have ever entered our atmosphere from
the sun, though we admit their existence in the solar spectrum before absorption. These state-
ments must not be understood as at all implying a denial of the action of water vapor, which
we find probably plays an important [lart in the i)henoinena with which we have been dealing.
The preceding cousiderafiiuis I have limited to the bearing of these observations on meteor-
ology, but I need hardly iioiiit out to the student of solar physics how greatly the knowledge of
the relative increment of the bine, violet, and ultra-violet region must raise our estimate of the
temperature at which such radiations were hrst emitted, or enlarge lui the relation of the ju'eeed-
ing work to celestial i)hysics in other ways.
The observations which have been detailed could hardly have been made at a better site than
they were, and I know of none in the country as good. All the comparisons of the work herein
cited as done at the sea-level (at Allegheny), with that at a great altitude, enhance our estimates
of the importance to meteorology of .systematic observations at a very great elevation. It wcuild
* .Siptemtnr tj, l''s4 _x|„. i-nadcr who iiiiy Ije iiiilisposecl to accept so urcat an all^i>^|>till1l witlioiu liirtlicr ili,,ciis-
jpt s.
a arcat ai.
all^..l■i.tio
11 witlioiu li
niul
of .ScicUC,
■ tor .Scpte
luljcr. lS-<4.
214 RESEAECHES ON SOLAR HEAT.
be of the greatest service to solar physics and to meteorology if an observatory for these objects
could be established on Mount Whitney, and I strongly recommend the site, for the purposes
named, as among the most desirable on the North American continent. Until such a permanent
observatory is established observations made under the extreme ditBculties attendant on such an
expedition as the present cannot possess the accuracy otherwise attainable, and everything which
has been described as to tbe hard conditions under which these were carried out will dispense me
from claiming for the results, where novel, a higher character than that of useful first ajiproxima-
tions in a field of research where so much of the highest interest yet remains.
I have already acknowledged my indebtedness to the military members of the expedition, liut
to all, both military and civil, I caunot but remember how much it owes for earnest and helpful
service beyond what the line of strict duty demanded. To Mr. J. E. Keeler, in particular, whose
ability and fertility of resource were tested in many varied capacities, and without whom, on more
than one occasion, we should have failed, particular acknowledgment is due. After the return of
the expedition, Mr. F. W. Very was joined with him aud others in the very long reductions. To
Mr. Very's conscientious care, and to his acquaintance with tlie subject of meteorology, I desire
to express my great iudebteduess, as well as to others who have assisted me iu the preparation of
the volume.
I caunot close without remembering that the expedition itself, and this account of it, are first
owing to the generosity of a citizen of Pittsburgh, a friend of the observatory, who does uot desire
the mention of his name as a donor, but to whom anything of use to knowledge here is prinuirily due.
S. P. LANGLEY.
Alleguexy Obseuvatoey, Allegheny, Pa., December ill, 1883.
APPENDICES
A I' P E N B I X 1 .
DISCUSSION OF THE METHOD EMPLOYED IX THE KEDUCTION OF PSVCHIIOM-
ET E 1 ; o I! s !•; 1 ; v at r» n s .
It is well known that the iiiclication.s of the i)syelironieter are only eoniparable with eaclj other
when certain conditions of environment are complied with. Kegnanlt himself has exjieriinentally
investigated the ma.niiitnde of the influence produced by chansed surroundings, and the consefiuent
deviation from his theory, and has found it to be great in many instances. As the conditions
which have been fund most conducive to accuracy were seldom present in the p.sychrometer
observations made during the expedition, it seemed desirable to examine the probable extent of
their influence, with a view to the further improvement of the results, if this should be found
possible. Regnaull's fornuda. adopted in the "Smithsonian Tables" (B, page !-)• is
.r=/- ''■'^" {f~t')li = f-A{t-t')h.
■' t;ii) — /' ^ ' • '• '
in which, for slight variations of temiierature, the coefticient A is iieaily constant.
In the Lone Pine observations (' averages about 15^ Centigrade, whence ' ' = .bOOSOT is
the value of ^1 used in the Lone Pine re<luctions. Kegnaulfs experinunits show that in the open
air a smaller value than this may be nsed, but in inclosed positions a greater one is necessary, on
account of the radiatiou from the walls of the iuclosure ; ami in a small inclosed chamber A may
become as great as .001280. This is the same thing as saying that the depression of the wet bulb
uuder these circumstances may need to be increased, for the purpose of our calculation, in the
proportion of o..- =l.ol».
The surroundings of the psychrometer at Mount Whitney appear to have been .very similar to
the "inclosed chamber" of Kegnault, and it is worth noting that a comparison of its indications
with those of a Itegnault's hygrometer showed the necessity of a nearly identical correction.
At Lone Pine the case was more open, allowing a freer circulation of air ; but, owing to the
constant in%'asion of dust, it is probable that the wick was seldom m a condition to allow of free
evaporation. A number of con)i)arisons of this in.strument with a Regnault's hygrometer seemed
to show that a correction, similar to that deduced for the mountain apparatus, was also desirable
for the psychrometer used at Lone Pine.
Table A.
l'i}mimiif:oii" of iKiichromeler utid Rnjnnidl'x hijgromrter.
[Wind, gentle or cilm.]
Mount Whitney. '
Dry-tralb thermometer 18°.62
Dew-point (psychroraeter) — 0 .45
Dew-point (RoL'nanlt's hygrometer) ! — 12 . n
Depression of (lew-point (psychrometer) 19.07
Depression of dew-point (Regnault's hyiirometer) -.- 31 -12
Katio i9:;;=i'''^ ;;t;«='^-^^
• tlbserver. O, E. M. t Observer, A, C, D.
ll is to be uut.-il tlmt Ers".->»lt's hygrometer itself indicates too low a rtew-poiut when it is ex]
(See .in article l.y C^.^a, •■ Snr riiy-rometrie." .I.oirn.ll de Phy.si.ine. tome II, a- sorie, p. -1.^0.)
12535— No. XV 28
218
RESEAECHES ON SOLAE HEAT.
The question of the iufliience of the wiiiil ujioii tlic jisycln'ometer ol)st'rv:itioiis is one which
requires more careful considerntiou.
A few comparisons of the psyehroiiieter and Keynaulfs hygrometer, taUeii during the ])revalenoe
of a wind described by the observer as "fresh," indicate a diminished factor for reduction of
depression of dew-jioint by the psychrometer to correspond with the same quantity as given by
the Eegnault hygrometer.*
Table B.
Comparison of psyrhromrtcr wtth licgjiaidVs hiigromilirr.
[Wiml, fresh. Station, Lone Pine. 0b,«ierTer, A. C. D.]
Dew-point
(psychrometer).
Dry-bulb.
Dew.point
(Eeg. hygr.).
0.
12°. 62
11 .41
4 .93
14 .25
1 .28
a
19». 89
23 .50
27 .39
22 .22
25 .94
a
90.50
9 .50
3 .39
8 .39
2 .56
Mean.. 8 .90 23 .79
6 .67
DepresBion of dew-point (paychrometer) 14°- 89
Depression of dew-point (Kegnault's hygrometer) 17 . 12
Katio 1 .15
Tlie summary of Lone Pine observations, in Table 150, shows an apparently systematic varmtion
in tlie computed force of vapor with varying \elocities of the wind as Ibllows :
Average values from a .smooth corve :
Calm 8. 8
Gentle 7.5
Fresli ■ 6. 1
Brisk 4.5
Gale 3.8
The extreme values of 8.8 mm. and 3.8 mm. for "calm" and "gale," respectivly, corre.spond to
dew-points of 0°.-t 0. and — L'°.4 C, and if the reduction were due to air-currents about the p.sychro-
meter, assuming an air temperature of 30^ C. we shoukl have 2(P.O C. and 3'2°.i C for the de-
pressions of the dew-point in the two cases, the ratio of which is 1.57, a smaller change than that
ob.served by Eegnault, who has demonstrated the eflect of the wind upon the p.sychrouicter by
passing dry air with various velocities through a tube containing a wet and a dry bulb tliermometer.
(See Annals de Chimie etde Physique, 3" s6r., tome XV, p. 201.).
The followino' are some of his figures:
As reduced by the ordinary tables, no account being taken of the wind, these values would be
obtained :
Temperatue
Temperature
of dew-point.
Depression of
dew.point.
From (1)
-..- 15O.0
0.
— 3". 3
—37 .7
0.
18". 3
iipletL' record of al)ove obMervjitions see paf;eR 171, 172.
REDrCTION OF PSYCHROMETER OKSERVATIOXS. 219
The above iiniiil)i'is illiistiatc tlic wide div t'lui'iicc of results coiiiiiiitcd by tlje tables from
suc'b unusual e\|ieriiiieiits, as well as tlie uiarKed actiou (it the wind when very dry.
A e<iuiijarisiiii of (1) and (!') shows that with a veli.eity of wind (1..!.". limes as -reat the dejires-
sion of the wet bulb was l.il times as yreat, and the <%deulaled de|.ressinn ol' the dew-point was
l'..S8 times as great as when a nioderate velocity of the air current was maintaineil.
It must be remembered that the absolute dryness of the air used in tliese (■xiierinients uf Reg-
uault inereases the errors in (|uesticiii to their greatest possible extent.
If the diminution nl' ai]Ue(ins vapor with inereasing wind which was oliserved at I.one I'iue
bad been altogether an instrnnii-nlal elleet, jirodm'ed. for examjile. by imperfeet eva|Mprati(Ui froin
a wick iucessantly clogged witli dust, the dilference between the indications ol Ihe psycliKiineler
and Regnault's hygrometer sliouhl have pr(i,i;rcssi\cly diminished wiili the increment of the wind,
and should even have been obliterated during a gale; but while the comparisons in the table give
some support to this explanation, it is probable that some part of the observed iliminution in the
indications of the psychrometer w itii nicreasing wind is not an instrumental iieculiarity. Imt an
actual fact, since the prexailing winds at Lone Pine ha\e blown acauss a wide expanse of desert,
whence it may well happen th;it an ini'reasing win<l should systematically diminish the absolute
amount of uuiistnre by biinging into this arid regicm increasing ijuaidities of the still drici' air of
the desert.
Hie obseivations on top of Ihe mountain are init suliiciently numerous to allbrd much help in
regard to this sulijcct. .'-lo tar as they go, the\ atford no iiulication of diminished moisture with
increasing wind. Whetlur this is owing to the instrument case being "as well shielded from air-
currents as could be obtained" is an ojien qnesticui, bat it raises a suspicion in regard to the mag-
nitude of the supposed iutlnence.
It is to be noted that when the southeast wind, so prevalent at Lone Pine, blew on the mount-
ain (which hapi)eued but seldom) it iirodnced a dimiuiiticm in the absolute moisture. (See, how-
ever, the description of the envinuimeut of the Mcmntain Camp and its lUdbable intluence on the
wiud, page Iso.)
It must, therefore, be concluded that a ]iart of the diminiilifui in the ]isycliiiimeter indicatimis
observed to occur at Lone Pine with im reading wind must be attiilmteil to instriimeiital |>e(ailiari-
ties, aud a l)art to the desert origin of the w ind, but the propmtional part to be ascribi'd to either
intlueuce remains uncertain.
While the dew-points obserx cd with Regnault's bj'grometer were probably hardly numerous
or accurate emmgh to be used lor cmrecling Regnault's psychrometer formula, it seemed )iossible
that they might be emiiloyeil to determine an emiiirical correction which, api)lied to the indicatiims
of the ]isychrometi-r, waiuhl counteract the eltcct of the pre)iidicial intluence froiu the instrnmeutal
environment. The opinion of the Signal Ser\ ice was therefore sought.
/..//./■ o/ Prof. S. i: I.HIUllai h> ihr Chirf .Si;/««/ lllli.rr. l/llilnl Stalls AnillJ.
Alleoiiexv Oi:'pa:\ atoky,
SunmUr -it. ISSl.
Shi : It iViiM til,- oiiiiii.iii nf Pr(. lessor Alilje that results ot)t.aine(l on Mount WLH ni-y liy the wet iind ilry hiilb
nrJKlit lie nl ,loiil,iliit |.rerisi,iri. mviiii; to tlie exceptioual rituio.spheric eouditioiis. I therefore made observations »i-
nmlt^inc.iisly with tlu-l;-i;iiaiill liy- et.i, tie- results so f.irjastiC.viu- Professor Abbe's predielion that they are ipiite
diserepant with eaeb other. As tlie tivatiieiit of the rase mvolves ipiestious of some iniportauee, I send a .opy .d our
preliminary rediietions of these lew eas.s wh, i,- «.■ have smiuitaueous readings of both iiistrumeuts.
