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SMITHSONIAN 
MISCELLANEOUS COLLECTIONS 



VOL. 63 




EVERY MAN IS A VALUABLE MEMBER OF SOCIETY WHO, BY HIS OBSERVATIONS, RESEARCHES. 
AND EXPERIMENTS, PROCURES KNOWLEDGE FOR MEN" — SMITHSON 



(Publication 2320) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

1914 



Z^t £or5 (gAitimoxi (pveee 

BALTIMORE, MD., U. S. A. 



ADVERTISEMENT 



The present series, entitled " Smithsonian Miscellaneous Collec- 
tions," is intended to embrace the principal publications issued 
directly by the Smithsonian Institution in octavo form; and is 
designed to contain reports on the present state of our knowledge 
of particular branches of science, instructions for collecting and 
digesting facts and materials for research, lists and synopses of 
species of the organic and inorganic world, reports of explorations, 
aids to bibliographical investigations, etc., generally prepared at the 
express request of the Institution. 

The " Smithsonian Contributions to Knowledge," in quarto form, 
embraces the records of extended original investigations and 
researches, resulting in what are believed to be new truths, and 
constituting positive additions to the sum of human knowledge. 

In both of these series each article bears a distinct number, and is 
also separately paged unless the entire volume relates to one subject. 
The date of the publication of each article is that given on its 
special title-page, and not that of the volume in which it is placed. 
In many cases papers have been published and largely distributed, 
several months before their combination into volumes. 

CHAS. D. WALCOTT, 
Secretary of the Smithsonian Institution. 



(Hi) 



CONTENTS 



1. Hinsdale, Guy. Atmospheric air in relation to tuberculosis. 

Published June 22, 1914. x+136 pp., 93 pis. (Publication 
Number 2254.) 

2. Clark, Austin Hobart. Notes on some specimens of a species 

of Onychophore (Oropcripatus corradoi) new to the fauna of 
Panama. February 21, 1914. 2 pp. (Pub. No. 2261.) 

3. GiLMORE, Charles, W. A new Ceratopsian dinosaur from the 

Upper Cretaceous of Montana, with note on Hypacrosaurus. 
March 21, 1914. 10 pp., 2 pis. (Pub. No. 2262.) 

4. PiTTiER, H. On the relationship of the genus Aulacocarpus, 

with description of a new Panamanian species. March 18, 
1914. 4 pp. (Pub. No. 2264.) 

5. Goldman, E. A. Descriptions of five new mammals from Pan- 

ama. March 14, 1914. 7 pp. (Pub. No. 2266.) 

6. FowLE, Frederick E. Smithsonian Physical Tables. Sixth 

revised edition. November 10, 1914. xxxvi + 355pp. (Pub. 
No. 2269.) 

7. Heller, Edmund. New subspecies of mammals from Equa- 

torial Africa. June 24, 1914. 12 pp. (Pub. No. 2272.) 

8. Explorations and field-work of the Smithsonian Institution in 

1913. November 22, 1914. 88 pp. (Pub. No. 2275.) 

9. McIndoo, N. E. The olfactory sense of insects. November 21, 

1914. 63 pp. (Pub. No. 2315.) 

10. Fewkes, J. Walter. Archeology of the Lower Mimbres Valley, 
New Mexico. December 18, 1914. 53 pp., 8 pis. (Pub. 
No. 2316.) 



(v) 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63. NUMBER ] 



ATMOSPHERIC AIR IN RELATION TO 
TUBERCULOSIS 

(With 93 Plates) 



BY 

GUY HINSDALE, A. M., M. D. 
Hot Springs, Virginia. 

Secretary of the American Climatological Association; Ex-President Pennsylvania Society for the 
Prevention of Tuberculosis; Fellow of the College of Physicians of Philadelphia; Associate Professor 
of Climatology, Medico-Chirurgical College; Member of the American Neurological Asso- 
ciation; Fellow of the Royal Society of Medicine, Great Britain; Corresponding 
Member of the International Anti-Tuberculosis Association, etc. 




(Publication 2254) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

1914 



ZU Botb (^afttmore (preee 

BALTIMORE, MD., H. S. A. 



ADVERTISEMENT 

The accompanying paper, by Dr. Guy Hinsdale, on " Atmospheric 
Air in Relation to Tuberculosis," is one of nearly a hundred essays 
entered in competition for a prize of $1,500 offered by the Smith- 
sonian Institution for the best treatise " On the Relation of Atmos- 
pheric Air to Tuberculosis," to be presented in connection with the 
International Congress on Tuberculosis held in Washington, Sep- 
tember 21 to October 12, 1908. The essays were submitted to a 
Committee of Award, consisting of Dr. William H. Welch, of Johns 
Hopkins University, Chairman ; Prof. William M. Davis, of Harvard 
University ; Dr. George M. Sternberg, Surgeon-General, U. S. A., 
Ret'd ; Dr. Simon Flexner, Director of Rockefeller Institute for 
Medical Research, New York ; Dr. Hermann M. Biggs, of New 
York, General Medical Officer, Department of Health, New York 
City; Dr. George Dock, Medical Department, Washington Univer- 
sity, St. Louis; and Dr. John S. Fulton, of Baltimore, Secretary 
General of the Congress on Tuberculosis. Upon the recommenda- 
tion of the committee, the prize was divided equally between Dr. 
Guy Hinsdale, of Hot Springs, Virginia, and Dr. S. Adolphus Knopf, 
of New York City. 

At the request of the Institution, Dr. Hinsdale has revised his 
essay so as to indicate some of the advances made in the study 
of the subject during the past five years. 

Charles D. Walcott, 
Secretarv of the Smithsonian Institution. 

Washington, December, 1913. 



TERMS OF COMPETITION 

SMITHSONIAN INSTITUTION 
HODGKINS FUND PRIZE 

In October, 1891, Thomas George Hodgkins, Esquire, of Setauket, 
New York, made a donation to the Smithsonian Institution, the in- 
come from a part of which was to be devoted to " the increase and 
diffusion of more exact knowledge in regard to the nature and prop- 
erties of atmospheric air in connection with the welfare of man." 
In furtherance of the donor's wishes, the Smithsonian Institution 
has from time to time oft'ered prizes, awarded medals, made grants 
for investigations, and issued publications. 

In connection with the approaching International Congress on 
Tuberculosis, which will be held in Washington, September 21 to 
October 12, 1908, a prize of $1,500 is offered for the best treatise 
" On the Relation of Atmospheric Air to Tuberculosis." Memoirs 
having relation to the cause, spread, prevention, or cure of tuberculo- 
sis are included within the general terms of the subject. 

Any memoir read before the International Congress on Tuberculo- 
sis, or sent to the Smithsonian Institution or to the Secretary-General 
of the Congress before its close, namely, October 12, 1908, will be 
considered in the competition. 

The memoirs may be written in English, French, German, Spanish 
or Italian. They should be submitted either in manuscript or type- 
written copy, or if in type, printed as manuscript. If written in 
German, they should be in Latin script. They will be examined and 
the prize awarded by a Committee appointed by the Secretary of the 
Smithsonian Institution in conjunction with the officers of the 
International Congress on Tuberculosis. 

Such memoirs must not have been published prior to the Congress. 
The Smithsonian Institution reserves the right to publish the treatise^ 
to which the prize is awarded. 

No condition as to the length of the treatises is established, it being 
expected that the practical results of important investigations will 
be set forth as convincingly and tersely as the subject will permit. 

The right is reserved to award no prize if in the judgment of the 
Committee no contribution is offered of sufficient merit to warrant 
such action. Charles D. Walcott, 

Secretary of the Smithsonian Institution. 

Washington, D. C, February 3, 1908. 



PREFACE 

The rapid progress in the antituberculosis movement throughout 
the world in the last five years has made it necessary to make some 
changes in the present essay as originally presented to the Smith- 
sonian Institution in 1908. Much that then seemed novel appears 
almost commonplace now. An extraordinary amount of research 
has been carried out with reference to the atmospheric air during 
these later years. The whole theory of ventilation has been stated 
in new terms; the presence of ozone in the atmosphere, a subject 
that has always appealed to the popular fancy since its discovery, 
has been restudied and its physiologic action assigned a value differ- 
ent from that commonly ascribed to it ; the properties of strong 
sunlight and Alpine air have been marshalled for the combat with 
surgical tuberculosis, particularly in children. 

Physiologists in Europe and America have lately made most in- 
teresting studies. of the blood at the higher altitudes and their obser- 
vations are constantly throwing new light on the entire subject of 
aerotherapy, replacing old impressions and beliefs with a scientific 
basis on which we may confidently build. 

There never was a time when the outdoor life and the accessories 
for the atmospheric treatment of all tuberculous persons were so 
well systematized and placed in harmony with the other hygienic 
measures adopted for their cure. 

What the result has been we have endeavored to show and what 
the future holds for us we are eagerly awaiting. 

May the Smithsonian Institution, through its Hodgkins Fund, 
continue to stimulate inquiry and disseminate the fruits of the 
worldwide efiforts to the better understanding of the great problems 
that yet remain unsolved. 

Guy Hinsdale. 

Hot Springs, Va., December, 1913. ' 



TABLE OF CONTENTS 

CHAPTER ■ PAGE 

I. Introduction i 

Difficulty of estimating the value of atmospheric air, aside 
from other agents in treating tubercular disease ; prevention 
of tuberculosis; sanatoria; pioneers in the treatment of tubercu- 
losis in America-; the Adirondack Cottage Sanitarium. 

II. Value of Forests: Micro-organisms, Atmospheric Impurities 4 

General benefit of forests; qualities of forest air and soil; car- 
bon dioxide ; oxygen ; Ozone ; use of forest reservations for sana- 
toria ; micro-organisms in the respiratory passages ; composition 
of expired air ; atmospheric impurities, coal and smoke, carbonic 
acid, sulphur dioxide, ammonia ; oxygen for tuberculous patients. 

III. Influence of Sea Air ; Inland Seas and Lakes 32 

Sea voyages; marine climate of islands ; Arctic climate; float- 
ing sanatoria ; seaside sanatoria for children ; seacoast and fogs ; 
fogs on the Pacific coast; radiation fogs; fogs in the moun- 
tains; sea air for surgical tuberculosis; air of inland seas and 
lakes. 

IV. Influence of Compressed and Rarefied Air ; High and Low Atmos- 

pheric Pressure ; Altitude 6r 

Discovery of the advantages of Colorado and California cli- 
mate for consumptives ; works of S. E. Solly, Charles Theodore 
Williams on Colorado; Jourdanet on Mexico; Paul Bert on 
diminished barometric pressure, etc. ; insolation ; diathermancy 
of the air; Alpine resorts; surgical tuberculosis treatment in 
Switzerland ; cases of high altitude treatment ; effect of cold 
beneficial; expansion of the thorax at the higher altitude; 
choice of cases for treatment at altitudes. 

V. Influence of Increased Atmospheric Pressure, Condensed Air 87 

The eff^ect of barometric changes on the spirits; artificially 
* compressed air, C. T. Williams, Von Vivenot ; pneumatic 
cabinet; Prof. Bier's treatment of surgical tuberculosis by arti- 
ficial hypersemia. 

VI. Artificial Pressure ; Breathing Exercises 98 

Pulmonary gymnastics; exercise at lowered air pressures; 
atmospheric compression of the affected lung, Murphy's 
Method, artificial pneumothorax ; song cure. 

VII. Fresh Air Schools for the Tuberculous ; Ventilation 103 

Waldschule or fresh air schools for tuberculous children; 
Providence fresh air school; defects of school buildings; hy- 
gienic safeguards in schools; rebreathed air; open air chapels 
and theatres; ventilation of dwellings. 



X TABLE OF CONTENTS 

PAGE 

VIII. Exercise in Tuberculosis ; Graduated Labor m 

Effect of exercise on the opsonic index of patients suffering 
from pulmonary tuberculosis; work of Dr. Paterson, Mr, In- 
man and Sir Almroth Wright. 

IX. Accessories for Fresh Air Treatment of Tuberculosis 120 

Tents; pavilion tents; tent houses; shacks; disused trolley 
cars; balconies; day camps; sleeping porches; pavilions; hospi- 
tal roof wards; detached cottages; sleeping canopies. 

X. Conclusions ^^ 



ATMOSPHERIC AIR IN RELATION TO TUBERCULOSIS 

By guy HINSDALE, A. M., M. D., Hot Springs, Va. 
(With 93 Plates) 

CHAPTER I. INTRODUCTION 

We are compelled to acknowledge at the outset the difficulty or 
impossibility of analyzing the relationship of atmospheric air to 
tuberculosis so as to isolate the influence of all other factors. It 
would be totally useless and impossible to consider air independent 
of sunlight, heat, rainfall, the configuration of the earth's surface; 
racial characteristics, social environment, including dwellings, cloth- 
ing, food, and drink. 

As a resultant of all these and many other factors in the tubercu- 
losis problem, we obtain the figures of mortality which are pub- 
lished from time to time by various cities, states, and nations. The 
problem seems incapable of solution. One might as well survey an 
oak that has grown for centuries and set out to determine the rela- 
tive value .of the atmospheric air, the sunlight, the rainfall, and the 
various constituents of the soil and its environment in producing 
the sturdy, deeply rooted, and wide-spreading tree which has seen 
ages come and go. 

The world-wide efforts now made to determine the nature of this 
infection and especially its bacteriologic and pathologic character 
are accompanied by a general effort to limit its spread. We are 
encouraged to believe that future generations will be provided with a 
practical and efficient method of destroying this insatiate monster. 

Undoubtedly we have begun at the right end, but we only began 
within the memory of nearly all of us, only thirty-two years ago, 
when the true cause of the disease was first isolated and revealed 
to the human eye. 

Previously we were as the blind leading the .blind, groping about 
in search of special climates, special foods or medicines, meeting 
with more or less success in so far as the dietetic, hygienic, out-of- 
door plan of treatment was carried out. These curative measures 
succeeded then, as they succeed now, but preventive measures 

Smithsonian Miscellaneous Collections, Vol. 63, No. 1 

I 



2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

worthy the name were entirely unknown. The enemy once revealed 
in its hiding place, and various facts in its life history determined, 
the logical result was a gradual — very gradual — dawn which prom- 
ised better things. Now the world has seen a great light and we 
wonder how intelligent men could have dwelt in those caverns of 
ignorance and even refused to come out for years while the men 
in the laboratory beckoned with signs which then seemed so uncer- 
tain but now so clear. As late as 1890 the medical mind did not 
grasp the necessity for preventive measures. As one asleep it heard 
voices but was slow to waken ; it starts and rubs its eyes and looks 
about, waiting for some word or message that will bring it to its 
senses. 

It was in 189 1 that the first society for the prevention of tuber- 
culosis was organized. This was started in France by M. Armain- 
gaud, of Bordeaux. The second w^as the Pennsylvania Society 
for the Prevention of Tuberculosis organized in Philadelphia in 
1892. These were the pioneers in Europe and America. They 
devoted their energies to a campaign with three cardinal features : 
(i) the education of the public in reference to the nature of the 
disease and its means of prevention; (2) the passage of suitable 
laws regarding notification, the restriction of expectoration, disin- 
fection, etc.; and (3) the care of consumptives and the establish- 
ment of sanatoria by public or private means in suitable localities. 

The wonderful growth of this movement for preventive measures 
is now seen in the establishment of 1,228 societies for the prevention 
of tuberculosis in America alone, and in the erection of 527 sanatoria 
in this country (1913).' The State of Pennsylvania alone has appro- 
priated in one Act of Legislature $2,000,000 for this purpose and 
one citizen of the state, Mr. Henry Phipps, has given an equal 
amount for the scientific study as well as the practical treatment 
of this disease in all its bearings.^ 



' The State of New York leads all other states in the number of new organi- 
zations and institutions established during the last two years. The total 
number of beds for consumptives in the United States now exceeds 33,000. 

^The Pennsylvania legislature appropriated $1,000,000 in 1907, $2,000,000 
in 1909, $2,624,808 in 191 1, and $2,659,660 in 1913 for tuberculosis work alone. 
This is under the direction of Dr. Samuel G. Dixon, the Commissioner of 
Health. 

There are at the present time two State Sanatoria in Pennsylvania in 
operation. 

Mont Alto, Franklin Co. 

No. of patients under treatment 957 

Elevation 1,650 ft. 



SMITHSONIAN MISCELLANEOUS COLLECTION 




Note:- The figures in Franklin County include the deaths at the State Sonotori 
The death rate for Franklin County exclusive of Mont Alto would be 1 

Peoth i 

I I 0-49 ^^ 



MAP SHOWING DISTRIBUTION OF PULMONARY TUBERCI 



VOL. 63, NO. 1, PL. 1 



ONWEALTH OF PENNSYLVANIA 
EPARTMENT OF HEALTH 
G. DIXON, M. D., COMMISSIONER 




iTuberculosis at Mont Alto, numbering 248 in 1912.; 



po.ooo. 
k9 



200 and above 



99 



P PENN 



SYLVANIA BY COUNTIES FOR THE YEAR 1912 



NO. I AIR AND TUBERCULOSIS — HINSDALE 3 

The late Dr. Henry I. Bowditch, of Boston, was one of the first 
physicians in America to recognize the value of constant out-door 
life in the treatment of tuberculosis and was accustomed to send 
such patients on easy journeys by carriage so that they might have 
the benefit of as much out-door air as possible, becoming gradually 
inured to the elements. 

The late Dr. Alfred L. Loomis, of New York, was one of the first 
to systematically send tuberculous patients to the Adirondack forest 
that they might have the benefit of the purest and most invigorating 
air obtainable and, like the physicians of ancient Rome who sent 
consumptive patients to the pine forests of Libya, he believed that 
the terebinthinate exhalations from the standing pines exerted a most 
beneficial influence on pulmonary affections. Dr. Loomis's results 
were so gratifying that he encouraged Dr. Edward L. Trudeau to 
care for such patients in the Adirondack Mountains throughout 
the year, and Dr. Trudeau, with his help, founded in 1884 the first 
sanatorium for tuberculosis in America." 

This Adirondack Cottage Sanitarium, now in its thirtieth year, 
has been the inspiration of sanatoria for tuberculosis throughout 
the country. Its success in restoring so many patients to health 
and usefulness is not wholly estimated in figures. It has established 



Cresson, Cambria Co. 

No. of patients under treatment : 2,37 

Elevation 2,550 ft. 

Hamburg, Berks Co. 

In the course of construction and will be completed some 
time in 1914. 

Capacity 480 

Elevation 55o ft. 

These institutions care for both incipient and far advanced cases. The 
interior arrangement of the sanatoria at Cresson and Hamburg is such that 
they can be used for the different classes of cases as demand may necessitate. 
There is a waiting list of those desiring admission to these institutions at all 
times. 

The State maintains 115 Tuberculosis Dispensaries, which are located 
throughout the 67 counties in the commonwealth. There are 220 physicians 
and 120 visiting nurses employed in these dispensaries. 

By the courtesy of Dr. Samuel G. Dixon, Commissioner of Health, we are 
able to show in a map the distribution of tuberculosis in the counties of Penn- 
sylvania (pi. i). This shows, as in an earlier map by the author, that the dis- 
ease is least prevalent in the higher, forest covered regions of the State. 

' A. L. Loomis, M. D. Evergreen Forests as a therapeutic agent in pul- 
monary phthisis (Trans. Amer. Climatological Ass., Vol. 4, 1887). See page 
134- 



4 SMlTirSONIAN MISCKLI.ANKOUS COLLECTIONS VOL. 63 

a ].ra(ti(al method of curt; ami lias done nmch to correct the earlier 
iiiir<iuii<lc(l and mischievous notions that jjrevailed as to what was 
necessary for the cure of tuberculosis. 

'J\-ikin^^ this institution as an example, let us see what bearing it 
may have on our 5.,'eneral subject, the relation of the atmospheric air 
to tuberculosis : 

(a) It is in the midst of an evergreen forest of over 10,000 square 
miles; (b) the atmosphere is pure, or at least as pure as may be ob- 
tained on the continent; (c) the air is moderately moist; (d) the 
rainfall averages 35 inches; (e) the air is moderately rarified, ow- 
ing I0 (f) an elevation of 1,750 feet; (g) owing to its northern 
situation, (latitude 44°) and its elevation (1,750 feet) (h) the 
climate is cold in winter and (i) subject to rather sudden changes 
with an annual range of 50° C. or 138° F. 

CHAPTER II. VALUE OF FORESTS, MICRO-ORGANISMS, 
ATMOSPHERIC IMPURITIES. 

GENERAL I'.ENEFIT OE FORESTS 

it has come to be an axiom in i)hthisiology that the air of an 
evergreen forest is eminently suitable for a ])atient with tuberculo- 
sis.* As we have previously mentioned, the pine forests of Libya 
were used two thousand years ago for the cure of " ulcerated lungs." 
At that ])eriod the pines abomided and gave the locality a reputation 
as a health resort for affections of the lungs. But the ravages of 
time, aided by fire and sword, not to s])eak of domestic needs, have 
obliterated all vestiges of these ancient forests. 

The successful institutions located in the Hartz Mountains, the 
Black Forest of Germany, in the Forest of Ardennes, the State 
Forest Reserve of I'cnnsylvania, .'uul the Adirondack Forest in New 
York owe much of their success to the abundant use of the purest 
air both day and night. 

lun-opean (iovernments h;ive long recognized the great value of 

' tlir i(.ll(.\\ iiiK (|U()lalinn from Pliny shows thai it was Kcnorally agreed 
ill his (lay that the forests and especially those which abound in pitch and 
balsam are (he most beneficial to consumptives or those who do not gather 
strength after loii^ illness, and ihal they are of more value than the voyage 
to Egypt: 

" Sylvas, eas duntaxat (piae picis resinaetpie gratia redantur, utilissimas 
esse i)hthisicis, aut qui longa aegritudinc non recolligant vires, satis constat ; 
ct ilium coeli acra plus ita quam navigationem Aegyptian proficere, plus quam 
lactis herbidos per nidiitium aestiva potus." — C. Plinii, Hist. Nat. lib. xxiv, 
Cap. C. 




CO Z D 



NO. I AIR AND TUBERCULOSIS HINSDALE 5 

their forests and have protected them by strictly enforcing intelHgent 
laws so that they may be forever preserved and improved. The his- 
tory of forestry in the United States and Canada has been that of 
ruthless, unrestrained, wholesale destruction of nearly all our 
standing" pine, and heavier spruce. In recent years, however, we have 
seen the establishment of Government reserves, State reserves, and 
State laws for their protection ; the organization of the American 
Forestry Association, the American Forest Congress, the Society 
for the Preservation of the Adirondack Forest; the Schools of For- 
estry at Yale, Harvard University and Mont Alto, Penna. All these 
remedial measures have come very late, but will undoubtedly exert 
a strong influence for good.^ 

Aside from the general beneficial influence of forests, universally 
recognized by climatologists, these natural parks have proved the 
means of restoring thousands of persons suffering from tuberculosis 
and diseases of the respiratory system. 

QUALITIES OF FOREST AIR AND SOIL 

The qualities of forest air and forest soil have been studied by 
E. Ebermayer ' who shows that, like that of the sea and mountains, 
forest air is freer from injurious gases, dust particles, and bacteria. 
It was shown that the vegetable components of the forest soil contain 
less nutritive matter (albuminoid, potash, and phosphates and ni- 
trates) for bacterial growth; that the temperature and moisture 
conditions are less favorable; that the sour humus of the forest 
soil is antagonistic to pathogenic bacteria; finally that, so far, no 
pathogenic microbes have ever been found in forest soil ; hence this 
soil may be called hygienically pure. 

The soil is protected from high winds by forest growth and under- 
growth ; the upper soil strata are slow to dry out and wind sweeping 
over them carries few micro-organisms into the air. As may be 
expected, fewer microbes are found in forest air than outside their 
limits. Serafini and Arata have proved this experimentally.' They 

' The chief forester of the United States has in 1913 under his care in 160 
forest reservations a total of 165,000,000 acres of forest land. The present 
Chief Forester has done excellent work in the prevention of serious forest 
fires. 

"^ E. Ebermayer: (i) Hygienic significance of forest air and forest soil. 
(2) Experiments regarding the significance of humus as a soil constituent; 
and influence of forest, different soils, and soil-covers on composition of air 
in the soil. Wollny, 1890 (Hygeia, August 15, 1891). 

* Serafini and Arata : Intorno all 'azione dei boschi sui mikro organismi 
transportati dai venti. 



6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

exposed plates in the forest air and on its outskirts and tabulated 
their countings of bacteria for forty successive days from May 6. 
They made three classes — molds, liquefying and non-liquefying 
bacteria. They found that, with one exception, one or two of these 
classes were always less numerous in the forest than on its outskirts 
and generally from twenty-three to twenty-eight times less. Serafini 
makes the point that bacteria coming from the outside are reduced in 
number by a sort of filtration process. Thus we see that the air of 
forests is comparatively free from endogenous and exogenous bac- 
teria — none of them in any case being pathogenic.^ 

CARBON DIOXIDE IN FORESTS 

Puchner shows that the air in the forest contains generally more 
carbonic acid gas than in the open, due to the decomposition of 
litter.^ But this difference must be almost inappreciable. As we 
know, the law of diffusion of gases renders it impossible for varia- 
tions in the relative proportion of the atmospheric constituents to be 
more than transitory. Diffusion is greatly favored by the winds 
which sweep through the tree tops, especially where they are not 
too crowded. 

The fact that so many sanatoria for tuberculosis are located in or 
near forests makes it very important to dwell a little longer on the 
constituents of the air in these localities. We know that forests, 
as well as all other forms of vegetal growth, take up large quantities 
of carbonic acid, retaining the carbon and rejecting the oxygen, 
and the question naturally arises, does it sensibly change the relative 
quality of either constituent so that the composition of the air is 
slightly different in the woods? Prof. Mark W. Harrington, lately 
chief of the United States Weather Bureau, undertook to answer 
that question, both with reference to carbonic acid, oxygen, and 
ozone, with some interesting results." Repeated observations show 
that each constituent is curiously uniform in quantity in the free 
air. It has been thought that carbonic acid is quite variable but 
the introduction of better methods of observation shows that, except 
in confined places where the gas is produced, the variations are very 



' See B. E. Fernow : Forest Influences, U. S. Dep. Agriculture, Forestry 
Division Bulletin No. 7, pp. 171-173. 

* H. Puchner: Investigations of the Carbonic Acid Contents of the Atmos- 
phere. 

* ,M. W. Harrington : Review of Forest Meteorological Observations, U. 
S. Dep. Agriculture, Forestry Division Bulletin No. 7, p. 105. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63. NO. 1, PL. 6 




DR. WALTHER'S SANATORIUM, NORDRACH-COLONIE, BLACK FOREST, GERMANY 




VIEW FROM THE ADIRONDACK COTTAGE SANITARIUM 

In the foreground are the pines and my only business in life Is to sit and look at them 

Courtesy of Journal of The Outdoor Life 



jjO. I AIR AND TUBERCULOSIS — HINSDALE 7 

small. A little study shows that the carbonic acid gas taken up by 
a forest is a very small quantity compared with that which passes 
the forest in the same time with the moving air. Grandeau ' esti- 
mated the annual product of carbon by a forest of beeches, spruces, 
or pines as about 2,700 pounds per acre. This corresponds to 9,900 
pounds of carbonic acid gas or 69,300 cubic feet. Now, if the aver- 
age motion of the air is five miles an hour, a low estimate, and the 
layer of air from which the gas is taken be estimated at one hundred 
feet thick, there would pass over an acre 550 million cubic feet in 
one hour. This air must contain about three parts in ten thousand 
of carbonic acid gas and the total amount of the latter per hour is 
165,000 cubic feet. But this is two and two-thirds, or more than 
twice as much as that taken up by the trees in the entire season, 
so that the air could provide in thirty minutes for the wants of the 
trees for the entire season. Prof. Harrington shows that the ratio 
of carbonic acid used to that furnished is only one part in 8,600. 

OXYGEN IN FORESTS 

Again, the additions of oxygen to the air would form a still 
smaller percentage of the oxygen already present, for this gas makes 
up 20.938 per cent of the air against a thirtieth of one per cent ob- 
tainable from this source. 

OZONE IN FORESTS 

The occurrence of ozone in the air of forests, especially coniferous 
forests, has been credited, since its discovery by Schoenbein in 1840, 
with affording remarkable health-giving qualities. This opinion has 
become firmly fixed in the minds of the public and, to a large extent, 
has been accepted by the medical profession as an evidence of high 
oxidizing power at once corrective of decaying vegetation and exhil- 
arating and curative to mankind. Popular behef usually has some 
basis for its existence ; indeed, meteorologists made regular estima- 
tions of ozone in the atmosphere by testing with sensitized papers 
and the results were published in connection with statistics of health 
resorts.' 

The Schonbein test is based on the power of ozone to free iodine 
from a solution of potassium iodide in contact with starch, when a 
violet color is developed in the sensitized paper. Unfortunately the 



' See Belgique Horticole, Vol. 35. 1885, p. 227. 

-See Transactions American Climatological Association, Vol. 5, p. 118. 



8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

discovery of important sources of error has destroyed the value of 
observations made in this manner. Other substances in the air 
have been found to act as reducing agents ; secondly, the color after 
having appeared may be altered or destroyed by substances, such as 
sulphurous acid and many organic substances. Again, the test acts 
only in a moist atmosphere and, besides that, varies in intensity 
according to the amount of the wind, so that, in a way, it is a 
measure of humidity and of wind. 

A more recent test, mentioned by Huggard as more sensitive, 
depends upon the use of what is known as tetra-paper, but is also 
considered uncertain. The full name of this reagent is tetramethyl- 
paraphenylendiamin paper. Notwithstanding the unsatisfactory na- 
ture of these tests, the conclusion seems to be accepted that ozone is 
more abundant in May and June and least abundant in December 
and January ; more abundant in the forests and the seashore and in 
mid-ocean and least abundant in towns where it commonly cannot be 
detected. The following quotation is from page 332 et seq. of Vol. 
I, Watts' Dictionary of Chemistry: 

Very little is known respecting the proportion of ozone in the atmosphere, 
or of the circumstances which influence its production. The ozonometnc 
methods hitherto devised are incapable of affording accurate quantitative 
estimations. Air over marshes or in places infested by malaria contains little 
or no ozone. No ozone can be detected in towns or in inhabited houses. 

Houzeau determines the relative amount of ozone in the air by exposing 
strips of red litmus paper dipped to half their length in a i per cent solution 
of potassium iodide. The paper in contact with ozone acquires a blue color 
from the action of the liberated potash upon the red litmus. The iodised 
litmus paper is preferable to iodised starch paper (Schonbein's test-paper) 
which exhibits a blue coloration with any reagent which liberates iodine, 
e. g., nitrous acid, chlorine, etc. From observations made with iodised litmus 
paper Houzeau concludes that ozone exists in the air normally, but the inten- 
sity with which it acts at any given point of the atmosphere is very variable. 
Country air contains at most ^^Aoo of its weight or yosVoo of its volume of 
ozone. The frequency of the ozone manifestations varies with the seasons, 
being greatest in the spring, strong in summer, v/eaker in autumn, and weakest 
in winter. The maximum of ozone is found in May and June, and the mini- 
mum in December and January. In general, ozone is more frequently ob- 
served on rainy days than in fine weather. Strong atmospheric disturbances, 
as thunder storms, gales, and hurricanes, are frequently accompanied by great 
manifestations of ozone. According to Houzeau, atmospheric electricity 
appears to be the most active cause of the formation of atmospheric ozone. 

It has been found that the air immediately above the tree tops 
and at the margin of the forest is richer in ozone than that of the 
interior, where a portion of it is utilized by the decaying vegetation. 
Ozone certainly aids in purifying the air by oxidizing animal or 




^ ? 



NO. I AIR AND TUBERCULOSIS— HINSDALE 9 

vegetable matter in process of decay and by uniting with the gases 
produced by their decomposition. It can, therefore, be found in con- 
siderable amounts where the air is particularly pure. This amount 
rarely exceeds one part in 10,000. " There is somewhat more ozone 
on mountains than on plains and most of all near the sea. Water is 
said by Carius to absorb 0.8 of its volume of ozone." ^ 

This statement by Mr. Russell seems to us extraordinary in view 
of the minute quantity contained in the atmosphere and apparently 
needs confirmation, especially in view of Russell's next statement 
that a great excess of ozone is destructive to life, and oxygen con- 
taining one two-hundred and fortieth part of ozone is rapidly fatal, 
and further, that even the ordinary quantity has bad effects in 
exacerbating bronchitis and bronchial colds, and some other affec- 
tions of the lungs. 

Ozone is not found in the streets of large towns or usually in 
inhabited rooms, but in very large, well ventilated rooms it is some- 
times, though rarely, detected. According to Russell it may be 
formed on the slow oxidation of phosphorus and of essential oils 
in the presence of moisture. When produced by electric discharges 
its pungency of odor is said to make it easily perceptible when pres- 
ent only to the extent of one volume in 2,500,000 volumes of air 
and the smell may sometimes be noticed on the sea beach. 

Since the discovery of ozone by Schonbein, not much has been 
learned about the actual origin of this allotropic form of oxygen. 
Its presence in and near forests and living plants has undoubtedly 
supported the popular view that the air of the forests is particularly 
healthful and that living plants in our apartments are likewise bene- 
ficial.' 

The existence of hydrogen peroxide in air was first established by Meissner 
in 1863, but we have no knowledge of the proportion in which it is present. 
All information as to its relative distribution is obtained from determinations 
of its amount in rain water and snow. The proportion seems to vary, like that 
of ozone, with the seasons of the year and with the temperature of the air. 
It is not improbable that the amount of hydrogen peroxide in air is greater 
than that of ozone, and it is possible that many so-called ozone manifestations 
are in reality due to peroxide of hydrogen. Watts' Dictionary of Chemistry. 



"^ Francis A. R. Russell : The Atmosphere in Relation to Human Life and 
Health, Smithsonian Miscellaneous Collections, Vol. 39 (Publication No. 
1072), 148 p., Washington, 1896. 

'^ See J. M. Anders : House Plants as Sanitary Agents, Lippincott & Co., 
1887. 



lO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

A recent paper by Sawyer, Beckwith and Skolfield ' of the Hygi- 
enic Laboratory of the CaHfornia State Board of Health, is one of 
the latest researches which discredit the claim made for ozone as a 
purifier of air. During recent years circulars have been issued in 
great numbers by manufacturers of apparatus stating that ozone 
is a " necessity " for the destruction of infectious germs and bac- 
terial life, for the sterilization of air in operating rooms for the 
purification of air in homes of persons suffering from contagious 
diseases and for giving to offices and homes the invigorating air of 
the country, seashore and mountains.' 

How false these claims are can readily be seen from the systematic 
work of these investigators, the details of which we cannot give 
here but to which the reader is referred. Among their conclusions 
are the following: 

During these tests certain physiologic effects of the " ozone " were noticed 
by the experimenters after they had been working around the machines. 
The immediate effect of inhaling the diluted gas was a feeling of dryness 
or tickling in the nasopharynx, and sometimes the irritation was felt in the 
chest. If the exposure was prolonged, watering of the eyes, and occasionally 
a slight headache, resulted. The smell of the " ozone " and its irritation was 
much more noticeable to persons who came suddenly under its influence than 
to those who were continuously exposed. 

1. The gaseous products of the two well-known ozone machines examined 
are irritating to the respiratory tract and, in considerable concentration, they 
will produce edema of the lungs and death in guinea-pigs. 

2. A concentration of the gaseous products sufficiently high to kill typhoid 
bacilli, staphylococci and streptococci, dried on glass rods, in the course of 
several hours, will kill guinea-pigs in a shorter time. Therefore these 
products have no value as bactericides in breathable air. 

3. Because the products of the ozone machines are irritating to the mucous 
membranes and are probably injurious in other ways, the machines should 
not be allowed in schools, offices or other places in which people remain for 
considerable periods of time. 

4. The ozone machines produce gases which mask disagreeable odors of 
moderate strength. In this way the machines can conceal faults in ventilation 
while not correcting them. Because the ozone machine covers unhygienic 
conditions in the air and at the same time produces new injurious substances, 
it cannot properly be classed as a hygienic device. 

Another paper even more elaborate than this was published at 
the same time by Edwin O. Jordan, Ph. D., and A. J. Carlson, Ph. D., 



* The Alleged Purification of Air by the Ozone Machine. Journ. Amer. 
Med. Ass., Sept. 27, 1913, p. 1013. 

* See Amer. Journ. Physiologic Therapeutics, Nov.-Dec, 191 1. 



KO. I AIR AND TUBERCULOSIS — HINSDALE II 

of Chicago/ This investigation was carried on at the suggestion of 
and under a grant from the Journal of the American Medical Asso- 
ciation. Their experiments were carried out (i) to determine the 
germicidal action of ozone on pure cultures under the conditions 
commonly used in testing disinfectants, and (2) to determine the 
effect of ozone on the ordinary air bacteria. They found, after a 
long series of experiments detailed in full in their paper, that no 
surely germicidal action on certain species of bacteria could be 
demonstrated by the usual disinfection tests with amounts of gaseous 
ozone ranging from 3 to 4.6 parts per million. The alleged effect of 
ozone on the ordinary air bacteria, if it occurs at all, is slight and 
irregular even when amounts of ozone far beyond the limit of phy- 
siologic tolerance are employed." The toxication of strong concen- 
trations of ozone through injury to the lungs was marked. Even 
in moderate amounts it produced an irritation of the sensory nerve 
endings of the throat and a headache due to irritation, corrosion 
and consequent hyperemia of the frontal sinuses. Consequently the 
use of this poisonous gas as a therapeutic agent is either valueless 
or injurious. 

USE OF FOREST RESERVATIONS FOR SANATORIA 

We cannot leave the subjects of forests and forest air without 
strongly advocating the use of forests and especially State and 
Governmental forest reserves for institutions, hospitals, and cfmps 
for the tuberculous. The State of Pennsylvania has large forestry 
reservations, amounting at present to 1,000 square miles in 23 coun- 
ties, and maintains a State School of Forestry, where young men are 
in training for its forest service. Acting under liberal forest laws, 
Dr. J. T. Rothrock, then State Forestry Commissioner, in 1903, an- 
nounced that citizens of Pennsylvania are entitled to the privilege 
of using the forestry reservation of the state under proper restric- 
tions as a residence while regaining health and recommended it espe- 
cially to those in need of fresh air treatment of tuberculosis. In 
the spring of that year Dr. Rothrock, with State aid, started the 
construction of a few small cabins for the use of such patients and 
called it the South Mountain Camp Sanatorium.' This is situated 



'Ozone: Its Bactericidal Physiologic and Deodorizing Action. (Journ. 
Amer. Med. Ass., Sept. 27, 1913, Vol. 61, pp. 1007-1012). 

' This is corroborated by the recent article by Konrich, Zur Verwendung 
der Ozone in der Lliftung. (Zeitschr. Hyg., 1913, Vol. IZ, 443-) 

=* Charities and Commonwealth, Dec. i, 1906. Journ. Amer. Med. Ass., 1907. 
Journal of the Outdoor Life, Jan., 1907, and Feb., 1908. 



12 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 



in Franklin County, Pennsylvania, in the southern tier of counties 
where the state owns 55,000 acres. The altitude of the camp is 
1,650 to 1,700 feet. It is now the site of the great State Sanatorium 
known as Mont Alto with a capacity of over 1,000 patients. 

At first the patients were obliged to provide and to prepare their 
own food, but the legislature afterward appropriated enough to 
enable the management to furnish food, and the results were better 
than before. Only patients in the incipient stages were admitted, 
and of the 141 so cared for (up to the year 1908) about 75 per 
cent were either much improved or cured. The charge to the patients 
was one dollar per week for all supplies and services, excepting 
washing and the care of their cabins and their persons. The large 
forestry reserve allows of an indefinite extension of this method of 
dealing with the disease, and the small expense seems to point to it 
as a way to provide for the large class of patients who must be cared 
for in the incipient stages if the disease is to be checked and its 
victims restored to society as safe and potent factors in industrial 
progress. Dr. Rothrock, who has just closed twenty years of distin- 
guished service to the state in the forestry commission, believes 
that the forest reservations furnish an answer to the further prob- 
lem of how to care for the consumptive whose disease is arrested, 
but whose financial condition demands that he must still be cared for 
until able to return to his home. Pennsylvania has nearly a million 
acres of forest reservation, much of which needs replanting with 
young trees. To do this requires a large number of men, and the 
task of raising and transplanting trees is mostly light outdoor labor, 
well suited to the convalescent consumptive. In addition, there are 
various forms of woodcraft, such as basket making and the manu- 
facture of small rustic articles that could easily be carried on under 
healthful conditions in the forests. The example of Pennsylvania 
suggests the propriety of other states taking similar steps and pro- 
viding for the large number of consumptives who need care in an 
inexpensive and at the same time effective manner. 

The United States Government should establish without delay 
large forest reserves in the Eastern, Middle, and Southern States. 
The White Mountains of New Hampshire and the Southern Appa- 
lachians should be placed under a system of Federal protection. It 
is encouraging to note that by a recent decision (November, 191 3) 
of the Courts of New Hampshire the way is opened for the condem- 
nation of mountain land in that State and indemnity has been 
awarded private owners for land so taken. 



NO. I AIR AND TUBERCULOSIS — HINSDALE I3 

The United States has 165,000,000 acres of national forests and 
France and Germany combined, 14,500,000 acres. 

The site of a model sanatorium for tuberculosis has the purest 
air or air nearly devoid of floating matter. It is only on very high 
mountain tops or in mid ocean, or in the Polar ice fields that we 
can have air free from suspended matter. The good results obtained 
in the higher Alpine sanatoria and in long sea voyages, in given 
cases of tuberculosis, are attributable in some degree to this absence 
of irritating or polluted atmosphere. In the more northern sanatoria, 
of which the Adirondack Cottage Sanitarium is a type, the long 
winter in which snow covers the ground for possibly five 
months, is always recognized as the best season for patients. The 
gain in health acquired during one winter equals that of two sum- 
mers. The added freedom which the snow covering provides against 
dust a.n'6. other atmospheric impurities may have its hygienic influ- 
ence for the cure of tuberculosis. 

MICRO-ORGANISMS IN RESPIRATORY PASSAGES 

It is interesting to learn something of the fate of micro-organisms 
when inhaled by a person in health or by those whose respiratory 
passages are already sufifering from irritation or disease. It has been 
calculated that upward of 14,000 organisms pass into the nasal cavi- 
ties in one hour's quiet respiration in the ordinary London atmos- 
phere.' Tyndall showed by his experiments with a ray of light 
in a dark chamber that expired air, or more exactly the last portion 
of the air of expiration is optically pure. In other words, respiration 
has freed the inhaled air from the particles of suspended matter 
with which it is laden. These experiments coincide with those of 
Gunning of Amsterdam in 1882 and those of Strauss and Dubreuil 
in 1887. Grancher has made many experiments with the expired air 
of phthisical patients and has never found in it the tubercle bacillus 
or its spores. Charrin, Karth, Cadeac, and Mallet have had corre- 
sponding results. 

These germs are probably all arrested before reaching the trachea ; 
they halt in the upper air passages. The interior of the g-reat majority 
of normal nasal cavities is perfectly aseptic. On the other hand 
the vestibules of the nares, the vibrissse lining them and all crusts 
formed there are generally swarming with bacteria. All germs are 
arrested here and the ciliated epithelium rapidly ejects them. 



'On Researches by Drs. St. Clair Thomson and R. T. Hewlet. Lancet, 
January 11, 1896. 



14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

By experiments on the mucous membrane of the dorsal wall of the 
pharynx, Thomson and Hewlet found that a particle of wet cork was 
conveyed at the rate of 25 mm. or one inch per minute. 

Wurtz and Lermoyez have published researches on the action of 
nasal mucus upon the anthrax bacillus and they hold that it exerts 
a bactericidal influence on all or nearly all pathogenic agents in dif- 
ferent degrees of intensity. 

Thomson and Hewlet corroborate this to the extent of saying 
that the nasal mucus " is possessed of the important property of 
exerting an inhibitory action on the growth of micro-organisms." 
Their experiments upon each other were very ingenious and highly 
interesting. They were able to demonstrate that in ordinary air of 
the laboratory under the conditions observed, 29 moulds and nine 
bacterial colonies developed ; whereas after passing through the nose 
the air contained only two moulds and no bacteria. 

On another occasion they found in nine liters of laboratory air, 
six moulds and four bacterial colonies, while the same quantity of 
air after passing through the nose exhibited one mould and no bac- 
teria. Thus they show that practically all, or nearly all, the micro- 
organisms of the air are arrested before reaching the naso-pharynx ; 
probably a majority are stopped by the vibrissse at the very entrance 
to the nose and those which do penetrate as far as the mucous 
membrane are rapidly eliminated. They state that the nasal mucus 
is an unfavorable soil for the growth of organisms and in this it is 
aided by the ciliated epithelium and lacrymal secretion. 

COMPOSITION OF EXPIRED AIR 

Dr. D. H. Bergey in 1893-4 made some experiments in the Labor- 
atory of Hygiene of the University of Pennsylvania under the pro- 
visions of the Hodgkins Fund of the Smithsonian Institution which 
are pertinent to this subject.^ These were conducted to ascertain 
whether the condensed moisture of air expired by men in ordinary, 
quiet respiration, contains any particulate organic matters, such as 
micro-organisms, epithelial scales, etc. The expired breath was con- 
ducted through melted gelatin contained in a half liter Erlenmayer 
flask, for twenty to thirty minutes. The gelatin was then hardened 



'J. S. Billings, S. Weir Mitchell, and D. H. Bergey: The Composition of 
Expired Air and Its Effects on Animal Life. Smithsonian Contributions to 
Knowledge, Vol. 29 (Publication 989), Washington, 1895. This investigation 
seemed to disprove the renowned experiments of Brown-Sequard and D'Ar- 
sonval in 1887. 



NO. I AIR AND TUBERCULOSIS — HINSDALE I5 

by rolling the flask in a shallow basin of ice-water, thus distributing 
the culture in a thin layer over the bottom and sides of the flask. 

These cultures were kept under observation for 20 to 30 days. 
About 150 cc. of gelatin was used for each experiment. The glass 
tube (b) of the apparatus used, which served for the entrance of the 
expired air, was inserted far enough to just impinge on the fluid 
culture medium in the flask, so that the air produced a slight agita- 
tion of the fluid in passing through the apparatus. The tube of 
entrance (b) is provided with a bulb-shaped enlargement which 
serves to retain any saliva that may flow into the tube. The tube 
(c) is closed with cotton so as to prevent the entrance of micro- 
organisms from this side of the apparatus, and a similar cotton plug 
is inserted in b when the apparatus is not in use. 




Apparatus for Determining the Presence of Bacteria in Expired Breath. 

It was found that the organisms developed in the cultures were 
all of the same character — a small yellow bacillus, common in labora- 
tory air. When special precautions were taken to sterilize the appa- 
ratus with dry heat for an hour previous to introducing the gelatin, 
besides the subsequent sterilization of the gelatin, the results were 
negative — no growths developed. If, after standing in the working 
room for several days, it was found that the culture medium was 
sterile, the expired breath was then conducted through the apparatus 
and the culture was kept under observation (for the specified time 
in the table) at the room temperature. The nature of the organisms 
that developed in the first two experiments, and the absence of any 
growth in the others, make it probable that they developed from 
spores that survived the fractional sterilization of the culture me- 
dium. It is improbable that they were carried in the expired breath. 
Dr. Bergey also made a careful examination of the fluid condensed 
from the expired air with high powers, both in hanging drops and in 
six dried and stained preparations, but nothing resembling bacteria 
or epithelium was found. 

The conclusion was reached that there is no evidence of a special 



l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

toxicity of the expired air. Billings, Mitchell, and Bergey say, in 
the monograph referred to, that the injurious effects of such air ob- 
served appeared to be due entirely to the diminution of oxygen, or 
the increase of carbonic acid, or to a combination of these two fac- 
tors. They consider that the principal, though not the only, causes 
of discomfort to people in crowded rooms are excessive temperature 
and unpleasant odors. 

We shall see, further on, that later studies show that the relative 
proportions of oxygen and carbonic acid are not per se such impor- 
tant factors. 

Dr. Milton J. Rosenau, professor of preventive medicine and 
hygiene in Harvard Medical School, said in his recent address^ on 
" Ether Day " at the Massachusetts General Hospital : 

One of the fallacies that has fallen is the relation of the air to the spread of 
infection. The virus of most communicable diseases was believed to be in 
the expired breath, or exhaled as emanations of some sort from the body. 
These emanations were said to be carried long distances — miles — on the wind. 
The easiest, and therefore the most natural way, to account for the spread 
of epidemic diseases was to consider them as air-borne. Nowadays the sani- 
tarian pays little heed to infection in the air except in droplet infection, and 
the radius of danger in the fine spray from the mouth and nose in coughing, 
sneezing and talking is limited to a few feet or yards at most. The more 
the air is studied the more it is acquitted as a vehicle for the spread of the 
communicable diseases. 

It was a great surprise when bacteriologists demonstrated that the expired 
breath ordinarily contains no bacteria. Most micro-organisms, even if wafted 
into the air soon die on account of the dryness, and especially if exposed to 
sunshine. The relation of the air to infection is nowhere better illustrated 
than in the practice of surgery. At first Lister and his followers attempted 
to disinfect the air in contact with the wound by carbolic sprays. Now the 
surgeon pays no heed to the air of a clean operating room, but ties a piece 
of gauze over his mouth and nose, and also over his hair, to prevent infective 
agents from falling into the wound from these sources. 

How complicated this entire subject is we can readily see from the 
review ' made by Dr. Henry Sewall, of Denver, of recent experimen- 
tal studies by Zuntz, Haldane, Rosenau and Amoss, Heymann, Paul, 
Ercklentz and Fliigge, Leonard Hill and others. This review de- 
serves to be read carefully. It sums up our latest knowledge and 
leads to some surprising conclusions. After describing the Black 
Hole of Calcutta, in which one hundred and forty-six Europeans 



^ Boston Medical and Surgical Journal, November 6, 1913. 

" On What do the Hygiene and Therapeutic Virtues of the Open Air De- 
pend? by Henry Sewall, Ph. D., M. D. (Journ. Amer. Med. Ass., Jan. 20, 
1912). 



NO. I AIR AND TUBERCULOSIS — HINSDALE ly 

were confined on the night of June, 1756, and only twenty-three 
survived, he shows that numberless observations have all led to the 
one conclusion that prolonged confinement in close air tends to lower 
vitality and increase the incidence of certain infections, especially pul- 
monary tuberculosis. However, it was found many years ago that 
animals and men can tolerate without distress an increase of car- 
bon dioxide in the air far beyond any concentration which it is likely 
to acquire under the worst conditions of crowding, provided the 
oxygen tension is maintained at a high level. Zuntz and Haldane 
and his associates show that the normal excitement of the respiratory 
nerve-center depends on the accumulation within it of carbon diox- 
ide, a waste product, which it is a prime object of respiration to 
remove. Sewall refers to Brown-Sequard and D'Arsonval's work 
and, as bearing on it, the very recent work of Rosenau and Amoss.' 
These workers condensed the vapor of human expiration and in- 
jected the liquid into guinea-pigs. No symptoms followed this pro- 
cedure. But after an appropriate interval of some weeks a little 
of the blood-serum from the person supplying the moisture was 
injected into the same animals. The outcome was an unmistakable 
anaphylactic reaction. According to current beliefs the result showed 
that the expired air must have contained proteid matter which sensi- 
tized the pigs toward proteids in the blood of persons from whom 
the first proteid was derived. The authors offer, as yet, no opinion 
as to whether the proteid in the expired air possesses hygienic 
significance. 

Prof. Sewall finds a suggestive analogy in the physiologic rela- 
tions of carbon dioxide which it is one of the chief objects of 
respiration to remove. Added to air in sufficient percentage it is 
deadly to animals, yet so far from its being useless in the body, Hal- 
dane and Priestley found that it must form four to five per cent of 
the alveolar air for the maintenance of normal respiratory move- 
ment, and a considerable lowering of its tension in the body would 
be followed by speedy death. Boycott and Haldane note that the 
subjective sense of invigoration and well-being excited by cold 
weather is associated with a high tension of carbon dioxide in the 
alveolar air.^ After summarizing the experiments of Heyman, Paul, 



' Organic Matter in the Expired Breath (Journal of Medical Research, 1911, 
Vol. 25, 35). 

' Haldane and Priestley : The Regulation of the Lung Ventilation (Journal 
of Physiology, 1905, Vol. 27, p. 225). 

Boycott and Haldane : The Effects of Low Atmospheric Pressure on Respi- 



l8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

and Ercklentz in Flugge's laboratory' which seem to show that, 
in people both well and sick, chemical changes in the character of the 
air in inhabited rooms exercise no deleterious effect on the health of 
the dwellers Dr. Sewall reviews Leonard Hill's work which shows 
that the motion of the air in the experimental chamber by means 
of electric fans almost entirely annulled the sense of discomfort.' 
He then cites the astonishing experiments of F. G. Benedict and 
R. D. Milner' who kept a subject for twenty-four hours in a cham- 
ber, the air of which held an average carbon dioxide content of 220 
parts per 10,000 or over seventy times the normal, together with a re- 
duction of oxygen to less than 19 per cent. The humidity was kept 
down and the temperature held uniform. The subject of the experi- 
ment suffered no discomfort. 

Boycott and Haldane, referred to above, express the opinion that 
" the alveolar carbon dioxide tends to a lower level in warm 
weather " and that this diminution in the alveolar carbon dioxide 
is associated with a feeling of warmth of a rather unpleasant kind 
rather than with any absolute point on the thermometer ; they hold 
that the rise in the carbon dioxide tension is associated with the 
general exhilaration and stimulation produced by cold air. 

And now comes Leonard Hill, the physiologist, of London, who 
with his staff at the London Hospital conducted several noteworthy 
experiments which he described before the Institution of Heating 
and Ventilating Engineers in March, 191 1.' In view of the fact that 



ration (Journal of Physiology, 1908, Vol. 37, p. 359). See also Preventive 
Medicine and Hygiene, by Milton J. Rosenau, M. D., Chapter 4, D. Appleton 
& Co., 1913. Prof. Rosenau's work contains the latest word on the bacteria 
and poisonous gases in the air, ventilation, etc. 

Thomas R. Crowder, M. D. : A Study of the Ventilation of Sleeping Cars 
(Archives of Internal Medicine, January, 191 1, and January, 1913). This 
elaborate investigation is illustrated by numerous diagrams showing the 
carbon dioxide content in the air from the aisles, the upper and lower 
berths and smoking rooms. 

' Zeitschrift f. Hygien. u. Infectionskr., 1905, Vol. 59. 

^Leonard Hill: The Relative Influence of Heat and Chemical Impurity 
of Close Air (Journal of Physiology, 1910, Vol. 41, p. 3). 

See also Leonard Hill, Martin Flack, James Mcintosh, R. A. Rowlands. 
H. B. Walker: The Influence of the Atmosphere on our Plealth and Com- 
fort in Confined and Crowded Places, Smithsonian Miscellaneous Collections, 
Vol. 60, No. 23, p. 96 (Publication 2170), 1913. 

' Experiments on the Metabolism of Matter and Energy in the Human 
Body, Bulletin 175, U. S. Dep. Agriculture Ofifice Experiment Station, 1907. 

*Journ. Amer. Med. Ass., April 8, 1911. 



NO. I AIR AND TUBERCULOSIS — HINSDALE IQ 

the London health authorities insist that in factories the percentage 
of carbon dioxide must not rise above the usual amount allowed, 
say ten parts in ten thousand, he remarks that the regulations do not 
prescribe any limitations of the wet-bulb temperature adding that 
while carbon dioxide does not do any harm whatever a wet-bulb 
temperature of 75° F. is very bad and ought not to be tolerated in 
any factory. All the current teaching of the hygiene of ventilation 
runs on the subject of chemical purity of the air; but according 
to Prof. Hill the essential thing in ventilation is heat, not chemical 
purity. It does not matter if there is i per cent more carbon dioxide 
and I per cent less of oxygen. In the worst ventilated rooms there 
is not I per cent less oxygen. The only effect of an excess of car- 
bon dioxide is to make one breathe a little more deeply. A much 
higher amount has to be attained to have any toxic effect. As to 
organic impurities derived from respiration there is no physiologic 
evidence of their toxicity or that they are of any importance ex- 
cept as an indicator of the number of bacteria in air. The way to 
keep air best from the physiologic point of view is shown by the 
following experiment performed by Hill at the London Hospital: 
Into a small chamber which holds about three cubic meters he put 
eight students and sealed them up air tight. They entered joking 
and lively and at the end of 44 minutes the wet bulb temperature 
had risen to 83° F. They had ceased to laugh and joke and the dry 
bulb stood at 87° F. They were wet with sweat and their faces 
were congested. The carbon dioxide had risen to 5.26 per cent and 
the oxygen had fallen to 15.1 per cent. Hill then put on three elec- 
tric fans and merely whirled the air about just as it was. The 
effect was like magic ; the students at once felt perfectly comfortable, 
but as soon as the fans stopped they felt as bad as ever and they 
cried out for the fans. These and other experiments related, accord- 
ing to Hill, show that all the discomfort from breathing air in a con- 
fined space is due to heat and moisture and not to carbon dioxide. 
Even after five repetitions of the experiment there were no after- 
eft'ects, such as headache. The obvious inference is that the air 
must be kept in motion to avoid bad effects. The open air treat- 
ment of disease is not altogether a matter of fresh air, but the 
constant cooling of the body by the circulation of air which makes 
us eat more and promotes activity. This leads to the general 
strengthening of the body because the blood is not only circulated 
by the heart but by every muscle in the body. 

There cannot be efficient circulation without constant movement 



20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

and activity. If there is constant cooling by ventilation, then a per- 
son is kept more active and the general health is improved. 
As Dr. M. J. Rosenau said in his recent address : 

Thus our entire conception of ventilation has changed, owing to the fact 
that we now do not believe that fresh air is particularly necessary in order 
to furnish us with more oxygen or to remove the slight excess of carbon 
dioxide. It is plain that it is heat stagnation that makes us feel so uncom- 
fortable in a poorly ventilated room rather than any change in the chemical 
composition of the air. It has been made perfectly clear from the work 
of Fliigge that one of the chief functions of fresh air is to help our heat-regu- 
lating mechanism maintain the normal temperature of the body. It is 
necessary to have some 2,000 to 3,000 cubic feet of air an hour to maintain 
our thermic equilibrium — just the amount that was formerly stated to be 
necessary to dilute the carbon dioxide and supply fresh oxygen. The prac- 
tice of ventilation, therefore, has not altered so much as has our reason for 
attaching importance to clean, cool, moving air, which has completely changed.' 

The foregoing resume is perhaps not complete without mentioning 
the recent work of Prof. Yandell Henderson, of Yale University, 
who has brought forward his " Acapnia " theory (acapnia meaning 
diminished carbon dioxide in the blood) . He says :' 

We have really at the present time no adequate scientific explanation for 
the health-stimulating properties of fresh air and the health-destroying influ- 
ence of bad ventilation. . . . The subject needs investigating along new lines 
rather than a rehearsal of old data. 

Dr. Crowder's recent experiments ' also furnish additional evidence 
against the theory that efficient ventilation consists in the chemical 
purity of the air, in its freedom from " a toxic organic substance." 
Even were a poisonous protein substance present in the expired air 
— a fact no experimenter has yet been able to demonstrate — the 
human organism under every-day conditions is apparently well able 
to adjust itself to the reinhalation of this hypothetic substance, since 
a considerable quantity of the expired air is always taken back into 
the lungs." 

We consider that experiments like these demonstrate most valu- 
able and practical truths and that is our excuse for introducing 
them so particularly in this place. When we consider that the aver- 
age man exhales from 9,000 to 10,800 liters of air in twenty- four 



' Boston Medical and Surgical Journal, Nov. 6, 1913. 

' Trans. Fifteenth International Congress on Hygiene and Demography, 
Vol. 7, p. 622. 

* Crowder, Thomas R. : The Reinspiration of Expired Air (Arch. Int. Med., 
October, 1913, p. 420). 

* Editorial in Journ. Amer. Med. Ass., Nov. 29, 1913. See also page 108. 



NO. I AIR AND TUBERCULOSIS HINSDALE 21 

hours' it would indeed be a terrible situation if it were true that 
the expired breath could convey pathogenic or other bacilli. The 
millions of bacilli which we take into the air passages are arrested 
in the air passages and for the most part mercifully destroyed by 
the secretion." In any event we have the assurance that the expired 
air is free from micro-organisms. With reference to tuberculosis 
this means that if healthy persons are exposed only to the expired air 
of tuberculous subjects no infection can occur. Only through bacilli 
contained in the sputum or in tiny drops of moisture coughed by 
the patient is the disease communicated ; and it is further probable 
that, as in the case of other infectious organisms, when once re- 
ceived into the nose and mouth and upper air passages, they quickly 
lose their activity or are soon extruded. (See page 13 et seq.) 

ATMOSPHERIC IMPURITIES 

In view of these facts it would scarcely seem necessary to state 
that for the treatment of all respiratory diseases and especially 
for the treatment of infections such as tuberculosis, which invades 
the larynx and the lungs, or for the treatment of patients whose 
throats and lungs owing to other infections, such as tonsillitis, 
pneumonia, or influenza, may be specially susceptible, no city air can 
be considered favorable. It is our duty to provide as nearly as possi- 
ble air with a very low bacterial content such as may be obtained in 
forests or in the neighborhood of the seashore. 

COAL AND SMOKE 

Aside from the presence of bacteria in the air of cities and towns 
there are other impurities which are of great disadvantage to tubercu- 
lous patients. The prevalent use of soft, or bituminous coal in Great 
Britain and America, especially in manufacturing centers, undoubt- 
edly shortens human life and hastens many a consumptive to his end. 
Volumes have been written on this subject and most valuable contri- 
butions have been made by Dr. J. B. Cohen, of Leeds, Mr. Francis 
A. R. Russell, Henry de Varigny and others, published in connection 
with the Hodgkins Fund.^ 



^ About 380 cubic feet which is equal to a volume yVs feet (220 cm.) in 
height, width, and thickness. 

" It has been calculated that in a town like London or Manchester, a man 
breathes in during ten hours 37,500.000 spores and germs. F. A. R. Russell. 

'See Smithsonian Miscellaneous Collections, Vol. 39, 1896 (Publications 
1071, 1072, 1073). 

See also " The Influence of Smoke on Acute and Chronic Lung Infections," 
by Wm. Charles White, M. D., and Paul Shuey, Pittsburg. Trans. Amer. 
Climatological Association, 1913. 



22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Dr. William Charles White and Paul Shuey, of Pittsburgh, have 
recently made a study of the influence of smoke on acute and chronic 
lung infections, selecting pneumonia and tuberculosis as a cause of 
death in Pittsburgh, St. Louis, Portland, Oregon, St. Paul, Cincin- 
nati, Chicago, Philadelphia, New York, New Orleans, Richmond, 
Cleveland, San Francisco, Indianapolis, Minneapolis, Memphis, Bos- 
ton, Mobile, and Los Angeles. They plotted the number of smoky 
days per year, 1907 to 1912, with the smokiest cities first and so on 
to the least in the order indicated above. The mortality for white 
population and total population and other data are noted on the ac- 
companying chart. This study is in some respects unsatisfactory, 
because of the difficulty of getting data as to smoky days. The con- 
clusion was that if we except Portland and St. Paul there is a 
general tendency of the tuberculosis death rate to rise as the number 
of smoky days in the city decreases. On the other hand, it will be 
seen that there is a general tendency for the number of deaths from 
pneumonia to fall as the number of smoky days in the city decreases. 
In this instance, also, Portland, St. Paul, and Boston must be ex- 
cepted. All this needs confirmation. 

It is a matter of common knowledge that coal miners are liable 
to a disease called fibrosis, anthracosis, or miners' consumption, in 
which the lungs receive and retain coal dust, which penetrates every 
nook and cranny of the lungs and adds one more element of danger 
to a most hazardous occupation. But we have it on the authority of 
Sir Frederick Treves that he had seen the lungs of many persons, 
who had lived in London, which were black from their surface to 
their innermost recesses. Such a condition, in his opinion, not only 
made it more difficult to resist disease, but started disease, and it was 
entirely due to dirt and soot inhaled. The black fog of London owes 
its color to coal smoke, which gives it its filthy, choking constituents, 
and kills people by thousands. Experiments showed that during 
a bad fog six tons of soot were deposited to the square mile.' 



^ Some six hundred years ago, the citizens of London petitioned King Ed- 
ward I to prohibit the use of " sea coal." He replied by making its use 
punishable by death. This stringent measure was repealed, however, but 
there was again considerable complaint in Queen Elizabeth's reign, and the 
nuisance created by coal smoke seems to have been definitely recognized 
at this period. Since this time there has been continual agitation, together 
with much legislation, both abroad and in this country. In the seventeenth 
century, King Charles II adopted repressive measures in London, and in the 
present century anti-smoke crusades have been frequent. In fact, the smoke 
problem will undoubtedly continue to demand attention until it is either 



NO. I 



AIR AND TUBERCULOSIS — HINSDALE 



23 



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24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The Lancet undertook by means of a system of gauges of its own 
design to estimate the annual deposit in London of all adventitious 
matter from the atmosphere. In the city proper it was calculated 
to be nearly five hundred tons to the square mile or about four and a 
half pounds per acre each day. Were it mere dirt it would not be so 
serious, but it is charged with gases and fluids of a deleterious char- 
acter such as sulphates, chlorides, ammonia, and carbon that is more 
or less oily and tarry. One of the experts employed by the Meteoro- 
logical Council in connection with the County Council of London, 
found that the sulphur contents of the coal ranged from one to two 
per cent and that from half a million to a million tons of sulphuric 
acid were diffused in the air every year. The loss to property from 
this erosive influence he estimated at about five and a half million 
pounds sterling. The effect upon health was a more elusive c|uestion, 
but stress was laid on the rise in death rate during foggy weather 
in which coal smoke plays a prominent part. Owing to the activity 
of the Coal Smoke Abatement Society, under the presidency of Sir 
William Richmond, atmospheric conditions are greatly improved, 
and it is claimed that there is a steady diminution in the number 
and density of the black fogs. 

In an article on London as a Health Resort and as a Sanitary City, 
by S. D. Clippingdale, M. D., Trans. Royal Society of Medicine, Feb- 
ruary, 1914, there is an interesting historical account of London air 
and fog, with a bibliography. 

CARBON DIOXIDE 

Parallel conditions are observed in cities like Leeds, Liverpool, 
Manchester, and Glasgow, and in less degree in cities like Pittsburgh, 
Cincinnati, Chicago, Cleveland, and St. Louis, during periods of 
comparatively calm, and of heavy and humid atmosphere. Egbert ' 
states that " it has been calculated that for every ton of coal burnt 
in London something like three tons of carbon dioxide are pro- 
duced," and as the city's coal consumption is over 30,000 tons per 
diem, its atmosphere must receive the enormous daily contamina- 
tion of about 300 tons of soot and 90,000 tons of carbonic acid every 
day ! How important, then, the adoption of practical means to 
abate the smoke nuisance ! Engineers assure us that such means 



entirely solved by the abolishment of the use of solid fuel or by the installa- 
tion of devices and methods which shall prevent the formation of smoke in 
furnaces, regardless of the nature of the fuel. 

^ Seneca Egbert : A Manual of Hygiene and Sanitation, Philadelphia, 1900. 

p. 74. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 25 

are perfectly feasible and economical. It does not need an engineer 
to assure us that they are hygienic. 

Prof. Charles Baskerville, of the College of the City of New York, 
has vigorously attacked the problem of smoke and other air impuri- 
ties. He shows ' that the sticky properties of soot are due to the tar 
contained in it. This tar adheres so tenaciously to everything that it 
is not easily removed by rain. In large manufacturing districts, par- 
ticularly in those where bituminous coal is used as fuel, vegetation 
is blackened, the leaves of trees are covered and the stomata are 
filled up, thus inhibiting the natural processes of transpiration and 
assimilation. In addition, the soot is frequently acid and the deposi- 
tion of acid along with soot is probably one of the principal causes 
of the early withering which is characteristic of the many forms of 
town vegetation. 

SULPHUR DIOXIDE 

Aside from the solid material which pollutes the atmosphere of 
cities, there are correspondingly enormous quantities of noxious 
gases which are equally injurious to persons with tubercular disease 
or other diseases of the respiratory tract. Mention has already been 
made of the vast amounts of carbonic acid gas generated by fur- 
naces, not to speak of the quantities exhaled by human beings. The 
production of this carbon dioxide by the combustion of coal offers 
a definite measure of the production of sulphur dioxide. These two 
gases have the same origin and the measure of one is the measure 
of the other. Recent studies by Prof. Theodore W. Schaefer, who 
has made many observations of the air of Kansas City during fogs, 
tend to show that the presence of sulphur dioxide has an unfavorable 
effect on persons suffering from bronchitis, pharyngitis, pneumonia, 
and asthma. In January, 1902, the heavy fogs occurring in St. 
Louis, Missouri, caused serious injury to the throat and lungs of 
prominent singers and in an action brought against the city and its 
chief smoke inspector, it was alleged that owing to the additional 
presence of smoke, suffocating gases, and acid, the health of the 
complainant was injured. In a mandamus proceeding it was asked 
that the authorities be compelled to abate the smoke nuisance. 

Prof. Schaefer has used the data mentioned previously as to the 
output of carbonic acid in London and states that he finds that at 
least 2,700 tons of sulphur dioxide are generated daily in that city 
and pass into surrounding atmosphere. This gas, after uniting with 

'Medical Record, New York, November 23, 30, 1912. 



26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

the oxygen and aqueous vapor of the air, is converted into sulphuric 
acid.' 

The presence of sulphur in coal, or in iron pyrites contained in 
coal, is responsible for this acid product and Prof. Schaefer believes 
that sulphur dioxide, being a very heavy gas, with a specific gravity 
of 2.25, is alone capable of creating a fog, or is at once shown when 
it is brought- in contact with the atmosphere, from which it absorbs 
aqueous vapor, causing dense, heavy fumes. The dust or carbon 
particles, coming in contact with this acid vapor, enhance its grav- 
ity materially. 

Prof. Baskerville some time ago made a number of determinations 
of the sulphur dioxide content of the air of New York city. Stations 
were established throughout greater New York city, including high 
ofifice buildings, parks, subways, stations, and railroad tunnels ; and 
very variable results, as might be expected, were obtained. The 
determinations may, in part, be thus summarized : 

Locality SO2 in parts in a million 

Elevated portion of city, near a 

high stack 3.14 

Various parks 0.84 (maximum; others negative) 

Railroad tunnels 8.54 — 31.50 

Subway None 

Downtown region 1.05 — 5.60 

Localities near a railroad 1.12 — 8.40 

In 1907, the residents of Stat en Island, as well as some on Long- 
Island, complained of the noxious nature of the air wafted over from 
various plants in New Jersey. This induced the Department of 
Health of the City of New York to investigate the air and vegetation 
in the vicinity of the Borough of Richmond, Staten Island, and 
some of the results obtained are given below by permission of the 
Department. 

Substance Impurity 

Air Trace of sulphuric acid 

Air 0.0066 per cent. SO2 by weight 

Air Trace of sulphuric acid 

Grass (three samples) Sulphuric acid present 

Grass 0.24 per cent SO3 

Grass 0.70 per cent SO3 

Leaves ' 0.19 per cent SO3 

Leaves 028 per cent SO3 

Soil 0.0015 per cent SO3 



^ Theodore W. Schaefer : The Contamination of the Air of our Cities with 
Sulphur Dioxide, the Cause of Respiratory Disease. Boston Medical and 
Surgical Journal, July 25, 1907. 



NO. I AIR AND TUBERCULOSIS HINSDALE 27 

These results do not really give us anything definite, as the com- 
parative factor is absent. 

Fog usually collects in the lower portions of a city, especially in 
depressed localities known as hollows, where it remains until dis- 
persed by air currents. The well-known increase of mortality in 
cities during the continued presence of heavy fog with these addi- 
tional contaminations have been recorded and commented upon for 
years. The heavy, suffocating, poisonous quality of sulphur dioxide 
is well known and has been the subject of several investigations. In 
general, it may be said that the chief symptoms of poisoning with 
sulphurous acid are those of irritation of the mucous membranes. 
Even in five parts in 10,000 it acts as an irritant, causing sneez- 
ing, coughing and lacrymation, bronchial irritation and catarrh 
(Cushny). It is also credited with causing pneumonia and Prof. 
Schaefer notes its power to produce asthma.^ Undoubtedly it would 
aggravate pulmonary and laryngeal tuberculosis and either delay 
or prevent a cure under the conditions described. 

AMMONIA IN THE AIR 

This gas is constantly present in the atmosphere, but in very 
minute quantities. Fifty years ago Boussingault and, later, Schloes- 
ing made careful investigations of this impurity of the atmosphere 
and devised ingenious methods of estimating" its amount in air and 
rain water. It usually exists only in combination with carbonic 
or nitric acid ; very little is free. Water absorbs it freely and it has 
been estimated that in France the annual rainfall brings to the 
earth in the form of nitrogen nearly 5 kilograms per acre. The 
presence of ammonia indicates organic putrefaction. Its amount 
does not usually exceed a very few parts per million. It is usually 
perceptible, as we all know, in and about stables. 

As far as any relation to tuberculosis is concerned, ammoniacal air 
has for us only a remote interest. At one time it was strongly advo- 
cated as a cure for pulmonary consumption and perhaps some his- 
toric details may be of interest here. 

Dr. Thomas Beddoes, of London, published in 1803, " Considera- 
tions on a Modified Atmosphere in Consumption Cases," and 
strongly advocated residence in a cow stable for such cases. One 
of his patients was Mrs. Finch, a daughter of Dr. Joseph Priestley, 



^ This accords with the conclusions of W. C. White and Paul Shuey, loc. cit. 
The relation of Sea Fog to Tuberculosis is considered in the next chapter, 
page 52. 



28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 6^ 

famous for his epoch-making discovery of Oxygen. The patient, 
from the description given, had a well-marked case of pulmonary 
tuberculosis in the second or third stage. She was placed in a stable 
14 by 20 feet and 9 feet high, and her bed was in a small recess a 
few inches above the ground of the stable, where two or three cows 
were kept. The temperature was maintained at 60° to 70° F. Mrs. 
Finch remained in this cow house nearly all the time from the 
autumn of 1799 until the spring of 1800. In a letter, dated August 
15, 1800, the patient wrote, " I am happy in being able to say that 
my chest continues perfectly well ; and from the difference of my 
feelings now, and some years back, I am more than ever a friend 
of the cows. I avoid colds and night air ; and by rides in the country 
am anxious to brace myself against winter and the necessity of a 
sea voyage." 

OXYGEN FOR TUBERCULOUS PATIENTS 

Shortly after the discovery of oxygen, physicians were stimulated 
to try the effect of various gases in the treatment of phthisis. Four- 
croy and Beddoes both observed the effects of the inhalation of 
oxygen and found that it accelerated the pulse and respiration, and, 
as they believed, increased inflammatory action so that they con- 
cluded that its effect was prejudicial. Beddoes held that in phthisis 
there is an excess of oxygen in the system and consequently, that 
free air was injurious to the patient. He says in the essay quoted 
previously ■} " As it seemed to me hopeless to propose residence in 
a cow house, I advised that the patient should live during the winter 
in a room fitted up so as to ensure the command of a steady tempera- 
ture. This advice was followed. Double doors and double windows 
were added to the bed room. The fire place was bricked up round 
the flue of a cast iron stove for giving out heated air." What a con- 
trast to the fresh air cure of the present day! But the doctor per- 
sisted in his plan of treatment until the patient died. 

The amount of oxygen present in the atmosphere, 20.938 per cent, 
is precisely adapted to the needs of animal life and the same propor- 
tion of oxygen is preserved in the atmosphere everywhere, without 
regard to altitude.^ It has been found that animals die if the ratio 
of oxygen is artificially decreased by as much as twenty-five per 



' Thomas Beddoes : Observations on the Medical and Domestic Manage- 
ment of the Consumptive. American edition, Troy, 1803, p. 42. 

' Analyses by Gay-Lussac of Air Collected at 7,000 meters ; and observa- 
tions by Dumas and Boussingault. 



NO. 1 AIR AND TUBERCULOSIS — HINSDALE 29 

cent ; but Paul Bert ' also showed that too much oxygen was equally 
prejudicial to life and, indeed, poisonous, animals dying in a super- 
oxygenated atmosphere as soon as their blood contains one-third 
more than the normal ratio of oxygen, because in such an atmos- 
phere the hemoglobin of the red blood corpuscles is saturated with 
oxygen — a fact which never occurs under normal conditions — and a 
proportion of this gas then dissolves in the serum of the blood 
Here lies the danger, for the tissues cannot withstand the presence 
of free, uncombined oxygen and death follows. The question imme- 
diately arises: Why do the tissues require combined oxygen and 
why does free oxygen kill them ? No one knows. Henry de Varigny, 
who deals with this subject with reference to aerobic and anaerobic 
organisms deals with this curious fact and acknowledges our limited 
knowledge on this point. He states, however, that while a certain 
increase in the ratio of oxygen results in death, lesser increases of 
a temporary character may be beneficial. Every poison kills, doubt- 
less, but there are doses which not only do not kill, but even confer 
benefit and improve health. 

Lorrain Smith has shown that oxygen at the tension of the atmos- 
pb.ere stimulates the lung-cells to active absorption; at a higher 
tension it acts as an irritant, or pathologic stimulant, and produces 
inflammation.'* 

As far as the respiratory processes are concerned the respiration 
of pure oxygen takes place without disturbing them for even in an 
atmosphere of pure oxygen animals breathe as though they were 
respiring normal atmospheric air."* 

Sir Humphrey Davy believed that when pure oxygen was inspired 
there is no more chemical change induced than occurs when atmos- 
pheric air is breathed; in other words, let the vital actions be a 
constant quantity, the addition of oxygen to the inspired air does 
not materially increase vital transformation. Fifty years ago there 
was great confusion in the minds of otherwise intelligent observers 
and false reasoning led them into grave errors. Those who, like 
Beddoes, believed that there was too much oxygen in the system held 
that the inhalation of air containing carbonic acid was the proper 
plan of treatment and this theory of hyper-oxidation was revived 



^ Paul Bert: La Pression Barometrique, 1878. 

See also monograph by F. G. Benedict quoted on page 31. 
- Lorrain Smith, in Journal of Physiology, 1899, Vol. 24, p. IQ- 
^ An American Text Book of Physiology, Vol. i. 



30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

by Baron von Liebig, who recommended that in phthisis the respira- 
tory action should be lessened/ 

The Boston Nutrition Laboratory of the Carnegie Institution of 
Washington has undertaken a most painstaking series of investiga- 
tions bearing on this subject. They include an examination of the 
comparative oxygen-content of uncontaminated outdoor air under 
all conditions as to wind direction and strength, temperature, cloud 
formation, barometer, and weather. In addition, samples of air were 
collected on the Atlantic Ocean, on the top of Pike's Peak, in the 
crowded streets of Boston, and in the New York and Boston sub- 
ways. The results of the analyses of uncontaminated outdoor air 
showed no material fluctuation in oxygen percentage in observations 
extending over many months and in spite of all possible alterations 
in weather and vegetative conditions. The average figures are 
0.031 per cent of carbon dioxide and 20.938 per cent oxygen. The 
ocean air and that from Pike's Peak gave essentially similar results. 

The extraordinary rapidity with which the local variations in the 
composition of the air are equalized is accentuated by the observa- 
tions on street air in the heart of the city, where the contaminating 
factors might be expected to be of sufficient magnitude to affect 
perceptibly the analytic data. Only the slightest trace of oxygen 
deficit is shown, with a minute corresponding carbon-dioxide incre- 
ment. Observations such as these tend to demonstrate the extent 
of the diffusion of gases and the establishment of equilibrium by air- 
currents. 

Most unexpected are the figures in regard to the extremely small 
extent to which the air was vitiated in the modern " tube " or sub- 
way, even during " rush " hours. There was, on the average, a 
fall of 0.03 per cent in oxygen accompanied by a rise of 0.032 
per cent in the carbon dioxide. Professor Benedict points out that 
while the measurement of carbon dioxide has been taken as an index 
of good or bad ventilation, the fact that the proportion of oxygen 
is actually lowered by an increase in the carbon dioxide has never 
before been clearly demonstrated. As a result of this, the determina- 
tion of the content of carbon dioxide in the air, which can be made 
with ease and accuracy, suffices to establish the approximate percent- 
age of oxygen. For every o.oi per cent increase in the atmospheric 
carbon dioxide one may safely assume a corresponding decrease 
in the percentage of oxygen. Aside from minor fluctuations ex- 



' See Edward Smith : Consumption, Its Early and Remediable Stages. 
Blanchard and Lea, Philadelphia, 1865. 



NO. I AIR AND TUBERCULOSIS HINSDALE 3 1 

plained above, it may now truly be said that " the air is a physical 
mixture with the definiteness of composition of a chemical com- 
pound." ' 

Since the introduction ' into medical practice of oxygen com- 
pressed in cylinders its use has been tried in tuberculous cases, but 
no satisfactory results have been obtained and its use is discontinued, 
except, so far as we know, in the hands of charlatans. 

The inhalation of oxygen gas may not per sc exert any curative 
action on a tuberculous lung, but that fact should not lead us to the 
conclusion that the voluntary respiration of an increased quantity 
of air is not beneficial. It is stated that the air in the central parts 
of the lungs is richer in carbonic acid than that found in the larger 
tubes and hence deep inspiration followed by deep expiration causes 
a larger amount of the air richer in carbonic acid, to be exhaled. 
From this the conclusion is drawn that increased chemical change 
will result, for if the carbon dioxide be removed from the air cells 
its place will be filled by quantities of the same gas which will escape 
from the blood. Furthermore, the removal of carbon dioxide from 
the blood facilitates and makes possible those metabolic changes 
which with a supply of suitable food improve nutrition. 

Nowadays we often speak of oxygen as synonymous with atmos- 
pheric air and in this sense we give it a prominent place in pulmonary 
therapeutics. We are tempted to reproduce the placard of an old 
boot-maker and chiropodist of fifty years ago which read : 

The best medicine! Two miles of oxygen three times a day. This is not 
only the best, but cheap and pleasant to take. It suits all ages and con- 
stitutions. It is patented by Infinite Wisdom, sealed with a signet divine. 
It cures cold feet, hot heads, pale faces, feeble lungs and bad tempers. 
If two or three take it together it has a still more striking effect. It has often 
been known to reconcile enemies, settle matrimonial quarrels and bring 
reluctant parties to a state of double blessedness. This medicine never fails. 
Spurious compounds are found in large towns ; but get into the country 
lanes, among green fields, or on the mountain top, and you have it in perfec- 
tion as prepared in the great laboratory of nature. 

Before taking this medicine . . . should be consulted on the understanding 
that corns, bunions, or bad nails, prevent its proper effects. 



' See the recent monograph by Benedict, F. G. : The Composition of the 
Atmosphere with Special Reference to Its Oxygen Content, Carnegie Insti- 
tution of Washington, Publication i66, 1912. Review in Journ. Amer. Med. 
Ass., Jan. 25, 1913. 

' The late Dr. Andrew H. Smith, of New York, was the first in the United 
States to use Oxygen in medical practice, i860. " Oxygen gas as a Remedy in 
Disease," A. H. Smith, 1870. 



32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The old London boot-maker had more wisdom than most of the 
doctors of his time. 

CHAPTER III. INFLUENCE OF SEA AIR; INLAND 
SEAS AND LAKES. 

SEA VOYAGES 

The value of sea air in tuberculosis has been discussed pro and 
con for ages and, like the tide, there is an ebb and flow of sentiment 
regarding its value in the treatment of tuberculosis. Undoubtedly 
there is, at present, a stronger belief in the efficacy of sea air in 
the various forms of tuberculosis than at any previous time. This is 
especially true as regards tuberculosis of the bones, the tuberculosis 
of children and in the important class of cases termed fibroid phthisis. 

Aretaeus, about 250 B. C, recommended sea voyages for the cure 
of consumption, and 300 years later Celsus advocated voyages from 
Italy to Egypt, if the patient were strong enough. Celsus was a 
layman whose learning was truly encyclopedic, but only his medical 
writings have survived. When the Roman sufferer from tubercu- 
losis was not able to make the sea voyage to Egypt he was sometimes 
advised to pass a large portion of his time sailing on the Tiber.* 

At Kreuznach, Ems, and other continental resorts, salt inhalations 
are given to patients with scrofulous and chronic bronchial affec- 
tions. Instead of trusting to sea breezes the patients are taken to 
halls where saline particles are present in a higher precentage than 
they can ever be at the sea side. They inhale the salt-laden air and 
make use of pulverization apparatus. Hours are spent in the open 
air near the " evaporating fences " so as to inhale salt air at interior 
stations. At Ems this treatment is carried out in pneumatic cham- 
bers capable of holding ten people in compressed atmosphere for 
about 1% hours. 

Sea air is of acknowledged purity as to micro-organisms, dust and 
adventitious gases. As previously remarked, there is at sea a maxi- 
mum of ozone and a minimum of all foreign deleterious substances. 
(See page 9.) Without considering, as yet, the amount of watery 
vapor in the air of the ocean and other features of ocean air such as 
its movement and temperature, we recognize some physical contents 
such as a minute quantity of sodium chloride, iodine and bromine 
as characteristic of sea air when contrasted with air from any other 



* " Opus est, si vires patiuntur, longa navigatione, coeli mutatione, sic 
ut densius quam id est, ex quo discedit aeger, petatur ; ideoque aptissime 
Alexandriam ex Italia itur." Celsus, De Med. lib. in. Cap. 22. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 8 








STORM AT BLACKPOOL ENGLAND. SHOWING HOW SALINE PARTICLES ENTER THE ATMOSPHERE 
Photographs by Courtesy of Dr. Leonard Malloy 



NO. I AIR AND TUBERCULOSIS — HINSDALE 33 

locality. The wind carries aloft fine particles derived from the crests 
of the waves and this saline matter from sea water and foam is 
constantly present near the surface and is carried for miles inland.' 
It is well known that plants near the seashore have a perceptible 
coating of saline matter which modifies their growth. 

As far as the present subject is concerned we have to deal with 
the influence on the tuberculous processes exerted by a marine cli- 
mate. This can be obtained by undertaking sea voyages or by a 
residence on islands, or on the seaboard. 

Ocean voyages were formerly strongly advocated as a means of 
cure in tuberculosis and were given an extended trial especially by 
English physicians. The constant commercial intercourse between 
England and her possessions all over the world made the practice 
easy and the results have been carefully weighed. Before the days 
of steam the typical ocean voyage from London to China or India 
involved vastly different conditions, as to time, route and accommo- 
dations. Some features will always be the same. Seasickness, the 
confined air of cabins, storm and wet will remain to harrass and ter- 
rify the traveler. But the clipper ships of the past are now, for 
the most part, doing duty as coal barges and the steam " tramp " 
and ocean liner carry the cargoes of the world. 

After ruling out the tramps, cattle ships, and the coasting schoon- 
ers, we have left a few sailing vessels still engaged in the East 
India trade and the fast liners. Modern systems of ventilation and 
cold storage have corrected some of the great disadvantages of the 
past and the presence of competent surgeons on board all the larger 
passenger steamers make the trip comparatively safe for a tubercu- 
lous patient if the necessity arises for him to make the voyage. But 
as a strictly therapeutic measure such trips are not to be recom- 
mended and in this we are supported by nearly all good authorities." 



^Two illustrations from a storm at Blackpool, England, are supplied by 
the courtesy of Dr. Leonard MoUoy. 

''Huggard, A., Handbook of Climatic Treatment, London, 1906, says: " Sea 
voyages were formerly in great repute for persons with phthisis; but it is 
now recognized that, except in certain well-defined instances they generally 
do harm. Only slight or mild cases without fever and without active symp- 
toms, are likely to benefit. The patients most suitable for a sea voyage are 
those in whom the disease has become partly or entirely arrested." Dr. 
Burney yet doubts whether phthisis at any stage is benefited by ocean travel. 
Prof. Charteris, of Glasgow, approves of a sea voyage in the early stage of 
phthisis in a young person, but after that stage all experience testifies that 
degeneration proceeds more rapidly on sea than on shore and the patient, 
if he reaches land, only does this to find a grave far away from the surround- 
ings of friends and home. 



34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Dr. W. E. Fisher, for many years surgeon to the Pacific Mail 
Steamship Co., while observing that patients affected with chronic 
diseases, such as phthisis, dyspepsia, etc., are not so liable to seasick- 
ness as others, states that a large percentage of tuberculous patients 
stand the sea voyage badly. Dr. Fisher's experience relates to the 
trip from New York to San Francisco by way of Panama. During 
the first part of the voyage until the Bahama Islands are reached, 
the invalid experiences bracing weather. From that point to the 
Isthmus and thence up the coast during the long voyage of three 
weeks or more, a distance of nearly three thousand miles, the tem- 
perature averages 90° in the shade and on many days rises as high 
as 95° or 96° F. This occurs during the winter months and is 
the direct cause of deaths on the voyage or shortly after arrival on 
the California coast. 

Dr. R. W. Felkin, of Edinburgh, says :^ " Fifteen years ago I used 
to advocate sea voyages in my lectures on Climatology in Edin- 
burgh, with great confidence; now I am more cautious. I do not 
send phthisical patients to sea as I once did. The risk of spreading 
infection is, to my thinking, too serious to be incurred. I well 
remember once sending two sisters to Australia ; the elder suffered 
from phthisis ; the younger was healthy. The elder certainly did 
gain some temporary benefit, but the younger sister and also a cabin 
companion became infected, and all three girls were in their graves 
within a year of their return to this country. I am sure that occupy- 
ing a joint cabin as they did caused the mischief." 

Dr. F. Parkes Weber, of London, takes a more hopeful view."" He 
says that sea voyages are often useful in the milder and quiescent 
forms of pulmonary tuberculosis, provided the patient's general con- 
dition be such as otherwise to fit him for life on shipboard. " Long 
voyages are to be preferred to all other methods of treatment in the 
case of male patients who have a taste for the sea, who are strong 
physically, or who possessed an originally strong constitution and 
were infected by * chance ' or when weakened by overwork, worry, 
improper hygienic conditions, or acute diseases." 

In pulmonary tuberculosis complicated by syphilis, or syphilitic 
phthisis, as it was formerly designated, a marine climate seems to 
be particularly suitable.^ 



^Journal of Balneology and Climatology, January, 1906. 
'F. Parkes Weber: System of Physiologic Therapeutics, Vol. 3, p. 87, 
Philadelphia, 1901. 
' See Roland G. Curtin, Trans. Amer. Climatological Ass., Vol. 4, p. 31. 



^fO. I AIR AND TUBERCULOSIS — HINSDALE 35 

The vicissitudes of sea-travel, the narrow cabins and the difficulty 
of obtaining a suitable diet, even such common requisites as milk and 
eggs, should be enough to condemn this plan. Tuberculosis patients 
ought not to travel more than is absolutely necessary. Imagine the 
bacteriological condition of a consumptive's stateroom, for instance, 
at the end of a month's voyage ! What sea-captain or steward would 
ever put such a cabin into a sanitary condition for the next pas- 
senger ? 

The author has some experience of life at sea under both sail and 
steam, although he has never taken very prolonged voyages. Taking 
into account the character of the food supply and the necessity of at 
least sleeping in small cabins and probably spending days in them, 
with uncertain medical attention ; and, besides this, the dangers of 
various kinds that pertain to seaports, the author feels bound to con- 
demn sea voyages for the tuberculous in any stage. 
" Non mutant morbum qui transemit mare." 
MARINE CLIMATE OF ISLANDS 

It is far better for the tuberculous patient to remain on terra Hrrna 
than to traverse the sea. Whatever is of value in the sea air can be 
obtained in islands such as Ireland, the Isle of Man, the Isle of 
Wight, Nantucket, the Isles of Shoals, Newfoundland, Long Island, 
the Bahamas, the Canaries, the Philippines, Samoa, and many other 
islands. 

Just as in the case of sea voyages, there are concomitant influ- 
ences, many of which are notoriously unfavorable, that in themselves 
over-balance any possible advantage from sea air. Take, for in- 
stance, the problem as it presents itself in Ireland or the Isle of Man. 
Among the various countries of the world Ireland stood fourth 
in the order of mortality from tuberculosis, being exceeded by Hun- 
gary, Austria, and Servia. During the last thirty-five years the 
mortality in Great Britain has been reduced one-half among females 
and one-third among males but, until 1907, there had been no such 
fall in Ireland. 

Sir John Byers, of Belfast, in his address' entitled "Why is 
Tuberculosis so Common in Ireland?" characterized its prevalence 
in that country as " appalling." Among the nine causes which are 
assigned for this condition of affairs attention is first directed to 
the damp climate. An investigation of places with rather worse con- 



^ The Lancet, January 25, 1908. See also Alfred E. Boyd, M. B. : Tubercu- 
losis and Pauperism in Ireland, British Journ. Tuberculosis, July, 1908, p- I59- 



36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

ditions of climate led Sir John to say on this point: "I cannot, 
therefore, admit that there is much in the dampness of the atmos- 
phere as a cause of tuberculosis in Ireland." Sir William Osier 
takes precisely the same ground and pointed out at the opening of 
the Tuberculosis Exhibit in Dublin, that Cornwall, with a much 
damper atmosphere than that of Ireland, was so free from the 
disease that consumptives were sent there. In Cardiff, Wales, with 
a damp climate and with the ground water in many places near the 
surface in the gravel and with the lower part of the town on a stifif 
marine clay, very retentive of moisture, the tuberculosis death rate 
for 1906 was only 1.20 per i,ooo. On the other hand in Belfast, 
with a smaller rainfall (34.57 inches as against 42.43 inches) the 
mortality was more than twice as much, or 2.77 per 1,000. The 
figures for 1906 were: 

Death rate 
from 
Rainfall tuberculosis 

inches per looo 

Manchester, notoriously damp, foggy and smoky 1.82 

Liverpool 1-82 

London 1.42 

Cardiff, Wales 42.81 1.20 

Bolton, England 42-43 i-H 

Belfast, Ireland 34-57 2.77 

Cork 4-53 

Dublin, Ireland 27.73 2.91 

North Dublin, Ireland 4-70 

After taking up in turn dampness of soil, emigration as a cause 
for tuberculosis, the asserted susceptibility of the Irish to tuberculo- 
sis, poverty and social position, food and drink and industries, and 
after weighing them carefully they were all discarded as insufficient 
causes of this mortality. The prime cause was declared to be want 
of Sanitary Reform and the prevalent domestic or home treatment 
of the advanced cases of pulmonary tuberculosis. 

Since 1907 an encouraging decline in the mortality from tuber- 
culosis has been noted. Whereas the rate for both sexes throughout 
Ireland was 273.6 per 100,000 in 1907 it had dropped by gradual 
stages to 215.2 in 1912. Sir William Thompson, the General Register 
for Ireland, justly attributes this well marked decrease during the 
past six years to the exertion of Her Excellency, the Countess of 
Aberdeen.^ 



^ Trans. National Association for the Prevention of Consumption and 
Other Forms of Tuberculosis, 5th Annual Conference, London, August 4 
and 5, 1913. See also Sir John Moore, Interstate Medical Journ., April, 1914. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 37 

Sir William shows that this decrease indicates 17,000 fewer people 
suffering from tuberculosis in Ireland in 19 12 than there were in 
1907. This corresponds to a decrease of nearly one-fifth of the 
total number of cases of tuberculosis. He seems hopeful that within 
the next few years the death-rate from tuberculosis in Ireland will 
not be above the average in other countries. 

Undoubtedly hygienic and philanthropic measures are entitled to 
the credit for this marked improvement and it gives us pleasure to 
note in this connection the remarkable work of Her Excellency, the 
Countess of Aberdeen. This noble woman founded in 1907 the 
Women's National Health Association of Ireland and a vigorous 
campaign was started which soon roused the whole country to a 
sense of responsibility in matters of public health and, in particular, 
to measures necessary for the prevention and cure of tuberculosis. 
The influence of this organization rapidly spread and within eight- 
een months no less than seventy branches had been opened through- 
out Ireland, for the most part opened in person by their excellencies, 
the Lord Lieutenant and Countess of Aberdeen, and now it has 150 
branches and 18,000 members. 

While undertaking the reduction of infant mortality, the improve- 
ment in the milk supply and better school hygiene, the association 
made a systematic attack on the prevalence of tuberculosis. This 
included home treatment and its strong ally, the tuberculosis dis- 
pensary, on a plan similar to that originated by Sir Robert Philip, of 
Edinburgh ; it included sanatorium treatment ; and it provided special 
treatment for advanced cases of tuberculosis. In this phase of the 
work the association had the benefit of £145,623. through the pro- 
visions of the National Insurance Act. Charitable Americans also 
contributed handsomely toward the erection of sanatoria now com- 
prising one thousand beds, the maintenance of dispensaries and of 
depots for the supply of pasteurized milk.' 

It is interesting to note that the Association also lent its support 
to the formation of an " Irish Goat Society," believing that the best 
way to meet the scarcity of milk experienced in many parts of Ire- 
land is to encourage the keeping of a good breed of milking goats.' 
Then, too, through the administration o"f the Laborer's Acts nearly 
fifty thousand cottages with garden plots ranging up to one acre 
have been built for rural laborers by rural sanitary authorities at an 
outlay of over £8,000,000. 

We have cited this remarkable campaign of the anti-tuberculosis 



' The late Mr. R. J. Collier and Mr. Nathan Straus. 



38 " SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

movement in Ireland to show how close are its relation to the broader 
field of general hygiene and sanitation and to show that such work 
pays ; and furthermore what great service one person of noble birth, 
by her foresight, solicitous care and untiring devotion, can initiate 
and carry out. As Prof. Thompson says: There is no doubt that 
it will rank as one of the greatest philanthropic efiforts of our time. 
Take the Isle of Man. This island in the Irish Sea has a popula- 
tion of over ten thousand and for six hundred years has been singu- 
larly free from the admixture of English, Irish, or Scotch blood. 
The island has a more equable climate than any other part of the 
British Isles. The mean annual temperature is 49° F. There is com- 
parative absence of frost, fog, or snow. But careful records since 
1880 show that the Manx tuberculosis death rate is about double 
that on the mainland.^ 

1880-82 1883-1897 

Isle of Man 31-63 25.70 per 10,000 

1S87 :893 

England and Wales i5-o8 I3-07 per 10,000 



14.28 12.17 per 10,000 

1889 1895 

14.35 12.43 per 10,000 

1890 1S96 

15.06 11.39 per 10,000 

The Bahamas and Bermuda in the Atlantic Ocean have a sub- 
tropical marine climate that experience shows to be far too relaxing 
and enervating for tuberculous patients. 

The Philippines and all other tropical islands are likewise entirely 
unsuited for tuberculous patients for the same reasons." Newfound- 
land, with a harsh, damp, colder air, is equally bad. 

Dr. Newsholme, of Brighton, President of the Epidemiological 
Section of the Royal Society of Medicine, in an elaborate inquiry 
into the principal causes of the reduction of the death rate from 
phthisis in different countries, came to the conclusion that the one 



'Charles A. Davies, M. D. : Tuberculosis in the Isle of Man (Tuberculosis, 
London, Oct., 1900). 

' According to Dr. Issac W. Brewer, U. S. A., " Notes on the Vital Sta- 
tistics of the Philippine Census of 1903-" American Medicine, Oct., 1906, the 
death rate from tuberculosis is one-third that in the United States. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 39 

common factor present in all cases where a fall was noted was the 
segregation of the patients in hospitals or sanatoria. In each country 
where the institutional has replaced the domestic relief of destitu- 
tion there has been a reduction of the death rate from phthisis which 
is roughly proportional to the change. 

As to the cause, then, of the spread of tuberculosis, we shall find 
that it probably always lies in ignorance, indifference and other moral 
or sociologic causes, and, in many of the cases cited, not to climatic 
or atmospheric conditions. 

Our opinion of sea air is fortunately not confined to that of the 
high seas or even that of islands. The sea air sweeps the mainland 
and, as we know, modifies the climate of all adjacent portions of the 
Continent. The great source of atmospheric moisture is found ulti- 
mately in the oceans. The invisible watery vapor and the visible 
clouds are carried inland and deposit their water over the Continent. 
The monsoons which are most highly developed in India and other 
parts of Asia, prevail also in Texas and on the Pacific coast of the 
United States. These seasonal winds are of great importance from 
a climatic standpoint and hence should be taken into account in ref- 
erence to the climatic treatment of tuberculosis.^ During the sum- 
mer and autumn in India these seasonal winds sweep inland from the 
sea and deluge the country with rain. This amounts, in the Khasi 
Hills, 200 miles north of the Bay of Bengal, to between 500 and 600 
inches a year and reaches its maximum at points about 1,400 meters, 
4,600 feet, above sea level. 

Fortunately in the United States these seasonal winds, while pres- 
ent, are not so dominant as climatic factors. We are more concerned 
in the present study with the diurnal winds of the seashore. The sea 
breeze which tempers the heat of our coasts is a distinctly beneficial 
feature of the shore and not only tends to moderate the heat of 
the summer day, but sweeps inland for fifty or a hundred miles the 
pure ocean air and provides all the desirable features of a marine 
climate. 

ARCTIC CLIMATE 

Passing still farther north we have the Arctic climate. It is 
marine or insular and cold. Arctic voyages have been proposed for 
the treatment of tuberculosis and, as adjuncts to the voyage, a sum- 
mer sojourn in the northern fjords -of Greenland. A trip of this 



^ See William Gordon : The Influence of Strong, Rainbearing Winds on 
the Prevalence of Phthisis, H. K. Lewis, London, 1910, Observations in 
Devonshire. 



40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

kind has been seriously planned by Dr. Frederick Sohon, of Wash- 
ington, D. C, but has never yet been carried out.^ 

It is a significant fact that Arctic explorers from Dr. Elisha Kent 
Kane down, including General A. W. Greely, Admiral Peary, Mr. W. 
S. Champ, Mr. Herbert L. Bridgman, the late Dr. Nicholas Senn, and 
others comment on the healthfulness of the Polar climate. Dr. 
Sohon made two voyages with Commander Peary, in 1896 and in 
1902, and states his opinion that in summer the Arctic regions are en- 
tirely suitable for, and beneficial to, the tuberculous, and that the un- 
equaled natural advantages for a cure can be practically utilized. Few 
understand the fascination which the Polar regions undoubtedly 
exert on all who enter that charmed circle. The expressions used by 
Arctic explorers seem so extravagant to the average mind. The 
late Professor Senn says : " Nature there lends such efiforts toward 
prophylaxis, as to leave no need for therapeutics." " 

The air of the Arctic regions is free from dust and germs. It is 
not, in itself, responsible for any disease which may be carried 
into Arctic settlements by ships' crews, or by means of the migration 
of animals or birds. Colds and catarrhal conditions are conspicu- 
ously absent. There is no pneumonia. The only " Arctic Fever " 
is that which explorers are almost sure to contract on their first 
visit and which has an annual periodicity. It is not a self-limited 
disease, as Admiral Peary can testify after nearly fourteen con- 
secutive summers in the Polar regions. 

Another feature of the atmosphere in the Arctic is absolute 
clearness and abundance of sunshine. Dr. Sohon, in 1902, exposed 
dishes of agar and introduced into culture tubes pebbles, bits of 
vegetation and water from the ground and from pools at Comman- 
der Peary's winter quarters. Of six dishes exposed for from one- 
half to two hours, two were sterile and four gathered only a com- 
mon white mould (P. glaucum). Only the hay bacillus was obtained 
from the pebbles. Water yielded the hay bacillus, B. liquefaciens, 
B. Uuorescens and an unclassified non-pathogenic saprophytic rod or- 
ganism. 



Frederick Sohon, M. D. : Personal Observations on the Advantages of Cer- 
tain Arctic Localities in the Treatment of Tuberculosis (American Medicine, 
April 23, 1904). 

Idem. The Therapeutic Merits pf the Arctic Climate Meteorological Data 
of a Summer Cruise (Journal American Medical Association, February 3, 
1906). 

"Nicholas Senn: Medical Affairs in the Heart of the Arctics (Journal 
American Medical Association, 1905, Vol. 45, pp. 1564, 1647). 



NO. I AIR AND TUBERCULOSIS — HINSDALE 4I 

The atmosphere has a bracing quahty and is always credited with 
developing a prodigious appetite. It is pointed out that a taste is 
developed for the kind of food the tuberculous patient needs, viz., 
fatty food and meat. The craving for this kind of food is usually 
accompanied by a corresponding adaptability to digest it and, in 
healthy subjects, flesh is always gained. Dr. Sohon says that in 
both of his trips to Greenland he has exceeded his usual maximum 
weight, gaining the first time thirty pounds in two months, and the 
second time nineteen pounds in six weeks. In the latter voyage 
even the crew made an average gain of ten pounds in weight. 

A large share of the beneficial influence of any atmospheric 
change is that which conduces to a good appetite and digestion. 
In this respect the summer Arctic voyage may fairly claim pre- 
eminence. With qualities such as these it is natural that, for a por- 
tion of the year at least, the merits of the Arctic climate in the treat- 
ment of tuberculosis should at least be considered. 

An atmospheric feature is its great penetrability for light and 
especially for the actinic and ultra-violet rays. Tanning of the skin 
always occurs and sunburn is not uncommon. During summer 
the sun never sets and, though not very high in the heavens, its 
generous rays must exert a very beneficial influence on any morbid 
process, especially of a tubercular type. Arctic plants develop rap- 
idly from seed to flower and seed again in surprising manner and 
the wild animals seem to be the largest and most vigorous of their 
kind. 

In judging of the weather to be encountered in the Arctic regions, 
we are too much inclined to recall the harrowing accounts of the 
ill-fated expeditions of the past; but in the Northern fjords of 
Greenland, some miles from the coast, or in the protected inland 
bays, the atmospheric conditions of summer are quite agreeable 
and are especially suitable for the open air treatment. 

The fluctuations of temperature are very moderate. The average 
minimum temperature between July 28 and September 6, between 
69° and 78° north latitude on these Greenland Fjords, was about 
38 F. ; the average maximum was 49° to 50°. Temperatures as 
high as 56° were recorded at North Star Bay and about 52° at Etah. 

The humidity averaged low. The records were made at 8 a. m. 
and 8 p. m., and, owing to the constant daylight, are much more 
representative estimates of relative humidity than in the case of 
records of relative humidity at those same hours in temperate lati- 
tudes. 



42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Maximum Minimum Average 

Humidity Humidity 

8 a. m. 8 p. m. 8 a. m. 8 p. m. 8 a. m. 8 p. m. 

New York 100 95 62 50 81.3 74-i 

Denver 90 90 4i I3 66.1 . 37-1 

North Star Bay 72 71 56 39 63.1 54- 

Etah, Greenland 81 70 40 35 57-6 S2.4 

The relative humidity was much lower while at anchor in the 
harbors of Northern Greenland than while en route through the 
Strait of Belle Isle and off Labrador and in Davis Strait and Smith's 
Sound. 

We have given some attention to this subject on account of the 
very enthusiastic claims made on behalf of the atmosphere of the 
Arctic regions during summer treatment of tuberculosis. Although 
the plans for sending a ship with tuberculous passengers on this 
voyage failed to be carried out owing to inability to get the neces- 
sary permission from the Danish Government to land at the north- 
ern ports of Greenland, it is possible that at some future time the 
attempt will again be made. 

The fact that Icelanders and Greenlanders may contract tubercu- 
losis in numbers and may die from it is not to be overlooked ; but 
the filth of winter quarters in the far North and the foul air of 
these huts is responsible for much of the illness of the native inhabi- 
tants. The Eskimo survives the dangers of the winter because he 
leads a totally different life in summer. It is difficult for those who 
have never been to the Polar regions to realize what a change is 
wrought by the advent of constant sunlight. This unique feature 
of the summer climate contributes to health and energy. The at- 
mosphere, free from all germs and dust, bracing in its quality, is 
a strong stimulant to bodily functions as gain in weight testifies. 

As a practical measure for the treatment of tuberculosis Arctic 
voyages have not yet been proved to be beneficial, although there is 
some presumptive evidence in their favor and, in view of the abund- 
ance of proof that the disease can be successfully combated at 
numberless places on the continent, such expeditions will scarcely 
meet with favor. 

FLOATING SANATORIA 

In 1896, Mr. M. O. Motschoutkovsky ^ advocated floating sanatoria 
for patients with incipient tuberculosis. These specially fitted ves- 
sels were to be shifted from port to port according to the season 
so as to get the most favorable climatic conditions. 



^The Lancet, April 4, 1906, p. 939. 



lllTHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1. PL. 9 




OPEN AIR CLASS ON FERRY BOAT " SOUTHFIELD," EAST RIVER, NEW YORK CITY. SLEEPING HOUR 

Courtesy of Dr. J. W. Brannan 




OPEN AIR SCHOOL FOR TUBERCULOUS CHILDREN. FERRY BOAT SOUTHFIELD," BELLEVUE 
HOSPITAL. SEE PAGE 43 



NO. I AIR AND TUBERCULOSIS — HINSDALE 43 

The vicissitudes of sea-travel, the narrow cabins and the difficulty 
of obtaining a suitable diet, even such common requisites as milk 
and eggs, ought to be enough to condemn this plan. Tuberculous 
patients ought not to travel more than is absolutely necessary. 
Old ferry boats have been recently utilized in Nev^ York as class- 
rooms for tuberculous scholars. The ferry boat " Southfield " has 
been equipped for this work through the Miss Spence's School 
Society under the direction and courtesy of Bellevue Hospital in 
cooperation with Dr. John Winters Brannan and Dr. J. Alexander 
Miller. 

There are three classes on the " Southfield " ; two for pulmonary 
cases of about thirty-six children; these classes being part of the 
regular Bellevue Clinic work and entirely supported by Bellevue. 

The third class is for tuberculous cripples with about twenty 
children. The cost of nurses and special equipment for this class 
together with incidental expenses is borne by the Spence School 
Society. 

The teachers for all three classes are supplied by the New York 
Board of Education so that they are a part of the regular school 
system.^ 

Owing to the fact that these old ferry boats seem to answer a 
useful purpose and in view of the reported use by the Italian Gov- 
ernment of three discarded men-of-war as floating sanatoria in the 
treatment of tuberculous patients, a request was made to the Navy 
Department of the United States for similar ships by the Fourth 
International Congress on School Hygiene at Buffalo, N. Y., August 
29, 1913, in a resolution, a portion of which is as follows: 

Whereas, It has been demonstrated in New York and other cities that 
discarded vessels lend themselves admirably to transformation into all-year- 
round hospitals and sanatoria for consumptive adults, sanatoria for children 
afflicted with joint and other types of tuberculosis, and into open air schools 
for tuberculous, anemic, and nervous children; 

Resolved, That the fourth International Congress on School Hygiene peti- 
tions the United States Government to place at the disposal of the various 
States of the Union as many of the discarded battleships and cruisers as possi- 
ble to be anchored according to their size in the rivers or at the seashore and 
to be utilized by the respective communities for open air schools, preven- 
toria, sanatorium schools for children, or hospital sanatoria for adults. 

The Secretary of the Navy, however, for the following very good 
reasons, declined. 



^ See Buffalo Medical Journal, 1907-8, Vol. 63, 4L 



44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

I am of the opinion that battleships are not suitable for floating sanatoria. 
This opinion is based on the following reasons. 

The cost of maintaining a battleship in proper sanitary and structural 
condition is very high. 

Battleships, particularly the older types, have very limited deck space, and 
this is so cut up by hatches, turrets, davits, cranes and w^inches that there 
are few spaces large enough for a cot. The cost of removing these obstruc- 
tions would be equivalent to that of building more suitable floating hospitals. 

The ventilation in the enclosed spaces of these vessels is so poor that it 
often has an unfavorable effect on those chosen especially for their health 
and vigor. Its effect on those already diseased could not be favorable. 
The openings are very small and admit but little sunlight ; it is necessary 
to use artificial light for a large part of the day. To correct these conditions 
would involve great expense, even if it were possible of accomplishment. 

The passages are narrow, the ladders steep and the hatches small, making 
transportation of the sick very difficult. 

Very respectfully, 

JosEPHus Daniels, 

Secretary of the Navy. 

Under the title " Una nave-scula-sanatorio per fanciulli predis- 
posti " Federico di Donate has urged this plan in Italy but up to the 
present the Italian Government has not assented. 

The remark has been made that : " If the right sort of ship could 
be sent to the right place in the right kind of weather with the 
right sort of patients, a great deal of good might result." 

SEASIDE SANATORIA FOR CHILDREN 

In the United States notable attempts have been made to utilize 
sea air in treating tubercular disease in children. Individual cases 
have been treated by sea air, but on a larger scale we should mention 
the experience of two institutions. 

In 1872, Dr. William H. Bennett, of Philadelphia, established the 
Children's Seashore House at Atlantic City, New Jersey. This in- 
stitution is open during the entire year, and in 19 12 more than 3,500 
mothers and children were cared for. Among the first patients ad- 
mitted to the Institution at its inception were the hospital children 
suffering from tubercular diseases of the bones, glands, and joints. 
The wonderful improvement wrought in such cases by the sea air 
led to a steadily increasing demand for their admission, and now 
throughout the year seventy beds are set apart for their care and 
treatment. 

The most notable and most recent attempt in the United States 
to treat cases of tuberculosis of the bones, joints and lymph nodes 
is at the Sea Breeze Hospital at Coney Island on the Atlantic 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 11 




TREATMENT OF POTT'S DISEASE OF THE SPINE ON A BRADFORD FRAME. SEA BREEZE 
HOSPITAL, SEA GATE, NEW YORK. PATIENTS REMAIN FOR MONTHS, NIGHT AND DAY, ON 
THESE FRAMES, BUT ARE REMOVED TWICE DAILY FOR BATHING AND POWDERING 
Courtesy of Dr. J W. Brannan 




SEA BREEZE HOSPITAL, SEA GATE, CONEY ISLAND, NEW YORK. MORE CITY CHILDREN ARE 
STARVED FOR SLEEP THAN FOR FOOD. VIEW AT 6 A. M. IN SPRING. CHILDREN SLEEPING TEN 
HOURS ON PORCH ALL NIGHT. CANVAS OVERHEAD ROLLED BACK. 



NO. I AIR AND TUBERCULOSIS HINSDALE 45 

Ocean, ten miles from New York City. This was undertaken by the 
New York Association for Improving the Condition of the Poor. 
Ten tents were erected on the beach and were opened to children 
between the ages of two and fourteen on June 6, 1904. These 
tents had a capacity of fifty patients. In the autumn permanent 
buildings were occupied and have since been used. While the 
main reliance has been on fresh sea air and good food, the very best 
surgical aid has been employed, and for all major operations the chil- 
dren were temporarily removed to hospitals in New York City. 
This co-operative arrangement is a great advantage to the seashore 
institution, as the distance is not great and avoids the necessity of 
enlarging the surgical staff and at the same time provides the highest 
surgical skill. To avoid mistakes most of the cases admitted are 
seen by at least one other surgeon besides the attending surgeon. 
While pulmonary cases are refused the staff admits severe, desperate, 
and even hopeless cases. 

In a recent report by two of the members of the staff ' there are 
histories of forty-two cases and illustrations of the methods of 
treatment ; but the noteworthy feature of the report is the prominence 
given to residence at .the seashore as the chief means of cure. The 
conclusions from seventy-six histories which form a basis of the re- 
port are as follows : 

(i) The seashore is the best place for treating children with tuberculous 
adenitis. The children make a better recovery here than elsewhere. Those 
with adenoids and enlarged tonsils should be submitted to an operation as a 
start of the cure. Sea air does not permit us to dispense with this. 

(2) The seashore is probably the best place for children with tuberculous 
joints, provided they can have there the same skilled orthopedic care as else- 
where. Their disease runs a somewhat milder and probably a shorter course, 
and the functional results are better than those obtained elsewhere. 

(3) Our results have been largely due to the careful attention (including 
feeding and nursing) which has been given the children. 

(4) Our results justify pushing the work. 

(5) A hospital such as this does better work than a public hospital under 
control of the municipality. 

(6) Many cases of co-called bone tuberculosis are in reality syphilis. 
We do not know whether there is anything " specific " about the seashore. 



'Leonard W. Ely and B. H. Whitbeck, Medical Record, March 7, 1908. 
See also Charlton Wallace, Medical Record, July 22, 1905; John Winters 
Brannan, Trans. American Climatological Association, 1905, P- 107; John 
Winters Brannan, Trans. National Association for the Study and Preven- 
tion of Tuberculosis, 1906. Roland Hammond: Heliotherapy as an Adjunct 
in the Treatment of Bone Disease, Amer. Journ. Orthopedic Surgery, May 
and October, 1913. 



46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

or whether children simply thrive better and so overcome more quickly their 
disease.^ 

As to treatment other than diet and fresh air, little need be said. We use 
plaster when we can in preference to braces. In Pott's disease we use first 
the Bradford frame, then plaster jackets; in hip joints, the short Lorenz 
spica. In knee-joint disease after the acute stages, we also use plaster-of- 
Paris. Patients with large cold abscesses are transferred to the Manhattan 
hospitals, where their abscesses are opened, wiped out, and sewn up again 
with proper asceptic precautions. 

On January 2ist of the present year, 1914, the author revisited 
Sea Breeze Hospital, Coney Island, New York, in order to see what 
is being- accomplished. Six cases of hip disease were being treated 
by partial exposure of the body to the sun. The patients were in 
bed on the balcony with the usual extension apparatus in place. 
General exposure, beginning with the feet and gradually involving 
the entire body, is not adopted at Sea Breeze, as a rule, and only the 
area of abdomen, hip and thigh adjacent to the diseased joint was 
exposed' to the air and sun. Continued cloudy and unfavorable 
weather had prevented much progress in the newer patients who 
were then undergoing treatment ; others who had been cured of 
serious tuberculous disease by the open-air method had recently been 
discharged. The fresh-air system is, however, well carried out, but 
not upon the naked body as in Switzerland and France. 

The temperature on the open balcony next to the wooden wall of 
the building was 62° F. at noon in the sun. It was the first bright 
day after weeks of storm and cloud. It is probable that the very 
encouraging experience of the last two years will lead to the adoption 
of Rollier's method in all its details as modified by the less favorable 
climatic conditions of this part of the Atlantic seaboard." 

Results at Sea Breeze Hospital in the treatment of tuberculosis of 
the bones, joints and glands have been so good that the city of New 
York has acquired a new location with 1,000 feet of beach front on 
what is known as Rockaway Point, ten miles beyond Coney Island. 
The plot runs back about 600 feet to Jamaica Bay and cost the city, 
after condemnation proceedings, $1,250,000. The plans include an 
arrangement of grounds and buildings which will involve a total 

^Charlton Wallace, M. D. : Surgical Tuberculosis and Its Treatment (Jour- 
nal of the Outdoor Life, March, 1913)- This author, who is Orthopedic 
Surgeon to St. Charles' Hospital. Long Island, and the East Side Free 
School for Crippled Children, New York, says: The author is not in a 
position to produce scientific proof that sea air is better than country air, 
but he does believe such to be the case, although there are some individual 
patients who do better in the country than at the seashore. 

" Heliotherapy is used at the Crawford Allen Hospital, Rhode Island. 



NO. I AIR AND TUBERCULOSIS HINSDALE 47 

outlay of $2,500,000 and there will be accoinmodation for i,ooo 
patients in the eight pavilions. Contracts for two of these pavilions 
have been let and will l)e paid for by a fund raised by the New York 
Association for Improving the Condition of the Poor. The new 
hospital will be turned over to the city of New York and will be con- 
ducted by Bellevue and Allied Hospitals. The plans include an 
immense playground running back to Jamaica Bay for the use of the 
public. 

Credit is due to Dr. John Winters Brannan, of New York, presi- 
dent of Bellevue and Allied Hospitals, for much of the great work 
which has so far taken about nine years to accomplish and for which 
America will be justly proud. 

Encouraged by the success at Sea Breeze, another hospital for 
surgical tuberculosis in children was started six years ago at Port 
Jefferson, on the north shore of Long Island, opposite the Sound. 
The situation is said to be ideal. It accommodates two hundred 
children and is a handsome fireproof structure. It is called St. 
Charles' Hospital ; it is under the active care of the " Daughters 
of Wisdom," a Roman Catholic Society. The children, according 
to Dr. Wallace, receive every physical, mental, spiritual and indus- 
trial care necessary to produce good moral men and women. It is 
an active orthopedic hospital admitting any deserving case and 
keeping him there until the lesions are healed. Patients in advanced 
stages of bone tuberculosis are received as well as those with pul- 
monary complication. Under the good hygienic surroundings at 
St. Charles' Hospital, the children have shown great improvement 
in every way. Dr. Wallace adds : " The removal of the diseased bone 
with the knife is no longer attempted, because such a procedure not 
only takes away the root from which the bone grows, but also fails 
to eradicate the aft'ected area. Reliance must therefore be placed 
on other than cutting methods for local treatment of the affected 
parts." Immobilization by plaster-of-Paris, properly applied and 
fresh air on the shore of Long Island Sound, conjoined with every 
other hygienic aid possible, constitute the line of treatment. 

The New York Hospital for Ruptured and Crippled has lately 
removed to a new site on a hill near the East River, where the 
outdoor treatment for the tuberculous cripple is carried out as well 
as it can be in a large city. 

In England it has long been customary to send scrofulous children 
and those with surgical tuberculosis to the eastern and southeast 
coast. At Margate the Royal Sea-Bathing Hospital, founded by 



48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Lettsom and Latham in 1791, is the oldest institution of the kind in 
Great Britain, and retains its pre-eminence. There are similar insti- 
tutions at Brighton, Bournemouth, Folkestone, and Ventnor, Isle of 
Wight (see plate 12). 

The impression prevails at present in England that sea air is the 
best for these cases. The bracing air suits them perfectly and 
children with tuberculous bones, joints, or glands can stand a 
much colder and fresher air than children with pulmonary disease. 
Sea air improves the general health and keeps nutrition at the 
highest level. Italy and France, however, take the lead in seashore 
sanatoria exclusively devoted to tuberculous children. They have 
been in existence on the Italian shore at Viareggio since 1856, and 
on the French coast since i860, and are conducted on a very exten- 
sive and systematic scale. The first sanatorium at Berck-sur-Mer 
was established in i860 by the city of Paris, and is almost exclusively 
for children suffering from tuberculous disease of the joints, bones 
and glands, and has at present considerably over one thousand beds 
and accommodates children from the poorest quarters of Paris.^ 

Two private hospitals for similar cases are located at Berck- 
Plage. One was founded by Baron Rothschild and is maintained 
by his widow and contains 600 beds. Four-fifths of the cases are 
surgical ; one-fifth, medical.^ The other is in Cazin Perrochaud and 
accommodates 200. At Pol-sur-Mer there is a similar institution 
maintained by the city of Lille, which is designed to have 900 
beds.* At Cannes there is an excellent private institution, the Villa 
Santa Maria, for the " cure helio-marine des tuberculoses chirurgi- 
cales " under the direction of D. A. Pascal. 

Besides these institutions for surgical tuberculosis there are others 
which are intended mainly for pulmonary tuberculosis. These are 
located at Hendaye, Ormesson, Villiers-sur-Marne and Noisy le 
Grand. There are now fifteen sanatoria on the French coast open 
throughout the year and, in addition, a number open for only a 
part of the year, containing in all over four thousand beds. In 1904 
there were twenty-three Italian hospitals distributed along the Medi- 
terranean and Adriatic shores of Italy, with over ten thousand beds. 



* See article by the author on " The Treatment of Surgical Tuberculosis," 
etc. Interstate Medical Journal, St. Louis, March, 1914. 

* See article by Douglas C. McMurtrie, Boston Medical and Surgical Jour- 
nal, Jan. 2, 1913. 

* See article by John W. Brannan, loc. cit. 





1 ' 






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1 |K^*^yP^'V 




^^■B^'S^I eft^lB^Blit t 







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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 13 





iS ^ 



WEST GALLERIES, MARITIME HOSPITAL FOR TUBERCULOSIS, BERCK-PLAGE, FRANCE. 300 BEDS 




SOUTH GALLERIES, MARITIME HOSPITAL FOR TUBERCULOSIS, BERCK-PLAGE, FRANCE. 216 BEDS 



NO. 1 AIR AND TUBERCULOSIS — HINSDALE 49 

These hospitals are said to be closed in winter. (Brannan.) Every 
other country in Europe, with the exception of Turkey and Greece, 
has one or more seashore sanatoria for tuberculous children, so that 
there are as many as seventy-five such hospitals on the shores of 
Europe. The Argentine Republic has two seashore sanatoria, one 
established twenty-three years ago with three hundred beds and a 
new one with five hundred beds. 

The plan of treatment at all these institutions is very simple and 
ought to have been carried out on this side of the Atlantic long ago. 
The brilliant experience at Sea Breeze, Coney Island, is simply due 
to a repetition of the methods adopted for decades in France and 
England. The regime at all these sanatoria is about the same. The 
patients are kept out of doors all day on the beach or on verandas, 
which are covered but are open on the front and sides. Four meals 
a day with unlimited milk are provided. All through the winter 
the children occupy themselves on the grounds or on the beach ; those 
confined to bed are on the open porches enjoying the sunshine and 
the sea air, the best tonics in the world, and developing a ruddy 
color and better general circulation than they have ever known. 
Their warm hands in the coldest winter weather is the wonder of 
all who visit them. At night the windows are wide open and the air 
has practically the same temperature as at any point on the coast, 
varying from 12° to 40° F. If the snow drifts in at night, as some- 
times happens, nobody seems to be the worse. The windows are, 
however, closed for a half hour morning and evening while the chil- 
dren are being washed and dressed. 

The surgeons at Berck-Plage, although engaged in active ortho- 
pedic work, are all firmly convinced that residence at the seashore, 
with the greater part of the twenty-four hours spent in the open air, 
does more for the children than could be accomplished even in the 
best appointed hospitals in the cities.' One of the surgeons at Mar- 
gate, after fifteen years of constant work in the wards, states his 
opinion that the knife plays a very secondary part to climatic and 
general influences. 

For an institution of this kind to attain the highest efficiency one 
thing seems plain ; the patients must be admitted at a very early age, 
not from six years old and upwards, but as early as two years of 
age. In this respect the French and American sanatoria have the 
advantage of the English. The point has been made that at six years 



* Each year during the early part of August vacation clinics are held, which 
are attended by large numbers of French and foreign physicians. 



50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

of age a child with tuberculous disease is often past cure. Aluch 
can be done with a tuberculosis case if " caught young." 

After serious operations, the surgeons at the seaside sanatoria note 
that progress is much more rapid when patients can live in the open 
air and the practical point has been discovered that subsequent dress- 
ings of a much more simple character are permissible under the open 
air regime. For instance, m Metropolitan hospitals the practice of 
packing and draining wounds has untold terrors for the unfortunate 
patients. Dr. Charlton Wallace found that at " Sea Breeze " tuber- 
culous sinuses heal more rapidly and permanently when all packing 
and drainage are omitted and only a sterile absorbent dressing is 
applied. As the general instability of these patients is- such as to 
cause them almost to collapse at the thought of having their wounds 
probed and packed, it led him to believe that they would gain 
strength and local resistance if they were not nervously upset at the 
time of each dressing. In the beginning, in order to ascertain 
whether there would be full drainage, comparisons were made of 
the amount of discharge, with and without the full dressing, and as 
there was no diminution he concluded that packing or tubing was not 
essential to drainage. Not only was the danger of infection less, 
no infected wound being observed, but he found that no sinus healed 
which still contained pus. This certainly simplifies the treatment of 
surgical wounds and the credit is given to the favorable atmospheric 
conditions. 

At Sea Breeze the children receive from one to two hours instruc- 
tion daily, the teachers being furnished by the Brooklyn Board of 
Education. It has been noted that the educational training given at 
this Sea Breeze Hospital has a most happy effect on the morals of 
the patients and at this early age much more can be accomplished 
in combating vice and ignorance, which constitute the greatest ob- 
stacles in dealing with the tuberculosis problem. 

(For open air schools for tuberculosjs children, Waldschule, etc., 
see pp. 103-107). 

In estimating the value of sea air in non-pulmonary tuberculosis 
in children, we naturally look to France for some data based on the 
enormous experience now extending over a period of nearly fifty 
years. During the last twenty years in France alone 60,000 children 
have been treated in these sanatoria and Dr. Brannan is authority for 
the following statement : 

Cures, 59 per cent. Decidedly improved.. 25 per cent 

Total of favorable results 84 per cent 

Cures in Pott's Disease 32 per cent 

Cures in glandular tuberculosis 74 per cent 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 14 




HELIOTHERAPY VIEW OF THE SOUTH GALLERIES OF THE MARINE HOSPITAL BERCK-PLAGE, 
HELIOTHERAPY^^^l^^ THE CHILDREN ARE EXPOSED ALL DAY NAKED TO THE SUN 




SEA BREEZE HOSPITAL, SEA GATE, NEW YORK. OPEN AIR SCHOOL 
Courtesy of Dr. J. W. Brannan 



SMITHSONIAN MISCtLLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 15 




HELIOTHERAPY. SEA BREEZE HOSPITAL, SEA GATE, NEW YORK, 

MARCH 18, 1913. CURED CASE OF TUBERCULOSIS OF THE KNEE. NO 

SINUS. 

Courtesy of Dr. Brannan 




, ^ 



HELIOTHERAPY AT SEA BREEZE HOSPITAL, SEA GATE, NEW YORK, OCTOBER, 1912. CHILDREN 
ON THE BEACH. CURED CASES OF TUBERCULOSIS OF THE WRIST AND ANKLE. THERE WERE 
OPEN SINUSES IN EACH CASE. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 5 I 

These results of the treatment of surgical tuberculosis at seashore 
sanatoria are much more favorable than in the case of pulmonary 
tuberculosis, in adults, in corresponding localities (see pp. 71-73). 

Nevertheless, the Department of Public Charities of the City of 
New York has just built and equipped at an expense of $3,500,000, 
a new hospital for adults having- pulmonary tuberculosis in the sec- 
ond or third stage. The site selected is on the highest point of Staten 
Island in New York Bay, 400 feet above tide and only five miles from 



^ See R. Russell, M. D. : Glandular Tabes, or the Use of Sea Water in 
Diseases of the Glands. London, 1750. 

Ehenezer Gilchrist, M. D. : The Use of Sea Voyages in Medicine. Lon- 
don, 177L 

Albert L. Gihon, M. D., U. S. N. : The Therapy of Ocean Climate (Trans. 
Amer. Climat. Ass., 1889, p. 50). 

M. Charteris, M. D. : Ocean Climate (Trans. Amer. Climat. Ass., 1890, p. 
278). 

Wm. Ewart, M. D., F. R. C. P. : The Present Position of the Treatment 
of Tuberculosis by Marine Climates (Journ. Balneology and Climatology, 
July, 1907). 

W. S. Wilson: The Ocean as a Health Resort, London, 1880. 

J. V. Shoemaker, M. D. : Ocean Travel for Health and Disease (The Lancet, 
July 23, 30, 1892). 

Hughes Bennett, M. D. : Life at Sea Medically Considered (Medical Times 
and Gazette, Vol. i, 1884, p. 244). 

Thomas B. Peacock, M. D. : Beneficial Influence of Sea Voyages in Some 
Forms of Disease (Medical Times and Gazette. Vol. 2, 1873, p. 687). 

John L. Adams : Report of 17 cases of Surgical Tuberculosis in Children 
(Boston Medical and Surgical Journal, 1906, Vol. 154, p. 17). 

A. Crosbee Dixey, M. R. C. P. : Edinb. Lancet, Vol. 2, 1888, p. 264. 

Boardman Reed : Effects of Sea Air Upon Diseases of the Respiratory 
Organs (Trans. Amer. Climat. Ass., Vol. t, 1884, p. 51). 

D'Espine, of Geneva. International Congress on Tuberculosis, Paris, Octo- 
ber, 1905. 

Armaingaud, of Bordeaux : International Congress on Tuberculosis, Paris, 
1905. 

Guy Hinsdale, M. D. : Treatment of Surgical Tuberculosis at the French 
Marine Hospitals and Alpine Sanatoria (Interstate Medical Journal, St. Louis, 
March, 1914). 

Trans. Congres de L' Association Internationale de Thalassotherapie, 
Cannes, April, 1914. 

See also Willy Meyer: Open-Air and Hyperdermic Treatment as Pow- 
erful Aids in the Management of Complicated Surgical Tuberculosis in 
Adults (Trans. Sixth International Congress on Tuberculosis, Washington, 
1908, Vol. 2, twenty illustrations). 

See also " Open Air Treatment of Tuberculosis," by the late Dr. DeForest 
Willard, ibid., page 257. Also Trans. Amer. Orthopedic Ass.. 1898. Shacks, 
bungalows, sleeping tents, sanatoria and day camps are discusssd. 



52: SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

the ocean. This new addition to New York's equipment has one 
thousand beds and is called the " Sea View Hospital." 

At the Second Annual Meeting of the National Association for the 
Study and Prevention of Tuberculosis held in Washington in 1906, 
the following resolution was offered by Dr. John W. Brannan and 
unanimously adopted : 

Whereas, Recent experience in Europe and in this country has shown that 
out-door Hfe in pure air has the same curative effect in surgical tuberculosis 
as in tuberculosis of the lungs, therefore, be it 

Resolved, That in the opinion of members of this Association hospitals 
and sanatoria should be established outside of cities either in the country or 
on the seashore for the treatment from its incipiency, of tuberculosis of 
bones, joints, and glands in children. 

SEACOAST AND FOGS 

Marine climates naturally include the strictly ocean climate and 
that of the seacoast. In the former sea air comes from every point 
of the compass. It is always moist and it is the most equable air that 
blows ; it is of infinite variety from the dead calm of the doldrums to 
the fierce gales of the North Atlantic. 

The atmosphere of the seacoast is naturally modified at times by 
continental influences. Indeed the characteristic " sea breeze " which 
springs up in the morning and subsides toward sun-down is brought 
about by the ascent of heated air back of the_ coast. The hotter the 
interior and the more rapidly this air ascends the stronger is the 
sea breeze which rushes shoreward from the ocean and penetrates 
for fifty or a hundred miles the adjoining country. 

But under other conditions land breezes occur and bring to the 
shore the Continental atmosphere of a totally different type. These 
atmospheric conflicts between sea and land involve most interesting 
meteorological problems ; they tend to lessen the equability of the 
purely marine or oceanic climate. Freezing weather is the product 
of the Continent and the descent of cold waves from the interior ; 
it brings to our northern seacoast frost and snow for a time, and 
never trespassing far upon the high seas. The seacoast has thus a 
mixture of two climates, but the sea air predominates and is never 
absent very long. 

There are well-known places in America and in the British Islands 
where the sea breeze greatly predominates ; Nova Scotia, Cape Cod, 
and Cape May in the United States ; Land's End and the Cornish 
Coast in England are cases in point. In such exposed situations the 
air is generally poorly adapted to the tuberculous patient. The air 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 16 




SEA BREEZE HOSPITAL, SEAGATE, NEW YORK. TREATMENT OF POTT'S DISEASE OF THE SPINE 

WITH PLASTER JACKETS AND HELIOTHERAPY 

Courtesy of Dr. J. W. Brannan 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 17 




FIG 1. HELIOTHERAPY FOR SURGICAL TUBERCULOSIS. DR. ROLLIER'S SANATORIUM, 
LEYSIN, SWITZERLAND. DORSAL EXPOSURE 




FIG 2. HELIOTHERAPY FOR SURGICAL TUBERCULOSIS. DR. ROLLIER'S SANATORIUM. 
From the author's article in Interstate Medical Journal, March, 1914 



NO. I AIR AND TUBERCULOSIS HINSDALE 53 

is said to be " too strong " and certainly for an all-the-year-round resi- 
dence the capes and headlands are too much at the mercy of high 
winds which render out-door life disagreeable. About Cape Cod, 
Nantucket, and Martha's Vineyard there is a peculiar liability to fog 
which is as unwelcome to the consumptive as it is to the mariner. 

The author has had experience with the fogs in these waters and 
considers it one of the great drawbacks to an otherwise agreeable 
climate. The summer and early autumn fogs of the eastern Maine 
coast and of the Bay of Fundy and Nova Scotia are worse in their 
chilly and penetrating qualities. The towns of Massachusetts on or 
near the seacoast seem to have somewhat more tuberculosis than 
those of the interior. 

Deaths from Pulmonary Tuberculosis in Massachusetts per 100,000 

Population 

Five Maritime Towns Five Inland Towns 

1903 1908-1912 1905 1908-1912 

Boston 224 155 Pittsfield 168 98 

Salem 154 iii Springfield 125 89 

New Bedford 164 124 Cliicopee 125 109 

Newburyport 181 131 Holyoke 154 I3I 

Plymouth 162 90 North Adams 81 98 

Average 177 122 Average 131 105 

Mr. Hiram F. Mills, of the Massachusetts State Board of Health, 
has lately published a most painstaking analysis of the mortality 
from tuberculosis in all the towns and cities of that state.^ 

He shows that there are sixty cities and towns bordering on the 
sea having a total population of about one-third of the entire state, 
or 1,293,625, in which the average death-rate per 100,000 for the five 
years, 1908-1912, was 135. During this period the rate for the entire 
state was 131. Omitting Boston, which has peculiar conditions, 
from both calculations the rate was 11 1 for the remaining 59 mari- 
time towns and cities against 124 for the remainder of the State. 
This throws the balance in favor of the seaboard. It should be 
noted that all the small and sparsely settled towns have low rates 
in almost regular gradation when compared with more and more 
populated districts. 

Boston has had a noteworthy decrease in its tuberculosis death 
rate as shown by the following figures representing the rate for the 
last five years, namely, 271, 283, 254, 176, 182, or a decrease of one- 
third in five years. There are sixteen small towns having an aggre- 



^ Address to the State Inspectors of Massachusetts, November 3, 1913. 
6 



54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

gate population of 5,540, in which there have been no deaths in all 
of the five years. 

The map shows several inland towns with a large death rate ow- 
ing to the presence of tuberculosis hospitals, asylums, and other insti- 
tutions. These are marked with an H (not readily seen in the 
reduced map) and include Rutland, Sharon, Lakeville, Bridgewater, 
North Reading, Medfield, Westborough, Westfield, Taunton, Dan- 
vers, and Monson. 

As Mr. Mills says : 

Forty years ago the death rate from consumption in Massachusetts was three 
times as great as it is now ; thirteen years ago it had been reduced one-half in 
the previous forty years ; to-day it has been reduced one-half in the past twenty 
years. There is no other State in the Union, in which records have been 
kept, where the reduction has been so much. From 1885 to 1909 it was more 
than twice as great as in England, Scotland, Ireland, The Netherlands, Bel- 
gium, Switzerland and Italy. The reduction is Prussia was 90 per cent of 
that in Massachusetts and that in Austria only 57 per cent. The registration 
system in Massachusetts is of the highest grade and in no other State or 
country of the world has such effective work been done and so much accom- 
plished in reducing the death rate from tuberculosis as in that Commonwealth. 

FOGS ON THE PACIFIC COAST 

It is this element of fog which renders so much of the Pacific 
coast of the United States unsuitable for tuberculous patients. The 
morning fogs are conspicuous features of the climate and are 
acknowledged sources of danger to tuberculous cases. They pene- 
trate as far as Los Angeles and Pasadena in the south, some eighteen 
miles from the coast ; they are common in San Francisco, and are 
carried by ocean atmospheric currents through the Golden Gate, 
sweeping the bay and up the Sacramento and San Joaquin valleys. 

There are portions of the California coast, as for example in the 
neighborhood of Santa Barbara, where the mountains are near the 
shore ; and beyond the mountains are deserts and necessarily an 
exceedingly dry atmosphere. The night air from the mountains 
brings with it a dry Continental quality ; the morning breezes bring 
a more humid air and possibly fog. In such localities fog is quickly 
scattered by the sun's heat and never penetrates very far inland. A 
suitable residence for tuberculous patients on the Pacific coast, as 
every native knows, is not found on the shore line but at some eleva- 
tion above the sea fairly well up on the hillsides or in well-situated 
valleys, like the Montecito Valley, where the dryer air of the interior 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 




STATE BOARD OF HEL\LTH 

MAP OF THE 

STATE OF MASSACHUSETTS. 

DEATHS FROM CONSUMPTION 



SCALE or MlUtS 
o X A e a 10 r& •« ift ta to at. fc < »e aa » 3t u jsm jm *k *a 4C 4« * 

k^l_.t-.l-.L^L.L-.L-iL.l-l-.U.UUI-.L-.l-. b r- U Ut-.UUI-. liut 



VOL. 63, NO. 1, PL. 




■^f^sftaHf.- 



NO. I AIR AND TUBERCULOSIS — HINSDALE 55 

checks the advent of fog- and where the early morning hours are as 
bright and dry as the afternoons/ 

RADIATION FOGS 

Fogs are born of the sea and of the land. The sea fog is obviously 
purer and less injurious than the smoke-laden fog of cities. There 
are fogs and fogs ; " dry " fogs and " wet " fogs ; the fogs of the 
coast and the fogs of mountain valleys and river courses ; but rarely 
of the plains. Radiation fogs are different from sea fogs ; in dry 
weather, on a cold still night when the lowest stratum of air is rap- 
idly cooled by contact with the cold radiating earth, the watery vapor 
is precipitated as minute globules. The colder the ground or the 
deeper and colder the water on which fog rests, the more persist- 
ent is the fog ; but as the sun warms the watery particles and over- 
comes the heat lost by radiation, the fog lifts and floats upward. It 
is bound to lift as its specific gravity diminishes. Slopes of hills, 
especially their southern sides, some hundreds of feet above the low- 
land or seashore, are thus comparatively free from these fogs and 
are much drier and warmer than lower places in the neighborhood. 
Such locations are far preferable to those of lower altitude. (Rus- 
sell.) 

FOGS IN THE MOUNTAINS 

And here we see how local geographic conditions modify the 
whole aspect of the question. On the North Atlantic Coast of the 
United States there are no mountain ranges ; one cannot get away 
from the fogs if he would ; while on the Pacific Coast, the mountains 
and their foot hills are comparatively near and one can be in full 
view of the seashore and yet be above the fog line. 

At Santa Barbara, one of the favorite California resorts for tuber- 
culous patients, fogs occur frequently from May until October, but 
are comparatively rare at other times. Dr. William H. Flint, who 
practiced there for thirteen years, says that the fogs creep in from 
the sea in the late afternoon, in the evening, or in the early morn- 
ing, disappearing at an uncertain hour the following forenoon. Occa- 
sionally fogs will persist all day and for a number of days consecu- 
tively. In May and June, 1903, a foggy period continued for 
seventeen days.* 



^ See A. G. McAdie : The Sun as a Fog Producer, Monthly Weather 
Review, Washington, 1913 (778-779). 
* Trans. Amer. Climat. Ass., 1904, P- 20. 



56 ' SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 63 

The late Dr. C. H. Alden, Asst. Surgeon General, U. S. A., who 
passed his later years, and died of tuberculosis, in Pasadena, Cali- 
fornia, says : 

The climate of Southern California is not a dry one, as some suppose. As this 
region lies along the coast, and its most frequented portions are nowhere very- 
distant from the water, the climate cannot be dry. The humidity lessens as one 
goes inland, but is always considerable, except in the uninhabited desert. The 
fogs which, in the absence of much rain, are a large factor in sustaining 
vegetation, penetrate many miles from the sea and add to the humidity. 
The fact that the hitmidity is not favorable for pulmonary tuberculosis 
which is at all advanced is evidently not appreciated as it should be. 
[Italics, author's.] 

Even as far as Redlands, over fifty miles from the coast, according 
to General Alden, who lived there for two winters, " fogs come up 
from the sea during the spring, but they are shorn of most of their 
moisture." Nevertheless, Redlands, from its comparative dryness, 
is a favorite place in winter for patients with pulmonary tuberculosis 
and they no doubt do better there than at Los Angeles, Pasadena, or 
at resorts directly on the coast. General Alden's conclusion is that 
while the mild temperatures and continuous sunshine of this region 
are favorable for the aged and the feeble from many causes, need- 
ing an out-door life, the warmth and moisture are unfavorable for 
cases of pulmonary tuberculosis that are at all advanced. 

In June, 1902, the author traveled through the mountains and vis- 
ited the principal resorts throughout California. The sea air with its 
frequent accompaniment of fog seemed to him too strong or fresh 
for tuberculous patients. North of Santa Barbara or Monterey the 
sea air is certainly cold and harsh during most of the year and, 
wherever it penetrates, tuberculous patients feel worse. This is par- 
ticularly true of the neighborhood of San Francisco. From the 
summit of Mt. Tamalpais, elevation 2,375 ^^et, on almost any sum- 
mer afternoon fog can be seen driving in from the Pacific and 
spreading over San Francisco Bay. As the sun descends the tem- 
perature of the air drops, so that saturation is reached. Fog results. 
Now on the southern California coast the cold, ocean atmospheric 
currents contain much less actual moisture than the warm, clear air 
on shore and the resultant mixture will now contain less water than 
the warm air did before and hence it is claimed with reason that 
notwithstanding the dripping roofs and wet pavements, there is less 
absolute moisture in the air than before the fog appeared. 

We did not find the California fog either so cold or chilling as we 
have observed it on the extreme eastern coast of Maine ; nor is it so 




U5 5 



NO. I AIR AND TUBERCULOSIS HINSDALE 57 

depressing and relaxing as the heavy misty weather observed in 
central and western Virginia mountain valleys during the rains of 
early summer and autumn, certainly not so depressing as the relax- 
ing moisture of the tropics. The California fogs have been likened 
to the Scotch mist. They never deter the fishermen from curing 
their fish on their racks along the seashore. Raisins and other fruit 
are dried in the open fields and residents claim that during the 
rainiest weather nothing molds or rots. (P. C Remondino.) 

Mr. Ford A. Carpenter, of the U. S. Weather Bureau, has published 
an interesting book, in which he gives a lucid description of the fogs 
of the Pacific Coast.* He shows that on that coast the maximum 
fog is reached in San Francisco, with moderately high averages 
north to the Canadian boundary and decreasing in frequency and 
duration with the latitude, San Diego having the least on the coast. 
He says that daylight fogs are practically unknown in San Diego. 
A " day with fog " is one on which there is one hour or more of 
fog dense enough to obscure objects one thousand feet distant. At 
San Diego the hours of greatest frequency were between eleven at 
night and six in the morning. Mr. Carpenter notes the beneficial 
effect of California fogs and says that it is impossible to measure 
accurately the amount of moisture conveyed by fog. There is no 
doubt that over a region covered by vegetation exposing a natural 
condensing surface, such as eucalyptus, palm, iceplant, etc., not less 
than a ton of water to the acre is thus distributed during the preva- 
lence of every dense fog. It also checks evaporation. 

" It is not fog in the generally accepted meaning, for this ' light 
veil ' is neither cold nor excessively moisture-laden. Neither is it 
high, for its altitude is less than a thousand feet. To one who has 
spent a few weeks of spring, summer or fall in southern California, 
the picturesque description of the musical Spanish el veto is quickly 
recognized as both expressive and truthful." " El velo de la lus " : 
" the veil that hides the light." " Velo qui cubre la lus del so " : 
"The veil which shades (covers) the light of the Sun." "El velo 
de la manana " : " The veil of the morning." 

There is probably no place on the entire coast line of the United 
States that offers so many climatic advantages for tuberculous 
patient as San Diego and its attractive neighbor, Coronado. 

It is a mistake to believe that because there is fog, the humidity 
is necessarily high during its presence. The United States Weather 



^ The climate and weather of San Diego, California. San Diego, 1913. See 
Review in Journ. Royal Meteorological Society, Jan., 1914. 



58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Bureau has taken pains to determine the relative humidity during 
fogs observed during ten years at Chicago on Lake Michigan. Ob- 
servations were made on ii8 foggy days by Dr. Frankenfield, whose 
results are given as follows : 

Relative humidity 90 per cent (or more) in 75 per cent of days. 
Relative humidity 80 to 90 per cent in 13 per cent of days. 
Relative humidity below 80 per cent in 12 per cent of days. 

The observer noted dense fog on one occasion when the relative 
humidity was as low as 52 per cent ; on another, when it was 58 per 
cent. 

The Pacific coast, as a whole, is much foggier than the Atlantic 
coast, because the winds on the Atlantic are mostly off-shore and 
consequently carry less moisture than the westerly on-shore winds of 
the Pacific. 

In the interior of the United States, especially the western half, 
the average number of foggy days per year is less than ten each 
year; in the Lake region the number rises to fifteen or twenty per 
annum. In isolated localities, local conditions increase this number 
greatly. 

At Colorado Springs genuine fogs occur, sometimes very dense 
and lasting all day, but they are uncommon and scarcely worth 
mentioning were not their existence so often denied. (Ely.) 

In the Adirondack Mountains fogs and mists are not uncommon 
along the rivers and on the lake shores in the early morning in the 
summer and autumn. They are examples of the radiation fogs 
already referred to and, like dew and frost, they are associated with 
clear weather. The presence of a light fog over an Adirondack lake 
in the early morning foretells a bright, sunny, warm day. 

Fogs are not at all unusual in the Alleghany and Blue Ridge 
Mountains. They follow river courses and settle in low valleys. 
The humidity attendant on the melting of snow or during the rains 
of early summer or autumn is not so readily exchanged for dryer 
air in the long narrow valleys as at the seaboard. In many localities 
the high ridges on either side shut out the direct rays of sunlight 
for several hours ; while at the seaboard there are no such natural 
barriers. 

At some of the higher elevations in the Blue Ridge Mountains 
of Pennsylvania, fog is noted during the summer and autumn. One 
observer, himself a tuberculous patient, recorded at Mount Pocono, 
in Monroe County, Pa., elevation 2,000 feet, fifteen days with fog 
part of the day, usually early morning, and seven with fog all day, 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63. NO. 1, PL. 23 




FIG 1. RUTLAND, MASSACHUSETTS STATE HOSPITAL FOR CONSUMPTIVES 




DAY CAMP FOR TUBERCULOUS PATIENTS, HOLYOKE, MASS. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 59 

between June i and December i. But this patient adds the signih- 
cant remark : " However, it seems ridiculous for me to find fault 
with Mount Pocono when I did so well there. My cough and expec- 
toration decreased considerably ; I gained five pounds and grew 
somewhat stronger."* 

At Rutland, Massachusetts, the site of the Massachusetts State 
Sanatorium, there were 24 days with fog for the year ending Novem- 
ber 30, 1907. Nevertheless, out of 4,334 cases of pulmonary tubercu- 
losis treated since its opening, 43.39 per cent of cases were arrested 
or apparently cured, and in addition, 47.38 per cent were improved." 

From what has been said, it is, therefore, not surprising that 
claims are made that there is a noticeable difiference in the character 
of fogs on the New England Coast.* Dr. Bowditch has described 
the fogs on the Maine Coast as sometimes " dry fogs." " The light 
vapory mist which drives in frequently from the sea has no definite 
sense of moisture as it strikes the face, and in the midst of it the air 
frequently feels dry. In the vicinity of Mount Desert, the presence 
of the mountains has, doubtless, an effect upon the quality of 
the atmosphere, and would partly account for what is often spoken 
of — the effect of sea and mountain air combined. Its peculiar dry- 
ness, even though on the coast, has been often so marked that I 
have frequently thought that certain phthisical patients, who need 
a dry bracing atmosphere, might improve there, although I have 
never quite dared to recommend it for such cases." 

SEA AIR FOR SURGICAL TUBERCULOSIS 

Halsted, of Baltimore, however, has recorded a favorable result 
in a case of tuberculous glands of the neck, treated simply by an out- 
door life on the Maine coast. The patient was a young lady of 
seventeen, whose cervical glands were actively inflamed and softened, 
the overlying skin having rapidly reddened and thinned during a 
treatment of six hours a day out of doors at a seashore further 
south. No operation was done, but she was sent to the Maine 
coast and lived out-of-doors day and night for four months. At the 
end of this period no one could tell, from the appearances, which 
side had been affected, and Halsted remarked that, to surgeons whose 
daily bread not long ago was tuberculous glands of the neck, such a 



* Journal of the Outdoor Life, February, 1908, p. 15. 

^ Eleventh Annual Report, 1907. 

'Vincent Y. Bowditch, Trans. Amer. Climat. Ass., 1897, p. 25. 



6o SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

resolution foretells a revolution in treatment." That revolution is, 
fortunately, to-day un fait accompli. 

Some of the European sanatoria of the best grade are in situations 
not altogether free from fogs and mists. This is true of Falkenstein, 
elevation 1,378 feet (420 m.), w^hose atmosphere is a little misty 
and foggy. 

AIR OF INLAND SEAS AND LAKES 

The region of the Great Lakes lying between the United States 
and Canada has been studiously avoided in selecting a site for any 
of the large sanatoria for tuberculosis. It is a matter of common 
observation that nasal, pharyngeal, and bronchial catarrhs are exceed- 
ingly common in adjacent districts. The lake winds are damp and 
are partly frozen during several months in the year, giving to the 
surrounding country a harsh climate. 

The lower lake region is also the favorite track of storms or 
cyclonic atmospheric movements which sweep the lakes and the 
St. Lawrence valley on their way to the seaboard. As these areas 
of low atmospheric pressure advance they are attended by increas- 
ing cloudiness in front and are usually followed by colder air from 
the Northwest, the fall in temperature being sufficient at times to 
constitute a cold wave.^ 

The winter storms on the Great Lakes are quite as violent as any 
on the seacoast, and on Lake Superior and Lake Huron floating 
ice may be seen in May and sometimes, in Lake Superior, as late 
as June. Lakes Michigan, Erie and Ontario are more southerly, but 
their shores are low and the skies are notably cloudy. The author 
has experience of the cold fogs of Lake Superior in July and 
August, and was impressed with their penetrating quality. A sum- 
mer spent on both the northern and southern shores of Lake Supe- 
rior was wonderfully exhilarating ; the air has a purity and stimulus 
such as one might expect from millions of miles of forest round- 
about. But not a single place on that vast shore can be recommended 
as a residence for a tuberculous patient. The vicissitudes of the 
weather are such that the approved methods of cure could not well 
be carried out. 



'Trans. Nat'l Ass. for the Study and Prevention of Tuberculosis, 1906. 

^To constitute a cold wave, so called, there must be a fall of twenty degrees 
or more in twenty-four hours, free of diurnal range and extending over an 
area of at least 50,000 square miles, the temperature somewhere in the area 
going as low as 36° F. 




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NO. I AIR AND TUBERCULOSIS HINSDALE 6l 

In the location of the state sanatorium for tuberculous patients 
in Minnesota, an interior and northerly location was wisely chosen, 
150 miles south of Lake Superior, at Lake Pokegama, near the head- 
waters of the Mississippi. 

The Wisconsin State Sanatorium has been located on Lake Neba- 
gamon, thirty miles from Lake Superior. 

Such small lakes as Lake Pokegama in Minnesota ; the Muskoka 
Lakes in Ontario, where the Canadian National Sanitarium Associa- 
tion has established two sanatoria for consumptives ; and the Saranac 
Lakes in the Adirondack Mountains, have no such power to modify 
the qualities of the atmosphere. Whatever influences are attributa- 
ble to these smaller bodies of water are small, compared with that 
of the forest and mountains. Undoubtedly a small lake is a desir- 
able feature in connection with a sanatorium, as it provides sources 
of amusement throughout the year and adds greatly to the beauty of 
the landscape. The writer spent six summers at Lake Placid in the 
Adirondack Mountains at an elevation of 1,860 feet. This is some- 
what more protected than the Saranac Lakes, St. Regis Lake or 
Long Lake, and, in his opinion, is quite as well suited as a residence 
for tuberculous patients as any other locality in the Adirondacks. 
The State of New York has built its large State Sanatorium at 
Ray Brook only four miles distant from Lake Placid. The State of 
Rhode Island has chosen Wallum Lake for its new Sanatorium, 
views of which are here given.^ 

CHAPTER IV. INFLUENCE OF COMPRESSED AND RAREFIED 
AIR; HIGH AND LOW ATMOSPHERIC PRES- 
SURE; ALTITUDE 

No phase of the tuberculosis question has been so vigorously 
debated as the influence of altitude ; no feature of the subject is so 
far from satisfactory solution. The battles between the Highlanders 
and the Lowlanders of Scotland seem to have been revived in the 
attempts to settle this question. Instead of the claymore and battle- 
axe, we have an array of statistics in serried columns marshalled by 
the leaders of the opposing forces. This history of the conflict 
would make as large a record as the Medical and Surgical History 
of the War of the Rebellion. And the end is not yet in sight. 

After trying for years to cure consumption by means of an " equa- 
ble climate " obtained at home by housing the patient behind double 

^The large German Sanatorium Grabosee is located on the shores of 
Lake Grabow. 



62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

windows, or by sending him to the islands of the sea, such as 
Madeira and the West Indies, the medical profession began to be im- 
pressed with the good results reported from the Rocky Mountains 
and the plains of the Western states and territories. 

In the rush to the California gold fields in 1849 and in the rapid 
emigration from Eastern states to Colorado, Utah, California, over- 
land in the " prairie schooner " and on horseback during subsequent 
years, the Western country became known for wonderful health- 
giving qualities. It was not long before Colorado became widely 
heralded as a health resort for consumptives. English physicians 
sent their patients to Colorado instead of sending them to Australia, 
Algiers, or to the Riviera and the results obtained were remarkable. 
The late Dr. S. E. Solly, who practiced in Colorado for thirty-three 
years, was sent from London on account of the higher altitude and 
better air of Colorado, and was one of a large number of English 
residents who have made their home in that state on account of 
pulmonary tuberculosis. 

In 1876, the late Dr. Charles Theodore Williams, of London, 
published his report to the International Medical Congress and in 
1894 issued his work on Aero-Therapeutics, in which are detailed 
the histories of 202 consumptives who were sent to Colorado at an 
altitude of 5,000 or 6,000 feet. They represented a residence of 350 
years at this elevation and the results were exceedingly satisfactory. 

Jourdanet, a French physician practicing in Mexico, published two 
works, one in 1861 and one in 1875, which undertook to explain the 
influence of barometric pressure and, incidentally, why, on the plain 
of Anahuac, 6,000 feet in elevation, there is an entire absence of 
pulmonary phthisis.* 

Jourdanet aided the great French physiologist, Paul Bert, in estab- 
lishing costly apparatus for investigating the physiological action of 
compressed and rarefied air and Paul Bert's classic work is an 
accepted authority on this subject. Later studies by Mosso and 
Marcet ^ should be noted, but it is impossible here to give more than 
passing notice. They show that a diminution of the barometric 
pressure increases the respiration rate and the volume of air respired, 
but if allowances are made for the increase of volume of the air 
at the lower pressure, the actual volume respired is less. Conversely, 



* D. Jourdanet : Influence de la Pression de TAir, Paris, 1875. Herrera 
and Lope: La Vie Sur Hants Plateaux, Hodgkins Prize Memoir, 1898. 

"An American Text-Book of Physiology, Phila., 1901, Vol. i, p. 434- 
Angello Mosso: Man in the High Alps (Der Mensch auf den Hochalpen, 
Leipsig, 1899), Translation by E. L. Kiesow, 1898. 



NO. 



AIR AND TUBERCULOSIS HINSDALE 63 



an increase of pressure lowers the rate and the volume of air 
respired. The effects of the respiration of rarefied air and com- 
pressed air on the circulation and on the composition of the blood 
are very marked and are of a complex character owing to the addi- 
tional influences of the abnormal pressure on the peripheral circula- 
tion. Not only is the circulation affected but, in the case of residence 
at high altitudes, the proportion of red blood corpuscles and of hemo- 
globin is notably increased. This increase in the red blood count 
at the higher altitudes, while not so great or so permanent as was 
at first supposed, is an established clinical fact and adds undoubted 
strength to the claim that altitude per se is a characteristic of the 
favorable climate for tuberculous patients. 

DIMINISHED ATMOSPHERIC PRESSURE 

The influence of diminished atmospheric pressure on the blood has 
been studied by Paul Bert in 1882,' Zuntz,' P. Regnard,' Viault," 
Egger,' Woolff," Koeppe,' Solly,' by W. A. Campbell and Gardiner 
and Hoagland," by L. S. Peters'" and by F. Laquer." One of the 



' Paul Bert, loc. cit., studied the blood of animals at La Paz, in Mexico, 
at an altitude of 12,140 feet (3,700 meters) and found that they had an 
oxygen-carrying capacity far in excess of that exhibited by the animals on 
the lower plains. 

" Zuntz : Experiments on the Pic du Midi, Elevation 9,000 feet. He empha- 
sized the possibility of an altered distribution of corpuscles. 

^ Regnard, P. : La Cure d'Altitude, 2eime Ed. Paris, i8g8. 

*Viault: Experiments at Merococha, Peru, elevation 14,275 feet. 1890. He 
noted that his blood contained 7 to 8 million red corpuscles per cubic milli- 
meter. 

"Egger: The Blood Changes in High Mountains, Verhandlungcn d. xii, 
Congr. Inner. Med., 1893. 

° Woolff: Verhandlungen d. xii. Congr. Inner Med. 1893, pp. 262-276. 

' Koeppe, xii. Congress fiir Inner. Med., 1893 ; Arch. Anat. Physiol., 189S, 
pp. 154-184. 

*S. E. Solly: Blood Changes Induced by Altitude. Trans, .\merican 
Climatological Association, 1899, p. iz^; also 1900, p. 204. 
S. E. Solly, Therapeutic Gazette, February, 1896. 

" Campbell and Hoagland : Trans. American Climatological Association, 
1901, p. 107. 

" For the effect of altitude, 6,000 feet, on blood pressure in tuberculous 
patients, see article by L. S. Peters, Silver City, New Mexico, in Archives 
of Internal Medicine, August, 1908 and October, 1913. The latter report 
covers 600 cases and shows that altitude tends to raise blood pressure rather 
than lower it both in consumptives and in normal persons living at high 
altitudes. 

"F. Laquer: Hohenclima und Blutncubildung, Deutsches Archiv fiir klin. 
Med. Leipzig, 1913, ex, Nos. 3 and 4, p. 189. 



64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

most thorough original studies is by Drs. Ossian, Schaumann and 
Emil Rosenquist, of Helsingfors, Finland/ Turban, also, has made 
a study of this subject.* 

Much of the earlier work has been proved incosrect as instru- 
mental and laboratory technic has been improved. Hematologic 
work has made rapid strides and several important correcting factors 
have been introduced. Attention has been called to the more rapid 
evaporation of blood samples at high altitudes where the climate is 
always dry and errors from this source are considerable. 

Not only that, but the human organism itself loses water more 
readily than at lower levels and so do animals used for experimental 
purposes. How much value should be given to these corrections we 
do not know, but there is evidently a revision downwards noticeable 
in nearly all the later studies of the blood count at high altitudes. 
Prof. Biirker, of Tiibingen, and his colleagues show at best only a 
comparatively small increase amounting to only four to eleven and a 
half per cent at an altitude of six thousand feet.^ 

These observers made comparative observations at Tiibingen 
(altitude 1,030 feet or 314 meters), and at the Sanatorium Schatzalp 
(altitude 6,150 feet or 1,874 meters, about 300 meters above Davos). 

Barker's findings, which appear to result from an exceptionally careful 
personal investigation with every precaution to avoid experimental error, show 
that altitude does exert an unquestionable influence on the blood in the direc- 
tion of an increase in both the number of erythrocytes and the content of 
hemoglobin. The increase is an absolute one, not merely relative. The red 
cells increased from 4 to 11.5 per cent, the hemoglobin from 7 to 10 per 
cent. These figures, it will be noted, are smaller than those usually given 
for the effect of moderate altitudes, yet they represent substantial and unde- 
niable gains quite in harmony with other previous observations. 

The responses of the different persons in Biirker's Alpine expedition varied 
in degree; but the qualitative examination of the blood established the fact 
that no hemoglobin derivative other than oxyhemoglobin was concerned in 



' Ossian, Schaumann and Rosenquist : Ueber die Natur d. Blutverander- 
ungen in Hohen Klima, Zeitschr. f. klin. Med., 1898, Band xxxv, Heft 1-4, 
pp. 126-170 and 315-349. 

''Turban, Munch. Med. Wochenschr., 1899, p. 792. 

^ See Editorial Altitude and the Blood Corpuscles, Journ. Amer. Med. Ass., 
February 3, 1912, p. 344; September 21, 1912 and November i, 1913. 

Biirker, K. ; Jooss, E. ; Moll, E., and Neumann, E. : Die physiologischen 
Wirkungen des Hohenklimas : II. Die Wirkung auf das Blut, gepriift durch 
tagliche Erythrozytenzahlungen und tagliche qualitative und quantitative 
Hamoglobinbestimmlungen im Blute von vier Versuchspersonen wahrend 
eines Monats, Ztschr. f. Biol, 1913, Vol. 61, 379. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 65 

the increment at altitudes. In agreement with most observers the adjustment 
of the blood to the new atmospheric conditions in ascending to higher levels 
occurs promptly ; there is a rapid increase in the factors involved at the 
start followed by a more gradual continuation of the effect ; but on returning 
toward the sea-level the blood does not resume its " low altitude " composi- 
tion so promptly. There may be a prolonged delay in the adjustment 
and return to normal figures.* 

Cohnheim ' regards evaporation as the cause of the concentration 
of blood under these conditions and that this is not due to a lack of 
oxygen. These studies in hematology have an important bearing on 
the course of tuberculosis at high altitudes, and constitute a very 
live question at the present day. 

Professor Cohnheim and Dr. Weber' have recently reported the results 
of examination of the blood of twenty-three persons who have been engaged 
for long periods in the operations of the railway ascending the Jungfrau peak 
in the Alps. Most of them spent considerable portions of their time at alti- 
tudes from 2,300 meters (7,546 feet, Eigergletscher Station) upward to 
3,450 meters (11,319 feet, Jungfraujoch Station). The importance of these 
observations lies in the fact that they furnish data regarding persons who 
have had prolonged experience in the higher altitudes so that the incidents 
of temporary residence and change of scene may be regarded as equalized or 
eliminated. They supplement the earlier records from the South American 
plateaus by results obtained with approved and up-to-date procedures. The 
new statistics agree in exhibiting values both for red blood-corpuscles and 
hemoglobin distinctly higher than the " normals " of sea level. Cohnheim 
maintains that the high figures thus obtained on a large scale from subjects 
accustomed to live at high atmospheric levels leave no alternative except to 
assume a new formation of corpuscles under such conditions. Where contrary 
conclusions have been reached — and there are many such — it is not unlikely 
that the period of residence was too brief to permit the stimulating effects 
of altitude to manifest themselves in any conspicuous way. 

The renewed assumption of an increased functioning of the hemopoietic 
organs at high altitudes has further been supported by observations conducted 
on Monte Rosa in the Alps relating to the regeneration of blood after severe 
anemias. In the international laboratory built on the Col d'Olen at an altitude 
of 2,900 meters (9,515 feet) and dedicated to the memory of Angelo Mosso, 
Laquer ' has found that dogs deprived by hemorrhage of half their blood- 
supply regenerate it in about sixteen days. Under precisely comparable 
experimental conditions twenty-seven days are required at lower levels for the 
restoration of the same blood loss. Laquer believes that the lower partial 
pressure of the oxygen is the effective stimulating factor in this more pro- 



* Editorial in Journ. Amer. Med. Ass., Nov. i, 1913, q. v. 

^ For a recent review of this subject see Cohnheim, O. : Physiologic des 
Alpinismus, II. Ergebn. d. Physiol., 1912, xii, 628; also Anglo-American 
Expedition to Pike's Peak, Journal Amer. Med. Ass., Aug. 10, 1912, p. 449. 

'Cohnheim, O., and Weber: Die Blutbildung im Hochgebirge, Deutsch, 
Arch. f. klin. Med., 1913, ex, 225. 



66 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 



nounced regeneration so strikingly shown at great heights. How long this 
latest explanation will withstand the attacks of the increasing number of 
Alpine physiologists remains to be seen.^ 

The latest observations show that arterial blood contains con- 
siderably more oxygen at high altitudes than at sea level. The 
pulmonary alveoli have a special power of extracting or secreting 
oxygen and this power is increased in high altitudes, this increase 
not disappearing until a considerable time after descent to sea level. 

W. R. Huggard, of London, an unbiassed and judicial observer, 
says : " The diminished frequency of tuberculosis with altitude may, 
I think, be taken as established." ' Hirsch ' held the same opinion and 
based his statement on statistics from various places. 

Thirteen years ago, Dr. Solly endeavored to show this statistically 
and arranged three tables which we append. 



TABLE I 
Comparative Results in Sanatoria in High and Low Climates 

COMBINED first AND SECOND-STAGE CASES ONLY 

(Taken from Dr. Walters, pp. 52 and 53) 



Altitude 



LOWLAND CLIMATES i 

Goerbersdorf (Manasse) ! 1,840 ft. 

Falkenstein (Dettweiler) 1.375 ft. 



Reiboldsgriin (Driver) 
Total 



HIGHLAND CLIMATES 



Leysin (Bernier) 
Davos (Turban) 



2,300 ft. 



4,150 ft. 

5.115 ft. 

Arosa (Jacobi) I 6,000 ft. 

Total 



Number of 
Cases 



3,615 
1,022 
2,000 

6,637 



Z1 
302 

259 
"598" 



Number 
Benefited 



Per Cent 



1,294 36 

746 -72, 

1,400 i 70 

3,440 ! Average. 51 



34 
269 
212 



92 
89 
82 



515 Average, 



71 



The total average of benefited in low climates was 71 per cent' 
" " " " " high " " 86 

1 Without Goerbersdorf. 

The Goerbersdorf reports up to 1884 are so much lower in the percent of 
benefited to the others — owing, perhaps, to some different method of estimating 
results, or, perhaps, to their being taken so many years ago, when the material 
was worse and the treatment perhaps not as efficient — that probably it would 
bring out the truth better to omit them. 



^Editorial in Journ. Amer. Med. Ass., July 26, 1913. 

''W. R. Huggard: A Handbook of Climatic Treatment, London, 1906, p. 
124. 

* Hirsch : Geographical and Historical Pathology, New Sydenham Society 
Translation, 1886, Vol. 3, p. 440. 



NO. I 



AIR AND TUBERCULOSIS — HINSDALE 



67 



TABLE II 
Comparative Results in Open Resorts in Low and High Climates 

ALL stages 
(Taken from Handbook of Climatology, Solly, pp. 132 and 133) 



Per Cent 



LOWLAND CLIMATES 

Desert Climates 

Island Climates 

Coast Climates .' 

Inland Climates 

Total 

HIGHLAND CLIMATES 
Alps (Davos) 

Colorado 

Total 



Number of 


Number 


Cases 


Benefited 


•154 


100 


568 


295 


2,328 


1,369 


136 


n 


3.186 


1,841 


2,027 


1. 551 


571 


420 


2,598 


1.971 



65 

52 

59 

57 

Average, 58 



Average, 76 



The to^al average of benefited in lowland climates was 57 per cent 
" " " " " " highland " " 76 per cent 

• The first table, Table I, deals with the comparative results in sana- 
toria in high and low climates, first and second stage cases combined 
being alone taken, and the different variety of forms of improvement 
being grouped under the head of benefited. Of the lowland sanatoria 
the lowest elevation above sea-level was 1,840 feet, and the highest 
3,300 feet. Of the highland climates the lowest elevation was 4,150 
feet, and the highest, 6,000 feet.. The total average percentage of 
benefited in low climates was 71, and in high climates 86. 

Table II gives comparative results in open resorts in low and 
high climates. The total average of benefited in lowland climates 
was 57 per cent, in highland climates 76 per cent. 

TABLE III 

Comparative Results in High and Low Climates in Open 

AND Closed Resorts 



Sanatoriums 


Per Cent 
Benefited 


Open Resorts 


LOWLAND climates 

Hygeia (A. Klebs) 


69 

76 

n 
74 

84 




Goerbersdorf (Brehmer) 




A dirondacks (Trudeau) 




Average 


Average percent of benefited, 58 


HIGHLAND CLIMATES 

Davos (Turban) 




Arosa (Jacobi) 




Average 


Average percent of benefited, 76 







68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Table III shows the comparative results in high and low climates 
in open and closed resorts. The cases, however, could not be ob- 
tained in first and second stage cases alone, but only of all stages 
combined. In lowland climates the closed sanatoria show 74 per cent 
benefited, and the open resorts 58 per cent benefited. In highland 
climates the closed sanatoria show 84 per cent benefited and the open 
resorts 76 per cent, exhibiting the relative superiority of sanatorium 
over open resort treatment in the two classes of climates, respec- 
tively. Doubtless the sanatorium cases were on the whole in better 
condition upon first coming under treatment than those in the open 
resorts and, therefore, the superiority of sanatorium treatment over 
open methods is probably not as great as it appears here ; but, never- 
theless, even if the material were exactly the same, the sanatoria 
would show a greater percentage of benefited over the open resorts. 