An opinion from the .Signal Office as to ihr ivl.itiv,- value of these instnuuentally discrepant delermiuatioiis I
should reeeive with interest.
.S. p. I.ANGLEY.
lieneral W. li. HaZICN, rl,i,f Sigmil llllini: ViiiUd StaUs Annij.
In regard to the above the following remarks by Professor Abbe were received from the Chief
Signal Office:
-l/enimuiirfiiiii ihlU'i} Xunmhir -Ji;. 1,-Sl. I!, marls i<ii 40-,';; Mi>.. IsSl.
The observations al Mount Whitney and l.niie Pine, as eoininuiii.ated by Pr.dessor I.aiigley, show larger iliserep-
aneies between the d.nv-poiiits oliserv.'d l.y KegnaiiU's apparatus ;ind those eoinpuied by the psychrometer Ihan are
usually found, for uistanee. on j.age ■.'. al tie- l.iwer laiiip. altitude l-J.imu feet ibar.nnetrie pressure not stated, but
220 RESEARCHES OX SOLAR HEAT.
assumed to 1"> iilimit -jll iuchcsl. im- dry-bulb 63"^ F. and for wet-bulb 15° F., the Regnault formula yivis a computed
dew-point ol about -Jf, V.. «liili- tin- observed dew-point is 9.5^ F., (.r lower by 16.5" F. The similar comparative ob-
servations made at Lone ?iue give observed dew-poiuts aluiost always lower than computeil acconliug to Professor
Langley by quantities varying between 0" and 18° F. Tlie former of these observations relates to an atmosphere
whose relative humidity is 10 or 'iS per cent., but for observations at Lone Pine the relative humidity is not given.
These discrepancies are much larger than those found by Regnault, Blauford, Belli, and otheis who have made
similar observations ill dry atmospheres and at low pressures, and I think that the explanation must consist partly in
the errois incideut to the use of the dew-point apparatus. Any more definite statement than this is iinimssible. owingto
the fact that nothing is said by Professor Langley as to whether he has corrected for baroiiutrie pressure and the
errors of his thermometers. The apparent effect of the wind is such as to indicate that he useil thick wicking
in place of thin uiuslin. His emiiirieal reductions for wicking and for wind are plausible, but should lie fonnded on a
large n'amber. of observed dew-points lielore being adopteil. If he still has the apparatus he sli.mld repeat these ob-
.servations iu the dry winter air.
Unless I know by personal inspection how carefnlly the dew jioint .Ti>paratus was handled I shonid advise the
adoption of the psychrometer work. If the observed dew-points are considered reliable jJcr sc, they can hereafter be
utilized iu connection with those made throughout the world to improve on Regnault's psychrometer formula, which
latter work has been undertaken by several, notably Belli. (.-<ee Zeitschrift fiir Meterologie, 1880 and 1881.)
Iu accordance witli tlir ailvirc (if Professor Abbe, tlie hygroinetic iiulicatiniis of tlie jisyeliro
meter have been adopteil without fatther correction.
Xole bi/ Fi-ofixxxr Ahhc. ,l„ii,t,tnj 31, 1.^-1. —Xot only did tlie iiieagerness of the data sent by Professor Langley forbid
deducing an eiiiiiineal loiieclnin apiiliealile to his iisyclinimetric results, but from a theoretical point of view it is
probable that the use of thick wicking on the wet-bulb so iiroticled it from the direct influence of radiation that
even when i-l' was large the correction for this item was reduced to a minimum : in other respects, of course, the use
of thick wickiug is objectionable, bnt as the Regnault dew-point api'aratns in very dry air and low dew-points gives
too low results. I think it preferable to retain Langiey's psyehiometrie results and reserve the observed dew-jioiufs (or
further discussion.
A P P K N n I X 2 .
EXPERIMENTAL DETERMINATION OF WAVELENGTHS IN THE INVISIBLE
PRISMATIC SPECTRUM.
(Note.— The following investigution was made at the expense of the Hache fund, and is published here by the
permission of its trustees. )
In Seiiteuiber. LS.sij while enj;aged a (ion iloiiut W'hitiiev, in iiieasiiriiig with a linear bolometer
the beat iu the invisible speetrnni of a dint pi ism. I came iipuu a hitherto uiiliiiowii eoUlband *
whose deviation indicated a (probably) very gretit wave length. We have had up to the present
time no way of measuring saeh wave-lengths directly, but are accustomed to determine them by-
more or less trtistwoithy extrapolation formula-. Ilir best known of which is Canchy's. Accord-
ingly, I attempted to calculate the wave-length by Caucliy's forniiila. but was at once conducted
to an impossible result. The formula, in other words, declared that no such inde.x of refraction
as I had measured was possible iu the prism in ques Jon. But the lueasuremeut was a fact beyond
dispute, and this drew my attention to the grossness of the errors to which the customary formulie
may lead.
Every jirism gives a dilfeiviit map of the siiectrum, nor when we find a band or line by the
I)rism have we any meaus of tixing the absolute place, exccjit by a reference to the normal or
wave-leugth scale, or to one derived from it.
It is desirable to deline, at the outset, the sen.se in which the term ''normal" is here used as
a synonym for ■■wave-length" sjicctrum.
The amount of energy in any region of the spi-i-liuni. such as that in any color, or between
any two specified limits, is a definite quantity, fixed by lads wliicli ate independent of our choice,
such as the nature of the radiant body, or the absorption which I lie ray has undergone. Beyoud
this, nature has no law which must govern us in reiu-csenting the distribution of the energy, and
all maps and charts of it are conventions.
If the length of the spectra formed by any two difleient agents, such as a prism and a giating,
be made equal, it does not then follow that the lengths of similar portions must be equal. In the
* Since designated as " 12."
WAVE-LEX(iTHS IX THE INVISIBLE PKISMATIO SI'ECTKUM. 221
case supposed we uliseivc, in f:ict, tliat tlic n-il |i(iitiiiii (for instance) of tlie prisinalic spectrum
will be narrower tlian tljc r<'il pdrtion (if tl]<' sccuml. lint since tlie anicmiit of enerj;y in tlii' red
must be reallv tlie same in butli, we nmst, in a ,i;rapliic rc]iresentation (if lliis eneri^y. incicase tlie
height of the urdinates in tlic red of the priMiiatic spcctinm, sd tliat tlie aieas sliall remain the
same.
The position of tlie maximnm ordinate is, then (in (ine sense), a matter of choice, and fixed
only by the scale we elect to cmjilny. We lind. tor instance, in the ]iiismatic spectrum, that this
ordinate is in sonic jiart (if the intra red. dcpcndiiiL; (m the p'ltii iil.ir prism used, while in the
grating siiectriiin it is. under the same ciicnmstanccs, always in one jiait (if tlie yellow : and we
might conceive of an ajiparatns which should always exhilnt it in the ultra-violet, or wliicli should
even .show the same energy at one wave length as at any other, or embody- any other arbitrary
mental picture of it. It is certainly a jiraclical cdnsideration of the first impurtance that no su(di
apparatus actually exists; but still, whether it exists (ir ikiI. in sd representing the distribution
of energy we should break no law except that iinpdseil by cunsidei jtieiis of simplicity and con-
venience.
Did the wurd •■ndrmal" then signify "absdlute" there would lie no spectrum exclnsivelv
entitled to such a name; tint in this cdniiectiini the Wdrd is alwa\s t(i be understood in its radical
meaning of an accepted rule or tyjie of cunstrnction. Such a t\iie exists in the wavelength
spectrum, and it has obtained general acceptance, not only (in accdunt iif its sinijilicitv and
convenience, but of its. al picsent. niiiipie claim td be a '• iiatiiial" (inc. It is pr(i|ierly distinyiiislied
as the •■natural" scale lidin its iidt ineiidy rcpicM'iiting a mental picture (if the disti ibutidii of tlie
energy under a very siin]ile law, but of actually lieiiu/ that which we do prdduce by onr most
efficient optical apparatus and make visible and measurable at will.
While we remain at liberty, then, to represent the energy siiectrum in terms of the wave-
fre(|uency or of the reciprocal ot the square of the wave-length, or of any other function of it, and
while we may often find occasion to use these scales for some special puriioses, we are (and all the
more especially that we habituallx speak in terms of the wave h'ligtli) le(l by cdiisideratidns of a
very practical kind to take as our iidrmal nr standard scale that (if the wa\elength itself.
Since we have this normal spectrum actually before ns, through the concave gratings
constructed by Professor Kowlaml, it may seem as though we might dispense with the prism, but this
is not as yet possible for the lower part of the spectrum, where oxerlapiiing spectra and feeble
heat here make the use nf the grating too ditlicnlt. If we cdiild use the siilar energy here, iidt in
the form of heat, but of chemical actidii, as in iihdtogiaphy. a yrcat advance might be made; and
there is reason, I believe, td Imiie that the lalmis nf I'mfcsMir Idiwhiml and Caiitain Abney w-ill
ere long do this for ns with ]irecisi(in. At iircscnt. hnwcver. we lia\e unly hear, and the thermo-
pile or the bolometer, which latter, though less sensitive than the camera, can be made, as I shall
show, to determine experimentally within known limits of error, the actual wave-lengths corre.
sponding to given indices of refraction, and hence to aftbrd here valid exiierimental data for jiassing
from the jirismatic spectrum td the nurmal diie. The reasdii why this so desirable intbrmatidn has
never been dlitained befiire is tudfold: (Istl While the measureiiient in ipicstidii can best be made
by means of a prism and grating conjointly, the heat, which in the hiwer prismatic spectrum is
very faint, becdines almost a \anisliiiig (jnantity when it has pa-sed the grating also, where the
heat is on the average less than une tenth that (riiiii the pi ism. \\ C must use, too, if pnssible, a
narrow aperture td register this heat, tbr a liniad one might inn accdiint of the ciimpression of the
infra-red by the prism ; cd\ er the ulmle lield. in which I's wmi; shdiild lie td discriminate: (L'd) AN'o
must have not only an iiistiiiinent mure sciimIivc than the ( ikhi tliermd|iile, lint we must ile\isc
some way of lixiug, with .in aiipi.ixiiiiatc piccishin. the iidiiit at which we are nieasiuiii^ when
that point is actually iin imIiIc.
The apparatus 1 have ilc\ is d tin this dimble iiiiipdsc has ihine its wdik with a degree nf
accuracy, which, if it may be called cunsidciablc, as cumparcd with what we have been used to
in heat nieasineincnts, is yet ncccss.inlx inteiinr to that dlitained by the e\e, and less than we may
hope for at siiiiie liitiiie time lidiii plidtngi apli\ . Nevertheless, it has, 1 believe, given experi-
mental data, very far outside the \ imIiIc siicclinm, by which we may either constrnct an emiiirical
formula and su)iiily its proper cdiistants sd that it will be trnstwoilhy within extended limits, di
222 RESEARCHES ON SOLAR HEAT.
test the exactness of such formula; as Caucby'is, RetUenbacher's, &c., wliieli, while i)rofessii)g a
theoretical basis, only agree in their results wiihiu the limits of the visible spectrum (from which
thej' have been iu fact derived, and where they are comijaratively unneeded). They contradict
each other, as will be seen, as soon as they are called on for information, in the region ontside of
it, where they would be chiefly useful.
The present work has been preceded by a new niaji of the invisible i)risniatic spectrum, where
the ab.scissiB were proi>ortional to the deviations in a certain prism (see Plate XI); and the
immediate object of this research is to pass from the arbitrardy spaced ])risinatic scale, belonging
to the particular prism in question, to a map on the normal r.nd absolutely general cue.
I should perhaps make the cautionary remark, that the general conclusions here offered, as to
the relation of wave-lengths and indices of refraction, have been drawn from observations on a
single jirism and have not been experimentally verified ou others. This is on account of the
extremely slow and laborious character of the process used (which has involved some mouths of labor
for this special prism). Though there seems no reason to doubt the generality of our conclusions,
it may be hoped that those experiments will be repeated with prisms of other material, and by other
observers, now that the prelinnnary obstacles have been removed.
In order to map the spectrum on the normal scale, where the wa\e-lengths are equally spaced,
from such a map as thatshowu in Plate XI ("Prismatic Spectrum"), in which the consideration of
wave-lengths does not enter, it is necessary to establish some relation between the wavelengths
of rays and their deviations, or between their wave-lengtlis and refractive indices, which are con-
nected with the deviations by the well-known formula
■ (a-fd)
sin -^-
n =
a
sm „
where (( = the refracting angle of tlie prism, d = the deviation, and n = the corresponding index
of refraction. In the visible spectrum the deviation, in any prism, of the Fraunhofer lines (whose
wave-lengths have been very accurately determined) can be measured by means of an eye-piece with
cross- wires; and, from a sufficient number of such measurements, by making ordioates propor-
tional to indices of refraction (or to deviations) and abscissa' proportional to wave-lengths, a carve
may be found whose equation is ii = {<.')>. or tl = (tr)A, representing the required relation to any
degree of exactness.
In the invi.siblespcctnim the ditliculties ai'c immensely greater, and demaml special means, not
only on account of this invisibility, but owing to the absori)tion of the prism and to its compress-
ing the rays.
The prism here used was nnide by Adam Hilger, of London, and its oi)tical propertes are iu
every way satisfactory. It is of a white flint, which has proved singularly transparent to the
longest solar waves. Its principal constants have already been given (p. l.'.iO).
APPAKATUS FOR 3IEASUKING OnSCUKE WAVE-LENGTHS.
In ISSli an apparatus was employed in which invisible rajs, after passing through the Hilger
l)rism, at a kuowu deviation, fell on a Rutherfurd leflecting grating (either of 081 lines to the
millimeter or half that number), from which the ditfractcd invisible ray fell on the bolometer at a
measured angle with tljc grating. By the use of the known formula (« s i=sin i -f- sin r) connect-
ing the angle of diti'raction with the wavc-lcngtli, tlie wave-length was then found.
Several determinations were thus made of wavelengths iu the upper i)art of the infra-red,
where the heat is relatnely great; but. tlnaigh the definition of tlie Kutlierfurd grating was
admirable, it was not large enough to sujiply sutticient heat to enable measures in the lower
infrared to be made with confidence.
In May, 1882, I had the good fortune to secure one of the very large concave gratings, then
newly constructed by Profes.sor Rowland, and which he was kind enough to make for me of a
very short focus, so as to give a specially hot spectrum. After many essays, during which a great
number of mechanical and optical arrangements for getting rid of the supcriio.sed spectra were
tried with unsatisfactory results, it became clear that, for this large and concave grating, it was
WAVE LKNGTHS I^T TFTE IXYISIBLE PRISMATIC SPECTRUM.
223
necessary to let the ray fall first iin it and then on the prism, tlins making- tlie wave-length the
known, and the deviation the nnknown, qnantity.
In the use of this form of grating the slit is iihieed in the circumference of a circle, whose
diameter is equal to the radius of curvature of the grating, and which touches its surface. The
spectra are then formed, without the need of collimator, observing telescope or any further
apparatus, all lying upon the circumference of tlie <ircle which contains the slit. The grating
which was employed ciuitains 18,050 lines, 14:.' to tlic millimeter (3,010 per inch), ruled on the sur-
face of a concave mirror of siieculum metal of 1"'.G3 (04 inches) radius of curvature, and exjioses a
ruled surface of li'D'"' (I'O square inches). By this large surface a spectrum is iiroduced sutti
ciently hot, even in its lower wave-lengths, to ettect the lioloineter strips after the various rctli-c-
tions and ab.sorptions to which the heat is necessarily sulijcctiMl in jiassing through the appaivitus.
Figure 17 illustrates the means finally adopted, and the <-(mrsc of the ra,\s thiDugh the api^a-
ratus; although, for the sake of distinctni'ss, the mechanicMl devices used to maintain the piiipcr
arrangements ot the parts aic omitted. The rays of liglit, coining from the I L' inch tlat mirrcir of
224 RESEARCHES ON SOLAR HEAT.
the large siderostiit, pas.s across the apparatus, and fall upon a 7 inch concave speculum at M, bj'
which at a distance of about 5 feet they are converged to a focus at Si. At this point is a vertical
slit, adjustable to any desired width by a double screw, which moves both jaws at once, so as to
keep the center always in the same place. This slit is protected from the great heat by a plate of
iron pierced with an aperture only a little larger than the slit when open to the usual width.
Beyond Si the rays diverge and fall upon the concave grating G. Directly opposite the grating is
a second slit, S,, also d(iu1)le acting, and the apparatus is so arranged that the two slits Si, S2, and
the gratingG, always lie upou the circumfereuce of a circle, whose diameter is Clinches; and there-
fore in whatever manner the slits may be placed, the light coming through Si forms a sharp spec"
trum upou S.>. A very massive arm carrying the grating, the slit Sj, and the heavy spectro-bolom-
eter, is pivoted at the center of the circle, so that the relative positions of these parts are un-
changed. The slit 82 is automatically kept diametrically opposite the grating, and on the normal
to its center.
The slit 82 is the slit of the spectro-bolometer, provided with the same attachments as when
used for mapping the visible spectrum (except that it is now fitted with simple collimating and ob-
jective lenses of the same special kind of diathermauous glass as the prism, instead of its own con-
cave mirror). Its eye-piece and the bolometer are interchangeable.
By means of the eye-piece aud graduated circle, the deviation and consequeutly the refractive
index of the rays passing through the slit can be determined, if they are visible. If they are in-
visible, their exact wave-length is known by a simple ocular observation of the visible oues, on
which they are superposed by the action of the grating, while their subsequent deviation is deter-
minable by the bolometer placed at B, provided they retain sufficient energy to affect the instru-
ment. It will be seen that according to this method all those invisible rays which are n times the
definitely known length of some vi.sible ray are caused to pass together through a slit, and then
through a prism, which sorts out the ray of the first spectrum from that of the second, that of the
second from that of the third, aud so on, so that the corresponding index of refraction may be de-
termined by observation with the eye in the case of the visible, with the bolometer in that of the
invisible ray.
To illustrate the use of the above described apparatus uiuler somewhat unfavorable circum-
stances, let us consider as an example the observations of June 13, LS82, which were taken far
down in the spectrum where the heat is feeble and the galvanometer deflection small, requiring a
widely open slit. The apparatus having been previously adjusted, and the sunlight properly di-
rected by the siderostat, the visible Fraunhofer Hue B, of the third spectrum of the gratiug, was
caused to fall upon the slit S., of the spectro-bolometer. Then, according to the theory of the
grating, there passed through this slit, rays having the wave-lciigtlis —
0//.O89 (3d spectrum, visilde).
1. 178 (2d spectrum, invisible).
1. 767 (1st spectrum, invisible).
The prism having been removed, and the telescoi^e brought into line, an image of S;, of the
same size as the .slit itself, was formed in the focus of the object lens, and on testing with the bolom-
eter, whose face was covered with a card-board screen pierced centrally with a 2"'"' slit, the heat
of this image produced a deflection of the galvanometer needle of about 30 divisions. The prism
was then replaced on the automatic holder and set to minimum deviation, and the image of the
slit, containing superposed rays whose combined efl'ect had produced the deflection just mentioned,
was separated into three similar images (as in Fig. IS),* each composed of nearly homogeneous
rays, aud of same dimen.sions as the slit S2. Of these three bands only the first or most refrangi-
ble, containing the Dj line, was visible, aud its deviation was found to be 17° 41', agreeing with
the value given by the table. It was the object of the experiment to find the place of the lower
invisible band, by groping for it, /. e., to determine its deviation by trials with the bolometer at
intervals sufficiently close to avoid the possibility of missing it altogether. According to Briot's
formula, the deviation should be io° 21', and in the preliminary search the circle was accordingly
•These three ini.Tge8, beiug composed of rays of different wave-leugtbs, could uot all be in focus at the !
time, since the collimator and objective of the spectrometer were simple lenses. The lenses were adjusted by
of a table of focal distances previously prepared, so as to throw a sharp (invisible) image of the baud to be detected.
WAVELENGTHS IN THE INVISIBLE PKISMATIC SPEOTRUM.
225
set to tins reading. Beginning at this point, and exposing the bolometer at every five minutes of
deviation, it was fonnd that the maxinuun etieet was obtained nearer 4.5^ 15'. The approximate
position having thus been found, the slit Si was narrowed to 13'""', and the following measurements
\m wf'-
''''t-fMf\
?. ■i'if"':i
iL 'T 1,; I'll !|i|| !|i:i||i|i: ' l!|:''ii:'{''li:|<|'
'^ I'li'ji'i r'l|i
' !■' ' ' III ll' 1 '• 'i' ' '.'1 1
■J. i, . ' 1 ''.!l'| !■ ■ i i;
I,', li.ii ■ '^
fs
'^ ■ ll 'i 1
lili'lilt
taken, the horizontal line givin
as it was moved through the spectrunj
med by Prism in determinal.ion of W^aV3-lenghh3.
the mean results of a .series of thirty exposures of the bolometer,
TAtiLE C.
Mitlwd ufJiiiiUiiij nfraiinibiUlii offnhle halt rai/»
45.10 45.15 45.20
The maximum reading at 45^ 10' corresponds to a coincidence of the 2mm. bolometer aper-
ture with the 2nini. iuvisible image of the slit, whose position is sought. I'mm a subsidiar.y
curve drawn thnmgh the points whose co-ordinates are respectively.
(.v=4B0 02', y=i-r>),
{.r=45° 07', l/=o.t'i),
{X=45° 10', i/=<3.0), \-c.,
it was concluded that the deviation of rays whose wave-length is 1.707 is 45° 10', and each
point in this determination being obtained from the mean of five observations, the result is partly
free from irregularities caused by changes in the state of the sky, and minute instrumental varia-
tions from extraneous causes, which here become of great relative importance, owing to tlic fcelib.'
heat measured.
Subsequent determinations, like the preceding, gave for the deviation of the same ray 45^ ()(!'
and 45° 07', and from a consideration of all the deviation adopted was (instead of 45° 21', as given
by Briot's formula) 45° OS', corresponding to a refractive index of 1.554!).
By means of measurements like the one described above, the deviations of various obscure
rays of known wave-lengths were determined. The indices of refraction were then computed liy
the usual formula
sin A (11 + ll)
table, wlicie. Imwcxer, only the
where (( = 02^ .'U' 4:!". The results are contained in the tolI(
results of succcsstiil days are given, most of the obscrvalions having been lust through chan;.
of the sky during the course of one determination:*
Table D.
Ejcpeiimeiilal cktermiiiation of d or u af a function of A (Hilgcr p,i«m}.
v;ition.s In
rful ami c
Date of observation.
June 13-;
.Itily 14 .
46 12
45 54
45 IC
45 08
44 45
44 25
1. 5654
1. 5625
1. 5362
1. 5549
■iiij; the
elaliou betv
n and ,1 can be coudiu-ti-il with at le
.stant .-Ifctrii' linlit as tiy siinliglit. Tlio latter only, Ik
125o5 — No. XV-
226 KESEAROHES ON SOLAR HEAT.
We observe tliat, wljere measures are taken in the [irismatic spectrum alone, we can generally
use with advantage a bolometer of as small an aperture as one fifth of a millimeter; but that
here it is advisable to open it to 2mm., owiug to the relative expansion of the spectrum, and to
the very feeble heat. Where such measures are taken in the shorter wave-lengths of the infra-
red, /. e., in the upper (invisible) grating spectrum, they are comparatively easy from the greater
heat, and can be made with a narrow aperture; but where in the lower invisible spectrum, as
here, they grow more and moi'e difficult as the wave-length increases, so that if we could repeat
each observation often enough, we should determine a separate probable error for each point of
the curve.
Owing to difSculties arising from the almost infinitesimal amount of heat in question, numerous
subsidiary observations are requisite for a single determination, which it therefore takes long to
make, the probable errors in the table being found in each case from betweeu 20 and 100 readings.
If it should possibly appear to the reader that in the three months of consecutive labor which were
given to this part of the work, more than six jwints might have been determined in the curve, he
is asked to remember that what is here difficult has till now been impossible. If we treat, in such
a case as that given above, the discrepancy of the cited determinations as being fairly typical (as
they appear to be), we shall obtain a probable error of about one minute of arc, and a comparison
of the different points with each other on the large curve exhibited indicates a similar result. It
will not appear improbable that this accuracy of setting should be attained by a bolometer whose
face covers many minutes of arc, when it is noted that in the given instance nearly 100 readings
are taken to fix the single determination. The error in the determination of a wavelength, again,
for one and the same error in deviation, increases rapidly as we go down the spectrum. If, then,
we regard the deviations as being correct, and ask in turn what the probable error of the corre-
sponding wave-length is, as given by our curve, we find that this probable error of A varies at each
point, but that it but slightly exceeds a unit of the second decimal place, in any case, for an error
of deviation of one minute of arc. The most satisfactory evidence, however, as to the degree of
accuracy attained, is derived by an inspection of the curve of observation on the original charts.