Table III also proves that climate exercises a beneficial influence 
over patients in closed sanatoriums as well as in open resorts. In 
all stages combined the percentage of benefited in sanatoria in 
low climates was 74 per cent, while in high climates it was 84 per 
cent. 

In the first and second stage cases combined (see in Table I), 
the difference in favor of mountain sanatoria is still greater — low- 
land sanatoria 71 per cent ; highland sanatoria 86 per cent.' 

The following is the classification of the National Association for 
the Study and Prevention of Tuberculosis adopted in May, 19 13. 
The data given in the table on page 69 are given in terms generally 
used up to that time. 

CLASSIFICATION OF SUBSEQUENT OBSERVATIONS 

Apparently Cured : All constitutional symptoms and expectoration with bacilli 
absent for a period of two years under ordinary conditions of life. 

Arrested: All constitutional symptoms and expectoration with bacilli absent 
for a period of six months; the physical signs to be those of a healed 
lesion. 

Apparently Arrested: All constitutional symptoms and expectoration with 
bacilli absent for a period of three months; the physical signs to be 
those of a healed lesion. 

Quiescent: Absence of all constitutional symptoms; expectoration and bacilli 
may or may not be present; physical signs stationary or retrogressive; the 
foregoing conditions to have existed for at least two months. 

Improved: Constitutional symptoms lessened or entirely absent; physical 
signs improved or unchanged; cough and expectoration with bacilli usu- 
ally present. 

Unimproved : All essential symptoms and signs unabated or increased. 

Died. 



"■ Dr. S. E. Solly, in the Philadelphia Medical Journal, December i, 1900. 



NO. I 



AIR AND TUBERCULOSIS — HINSDALE 



69 



It is practically impossible to draw accurate conclusions from data 
furnished by different institutions, under such wide variations as to 
the character of the patients and varying standards as to what 
constitutes an apparent cure or arrested disease. A glance at the 
chart or table shows that good results are obtained at all eleva- 



Sanatoria 


a 
2 

> 


< 


•0 

St; 
.«< 

Q 


■a 

> 



u 

a 


> 
U 

a 
E 
'5 


13 

5 


u 


Stage 


Sharon, Mass. 


feet 
250 


per 
cent 
56 


per 
cent 
18 


per 
cent 
33 


per 

cent 

9 


per 
cent 


1891-1911 


All 


Barlow, Los Angeles, Cal. 


300 


3 

16 
31-14 


4 
6 
16 

14.7 


40 
39-5 
42.8 
32-8 


35 
27-5 

1-8 


13 

22 
1-7 
6-S 


1907 
1903-7 
1912 
1913 


All 

Ichiefly ad- 
J vanced 


Wallum Lake, R. I. (State) 


650 


8.S 


32.9 


33-6 


23-7 


I 


Previous 
to 1912 


Iaii 






6.7 


27.4 


38.3 


24-9 


2-5 


1912 


J 


Muskoka, Canada 


700 


5-54 


20.8 


45-41 


24.56 


3-67 


1902-12 


All 


Pottenger, Monrovia, Cal. 
(Private) 


1000 


68 
25 


21 
so 
33 


11 
17 
36 






1909 
to 
1912 


^Incipient 


4 
8 


4 
15 


< Second 
iThird 


Otisville, N. Y. (State) 


1200 


12 


47-3 


27-7 


10.5 


1-3 


1913 


All 


Rutland, Mass. (State) 


1165 


26.1 


35-6 


29-5 


9 




1906 


Early 


New Jersey State (Glen 
Gardner) 


900 


12 


29 


42 


16 


I 


1912 


All 


White Haven, Pa. (Free 
Hospital) 


1250 




17. 1 


59-9 


13-7 


3-3 


1901-13 


All 


Adirondack Cott. Sanitarium, 
Saranac Lake, N. Y. 


1750 


48-3 i 36.3 

8.8 ' '^ " 




15-4 
43 


4.2 


1885-1911 


Incipient 
Moderately and 




'*"■" 




far advanced 


Ray Brook, Adirondacks,N. Y. 
(State) 


163s 


34-4 


31.6 


17-3 


14 


•9 


1912 


All 


New Mexico Cottage Sanita- 
rium, Silver City (600 cases. 
Private) 


6000 


83 
SO 


17 
33 








1904-13 


Incipient 


8 


6 


2 


19% 
Moderately ad- 




vanced, 19% 






13 


30 


25 


26 


4 




Far advanced 






62% 


U. S. Public Health Service 
Sanatorium, Fort Stanton, 
N. M. (For Sailors) 


6231 


II. 7 


IS 


29.1 


9-5 


34-5 


1899-1912 


All 


U. S. Army Hospital, Fort 
Bayard, N. M. 


6400 


2.02 2.87 
4.78 11.40 


69.2; 
52.38 


19-59 
23.80 


6.25 
7.64 


1911 
1912 


All 
All 



tions. The best results are claimed in incipient cases by the Potten- 
ger (Private) Sanatorium, Monrovia, California, i,ooo feet, and 
New Mexico Cottage Sanatorium, Silver City, New Mexico, 6,000 
feet. 

INSOLATION. DIATHERMANCY OF AIR. ALPINE RESORTS 

Associated with diminished atmospheric pressure are other impor- 
tant and inseparable atmospheric qualities which contribute largely 



•JO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

to the resultant influence on man's welfare in the higher altitudes. 
These other qualities have a special influence on pulmonary tubercu- 
losis and should be recognized in estimating the effect on patients 
of this class. 

We have, first, greater insolation. The part played by the earth's 
atmosphere in arresting the sun's rays is very important and second 
only to the influence of the atmosphere of the sun itself in arresting 
the radiation of light and heat from the sun. Slight changes in the 
sun's atmosphere would speedily alter the terrestrial climate. On 
the earth's surface at sea level the energy of light of the sun and that 
of the heat rays are considerably less than at the higher altitudes and 
recent measurements are of great interest and practical value. 

Dr. Julius Hann, the great meteorologist of Vienna, has noted that 
on the lower plains thirty to forty per cent of the total amount of 
the sun's heat was absorbed by the earth's atmosphere, whereas at 
the summit of Mt. Blanc, at 15,730 feet (4,810 meters) elevation, 
nearly one-half of the absorbing mass of the air is lost and the 
amount of the sun's heat absorbed was not more than 6 per cent. 
One can readily understand that when the resistance is removed 
the light rays are more effective than at sea level. The late Prof. 
S. P. Langley showed by delicate measurements at this height that 
the blue end of the spectrum grows to many times its intensity at sea 
level." This marked diathermancy of the atmosphere goes hand in 
hand with altitude. The increased facility with which the solar rays 
are transmitted through an attenuated air accounts for the tan and 
sunburn so readily acquired on mountain tops and this quality is, in 
the author's opinion, of value in the prevention and treatment of 
tuberculosis. 

Owing to the increased diathermancy of the atmosphere at ele- 
vated stations there is a remarkable difference between the atmos- 
pheric temperature in the sun and in the shade. At the higher Alpine 
resorts for tuberculous patients, such as Davos (5,200 feet), St. 
Moritz (6,000 feet), Arosa (6,100 feet), and Leysin (4,757 feet), 
the excessive heat in the sun compared with shade temperatures in 
winter favors the outdoor life during the " invalid's day." It also, 
mcidentally, impresses all newly arrived visitors as a marvellous cli- 
matic feature. At St. Moritz, now a fashionable winter resort, ladies 
find parasols almost a necessity while friends are skating, and those 



^ S. P. Langley : Researches on Solar Heat and Its Absorption by the 
Earth's Atmosphere. Papers of the U. S. Weather Bureau, No. 15, Wash- 
ington, 1884, p. 242. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 7I 

who indulge in this Alpine pastime revel in summer clothing. Al- 
though the climate is a cold one it is characterized by great diurnal 
ranges of temperature, freedom from dust, winds and fogs, and emi- 
nently suitable for the climatic cure. 

As the snow lies on the ground at these resorts for from three to 
five months, sleighing, skating, skiing and tobogganing are popular 
and some of these sports are allowable in suitable cases of tuberculo- 
sis. In March or April the snow melts and the roads become slushy 
and muddy, so that the air becomes very damp, and patients are 
accustomed to make temporary visits to lower stations, such as 
Wiesen (4,760 feet), Seewis (2,985 feet), Thusis (2,448 feet), Gais 
in Appenzell (2,820 feet), or Ragaz (1,709 feet), returning later to 
the higher stations.* 

SURGICAL TUBERCULOSIS TREATMENT IN SWITZERLAND 

No chapter on high altitude treatment would be complete at the 
present time without noting the brilliant success of Dr. A. RoUier 
in the treatment of surgical tuberculosis at Leysin, in the Vaudois 
Alps, Switzerland. This station has an altitude of about 4,500 feet 
above sea level. The hospital buildings face the south and are pro- 
tected by mountain ranges from the cold winds of the north and 
west." Rollier states that even in midwinter, with snow on the 
ground, the temperature on the sunny balconies is often as high 
as 95° to 120° F. Owing to the purity of the atmosphere and 
the absence of moisture there is little loss of the luminous and 
caloric radiation of the sun. Rollier established his first hospital for 
the treatment of tuberculosis of the bones and joints in 1903, but it 
is only during the last two or three years that his method has 
attracted so much attention, though Bernard, of Samaden, had prac- 
ticed it in the pure mountain air of Graubunden in the Engadine ; 
and probably this influenced Rollier to select an elevated site for his 
hospitals. These are three in number and are located at 1,250, 1,350 
and 1,500 meters, or 3,800, 4,100 and 4,500 feet. The exposure of 



' See Walter B. Piatt, M. D. : The Climate of St. Moritz, Upper Engadine, 
Switzerland (Trans. Amer. Climat. Ass., Vol. 4, p. 137)- 

Arnold C. Klebs : St. Moritz, Engadine (Trans. Amer. Climat. Ass., 1906, 
Vol. 22, p. is). 

" See description by John Winters Brannan, ,M. D., Medical Record, June 7, 
1913. Also Rollier, Paris Medical, January 7, 191 1, and February, 1913. 
The author is indebted to Dr. Brannan for his data and to Dr. Rollier for the 
illustrations and descriptions of his method. 



72 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

the patient to the sun is the essential feature and after three to ten 
days of accHmatization indoors he begins with five minute exposures 
of the feet, five times a day. This is steadily increased as pigmenta- 
tion appears until finally the entire surface of the body is exposed 
from sunrise to sunset. The head is, however, protected with white 
caps and shaded glasses. With the development of the pigmentation 
the cure progresses until recovery is complete. Dr. Rollier has sent 
us photographs of a boy who had 32 foci of tuberculosis, even the 
lungs being involved. This boy was considered cured after fifteen 
months of treatment. See plate 26. 

In another case there were multiple lesions, including a badly dis- 
organized and anchylosed elbow with seven sinuses and a history 
of three resections of the joint and forearm. This boy also made 
a good recovery with complete return of function, full flexion and 
full extension. See plate 27. Dr. Brannan adds that he has seen 
many such cures at " See Breeze " and has kindly furnished photo- 
graphs of some of these patients. See plate 16. 

According to Rollier the pigmentation is the important element 
in the cure, inasmuch as it affords to the skin a remarkable resist- 
ance, favors the cicatrization of wounds and confers a local immunity 
to microbic infections. On days when there is no sunshine recourse is 
had to radiotherapy for the adults and the Bier treatment (local 
lowering of atmospheric pressure) for the children ; at all times, 
whether the sun shines or not, the skin has its bath of air and light. 

Two hundred beds in Rollier's sanatoria are reserved for children. 

Dr. Rollier presented to the XVII International Medical Congress 
at London in 19 13, a resume of his method of heliotherapy and 
refers to eighteen separate communications to medical literature, in 
which he and his associates have described the method. Among other 
things we notice that he reports the number of adults having external 
tuberculosis treated by him as greater than that of children, 522 to 
477. The prognosis for the former is as favorable as for the latter 
and the duration of treatment is never much longer. In Rollier's 
paper, referred to, all his cases for the past eleven years are tabu- 
lated and out of 1,129 patients, 951 are reported cured. Of the total 
number only three underwent the operation of resection. These 
were cases of gonorrheal arthritis ; one was adult of over fifty years. 
Two cases of tuberculosis of the foot were treated by amputation ; 
both were adults of over sixty years. 

Rollier uses fixation by means of plaster, especially in Pott's Dis- 
ease, but in all cases insists strenuously that the tuberculous joint 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1. PL. 27 







FOUR ILLUSTRATIONS OF THE SAME CHILD. HE WAS ADMITTED TO DR. ROLLIER'S SANATORIUM, 
LEYSIN, AT THE AGE OF FIVE, WITH NUMEROUS TUBERCULOUS FOCI IN THE BONE AND PERIOSTEUM 
AND ABOUT THE RIGHT EYE. THERE WAS TUBERCULOSIS OF THE ELBOW AND RIGHT FOREARM. 
THREE PREVIOUS OPERATIONS. SEVEN FISTULOUS OPENINGS IN THE ELBOW; SEVEN IN THE FACE. 
JOINTS IMMOVABLE; GENERAL CONDITION BAD. THE TWO LOWER VIEWS SHOW THAT AT THE END 
OF ONE YEAR THE OPEN SORE HAD HEALED. CHILD VIGOROUS. 



NO. I AIR AND TUBERCULOSIS HINSDALE 73 

or other site of the disease must not be covered over by any unre- 
movable apparatus so as to interfere with the full exposure to the 
sunlight. Rollier's last paper goes very fully into the technic of 
heliotherapy and the reader is referred to this and to the fully illus- 
trated paper in " Paris Medical," February, 1913, in which there are 
forty-five remarkable photographs covering the most interesting fea- 
tures of this work. It is at present attracting great attention and 
x\merican physicians can find in the recent review of Rollier's work 
by Dr. Henry Dietrich, of Los Angeles, California, an excellent 
summary of its theory and practice.^ 

Rollier,^ in his address before the Gesellschaft deutscher Natur- 
forscher and Aerzte in Miinster in 1912, says: 

It is in surgical tuberculosis that we have seen the best results from helio- 
therapy, and we have made the treatment of it our life work. As a result 
of my experience in the use of the light-cure in higher altitudes, based on an 
experience of nine years, I maintain to-day that the cure of surgical tubercu- 
losis in all its forms, in all stages, as well as at every age of life, can be 
accomplished. 

The closed surgical tuberculosis always heals, if one will only be patient, 
and above all if one understands how to keep it closed. To transform a 
closed tuberculosis into an open one means to increase the gravity of the case 
a hundredfold. A diminution of the vitality of the tissues is the inevitable 

consequence To regard a surgical tuberculosis as a local disease which 

can be cured by local treatment alone is a ruinous error. On the contrary. 



'Journ. Amer. Med. Ass., December 20, 1913, p. 2232. 

° References: Rollier (Verhandl. d. Gesellsch. f. Kinderheilk. d. 84 Ver- 
samml. d. Gesellsch. deutsch. Naturforsch. u. Aerzte in Munster), 1912. A 
report of 650 cases in which 355 patients were adults and 295 children. There 
were 450 cases of closed surgical tuberculosis and 200 cases of open surgical 
tuberculosis. In the cases of closed surgical tuberculosis 393 patients were 
cured, 41 improved, 11 remained stationary, and 5 died. Of the patients with 
open surgical tuberculosis, 137 were cured, 29 improved, 14 remained sta- 
tionary, and 20 died. 

Rollier and Rosselet: Sur le role du pigment epidermique et de la chloro- 
phylle (Bulletin de la Soc. des sciences nat. 1908). 

Rollier and Hallopeau : Sur les cures solaires directes des tuberculoses dans 
les stations d'altitude. Communication a I'Academie de Medecine, Paris (Bul- 
letin de I'A. d. Med., 1908, page 422). 

Rollier and Borel : Heliotherapie de la tuberculose primaire de la conjonc- 
tive (Rev. med. de la Suisse romande, 20 avril 1912). 

Witqier, T. and Franzoni, A.: Deutsch. Zeitschrift fiir Chirurgie, No. 114. 

P. F. Armand-DeHlle: L'Heliotherapie, Masson et Cie, Paris, 1914. 

P. Vignard and P. Jouffray: La Cure Solaire des Tuberculoses Chirurgi- 
cales, Masson et Cie, Paris. 



74 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

it is a general affection which requires general treatment. Of all infectious 
diseases it is the one in which the individual resistance plays a deciding part. 
Our first effort, therefore, is directed to improve general conditions and thus 
to bring about a healing of the local focus by treatment of the entire system. 
A rational local treatment is necessary as well, provided it is not tog one- 
sided. 

In cases of spondylitis, or Pott's disease, the children wear jackets 
having a large fenestrum cut anteriorly, as the vertebrae in children 
are not much further removed from the surface of the abdomen than 
from that of the back. After healing is verified by X-ray a celluloid 
corset is worn. One or two years are required for the cure. Plate 
29 shows a girl thus cured of pronounced Pott's disease with gib- 
bosity, and paraplegia and muscular atrophy. There was complete 
healing after fifteen months of the solar cure which the illustration 
well shows. 

CASES OF HIGH ALTITUDE TREATMENT 

As illustrations of the good efifect of high altitude treatment, two 
cases from the practice of the late Dr. Charles Theodore Williams, 
of London, may be cited. They were both cured at St. Moritz 
(6,000 feet). 

Miss C, aged i8, was first seen by Dr. Williams, July 20, 1887. 
She had lost a sister from tuberculosis and she had a history of 
cough and expectoration for five months and wasting and night 
sweats for two months ; total loss of appetite and aspect very pallid. 
Slight dulness, crepitation in first interspace to the right. Ordered 
to St. Moritz for the winter. In the spring the patient spent six 
weeks in Wiesen, elevation 4,760 feet. She entirely lost her cough 
and expectoration, gained twenty-four pounds in weight and became 
well bronzed, looking the picture of health. Her chest increased 
enormously in circumference a'nd measured, on full expiration, five 
inches more at the level of the second rib than before she left 
England. She stated that she had burst all her clothes. Careful 
examination at the end of eleven months, when these later notes 
were taken, showed great development of the thorax and hyper-reso- 
nance everywhere, but no abnormal physical signs. After more than 
three years in England the chest measurement had somewhat de- 
creased. 

Another patient, Miss R., aged 21, was seen in November, 1879, 
with a history of cough with expectoration, loss of flesh, night 
sweats, pain in the left chest and evening pyrexia of a month's dura- 





o ^ 

uj 9 

a z 

D -J 

UJ O 

o 



5: H 



h < 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 29 




FIG. 1. HELIOTHERAPY AND IMMOBILIZATION IN PLASTER FOR SURGICAL TUBERCULOSIS. BAL- 
CONY OF DR. ROLLIER'S SANATORIUM, " LE CHALET," LEYSIN, SWITZERLAND. THE JACKETS 
HAVE LARGE OPENINGS TO ALLOW ACCESS OF SUNLIGHT TO THE DISEASED SPINES. SOME 
PATIENTS IN DORSAL POSITION ; OTHERS IN VENTRAL POSITION. 



■^ss^M 




FIG. 2. CHILDREN WHO CAME TO DR. ROLLIER VERY SICK NOW INDULGE IN WINTER SPORTS. NO 
CLOTHING BUT CAPS AND LOIN CLOTHS. NOTE THE MUSCULATURE OF THE CHILDREN FORMERLY 
SUBJECTS OF COXALGIA, ARTHRITIS, PERITONITIS AND ADENITIS. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 75 

tion. Dullness and deficient breath sounds were detected close to the 
left scapula. After three years of unsuccessful treatment in Eng- 
land, during which time two winters were spent at Hyeres, on the 
Mediterranean, losing ground and growing thinner and showing evi- 
dence of commencing disease in the opposite lung, she was sent for 
the winter to St. Moritz. She returned the following May vigorous 
and well bronzed, having taken plenty of exercise, skating, walking, 
and tobogganing. She had lost all cough and had gained much 
strength. The chest measurement showed an increase of one inch. 
The whole thorax was found hyper-resonant and no physical signs 
of consolidation could be detected. After eleven years of residence 
subsequently in England, she was free from chest symptoms. 

In this case, notwithstanding the improvement following two 
winters spent at Hyeres, at sea level, the disease was not arrested 
and increased the following year. But during one winter's residence 
at St. Moritz, elevation 6,000 feet (diminished atmospheric pressure 
and out-door life with winter sports), there was complete arrest of 
the disease, as the experience of eleven years with absence of phy- 
sical signs testifies. 

There is a wealth of clinical material to show the advantages 
of high altitude treatment at the well-known European and Ameri- 
can resorts. Sir Hermann Weber, of London, and his son, Dr. F. 
Parkes Weber, have had a long and favorable experience in the treat- 
ment of pulmonary tuberculosis in high altitudes and they support 
Dr. C. T. Williams in a higher estimate of treatment of this disease 
at high elevations as contrasted with results at the sea level. 

Twenty-five years ago Sir Hermann Weber stated that out of 106 
tuberculous patients sent to high altitudes, 38 were cured, either 
permanently or temporarily, 16 were stationary or but slightly im- 
proved and 10 deteriorated. More than half of the cases in the first 
stage were cured. 

The American statistics of Drs. Samuel A. Fisk,' W. A. Jayne,' 
S. E. Solly,' Charles Denison and S. G. Bonney, all of Colorado, 



'Fisk, Samuel A.: Concerning Colorado (Medical News, Sept. 16, 1899); 
Climate of Colorado (Trans. Amer. Climat. Ass., 1888, p. 11). 

''Jayne, W. A.: Climate of Colorado and Its Effects (Trans. Amer. Cli- 
mat. Ass., 1888). 

* Solly, S. E. : Invalids Suited for Colorado Springs (Trans. Amer. Climat. 
Ass., 1888, p. 34). 



76 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

are certainly convincing as to the effect of high altitude treatment 
in the cure of pulmonary tuberculosis/ 

Solly said in 1888, " Taking the medical profession throughout 
the world, it is unquestionable that a large majority of those who 
have made a study of the subject believe that where a change is 
made, a change to an elevated country is the most likely to benefit 
a consumptive." 

Solly lived for thirty-three years in Colorado after having re- 
moved, as a tuberculous invalid, from England. Every one of the 
physicians mentioned above went to Denver or Colorado Springs as 
a tuberculous patient, recovered his health there, acquired a repu- 
tation and successful practice during fifteen to thirty years of resi- 
dence and the majority are alive to-day (1913). Those who died 
succumbed to other affections. 

According to Solly, 76 per cent of all patients, good, bad and 
indifferent, and 89 per cent of those in the first stage that undergo 
climatic treatment in Colorado are benefited. Would such patients 
as we have mentioned have derived equal and as lasting benefit at 
Alpine Stations, such as Davos or St. Moritz, which have a corre- 
sponding altitude and an equal barometric pressure ? Judging from 
recorded clinical experience, we believe that they probably would 
have done equally well. We can never know absolutely. Would 
they have done equally well at sea-level or at very moderate altitude ? 
None of the physician-patients whose names are quoted would admit, 
it. 

Dr. Solly, with his inimitable humor once remarked, " If I were 
living in London to-day, I'd be dead." In all human probability most, 
if not all of them, are fair examples of the curative power of the 
Colorado climate. 

Of late there have been dissenting voices, challenging some of the 
cardinal principles involved in the altitude treatment of tuberculosis. 
Not only altitude, with its concomitant rarefied atmosphere, but even 
sunlight itself which lightens the heart of every invalid, have both 
been denied the value so generally assigned them in tuberculo- 



^ Charles Theodore Williams: Aerotherapeutics, or the Treatment of Lung 
Diseases by Climate. The Lumleian Lectures, 1893 ; Macmillan, 1894, pp. 
111-179. 

Charles Denison : Dryness and Elevation the Most Important Elements in 
the Climatic Treatment of Phthisis (Trans. Amer. Climat. Ass., Vol. i, 
1884, p. 22). 



NO. I AIR AND TUBERCULOSIS — HINSDALE 'J'J 

therapy. These discordant notes find utterances among those who 
have been compelled to treat the poorer class of consumptives in our 
cities at the seaboard and who have obtained some excellent results. 
Stress is laid on the beneficial influence, for example, of cold.^ The 
fact that patients improve more in winter than in summer is cited 
to prove that " cold air in itself seems to cure in a manner which 
nothing else can accomplish. * * * Sunshine is not essential — 
excellent results may be obtained in climates where the sun is rarely 
seen. Mere outdoor living seems to be the essential element, and 
yet there does not seem to be any doubt that quicker results are ob- 
tained in the cold season than in the summer." 

EFFECT OF COLD AIR 

There is truth in the proposition that cold air is better for the 
consumptive than heated air. It is usually purer and is unquestion- 
ably more stimulating to the vital forces. Warm sleeping rooms are 
positively bad because of deficient ventilation. Warmth debilitates 
and opens the way to bacterial invasion. Hot weather is relaxing, 
while moderate cold, or greater cold with proper safeguards, acts as 
a tonic and fortifies the well and sick alike against disease. 

The good efifect of cold air in tuberculosis is commonly noted by 
physicians and patients. The following extract from a letter from 
a tuberculous patient, dated Saranac Lake, New York, February 
19, 1908, is interesting: 

I have not felt the cold up here this winter as I feared I might, although 
the mercury has nearly disappeared on one or two memorable nights. 46° 
below zero is the coldest I have seen it but it was reported 50° below in the 
village. I am quite used to the cold now as I sit out on the porch all day 
and have not missed a day yet; but there is one redeeming feature about the 
cold up here and that is that zero weather does not seem nearly so cold 
as 20° above in Philadelphia. I really do not begin to feel it until it gets to 
20° below, although it is usually too cold to use my hands even in milder 
weather. J. D. 

This patient was 22 years old, had been at Saranac fifteen months 
and is reported perfectly well and weighs 180 pounds. He is ap- 
parently cured. He remains well, Nov., 1913. 



' Editorial, American Medicine, Philadelphia, January 20, igo6. 
See A. D. Blackader, M. D. : The Advantages of a Cold, Dry Climate in the 
Treatment of Some Forms of Disease (N. Y. Med. Journ., Aug. 3, 1912). 



78 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The minimum temperature at Saranac Lake for 19 12 was — 32° 
F. on January 25, and the maximum was 88° F. on July 10. The 
mean temperature was 40.98° F. The total precipitation was 43.19 
inches, with a total snowfall of 124.24 inches. Clear days, 153 ; 
partly cloudy, 'j'] \ cloudy, 136. 

The extract here reproduced from a letter dated Saranac Lake, 
July, 1886, is interesting-. It was addressed to the author. 











The best and clearest statement of seasonal influence on body 
weight of consumptives that we know of was made by Dr. N. B. 
Burns, of the North Reading State Sanatorium, Massachusetts. His 
observations are based on one thousand patients during three years. 
Fully forty per cent of the cases admitted to this sanatorium were of 
the far advanced and progressive type. It was noted that August, 
September and October show that the largest percentage of patients 
gaining, while the three months immediately preceding show the 
opposite. 

Dr. Burns also charted the aggregate gain in pounds of the male 
patients treated at North Reading, December, 1911 to 1912, inclusive. 
There was a rise in January and February, 191 2, to 850 pounds for 
76 patients which was maintained well through March and April. 



NO. I 



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82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

There was a subsequent sharp decline in May, the index dropping 
250 points. This fall continued without interruption in June, to cul- 
minate July II, at the low point for 1912. 

The conclusion of this study was : 

Phthisical patients are apt to lose rapidly in weight and general 
condition in May, June, and the first two weeks in July, which season 
constitutes an unfavorable and critical period. 

Phthisical patients make an extraordinary recovery in weight and 
general condition in the month of August, which is a surprisingly 
favorable time of the year. 

August, September, January and February are the most propitious 
months for obtaining successful results in treating pulmonary tuber- 
culosis. 

Forced feeding in the unfavorable season seems to have availed 
very little in limited number of cases studied at North Reading. 

We have already referred to the beneficial influences of the Arctic 
summer climate (see pages 39-42), and we attributed much of it 
to the perpetual sunshine ; consequently we cannot agree to the 
illogical statement that sunshine is not essential. We believe that the 
" Fireside Cure " has no place in the treatment of tuberculosis and 
we must admit that whereas only a few years ago the cold air 
fiend, who slept with windows wide open in the coldest winter, was 
considered a crank, he now has been proved to be the only sensible 
one among us.* 

EXPANSION OF THORAX AT HIGH ALTITUDES 

Without dwelling further at this time on the efifect of cold air 
compared with warm air on tuberculous disease (see pp. 28, 40, 
71), we must note some of the undeniable effects of diminished 
atmospheric pressure on physical development and especially on the 
thorax and pulmonary tissue. 

One striking change is the expansion of the thorax in various 
directions and a corresponding increase in the mobility of the tho- 
racic walls. We have previously referred to one case in which the 
circumference increased five inches during a residence at St. Moritz, 
elevation 6,100 feet. (See page 74.) Changes of from one to 
three inches are more commonly noted even at much more moderate 
elevations. These changes are conveniently recorded by means of 



^ American Medicine, loc. cit. 



NO. I AIR AND TUBERCULOSIS HINSDALE 83 

the instrument known as the cyrtometer which gives accurate trac- 
ings for recording the progress of the patient/ 

Inasmuch as tuberculous patients in whom the disease is actively 
progressing show a shrinking of the perimeter pari passu with the 
advance of the disease, and those who are recovering show an in- 
creasing circumference, it is a fair inference that the physiologic 
increase in thoracic measurements due to residence in the higher alti- 
tudes is an advantage in the prevention and treatment of pulmonary 
tuberculosis. Man is not adapted to live permanently at altitudes 
above 13,000 to 16,000 feet (4,000-5,000 meters), but at somewhat 
lower elevations as, for instance, at 10,000 feet we have some thriv- 
ing cities such as Leadville and Cripple Creek in Colorado, and Quito 
in Equador, elevations 10,000 and 9,350 feet (3,000 and 2,850 
meters). The altitude of the permanent habitations in the Ortler 
Alps is about 5,450 feet (1,640 meters), and that of the highest 
health stations from 5,000 to 7,000 feet (Arosa). It is a well-known 
fact that the Indians of the Andes, the Swiss guides, the Tyrolese 
hunters and other mountain dwellers have a large thorax with corre- 
spondingly deep inspiratory power and remarkable endurance.' The 
increased respiration and the quickening of the circulation promote 
health and vigor in mountain races and comparisons between the 
highlanders and those in deep and flat valleys are always in favor 
of the former. All observers have remarked on the immunity from 
disease, and especially scrofulous and tuberculous disease, charac- 
teristic of mountain races, provided they live in the open, avoid over- 
crowding, have sufficient and suitable food and observe ordinary 
hygienic methods of life. Failure in this respect provides an opening 
for tuberculosis which, as we well know, is the scourge of the 
North American Indian and his relatives in Mexico and South 
America. Even in Quito, that city of remarkable equability, where 
it is perpetual spring, tuberculosis has effected an entrance, and 
enters largely into the mortality lists.' In Bogota, South America, 
in La-Paz, Mexico (elevation 11,000 feet, 3,360 meters) and in other 
densely populated towns in these countries, the later records show 
increasing numbers of cases of tuberculosis. This fact, however, 



' See Minor, Charles L. : The Cyrtometer ; A Neglected Instrument of 
Pulmonary Diagnosis and Prognosis (Trans. Amer. Climat. Ass., 1903, p. 
221). 

' " Mexican Indians, though of medium height, have unusually large and 
wide chests, quite out of proportion to their size." Jourdanet. 

""Jacoby: These de Paris, 1888. Quoted by Huggard. 



84 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

should not afford the slightest ground for controverting the general 
proposition that life at altitudes of from 3,000 to 6,000 feet favors 
immunity from tuberculosis and the cure of the disease in suitable 
cases. 

CHOICE OF CASES FOR HIGH ALTITUDE 

The question then arises, what are suitable cases for altitude treat- 
ment? What kind of patients may be sent to stations of lower 
barometric pressure? 

In choosing a location, the late Dr. F. I. Knight, of Boston, for- 
mulated some opinions based on his long experience.' He limited 
the age of those resorting to altitudes to fifty years. In temperament 
he preferred the phlegmatic to the nervous, with an irritable heart, 
frequent pulse, and inability to resist cold ; and with the latter we 
must be careful not to include those who show nervous irritability 
from disease, not temperament, as they are generally benefited in 
high places. As regards disease, he first considered cases of early 
infection of the apices of the lungs with little constitutional disturb- 
ance, and, although these generally do well under most conditions, 
yet considerable experience assured him that more recover in high 
altitudes than elsewhere. 

It is best to begin with low altitude in patients with more advanced 
disease showing some consolidation but no excavation ; also when 
both apices or much of one lung is involved and the pulse and tem- 
perature are both over 100. 

Hemorrhagic cases, early cases with hemoptysis and without much 
fever are benefited by high altitudes. Patients with advanced dis- 
ease, those with cavities or severe hectic symptoms should not be 
sent to high altitudes. A small, quiet cavity is not a counter-indica- 
tion ; hectic symptoms are counter-indications. 

This accords with the latest report from the U. S. Public Health 
Service Sanatorium at Fort Stanton, New Mexico, altitude 6,231 
feet. Dr. F. C. Smith reports 56 deaths from pulmonary hemor- 
rhage in a total of 524 patients since the hospital was opened in 
1899. His conclusion is that pulmonary hemorrhage is not more 
frequent at high altitude than at sea level, but the results are perhaps 
more often serious, especially in those with impaired circulation." 



' Trans. Amer. Climat. Ass., 1888, p. 50. 

'Public Health Reports, U. S. Public Health Service, No. 51, by F. C. 
Smith, Passed Ass't Surgeon, Washington, 1910. See also Report No. 93, 
Washington, 1912. 




5 > 



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NO. I AIR AND TUBERCULOSIS HINSDALE 85 

Patients in an acute condition should not be sent. Cases of fibroid 
phthisis, in Dr. Knight's opinion, are not suitable. Convalescents 
from pneumonia or pleurisy are usually well suited for elevated 
regions. Advanced cases of tubercular laryngitis, if good local treat- 
ment and freedom from dust can be obtained, may do no worse in 
elevated regions than elsewhere. 

In cases complicated by cardiac dilatation we cannot advise alti- 
tude ; but a cardiac murmur resulting from a long-past attack of 
endocarditis with no sign of enlargement or deranged circulation 
should not prevent. Nervous derangements of the heart are usually 
counter-indications. 

The observations made at the United States Public Health Sana- 
torium at Fort Stanton, New Mexico, by Surgeon F. C. Smith, of the 
service are commended as a valuable contribution to the Relation of 
Climate to the Treatment of Pulmonary Tuberculosis. This sana- 
torium is open to sailors in the merchant marine and they are trans- 
ferred from the twenty-two marine hospitals on the coasts and 
rivers to this admirable inland sanatorium. It was found that the 
results have been nearly three times as good in the cases which left 
the home stations, i. e., the local marine hospitals, without fever as 
in those who had a temperature of 38° C. (100.4° F-) or more 
within two weeks of departure. The deaths in those leaving afe- 
brile were to those leaving with fever as 22 to 59 ; the arrests, as 
19 to 7>4 ; the apparent cures, as 10 to 3. Dr. Smith holds that the 
case that should be sent to a distant climate immediately upon diag- 
nosis is exceptional and he also adds that neglect to make an 
early diagnosis does not warrant precipitate haste in sending the vic- 
tim away when it is finally established. The psychologic moment 
for a climatic change is when there is a comparative quiescence of 
the lung process under treatment at home, when nutrition is im- 
proved and further improvement is slow (Francine). Climatic 
change, however, must sometimes be made, as we will see later on, 
when the hoped for stage of quiescence does not occur. 

Before allowing patients with pulmonary diseases to go long dis- 
tances or to make any great change to higher altitudes, some caution 
should be given. In the first place, patients should not make any 
physical exertion for two or three weeks after arrival. The air may be 
stimulating, there may be sights to see and many dangerous invitations 
given, but it is absolutely necessary that the patient should be ad- 
justed to the new atmospheric conditions. Acclimatization is neces- 
sary to comfort and safety. In the old days it was accomplished by the 
slow ride in the stage-coach over the plains. We cannot go back to the 



86 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

old methods, and therefore we must exercise greater caution. No fe- 
brile case should be sent on these journeys or to any elevated resort. 
Hemorrhage is not a counter-indication to a change of altitude, and 
it is not any more liable to occur at five to six thousand feet than 
at sea-level. However, no advanced case of pulmonary tuberculosis 
should be sent away. Financial considerations are highly important. 
Expenses are usually underestimated, and the want of sufficient 
means, the need to economize as regards the necessities, not to speak 
of the luxuries, of life, is a dreadful handicap, and should bar out 
many a case that succumbs for want of the very comforts he had 
left behind. It would be far better for such patients if they should 
enter some special hospital or sanitarium for consumption, such as 
are found in most of our Eastern States. 

No one should be sent away without definite and satisfactory 
knowledge of the place to which he is sent, and without a letter of 
introduction to some favorably known practitioner containing a state- 
ment of the main points in the case. 

In matters of climate, as in many other fi.elds, it is the man behind 
the climate who will help the patient, save him from errors and in- 
discretions, advise him and direct him as to local surroundings, and 
enable him so to live that his disease shall be arrested. 

Some localities favorable for tuberculous patients have already 
been mentioned. Taking the country as a whole we naturally look 
to the elevated, sparsely settled regions of Colorado, New Mexico, 
Wyoming, Montana, Nevada, Utah, Arizona and California. The 
slopes of the Rocky Mountains and the Great Basin are justly en- 
titled to first choice, provided always that other safeguards than 
climate are to had for the protection, the comfort and nutriment 
of the patient. Texas, especially the central and higher western por- 
tion, must be included in this great area. Life in Texas was for- 
merly rather too rough and food and accommodations were too 
primitive for fastidious people, but now at places like San Antonio 
and El Paso, these defects have been remedied. The winter climate 
of Texas is very agreeable, except when the Texas norther descends 
and holds everything in an icy clasp. However, this is not alto- 
gether a disadvantage, if not too severe. 

Florida suits some cases of phthisis. The interior of the state is 
sandy and the winter and spring climate is excellent. The culti- 
vation of orange groves and other agricultural features of the state 
have given many a patient a profitable occupation that he would 
never have found elsewhere. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 87 

Thomasville, in Georgia, sixteen miles from the Florida line, 
and Aiken and Camden, in South Carolina, have long had a reputa- 
tion for the relief of pulmonary affections. Asheville, North Caro- 
lina, is more elevated (2,300 feet) and has an excellent " all the year 
round " climate. Special attention is given to tuberculous patients 
at this resort, and this is something" that cannot be said of all the 
g-ood places. In Pennsylvania, suitable places are found in the 
Pocono Mountains, at White Haven, Kane, Cresson, Mont Alto and 
Hamburg-. In New Jersey, there are Lakewood, Brown's Mills, 
Haddonfield, Vineland, and, for special cases, such as chronic fibroid 
phthisis, we may advise Atlantic City. 

In New York, there are the Adirondacks, especially the vicinity 
of Saranac ; Loomis, in Sullivan County, where there is an excellent 
sanatorium. In New England, there are institutions at Rutland 
and Sharon, Massachusetts ; Wallum Lake, Rhode Island ; Walling- 
ford, Connecticut. But, as we have said before, the choice of a 
place, whether near home or at a distant point involves all the ques- 
tions of diagnosis, of temperament, of financial resources, all of 
which the physician must weigh as conscientiously as though his own 
life depended on it. 

Of late, English physicians have been making more extended use 
of the higher Alpine resorts. Among these, Davos Platz, altitude 
5,200 feet; St. Moritz, 6,000 feet; Arosa, 6,100 feet; and Leysin, 
4,712 feet, are usually chosen. Their chief characteristics are an 
atmosphere of dry, still, cold, rarefied air ; absence of fog, few 
clouds and very little wind. There is, therefore, strong sunlight 
with a grateful warmth in the sun's rays. 

In selecting cases for treatment by change of climate, we must 
exercise as much discrimination as in applying any other remedial 
measure. Indeed, more caution should be used, for the patient will 
pass out of observation and in most cases the advice given involves 
the most vital consequences. 

CHAPTER V. INFLUENCE OF INCREASED ATMOSPHERIC 
PRESSURE; CONDENSED AIR 

Celsus, in treating of pulmonary tuberculosis in the first century 
A. D., advocated a change of climate and to " seek a denser air 
than one lives in." ^ 

A few places in California and in Asia Minor are below sea-level. 



^ De Medicina, Paris edition, Delahay, 1855. 



88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

But the consequent increased atmospheric pressure in these localities 
is not in itself worthy of note. Such desolate regions as the Dead 
Sea, the Mojave Desert, Death Valley, and Salton Lake, California, 
are entirely unsuited for the tuberculous, and, for obvious reasons, 
all subterranean pressures are out of the question. Divers and 
caisson workers become anemic and hence artificial pressures in- 
creased beyond the normal at sea level are injurious. 

Even the natural variations in atmospheric pressure at any given 
station may be sufficient to have some appreciable influence, per se, 
on the course of pulmonary tuberculosis. Changes of pressure of 
20 mm. (.7874 inches) occasionally take place, but they are com- 
parable to a gradual change of level amounting to only 200 meters 
(656 feet), and it has been assumed that no appreciable physiologic 
eft'ects can be attributed to these gradual alterations, at least as far 
as tubercular diseases are concerned. Hann ^ and Thomas ^ state 
that in experiments with pneumatic chambers, pressure changes 
amounting to 300 mm. (11.8 inches) a day have been produced 
without causing any notable injurious effects upon the sick persons 
concerned in these experiments. 

EFFECT OF BAROMETRIC CHANGES ON THE SPIRITS 

As the barometric pressure in any given place falls the cloudiness 
usually increases, the temperature rises, the wind increases, and 
precipitation is liable to occur ; as the pressure rises the skies clear, 
the temperature falls and the winds shift to the west or northwest. 
The spirits and general morale of all patients usually improve with 
a rising barometer unless prolonged wind storms accompany such a 
change. Whatever improvement accompanies a rising barometer 
is due to the stimulus of cold or the return of sunshine and dryer 
air. 

Dr. Charles C. Browning, of Los Angeles, has studied the effect 
of some atmospheric conditions on tuberculous patients.' In his 
first report it appeared that unseasonable or very sudden changes 
in temperature influenced temperature of patients, while equal or 
greater changes occurring slowly did not. Of hemorrhages occur- 
ring in groups about four times the number occurred when there 



'Julius Hann: Handbook of Climatology, Macmillan, 1903, p. 71. 
^Thomas, in Beitrage zur Allgemeinen Klimatologie, Erlangen, 1872. 
■* Trans. American Climatological Ass., 1908 ; idem, 1913, p. 189. 



NO. I 



AIR AND TUBERCULOSIS — HINSDALE 



89 



AUGUST 1912 




Febrile" 



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Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric pressure, 
temperature and humidity. Courtesy of Dr. C. C. Browning, Los Angeles, Cal. 



90 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 



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60 

50 

L 40 
























































































































f 






















A 


















,l\ 


A 




















A 


f\ 






A 


A 




A 


A 




h 


/^ 


A 




A 


A 


r 






V 


J\l\ 


A 




A 


A 


A 


A 


/ 


I 


r 


s/ 


\/^ 


/ 


/ 


X 


/ 


/ 


/^ 




J 


^ 


V 




V^ 


y\ 


/ 








V 


V V' 


v/N 


n 


/ 


\J 


V^ 


/ 










V 


V 


V 


y 








¥ 




V 






V 


1/ 
















V 


y 


V 


V 


































































Humidity 


' 90 
80 
70 
60 

50 

40 

30 

_20_ 


V 


— 


— 














































A 


A 


A 


1 










^. 


A 


\ 


K 


A 


A 


^y 






\ 














'S, 




\y 


\ 


^ 


'\ 


'\ 




V 


y 


A 






K 


' \ 


\ 1 


\ 


V 


A, 


\ 


'V 




^i 


V 


\ 










p^ 






V 


V 


V 


\ 






V 


\ 


A 


^ ) 


\ 




V 






V 


\ 










\ 








. 
















' 








•' 


\tM 


Y 












V 










V 






% 


\i 


















y 








V 
































'v 


v 


















\ 








































V 




















y 






























































99 

Temp. gg 

Afebrile < 97 

90 

(Pulse go 

70 






























































^ 


~A 


r.^ 


:">^ 


■J^ 


■"5^ 


■7^ 


-r 


r*^ 


-/ 


-/N 


:'^ 


-/* 


>•/< 


•yv 


-/ 


-^ 


-?*■ 


*A 


^ 


i~A 


-A 


::<^ 


"^ 


"T 


"■^ 


-A 


■7* 


-/^ 


z^ 


w 


V 




V 


W 


V 


V 






V 


V 


V 


V 


V 


V 










V 


s/ 




V^ 


s/ 




V 


V 


































































7^ 


^! 


Si^- 


t^ 


LyS 


^ 


^ 


s^ 


/- 


e! 


y 


V* 


^ 


v^ 


^7^ 


7* 


^ 


■7^ 


r/^ 


-7^ 


/-^ 


^^ 


^ 


^ 


1~A 


■r 


rA 


:V 


^ 


f/ 






























" 
































lOZ 


























































































































Febrile • 


Temp., 00 
99 
96 
110 

.Pulse 100 


h 


/ 


. 


A 




/'/^ 


A 






X 


/^ 


« 


ft 








A 


h 


/^ 


A 


A 




A 


A 


I 


y 


it 


A 


/ 




V 


1/ 


V 




r^ 


Y 


/ 






/ 


/ 


y^ 


/ 


V' 


^A 


/ 


7 


J 




/^ 


/ 


\/ 


/ 


/^ 


J 


7 


/ 


/ 


J 


1 




¥ 
















V 




¥ 


V 


• 


V 


Y 


Y 


V 






V 


y 


V 


» 


V 


Y 


ir 


V 


y 


































































A. 


/ 


/ 






iA 


A 








A 


/ 








A 


A 




A 




/\ 


K 




A 


./ 


A 




/ 


V 


1/ 


Y 


V 


V 




;/' 


V 


v^ 


^ 


7' 


s^ 


/ 


V 


v^ 


^' 


^ 


^ 


1/ 


^ 


/ 


V 


v- 


^ 


v^ 


v' 


V 


V 


^ 


80 






























































Hemorrhages 














































BS 






H 






wm 


Deaths 




+ 




+ 




+ 




+ 




+ 


+ 


+ 




+ 
















++ 






+ 




+ 


^ 




+ 



Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric pressure, 
temperature and humidity. Courtesy of Dr. C. C. Browning, Los Angeles, Cal. 



NO. I 



AIR AND TUBERCULOSIS HINSDALE 



91 



OCTOBER 1912 
DATE |l|2l3l4|5|6|7|e|9|l0|ll | 12| 13 j I4-| 15 | 16 1 17 1 18 1 19 |20|2I |22|23|24|25l26|27|28|29[30 [31 | 


Barometer. 


10 ^^^1 L— j- j^ -j~ 


'°Z ^\ ^ x^ '^^'^"^'^v- ^V^-^ ^^^"^ ^"^ 


1°-^-^, J ^x^ ^ ^^^ 


7o\j tZ ^ ^ 


29-6 2! - 


Thermomet 


To ^ ^^^^t-h 


^r 70 ^-A -A^^T^H^^\l-T-W^-A -*-A-*H^^-A-it -TT-A-/ 


1 IoZ3^ -^-AjSJl^ZfL^^ ^ ^^J^^X^AJ^J^J^J^^^^X 


i,o cA/-^-^-^-^^^^^ j- *-^^^)r^^\t-^^^i/~t^ 


40 


Humidity 




^° ^ NjVl_ r. .^>l_AAa_a A„/L__t_ 


fo A]^^V^ \ i\t ^r^t'^t^^^^X-JV 


1° \ ^^YV^X ^ i^ XtX 


\ ,0 ^ -^'^ ir- 7 Art-A 


1. ■ t tC X ^ 3 


^0 i>v- ^t^^^ ^ 


30 -^Si. ^X^ ^ 


^ 10 }L — 


7 
Afebrile' 
P 


emp. „„ -^ -A-A -^- 7\-Ar-A 3^-A.-/\ •A-/'<^ -ArA-A-f^- f\-A:h-ts^:fiJ:f^zh:fi-Jsdhz&:t. 






uisefo^^^:^^;^^'^^^-^^^^*^^^^'^'^^^^^^^^'^"^- 




T 
Febrile •■ 
P 




, !oo -J«_ji_a — /-j>^ J\-J5-A^-J\^-/\-A-^-A^;r-JrJ-^-A-AH5-A-A-A-^-A-A7 


^llrZtzlSxXXJ^XTl^XXXlU-^^ 


llrAr /-/ ^v-\hf^\/-/ /^/-/^rr"*' "^^^v Y V « r^v irv^r- \rv- 


"° }i A s-> i 1 A A A A yvYS . ^ 


,,se'00_^_^^_^^^^^^^^//^^^^^/^////v^^^/-V*/ 


80 • [ 1 :tj: 


Hemorrhages <=> r^aB"^^ "T^y -n-naa i_i i_j — 1 xa l_, — -j-,- 
" Deaths "^h"!"^ ■*■! + + + + +++ + ^"'■/+ '"' 



Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric pressure, 
temperature and humidity. Courtesy of Dr. C. C. Browning, Los Angeles, Cal. 



92 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 







JANUAR> 


f 1913 






















































DATE 


1 


2 


3 


4 


5 


6 


7 


6 


9 


10 


11 


12 


13 


14 


15 


16 


17 


le 


19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 


31 


Barometer ^ 


40 
30 
20 

10 

3000 

90 

60 

129-70 










































































, 










r 


-\ 








































> 


\, 








/ 










/ 


\ 












^, 




























/ 


\ 








/ 








^ 














/ 


s 


S 










N 








^ 


y 


\ 








V 






/ 






1 


/ 








s 




y 






^ 




\, 


N 


/ 




"^ 


^ 


"S^ 








\ 






\^ 




N 






\, 


/ 










N^ 












V 




























V 


r' 






V 




















































V 






















































Thermomete 


80 
70 
.1 60 
50 
40 
30 
^ 20 






71 










































































































A 








A 




V I . 


















A 














a 








A 


A 


A 


K 


/I 


A 


. 




r 




1a 








A 




n 


A 


A 


A 


1 ^ 




A 


A 


A 


/N 


/ 




>A 


A 


/ 


V 


\/' 


V 


/' 


lA 


.A 


/ 


I 






V 


\A 


A 




/ 


kA 


/ 


/ 


^ 


V 


^ 


V^' 


>/ 




/ 




V 




r 


y 


y 






V 




y 


V ' 


/ 










V 


/^ 




V 












































































































Humidity 


90 
60 
70 
60 
' 50 
40 
30 
ZO 
10 
^ 


















1 












,^ 






















k 




1 


\> 


h 


















A 












/ 


V 


\ 


/— 


(\. 
















A 




Ay 


V 


\ 
















\ 




/ 


\, 




y 










\ 






'\ 












V 


' V 




\ 


\ 




j 












1 


y 


/ 


\ 




/ 












\ 




\ 


A 






1 




\i 












1 














\ 


' 






r 
















V 




k 




1 




V 










\ 


1 








A 






Y 




























\ 


1 














\ 


1 






1 


\ 




































v 
















\ 




\ A 


1 






















































\n 


J 


















































































































Te 
Afebrile •< 

Pu 


98 
97 

90 

Ise 80 

70 
































































-P 


U 


p^ 


;^ 


^ 


^ 


^ 


-- 


-r; 


r/^ 


-f^ 


TV 


-A 


- — 


-K" 


-^, 


:A 


7^ 


^ 


.■A 


7S 


"iA 


-^ 


bA-^ 


i7^ 


",A 


Z^ 


LA 


t^ 


^ 






[r 


y^' 


■/ > 


l/V>«/ V 








• 








V 


s/^ 


V 






-A 


, 




^ 


/\ 










A 






/. 


^A 












A 


A 










A 


.A 


uA 


r 


y-W-i 


y^ 


^^ 


U- 


Sw'-S 


^ 


•^ 


s/- 


y!- 


yj 


s<:j 


Its 


^ 


-<^i-sA 


/' 


y- 


y. 


^J^- 


fvj 


S(^S 


LA 


[^4^5 


^_ 






y_. 




























































Te 
Febrile •■ 

Pu 


101 

99 

98 

1 10 

Ise '°° 
90 

eo 




























































A 


A 


r^ 


« 




« 


A 


1 




A 


/ 


A 


A 


A 


A 


A 


A 


A 


/ 


A 


A A 


A 


A A 


A 


A 


A 


A^ A 


/ 


P 


A/ 


V 


i/^ 


/' 


/ 


J 




V 


/ 


P 


\r 


J^ 


>/^ 


/ 


\r 


V 


/ 


l/ 


Af^ 


/^ 


Ar 


/^ 


\Aiy\n 


/ 


r^V » 


» 


V 


V 


/ 


( 




y 


y 


V 


V 


V 


V 


V 


V 


y 


r 


V 


V 


V 


V 


y 




y 


V 


y 


• » Y 1 










/v 






















































As 


A 


f\ 




A 




A 


A 


,/v 


A 


/ 


.'^ 


u^ 






A 


/v 


.,A 


A 




A 


A 




A 


L,A 


..A 


A A 


/ 


1 


y 


v> 


/ 


\r 


/^ 


/ 


\j^ 


/ 


■/ 


y/ 


s/ 


V 


»' 


V 


S/^ 


/^ 


w' 


V' 


V 


• 1 


^ 


V^ 


S/^ 


^/^ 


/ 


V ^ 


V 


/ 


V 


y 














V 
















































Hemorrhages 








\ 






a 








□ 












□ 


□ 


□ 




□ 


■ 




□ 












Deaths 




++ 




+ A 


+ ++ 


.. 










+ 


+ 




+ 








+ 






+ 


+ 
++ 




" 


++ 






+ 


+ 



Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric pressure, 
temperature and humidity. Courtesy of Dr. C. C. Browning, Los Angeles, Cal. 



J 



NO. ] 



AIR AND TUBERCULOSIS — HINSDALE 



93 



FEBRUARY 1913. 

DATE |l|2|3|4-|5|6|7|8|9|l0|ll | 12 | 13 ] 14| 15 | 16 ] 17 1 18| 19 |20|2I |22l23l24]25|26|27|28| 


Barometer.* 


f 


20 Z^N^ -^ 


iS ^^ /^ ^ t- 






c.r. ^-V / V^^"^ L ' 


70 ^ V ^ 


60 A^'^ 


50 ^^ 


29-40 V 


Thermomete 




60 K^hhr^nl^hKtttilJKK f 


A 5oy^Z/iA^^^^7-y ^L^/ZA-^PT^A^^v^^^^^^J 


su^*^i^^*- *-»— r-«^|^i'-)f- t^'^'Sj^sr^^^^T^^'f^ 


^ no 


Humidity 




9oV- «- tLftk,*—- 1- A^\- 


Io\ »_ vvt -vi^tt ^i-J- -Jl / t 4- 


7oi^ Sa:_^^^±«_7^ it -v^Xa: jCz X^/X 


i lo ^ xZ ^rr XT z XX ixt X x_. 


60 ^ -V ^^ il^ ^T^t^ ^^ ±7 


4? ^ iz: is it 


i 30 V /V 1^' 


Te 
Afebrile. 

Pu 




-P 99 ;4^^^v^^^i2?-;^5A;^7^^^^^^^^-^^^^^?t'5^^ 


'" «°h4yi4i^ 


70 


Te 
Febrile. 

F-u 


101 


mnioo A A ^ / /i A / //AjAaA/^ / n l\ )J /^^ y R K A XA / 


^oo/A/\/\/yvvv^^//^///\A/A/fy 


99/'ir/Y'»*« i)li\/)lVYYl**YViitV 


1 10 




'*^ 90 T^v^^^'r'^^^i^r'^^^^'r^sr^rs^^Ay'K/^^^T^^y 


60 V <r V k^ pi / 


Kcmorrhages L'- ■ "^ a a ■ ■ 


Deaths + ++++ + /+ + + + ++ + + + /+ + + ++t + 



Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric 
pressure, temperature and humidity. Courtesy of Dr. C. C. Browning, Los 
Angeles, Cal. 



94 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 



MAR 
DATE 1 1 2 


:h 1913. 
3 4 5 6 7 6 


9 10 II 12 1 


3 14 15 16 17 1 


8 19 20 21 22 23 24 25 2 


6 27 28 29 30 31 


Barometer 














IW 






ys^ 


.^ 




10 ^s^ 


^"V 


/\ 


y^ s^ 


z 


"^S^ ^ 


< .10-00 


^^ z 


A ^^ 


S,'* 


s^ ^_*^ fcs^v^ 


x-^'^^^ 


QO 


5^ 


^ Z- 




^^\^^ ^ 


^ 


80 




\ y^ 








I 20-70 




^^ 








Thermomel 


[ ''O 




















J 






Til ^H A 




-/-» 


7 


-» -k 


-e'' 60 ^^ 


ZftTtTT 


^S, it 


-_^ a/A 




AlAJSTSt 


5^7^ 


/ t * » » 


J~t^7^y 


l^f^a 


^A/ /a /vA/y 


^^TL^^r 


OU / j^ 


» 


inir^Sf^v 


» » 


y '' v\/ / / » 


If » 


I 30 








* 




Humidit 






lU 4 




1 1 


r 






/Va ^ 




44vt^l-/t 


t ^-^ 






N t-j- 


V Z 


\/li V v\'\/\ 


^t^ 




^^ 


~ A^ 


A y^ 


1/ V \j \k 


\N 


/^ foL.^ 


T ^ 


^ 


^L_ T 


4 ^^lit- 


^-v^ 


4-0 1 

30 


J^^f^ *- 




t At 




r 


^\\/t7 




v^ / 




i^ 


?0 


V \/ v^ 




A/^ 






I 10 












T 

Afebrile" 

Pi 


0,0 












-"'P- eg -A 7^ 


rA/^AhA^:^ 


^^^ 


-^txtSg^jA:; 


^'f'T^-f^Z^ 7^'f^./t/ 


'^r/«L^^^^^^ 


° / V 1 


V V V V » V 




V ' / V Y^y » V 


V * •^ y 




><« >« A >^ -A .A 


«, /A y^ Ai ^ 


a^Aa^^ 


. > A .• A A ^. ^rf" 


V /sy^L/A j*L / 


ilse an /-"^ 




/jc.l^-icV 


rNL>c__ _!, 


t.^rZ^^T^yZYlZ. 


>^f_«:J/V- 


70 












T 
Febrile. 

P 


101 ' 












100 aI a 


^J\Z^^^^ 


A A A jH 


/ / A A f\ 




A /\ >< i^ > / 


^'"p cc^ N 


\fui\f\tu:t 


\blJl^{i 


f\/XTTu 


'/JAnA/^N 


^T^xy^t 


Qe 


v-v-v-y-jrir 




Y Y Y ^ ^ 


*-V-t^/-f-)[-f^r 


Y V V Y Y 


no 












1 ^ 100 A A 


A Al A /lj^ 


i^ A i^i iA 


/, yA A A /V J 




\JsJsj!sAJ 


^'=" 90i^7^ 


^^r^r\-fr^ 




V ^/^/ V 


'^y^/^A/_^^^'^ 




eo 












HemorrhaSes 


■ ■ 


■ 


a 


a m 


-^- D a a 44: 


Deaths 


■^ .■*; 


-f- -<- + ' 


+ + H 


h + + + 


+ 



Relation of pulmonary hemorrhages and deaths from tuberculosis to barometric pressure, 
temperature and humidity. Courtesy of Dr. C. C. Browning, Los Angeles, Cal. 



NO. I 



AIR AND TUBERCULOSIS HINSDALE 



95 



was a barometric pressure change exceeding .3 of an inch within 
twenty-four hours than when the change was less. The hemor- 
rhages appeared to be more frequent if there had been a change in 
the opposite direction — a sudden fall. The cases observed were all 
in the advanced stage. The conditions which appear to influence 
groups of hemorrhages and deaths are barometric pressure, humidity 
and cloudiness, each in turn appearing to be the most prominent 







s 


s 








































90 




/ 


V 








































^ 




\ 


V 






































60 








\ 


,80 


































8/ 










K, 


































7 


70 








, 




V 








*• 


'•* 








**^ 


'*• 


... 


... 


% 






/ 


.•• 


• •• 


>•* 






\ 


^ 


^ 


k 


s 


^.' 


'•' 










•• 


'*•« 


V, 


%^ 






60 












.••*' 


— . 


~m* 


«•*" 


6 


»■ 


6 


K 


s 












!><< 


B2 


-.. 




> 


*•• 


••' 


" 


















> 








/ 


59 






>^ ( 


50 


»•*■ 






























\ 


/ 


r 








































> 


9 












40 


























































































30 














































P-^ 


i 


V 


































? 


5 










' 


s. 




^ 


{ 


i 


( 






) 


% 












^ 


y 


\ 




20 




' 








^ 


V 








\ 






/ 


\ 










^ 


Z' 






\ 


10 


\ 






/' 


\ 










\ 


/ 






\ 


t-- 


-^ 


y 










li 


^ 


^ 


/ 






\ 








^ 


'a 














/ 


s 













\ 


/ 








■ ^ 


^ 






















































^ 





















•Deaths from 
Tuberculosis -1910 



Humidity 
"~i Temperature 



Deaths, L.A.Co. 
Hospital 



Elevation 293 ft. 



Chart showing deaths from tuberculosis in the Los Angeles County Hospital 
and in the city of Los Angeles in 1910. Rainfall, mean monthly temper- 
ature and relative humidity are also shown. Courtesy of Dr. C. C. 
Browning. 



index in exerting a limited determining influence. This is shown in 
the two charts for November and December, 1912. Dr. Browning's 
paper contains charts for six other months. 

Dr. Browning notes the influence of fog and remarks that the 
" high fog " is regarded by many as one of the most desirable fac- 
tors of the Southern California climatic condition. It is not fog 
in the generally accepted meaning, for this " light veil " is neither 
cold nor excessively moisture laden ; neither is it high, for its altitude 
is less than a thousand feet. 



96 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

When the barometer is gradually rising and the humidity slowly 
falling and the sky clear or clearing, patients are pleasant, in some 
cases jovial and inclined to be optimistic as to the future. 

When the barometer is either gradually or rapidly falling and the 
humidity rising and becoming more oppressive as the hours go by, 
and the day is foggy with little or no sunshine, the effect on patients is 
entirely different. They become pessimistic, cross and very irrit- 
able. During the so-called " northers," when the barometer falls, 
then rises rapidly with clear weather and a quick drop in the humid- 
ity as from 75 per cent to 20 per cent in twenty-four hours, there 
is a marked drying of the mucous membrane, causing great discom- 
fort in some and comfort in others. 

ARTIFICIALLY COMPRESSED AIR 

Artificially compressed air has been used by Oertel, Simonoff and 
Charles Theodore Williams in pulmonary tuberculosis. The first 
two claimed great improvement resulting from its use ; but Williams 
did not find such favorable effects.' In nine cases submitted to the 
compressed air bath, hemorrhage was brought on in two while in the 
bath ; in four others hemorrhage occurred but could not be distinctly 
connected with this form of treatment. There was usually some 
gain in weight and diminished cough and expectoration, and appar- 
ently the respiration became freer in the unaffected portions of the 
lungs. Beyond the opening up or aeration of portions of the lung 
which had not been brought into play for some time, there seemed 
to be no special change for the better. Compressed air in Williams's 
experience did not facilitate the absorption of lung consolidation or 
infiltration. 

At the Brompton Hospital a large wrought iron chamber was con- 
structed about ten feet in diameter by eight feet in height, and ac- 
commodated four patients. It had thick glass windows and a closely 
fitting door. By means of inlet and outlet pipes compressed air was 
introduced and allowed to escape. The outer air from a pure source 
was filtered through cotton and pumped into the receiver. The pres- 
sure was gradually increased after the patients were inside the tank 
until it reached ten pounds or two-thirds of an atmosphere above the 
normal. Half an hour was spent in increasing the pressure, one hour 
in maintaining it at the highest point required, and half an hour in 



* Charles Theodore Williams : Compressed Air Bath and Its Uses in the 
Treatment of Disease, London; Smith, Elder & Co., 1885, and Aerotherapeu- 
tics. Macmillan, London, 1894, p. 106. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 97 

reducing it; so that two hours were consumed in its application 
therapeutically. 

A practical difficulty was encountered in keeping the compressed 
air sufficiently cool to be comfortable, owing to the fact that air invari- 
ably rises in temperature during compression and cools during rare- 
faction ; so that in warm days ice had to be used about the reservoir. 

Von Vivenot, in a careful series of experiments, showed that the 
influence of compressed air on the respiratory capacity was to per- 
manently raise it. When used for two hours every day it is found 
to increase daily from 20 ccm. to 30 ccm. above the previous day's 
record. Von Vivenot took 122 compressed air baths during 143 days 
and his respiratory capacity was raised from 3051 ccm. to 3794 ccm. 
and, in compressed air, to 3981 ccm. This increased capacity was 
reached in three and a half months, after 91 baths and was after- 
ward maintained at practically the same level." 

An increase in respiratory capacity has been noted by other ob- 
servers, but the respiration rate is always lowered and in almost all 
cases there is a similar lowering of the pulse rate. 

PNEUMATIC CABINET 

These experimental results naturally appealed to phthisiologists 
and patients were treated at Brompton, as we have mentioned, and 
in the United States by means of Ketchum's pneumatic cabinet or 
similar devices. There is no doubt but that the method was given 
a fair trial, but it has been found wanting. The pneumatic cabinets 
installed at considerable expense at the Loomis Sanitarium at Liberty, 
at the Rush Hospital in Philadelphia and at Saranac, are rusting 
away or consigned to the scrap heap. The simpler and more natural 
method of outdoor life is found much more safe, rational and effect- 
ive.'' 

See J. Solis Cohen: The Use of Compressed and Rarefied Air as a 
Substitute for Change of Climate in the Treatment of Pulmonary Phthisis. 
(Trans. Amer. Climat. Ass., Vol. i, 1885). 

V. Y. Bowditch : 1 en Months Experience with Pneumatic Differentiation, 
ibid., 1886, 47. 

A. S. Houghton, Journ. Amer. Med. Ass., Nov. 7, 1885. 

C. E. Quimby, Trans. Amer. Climat. Ass., Vol. 9, p. 33- 

Isaac Hull Piatt, Trans. Amer. Climat. Ass., Vol. 3, P- 76. 



' Paul Bert, op. cit., p. 439. 

Huggard, W. R. : Handbook of Climatic Treatment, p. 109. 
' At Sharon Sanatorium it is still used in some cases as a means of calis- 
thenics for the chest and is thought to be of value 



98 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Tiegel, New Yorker Medicinische Presse, April, 1887. 

E. L. Trudeau, Trans. Amer. Climat. Ass., 1886, p. 41. 

Ketchum: Physics of Pneumatic Differentiation (Medical Record, Jan. 9, 



Waldenburg, Pneumatische Behandlung, Berlin. 
J. T. Whittaker, Gaillard's Med. Journ., August, 1885, p. 208. 
Herbert F. Williams, Journ. Amer. Med. Ass., Aug. 14, 1885. 
Herbert F. Williams, Trans. Amer. Climat. Ass., 1886, p. 17. 
B. F. Westbrook, Trans. Amer. Climat. Ass., 1887, p. 102. 

ARTIFICIAL HYPEREMIA 

We must here refer to an important advance in the treatment of 
surgical tuberculosis in which artificial changes in the atmospheric 
pressure play a prominent part. Prof. Bier, of Bonn, first used his 
famous method in treating tuberculosis of joints; he used the 
" Stauungsbinde." He also uses cupping glasses of various shapes 
so that they may be applied to various parts. The rarefaction 
of the air is accompHshed by a rubber ball or a pump, according 
to the size of the glass. After opening tuberculosis lymphatic glands 
and tuberculous abscesses in connection with joints, the cupping 
glasses are applied and the claim is made that this process avoids 
mixed infections. Tampons and drains, also, are found to be unnec- 
essary. 

In treating a member, for instance the hand, Bier uses a glass 
cylinder provided with a cuff and a rubber band, so that the whole 
hand is hermetically sealed and by means of the pump the air is 
partially exhausted. By similar apparatus Prof. Bier, Dr. V. 
Schmieden, Dr. Willy Meyer, Ewart, and others all over the world 
have treated successfully cases of surgical tuberculosis so that the 
method has an established place in tuberculo-therapy." 

CHAPTER VI. ARTIFICIAL PRESSURE; BREATHING 
EXERCISES 

Radical differences of opinion exist as to the use of artificial varia- 
tions of pressure, or pneumatic differentiation, in pulmonary tubercu- 
losis and also as to the larger question as to whether the diseased 
lung should be set at rest or invited to expand. 

The respiration of artificially compressed or rarefied air for 
limited periods, such as half an hour or two hours, has been con- 
sidered, but this form of pulmonary gymnastics has given way to 



^August Bier: Hyperaemie als Heilmittel, Stli edition. Prof. Bier advises 
a long continued residence at the seashore in cases of surgical tuberculosis. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 99 

more natural methods of accomplishing" the results aimed at. The 
judicious use of exercises has been advocated for centuries and this 
plan of treatment has passed through most interesting phases, long 
advocated, then condemned and later revived. Some of the recent 
advocates of exercise by graduated labor invoke the very latest 
knowledge of the pathology of tuberculosis in support of this method. 

The bad effects of exercise on tuberculosis patients at the well- 
known climatic stations have been widely commented on and number- 
less histories of patients going to their death when caution might 
have saved them are on record. Patients going from the lower ele- 
vations to altitudes of five and six thousand feet do not seem to 
realize at first how necessary are rest and thorough acclimatization 
for their safety during the earlier weeks or months of treatment. 
The higher stations are natural gymnasia where diseased lungs may 
be trained or overtrained ; where accidents may happen to the inex- 
perienced and rash, or even to the old time expert if he neglects to 
exercise proper judgment. No fall from the trapeze is more fatal 
in its effect than some mountain expedition or other adventure by 
the tuberculous patient. Dr. Solly was wont to say that nowhere is 
the invalid fool more quickly punished for his folly than in Colorado. 

We are concerned, at present, with exercise as it relates to the 
breathing habit and the aeration of the diseased lung. Exercises 
and improved breathing habits can be carried out and acquired at the 
sea-level or at higher elevations. We believe that at the moderate 
or higher altitudes breathing exercises are more effective for good 
and tend more fully to develop the thoracic movements and capacity 
than at the lower levels (see page 62). Minor has recently reviewed 
this subject in a paper on the " Use and Abuse of Pulmonary Gym- 
nastics in the Treatment of Tuberculosis " and holds that they are 
beneficial in properly selected cases. That such measures are abused 
by those who use them indiscriminately and unintelligently we all 
know. 

ATMOSPHERIC COMPRESSION OF LUNG 

Fifteen years ago Cornet came out strongly against exercises and 
others of experience take even more radical ground. The principle 
of rest has been carried to such an extreme that surgical measures, 
such as strapping the affected side to insure complete immobilization, 
have been adopted.^ The most radical measure was the introduction 



* Charles Denison, Trans. Amer. Climat. Ass., Vol. 21, 1905. 



lOO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

into the pleural cavity of nitrogen gas, or atmospheric air, so as to 
compress the lung and prevent as nearly as possible all motion. The 
credit for devising this operation and first performing it, belongs to 
Forlanini, but it v^as first practiced in America by Dr. John B. 
Murphy,' of Chicago, and has been repeatedly used by many others 
in Europe and America, including the late Dr. Henry P. Lbomis,* 
Dr. Cleaveland Floyd and Dr. Samuel Robinson, of Boston, Dr. L. 
Brauer, Prof. T. Beneke, of Hamburg, Dr. H. L. Barnes and Dr. 
F. T. Fulton, of Rhode Island. 

ARTIFICIAL PNEUMOTHORAX 

Prof. Theodore Beneke, of Hamburg, says' that Forlanini con- 
ceived the idea of placing the affected lung at rest by artificial 
pneumothorax as early as 1882 ; he put it in practice in 1888 ; Brauer 
and Ad. Schmidt performed it in 1906. Murphy seems to have 
developed his operation without any knowledge of Forlanini's work. 
The operation has been performed in Germany, according to Beneke, 
by hundreds of physicians on several thousand patients. The opera- 
tion is meeting with great favor in America." 

The clinical observation that the occurrence of pleuritic effusion 
in tuberculous cases was followed by an arrest of the symptoms of 
the primary disease if the effusion were left undisturbed; and, 
further, the unfavorable results which follow tapping in other cases, 
or when later adopted in cases of quiescent during the presence of 
the effusion led to this method of artificially producing immobility. 
Pleuritic effusion is intimately connected with pulmonary tuberculo- 
sis in a majority of cases and, if not purulent, should probably be 
left undisturbed. 

Loomis followed Murphy's technique, using a special apparatus 
for the injection of pure nitrogen gas by means of which from fifty 



'John B. Murphy: The Surgery of the Lungs (Journ. Amer. Med. Ass., 
1898). Also Surgical Clinics of Dr. John B. Murphy, December, 1913. W. B. 
Saunders Co., Phila. ; also Interstate Medical Journ., March, 1914. 

^ Henry P. Loomis: Some Personal Observations on the Effects of Intra- 
pleural Injections of Nitrogen Gas in Tuberculosis (Trans. Amer. Climat. 
Ass., 1900; Med. Record, Sept. 29, 1900). 

This method was first proposed by Prof. Carlo Forlanini, of Pavia, Italy, 
at the International Medical Congress, Rome, 1894. 

' Ueber den kunstlichen Pneumothorax, " Tuberculosis." Berlin, Nov., 1913. 

" See article by Dunham and Rockhill, with discussion by C. L. Minor, 
Journ. Amer. Med. Ass., Sept. 13, 1913. 



NO. I AIR AND TUBERCULOSIS HINSDALE lOI 

to two hundred cubic inches were introduced into the pleural cavity 
on the affected side' 

The nitrogen gas introduced into the pleural cavity does not re- 
main long without being absorbed, and in order to keep the lung 
immobilized for six months or more, repeated injections are required. 
When ordinary atmospheric air gains entrance to the pleural cavity 
it constitutes the condition known as pneumothorax, and if the pneu- 
mothorax becomes closed, the oxygen steadily diminishes and finally 
disappears, the carbon dioxide decreases and the last element to 
disappear is the nitrogen. This fact has been determined by chemical 
analysis by Dory, Bouveret, LeConte, Ewald (Loomis) . The respira- 
tions are always increased after the injections and the pulse rate is 
lowered. A notable effect in Dr. Loomis' cases was the absolute con- 
trol of pulmonary hemorrhage in cases where all other measurd^ 
failed. 

Dr. Loomis' experience in eighteen cases treated by injections 
of nitrogen gas was uniformly favorable, although not -curative. 
Probably the fact that pulmonary hemorrhage is controlled is the 
chief value of the method, though gain in weight followed the adop- 
tion of this measure in all the cases. 

SONG CURE 

One method of pulmonary exercise lately advocated for tubercu- 
lous patients is by singing.^ Singing invokes correct nasal breath- 
ing and a maintenance of the elasticity and proper expansion of the 
chest. The necessary breathing exercises promote an increased func- 
tional activity of all parts of the lungs, including the apices where 
tuberculosis usually first becomes evident. It is here that expansion 
is most limited and the prevalent opinion is that this comparative 
inactivity is a strong factor in the tendency of the disease. 

The " song cure " may be suitable in some cases of pulmonary 



' For a good description of the latest apparatus and a discussion of the 
most approved methods see articles by Harry Lee Barnes and Frank Taylor 
Fulton, and by Samuel Robinson and Cleaveland Floyd, Transactions of the 
American Climatological Association, 1913, pp. 160-188, and. 1911, pp. 289-383. 
A bibliography is given in Transactions, 1913, p. 170- 

See also Trans. American Sanatorium Association, 8th spring meeting, p. 
16. Discussion by H. D. Chadwick, W. A. Griffin, E. S. Bullock, G. W. Hol- 
den, J. J. Lloyd, Jr., L. Brown, J. Roddick Byers. 

See also Samuel Robinson, "Practical Treatment," edited by Musser and 
Kelly, W. B. Saunders Co., Philadelphia, 1911, Vol. 3, p. 254- 

"Drs. Leslie and Horsford, The Hospital, London, Jan. 25, 1908. 



102 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

tuberculosis, but in laryngeal cases it would be counter-indicated. 
Its practice in pulmonary cases has not been adopted to any very 
great extent ; but it would seem to have some advantages as it does 
not involve great muscular fatigue. 

It is well known that public speakers with pulmonary tuberculosis 
cannot continue this practice with impunity. Their tendency to 
attempt to increase their weakening vocal powers by forcing the air 
outward has a bad influence on the lungs. Bad habits of speaking 
and lack of training are probably accountable for these bad results. 
Artistic breathing should be cultivated and all public speaking in 
crowded and badly ventilated halls should be avoided.^ Knopf refers 
to cases of phthisis ' which had even passed the incipient stage 
and were cured after following the occupation of street singer or 
speaker. He cites the case of an English lady who became an 
evangelist, addressing crowds of people every night in open air meet- 
ings and who was actually cured of her tuberculous disease after 
following this calling for a year. 

Our own experience leads us to believe this to be an exceptional 
result. Having had some experience in treating members of the 
Salvation Army in various grades of the service, the impression 
gained was that tubercular disease was quite common among them 
and that their life of exposure, unhygienic quarters, insufficient food 
and excessive use of the voice rendered them an easy prey to con- 
sumption. The voice is almost always over-strained and hoarse and 
the open air life the members lead is accompanied by hardships 
which over-balance any favorable features in their nomadic exist- 
ence. 

Open air singing, properly employed, as in the German Army, 
is, no doubt, beneficial. This should be encouraged by all military 
authorities. It relieves the tedium of the march and invigorates the 
soldier. Barth, of Koslin, has made a thorough study of the efifects 
of singing on the action of the lungs and heart, on diseases of the 
heart, on the pulmonary circulation, on the blood, the vocal appara- 
tus, the upper air passages, the general health, the development of 



^George Hudson Makuen : Artistic Breathing (Philadelphia Medical Jour- 
nal, Sept. 3, 1898). 

^ S. A. Knopf : Respiratory Exercises in the Prevention and Treatment 
of Pulmonary Diseases (Johns Hopkins Medical Bulletin, Sept. 1901). 

See also John H. Pryor, Deep Breathing as a Therapeutic and Preventive 
Measure in Certain Diseases of the Lungs (Trans. Amer. Climat. Ass., Vol. 
22, 1906, p. 251). 



NO. I AIR AND TUBERCULOSIS — HINSDALE IO3 

the chest, on metabolism and on the activity of the digestive organs, 
and has come to the conclusion that singing is one of the exercises 
most conducive to health. (Knopf.) 

CHAPTER VII. FRESH AIR SCHOOLS FOR THE TUBERCULOUS; 

VENTILATION 

Under the name of " Waldschule " these have recently been estab- 
lished in Germany. The first was opened at Charlottenburg, Berlin, 
August I, 1904, and closed its first term October 29th of the same 
year with 120 scholars. The results of the first year were very 
encouraging, the average increase in the weight of the children 
was five pounds, and the Forest School has been regularly opened 
each year. 

The credit of its establishment belongs to the " Vaterliindischer 
Frauenverein " of Charlottenburg. This patriotic association of 
women selected children either suspected of tuberculosis or with 
the disease already established for the Forest School. In this way 
educational facilities are provided for children whose condition ren- 
ders them unsuitable for the public schools and at the same time 
avoids the necessity of sending them to sanatoria where there is little 
or no provision for teaching. 

At Charlottenburg they put up so-called " Doecker barracks " or 
transportable buildings of light construction. There was one school 
barrack, containing two class-rooms and one teachers' room. The 
second barrack was used for household purposes. There was also 
an open " liege-halle " towards the south where the children may 
remain during bad weather. A light frame structure contains wash 
rooms and a bath-room with tub and douche. Three schoolmasters 
and one schoolmistress give instruction. The children were dis- 
tributed in six classes of about twenty each. This is smaller than 
in the public schools where there are from forty-five to sixty in a 
class. The sessions never lasted over two hours continuously." 

This school has now grown so as to accommodate 240 children. 

A second school is located in ]\I.-Gladbach in the Rheinprovinz. 
It was opened in 1906 for sixty children between eight and fourteen 
years of age. 

A third one is in Muhlhausen, Reichslande, Elsass-Lothringen, 
Southwest Germany. It was opened in 1906 and the physician in 
charge is Dr. Bienstock. 



' For further particulars of this school, see article by Dr. J. Nietner, Tuber- 
culosis, May. 1905. 



104 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

A fourth is the Forest School in the Mctoria Louise Children's 
Sanatorium at Hohenlychen. It was established August i, 1903. 
Pastor A'lickley is in charge. These are the pioneer schools and 
many others have since been established. 

The most successful private open air schools in Germany are 
conducted by Prof. Dr. Gustav Pannwitz, the honorary secretary 
of the International Association for the Prevention of Tuberculosis. 
They are situated at Hohenlychen, about tv^o hours by rail from Ber- 
lin, near Templin, on the hilly plateau which is called the " Mecklen- 
burgisch — Pommersche — Seenplatte," between the East Sea and 
Spree Rivers. There are extensive forests of fir, a large lake with 
an island of 240 acres belonging to the school. It is conducted on 
the most modern hygienic principles. 

An open air school was established at Bostall-Heath, near Wool- 
wich, England, in 1907 ; in France, at Lyons, Vincennes and Bou- 
logne ; in Switzerland, at Lausanne, open from June 5 to Septem- 
ber 23, at Zurich and Geneva. The " Rayon de Soleil " at Geneva, is 
for very young children ; so also " Les Oisillons " at Lausanne. 

In the United States the first fresh air school for tuberculous 
children was established in Providence, Rhode Island. Dr. Ellen A. 
Stone and Dr. Mary S. Packard had a small day camp during the 
surnmer.of 1907 for children suspected of having tuberculosis. They 
soon became convinced that a fresh air school ought to be started 
for the benefit of the tuberculous children of Providence and they 
asked the help of Dr. Jay Perkins, Chairman of the Providence 
League for the Suppression of Tuberculosis in getting a single 
small school, necessarily ungraded, for those children, arranged 
so as to approximate an out of door school. At the camp which these 
physicians had been conducting there were about ten children who 
would soon have to go back to the ordinary schools or else would 
be at home in close rooms. 

In response to this appeal Dr. Perkins enHsted the sympathy of the 
Superintendent of Schools, Mr. Walter H. Small, and with Judge 
Rueckert and Dr. Charles V. Chapin, the school committee estab- 
lished the first fresh air public school in America. 

A school house not then in use and centrally located was requested 
for use and granted, and the necessary changes were made. The 
result was that they had to begin with a room on the second floor 
the full size of the building, about 40 by 25 feet, with windows on 
three sides. The brick wall on one-half of the southerly side was 
removed and windows substituted, these windows extending from 
near the floor to the ceiling, with hinges at the top and pulleys ar- 



NO. I AIR AND TUBERCULOSIS HINSDALE IO5 

ranged so that the lower end can be raised to the ceihng, thus leaving 
this half of the room completely open to the south. Each school 
desk and its accompanying seat is arranged on an individual wooden 
support so that, while stationary as regards each other, each desk 
and seat can be moved as desired, and thus any arrangement of seats 
may be made. The school is an ungraded one (the ages running 
from 7 to 13 years), and as such limited to 25 pupils. The school 
hours are from 9 to 11.45 a. m., and from 1.45 to 3.30 p. m., with a 
recess from 10.15 to 10.45. Towards the end of this recess each 
pupil is served a cup of hot soup. Each pupil has a sitting-out bag 
of the standard type and in very cold weather has a hot soapstone 
in the bottom of the bag. In the end of the room not open to the 
south a good fire k kept going, thus partially warming the air and 
keeping that end of the room moderately warm, the pupils' seats all 
being in the other end. 

One interesting feature in connection with the school is that, 
though these children come from poor homes and there has been an 
extensive epidemic of " colds " in winter, especially affecting the 
nose and throat, no child in the school has had even a " cold in the 
head." On being enrolled, each child is weighed, measured, and 
the hemoglobin tested. The League furnishes the sitting-out bags 
and soapstones and some clothing, the city paying all other expenses. 

Thus the credit for suggesting the school belongs to Drs. Packard 
and Stone, but the work was developed and carried on through the 
efforts of the League. Most of the children for the school are 
selected in the first instance by the head tuberculosis nurse and sec- 
ondly by the physicians on the League Committee. All of them 
are from within walking distance of the school. Dr. Stone is one 
of the Medical Inspectors of the Public Schools and the other Medi- 
cal Inspector, Dr. Charles E. Hawkes, was added to the committee. 

Providence was the first city in the country to establish special 
schools for the mentally deficient and the school department is to be 
highly complimented because of the enthusiasm and energy with 
which they took up the establishment of a special school for the 
physically deficient as soon as the matter was presented to them. 

This Fresh Air School in Providence was opened on January 27, 
1908, with ten pupils, and soon twenty were enrolled. Hot soap- 
stones, sitting-out bags, hot drinks at recess, frequent trips to the 
stove, breathing exercises, marching, bending movements, and uni- 
form work in singing are prominent features of the pioneer fresh-air 
school in America.^ 



' Ellen A. Stone, M. D., Journal of the Outdoor Life, May, 1908. 



I06 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The instruction of children at the Sea Breeze Hospital for 
Tuberculous Children at Coney Island is provided by the Board of 
Public Education of Brooklyn, New York, and the Board deserves 
credit for thus cooperating- with the Sanatorium. Provision is now 
made in the larger cities for the regular and systematic education 
out of doors of tuberculous children in the community at large and 
the success of this movement is attested by the fact that on May 
I, 191 3, there were 177 open air schools in the United States, five 
of these are in Rhode Island ; thirty in Manhattan ; twenty in 
P'rooklyn. 

See also Jay Perkins, M. D. : Fresh Air Schools — How They Accomplish 
Their Result (Journal of the Outdoor Life, New York, June, 1912). 

Les EColes de Plein Air, leur valeur prophylatique dans la Lutte Anti- 
Tuberculose, "Tuberculosis," Berlin, Nov., 191 1. 

The Open-Air School, Anna Garlin Spencer, Trans. Sixth International 
Congress, Washington, 1908, Vol. 2, p. 612. 

Open Air Schools, Thomas Wray Grayson, M. D., Therapeutic Gazette, 
Nov., 1913, p. 27. Also John V. Van Pelt, Interstate Med. Journ., April, 1914. 

In order to control tuberculosis efifectively we shall have to make 
more determined efforts to reach the school children and even those 
of earlier years. Tuberculosis is latent in thousands of children 
in every large city ; sooner or later it becomes manifest as vital resist- 
ance becomes lowered. A recent view, prevailing in France and 
Germany, is that all tuberculous infections are made in infancy 
and childhood, the disease lying- latent, from one cause or another, 
until the individual resistance, weakened by successive colds, pneu- 
monia, grippe or other infections, or exposure to reinfection, finally 
yields and tuberculosis is actively established. Both laboratory and 
clinical experience point to a much earlier primary infection than we 
have been accustomed to believe and hence too much stress cannot 
be laid on the importance of better ventilated schools and the estab- 
lishment of more " fresh-air schools" in every city of the country. 
These should be located near parks, if possible, or at least have ex- 
tensive play grounds.' They should be conducted also for the benefit 
of children who may be anemic, nervous, and not necessarily tubercu- 
lous ; and also for apparently healthy children. The best example of 
the outdoor school for normal children has been opened at Bryn Mawr 
College, Pennsylvania, as the Phebe Anna Thorne Model School. 



' Henry Barton Jacobs, M. D., Journal of the Outdoor Life, April, 1908. 

J. H. Lowman, M. D., Trans. Nat. Ass. for the Study and Prevention of 
Tuberculosis, 1907. 

The three Elizabeth McCormick Schools, in Chicago, are admirable ex- 
amples of the open air school. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 34 




FIG. 1. ■ RAYON DE SOLEIL," GENEVA, SWITZERLAND. DAY CAMP FOR ANEMIC AND 
DELICATE CHILDREN 




FIG. 2. FOREST SCHOOL, GENEVA, SWITZERLAND 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 35 




FIG. 1. OPEN AIR SCHOOL ESTABLISHED BY THE CIVIC CLUB, PITTSBURGH, PENNA. STUDY 

HOUR; WARM WEATHER 




OPEN AIR SCHOOL ESTABLISHED BY THE CIVIC CLUB, PITTSBURGH. 
HOUR; COLD WEATHER 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 36 




OPEN AIR SCHOOL ESTABLISHED BY THE CIVIC CLUB, PITTSBURGH, PENNA. RESTING HOUR 



SMITHSONIAN MISCELLANEOUS COLLECTIDNS 



VOL. 63, NO. 1, PL. 38 




FIG. 1 . FRESH AIR SCHOOL ESTABLISHED BY THE CIVIC CLUB, PITTSBURGH, PENNA 




FIG. 2. OPEN AIR CLASS FOR ANEMIC CHILDREN AT PUBLIC SCHOOL NO. 21, NEW YORK CITY 
Courtesy of Dr. J. W. Brannan 



NO. I AIR AND TUBERCULOSIS HINSDALE lOJ 

Other private schools are advertising open air classrooms, e. g., the 
Horace Mann School, the Packer Institute of Brooklyn and the 
Brooklyn High School. 

All measures to preserve the purity of air and its freedom from 
dust should be rigidly enforced in schools. Bad ventilation is the rule 
except in the most modern school buildings. After two hours the air 
is depressing and carbonic acid is usually found in excess. The 
problem of how to deal with dust is a difficult one in schools, owing 
to the expense of really efficient methods. The floors should not 
have open crevices and dry sweeping should not be allowed. Sweep- 
ing with wet saw dust is probably the most effective, and at the 
end of each term a thorough bacteriological dust disinfection should 
be carried out by the Department of Health. Dr. J. H. Lowman, 
of Cleveland, who has instituted great reforms in the hygiene of 
the schools of that city, recommends not formaldehyde, but that the 
walls should be cleaned or painted, the furniture washed and the 
floors treated with dilute solutions of chloride of lime. 

We recognize tuberculosis to be one of the greatest dangers to 
school children, for at the tenth year the Prussian statistics show 
that out of lOO boys who die, 9.26 die of tuberculosis, and out of 
100 girls, 12.02 die of tuberculosis ; hence the importance of all hygr- 
enic safeguards against this malady. 

Tracheo-bronchial tuberculosis and tuberculosis of the lymphatic 
system are the forms most commonly encountered and strict medical 
inspection will reveal large numbers of children for whom fresh air 
schools or sanatorium schools should be provided. In New York 
City, out of about one hundred thousand children examined in 1905- 
1906, over one thousand were found to have pulmonary disease, and 
in almost every case it was the first intimation to the mother that her 
child had pulmonary tuberculosis. 

Besides the Waldschule of Germany there are specially constructed 
sanatorium schools in Milan, Italy, and vacation colonies have been 
established near Geneva, the Swiss Government supplying the 
teacher while philanthropy supports the schools. In Denmark, 
where the outing vacations are so thoroughly systematized, the 
teachers are supplied by the state. The United States show prom- 
ise of carrying out this enlightened method of dealing with the 
tuberculous problem. Outdoor schools are conducted successfully 
in connection with private camps for boys and girls. Many of these 
are in New Hampshire and Maine, in the vicinity of the Rangeley 
Lakes, and in Oxford County. 



I08 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

IMPORTANCE OF VENTILATION 

The first desideratum in tuberculo-therapy and in the prevention 
of tuberculosis is abundant and free ventilation. The dwelling, the 
bedroom, the workshop, the office, the church, the schoolroom, the 
theatre, the modern subway are one and all dangerous in proportion, 
as their atmosphere is composed of dead or rebreathed air. Not 
only is tuberculosis favored by unhygienic surroundings and vitiated 
atmosphere in particular, but no other agent, not excepting alcohol 
and bad food, so surely undermines the constitution and renders 
it unable to resist disease. Air that has once been breathed, ought 
not to be breathed again. Out of doors the danger is minimized ; 
indoors we usually breathe and rebreathe the contained air again 
and again. To some extent, of course, this cannot be avoided, but 
we should endeavor to reduce it to a minimum. This subject has 
been recently investigated by Dr. Thomas R. Crowder, who studied 
by ingenious methods the elTect of such factors as change of posi- 
tion, body motion, different types of breathing and different tempera- 
tures and, in addition, has determined the conditions that obtain on 
the sleeping porch and in the open air. Nasal breathing was the 
type examined, since in mouth breathing there is, under favorable 
circumstances, little reinspiration." 

The conclusions that may fairly be drawn from Crowder's work are 
that (i) a person remaining quiet and indoors will immediately rebreathe 
from I to 2 per cent of his own expired air; (2) when lying in bed the 
percentage is higher, rising to from 4 to 10 per cent, depending on the position 
assumed wh'ile sleeping. " Nor does sleeping in the open insure pure air 
for breathing. The same influences here produce the same relative results 
that they do inside. When one buries his head betw^een pillow and bed clothes 
for the sake of warmth, reinspiration is inevitable, and it is not necessarily 
small in amount." In addition, it must be noted that at each inspiration we 
reinhale not only some of the air just exhaled, but also the air contained in 
the nose and larger bronchi — the so-called " dead-space " air. This may 
amount to one-third of the whole volume in quiet inspiration and not less 
than one-tenth in deep breathing. 

The significance of this study in connection with questions of ventilation 
is obvious. Since even under the most favorable conditions we cannot avoid 
drawing back into the lungs some of the air that has just passed out of them, 
not much importance can be attached to the slight variations in carbon 
dioxide content which occur in the air of rooms. 



^ The Reinspiration of Expired Air. Archives of Internal Medicine, Chi- 
cago, October, 1913, p. 1936. Journ. Amer. Med. Ass., Editorial, Nov. 29, 1913, 
p. 1986. 



NO. I AIR AND TUBERCULOSIS HINSDALE IO9 

OPEN AIR CHAPELS AND THEATRES 

It is remarkable how inconsistent we all are in matters of hygiene. 
Medical men are often among the worst ofifenders. Their offices 
are commonly stufify, their conventions and social gatherings are 
often held in inadequate halls in which vitiated air, sometimes reek- 
ing with smoke, is perfectly abominable. 

If to do were as easy as to know what 'twere well to do 
Then chapels had been churches and poor men's cottages princes' 
palaces. 

We cannot go back to the time of the Druids or worship in 
groves after the manner of the Greeks, but it seems fitting here to 
call attention to one chapel that has been specially constructed for 
out-of-door worship and that is destined to be a model for many a 
sanatorium at least. This has been constructed for the famous 
King Edward VII Sanatorium near Midhurst, in Sussex, England. 
The accompanying illustration of this unique chapel marks a step in 
advance in sanatorium construction. It is in the Moorish style, 
shaped like a broad letter V. The double rows of coluinns of the 
cloister are on the southerly side, the pulpit and chancel are in the 
apex and the northerly sides forming the inner walls are provided 
with arched apertures so that the patients may sit absolutely in tjie 
open air but with sufficient protection from the weather at all seasons. 
In fair weather services are held under the sky in the open space 
in front of the building between its extended arms. The illustra- 
tion shows this very beautifully. 

Open air theatres were built by the Greeks and Romans and the 
remains of these structures are among the most interesting of ancient 
ruins. In Europe the Passion Play at Bayreuth is enacted wholly out 
of doors, but is entirely apart from our subject except so far as it 
demonstrates the possibilities of out-of-door representation. The 
low theatre and concert hall are invariably hot and stuffy and un- 
doubtedly foster tuberculosis by inadequate ventilation. It would be 
better if we could have some theatres or assembly halls with per- 
fectly free circulation of air. 

The Groton School in Connecticut has lately undertaken to build 
an outdoor gymnasium, so that the boys shall have the advantage of 
exercise in the open air rather than in an enclosed building. This is 
the first school we know of to adopt this admirable plan. 

VENTILATION OF DWELLINGS 

Ordinary dwellings are terribly deficient as regards ventilation. 
The country dwellings of the poor are strangely defective in this 



no SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

respect. It has been said that the reason why the air in rural dis- 
tricts is so pure is that the poor country people have all the bad air 
shut up in their houses. There is a great deal of truth in this. 
Doctors are constantly struggling with the strange aversion that 
the rural population has regarding sufficient air in the bedrooms. 
As soon as night falls the windows and doors are tightly closed and 
the kerosene lamp adds to the pollution of the air. It is a common 
experience to find the doors and windows kept closely shut owing to 
the deeply rooted fear of catching cold. In European countries the 
windows of many of the older dwellings were originally intended for 
light and not for air, and are merely panes of glass built into the wall 
and not intended to be opened. Others are so badly constructed that 
the upper sash cannot be lowered and the lower sash is scarcely ever 
raised more than a few inches. 

The children in. many country cottages instead of being rosy and 
robust, as they should be with healthy surroundings, are frequently 
pale and bloodless on account of this bad air. This deticient venti- 
lation of country houses and the bad food so common, where milk 
and eggs ought to be so plentiful and good, conspire to give to some 
country populations a bad start in the earlier years. No better ex- 
ample can be cited than that of the " poor whites " of the Southern 
United States. Indolence, ignorance, general helplessness and 
inertia are their characteristics. Their children are pale and gaunt, 
and their living quarters are horrible beyond description. It is a 
wonder the death rate among them is not greater than it is.' 

It seems very strange, but it is a fact, that about seventy years 
ago a proposition was made to use the Mammoth Cave in Ken- 
tucky as a winter resort for invalids. Sixteen consumptives were 
sent there to gain the reputed benefit from the equable temperature 
and asserted purity of the air in that cavern. Five of these patients 
died and the others were injured as a result of the darkness and 
dampness combined. That such an irrational and cruel experiment 
should have been tried seems incomprehensible at the present day.^ 



' The death rate from pulmonary tuberculosis for Virginia during the year 
ending June 30, 1913, was for whites 98.4, and for colored 256 per 100,000. 
The state rate was estimated at 148. 

" See Croghan : The Mammoth Cave as a Winter Resort for Invalids (Bos- 
ton Medical and Surgical Journal, 1843, Vol. 28, p. 188). 

Daniel Drake, M. D. : Western Journal of Medicine and Surgery, Louis- 
ville, Kentucky, 1843, Vol. 7, p. 78. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 42 




OPEN AIR DINING HALL. DR. WALTHER'S SANATORIUM. NORDRACH-COLONIE, BLACK 
FOREST, GERMANY 




LAWN CUTTING.' ^GRADUATED LABOR IN PULMONARY TUBERCULOSIS. SANATORIUM OF THE 
BROMPTON HOSPITAL, FRIMLEY, ENGLAND 



NO. I AIR AND TUBERCULOSIS — HINSDALE III 

CHAPTER VIII. EXERCISE IN TUBERCULOSIS; GRADUATED 

LABOR 

The Nordrach system of treatment of pulmonary tuberculosis car- 
ried out by Dr. Walther and that of his predecessor, Dr. Brehmer, 
at Goebersdorf, in Silesia, involves much exercise in addition to 
fresh air and alimentation ; the Dettweiler system enjoins rest in 
the open air with superalimentation. McLean's dictum is: " If the 
phthisical patient would live, he must work for it." ^ Probably this 
advice should not be taken too literally, at least by every tuberculous 
patient ; but graduated physical exercise has a very important and 
useful place in the treatment of most patients. Brehmer advocated 
hill-climbing, while Walther advises graduated walking exercises, 
in some cases to the extent of walking twenty miles a day. Whether 
one practices walking, or hill-climbing or graduated labor, we cannot 
dissociate from these measures the effect of atmospheric air, in its 
various qualities, upon the lungs and the accompanying stimulation of 
the pulmonary and general circulation. Two recent papers by London 
practitioners are full of such suggestive thoughts on this subject that 
we call special attention to them. They are considered by some as 
marking an epoch in the treatment of pulmonary tuberculosis. 

At a meeting of the Medical Society of London, January 13, 1908, 
Dr. Marcus S. Paterson, the Medical Superintendent of the Bromp- 
ton Hospital Sanatorium, at Frimley, read a paper on " Graduated 
Labor in Pulmonary Tuberculosis " which was supplemented by an- 
other on the " Effect of Exercise on the Opsonic Index of Patients 
Suffering from Pulmonary Tuberculosis," by Dr. A. C. Inman, Super- 
intendent of the Laboratories, Brompton Hospital.* 

The patients for whom Paterson instituted graduated labor were 
selected cases sent from the Brompton Hospital in London to its 
Sanatorium at Frimley, at an elevation of 380 feet in the country. 

He was induced to carry out this plan of treatment after seeing 
tuberculous patients who did well while working under unfavorable 
surroundings ; but he believed that under careful regulation of labor 
and with very careful observation of the temperature records, he 
might safely proceed. The exercises adopted involved all the 
muscles of the trunk and extremities and this was thought to be 
better than walking exercises in which the lower limbs were chiefly 
employed. The use of the upper limbs seemed more likely to favor 



^ McLean : Personal Observation in Phthisis Pulmonalis (Journal Amer. 
Med. Ass., February, 1898). 
^ The Lancet, January 25, 1908. 



112 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

the. expansion of the lungs. It was not forgotten that the common 
objections to this plan of treatment are, (i) that the disease would 
become active again under the strain; and (2) that the exertion 
would tend to produce hemoptysis. Considerable tact and personal 
influence must have been exerted to get the patients to carry out a 
plan which involved increasing labor and measures that are generally 
considered positively harmful. 

The first exercise ordered was walking, the distance being gradu- 
ally increased up to ten miles a day. When a patient had reached 
this stage he was given a basket in which to carry mould for spread- 
ing on the lawns. No case of hemoptysis or of pyrexia occurred 
among these patients. When they had been on this grade with noth- 
ing but beneficial results for from three weeks to a month, they 
were given boys' spades with which to dig for five minutes followed 
by an interval of five minutes for a rest. After a few weeks, several 
of the patients on this work, who were doing well, were allowed to 
work as hard as possible with their small spades without any inter- 
vals for rest. As they had all improved on this labor larger shovels 
were obtained, and it was found that the patients were able to use 
them without the occurrence of hemoptysis or a rise of temperature. 
About this time many of the patients were feeling so well that it be- 
came necessary to restrain them from doing too much. 

These results in a few cases creates a most favorable sentiment 
among the other patients so that the system was extended generally, 
with great care and minute supervision. Harder work was pre- 
scribed for patients who could be trusted even to the use of spades, 
shovels and five "pound pick-axes. The patients all expressed the 
opinion that the work did them good and that the harder they 
worked the better they felt. Many patients have written to Dr. 
Paterson to say that they date their improvement from the com- 
mencement of the labor, and that they think the hardest work did 
them the most good. It certainly speaks well for the strict supervision 
of these patients that no accidents occurred of a serious nature, 
though several developed fever and, subsequently, pleurisy. One 
patient was laid up for two months and was much worse at the end of 
that time, though eventually he did well and returned to work, though 
the extent of his disease was increased through overexertion. 

The suitability of cases for graduated labor rests on a very careful 
physical examination, importance being laid on the general muscular 
and physical development. Marked wasting and poor development 
is, naturally, a bar to this method of treatment. The resisting power 




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NO. I AIR AND TUBERCULOSIS — HINSDALE II3 

of a patient with a very limited lesion is an unknown quantity and 
has to be determined, whereas a patient with a lesion involving four 
lobes may remain at work for some time and exhibit a good initial 
resisting power. 

Dr. Paterson lays very great stress on the temperature taken in the 
mouth. If this is or has been 99° F. or over during the week 
preceding admission to the sanatorium, the patient is put to bed 
after the journey. So long as the temperature remains at 99° F. 
in the case of men or 99.6° F. in the case of women, the patient 
is not allowed up for any purpose. So long as the temperature is 
unaffected by exertion the patient is gradually allowed up for longer 
and longer periods. Patients with apparently limited disease, but 
who are in poor general condition and without fever, are allowed 
to be up all day, but are not permitted to take further exercise 
than is entailed by walking to and from the dining hall for their 
meals. The remainder of the day is spent in resting. As their con- 
dition improves they are allowed to walk half a mile a day, and so 
on, until a distance of six miles a day is reached. The rate of in- 
crease in the amount of exercise depends upon such factors as the 
patient's disposition, weight and appetite. 
The grades of work are briefly as follows : 
(A i) Walking from one-half to ten miles daily. 

( 1 ) Carrying baskets of mould or other material. 

(2) Using a small shovel. 

(3) Using a large shovel. 

(4) Using a five-pound pick-axe. 

(5) Using a pick-axe for six hours a day. 

Patients in grades i, 2, 3, and 4, work four hours a day. 

The basket work in which about eight pounds of earth are carried 
is considered the most important and, as a rule, patients spend far 
more time in this work than in any other. It brings into use all the 
muscles. 

Work has a wholesome effect on the mind. If the patient is at 
first sullen and apathetic, the improvement in physical condition 
quickly begets a lively and cheerful mental attitude, and one that 
seeks work rather than to shirk it. 

During 1905 and 1906 the number of patients discharged from 
this sanatorium was 164, and they all returned to their previous 
occupations, whatever they happened to be, and not to light, outdoor 
work. They were fitted by the line of treatment which we have de- 
scribed for effective wage earning. 



114 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

We have dwelt quite fully on this innovation in tuberculo-therapy 
because it gives promise of good, practical results and, further, be- 
cause it is so radically difit'erent from the prevailing methods adopted 
in most sanatoria. But, the most interesting feature is the explana- 
tion which is ofit'ered to account for the benefits which has accrued. 
This explanation is set forth in an elaborate study made by A. C. 
Inman, M. B., the superintendent of the laboratories of the Bromp- 
ton Hospital, on the " Effect of Exercise on the Opsonic Index of 
Patients Suffering from Pulmonary Tuberculosis."^ 

This study of Inman's was prompted and made possible by the 
brilliant work of Sir Almroth Wright. Wright showed in his Har- 
veian Lecture in New York, that there are three great agencies by 
which immunizing responses can be evoked in the organism; 

(i) By the inoculation of bacterial vaccines. 

(2) By artificially induced auto-inoculations. 

(3) Ey spontaneous auto-inoculations. 

Wright had previously elucidated the subject of vaccine therapy 
by constructing curves from the opsonic indices of patients vacci- 
nated against their infection and in this manner traced a definite 
train of events which follow upon a single inoculation. The succes- 
sive phases were termed the negative phase, the positive phase and 
the phase of maintained high level. Freeman, working in Wright's 
laboratory, then took up the subject of massage in its efifect on gono- 
coccal joints showing that "Auto-inoculations follow upon all active 
and passive movements which affect a focus of infection and upon 
all vascular changes which activate the lymph-stream in such a 
focus." 

Wright's dictum was that " where in association with a bacterial 
invasion of the organism bacteria or bacterial products pass into 
the general lymph, and blood-stream, intoxication effects and im- 
3iiunizing responses, similar to those which follow upon the inocula- 
tion of bacterial vaccines, must inevitably supervene." It is a per- 
fectly logical conclusion, then, that nature cures bacterial infections 
through such auto-inoculations. Inman set himself to find out what 
the body is doing of itself and what value extraneous circumstances, 
such as physical exercise, have in aiding these attempts on the part 
of the body. Inman's work was conducted on a carefully planned 
technique, controlled and checked at all points, using forty-three 
patients in the sanatorium treated by the System of Graduated Labor. 

Inman found that in 41 out of 43 cases the opsonic index w^as at 



' Read before the Medical Society of London, January 13, 1908. 







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NO. I AIR AND TUBERCULOSIS HINSDALE II5 

some time of the day well above the normal, and what is of even 
more importance, in no case did the exercise, even though severe, 
lower the index below the normal line — that is, the auto-inoculation 
was never so great as to produce a negative phase and, therefore, 
never in excess. 

It was observed during these investigations that in some bloods examined, 
tuberculo-agglutinins appeared in association with the immune tuberculo- 
opsonins. This must be taken as another evidence of an immunizing response 
on the part of the organism. When the difficulties of such a method of treat- 
ment and the danger of the weapon employed are taken into consideration 
It will be readily understood that every now and then, in spite of the most 
careful supervision, an excessive auto-inoculation must take place. Such an 
over-dose is readily recognized clinically. A patient doing well on the ■ 
grade of work prescribed for him and with no abnormality of temperature 
suddenly complains of feeling tired, of loss of appetite and of headache; 
and the temperature chart registers an elevation to 99° or 100° F. These 
are precisely the symptoms which are found during the negative phase after 
an excessive dose of bacterial vaccine. 

Thus we have a new scientific test by which the efifect of physical 
exercise on the blood of patients has been traced. As Inman says : 

The opsonic index has shown that the exercise has supplied the stimulus 
needed to induce artificial auto-inoculation, and that this systematic gradua- 
tion has regulated this in point of time and amount. This co-operation with 
the natural efforts of the blood has enabled Dr. Paterson to send his patients 
back to their accustomed work, however hard it may be. But the investigation 
has done more than explain a successful mode of treatment. Dr. Paterson 
agrees with me that with the aid of the opsonic index he can regulate the 
stimulus with scientific accuracy and obtain his results more certainly and 
more rapidly. This, of course, involves work in the laboratory. But it also 
means a more rapid and a more certain discharge of the patient which is the 
main object of the sanatorium. 

Fresh air, exercise, and proper food seem then to constitute the 
foundation of successful treatment of tuberculosis. The improve- 
ment of the general condition of the patient and life in the open air 
evidently needs to be supplemented by certain exercise so as to pro- 
duce a series of auto-inoculations and probably the best method yet 
devised is by the system of graduated labor just described. 

All sorts of exercises such as horseback riding, golfing, light 
dumb-bell exercises and other calisthenics have been practiced for 
many years in treating tuberculosis ; walking exercises have been the 
feature of some of the German sanatoria referred to ; patients sent 
to the western states and territories almost invariably practiced out- 
door exercises, some with great harm and some with benefit. 
Neither physician nor patient in most instances regulated these exer- 



Il6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

cises intelligently, but groped in the dark, never dreaming of the 
underlying principles as explained by laboratory studies of Sir Alm- 
roth Wright, Paterson, Inman, and others. We trust that further 
studies and the application of the same method in Europe and 
America will fix the value of exercise in tuberculosis. 

A somewhat similar system of graduated labor has been adopted 
in the King Edward VII Sanatorium near Midhurst, England. 
Light work in the gardens and grounds is prescribed in lieu of some 
of the walking exercise and forms part of the regular treatment. 
Practical gardening in the grounds and flower beds is utilized. The 
lightest labor consists of weeding, hoeing and edging paths and bor- 
ders, gathering seeds, plucking dead flowers, pruning, etc. Some- 
what harder exercise consists in wheeling soil to the lawns and 
spreading it, clearing ground of stones and taking them away in 
barrows, and in leveling new ground after being broken up. The 
heaviest work is that of digging and trenching unbroken ground, 
moving, rolling, etc. Paths through the pine woods have also been 
constructed. In this particular work the breaking up of the ground 
with picks and clearing away the roots from neighboring trees was 
allotted to the first division of patients. The second division cleared 
away the broken ground and roughly leveled it. The third division 
finished the leveling of the paths with rakes and tidied up the edges.* 

Free patients at the King's Sanatorium have made a cinder tennis 
court ; they have cut down and sawed fire wood ; they have an open 
air carpenter shop and an instructor in carpentry, who is himself a 
patient ; they care for the poultry and make the runs for the fowls. 
In this way patients are constantly occupied. 

Although the system of graduated exercises, or labor, adopted 
at the sanatoria referred to, has attracted wide notice and its princi- 
ples were there first placed on a highly scientific basis, there were 
previous attempts to do this in an intelligent and rational manner. 
Sir Robert Philip, at Edinburgh, over twenty years ago, before the 
bacteriology of tuberculosis had been so well developed, prescribed 
practically the same thing as a therapeutic measure of definite dos- 
age. He had had classes of selected patients who came at fixed 
hours to take regular training with regard to posture and healthy 
respiratory movement. More especially the young were taught the 
value of a healthy form of chest, the principles of nose-breathing 
and full diaphragmatic movement. " In addition to this, meas- 
ured walks of varying amount and gradient were prescribed exactly 



* Noel Dean Bardswell, Tuberculosis, Berlin, May, 1908. 



NO. I AIR AND TUBERCULOSIS — HINSDALE 11/ 

as we prescribe medicines. Thus we had walks radiating from the 
dispensary round the meadows, walks over the Bruntsfield Links 
and walks in various directions on the slopes of Arthur's Seat. The 
patients reported, at successive visits, their experience in carrying out 
such instructions and notes were made of the effects produced." 
Here we see the germ of the class method so well developed and 
practiced by Pratt, of Boston, although he is an apostle of rest 
rather than labor. 

The results in Philip's hands were eminently satisfactory. " The 
patients did remarkably well and no accident was traced to the 
adoption of active movement instead of rest. The experience led to 
a change in my outlook in relation to the meaning of treatment in 
tuberculosis." Philip came to the conclusion that by the establish- 
ment of hospitals or sanatoria for patients in the earlier stages of 
tuberculosis " we might hope to achieve permanent cures to a degree 
not dreamt of, by elaboration of the principle of regulated exercises 
and graded activity of all kinds." These conclusions were justified 
by the results obtained " in the home treatment undertaken for so 
many years at the Victoria Dispensary and in the systematized 
regime of work at the Royal Victoria Hospital and the recently 
opened Farm Colony." 

Sir Robert Philip lays great stress on the well-known fact that 
there is a progressive intoxication in tuberculosis and the toxins pro- 
duced by the tubercle bacillus appear to exert their vicious influence 
particularly on the neuromuscular apparatus. The toxin is especially 
a muscle poison.^ There is a visible and palpable progressive wasting 
of the muscles, both of the trunk and the extremities, with advancing 
flaccidity and increased myotatic irritability. It is an expression of 
malnutrition, a muscular dystrophy dependent on intoxication. The 
obvious conclusion is that by the institution of natural movements 
the physiologic cure of " recreation " is assisted and health gradu- 
ally returns. 

Sir Robert's scheme of physical treatment at the Royal Victoria 
Hospital is worthy of mention. On admission each patient is placed 
at complete rest. During this stage, in addition to minute examina- 
tion of every organ, the patients general condition is carefully ob- 
served. According to the estimate which is made the length of the 
resting period is fixed. Thereafter, in the absence of counter-indica- 
tion, the patient is gradually advanced through the other stages. 



^R. W. Philip, Trans. International Med. Congress, Washington, 1887, 
Vol. I, p. 205. 



Il8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The dose of exercise is increased or diminished as the temperature 
chart, pulse rate and other indications suggest. A colored badge is 
given to the patient to denote the stage he has reached. 

I. Resting Stage, as noted above. (White Badge.) 

II. Stage of Regulated Exercises. (Yellow Badge.) This includes (i) 
walking % to S miles; (a) on the level; (b) on sloping ground. (2) Various 
respiratory exercises once or twice a day. (3) Other forms of movements 
to improve carriage of shoulders, head, chest, etc. 

III. Stage of Regulated Work. (Pale Blue Badge.) 

IIIA. Picking up papers, leaves and other light rubbish on the grounds; 
knitting; sewing; drawing. 

IIIB. (Green Badge.) Emptying waste garden boxes and assisting to carry 
away rubbish. Carrying light baskets for various garden purposes. Light 
painting work, wiping shelters ; setting tables and laying cloth in patients' 
dining room; cleaning silver, brasses, taps, etc. 

inc. (Deep Blue Badge.) Raking, hoeing; mowing; sweeping leaves; 
light wheel-barrow ; heavier painting work ; sweeping shelters ; scrubbing 
floors ; cleaning knives ; assisting in laundry ; washing dishes. 

HID. (Red Badge.) Digging; sawing; carrying heavy baskets for various 
gardening purposes; wheeling and drawing full wheel-barrow and other 
heavy gardening work. Window cleaning and polishing floors ; sweeping 
and cleaning court yard. Carpentering; joinering; engineering; attending 
boiler; errands. 

An institution providing diversified occupations has a great advan- 
tage over one w^hose patients are restricted to walking exercises and 
where the women are employed in kitchen work and the men as 
laboratory orderlies, assistants in the drug rooms, clerks and so on. 
It is well to vary the walking exercise with manual labor. Patients 
welcome it and take a great interest in the various occupations they 
are put to. They acquire confidence in themselves as they see their 
muscular tone improving and some prospect of resuming useful 
occupations. 

With various modifications suggested by local conditions the sys- 
tem of graduated labor described above is now adopted at various 
institutions in America ; in many cases, however, the economic aspect 
of the plan of treatment apparently overshadows the therapeutic 
features ; probably the best examples of the method are at the Loomis 
Sanatorium, New York, Otisville State Sanatorium, New York, The 
Adirondack Cottage Sanitarium, New York, The North Reading 
State Sanatorium, Massachusetts, and The Barlow Sanatorium, Los 
Angeles, California. Dr. Barlow has kindly sent me the following 
description of the method he has carried out : 

This institution is semi-charitable and re^ceives cases in all stages. 
You ask me to send you a statement of our use of graduated labor. I will 
give you the facts as we handle the matter, which is somewhat modified to 







:f 



*\ 







NO. I AIR AND TUBERCULOSIS — HINSDALE IIQ 

meet the needs of our institution. It seems to me that every institution must 
modify this according to the facilities at command. Our working plan is as 
follows : 

All the patients without any fever are kept absolutely quiet for the first 
two or three weeks, except that they are allowed to go to the dining room 
for meals. If, during this time, there is no elevation of temperature, no 
marked acceleration of pulse, and no loss of weight, they are started on exer- 
cise, beginning with ten minutes' walking twice a day. If they continue to do 
well, gain weight, temperature remains normal, and progress of physical signs 
is favorable, then exercise is increased every two weeks. The amount of 
exercise is charted for each patient ; one copy posted on the bulletin board, 
and one copy retained by the nurse in charge of the order, to check up the 
allowance for each patient. Patients who have more than ten minutes' exer- 
cise twice a day make their own beds and keep their rooms in order, except 
the heavy cleaning. After patients have reached an allowance of thirty 
minutes twice a day, they are assigned to more practical work about the 
place or grounds. In making these assignments, the patient's physical condi- 
tion and progress, former, and probably future, occupation are considered. 
Most of these assignments are changed each month, the effort being to try to 
increase the work each month. The work done includes the setting of tables 
in the dining room, removing and washing dishes, work in the diet kitchen, 
looking after books and pamphlets in the library, cataloguing books, statisti- 
cal work, stenography and typewriting, carrying mail, light repairs about 
buildings, care of paths and summer-houses, sprinkling during dry weather, 
and operating the incinerator. Many patients are assigned to flower beds of 
their own, or to doing light work in caring for the sanatorium grounds. In 
carrying out this exercise or labor, careful watch is kept over patients, and 
if any elevation of temperature, acceleration of pulse, or extension of physical 
signs are observed, they are put back to rest. The purposes that this exercise 
and labor seem to serve are, recreation, stimulating the appetite and digestion, 
building up healthy tissue, inducing healthy sleep, and testing the patients 
against relapses when they resume their normal way of living after being dis- 
charged. We find that patients who accept the occupation cheerfully make 
better progress mentally and physically than those who resent being assigned 
to duties. 

For patients with an elevation of temperature 99° or over, acceleration of 
pulse, either loss or no gain in weight, or who do not show improvement in 
other ways, rest is continued, and exercise or assigned work is deferred. 

At the present time (December 11, 1913), there are 43 patients in the 
sanatorium. Ten are in the infirmary ; thirty-three in open-air cottages ; of 
the latter twenty-seven are doing their own work, and twenty-five additional 
assigned work. Of the six in open air cottages not doing their own work, 
three are new patients who have been recently admitted and not under obser- 
vation a sufficient time for report. 

REFERENCES TO WORKS ON EXERCISE AND WORK 

Sir Robert W. Philip: Rest and Movement in Tuberculosis (British Medi- 
cal Journal, December 24, 1910). 

Albert Robin: How Consumption is Cured by Work (Therapeutic Gazette, 
December, 191 1, p. 854-865). 



I20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Lawrason Brown and F. H. Heise : Properly Regulated Rest and Exercise 
in Pulmonary Tuberculosis (Journal of the Out-Door Life, August, 1912). 

J. W. Flinn: Rest and Repair in Pulmonary Tuberculosis (Journ. Amer. 
Med. Ass., Aug. 16, 1913, p. 466). 

L. Teleky: Choice of Occupation with Regard to Tuberculosis (Wien. 
klin. Wochnschr., March 13, 1913; abstr., Journal Amer. Med. Ass., April 26, 
1913, P- 1336). 

S. R. C. Halcomb: Graduated Labor in Pulmonary Tuberculosis (Military 
Surgeon, February, 1913 ; abstr., Journ. Amer. Med. Ass., Oct. 26, 1912, p. 
1564). 

J. W. Allan: Graduated Labor at Bellefield Sanatorium (Glasgow Med. 
Journ., January, 1911; abstr., Journ. Amer, Med. Ass., Feb. 4, 1911, p. 384)- 

A. P. Francine : Rest, Exercise and Food in the Management of Tubercu- 
losis (New York Med. Jour., Dec. 31, 1910; abstr., Journ. Amer. Med. Ass., 
Oct. 29, 1910). 

M. Paterson : Treatment of Pulmonary Tuberculosis by Graduated Rest 
and Exercise (Practitioner, January, 1913). 

C. C. MacCorison and N. B. Burns: Method of Recording Exercise Data 
in Sanatorium for Consumptives (Boston Med. and Surg. Journ., May 9, 
1912). 

CHAPTER IX. ACCESSORIES FOR THE FRESH AIR TREAT- 
MENT OF TUBERCULOSIS 

It would be impossible to carry out the fresh air treatment of 
tuberculosis without some special facilities or accessories. These 
vary somewhat in accordance with the plan of treatment, whether 
singly or collectively ; or in cities, forests, or plains. Among these 
accessories we include : ( i ) Tents ; pavilion tents. '(2) Tent houses ; 
shacks, "lean-tos." (3) Disused trolley cars. (4) Balconies or 
leigeterrasse for day use. (5) Day camps. (6) Sleeping porches 
or balconies. (7) Wooden pavilions. (8) Glass pavilions. (9) 
Hospital roof wards. (10) Detached Cottages. (11) Sleeping 
canopies. 

Tents. — Tents have the advantage of low cost, portability, and the 
fact that they are adapted for almost any locality, whether in the 
city, the forest, or the plains. In the city a tent for the use of a 
tuberculous patient usually attracts too much notice and unfavorable 
comment unless placed in a rural district. It is possible, however, 
to erect tents in the heart of a great city, hundreds of feet above the 
ground where an abundance of pure air and sunlight are obtained. 
The modern hotel or ofBce building can furnish a far better site, in 
these particulars, than many rural districts. The author is not aware 
of any extensive use of tall buildings for the treatment of pulmonary 
tuberculosis, but it would seem to be an entirely feasible proposition. 




< o 

I- CD 

ir 

O d 



NO. I AIR AND TUBERCULOSIS — HINSDALE 121 

Anyone who will read the interesting story by Van Tassel Sutphen 
entitled " The Negative Pole," ' will find the history of an interesting 
case of pulmonary tuberculosis cufed by residence of eighteen months 
on the top of a modern " skyscraper," The patient had been advised 
to remove to Arizona, but circumstances made this advice impossible 
to follow ; as an alternative measure he isolated himself almost en- 
tirely from the world in the midst of a metropolis, and was rewarded 
by a complete cure. The imaginative author of this original story 
assigns to the patient a much more difficult role than need be assumed 
by anyone who may follow the general line of treatment and perhaps 
we may hear of many who may be encouraged to carry out the plan 
suggested. 

In the forest during the warmer season tents are almost indispensa- 
ble. A substantial tent properly erected, protected with a " fly " and 
with a surrounding trench to provide for excessive rainfall, can be 
made a comfortable and healthful habitation during a large part of 
the year. 

The ventilation of tents, and their heating in cold weather, have 
received a great deal of study, and as they are perfected in these 
respects their suitability for a continuous residence throughout the 
year has been proved. Tents can be made storm proof and almost 
as comfortable in stormy weather as an ordinary building. On 
Blackwell's Island and on Ward's Island, New York City, tents are 
in constant use, with astonishing success for tuberculous patients. 

At the Manhattan State Hospital East, for the insane, Ward's 
Island, New York City, the late Dr. A. E. Macdonald instituted, in 
1901, a tent colony for the tuberculous patients. 

This experiment resulted most favorably and led to the extension 
of the outdoor treatment to other classes of the insane besides the 
consumptives. For thirteen years the consumptive insane on Ward's 
Island have been treated in tents and pavilions. Tuberculous infec- 
tion has been removed from the wards and 11.39 P^^ cent of patients 
are reported to have had their tubercular disease arrested. They 
almost invariably gained flesh ; one is reported to have gained 79.5 
lbs, (Eighth Annual Report, Manhattan State Hosp., New York.) 
In the Eighth Annual Report the following comment is made : " In 
our experience the winter months have proven to be the most favor- 
able for these patients, despite popular opinion to the contrary, and 
likewise it is seen that the summer month of July was in a decided 
manner proven to be the least favorable of the year." 



^ Harper's Magazine, July, 1908. 



122 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

The accompanying illustrations show fully the initial stage of this 
experiment in a portion of New York City having many natural 
beauties. But in the course of time it was apparently realized that 
the same results might be obtained with other structures of a more 
permanent character and I am informed by Dr. William Mabon, the 
superintendent and medical director, that the tents have been replaced 
by wooden and glass camps. The reason for this change is that 
the tents were found to be very close and unsatisfactory in wet 
weather, whereas the wooden camps can be opened and ventilated 
under all conditions of weather. 

Pavilion Tents.— On Blackwell's Island, New York, the Metropoli- 
tan Hospital makes use of twelve paviHon tents with a capacity for 
142 patients. Steam pipes are arranged in a double circuit and in 
some cases stoves render these pavilion tents comfortable in winter 
and were preferred by the majority of the patients, in the coldest 
weather, to the ordinary quarters in the main building of the hos- 
pital. These pavilion tents were devised by Dr. A. M. Holmes, of 
Denver. 

The tent devised by Dr. Charles Fox Gardiner, of Colorado 
Springs, is largely used in western sanatoria and has some notable 
advantages. It is of conical shape, like the Sibley army tent, with 
a ventilator at the apex of the cone which may be opened or shut. 
The board floor has an air space beneath and air inlets opening 
at the floor between the interior wainscoting and the tent wall 
supplying air at the height of three or four feet above the floor. 
This is an improvement over the method of allowing air to enter 
at the floor. These inlets are controlled by hinged lids. This tent 
avoids the use of a center pole, pegs, or guy-ropes, as it is sup- 
ported by two-by-four-inch timbers reinforced by angle irons and 
plates. This tent costs from $90 to $100 and is thoroughly practical. 
It is not unlike the Nordrach tent. (See plate 55.) 

The tent devised by Dr. H. L. Ulrich, of Minneapolis, is simpler 
and less expensive. It consists of a wall tent with ridge pole for the 
tent, and another 12 inches clear above it for the " fly." There 
are ventilating openings on either side of the tent ridge. The tent 
and "fly" are secured by guy-ropes and pegs and all four sides 
may be rolled up and lowered as required. A stove may be used 
in cold weather. A tent 10 by 12 feet costs $22.50. 

Other excellent tents have been devised by Prof. Irving Fisher, of 
New Haven, Dr. Mary Lapham, of Highland, N. C.,' and Dr. James 
A. Hart, of Geneva, New York, and Colorado Springs. 



^American Medicine, Phila., 1905, Vol. 9, 517- 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 53 




FIG. 1. MANHATTAN STATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. 

THE TUBERCULOUS INSANE 



TENTS FOR 




FIG. 2. MANHATTAN blATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. CAMP C, FOR 
DEMENTED AND UNCLEANLY TUBERCULOSIS INSANE PATIENTS 



SMITHSOMA\ MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 54 




yf'^ ^ % 






FIG. 1. MANHATTAN STATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. TENTS FOR 
THE TUBERCULOUS INSANE. SUMMER LOCATION 




FIG. 2. MANHATTAN STATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. CAMP A, FOR 
THE TUBERCULOUS INSANE. SUMMER LOCATION 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 55 




TENT DEVISED BY DR. CHARLES F. GARDINER, COLORADO 
SPRINGS. SEE PAGE 122 




FIG. 2. MANHATTAN STATE HUbHiTAL, EAST, CAMP A. INSANE TUBERCULOUS PATIENTS. 
REVOLVING TENT CONSTRUCTED SO AS TO BE EASILY TURNED IN ACCORDANCE WITH THE DIREC 
TION OF SUN AND WIND. 




2 t- 



- => 5 
5" iLi o 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. t, PL. 57 




— .iMJilMi ««i iHtti 



FIG. 1. MANHATTAN STATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. NEW OPEN 
SHELTER FOR THE TUBERCULOUS INSANE 




FIG. 2. LOOMIS SANATORIUM, SULLIVAN COUNTY, NEW YORK. SLEEPING GALLERY IN 

GUILD LEAN-TO 




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NO. I AIR AND TUBERCULOSIS — HINSDALE I23 

The evolution of the tent and open air shelter into the tent house, 
shack, and cottage, is an interesting feature of the open air treatment 
of tuberculosis. 

"Lean-to." — The open air shelter and "lean-to" are somewhat 
alike. The latter has been long used by sportsmen and others in 
our northern forests, and has been greatly amplified for sanatorium 
purposes. The roof of the " lean-to " slopes directly back from its 
front or there may be a ridge placed close to the front or southerly 
side of the structure. The roof slopes well toward the back, but is 
short in front and allows free access of air and light. Canvass or 
screens are arranged to hang in front as a protection from wind or 
rain, and to insure privacy. For a full description of a " lean-to " 
the reader is referred to Dr. H. M. King's description with plans in 
" Some Methods of Housing," Charity Organization Society, New 
York. 

Excellent " lean-tos " or open air shelters are in use all the year 
at the Royal Victoria Hospital, Edinburgh, Scotland, as seen in the 
illustration kindly supplied by Sir Robert Philip. (See plate 56.) 

Pavilion tents are amplifications of the tent cottage, and are 
adapted for ten or twelve beds. As described by Mr. Homer Folks, 
they are sixteen by thirty-two feet long; the walls are eight feet 
high ; the roof is fifteen feet high at the ridge and the floor of the 
tent is sixteen inches above the ground with free citculation of air 
underneath. 

Tent Houses adapted for use in the New England and Middle 
States are naturally different from those in use in New Mexico and 
Arizona, where rain and snow are uncommon. The accompanying 
illustrations show a row of six tent houses and a single tent house 
at the U. S. Public Health Sanatorium at Fort Stanton, New Mexico, 
for consumptive sailors, under the care of the United States Public 
Health Service. The roof has a slight incline and the sides are ar- 
ranged to give free ventilation as well as shelter when required. 

Trolley Cars. — Superannuated and disused trolley cars were first 
used for tuberculosis patients by Dr. W. H. Peters, of Providence, 
Rhode Island, at the Pine Ridge Camp near that city. With slight 
alterations and at very little expense these cars may serve a useful 
purpose in connection with the outdoor treatment of tuberculosis at 
all seasons. Once located on a convenient site they have many ad- 
vantages over the ordinary shack, affording a maximum of light and 
air and good protection against storms with their adjustable windows 
and doors. The author visited Pine Ridge Camp and can testify to 



124 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

their efficiency ; the camp itself was discontinued after the erection 
of the fine State Sanatorium for tuberculosis at Wallum Lake. 
Trolley cars were also used at the Camp Auxiliary, Montefiore Home, 
Bedford, New York. (See plates 67 and 68.) 

The Balcony, or Liege-terrasse as it is known in Germany, is a nec- 
essary adjunct of any sanatorium for tuberculosis. Plate 71 shows a 
covered or partly sheltered balcony in use at a large private sana- 
torium in St. Blasien in the Black Forest, Germany. Plate 89 shows 
an open or uncovered balcony at the Sharon Sanatorium, Massa- 
chusetts. In June, 1908, the author visited the latter sanatorium with 
the Medical Director, Dr. Vincent Y. Bowditch, and can bear wit- 
ness to the excellent arrangements for the outdoor treatment of 
tuberculosis carried out at this institution. 

The records, now extending over 22 years, show that about 50 
per cent of all cases, and 72 per cent of all incipient cases have been 
arrested or cured.' Of the 160 arrested cases treated between 1891 
and 1906, 133 or 83 per cent were still living and well in 1908, most 
of them house-keepers and wage earners; in addition, 3.7 per cent 
were doing well at last accounts, but were not recently heard from. 

We have given the particulars of these cases treated at Sharon 
Sanatorium because the results are remarkably good being obtained 
at an elevation of 250 feet above sea level, about 15 miles from 
Massachusetts Bay, and about 20 miles from Boston. Sharon is near 
enough to the ocean to be affected by the sea breeze during the hot 
weather. 

Day Camps; Walderholiingstdtten. — The daily care of consump- 
tives at a day camp for the outpatients of a general hospital had its 
origin about the same time in both Boston and Berlin. It was pro- 
posed by Dr. A. K. Stone and Dr. E. P. Joslin in 1905 in Boston, 
and provision was made at the Mattapan Day Camps and at the 
House of the Good Samaritan for ambulatory patients. Plates 72-74 
show how this is carried out. In July, 1908, fifty consumptives too 
ill to be benefited by treatment at the Massachusetts General Hos- 
pital were transferred to the new home of the Boston Consumptives' 
Hospital on the Conness estate, Mattapan, and entered on treatment 
which it was hoped would culminate in their improvement to an ex- 
tent that should warrant their entrance into the state institution. 
They went to the camp in the morning and returned to their homes 



' See V. Y. Bowditch, Boston Medical and Surg. Journ., June 22, 1899. 
See V. Y. Bowditch, Journ. Amer. Med. Ass., Nov. 14, I903- 
See V. Y. Bowditch, Trans. Amer. Climatological Ass., 1907, p. 168. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 93, NO. 1, PL. 




FIG. 1. OLD TROLLEY CAR THAT WAS USED BY MOTHER AND CHILD AT THE PINE RIDGE 

CAMP FOR CONSUMPTIVES, NEAR PROVIDENCE, RHODE ISLAND 

Photograph by Courtesy of Dr. W. H. Peters, Providence 




' # ^ 







1k^ 



fc' 








FIG. 2. ESTES PARK, COLORADO. IDEAL SUMMER RESIDENCE, WITH SPACIOUS PORCHES FOR 
PULMONARY INVALIDS. SLOPING GROUND, SANDY SOIL, MOUNTAINOUS BACK-GROUND AFFORDING 
PROTECTION FROM WIND AND DUST. 

Courtesy of Dr. S. G. Bonney 



NO. I AIR AND TUBERCULOSIS HINSDALE I25 

at night. Those given preference in treatment were patients whose 
dependents, circumstances, and health most demanded it. The new 
hospital and its location are picturesque as well as healthful, and 
patients are able to remain throughout the winter. The main build- 
ing is 125 feet long and contains dining-room, kitchen, examination 
and rest rooms, and has a spacious veranda facing the south. It is 
designed to accommodate 150 patients, in the two pavilions, two cot- 
tages, and children's building. The Day Camp has proved to be a 
great success. 

Day camps, when properly conducted, have an immense value on 
educational lines. In addition they remove for a time the sources 
of infection from the community and from the homes. These 
patients cannot always go to a sanatorium but in this way receive 
proper care during a large part of the day and may eventually avoid 
the necessity of going to a sanatorium ; others who need sanatorium 
care are provided for, pending admission ; and after discharge from 
the sanatorium the camp helps to complete the cure. Dr. Otis does 
not believe that these camps are destined to become a permanent 
therapeutic measure in conducting the cure. 

The best location for day camps is in the forest. In Germany they 
are known as Walderholungstatte and there are over eighty of them 
scattered throughout the Empire. Those who are only slightly af- 
fected with tuberculosis, or are convalescent from it, pass the day in 
camp and return at night to their homes. The accompanying illus- 
tration (pi. ']6^ shows these camps for adults and children at 
Kuhfelde, Germany. These forest convalescent homes are greatly 
favored by the German insurance societies and sick lodges. Their 
benefits are extended to the children of patients. 

Germany must be given credit for making the greatest discoveries 
and for instituting the most rational methods of treatment in connec- 
tion with tuberculosis. The most thorough measures are adopted 
by the Imperial Government, the industrial insurance companies and 
by the medical profession of Germany. 

According to' the business report of the German Central Com- 
mittee for the campaign against tuberculosis, there were in Germany 
in 1908 99 popular sanatoria for adults affected with disease of the 
lungs. These have 10,539 beds, 6,500 for men and 4,039 for women ; 
in addition there are 36 private sanatoria with 2,175 beds, so that 
in all, 12,714 beds for adult tuberculosis patients are available. For 
children with pronounced tuberculosis there are 18 sanatoria with 
875 beds ; besides there are 73 institutions, with 6,348 beds, in which 



126 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

are received only " scrofulous " children and those who are threat- 
ened with tuberculosis. During the last five years these facilities 
have been greatly increased; 31,022 insured persons were treated 
in the sanatoria during a total of 2,312,850 days of care, at a cost of 
11,483,033 marks ($2,755,928). On an average, each person treated 
received 75 days of care at a cost of 370.16 marks ($88.84) or 4.96 
marks ($1.19) per person for each day of care. 

Night Camps.- — -These aftord open air conditions of sleeping, either 
for patients with arrested tuberculosis who pursue their occupation 
by day in the nearby city, or with disease still unarrested but who are 
able, or from necessity are compelled to work by day.' 

Sleeping porches and balconies. — Sleeping out of doors requires 
special arrangements which are not usually found in cities. The 
ordinary dwelling, apartment house, or tenement has no provision for 
this innovation in tuberculo-therapy. Suburban and country houses 
or those in the less crowded cities are better adapted for the con- 
version of an upper porch or balcony into a sleeping apartment. 
In Denver, for instance, the practice is common enough to excite 
little comment. Detached houses are usually easily fitted with the 
necessary screened enclosures.^ 

Pavilions are more substantial and permanent than the forms of 
shelter previously referred to. Where large numbers of patients 
must be cared for at a minimum of expense the pavilion system has 
distinct advantages, especially for night use. At the Metropolitan 
Hospital, Blackwell's Island, New York City, about one-third of all 
consumptives under hospital care in New York are there provided 
for in the tent pavilions referred to on page 123 ; these tent pavilions 
cost about $12.00 per bed or $144.00 for a tent pavilion with a capac- 
ity of 12 beds. 

At the Manhattan State Hospital for the Insane, Ward's Island, 
New York, more substantial and permanent pavilions have been con- 
structed of wood and glass and have displaced the cloth tents. These 
pavilions are heated by steam, lighted by electricity, and have remov- 
able glass sides permitting a free circulation of air and light all the 
time. Their per capita cost is about $100. 

In addition, there are camps for both the men and the women 
with a total capacity of 175 patients. In summer some canvas tents 



* E. O. Otis: Institutions for the Prevention and Cure of Tuberculosis, 
Boston Med. and Surg. Journ., Aug. i, 1912. 

^ See " Directions for Living and Sleeping in the Open Air," National Ass. 
Tuberculosis, 1910. See T. S. Carrington : Interstate Med. Journ., April, 
1914. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. I, PL. 72 




FIG. 1. DAY CAMP FOR TUBERCULOSIS PATIENTS, HOUSE OF THE GOOD 
SAMARITAN, BOSTON 




A DAY CAMP FOR TUBERCULOUS PATIENTS AT THE HOUSE OF THE GOOD 
SAMARITAN, BOSTON, NEAR THE HARVARD MEDICAL SCHOOL 




^4 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63. NO. 1. PL. 77 




FIG. 1. DIET KITCHEN. DAY CAMP AT PARKER HILL, BOSTON, MASSACHUSETTS 




FIG. 2. SLEEPING BALCONY USED BY A PATIENT IN HAVERHILL, MASSACHUSETTS 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO 1, PL. 78 




SLEEPING PORCH IN A CROWDED DISTRICT OF PHILADELPHIA 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. I, PL.; 79 




DOUBLE SLEEPING PORCH WITH EASTERN AND SOUTHERN EXPOSURES. THIS SUMMER RESI- 
DENCE IN ESTES PARK, COLORADO, IS PROVIDED WITH PORCHES ON ALL SIDES SAVE THE NORTH, 
WHICH IS PROTECTED BY THE ROCKY FORMATION IN THE BACKGROUND. THE PORCH IS COV- 
ERED WITH A PERMANENT ROOF. 

Courtesy of Dr. S. G. Bonney 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 80 



\, 




CITY RESIDENCE WITH IDEAL UPPER DOUBLE SLEEPING PORCH CONNECTED 

WITH BEDROOM. SHEATHING AT THE BASE, WIRE SCREENING, AWNINGS, 

ELECTRIC LIGHT. 

Courtesy of Dr. S. G. Bonney, Denver 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 83 




FIG. 1. MANHATTAN STATE HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. NEW PAVILIONS 

FOR THE TUBERCULOUS INSANE 

Courtesy of Dr. William Mabon 




FIG. 2. MANHATTAN STATE' HOSPITAL, EAST, WARD'S ISLAND, NEW YORK CITY. NEW GLASS 

PAVILION FOR THE TUBERCULOUS INSANE. WINTER 

Courtesy of Dr. William Mabon 



I 




SMITHSOMAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 85 




FIG. 1. KIOSK AND OPEN DECK ADJOINING WARDS FOR EARLY CASES OF TUBERCULOSIS, PHIPPS 

INSTITUTE, IN A VERY OLD AND CROWDED PART OF PHILADELPHIA 

Courtesy of Dr. 0. J. Hatfield, D. rector 




FIG. 2. BELLEVUE HOSPITAL, NEW YORK CITY. ROOF WAKD ("OH CHILDREN 
Courtesy of Dr. .1. W. Brannan 



NO. I AIR AND TUBERCULOSIS — HINSDALE 12/ 

are used. The accompanying photograph (pi. 83), kindly furnished 
by Dr. Wm. Mabon, the superintendent, shows the character of the 
pavilion. 

In the Royal Victoria Hospital for Consumptives, Edinburgh, 
Scotland, still more substantial and expensive pavilions are in use 
as seen from the illustrations (pi. 84) kindly furnished by Dr. R. 
W. Philip. 

Roof Gardens. — At the Philadelphia Hospital the first attempt to 
segregate tuberculous patients for the fresh air cure was by means 
of a roof garden ward. This was a vast improvement over the pre- 
vious method of indoor confinement and was greatly appreciated by 
the patients. The roof garden ward was in use winter and summer, 
but later gave way to the six glass pavilions erected at an expense 
of over $112,000. 

Each pavilion is intended to accommodate eighteen patients, usu- 
ally in an advanced stage of tuberculosis. Each is separate in itself 
with walls and roof of glass and only sufficient metal work to give 
proper support. The floors are of cement so as to be as smooth and 
non-absorbent as possible. Including the porches, which are also 
enclosed in glass, each pavilion measures 39 by 70 feet. The glass 
is arranged in frames in both walls and porches and by means of 
automatic devices one side of the building or all three sides may 
be thrown open. Screens or shades are arranged to prevent too 
much access of the sun. The system of ventilation and heating is 
considered ample. 

Detached Cottages. — At the Nordrach Ranch Sanatorium, three 
miles from Colorado Springs, independent cottages resembling tents 
are used. These are economical and insure privacy and sufficient 
protection. The system is adopted from that in use in Nordrach, 
Germany. 

The highest development of housing for the tuberculous patient 
is undoubtedly the independent cottage. It is necessarily expensive, 
but the patient fortunate enough to be its inmate has a maximum of 
comfort and at the same time is in the enjoyment of the best atmos- 
pheric conditions night and day. At the Loomis Sanatorium where 
the snow lies on the ground more than four months in the year, and 
at Saranac Lake, in the Adirondack Mountains, where the winters 
are even longer and more severe, the independent cottage is a dis- 
tinctive feature. 

Sleeping Canopies. — Detachable windows may be applied to tents, 
pavilions, or ordinary dwellings, so as to allow patients to breathe 



128 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

by day and night the outer air uncontaminated by others occupying 
the same room or dwelHng. Devices suitable for any window may 
be obtained. It is thus possible in a hospital ward to have half a 
dozen patients breathe the outer air while the ward is kept warm. 
The tent can come over the end of the regular hospital bed so that 
patients sleeping in wards where miscellaneous cases are received, 
may nevertheless have the full benefit of the outer air. By means 
of thick celluloid the patient may be readily seen. The celluloid 
window may be raised to give the patient drink and nourishment. 

Plate 93 shows the Walsh Window Tent applied to the window 
of an ordinary dwelling.' 

CHAPTER X. CONCLUSIONS. 

There are some people, especially those of a skeptical or combative 
tendency, who refuse to admit that climate plays any important role 
in the cure of tuberculosis. One of these who was formerly in charge 
of a widely known institution for the study and treatment of tuber- 
culosis has said: " I desire to go on record as believing that there 
is no therapeutic value in climate." This same physician probably 
owes his life to the fact that thirty-five years or more ago he left 
the city and removed to the mountains of Pennsylvania for the relief 
of a pulmonary disease and recovered. Such an attitude is a study 
for the psychologists and would hardly seem deserving of serious 
attention, except that we hear such statements as this: "If a case 
of consumption cannot be cured in its home climate it cannot be 
cured anywhere." 

I think there is no doubt that if any of us were told that he is 
in the incipient stage of tuberculosis he would immediately take steps 
to familiarize himself with the line of treatment which would, before 
much time had elasped, involve leaving Boston, New York, Phila- 
delphia, or Chicago, as the case might be, and so live as to enjoy 
what air and sunshine and other atmospheric features might afford. 

One reason why home climates, if such a term may be permissible, 
have grown in favor is that it has been found necessary to estab- 
lish a large number of State sanatoria, or at least to seek aid for 
private sanatoria from some of our State legislatures. It is a matter 
of expediency to have such sanatoria and legislators must be con- 
vinced that good results or, if necessary, the best results, can be 
obtained close at hand. We are all heartily in favor of such institu- 



^ For the history of this tent see Knopf and McLaughlin, N. Y. Med. Journ., 
IQOS, Vol. 81, 425. 



NO. I AIR AND TUBERCULOSIS — HINSDALE I29 

tions whether or not we should wish to stake our chances of recovery 
in any of them. 

Of course we do not claim that there is any specific climate for 
tuberculosis and the long search for such climate, a search lasting 
for nearly two thousand years, is apparently at an end. 

Now what is there left to us, and what do we understand by a 
climatic change? 

We all know that the New England climate is changeable, that is, 
the meteorological conditions are constantly varying just as they 
also vary in the Mississippi Valley and along the Atlantic seaboard. 
But the New England climate is p^eculiarly unstable and, as Charles 
Dudley Warner has said, " New England is the battle-ground of 
the weather." 

We have a change of climate when we leave the hot city in summer 
and go a few miles to the shore. We have floating hospitals so that this 
climatic change may stimulate a sick child to recovery. A so-called 
" home-climate " may work a cure or aid in a cure because we leave 
the climate of our homes, often too dry with furnace heat, too poorly 
ventilated, too damp from lack of sun, and remove to more hygienic 
dwellings in the same locality where sun and air and cleanliness 
abound. 

But, to take up the principal question at issue, the first thing usu- 
ally asked is whether one should go to the Adirondacks, Colorado, 
New Mexico, Arizona, California, or elsewhere, in order to get 
what is so frequently claimed to be the greatest climatic advantages. 
No one who has visited these localities can fail to be impressed with 
the living examples of recovery from tuberculosis. Denver, Colo- 
rado Springs, and innumerable towns in southern California abound 
in doctors who have practically recovered from this disease and are 
earning a living that is the envy of their eastern confreres. 

Would they have recovered in their eastern homes ? Almost to a 
man they answer " No." I have never heard of an exception. But 
the case is hard to prove from such ex parte evidence. However, 
it is interesting to note Dr. H. B. Dunham's conclusion. He stated 
in 1904, after visiting discharged Massachusetts State Sanatorium 
patients in the west, and after comparing Massachusetts Sanatorium 
statistics with those of the U. S. Army Sanatorium at Fort Bayard, 
New Mexico, that "the results corroborate our beliefs in the effi- 
cacy of residence in dry climates, but with a smaller margin in its 
favor than was anticipated." The proportion of people adapted for 
treatment in these extremes of climate must be more equal than 



130 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

thought possible by cHmatologists generally. That is to say, a small 
majority of the patients at Rutland, Mass., would probably do better 
at Fort Bayard, New Mexico, and a large minority might do better 
at Rutland. But no one can say positively, in any given case, what 
would have been the outcome had he chosen differently. 

We need not discuss the bearing of what to do for the poor or 
what to do for the rich, or the question of food, or the physician's 
management ; these are important and may govern the choice, but 
v/hat we want is an answer to the abstract question of the influence 
of climate. 

We believe that climate may be utilised as an adjuvant of great 
value for carrying out the hygienic, dietetic treatment of all forms 
of tuberculosis and of many other diseases. There are some elements 
of climate that have a more positive influence in hastening cure than 
others. The first place must be assigned to an abundance of air, 
which is as nearly as possible bacteriologically and chemically pure. 
It goes without saying that city air is polluted by smoke and dust 
and all dwellings, whether in the city or the country, are far below 
the standard of purity desirable. Only on the sea or at the highest 
elevations do we find air really pure, but we can approximate it by 
living out of doors. There is a climate of the city, a suburban 
climate, a climate of the country, woods, and plains, all differing 
as regards purity of air. We are all probably agreed on this point. 

Next comes the subject of sunshine. We admit that good results 
are obtained in cloudy regions as, for instance, in the Adirondacks 
and at Rutland ; but there is at least no objection to sunshine, and I 
believe that the moral effect of bright sunny days and plenty of them 
is very great. Invalids always welcome the sun. We can protect 
ourselves from too much sun if need be, and I, for one, believe that 
sunlight does a vast amount of good and sunny regions are much to 
be preferred, other things being equal. That is the great asset of 
our western plains and mountains ; and it is a real asset that counts. 
Of course there are exceptions. Tastes differ. Dr. Solly used to 
relate the story of one of his countrymen who had been sojourning 
in Colorado and finally returned to England. As he landed in a fog 
and found himself home again, he exclaimed, " Thank God ! I am 
out of that beastly sunshine." I do not suppose he intended to be 
irrational or ungrateful for the greatest of all natural gifts. 

Now, what other climatic conditions besides pure air and abundant 
sunshine have we to help us? Is a cool climate or a warm climate 
the best ? Is a dry or humid climate to be preferred ? These quali- 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 







FIG. 1. SHACK WITH SCREENED PORCH. ESTES PARK, COLORADO 
Courtesy of Dr. S. G. Bonney 




FiG. 2 WELCm's RtsMHT. F VE MILES FROM LVONr-. i:-L..'RADO. SIX ROOM COTTAGE SOME- 
WHAT PRIMITIVE BUT WITH AMPLE SCREENED PORCH. SHELTERED FROM NORTH AND WEST 

WINDS. 

Courtesy of Dr. S. G. Bonney 



pM'<i0- 




SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 




FIG. 1. ANNE M. LOOMIS MEMORIAL COTTAGE— (NEW INDEPENDENT UNIT) LOOMIS SANATORIUM 

SULLIVAN COUNTY, NEW YORK 




FIG. 2. LOOMIS SANATORIUM, SULLIVAN COUNTY, NEW YORK. ONE OF THE EAST PORCHE 
THE MARY LEWIS RECEPTION HOSPITAL 



NO. I AIR AND TUBERCULOSIS — HINSDALE I3I 

ties of temperature and humidity may as well be considered together. 
Undoubtedly for the majority of cases in the first stage the climate 
should be dry and the temperature comfortable — not warm enough to 
be relaxing, but not so cold as to be repellent and restrict exercise or 
out-of-door life. It is true that in special localities better results 
are obtained during the cold months than during the summer. This 
is true of the Adirondack Cottage Sanitarium in the State of New 
York. One reason for this is that in winter the lakes and ponds 
are frozen and covered with dry snow; the air is drier. It is far 
enough north and at a sufficient altitude to escape the alternate freez- 
ing and thawing that is experienced in New York City, where un- 
questionably it is less favorable for the consumptive during the cold 
season than during the warm months. Take Florida and South 
Carolina : Undoubtedly the best season there is during the winter 
months, as the summers are oppressively warm and wet. The 
winter is the dry season and the temperature is comfortable. The 
interior of Florida forty or fifty miles from either coast is reasonably 
dry. As far as Arizona and New Mexico are concerned, the sum- 
mers are too hot at all the lower elevations for any invalid, but at 
the higher elevations, 5,000 or 6,000 or 7,000 feet, the summer heat 
is not oppressive. Along the southern coast of California and at 
many of the resorts somewhat inland, as good results are obtained 
in summer as in winter, although the latter is the more fashionable 
season for eastern visitors. The southern California resorts which 
have been most frequented by consumptives vary greatly between 
themselves as regards the important question of humidity. That a 
place is frequented by consumptives does not prove that it is a desir- 
able place for them. Many of them are misguided, wandering in- 
valids, sent out from the east with little or no judgment as to their 
individual needs and with no proper knowledge on the part of their 
medical advisers as to the humidity or local character of the places 
to which they are destined. A man, for instance, will go to Los 
Angeles. It does not take him long to find out that while the air 
is fairly dry from ii a. m. to 5 p. m., it is always damp at night. 
Six hours out of twenty- four are dry, the remaining eighteen are 
decidedly damp. The physicians of Los Angeles do not claim that 
their climate is a suitable one for cases of tuberculosis and usually 
send these cases to the interior stations, such as Redlands or River- 
side, Monrovia or Altadena. Many are sent to Arizona. Experience 
shows that consumptives do better if they avoid the coast region. 
Or, if near the coast, as at Santa Barbara, they are better if they 



132 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

find a site at some elevation on the hillside or in the mountain val- 
leys beyond the reach of the morning fog and the excessive humidity 
at the shore/ The records of the Weather Bureau show that these 
places on the coast or within reach of the fogs which penetrate 
inland have a greater humidity than Boston or New York, the mean 
annual absolute humidity for Santa Barbara, Los Angeles, and San 
Diego being given at 4.20, 4.42 and 4.34 grains, more than one-third 
more than that of New York and Boston, 3.19 grains and 2.84 grains. 
The mean annual relative humidity of all these places mentioned is 
from "JT. to 73 per cent. But the advantage of places like Santa Bar- 
bara, San Diego, Redlands, and Riverside, lies in the fact that the 
mean annual humidity shows a remarkable variation during the 
twenty-four hours compared with places like Boston, New York, or 
Philadelphia, where the daily range is much less. At Redlands, fifty 
miles inland from the Pacific Ocean, one of the best known stations, 
the hygrometer has been known to indicate in fair weather 55 per cent 
at 4.30 p. m., and 80 per cent at 6.00 p. m. The relative humidity 
is sometimes as low as 30 per cent for a limited time during the 
day, and 70 to 80 per cent at night when the temperature is from 
44° to 60° F. 

It may as well be stated that the government records of humidity 
are quite misleading when we use them to judge of the climate of 
any given place. The observations are made at 8 a. m. and 8 p. m., 
but in the invalid's day, made up of the intervening hours, the rela- 
tive humidity reaches a much lower mark than the records show. 
I often observe a relative humidity in Virginia of 25 or 30 per cent 
at 2 p. m., and 95 or 98 per cent at night or in the early morning, 
especially when dew falls after a bright, invigorating day. I think 
that people, whether sick or well, adjust themselves to these natural 
changes of humidity if properly clothed and constantly in the open 
air ; but when subject to rapid changes in humidity, as in going back 
and forth from the excessively dry air of a house in winter to the 
damp air outside, the demands upon the mucous membranes are 
very great and such frequent and violent changes certainly do harm 
to susceptible people. Such rapid variations or alterations of the 
humidity of the inspired air I think are as bad as would be rapid 
alternations of altitude involving variations of several thousand feet. 

Some patients, however, seem to do better with a humidity greater 
than that chosen for others. If we have a low relative humidity 



^ See W. Jarvis Barlow, M. D. : Climate in the Treatment of Pulmonary 
Tuberculosis (Journ. Amer. Medical Association, October 28, 1911). 



NO. I AIR AND TUBERCULOSIS HINSDALE 133 

and at the same time a moderately low temperature the general 
effect is tonic and it is beneficial in conditions of irritability of the 
respiratory mucous membrane; but if the temperature is very low 
this may be rather irritating. We find atmospheric conditions like 
this from Minnesota to the Rockies and through Manitoba and 
Alberta. 

The combination of high relative humidity and low temperature 
certainly favors catarrh and we have such conditions all winter 
long in the region of the Great Lakes and in New York and New 
England. Probably the best combination is a low humidity and a 
moderately cool temperature ; the average tuberculous patient makes 
his best gains after August first and in subsequent cold, dry weather 
when such conditions prevail. But of course there are exceptions 
and some do better with a high relative humidity and a warm tem- 
perature ; these are not numerous and probably include more of the 
patients in later stages when expectoration is profuse and vitality is 
low- 

The old idea about equability of temperature, at least between the 
temperature of midday and midnight, is not of great importance;* 
all mountainous stations show great variations in this respect. Some 
variability tends to stimulate the vital activities, but in older people 
and those who are feeble great variability is a disadvantage. 

As far as altitude is concerned it probably has not, per se, any 
great influence ; certainly to my mind not so much as we used to 
think. However, altitude is incidentally associated with mountain 
life or life on the plains, with more sun, less moisture, and scattered 
population. We should not forget that surgical tuberculosis is al- 
ways favorably influenced by a seashore residence suitably chosen. 

I never shall forget the wonderful impression made on visiting 
the Sea Breeze Hospital for Tuberculous Children on Long Island, 
New York. Constant outdoor life in all weather works miraculous 
cures after the most formidable operations for bone tuberculosis and 
in many cases renders them wholly unnecessary in patients whose 
physical condition on admission was most unpromising. All the 
great French and Italian sanatoria for tuberculous children are 
located on the seashore. 

Among the numberless histories of the climatic cure I will give 
only one and I think I may safely let it stand as a good example by 
which to let the argument rest. The history is that of a physician 
whom we all love and respect. It was published, together with 
twenty other carefully recorded histories, by that prince of clinicians, 



134 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

the late Dr. Alfred L. Loomis, in the Medical Record and formed 
a part of a paper read before the Medical Society of the State of 
New York in 1879, a paper which we commend to your attention. 
Dr. Loomis says: 

At the age of twenty-five this patient, being of good family history, began 
to lose his health in the winter of 1872. His symptoms were rapidly becoming 
urgent; he was examined by several physicians. Extensive consolidation at 
the left apex was found, extending posteriorly nearly to the angle of the 
scapula; on the right side nothing was discovered save slight pleuritic ad- 
hesions at the apex. 

He was ordered south, but returned in the spring in no way benefited. 
On the contrary, night-sweating had set in, and his fever was higher. In 
the latter part of May he started for the Adirondacks, the ride in the stage 
being accomplished on an improvised bed. His condition at this time was 
most unpromising; he had daily fever, night sweats, profuse and purulent 
expectoration, had lost his appetite and was obliged constantly to have 
recourse to stimulants. Weight about 134 pounds. He began to improve 
at once, his appetite returned, all his symptoms decreased in severity, 
and after a stay of more than three months he returned to New York 
weighing 146 pounds, with only slight morning cough, presenting the appear- 
ance of a man in good health. A few days after his arrival in New York 
he had a chill, all his old symptoms returned and he was advised to leave 
for St. Paul, Minnesota, where he spent the entire winter. He did badly 
there ; was sick the greater portion of the winter. In the spring of 1873 
he again went to the Adirondacks. At this time he was in a most debilitated 
state, was anemic, emaciated, had daily hectic fever, constant cough, and pro- 
fuse purulent expectoration. 

The marked improvement did not commence at once as it did the previous 
summer, and the first of September found him in a wretched condition. I 
then examined him for the first time and found complete consolidation of the 
left lung over the scapula and suprascapular space, with pleuritic thickenings 
and adhesions over the infraclavicular space. On coughing, bronchial rales 
of large and small size were heard over the consolidated portion of the lung. 
Over the right infraclavicular region the respiratory murmur was feeble, 
and on full inspiration pleuritic friction sounds were heard. I advised him 
to remain at St. Regis Lake during the winter, and although he was repeatedly 
warned that such a step would prove fatal, he followed my advice. 

From this time he began slowly to improve. Since that time he has lived 
in this region. At the present time his weight is 158 pounds, gain of 22 
pounds since he first went to the Adirondacks in 1873, and ten pounds more 
than was his weight in health. He has slight morning cough and expectora- 
tion, his pulse is from 72 to 85 and he presents the appearance of a person 
in good health. In his lungs evidences still remain of the disease he has so 
many years combated. 

Although he has made three attempts to live in New York, at intervals 
of two years, each time his removal from the mountains has been followed 
within ten days by a chill, and a return of pneumonic symptoms — symptoms 
so ominous that he has become convinced that it will be necessary for him 
to remain in the Adirondack region for some time to come. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 1, PL. 90 




Ife^. 



FIG. 1. LOOMIS SANATORIUM, SULLIVAN COUNTY, NEW YORK 




FIG. 2. LOOMIS SANATORIUM, SULLIVAN COUNTY, NEW YORK. PORCH OF OLD INFIRMARY 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. «^. NO. 1. PL. 91 




FIG. 1. PARTIAL V:EVv' 



PE.\.NSyL/A.N!A'S STATE SANATORIUV FOR TUBERCULOSIS, NUMBER 
MONT ALTO, FRANKLIN COUNTY 




PENNSYLVANIA'S STATE SANATORIUM FOR TUBERCULOSIS, NUMBER 3. HAMBURG, 
BERKS COUNTY 



SMJTHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. S3, NO. 1, PL 92 




PARTIAL VIEW OF PENNSYLVANIA'S STATE SANATORIUM FOR TUBERCULOSIS, NUMBER 2, 

CRESSON, CAMBRIA COUNTY 

This property, formerly a popular summer resort hotel, was presented to the State by Mr. 

Andrew Carnegie for sanatorium purposes 



8MITH30NIAN MISCELLANEOUS COLLECTIONS 



VOL. 63, NO. 




THE WALSH WINDOW TENT. ALTHOUGH LYING IN THE BEDROOM THE SLEEPER HAS FREE 
ACCESS TO THE OUTER AIR 



NO. I AIR AND TUI'.KKCULOSIS HINSDALK I 35 

Wc all know the after history of this patient. Thank God, he is 
still living, still working, and there are thousands living to-day who 
owe their lives to the example which he has set them. lie seized the 
principles of climatic treatment and adapted it to the individual. 

I recently sent the following question to the deans of medical 
colleges in Boston, Chicago, New Orleans, Los Angeles, and Mon- 
treal. T knew nothing of the views of these men on this su1)jcct 
except one; of course wc all know that every one from California 
has decided views on climate. The question was : 

What would you do for yourself climatically if you were told for 
the first time that you had incipient pulmonary tuberculosis? 

Here are the answers : 

I would strike for the wild pine woods of northern Michigan or Wisconsin 
and stay there. — A. R. Edwards, Chicago. 

In answer to your question I may say that if I had incipif-nt tuberculosis 
r should either go to Saranac or St. Agathe in Canada and employ the open 
air treatment. — F. J. Shepherd, McGill University, Montreal. 

In answer to your question of December 26, I would say that I would 
treat myself as I do patients on whom I make the diagnosis of incipient pul- 
monary tuberculosis, that is, refer them to a local man who sjtecializcs in this 
disease, and ask him to look them over and refer them for climatic treatment 
in accordance with his knowledge of climatic conditions suitable to the indi- 
vidual case. Were I to start out to select a climate for myself, I would be 
much more influenced by the physician under whose care I would come in the 
new place than by the actual climate, and would probably select either Saranac 
Lake or Asheville, N. C, as I know and have confidence in physicians in each 
place. Were they to decide that I was better suited to some other climate, 
I would move on under their advice. If it were possible, I believe that I 
would undoubtedly leave Boston, had I incipient tuberculosis. 

Very truly yours, 

Hknry A. Christian, 

Boston. 

If I had to answer your question categorically I would say that I would 
ask the advice of one or two men living in my own community as to what 
I should do for myself climatically if I were told for the first time that I 
had incipient pulmonary tuberculosis. 

The practice among the profession in New Orleans is to send patients to 
St. Tammany Parish, in Louisiana, where the growth of piney woods is thick 
and ozone plentiful. When the particular case justifies, the patient is sent 
to the plains of Arizona or New Mexico, and, rarely, to El Paso, Texas. A 
few patients go to Colorado. — Isadore Dyer, Tulane University, New Or- 
leans, La. 

Perhaps I can best answer this personally by telling you what I did when I 
was told this very thing fifteen years ago. Having contracted tuberculosis 
in New York city I sought a better climate for an outdoor life, spending 
the first summer in the Adirondack Mountains and in November of that year 



136 , SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

going to California, where I lived for one year in the foothill region near 
the coast at an elevation of 1,000 feet, free from responsibility and work. 
After the first year I never had any return of my pulmonary tuberculosis. 

I believe a change of climate is more a question of finances- than anything 
else. If one has not the necessary means to have what is right in a different 
climate his chances for a cure are much better with home treatment, but 
when a better climate can conveniently be added to other measures of treat- 
ment for pulmonary tuberculosis it should be advised. — W. Jarvis Barlow, 
Univ. of Southern California, Los Angeles, Cal. 

Note. — For the bibliography of tuberculosis in its various relations the reader 
is referred to the Index Catalogue of the Surgeon-General's Library, U. S. 
Army, Volume 18, Second Series, Washington, 1913. This bibliography em- 
braces 412 pages in double columns, an invaluable contribution to the history 
and literature of this subject. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63, NUMBER 2 



Notes on Some Specimens of a Species 
Onychophore (Oroperipatus corradoi) 
New to the Fauna of Panama 



BY 



AUSTIN HOBART CLARK 




(Publication 2261) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

FEBRUARY 21, 1914 



ZU ^ovi> (gaitimovt (preea 

B\I.TIMORr:, MD., V. S. A. 



NOTES ON SOME SPECIMENS OF A SPECIES OF 

ONYCHOPHORE (OROPERIPATUS CORRADOI) 

NEW TO THE FAUNA OF PANAMA 

By AUSTIN HOBART CLARK 

Through Professor T. D. A. Cockerell I have recently received 
four specimens of a species of Peripatus collected at Ancon, Canal 
Zone, by Mr. J- Zetek, which represent'a genus, as well as a species, 
not previously definitely known as an inhabitant of the region. 

These specimens are now in the collection of the United States 
National Museum. 

OROPERIPATUS CORRADOI (Camerano) 

J'l-ri flatus corradoi 1898. Camerano. Boll. Mus. Zool. ed Anat. comp. di 
Torino, vol. 13, No. .316, p. 2. — 1898. Camerano, Atti R. Ace. Sci. di 
Torino (2), vol. 33, pp. 308-310, figs. A and B; p. 591. — 1905. Bouvier, 
Ann. des. sci. nat. (9), vol. 2, p. 120, pi. 3, fig. 15 ; pi. 4, figs. 29, 30; text 
figs. 6, p. 15; 18, p. 20; 42, p. 38; 63, p. 124; 64 and 65, p. 125 (the 
complete synonymy is given). 

Oropcrifatiis corradoi nn3. A. H. Ci.ark, Proc. Biol. Soc. Washington, vol. 
26, p. 16. 

Locality.- — Ancon, l\anama Canal Zone. 

Material. — Four specimens, two males and two females. 

Notes. — One of the females is 34 mm. long and 4 mm. broad, and 
possesses twenty-seven pairs of ambulatory legs ; the other is 34 mm. 
long and 3.5 mm. broad, with twenty-nine pairs of ambulatory legs. 

Of the males one is 19 mm. long and 2.3 mm. broad, with twenty- 
four pairs of ambulatory legs, and the other is 19 mm. long and 2.5 
mm. broad, with twenty-five pairs of ambulatory legs. 

All the specimens are dorsally dark brown in color, with a narrow 
median line of darker, and ventrally light brown. 

The dorsal folds in the two females are all of approximately the 
same width, but in the males there is a more or less distinct alterna- 
tion of broader and narrower folds; there are no incomplete folds. 

Some of the primary papillae of the back are very much more 
developed than the others, and lighter in color, and these enlarged 
light colored papilUe show a more or less regular arrangement which, 
however, is very much less evident in the females than in the males. 

Smithsonian Miscellaneous Collections, Vol. 63, No. 2. 

I 



2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

There is a regular line of these papillse on either side of the median 
dorsal dark line, which gradually becomes irregular and disappears 
somewhat before the middle of the body. There are two scalloped 
rows, one along each of the outer margins of the dorsal surface of 
the body, consisting of a series of arcs of which the convexity is 
above each of the ambulatory legs ; beyond these in the males there 
are similar lines with the arcs alternating with those in the inner 
rows, their convexity being between the legs, and reaching down 
to the level of the leg bases. Between the median and lateral lines 
the enlarged papillae are arranged in a sinuous and more or less 
irregular line, with scattered ones on either side of it; but toward 
the posterior part of the body they become less and less numerous, 
and more and more irregular in their position. 

All of the legs are provided with feet. 

The creeping pads consist each of four arcs of nearly equal width, 
of which the fourth is about as long as the second. 

The urinary tubercle which, in reference to the short diameter of 
the third arc is approximately central in position, divides the third 
arc into two parts, of which the posterior is much smaller than the 
anterior, and is entirely separated from the tubercle, which is broadly 
united with the anterior portion. The conditions in these specimens 
is well represented in Bouvier's figure. 

Remarks. — These individuals appear to agree with the specimens 
of Oroperipatus corradoi from Guayaquil as described by Bouvier. 

Range.— Oroperipatus corradoi is now known from Quito, Balzar 
and Guayaquil, Ecuador, and from Ancon, Panama Canal Zone. 

List of the Species of Onychophores Knoivn from the Isthmus 

of Panama 
Oroperipatus corradoi (Camerano). 
Oroperipatus eiseni (Wheeler)'. 
Macroperipatus geayi (Bouvier). 
Epiperipatus hrasiliensis (Bouvier). 
Epiperipatiis edwardsii (Blanchard). 

^ This species has not actually been taken on the isthmus, but as it ranges 
from Tepic, Mexico, south to the Rio Purus, Brazil, it probably occurs there. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63. NUMBER 3 



A New Ceratopsian Dinosaur from the Upper 

Cretaceous of Montana, with Note 

on Hypacrosaurus 



(With Two Plates) 



CHARLES W. GILMORE 
Assistant Curator of Fossil Reptiles, U. S. National Museum 






(Publication 2262) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

MARCH 21, 1914 



Z^i Boxb (§aitimoxt (preee 

liALTIMOIlK, Ml)., U. S. A. 



A NEW CERATOPSIAN DINOSAUR FROM THE UPPER 

CRETACEOUS OF MONTANA, WITH NOTE 

ON HYPACROSAURUS ' 

By CHARLES W. GILMORE 

assistant curator of fo.ssii, reptiles, u. s. national museum. 

(With Two Plates) 

INTRODUCTION 

The fossil remains upon which the present communication is 
l)ased were collected by the writ^er during the summer of 1913 
while working under the auspices of the U. S. Geological Survey 
on the lUackfeet Indian Reservation in northwestern Montana. The 
partial skeletons of five individuals were found and these supple- 
ment one another to such an extent that nearly all parts of the skele- 
ton are represented. The skull presents some anatomical features 
not heretofore known in the Ceratopsia and the new genus and spe- 
cies Brachyccratops iiiontancnsis is here proposed. 

This new form is the smallest known re]>resentative among the 
Ceratopsian dinosaurs and in several respects strikingly different 
from any of its allied contemporaries. 

The present paper is preliminary. Upon the completion of the 
preparatory work now in progress a more detailed account of the 
skeletal anatomy and a discussion of its affinities will be given. 

BRACHYCERATOPS MONTANENSIS, new genus and species 
Type. — Cat. No. 7951 U. S. Xat. Mus. A considerable portion 
of a disarticulated skull ii. e., nasals, prefrontals, postfrontals, 
])Ostorbitals, premaxillaries, maxillaries, alisphenoid), with which is 
provisionally associated a fragmentary part of the frill and a right 
dentary and a predentary. 

Type locality.— N. E. >4 Sec. 16, T 37 N, R 8 W. Milk River, 
Ijlackfeet Indian Reservation, Teton County, Montana. 

Paratypes. — Cat. No. 7952, U. S. Nat. ^lus. Rostral and portions 
of the premaxillaries; Cat. No. 7953 U. S. Nat. Mus. Sacrum, 



' Published by ])ermission of the Director of the U. S. Geological Survey. 
Smithsonian Miscellaneous Collections. Vol. 63, No. 3 



2 SMITHSONIAX MISCELLANEOUS COLLECTIONS VOL. 63 

complete pelvis and articulated caudal series of 45 vertebrje con- 
tinuing to the tip of the tail; Cat. No. 7957, U. S. Nat. Mus. Tw^o 
tarsals of the distal row, four articulated metatarsals, a portion of 
the fifth, and eleven phalanges. 

Localities. — Same as the type. 