For we are now prepared to draw a curve expressing graphically the relation between deviations
or refractive indices and wave-lengths, extending throughout both the visible and invisible parts of
the spectrum. Plotting the points given by the data in Table D, and drawing a smooth curve
through them, we obtain the "curve of observation" showing n as a function of A in the lower curve
of Plate XIX, and d as a function of A in the curve of Plate XX, where the x'oints obtained by
observation are distinguished by small dots.
There would be no gain in accuracy, at this stage, in attempting to work from a formula rep-
resenting the equation of the curve obtained, as the grajjhical construction is fully as trustworthy
as the data. This I say with special reference to the large original charts* which have been drawn
by Jlr. J. E. Keeler, of this observatory, and which seem to me favorable specimens of the accu-
racy attainable by this method.
We are now prepared to test the accuracy of the various formnUf connecting refraction with
wave-length, though it will be convenient to first prepare a table showing what this relation is in
the visible part of tlie si)ectrum of the prism employed.
In the following table the deviations in the visible spectrum were measured by the spectro-
meter, reading to 10" of arc, which has been already described, in which for this special purpose
the bolometer was replaced by an achromatic observing telescope with a micrometer eye-piece, and
tlic indices of refraction were computed by the usual formula. "O" in the ultra violet was meas-
ured by aid of a Soret fluorescent eye piece, and its wavelength is from Cornu. The other wave-
lengtlis are taken from Angstrom. But the unit is here the wnV/on = y„Joiy millimeter = (10,000
times the unit of Angstrom's scale). "A" is here the symbol for the wave-length.
*■ These original cbarts were exhibited to the meinliers of the National Academy of Scieuces, at Washiugt
April, W83. The engraviug here given in illustration, being on a much reduced scale, will merely indicate the (
ueas of iuterpolation possible by the originals.
i
40 60
226 KESEAROHES ON SOLAR HEAT.
We observe tliat, where measures are taken in tlie [irismatic! spectrum alone, we can generally
use with advantage a bolometer of as small an aperture as one fifth of a millimeter; but that
here it is advisable to open it to 2nim., owing to the relative expansion of the spectrum, and to
the very feeble heat. Where such measures are taken in the shorter wave-lengths of the infra-
red, /. (-., in the upjter (invisible) grating spectrum, they are comparatively ea.sy from the greater
heat, and can be made with a narrow aperture; but where in the lower invisible spectrum, as
here, they grow more and more dilBcult as the wave-length increases, so that if we could repeat
each observation often enough, we should determine a separate probable error for each point of
the curve.
Owing to difflculties arising from the almost infinitesimal amount of heat in question, numerous
subsidiary observations are requisite for a single determination, which it therefore takes long to
make, the probable errors in the table being found in each case from between 20 and 100 readings.
If it should jDossibly appear to the reader that in the three months of consecutive labor which were
given to this part of the work, more than six jwiuts might have been determined in the curve, he
is asked to remember that what is here difficult has till now been impossible. If we treat, in such
a case as that given above, the discrepancy of the cited determinations as being fairly typical (as
they apjiear to be), we shall obtain a probable error of about one minute of arc, and a comparison
of the different points with each other on the large curve exhibited indicates a similar result. It
will not appear improbable that this accuracy of .setting should be attained by a bolometer whose
face covers many minutes of arc, when it is noted that in the given instance nearly 100 readings
are taken to fix the single determination. The error in the determination of a wavelength, again,
for one and the same error in deviation, increases rapidly as we go down the spectrum. If, then,
we regard the deviations as being correct, and ask in turn what the probable error of the corre-
sponding wave-length is, as given by our curve, we find that this probable error of A varies at each
X>oint, but that it but slightly exceeds a unit of the second decimal place, in any case, for an error
of deviation of one minute of arc. The most satisfactory evidence, however, as to the degree of
accuracy attained, is derived by an inspection of the curve of observation on the original charts.
For we are now prepared to draw a curve expressing graphically the relation between deviations
or refractive indices and wave-lengths, extending throughout both the visil)le and invisible parts of
the spectrum. Plotting the points given by the data in Table D, and drawing a smooth curve
through them, we obtain the "curve of observation" showiug ti as a function of A in the lower curve
of Plate XIX, and d as a function of A in the curv^e of Plate XX, where the points obtained by
observation are distinguished by small dots.
There would be no gain in accuracy, at this stage, in attempting to work from a formula rep-
resenting the equation of the curve obtained, as the graphical construction is fully as trustworthy
as the (lata. This I say with special reference to the large original charts* which have been drawn
by Mr. J. E. Keeler, of this observatory, and which seem to me favorable specimens of the accu-
racy attainable by this method.
We are now prepared to test the accuracy of the various formnlw connecting refraction with
wave length, though it will be convenient to first prei)are a table showing what this relation is in
the visible part of the spectrum of the prism eiuidoyed.
In the following table the deviations in the visible spectrum were measured by the spectro-
meter, reading to 10" of arc, which has been already described, in which for this special purpose
the biiloiiieter was replaced by an achromatic observing telescope with a micrometer eye-piece, and
tile imiiccs lit refraction were computed by the usual formula. "O" in the ultra violet was meas-
unil liy aid of a Soret fluorescent eye piece, and its wavelength is from Cornu. The other wave-
leii.utlis are taken from Angstrom. But the unit is here the ffl(f;-Ort = joJou "'il'inieter= (10,000
limes the unit of Angstroni's scale). "A" is here the symbol for the wave-length.
^ Tliese original cbjirts were exhibited to the meniberB of the National Academy of Sciences, at Washingtou, in
April, 1H83. Tile engraving here given in illustration, being on a much reduced scale, will merely indicate the exact-
ness of interpolation possible by the originals.
)200
)IOO
I
\
\
900
800
'
\
■^
"^^^
i5^
^^
:~ -
600
500
-^~-
^
~~
^
■ —---
— — -. 'Z^u/a
r_
-~~~
- — _
----.
■/EKerUr
D,i
100 120 1.40 160
PLATE XIX,
Curve ii=f (X) for the Hilger Prism.
2.20 2 40
4^
4^
o
oo
4^
O
_____
_^
\ __^
^
^^""^
z'
/
.
/
/
7
1
! 1
WAVELENGTHS IN THE INVISIBLE PRISMATIC SPECTRUM.
227
The following indices in the visible spectrum on which the coniputations lor tcstiii}; tin- Inr
mulw are founded are trustworthy to the fourth decimal place here given :
Table B.
Oiserrcd Indicen in risible, spectmyi of Hilgrr prism.
Line.
*
d
n
^
o .
A
0 78009
46 49
05
C
. ' 0.65618
47 15
45
1. 57.5V
Di
0. 58890
47 41
15
1. 5798
48 21
18 44
05
15
1. 5862
1. 5899
F
1 0.48606
Hi
0 ;i9679
50 34
05
1. 61170
0
0. 34400
52 43
00
1. 6260
A smooth curve drawn through the points, whose positions are given by the above table, rep-
resents with accuracy the relation between n and A in the visible part of the spectrum. This
method is, however, obviously inapplicable to the very extended invisible portion below the A
line ; and accordingly attempts were first made to efiect the determination of corresponding indices
and wavelengths by extending the curve derived from the above observations by means of for-
mula'. Several formuhe have, it will be remembered, been projjosed by physicists, expressing »
as a lunction of A, and containing constants wliich are to be determined l)y observation. But it
has never bitherto been possible to test these formuhe far from the visible spectrum, whence their
constants have been in fact derived.
This desirable test we are now prepared to apply. The simplest as well as the most widely,
nsed formula is that of Cauchy, which, as it is commonly written,
(«="+i+xO
/V "^ A
contains three unknown (piantities requiring for their determination three simultan
Selecting the lines A, D, and H for this purpose, we have from the table just
e()Uations —
1.5714 = f( 4- ,M -riiuKivJ + /iTTcdMiiH 1.5i98 = «+ /ii K«xno\2 +
s eiiiiafions.
L^n the three
(0.
ri.i(»(iit)- ^ (o.Toouii)^
l.(i070 = (( +
from which by elimination
,( = 1.55!«, h-^
so tliat tor this prism, the formula becomes,
H = 1.5593 + '
(O.3'J«70)-
+
(0.588!>())'
c
' (0.30070)'
f = 0.0001137
0.0001137
(O.5.S.S0O)*
which, we find on trial, satisfies the observations in the visible part of the spectriiiii within very
narrow limits. When, however, we attempt to extend the application of the foniiuhi to the infra
red region, its results are not so satisfactory. Since h and o are both positive, tlie least value
which n can have, in our prism, according to the formula, is a, or 1.5503, coriesponding to a
deviation of 45"^ 35', whereas the bolometricr measurements show that in this prism tlie solar
spectrum, after absorption, extends as low as 44'^, with every sign that if it do not extend yet farther,
it is not on account of the prism, but because lielow this point t!ie heat is absorbed by sonic ingredient
of our atmosphere.
We conclude, then, that Cauchy's formula gives grossly erroneous results, when extended far
beyond the limits within which the observations on which it is founded are made. Its implicit
as.sertion that the lower limit of the jirismatic spectrum (however great the wave length of the
ray transmitted) is not so f.ir below A as A is lielow D, is alisolutely contradicted liy these
experiments; and all extra-polations made by it, far from the visible speetriiiii in which its constants
have been determined, are wholly untrustworthy, as will appear more fully later.
228
kksp:arches on solar heat.
Eedtenbacher proposes the formula.
--a + hr- + ^^
for expressing the same relation. Using tlie same lines as before for ileterinining tbe unknown
constants, we have for the Hilger prism
A = 0.412297 - ().01I()!)3711A- — '^'■f"*39220
a formula which also satisfies the observations in the visible spectrum, but fails when extended to
the invisible. The curve representing it has a minimum point, corresponding to n^ 1.5647, for a
value of A found from the equation A^ = f , or, in the special case of the formula above, where -^ is
b b
positive, A ^1.430; so that for every value of « greater than 1.5647 there are two real values of A.
This formula, therefore, is even less satisfactory than that of Cauchy.
Briot gives a formula which has been asserted by other investigators* to represent satisfactorily
the results of observation througiiout the whole spectrum, namely :
1
= <( + i
CaD+KSVKS)
From four equations like this, using values of ii and A, corresponding to the Fraunhofer lines
A, C, F, and H, the values of the constants were determiuedt as follows:
= 0.4102S,
;*= -0.0013495,
-0.00000.3379,
i-=-|- 0.0022329.
With the aid of these constants, the wavelengths corresponding to given refractive indices
were computed, and a curve representing the formula was plotted. This curve, as well as tho.se
rejjresentiug Cauchy's and IJedtenbaoher's forinulrt, is shown in Plate XIX, where we may obtain
by simple inspection the actual error.s of all the formula? in question, or we nuiy take them from
the following table, whose results, I hope, will supi)ly useful data for those who are interested in
theories of dispersion.
Table F.
Apiiror
•-leiiijlhx hn Biiol's, Caiichij's. and Redleilbacher's foi
[Comjyarison of theories ii'ith observatiou).
n„hi\ for ruhl haiuJx
71 1 1 Wave-lengtbs derived by extrapolation.
Observed.
By observa- i
From Briot'3
fornmla-
From Cauchy'a
formula.
From Redtenbacher's forraula.
A ValQe.
Error.
Value,
Error.
I. Value. 1 Error, 11. Value,
Errcu'.
0.000
0.000
0.000
0.001
0.001
0.002
0.040
0,760
0,818
0,853
0,900
0,920
0,900
1, 270
1,730
2,460
0. 000
0.003
0.003
0.010
0.010
0.020
0.140
0.460
1.100
0, 700 0 000
0, 820 ; 0. 005
0, 862 0, 012
0,915 0,025
0, 941 0, 031
0, 990 0, 050
Imag nary.
1. 5678 0. 890 1). 891
1.5674 0.910 0.911
1. 5668 ' 0. 940 0. 942
1,5636 1.130 1.170
2,230
2,170
2,060
Imag
1,340
1,260
1.120
nary.