Horizon. — From the upper part of an Upper Cretaceous formation 
soon to be described by the U. S. Geological Survey, which includes 
the equivalent of the Judith River formation and some older beds. 
The fossiliferous horizon is also the equivalent of the upper part 
of the Belly River formation, as described in neighboring areas of 
Canada. 

Generic and specific characters. — Typically of small size. Skull 
with facial portion much abbreviated, and deep vertically. Supra- 
orbital horn cores small. Nasal horn core outgrowth from nasals, 
large, slightly recurved, laterally compressed, and divided longitudi- 
nally by median suture. Frill with comparatively sharp median 
crest, fenestrse apparently of small size, and entirely within the 
median element. Supratemporal fossae opening widely behind. Bor- 
der of frill scalloped, but without separate marginal ossifications. 
Dentition as compared with Triceratops greatly reduced. 

Description of skull. — The description to follow is devoted en- 
tirely to a consideration of the skull, since it shows characters of 
sufficient importance to readily distinguish it from all the other 
known members of the Ceratopsian group, which in the greater num- 
ber of instances have also been established upon cranial material. 

When found, the skull was entirely disarticulated, but the excel- 
lent state of preservation of the bone and the absence of distortion 
by crushing rendered the assembling of the scattered elements a 
comparatively easy matter. This specimen is of the utmost impor- 
tance in the evidence it gives for the proper interpretation of the 
cranial elements, and especially the positive information it affords 
relating to those parts of the Ceratopsian cranium now somewhat 
in controversy. 

In the above diagnosis of the genus and species, it is stated to be 
typically of small size. While this statement is true so far as 
applied to the known specimens, it should also be stated that to 
some extent the small size of these specimens may be due to the 
immaturity of the individuals. The open sutures of the skull, 
sacrum, and vertebra? all testify to the youth of the animals. 

Viewing the skull in profile (pi. i), one is especially impressed by 
the great abbreviation of the facial portion, when compared with the 



NO. 3 NEW CERATOPSIAN DINOSAUR GILMORE 3 

Ceratopsians of the Lance formation. It is to this shortening that 
the generic name refers. The narial opening, as in other known 
Judith River and Belly River forms, is situated well forward and 
under the nasal horn, whereas in the later and more, highly special- 
ized Tricciatops this orifice is ^entirely posterior to that horn. The 
distance between the nasal and supraorbital horns, as seen in the 
upper outline, is exceedingly short, due largely to the shortened 
nasal bones and the great fore and aft development of the basal 
portion of the nasal horn and also to the forward position over the 
orbits of the small brow horns. 

The exact pitch of the frill portion in relation to the anterior part 
of the skull cannot be positively determined, though in the drawing 
it has been placed in accordance with the evidence of articulated 
skulls. 

This specimen brings to light an entirely new phase of nasal horn 
development and one which, so far as our previous knowledge goes, 
appears to be unique among dinosaurs. Reference is made here to 
the longitudinal separation of the horn core into two halves by the 
nasal suture. This also indicates the nasal horn to be an outgrowth 
from the nasal bones instead of having originated from a separate 
center of ossification, as is the case in the more specialized Tricera- 
tops. It appears quite probable there are some of the described 
Belly River species that will also show a similar mode -of nasal horn 
development when juvenile specimens are found. 

The nasals are especially deep and massive, due to the develop- 
ment on their superior surfaces of the nasal horn cores. Posteriorly 
they present a pointed process with a beveled underlapping surface 
for contact with the prefrontals (the frontals and lachrymals of 
authors). Laterally they send down a deep extension to meet the 
premaxillary, and anteriorly the arched ventral borders of the nasal 
bones form the upper half of the boundary of the narial ori- 
fice. Anteriorly they send out vertically flattened processes (see p, 
fig. i) between which are received the ascending processes of the 
premaxillas. This nasal process appears to end about 32 mm. in ad- 
vance of the forward line of the horn core, so that the upper outline 
of the beak is formed largely by the premaxillaries. The horn has 
a broad fore and aft extent at its base, but tapers rapidly to a bluntly 
pointed horn of moderate height. Transversely it is much com- 
pressed at the base, though inclined to expand somewhat toward 
the summit. The horn as a whole is directed somewhat forward, 
but the curve of the posterior side is such as to give the impression 



4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

that its upper part is slightly recurved. The surfaces of the upper 
half are roughened and grooved by vascular impressions. 

On the tip of the left half of the nasal horn is a small, flattened 
oval bony ossicle, which rests in a shallow depression or pit on the 
apex of the horn as shown at os, figure i. This ossicle is a distinct 
element from the underlying bone and may represent the incipient 
horn of later Ceratopsians where it is known to be developed from a 
center of ossification distinct from the nasal bones. 



'OS 




Fig. i. — Nasals and nasal horn cores of Brachyccratops montancnsis. Type : 
Cat. No. 7951 U. S. Nat. Mus., Yi Nat. size. A, side view; B, front view; c, 
surface for contact with the premaxillaries ; /, surface for articulation of pre- 
frontal ; no. anterior nasal opening; os, ossicle on top of horn core; p, anterior 
process of nasal ; po, orifice for superior processes of premaxillaries ; s, suture 
separating two halves of nasal horn. 



The maxillaries are of triangular outline with alveoli for twenty 
teeth in the functional row. As compared wath Triccratops this is 
a greatly reduced number, Triccratops having forty alveoli in the 
maxillary. In this specimen all of the functional teeth have fallen 
out, but two or more germ teeth are still retained and these give 
some idea of their character. 



NO. 3 NEW CF.RATOPSIAN DINOSAUR GILMORE 5 

The true extent of the postfroiitals in the Ceratopsian skull is here 
correctly determined for the first time. Authorities have heretofore 
considered the post frontal as extending from the median line out- 
ward and including all of that portion of the skull here designated 
as postf rental and postorbital (see pi. 2). In this specimen a longi- 
tudinal suture just internal to the base of the supraorbital horn 
core separates it into two distinct elements. The inner portion all 
paleontologists agree in calling the postfrontal, the outer appears 
without question to represent the postorbital. Von Huene/ in 191 2, 
in a skull of Triccratops prorsus regarded that portion forming the 
posterior boundary of the orbit as representing the whole of the post- 
orbital, but the writer now questions the correctness of this determi- 
nation in the genus Triccratops, in so far as regarding it as repre- 
senting the entire postorbital. 

In Brachyceratops the postfrontal is a somewhat irregularly trian- 
gular bone, longer than wide, which unites by suture on the median 
line Avith'its fellow of the opposite side. 

Anteriorly the combined postfrontals terminate in a pointed pro- 
jection that is interposed between the deeply emarginate posterior 
borders of the prefrontals. Posteriorly and on either side of the 
postfrontal foramen these bones articulate by suture with the median 
element of the frill. A toothed external border unites with the post- 
orbital. Beginning between the horn cores the median upper sur- 
faces of the postfrontals are angularly depressed, gradually deepen- 
ing and widening transversely as they approach the fontenelle much 
as in Styracosaurus alhertcnsis Lambe, see E, plate II, The Ottawa 
Naturalist, Vol. 27, 1913. 

The postorbital gives rise to the small supraorbital horn core and 
forms nearly one-half of the orbital border. Posterior to this horn 
which is situated on the extreme anterior end, the bone flares out 
into a wide expanded portion, much deflected externally, with a 
curved posterior border, the inner half of which forms a portion 
of the outer boundary of the supratemporal fossa, the outer half 
having an underlapping sutural edge for articulation with the squa- 
mosal. The straight inferior edge meets the jugal which is missing 
in this specimen. 

The thickened anterior border shows a sutural edge for union with 
the missing supraorbital bone. On the median inferior surface is 
a shallow pit which receives the outer end of the alisphenoid, as it 
does in Stegosaitnts and Camptosaurus. 



' Neues Jahrbuch, 1912, fig. 3, p. 151. 



6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Immediately above the orbit on the anterior part of the postorbital 
there rises a low horn core, the upper extremity being obtusely 
rounded from a lateral aspect, see po.h plate i, but sharply pointed 
when viewed from the front. The external surface of this horn 
is plane, the internal strongly convex, with the antero-posterior 
diameter greatly exceeding the transverse, the total height of the 
horn above the orbit being 35 mm. These horn cores appear to be 
outgrowths from the postorbital bones unless they include a posterior 
supraorbital element such as has recently been found in the skull 
of Stegosaurns. However that may be, there is no trace of such a 
division in the postorbitals of this specimen. This again raises the 
question of the proper designation of these horns which have been 
called successively postfrontal and supraorbital horti cores. If an 
outgrowth from the postorbital bone, as the present specimen appears 
to indicate, the term postorbital horn core would be a more appropri- 
ate designation. 

The prefrontals (the frontals and lachrymals of autliors) are 
deeply emarginate anteriorly and receive between them the pointed 
posterior ends of the nasals. 

The prefrontal is a c|uadrangular plate of bone diagonally placed 
filling the interspace between the postfrontal and nasal bones. Its 
thickened posterior end contributes to the inner part of the anterior 
boundary of the orbit. Near the posterior termination a narrow 
vertical sutural surface {so, pi. 2) on the external side was for the 
articulation of the small supraorbital bone that is missing. This ele- 
ment would have completed the thickened projecting orbital border 
immediately in front of the eye and which forms such a conspicuous 
feature of the Ceratopsian skull. On the upper posterior end of the 
prefrontal a pointed peg-like projection is received in a correspond- 
ing pit in the anterior border of the postfrontal, thus strengthening 
the union of these two bones. The prefrontal is just barely in con- 
tact with the postorbital at the base of the postorbital horn core. 

The relationships of the pre- and postfrontals in Brachyccratops is 
an unusual one, for in most dinosaurian crania the frontal is inter- 
posed between them, and so far as the writer is aware the above 
condition is only found in Stegosaurus among the dinosauria and in 
•some of the Permian reptilia. Von Huene has shown, and the writer 
believes correctly too, that the frontal in Triceratops has been en- 
tirely excluded from the dorsal surface of the skull. 

The frill is represented by the median elements from two individu- 
als. Both have portions missing, but the better preserved one is 



NO. 3 NEW CKRATOPSIAN DINOSAUR GILMORE J 

provisionally associated with the type as shown in plates i and 2. 
This association, however, is only provisional in so far as it applies 
to the recognition of the proper individual, for it can be said without 
question that all the bones found belong to the same kind of an 
animal. 

The dermo-supraoccipital or interparietal, for surely it cannot be 
the parietal as Hay ' and von Huene ' have clearly shown, is united 
by suture with the anterior portion of the skull at the postfrontal 
foramen. The median part of the interparietal is sharply ridged, ex- 
cepting the posterior extremity, where it flattens out into a thinner 
portion with an emarginate median border. Between the fenestrse 
the median bar, in cross section, is triangular. The superior surface 
of this ridge forward of its narrowest part between the fenestrse 
presents three low longitudinal swellings arranged one in front of 
the other. Proximally the median portion is greatly compressed 
transversely into a short neck, forward of which it again widens into 
a much depressed end that articulates laterally with the postfrontals 
and with them forms the upper boundaries of the postfrontal fora- 
men, see jo, plate 2. Between these two lateral portions the median 
surface is deeply concave and slopes downward to a heavy truncated 
border that in all probability was suturally united with the parietals. 
In Brachyceratops at least, the parietal was entirely excluded from the 
dorsal aspect, and it is presumed that similar conditions obtained 
in Triceratops, although von Huene was inclined to regard a small 
]:)ortion of the median part of the frill posterior to the postfrontal 
foramen in that genus as being parietal. 

The bone surrounding the frill fenestrse is very thin, but toward 
the lateral free edges and posteriorly it becomes thickened. Proxi- 
mally it remains thin where it forms the floor of the supratemporal 
fossa but thickens toward the sutural border for the squamosal. The 
exact shape and extent of the frill fenestrae cannot be accurately 
determined from the available specimens, but it is readily apparent 
that they were of comparatively small size. The surfaces of the frill 
are relatively smooth and without the ramifying system of vascular 
grooves of the later Ceratopsians. There were no epoccipital bones 
on the margins of the frill, but on either side of the median emargi- 
nation a series of prominences give to the periphery much the same 
peculiar scalloped effect found in the Triceratops frill with its sepa- 
rate ossifications. 



^ Proc. U. S. Nat. Mus. vol. 2,^, 1909, p. 97. 

' Neues Jahrbuch, 1912, pp. 150-156, figs. 3, 4, 5 and 6. 



8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Laterally the median portion unites with the squamosal by a 
straight sutural edge that is directed forward and inward toward the 
center of the skull. A triangular outward projection with an upper 
striated surface at the anterior termination of the squamosal suture 
represents a surface that was overlapped by the articulated squamos- 
als (s.s., plate I ). A low. sharp, diagonally directed ridge apparently 
indicates the posterior extent of the overlap of the squamosal. The 
squamosals are missing, but those as in other primitive Ceratopsians 
appear to have been short and broad. 

The rostral is missing from the type, but is present in a slightly 
smaller individual (Cat. No. 7952, U. S. Nat. Alus.). (See fig. 2.) 
In general aspect it resembles the rostral of Triceratops, but wdth a 





/> 



Fig. 2. — Rostral of Brachyceratops )iioiitaiicnsis. Paratype : Cat. No. 7952 
U. S. Nat. Mus., 14 nat. size. a. side view ; b, posterior view ; s. superior 
process ; p, posterior processes. 

less curved anterior border. Externally the surfaces are pitted and 
grooved and in life were doubtless covered by a horny sheath. 

The predentary except for its much smaller size is indistinguish- 
able from that of Triceratops. It is to be distinguished from the 
predentary of Monocloniiis dazvsoiii Lambe by the upward turned 
apex of the anterior end. 

The dentary is stout, gradually narrowing vertically toward the 
front, the anterior end being especially depressed and unusually 
broad transversely, this end being nearly at right angles to the pos- 
terior portion. Near the posterior end on the external surface a 
stout coronoid process is developed, extending well above the dental 
border. It is compressed transversely but widens antero-posteriorly 
with a hooked forward process as in other primitive Ceratopsians. 
Beginning at the base of this process, a low, broad ridge extends 



NO. 3 



NEW CERATOI'SIAN DINOSAUR GILMORE 



forward at about mid-height along the outer side of the dentary. 
Above and below this ridge the outer surface retreats obliquely in- 
ward. 

\'iewed from above, the dental border is straight but is obliquely 
placed in relation to the lower portion, that is, it passes from the inner 
posterior margin to the outer anterior margin of the jaw. Beneath 
the coronoid process there is a deep mandibular fossa which extends 
forward about one-third the length of the dentary. On the inner 
side there is the usual row of foramina, leading into the dental cham- 
ber. The exact number of alveoli cannot be determined at this 
time, although the tooth series is relatively shorter than in either 
Ccratops or Triceratops. 




,TrL 



Fig. 3. — Dentary of Brachyccraiops iiw)itancnsis. Type: Cat. No. 7951 
U. S. Nat. Mus., 1/2 nat. size, c, coronoid process ; m, mental foramen ; sp, 
surface for predentary. 

At this time little can be said regarding the affinities of Brachy- 
ceratops, though it would appear most nearly allied to Monoclonius, 
as shown by its small size, the small brow horns of similar shape, 
large nasal horn and crenulated margin of the frill without separate 
marginal ossifications. 

It is readily distinguished, however, from all known Ceratopsians 
by the longitudinal suture of the nasal horn, the small fenestrse 
wholly within the median frill element, and the greatly abbreviated 
facial portion of the skull. It is also apparent that there are other 
distinguishing features in the skeleton which is to be described 
later. 

The striking resemblance of the fragment of a skull figured by 
Hatcher as Monoclon'uis crassns ' to the homologous parts of the 



'Monog. U. S. Geol. Survey, Vol. 49, 1907, p. 74, fig. 76. 



lO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 6^ 

present specimen leads the writer to suggest its possible identification 
with the present genus; Hatcher regarded it as belonging to a smaller 
and distinct individual from the type of that species and he also ob- 
serves : " I describe and figure this element in this connection not 
out of regard for any certain additional characters it may furnish 
distinctive of the present genus and species [Monoclonius crassus] 
but rather for the information which it affords relative to the homol- 
ogies of certain cranial elements in the Ceratopsia as a group." 
The great similarity of the horn-cores with those of Brachyceratops 
lends much color to the above suggestion. 

MEASUREMENTS ^,„_ 

Greatest length of skull, about 565 

Greatest breadth of skull, estimated 400 

Expanse of frontal region at base of brow horn cores 90 

Greatest width of nasals 58 

Length of interparietal along median line 3i5 

Height of nasal horn core above border of narial orifice 125 

Greatest width of postf rontals 80 

Greatest length of combined post- and prefrontals 126 

NOTE ON HYPACROSAURUS 

I wish to announce the discovery in northwestern Montana, in 
beds equivalent to the upper part of the Belly River formation, of 
the Trachodont reptile Hypacrosaurus^ A considerable portion of 
the skeleton (Cat. No. 7948, U. S. Nat. Mus.) of one individual 
was recovered, and at this time (the specimen not being entirely 
prepared) I am unable to distinguish it specifically from the type 
and only known species, H. altispinus Brown, from the Edmonton 
Cretaceous of Canada. 

^Barnum Brown: A New Trachodont Dinosaur Hypacrosaurus, from the 
Edmonton Cretaceous of Alberta. (Bull. Amer. Mus. Nat. Hist., Vol. 32, 
1913. pp. 395-406.) ' 



I 



i 



EXPLANATION OF PLATE i 

Lateral view of the skull of Brachyccratops montaiiensis. Type : Cat. No. 
7951 U. S. Nat. Mus., }i nat. size, d, dentary ; /, fenestra in frill ; if, infra- 
orbital foramen; in.p, interparietal; ;', jugal; /, lachrymal; vix, maxillary; n, 
nasal ; nh, nasal horn cores ; no, anterior narial opening ; 0, orbit ; os, ossicle 
on top of nasal horn core ; pd, predentary ; pf, prefrontal ; pm.v, premaxillary ; 
po, postorbital ; po.h, postorbital horn core ; r, rostral ; s, suture separating 
halves of nasal horn ; sq, squamosal ; so, sutural border on prefrontal for 
small supraorbital ; .y...?, sutural surfaces for squamosal ; st.f, supratemporal 
fossa. 



EXPLANATION OF PLATE 2 

Superior view of the skull of Brachyccratops montaiiensis. Type: Cat. No. 
7951 U. S. Nat. Mus., %. nat. size. /, fenestra in frill; fo, postfrontal fora- 
men; in.p, interparietal; n, nasal; nh, nasal horn cores; pf, prefrontal; po, 
postorbital; poh, postorbital horn core; p.tf, postfrontal; s, suture repre- 
senting halves of the nasal horn core ; so, sutural border for missing supra- 
orbital bone ; sq, squamosal ; s.tf, supratemporal fossa. 








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SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63, NUMBER 4 



ON THE RELATIONSHIP OF THE GENUS 

AULACOCARPUS, WITH DESCRIPTION 

OF A NEW PANAMANIAN SPECIES 



BY 
H. PITTIER 




(Publication 2264) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

MARCH 18, 1914 



ZU iSorJi d^aitimovt (preee 

BALTIMORE, MD., U. S. A. 



ON THE RELATIONSHIP OF THE GENUS AULACOCAR- 
PUS, WITH DESCRIPTION OF A NEW PANA- 
MANIAN SPECIES 

By H. PITTIER 

The genus Aulacocarpus, as originally regarded ' by its founder, 
Dr. O. Berg, included two species, A. Sellowianus Berg, from Brazil, 
and A. crassifolius (Benth.) Berg, from Colombia. The latter was 
first described as Campomanesia crassifolia Benth. ,^ upon material 
collected by the botanists of the Sulphur voyage on Gorgona Island, 
off the Pacific coast of Colombia, between Buenaventura and Tumaco. 
The Flora of the British West Indies by Grisebach contains ^ the de- 
scription of a new species, A. quadrangularis, from Antigua and 
Guadeloupe Islands ; and subsequently the same author added his A. 
Wrightii, originally collected in Eastern Cuba.* 

Thus, in 1866 Aulacocarpus had been increased to four species,' 
but the flower of none of these had ever been described. Taking 
into consideration the general distribution of the Myrtaceae, it was 
but logical, in the absence of more complete information, to find a 
place for this genus among the Myrtoideae, which are widely dis- 
persed in America. According" to Berg, its affinities were with Cam- 
pomanesia, a supposition which was strengthened by the original 
inclusion in this genus of one of the species of Aulacocarpus. On 
the other hand, Niedenzu, taking as a basis the embryonic characters, 
places it among the Eugeniinae. 

During his exploration of the forests of Eastern Panama, in 191 1, 
the writer had the good fortune to discover a new representative of 
Aulacocarpus in the shape of a medium-sized tree, from which her- 
barium specimens were obtained, the flowers being preserved in alco- 
hol. The description of these shows that, contrary to every expecta- 
tion, Aulacocarpus is not a true Myrtoid, but must be placed among 



^ Linnaea 27 : 345- 1856- Martius, Fl. Bras. 14' : 380. 1857. 
' Bot. Voy. Sulphur 97. pi. 37. 1844. 

* Page 239. 

* Cat. PL Cub. 90. 1866. 

'Niedenzu, however, ignores Grisebach's Antillean species (Engl. & Prantl, 
Pflanzenfam. 3' : 83. iJ 



Smithsonian Miscellaneous Collections Vol. 63, No. 4 

I 



2 • SMrnisoMAX miscellankous collrctioxs vol. 63 

the Leptospermoideae, also represented in South America by the 
Chilean genus Tepualia. This will be made clear by the following 
amended and completed description : 

AULACOCARPUS Berg. 

Receptacle forming a crater-like cup above the ovary. Sepals 5, 
short, obtuse or acute. Petals 5, unguiculate, apiculate. Stamens 
10, mserted on the margin of the receptacle, 5 opposite to, 5 alternate 
with the sepals, curved outward beyond the corolla, the basifixed 
2-celled anthers hanging around the receptacle ; anther cells longitu- 
dinally dehiscent. Ovary 5-celled, each cell with 5 (or 4) ovules; 
style simple, truncate. Drupe depressed-globose, horny or sublignose, 
5 to i-celled, each cell with I seed. Seed albuminose, covered with a 
thick, suberose testa. Cotyledons plano-convex, thick ; radicle basal, 
very short. Trees with very hard wood ; leaves opposite, exstipulate, 
thick, obscurely veined ; flowers single or few in a cluster, pseudo- 
axillar3^ 

Species 5, Tropical American. 

On account of its fundamental characters, viz. : exalbuminose seed, 
short basal radicle, ovate-depressed seeds, indehiscent woody drupe, 
5-celled ovary, and 10 stamens, with basifixed anthers, Aulacocarpus 
would take perhaps an intermediary position between the Calotham- 
ninae and the Chamaelauciae. The genus does not naturally fit into 
any of the present divisions of the Leptospermoideae, although there 
can be no doubt as to its belonging to this subfamily. 

The collection and study of new materials of the 4 species of 
Aulacocarpus already described is highly desirable and it is not un- 
likely that a better knowledge of the genus will result in a reduction 
of the number of species. My own specimens do not agree with any 
existing description, and so 1 have presumed to describe them under 
a new name. 

AULACOCARPUS COMPLETENS, sp. nov. 

A tree up to about 18 meters high and 35 to 40 cm. in diameter at 
the base. Crown elongate ; trunk continuous. Bark smooth, grayish. 
Entirely glabrous. 

Leaves opposite, large, coriaceous, short-petiolate. Stipules none. 
Petioles thick. 4 to 5 mm. long. Leaf blades 14 to 25 cm. long, 5 to 
II cm. broad, ovate-elliptic (broader toward the base), cordate to 



NO. 4 



THli CKNirS AULACOCARPUS I'lTlIER 



truncate at the base, narrowly acuminate at tip, light green above, 
paler and sometimes brownish beneath. Costa impressed above, very 
l)rominent beneath ; primary veins numerous, almost straight and 
parallel, slightly prominent above and underneath. 

Flowers single or aggregate at nodes on old wood (never on the 
year's growth). Pedicels slender, 12 to 15 nmi. long, bearing at the 
middle one pair of small bractlets, these clasping", ovate-acute, per- 
sistent, abotit 2 mm. long. Receptacle funnel-sha])ed or obconic, 
growing much above the ovary. Sepals 5, coriaceous, thick, ovate- 
triangular and acute at the tip, caducous, about 6 mm. long and 4 
mm. broad at the base. Petals 5, retiexed, pink, irregularly and broadly- 
ovate, apiculate, with a short, broad claw and a pair of rounded 
basal winglets ; margin irregularly denticulate or sublacerate ; length 
II mm., breadth 9 mm. Stamens 10, inserted on margin of recepta- 
cle and alternately opposite to sepals and petals; filaments about 10 




Floral details of Aiilococarpus complctens: a, petal; b, stamen; fc^ anther, 
ventral side; b", anther, dorsal side; c, cross-section of ovary. Enlarged 4 
times. 



mm. long, bending outwards ; anthers 6 to 6.5 mm. long, golden 
yellow, basifixed, introrse, with a large ovate, glandular, porelike 
structure at about the middle of the ventral side, and four small 
glands near the tip ; cells longitudinally dehiscent. Ovary 5-celled, 
each cell with 5 or 4 ovules : style glabrous, terete, truncate, about 
y.~, mm. long. 

Fruit dry, 4 to i -celled, globose-depressed in the first case, with 
the cells showing outside, globose and crowned with the cuplike re- 
ceptacular overgrowth when i -celled; pericarp thick, hard, greenish 
outside at maturity ; cells i-seeded. Seeds large, ovoid and slightlx- 
compressed laterally, their length 11 mm., the longest diameter 9 
mm. 



4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

Panama : Hills back of Puerto Obaldia, San Bias Coast ; flowers 
and fruit, August 30, 1911 ; Pittier 4310 (type, U. S. Nat. Herb. Nos. 

479435-7)- 

This remarkable species differs from A. crassifolius (Benth.) 
Berg in its larger leaves, these almost always deeply emarginate 
at the base, and in having the lobes of the calyx long, acute, triangu- 
lar, and caducous. Further, our species is a relatively large tree, 
while the latter, compared in its habit with Calycolpiis glaher, is 
barely more than a shrub. The wood is very hard and known under 
the name " gasparillo." 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63, NUMBER 5 



DESCRIPTIONS OF FIVE NEW MAMMALS 
FROM PANAMA 



BY 

E A. GOLDMAN 



fPrW 



(Publication 2266) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

MARCH 14, 1914 



Zt)t £or& (§(iitimoxt (preea 

BALTIMORE, MD., U. S. A. 



DESCRIPTIONS OF FIVE NEW MAMMALS FROM 

PANAMA 

By E. a. GOLDMAN 

Additional determinations of mammals obtained by the writer, 
while assigned to the Smithsonian Biological Survey of the Panama 
Canal Zone, reveal five hitherto unrecognized forms which are de- 
scribed below. 

For the loan of types and other material for comparison I am 
indebted to Dr. J. A. Allen of the American Museum of Natural 
History, New York City, and to Mr. Samuel Henshaw of the Mu- 
seum of Comparative Zoology, Cambridge, Massachusetts. 

CHIRONECTES PANAMENSIS, new species 

Type from Cana (altitude 2,000 feet), eastern Panama. No. 
179164, skin and skull, male, old adult, U. S. National Museum (Bio- 
logical Survey Collection) ; collected by E. A. Goldman, March 23, 
1912. Original number 21562. 

General characters. — Similar to C. minimus of Guiana in size and 
color, but differing in cranial details, especially the longer braincase 
and much longer, evenly tapering, and posteriorly pointed nasals. 

Color. — Color pattern about as in C. minimus, but light facial 
areas apparently less distinct ; dark brown or black of forearms ex- 
tending down over the thinly haired first phalanges of three median 
digits, the terminal phalanges white or light flesh color as in mini- 
mus; hairy base of tail dark all round. 

Skull. — Similar to that of C minimus, but braincase more elon- 
gated, the well-developed lambdoid crest projecting posteriorly over 
foramen magnum ; nasals longer, encroaching farther on frontal 
platform, the ends pointed instead of truncate, and the sides not con- 
stricted near middle ; ascending branches of premaxillae reaching 
farther posteriorly along sides of nasals ; fronto-parietal suture con- 
vex posteriorly; inner sides of parietals longer; sagittal crest well 
developed. 

Measurements. — Type: Total length, 651 mm.; tail vertebrae, 
386; hind foot, y2. Skull (type) : Greatest length, 74.2; condylo- 
basal length, 72.3 ; zygomatic breadth, 43.8 ; length of nasals, 33 ; 

Smithsonian'Miscellaneous Collections, Vol. 63, No. 5. 



2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

greatest breadth of nasals, 11 ; interorbital breadth, 14.1 ; postorbital 
breadth, 8.5 ; palatal length, 45.6 ; upper molariform tooth row, 26.4 ; 
upper premolar series, 11. 6. 

Remarks. — While the water opossum of Middle America and Co- 
lombia is very similar in size and color to C. minimus of north- 
eastern South America it differs in numerous cranial details from 
that animal as figured by Burmeister." The nasals are conspicuously 
longer and very diiTerent in form. The sagittal crest develops in 
both sexes early in life. In a specimen from Rio Frio, Cauca River, 
Colombia, the tail is black to the tip. 

Specimens examined. — Total number, ii, as follows: 

Panama: Cana (type), i. 

Costa Rica : San Jose, i ; exact localities unknown, 3. 

Nicaragua: Matagalpa, i. 

Colombia : Bagado, i ; Barbacoas, i ; Guanchito, i ; Porto Frio, 
Cauca River, i; Palmira, i. 

LONCHOPHYLLA CONCAVA, new species 

Type from Cana (altitude 2,000 feet), eastern Panama. No. 
179621, skin and skull, male adult, U. S. National Museum (Bio- 
logical Survey Collection), collected by E. A. Goldman, May 20, 
1 91 2. Original number 21 701. 

General characters. — Similar in size to L. mordax, but color 
darker; cranial and dental characters different, the second upper 
premolar notably narrower, and in the reduced development of the 
internal lobe more like that of the much larger species, L. hesperia. 

Color. — About as in Glossopliaga soricina; general color of upper 
parts near warm sepia (Ridgway, Color Standards and Nomencla- 
ture, 1912), the under parts and basal color of fur of upper parts 
somewhat paler. 

.Skull. — Broader and more massive than that of L. mordax, the 
l)raincase larger and more fully inflated ; interpterygoid fossa 
broader ; coronoid process lower, the upper outline more broadly 
rounded ; angle of mandible longer ; incisors slightly larger ; second 
upper premolar much less extended transversely owing to reduction 
in size of inner lobe; molar crowns more quadrate, less triangular 
in outline. Compared with that of L. hesperia the skull is much 
smaller and relatively shorter and broader, the braincase relatively 
larger but flatter above ; coronoid process with less broadly rounded 



' Fauna Brasiliens, pp. 72-73, pi. 11, figs 3-4, 1856. 



NO. 5 NEW MAMMALS FROM PANAMA GOLDMAN 3 

upper outline ; dentition similar, but relatively heavier, the premolar 
series less widely spaced ; third upper molar nearly as large as sec- 
ond (decidedly smaller in hcspcria). 

Measurements. — Type (measured in flesh) : Total length, 68 mm. ; 
tail vertebrae, lo; tibia, i2.'/; hind foot, ii; forearm, 33.9. Skull 
(type): Greatest length, 23.4; condylobasal length, 22.4; interor- 
bital breadth, 4.6 ; breadth of braincase, 9.3 ; mastoid breadth, 9.8 ; 
depth of braincase at middle, 6.9; palatal length, 12.3; length of 
mandible, 16.8 ; maxillary tooth row, 8. 

Remarks. — In the general form of the skull this species is in all 
essential respects like L. mordax and L. robusta and unlike L. hes- 
peria in which the skull is relatively much narrower and more 
elongated. The narrowness and C haeronycteris-liko. appearance of 
the skull of L. hespcria has been pointed out by Mr. Gerrit S. Miller, 
Jr.^ The greater relative as well as actual length of the rostrum 
in hesperia leaves the third upper molar implanted well in front of 
the maxillary processes of the zygoma as in the genus Chaeronyc- 
teris instead of in the same horizontal plane with these processes 
as in mordax and robusta. In the narrowness of the second upper 
premolar, however, L. concava approaches hesperia, the conspicu- 
ous inner lobe present in mordax and robusta being reduced to a 
slight swelling bearing a small cusp. The coronoid process in con- 
cava is somewhat intermediate in shape between the high angular 
form seen in mordax and the low, broadly rounded upper outline 
of hesperia. 

A small bat, Lionycteris spurrelU, from northwestern Colombia, 
has recently been described by Mr. Oldfield Thomas and made the 
type of a new genus characterized by the narrowness of the upper 
premolars. L. concava may possibly require comparison with the 
Colombian species which is based on an immature individual. But, 
allowing for immaturity, the cranial dimensions given are so differ- 
ent (greatest length, 18.7 in spurrelU, 23.4 in concava) that the spe- 
cific identity of the two seems very improbable. 

Specimens examined. — One, the type. 

LUTRA REPANDA, new species 

Type from Cana (altitude 2,000 feet), eastern Panama. No. 
179974, skin and skull, male adult, U. S. National Museum (Bio- 
logical Survey Collection), collected by E. A. Goldman, May 30, 
19 1 2. Original number 21758. 



^ Proc. U. S. Nat. Mus., vol. 42, No. 1882, p. 24, March 6, 1912. 



4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

General characters. — A small form with low, flat skull closely 
allied to L. columbiana, but differing in dental and, slight cranial 
characters, especially the lesser transverse extent of the large upper 
molariform teeth. Differing from L. latidens in much smaller size 
as well as cranial details. 

Color. — Entire upper parts warm sepia or mars brown (Ridgway, 
1912) ; under parts grayish brown, palest on throat, pectoral and 
inguinal regions ; lips and inner sides of forelegs soiled whitish. 

Skull. — Similar in size to that of L. colombiana; rostrum and 
interorbital space narrower; lachrymal eminence more prominent, 
projecting as a distant process on anterior border of orbit; jugal 
less extended vertically but bearing a postorbital process as in colom- 
biana; palate reaching farther posteriorly beyond molars; upper 
carnassial narrower, with inner lobe less produced posteriorly, leav- 
ing a gap which is absent in colombiana; upper molar narrower, the 
postero-external cusp set inward, giving the crown a less evenly rec- 
tangular outline. Contrasted with that of L. latidens the skull is 
very much smaller, with flatter frontal region. 

Measurements. — Type: Total length, 1085 mm.; tail vertebrae, 
500; hind foot, 119. An adult female from Gatun, Canal Zone: 
1095; 463; III. Skull (type) : Condylobasal length, 109. i ; zygo- 
matic breadth, 72; interorbital breadth, 23.1; postorbital breadth, 
16.8; mastoid breadth, 69.9; palatal length, 49.8; maxillary tooth 
row, 36.1 ; alveolar length of upper carnassial, 12.4 ; alveolar breadth 
of upper carnassial, 10. 

Remarks. — The otter of Panama, like other Middle American 
forms of Lutra, has the nose pad haired to near the upper border of 
the nostrils; the soles of the feet are entirely naked; the tufts of 
hair under the toes and the granular tubercles present on the soles 
of the hind feet in L. canadensis are absent. The frontal region is 
flatter in skulls of L. repanda than in the skull of the type of L. 
colombiana, but the more swollen condition of the latter may be due 
to the presence of the parasites that frequent the frontal sinuses 
in Mustelidae. 

Specimens examined. — Two, from localities as follows: 
Panama: Cana (type), i. 
Canal Zone: Gatun, i. 

FELIS PIRRENSIS, new species 
Type from Cana (altitude 2,000 feet), eastern Panama, No. 
1 79 1 62, skin and skull, female adult, U. S: National Museum (Bio- 
logical Survey Collection) ; collected by E. A. Goldman, March 22, 
19 1 2. Original number 21559. 



NO. 5 NEW Mx\iMMALS FROM PANAMA — GOLDMAN 5 

General characters. — A large, long-tailed tiger-cat, probably a 
member of the F. pardinoides group. Pelage rather long and soft ; 
fur of nape not reversed ; skull large with narrowly spreading zygo- 
mata and fully inflated audital bullae. 

Color. — Ground color of upper parts ochraceous tawny (Ridgway, 
1912), nearly uniform from nape to base of tail, but becoming 
somewhat paler on head and paling through cinnamon buff to pink- 
ish buff along lower part of sides; general upper surface heavily 
lined and spotted with black, the spots on sides more or less com- 
pletely encircling tawny areas, or forming rosettes; back of neck 
with a narrow median black line and two broader parallel lines, one 
on each side ; shoulders marked by heavy diagonal stripes extending 
from near a rounded solid black median spot downward and for- 
ward on each side ; posterior part of back with two narrow central 
lines extending to near base of tail; under parts white, heavily 
spotted with black across abdomen, and with black bars, one across 
throat and one across neck; outer- sides of- forearms and hind legs 
cinnamon buffy, spotted with black ; feet buft'y grayish interrupted 
by small black markings ; ears deep black, with white submarginal 
spots and buffy edges ; tail with about 12 broad, irregular, but nearly 
complete black rings, the narrow interspaces buffy above and white 
below. 

Skull. — Large and rather elongated, the vault of braincase highest 
near f ronto-parietal suture ; frontal region broad ; zygomata slightly 
spreading posteriorly, the squamosal arms not strongly bowed out- 
ward ; palate narrow ; audital bullae large and much inflated anteri- 
orly. 

Measurements. — Type : Total length, 963 mm. ; tail vertebrae, 440 ; 
hind foot, 131. 5. Skull (type) : Greatest length, 99.6; condylobasal 
length, 95.6; zygomatic breadth, 62.8; interorbital breadth, 18.5; 
length of nasals (median line), 17.6; greatest breadth of nasals, 13; 
intertemporal breadth of braincase, 34 ; breadth between tips of post- 
orbital processes, 51.5; length of palate, 38.5; length of upper in- 
cisive tooth row, 12.2; alveolar length (outer side) of upper car- 
nassial, 11.6. 

Remarks. — This tiger cat is provisionally referred to the little 
known F. pardinoides group. In size it seems nearer to the F. wiedii 
group, but it lacks the reversed pelage of nape commonly ascribed 
to that group. Moreover, the skull is more elongated than in the 
available Mexican and Brazilian specimens used for comparison 
and assumed to represent the F. wiedii group. It may be similar 



6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 63 

to F. pardinoides oncilla Thomas, from Volcan de Irazti, Costa Rica, 
but the type of the latter without skull is described as a much smaller 
animal with clay colored under parts. No comparison with the 
forms of Felis pajeros seems necessary. 
Specimens examined. — One, the type. 

AOTUS ZONALIS, new species 

Type from Gatun (altitude loo feet), Canal Zone, Panama, No. 
1 7 123 1, skin and skull, female adult, U. S. National Museum (Bio- 
logical Survey Collection) ; collected by E. A. Goldman, April 29, 
1911. Original number 21101. 

General characters. — Resembling A. griseimemhra, but general 
color more buffy, less grayish ; skull broader and differing in numer- 
ous details ; dentition heavier. 

Color. — General shade of upper parts, limbs and upper base of 
tail near wood brown (Ridgway, 1912) with a buffy suff'usion, this 
color more or less heavily overlaid with russet and black along 
median line of back ; head marked with narrow black lateral lines 
converging to a point on back of neck, and a black median frontal 
line extending from between eyes to crown ; white spots above and 
below eyes ; sides of neck grayish in some specimens ; under parts 
light ochraceous-buff ; feet blackish ; proximal third of under side 
of tail usually stained with chestnut, the distal two-thirds black all 
round. 

Skull. — Similar in general size to that of ^. griseimemhra, but 
broader, the greater breadth most noticeable in the braincase ; inter- 
orbital region more depressed, materially altering the facial angle; 
frontals less extended posteriorly between parietals ; parietals joined 
by a longer suture owing to lesser posterior development of frontals ; 
supraoccipital reaching farther upward in a wedge-shaped extension 
between parietals ; zygomatic portion of jugal heavier ; audital bullae 
less inflated in front of meatus ; mandible broader and heavier, the 
angle more everted ; molariform teeth heavier. 

Measurements. — Type: Total' length, 683 mm.; tail vertebrae, 
400; hind foot, 90. Average of two adult female topotypes: 
637 (620-654) ; 357 (325-390) ; 85.5 (83-88). An adult male from 
Boca de Cupe: 670; 360; 90. Skull (type) : Greatest length, 60.9; 
condylobasal length, 47.2 ; zygomatic breadth, 37.5 ; breadth between 
outer sides of orbits, 43.3; postorbital breadth, 31.5; mastoid 
breadth, 33.8 ; interorbital breadth, 5.2 ; palatal length, 17.5 ; maxil- 
lary tooth row, 18.3. 



NO. 5 NEW MAMMALS FROM PANAMA — GOLDMAN "J 

Remarks. — This species, the only known nocturnal monkey of 
Panama, closely resembles A. griseimembra of the Santa Marta 
region of Colombia in external appearance, the principal difference 
being a more general buffy suffusion of the body and limbs. The 
skull, however, differs in many important respects and the larger 
molariform teeth of the Panama animal would alone serve as a dis- 
tinguishing character. 

Specimens examined. — Total number, lo, from localities as fol- 
lows: 

Canal Zone: Gatun (type locality), 4. 

Panama : Cana, 3 ; Boca de Cupe, 3. 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 

VOLUME 63, NUMBER 6 



SMITHSONIAN 

PHYSICAL TABLES 

SIXTH REVISED EDITION 



PREPARED BY 

FREDERICK E. FOWLE 

AID, SMITHSONIAN ASTROPHYSICAL OBSERVATORY 






/fi 




m 



S^-^ 



(Publication 2269) 



CITY OF WASHINGTON 

PUBLISHED BY THE SMITHSONIAN INSTITUTION 

1914 



^ 



ADVERTISEMENT. 

In connection with the system of meteorological observations established by 
the Smithsonian Institution about 1850, a series of meteorological tables was 
compiled by Dr. Arnold Guyot, at the request of Secretary Henry, and the first 
edition was published in 1852. Though primarily designed for meteorological 
observers reporting to the Smithsonian Institution, the tables were so widely used 
by physicists that it seemed desirable to recast the work entirely. It was decided 
to publish three sets of tables, each representative of the latest knowledge in its 
field, and independent of one another, but forming a homogeneous series. The 
first of the new series. Meteorological Tables, was published in 1893, the second, 
Geographical Tables, in 1894, and the third, Physical Tables, in 1896. In 1909 
yet another volume was added, so that the series now comprises : Smithsonian 
Meteorological Tables, Smithsonian Geographical Tables, Smithsonian Physical 
Tables, and Smithsonian Mathematical Tables, 

The fourteen years which had elapsed in 19 10 since the publication of the first 
edition of the Physical Tables, prepared by Professor Thomas Gray, had brought 
such changes in the material upon which the tables must be based that it became 
necessary to make a radical revision for the sth revised edition issued in 1910. 
That revision has been still further continued for the present sixth edition. 

Charles D. Walcott, 
Secretary of the Smithsonian Institution, 
yune, 19 14. 



PREFACE TO THE 5™ REVISED EDITION. \ 

The present Smithsonian Physical Tables are the outcome of a radical revision 
of the set of tables compiled by Professor Thomas Gray in 1896. Recent data 
and many new tables have been added for which the references to the sources 
have been made more complete ; and several mathematical tables have been 
added, — some of them especially computed for this work. The inclusion of these 
mathematical tables seems warranted by the demand for them. In order to pre- 
serve a uniform change of argument and to facilitate comparison, many of the 
numbers given in some tables have been obtained by interpolation in the data 
actually given in the papers quoted. 

Our gratitude is expressed for many suggestions and for help in the improve- 
ment of the present edition : to the U. S. Bureau of Standards for the revision of 
the electrical, magnetic, and metrological tables and other suggestions ; to the 
U. S. Coast and Geodetic Survey for the revision of the magnetic and geodetic 
tables ; to the U. S. Geological Survey for various data ; to Mr. Van Orstrand for 
several of the mathematical tables ; to Mr. Wead for the data on the musical 
scales ; to Mr. Sosman for the new physical-chemistry data ; to Messrs. Abbot, 
Becker, Lanza, Rosa, and Wood ; to the U. S. Bureau of Forestry and to others. 
We are also under obligation to the authors and publishers of Landolt-Bornstein- 
Meyerhoffer's Physikalisch-chemische Tabellen (1905) and B. O. Peirce's Mathe- 
matical Tables for the use of certain tables. 

It is hardly possible that any series of tables involving so much transcribing, 
interpolation, and calculation should be entirely free from errors, and the Smith- 
sonian Institution will be grateful, not only for notice of whatever errors may be 
found, but also for suggestions as to other changes which may seem advisable for 
later editions. 

F. E. FowLE. 

ASTROPHYSICAL OBSERVATORY 

OF THE Smithsonian Institution, 
June, 1910 

PREFACE TO THE 6th REVISED EDITION. 

The revision commenced for the fifth edition has been Continued ; a large pro- 
portion of the tables have been rechecked, typographical errors corrected, later 
data inserted and many new tables are added, including among others a new set of 
wire tables from advance sheets courteously given by the Bureau of Standards, 
new mathematical tables computed by Mr. Van Orstrand and those on Rontgen 
rays and radioactivity. The number of tables has been increased from 335 to 
over 400. We express our gratitude to the Bureau of Standards, to the Geophysical 
Laboratory, the Geological Survey, and to those who have helped through sug- 
gested improvements, new data, or by calling our attention to errors in the earlier 
editions. 

F. E. FowLE. 

ASTROPHYSICAL OBSERVATORY 

OF THE Smithsonian Institution, 
October, 191 3. 



TABLE OF CONTENTS. 



Introduction on units of measurement and conversion factors 
Units of measurement : general discussion .... 
Dimension formulae for dynamic units 

" " " heat units 

" of electric and magnetic units •• general discussion 

" formulae in electrostatic system .... 

" " " electromagnetic system 

Practical units of electricity, legalization of . 



PAGE 

xvii 
xvii 
xix 

XXV 

xxvii 

xxviii 

xxxi 

XXXV 



TABLE 
I. 



4- 

5- 
6. 

7- 
8. 

9- 

ID. 
II. 
12. 

13- 
14. 

15- 
16. 

i7. 



Formulae for conversion factors : (a) Fundamental units ... 2 

(i>) Derived units ... 2 

I. Geometric and dynamic units 2 

II. Heat units .... 3 

III. Magnetic and electric units 3 
Tables for converting U. S. weights and measures : 

(i) Customary to metric ........ 5 

(2) Metric to customary ........ 6 

Equivalents of metric and British imperial weights and measures : 

(i) Metric to imperial . 7 

(2) Multiples, metric to imperial 8 

(3) Imperial to metric ........ g 

(4) Multiples, imperial to metric . . . . . .10 

Volume of a glass vessel from weight of its volume of water or mercury 1 1 

Derivatives and integrals 12 

Series 13 

Mathematical constants .14 

Reciprocals, squares, cubes and square roots of nattiral numbers . 15 

Logarithms, 1000-2000 ......... 24 

Logarithms 26 

Antilogarithms 28 

Antilogarithms, .9000-1.0000 ........ 30 

Circular (trigonometric) functions, argument (°, '•) . . . -32 
" " " argument (radians) . . -37 

Logarithmic factorials, n!, n = i to 100 40 

Hyperbolic functions 41 

Factorials, 1-20 47 



VI 



CONTENTS. 



19. 
20. 

21. 

22. 

23- 
24. 

25- 

26. 

27. 

28. 
29. 

so- 
32. 



Exponential functions ^ . . 48 

Values of e^'^ and ^~* and their logarithms 



34- 
35- 



36 

37 

38 

39 
40 

41 
42 

43 
44 

45 
46 

47 
48 

49 
50 
51 



" " ^4 and^" " " " 

Vt — Vt 

" " dr~'^and ^ * "* " " 

" " e^ and <?~-^ and " " for fractional values of x 

Probability of errors of observations : probability integral 



Values of 0.6745 ^/ 

" " 0.6745 J-^^ 
\n{ii—\) 



" 0.8453 



\n(n — i) 



" 0.8453 „^/ ■ 



;^2. Value for^ ^(i — sin26sin^<^)±id$ for different values of 6 ; also the cor- 



responding logarithms 

Moments of inertia, radii of gyration, corresponding weights 
Strength of materials : (a) metals 
(^) stones 

(<r) brick .... 
(d) concretes . 
" " *' timber tests 



Moduli of rigidity 

Variation of the moduli of rigidity with the temperature 
Young's modulus ....... 

Compressibility of the more important solid elements 
Hardness ........ 

Relative hardness of the elements 

Poisson's ratio ....... 

Elastic moduli of crystals, formulae 

" " " " numerical results 

Compressibility of O, air, N, H at different pressures and temperatures 
" " ethylene " " 

" " carbon dioxide at " ** 

" ** gases, values of a . 



54 

55 

55 
56 
56 
57 

57 
58 
58 
58 



Least-squares formulae 59 

Inverse of probability integral. Diffusion 60 

Logarithms of the gamma function T{n) for values of n between i and 2 62 

Values for the first seven zonal harmonics from 6 = 0° to ^=90° . 64 



66 
67 
68 
68 
68 
68 
69 
70 
71 
71 
72 

73 
73 
73 
73 
74 

75 
76 

76 
76 

77 
77 



CONTENTS. 



Vll 



52- 
53- 
54- 
55- 
56. 
57- 
58. 
59- 
60. 
61. 
62. 

^3- 

64. 
65. 
66. 
67. 
68. 
69. 
70. 

71- 

72. 

73- 
74- 

75- 
76. 

77- 
78. 

79- 
80. 
81. 
82. 

83- 
84. 

85. 
86. 
87. 
88. 
89. 
90. 
91. 
92. 

93- 

94. 

95- 
96. 



Compressibility of air and oxygen between 18° and 22°C 

Relation between pressure, temperature and volume of sulphur dioxide 

" " " " " " " ammonia 

Compressibility of liquids 

" " solids 

Specific gravities corresponding to the Baumd scale 
Reduction of weighings in air to vacuo 

" densities " " " " 
Densities of the solid and liquid elements 

" " various woods . 

" " " solids . 
" " alloys . 

" " " natural and artificial minerals 

" " molten tin and tin-lead eutectic 
Weight in grams per square meter of sheet metal 

" " various common units of sheet metal . 
Densities of various liquids 

" " '* gases ....... 

" '« " aqueous solutions of salts, bases and acids 
Density of water free from air between 0° and 36° C . 
Volume of water at temperatures between 0° and 36° C in terms of its 

volume at the temperature of maximum density . . . . 
Density and volume of water at different temperatures from-io to 25o°C 

" " " " mercury at " " " -10 " 36o°C 

Densities aqueous ethyl alcohol. Temp, variation . . . . 

" " mixtures methyl alcohol, cane-sugar or sulphuric acid 

Velocity of sound in solids . 

'* " " " liquids and gases . 
Musical scales 



Acceleration of gravity at sea level and different latitudes . 

Results of some of the more recent gravity determinations . 

Value of gravity at some of the U. S. C. and G. Survey stations 

Length of seconds pendulum for sea level and different latitudes 

Determinations of the length of the seconds pendulum 

Miscellaneous geodetic data 

Lengths of degrees on earth's surface 

Miscellaneous astronomical data . 

Planetary data .... 

Equation of time .... 

Miscellaneous astronomical data . 

Terrestrial magnetism : secular change of declination 

" " dip or inclination . 

" " secular change of dip 

" ** horizontal intensity 

«* " secular change of horizontal intensity 



77 

78 
78 

79 
80 
81 
82 
82 
83 

85 
86 

87 
88 
88 
89 
89 
90 

91 
92 

94 

95 
96 

97 

98 

100 

lOI 

102 
103 
103 
104 

105 
106 
107 
107 
108 
108 
109 
no 
no 
no 
III 
113 
113 
114 
114 



VUl 



CONTENTS. 



ty 



97. Terrestrial magnetism : total intensity 

98. " " secular change of total intens 

99. " " agonic line . 
100. Magnetic elements at magnetic observatories 
loi. Pressure of mercury and water columns 

102. Reduction of barometer to standard temperature 

103. " " " " " gravity, inch and metric scales 

104. " " *' " latitude 45° : inch scale 

105. " " " " " " metric scale 

106. Correction of barometer for capillarity : inch and metric scale . 

107. Volume of mercury meniscus in cu. mm. ..... 

108. Aerodynamics : data for wind pressures 

109. " " " the soaring of planes .... 
no. Coefficients of friction . . 

111. Lubricants 

112. " for cutting tools 

113. a Viscosity of water at different temperatures .... 
b Specific viscosity of water at different temperatures 

114. Coefficients of viscosity for solutions of alcohol in water . 

115. Specific viscosity of mineral oils 

116. " " " various oils 

117. Viscosity of various liquids 

118. " " " " temperature variation 

119. Specific viscosity of solutions : variation with density and temperature 

120. " " " " atomic concentrations 

121. Viscosity of gases and vapors 

122. " " air 2o?2 C 

123. " " gases and vapors, temperature variation . 

124. Diffusion of an aqueous solution into pure water 

125. " *' vapors 

126. " " gases and vapors 

127. " " metals into metals 

128. Solubility of inorganic salts in water : temperature variation 

129. " ** a few organic salts in water : temperature variation 

130. " " gases in water 

131. " , change produced by uniform pressure 
T32. Absorption of gases by liquids 

133. Capillarity and surface tension : water and alcohol in air . 

134. " " " " miscellaneous liquids in air 

135. " " " " aqueous solutions of salts . 

136. Capillarity and surface tension : liquids in contact with air, water or 

mercury .......... 

137. Capillarity and surface tension : liquids at solidifying point 

138. " " *' " thickness of soap films 

139. Vapor pressures 

140. " " of ethyl alcohol 



CONTENTS. 



378^ 



141. Vapor pressures of methyl alcohol .... 

142. " " and temperatures: (a) carbon disulphide 

(d) chlorobenzine 
(c) bromobenzine 
(^) aniline . 

(e) methyl salkjX'late 
(/) bromonaphmaline 
(g) mercury 

143. Vapor pressure of solutions of salts in water 

144. Pressure of saturated aqueous vapor at low temperature over ice 

145. " " " " " " " " " water 

146. " " « " " o°t0 5o°C 
147- " " " " " 50° to 374° C . 

148. Weight in grains of aqueous vapor in a cubic foot of saturated air 

149. " " grams " " " " " " meter of " " 

150. Hygrometry, vapor pressure in the atmosphere 

151. " dew-points .... 

152. Relative humidity 

153. Values of 0.378^ in the atmospheric pressure equation /i = B — o 

154. Table for facilitating the calculation of /i/ySo 
^55- Logarithms of ^7760 for values of A between 80 and 800 

156. Values of 1+0.00367 /: 

(a) for values of / between 0° and 10° C, by tenths . 
{^) " " " " " - 90° '• + 1990° C, by tens 

(c) Logarithms for / "—49° " +399° C, by units 
(^) " " " " 400° " 1990° C, by tens . 

157. Determination of heights by the barometer 

158. Barometric pressures corresponding to different temperatures of the 

boiling-point of water : 

(a) Common measure 

(d) Metric measure 

159. International Primary wave-length standard, Red Cd. line . 

160. " Secondary " standards Fe. arc lines . 

161. Additional standard Fe. lines 

162. Stronger lines of some of the elements .... 

163. Rowland's standard solar wave-lengths (also corrections) . 

164. Tertiary standard wave-lengths Fe. arc lines 

165. Wave-lengths of the Fraunhofer lines 

166. Photometric standards 

167. Intrinsic brightness of various lights 

168. Visibility of white lights 

169. Efficiency of various electric lights 

170. Sensitiveness of the eye to radiation of different wave-lengths 

(threshold) intensities 

171. Sensitiveness of the eye : greater intensities 

172. Sensibility of the eye to small differences of intensity (Fechner) 



low 



CONTENTS. 



173- 
174. 

175- 
176. 

177. 
178. 
179. 
180. 
181. 
182. 

183. 

184. 

185. 

186. 

187. 

188. 
189. 

190. 

191. 

192. 

193- 
194. 

195- 
196. 

197. 
198. 



199. 

200. 
201. 

202. 

203. 

204. 

205. 

206. 

207. 

208. 

209. 

210. 
211. 
212. 
213. 
214. 
215. 



The solar constant and temperature .... 
Solar spectrum energy ; atmospheric transparency 
Distribution of solar energy in spectrum 
Distribution of intensity of radiation over solar disk . 
Transmissibility of radiation by dry and moist air 

Brightness of sk^ 

Relative intensmes of sun- and sky-light 

Air masses ....••••• 

Relative intensities of solar radiation — monthly change 

Mean monthly and yearly temperatures 

Indices of refraction of Jena glasses .... 

" ** " u « u .... 

'« " '< « a " temperature coefficients 

" " *' for rock salt .... 

" « " " " " temperature coefficients 

" " " " sylvine 

'« " " " fluorite 

" «' « " " temperature coefficients 

" " " " Iceland spar 

" " " " nitroso-dimethyl-aniline 

" " " " quartz 

" " " " various alums 

" " " " " monorefringents 

" •' " " " uniaxial crystals 

<' " " *' " biaxial crystals 

" '* " " solutions of salts and acids : 

(a) solutions in water 
(I?) " " alcohol . 

(r) " " potassium permanganate 

*' " " " various liquids 

" •' ** " gases and vapors . 

Standard refractive media : n = 1.74 to 1.87 
" " '' n= 1.68 to 210 

" " " «= 1.546 to 1.682 . 

Optical constants of metals — (definitions) 



Reflecting power of metals 

Reflection of light, perpendicular incidence : various values 
" " " incidence varying : n near unity 
" " " " " « = i.55 . 

Reflection from metals 

" " various materials .... 

Transmissibility of radiation by Jena glasses 

«« " " " " ultra-violet glasses 



of n 



CONTENTS. 



XI 



«l6. 

217. 

218. 

219. 

219a. 

220. 

221. 

222. 

223. 

224. 

225. 

226. 

227. 

228. 

229. 

230. 

231. 



232. 

233- 
234- 

235- 
236. 

237- 
238. 

239- 
240. 
241. 
242. 

243- 
244. 



245- 
246. 
247. 
248. 
249. 
250. 



. 203 
and quartz 203 

• 204 



Transmissibility of radiation by alum, rock salt, sylvine, fluorite, Ice 

land spar, quartz .... 
Color screens (Landolt) 
(Wood) 
" " (Jena glasses) 

Transmissibility of radiation by water 
Rotation of the plane of polarized light by solutions . 

" " " " " " " sodium chlorate 

Colors of thin films, Newton's rings .... 
Thermal conductivity of metals and alloys . 
Thermal conductivity at high temperature . 
" '* of various substances 

'* " " water and salt solutions 

'* " *' organic liquids 

" " " gases 

Diffusivitles 

Heat of combustion 

Heat values and analyses of various fuels : {a) coals . 

(b) peats . 

(c) liquid fuels 
Chemical and physical properties of explosives 
Heat of combination .... 
Latent heat of vaporization 

" " " fusion .... 
Melting-points of the chemical elements 
Boiling-points " " " " 

Densities, melting and boiling points, inorganic compounds 
Effect of pressure on melting points . 

" " " " freezing point of water 
Melting points of various mixtures of metals 



points of organic compounds 



Low-melting-point alloys 
Densities, melting-points, boiling- 

{d) Paraffin series . 

(b) Olefine series 

{c) Acetylene series 

{(f) Monatomic alcohols 

(<?) Alcoholic ethers 

(/) Ethyl ethers 

{g) Miscellaneous . 
Transformation and melting-points, minerals and 
Lowering of freezing-points by salts in solution 
Raising of boiling-points by salts in solution 
Freezing mixtures ..... 
Critical temperatures, pressure, volumes and densities of gases 
Coefficients of linear expansion of the chemical elements . 



eutectics 



xu 



CONTENTS. 



251. 
252. 
253- 
254- 

255- 

256. 

257- 
258. 

259- 

260. 
261. 
262. 

263. 

264. 
265. 

266. 

267. 

268. 

269. 
270. 
271. 
272. 

273- 
274. 

275- 
276. 

277. 
278. 
279. 
280. 
281. 
282. 
283. 
284. 
285. 
286. 
287. 
288. 
289. 

290. 
291. 
292. 

293- 
294. 



Coefficients of linear expansion of miscellaneous substances . . 233 

" *' cubical " " crystalline and other solids . . 234 

" " " " liquids 235 

'* " thermal expansion of gases 236 

Mechanical equivalent of heat : various data 237 

" " " " adopted values (Ames) . . . 237 

" " " '* conversion values .... 237 

Specific heats of the chemical elements 238 

" " " water and mercury 239 

Additional specific heats of the elements 240 

Mean specific heats of quartz, silica glass and platinum . . .240 

Specific heats of various solids 241 

" " " " liquids 241 

" " " *' minerals and rocks 242 

" " " " gases and vapors 243 

Gas and mercury thermometers : formulae 244 

Comparison of hydrogen and 16'" thermometers : 0° to 100° C . 244 

" «' " " 59'" " 0° to 100° C. . 244 

" " " " 16'" and 59"' thermometers: -5° to-35°C. 244 

Comparison of air and 16"' glass thermometers: 0° to 300° C. . . 245 

" " «' " 59"' " " 100° to 200° C. . 245 

" " hydrogen and various mercury thermometers . . 246 

" " air and high temperature (59"') mercury thermometer . 246 

" " H., toluol, alcohol, petrol ether, pentane thermometers 246 

Platinum resistance thermometry 247 

Thermodynamic scale ; temperature of ice-point .... 247 

Standard points for calibration of thermometers .... 247 

Stem correction for thermometers 248 

.... 249 

. 249 

Calibration of thermo-element Pt.-Pt. Rh 250 

" " " " Cu-Constantan 250 

Radiation formulae and constants for perfect radiator . . . .251 

" in calories for perfect radiators at various temperatures . 251 

" distribution in spectrum at various temperatures . .251 

Cooling by radiation and convection : ordinary pressures . 

" " " " " different pressures . 

" " " " " very small pressures 

" " " " " temperature and pressure effects 

Properties and constants of saturated steam : metric measure 

•' " " " " " common measure . 

Ratio of the electrostatic to the electromagnetic unit of electricity 
Electromotive force of standard cells : absolute current measures 

Data for voltaic cells : {a) double fluid cells 

(J?) single fluid cells 

(<r) standard cells 



CONTENTS. 



xm 



294. 

295- 

296. 
297. 
298. 
299. 
300. 
301. 
302. 

303- 
304- 

305- 
306. 

307- 
308. 

309- 
310. 

311- 
312. 

3^3- 
314- 

315- 
316. 

317- 
318. 

319- 
320. 
321. 
322. 

323- 
324- 

325- 
326. 

327- 
328. 

329- 
330- 
331- 
332. 
333- 
334- 
335- 
336. 
337- 
338- 



Data for voltaic cells : (^) secondary (storage) cells . . . . 
Contact differences of potential, solids with liquids and liquids with 

liquids in air 

Contact differences of potential, solids with solids in air 
Potential difference between metals in various salt solutions 
Thermoelectric powers 

" " with alloys 

" " " platinum 

<' '* of Pt. with Pt. Rh. alloys 

Peltier effect 

" " Fe-constantan, Cu-constantan 

" " E. M. F. in volts . 

Various determinations of the ohm 
Specific resistance of metallic wires . 
Specific resistance of metals 
Temperature resistance coefficient 
Conductivities of three-metal and other alloys 

" alloys .... 
Allowable carrying capacity rubber-covered copper wires . 
Resistance of metals and alloys at low temperatures . 
Temperature variation of electrical resistance of glass, porcelain 
Temperature resistance coefficients of glass, porcelain, quartz 

Tabular comparison of wire gages 

Wire tables. Mass and volume resistivities of Cu. and Al. 
" " Temperature coefficients of copper 

" *' Reduction to standard temperatures 

" " Standard annealed copper wire, English units 

<' " " " " " metric units 

" " Hand-drawn aluminum wire, English units . 

" " " " " " metric units 

Dielectric strength ; steady potential for spark in air . 

" " alternating potential for spark in air . 

" " potentials for longer sparks in air 

" *' effect of (air) pressure .... 

" ** of various materials .... 

" ** " kerosene ...... 

Electric resistance with alternating currents (straight wires) 
" " for high frequencies .... 

Wireless telegraphy ; wave-lengths, frequencies, oscillation constant 

" " radiation resistance for various wave-lengths 

International atomic weights and electrochemical equivalents 

Conductivity of a few dilute solutions 

Electrochemical equivalents and densities of nearly normal solutions 
Specific molecular conductivity of solutions .... 
" " *' " " limiting values 

" " " *' ** temperature coefficients 



263 



CONTENTS. 



339- 
34°- 
341- 
342- 
343- 
344- 

345- 

346. 
347- 
348. 

349- 
350- 
351- 
352. 
353- 



354- 
355- 
356. 
357- 
358. 

359- 
360. 
361. 
362. 

2^3- 
364- 
365- 
366. 

367- 
368. 

369- 
37°- 
371- 
372- 
373- 
374- 
375- 
376- 
377- 
378. 



Equivalent conductivity of salts, acids, bases in solution 

" " " some additional salts in solution 

" conductance of the separate ions 

Hydrolisis of ammonium acetate : ionization of water 
Dielectric constants (specific inductive capacity) of gases 

" " " " " " " temperature 

coefficient 

Dielectric constants (specific inductive capacity) of gases: pressure co 

efficient 

Dielectric constants of liquids ..... 

" " " " temperature coefficient . 

" " " liquefied gases 

" " " standard solutions for calibrations 

" " " solids 

" " " crystals 

Permeability of iron rings and wire, various inductions 
Permeability of transformer iron : 

(a) specimen of Westinghouse No. 8 transformer 

(d) " " " " 6 

(c) " " " " 4 " 

(//) " " Thomson-Houston 1500-watt transformer . 

Magnetic properties of iron and steel . 

" " " cast iron in intense fields 

" corrections for ring specimens 
Composition and magnetic properties of iron and steel 
Permeability of some of the specimens in Table 303 
Magnetic properties of soft iron at 0° and 100° C. 

" " " steel at 0° and 100° C. . 

" " " cobalt at 100° C. . 

" nickel " " " . 

" " " magnetite 

" " " Lowmoor wrought iron . 

" " " Vicker's tool steel . 

" " " Hadfield's manganese steel 

Saturation values for different steels . 
Magnetic properties of iron in very weak fields . 
Dissipation of energy in cyclic magnetization of magnetic substances 

" " " " " " " cable transformers 

Demagnetizing factors for rods ....... 

" " Shuddemagen's values .... 

Dissipation of energy in cyclic magnetization of various substances 

" " " " " " " transformer steels 

Magneto-optic rotation, formulae : Verdet's constant . 

" " " in solids ...... 

" " " " liquids 

" " " " solutions of salts and acids in water . 



CONTENTS. 



XV 



379. Magneto-optic rotation, gases . 

380. Verdet's and Kundt's constants . 

381. Values of Kerr's constant .... 

382. Dispersion of Kerr's effect. IngersoU's values 

383. " " " " Foote's 

384. Magnetic susceptibility .... 

385. Variation of the resistance of bismuth in magne 

386. " " " " " nickel " 

387. " " " " " various metals in a 

388. Transverse galvanomagnetic and thermomagnet 

389. Variation of the Hall constant with the tempera 

390. Rontgen rays (x-rays) ionization due to 

391. " " Secondary Rontgen rays 

392. " " " Cathodic rays 

393. " " '* absorption coefficients 

394. X-R spectra and atomic numbers 

395. Radioactivity: production of phosphorescence 

396. " " " a-particles 

397. " heating effects 

398. " various constants 

399. " stopping powers for a rays . 

400. " ♦' " " ^ " 

401. " " *' " y « 

402. " ions produced by the a, ^, and y 

403. " radium emanation ; units 

404. " vapor pressure of Ra emanation 

405. " spectra .... 

406. Miscellaneous constants, molecular, atomic, etc. 

407. Periodic system of the elements . 

Definitions of units 

Index 



ic field 

a 

magnetic 
c effects 
ure 



field 



rays 



330 
330 
331 
33^ 
33^ 
332 
333 
333 
333 
334 
334 
335 
335 
335 
33^ 
336 
337 
337 
337 
338 
340 
340 
340 
341 
341 
341 
341 
342 
343 

345 
349 



INTRODUCTION. 



UNITS OF MEASUREMENT AND CONVERSION FORMULA. 

Units. — The quantitative measure of anything is a number which expresses the 
ratio of the magnitude of the thing to the magnitude of some other thing of the 
same kind. In order that the number expressing the measure may be intelligi- 
ble, the magnitude of the thing used for comparison must be known. This leads 
to the conventional choice of certain magnitudes as units of measurement, and 
any other magnitude is then simply expressed by a number which tells how many 
magnitudes equal to the unit of the same kind of magnitude it contains. For 
example, the distance between two places may be stated as a certain number of 
miles or of yards or of feet. In the first case, the mile is assumed as a known 
distance ; in the second, the yard, and in the third, the foot. What is sought for 
in the statement is to convey an idea of the distance by describing it in terms of 
distances which are either familiar or easily referred to for comparison. Similarly 
quantities of matter are referred to as so many tons or pounds or grains and so 
forth, and intervals of time as a number of hours or minutes or seconds. Gen- 
erally in ordinary affairs such statements appeal to experience ; but, whether this 
be so or not, the statement must involve some magnitude as a fundamental quan- 
tity, and this must be of such a character that, if it is not known, it can be readily 
referred to. We become familiar with the length of a mile by walking over dis- 
tances expressed in miles, with the length of a yard or a foot by examining a yard 
or a foot measure and comparing it with something easily referred to, — say our 
own height, the length of our foot or step, — and similarly for quantities of other 
kinds. This leads us to be able to form a mental picture of such magnitudes 
when the numbers expressing them are stated, and hence to follow intelligently 
descriptions of the results of scientific work. The possession of copies of the 
units enables us by proper comparisons to find the magnitude-numbers express- 
ing physical quantities for ourselves. The numbers descriptive of any quan- 
tity must depend on the intrinsic magnitude of the unit in terms of which it is 
described. Thus a mile is 1760 yards, or 5280 feet, and hence when a mile is 
taken as the unit the magnitude-number for the distance is i, when a yard is taken 
as the unit the magnitude-number is 1760, and when a foot is taken it is 5280. 
Thus, to obtain the magnitude-number for a quantity in terms of a new unit when 
it is already known in terms of another we have to multiply the old magnitude- 
number by the ratio of the intrinsic values of the old and new units ; that is, by 
the number of the new units required to make one of the old. 



Xviii INTRODUCTION. 

Fundamental Units of Length and Mass. — It is desirable that as few 
different kinds of unit quantities as possible should be introduced into our measure- 
ments, and since it has been found possible and convenient to express a large 
number of physical quantities in terms of length or mass or time units and com- 
binations of these, they have been very generally adopted as fundamental units. 
Two systems of such units are used in this country for scientific measurements, 
namely, the customary, and the French or metric, systems. Tables of conversion 
factors are given in the book for facilitating comparisons between quantities ex- 
pressed in terms of one system with similar quantities expressed in the other. In 
the customary system the standard unit of length is the yard and is now defined 
as 3600/3937 meter. The unit of mass is the avoirdupois pound and is defined 
as 1/2.20462 kilogram. 

The British yard is defined as the " straight line or distance (at 62° F.) between 
the transverse lines in the two gold plugs in the bronze bar deposited in the office 
of the exchequer." The British standard of mass is the pound avoirdupois and 
is the mass of a piece of platinum marked "P. S. 1844, i lb.," preserved in the 
exchequer office. 

In the metric system the standard of length is the meter and is defined as the 
distance between two lines at 0° Centrigrade on a platinum iridium bar deposited 
at the International Bureau of Weights and Measures. This bar is known as the 
International Prototype Meter, and its length was derived from the " metre des 
Archives," which was made by Borda. Copies of the International Prototype 
Meter are possessed by the various governments, and are called " National 
Prototypes." 

Borda, Delambre, Laplace, and others, acting as a committee of the French 
Academy, recommended that the standard unit of length should be the ten mil- 
lionth part of the length, from the equator to the pole, of the meridian passing 
through Paris. In 1795 the French Republic passed a decree making this the 
legal standard of length, and an arc of the meridian extending from Dunkirk to 
Barcelona was measured by Delambre and Mechain for the purpose of realizing 
the standard. From the results of that measurement the meter bar was made 
by Borda. The meter is not now defined in terms of the meridian length, and 
hence subsequent measurements of the length of the meridian have not affected 
the length of the meter. 

The metric standard of mass is the kilogram and is defined as the mass of a 
piece of platinum-iridium deposited at the International Bureau of Weights and 
Measures. This standard is known as the International Prototype Kilogram. 
Its mass is equal to that of the older standard, the "kilogramme des Archives," 
■made by Borda and intended to have the same mass as a cubic decimeter of dis- 
tilled water at the temperature of 4° C. Copies of the International Prototype 
Kilogram are possessed by the various governments, and as in the case of the 
meter standards are called National Prototypes. 



INTRODUCTION. xix 

Comparisons of the French and customary standards are given in tabular form 
in Table 2 ; and similarly Table 3, differing slightly, compares the British and 
French systems. In the metric system the decimal subdivision is used, and thus 
we have the decimeter, the centimeter, and the millimeter as subdivisions, and 
the dekameter, hektometer, and kilometer as multiples. The centimeter is most 
commonly used in scientific work. 



Time. — The unit of time in both the systems here referred to is the mean 
solar second, or the 86,400th part of the mean solar day. The unit of time is 
thus founded on the average time required for the earth to make one revolution 
on its axis relatively to the sun as a fixed point of reference. 



Derived Units. — Units of quantities depending on powers greater than unity 
of the fundamental length, mass, and time units, or on combinations of different 
powers of these units, are called "derived units." Thus, the unit of area and of 
volume are respectively the area of a square whose side is the unit of length and 
the volume of a cube whose edge is the unit of length. Suppose that the area of 
a surface is expressed in terms of the foot as fundamental unit, and we wish to 
find the area-number when the yard is taken as fundamental unit. The yard is 
3 times as long as the foot, and therefore the area of a square whose side is a 
yard is 3 X 3 times as great as that whose side is a foot. Thus, the surface will 
only make one ninth as many units of area when the yard is the unit of length as 
it will make when the foot is that unit. To transform, then, from the foot as old 
unit to the yard as new unit, we have to multiply the old area-number by 1/9, or by 
the ratio of the magnitude of the old to that of the new unit of area. This is the 
same rule as that given above, but it is usually more convenient to express the 
transformations in terms of the fundamental units directly. In the above cace, 
since on the method of measurement here adopted an area-number is the product 
of a length-number by a length-number the ratio of two units is the square of the 
ratio of the intrinsic values of the two units of length. Hence, if / be the ratio 
of the magnitude of the old to that of the new unit of length, the ratio of the cor- 
responding units of area is /'. Similarly the ratio of two units of volume will be 
P, and so on for other quantities. 



Dimensional Formulse. — It is convenient to adopt symbols for the ratios 
of length units, mass units, and time units, and adhere to their use throughout ; 
and in what follows, the small letters, /, m, t, will be used for these ratios. These 
letters will always represent simple numbers, but the magnitude of the number 
will depend on the relative magnitudes of the units the ratios of which they repre- 
sent. When the values of the numbers represented by /, w, / are known, and the 
powers of /, ;;/, and / involved in any particular unit are also known, the factor for 
transformation is at once obtained. Thus, in the above example, the value of / 
was 1/3 and the power of / involved in the expression for area is /- ; hence, the 
factor for transforming from square feet to square yards is 1/9. These factors 



XX INTRODUCTION. 

have been called by Prof. James Thomson "change ratios," which seems an 
appropriate term. The term " conversion factor " is perhaps more generally 
known, and has been used throughout this book. 

Conversion Factor. — In order to determine the symbolic expression for the 
conversion factor for any physical quantity, it is sufficient to determine the degree 
to which the quantities length, mass, and time are involved in the quantity. Thus, 
a velocity is expressed by the ratio of the number representing a length to that 
representing an interval of time, or L/T, an acceleration by a velocity-number 
divided by an interval of time-number, or L/T'^, and so on, and the correspond- 
ing ratios of units must therefore enter to precisely the same degree. The fac- 
tors would thus be for the above cases, ///and Ijt"^. Equations of the form above 
given for velocity and acceleration which show the dimensions of the quantity in 
terms of the fundamental units are called " dimensional equations." Thus 

E = ML'^T-^ 

is the dimensional equation for energy, and ML'^T"^ is the dimensional formula 
for energy. 

In general, if we have an equation for a physical quantity 

Q = CL^M^T^, 

where C is a constant and LMT represents length, mass, and time in terms of one 
set of units, and we wish to transform to another set of units in terms of which 

LMT 

the length, mass, and time are L,M,T,, we have to find the value of ~,~,p^, which 
° ' ' ' LMT 

in accordance with the convention adopted above will be / m /, or the ratios of 

the magnitudes of the old to those of the new units. 

Thus Ly = L/, My = Mw, T;=:T/, and if Qy be the new quantity-number 

Qy = CLy^My'-Ty^ 

= CL"/»M*»z''T7' = Q^m% 

or the conversion factor is l"m^^, a quantity of precisely the same form as the 
dimension formula L^M^T". 

We now proceed to form the dimensional and conversion factor formulae for 
the more commonly occurring derived units. 

1. Area. — The unit of area is the square the side of which is measured by 
the unit of length. The area of a surface is therefore expressed as 

S = CL'', 

where C is a constant depending on the shape of the boundary of the surface 
and L a linear dimension. For example, if the surface be square and L be the 
length of a side C is unity. If the boundary be a circle and L be a diameter 
C = 7r/4, and so on. The dimensional formula is thus L\ and the conversion 
factor l'\ 

2. Volume. — The unit of volume is the volume of a cube the edge of which 
is measured by the unit of length. The volume of a body is therefore expressed as 



INTRODUCTION. Xxi 

V = CU, 

where as before C is a constant depending on the shape of the boundary. The 
dimensional formula is L** and the conversion factor P. 

3. Density. — The density of a substance is the quantity of matter in the unit 
of volume. The dimension formula is therefore M/V or ML~^, and conversion 
factor ;;//~^. 

Example. — The density of a body is 150 in pounds per cubic foot: required 
the density in grains per cubic inch. 

Here m is the number of grains in a pound := 7000, and / is the number of 
inches in a foot:^ 12 ; .*. nil"^ = 7000/12^ = 4-051. Hence the density is 150 X 
4.051 =607.6 in grains per cubic inch. 

Note. — The specific gravity of a body is the ratio of its density to the density of a standard 
substance. The dimension formula and conversion factor are therefore both unity. 

4. Velocity. — The velocity of a body at any instant is given by the equation 

v= — --, or velocity is the ratio of a length-number to a time-number. The di- 
a 1 

mension formula is LT~\ and the conversion factor //~^ 

Example. — A train has a velocity of 60 miles an hour : what is its velocity in 

feet per second ? 

Here /= 5280 and / = 3600 ;.*. //~^ = ^5.- — =^=1.467. Hence the velo- 

3600 30 

city = 60 X 1.467 = 88.0 in feet per second. 

5. Angle. — An angle is measured by the ratio of the length of an arc to the 
length of the radius of the arc. The dimension formula and the conversion 
factor are therefore both unity. 

6. Angular Velocity. — Angular velocity is the ratio of the magnitude of the 
angle described in an interval of time to the length of the interval. The dimen- 
sion formula is therefore T~\ and the conversion factor is t~'^. 

7. Linear Acceleration. — Acceleration is the rate of change of velocity or 

dv 
a = — ■• The dimension formula is therefore VT~^ or LT~l and the conversion 
dt ' 

factor is //~^ 

Example. — A body acquires velocity at a uniform rate, and at the end of one 
minute is moving at the rate of 20 kilometers per hour: what is the acceleration 
in centimeters per second per second ? 

Since the velocity gained was 20 kilometers per hour in one minute, the accel- 
eration was 1200 kilometers per hour per hour. 

Here /= 100 000 and /=36oo ; .•. //'■■^ = 100 000/3600^= .00771, and there- 
fore acceleration ::= .00771 X 1200 = 9.26 centimeters per second. 

8. Angular Acceleration. — Angular acceleration is rate of change of angu- 



XXn INTRODUCTION. 

lar velocity. The dimensional formula is thus — ^ — -—^ or T~^, and the 

conversion factor t~'\ 

g. Solid Angle. — A solid angle is measured by the ratio of the surface of 
the portion of a sphere enclosed by the conical surface forming the angle to the 
square of radius of the spherical surface, the centre of the sphere being at the 

vertex of the cone. The dimensional formula is therefore — — ^ or i, and hence 
the conversion factor is also i. 

10. Curvature. — Curvature is measured by the rate of change of direction of 
the curve with reference to distance measured along the curve as independent 

variable. The dimension formula is therefore , — ^^ or L~\ and the conversion 

length 

factor is Z"^. 

11. Tortuosity. — Tortuosity is measured by the rate of rotation of the tan- 
gent plane round the tangent to the curve of reference when length along the 

curve is independent variable. The dimension formula is therefore ,~^ — or 

length 

L~\ and the conversion factor is /~^. 

12. Specific Curvature of a Surface. — This was defined by Gauss to be. 
at any point of the surface, the ratio of the solid angle enclosed by a surface 
formed by moving a normal to the surface round the periphery of a small area 
containing the point, to the magnitude of the area. The dimensional formula is 

therefore ^:— or Lr\ and the conversion factor is thus /~^. 

surface 

13. Momentum. — Tkis is quantity of motion in the Newtonian sense, and is, 
at any instant, measured by the product of the mass-number and the velocity- 
number for the body. 

Thus the dimension formula is MV or MLT~\ and the conversion factor m//~^. 

Example. — A mass of 10 pounds is moving with a velocity of 30 feet per sec- 
ond: what is its momentum when the centimeter, the gram, and the second are 
fundamental units ? 

Here 7;/ = 453.59, 7=30.48, and /= i ; .-. w//-^ = 453.59 X 30-48= 13825. 
The momentum is thus 13825 X 10 X 30 = 4 147 500. 

14. Moment of Momentum. — The moment of momentum of a body with 
reference to a point is the product of its momentum-number and the number 
expressing the distance of its line of motion from the point. The dimensional 
formula is thus ML'^T"'^, and hence the conversion factor is mPt"'^. 

15. Moment of Inertia. — The moment of inertia of a body round any axis 
is expressed by the formula 2wr^, where m is the mass of any particle of the body 



INTRODUCTION. XXl'.I 

and r its distance from the axis. The dimension formula for the sum is clearly 
the same as for each element, and hence is ML^ The conversion factor is there- 
fore mV-. 

i6. Angular Momentum. — The angular momentum of a body round any 
axis is the product of the numbers expressing the moment of inertia and the 
angular velocity of the body. The dimensional formula and the conversion fac- 
tor are therefore the same as for moment of momentum given above. 

17. Force. — A force is measured by the rate of change of momentum it is 
capable of producing. The dimension formulae for force and '• time rate of 
change of momentum " are therefore the same, and are expressed by the ratio 
of momentum-number to time-number or MLT"^. The conversion factor is thus 
mlt-''. 

Note. — When mass is expressed in pounds, length in feet, and time in seconds, the unit force 
is called the poundal. When grams, centimeters, and seconds are the corresponding units the unit 
of force is called the dyne. 

Example. Find the number of dynes in 25 poundals. 

Here ;;/ = 453-59' ^ = 3o-48, and t= i ; .-. w//-^^ 453.59 X 30.48 = 13825 
nearly. The number of dynes is thus 13825 X 25 = 345625 approximately. 

18. Moment of a Couple, Torque, or Twisting Motive. — These are dif- 
ferent names for a quantity which can be expressed as the product of two numbers 
representing a force and a length. The dimension formula is therefore FL or 
ML^T"^, and the conversion factor is mPt~^. 

ig. Intensity of a Stress. — The intensity of a stress is the ratio of the num- 
ber expressing the total stress to the number expressing the area over which the 
stress is distributed. The dimensional formula is thus FL~^ or ML~^T~^, and the 
conversion factor is ml~^t~'. 

20. Intensity of Attraction, or " Force at a Point." — This is the force of 
attraction per unit mass on a body placed at the point, and the dimensional for- 
mula is therefore FM~'^ or LT~^, the same as acceleration. The conversion fac- 
tors for acceleration therefore apply. 

21. Absolute Force of a Centre of Attraction, or '♦ Strength of a Cen- 
tre." — This is the intensity of force at unit distance from the centre, and is there- 
fore the force per unit mass at any point multiplied by the square of the distance 
from the centre. The dimensional formula thus becomes FL^M~^ or L^T~^. The 
conversion factor is therefore l^t~'^. 

22. Modulus of Elasticity. — A modulus of elasticity is the ratio of stress 
intensity to percentage strain. The dimension of percentage strain is a length 
divided by a length, and is therefore unity. Hence, the dimensional formula of a 
modulus of elasticity is the same as that of stress intensity, or ML~^T~', and the 
conversion factor is thus also ;«/~V~^. 



Xxiv INTRODUCTION. 

23. Work and Energy. — When the point of application of a force, acting on 
a body, moves in the direction of the force, work is done by the force, and the 
amount is measured by the product of the force and displacement numbers. The 
dimensional formula is therefore FL or ML^T~^. 

The work done by the force either produces a change in the velocity of the body 
or a change of shape or configuration of the body, or both. In the first case it 
produces a change of kinetic energy, in the second a change of potential energy. 
The dimension formulae of energy and work, representing quantities of the same 
kind, are identical, and the conversion factor for both is mlH~'^. 

24. Resilience. — This is the work done per unit volume of a body in distort- 
ing it to the elastic limit or in producing rupture. The dimension formula is there- 
fore ML^T-'^L-^ or ML-^T-^, and the conversion factor ml-H-^. 

25. Power, or Activity. — Power — or, as it is now very commonly called, ac- 
tivity — is defined as the time rate of doing work, or if W represent work and P power 

P = — — . The dimensional formula is therefore WT~^ or ML^~^ and the con- 
dt 

version factor mPt~^, or for problems in gravitation units more conveniently _/7/~\ 

where/ stands for the force factor. 

Examples, {a) Find the number of gram centimeters in one foot pound. 

Here the units of force are the attraction of the earth on the pound * and 
the gram of matter, and the conversion factor is fi, where / is 453.59 and / is 
30.48. 

Hence the number is 453.59 X 30.48 = 13825. 

(J)) Find the number of foot poundals in i 000 000 centimeter dynes. 
Here m = i/453-59» ^= 1/30.48, and t=\; .: mPr^ = i/453-59 X 30-48^ 
and io^mPr'= 107453.59 X 3o-48'= 2.373. 