X 1. 5570 1. 540
J, 1. 5572 1. 580
1.800
2.105
to
2.260
2. 460
2.524
0.220
0.295
to
0.390
0.480
0.494
n ? to to
Note. — A part of the above values of n, wljere detenxiJDed from oljservation "by the bolometer, are liable
.0 error in the fourth decimal place. For probable errors of A, as observed, see Tabic D. " \ Observed" ia
jither from a direct observation or from an interpolation between two closely contiguous observations.
*Moiito!i, Comptes Rendus, tome 89, page 297, tome 88, page 1190.
t This formula has tbe practical inconvenience of leading to cubic equations either in ii- or A-, the solution of
ich is so tedious as to forbid ita use where many places are to bo independently found. I have been aided in the
sent Icu-thy nnnurical computations by Prof. M. B. Goff.
WAVELENGTHS IN THE INVISIBLE PRISMATK! SPEOTKUM. 229
It is evident that Briot'.s foniuila, tlioiigli not exact, yet gives results niiu-li more trustwortliy
than the others considered, and it was enii)loye(l in constructing provisional niajis of the normal
spectrum from the prismatic until an apparatus was completed for detcrMiining the \va;c lengths
of the invisible rays by direct measurement.
We must evidently conclude, from the numbers in Table F and from the curve in I'late XIX
which embodies them, that wc in reality can scarcely assign any limit to the extent of the infra-red
prismatic spectrum, and that, far from the curve having an asymptote parallel to the axis of X, as
Cauchy's theory requires, our curve, so far as we can follow it, rather tends to ultimately coincide
with a straight line cutting the axis at a liuite angle, and (if this axis jiass tliroiigli the point h = 1)
at a great distance from the origin.
With the danger of estra-polations luvsented to us in sueli exani]il<s as lia\i> been cited, we
shall not attempt to generalize the results of our obserxaticms fuitber than to remark that, for the
prism in question, we tind that the deviation tends within the limits of observation to become pro-
portional to the wavelengths as the deviation diminishes, and that, as far as we can see at pres-
ent, there is scarcely any limit to the wavelength our prism can transmit except that tixed by its
absorptive ettect.
The approximate limit of the solar spectrum of the Hilger prism is at ii = 1 .'iV','>, which,
according to Briot's formnla, corresponds nearly to 3.7.4, but which, according t" our bolometric
observations, corresponds to an actual wavelength of 2,«.S. For this same jioint. as will lie .seen by
Table F, the values by Cauchy"s formula are impossible and those by Kedtenbaelier's formula are
imaginary.
We may add that Briot's formula gives a point of iutiexion near /- = -;■. In other words, the
curve, which up to near the limits of our chart (Fig. 2) has been con\ex to the axis of A, there
becomes concave, and, as we lind, would cut the axis near /. = 16," (/. r., for » = ] /. = lO-.d). These
values of ours for Briot's formula rest, it will be remembered, on extra]iolafions foundi.'d on meas-
ures in the visible spectrum.
"WAYE-LENCTHS OF COLD LINES IN INFRAKED rKIS:*rATII' St'ICCTIiU Jt.
The following values (in Table G) from Mouton, Abney, and Draper are the only ones I know
previous to my owu measures where the wave-lengths of any cold lines are given wiili a|i|iidximate
accuracy. Of these it is just to distinguish those b.y Abney as possessing a di-gice df exactness
before unknown. There aie some doulits about the band /. = 1. .■_',(> having really been observed
before, but I have included this among tliose whose existence was known nr suspected before
my measures.
The values here given were olitained by me in IS8-', and first publishe(l in the ('(laiptes Hen-
dus for September 11, ISSl', iu tlie form of charts which were drawn from them. These charts
were so much reduced by the engraver that, though these values are still detei niinalile from
them, it may be convenient to repeat them here iu their original tabular form, with the addition
of the ]irobable errors :
230
KESEAROHES o:N SOLAK HEAT.
Table G.
Tiihir 11/ (lurk baiid.i in iiifru-red portiuii 0/ sjicctniii
A
n (Hilger prism).
d (Hilger prism).
Remarks.
0.S15
1. 5697
46" sn'.o
Tliia line I hare certiiinly seen, but with difficulty. It'
is near Tlie utninst limit of the visible spectrum. It
appear" to coincid.. witli Captain Abnev'a 2 and with
Iliap.-i s„
0.850
1. 5687
46° 33'. 0
Onllipv.M IniNl ,il ii.ihilit.v. orbeTondit.thereisinfact
sum., mi. , 1 1 IV :i. Ill its having been seen at all. Ap-
1. 5678
46° 27'. 5
Quit.- :„ n , ,,- ;„; \ii„ ,^ I,,i. a heavy line
0.908
1. 5674
46° 25'. 0
0.935
1. 51168
46° 21'. 0
Very 11 1,1 1 ■ '1 , . ■ , , ... ,11 ,: . 1,1 Mr interruption
of llh .!,■■_ . II . III., ,,|i1h «-,>ii1,1 lie
niUrll I,. .,',, 1 1 1 1,;;. , |. . \ if m.i, |, , ||,.. eX-
tivnii. liiiiii niiM . i. . .11. •• Ill ..^ ti.liis
own -1, 111, II. 1,1 11 ,- i.i, 1 ■ 1 , . , . . ' , _ ,1 ,1, La-
mai,~l.|, • . Ii. ..!,.! . . : . iiii..|iii,-.lrleoted
sniiii ' ■ '■ , ,' ■' 1 bv Draper.
Til.' \ I ., , 1 .ii.l.aUethatitis
1.130
1. 5636
40° 1'. 0
Still 1 1 . . 1 .i .' 1 1 i.ii.linir. Thi.^Iine
is Ki" 1 >l 1' 'I'Jlli of l.'230(!).
by 111 ■.••. ..! 1 Mil. , , l.i.lMi, ,i,i|i:,n.ntly
caii-.-il ■ ' ■ 1 'I'-i ■ .■•■' 1. I'l. 1..I ter
1.270
1.5616
45° 49'. 0
Incoii.|.i ..
1.360
1. 5604
45° 41'. 0
Vervii II ' 1 ,.iiii_ ..il.iiilioth
sill.- - . .■ . . •.: 1 ,, 1 1 1 1, .1 iii.l iiliiiost
alK.iliii, 1 , !,• II ,1 1 , „ II . ,1, ii.. 1,1, iitiiiable
Willi .> .1 , ,11 i II 1 ; 1. : , 1 .. ,,, III I,am,in,^lvy'»
I'iii.. 1 . II 1 !• II !• 1:!, or Mouton's
l|i t- 1 ■ 1 , , !■ i. - .1,1.. difScullv in
dil. 11,1 1. ii. ;, , j .1 1 1 Thecoldest
pail.il It ^.1 I 111. [!• ii.i-i .1 -. .. .. ;. ii_::i..l 1.36. From the
ob."erviiti..us at .\ll.'ulii-iiy it i^ aiKspL'._te(l to be of lellu-
1.540
1.585
1. 5576
1.5571
45° 26'. 0
45° 22'. 5
i Inconspicuous lines
1.805-1.870
1. 5544-1. 5535
45° 5'.0-45° 1'. 0
This i. 111. ,1. li ...M li.iiil mi, ill, .III .r,,., II, ,,,1,111 -ir.iunt
Whim. II . ii 1' • , , 1 , . ' . . 1 . ..| |,l,.|rfT
in 111,. 1! Ii. . , 1. . : 1. II 1...1 . . ■ Hi i . ..I.I, and
sli-lii . II 1. !■. . .1 1 . 1 . . .■ liza-
bl.' 11 ■ i.ii.liably
of 1. 1' 1. .,■ . 1 . .• . _ • 11 ,. -,iiV.TBd
mil\'_' '.' ' , 1 - . . . ■. . _i .' .V .|. ,",'l,b-8°
n, u..l'll i» ilii- lii.sl" lu ilii.»p,..l'i'i'iiu.'l,u'i'ili'at'iti3
the last of thu tile.it aud euuspieuous intenuptiuna of
1. 983
1. 5.120
44'5 53'. 0
2.037
1.5515
44° 49'. 0
Small l.ut .leliiiile lin... The.ni- two lin.-a arc the last dis-
2^.7.1 1 " .... 1 1 ..1 . . . . ii..rtrv,
wlii. Ii . .. ... . - .ii,.,ned.
BcM.i.. itlOUS
of .-11. ._ ' 1 , 1 ,. . .„„„tl,6
can 1. ■ .1 ■ .. li.voud
this ] ..i .' ■ ■ 1 ■ . ... .il.sorp-
Eeyoml it. very jiniliably the eaillrH owli riiiliii'tiona"into
space are checked by its owu envelope.
DI.STRUUTTIO^ OF ENEKtiY l:S THE StIUJIAL .'^PECTIir 51.
The curve (7={/)/\ given in Plate XX enables us to inai'k ott'a wave-length scale upon the map
of the prismatic spectrum without auy extrapolation between our present extreme points of
observation, a deviation of 52° 43' (corresponding to A =0»..'?-14), and a deviation of 44° 25' (corre-
sponding to A=2''.35(i), and also to construct a map in which the wave-length scale is an ordinary
scale of equal part.s, but in which the degrees of deviation, if represented, would be unequally
spaced. Such a chart of the normal spectrum, has, as we have already remarked, Jhe advantage
of being entirely independent of anj' particular prism or grating, and consequently of being
directly comparable with all other maps of the same kind.
If, besides making a map of the normal spectrum, we wi.sh to construct a curve rei)resenting
the corresponding distribution of energy, a further consideration of the relations existing between
WAVE LENGTHS IN THE INVISIBLE PRISMATIC SPECTRl'M.
231
the two charts is iiecessaiy. Tlic law of dispersion of the prism causes tlie distribution of energy
in its spectrum to be i|uite (lillcrciit from what would have been observed with a diftraction
grating.* Disregarding tlic al>siiihiiig action of the apparatus, the amount of heat between two
defiuite wave-lengtlis. as lictwccn tlic A and I; lines, should be the same in l>oth spectra, provided
F,g.ja.
the total i|uantity of heat is the same in both. The area between any two onlinate.s of tljc (airve
in I'Uite XI (|)risnuitic spectrum) may be considered to represent tlie amount of lieat in the part
of the spectrum included between them, and the total area of the curve represents the total
amount of heat. If, then, we suppose the area of the normal curve required to be the same as that
of the prismatic, the condition to lie liiHilled by the tbriiier curve is that the area, included between
the ordinates at any two wav('-lenj;llis, sliall be e(|nal to that included between the same wave-
lengths in the latter: and from this condition we can deduce a rule for etfecting the required
transformation.!
Lay off upon a line A I! (I'ig. I'.t) any convenient distant-e and divide it into cipial spaces to
represent the normal wave-length scale, and upon a line C 1), at right angles to the first, lay otf
the same distance and divide it into the same number of parts, spaced according to the law of
* J. W. Draper, Pliiloiiopbical Magaz
t See .1. MuUer, Poggendorff's Annate
Comptes ReDdus, tome ."rO, page Sl'ti.
:ie, votuine 44, page 104, 1872.
, Baud 105; Landqtust, Poggendorft", Annalen, Baud 155, Seite 146; Mouton,
232
RESEARCHES ON SOLAR UEAT.
dispersion of the piisin. ;is in tbe wave-lougth scale marked on the bottom of the prismatic chart
(see PKite XI). Erect ordiiiates at the points of division, and mark them with the proper wave-
lengths, bcgiuuins on both lines at the ends which lie nearest to each other, as in Fig. 1!>, where
five ordinatcs arc slidwn. Through the intersection of corresponding ordiuates, draw the curve
E F, and upon CD draw the curve of distribution of energy in the prismatic spectrum.
Fiy.^O.
> tli3 Normal Spa
Let ", fig. 2(1. he a very small wave-length interval on the prismatic scale; c, the same inter-
val on tlie mirmal scale; ami h and f?, the average heights of the energy curves over the two
intervals rcsijcctively: tbe shaded part of the figure reiiresenting therefore the portion of the total
area included between these limits; f/'isa portion of the curve EF, fig. 19. Then according to
the condition of transformation
cd = ah
whence
From
h:(l:
'trical coiisiilcratious
tan ip
the inter?
'ctioiis of the two pairs of ordinates
where (f is the angle wliicli tlie <'lioid EF joiiiinj]
makes with AB, coiise()ueiitly
/*:</:: 1 : tan <f
froin which
d = h tan c-
Now when a and c are indefinitely small hdw\ d are the ordinates of the prismatic and normal
energy curves respectively, at a given wave-length, and c is the angle formed by the tangent to
BF at their jioint of intersection. Hence to find the height of the normal curve at a given wave-
length, the corresponding ordinate of the prismatic curve must be multiplied by tan <f.
WAYE-LENr.TIIS IN THE INVISIBLE PRISMATIC SPECTUrM. 233
Such ii construction was iipiilicd to tin- |irisiiiatic- i'iii'r,;;v curve ol' tlie Ililui'r ]irisni. resulting
in tbe following- table (H). wliicli cxliiMr^ lor cxciy tmtl) ot tin- unll wavclcngi li : (li, tlieilevia-
tions of even wave-lengtlis in tljc spcctruui of the liilger prism: (-). lljc urdiiiati's nt llic prismatic
curve of energy in this spectrum as given liy oliservation with the liolcuneter (the dotted liimnding
curve of Plate XI), -'prismatic spectrum " : (.">). the values of tan c- obtained by estimaticin Iroiii tlie
plotted curve EF, fig. 39; (4), tljc (U-dinates of tlie norujal energy curve, whicli. (jU lieing plotted,
give the outer dotted curve in Plate Xll CMiormal spectrum").
Table II.— Table /ur /aciliUilinil tlir roiislnwi'wn »/ Hit- iinniiid enmiy ain-e when the ilhh'ilniliuii ,/ Ihe nnr<jii in Ihrpiigniittic
A.
50
(1.
27 40
Priauiatic
ordinatca.
Tan 4..
Nnrmal
ordinates.
i 0.40
6.5
9. 820
64
0.50
4S
:i4 00
57
4. 226
241
0.60
47
35 '.'O
134
2.3S0
319
0.70
47
03 00
210
1.450
305
; 0. 60
46 41 40
260
l.OOU
266
U. 90
46
25 40
316
.720
228
1.00
40
14 30
342
.600
205
1.10
40 04 30
336
. 5.50
185
1.20
55 30
311
.520
162
1.30
45
40 40
260
.4SIS
139
r5o
45
20 30
222
!463
103
1.00
45
21 00
193
.446
87
1.70
45
13 20
170
.436
74
1.80
45
05 40
147
.429
63
1.90
4t
5» 10
125
.423
53
2. OO
103
.416
43
2.10
44
43 20
.414
35
2.20
44
30 00
67
.411
28
2.30
44
2H 40
51
.409
21
2.40
44
21 30
36
.407
15
2. 50
44
14 30
.405
9
2.60
44
07 30
10
.403
4
2.70
44 00 30
3.
.401
1.2
The true normal energy curve with all its inflections, maxima and iiiiriima. is easily drawn
after this dotted curve is plotted, fnr the ]iaits of the ordinate (d' the laller liejnw and alxjve its
intersection with the former irregular curve bear tlie same pidportiori to each other as in the pris-
matic spectrum, and we thus finally attain the object of the preceding lalmr.
If, now, it is desirable t<i map the distribution of the energy mi any other scale, such as that
on whicli the abscissa- are proportional to the times of vibration, this can Im- done with facility.
Thus in the suppo.sed instance \\t- have only to lind , correspiuiding toeacli wave length iiiorderto
get the ab.sciss*,and(observingthat since.' now = , ,. = — ,,)toiise tin- multiplying lact(U- ,_,
to obtain thelength of the new abscis.^a- Iromtheidd inea<di instance. If tliclciiL;tli oftlic neweiiergy
curve between the limiting |icrpcndicnlars( wliii-h now represent the reciprocals of the wave leiigtli)
is to be the same as in the old we must introduce a c<uistaiit multiplier, ii, writing the e(iiiation of
the interpolating curve .r = , so that the multiplying factor becmnes — , . Tims if tin- limiting
ordinates of the wave-Iengtli energv curve are -\ ,, A,,, and we are to have the condition,
a- 0 "-'-'-
then,
" = A . X A,,.
If the mean ordinate of any small area of the inu'inal energy enr\e lietwcen any given limits,
A„, A„ is denoted liy i/,. and tliat of the correspoiidiiig area of tiie new ciuve liy //, simi- ihe areas are
to be the same, we have (I I ^ — , 1// = (A, — Aj ;/i. "lience ,v = ' x ,i/i. wliicli at the limit lie-
comes II = ' ,!/i. Hence to obtain the new ordinates, the old ones must be multiplied by tlie recip-
rocals of the factors for abscissa-, m by
The curve EF, Fig. 19, if represented by a formula would give ri.se to an expressicui of the
form d = [if] X, the abscisste measured along AH being proportional to the wave lengt lis, and the
12535— No. XV 30
234 RESEAECHES ON SOLAK HEAT.
ordinati's pariilli'l to CD, to the deviations. It is tlieretbre a curve similar to that in Plate XX,
except tliat tlie aliscissa' ami ordiuates are drawn on ditl'erent scales. Since tan c = ,, = „ ,
the factors for iiinlti|ilvinjx the prismatic ordinates may be computed, provided tlie curve EF can
be exactly expressed hy a formula, and for the preliminary reduction this was done, the values of
ij-, being computed from Briot's formula, and t from the relation h = ^ — ." , — When, how-
ever, it was shown by the measurements of obscure rays that Briot's formula, obtained by obser-
vations ill tlic visilile spectrum, does not exactly express the law of dispersion, the table of factors
thus prepared, was of course abandoned and the graphical method described above was substituted.
I have drawn in this way (on a smaller scale than that of the normaror prismatic curves, and
following the smooth curve in the former as my original) four ditterent schemes for the distribu-
tion of the energy. (See Plate XXI.) Fig. B represents the distribution of solar energy after
absorption by our atmosphere ou the scale of wave-frequency (general equation of interpolating
curve ■'■=, ) proposed by Mr. Stoney. Fig. C represents the distrilmtion according to a proposal
(.f=logA) of Lord Rayleigh.
Fig. D is quite ditfereut from any of the preceding. It gives the distribution on a scale I
have never seen pr(i)iosed, but which I have found useful. In this the bounding curve is a straight
line parallel to the axis of X (y = constant). This is not merel}' suggestive as illustrating what has
already been remarked here as to the conventional character of the methods of showing the dis-
tribution of the energy, but it has more practical uses. lu this particular construction it is evi-
dent in fact that the sums of the energies, between any two wave-lengths whatever, are directly
proportional to the distance between the ordinates, measured on the axis of X. If, then, we desire
(for instance) to know what relation the invisible bears to the visible heat, or to inquire about
what jioint in the sjjectrum the energy is equally distributed, &c., these and similar problems are
solved through Fig. D by simple inspection.
I have not been able as yet to repeat the preceding determinations upon the lower part of the
spectrum as often as I could wish. They are susceptible of improved accuracy by still longer
experiment, but I think that within the limits of error indicated they may already be useful. I
should add that throughout this investigation I have received constant and valuable aid from Mr.
J. E. Keeler, not oidy in the graphical constructions, but in the experiments and in the computa-
tions, through all the details of which his aid has been more that of a coadjutor than au assistant.
ALLECriiENY Observatory,
AUefihoni, Pa., October, 1SS3.
Since the above was in type I have seen the interesting article by Mr. H. Becqnerel in the
Aunales de Chimie ct de Physique, for September, 1883.
The wave leiigtlis assigned by M. Becquerel to the band at the limit of his researches, 1,440
to 1,500, appear to nie too great, for this limit corresponds to the band whose wave-length is
given at l''.3l) to li^.ol on my chart, published in the Comptes Rendus of the previous year (Sep-
tember 11, 1SS2), and on a larger scale in the American Journal of Science, for March, 1883, and
in the Anuales de Chimie et de Physique, for August of this year. I regret that M. Becquerel has
not read the article in the Comptes Kendus. Had he done so he would have seen that the wave-
lengths there given were not conjectural, but directly determined by a very laborious but the only
practical method from the direct use of a gratiug. They were the result, in fact, of the measure-
ments I have just described, and were specially intended to give information about the unknown
region extending l)eyonil the limit of M. Becquerel's researches, such as the great newly discovered
bandil, for instance, which stretches from wave-lengths If'.SOto l''.!tO, while JI. Becquerel's furthest
band, as I have said, is at l''.4S. The present memoir will show what degree of reliance maj' be
placed on these measurements.
V
234 EESEAECHES ON SOLAR HEAT.
ordinate's iiiu-iillcl to C'I>, to the deviations. It is tlierotbre a curve similar to that in Plate XX,
except tliat tlie abscissa/ and ordinates are drawn on dift'erent scales. Since tan c = ,, = ,-, ,
the factors for multii)l.Ying the prismatic ordinates may be computed, pi'ovided the curve EF can
be exactly expressed by a formula, and for the preliminary reduction this was done, the values of
j^ being computed from Briot's formula, and 7- from the relation n = ^ — 5 Wheu, how-
ttA ® ^ ' an sin i a . '
ever, it was shown by the measurements of obscure rays that Briot's formula, obtained by obser-
vations ill tli<' visilile spectrum, does not exactly express the law of dispersion, the table of factors
thus prepared, was of course abandoned and the graphical method described above was substituted.
I have drawn in this way (on a smaller scale than that of the uormal'or prismatic curves, and
following tlie smooth curve in the former as my original) four dittereut schemes for the distribu-
tion of the energy. (See Plate XXI.) Fig. B represents the distribution of solar energy after
absorption by our atmosphere on the scale of wave-frequency (general equation of interpolating
1
^\
(.(■=logA) of Lord Eayleigh.
Fig. D is quite dift'erent from any of the preceding. It gives the distribution on a scale I
have never seen proposed, but which I have found useful. In this the bounding curve is a atfaigltt
line parallel to the axis of X (;/=constaut). This is not merely suggestive as illustrating what has
already been remarked here as to the conventional character of the methods of showing the dis-
tribution of the energj', but it has more practical uses. lu this particular construction it is evi-
dent in fact that the sums of the energies, between any two wave-lengths whatever, are directly
proportional to the distance between the ordinates, measured on the axis of X. If, then, we desire
(for instance) to know what relation the invisible bears to the visible heat, or to inquire about
what point in the spectrum the energy is equally distributed, iS:c., these and similar ])r(ibleriis are
solved through Fig. D by simple inspection.
I have not been able as yet to repeat the preceding determinations upon the lower part of the
spectrum as often as I could wish. They are susceptible of improved accuracy by still longer
experiment, but I think that within the limits of error indicated they may already be useful. I
should add that throughout this investigation I have received constant and valuable aid from Mr.
J. E. Keeler, not only in the graphical constructions, but in the experiments and in the computa-
tions, through all the details of which his aid has been more that of a coadjutor than an assistant.
Allegheny Observatory,
Allefihcnn, Pa., Ortoher, 1SS3.
Since the above was in type I have seen the interesting article by Mr. H. Becquerel in the
Anuales de Chimie et de Physique, for September, 1883.
The wave-lengths assigned by M. Becquerel to the band at the limit of his researches, 1,440
to 1,500, ajipear to me too great, for this limit corresponds to the band whose wave-length is
given at l''.3l> to 1''.37 on my chart, published in the Oomptes Rendus of the previous year (Sep-
tember 11, 1882), and on a larger scale in the American Journal of Science, for March, 1883, and
in the Annales de Ohimie et de Physique, for August of this year. I regret that M. Becquerel has
not read the article in the Comptes Rendus. Had he done so he would have seen that the wave-
lengths there given were not conjectural, but directly determined by a very laborious but the only
practical method from the direct use of a grating. They were the result, in fact, of the measure-
ments I have just described, and were specially intended to give information about the unknown
region extending beyund tlie limit of M. Becquerers researches, such as the great newly discovered
band XI, for instance, which stretches from wave-lengths 1''.80 to l^.OO, while M. Becquerefs furthest
baud, as I have said, is at 1''.48. The present memoir will show what degree of reliance may be
placed on these measurements.
WAVE-LENGTHS IN THE INVISIBLE PRISMATIC SPEOTKr:\I.
235
It is understood tlint a i)l]Otonrapliic inaji ot tlif s])i'ctnim to It^M (and tlieicforo coxri-iiiy tlir
f;ronnd of ]\I. r.ecciUfrt'I's iiapcr, liiit not extending as tar as my ".O"'), will sliortly lie |inlilislieil
from the joint labors of Professor Rowland and Captain Abney, and as tlieir results will ]irobably
be aceepted on all hands as more exact than the preliminary exjilorations m which M. l!<'C(|uerel
and myself have been engaged, we may await its appearance for the determination of a part of the
Iioiuts in question.
I would call attention to the fact that M. llec<|nerel has stated that the furthest band known
to him in Septend>er, 1.S83 (except from my own researches), had a wavedcn^th of not over
l/z.od, according to his own estimate.