(c) If gravity produces an acceleration of 32.2 feet per second per second, how 
many watts are required to make one horse-power ? 

One horse-power is 550 foot pounds per second, or 550 X 32.2 = 17710 foot 
poundals per second. One watt is 10'' ergs per second, that is, 10'^ dyne centi- 
meters per second. The conversion factor is mPt^', where »« = 453-59, / = 30.48, 
and /= I, and the result has to be divided by 10'', the number of dyne centime- 
ters per second in the watt. 

Hence, ly-j 10 mPr^ 10' = 17710X 453-59 X 30.48710''= 746.3. 

(d) How many gram centimeters per second correspond to 33000 foot pounds 
per minute ? 

The conversion factor suitable for this case isy?/'\ where/is 453.59, /is 30.48, 
and / is 60. 

Hence, 33000//'^ =133000 X 453-59 X 30.48/60 = 7 604000 nearly. 

* It is important to remember that in problems like that here given the term " pound " or 
" gram " refers to force and not to mass. 



INTRODUCTION. XXV 



HEAT UNITS. 

I. If heat be measured in dynamical units its dimensions are the same as those 
of energy, namely ML^T~^ The most common measurements, however, are 
made in thermal units, that is, in terms of the amount of heat required to raise 
the temperature of unit mass of water one degree of temperature at some stated 
temperature. This method of measurement involves the unit of mass and some 
unit of temperature ; and hence, if we denote temperature-numbers by© and their 
conversion factors by 6, the dimensional formula and conversion factor for quan- 
tity of heat will be M0 and mO respectively. The relative amount of heat com- 
pared with water as standard substance required to raise unit mass of different 
substances one degree in temperature is called their specific heat, and is a simple 
number. 

Unit volume is sometimes used instead of unit mass in the measurement of 
heat, the units being then called thermometric units. The dimensional formula 
is in that case changed by the substitution of volume for mass, and becomes U®, 
and hence the conversion factor is to be calculated from the formula P9. 



For other physical quantities involving heat we have: — 



2. Coefficient of Expansion. — The coefficient of expansion of a substance 
is equal to the ratio of the change of length per unit length (linear), or change 
of volume per unit volume (voluminal) to the change of temperature. These 
ratios are simple numbers, and the change of temperature is inversely as the mag- 
nitude of the unit of temperature. Hence the dimensional and conversion-factor 
formulee are 0~^ and 6~'^. 



3. Conductivity, or Specific Conductance. — This is the quantity of heat 
transmitted per unit of time per unit of surface per unit of temperature gradient. 
The equation for conductivity is therefore, with H as quantity of heat, 

K = 



and the dimensional f ormula ^rpp = py^, which gives w/~V~^ for conversion factor. 

In thermometric units the formula becomes L^T~^ which properly represents 
diffusivity. In dynamical units H becomes ML'^T"^, and the formula changes to 
MLT~^©~^ The conversion factors obtained from these are /V~i and mit~^6~^ 
respectively. 



XXvi INTRODUCTION. 

4. Thermal Capacity. — This is the product of the number for mass and 
the specific heat, and hence the dimensional formula and conversion factor are 
simply M and m. 

5. Latent Heat. — Latent heat is the ratio of the number representing the 
quantity of heat required to change the state of a body to the number represent- 
ing the quantity of matter in the body. The dimensional formula is therefore 
M0/M or ©, and hence the conversion factor is simply the ratio of the tempera- 
ture units or Q. In dynamical units the factor is Pt~'^.* 

6. Joule's Equivalent. — Joule's dynamical equivalent is connected with 
quantity of heat by the equation 

ML2T-2=JH or JM0. 

This gives for the dimensional formula of J the expression L^T~^©~^ The conver- 
sion factor is thus represented by Pi~^&~^. When heat is measured in dynamical 
units J is a simple number. 

7. Entropy. — The entropy of a body is directly proportional to the quantity 
of heat it contains and inversely proportional to its temperature. The dimen- 
sional formula is thus M©/0 or M, and the conversion factor is fu. When heat is 
measured in dynamical units the factor is mr't~^B~^. 

Examples, (a) Find the relation between the British thermal unit, the calorie, 
and the therm. 

Neglecting the variation of the specific heat of water with temperature, or de- 
fining all the units for the same temperature of the standard substance, we have 
the following definitions. The British thermal unit is the quantity of heat required 
to raise the temperature of one pound of water 1° F. The calorie is the quan- 
tity of heat required to raise the temperature of one kilogramme of water 1° C 
The therm is the quantity of heat required to raise the temperature of one gramme 
of water 1° C. Hence : — 

(i) To find the number of calories in one British thermal unit, we have 
w = . 45359 and 6 = 5; .'. ^6 = . 45359 X 5/9 = -25i99- 

(2) To find the number of therms in one calorie, m=^\ooo and 6=1; 
.'. mO=: 1000. 

It follows at once that the number of therms in one British thermal unit is 
1000 X -25199 = 251.99. 

(li) What is the relation between the foot grain second Fahrenheit-degree and 
the centimetre gramme second Centigrade-degree units of conductivity ? 

The number of the latter units in one of the former is given by the for- 

* It will be noticed that when © is given the dimension formula L^T-^ the formulae in thermal 
and dynamical units are always identical. The thermometric units practically suppress mass. 



INTRODUCTION. XX\ ii 

mula ml~^t~^6°, where w = . 064799, ^=3o-48> ^"<i /= i, and is therefore = 
.064799/30.48 = 2.126 X io~^- 

(^•) Find the relation between the units stated in {b) for emissivity. 

In this case the conversion formula is ml^'-t"^, where i?il and t have the 
same value as before. Hence the number of the latter units in the former is 
0.064 799/30.48- = 6.975 X lo-^ 

{d) Find the number of centimeter gram second units in the inch grain 
hour unit of emissivity. 

Here the formula is mlr-t'~'^, where w = 0.064 799, ^=2.54, and / = 36oo. 
Therefore the required number is 0.064799/2.54"^ X 3600 = 2.790 X io~'^- 

(f) If Joule's equivalent be 776 foot pounds per pound of water per degree 
Fahrenheit, what will be its value in gravitation units when the metre, the 
kilogramme, and the degree Centigrade are units ? 

The conversion factor in this case is ,,_, or 10 ', where / = -3048 and 

d-^ = 1.8; .-. 776 X .3048 X 1.8 = 425.7. 

(/) If Joule's equivalent be 24832 foot poundals when the degree Fahren- 
heit is unit of* temperature, what will be its value when kilogram meter second 
and degree-Centigrade units are used ? 

The conversion factor is Vr-Q"^, where /= .3048, / = i, and 0~^ = 1.8 ; 
.'. 24832 X r-r'-O-^ = 24832 X .3048' X 1.8 =4152.5. 

In gravitation units this would give 4152. 5/9. 81 =423.3. 



ELECTRIC AND MAGNETIC UNITS. 

There are two systems of these units, the electrostatic and the electromagnetic 
systems, which differ from each other because of the different fundamental suppo- 
sitions on which they are based. In the electrostatic system the repulsive force 
between two quantities of static electricity is made the basis. This connects force, 

quantity of electricity, and length by the equation /=c? ^, where / is force, a a 

quantity depending on the units employed and on the nature of the medium, q and 
q^ quantities of electricity, and / the distance between q and q^. The magnitude of 
the force / for any particular values of q, q^ and / depends on a property of the 
medium across which the force takes place called its inductive capacity. The in- 
ductive capacity of air has generally been assumed as unity, and the inductive 
capacity of other media expressed as a number representing the ratio of the induc- 
tive capacity of the medium to that of air. These numbers are known as the spe- 
cific inductive capacities of the media. According to the ordinary assumption, 
then, of air as the standard medium, we obtain unit quantity of electricity when 
in the above equation ^ = ^y, andy^ a^ and / are each unity. A formal definition 
is given below. 

In the electromagnetic system the repulsion between two magnetic poles or 



XXVlll INTRODUCTION. 

quantities of magnetism is taken as the basis. In tliis system the quantities force, 
quantity of magnetism, and length are connected by an equation of the form 

r mm, 

where w and m^ are in this case quantities of magnetism, and the otlier symbols 
have the same meaning as before. In this case it has been usual to assume the 
magnetic inductive capacity of air to be unity, and to express the magnetic induc- 
tive capacity of other media as a simple number representing the ratio of the in- 
ductive capacity of the medium to that of air. These numbers, by analogy with 
specific inductive capacity for electricity, might be called specific inductive capac- 
ities for magnetism. They are usually called permeabilities. ( Vide Thomson, 
" Papers on Electrostatics and Magnetism," p. 484.) In this case, also, like that 
for electricity, the unit quantity of magnetism is obtained by making in = Wy, and 
/, a, and / each unity. 

In both these cases the intrinsic inductive capacity of the standard medium is 
suppressed, and hence also that of all other media. Whether this be done or not, 
direct experiment has to be resorted to for the determination of the absolute val- 
ues of the units and the relations of the units in the one system to those in the 
other. The character of this relation can be directly inferred from the dimen- 
sional formulae of the different quantities, but these can give no information as to 
the relative absolute values of the units in the two systems. Prof. Riicker has 
suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist- 
ence of the suppressed properties by putting symbols for them in the dimensional 
formulae. This has the advantage of showing how the magnitudes of the different 
units would be affected by a change in the standard medium, or by making the 
standard medium different for the two systems. In accordance with this idea, the 
symbols K and P have been introduced into the formulce given below to represent 
inductive capacity in the electrostatic and the electromagnetic systems respectively. 
In the conversion formulae A and/ are the ordinary specific inductive capacities 
and permeabilities of the media when air is taken as the standard, or generally 
those with reference to the first medium taken as standard. The ordinary for- 
mulae may be obtained by putting K and P equal to unity. 



ELECTROSTATIC UNITS. 

1. Quantity of Electricity. — The unit quantity of electricity is defined as 
that quantity which if concentrated at a point and placed at unit distance from an 
equal and similarly concentrated quantity repels it, or is repelled by it, with unit 
force. The medium or dielectric is usually taken as air, and the other units in ac- 
cordance with the centimeter gram second system. 

In this case we have the force of repulsion proportional directly to the square 
of the quantity of electricity and inversely to the square of the distance between 
the quantities and to the inductive capacity. The dimensional formula is there- 
fore the same as that for [force X length^ X inductive capacity]^ or M*L^T~^K^, 
and the conversion factor is mHH~'^k^. 



A 



INTRODUCTION. Xxix 

2. Electric Surface Density and Electric Displacement. — The density 
of an electric distribution at any point on a surface is measured by the quantity 
per unit of area, and the electric displacement at any point in a dielectric is mea- 
sured by the quantity displaced per unit of area. These quantities have therefore 
the same dimensional formula, namely, the ratio of the formulas for quantity of 
electricity and for area or M*L~iT~^K^, and the conversion factor jn^l~H~'^kK 

3. Electric Force at a Point, or Intensity of Electric Field. — This is 
measured by the ratio of the magnitude of the force on a quantity of electricity at 
a point to the magnitude of the quantity of electricity. The dimensional formula 
is therefore the ratio of the formulae for force and electric quantity, or 

which gives the conversion factor ni'l~^-t~^k~^-. 

4. Electric Potential and Electromotive Force. — Change of potential 
is proportional to the work done per unit of electricity in producing the change. 
The dimensional formula is therefore the ratio of the formulae for work and elec- 
tric quantity, or 

^^^^'"'^ = M^L^T-^K-^ 
MiL^T-^K* ' 

which gives the conversion factor m^l^t~^k~^-. 

5. Capacity of a Conductor. — The capacity of an insulated conductor is 
proportional to the ratio of the numbers representing the quantity of electricity in 
a charge and the potential of the charge. The dimensional formula is thus the 
ratio of the two formulae for electric quantity and potential, or 

M^L'T-^K^ _ 

M^L^T-^K-i ' 

which gives Ik for conversion factor. When K is taken as unity, as in the ordinary 
units, the capacity of an insulated conductor is simply a length. 

6. Specific Inductive Capacity. — This is the ratio of the inductive cap?c- 
ity of the substance to that of a standard substance, and hence the dimensional 
formula is K/K or i.* 

7. Electric Current. — Current is quantity flowing past a point per unit of 
time. The dimensional formula is thus the ratio of the formulae for electric quan- 
tity and for time, or 

and the conversion factor inrPf^k^- . 

m 

* According to the ordinary definition referred to air as standard medium, the specific inductive 
capacity of a substance is K, or is identical in dimensions with what is here taken as inductive ca- 
pacity. Hence in that case the conversion factor must be taken as i on the electrostatic and as 
t~^t^ on the electromagnetic system. 



XXX INTRODUCTION. 

8. Conductivity, or Specific * Conductance. — This, like the corresponding 
term for heat, is quantity per unit area per unit potential gradient per unit of time. 
The dimensional formula is therefore 

M-L^T-^K* T-^K or electric quantity ^ 

,M'L*T~^K~tp ' area X potential gradient X time 

^' L 

The conversion factor is t~'^k. 

9. Specific* Resistance. — This is the reciprocal of conductivity as above 
defined, and hence the dimensional formula and conversion factor are respec- 
tively TK-^ and tk'^. 

10. Conductance. — The conductance of any part of an electric circuit, not 
containing a source of electromotive force, is the ratio of the numbers represent- 
ing the current fiowing through it and the difference of potential between its ends. 
The dimensional formula is thus the ratio of the formula for current and poten- 
tial, or 

MiL^T-^K^ _ ^^ 
M^LiT-^K-^-^ ' 

from which we get the conversion factor It~'^k, 

11. Resistance. — This is the reciprocal of conluctance, and therefore the 
dimensional formula and the couversiou factor are respectively ly^'TK"' auJ 
l-Hk-\ 



EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS, 

{a) find the factor for converting quantity of electricity expressed in foot grain 
second units to the same expressed in c. g. s. units. 

By (i) the formula is ?«7'V^U'-, in which in this case Jti = 0.064S, /= 30.48, / = 
I, and k^ 1 ; .-. the factor is 0.0648^ X 30.48^ = 4.2836. 

(d) Find the factor required to convert electric potential from millimeter milli- 
gram second units to c. g. s. units. 

By (4) the formula is ;«-/-7~^/^~*, and in this case ?n = o.ooi, /= o.i, /*= i, and 
/('=i; .•. the factor ^ O.OOI- X 0.1-:= o.oi. 

(c) Find the factor required to convert from foot grain second and specific in- 
ductive capacity 6 units to c. g. s. units. 

By (s) the formula is //&, and in this case /= 30.48 and ^=^6; .'. the factor 
= 30.48X6=182.88. 

* The term "specific," as used here and in 9, refers conductance and resistance to that between%i 
the ends of a bar of unit section and unit length, and hence is different from the same term in 
specific heat, specific inductivity, capacity, etc., which refer to a standard substance. 



INTRODUCTION. XXxi 



ELECTROMAGNETIC UNITS. 

As stated above, these units bear the same relation to unit quantity of magne- 
tism that the electric units do to quantity of electricity. Thus, when inductive 
capacity is suppressed, the dimensional formula for magnetic quantity on this sys- 
tem is the same as that for electric quantity on the electrostatic system. All quan- 
tities in this system which only differ from corresponding quantities defined above 
by the substitution of magnetic for electric quantity may have their dimensional 
formulas derived from those of the corresponding quantity by substituting P 
for K. 

1. Magnetic Pole, or Quantity of Magnetism. — Two unit quantities of 
magnetism concentrated at points unit distance apart repel each other with unit 
force. The dimensional formula is thus the same as for [force X length^ X in- 
ductive capacity]- or M-L^T~^P-, and the conversion factor is w-/-/"-'/^ 

2. Density of Surface Distribution of Magnetism. — This is measured 
by quantity of magnetism per unit area, and the dimension formula is therefore 
the ratio of the expressions for magnetic quantity and for area, or M-L~-T~^P*, 
which gives the conversion factor 7;r/""^/~^/*. 

3. Magnetic Force at a Point, or Intensity of Magnetic Field. — The 

number for this is the ratio of the numbers representing the magnitudes of the 

force on a magnetic pole placed at the point and the magnitude of the magnetic 

pole. 

The dimensional formula is therefore the ratio of the expressions for force and 

magnetic quantity, or 

MLT-2 



M^L'T-ipi 
and the conversion factor m^l~^t~'^p~^. 



M*L-^T-ip-J, 



4. Magnetic Potential. — The magnetic potential at a point is measured by 
the work which is required to bring unit quantity of positive magnetism from zero 
potential to the point. The dimensional formula is thus the ratio of the formula 
for work and magnetic quantity, or 

ATT 27^-2 
M^LiT-^P5 ' 

which gives the conversion factor ?«*/-/~'/~^ 

5. Magnetic Moment. — This is the product of the numbers for pole 
strength and length of a magnet. The dimensional formula is therefore the pro- 
duct of the formute for magnetic quantity and length, or M L'T~^P-, and the con- 
version factor w-/-/~'/-. 

6. Intensity of Magnetization. — The intensity of magnetization of any por- 
tion of a magnetized body is the ratio of the numbers representing the magni- 



XXXli INTRODUCTION. 

tude of the magnetic moment of that portion and its volume. The dimensional 
formula is therefore the ratio of the formulae for magnetic moment and volume, or 

M!I^' = M.L-.T-P.. 

The conversion factor is therefore m^t~^-t~^p^. 

7. Magnetic Permeability,* or Specific Magnetic Inductive Capacity. 

— This is the analogue in magnetism to specific inductive capacity in electricity. 
It is the ratio of the magnetic induction in the substance to the magnetic induc- 
tion in the field which produces the magnetization, and therefore its dimensional 
formula and conversion factor are unity. 

8. Magnetic Susceptibility. — This is the ratio of the numbers which repre- 
sent the values of the intensity of magnetization produced and the intensity of the 
magnetic field producing it. The dimensional formula is therefore the ratio of 
the formulae for intensity of magnetization and magnetic field or 

M^L-iT-ipi 



M*L-*T-ip-4 



or P. 



The conversion factor is therefore /, and both the dimensional formula and con- 
version factor are unity in the ordinary system. 

9. Current Strength. — A current of strength c flowing round a circle of 
radius r produces a magnetic field at the centre of intensity 2iTclr. The dimen- 
sional formula is therefore the product of the formulae for magnetic field intensity 
and length, or M^L*T~^P"'*, which gives the conversion factor mH^-t~'^p~^. 

10. Current Density, or Strength of Cvirrent at a Point. — This is the 
ratio of the numbers for current strength and area. The dimensional formula 
and the conversion factor are therefore M^L~*T~^P~- and m^t'H'~^p~^. 

11. Quantity of Electricity. — This is the product of the numbers for cur- 
rent and time. The dimensional formula is therefore M*L*T-^P-^ X T= M^L*P~*, 
and the conversion factor m^l^p"^. 

12. Electric Potential, or Electromotive Force. — As in the electrostatic 
system, this is the ratio of the numbers for work and quantity of electricity. The 
dimensional formula is therefore 

WUP=i-^^^ P, 

and the conversion factor mH^t~^p^. 

* Permeability, as ordinarily taken with the standard medium as unity, has the same dimension 
formula and conversion factor as that which is here taken as magnetic inductive capacity. Hence 
for ordinary transformations the conversion factor should be taken as i in the electromagnetic and 
J~2/2 in the electrostatic systems. 



INTRODUCTION. XXxiii 



13. Electrostatic Capacity. — This is the ratio of the numbers for quantity 
of electricity and difference of potential. The dimensional formula is therefore 



M^L«T-^Pi 

and the conversion factor l~^t-p~^. 



L-iT2p^ 



14. Resistance of a Conductor. — The resistance of a conductor or elec- 
trode is the ratio of the numbers for difference of potential between its ends and 
the constant current it is capable of producing. The dimensional formula is 
therefore the ratio of those for potential and current or 

M^L»T::!Pi_TT-ip 

M^LiT-ip-i 

The conversion factor thus becomes it~'^p, and in the ordinary system resistance 
has the same conversion factor as velocity. 

15. Conductance. — This is the reciprocal of resistance, and hence the dimen- 
sional formula and conversion factor are respectively L~^TP~^ and l~'^tp~^. 

16. Conductivity, or Specific Conductance. — This is quantity of electric- 
ity transmitted per unit of area per unit of potential gradient per unit of time. 
The dimensional formula is therefore derived from those of the quantities men- 
tioned as follows : — 

M^L^P-^ _ , 

L L— T 

The conversion factor is therefore l~Hp~\ 

17. Specific Resistance. — This is the reciprocal of conductivity as defined 
in 16, and hence the dimensional formula and conversion factor are respectively 
L'^T-ip and fr^p. 

i8. Coefficient of Self-induction, or Inductance, or Electro-kinetic In- 
ertia. — These are for any circuit the electromotive force produced in it by unit 
rate of variation of the current through it. The dimensional formula is therefore 
the product of the formulae for electromotive force and time divided by that for 
current or 

MJLST-'^pi 



MiL*T-ip-4 



X T = LP. 



The conversion factor is therefore Ip, and in the ordinary system is the same as 
that for length. 

19. Coefficient of Mutual Induction. — The mutual induction of two cir- 
cuits is the electromotive force produced in one per unit rate of variation of the 
current in the other. The dimensional formula and the conversion factor are 
therefore the same as those for self-induction. 



xxxiv INTRODUCTION. 

20. Electro-kinetic Momentum. — The number for this is the product of 
the numbers for current and for electro-kinetic inertia. The dimensional formula 
is therefore the product of the formulae for these quantities, or M*L^T~^P~^ X LP 
= M-L-T~^P^, and the conversion factor is mHH~'^p^, 

21. Electromotive Force at a Point. — The number for this quantity is 
the ratio of the numbers for electric potential or electromotive force as given in 
12, and for length. The dimensional formula is therefore M-L*T~^P-, and the 
conversion factor w-/-^~^/*. 

22. Vector Potential. — This is time integral of electromotive force at a 
point, or the electro-kinetic momentum at a point. The dimensional formula 
may therefore be derived from 21 by multiplying by T, or from 20 by dividing 
by L. It is therefore M^L-T~^P^, and the conversion factor ;?/-/V~^-. 

23. Thermoelectric Height. — This is measured by the ratio of the num- 
bers for electromotive force and for temperature. The dimensional formula is 
therefore the ratio of the formulae for these two quantities, or M*L^T~"P^©~^, and 
the conversion factor mHH~'^f'B~^. 

24. Specific Heat of Electricity. — This quantity is measured in the same 
way as 23, and hence has the same formulae. 

25. Coefficient of Peltier Effect. — This is measured by the ratio of the 
numbers for quantity of heat and for quantity of electricity. The dimensional 
formula is therefore 

_^ = M^L-iP^©, 
M^L^P-i ' 

and the conversion factor m^l~^p^9. 



EXAMPLES OF CONVERSION IN ELECTROMAGNETIC UNITS. 

{a) Find the factor required to convert intensity of magnetic field from foot 
gi'ain minute units to c. g. s. units. 

By (3) the formula is in^t~H~^p~^-, and in this case m = 0.0648, /= 30.48, / = 
60, and/ = I ; .". the factors = 0.0648- X 30.48^- X 6o~^ 1= 0.00076847. 

Similarly to convert from foot grain second units to c. g. s. units the factor is 
0.0648* X 30.48"- = 0.046 108. 

(^) How many c. g. s. units of magnetic moment make one foot grain second 
unit of the same quantity .'' 

By (5) the formula is »?V*/~^/-, and the values for this problem are pi = 0.0648, 
,/= 30.48, t = I, and/ = I ; .*. the number = 0.0648* X 30-48^= 1305.6. 

(<r) If the intensity of magnetization of a steel bar be 700 in c. g. s. units, what 
will it be in millimeter milligram second units ? 



INTRODUCTION. XXXV 

By (6) the formula is w^/^/"^/^, and in this case m = looo, /= lo, ^= i, and 
p ■= 1 ; .•. the intensity = 700 X 1000^ X 10^ = 70000. 

(d) Find the factor required to convert current strength from c. g. s. units to 
earth quadrant io~" gram and second units. 

By (9) the formula is wV-/~^/~*, and the values of these quantities are here m = 
10", /= io~^ t= I, and/ = I i .'. the factor = loH x io~2= 10. 

(1?) P'ind the factor required to convert resistance expressed in c. g. s. units into 
the same expressed in earth-quadrant io~" gram and second units. 

By (14) the formula is /t~^J>, and for this case /= io~', /= i, and / = i ; 
.*. the factor =: io~^ 

(/) Find the factor required to convert electromotive force from earth-quadrant 
io~" gram and second units to c. g. s. units. 

By (12) the formula is m^/U~^/>\ and for this case m ^ io~", /= 10^, f=i, 
and/ = I ; .'. the factor = 10*. 



PRACTICAL UNITS. 

In practical electrical measurements the units adopted are either multiples or 
submultiples of the units founded on the centimeter, the gram, and the second 
as fundamental units, and air is taken as the standard medium, for which K and P 
are assumed unity. The following, quoted from the report to the Honorable the 
Secretary of State, under date of November 6th, 1893, by the delegates repre- 
senting the United States, gives the ordinary units with their names and values 
as defined by the International Congress at Chicago in 1893 : — 

" Resolved, That the several governments represented by the delegates of this 
International Congress of Electricians be, and they are hereby, recommended to 
formally adopt as legal units of electrical measure the following : As a unit of re- 
sistance, the internatiojial oh77i, which is based upon the ohm equal to 10® units of 
resistance of the C G. S. system of electro-magnetic units, and is represented 
by the resistance offered to an unvarying electric current by a column of mercury 
at the temperature of melting ice 14.4521 grams in mass, of a constant cross- 
sectional area and of the length of 106.3 centimeters. 

" As a unit of current, the interfiational ampere, which is one tenth of the unit of 
current of the C. G. S. system of electro-magnetic units, and which is represented 
sufficiently well for practical use by the unvarying current which, when passed 
through a solution of nitrate of silver in water, and in accordance with accom- 
panying specifications,* deposits silver at the rate of 0.001118 of a gram per 
second. 

* " In the following specification the term ' silver voltameter' means the arrangement of appara- 
tus by means of which an electric current is passed through a solution of nitrate of silver in water. 
The silver voltameter measures the total electrical quantity which has passed during the time of 
the experiment, and by noting this time the time average of the current, or, if the current has been 
kept constant, the current itself can be deduced. 

" In employing the silver voltameter to measure currents of about one ampere, the foll-Jwmg 
arrangements should be adopted : — 



XXXVl INTRODUCTION. 

" As a unit of electromotive force, the international volt, which is the electro- 
motive force that, steadily applied to a conductor whose resistance is one interna- 
tional ohm, will produce a current of one international ampere, and which is rep- 
resented sufificiently well for practical use by \%%^ of the electromotive force 
between the poles or electrodes of the voltaic cell known as Clark's cell, at a tem- 
perature of 15° C, and prepared in the manner described in the accompanying 
specification.* 

" As a unit of quantity, the ifiternational coulomb, which is the quantity of elec- 
tricity transferred by a current of one international ampere in one second. 

"As a unit of capacity, the international farad, which is the capacity of a con- 
denser charged to a potential of one international volt by one international cou- 
lomb of electricity.f 

" As a unit of work, the Joule, which is equal to 10'' units of work in the c. g. s. 
system, and which is represented sufficiently well for practical use by the energy 
expended in one second by an international ampere in an international ohm. 

" As a unit of power, the watt, which is equal to 10'' units of power in the c. g. s. 
system, and which is represented sufficiently well for practical use by the work 
done at the rate of one joule per second. 

" As the unit of induction, the henry, which is the induction in a circuit when 
the electromotive force induced in this circuit is one international volt, while the 
inducing current varies at the rate of one ampere per second. 

" The Chamber also voted that it was not wise to adopt or recommend a stand- 
ard of light at the present time." 

By an Act of Congress approved July 12th, 1894, the units recommended by 
the Chicago Congress were adopted in this country with only some unimportant 
verbal changes in the definitions. 

By an Order in Council of date August 23d, 1894, the British Board of Trade 
adopted the ohm, the ampere, and the volt, substantially as recommended by 
the Chicago Congress. The other units were not legalized in Great Britain. 
They are, however, in general use in that country and all over the world. 

" The kathode on which the silver is to be deposited should take the form of a platinum bowl 
not less than 10 centimeters in diameter and from 4 to 5 centimeters in depth. 

" The anode should be a plate of pure silver some 30 square centimeters in area and 2 or 3 
millimeters in thickness. 

" This is supported horizontally in the liquid near the top of the solution by a platinum wire 
passed through holes in the plate at opposite corners. To prevent the disintegrated silver which 
is formed on the anode from falling on to the kathode, the anode should be wrapped round with 
pure filter paper, secured at the back with sealing wax. 

"The liquid should consist of a neutral solution of pure silver nitrate, containing about 15 parts 
by weight of the nitrate to 85 parts of water. 

"The resistance of the voltameter changes somewhat as the current passes. To prevent these 
changes having too great an effect on the current, some resistance besides that of the voltameter 
should be inserted in the circuit. The total metallic resistance of the circuit should not be less 
than 10 ohms." 

* A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, was appointed to pre- 
pare specifications for the Clark's cell, but no report was made, on account of Helmholtz's death. 

t The one millionth part of the farad is more commonly used in practical measurements, and is 
called the microfarad. 



PHYSICAL TABLES 



Table 1 . 
FUNDAMENTAL AND DERIVED UNITS. 



To change a quantity from one system of units to another : substitute in the correspond- 
ing conversion factor from the following table the ratio of the magnitudes of the old units 
to the new and multiply the old quantity by the resulting number. For example : to reduce 
velocity in miles per hour to feet per second, the conversion factor is lt-'^\ /=528o/i, 
/=36oo/i, therefore the factor=52So/36oo=i.467. 

{a) Fundamental Units. 


Name of Unit. 


Symbol. 


Conversion Factor. 


Length. 

Mass. 

Time. 

Temperature. 

Electric Inductive Capacity. 

Magnetic Inductive Capacity. 


L 

M 
T 
© 
K 
P 


/ 

m 
t 
6 
k 
P 


if) Derived Units. 
/ Geometric and Dynamic Units. 


Name of Unit. 


Conversion Factor. 


Area. 
Volume. 
Angle. 
Solid Angle. 
Curvature. 
Tortuosity. 

Specific curvature of a surface. 
Angular velocity. 
Angular acceleration. 
Linear velocity. 
Linear acceleration. 
Density. 

Moment of inertia. 

Intensity of attraction, or "force at a point." 
Absolute force of a centre of attraction, or " strength \ 
of a centre." j 
Momentum. 

Moment of momentum, or angular momentum. 
Force. 

Moment of a couple, or torque. 
Intensity of stress. 
Modulus of elasticity. 
Work and energy. 
Resilience. 
Power or activity. 


I 
I 

/-I 

/-^ 

/-=> 

t-^ 

/-2 

It-^ 

It-^ 

m /-3 

ml"" 

It-'' 

l^t-^ 

mlt-^ 

ml^t-^ 

mlt-'' 

mlU-"" 

ml-U-'' 

ml-U-"" 

ml'^t'^ 

m /-' /-' 

m/^t-^ 



Smithsonian Tables. 



Table 1 . 
FUNDAMENTAL AND DERIVED UNITS. 



11. Heat Units. 


Name of Unit. 


Conversion Factor. 


Quantity of heat (thermal units). 

" " (thermometric units). 

" *' (dynamical units). 
Coefficient of thermal expansion. 
Conductivity (thermal units). 

" (thermometric units), or diffusivity. 
" (dynamical units). 
Thermal capacity. 
Latent heat (thermal units). 

" " (dynamical units). 
Joule's equivalent. 
Entropy (heat measured in thermal units). 

" ( " " " dynamical units). 


m e 
m 1 1-^ e-^ 

m 

e 
I'^t-'^e 

m 

m P t-"" 6 


///. Magnetic and Electric Units. 


Name of Unit. 


Conversion factor 
for electrostatic 
system. 


Conversion factor 
for electromag- 
netic system. 


Magnetic pole, or quantity of mag- \ 

netism. f 
Density of surface distribution of) 

magnetism. j 
Intensity of magnetic field. 
Magnetic potential. 
Magnetic moment. 
Intensity of magnetisation. 
Magnetic permeability. 
Magnetic susceptibility and mag-) 

netic inductive capacity. ) 
Quantity of electricity. 
Electric surface density and electric ) 

displacement. j 
Intensity of electric field. 
Electric potential and e. m. f. 
Capacity of a condenser. 
Inductive capacity. 
Specific inductive capacity. 
Electric current. 


m^ li t--" k^ 

I 

m^ t^ r' ki 

mi /-i t-^ k-i 
wi li t-^ k-^ 
Ik 
k 

I 


mi r^ r^pi 

mi l-i t-'^pi 
mi /-* t-^p-i 

milif^p-i 

mil^r^pi 
mil-'^t-^p^ 

I 

p 

mi li /-4 

mi Mp-^ 

mi li ir-'^pi 
mi /5 t-'^pi 

t-^ t^p-^ 
l-^ t^p-"- 

I 

mi li t-^p-i 



Smithsonian Tables. 



Table 1. 
FUNDAMENTAL AND DERIVED UNITS. 



///. Magnetic and Electric Units. 








Conversion factor 


Conversion factor 


Name of Unit. 


for electrostatic 


for electromag- 






system. 


netic system. 




Conductivity, 


t--" k 


i^2 /^-i 


Specific resistance. 


tk-^ 


p t-^p 




Conductance. 


It-'' k 


t-^ tp-'^ 




Resistance. 


t-' t k-' 


It-'^p 




Coefficient of self induction and) 
coefficient of mutual induction. j 


/-^ /2 ^-1 


ip 








Electrokinetic momentum. 


m"^ l^ k-^ 


mi n t-'^pi 




Electromotive force at a point. 


m"^ /-* t-^ k-^ 


mi li r^pi 




Vector potential. 


m^ ri k-i 


mi lit-^pi 




Thermoelectric height and specific) 
heat of electricity. j 


mi n t-' k-i 6-^ 


mi /' rV- ^' 










Coefficient of Peltier effect. 


mi /-' t k-i e 


mi l-ipiQ 





Smithsonian Tables. 



Table 2. 
TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES.* 

(1) CUSTOMARY TO METRIC. 



LINEAR. 


CAPACITY. 






Inches 

to 

millimeters. 


Feet to 
meters. 


Yards to 
meters. 


Miles 

to 

kilometers. 




Fluid 
drams to 

milliliters 

or cubic 

centimeters. 


Fluid 

ounces 

to 

milliliters. 


Liquid 

quarts to 

liters. 


Gallons to 
liters. 




I 

2 

3 
4 
5 
6 

7 
8 

9 


25.4001 

50.8001 

76.2002 

101.6002 

127.0003 

152.4003 
177.8004 
203.2004 
228.6005 


0.304801 
0.609601 
0.914402 
1. 219202 

1.524003 

I.S2S804 
2.133604 
2.438405 
2.743205 


0.914402 
1.828804 

2.743205 
3.657607 
4.572009 

5.48641 1 
6.400813 

7-315215 
8.229616 


1.60935 
3.21869 
4.82804 

6.43739 
8.04674 

9.65608 
11.26543 
12.87478 
14.48412 


I 
2 
3 

\4 
5 
6 

7 
8 

9 


3-70 

7-39 
11.09 

14.79 
18.48 

22.18 
25.88 
29-57 
33-27 


29-57 

59.15 

88.72 

118.29 

147.87 

177-44 
207.01 
236.58 
266.16 


0-94633 
1.89267 
2.83900 

3-78533 
4-73167 

5.67S00 
6.62433 
7.57066 
8.51700 


3-78533 

7-57066 

11.35600 

15-I4133 
18.92666 

22.71199 

26.49733 
30.28266 
34.06799 




SQUARE. 


WEIGHT. 




I 

2 

3 
4 
5 
6 

7 
8 

9 


Square 
inches to 
square cen- 
timeters. 


Square feet 
to square 
decimeters. 


Square 
yards to 
square 
meters. 


Acres to 
hectares. 




Grains to 
milligrams. 


Avoirdu- 
pois ounces 
to grams. 


Avoirdu- 
pois pounds 
to kilo- 
grams. 


Troy 

ounces to 

grams. 




6.452 
12.903 

19-355 

25.807 
32.258 

38.710 
45.161 

5>-6i3 

58.065 


9.290 
18.581 
27.871 
37.161 
46.452 

55-742 
65.032 

74-323 
83-613 


0.836 
1.672 
2.508 

3-345 
4.181 

5-017 
S-853 
6.689 

7-525 


0.4047 
0.8094 
I.2141 
I.6187 
2-0234 

2.4281 
2.8328 

3-2375 
3-6422 


I 
2 
3 
4 
5 
6 

7 
8 

9 


64.7989 
129.5978 
194.3968 
259-1957 
323-9946 

388.7935 
453-5924 

5'8-39i3 
583-1903 


28.3495 

56.6991 

85.0486 

1 13.3981 

141.7476 

170.0972 
198.4467 
226.7962 
255-1457 


0.45359 
0.907 1 8 
1.3607S 
1.81437 
2.26796 

2.72x55 

3-17515 
3.62874 
4-08233 


31.10348 

62.20696 1 

93-31044! 
124.41392 

155-5174OJ 

186.620S8' 

217-72437 
24S.S27S5 

279-93133 








CUBI 


C. 




I Gunter's chain = 
I sq. statute mile = 
I fathom = 


20.1168 meters. 

259.000 hectares. 

1.S29 meters. 






Cubic 
inches to 
cubic cen- 
timeters. 


Cubic feet 
to cubic 
meters. 


Cubic 
yards to 

cubic 
meters. 


Bushels to 
hectoliters. 




I 

2 

3 

4 
5 
6 

7 
8 

9 


16.3S7 

32-774 
49.161 

65-549 
81.936 

98.323 
II4.7IO 
131.097 
147.484 


0.02832 
0.05663 
0.08495 
O.II327 
O.I4159 

0.16990 
0.19822 
0.22654 
0.25485 


0.765 
1.529 
2.294 
3-058 
3-823 

4.587 

6.I16 
6.881 


0-35239 
0.70479 
I.05718 
1.40957 
1.76196 

2.11436 
2.46675 
2.81914 
3-I7154 




I nautical 
I foot 
I avoir, pc 
15432-3563^ 


mile = 

und = 
) grains = 


1853.25 meters. 

0.304S01 meter. 

453.5924277 grams. 

1. 000 kilogram. 





According to an executive order dated April 15, 1893, the United States yard is defined as 3600/3937 meter, and 
the avoirdupois pound as 1/2.20462 kilogram. , r , j ,^j v n • r- >. j 

I meter (international prototype) = 15S3164.13 times the wave-length of the red Cd. line. iJenoit, tabryand 
Perot. C. R. 144, 1907 differs only in the decimal portion from the measure of Michelson and Benoit 14 years earlier. 

The length of the nautical mile given above and adopted by the U. S. Coast and Geodetic Survey many years ago, 
is defined as that of a minute of arc of a great circle of a sphere wfhose surface equals that of the earth (Clarke's Sphe- 
roid of 1866). „ r f. , J 

* Quoted from sheets issued by the United States Bureau of Standards. 
Smithsonian Tables. 



Table 2 {continued). 
TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES. 

(2) METRIC TO CUSTOMARY. 



LINEAR. 


CAPACITY. 






Meters to 
inches. 


Meters to 
feet. 


Meters to 
yards, 


Kilometers 
to miles. 




Millili- 
ters or 
cubic cen- 
timeters 
to fluid 
drams. 


Centi- 
liters to 

fluid 
ounces. 


Liters 

to 
quarts. 


Deca- 
liters 
to 
gallons. 


Hecto- 
liters 
to 
bushels. 




I 

2 

3 

4 
5 


39.3700 

78.7400 

1 18. 1 100 

157.4800 

196.8500 


3.28083 
6.56167 
9.84250 

13-12333 
16.40417 


1. 09361 1 

2.187222 
3-280833 
4-374444 
5.468056 


0.62137 

1.24274 
1.864 11 
2.48548 
3.10685 


I 

2 
3 

4 
5 


0.27 

0-54 
0.81 
1.08 
1-35 


0.676 
I.O14 

1-353 
1. 69 1 


1.0567 
2.II34 
3.1701 
4.2268 
5-2836 


2.6418 
5-2836 

7-9253 
10.5671 
13.2089 


2.8378 

S-6756 

8-5135 

"-3513 

14.1891 




6 

7 
8 

9 


236.2200 
275.5900 
314.9600 
354.3300 


19.6S500 
22.96583 
26.24667 
29.52750 


6.561667 
7-655278 
8.748889 
9.842500 


3.72822 

4-34959 
4.97096 

5-59233 


6 

7 
8 

9 


1.62 
1.89 
2.16 
2-43 


2.029 
2.367 
2-705 
3-043 


6.3403 
7.3970 
8.4537 
9.5104 


15-8507 
18.4924 
21.1342 
23.7760 


17.0269 
19.8647 
22.7026 
25.5404 




SQUARE. 


WEIGHT. 




I 

2 

3 

4 
5 


Square 

centimeters 

to square 

inches. 


Square 

meters to 

square 

feel. 


Square 

meters to 

square 

yards. 


Hectares 
to acres. 




Milli- 
grams to 
grains. 


Kilo- 
grams to 
grains. 


Hecto- 
grams to 
ounces _ 
avoirdupois. 


Kilo- 
grams to 
pounds 
avoirdupois. 




0.1550 
0.3100 
0.4650 
0.6200 
0.7750 


10.764 
21.528 
32.292 
43-055 
53-819 


1. 196 

4.784 
5.980 


2.471 
4.942 

7-413 
9.884 

12355 


I 
2 
3 
4 

5 


0.01543 
0.03086 
0.04630 
0.06173 
0.07716 


15432-36 
30864.7 1 
46297.07 
61729.43 
77161.78 


3-5274 

7.0548 

10.5822 

14.1096 

17.6370 


2.20462 
4.40924 
6.61387 
8.81849 
II.023II 




6 

7 
|8 

9 


0.9300 
1.0850 
1.2400 
1-3950 


64-583 

75-347 
86.1 1 1 

96.875 


7.176 
8.372 
9.568 
10.764 


14.826 
17.297 
19.768 
22.239 


6 

7 
8 

9 


0.09259 
0.10803 
0.12346 
0.13889 


92594.14 
108026.49 
123458.85 
138891.21 


21.1644 
24.6918 
28.2192 
31.7466 


13-22773 
15-43236 
17.63698 
19.84160 




1 CUBIC. 


WEIGHT. 




1 

I 

3 


Cubic 

centimeters 

to cubic 

inches. 


Cubic 

decimeters 

to cubic 

inches. 


Cubic 

meters to 

cubic 

feet. 


Cubic 

meters to 

cubic 

yards. 




Quintals to 
pounds av. 


Milliers or 

tonnes to pounds 

av. 


Kilograms 

to ounces 

Troy. 




0.0610 
0.1220 
O.183I 

0.2441 
0.3051 


61.023 
122.047 
183.070 
244.094 
305- "7 


35-314 

70.269 

105.943 

141.258 

176.572 


1.308 
2.616 
3-924 
5-232 
6.540 


I 
2 
3 
4 
5 


220.46 
440.92 
661.39 
881.85 
1 102.31 


2204.6 
4409.2 
6613.9 
8818.5 
IIO23.I 


32-1507 

64-3015 

96.4522 

I2S.6030 

160.7537 




!6 

'7 

18 

l1 


0.3661 
0.4272 
0.4882 
0.5492 


366.140 
427.164 
488.187 
549.210 


211.887 
247.201 
282.516 
317.830 


7.848 
9.156 
10.464 
II.77I 


6 

7 
8 

9 


1322.77 

1543-24 
1763.70 
1984.16 


13227.7 

15432-4 
17637.0 
1 984 1. 6 


192.9045 
225.0552 
257.2059 
289.3567 





By the concurrent action of the principal governments of the world an International Bureau of \Veights and 
Measures has been established near Paris. Under the direction of the International Committee, two ingots were 
cast of pure platinum-iridium in the proportion of g parts of the former to i of the latter metal. From one of these 
a certain number of kilograms were prepared, from the other a definite number of meter bars. These standards of 
weight and length were intercompared, without preference, and certain ones were selected as International proto- 
type standards. The others were distributed by lot, in September, iSSg, to the different governments, and are called 
National prototype standards. Those apportioned to the United States were received in 1890, and are kept at the 
Bureau of Standards in Washington, D. C. 

The metric system was legalized in the United States in 1S66. 

The International Standard Meter is derived from the M^tre des Archives, and its length is defined by the 
distance between two lines at 0° Centigrade, on a platinum-iridium bar deposited at the International Bureau of 
Weights and Measures. 

The International Standard Kilogram is a mass of platinum-iridium deposited at the same place, and its weight 
in vacuo is the same as that of the Kilogram des Archives. 

The liter is equal to the quantity of pure water at 4° C, 760 mm. Hg. pressure which weighs i kilogram = 1.000027 
cu. dm. (Trav. et Mem. Bureau Intern, des P. et M. 14, 1910, Benoit.; 

Smithsonian Tables. 



Table 3. 

EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS 

AND MEASURES."- 

(1) METRIC TO IMPERIAL 



LINEAR MEASURE. 



I millimeter (mm.) { 
(.001 m.) 5 

I centimeter (.01 m.) 
I decimeter (.1 m) 

I METER (m.) 



I dekameter 

(10 m.) 
I hectometer 

(100 m.) 
I kilometer 

(1,000 m.) 
I myriameter 

( 10,000 ra.) 
I micron . . 



-1 



= 0.03937 m. 

= 0-39370 " 
3.93701 " 
39.370113 " 
3.280843 ft. 
1.09361425 yds. 

= 10.93614 
= 109.361425 
= 0.62137 mile. 
= 6.21372 miles. 
= o.coi mm. 



SQUARE MEASURE. 



I sq. centimeter . . 
I sq. decimeter 

(100 sq. centm.) 
I sq. meter or centi- 

are (100 sq. dcm.) 
I ARE (100 sq. m.) 
I hectare (100 ares 

or 10,000 sq. m.) 



. = 0.1550 sq. in. 

[= 15-500 sq. in. 

I __ j 10.7639 sq. ft. 

( j 1. 1960 sq. yds. 

= 119.60 sq. yds. 

[ = 2-47 1 1 acres. 



CUBIC MEASURE. 



I cub. centimeter 

(c.c.) (1,000 cubic 

millimeters) 
I eub. decimeter 

(c.d.) (1,000 cubic 

centimeters) 

I CUB. METER 

or stere 
(1,000 c.d.) 






0.0610 cub. in. 



61.024 



_ ( 35.3148 cub. ft. 
I 1-307954 cub. yds. 



MEASURE OF CAPACITY. 



1 milliliter (ml.) (.001 
liter) 

I centiliter (.01 liter) 

I deciliter (.1 liter) . 
I LITER (1,000 cub. 
centimeters or i 
cub. decimeter) 
I dekaliter (10 liters) 
I hectoliter (100 " ) 
I kiloliter (1,000 " ) 



= 1 



0.0610 cub. in. 

0.61024 " " 
0.070 gill. 
0.176 pint. 



= 1.75980 pints. 

= 2.200 gallons, 

= 2.75 bushels. 

= 3-437 quarters. 



APOTHECARIES' MEASURE. 



I cubic centi- ) 
meter (i > 
gram w't) ) 

I cub. millimeter : 



( 0.03520 fluid ounce. 
:< 0.28157 fluid drachm. 

( 15.43236 grains weight. 
= 0.01693 minim. 



AVOIRDUPOIS WEIGHT. 



I milligram (mgr.) . . 
I centigram (.01 gram.) 
I decigram (.i " ) 

I GRAM 

I dekagram (10 gram.) 
I hectogram (100 " ) 

I KILOGRAM (1,000" ) 

I myriagram (10 kilog.) 
I quintal (100 " ) 



I millier or tonne 
(1,000 kilog.) 



= 0.01543 gram. 
= 0.15432 " 
= 1-54324 grains. 
=15.43236 " 
= 5.64383 drams. 

= 3-52739 oz- 
( 2.2046223 lb- 

= ] 15432-3564 
( grains. 

=22.04622 lbs. 
1. 96841 cwt. 



> . . = 0.9S42 ton. 



TROY WEIGHT. 



f IS- 



0.03215 oz. Troy. 

64301 pennyweight. 
5.43236 grains. 



APOTHECARIES' WEIGHT. 

0.25721 drachm. 
= •{ 0.77162 scruple. 
15-43236 grains. 



Note. — The Meter is the length, at the temperature of o° C, of the platinum-iridium bar deposited at the 
International Bureau of Weights and Measures at Sfevres, near Paris, France. 

The present legal equivalent of the meter is 39.370113 inches, as above stated. 

The Kilogram is the mass of a platinum-iridium weight deposited at the same place. 

The Liter contains one kilogram weight of distilled water at its maximum density (4° C), the barometer being 
at 760 millimeters. 

*In accordance with the schedule adopted under the Weights and Measures (metric system) Act, 1897. 
Smithsonian Tables. 



Table 3. 

EQUIVALENTS OF METRIC AND BRITISH IWIPERIAL WEIGHTS 
AND MEASURES. 









(2) f 


vIETRIC TO 


MPERIAL 








LINEAR MEASURE. 


MEASURE OF CAPACITY. 




Millimeters 


Meters 


Meters 


Kilo- 




Liters 


Dekaliters 


Hectoliters 


Kiloliters 




to 


to 


to 


meters to 




to 


to 


to 


to 




inches. 


feet. 


yards. 


miles. 




pmts. 


gallons 


bushels. 


quarters. 


I 


0-0393701 1 


3.28084 


1. 0936 1 


0.62137 


I 


1.75980 


2.19975 


2.74969 


3-43712 


2 


0.07874023 


6.56169 


2.18723 


1.24274 


2 


3-51961 


4-39951 


5-49938 


6.87423 


1 


O.I 181 1034 


9.84253 


3.28084 


1. 864 1 2 


3 


5.27941 


6.59926 


8.24908 


10-31 135 


4 


0.15748045 


13-12337 


437446 


2.48549 


4 


7.03921 


8.79902 


10.99877 


13.74846 


5 


O.196S5056 


16.40421 


5.46807 


3.10686 


5 


8.79902 


10.99877 


13.74846 


17.18558 


6 


0.23622068 


19.6S506 


6.56169 


3.72823 


6 


10.55882 


13.19852 


16.49815 


20.62269 


7 


0-27559079 


22.96590 


7-65530 


4.34960 


7 


12.31862 


15.39828 


19.24785 


24.05981 


8 


0.31496090 


26.24674 


8.74891 


4.97097 


8 


14.07842 


17.59803 


21.99754 


27.49692 


9 


0.35433102 


29.52758 


9-84253 


5-59235 


9 


15.83823 


19.79778 


24-74723 


30.93404 


SQUARE MEASURE. 


WEIGHT (Avoirdupois). 




Square 


Square 


Square 






Milli- 




Kilo- 


Quintals 




centimeters 


meters to 


meters to 


Hectares 




grams 


Kilograms 


grams 


to 




to square 


square 


square 


to acres. 




to 


to grams. 


to 


hundred- 




inches. 


feet. 


yards. 




I 


grains. 




pounds. 


weights. 


I 


0.15500 


10.76393 


I- 19599 


2.47 1 1 


0.01543 


15432.356 


2.20462 


1. 96841 


2 


0.31000 


21.52786 


2.39198 


4.9421 


2 


0.03086 


30864.713 


4.40924 


3-9.3683 


^ 


0.46500 


32.29179 


3.58798 


7-4132 


3 


0.04630 


46297.069 


6.61387 


5-90524 


4 


0.62000 


43-05572 


4-78397 


9.8842 


4 


0.06173 


61729.426 


8.81849 


7-87365 


5 


0.77500 


53-^1965 


5.97996 


12.3553 


5 


0.07716 


77161.782 


1 1. 0231 1 


9.84206 


6 


0.93000 


64-58357 


7-17595 


14.8263 


6 


0.09259 


92594-138 


13-22773 


1 1. 81048 


7 


i.oSsoo 


75-34750 


8.37194 


17.2974 


7 


0.10803 


I0S026.495 


15-43236 


13.77889 


8 


1.24000 


86.1 1 143 


9.56794 


19.7685 


8 


0.12346 


123458-851 


17.63698 


15-74730 


9 


I-3950I 


96.87536 


10.76393 


22.2395 


9 


0.13889 


138891.208 


19.84160 


17.71572 


CUBIC MEASURE. 


Apothe- 
caries' 
Measure. 


Avoirdupois 
(cont.) 


Troy Weight. 


Apothe- 
caries' 
Weight. 




Cubic 


Cubic 


Cubic 


Cub. cen- 










Grams 




decimeters 
to cubic 
inches. 


meters to 
cubic 
feet. 


meters to 
cubic 
yards. 


timeters 
to fluid 
drachms. 




tonnes to 
tons. 


to ounces 
Troy. 


to penny- 
weights. 


to 
scruples. 


I 


61.02390 


35-31476 


1-30795 


0.28157 


I 


0.98421 


0.03215 


0.64301 


0.77162 


2 


122.04781 


70.62952 


2.61591 


0.56314 


2 


1. 9684 1 


0.06430 


1.28603 


1-54324 


3 


183.07171 


105.94428 


3.92386 


0.84471 


3 


2.95262 


0.09645 


1.92904 


2.31485 


4 


244.09561 


141.25904 


5.23182 


1. 12627 


4 


3-93683 


0.12860 


2.57206 


3.08647 


5 


305.11952 


176.57379 


6.53977 


1.40784 


5 


4.92103 


0.16075 


3.21507 


3.85809 


6 


366.14342 


211.88855 


7.84772 


1. 6894 1 


6 


5.90524 


0.19290 


3.85809 


4.62971 


7 


427.16732 


247.20331 


9.15568 


1.97098 


7 


6.88944 


0.22506 


4.5OIIO 


5.40132 


8 


488.19123 


282.51807 


10.46363 


2.25255 


8 


7.87365 


0.25721 


5-14412 


6.17294 


9 


549-21513 


3i7-«3283 


II.77159 


2.53412 


9 


8.85786 


0.28936 


5-78713 


6.94456 


Smithsonian Tables. 















Table 3. 



EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS 
AND MEASURES. 

(3) IMPERIAL TO METRIC. 



LINEAR MEASURE. 



I inch = 

I foot (i2 in.) . . = 
I YARD (3 ft.) . . = 
I pole ( 5i yd. ) . . = 

I chain (22 yd. or ) 

100 links) ) 

I furlong (220 yd.) = 

I mile (1,760 yd.) . = 



I 25.400 milli- 
I meters. 
0.304S0 meter. 

0.914399 " 
5.0292 meters. 

20.1168 " 

201. 16S " 
1.6093 kilo- 
meters. 



SQUARE MEASURE. 



I square inch 

I sq. ft. (144 sq. in.) 



( 6.4516 sq. cen- 
( timeters. 

( 9.2903 sq. deci- 
) meters. 



r -, \ 0.S36126 sq. 

I SQ. YARD (9 sq. ft.) = -J meters. 

u / 1 1 \ i -5--93 sq. me- 

I perch (3oi sq. yd.) = j \/^l 

I rood (40 perches) = 10.117 ares. 

I ACRE U840 sq. yd.) = 0.4046S hectare. 

I sq. mile (640 acres) = | 259.00 hectares. 



CUBIC MEASURE. 

I cub. inch = 16.3S7 cub. centimeters. 
I cub. foot (1728 / _ (0.02S317 cub. me- 

cub. in.) i~ < ter, or 28.317 

( cub. decimeters, 
I CUB. YARD (27 ) 0.76455 cub. meter. 

cub. ft.) ) 



APOTHECARIES' MEASURE. 



I gallon (8 pints or 

160 fluid ounces) 
I fluid ounce, f 5 

(8 drachms) 
I fluid drachm, f 5 I 

(60 minims) ) 

I minim, m (0.91 146 ( 

grain weight) J 



= 4.5459631 liters. 

{ 28.4123 cubic 
\ centimeters. 
_ I 3-5515 cubic 
J centimeters. 
0.05919 cubic 
centimeters. 



-1 



Note. — The Apothecaries' gallon is of the same 
capacity as the Imperial gallon. 



MEASURE OF CAPACITY. 

I gill = 1.42 deciliters. 

I pint (4 gills) . . . = 0.568 liter. 
I quart (2 pints) . . = 1.136 Hters. 
I GALLON (4 quarts) = 4.5459631 " 
I peck ( 2 galls.) . . = 9.092 " 

I bushel (8 galls.) . — 3.6;i7 dekaliters. 
I quarter (8 bushels) = 2.909 hectoliters. 



AVOIRDUPOIS WEIGHT. 



r gram .... 

I dram .... 
I ounce (16 dr.) . 
I POUND (16 oz. or 

7,000 grains) 
I stone (14 lb.) . 
I quarter (28 lb.) 
I hundredweight I 

(112 lb.) ( 



= 1 



h 



I ton (20 cwt. ) . =: 



64.8 m i 11 i - 
grams. 
1.772 grams. 
28.350 " 

0.45359243 kilogr. 

6.350 

12.70 " 

50.80 " 

0.5080 quintal. 
1.0160 tonnes 
or 1016 kilo- 
grams. 



TROY WEIGHT. 



I Troy OUNCE (480 J _ 31.1035 grams, 
grams avoir.) j -^ ■'^ * 



I pennyweight (24 ^ 

grains) 



1.5552 



Note. — The Troy grain is of the same weight as 

the Avoirdupois grain. 



APOTHECARIES' WEIGHT. 



I ounce (8 drachms) 
I drachm, 5 i (3 scru- I 

pies) J 

I scruple, 9i (20 ) 

grains) ) 



= 31-1035 grams. 
= 3.888 

= 1.296 " 



Note. — The Apothecaries' ounce is of the same 
weight as the Troy ounce. The Apothecaries' 
grain is also of the same weight as the Avoirdupois 
grain. 



Note. — The Yard is the length at 62° Fahr., marked on a bronze bar deposited with the Board of Trade. 

The Pound is the weight of a piece o£ platinum weighed in vacuo at the temperature of 0° C, and which is als» 
deposited with the Board of Trade. . 

The Gallon contains 10 lb. weight of distilled water at the temperature of 62° Fahr., the barometer being at 
30 inches. 
Smithsonian Tables. 



10 Table 3. 

EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS 
AND MEASURES. 

(4) IMPERIAL TO METRIC. 





LINEAR MEASURE. 


MEASURE OF CAPACITY. 








Inches 

to 

centimeters. 


Feet 

to 

meters. 


Yards 

to 
meters. 


Miles 
to kilo- 
meters. 




Quarts 

to 
liters. 


Gallons 

to 

liters. 


Bushels 

to 

dekaliters. 


Quarters 

to 

hectoliters. 






1 

2 

3 
4 

5 

6 

7 
8 

9 


2-539998 
5.079996 

7.619993 
10.159991 
12.699989 

15.239987 
17.779984 
20.319982 
22.859980 


0.30480 
0.60960 
0.91440 
1. 21920 
1.52400 

1.82880 
2.13360 
2.43840 
2.74320 


0.91440 
1.82880 
2.74320 
3-65760 
4.57200 

5.48640 
6.40080 

7-31519 
8.22959 


1.60934 

3.21869 
4.82803 

6.43737 
8.04671 

9.65606 
11.26540 
12.87474 
I4.4840S 


I 

2 

3 

4 
5 

6 

7 
8 

9 


1.13649 

2.27298 

3-40947 
4.54596 
5-68245 

6.81894 

7-95544 
9.09193 
10.22842 


4-54596 

9.09193 

I3-637S9 

18.18385 

22.72982 

27.27578 
31.82174 
36.36770 
40.91367 


3-63677 

7-27354 
10.91031 
14.54708 
18.18385 

21.82062 

25-45739 
29.09416 

32.73093 


2.90942 

5-81883 

§.7282^ 

11.63767 

14.54708 

17.45650 
20.36591 

23-27533 
26.18475 






SQUARE MEASURE. 


WEIGHT (Avoirdupois). 






I 

2 

3 
4 
5 

6 

7 
8 

9 


Square 

inches 

to square 

centimeters. 


Square 

feet 

to square 

decimeters. 


Square 
yards to 
square 
meters. 


Acres to 
hectares. 




Grains 
to milli- 
grams. 


Ounces to 
grams. 


Pounds 
to kilo- 
grams. 


Hundred- 
weights to 
quintals. 






6.45159 
12.90318 

19-35477 
25.80636 

32-25794 

38-70953 
45.16112 
51.6127I 
58. 06430 


9.29029 

18.58058 
27.870S6 
37-16115 
46.45144 

55-74173 
65.03201 
74.32230 
83.61259 


0.83613 
1.67225 
2.50838 
3-34450 
4.18063 

5.01676 
5.85288 
6.68901 
7-52513 


0.40468 
O.S0937 
1.21405 
1.61874 
2.02342 

2.42811 
2.83279 
3-23748 
3.64216 


I 

2 

3 
4 

5 

6 

7 
8 

9 


64.79S92 
129.59784 
194-39675 
259.19567 

323-99459 

388.79351 
453-59243 
518.39135 
5S3. 19026 


28.34953 

56.69905 

85.04858 

1 13.3981 1 

141.74763 

170.09716 
198.44669 
226.79621 
255-14574 


0.45359 
0.907 1 8 
1.36078 
1.81437 
2.26796 

2.72155 
3-17515 
3-62874 
4.08233 


0.50802 

1. 01 605 

1.52407 
2.03209 
2.54012 

3.04814 
3-55616 
4.06419 
4.57221 






CUBIC MEASURE. 


Apothe- 
caries' 
Measure. 


Avoirdupois 
(cont.). 


Trov Weight. 


Apothe- 
caries' 
Weight. 






1 
2 

3 

4 
5 

6 

7 
8 

9 


Cubic 

inches 

to cubic 

centimeters. 


Cubic feet 

to 

cubic 

meters. 


Cubic 
yards 
to cubic 
meters. 


Fluid 
drachms 
to cubic 

cenli- 
meters. 




Tons to 

milliers or 

tonnes. 


Ounces to 
grams. 


Penny- 
weights to 
grams. 


Scruples 

to 
grams. 






16.38702 

32-77404 
49.16106 
65.54808 
81.93511 

98.32213 
114.70915 
1 3 1. 0961 7 
147.48319 


0.02832 
0.05663 
O.0S495 
O.I1327 
O.14158 

0.16990 
O.19S22 
0.22653 
0.25485 


0.76455 
I.52911 
2.29366 
3.05821 
3.82276 

4-58732 
5-35187 
6. II 642 
6.88098 


3-55153 

7.10307 

10.65460 

14.20613 

17.75767 

21.30920 
24.S6074 
28.41227 
31.96380 


I 

2 

3 

4 

5 

6 

7 
8 

9 


1.01605 
2.03209 
3.04814 
4.06419 

5.08024 

6.09628 
7-II233 
8.12S38 
9.14442 


31.10348 
62.20696 

93-31044 
124.41392 
155-51740 

186.62088 
217.72437 
248.82785 
279-93133 


1-55517 
3-IIO35 
4.66552 
6.22070 
7-77587 

9-33104 
IO.8S622 
12.44139 
13-99657 


1.29598 
2.59196 
3.88794 
5-1S391 
6.47989 

7-77587 

9.07185 

10.36783 

11.66381 





Smithsonian Tables. 



V=PR =/^' 
a 



If a glass vessel contains 2XfQ,P grammes of mercury, weighted with brass weights in air at 
760 mm. pressure, then its volume in c. cm. 

at the same temperature, t, : 

at another temperature, h, : V = PRx = P pfd \\-\-1 {h- t)\ 
I / = the weight, reduced to vacuum, of the mass of mercury or water which, weighed with brass 
weights, equals i gram ; 
d = the density of mercury or water at z"" C, 
and 7 = 0.000 025, is the cubical expansion coefficient of glass. 



Table 4. 



II 



VOLUME OF A CLASS VESSEL FROM THE WEIGHT OF ITS EQUIVALENT 
VOLUME OF MERCURY OR WATER. 







WATER. 






MERCURY. 




Temper- 














cLtur6 

t 


n. 


Jil, 4 = 10°. 


/?1, ^J = 20°. 


a. 


/?!, ti = 10°. 


/?!, ^1 = 20°. 


0° 


1.001192 


1.001443 


1. 001 693 


0-0735499 


0.0735683 


0.0735867 


I 


ii33 


1358 


1609 


5633 


5798 


5982 


2 


1092 


1292 


1542 


5766 


5914 


6098 


3 


1068 


1243 


1493 


5900 


6029 


6213 


4 


1060 


I2I0 


1460 


6033 


6144 


6328 


S 


1068 


1 193 


1443 


6167 


6259 


6443 


6 


I. CO 1 092 


I.OOII92 


I.OOI442 


0.0736301 


0.0736374 


0.0736558 


7 


1131 


1206 


1456 


6434 


6490 


6674 


8 


1 184 


1234 


1485 


6568 


6605 


6789 


9 


1252 


1277 


1527 


6702 


6720 


6904 


10 


1333 


1333 


1584 


6835 


6835 


7020 


II 


1.001428 


1. 00 1 403 


1. 001653 


0.0736969 


0.0736951 


0.073713s 


12 


1536 


i486 


1736 


7103 


7066 


7250 


13 


1657 


1582 


1832 


7236 


718I 


7365 


14 


1790 


1690 


1940 


7370 


7297 


7481 


IS 


1935 


I8IO 


2060 


7504 


7412 


7596 


16 


1.002092 


I.OOI942 


I.002I93 


0.0737637 


0.0737527 


0.0737711 


17 


2261 


2086 


2337 


7771 


7642 


7826 


18 


2441 


2241 


2491 


7905 


7757 


7941 


19 


2633 


2407 


2658 


8039 


7872 


8057 


20 


2835 


2584 


2835 


8172 


7988 


8172 


21 


1.003048 


1.002772 


1.003023 


0.0738306 


0.0738103 


0.0738288 


22 


3271 


2970 


3220 


8440 


8218 


8403 


23 


3504 


3178 


3429 


8573 


8333 


8518 


24 


3748 


3396 


3647 


8707 


8449 


S633 


25 


4001 


3624 


3875 


8841 


8564 


8748 


26 


1.004264 


1.003862 


I.004II3 


0.0738974 


0.0738679 


0.0738864 


27 


4537 


4IIO 


4361 


9108 


8794 


S979 


28 


4818 


4366 


4616 


9242 


8910 


9094 


29 


5110 


4632 


4884 


9376 


9025 


9210 


30 


5410 


4908 


5159 


9510 


9140 


9325 



Taken from Landolt, Bornstein, and Meyerhoffer's Physikalisch-Chemische Tabellen. 
Smithsonian Tables. 



12 



Table 5. 
DERIVATIVES AND INTEGRALS.* 









x"+i 


d ax 


= adx 


/a;" (fa: 


= , unless n= — i 


d uv 


/ dv du\ , 

/ du dv\ 


rdx 

J X 


= logx 


d^ 


_ dx dx dx 


fe^dx 


= e* 


V 


\ l|2 / 






d*" 


= nacn-i dx 


fc^Hx 


=- go^ 
a 


df{u) 


-df(-\f.dx 
du dx 


fx e«^ dx 




de^ 


= e^dx 


/log a; dx 


= X log x-x 


de«« 


= a e«^ dx 


fu dv 


= u v—fv du 


d loge X 


= - dx 

X 


/{a+hxY dx 




dx^ 


= X'^ (l+logeX) 






d sin a; 


= cos X dx 


fia^W)-^ dx 


= itan-i^ = 

a a 

I . , X 

- sin— 1 


Va;2 + oi 


d cos a; 


= -sin X dx 


fW-x^Y^dx 


I , a+x 
= — log 

20 ° a-x 


d tan re 


= sec' X dx 


/(a2-a;=)-i dx 


= sin-i -, or — cos— ^ - 

a a 


d cot X 


= — csc2 X dx 


fx{a''±x'')-^dx 


= ±ia'±x')i 


J sec X 


= tan a; sec x dx 


ysin^ X dx 


= —J cos xsin x+2 X 


d CSC X 


— —cot a; . scs a; dx 


y cos2 X dx 


= 1 sin X cos x+5 * 


d sin-i a; 


= {l-X^)-i dx 


ysin X cos X dx 


= i sin2 X 


d cos-i a; 


= -{l-x'~)-i dx 


/(sin X cos x)-' 


dx = log tan X 


<i tan-i X 


= {i+x^)-^dx 


/tan X (/x 


= -log cos X 


d cot-i a; 


= -(i+x^)-idx 


/tan2 X c?x 


= tan X— X 


J sec-i X 


= x-^ (a;2-i)-i dx 


/cot X c?x 


= log sin X 


d csc-i a;] 


= -x-^ (ar--i)-^ dx 


/cot2 X c?x 


= — cot X— X 


d sinh X 


= cosh x dx 


/esc X dx 


= log tan ^ X 


(i cosh X 


= sinh X dx 


fx sin X dx 


= sin X— X cos X 


d tanh a; 


= sech' X dx 


f X cos X dx 


= cosx + x sinx 


c? coth X 


= — csch2 X dx 


/tanh xdx 


= log cosh X 


d sech « 


= —sech x tanh dx 


/ coth X dx 


= log sinh X 


d csch * 


= —csch X ■ coth a; dx 


/sech X dx 


= 2 tan-i ea;=g(J j^ 


(i sinh— 1 X 


^{x^+l)-i dx 


/csch X dx 


= log tanh - 


d cosh-i X 


= (a;2-i)-i da; 


fx sinh X dx 


= X cosh X— sinh x 


d tanh-i x 


= {i-x^)-'^dx 


fx cosh X dx 


=^ X sinh X— cosh x 


d coth-i x 


= {i-x^)-'dx 


/sinh- X dx 


= i (sinh xcosh x— x) 


d sech-i X 


= -a;-Mi-a;')-* dx 


/cOSh2 ^ J;j; 


= 1 (sinh X cosh x+x) 


d csch-i 3f 


= -x-i (a;-+i)-i 


/sinh X cosh xdx =| cosh (2 x) 



* See also accompanying table of derivatives. For example : /cos. x dx = sin. x + constant. 
Smithsonian Tables. 



Table 6. 13 

SERIES. 



(jc + y)n = x^+ - «»-! y + - ' ^'\ '^ x"-2 j'^ + . 



n(n — i) . . . (n—m+i) ^ ^ , , ^ ox 

(X ± x)n =.±nx+ -i^I^ ± "<"-^^ ^r^-^^' + ■ . ■ + ^-f-^4^+ • • • (:cK I) 
2! 3 ! (h— kJ! k ! 

(i ± «) " = I T ««-1 — — x^ T -, + • • • 

(i ± *)-! = I T x+x^ T a;»+a;< T a;5+ . . . (a;2<i) 

(I ± a;)-2 -= I T 2x+3:c2 T 4a;3+5x^ T 6a;5+ . . . (a;-<i) 

A2 A» Taylor's 

/(;c+A) ^/ (;c)+A/' {x) + ^ /" W + • • • + ^ /^"' W + . . . ^ series. 

V -1-2 /rw Maclaurin's 

/ (^) =/ (<') + 7 /' (^) + fl /" ('') + ••• ,n / '''' (0) + ... series. 

,. / i\ I I I I 

A*2 vO /y'4 

2I 3! 4I 

(x\oeaY fa; log fl)' / „ ^ n 

a* = i+a;loga+ ^ V" + ^^ 7-^+ (oiKcc) 

2! 3! 

= {x-i)-h{x-iy + \{x-iy - ... (2>Ar>o) 

\_x+i ^\x+ij S\x+iJ J 

log (I + :r) = 3; - i :c2 + § a;8 - i X* + (x2<i) 



sin X = -. (e'^ - e-'^) = a; - ^, + ^ - f, + . . . (x2<oo) 



3"! 5' 7 
I 



(gtx + e-ix) = 1 ^^^ ;-7r, +... = !- versinx (x2<cc) 

2 ! 4 ■ o ! 



x' 2.r^ I7.r^ 62 

tan .r = X + - + — ^4- ~ + ^5—; x^ + 
3 15 315 2b35 



(-?) 



sin-i :e = - - C0S.-1 ;c-x+^ + --^-- + - •^•^•-+... (x2<i) 

2 62452467 

tan-i X = - - cot.-i X = X x' + - .x= x'' + . . . (x2<i) 

2 3 5 7 

Till. / 5V. ,N 

2 X 3x' Sx* 



sinh X = - (e* - e-*) =x+ -+— + -,+.•• (x''<oo) 

2 ^ 3! 5! 7I 



Smithsonian Tables. 



14 



Table 6 (continued). 

SERIES. 



cosh ^ = i (fiX + e-x) = I + |. 4- 1^ + ^j + . . . 


(x2<x.) 


I 2 17 

tanh X = X x'+ — x^ — — x'^ + . . . 

3 15 315 


(x'~<l^') 


... I a;« I 3 s;6 i 3 5 :»;^ , 

sinh-i a; = a; \. - . - . ._. +... 

23 245 2467 


{X^<1) 


II 131 I 3 5 I 

= log 2^- +------,+ -- g ^-^ - .. . 


{x^>i) 


,, , II 131 I35I 
COSh-» ^ = log 2^ - - -, - - ^ -, - - - ^ g^, - . .. 


{x'>i) 


tanh-1 ^ = ^+_a;3+;r5_f.j.7 4.... 


{X^<1) 


I , I . 61 , 

gda; = = a;-7:<^'H cc^ x^ + . . . 

^ 6 24 5040 


(x small) 


ir , I sech^a; i -5 sech ^x 

= sech. X ... 

2 23 245 


(x large) 


X = gd-l = 0+^ .^3 +^05+ ^ 0^ + . . . 


(-0 


/ (:c) = - bo, + b, cos — + b^ cos — + . . . 

2 C C 




. irx _ 2irx , 

4- ai sin 1-02 cos f- . . 

c c 


.(~c<x<c) 


am - - y I ^ / W sin ^ (fa; 




I /" -f- c ^ , . w TT a; 
hm = -J -c /(^)cos ^ (fa; 





Table 7. -MATHEMATICAL CONSTANTS. 



e = 2.71828 1S285 


Numbers. 
TT = 3.I4I59 26536 


Logarithms. 
0.49714 98727 


e-i = 0.36787 94412 


TT^ = 9.86960 4401 I 


0.99429 97454 


M = logioc = 0.43429 44819 


- = 0.31830 98862 


9.50285 01273 


(M)-i = loge 10 = 2.30258 50930 
logiologioe= 9-63778 431 13 


\/7r = 1.77245 38509 
— = 0.88622 69255 


0.24857 49363 

9-94754 49407 


Iogio2 = 0.30102 99957 


-^ = 0.56418 95835 


9.75142 50637 


l0ge2 = 0.69314 71806 


-^ = 1. 12837 91671 


0.05245 50593 


logioa; = M.log^a; 


yjl = 1-25331 41373 


0.09S05 99385 


logij;c = logeo;. log^e 


■xj- = 0.79788 45608 


9.90194 00615 


= log<,a; H- logeB 
loge IT = 1. 14472 9S858 


1 7 = 0.78539 81634 
4 

^ = 0.443 1 1 34627 
4 


9.8950S 98814 
9.64651 49450 


p = 0.47693 62762 


1 TT = 4.18879 02048 


0.6220S 86093 
0.03520 45477 


logp = 9.67846 03565 


/ 1-08443 75514 

V 2 IT 



Smithsonian Tables. 











Table 8. 








I 


5 


VALUES OF 


RECIPROCALS, SQUARES, 


CUBES, 


SQUARE ROOTS, OF 








NATURAL 


NUMBERS. 








n 


1 000.1 


tfi 


«3 


V« 


« 


1000.^ 


«2 


«3 


<n 




10 


100.000 


100 


1000 


3-f623 


65 


15.3846 


4225 


274625 


8.0623 




II 


90.9091 


121 


1331 


3-3 '66 


66 


i5-'5i5 


4356 


2S7496 


8.1240 




12 


83-3333 


144 


1728 


3-4641 


67 


14.9254 


4489 


300763 


8.1854 




13 


76.9231 


169 


2197 


3.6056 


68 


14.7059 


4624 


314432 


8.2462 




14 


71.42S6 


196 


2744 


3-7417 


69 


14.4928 


4761 


328509 


8.3066 




15 


66.6667 


225 


3375 


3-8730 


70 


14.2857 


4900 


343000 


8.3666 




16 


62.5000 


256 


4096 


4.0000 


71 


14.0845 


5041 


3579'! 


8.4261 




17 


588^35 


289 


4913 


4-1231 


72 


13.8889 


5'84 


373248 


8.4853 




18 


55-5556 


324 


5832 


4.2426 


73 


13.6986 


5329 


389017 


8.5440 




19 


52.6316 


361 


6859 


4-3589 


74 


13-5135 


5476 


405224 


8.6023 




20 


50.0000 


400 


8000 


4.4721 


75 


13-3333 


5625 


421875 


8.6603 




21 


47.6190 


441 


9261 


4.5826 


76 


13-1579 


5776 


438976 


8.7178 




22 


45-4545 


484 


10648 


4.6904 


17 


12.9870 


5929 


456533 


8.7750 




23 


43-4783 


529 


12167 


4-7958 


78 


12.8205 


6084 


474552 


8.8318 




24 


41.6667 


576 


13824 


4.8990 


79 


12.6582 


6241 


493039 


8.88S2 




25 


40.0000 


625 


15625 


5.0000 


80 


12.5000 


6400 


512000 


8.9443 




26 


38.4615 


676 


17576 


5-0990 


81 


12.3457 


6561 


531441 


9.0000 




27 


37-0370 


729 


19683 


5.1962 


82 


12.1951 


6724 


551368 


9-0554 




28 


3S-7'43 


784 


21952 


5-2915 


f3 


12.0482 


6889 


571787 


9. 11 04 




29 


34-4S28 


841 


24389 


5-3852 


84 


11.9048 


7056 


592704 


9.1652 




30 


2,3-?>?>33 


900 


27000 


5-4772 


85 


11.7647 


7225 


614125 


9.2195 




31 


32.2581 


961 


29791 


5-5678 


86 


[ 1.6279 


7396 


636056 


9.2736 




32 


31.2500 


1024 


3276S 


5-6569 


87 


11.4943 


7569 


658503 


9-3274 




33 


30-3030 


1089 


35937 


5-7446 


88 


11.3636 


7744 


681472 


9.3S08 




34 


29.4118 


1156 


39304 


5-8310 


89 


11.2360 


7921 


704969 


9-4340 




35 


28.5714 


1225 


42875 


5.9161 


90 


ii.iiii 


8100 


729000 


9.4868 




36 


27.7778 


1296 


46656 


6.0000 


91 


10.9890 


82S1 


753571 


9-5394 




37 


27.0270 


1369 


50653 


6.0S28 


92 


10.8696 


8464 


7786S8 


9-5917 




38 


26.3158 


1444 


54872 


6.1644 


93 


10.7527 


8649 


804357 


9-6437 




39 


25.6410 


1521 


593 '9 


6.2450 


94 


10.6383 


8836 


830584 


9-6954 




40 


25.0000 


1600 


64000 


6.3246 


95 


10.5263 


9025 


857375 


9.7468 




41 


24.3902 


1681 


68921 


6.4031 


96 


10.4167 


9216 


884736 


9.79S0 




42 


23.8095 


1764 


74088 


6.4807 


97 


10.3093 


9409 


912673 


9.8489 




43 


23.2558 


1849 


^9507 


6.5574 


98 


10.2041 


9604 


941192 


9.S995 




44 


22.7273 


1936 


85184 


6.6332 


99 


lO.IOIO 


9801 


970299 


9-9499 




45 


22.2222 


2025 


91125 


6.7082 


100 


10.0000 


1 0000 


I 000000 


10.0000 




46 


21.7391 


2116 


97336 


6.7823 


lOI 


9.90099 


I020I 


1030301 


10.0499 




47 


21.2766 


2209 


103823 


6.8557 


T02 


9.80392 


10404 


1061208 


10.0995 




48 


20.8333 


2304 


1 10592 


6.9282 


103 


9.70874 


10609 


1092727 


10.1489 




49 


20.4082 


2401 


1 1 7649 


7.0000 


104 


9.61538 


I0816 


1 1 24864 


10.1980 




50 


20.0000 


2500 


125000 


7.0711 


105 


9-52381 


I 1025 


II 57625 


10.2470 




51 


19.6078 


2601 


132651 


7.1414 


106 


9-43396 


1 1 236 


1191016 


10.2956 




52 


19.230S 


2704 


1 40608 


7.2111 


107 


9-34579 


I 1449 


1225043 


10.3441 




S3 


18.8679 


2809 


14SS77 


7.2801 


108 


9.25926 


1 1 664 


1 2597 1 2 


•0-3923 




54 


18.5185 


2916 


1 57464 


7-34S5 


109 


9-17431 


nSSi 


1295029 


10.4403 




55 


18.1818 


3025 


166375 


7.4x62 


110 


9.09091 


12100 


1331000 


10.4S81 




56 


17-8571 


3136 


175616 


7-4833 


III 


9.00901 


12321 


I 36763 I 


'0-5357 




57 


17-5439 


3249 


185193 


7-5498 


112 


8.92857 


12544 


1404928 


10.5830 




58 


17.2414 


3364 


195112 


7.6158 


"3 


8.84956 


12769 


1442897 


10.6301 




59 


16.9492 


34S1 


205379 


7.68U 


114 


8.77193 


12996 


1 48 1 544 


10.6771 




60 


16.6667 


3600 


216000 


7.7460 


115 


8.69565 


13225 


X 52087 5 


10.7238 




61 


16.3934 


3721 


226981 


7.8102 


116 


8.62069 


13456 


1 560896 


10.7703 




62 


16.1290 


3844 


238328 


7.8740 


"7 


8.54701 


13689 


1601613 


10.8167 




63 


15-8730 


3969 


250047 


7-9373 


118 


8.47458 


13924 


1643032 


10.S628 




64 


15.6250 


4096 


262144 


8.0000 


119 


8.40336 


14161 


1 685 1 59 


10.9087 





Smithsonian Tables. 



I 6 Table 8 {continued). 

VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, 
OF NATURAL NUMBERS. 



n 


1000.^ 


«2 


«3 


v« 


« 


1 000. J 


«2 


«3 


y/« 




120 


8-33333 


14400 


1728000 


10.9545 


. 175 


5.71429 


30625 


5359375 


13.228S 




121 


8.26446 


1 464 1 


I77156I 


1 1 .0000 


176 


5.68182 


30976 


5451776 


13.2665 




122 


8.19672 


I4S84 


181584S 


11.0454 


^77 


5-64972 


31329 


5545233 


13-3041 




123 


8.13008 


I5129 


1860867 


11.0905 


178 


5.61798 


31684 


5639752 


13-3417 




124 


8.06452 


15376 


1906624 


"■1355 


179 


5-58659 


32041 


5735339 


13-3791 




125 


8.00000 


15625 


I953I25 


1 1. 1803 


180 


5-55556 


32400 


5832000 


13.4164 




126 


7-93651 


15876 


2000376 


11.2250 


181 


5.52486 


32761 


592974' 


■3-4536 




127 


7.87402 


16129 


2048383 


11.2694 


182 


5-49451 


33124 


602S568 


134907 




1 28 


7.81250 


16384 


2097152 


11-3137 


183 


5.46448 


33489 


6128487 


13-5277 




129 


7-75194 


1 664 1 


2146689 


"•3578 


184 


5-43478 


33856 


6229504 


13-5647 




130 


7.69231 


16900 


2197000 


II.40I8 


185 


5-40541 


34225 


6331625 


13.6015 




131 


7-63359 


I7161 


2248091 


11-4455 


186 


5-37634 


34596 


6434856 


13.6382 




132 


7-5757(3 


17424 


2299968 


1 1. 489 1 


187 


5-34759 


34969 


6539203 


13-6748 




133 


7.51880 


17689 


2352637 


11.5326 


188 


5-31915 


35344 


6644672 


13-7113 




134 


7.46269 


17956 


2406104 


"•5758 


189 


5.29101 


35721 


6751269 


13-7477 




135 


7.40741 


1S225 


2460375 


1 1. 61 90 


190 


5.26316 


36100 


6859000 


13.7840 




136 


7-35294 


18496 


2515456 


11.6619 


191 


5-23560 


36481 


696787 1 


13.8203 




137 


7.29927 


18769 


2571353 


11.7047 


192 


5-20833 


36864 


7077888 


13.8564 




138 


7.24638 


19044 


2628072 


11-7473 


193 


5-18135 


37249 


7189057 


13.8924 




139 


7.19424 


19321 


2685619 


11.7898 


194 


5.15464 


37636 


7301384 


13.9284 




140 


7.14286 


19600 


2744000 


11.8322 


195 


5.12821 


38025 


7414875 


13.9642 




141 


7.09220 


1 988 1 


2803221 


11.8743 


196 


5.10204 


38416 


7529536 


1 4.0000 




142 


7.04225 


20164 


2863288 


11.9164 


197 


5.07614 


38809 


7645373 


14-0357 




143 


6.99301 


20449 


2924207 


11.9583 


198 


5-05051 


39204 


7762392 


14.0712 




144 


6.94444 


20736 


2985984 


12.0000 


199 


5-02513 


39601 


7880599 


14.1067 




145 


6.S9655 


21025 


3048625 


12.0416 


200 


5.00000 


40000 


8000000 


14.1421 




146 


6.84932 


21316 


3II2I36 


1 2.0830 


201 


4-97512 


40401 


8 1 20601 


14-1774 




147 


6.80272 


21609 


3176523 


12.1244 


202 


4.95050 


40804 


8242408 


14.2127 




148 


6.75676 


21904 


3241792 


12.1655 


203 


4.9261 1 


41209 


8365427 


14.2478 




149 


6.71141 


22201 


3307949 


12.2066 


204 


4.90196 


41616 


8489664 


14.2829 




150 


6.66667 


22500 


3375000 


12.2474 


205 


4.87805 


42025 


8615125 


14.3178 




151 


6.62252 


22801 


3442951 


12.2882 


206 


4-85437 


42436 


8741816 


14-3527 




152 


6.57S95 


23104 


351 1808 


12.3288 


207 


4.83092 


42849 


8S69743 


14-3875 




153 


6-53595 


23409 


35S1577 


12.3693 


208 


4.80769 


43264 


8998912 


14.4222 




154 


6.49351 


23716 


3652264 


12.4097 


209 


4.78469 


43681 


9129329 


14.456S 


1 


155 


6.45161 


24025 


372387s 


12.4499 


210 


4.76190 


44100 


9261000 


14.4914 


1 


156 


6.41026 


24336 


3796416 


12.4900 


211 


4-73934 


44521 


9393931 


14.5258 


1 


157 


6.36943 


24649 


3869893 


12.5300 


212 


4.71698 


44944 


9528128 


14.5602 


1 


158 


6.3291 1 


24964 


3944312 


12.5698 


213 


4.69484 


45369 


9663597 


14-5945 


1 


159 


6.2S931 


25281 


4019679 


1 2.6095 


214 


4.67290 


45796 


9800344 


14.6287 




160 


6.25000 


25600 


4096000 


12.6491 


215 


4.65116 


46225 


9938375 


14.6629 




161 


6.21118 


25921 


4173281 


12.6886 


216 


4.62963 


46656 


10077696 


14.6969 




162 


6.17284 


26244 


4251528 


12.7279 


217 


4.60829 47089 


10218313 


14.7309 




163 


6.13497 


26569 


4330747 


12.7671 


218 


4.58716 


47524 


10360232 


14.7648 




164 


6.09756 


26896 


4410944 


12.8062 


219 


4.56621 


47961 


10503459 


14.7986 




165 


6.06061 


27225 


4492125 


12.8452 


220 


4-54545 


48400 


10648000 


14.8324 




166 


6.02410 


27556 


4574296 


12.8841 


221 


4.52489 


48841 


10793861 


14.8661 




167 


5.9S802 


27889 


4657463 


12.9228 


222 


4.50450 


49284 


10941048 


14-8997 




168 


5-95238 


28224 


4741632 


12.9615 


223 


4.48430 


49729 


110S9567 


14-9332 




169 


5.91716 


28561 


4826809 


13.0000 


224 


4.46429 


50176 


11239424 


14.9666 




170 


5.88235 


28900 


4913000 


13.0384 


225 


4.44444 


50625 


11390625 


1 5.0000 




171 


5.84795 


29241 


50002 1 1 


13.0767 


226 


4.42478 


51076 


11543176 


15-0333 




172 


5-81395 


29584 


5088448 


13.1149 


227 


4.40529 


51529 


1 1697083 


15.0665 




173 


5-78035 


29929 51777I7 


13-1529 


228 


4-38596 


51984 


11852352 


15.0997 




174 


5-74713 


30276 5268024 


13.1909 


229 


4.36681 


52441 


I 200S989 


15-1327 





SMtTHSONIAN TABLES. 