APPENDIX a .
EXPEKIMENTAL DETEimiXATION OF THE INFLUENCE OF ('( iN\ K( TK >N ('III
REI^TS I'PON THE LOSS OK (iAlX OF Ti;il PEEATUKE l;V A TIU:i;,M( »,\n:TEi;
BDLP..
Several series of experiments were made to ascertain the dillerenci' in the latc ol heating or
cooling of a thermometer ludb in air and in rariio. The linlb was inclosed in the centei' of a thin
copper globe o centinieleis in diameter, the stem and aaexhansling tnlie of glass being sealed.
The apparatus was connecteil to an <jr(lii]ary Siirengel's pnmii. and a \a<'niin] maile to williin half
a millinu'ter of mercury. The glass tube was then sealed in the tiaiiie of a lamp and the whole
was innnersed in hot water kept constantly stiired, the temperatures of the water and of the inner
thermonieter being recorded from minute to minute. A minute portion of the heat ac(|iiin-d liy
the inner thermometer is received l)y coudnction along the glass stem, and a very small amount
by the convection of the trifling i|uantity of air remaining; but by far the greater part is ladiated
to the bulb from the copper globe, which is blacUened within. The rejielition of the experirjH'nl
with the globe sealed but liill of air enables us to disciiminate between the etfect of radiation and
of convection. The tirst experiments were made with at hern eter (Oreen. 4."iS() graduated from
0° to G(l^ C. in tenths of a degree, having a clear spheiieal bulb 1/2-' ceiitinieters in <lianK'tei'.
Tlie sncceeiling ones were carried on with a lilackened bulb-thermonu'ter (Ilandiu, ST.'IT) which lias
been used in the large Violle actinometer in the measurement of solar r idiation. The observers
had acquired expertness by much previous practice in reading to hiiiulreilths of a de;;iee, and a
single hundredth will represent more than tlie iirobalile error ot one reading.
llarch 27. 16;
■r>,„i,e
c
opper globe dipped i
n hot wate
'■
Cn
pper glolie dipped in
.-..Id water.
Time.
Temper. l\T,,^^„ '
oAva'ter. '''«*■
Defi-
Iciency.
First dif.
fereoce.
Time.
Temper- ' j;,.^.^^
ol-'witer. ■'''•'*■
Excess, f
irat dif-
•ul.-nee.
Uinu,..
o
„
0
„
.,
IhuiU:
0
1
40.50
40.22
20.50
23.88
20.00
17.34
0
1
4.42
4.47
31.60
28.30
27. 18 .'
23. 83
""i'm"
■■3.' 35"
2
39.98
25.00
14.98
2.30
2
4.51
2.5, 35
20 84
2.99
3
39. 75
27.00
12. 75
2.23
3
4. ,50
22,65
18. 09
2.75
4
39.54
28.78
10.76
1.99
4.60
211. 28
15.li8
2. 41
5
39.33
30.31
9.02
1.74
5
4.64
18.15
13. 51
2. 17
6
39.13
31.01
7.52
1..50
6
4.68
16.27
11. .59
1.92
7
38. 94 ' 32. 69
6. 25
1.27
4.72
14.65
9. m
1, 66
8
38. 74 1 33. 62
5.12
1.13
s
4.77
13, 21
8. U
1 49
!)
38. 58 1 34. 38
4,20
.92
9
4.81
12, 00
7 19
1 J 5
10
38. 42 1 35. 00
3.42
.78
10
4.86
10.93
r. 117
1 12
11
12
38. 28 1 35. 50
38. 15 1 35. 89
2.78
•-^,
12
4.89
4.93
111. 05
9.34
4 t"
75
13
38.04 ' 36 19
\.h
!Ji
13
4. 98 8, 07
3 09
14
1.1
37. 94 30 38
37. 84 3f.. .57
1.50
!2l)
15
5^07
7' 60
'i 11
.04
16
37. 74 1 30. 70
l!o4
'.23
16
5.11
7120!
ZUH
!44
236
EESEAKCHES ON SOLAR HEAT.
Ill tilt' al»(>ve the copper globe was dipjieil in tlie water at least 30 seconds before the first
reailiiig. Tlie teiiipeiature of tlie water itself was taken e\eiy minute, and niinnte irregularities
found corrected by a siuootli cnrve, the ordiiiates of wliicli 5;i\ e tlie values in the column beaded
"Temperature uf water."
[Kt'petitioD of last experiment with ai
upper slobe. Ba;
All else as before.]
Copper plol
e dipped i
n hot water.
Copper globe
dipped i
1 cold wat
-
Time
Ten^per-
of water.
Green.
4.'i84.
Defl. . First dif.
ciency. ! leience.
Temper-
Time, atiire
of water.
Green,
4584.
Excess.
Firstdit-
ference.
Minut
S o
o
o
2Iumtcs. °
o
o
o
0 4.62
1
41. U2
23. 57
17. 45 4. 86
1 4.65
2.5. 87
5.56
2
411. 60
26.58
14. 22 3. 23 ■
2
4.69
21. 52
16,83
4.39
3
40. .18
29.23
11. 35 2. 87
3
4.72
18.11
13.39
3.44
4
40. 38
31.44
8. 94 2. 41
4
4.76
1.5.40
10.64
2.75
5
40,17
33.12
7.05 1 1.89
5
4.80
13.28
8.48
2.16
6
39.99
34.46
5.53 1.52
6
4.83
11.65
6.82
1.66
7
39. fO
3f.. 46
4. 34 1 1. 19
7
4.86
10.30
5.44
1.38
8
39. 63
36.21
3. 42 . 92
8
4.90
9.32
4.42
1.02
9
39.48
36.76
2. 72 1 . 70
9
4.93
8.51
3. .58
.84
;o
39. 33
37.18
2.15 I .57
10
4.97
7.78
2.81
.77
11
39.1!)
37 49
11
[March 27,1883. The
i(o=BaudiD, 87:
The copper globe was dipped i
c
opper glol
e dipped i
n liot water.
Copper globe dipped i
1 cold water.
Time.
Tempcr-
of water.
Eandin,
8737,
Defi-
ciency.
First dif-
ference.
Time.
Temppr-
of water.
B udin,
8737.
Excess.
Firstdif-
ference.
Slintdes.
„
o
„
^
Mhintee.
0
o
o
o
0
34.80
17,95
16.85
6.44
28.08
21.64
1
34.67
20. 10
14.57
1
6.47
24.41
17.94
3.70
34.56
21,74
12. 82
1.75
2
6. 50
21.30
14-80
3.14
3
34.44
23.76
10.68
2.14
3
6. .53
18.75
12-22
2.58
4
34. 34
25.43
8.91
1.77
4
6.56
16.62
10.06
2,16
5
31. 23
26.90
7.32
1.59
5
6,58
14,80
8.22
1,S4
6
34.12
28.04
6.08
1.24
6
0.61
13.-30
6.69
1.53
7
34.00
29.00
5.00
1.1)8
7
0.04
12. 05
5.41
1.28
8
- 33.89
29.80
4 09
.91
8
6.67
11.00
4.33
1.08
9
33,78
30.38
3.40
.69
9
6.70
10, 15
3-45
.88
10
33.68
30.84
2,84
.50
10
0.73
9.46
2.73
.72
11
33. 58
31.21
2.37
.47
11
6.76
8.91
2.15
.58
12
33.47
31.47
2.00
.37
6.78
8.41
1.03
.52
13
33. 37
31.68
1.09
.31
13
6,81
8. 04
1.23
.40
14
33.27
31.82
1.45
.24
14
6,84
7.76
.92
.31
15
33.17
31.90
1.27
.18
15
6,86
7.50
.64
.28
1 of last experiment with air in copper globe. All elae fla before.]
t
,pi,er glol
c ,li].pe.l i
u hot watt
-
'■
i])Iicr glob
e rt.pped i
cold water. 1
Time.
Temper.
Ban din,
8737.
nefl.
fieieuey.
Fiistdif-
feience.
Time.
Temper-
ature
ofwater.
Baiidin,
8737.
Excess.
First dif-
feienee.
Mhii.les-
„
„
o
o
Minutes.
0
o
„
o
34.80
34.70
16 42
20, 96
18.38
13. 74
?
4.73
4.76
25. 70
20.03
20.97
15.27
4.64
5.70
34.00
23. 53
11.07
2.07
4.81
16.18
11.37
3.90
3
34. 50
2.5. SO
8.70
2 37
3
4.84
13. 32
8.48
2.88
4
34.41
27.76
6.65
2.05
4
11.24
6.36
2.12
5
34. 31
29.18
5.13
1.52
5
4.02
9.72
4.80
1.56
6
34.22
30.20
4.02
1.11
6
4. 1)5
8,57
3.62
1. 18
7
34. 12
30. 95
3.17
.85
7
4.99
7 70
2.71
.91
8
34. 02
31.47
2. 55
.62
y
5. 02
7 00
2. 114
. 07
9
33. 92
31.90
2 02
.53
9
5 06
6,59
1,,53 ..51
10
33. 84
32.18
1,06
.36
10
,5. 10
0, 21
1,11 .K
33. 74
32. 39
1.35
.31
11
5. 14
5 98
.84 . .27
12
33. 05
3'' 50
1.15
"'0
12
5.18
5.72
.51
.30
13
33. 50
32 611
.96
.19
13
5.21
,5. ,59
.38
.16
14
In
33.46
33. 37
32. 67
32. 70
!67
.17
.12
14
15
5.25
5, 28
5.41
5, 37
.16
.09
!o7
16
33.28
32. 67
.61
.00 j
16
5.32
5.27
-.05
.14
INFLTTENOB OF COJSIVECTION CURRENTS.
237
|Marcb30. 1883; The
II = 22° to 24=
Till.
i-i.pii
r glol,„ 1
.ivjnp bei
u cooleil
u suo
V ia
_
■lip|,
•cl in liiit \
aler.
Ti
.e.
Temper-
ature of
Bntidin,
8737.
Defi-
ciency.
First
feren
ait-
Min
1)
Sec.
UO
3.5. 26
3.00
32.26
■>
0
15
35.24
30.72
'i.'sif
1. .52 (.
1.19 1
0
0
30
45
35. 22
35.21
e.02
7.20
29. 20
28. 01
5.55
1
00
35.19
8.48
26.71
1.30 1
1
15
35.17
9.40
25.77
.94)
1
30
35.10
10.39
24.77
i.ool
4.08
1
45
35.14
11.41
23 73
1. 04 (■
00
35. 13
12.50
22.63
i.ioj
3
00
35.00
16. 02
19.04
3.59
4
00
35, 00
10.19
15.81
3.23
5
00
34.94
21.91
13.03
2.78
6
00
34.87
24.18
10.69
2.34
7
00
34.81
26 04
8.77
1.92
8
00
34.75
27.57
7.18
1.59
9
00
34.70
28. 90
5.80
1.38
10
00
34. 04
29.78
4.86
.94
Jl
00
34. -,St
30. 63
3.96
.90
12
00
34.54
31,21
3. 33
.03
13
00
34. 40
31.69
2.80
.53
14
00
34.43
32. 12
2.31
.49
15
00
34.39
32. 43
1.96
.35
16
00
34.34
32.64
1.70
.20
17
00
34.30
32.81
1.49
.21
18
00
34.25
32.97
1.28.
.21
14 00
16 00
16 00
Temper,
atnre of
Hamlin,
8737.
2.62
35.64
2.05
34. 60
2.68
33.16
2. 72
31 87
2.75
30.48
2.78
29.25
2.82
28.00
2.85
27. 00
2.88
25.78
3.02
21.65
3.15
18.38
3. 28
15,69
3.41
13.45
3.54
11.66
3.67
10.15
3.80
8.98
3.94
7.99
4^18
6 60
4.30
4.42
4..i4
6 12
5.70
6.42
5.21
33.02
31.65
;io. 48
27.73
2.5.18
24.15
22.90
18.03
12.41
10.04
8.12
0.48
5.18
4.05
3.14
2.42
1.82
1.28
.88
..55
.25
1.64
1.30
1.13
The copper globe 1
aving been cooled
n snow to
The copper globe having been heated
n hot water
about 3°
is dipped
n hot water at about 35°.
to about 35° ia dipped in cold
water at ah
out 30.
Fir.st difier-
Time.
Temper-
ature of
Eaiidin,
Defl
First difler-
Temper-
Time, ature of
Baudin.
8737.
E.>;ces8.
water.
8737
ence.
water.
Min. Sec. »
Min. Sec.
.-,
c, o
0 00
35. 17
3 50
31,67
0 00 3.27
3.5. 50
32. 23
0 15
35.15
5. 35
29.80
1,87 ')
0 IS 3.29
33. 22
29. 93
"2.'30 1
0 30
3.5. 13
8.02
27.11
2. 69 1 0 .,
2„5,8..55
0 30
3.32
31.10
27.78
2- 15 I „ ,,,
J g^ 8.33
0 45
35.11
10.05
25.06
0 45
3.34
29.28
2.5. 94
1 00
35, 10
11.98
23.12
1.94 J
1 00
3.36
27.26
23.90
2, 04 J
1 15
35.08
13.63
21.45
1.67)
1.57 [„„
1 15
3.38
2.5. 08
21.70
2. 20 )
1 30
35. 06
15.18
19.88
1 30
3.41
23.46
20. 05
1. 65 „ „„
I. 00 1 ^- ^^
1 45
35.04
16 35
18.69
1.19| ^■'''
1 45
3.43
22.48
19.05
2 00
3,5. 02
17.60
17.42
1.27 J
2 00
3.15
20.99
17.54
l.,51J
3 00
34.95
21.35
13.00
3 00
3.55
1 6. ,52
12 97
4. ,57
4 00
34.87
24.48
10,39
3'2I
4 00
3.64
13, 38
9-74
3.23
5 00
34.80
20.92
7,88
2. 51
5 00
3.73
11.02
7.29
2.45
6 00
34.72
28.70
6 02
1.86
6 00
3.82
9.31
.5.49
1.80
7 00
34. 65
30.01
4.64
1.38
7 00
3.91
8.13
4-22
1.27
8 00
34. 57
30.97
3.60
1.04
8 00
4.00
7.20
3.20
1.02
9 00
34.50
31.62
2.88
.72
9 00
4.09
6 41
2. ;i2
.88
10 00
34.42
32. 12
2.30
.58
10 00
4.19
5.92
1.73
.59
11 00
34.31
32.48
1.86
11 00
4.28
,5,60
1.32
.41
12 00
34.27
32.76
1.51
.35
12 00
4.37
,5,24
.87
13 00
34.20
32,98
1.22
.29
13 00
4.46
.56
.'si
14 00
34.12
33.07
1. 05
.17
14 00
4.56
4:89
.33
.23
15 00
34.05
33. 10
.89
.16
15 00
4.64
4,80
.16
.17
16 00
33.98
33.21
.12
16 00
4.72
4,72
.00
.16
•Int.
alsi
In till' last foiiv siMU'.s. rrailinys t'Vcr\ I."i .si'iiinil.s tor tlir tiist L' Miiiiiitr,^ wni- iittciiijitiMl : tlie
iiiterviil.s of time were, liowL'Vi'i', .soiiiewliat ini'f;iilar, a,s tin- olrsci \ t-il latr.s ol Inciting or cooling
show : but the observation,? are siifticient to prove tliat tlic cdjiiirr l;1ijI>c iiri|iiiir> tlie temperature
of tbe surrounding water very rapidly; indeed, it niirst )ii.irtiially do ,-ci in a ,siiii;lc second, since
the rate of beating or cooling for the first 15 seconds agrees fairly, at least within the limits of
errors of observation, with the subsequent rates.
According to the law of Newton, radiation is jiroportional to teiii)ieiatiiir. and it is very com-
monly assumed that within the liiniteil range of temperature, with wliicli \vr air here dealing, nil
losses are proportional to tem|)eraturo also. This cannot be really the case in thcoiy. and it
does not ajipear to be so in practice from the observations of Duhing and Tctit. < 'unsidciing the
238
RESEARCHES OX SOLAR HEAT.
importance of the suliject in oiiractiuometiic investigations, we bave thought it desivalile to make
a series ofexiieriments on the rates of beating and cooling in air and iu vacuo with the thermometers
actually used at Mount Whitney and elsewhere, and it is the results of these which we have just given.
In the assumption just allnded to, the loss of heat duiing a time, (It, is proportional to the excess of
temperature, f), whence ^=C e~"''. This is the equation of a logarithmic curve in which the tempera-,
tures of excess at equal intervals of time should bear a constant ratio to each other. We may deter-
mine whether it is a logarithmic curve by any of its characteristic jwoperties, but conveniently here
by noting whether the subtangeuts are constant, as in this case they should be. We can calculate
these actual subtangeuts from the equation just given, or we can draw smooth curves through the
points represented by the preceding ol)servati(^ns, pass a logarithmic curve through three points
in the smooth curve, and thns determine the logarithmic curve most nearly agreeing with the
observed one. We then Hnd thr snlitangents of the latter and determine how far and in what
way the actual curve agrees with that which would be given if all losses were strictly in propor-
tion to temperature. The results of this latter procedure are given iu the two following tables:
Table of suhtanijenta nhowiiiij llie rate of Iieathig idid aioliinj.
OBSERTATIOKS OF MAECH 27. 18f3,
s
Heating ir
Heating in
air.
Cooling iu
Cooling in
air.
Suhtaugents
Siibtangents
SnbtangeDt.s
Subt.iDgents
p
trom smooth
from smooth
5
trom smooth
from smooth
a
curve.
curve.
a
curve.
curve.
0
6.40
4.40
0
5.30
2.90
1
6.30
4.15
1
5.38
3.25
2
5.80
3.eo
2
5.45
3.55
3
5.55
3.75
3
5.50
3.68
4
5.34
3.75
1
5.60
3.70
5.10
3.75
5
5.70
3.75
6
4.90
3 75
6
5.75
3.75
4,80
3.75
7
5.80
3.75
3.75
8
5.90
3.75
4.60
3.75
9
5.95
3.75
10
4.60
3.75
10
6.05
3.75
11
12
4.65
4 80
3.75
3.7o
11
12
6.15
6.28
3.75
3.75
lit
5 00
3.75
13
6.56
3.75
3.75
14
6.70
3.75
15
3.75
OBSEEVATIONS OF MAKCH 30, 1883.
1
Heating in
Heating in
^
Cooling in
Cooling in
Subtangeuts
Subtangeuts
Subtangeuts
Subtangents
^
from smooth
from smooth
5
from smooth
from smooth
a
cnive.
a
cui\e.
curvt.
0
5. 85
3,60
0
5.22
3.35
3.60
1
5.22
3.45
5. .50
3.60
3
5.22
3.50
5 40
3.00
3
5.22
3.55
5.35
3.60
4
5.22
3.60
5.25
3.60
3.22
3.65
5.23
3.60
6
5.22
3.70
3.60
7
5.22
3.72
5.23
3,60
8
5.22
3.74
5.25
3,00
9
5.22
3,75
5.30
3.60
10
5.22
3,74
5.35
3.60
11
5.22
5.45
3.60
12
5.22
3.65
5. 50
3. GO
13
.5. 22 .
3.58
.5,70
3.60
14
5.22
3.48
15
5 85
3.60
lo
5 22
3.35
In these tallies tlic progressive diflei'i-nces in the stibtangents, though not excessive, on the
whole indicate a departure from the logarithmic law".
A method, perhaps in some respects preferable, is the drawing of supplementary curves in
which the rates of heating or cooling, for each excess of teinperature, are made the ordinates
INFLUEISrCE OF COXA'ECTION CURRENTS. 239
These ordinates sboulil fall on a strainiit line in case the curve is a logarithmic one. They do so,
iu fact, in the case of the heating and cooling in vacuo within the linjits of observation; but in the
case of the heating and cooling in air, there is a slight but systematic departure, indicating that
the loss by convection is luit proportional to the excess of temperature, but that, for ordinary air
pressures, the convection increases with great rapidity until the diflerence between the tempera-
ture of the thermometer and its enclosure is as much as 1(1 or l."i degrees Centigrade, after which,
for still greater difterences the eonvectiou increases at a smaller and nearly eoustant rate. It is
thus shown from these observations th;it Newton's law, although nearly representing the loss by
radiation alone for slight excesses of temperature, does not hold good for all losses, a <leductiou of
importance iu relation to the theory of the globe actiuomiter, of which we have made so uuichuse.
Il^DEX
A.Re(lLicti"i[.il iiiiliMl Kite, hill
B.Vorilillx'll.-.l ,„u•[u,l\^,l^
C. 11tti-rniiiiiilic.li 1,1 iiiiii.uul, 1,
peifLTt itbsiii-ptiiiii ut' till
li. For liniiliisbeil t xposuri'
E mill F. For sk v radiation . . .
irisloriiial iiitrocliii-lii.1
Rcsiilta of, a
IS atl'crting tho
tlii-iir'
siiac-ii
risEiivATlras-
i:.-iliu:tiiin o
Diaiiusslon (
)f IlH'tllOll ,-IMII
lojoil
Foi 1,,,.,
.1 n,i 111, .xpeil
itiim .
Tr
EouKiier's IVinmila lor tin- .lit.riiiiiiat
Melloni's (li.srovery ..
Illuatrated, asiU-termiiii.l l.y tlio Mu
lonii'tor observations
lutroductioi
Itcasou for c
DcaciilJlioii
t.)ii Hular ilitJVartioii ain-ct
At Alle^lii-iiy
Cai.oKIE:
DetiuitioD of (foot note)
C'Al
General proportion of, in atiiioaplier
At Mount Wliil
liiiri ase witli ascent into the atniospbc
Of darii boat, and of cold band.i
urliiilit, .lelinitionof
Hi.'
lelbe
of tra
Wavcknslbs of, in ii
'ECTIOX CUUHEST6:
InHiienco of, upon lo;
tbermonieter bn
General aci-eptauce as to absorption of , . .
Conclnsions arrived at as tlie i eaiilt of obji
Coetticient of trausniission of
liistribntion of, in tbe normal speetrnm . .
At Lone Piiii- and Monnt Wliitney
1253J— No. XV ol
]'<niilU.t'.-i f.
At Alli-Sliri
At Lorn- Pii
Mil, Mount Wbitne
( 'oii.Hiil'ratioii of, in ■oniieetion with telluric lines
rnliiiiiiKuy .,b»,ivatiouson,at Allegbeny
I :oi le.tions for preliminary observations
Etii-rt of, upon temperature in direet aunsbine ,.
r.asis for tbeory of
('ouuectiou between, and atiuospbel'ie moisture
(ieneral belief as to aetion of
lof
lllu
f (fo.
Kolation of, to siinlifbl, as deti riuined at Allesli.ny
SOI.AU fONSTANT :
Ilelined
BoUKuer'a tlit'ory tor deterraiuatiuii of (iiMc foot-uotel-
Approsiniate value of, as determined at Allegheny ....
Follies' appliealioii „1 Melloiii's discovery to tile ileter-
Violle s valu
i'ri
'rei»e''i^""aimi"
llK
of as dedi
aei-d from
obsi
srvati
on
tlirou^di small.
11 air.niass
IS
111-
Ma
leluiiuationof. In
.xiuiiini ami uiiuii
llie study
iium value;
of lioniogei
9 of
ions
rays
Ifil
iiimary of lesiills
ist pioiiable viilui
ill regard 1
lot lie deter
mim
itmni
''
Ito
242
Greater than ordinarily believed 33
Difficulty ill ascertaiuing amount of. receivi-d at tbe
earth's surface 45
PyiLelioiiK'Iricohsi'rvationson 01
Kolation nf.'tobeafoi' the stars (foot note) 1-2
Trausiiiissibilityor increases with iucreasi^ in wavi--
Ieu;;tlis KliJ, If.l
Slit;hl iiiliu.-iice <.r, u\nm leiupi-Malinv ul the *;aith .... -ij
Aiijiaratus lui' observation of . - IGiJ
Action of atmospheric moisture in niodihcatioii uf ... 1J^4
Relation of, lo suns.heat (fuot note) 122
Value of atin..s]jl.erii' Ininsiiiissioii <.f ISf.
As derived by Ponillet 47
Theory of , a.s aftected by observations 12'j
Theory of, as aflected by observatious on uditiirual
radiation ICO
Of globe actinometers. determiuation of water eciuiva-
Icntaof 7S
Loas or gain of temperature by, icilueiic.ea by couvec
tion currents 235
VaVK-T.KXG'IIIS:
Effect of increase of, ujion transuiissibility of solar
beat 133,151
Limit of. in idiaervatiou 209
Kxiierimental determination of, in invisible spectrum . 220
A|ii)ai;Ltus I'nr tbf mensure uf obscure 222
(It .■i.lilliuts in iufra-rcii prismatic spectrum 229
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