Table 8 {cotitiniud). I 7 

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS, OF 

NATURAL NUMBERS. 



n 


iooo.i 


«2 


«8 


v« 


n 


1000.' 


«2 


«3 


v« 


230 


4-34783 


52900 


12 167000 


15.1658 


285 


3-50877 


81225 


23I49125 


16.8819 


231 


4.32900 


53361 


12326391 


15.1987 


286 


3.49650 


81796 


23393656 


16.91 15 


232 


4-31034 


53824 


I24S7168 


15-2315 


287 


.3-48432 


82369 


23639903 


16.941 1 


233 


4.29185 


54289 


12649337 


1 5.2643 


288 


3.47222 


82944 


23887872 


16.9706 


234 


4-27350 


54756 


12812904 


15.2971 


289 


3.46021 


83521 


24137569 


17.0000 


235 


4-25532 


55225 


I2977S75 


15-3297 


290 


3.44828 


84 1 00 


24389000 


17.0294 


236 


4.23729 


55696 


13144256 


'5-3623 


291 


3 43643 


846S1 


24642171 


: 17-0587 


237 


4.21941 


56169 


I33I2053 


15-3948 


292 


3.42466 


85264 


24897088 


17.0880 


23S 


4.20168 


56644 


I3481272 


15.4272 


293 


3-41297 


85849 


25153757 


17-1172 


239 


4.IS4IO 


57121 


I365I919 


15.4596 


294 


3.40136 


86436 


25412x84 


17.1464 


240 


4.16667 


57600 


I 38 24000 


15.4919 


295 


3-38983 


87025 


25672375 


17.1756 


241 


4.14938 


58081 


1 3997 52 1 


15-5242 


296 


3-37838 


87616 


25934336 


17.2047 


242 


4-13223 


58564 


14172488 


15-5563 


297 


3.36700 


88209 


2619S073 


17-2337 


243 


4-11523 


59049 


14348907 


15.5885 


298 


3-3S570 


88804 


26463592 


17.2627 


244 


4.09836 


59536 


14526784 


15.6205 


299 


3-34448 


89401 


26730899 


17.2916 


245 


4.08163 


60025 


14706125 


15.6525 


300 


3-33333 


90000 


27000000 


17.3205 


246 


4.06504 60516 


14886936 


15.6844 


301 


3-32226 


90601 


27270901 


17-3494 


247 


4.04858 


61009 


15069223 


15.7162 


302 


3-3"26 


91204 


27543608 


17-3781 


248 


4.03226 


61504 


15252992 


15.7480 


303 


3-30033 


91809 


27818127 


17.4069 


249 


4.01606 


62001 


15438249 


15-7797 


304 


3.28947 


92416 


28094464 


17-4356 


250 


4.00000 


62500 


15625000 


15.8114 


305 


3.27869 


93025 


28372625 


17.4642 


251 


3.98406 


63001 


15S13251 


15.8430 


306 


3-26797 


93636 


28652616 


17.4929 


252 


3.96825 


63504 


16003008 


15-8745 


307 


3-25733 


94249 


28934443 


17-5214 


253 


3-95257 


64009 


16194277 


15.9060 


308 


3-24675 


94864 


292181I2 


17-5499 


254 


3-93701 


64516 


16387064 


15-9374 


309 


3.23625 


95481 


29503629 


17-5784 


255 


3-92157 


65025 


16581375 


15.9687 


310 


3.22581 


96100 


29791000 


17.6068 


256 


3.90625 


65536 


16777216 


1 6.0000 


3" 


3-21543 


96721 


30080231 


17-6352 


2 57 


3-89105 


66049 


16974593 


16.0312 


312 


3.20513 


97344 


30371328 


17.6635 


258 


3-87597 


66564 


17173512 


16.0624 


313 


3.19489 


97969 


30664297 


17.6918 


259 


3.86100 


67081 


17373979 


16.0935 


314 


3. 1 847 1 


98596 


30959144 


17.7200 


260 


3.84615 


67600 


17576000 


16.1245 


315 


3.17460 


99225 


31255875 


17.7482 


261 


3-83142 


68121 


17779581 


16.1555 


3'6 


3.16456 


99856 


31554496 


17.7764 


262 


3.81679 


68644 


17984728 


16.1864 


317 


3-15457 


100489 


31855OI3 


17.8045 


263 


3.S022S 


69169 


1S191447 


16.2173 


318 


3-14465 


101124 


32157432 


17.8326 


264 


3.7S7SS 


69696 


18399744 


16.2481 


319 


3.13480 


101761 


32461759 


17.8606 


265 


3-77358 


70225 


18609625 


16.2788 


320 


3.12500 


102400 


32768000 


17.8885 


266 


3-75940 


70756 


18S21096 


16.3095 


321 


3-"5;6 


1 0304 1 


33076161 


17.9165 


267 


3-74532 


71289 


1 9034 1 63 


16.3401 


322 


310559 


103684 


33386248 


17.9444 


268 


3-73134 


71824 


19248832 


16.3707 


323 


309598 


104329 


33698267 


17.9722 


269 


3-71747 


72361 


19465109 


16.4012 


324 


3.08642 


104976 


34012224 


18.0000 


270 


3-70370 


72900 


19683000 


16.4317 


325 


3.07692 


105625 


34328125 


18.0278 


271 


3.69004 


73441 


199025 1 1 


16.4621 


326 


3.06748 


106276 


34645976 


18.0555 


272 


3.67647 


73984 


20123648 


16.4924 


327 


3.05S10 


106929 


34965783 


18.0831 


273 


3.66300 


74529 


20346417 


16.5227 


328 


3.04878 


107584 


35287552 


18.1108 


274 


3.64964 


75076 


20570824 


16.5529 


329 


3-03951 


I 0824 I 


35611289 


18.1384 


275 


3-63636 


75625 


20796875 


16.5831 


330 


3-03030 


108900 


35937000 


18.1659 


276 


3.62319 


76176 


21024576 


16.6132 


331 


3.021 1 5 


I 0956 I 


36264691 


18.1934 


277 


3.61011 


76729 


21253933 


16.6433 


332 


3.01205 


110224 


36594368 


18.2209 


278 


3-59712 


77284 


21484952 


16.6733 


m 


3.00300 


II 0889 


36926037 


18.2483 


279 


358423 


77841 


21717639 


16.7033 


334 


2.99401 


111556 


37259704 


18,2757 


280 


3-57143 


7S400 


21952000 


16.7332 


335 


2.98507 


112225 


37595375 


18.3030 


281 


3-55872 


7S961 


221S8041 


16.7631 


336 


2.97619 


1 1 2896 


37933056 


18.3303 


2S2 


3-54610 


79524 


22425768 


16.7929 : 


ZZl 


2.96736 


1 1 3569 


38272753 


18.3576 


283 


3-53357 


800S9 


22665187 


16.8226 


338 


2.95858 


1 14244 


38614472 


18.3S48 


284 


3.52113 


80656 


22906304 1 


16.8523 


339 


2.94985 


114921 


38958219 


18.4120 



Smithsonian Tables. 



i8 



Table 8 {.continued'). 



VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 
OF NATURAL NUMBERS. 



n 


lOOO.i 


«2 


«» 


V« 


« 


lOOO.i 


«2 


«3 


v« 


340 


2.941 18 


I I 5600 


39304000 


18.4391 


395 


2-53165 


156025 


61629875 


19.8746 


341 


2-93255 


1 1 628 1 


39651821 


18.4662 


396 


2-52525 


I 56816 


62099136 


19.8997 


342 


2.92398 


1 1 6964 


40001688 


18.4932 


397 


2.51889 


157609 


62570773 


19.9249 


343 


2.91545 


1 1 7649 


40353607 


18.5203 


398 


2.51256 


I 58404 


63044792 


19.9499 


344 


2.90698 


1 18336 


40707584 


18.5472 


399 


2.50627 


1 5920 1 


63521199 


19.9750 


345 


2.89855 


1 19025 


41063625 


18.5742 


400 


2.50000 


160000 


64000000 


20.0000 


346 


2.89017 


II9716 


41421736 


18.6011 


401 


2-49377 


1 6080 1 


64481201 


20.0250 


347 


2.88 1 84 


I 20409 


41781923 


18.6279 


402 


2.48756 


161604 


64964808 


20.0499 


343 


2.87356 


121 104 


42I44I92 


18.6548 


403 


2.48139 


162409 


65450827 


20.0749 


349 


2.S6533 


I2180I 


42508549 


18.6815 


404 


2.47525 


163216 


65939264 


20.0998 


350 


2.85714 


122500 


42875000 


18.7083 


405 


2.46914 


164025 


66430125 


20.1246 


351 


2.84900 


I 23201 


43243551 


18.7350 


406 


2.46305 


164836 


66923416 


20.1494 


352 


2.84091 


123904 


43614208 


18.7617 


407 


2.45700 


165649 


67419143 


20.1742 


353 


2.83286 


1 24609 


43986977 


18.7883 


408 


2.45098 


1 66464 


679I7312 


20.1990 


354 


2.82486 


125316 


44361864 


18.8149 


409 


2.44499 


167281 


68417929 


20.2237 


355 


2.81690 


126025 


44738875 


18.8414 


410 


2.43902 


1681OO 


6S92IOOO 


20.2485 


356 


2.80S99 


126736 


45118016 


18.8680 


411 


2-43309 


I 6892 I 


69426531 


20.2731 


357 


2.80112 


127449 


45499293 


18.8944 


412 


2.42718 


169744 


69934528 


20.2978 


358 


2.79330 


I 28 1 64 


45882712 


18.9209 


413 


2.42131 


170569 


70444997 


20.3224 


359 


2.78552 


I 2888 I 


46268279 


18.9473 


414 


2.41546 


I71396 


70957944 


20.3470 


360 


2.77778 


I 29600 


46656000 


18.9737 


415 


2.40964 


172225 


71473375 


20.3715 


361 


2.77008 


130321 


47045881 


19.0000 


416 


2-40385 


173056 


71991296 


20.3961 


362 


2.76243 


I3IO44 


47437928 


19.0263 


417 


2.39808 


I73S89 


72511713 


20.4206 


363 


2.75482 


I3I769 


47832147 


19.0526 


418 


2-39234 


174724 


73034632 


20.4450 


364 


2.74725 


132496 


48228544 


19.0788 


419 


2-38663 


I75561 


73560059 


20.4695 


365 


2-73973 


133225 


48627125 


19.1050 


420 


2.38095 


176400 


74088000 


20.4939 


366 


2.73224 


133956 


49027896 


19.1311 


421 


2-37530 


177241 


74618461 


20.5183 


367 


2.724S0 


134689 


49430863 


19.1572 


422 


2.36967 


178084 


75151448 


20.5426 


368 


2.71739 


135424 


49836032 


19-1833 


423 


2.36407 


178929 


75686967 


20.5670 


369 


2.71003 


136161 


50243409 


19.2094 


424 


2-35849 


179776 


76225024 


20-5913 


370 


2.70270 


1 36900 


50653000 


19-2354 


425 


2-35294 


180625 


76765625 


20.6155 


371 


2-69542 


I 37641 


5106481 1 


19.2614 


426 


2-34742 


181476 


77308776 


20.6398 


372 


2.68817 


138384 


51478848 


19.2873 


427 


2.34192 


182329 


77854483 


20.6640 


373 


2.6S097 


I39129 


5i895i'7 


19.3132 


428 


2-33645 


183184 


78402752 


20.6882 


374 


2.673S0 


139876 


52313624 


19-3391 


429 


2.33100 


I 8404 I 


78953589 


20.7123 


375 


2.66667 


140625 


52734375 


19.3649 


430 


2-32558 


184900 


79507000 


20.7364 


376 


2.65957 


I41376 


53157376 


19.3907 


43' 


2.32019 


185761 


80062991 


20.7605 


377 


2.65252 


142129 


53582633 


19.4165 


432 


2.314S1 


186624 


80621568 


20.7846 


37S 


2.64550 


142884 


54010152 


19.4422 


433 


2.30947 


187489 


81182737 


20.8087 


379 


2.63852 


1 4364 1 


54439939 


19.4679 


434 


2.30415 


188356 


81746504 


20.8327 


380 


2.63158 


144400 


54872000 


19.4936 


435 


2.298S5 


189225 


82312875 


20.8567 


38" 


2.62467 


I45161 


55306341 


19.5192 


436 


2-29358 


1 90096 


82881856 


20.8806 


382 


2.61780 


145924 


55742968 


19.5448 


437 


2.28833 


1 90969 


83453453 


20.9045 


3S3 


2.61097 


146689 


56181887 


19.5704 


438 


2.2831 1 


191844 


84027672 


20.9284 


384 


2.60417 


147456 


56623104 


'9-5959 


439 


2.27790 


192721 


84604519 


20.9523 


385 


2.59740 


148225 


57066625 


19.6214 


440 


2.27273 


193600 


85184000 


20.9762 


386 


2.59067 


148996 


57512456 


19.6469 


441 


2.26757 


194481 


85766121 


2 1 .0000 


387 


2-58398 


149769 


57960603 


19.6723 


442 


2.26244 


195364 


86350888 


21.0238 


388 


2-57732 


150544 


58411072 


19.6977 


443 


2-25734 


196249 


86938307 


21.0476 


389 


2.57069 


I5I32I 


58863869 


19.7231 


444 


2.25225 


197136 


87528384 


21.0713 


390 


2.56410 


I52IOO 


59319000 


19.7484 


445 


2.24719 


198025 


8812II25 


21.0950 


391 


2-55754 


152881 


59776471 


19-7737 


446 


2.24215 


198916 


88716536 


21.1187 


392 


2.55102 


153664 


60236288 


19.7990 


447 


2.23714 


I 99809 


89314623 


21.1424 


393 


2-54453 


154449 


60698457 


19.8242 


448 


2.23214 


200704 


89915392 


21.1660 


394 


2.53807 


155236 


61162984 


19.8494 


449 


2.22717 


20160I 


90518849 


21.1896 



Smithsonian Tables. 



Table 8 (continued). IQ 

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 









OF NATURAL NUMBERS 


• 






n 


looo.i 


«2 


«8 


V« 


n 


lOOO.i 


«2 


„3 


V« 


450 


2.22222 


202500 


91 1 25000 


21.2132 


505 


1.98020 


255025 


128787625 


22.4722 


45' 


2.21729 


203401 


9I73385I 


21.2368 ; 


506 


1.97628 


256036 


I29554216 


22.4944 


452 


2.21239 


204304 


92345408 


21.2603 1 


507 


1.97239 


257049 


130323843 


22.5167 


453 


2.20751 


205209 


92959677 


21.2838 


508 


1.96850 


25S0O4 


1 3 10965 1 2 


22.5389 


454 


2.20264 


2061 16 


93576664 


21.3073 


509 


1.96464 


259081 


131872229 


22.5610 


455 


2.19780 


207025 


94196375 


21.3307 


510 


1 .96078 


260100 


I3265IOOO 


22.5832 


456 


2.1929S 


207936 


94S18816 


21-3542 


511 


1.95695 


261I2I 


1 3343283 1 


22.6053 


457 


2.1SS18 


208849 


95443993 


21.3776 


512 


I-953I2 


262144 


I342I7728 


22.6274 


458 


2.18341 


209764 


9607 1 9 1 2 


21.4009 


513 


1.94932 


263169 


135005697 


22.6495 


459 


2.17865 


2I0681 


96702579 


21.4243 


514 


1.94553 


264196 


135796744 


22.6716 


460 


2.17391 


21 1600 


97336000 


21.4476 


515 


1-94175 


265225 


136590875 


22.6936 


461 


2.16920 


21252I 


97972181 


21.4709 


516 


1.93798 


266256 


I 37 38S096 


22.7156 


462 


2.16450 


213444 


9861 1 1 28 


21.4942 


517 


1-93424 


267289 


138188413 


22.7376 


463 


2.15983 


214369 


99252847 


21.5174 


518 


1.93050 


268324 


138991832 


22.7596 


464 


2.15517 


215296 


99897344 


21.5407 


519 


1.92678 


269361 


139798359 


22.7816 


465 


2.15054 


216225 


100544625 


21.5639 


520 


1.92308 


270400 


140608000 


22.8035 


466 


2.14592 


217156 


10 1 194696 


21.5870 


521 


1.91939 


27144I 


141420761 


22.8254 


467 


-•14133 


2 I S089 


101847563 


21.6102 


522 


1.91571 


272484 


142236648 


22.8473 


468 


^■13675 


219024 


102503232 


21-6333 


523 


'■91205 


273529 


143055667 


22.8692 


469 


2.13220 


2I9961 


103161709 


21.6564 


524 


1 .90840 


274576 


143877824 


22.8910 


470 


2.12766 


220900 


103823000 


21.6795 


525 


1.90476 


275625 


I 447031 25 


22.9129 


471 


2.12314 


22184I 


104487111 


21.7025 


526 


1.901 14 


276676 


145531576 


22.9347 


472 


2.1 1864 


222784 


1 05 1 54048 


21.7256 


527 


1-89753 


277729 


1 46363 1 83 


22.9565 


473 


2.1 1416 


223729 


105823817 


21.7486 


528 


1.89394 


278784 


147 197952 


22.9783 


474 


2.10970 


224676 


106496424 


21.7715 


529 


1.89036 


279841 


148035889 


23.0000 


475 


2.10526 


225625 


107171875 


21.7945 


530 


1.8S679 


280900 


148877000 


23.0217 


476 


2.10084 


226576 


107850176 


21.8174 


53' 


1.8S324 


281961 


149721291 


23-0434 


477 


2.09644 


227529 


108531333 


21.8403 i 


532 


1.87970 


283024 


1 50568768 


23.0651 


478 


2.09205 


228484 


109215352 


21.8632 


533 


1.87617 


284089 


151419437 


23.0868 


479 


2.0876S 


229441 


109902239 


2I.S861 


534 


1.87266 


285156 


152273304 


23.1084 


480 


2-08333 


230400 


1 10592000 


21.9089 


535 


1. 869 1 6 


286225 


1 53130375 


23.1301 


481 


2.07900 


23I361 


1 1 128464 1 


21.9317 


536 


1.86567 


287296 


153990656 


23-1517 


482 


2.07469 


232324 


111980168 


21.9545 


537 


1.86220 


28S369 


1 548541 53 


23-1733 


483 


2.07039 


2332S9 


1 1 2678587 


21.9773 


538 


1.S5874 


289444 


155720872 


23.1948 


484 


2.06612 


234256 


1 1 3379904 


22.0000 


539 


1.85529 


290521 


1 565908 1 9 


23.2164 


485 


2.06186 


235225 


114084125 


22.0227 


540 


1.85185 


291600 


157464000 


232379 


486 


2.05761 


236196 


114791256 


22.0454 


541 


1.84843 


2926S1 


1 5834042 1 


23-2594 


487 


2-05339 


237169 


I '5501303 


22.0681 


542 


1.84502 


293764 


I 592200S8 


23.2809 


488 


2.04918 


238144 


116214272 


22.0907 


543 


1.84162 


294849 


1 60 1 03007 


23.3024 


4S9 


2.04499 


239I2I 


11 6930 I 69 


22.1133 


544 


1.83824 


295936 


I 60989 I 84 


23-3238 


490 


2.04082 


240100 


1 17649000 


22.1359 


545 


1.83486 


297025 


161878625 


23-3452 


491 


2.03666 


241081 


118370771 


22.1585 


546 


I -831 50 


298 1 1 6 


162771336 


23.3666 


492 


2-03252 


242064 


1 19095488 


22.1S1I 


547 


1.82815 


299209 


163667323 


23.3880 


493 


2.02840 


243049 


1 19823 1 57 


22.2036 


548 


1.82482 


300304 


164566592 


23.4094 


494 


2.02429 


244036 


120553784 


22.2261 


549 


1. 82 1 49 


301401 


165469149 


23-4307 


495 


2.02020 


245025 


121287375 


22.2486 


550 


1.81818 


302500 


166375000 


23.4521 


496 


2.01613 


246016 


122023936 


22.2711 


551 


1. 8 1 488 


303601 


167284151 


23.4734 


497 


2.01207 


247009 


122763473 


22.2935 


552 


1.81159 


304704 


I 68 I 96608 


23.4947 


49S 


2.00803 


248004 


123505992 


22.3159 


553 


1.80832 


305809 


169112377 


23.5160 


499 


2.00401 


249001 


124251499 


22.3383 


554 


1.80505 


306916 


I 70031 464 


23.5372 


500 


2.00000 


250000 


125000000 


22.3607 


555 


1.80180 


308025 


17095387s 


23-5584 


501 


1. 9960 1 


25IOOI 


125751501 


22.3830 


556 


1.79856 


309136 


171879616 


23.5797 


502 


1.99203 


252004 


1 26506008 


22.4054 


557 


1-79533 


310249 


172808693 


2'?. 6008 


503 


1.98807 


253009 


127263527 


22.4277 


558 


1.79211 


311364 


173741112 


23.6220 


504 


1. 9841 3 


254016 


128024064 


22.4499 


559 


1. 78891 


31 2481 


174676879 


23.6432 



Smithsonian Tables. 



20 



Table 8 {continued). 



VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 
OF NATURAL NUMBERS. 



n 
560 


lOOO.i 


«2 


«3 


v« 


n 
615 


lOOO.i 


«2 


«3 


v« 


1 7857 1 


313600 


175616000 


23.6643 


1.62602 


378225 


232608375 


24-7992 


561 


1-78253 


31472I 


I76558481 


23.6854 


616 


1.62338 


379456 


233744896 


24.8193 


562 


1.77936 


315844 


177504328 


23.7065 


617 


1.62075 


380689 


234885113 


24.8395 


563 


1.77620 


316969 


178453547 


23.7276 


618 


I.6I8I2 


381924 


236029032 


24.8596 


564 


177305 


318096 


179406144 


23-7487 


619 


I.6I55I 


383161 


237176659 


24.8797 


565 


1. 76991 


319225 


1 80362 1 25 


23.7697 


620 


1. 61 290 


384400 


238328000 


24.8998 


566 


1.76678 


320356 


181321496 


23.7908 


621 


I.6I03I 


385641 


239483061 


24.9199 


567 


1.76367 


321489 


182284263 


23.8118 


622 


1.60772 


386884 


240641848 


24-9399 


568 


1.76056 


322624 


183250432 


23-8328 


623 


1. 60514 


388129 


241804367 


24.9600 


569 


175747 


323761 


1S422OOO9 


23-8537 


624 


1.60256 


389376 


242970624 


24.9800 


570 


175439 


324900 


I 85 I 93000 


23.8747 


625 


1 .60000 


390625 


244140625 


25.0000 


571 


I75I3I 


326041 


1861694II 


23.8956 


626 


1-59744 


391876 


245314376 


25.0200 


572 


174825 


327184 


187 149248 


23.9165 


627 


1.59490 


393129 


246491883 


25.0400 


573 


1.74520 


328329 


I88132517 


23-9374 


628 


1.59236 


394384 


247673152 


25.0599 


574 


I.742I6 


329476 


189119224 


23-9583 


629 


1.58983 


395641 


24S858189 


25.0799 


575 


I739I3 


330625 


I9OIO9375 


23.9792 


630 


1-58730 


396900 


250047000 


25.0998 


576 


I.736II 


331776 


191 102976 


24.0000 


^J' 


1.58479 


398161 


25123959I 


25-1197 


577 


I733IO 


332929 


I 92 I 00033 


24.0208 


632 


1.58228 


399424 


252435968 


25.1396 


573 


I.730IO 


3340S4 


I93IOO552 


24.0416 


633 


1-57978 


400689 


253636137 


25-1595 


579 


I.727I2 


335241 


I 94 I 04539 


24.0624 


634 


1-57729 


401956 


254S4OIO4 


25-1794 


580 


I.724I4 


336400 


1 95 1 12000 


24.0832 


635 


1.57480 


403225 


256047875 


25.1992 


^l' 


I.72II7 


337561 


196122941 


24.1039 


636 


1-57233 


404496 


257259456 


25.2190 


5S2 


I.7IS2I 


338724 


197 1 37368 


24.1247 


637 


1.56986 


405769 


258474853 


25.2389 


5^^ 


I.7I527 


339889 


198155287 


24.1454 


638 


1.56740 


407044 


259694072 


25-2587 


584 


I7I233 


341056 


199176704 


24.1661 


639 


1.56495 


408321 


260917 1 19 


25.2784 


585 


1.70940 


342225 


200201625 


24.1868 


640 


1.56250 


409600 


262144000 


25.2982 


586 


1.70648 


343396 


201230056 


24.2074 


641 


1.56006 


410881 


263374721 


25.3180 


5S7 


1.70358 


344569 


202262003 


24.2281 


642 


1-55763 


4I2164 


2646092SS 


25-3377 


588 


1.70068 


345744 


203297472 


24.2487 


643 


1-55521 


413449 


265847707 


25-3574 


589 


1.69779 


346921 


204336469 


24.2693 


644 


1.55280 


414736 


267089984 


25-3772 


590 


1.69492 


348100 


205379000 


24.2899 


645 


1-55039 


416025 


268336125 


253969 


591 


1.69205 


349281 


206425071 


24.3105 


646 


1-54799 


417316 


2695S6136 


25.4165 


592 


1. 68919 


350464 


207474688 


24-3311 


647 


1.54560 


418609 


270840023 


25.4362 


593 


1.68634 


351649 


208527857 


24.3516 


648 


1-54321 


419904 


272097792 


25-4558 


594 


1.68350 


352836 


209584584 


24.3721 


649 


1.54083 


42I2OI 


273359449 


25-4755 


595 


1.68067 


354025 


210644875 


24.3926 


650 


1.53846 


422500 


274625000 


25-495' 


596 


1.67785 


355216 


21 1708736 


24.4131 


651 


1.53610 


423801 


275S9445I 


25-5147 


597 


1.67504 


356409 


212776173 


24-4336 


652 


1-53374 


425104 


277167808 


25-5343 


i98 


1.67224 


357604 


213847192 


24.4540 


653 


1-53139 


426409 


278445077 


25-5539 


599 


1.66945 


358801 


214921799 


24-4745 


654 


1.52905 


427716 


279726264 


25-5734 


600 


1.66667 


360000 


216000000 


24.4949 


655 


1.52672 


429025 


281OII375 


25-5930 


601 


1.66389 


361 201 


217081801 


24-5153 


656 


1-52439 


430336 


282300416 


25.6125 


602 


I.66II3 


362404 


21816720S 


24-5357 


657 


1.52207 


431649 


283593393 


25.6320 


603 


1.65837 


363609 


219256227 


24.5561 


658 


1. 51976 


432964 


284890312 


25-6515 


604 


1-65563 


364816 


220348864 


24.5764 


659 


1-51745 


4342S1 


28619II79 


25.6710 


605 


1.65289 


366025 


221445125 


24.5967 


660 


1-51515 


435600 


287496000 


25.6905 


606 


1-65017 


367236 


222545016 


24.6171 


661 


1. 51286 


436921 


288804781 


25-7099 


607 


1.64745 


368449 


223648543 


24-6374 


662 


1-51057 


438244 


29OII7528 


25.7294 


608 


1.64474 


369664 


224755712 


24-6577 


663 


1.50S30 


439569 


291434247 


25.7488 


609 


1 .64204 


370881 


225866529 


24.6779 


664 


1.50602 


440896 


292754944 


25.7682 


610 


1-63934 


372100 


226981000 


24.6982 


665 


1.50376 


442225 


294079625 


25.7876 


611 


1.63666 


373321 


2280991 31 


24.7184 


666 


1. 50150 


443556 


295408296 


25.8070 


612 


1-63399 


374544 


229220928 


24.7386 


667 


1.49925 


444889 


296740963 


25.8263 


6t3 


I.63I32 


375769 


230346397 


24.7588 


668 


1.49701 


446224 


298077632 


25.8457 


614 


1.62866 


376996 


231475544 


24.7790 


669 


1-49477 


447561 


299418309 


25.S650 



Smithsonian Tables. 



Table 8 {continued). 2 I 

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 
OF NATURAL NUMBERS. 



n 
670 


lOOO.i 


«2 


,fi 


v« 


n 
725 


1 000.1 


«2 


»8 


v« 


1.49254 


448900 


300763000 


25.8844 


1-37931 


525625 


381078125 


26.9258 


671 


1.4903 1 


450241 


3021 11711 


259037 


726 


1-37741 


527076 


382657176 


26.9444 


672 


1. 488 10 


451584 


303464448 


25.9230 


727 


1-37552 


528529 


384240583 


26.9629 


<^VZ 


1.48588 


452929 


304821217 


25.9422 


728 


1-37363 


529984 


385828352 


26.9815 


674 


1.48368 


454276 


306182024 


25.9615 


729 


1-37174 


531441 


387420489 


27.0000 


675 


r. 48 1 48 


455625 


307546875 


25.9808 


730 


1.36986 


532900 


389017000 


27.0185 


676 


1.47929 


456976 


308915776 


26.0000 


73' 


1.36799 


534361 


390617891 


27.0370 


677 


1.47710 


458329 


310288733 


26.0192 


732 


1.36612 


535824 


392223168 


27-0555 


678 


1-47493 


459684 


31 1665752 


26.0384 


7io 


1.36426 


537289 


393832837 


27.0740 


679 


147275 


461 04 1 


313046839 


26.0576 


734 


1.36240 


538756 


395446904 


27.0924 


680 


1.47059 


462400 


314432000 


26.0768 


735 


1.36054 


540225 


397065375 


27.X109 


68 r 


1.46843 


463761 


315821241 


26.0960 


736 


1.35870 


541696 


398688256 


27.1293 


682 


1.46628 


465124 


317214568 


26.11 5 1 


737 


1-35685 


543169 


400315553 


27.1477 


683 


1.46413 


466489 


318611987 


26.1343 


738 


1-35501 


544644 


401947272 


27.1662 


684 


1.46199 


467856 


320013504 


26.1534 


739 


1-35318 


5461 2 I 


403583419 


27.1846 


685 


I -4595 5 


469225 


321419125 


26.1725 


740 


1-35135 


547600 


405224000 


27.2029 


686 


1-45773 


470596 


322828856 


26.1916 


741 


1-34953 


549081 


406S6902 I 


27.2213 


687 


1.45560 


471969 


324242703 


26.2107 


742 


I -3477 1 


550564 


408518488 


27.2397 


688 


1-45349 


473344 


325660672 


26.2298 


743 


1.34590 


552049 


4IOI72407 


27.2580 


6S9 


i-45'3S 


474721 


3270S2769 


26.2488 


744 


1.34409 


553536 


41 1830784 


27.2764 


690 


1.4492S 


476100 


328509000 


26.2679 


745 


1.34228 


555025 


413493625 


27-2947 


691 


1.447 1 8 


477481 


329939371 


26.2S69 i 


! 746 


1.34048 


556516 


415160936 


27.3130 


692 


1.44509 


47S864 


331373888 


26.3059 


747 


1.33869 


55S009 


416S32723 


^7-0^3 


693 


1.44300 


480249 


332812557 


26.3249 


748 


1.33690 


559504 


418508992 


27.3496 


694 


1.44092 


48 1 636 


334255384 


26.3439 


749 


1-33511 


56100 1 


420189749 


27-3679 


695 


1-43885 


483025 


335702375 


26.3629 


750 


1-33333 


562500 


421875000 


27.3861 


696 


1.43678 


4S4416 


337153536 


26.3818 


751 


1-33156 


564001 


423564751 


27.4044 


697 


1-43472 


485S09 


338608873 


26.4008 


752 


1.32979 


565504 


425259008 


27.4226 


698 


1.43266 


4S7204 


340368392 


26.4197 


753 


1.32802 


567009 


426957777 


27.4408 


699 


1.43062 


488601 


341532099 


26.4386 


754 


1.32626 


568516 


428661064 


27.4591 


700 


1.42S57 


490000 


343000000 


26.4575 


755 


1.32450 


570025 


430368S75 


27-4773 


701 


1.42653 


491401 


344472 10 1 


26.4764 


756 


1-32275 


571536 


432081216 


27-4955 


702 


1.42450 


492804 


345948408 


26.4953 


1 757 


1.32100 


573049 


433798093 


27.5136 


703 


1.42248 


494209 


347428927 


26.5141 


758 


1.31926 


574564 


435519512 


27-53'8 


704 


1.4204s 


495616 


348913664 


26.5330 


759 


1-31752 


576081 


437245479 


27.5500 


705 


1.41844 


497025 


350402625 


26.5518 


760 


1-31579 


577600 


438976000 


27.5681 


706 


1. 41 643 


498436 


351895816 


26.5707 


761 


1. 3 1406 


5791 2 I 


44071 1 08 1 


27.^^862 


707 


1. 4 1 443 


499849 


353393243 


26.5895 


762 


I -3 1 234 


5S0644 


442450728 


27.6043 


708 


1.41243 


501264 


354894912 


26.6083 


763 


1.31062 


582169 


444194947 


27.6225 


709 


1. 41 044 


502681 


356400829 


26.6271 


764 


1.30890 


583696 


445943744 


27.6405 


710 


1.40845 


504100 


35791 1000 


26.6458 


765 


1.307 19 


585225 


447697125 


27.6586 


711 


1.40647 


505521 


359425431 


26.6646 


766 


1.30548 


586756 


449455096 


27.6767 


712 


1.40449 


506944 


360944128 


26.6833 


767 


1-30378 


588289 


451217663 


27.694S 


7^2, 


1.40252 


508369 


362467097 


26.7021 


768 


1.30208 


589824 


4529S4S32 


27.7128 


714 


1.40056 


509796 


363994344 


26.7208 


769 


1.30039 


591361 


454756609 


27.7308 


715 


1.39860 


511225 


365525875 


26.7395 


770 


1.29870 


592900 


456533000 


27.7489 


716 


1.39665 


512656 


367061696 


26.7582 


771 


1.29702 


594441 


45831401 1 


27.7669 


717 


1.39470 


514089 


368601813 


26.7769 


772 


1-29534 


595984 


460099648 


27-7849 


718 


1.39276 


515524 


370146232 


26.7955 


m 


1.29366 


597529 


461S89917 


27.8029 


719 


1.39082 


516961 


371694959 


26.8142 


774 


1.29199 


599076 


4636S4824 


27.8209 


720 


1.3S889 


518400 


373248000 


26.8328 


775 


1.29032 


600625 


465484375 


27.8388 


721 


1.3S696 


519841 


374805361 


26.8514 


776 


1.28866 


602176 


46728S576 


27.8568 


722 


1.38504 


521284 


376367048 


26.8701 


777 


1.28700 


603729 


469097433 


27.8747 


723 


1-38313 


522729 


377933067 


26.8887 


77S 


1-28535 


605284 


470910952 


27.8927 


724 


1.38122 


524176 


379503424 


26.9072 


779 


1.28370 


606S4I 


472729139 


27.9106 



Smithsonian Tables. 



2 2 Table 8 (conHnued). 

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 
OF NATURAL NUMBERS. 



n 
780 


1 000. 1 


«2 


«3 


v« 


n 
835 


1000.^ 


«2 


«3 


n/« 


1.28205 


608400 


474552000 


27.9285 


1. 19760 


697225 


582182875 


28.8964 


7S1 


1. 2804 1 


609961 


476379541 


27.9464 


836 


1.19617 


69S896 


5S4277056 


28.9137 


782 


1.27877 


611524 


478211768 


27-9643 


837 


I -19474 


700569 


586376253 


2S.93IO 


7S3 


1.27714 


613089 


4800486S7 


27.9821 


83S 


1-19332 


702244 


5S84S0472 


28.9482 


784 


1.27551 


614656 


481890304 


28.0000 


839 


1.19190 


703921 


590589719 


28.9655 


785 


1.27389 


616225 


483736625 


28.0179 


840 


1. 1 9048 


705600 


592704000 


28.9828 


786 


1.27226 


617796 


485587656 


28.0357 


841 


1. 1 8906 


7072S1 


594S2332I 


29.0000 


787 


1.27065 


619369 


487443403 


28.0535 


842 


1.18765 


708964 


5969476S8 


29.0172 


78S 


1.26904 


620944 


489303S72 


28.0713 


843 


1. 18624 


710649 


599077107 


29.0345 


789 


1.26743 


622521 


491 169069 


28.0891 


844 


1. 1 8483 


712336 


601 2 II 584 


29.0517 


790 


1.26582 


624100 


493039000 


28.1069 


845 


I -18343 


714025 


603351125 


29.0689 


791 


1.26422 


625681 


4949 1 367 1 


28.1247 


S46 


1. 1 8203 


715716 


605495736 


29.0861 


79- 


1.26263 


627264 


496793088 


28.1425 i 


847 


1 . 1 8064 


717409 


607645423 


29.1033 


793 


1.26103 


628849 


498677257 


28.1603 


848 


1. 17925 


719104 


609S0OI92 


29.1204 


794 


1-25943 


630436 


500566184 


28.1780 


849 


1. 17786 


720801 


611960049 


29.1376 


795 


1.25786 


632025 


502459875 


28.1957 


850 


1-17647 


722500 


614I25OOO 


29.1548 


796 


1.25628 


633616 


504358336 


28.2135 


851 


1. 17509 


724201 


61629505I 


29.1719 


797 


1-25471 


635209 


506261573 


28.2312 


852 


I-17371 


725904 


61847020S 


29.1890 


798 


1-25313 


636S04 


508169592 


28.2489 


853 


1-17233 


727609 


620650477 


29.2062 


799 


1.25156 


638401 


510082399 


28.2666 


854 


1. 1 7096 


729316 


62283 5S64 


29.2233 


800 


1.25000 


640000 


512000000 


28.2843 


855 


1. 16959 


731025 


625026375 


29.2404 


801 


1.24844 


64160I 


5 1 392 240 1 


28.3019 


856 


1. 1 6822 


732736 


627222016 


29-2575 


802 


1.24688 


643204 


51584960S 


28.3196 


857 


1. 1 6686 


734449 


629422793 


29.2746 


803 


1-24533 


644S09 


517781627 


28.3373 


858 


1. 16550 


736164 


63162S7I2 


29.2916 


804 


1.24378 


646416 


5 1 97 1 8464 


28.3549 


859 


1.16414 


737881 


633S39779 


29-3087 


805 


1.24224 


648025 


521660125 


28.3725 


860 


1. 16279 


739600 


636056000 


29.3258 


806 


1.24069 


649636 


523606616 


28.3901 


861 


1.16144 


741321 


63S277381 


29.3428 


807 


1. 239 1 6 


651249 


525557943 


28.4077 


1 862 


1.16009 


743044 


640503928 


29.3598 


808 


1.23762 


652864 


527514112 


28.4253 


863 


1.15875 


744769 


642735647 


29.3769 


809 


1.23609 


654481 


529475129 


28.4429 


864 


1-15741 


746496 


644972544 


29-3939 


810 


1-23457 


656100 


531441000 


28.4605 


865 


1. 1 5607 


748225 


647214625 


29.4109 


8ri 


1-23305 


657721 


53341 1731 


28.4781 


866 


1-15473 


749956 


649461896 


29.4279 


812 


'•23153 


659344 


53538732S 


28.4956 


867 


1-15340 


751689 


651714363 


29.4449 


813 


1. 23001 


660969 


537367797 


28.5132 


868 


1.15207 


753424 


653972032 


29.4618 


814 


1.22850 


662596 


539353144 


28.5307 


869 


1-15075 


755161 


656234909 


29.47S8 


815 


1.22699 


664225 


541343375 


28.5482 


870 


1.14943 


756900 


658503000 


29.4958 


816 


1.22549 


665856 


543338496 


28.5657 


871 


1.14S11 


758641 


66077631 I 


295127 


817 


1.22399 


667489 


545338513 


28.5832 


S72 


1. 1 4679 


760384 


663054S4S 


29.5296 


81S 


1.22249 


669124 


547343432 


28.6007 


873 


1. 14548 


762129 


665338617 


29.5466 


819 


1. 22100 


670761 


549353259 


28.6182 


874 


1.14416 


763876 


667627624 


29-5635 


820 


1.21951 


672400 


551368000 


28.6356 


875 


1. 14286 


765625 


669921875 


29.5804 


821 


1. 21803 


674041 


553387661 


28.6531 


876 


1-14155 


767376 


672221376 


295973 


822 


1.21655 


675684 


555412248 


28.6705 


i 877 


1. 14025 


769129 


674526133 


29.6142 


823 


1.2 1 507 


677329 


557441767 


28.6S80 


878 


1-13S95 


770884 


676836152 


29.6311 


824 


1-21359 


678976 


559476224 


28.7054 


879 


1. 13766 


772641 


679151439 


29.6479 


825 


1.21212 


680625 


561515625 


28.7228 


880 


1.13636 


774400 


681472000 


29.6648 


826 


1.21065 


6S2276 


563559976 


28.7402 


881 


1-13507 


776161 


683797841 


29.6816 


827 


1.20919 


683929 


565609283 


28.7576 1 


882 


1-13379 


777924 


68612S968 


29.6985 


828 


1.20773 


685584 


567663552 


28.7750 


883 


1.13250 


779689 


688465387 


29-7153 


829 


1.20627 


687241 


569722789 


28.7924 


884 


1.13122 


781456 


690807104 


29.7321 


830 


1.20482 


688900 


571787000 


28.8097 


885 


I.I 2994 


783225 


693154125 


29.7489 


831 


1,20337 


690561 


573856191 


28.8271 


886 


1. 1 2867 


784996 


695506456 


29.7658 


832 


1. 20192 


692224 


57593036S 


28.8444 


8S7 


1.12740 


7S6769 


697864103 


29.7825 


833 


1 .20048 


693889 


578009537 


28.8617 


888 


1.12613 


788544 


700227072 


29-7993 


834 


1. 19904 


695556 


5S0093704 


28.8791 


889 


1.12486 


790321 


702595369 


29.8161 



Smithsonian Tables. 



TABLE 8 (continued). 2 3 

VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS 
OF NATURAL NUMBERS. 



n 


1 000. 1 


«- 


«3 


v« 


« 


lOOO.^ 


«2 


«3 


V« 


890 


I.I 2360 


792100 


704969000 


29.8329 


945 


1.05820 


893025 


84390S625 


30-7409 


891 


1. 12233 


793881 


707347971 


29.8496 


946 


1.05708 


894916 


846590536 


30-7571 


S92 


1.12108 


795664 


709732288 


29.8664 


947 


1-05597 


896809 


849278123 


30-7734 


^^93 


I.I 1982 


797449 


712121957 


29.8831 


948 


1.05485 


898704 


85 1 97 1 392 


30.7896 


894 


1. 11857 


799236 


7 1 45 1 6984 


29.8998 


949 


1-05374 


900601 


854670349 


30.8058 


895 


1.11732 


801025 


71691737s 


29.9166 


950 


1.05263 


902500 


857375000 


30.8221 


896 


I.I 1607 


802S16 


719323136 


29-9333 


951 


I.05I52 


904401 


860085351 


30.8383 


897 


I.I 1483 


804609 


721734273 


29.9500 


952 


1.05042 


906304 


862801408 


3O-S545 


898 


i-"359 


806404 


724150792 


29.9666 


953 


1.04932 


908209 


865523177 


30.8707 


S99 


I-II23S 


808201 


726572699 


29-9833 


954 


1.04822 


910116 


868250664 


30.8869 


900 


I. mil 


810000 


729000000 


30.0000 


955 


1.047 1 2 


912025 


870983875 


30.9031 


901 


1. 10988 


811801 


731432701 


30.0167 


956 


1 .04603 


913936 


873722816 


30.9192 


902 


1. 1 0865 


813604 


733870808 


30-0333 


957 


1.04493 


915849 


876467493 


30-9354 


903 


I. 10742 


8 1 5409 


7363M327 


30.0500 


958 


1.04384 


917764 


8792179I2 


30-9516 


904 


1.10619 


817216 


738763264 


30.0666 


959 


1.04275 


9I9681 


881974079 


30.9677 


905 


1. 10497 


819025 


741217625 


30.0832 


960 


1. 04 1 67 


921600 


884736000 


30.9839 


906 


1-10375 


820836 


743677416 


30.0998 


961 


1 .04058 


923521 


887503681 


31.0000 


907 


1. 10254 


822649 


746142643 


30.1164 


962 


1.03950 


925444 


890277128 


31.0161 


908 


1.10132 


824464 


74861 331 2 


30-1330 


963 


1.03842 


927369 


893056347 


31.0322 


909 


I.IOOII 


826281 


751089429 


30.1496 


964 


1-03734 


929296 


895841344 


31.0483 


910 


1.09890 


828100 


753571000 


30.1662 


965 


1.03627 


931225 


898632125 


31.0644 


911 


1.09769 


829921 


75605S031 


30.1828 


966 


1.03520 


933156 


901428696 


31.0805 


912 


1.09649 ' 831744 ! 758550528 


30-1993 


.997 


I -034 1 3 


935089 


904231063 


31.0966 


913 


1.09529 1 833569 


76104S497 


30.2159 


968 


1.03306 


937024 


907039232 


31-1127 


914 


1.09409 


S35396 


763551944 


30.2324 


969 


1. 03 1 99 


938961 


909853209 


31.1288 


915 


1 .09290 


837225 


766060875 


30.2490 


970 


1.03093 


940900 


912673000 


31.1448 


916 


1. 091 70 


839056 


768575296 


30.2655 


971 


1.02987 


942841 


91 549861 I 


31.1609 


9'7 


1. 0905 1 


840889 


771095213 


30.2820 


972 


1. 0288 1 


944784 


918330048 


31.1769 


91S 


1.08932 


842724 


773620632 


30.2985 


973 


1.02775 


946729 


92II673I7 


31.1929 


919 


1. 088 1 4 


844561 


776151559 


30.3150 


974 


1.02669 


948676 


924010424 


31.2090 


920 


1.08696 


S46400 


77868S000 


30-3315 


975 


1.02564 


950625 


92685937s 


31.2250 


921 


1.08578 


S48241 


781 229961 


30-3480 


976 


1.02459 


952576 


9297I4176 


31.2410 


922 


1 .08460 


850084 


7S3777448 


30-3645 


977 


1-0-354 


954529 


932574S33 


3'.2570 


9-3 


1.08342 


851929 


786330467 


30.3809 


978 


1.02249 


956484 


935441352 


31.2730 


924 


1.08225 


853776 


7S8889024 


30-3974 


979 


1. 02 145 


958441 


938313739 


31.2S90 


925 


1. 08 1 08 


855625 


791453125 


30.4138 


980 


1. 02041 


960400 


941 192000 


31.3050 


926 


1. 0799 1 


857476 


794022776 


30-4302 


981 


1. 01 937 


962361 


944O7614I 


31.3209 


927 


1.07875 


8593-9 


796597983 


30.4467 


982 


1.01833 


964324 


946966168 


31-3369 


928 


1.07759 


861 1S4 


799178752 


30.4631 


983 


1.01729 


966289 


949862087 


31-352S 


929 


1.07643 


863041 


801765089 


30-4795 


984 


1.01626 


968256 


952763904 


31-3688 


930 


1.07527 


864900 


804357000 


30.4959 


985 


1.01523 


970225 


955671625 


31-3847 


931 


1. 074 1 1 


S66761 


806954491 


30.5123 


986 


1. 01420 


972196 


95S585256 


3 1 .4006 


932 


1.07296 


S68624 


809557568 


30.5287 


987 


1-01317 


974169 


961 504803 


31.4166 


933 


1.07181 


870489 


81 2 166237 


30.5450 


988 


1.01215 


976144 


964430272 


31-4325 


934 


1.07066 


872356 


814780504 


30.5614 


989 


1.01112 


97812I 


967361669 


31.4484 


935 


1.06952 


874225 


817400375 


30.5778 


990 


I.OIOIO 


980100 


970299000 


31.4643 


936 


1.06838 


876096 


820025856 


30.5941 


991 


1.00908 


98 208 1 


973242271 


31.4S02 


937 


1.06724 


877969 


822656953 


30.6105 


992 


1 .00806 


984064 


97619I488 


31.4960 


938 


1. 066 10 


879844 


825293672 


30.6268 


993 


1.00705 


986049 


979146657 


31.5119 


939 


1.06496 


881721 


827936019 


30.6431 


994 


1 .00604 


988036 


982107784 


31.5278 


940 


1.06383 


883600 


830584000 


30.6594 


995 


1.00503 


990025 


985074875 


31-5436 


941 


1.06270 


885481 


833237621 


30.6757 


996 


1 .00402 


992016 


988047936 


31.5595 


942 


1. 061 57 


887364 


835896888 


30.6920 


997 


1. 0030 1 


994009 


991026973 


31-5753 


943 


1.06045 


889249 


838561807 


30.7083 


998 


1.00200 


996004 


99401 1992 


31-5911 


944 


1.05932 


891 136 


841232384 


30-7246 


999 


1. 00 1 00 


99SOOI 


997002999 


31.6070 



Smithsonian Tables. 



24 



Table 9. 
LOGARITHMS. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


100 


0000 


0004 


0009 


0013 


0017 


0022 


0026 


0030 


<^ZS 


0039 


0043 


lOI 


0043 


004S 


0052 


0056 


0060 


0065 


0069 


0073 


0077 


0082 


0086 


I02 


0086 


0090 


0095 


0099 


0103 


0107 


OIII 


01 16 


0120 


0124 


0128 


103 


0128 


0133 


0137 


0141 


0145 


0149 


0154 


0158 


0162 


0166 


0170 


104 


0170 


0175 


0179 


0183 


0187 


0191 


0195 


0199 


0204 


0208 


0212 


105 


0212 


0216 


0220 


0224 


0228 


0233 


0237 


0241 


0245 


0249 


0253 


106 


0253 


0257 


0261 


0265 


0269 


0273 


0278 


0282 


0286 


0290 


0294 


107 


0294 


0298 


0302 


0306 


0310 


0314 


0318 


0322 


0326 


0330 


0334 


108 


0334 


0338 


0342 


0346 


0350 


0354 


0358 


0362 


0366 


037.0 


0374 


109 


0374 


0378 


0382 


03S6 


0390 


0394 


0398 


0402 


0406 


0410 


0414 


110 


0414 


0418 


0422 


0426 


0430 


0434 


0438 


0441 


0445 


0449 


0453 


III 


0453 


0457 


0461 


0465 


0469 


0473 


0477 


0481 


0484 


0488 


0492 


112 


0492 


0496 


0500 


0504 


0508 


0512 


0515 


0519 


0523 


0527 


0531 


113 


0531 


0535 


0538 


0542 


0546 


0550 


0554 


0558 


0561 


0565 


0569 


114 


0569 


0573 


0577 


0580 


0584 


0588 


0592 


0596 


0599 


0603 


0607 


115 


0607 


061 1 


0615 


0618 


0622 


0626 


0630 


0633 


0637 


0641 


0645 


116 


0645 


0648 


0652 


0656 


0660 


0663 


0667 


0671 


0674 


0678 


0682 


H7 


0682 


0686 


0689 


0693 


0697 


0700 


0704 


0708 


07 1 1 


0715 


0719 


n8 


0719 


0722 


0726 


0730 


0734 


0737 


0741 


0745 


0748 


0752 


0755 


119 


07 55 


0759 


0763 


0766 


0770 


0774 


0777 


0781 


0785 


0788 


0792 


120 


0792 


0795 


0799 


0803 


0806 


0810 


0813 


0817 


0821 


0824 


0828 


121 


08 28 


0S31 


0S35 


0839 


0842 


0846 


0849 


0853 


0856 


0S60 


0864 


122 


0864 


0867 


0871 


0874 


0878 


0881 


0885 


08S8 


0892 


0S96 


0S99 


123 


0899 


0903 


0906 


0910 


0913 


0917 


0920 


0924 


0927 


0931 


0934 


124 


0934 


0938 


0941 


0945 


0948 


0952 


0955 


0959 


0962 


0966 


0969 


125 


0969 


0973 


0976 


0980 


09S3 


0986 


0990 


0993 


0997 


1000 


1004 


126 


1004 


1007 


lOII 


1014 


1017 


1021 


1024 


1028 


1031 


1035 


1038 


127 


1038 


1041 


1045 


1048 


1052 


1055 


1059 


1062 


1065 


1069 


1072 


128 


1072 


1075 


1079 


10S2 


1086 


1089 


1092 


1096 


1099 


1103 


1 106 


129 


1 106 


1 109 


1113 


1116 


1119 


1123 


1 1 26 


1129 


^^32> 


1 136 


"39 


130 


"39 


"43 


1 146 


"49 


"53 


1156 


"59 


1 163 


1 166 


1 169 


"73 


131 


"73 


1 176 


"79 


1 183 


1 186 


1 189 


"93 


1 196 


"99 


1202 


1206 


132 


1206 


1209 


1212 


1216 


1219 


1222 


1225 


1229 


1232 


'^^5 


1239 


133 


1239 


1242 


1245 


1248 


1252 


1255 


1258 


1 261 


1265 


1268 


1271 


134 


1 27 1 


1-74 


1278 


12S1 


12S4 


1287 


1290 


1294 


1297 


1300 


1303 


135 


1303 


1307 


1310 


1313 


1316 


1319 


1323 


1326 


1329 


1332 


1335 


136 


1335 


1339 


1342 


1345 


134S 


1 35 1 


'355 


1358 


1361 


1364 


1367 


^2,7 


1367 


1370 


1374 


1377 


1380 


1383 


1386 


13S9 


1392 


1396 


1399 


138 


1399 


1402 


1405 


1408 


1411 


1414 


1418 


1421 


1424 


1427 


1430 


139 


1430 


1433 


1436 


1440 


1443 


1446 


1449 


1452 


1455 


1458 


1461 


140 


1461 


1464 


1467 


1 47 1 


1474 


1477 


1480 


14S3 


i486 


1489 


1492 


141 


1492 


1495 


1498 


1 501 


1504 


1508 


1511 


1514 


1517 


1520 


1523 


142 


1523 


1526 


1529 


1532 


1535 


1538 


1 541 


1544 


1547 


1550 


1553 


U3 


1553 


1556 


1559 


1562 


1565 


1569 


1572 


1575 


1578 


1581 


1584 


144 


1584 


1587 


1590 


1593 


1596 


1599 


1602 


1605 


1608 


1611 


1614 


145 


1614 


1617 


1620 


1623 


1626 


1629 


1632 


1635 


1638 


1 641 


1644 


146 


1644 


1647 


1649 


1652 


1655 


1658 


i66i 


1664 


1667 


1670 


1673 


147 


1673 


1676 


1679 


1682 


1685 


1688 


1691 


1694 


1697 


1700 


1703 


148 


1703 


1706 


1708 


1711 


1714 


1717 


1720 


1723 


1726 


1729 


1732 


149 


1732 


1735 


1738 


1741 


1744 


1746 


1749 


1752 


1755 


1758 


1761 



Smithsonian Tables. 



Table 9 (continued). 

LOGARITHMS. 



25 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


150 


1761 


1764 


1767 


1770 


1772 


I77S 


1778 


1781 


1784 


1787 


1790 


151 


1790 


•793 


1796 


1798 


1801 


1804 


1807 


1810 


1813 


1816 


1818 


152 


181S 


1821 


1824 


1827 


1830 


1833 


1836 


1838 


1841 


1844 


1847 


153 


1847 


1850 


18S3 
1881 


1855 


1858 


1861 


1864 


1867 


1870 


1872 


1875 


154 


1875 


1878 


1884 


1886 


1889 


1892 


1895 


1898 


1901 


1903 


155 


1903 


1906 


1909 


1912 


1915 


1917 


1920 


1923 


1926 


1928 


1931 


156 


'93' 


1934 


1937 


1940 


1942 


1945 


1948 


1951 


1953 


1956 


1959 


157 


1959 


1962 


1965 


1967 


1970 


'973 


1976 


197S 


1981 


1984 


1987 


158 


19S7 


19S9 


1992 


1995 


1998 


2000 


2003 


2006 


2009 


201 1 


2014 


159 


2014 


2017 


2019 


2022 


2025 


2028 


2030 


2033 


2036 


2038 


2041 


160 


2041 


2044 


2047 


2049 


2052 


2055 


2057 


2060 


2063 


2066 


2068 


161 


206S 


2071 


2074 


2076 


2079 


2082 


2084 


2087 


2090 


2092 


2095 


162 


2095 


2098 


2101 


2103 


2106 


2109 


2111 


2114 


2117 


2119 


2122 


163 


2122 


2125 


2127 


2130 


2133 


2135 


2138 


2140 


2143 


2146 


2148 


164 


2148 


2151 


2154 


2156 


2159 


2162 


2164 


2167 


2170 


2172 


2175 


165 


2175 


2177 


2180 


2183 


2185 


2188 


2191 


2193 


2196 


2198 


2201 


166 


2201 


2204 


2206 


2209 


2212 


2214 


2217 


2219 


2222 


2225 


2227 


167 


2227 


2230 


2232 


2235 


2238 


2240 


2243 


2245 


2248 


2251 


2253 


168 


2253 


2256 


225S 


2261 


2263 


2266 


2269 


2271 


2274 


2276 


2279 


169 


2279 


2281 


2284 


2287 


2289 


2292 


2294 


2297 


2299 


2302 


2304 


170 


2304 


2307 


2310 


2312 


2315 


2317 


2320 


2322 


2325 


2327 


2330 


171 


2330 


2333 


2335 


2338 


2340 


2343 


2345 


2348 


2350 


2353 


2355 


172 


2355 


2358 


2360 


2363 


2365 


2368 


2370 


2373 


2375 


2378 


2380 


^13 


23S0 


2383 


2385 


2388 


2390 


2393 


2395 


2398 


2400 


2403 


2405 


174 


2405 


2408 


2410 


2413 


2415 


2418 


2420 


2423 


2425 


2428 


2430 


175 


2430 


2433 


2435 


2438 


2440 


2443 


2445 


2448 


2450 


2453 


2455 


176 


2455 


2458 


2460 


2463 


2465 


2467 


2470 


2472 


2475 


2477 


2480 


177 


2480 


2482 


2485 


2487 


2490 


2492 


2494 


2497 


2499 


2502 


2504 


178 


2504 


2507 


2509 


2512 


2514 


2516 


2519 


2521 


2524 


2526 


2529 


179 


2529 


2531 


2533 


2536 


2538 


2541 


2543 


2545 


2548 


2550 


2553 


180 


2553 


2555 


2558 


2560 


2562 


2565 


2567 


2570 


2572 


2574 


2577 


181 


2577 


2579 


2582 


2584 


2586 


2589 


2591 


2594 


2596 


2598 


2601 


182 


2601 


2603 


2605 


2608 


2610 


2613 


2615 


2617 


2620 


2622 


^^'^ 


1S3 


262^ 
264S 


2627 


2629 


2632 


2634 


2636 


2639 


2641 


2643 


2646 


2648 


1S4 


2651 


2653 


265s 


2658 


2660 


2662 


2665 


2667 


2669 


2672 


185 


2672 


2674 


2676 


2679 


2681 


2683 


2686 


2688 


2690 


2693 


2695 


1S6 


2695 


2697 


2700 


2702 


2704 


2707 


2709 


2711 


2714 


2716 


2718 


187 


2718 


2721 


2723 


2725 


2728 


2730 


2732 


2735 


2737 


2739 


2742 


188 


2742 


2744 


2746 


2749 


2751 


2753 


2755 


2758 


2760 


2762 


2765 


189 


2765 


2767 


2769 


2772 


2774 


2776 


2778 


2781 


2783 


2785 


2788 


190 


2788 


2790 


2792 


2794 


2797 


2799 


2801 


2804 


2806 


2808 


2810 


191 


2810 


2813 


2815 


2817 


2819 


2822 


2824 


2826 


2828 


2S31 


^0^^ 


192 


2833 


2835 


2838 


2840 


2842 


2844 


2847 


2849 


2851 


'l^l 


2856 


193 


2S56 


2858 


2860 


2S62 


2865 


2867 


2869 


2871 


2874 


2876 


2878 


194 


2878 


2880 


2S82 


28S5 


2887 


2889 


2891 


2S94 


2896 


2898 


2900 


195 


2900 


2903 


2905 


2907 


2909 


291 1 


2914 


2916 


2918 


2920 


2923 


196 


2923 


2925 


2927 


2929 


2931 


2934 


2936 


2938 


2940 


2942 


2945 


197 


2945 


2947 


2949 


2951 


2953 


2956 


2958 


2960 


2962 


2964 


2967 


198 


2967 


2969 


2971 


2973 


2975 


2978 


2980 


2982 


2984 


2986 


2989 


199 


2989 


2991 


2993 


2995 


2997 


2999 


3002 


3004 


3006 


3008 


3010 



Smithsonian Tables. 



26 



Table 10. 
LOGARITHMS. 



N 





1 


2 


3 


4 


5 


6 


7 


8 


9 


P.P. 1 


1 


2 


3 


4 

17 
15 
14 
13 
12 


5 

21 
19 
17 
16 

15 


10 

II 

12 

14 


0000 
0414 
0792 

1139 
1461 


0043 

0453 
0828 

1173 
1492 


0086 
0492 
0864 
1206 
1523 


0128 

0531 
0S99 

1239 
1553 


0170 
0569 

0934 
1271 

1584 


0212 
0607 
0969 

1303 
1614 


0253 
0645 
1004 

1335 
1644 


0294 
0682 
1038 
1367 
1673 


0334 
0719 
1072 
1399 
1703 


0374 
07S5 
1 106 

1430 
1732 


4 
4 
3 
3 
3 


8 
8 

7 
6 
6 


12 
II 
10 
10 
9 


15 

i6 

17 
i8 

19 


1761 
2041 
2304 

2553 
2788 


1790 
2068 
2330 

2577 
2810 


1818 

2095 
2355 
2601 

2833 


1847 
2122 

23S0 
2625 
2856 


1875 
2148 
2405 
2648 
2878 


1903 
2175 
2430 
2672 
2900 


1931 

2201 

2455 
2695 

2923 


1959 
2227 
2480 
2718 
2945 


1987 

2253 
2504 

2742 
2967 


2014 

2279 
2529 
2765 
2989 


3 

3 
2 
2 
2 


6 

5 
5 
5 
4 


8 
8 
7 
7 
7 


II 
II 

10 
9 
9 


14 
13 
12 
12 
II 


20 

21 

22 

23 

24 


3010 
3222 

3424 
3617 
3802 


3032 

3243 
3444 
3636 
3820 


3054 
3263 
3464 
3655 
3838 


3075 
3284 
3483 
3674 
3856 


3096 

3304 
3502 
3692 
3874 


3118 

3324 
3522 

3892 


3139 
3345 
3541 
3729 
3909 


3160 

3365 
3560 
3747 
3927 


3181 
3385 

3766 
3945 


3201 
3404 
3598 
3784 
3962 


2 
2 
2 
2 

2 


4 
4 
4 
4 
4 


6 
6 
6 
5 

5 


8 
8 
8 
7 
7 


II 

10 
10 
9 
9 


25 

26 
27 
28 
29 


3979 
4150 
4314 
4472 
4624 


3997 
4166 

4330 
4487 

4639 


4014 
4183 
4346 
4502 
4654 


4031 
4200 
4362 
4518 
4669 


4048 
4216 
4378 

4533 
4683 


4065 
4232 

4393 
4548 
4698 


4082 
4249 
4409 
4564 
4713 


4099 
4265 
4425 
4579 
4728 


4116 

4281 
4440 

4594 
4742 


4133 
4298 
4456 
4609 
4757 


2 
2 
2 
2 
I 


3 
3 
3 
3 
3 


5 
5 
5 
5 
4 


7 
7 
6 
6 
6 


9 

8 
8 
8 
7 


30 

31 

32 
33 
34 


4771 
4914 

5051 
5185 
5315 


4786 
4928 
5065 
5198 
5328 


4800 
4942 
5079 
5211 
5340 


4814 

4955 
5092 

5224 

5353 


4829 
4969 
5105 

5237 
5366 


4843 
4983 
5119 

5250 
5378 


4857 
4997 
5132 
5263 
5391 


4871 
501 1 

5145 
5276 

5403 


4886 
5024 
5159 
5289 
54'6 


4900 
5038 
5172 
5302 
5428 




3 
3 
3 
3 
3 


4 

4 
4 
4 
4 


6 
6 

5 
5 
5 


7 
7 
7 
6 
6 


35 

36 
Z7 
38 
39 


5441 
5563 
56S2 

5798 
591 1 


5453 
5575 
5694 
5809 

5922 


5465 
5587 
5705 
5821 

5933 


5478 
5599 
5717 
5832 
5944 


5490 
5611 

5729 
5843 
5955 


5502 
5623 
5740 

5855 
5966 


5514 
5635 
5752 
5866 

5977 


5527 
5647 
5763 
5877 
5988 


5539 

5658 
5775 
5888 

5999 


5551 
5670 
5786 

5899 
6010 




2 
2 


4 
4 
3 
3 
3 


5 
5 
5 
5 
4 


6 
6 
6 
6 
6 


40 

41 

42 

43 
44 


6021 
6128 
6232 
6335 
643 s 


6031 
6138 
6243 

6345 
6444 


6042 
6149 
6253 
6355 
6454 


6160 
6263 

6464 


6064 
6170 
6274 

6375 
6474 


6075 
6180 
62S4 
63S5 
6484 


60S 5 
6r9i 
6294 
6395 
6493 


6096 
6201 
6304 
6405 
6503 


6107 
6212 
6314 
6415 
6513 


6117 
6222 
6325 
6425 
6522 




2 
2 
2 
2 
2 


3 
3 
3 
3 
3 


4 
4 
4 
4 
4 


S 
5 
5 
5 
5 


45 

46 

47 
48 

49 


6532 
6628 
6721 
6S12 
6902 


6542 
6637 
6730 
6821 
691 1 


6551 

6646 

6739 
6830 
6920 


6561 
6656 
6749 
6839 
6928 


6571 
6665 
6758 
6848 

6937 


6580 
6675 
6767 
6857 
6946 


6590 
6684 
6776 
6866 
6955 


6599 
6693 
6785 
6875 
6964 


6609 
6702 
6794 
6884 
6972 


6618 
6712 
d8o3 
6893 
6981 




2 

2 
2 
2 
2 


3 

3 
3 
3 
3 


4 
4 
4 
4 
4 


5 
5 
5 
4 
4 


50 

51 

52 
53 
54 


6990 
7076 
7160 
7243 
7324 


6998 
7084 
7168 
7251 
7332 


7007 

7093 

7177 

7259 
7340 


7016 
7101 
7185 
7267 
7348 


7024 
7110 
7193 

7275 
7356 


7033 
7118 
7202 
7284 
7364 


7042 
7126 
7210 
7292 
7372 


7050 

7135 
7218 
7300 
7380 


7059 
7143 
7226 

7308 
7388 


7067 
7152 
7235 
7316 
7396 




2 
2 
2 
2 
2 


3 
3 
2 
2 
2 


3 
3 
3 
3 
3 


4 
4 
4 
4 

4 



Smithsonian Tables. 



Table 1 iconthmed). 
LOGARITHMS. 



27 


























P.P. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 




1 


2 


3 


4 


5 


55 


7404 


7412 


7419 


7427 


7435 


7443 


7451 


7459 


7466 


7474 




2 


2 


3 


4 


56 


7482 


7490 


7497 


7505 


75'3 


7520 


7528 


7536 


7543 


7551 




2 


2 


3 


4 


57 


7559 


7566 


7574 


7582 


7589 


7597 


7604 


7612 


7619 


7627 




2 


2 


3 


4 


5S 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7694 


7701 






2 


3 


4 


59 


7709 


7716 


7723 


7731 


7738 


7745 


7752 


7760 


7767 


7774 






2 


3 


4 


60 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 






2 


3 


4 


6i 


7S53 


7860 


7868 


7875 


7882 


7889 


7896 


7903 


7910 


7917 






2 


3 


4 


62 


7924 


7931 


7938 


7945 


7952 


7959 


7966 


7973 


7980 


7987 






2 


3 


3 


63 


7993 


8000 


8007 


8014 


8021 


8028 


803s 


8041 


8048 


8055 






2 


3 


3 


64 


8062 


8069 


8075 


80S2 


8089 


8096 


8l02 


8109 


8116 


8l22 






2 


3 


3 


65 


8129 


8136 


8142 


8149 


8156 


8162 


8169 


8176 


8182 


8189 






2 


3 


3 


66 


8195 


8202 


8209 


8215 


8222 


8228 


8235 


8241 


8248 


8254 






2 


3 


3 


67 


8261 


8267 


8274 


8280 


8287 


8293 


8299 


8306 


8312 


83'9 






2 


3 


3 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


8382 






2 


3 


3 


69 


8388 


8395 


8401 


8407 


8414 


8420 


S426 


8432 


8439 


8445 






2 


3 


3 


70 


S451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8506 






2 


2 


3 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


8555 


8561 


8567 






2 


2 


3 


72 


8573 


8579 


8585 


8591 


8597 


8603 


8609 


8615 


8621 


8627 






2 


2 


3 


73 


8633 


8639 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 






2 


2 


3 


74 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


8739 


8745 






2 


2 


3 


75 


8751 


8756 


8762 


8768 


8774 


8779 


878s 


8791 


8797 


S802 






2 


2 


3 


76 


8808 


8814 


8820 


8825 


8831 


8837 


8842 


8848 


8854 


8859 






2 


2 


3 


77 


8865 


8S71 


8876 


8882 


8887 


8893 


8899 


8904 


8910 


8915 






2 


2 


3 


78 


8921 


8927 


8932 


8938 


8943 


8949 


8954 


8960 


8965 


8971 






2 


2 


3 


79 


8976 


89S2 


8987 


8993 


8998 


9004 


9009 


9015 


9020 


9025 






2 


2 


3 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 






2 


2 


3 


81 


9085 


9090 


9096 


9101 


9106 


9112 


9II7 


9122 


9128 


9133 






2 


2 


3 


82 


9138 


9143 


9149 


9154 


9159 


9165 


9170 


9175 


9180 


9186 






2 


2 


3 


83 


9191 


9196 


9201 


9206 


9212 


9217 


9222 


9227 


9232 


9238 






2 


2 


3 


84 


9243 


9248 


9253 


9258 


9263 


9269 


9274 


9279 


9284 


9289 






2 


2 


3 


85 


9294 


9299 


9304 


9309 


9315 


9320 


9325 


9330 


9335 


9340 






2 


2 


3 


86 


934S 


9350 


9355 


9360 


9365 


9370 


9375 


9380 


9385 


9390 






2 


2 


3 


87 


9395 


9400 


9405 


9410 


9415 


9420 


9425 


9430 


9435 


9440 









2 


2 


88 


9445 


9450 


9455 


9460 


9465 


9469 


9474 


9479 


9484 


9489 









2 


2 


89 


9494 


9499 


9504 


9509 


9513 


9518 


9523 


9528 


9533 


9538 









2 


2 


90 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 









2 


2 


91 


9590 


9595 


9600 


9605 


9609 


9614 


9619 


9624 


9628 


9633 









2 


2 


92 


9638 


9643 


9647 


9652 


9657 


9661 


9666 


9671 


9675 


9680 









2 


2 


93 


9685 


9689 


9694 


9699 


9703 


9708 


9713 


9717 


9722 


9727 









2 


2 


94 


9731 


9736 


9741 


9745 


9750 


9754 


9759 


9763 


9768 


9773 









2 


2 


95 


9777 


9782 


9786 


9791 


9795 


9800 


9805 


9809 


9814 


9S18 









2 


2 


96 


9823 


9827 


9832 


9836 


9841 


9S45 


9850 


9854 


98 59 


9S63 









2 


2 


97 


9S68 


9872 


9877 


9881 


9886 


9S90 


9894 


9S99 


9903 


9908 









2 


2 


98 


9912 


9917 


9921 


9926 


9930 


9934 


9939 


9943 


9948 


9952 









2 


2 


99 


9956 


9961 


9965 


9969 


9974 


9978 


9983 


9987 


9991 


9996 









~ 


2 



Smithsonian Tables. 



28 



Table 1 1 . 
ANTILOGARITHMS. 

























P.P. 







1 


2 


3 


4 


5 


6 


7 


8 


9 






1 


2 


3 


4 


5 


.00 


1000 


1002 


1005 


1007 


1009 


[012 


1014 


1016 


1019 


1021 












I 


.OI 


1023 


1026 


1028 


1030 


1033 


1035 


1038 


1040 


1042 


1045 










i ' " 


.02 


1047 


1050 


1052 


1054 


1057 


1059 


1062 


1064 


1067 


1069 














■03 


1072 


1074 


1076 


1079 


108 1 


IOS4 


ro86 


1089 


1 091 


1094 














.04 


1096 


1099 


1 102 


1 104 


1 107 


1 1 09 


1112 


III4 


1117 


1119 





I 








.05 


1122 


1125 


1127 


1 1 30 


1132 


1135 


1 138 


1 140 


IM3 


1 146 













.06 


1 148 


1151 


1153 


1 1 56 


1159 


I161 


1 164 


1 167 


1 169 


1172 













.07 


II7S 


1178 


1 180 


1183 


1 186 


1189 


1191 


1 194 


1 197 


1 199 













.08 


1202 


1205 


1208 


1211 


1213 


I216 


1219 


1222 


1225 


1227 













.09 


1230 


1233 


1236 


1239 


1242 


1245 


1247 


1250 


1253 


1256 













.10 


1259 


1262 


1265 


1268 


1271 


1274 


1276 


1279 


1282 


1285 











I 


.11 


1288 


1291 


1294 


1297 


1300 


1303 


1306 


1309 


1312 


1315 











2 


.12 


1318 


1321 


1324 


1327 


1330 


1334 


1337 


1340 


1343 


1346 











2 


•13 


1349 


1352 


1355 


1358 


1361 


•365 


1368 


1371 


1374 


1377 











2 


.14 


1380 


1384 


1387 


1390 


1393 


1396 


1400 


1403 


1406 


1409 











2 


.15 


1413 


1416 


1419 


1422 


1426 


1429 


1432 


1435 


1439 


1442 











2 


.16 


1445 


1449 


1452 


1455 


1459 


1462 


1466 


1469 


1472 


1476 











2 


•17 


1479 


1483 


i486 


1489 


1493 


1496 


1500 


1503 


1507 


1510 











2 


.18 


1514 


1517 


1521 


1524 


1528 


I 531 


1535 


1538 


1542 


1545 











2 


.19 


1549 


1552 


1556 


1560 


1563 


1567 


1570 


1574 


1578 


1581 











2 


.20 


1585 


1589 


1592 


1596 


1600 


1603 


1607 


1611 


1614 


1618 









I 


2 


.21 


1622 


1626 


1629 


1633 


1637 


I64I 


1644 


1648 


1652 


1656 







I 


2 


2 


.22 


1660 


1663 


1667 


167 1 


1675 


1679 


1683 


16S7 


1690 


1694 









2 


2 


•23 


1698 


1702 


1706 


1710 


1714 


I718 


1722 


1726 


1730 


1734 









2 


2 


.24 


1738 


1742 


1746 


1750 


1754 


1758 


1762 


1766 


1770 


1774 









2 


2 


.25 


1778 


1782 


1786 


1791 


1795 


1799 


1803 


1807 


1811 


1816 









2 


2 


.26 


1820 


1824 


1828 


1832 


1837 


184I 


1845 


1849 


1854 


1858 









2 


2 


.27 


1862 


1866 


1871 


1875 


1879 


1884 


1888 


1892 


1897 


1 901 









2 


2 


.28 


1905 


1910 


1914 


1919 


1923 


1928 


1932 


1936 


1 941 


1945 









2 


2 


.29 


1950 


1954 


1959 


1963 


1968 


1972 


1977 


19S2 


1986 


1 991 









2 


2 


.30 


1995 


2000 


2004 


2009 


2014 


2018 


2023 


2028 


2032 


2037 









2 


2 


•31 


2042 


2046 


2051 


2056 


2061 


2065 


2070 


2075 


20S0 


2084 









2 


2 


•32 


20S9 


2094 


2099 


2104 


2109 


2II3 


2118 


2123 


2128 


2133 









2 


2 


•33 


2138 


2143 


2148 


2153 


2158 


2163 


2168 


2173 


2178 


2183 









2 


2 


•34 


2188 


2193 


2198 


2203 


2208 


2213 


2218 


2223 


2228 


2234 


I 




2 


2 


3 


.35 


2239 


2244 


2249 


2254 


2259 


2265 


2270 


2275 


2280 


2286 






2 


2 


3 


•36 


2291 


2296 


2301 


2307 


2312 


2317 


2323 


2328 


^333 


2339 






2 


2 


3 


•37 


2344 


2350 


2355 


2360 


2366 


2371 


2377 


2382 


2388 


2393 






2 


2 


3 


•38 


2399 


2404 


2410 


2415 


2421 


2427 


2432 


2438 


2443 


2449 






2 


2 


3 


•39 


2455 


2460 


2466 


2472 


2477 


2483 


2489 


2495 


2500 


2506 






2 


2 


3 


.40 


2512 


2518 


2523 


2529 


2535 


2541 


2547 


2553 


"559 


2564 






2 


2 


3 


.41 


2570 


2576 


2582 


2588 


2594 


2600 


2606 


2612 


2618 


2624 






2 


2 


3 


.42 


2630 


2636 


2642 


2649 


2655 


2661 


2667 


2673 


2679 


2685 






2 


2 


3 


•43 


2692 


2698 


2704 


2710 


2716 


2723 


2729 


2735 


2742 


2748 






2 


3 


3 


•44 


2754 


2761 


2767 


2773 


2780 


2786 


2793 


2799 


2805 


2812 






2 


3 


3 


.45 


2818 


2825 


2831 


2838 


2844 


2851 


2858 


2864 


2871 


2877 






2 


3 


3 


.46 


2S84 


2891 


2897 


2904 


2911 


2917 


2924 


2931 


2938 


2944 






2 


3 


3 


•47 


2951 


2958 


2965 


2972 


2979 


2985 


2992 


2999 


3006 


3013 






2 


3 


3 


.48 


3020 


3027 


3034 


3041 


3048 


3055 


3062 


3069 


3076 


3083 






2 


3 


4 


•49 


3090 


3097 


3105 


3II2 


3119 


3126 


3133 


3141 


3148 


3155 






2 


3 


4 



Smithsonian Tables. 



Table 1 1 (contimud). 
ANTILOGARITHMS. 



29 








1 


2 


3 


4 


5 


6 


7 


8 


9 


P.P. 1 




1 


2 


3 


4 


5 


.50 


3162 


3170 


3177 


3184 


3192 


3199 


3206 


3214 


3221 


3228 




I 


2 


3 


4 


•51 


y--,(> 


3243 


3251 


3258 


3266 


3273 


3281 


3289 


3296 


3304 




2 


2 


3 


4 


•52 


33" 


3319 


3327 


3334 


3342 


3350 


3357 


3365 


ZVi 


3381 




2 


2 


3 


4 


•53 


33S8 


3396 


3404 


3412 


3420 


3428 


34.36 


3443 


3451 


3459 




2 


2 


3 


4 


•54 


3467 


3475 


3483 


3491 


3499 


3508 


3516 


3524 


3532 


3540 




2 


2 


3 


4 


.55 


354S 


355^ 


3565 


3573 


35S1 


3589 


3597 


3606 


3614 


3622 




2 


2 


3 


4 


•56 


3631 


3639 


3648 


3656 


3664 


3673 


3681 


3690 


3698 


3707 




2 


3 


3 


4 


•57 


3715 


3724 


3733 


3741 


3750 


3758 


3767 


3776 


3784 


3793 




2 


3 


3 


4 


.58 


3802 


381 1 


3819 


3S28 


3837 


3846 


3855 


3S64 


3873 


3S82 




2 


3 


4 


4 


•59 


3890 


3899 


390S 


3917 


3926 


3936 


3945 


3954 


3963 


3972 




2 


3 


4 


5 


.60 


3981 


3990 


3999 


4009 


4018 


4027 


4036 


4046 


4055 


4064 




2 


3 


4 


5 


.61 


4074 


4083 


4093 


4102 


4111 


4121 


4130 


4140 


4150 


4159 




2 


3 


4 


5 


.62 


4169 


4178 


418S 


4198 


4207 


4217 


4227 


4236 


4246 


4256 




2 


3 


4 


5 


•63 


4266 


4276 


4285 


4295 


4305 


4315 


4325 


4335 


4345 


4355 




2 


3 


4 


5 


.64 


4365 


437S 


4385 


4395 


4406 


4416 


4426 


4436 


4446 


4457 




2 


3 


4 


5 


.65 


4467 


4477 


44S7 


4498 


450S 


4519 


4529 


4539 


4550 


4560 




2 


3 


4 


5 


.66 


4571 


4581 


4592 


4603 


4613 


4624 


4634 


4645 


4656 


4667 




2 


3 


4 


5 


.67 


4677 


46SS 


4699 


4710 


4721 


4732 


4742 


4753 


4764 


4775 




2 


3 


4 


5 


.6S 


47S6 


4797 


4808 


4819 


4S31 


4S42 


4853 


4864 


4875 


4887 




2 


3 


4 


6 


.69 


4S9S 


4909 


4920 


4932 


4943 


4955 


4966 


4977 


4989 


5000 




2 


3 


5 


6 


.70 


5012 


5023 


503s 


5047 


5058 


5070 


5082 


5093 


5105 


5117 




2 


4 


5 


6 


•71 


5129 


5140 


5152 


5164 


5176 


51S8 


5200 


5212 


5224 


5236 




2 


4 


5 


6 


.72 


5248 


5260 


5272 


52S4 


5297 


5309 


5321 


5333 


5346 


5358 




2 


4 


5 


6 


■73 


5370 


5383 


5395 


5408 


5420 


5433 


5445 


5458 


5470 


5483 




3 


4 


5 


6 


■7A 


5495 


5508 


5521 


5534 


5546 


5559 


5572 


55S5 


5598 


5610 




3 


4 


5 


6 


.75 


5623 


5636 


5649 


5662 


5675 


5689 


5702 


5715 


5728 


5741 




3 


4 


5 


7 


.76 


5754 


576S 


5781 


5794 


5S08 


5821 


5834 


5848 


5S61 


5875 




3 


4 


5 


7 


•77 


58SS 


5902 


5916 


5929 


5943 


5957 


5970 


5984 


5998 


6012 




3 


4 


5 


7 


.78 


6026 


6039 


6053 


6067 


6081 


6095 


6109 


6124 


6138 


6152 




3 


4 


6 


7 


•79 


6166 


6180 


6194 


6209 


6223 


6237 


6252 


6266 


6281 


6295 




3 


4 


6 


7 


.80 


6310 


6324 


6339 


6353 


6368 


6383 


6397 


6412 


6427 


6442 


I 


3 


4 


6 


7 


.8i 


6457 


6471 


6486 


6501 


6516 


6531 


6546 


6561 


6577 


6592 


2 


3 


5 


6 


8 


.82 


6607 


6622 


6637 


6653 


6668 


66S3 


6699 


6714 


6730 


6745 


2 


3 


5 


6 


8 


•83 


6761 


6776 


6792 


6808 


6823 


6S39 


6855 


6871 


6887 


6902 


2 


3 


5 


6 


8 


.84 


6918 


6934 


6950 


6966 


69S2 


6998 


7015 


7031 


7047 


7063 


2 


3 


5 


6 


8 


.85 


7079 


7096 


7112 


7129 


7145 


7161 


7178 


7194 


7211 


7228 


2 


3 


5 


7 


8 


.86 


7244 


7261 


7278 


7295 


73" 


7328 


7345 


7362 


7379 


7396 


2 


3 


5 


7 


8 


.87 


7413 


7430 


7447 


7464 


7482 


7499 


7516 


7534 


7551 


7568 


2 


3 


5 


7 


9 


.88 


75S6 


7603 


7621 


763S 


7656 


7674 


7691 


7709 


7727 


7745 


2 


4 


5 


7 


9 


.89 


7762 


7780 


7798 


7816 


7834 


7S52 


7870 


78S9 


7907 


7925 


2 


4 


5 


7 


9 


.90 


7943 


7962 


7980 


7998 


8017 


803s 


8054 


8072 


8091 


8110 


2 


4 


6 


7 


9 


.91 


S128 


8147 


8166 


8185 


8204 


8222 


8241 


8260 


8279 


8299 


2 


4 


6 


8 


9 


.92 


S318 


^T:,! 


8356 


S375 


8395 


8414 


8433 


8453 


8472 


8492 


2 


4 


6 


8 


10 


•93 


85U 


8S3I 


8551 


8570 


8590 


8610 


8630 


S650 


8670 


8690 


2 


4 


6 


8 


10 


•94 


8710 


8730 


8750 


8770 


8790 


8810 


8831 


8851 


8872 


8S92 


2 


4 


6 


8 


10 


.95 


8913 


8933 


8954 


8974 


8995 


9016 


9036 


9057 


9078 


9099 


2 


4 


6 


8 


10 


.96 


9120 


9141 


9162 


9183 


9204 


9226 


9247 


9268 


9290 


9311 


2 


4 


6 


8 


II 


•97 


9333 


9354 


9376 


9397 


9419 


9441 


9462 


9484 


9506 


9528 


2 


4 


7 


9 


II 


.98 


9550 


9572 


9594 


9616 


9638 


9661 


9683 


9705 


9727 


9750 


2 


4 


7 


9 


II 


•99 


9772 


9795 


9817 


9840 


9863 


9886 


9908 


9931 


9954 


9977 


2 


5 


7 


9 


II 


Smith: 


IONIAN 


Tables. 
















• 













Table 12. 
ANTILOGARITHMS. 








12 3 


4 1 5 


6 


7 


8 9 


10 


.900 


7943 


7945 7947 7949 


7951 7952 


7954 


7956 


7958 ' 7960 


7962 ' 


.901 


7962 


7963 7965 1 7967 


7969 I 79/1 


, 7973 


7974 ; 7976 7978 


7980 


.902 


79S0 


79S2 7984 1 7985 


l^l ^989 


i sSJ 


7993 


7995 7997 


799S 


•903 


799^ 


8000 S002 1 8004 


8006 800S 




Sou 


8013 1 8015 


8017 


i -904 


8017 


S019 


S020 8022 


8024 8026 


8028 


8030 


8032 S033 


8035 


.905 


8035 


S037 


8039 1 8041 


8043 8045 


8046 


8048 


8050 8052 


80 ;4 


; .906 


S054 


S056 8057 8059 


8061 8063 


8065 


8067 


8069 8070 


8072 


. .907 


S072 


S074 


8076 807S 


80S0 8082 


8084 


8085 


8087 8089 


S091 


i .90S 


8091 


8093 


8095 S097 


8098 8100 


8102 


8104 


8106 810S 


8110 


.909 


Siio 


8111 


8113 


8115 


S117 


81 19 


8121 


8123 


8125 8126 


81 28 


.910 


8128 


8130 


8132 


8134 


8136 


8138 


8140 


8141 


S143 ' 8145 


8147 


1 -9" 


8147 


8149 


8151 ! 8153 


8155 


8156 


8158 


8160 


8162 8164 


8166 


.912 


8166 


8168 


8170 8171 


8173 


8175 


8177 


8179 


8181 8183 


8185 


■913 


S1S5 


8187 


8188 8190 


8192 


8194 


8196 


8198 


8200 8202 


8204 1 


.914 


8204 


S205 


8207 8209 


821 1 


8213 


8215 


8217 


8219 8221 


8222 


.915 


S222 


S224 


8226 8228 


8230 


8232 


8234 


8236 


S238 8239 


8241 


.916 


S241 


8243 


8245 : 8247 


8249 


8251 8253 


8255 


8257 S258 


8260 


.917 


8260 


8262 


8264 8266 


826S 


8270 8272 


8274 


8276 8278 


8279 


.91S 


8279 


8281 


8283 8285 


82S7 


8289 8291 


8293 


8295 S297 


8299 


.919 


8299 


S300 


8302 


8304 


8306 


830S 8310 


8312 


8314 8316 


831S 


.920 


S31S 


8320 


8321 


8323 


8325 


8327 ! S329 


8331 


8333 8335 


f337 


.921 


8337 


S339 


8341 8343 


8344 


8^6 8348 


8350 


8352 8354 


83 ;o 


.922 


8356 


835S 


8360 8362 


8364 


8366 


8368 


8370 


837 1 8373 


8375 


! 923 


8375 


S377 


8379 8381 


8383 


8385 


8387 


8389 


8391 8393 


8395 


1 -9-4 


S395 


8397 


839S S400 


8402 


8404 


8406 


840S 


8410 ! 8412 


8414 


.925 


8414 


S416 


8418 8420 


8422 


8424 


8426 


842S 


8429 8431 


8433 


.926 


8433 


8435 


8437 8439 


8441 


8443 


8445 


8447 


8449 8451 


8453 


.927 


8453 


8455 


8457 8459 


8461 1 8463 


8464 


8466 


846S 8470 


8472 


.92S 


8472 


8474 


8476 • 8478 


8480 


8482 


8484 


8486 


8488 8490 


8492 


•9-9 


8492 


8494 


S496 j 8498 


8500 


8502 


8504 


8506 


8507 j 8509 


8511 


.930 


8;ii 


S5T3 


8515 ! 8517 


8519 


8521 


8523 


8525 


8527 8529 


S531 


•931 


S531 


8533 


S535 , 8537 


8539 


8541 


8543 


8545 


8547 ! 8549 


8;^i 


•932 


S551 


8553 


8555 8557 


S559 


8561 


8562 


8564 8;66 856S 


8570 


•933 


8-0 


8572 


8574 ' 8576 


8578 


8580 8582 


8584 8;S6 858S 


0590 


•934 


8590 


8592 


8594 1 8596 


8598 


8600 


8602 


8604 S606 8608 


8610 


.935 


S61C 


S612 


8614 ; 8616 


8618 


8620 


8622 


8624 8626 8628 


8630 


•930 


S630 


S632 


8634 8636 


8638 


8640 


8642 


S644 8646 8648 


86 ;o 


1 -937 


S650 


8652 


8654 ; 8656 


86^8 


8660 


8662 


8664 , 8666 8668 


86-0 


' •938 


S670 


8672 8674 8676 


8678 


8680 


86S2 


86S4 8686 8688 


8690 


•939 


8690 


8692 8694 


8696 


8698 


8700 


8702 


8704 8706 8708 


8710 , 


.940 


87 10 


8712 S714 


8716 


8718 


8720 


8722 


8724 8726 8728 


8:^,0 


.941 


8730 


8732 S734 ; 8736 


8738 ; 8740 8742 


8744 S746 8748 


8:;c 


; .942 


8750 


8752 8754 1 8756 


87 58 ' 8760 8762 


8764 8766 876S 


87-0 


1 ^943 


8770 


8772 8774 8776 


8778 8780 8782 


8784 8786 8:88 


8-O0 


1 -944 


8790 


S792 ; S794 8796 


879S S800 8S02 

1 


S804 SS06 880S 


88 10 


.945 


SSio 


8S13 8S15 8S17 


8819 8821 SS23 


8S25 


8S27 8829 


8831 


.946 


SS^ii 


SS33 8S35 8S37 


8839 


8S41 8843 


8S45 


8S47 8849 


8S;i 


•947 


SS51 


88^3 88 ;5 8857 


8S59 


8S61 8S63 


8865 


8S67 8S70 


8872 


■94S 


SS72 


SS-4 8876 SS78 


8SS0 


8SS2 ' 8SS4 


8886 


SS88 8890 


S8q2 


•949 


SS92 


SS94 SS96 SS98 


8900 8902 8904 


S9C6 


SooS S910 


i 



Smithsonian Tables. 



Table 1 2 {contimted). 
ANTILOGARITHMS. 



31 








1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


.950 


8913 


8915 


8917 


8919 


8921 


8923 


8925 


8927 


8929 


8931 


8933 


•951 


8933 


8935 


8937 


8939 


8941 


8943 


8945 


8947 


8950 


8952 


8954 


.952 


8954 


S956 


8958 


8960 


8962 


8964 


8966 


8968 


8970 


8972 


8974 


•953 


S974 


8976 


897S 


8980 


8983 


8985 


8987 


8989 


8991 


8993 


8995 


•954 


8995 


8997 


8999 


9001 


9003 


9005 


9007 


9009 


9012 


9014 


9016 


.955 


9016 


9018 


9020 


9022 


9024 


9026 


9028 


9030 


9032 


9034 


9036 


.956 


9036 


9039 


9041 


9043 


9045 


9047 


9049 


9051 


9053 


9055 


9057 


•957 


9057 


9059 


9061 


9064 


ao66 


9068 


9070 


9072 


9074 


9076 


9078 


•95^^ 


9078 


9080 


9082 


9084 


9087 


9089 


9091 


9093 


9095 


9097 


9099 


•959 


9099 


9101 


9103 


9105 


9108 


9110 


9112 


9114 


9116 


91 18 


9120 


.960 


9120 


9122 


9124 


9126 


9129 


9131 


9133 


9^35 


9137 


9139 


9141 


.961 


9141 


9143 


9145 


9147 


9150 


9152 


9154 


9156 


9158 


9160 


9162 


.962 


9162 


9164 


9166 


9169 


9171 


9173 


9175 


9177 


9179 


9181 


9183 


•963 


9183 


91S5 


91S8 


9190 


9192 


9194 


9196 


9198 


9200 


9202 


9204 


.964 


9204 


9207 


9209 


9211 


9213 


9215 


9217 


9219 


9221 


9224 


9226 


.965 


9226 


9228 


9230 


9232 


9234 


9236 


9238 


9241 


9243 


9245 


9247 


.966 


9247 


9249 


9251 


9253 


9256 


9258 


9260 


9262 


9264 


9266 


9268 


.967 


9268 


9270 


9273 


9275 


9277 


9279 


9281 


9283 


9285 


9288 


9290 


.96S 


9290 


9292 


9294 


9296 


9298 


9300 


9303 


9305 


9307 


9309 


93" 


.969 


9311 


93'3 


9315 


9318 


9320 


9322 


9324 


9326 


9328 


9330 


9333 


.970 


9333 


9335 


9337 


9339 


9341 


9343 


9345 


9348 


9350 


9352 


9354 


.971 


9354 


9356 


9358 


9361 


9363 


9365 


9367 


9369 


9371 


9373 


9376 


.972 


9376 


9378 


9380 


9382 


9384 


9386 


9389 


9391 


9393 


9395 


9397 


•973 


9397 


9399 


9402 


9404 


9406 


9408 


9410 


9412 


9415 


9417 


9419 


•974 


9419 


9421 


9423 


9425 


942S 


9430 


9432 


9434 


9436 


9438 


9441 


.975 


9441 


9443 


9445 


9447 


9449 


9451 


9454 


9456 


9458 


9460 


9462 


.976 


9462 


9465 


9467 


9469 


9471 


9473 


9475 


9478 


9480 


94S2 


9484 


•977 


94S4 


9486 


9489 


9491 


9493 


9495 


9497 


9499 


9502 


9504 


9506 


.97S 


9506 


9508 


95to 


9513 


9515 


9517 


9519 


9521 


9524 


9526 


9528 


•979 


95-8 


9530 


9532 


9535 


9537 


9539 


9541 


9543 


9546 


9548 


9550 


980 


9550 


9552 


9554 


9557 


9559 


9561 


9563 


9565 


9568 


9570 


9572 


.98 1 


9572 


9574 


9576 


9579 


9581 


9583 


9585 


9587 


9590 


9592 


9594 


.9S2 


9594 


9596 


9598 


9601 


9603 


9605 


9607 


9609 


9612 


9614 


9616 


•9S3 


9616 


9618 


9621 


9623 


9625 


9627 


9629 


9632 


9634 


9636 


9638 


•9S4 


9638 


9641 


9643 


9645 


9647 


9649 


9652 


9654 


9656 


9658 


9661 


.985 


9661 


9663 


9665 


9667 


9669 


9672 


9674 


9676 


9678 


9681 


9683 


.9S6 


9683 


96S5 


9687 


9689 


9692 


9694 


9696 


9698 


9701 


9703 


9705 


•9S7 


9705 


9707 


9710 


9712 


9714 


9716 


9719 


9721 


9723 


972^ 


9727 


.9S8 


97-7 


9730 


9732 


9734 


9736 


9739 


9741 


9743 


9745 


9748 


9750 


.989 


9750 


9752 


9754 


9757 


9759 


9761 


9763 


9766 


9768 


9770 


9772 


.990 


9772 


9775 


9777 


9779 


9781 


9784 


9786 


9788 


9790 


9793 


9795 


.991 


9795 


9797 


9799 


9802 


9804 


9806 


9808 


981 1 


9^'^ 


9815 


9817 


.992 


9817 


9820 


9822 


9824 


9827 


9829 


9831 


9833 


9836 


9838 


9840 


•993 


9840 


9842 


9845 


9847 


9849 


9851 


9854 


9856 


9858 


9^61 


9^^3 


•994 


9863 


9865 


9867 


9870 


9872 


9874 


9876 


9879 


9881 


9883 


9886 


.995 


9S86 


98SS 


9890 


9892 


9895 


9897 


9899 


9901 


9904 


9906 


9908 


.996 


990S 


991 1 


9913 


9915 


9917 


9920 


9922 


9924 


9927 


9929 


9931 


•997 


9931 


9933 


9936 


9938 


9940 


9943 


9945 


9947 9949 


9952 


9954 


.998 


9954 


9956 


9959 


9961 


9963 


9966 


9968 


9970 9972 


9975 


9977 


•999 


9977 


9979 9982 


9984 


9986 


9988 


9991 


9993 9995 9998 


0000 


,' 8MITHS0^ 


IAN Tab 


LES. 





















32 



Table 13. 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 

(Taken from B. O. Peirce's " Short Table of Integrals," Ginn & Co.) 





1 frl 




SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 






Nat. Log. 


Nat. Log. 


Nat. Log. 


Nat. 


Log. 


O.OOOO 


0°00' 


.0000 00 


1 .0000 0.0000 


.0000 CO 


CO 


CO 


9o°oo' 


1.5708 


0.0029 


10 


.0029 7.4637 


1 .0000 .0000 


.0029 7.4637 


343-77 


2-5363 


50 


1-5679 


0.0058 


20 


.0058 .7648 


1. 0000 .0000 


.0058 .7648 


171.89 


•2352 


40 


1.5650 


0.0087 


30 


.0087 .9408 


1 .0000 .0000 


.0087 .9409 


114.59 


.0591 


30 


1. 5621 


0.0II6 


40 


.0116 8.0658 


.9999 .0000 


.0116 8.0658 


85.940 


1-9342 


20 


1-5592 


0.0145 


50 


•0145 -1627 


.9999 .0000 


.0145 .1627 


68.750 


•8373 


10 


1-5563 


0.0175 


I°00' 


.0175 8.2419 


.9998 9.9999 


.0175 8.2419 


57-290 


1-7581 


89°oo' 


1-5533 


0.0204 


10 


.0204 .3088 


.9998 .9999 


.0204 .3089 


49.104 


.6911 


50 


1-5504 


0.0233 


20 


.0233 .3668 


•9997 -9999 


•0233 .3669 


42.964 


-6331 


40 


1-5475 


0.0262 


30 


.0262 .4179 


.9997 .9999 


.0262 .4181 


38.188 


.5819 


30 


1.5446 


0.0291 


40 


.0291 .4637 


.9996 .9998 


.0291 .4638 


34^368 


-5362 


20 


1-5417 


0.0320 


50 


.0320 .5050 


-9995 -9998 


•0320 .5053 


31.242 


-4947 


10 


1-5388 


0.0349 


2°00' 


.0349 8.5428 


•9994 9-9997 


.0349 8.5431 


28.636 


1.4569 


S8°oo' 


1-5359 


0.0378 


10 


•0378 .5776 


•9993 ^9997 


•0378 .5779 


26.432 


.4221 


50 


'•5330 


0.0407 


20 


.0407 .6097 


•9992 ^9996 


.0407 .6101 


24^542 


•3899 


40 


1-5301 


0.0436 


30 


.0436 .6397 


•9990 -9996 


.0437 .6401 


22.904 


•3599 


30 


1.5272 


0.0465 


40 


.0465 .6677 


•9989 ^9995 


.0466 .6682 


21.470 


•3318 


20 


1-5243 


0.0495 


50 


.0494 .6940 


.9988 .9995 


.0495 ^6945 


20.206 


•3055 


10 


1-5213 


0.0524 


3°oo' 


.0523 8.7188 


.99S6 9.9994 


.0524 8.7194 


19.081 


1.2806 


87°oo' 


1.5184 


0-0553 


10 


•0552 .7423 


•9985 -9993 


•0553 -7429 


18.075 


-2571 


50 


1-5155 


0.0582 


20 


.0581 .7645 


.9983 ^9993 


.0582 .7652 


17.169 


.2348 


40 


1.5126 


0.061 1 


30 


.0610 .7857 


.9981 .9992 


.0612 .7865 


16.350 


•2135 


30 


1-5097 


0.0640 


40 


.0640 .8059 


.9980 .999 1 


.0641 .8067 


15.605 


-'933 


20 


1.5068 


0.0669 


50 


.0669 .8251 


.9978 .9990 


.0670 .8261 


14.924 


•1739 


10 


1-5039 


0.0698 


4°oo' 


.0698 8.8436 


.9976 9.9989 


.0699 8.8446 


14.301 


1-1554 


86°oo' 


1.5010 


0.0727 


10 


.0727 .8613 


-9974 -9989 


.0729 .8624 


13-727 


-1376 


50 


1.4981 


0.0756 


20 


.0756 .8783 


.9971 .9988 


•0758 -8795 


13-197 


.1205 


40 


J -4952 


0.0785 


30 


.0785 .8946 


.9969 .9987 


.0787 .8960 


12.706 


.1040 


30 


1.4923 


0.0814 


40 


.0814 .9104 


.9967 .9986 


.0816 .9118 


12.251 


.0S82 


20 


1.4893 


0.0844 


50 


.0843 .9256 


.9964 .9985 


.0846 .9272 


11.826 


.0728 


10 


1.4864 


0.0873 


5°oo' 


•0872 8.9403 


.9962 9.9983 


.0875 8.9420 


11.430 


1.05S0 


85°oo' 


1-4835 


0.0902 


10 


•0901 .9545 


•9959 -9982 


•0904 -9563 


11.059 


•0437 


50 


1.4806 


0.0931 


20 


.0929 .9682 


-9957 -9981 


.0934 .9701 


10.712 


.0299 


40 


1-4777 


0.0960 


30 


•0958 .9816 


-9954 -9980 


-0963 -9836 


10.385 


.0164 


30 


1.4748 


0.0989 


40 


•0987 .9945 


.9951 .9979 


.0992 .9966 


10.078 


.0034 


20 


1.4719 


O.IOI8 


SO 


.1016 9.0070 


-9948 -9977 


.1022 9.0093 


9.7S82 


0.9907 


10 


1.4690 


0.1047 


6°oo 


.1045 9-0192 


-9945 9-9976 


.1051 9.0216 


9-5144 


0.9784 


84°oo' 


1.4661 
1.4632 


0.1076 


10 


.1074 .0311 


•9942 .9975 


.1080 .0336 


9-2553 


.9664 


50 


O.I 105 


20 


.1103 .0426 


-9939 -9973 


.1110 .0453 


9.0098 


•9547 


40 


1.4603 


0.1134 


30 


.1132 .0539 


.9936 .9972 


.1139 .0567 


8.7769 


-9433 


30 


1-4574 


0.1164 


40 


.1161 .0648 


•9932 -9971 


.1169 .0678 


8-5555 


.9322 


20 


1.4544 


O.I 193 


50 


.1190 .0755 


.9929 .9969 


.1198 .0786 


8-3450 


.9214 


10 


I-45I5 


0.1222 


7°oo' 


.1219 9.0859 


•9925 9-9968 


.1228 9.0891 


8.1443 


0.9109 


83°oo' 


1.4486 


O.I25I 


10 


.1248 .0961 


.9922 .9966 


-1257 .0995 


7-9530 


-9005 


50 


1-4457 


0.1280 


20 


.1276 .1060 


.9918 .9964 


.1287 .1096 


7.7704 


.8904 


40 


1.4428 , 


0.1309 


30 


•1305 -1157 


.9914 .9963 


.1317 .1194 


7-5958 


.8806 


30 


1-4399 j 


0.1338 


40 


•1334 -1252 


.9911 .9961 


.1346 .1291 


7.4287 


.8709 


20 


1-4370 


0.1367 


50 


■^i'^3 -1345 


-9907 .9959 


.1376 .1385 


7.2687 


.8615 


10 


I -434 1 


0.1396 


8°oo' 


.1392 9.1436 


•9903 9-9958 


.1405 9.1478 


7.1154 


0.8522 


82°00' 


1.4312 


0.1425 


10 


.1421 .1525 


-9899 -9956 


•1435 -1569 


6.9682 


.8431 


50 


1.4283 


0.1454 


20 


.1449 .1612 


■9894 -9954 


.1465 .1658 


6.8269 


.8342 


40 


1-4254 , 


0.1484 


30 


.1478 .1697 


.9890 .9952 


•1495 -1745 


6.6912 


-8255 


30 


1.4224 


O.I5I3 


40 


.1507 .1781 


.9886 -9950 


.1524 .1831 


6.5606 


.8169 


20 


1.4195 . 


0.1542 


50 


.1536 .1863 


.9881 .9948 


.1554 .1915 


6.4348 


.8085 


10 


1.4166 


O.I57I 


9°oo' 


.1564 9.1943 


.9877 9.9946 


.1584 9-1997 


6-3138 


0.8003 


8i°oo' 


1.4137 






Nat. Log. 


Nat. Log. 


Nat. Log. 


Nat. 


Log. 


t/i 




COSINES. 


SINES. 


COTAN- 
GENTS. 


TANGENTS. 



Smithsonian Tables. 



Table 13 {coiuinued). 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



33 








SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 






Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


0.1571 


9°oo' 


.1564 


9-1943 


.9877 


9.9946 


.1584 


9.1997 


6.3 > 38 


0.8003 


8i°oo' 


1.4137 


0. 1 600 


10 


•1593 


.2022 


.9872 


•9944 


.1614 


.2078 


6.1970 


.7922 


50 


1.4108 


0.1629 


20 


.162.2 


.2100 


.9868 


.9942 


.1644 


.2158 


6.0844 


.7842 


40 


1.4079 


0.1658 


30 


.1650 


.2176 


,9863 


.9940 


•1673 


.2236 


5-9758 


.7764 


30 


1.4050 


0.1687 


40 


.1679 


.2251 


.9858 


•9938 


•1703 


•23J3 


5.8708 


.7687 


20 


1.4021 


0.1716 


50 


.1708 


.2324 


•9853 


•9936 


•1733 


.2389 


5-7694 


.7611 


10 


1.3992 


0.1745 


io°oo' 


•1736 


9-2397 


.9848 


9-9934 


•1763 


9.2463 


5-6713 


0-7537 


8o°oo' 


1-3963 


0.1774 


10 


•1765 


.2468 


•9843 


•993' 


•1793 


•2536 


5-5764 


•7464 i 


50 


1-3934 


0.1804 


20 


.1794 


•253S 


.9838 


.9929 


.1823 


.2609 


5-4845 


•7391 i 


40 


1.3904 


0.1833 


30 


.1822 


.2606 


•9833 


.9927 


•1853 


.2680 


5-3955 


.7320 


30 


1-3875 


0.1862 


40 


.1851 


.2674 


.9827 


.9924 


.1883 


.2750 


5-3093 


.7250 


20 


1.3846 


0.189 1 


50 


.1880 


.2740 


.9822 


.9922 


.1914 


.2819 


5-2257 


.7181 


10 


1.3817 


0.1920 


1 1°00' 


.1908 


9.2806 


.9816 


9.9919 


.1944 


9.2887 


5.1446 


O.7113 


79°oo' 


1.3788 


0.1949 


10 


•■937 


.2870 


.9811 


•99 '7 


.1974 


•2953 


5.0658 


.7047 


50 


1-3759 


0.1 97S 


20 


.1965 


.2934 


.9805 


.9914 


.2004 


•3020 


4.9894 


.6980 


40 


1-3730 


0.2007 


30 


.1994 


.2997 


•9799 


.9912 


•2035 


•30S5 


4.9152 


.6915 


30 


1. 3701 


0.2036 


40 


.2022 


•305S 


•9793 


■9909 


.2065 


•3149 


4.8430 


.68^1 


20 


1.3672 


0.2065 


50 


.2051 


•3119 


•9787 


.9907 


.2095 


.3212 


4.7729 


.67S8 


10 


1^3643 


0.2094 


I2°00' 


.2079 


9-3179 


.9781 


9.9904 


.2126 


9^3275 


4.7046 


0.6725 


78°oo' 


1.3614 


0.2123 


10 


.2108 


•3238 


-9775 


.9901 


.2156 


•3336 


4.6382 


.6664 


50 


1-3584 


0-2153 


20 


.2136 


.3296 


.9769 


•9899 


.2186 


•3397 


4.5736 


.6603 


40 


1-3555 


0.2182 


30 


.2164 


■3353 


•9763 


.9S96 


.2217 


•345S 


4-5'07 


.6542 


30 


1-3526 


0.221 1 


40 


.2193 


.3410 


•9757 


•9893 


.2247 


•3517 


4.4494 


•6483 


20 


1-3497 


0.2240 


50 


.2221 


.3466 


.9750 


.9890 


.2278 


•3576 


4.3897 


.6424 


10 


1.3468 


0.2269 


i3°oo' 


.2250 


9-3521 


•9744 


9.9887 


.2309 


9^3634 


4-3315 


0.6366 


77°oo' 


1-3439 


0.2298 


10 


.2278 


-3575 


•9737 


.9S84 


•2339 


.3691 


4-2747 


•6309 


50 


1.3410 


0.2327 


20 


.2306 


.3629 


•9730 


.9881 


.2370 


•3748 


4-2193 


.6252 


40 


•■3381 


0.2356 


30 


•2334 


.3682 


•9724 


.9878 


.2401 


.3804 


4-1653 


.6196 


30 


1-3352 


0.2385 


40 


■2363 


•3734 


.9717 


-9S75 


.2432 


•3859 


4. 1 1 26 


.6141 


20 


1-3323 


0.2414 


50 


.2391 


.3786 


.9710 


.9872 


.2462 


•3914 


4.061 1 


.6086 


10 


1-3294 


0.2443 


i4°oo' 


.2419 


9-3837 


■9703 


9.9869 


•2493 


9.3968 


4.0108 


0.6032 


76°oo' 


1.3265 


0.2473 


I0# 


•2447 


.3887 


.9696 


.9866 


.2524 


.4021 


3-9617 


•5979 


50 


1-3235 


0.2502 


20 


.2476 


•3937 


.9689 


.9863 


.2555 


.4074 


3-9136 


.5926 


40 


1.3206 


0.2531 


30 


.2504 


.3986 


.9681 


•98 59 


.2586 


.4127 


3-8667 


•5873 


30 


••3177 


0.2560 


40 


•2532 


.4035 


.9674 


.9856 


.2617 


.4178 


3.8208 


•5822 


20 


1.3148 


0.2589 


50 


.2560 


.4083 


.9667 


•9S53 


.2648 


.4230 


3.7760 


•5770 


10 


1.3119 


0.261S 


1 5°oo' 


.2588 


9.4130 


•9659 


9.9849 


.2679 


9.4281 


3^7321 


0.5719 


75°oo' 


1.3090 


0.2647 


10 


.2616 


.4177 


.9652 


.9846 


.2711 


•4331 


3.6891 


.5669 


50 


1.3061 


0.2676 


20 


.2644 


.4223 


.9644 


.9843 


.2742 


.4381 


3-6470 


.5619 


40 


1-3032 


0.2705 


30 


.2672 


.4269 


.9636 


•9839 


•2773 


•4430 


3-6059 


•5570 


30 


1-3003 


0.2734 


40 


.2700 


•4314 


.9628 


.9S36 


.2805 


•4479 


3-5656 


.5521 


20 


1.2974 


0.2763 


50 


.2728 


-4359 


.9621 


•9S32 


.2836 


•4527 


3-5261 


•5473 


10 


1.2945 


0.2793 


i6°oo' 


.2756 


9.4403 


.9613 


9.9828 


.2867 


9^4575 


3-4874 


0.5425 


74°oo' 


1.2915 


0.2822 


10 


.2784 


•4447 


•9605 


.9825 


.2899 


.4622 


3-4495 


•5378 


50 


1.28S6 


0.2851 


20 


.2812 


.4491 


.9596 


.9821 


•2931 


.4669 


3-4I24 


•5331 


40 


1.2857 


0.2S80 


30 


.2840 


•4533 


.9588 


.9817 


.2962 


.4716 


3-3759 


.5284 


30 


1.2S28 


0.2909 


40 


.2868 


•4576 


.9580 


.9814 


•2994 


.4762 


3-3402 


•5238 


20 


1.2799 


0.2938 


50 


.2896 


.4618 


•9572 


.9810 


.3026 


.4808 


3-3052 


.5192 


10 


1.2770 


0.2967 


i7°oo' 


.2924 


9.4659 


-9563 


9.9806 


•3057 


9-4853 


3-2709 


0.5147 


73°oo' 


1. 2741 


0.2996 


10 


.2952 


.4700 


-9555 


.9802 


.3089 


.489S 


3-2371 


.5102 


50 


1. 2712 


0.3025 


20 


.2979 


.4741 


■9546 


•9798 


.3121 


•4943 


3.2041 


•5057 


40 


1.2683 


0.3054 


30 


.3007 


•4781 


-9537 


•9794 


•3153 


.4987 


3.1716 


•5013 


30 


1.2654 


0.3083 


40 


■3035 


.4S21 


.9528 


•9790 


•3185 


•5031 


3-1397 


.4969 


20 


1.2625 


0-3113 


50 


.3062 


.4861 


.9520 


.9786 


.3217 


•5075 


3.1084 


•4925 


10 


1-2595 


0.3142 


i8°oo' 


.3090 


9.4900 


•95" 


9.9782 


•3249 


9.51 18 


3-0777 


0.4882 


72°oo' 


1.2566 






Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


c/5 




0^ 


COSINES 


SINES. 


COTAN- 
GENTS. 


TANGENTS 



Smithsonian Tables. 



34 



Table 1 3 (continued). 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 





in 




SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 






Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


0.3142 


i8°oo' 


.3090 


9.4900 


•951 1 


9.9782 


•3249 


9.5118 


3^0777 


O.4SS2 


72°oo' 


1.2566 


0.3I7I 


10 


.3118 


•4939 


.9502 


.9778 


.3281 


.5161 


3-0475 


.4839 


so 


'•2537 


0.3200 


20 


•3145 


•4977 


.9492 


•9774 


•33'4 


•5203 


3-0178 


•4797 


40 


1.2508 


0.3229 


30 


•3 '73 


•5015 


■9483 


.9770 


•3346 


■5245 


2.9887 


•47 55 


30 


1.2479 


0.3258 


40 


.3201 


•5052 


-9474 


.9765 


•3378 


.5287 


2.9600 


•4713 


20 


1.2450 


0.3287 


50 


.3228 


.5090 


•9465 


.9761 


•341 1 


•5329 


2.9319 


.4671 


10 


1. 2421 


0.3316 


i9°oo' 


•3256 


9.5126 


•9455 


9^9757 


•3443 


9^5370 


2.9042 


0.4630 


7i°oo' 


1.2392 


0-3345 


10 


•3283 


•5163 


•9446 


.9752 


•3476 


.5411 


2.S770 


.4589 


SO 


'-2363 


0.3374 


20 


•3311 


.5199 


.9436 


.9748 


•3508 


•5451 


2.8502 


•4549 


40 


1-2334 


0.3403 


30 


•3338 


•5235 


.9426 


•9743 


•3541 


•5491 


2.8239 


•4509 


30 


'•2305 


0-3432 


40 


■3365 


•5270 


.9417 


•9739 


•3574 


•5531 


2.7980 


.4469 


20 


1.2275 


0.3462 


50 


•3393 


•5306 


•9407 


•9734 


.3607 


•5571 


2.7725 


•4429 


10 


1.2246 


0.3491 


20°00' 


.3420 


9^5341 


•9397 


9-9730 


.3640 


9.561 1 


2.7475 


0.4389 


70°oo' 


1.2217 


0.3520 


10 


•3448 


•5375 


-9387 


.9725 


•3673 


.5650 


2.7228 


•4350 


50 


1.2188 


0-3549 


20 


•3475 


.5409 


•9377 


.9721 


.3706 


.5689 


2.6985 


•43" 


40 


1.2159 


0.3578 


30 


.3502 


•5443 


•9367 


•9716 


•3739 


•5727 


2.6746 


•4273 


30 


1. 2130 


0.3607 


40 


•3529 


•5477 


•9356 


.9711 


•3772 


•5766 


2.651 1 


•4234 


20 


1.2101 


0.3636 


SO 


•3557 


•5510 


■9346 


.9706 


.3805 


•5804 


2.6279 


.4196 


10 


1.2072 


0.3665 


2I°00' 


•3584 


9-5543 


•9336 


9.9702 


•3839 


9.5842 


2.6051 


0.4158 


69°oo' 


1.2043 


0.3694 


10 


.3611 


•5576 


-9325 


.9697 


.3872 


•5879 


2.5826 


.4121 


50 


1. 2014 


0.3723 


20 


.3638 


.5609 


-9315 


.9692 


.3906 


•59 '7 


2.5605 


.4083 


40 


1-1985 


0.3752 


30 


•3665 


.5641 


•9304 


.9687 


•3939 


•5954 


2.5386 


.4046 


30 


1. 1956 


0.3782 


40 


.3692 


•5673 


•9293 


.9682 


•3973 


•5991 


2.5172 


.4009 


20 


1. 1926 


0.3S11 


50 


•3719 


•5704 


.9283 


.9677 


.4006 


.6028 


2.4960 


•3972 


10 


1. 1897 


0.3840 


22°00' 


■3746 


9^5736 


.9272 


9.9672 


.4040 


9.6064 


2.4751 


0^3936 


68°oo' 


1. 1868 


0.3869 


10 


•3773 


.5767 


.9261 


.9667 


•4074 


.6100 


2.4545 


.3900 


SO 


1.1839 


0.3898 


20 


.3800 


•5798 


-9250 


.9661 


.4108 


.6136 


2.4342 


•3864 


40 


1.1810 


0.3927 


30 


•3827 


•5828 


-9239 


•9656 


.4142 


.6172 


2.4142 


•3828 


30 


1.1781 


0.3956 


40 


■3854 


•5859 


.9228 


.9651 


.4176 


.6208 


2.3945 


•3792 


20 


1. 1752 


0.3985 


50 


.3881 


.5889 


.9216 


.9646 


.4210 


.6243 


2^3750 


•3757 


10 


1. 1723 


0.4014 


23°oo' 


-3907 


9.5919 


•9205 


9.9640 


.4245 


9.6279 


2^3559 


0.3721 


67°oo' 


1. 1694 


0.4043 


10 


•3934 


•5948 


•9 '94 


•9635 


.4279 


.6314 


2.3369 


.3686 


► 50 


1. 1665 


0.4072 


20 


.3961 


•5978 


.9182 


.9629 


•43 '4 


.6348 


2.3'83 


■3652 


40 


1.1636 


0.4102 


30 


•3987 


.6007 


.9171 


•9624 


•4348 


•6383 


2.2998 


•3617 


30 


1. 1606 


0.4131 


40 


.4014 


.6036 


-9 '59 


.9618 


•4383 


.6417 


2.2817 


•3583 


20 


1. 1577 


0.4160 


50 


.4041 


.6065 


•9 '47 


.9613 


.4417 


•6452 


2.2637 


•3548 


10 


1. 1548 


0.4189 


24°oo' 


.4067 


9.6093 


•9 '35 


9.9607 


•4452 


9.6486 


2.2460 


0.3514 


66°oo' 


1.1519 


0.4218 


10 


■4094 


.6121 


.9124 


.9602 


•4487 


.6520 


2.2286 


•3480 


50 


1.1490 


0.4247 


20 


.4120 


.6149 


.9(12 


•9596 


•4522 


•^553 


2.2113 


•3447 


40 


1. 1461 


0.4276 


30 


.4147 


.6177 


.9100 


.9590 


•4557 


.6587 


2.1943 


•34 '3 


30 


1.1432 


0.4305 


40 


.4173 


•6205 


.9088 


.9584 


•4592 


.6620 


2.1775 


•33S0 


20 


1. 1403 


0.4334 


50 


.4200 


.6232 


•9075 


•9579 


.4628 


.6654 


2.1609 


•3346 


10 


'•1374 


0.4363 


25°oo' 


.4226 


9-6259 


•9063 


9-9573 


.4663 


9.6687 


2.1445 


0.3313 


65°oo' 


'•'345 


0.4392 


10 


•4253 


.6286 


.9051 


.9567 


.4699 


.6720 


2.1283 


.3280 


50 


1.1316 


0.4422 


20 


•4279 


•6313 


•9038 


.9561 


•4734 


.6752 


2.1123 


•3248 


40 


1. 1286 


0.4451 


30 


•4305 


.6340 


.9026 


•9555 


•4770 


•6785 


2.0965 


•3215 


30 


1.1257 


0.4480 


40 


•4331 


.6366 


.9013 


•9549 


.4S06 


.68 1 7 


2.0809 


•3 '83 


20 


1.1228 


0.4509 


50 


•4358 


.6392 


.9001 


•9543 


.4841 


.6850 


2.0655 


•3 '50 


10 


1.1199 


04538 


26°oo' 


•4384 


9.6418 


.8988 


9-9537 


-4877 


9.6882 


2.0503 


0.3118 


64°oo' 


1.1170 


0.4567 


10 


.4410 


•6444 -8975 


•9530 


•49 '3 


.6914 


2-0353 


.30S6 


50 


1. 1141 


0.4596 


20 


■4436 


.6470 


.8962 


•9524 


.4950 


.6946 


2.0204 


•3054 


40 


1. 1112 


0.4625 


30 


.4462 


•6495 


.8949 


.9518 


.4986 


.6977 


2.0057 


•3023 


30 


1.1083 


0.4654 


40 


.4488 


.6521 


.8936 


.9512 


.5022 


.7009 


1.9912 


.2991 


20 


1. 1054 


0.4683 


50 


•4514 


.6546 


.8923 


•9505 


•5059 


.7040 


1.9768 


.2960 


10 


1. 1025 


0.4712 


27°oo' 


.4540 


9.6570 


.8910 


9.9499 


•5095 


9.7072 


1.9626 


0.2928 


63°oo' 


1.0996 






Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


tn 

1 u 




RADI- 
ANS. 


COSINES. 


SINES. 


COTAN- 
GENTS. 


TANGENTS, 



Smithsonian Tables. 



Table 1 3 (.continued). 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



35 



¥ 
«< 





SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 








Nat. Log. 


Nat. Log. 


Nat. Log. 


Nat. Log. 




0.4712 


27°oo' 


•4540 9-6570 


.8910 9.9499 


.5095 9.7072 


1.9626 0.2928 


63°oo' 


1.0996 




0.4741 


10 


.4566 .6595 


•8897 -9492 


.5132 .7103 


1.9486 .2897 


50 


1.0966 




0.4771 


20 


.4592 .6620 


.8884 .9486 


.5169 .7134 


1.9347 .2866 


40 


1-0937 




0.4S00 


30 


.4617 .6644 


.8870 .9479 


.5206 .7165 


1.9210 .2835 


30 


1.0908 




0.4S29 


40 


.4643 .6668 


.8857 .9473 


.5243 .7196 


1.9074 .2804 


20 


1.0S79 




0.4858 


50 


.4669 .6692 


.8843 -9466 


.5280 .7226 


1.8940 .2774 


10 


1.0850 




0.4887 


28°oo' 


.4695 9.6716 


.8829 9.9459 


-5317 9-7257 


1.8807 0.2743 


62°oo' 


1.0821 




0.4916 


10 


.4720 .6740 


-8816 .9453 


•5354 -7287 


1.8676 .2713 


so 


1.0792 




0.4945 


20 


-4746 .6763 


.8802 .9446 


•5392 .73^7 


1.8546 .2683 


40 


1.0763 




0.4974 


30 


.4772 .6787 


.8788 .9439 


.5430 .7348 


1.8418 .2652 


30 


1.0734 




0.5003 


40 


.4797 -6810 


•8774 -9432 


■5467 -7378 


1.8291 .2622 


20 


1.0705 




0.5032 


50 


-4823 .6833 


.8760 ,9425 


-5505 -7408 


1.8165 -2592 


10 


1.0676 




0.5061 


29°00' 


.4S48 9.6856 


.8746 9.9418 


-5543 9-7438 


1.8040 0.2562 


6i°oo' 


1.0647 




0.5091 


10 


.4S74 .6878 


-8732 -9411 


-5581 -7467 


1-7917 -2533 


50 


1.0617 




0.5120 


20 


.4899 .6901 


.8718 .9404 


.5619 .7497 


1.7796 .2503 


40 


1.05S8 




0.5149 


30 


.4924 .6923 


-8704 -9397 


.5658 .7526 


1.7675 .2474 


30 


1-0559 




0.5178 


40 


.4950 .6946 


•8689 .9390 


.5696 .7556 


1.7556 .2444 


20 


1.0530 




0.5207 


50 


•4975 -6968 


-8675 -9383 


-5735 -7585 


1.7437 .2415 


10 


1.0501 




0.5236 


30°oo' 


.5000 9.6990 


.8660 9.9375 


-5774 9-7614 


I.7321 0.2386 


do'oo' 


1.0472 




0.5265 


10 


.5025 .7012 


.8646 .9368 


.5812 .7644 


1.7205 .2356 


50 


1.0443 




0.5294 


20 


.5050 .7033 


.8631 .9361 


•5851 -7673 


1.7090 .2327 


40 


1.0414 




0'5323 


30 


-5075 -7055 


.8616 .9353 


.5890 .7701 


1.6977 -2299 


30 


1.0385 




0-5352 


40 


.5100 .7076 


.8601 .9346 


-5930 -7730 


1.6S64 .2270 


20 


1-0356 




o-53«i 


50 


.5125 .7097 


•8587 -9338 


-5969 -7759 


1.6753 -2241 


10 


1.0327 




0.541 1 


3i°oo' 


.5150 9.7118 


•8572 9-9331 


.6009 9.7788 


1.6643 0.2212 


59°oo' 


1.0297 




0.5440 


10 


•5'75 -7139 


■8557 -9323 


.6048 .7816 


1.6534 .2184 


50 


1.0268 




0.5469 


20 


.5200 .7160 


-8542 .93.15 


.6088 .7845 


1.6426 .2155 


40 


1.0239 




0.5498 


30 


.5225 .7181 


.8526 .9308 


.6128 .7873 


1.6319 .2127 


30 


1. 02 10 




0.5527 


40 


.5250 .7201 


.8511 .9300 


.6168 .7902 


1.6212 .2098 


20 


1.0181 




0-5556 


50 


.5275 .7222 


.8496 .9292 


.6208 .7930 


1.6107 .2070 


10 


1.0152 




0-5585 


32°00' 


.5299 9.7242 


.8480 9.9284 


•6249 9-7958 


1.6003 0.2042 


58°oo' 


1.0123 




0.5614 


10 


.5324 .7262 


.8465 .9276 


.6289 .7986 


1.5900 .2014 


50 


1.0094 




0.5643 


20 


.5348 .7282 


.8450 .9268 


.6330 .8014 


1.5798 .1986 


40 


1.0065 




0.5672 


30 


-5373 -7302 


.8434 .9260 


.6371 .8042 


1-5697 -1958 


30 


1 .0036 




0.5701 


40 


-5398 -7322 


.8418 .9252 


.6412 .8070 


1-5597 -1930 


20 


1 .0007 




0-5730 


50 


.5422 .7342 


.8403 .9244 


.6453 .8097 


1.5497 .1903 


10 


0.9977 




0.5760 


33000' 


-5446 9-7361 


-8387 9-9236 


.6494 9.8125 


1.5399 0.1875 


57°oo' 


0.9948 




0.5789 


10 


.5471 -7380 


.8371 .9228 


.6536 .8153 


1. 5301 .1847 


50 


0.9919 




0.5S18 


20 


.5495 .7400 


-8355 -9219 


.6577 .8180 


1.5204 .1820 


40 


0.9S90 




0.5847 


30 


-5519 -7419 


•8339 -9211 


.6619 .8208 


1.5108 .1792 


30 


0.9S61 




0.5876 


40 


-5544 -7438 


.8323 .9203 


.6661 .8235 


1.5013 .1765 


20 


0.9832 




0-5905 


50 


.5568 .7457 


•8307 -9194 


.6703 .8263 


1.4919 .1737 


10 


0.9803 




0-5934 


34°oo' 


-5592 9-7476 


.8290 9.9186 


.6745 9.8290 


1.4826 0.1710 


56°oo' 


0.9774 




0.5963 


10 


.5616 .7494 


.8274 .9177 


-6787 .8317 


1.4733 -1683 


50 


0.9745 




0.5992 


20 


.5640 .7513 


.8258 .9169 


.6830 .8344 


1.464 1 .1656 


40 


0.9716 




0.602 1 


30 


.5664 .7531 


.8241 .9160 


-6873 -8371 


1.4550 .1629 


30 


0.9687 




0.6050 


40 


.5688 .7550 


.8225 .9151 


.6916 .8398 


1.4460 .1602 


20 


0.9657 




0.6080 


50 


.5712 .7568 


.8208 .9142 


.6959 .8425 


1-4370 .1575 


10 


0.9628 




0.6109 


35°oo' 


-5736 9-7586 


.8192 9.9134 


.7002 9.8452 


1.4281 0.1548 


S5°oo' 


0.9599 




0.6138 


10 


.5760 .7604 


.8175 .9125 


.7046 .8479 


1.4193 .1521 


50 


0.9570 




0.6167 


20 


.5783 .7622 


.8158 .9116 


.7089 .8506 


1.4106 .1494 


40 


0.9541 




0.6196 


30 


.5807 .7640 


.8141 .9107 


-7133 -8533 


1.4019 .1467 


30 


0.9512 




0.6225 


40 


-5831 -7657 


.8124 .9098 


-7177 -8559 


1.3934 .1441 


20 


0.9483 




0.6254 


50 


-5854 .7675 


.8107 .9089 


.7221 .8586 


1.3848 .1414 


10 


0.9454 




0.6283 


36°oo' 


.5878 9.7692 


,8090 9.9080 


.7265 9.8613 


1.3764 0.1387 


S4°oo' 


0.9425 








Nat. Log. 


Nat. Log. 


Nat. Log. 


Nat. Log. 









COSINES. 


SINES. 


COTAN- 
GENTS. 


TANGENTS. 





Smithsonian Tables. 



36 



Table 1 3 [continued). 

CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



0.6283 
0.6312 
0.6341 
0.6370 
0.6400 
0.6429 

0.6458 
0.6487 
0.6516 
0.6545 
0.6574 
0.6603 

0.6632 
0.6661 
0.6690 
0.6720 
0.6749 
0.6778 

0.6807 
0.6836 
0.6S65 
0.6S94 
0.6923 
0.6952 

0.6981 
0.7010 
0.7039 
0.7069 
0.7098 
0.7127 

0.7156 
0.7185 
0.7214 

0.7243 
0.7272 
0.7301 

07330 
0.7359 
0.7389 
0.7418 

0-7447 
0.7476 

0.7505 
07 534 
0.7563 
0.7592 
0.7621 
0.7650 

0.7679 
0.7709 

0773'^ 
0.7767 
0.7796 
0.7825 

0.7854 



WW 

o 



^6°oo' 



30 

40 

50 

37°oo' 



30 
40 
50 
38°oo' 
10 
20 

30 
40 

50 

39°oo' 



40 
50 

40°oo' 
10 
20 
30 
40 
50 

4i°oo' 
10 
20 

30 
40 

50 

42°00' 

10 
20 

30 
40 

so 

43°oo' 
10 
20 
30 
40 
50 

44°oo' 



30 

40 

50 
45°oo' 



SINES. 



Nat. Log. 



5878 
5901 
5925 
5948 
5972 

5995 
6018 
6041 
6065 
60S8 
6111 
6134 
6157 
6180 
6202 
6225 
6248 
6271 

6293 
6316 
6338 
6361 

63S3 
6406 



9.7692 
.7710 
7727 
7744 
.7761 
7778 

97795 
.7811 

7828 

7844 
.7861 

7877 

97893 
.7910 
.7926 
7941 
7957 
7973 

97989 



.8020 
.8035 
.8050 
.8066 



6428 9.8081 

6450 .8096 

6472 .Bin 

6494 -8125 

6517 .8140 

6539 -8155 

6561 9.8169 

6583 .8184 

6604 .8198 

6626 .8213 

6648 .8227 

6670 .8241 

6691 9.8255 

6713 .8269 

6734 -8283 

6756 .8297 

6777 .8311 

6799 .8324 

6820 9.8338 

6841 .8351 

6862 .8365 

6884 .8378 

6905 -8391 

6926 .8405 

6947 9.8418 

6967 .8431 

69S8 .8444 

7009 .8457 

7030 .8469 

7050 .8482 

7071 9.849s 



Nat. Log. 



COSINES. 



COSINES. TANGENTS. 



Nat. Log. Nat. Log. 



,8ogo g.9080 

,8073 .9070 

,8056 .9061 

8039 .9052 

,8021 .9042 

,8004 .9033 

7986 9.9023 

7969 .9014 

,7951 .9004 

7934 -8995 

7916 .8985 

7898 .8975 

,7880 9.8965 

7S62 .8955 

7844 .8945 

7826 .8935 

7808 .8925 

7790 -8915 

7771 9.8905 

7753 -8895 

7735 -8884 

7716 .8874 

7698 .8864 

7679 .8853 

7660 9.8843 

7642 .8832 

,7623 .8821 

7604 .8810 

7585 .8800 

7566 .8789 

7547 9-8778 

.7528 .8767 

7509 -8756 

7490 .8745 

7470 .8733 

,7451 .8722 

7431 9.87 1 1 

7412 .8699 

7392 .8688 

7373 -8676 

7353 -8665 

73Z2, -8653 

.7314 9.8641 

,7294 .8629 

.7274 .8618 

.7254 .8606 

,7234 .8594 

.7214 .8582 

7193 9-8569 

7173 -8557 

■7153 -8545 

7133 -8532 

.7112 .8520 

.7092 .8507 

.7071 9.8495 



Nat Log. 



SINES. 



7265 

7310 

7355 
7400 

7445 
7490 

7536 

7581 
7627 

7673 
7720 
7766 

7813 
7860 

7907 
7954 
8002 
8050 



9-8613 
.8639 
.8666 
.8692 
.8718 
.8745 

9.8771 

•8797 
.8824 
.8850 
.8876 
.8902 

9.8928 

•8954 
.8980 
.9006 
.9032 
.9058 

9.9084 
.9110 

•9135 
.9161 
.9187 
.9212 

9.9238 
.9264 
.92S9 
-9315 
•9341 
.9366 

9.9392 
.9417 

•9443 
.9468 

•9494 
•9519 

9-9544 
•9570 

•9595 
.9621 
.9646 
.9671 

9.9697 
.9722 

•9747 
.9772 
.9798 
•9823 
9.9848 

•9874 
.9899 
.9924 
•9949 
•9975 
1. 0000 0.0000 



8146 
8195 
8243 
8292 

8342 

8391 
8441 
8491 
8541 
8591 
8642 

8693 

8744 
8796 
8847 
8899 
8952 

9004 

9057 
9110 
9163 
9217 
9271 

9325 
9380 

9435 
9490 

9545 
9601 

9657 

9713 
9770 
9827 
9884 
9942 



Nat. Log. 



COTAN- 
GENTS, 



COTANGENTS 



Nat. Log. 



3764 
3680 

3597 
3514 
3432 
3351 
3270 
3190 
31II 

3032 
2954 
2876 

2799 
2723 
2647 
2572 
2497 
2423 

2349 
2276 
2203 
2131 
2059 
1988 

1918 

1847 
1778 
1708 
1640 
1571 

1504 
1436 
1369 

1303 
1237 
II71 

1 106 
IO41 
0977 

0913 
0850 
0786 

0724 
0661 
0599 
0538 
0477 
0416 

035s 
0295 

0235 
0176 
0117 

.0058 

0000 



0.1387 
.1361 

•1334 

.130S 
.1282 
.1255 

0.1229 
.1203 
.1176 
.1150 
.1124 
.1098 

0.1072 
.1046 
.I020 

•0994 
.O96S 
.0942 

0.0916 
.0890 
.0865 
.0839 
.0813 
.0788 

0.0762 
.0736 
.0711 
.0685 
.0659 
.0634 

0.0608 
•0583 
•0557 
•0532 
.0506 
.O4S1 

0.0456 
.0430 
.0405 
•0379 
•0354 
•0329 

0.0303 
.0278 

•0253 
.O22S 
.0202 
.0177 

0.0152 
.0126 
.0101 
.0076 
•0051 
.0025 

0.0000 



Nat. Log. 



TANGENTS. 



54"oo' 

50 
40 

30 
20 
10 

53°oo' 

50 
40 

30 
20 
10 

52°00' 

50 
40 
30 

20 

10 

5i°oo' 

50 

40 



ID 

5o°oo' 
50 
40 



10 

49°oo' 

50 
40 

30 
20 
10 

48°oo' 

50 
40 
30 
20 
10 

47°oo' 

50 
40 

30 
20 
10 

46°oo' 

50 
40 



10 



45"oo' 



t/5 

wa 
o 



Smithsonian Tables. 



Table 14. 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



< 

s 

< 


SINES. 


COSINES. 


TANGENTS 


COTANGENTS. 


w 
w 


w 
Q 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


o.oo 


0.00000 


— 00 


1 .00000 


0.00000 


— 00 


— 00 


C<3 


00 


oo°oo' 


.01 


.01000 


7.99999 


0.99995 


9.99998 


0.0 1 000 


8.00001 


99.997 


1.99999 


0034 


.02 


.02000 


8. 30 1 00 


.99980 


.99991 


.02000 


.30109 


49-993 


.69891 


01 09 


•03 


.03000 


.47706 


•99955 


.99980 


.03001 


•47725 


33^323 


.52275 


01 43 


.04 


.03999 


.60194 


.99920 


.99965 


.04002 


.60229 


24.9S7 


.39771 


02 18 


0.05 


0.04998 


8.69879 


0.99875 


9.99946 


0.05004 


8^69933 


19.983 


1.30067 


02°52' 


.06 


.05996 


•77789 


.99820 


.99922 


.06007 


•77867 


16.647 


•22133 


03 26 


.07 


.06994 


•84474 


•99755 


.99894 


.07011 


.84581 


14.262 


.15419 


04 01 


.08 


■07991 


.90263 


.99680 


.99S61 


.08017 


.90402 


12.473 


.09598 


0435 


.09 


.08988 


•95366 


•99595 


.99S24 


.09024 


•95542 


II. 08 1 


.04458 


0509 


O.IO 


0.09983 


8.99928 


0.99500 


9.99782 


0.10033 


9.00145 


9.9666 


0-99855 


05°44' 


.1 1 


.10978 


9.04052 


.99396 


•99737 


.11045 


•04315 


9-0542 


•95685 


06 18 


.12 


.11971 


.07814 


.99281 


.996S7 


.12058 


.08127 


8-2933 


.91873 


06 53 


•13 


.12963 


.1 1272 


.99156 


.99632 


■13074 


.11640 


7.6489 


.8S360 


07 27 


.14 


•13954 


.14471 


.99022 


•99573 


.14092 


.14S98 


7.0961 


.85102 


08 01 


0.15 


0.14944 


9.17446 


0.98877 


9.99510 


O.15114 


9^17937 


6.6166 


0.82063 


oS°36' 


.16 


•15932 


.20227 


•98723 


.99442 


.16138 


.20785 


6.1966 


.79215 


09 10 


•17 


.16918 


.22836 


.98558 


•99369 


.17166 


.23466 


5-8256 


•76534 


0944 


.18 


•17903 


•25292 


•98384 


•99293 


.18197 


.26000 


5-4954 


.74000 


10 19 


.19 


.18886 


.27614 


.98200 


.99211 


.19232 


.28402 


5.1997 


.71598 


10 53 


0.20 


C.19867 


9.29813 


0.9S007 


9.99126 


0.20271 


9.30688 


4-9332 


0.69312 


II°28' 


.21 


.20846 


.31902 


•97803 


•99035 


.21314 


.32867 


4.6917 


•67133 


12 02 


.22 


.21823 


■33891 


•97590 


.9S940 


.22362 


•34951 


4.4719 


.65049 


1236 


■23 


.22798 


•35789 


•97367 


.98841 


•23414 


.36948 


4.2709 


.63052 


13 II 


.24 


.23770 


■37603 


•97134 


• ^98737 


.24472 


.38866 


4.0864 


.61134 


1345 


0.25 


0.24740 


939341 


0.96S91 


9.98628 


©■25534 


9.40712 


3-9163 


0.59288 


I4°i9' 


.26 


.25708 


.41007 


.96639 


•98515 


.26602 


.42491 


3-7592 


•57509 


14 54 


.27 


.26673 


.42607 


•96377 


•98397 


.27676 


.44210 


3-6133 


•55790 


1528 


.28 


.27636 


.44147 


.96106 


•98275 


.28755 


.45872 


3-4776 


.54128 


1603 


.29 


.28595 


.45629 


•95824 


.98148 


.29841 


.47482 


3-35II 


•52518 


1637 


0.30 


0.29552 


947059 


0^95534 


9.98016 


©■ 30934 


9.49043 


3-2327 


0.50957 


i7°ii' 


•31 


.30506 


.48438 


■95233 


.97879 


.32033 


•50559 


3.1218 


.49441 


17 46 


•32 


•31457 


■49771 


.94924 


■97737 


•33139 


•52034 


3.0176 


.47966 


18 20 


•33 


.32404 


.51060 


.94604 


•97591 


•34252 


•53469 


2.9195 


.46531 


18 54 


•34 


•33349 


■52308 


•94275 


•97440 


•35374 


.54868 


2.8270 


.45132 


1929 


0-35 


0.34290 


9-53516 


0-93937 


9.97284 


0.36503 


9-56233 


2-7395 


0.43767 


20°03' 


•36 


•35227 


.546S8 


•93590 


■97123 


.37640 


•57565 


2.6567 


•42435 


20 38 


•37 


.36162 


.55825 


•93233 


■96957 


.38786 


.58868 


2.5782 


•4''32 


21 12 


•38 


.37092 


.56928 


.92866 


.967S6 


•39941 


.60142 


2.5037 


•39858 


21 46 


•39 


.38019 


.58000 


.92491 


.96610 


.41105 


.61390 


2.432S 


.38610 


22 21 


0.40 


0.38942 


9.59042 


0.92106 


9.96429 


0.42279 


9.62613 


2.3652 


0^37387 


22°55' 


.41 


.39861 


.60055 


.91712 


■96243 


.43463 


.63812 


2.3008 


.36188 


23 29 


.42 


.40776 


.61041 


.91309 


.96051 


■44657 


.64989 


2-2393 


.35011 


24 04 


•43 


.41687 


.62000 


.90897 


■95855 


.45862 


.66145 


2.1804 


•33855 


24 38 


•44 


•42594 


•62935 


•90475 


•95653 


.47078 


.67282 


2.1241 


.32718 


25 13 


0.45 


0.43497 


9-63845 


0.90045 


9.95446 


0.48306 


9.68400 


2.0702 


0.31600 


25°47' 


.46 


•44395 


•64733 


.89605 


•95233 


.49545 


.69500 


2.0184 


.30500 


26 21 


•47 


.45289 


•65599 


•89157 


•95015 


.50797 


.70583 


1.9686 


.29417 


26 56 


.48 


.46178 


.66443 


.8S699 


.94792 


.52061 


.71651 


1.9208 


.2S349 


27 30 


•49 


•47063 


.67268 


.88233 


•94563 


•53339 


.72704 


1.8748 


.27296 


28 04 


50 


0-47943 


9.68072 


0.87758 


9-94329 


0.54630 


9^73743 


1-8305 


0.26257 


28°39' 



Smithsonian Tables. 



38 



Table 1 4 (^continued). 

CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



< 

s 

< 

'A 


SINES. 


COSINES. 


TANGENTS 


COTANGENTS. 


w 
w 



w 
Q 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


0.50 


0-47943 


9.6807 2 


0.87758 


9-94329 


0.54630 


9-73743 


1.8305 


0.26257 


28°39' 


•SI 


.48818 


.68858 


•87274 


.94089 


•55936 


.74769 


.7878 


•2523' 


29 13 


•52 


.496S8 


.69625 


.86782 


•93843 


-57256 


.75782 


•7465 


.242.8 


2948 


•S3 


•50553 


•70375 


.86281 


•9359' 


•58592 


.76784 


.7067 


.23216 


30 22 


•54 


.51414 


.71108 


.85771 


•93334 


•59943 


•77774 


.6683 


.22226 


3056 


0.55 


0.52269 


9-71824 


0.85252 


9.93071 


0-61311 


9-78754 


I.6310 


0.21246 


3i°3i' 


.56 


•53' 19 


•72525 


.84726 


.9280. 


.62695 


•79723 


•5950 


.20277 


3205 


•57 


•53963 


.732.0 


.84.90 


.92526 


-64097 


.806S4 


.5601 


.193.6 


32 40 


.58 


.54802 


.73880 


.83646 


.92245 


•655'7 


•81635 


•5263 


•18365 


Zi 14 


•59 


•55636 


•74536 


.83094 


•9'957 


.66956 


.82579 


•4935 


.17421 


3348 


0.60 


0.56464 


9^75177 


0.82534 


9.9.663 


0.68414 


9-83514 


1. 461 7 


0.16486 


34°23' 


.61 


•572S7 


•75805 


.81965 


•91363 


.69892 


•84443 


.4308 


•15557 


34 57 


.62 


.58104 


.76420 


.81388 


.91056 


•7 '39' 


•85364 


.4007 


.14636 


35 3' 


.63 


•58914 


.77022 


.80803 


•90743 


.72911 


.86280 


•37 '5 


.13720 


3606 


.64 


.59720 


.77612 


.80210 


.90423 


•74454 


.87189 


•3431 


.12811 


3640 


0.65 


0.60519 


9.7S189 


0.79608 


9.90096 


0.76020 


9.88093 


'•3'54 


O.I 1907 


37°i5' 


.66 


.6.3.2 


•78754 


.78999 


.89762 


.77610 


.88992 


.2885 


.11008 


37 49 


.67 


.62099 


.79308 


.78382 


.89422 


.79225 


.89S86 


.2622 


.101.4 


3823 


.68 


.62879 


.79851 


•77757 


.89074 


.80866 


•90777 


•2366 


.09223 


38 58 


.69 


.63654 


.80382 


.77125 


.88719 


•82534 


.91663 


.21.6 


•08337 


3932 


0.70 


0.64422 


9.80903 


0.76484 


9.88357 


0.84229 


9-92546 


1. 1872 


0-07454 


40°o6' 


•71 


•65183 


.8.414 


•75836 


.87988 


•85953 


•93426 


.1634 


•06574 


4041 


•72 


•65938 


.8.914 


.75181 


.87611 


.87707 


•94303 


.1402 


.05697 


4. 15 


■11 


.66687 


.82404 


•74517 


.87226 


.89492 


.95.78 


-1174 


.04822 


41 50 


•74 


.67429 


.82885 


•73847 


•86S33 


•9 '309 


■ -96051 


•0952 


.03949 


42 24 


0.75 


0.68.64 


9-83355 


0-73169 


9-86433 


0.93160 


9.96923 


I -0734 


0.03077 


42°58' 


.76 


.68892 


.838.7 


•72484 


.86024 


.95045 


•97793 


.0521 


.02207 


43 33 


•77 


.69614 


.84269 


.71791 


.85607 


.96967 


.98662 


•0313 


•01338 


44 07 


•78 


.70328 


•84713 


.71091 


.85182 


.98926 


9-9953' 


1.0.09 


.00469 


44 41 


•79 


•71035 


•85147 


•70385 


.84748 


1 .0092 


0.00400 


0.99084 


9.99600 


45 16 


0.80 


0.71736 


9-85573 


0.69671 


9-84305 


1.0296 


0-0 1 2 68 


0.97 1 21 


9.98732 


45°So' 


.81 


.72429 


.85991 


•68950 


•83853 


-0505 


.02.38 


•95197 


.97862 


46 25 


.82 


•7311S 


.86400 


.68222 


•83393 


.0717 


.03008 


•93309 


.96992 


46 59 


•83 


•73793 


.86802 


.67488 


.82922 


•0934 


•03879 


•9'4S5 


.9612. 


47 33 


.84 


.74464 


.87.95 


.66746 


.82443 


.1156 


.04752 


•89635 


•95248 


48 08 


0.85 


0.75.28 


9.87580 


0.65998 


9^8i953 


1-1383 


0.05627 


0.87848 


9^94373 


48°42' 


.86 


•75784 


.87958 


.65244 


.8.454 


.16.6 


.06504 


.86091 


•93496 


49 16 


.87 


•76433 


.88328 


.64483 


.80944 


■1853 


•07384 


•^^^5 


.926.6 


49 51 


.88 


•77074 


.88691 


•63715 


.80424 


.2097 


.08266 


.82668 


•9'734 


5025 


.89 


.77707 


.89046 


.62941 


.79894 


.2346 


•09153 


.80998 


.90847 


5' 00 


0.90 


0-78333 


9-89394 


0.62 161 


9-79352 


1.2602 


0.10043 


0^79355 


9-89957 


5'°34' 


.91 


•78950 


•89735 


•61375 


.78799 


.2864 


•10937 


•77738 


.89063 


52 08 


.92 


.79560 


.90070 


.60582 


.78234 


•3133 


.1.835 


.76.46 


.88.65 


52 43 


■93 


.80.62 


•90397 


•59783 


.77658 


•3409 


•12739 


•74578 


.8726. 


53 17 


•94 


.80756 


.90717 


.58979 


.77070 


.3692 


.13648 


•73034 


•86352 


53 51 


0.95 


0.81342 


9.91031 


0.58168 


9.76469 


1-3984 


0.14563 


0-715" 


9-85437 


54°26' 


.96 


.81919 


•91339 


•57352 


•75855 


.42S4 


• 154S4 


.70010 


.84516 


5500 


•97 


.82489 


.91639 


•56530 


.75228 


.4592 


..6412 


•68531 


.83588 


55 35 


.98 


.83050 


•91934 


•S5702 


•74587 


.49.0 


•17347 


.67071 


•82653 


5609 


•99 


•83603 


.92222 


.54869 


•73933 


•5237 


.18289 


.65631 


.81711 


5643 


1. 00 


0.84147 


9.92504 


0.54030 


9.73264 


1-5574 


0-19240 


0.64209 


9.80760 


57°i8' 



Smithsonian Tables. 



Table 14 (continued). 
CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 



39 



< 

5 
< 


SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 





Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


I.OO 


0.84147 


9.92504 


0.54030 


9.73264 


1-5574 


0.19240 


0.64209 


9.80760 


57°i8' 


.OI 


.84683 


.92780 


.53186 


.725S0 


.5922 


.20200 


.62806 


.79800 


57 52 


.02 


.8521 1 


.93049 


■52337 


.71881 


.6281 


.21169 


.61420 


.78831 


58 27 


•03 


•85730 


•93313 


.51482 


.71165 


.6652 


.22148 


.60051 


•77852 


5901 


.04 


.86240 


•93571 


.50622 


•70434 


.7036 


■23137 


.58699 


.76863 


59 35 


1.05 


0.S6742 


9-93823 


0.49757 


9.69686 


'■7433 


0.24138 


0.57362 


9.75862 


60° 10' 


.06 


.87236 


.94069 


.48887 


.68920 


.7844 


■25150 


.56040 


.74850 


60 44 


.07 


.87720 


.94310 


.48012 


•68135 


.8270 


.26175 


.54734 


•73825 


61 18 


.oS 


.88196 


•94545 


•47133 


•67332 


.8712 


.27212 


.53441 


.72788 


61 53 


.09 


.88663 


•94774 


.46249 


.66510 


.9171 


.28264 


.52162 


.71736 


62 27 


1. 10 


0.891 2 1 


9.94998 


0.45360 


9.65667 


1.9648 


o^2933i 


0.50897 


9.70669 


63°02' 


.11 


.89570 


.95216 


.44466 


.64803 


2.0143 


•30413 


.49644 


-69587 


6336 


.12 


.90010 


•95429 


.43568 


•63917 


.0660 


.31512 


.48404 


.68488 


64 10 


•13 


.90441 


•95f>37 


.42666 


.63008 


.1198 


.32628 


■47175 


.67372 


6445 


.14 


.90863 


•95839 


■41759 


.62075 


•1759 


'337(>3 


■45959 


.66237 


65 19 


1. 15 


0.91276 


9.96036 


0.40849 


9.61 118 


2-2345 


0.34918 


0-44753 


9.65082 


65°53' 


.16 


.91680 


.96228 


•39934 


■60134 


.2958 


•36093 


•43558 


•63907 


66 28 


•17 


•92075 


.96414 


•39015 


•59123 


.3600 


•37291 


•42373 


.62709 


67 02 


.18 


.92461 


.96596 


.38092 


•58084 


•4273 


.385.2 


.41199 


.61488 


67 37 


.19 


.92837 


.96772 


.37166 


•57015 


■4979 


•39757 


■40034 


.60243 


68 II 


1.20 


0.93204 


9-96943 


0.36236 


9-55914 


2.5722 


0.41030 


0.38878 


9.58970 


68°45' 


.21 


.93562 


.97110 


•35302 


.54780 


•6503 


■42330 


■3773^ 


■57670 


69 20 


.22 


.93910 


.97271 


•34365 


•5361 1 


.7328 


.43660 


•36593 


•56340 


69 54 


•23 


.94249 


.97428 


•33424 


.52406 


.8198 


•45022 


•35463 


•54978 


70 28 


.24 


•94578 


•97579 


.32480 


.51161 


.9119 


.46418 


-34341 


•53582 


71 03 


1.25 


0.94898 


9.97726 


0-31532 


9.4987 s 


3.0096 


0.47850 


0.33227 


9-52150 


7i°37' 


.26 


.95209 


.97868 


■30582 


.48546 


■1133 


.49322 


.32121 


.50678 


72 12 


.27 


.95510 


.98005 


.29628 


.47170 


.2236 


•50835 


.31021 


-49165 


72 46 


.28 


.95802 


•98137 


.28672 


•45745 


•3413 


■52392 


.29928 


.47608 


73 20 


.29 


.960S4 


.98265 


.27712 


.44267 


.4672 


-53998 


.28842 


.46002 


73 55 


1.30 


0.96356 


9.98388 


0.26750 


9.42732 


3.6021 


0.55656 


0.27762 


9-44344 


74°29' 


•31 


.96618 


.98 506 


•25785 


•41 137 


•7471 


■57369 


.26687 


.42631 


7503 


•32 


.96872 


.98620 


.24818 


•39476 


•9033 


.59144 


.25619 


.40856 


7538 


•33 


•971 15 


.98729 


.23848 


•37744 


4-0723 


.60984 


•24556 


.39016 


76 12 


•34 


•97348 


•98833 


.22875 


•35937 


•2556 


.62896 


•23498 


•37104 


7647 


1-35 


0.97572 


9-98933 


0.21901 


9.34046 


4-4552 


0.64887 


0.22446 


9-35113 


77°2i' 


•36 


.97786 


.99028 


.20924 


.32064 


•6734 


.66964 


.21398 


■33036 


77 55 


•37 


.97991 


.99119 


.19945 


.29983 


•9131 


•69135 


■20354 


■30865 


78 30 


•38 


.981S5 


•99205 


.18964 


■27793 


5-1774 


.71411 


•19315 


.28589 


7904 


•39 


.98370 


.99286 


.17981 


.25482 


•4707 


.73804 


.18279 


.26196 


7938 


1.40 


0.98545 


9-99363 


0. 1 6997 


9.23036 


5-7979 


0.76327 


0.17248 


9-23673 


8o°i3' 


.41 


.98710 


•99436 


.16010 


.20440 


6.1654 


.78996 


.16220 


.21004 


8047 


.42 


.98S65 


.99504 


■15023 


.17674 


6.5811 


.81830 


•15195 


.18170 


81 22 


•43 


.99010 


.99568 


■ 14033 


.14716 


7-0555 


■84853 


•14173 


.15147 


81 56 


■44 


.99146 


.99627 


.13042 


•11536 


7.6018 


.88092 


•13155 


.11908 


82 30 


1.45 


0.99271 


9.99682 


0.12050 


9.08100 


^o-'^^ll 


0.91583 


0.12139 


9.08417 


83°os' 


.46 


•99387 


•99733 


.11057 


.04364 


8.9886 


■95369 


.11125 


.04631 


8339 


•47 


.99492 


.99779 


.10063 


.00271 


9.8874 


•99508 


.10114 


.00492 


84 13 


.48 


•99588 


.99821 


.09067 


8.95747 


10.983 


1.04074 


.09105 


8.95926 


84 48 


.49 


.99674 


.99858 


.0807 1 


.90692 


12.350 


.09166 


.08097 


.90834 


8522 


1.50 


0.99749 


9.99891 


0.07074 


8.84965 


I4.IOI 


1. 14926 


0.07091 


8.85074 


85°57' 



Smithsonian Tables. 



40 



Tables 1 4 {continued) AND 1 5. 

CIRCULAR FUNCTIONS AND FACTORIALS. 

TABLE 14 {continued). — Circular (Trigonometric) Functions. 





z 

< 


SINES. 


COSINES. 


TANGENTS. 


COTANGENTS. 


W 


a 

Q 


< 


Nat. 


Log 


Nat. 


Log 


Nat. 


Log. 


Nat. 


Log. 


1.50 


0.99749 


9.99891 


0.07074 


8.S4965 


I4.IOI 


1. 1 4926 


0.07091 


8.85074 


85°57' 




51 


.99S15 


.99920 


.06076 


.78361 


16.428 


•21559 


.06087 


•78441 


8631 




S2 


.99871 


.99944 


.05077 


•70565 


19.670 


•29379 


.05084 


.70621 


87 05 




S.l 


.99917 


.99964 


.04079 


.61050 


24.498 


.38914 


.040S2 


.610S6 


87 40 




54 


•99953 


•99979 


.03079 


.48843 


32.461 


.51136 


.030S1 


.48S64 


88 14 


I 


ss 


0.99978 


9.99991 


0.02079 


8.31796 


48.078 


1. 68 1 95 


O.O20S0 


8.31805 


88°49' 




Sb 


0.99994 


9.99997 


.01080 


8.03327 


92.621 


1.96671 


.oioSo 


8.03329 


8923 




S7 


[ .00000 


0.00000 


.00080 


6.90109 


1255.8 


3.09891 


.00080 


6.90109 


«9 57 




S« 


0.99996 


9.9999S 


-.00920 


7.9639611 


108.65 


2.03603 


-.00920 


7.9639711 


90 32 




59 


0.99982 


9.99992 


-.01920 


8.2833611 


52.067 


1.71656 


-.01921 


8.28344n 


91 06 


1.60 


0-99957 


9.99981 


-0.02920 


8.4653811 


34-233 


1-53444 


-0.02921 


8.46556:1 


9i°4o' 



90°= 1.570 7963 radians. 



TABLE 15. — Logarithmic Factorials. 

Logarithms of the products 1.2.3 '^ '' from i to 100. 

See Table 17 for Factorials i to 20. 
See Table 31 for log. r (« + 0? values of n between i and 2. 



1 


log («.') 


n. 


log («.') 


n. 


log («.') 


«. 


log («.') 


0.000000 


26 


26.605619 


51 


66.190645 


76 


111.275425 


2 


0.301030 


27 


28.036983 


52 


67.906648 


77 


113.161916 


3 


0.778I5I 


28 


29.484141 


S3 


69.630924 


78 


II 5.05401 1 


4 


1.380211 


29 


30.946539 


S4 


71-363318 


79 


116.951638 


5 


2.079181 


30 


32.423660 


55 


73.103681 


80 


118.854728 


6 


2-857332 


31 


33.915022 


56 


74.851869 


81 


120.763213 


7 


3-702431 


32 


35.420172 


S7 


76.607744 


82 


122.677027 


8 


4.605521 


33 


36.9386S6 


S8 


78.371172 


83 


124.596105 


Q 


5-559763 


34 


38.470165 


59 


80.142024 


84 


126.520384 


10 


6^559763 


35 


40.014233 


60 


81.920175 


85 


128.449803 


11 


7.60II56 


36 


41.57053s 


61 


83-705505 


86 


130-384301 


12 


8-680337 


37 


43-138737 


62 


85.497896 


87 


132.323821 


13 


9.794280 


38 


44.718520 


63 


87-297237 


88 


134.268303 


14 


10.940408 


39 


46.309585 


64 


89.103417 


89 


136.217693 


15 


12.116500 


40 


47.911645 


65 


90.916330 


90 


138.171936 


16 


13.320620 


41 


49.524429 


66 


92-735874 


91 


140.130977 


17 


14.551069 


42 


51.147678 


67 


94.561949 


92 


142.094765 


18 


15.806341 


43 


52.781147 


68 


96-394458 


93 


144.063248 


iq 


17.085095 


44 


54-424599 


69 


98-233307 


94 


146.036376 


20 


18.386125 


45 


56.077812 


70 


100.078405 


95 


148.0x4099 


21 


19.708344 


46 


57.740570 


71 


101.929663 


96 


149-996371 


22 


21.050767 


47 


59.412668 


72 


103.786996 


97 


I5I.9S3142 


23 


22.412494 


48 


61.093909 ! 


73 


105.650319 


98 


153-974368 


24 


23.792706 


49 


62.784105 


74 


107.519550 


99 


155.970004 


25 


25.190646 


50 


64.483075 


75 


109.394612 


100 


157.970004 



Smithsonian Tables. 



Table 1 6. 
HYPERBOLIC FUNCTIONS. 



41 





sin 


1. u 


cosh, u 


tan 


h. u 


coth. u 


gd u 


u 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


0.00 


0.00000 


00 


1. 00000 


0.00000 


0.00000 


00 


00 


00 


oo°oo' 


.OI 


.01000 


8.00001 


.00005 


.00002 


.01000 


7.99999 


100.003 


2.00001 


34 


.02 


.02000 


.30106 


.00020 


.00009 


.02000 


8.30097 


50.007 


1.69903 


I 09 


■03 


.03000 


•47719 


.00045 


.00020 


.02999 


.47699 


33^343 


1-52301 


I 43 


.04 


.04001 


.60218 


.00080 


.00035 


.03998 


.60183 


25.013 


1. 398 1 7 


2 17 


0.05 


0.05002 


8.69915 


I.OOI25 


0.00054 


0.04996 


8.69861 


20.017 


1. 30 1 39 


2 52 


.06 


.06004 


.77841 


.00180 


.00078 


•05993 


-77763 


16.687 


.22237 


3 26 


.07 


.07006 


.84545 


.00245 


.00106 


.06989 


.84439 


14.309 


.15561 


4 00 


.08 


.08009 


•90355 


.00320 


•00 1 39 


.07983 


.90216 


12.527 


.09784 


4 35 


.09 


.09012 


•95483 


.00405 


.00176 


.08976 


•95307 


11. 141 


.04693 


5 09 


O.IO 


O.IOOI7 


9.00072 


1.00500 


0.00217 


0.09967 


8.99856 


10.0333 


1. 00 1 44 


5 43 i 


.11 


.11022 


.04227 


.00606 


.00262 


.10956 


9.03965 


9^1275 


0.96035 


6 17 


.12 


.12029 


.0S022 


.00721 


.00312 


•II943 


.07710 


8.3733 


.92290 


6 52 


•13 


■^3037 


.11517 


.00846 


.00366 


.12927 


.III5I 


7-7356 


.88849 


7 26 


.14 


.14046 


•14755 


.00982 


.00434 


.13909 


•14330 


7.189s 


•85670 


8 00 


0.15 


0.15056 


9.17772 


I.OII27 


0.00487 


0.14889 


9.17285 


6.7166 


O.S2715 


8 34 


.16 


. 1 6068 


.20597 


.01283 


.00554 


.15865 


.20044 


6.3032 


•79956 


9 08 


•17 


.I70S2 


•23254 


.01448 


.00625 


.16838 


.22629 


5^9389 


•77371 


9 42 


.18 


.1S097 


.25762 


.01624 


.00700 


.17808 


.25062 


5^6154 


•74938 


10 15 


.19 


.19115 


.28136 


.01810 


.00779 


.18775 


•27357 


53263 


•72643 


10 49 


0.20 


0.20134 


9.30392 


1.02007 


0.00863 


0.19738 


9.29529 


5.0665 


0.70471 


1 

II 23 


.21 


•2II55 


•32541 


.02213 


.00951 


.20697 


•3 '590 


4^83 1 7 


.68410 


II 57 


.22 


.22178 


•34592 


.02430 


.01043 


.21652 


•33549 


4.6186 


.66451 


12 30 


•23 


.23203 


•36555 


.02657 


.01139 


.22603 


•35416 


4.4242 


.64584 


13 04 


.24 


.24231 


•38437 


.02894 


.01239 


•23550 


•37198 


4.2464 


.62802 


13 37 


0.25 


0.25261 


9.40245 


I.0314I 


0-01343 


0.24492 


9.38902 


4.0S30 


0.61098 


14 II 


.26 


.26294 


.41986 


•03399 


.01452 


•25430 


•40534 


3^9324 


•59466 


14 44 


•27 


.27329 


•43663 


.03667 


.01564 


.26362 


.42099 


3^7933 


•S790I 


15 17 


.28 


•28367 


.452S2 


•03946 


.01 68 1 


.27291 


.43601 


36643 


•56399 


15 50 


.29 


.29408 


.46847 


•0423s 


.01801 


•282.3 


.45046 


3^5444 


•549S4 


16 23 


0.30 


0.30452 


9.48362 


1.04534 


0.01926 


O.29131 


9.46436 


3-4327 


0^53564 


16 56 


•31 


.31499 


.49830 


.04844 


.02054 


.30044 


•47775 


•3285 


•52225 


17 29 


1 .32 


•32549 


.51254 


.05164 


.02187 


•30951 


.49067 


•2309 


•50933 


18 02 


, -33 


.33602 


•52637 


•05495 


.02323 


•3'852 


•50314 


•1395 


.49686 


18 34 


•34 


•34659 


•53981 


.05836 


.02463 


•32748 


•51518 


•0536 


.48482 


19 07 


0.35 


0-35719 


9.55290 


r.o6i88 


0.02607 


0.33638 


9.52682 


2.9729 


0.47318 


19 39 


•36 


•367S3 


.56564 


.06550 


•02755 


•34521 


•53S09 


.8968 


.46191 


20 12 


•37 


•37S5O 


•57S07 


.06923 


.02907 


•35399 


.54899 


.8249 


.45101 


20 44 1 


1 .38 


.38921 


.59019 


•07307 


•03063 


•36271 


•55956 


•7570 


.44044 


21 16 


1 -39 


.39996 


.60202 


.07702 


.03222 


•37136 


.56980 


.6928 


.43020 


21 48 i 

1 


0.40 


0.41075 


9.61358 


1. 08107 


0-03385 


0-37995 


9-57973 


2.6319 


0.42027 


22 20 


■41 


.42158 


.62488 


•08523 


•03552 


.38847 


•58936 


•5742 


.41064 


22 52 


.42 


.43246 


•63594 


.08950 


•03723 


•39693 


.59871 


•5193 


.40129 


23 23 


.43 


•44337 


.64677 


.09388 


.03897 


•40532 


.60780 


.4672 


.39220 


23 55 


•44 


•45434 


•6573S 


.09837 


•04075 


.41364 


.61663 


■4175 


•38337 


24 26 


0.45 


0.46534 


9.66777 


1. 102970 


.04256 


0.42190 


9.62521 


2.3702 


0.37479 


24 57 ' 


.46 


.47640 


•67797 


.10768 


.04441 


.4300S 


•63355 


•3251 


.36645 


25 28 1 


•47 


.487 so 


.68797 


.11250 


.04630 


.43S20 


.64167 


.2821 


•35833 


25 59 1 


.48 


.49865 


.69779 


."743 


.04822 


.44624 


.64957 


.2409 


•35043 


26 30 


•49 


.50984 


•70744 


.12247 


.05018 


.45422 


.65726 


.2016 


•34274 


27 01 1 


0.50 


0.52110 


9.71692 


1. 12763 


0.05217 


0.46212 


9.66475 


2.1640 


0^33525 


27 31 i 

1 



Smithsonian Tables. 



42 



Table 1 6 {continued). 
HYBERBOLIC FUNCTIONS. 





sinh 


. u 


cosh 


. u 


tanh 


. u 


coth 


. u 






u 


















gd u 




Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 




0.50 


O.52IIO 


9.71692 


1. 12763 


0.05217 


0.46212 


9.66475 


2.1640 


0-33525 


27°3i' 


•51 


•53240 


.72624 


.13289 


.05419 


•46995 


.67205 


.1279 


•32795 


28 02 




1 -5- 


•54375 


•73540 


.13827 


.05625 


.47770 


.67916 


-0934 


.32084 


28 32 




•53 


.55516 


.74442 


•14377 


.05834 


.48538 


.68608 


.0602 


•31392 


29 02 




•54 


.56663 


•75330 


.14938 


.06046 


•49299 


.69284 


.0284 


.30716 


29 32 




0^55 


0.57815 


9.76204 


I.15510 


0.06262 


0.50052 


9.69942 


1.9079 


0.30058 


30 02 




•56 


•58973 


.77065 


.16094 


.064S I 


.50798 


.70584 


.9686 


.29416 


30 32 




•57 


.60137 


•77914 


. 1 6690 


.06703 


.51536 


.71211 


.9404 


.28789 


31 01 




•58 


.61307 


.78751 


.17297 


.06929 


.52267 


.71822 


il^^ 


.2S178 


31 31 




.59 


.62483 


•79576 


.17916 


.07157 


.52990 


.72419 


.8872 


.27581 


32 00 




0.60 


0.63665 


9.80390 


1.18547 


0.07389 


0-53705 


9.73001 


1.8620 


0.26999 


32 29 




.61 


.64854 


.81194 


.191S9 


.07624 


■54413 


•73570 


.8378 


.26430 


32 58 




.62 


.66049 


.81987 


.19844 


.07861 


•55113 


.74125 


.8145 


•25875 


33 27 




63 


.67251 


.82770 


.20510 


.08102 


■55805 


.74667 


.7919 


•25333 


33 55 




.64 


.68459 


•83543 


.21189 


.08346 


•56490 


•75197 


•7702 


.24803 


34 24 




0.65 


0.6967 5 


9.84308 


1. 21879 


0.08593 


0.57167 


9^75715 


1-7493 


0.24285 


34 52 




.66 


.70S97 


.85063 


.22582 


.08843 


•57836 


.76220 


.7290 


.23780 


35 20 




.67 


.72126 


.85S09 


.23297 


.09095 


•58498 


.76714 


-7095 


.23286 


3548 




.68 


•73363 


.86548 


.24025 


.09351 


•59152 


•77 '97 


.6906 


.22803 


36 16 




.69 


.74607 


.87278 


•24765 


.09609 


•59798 


.77669 


.6723 


•22331 


36 44 




070 


0.75858 


9.88000 


1.25517 


0.09870 


0.60437 


9.78130 


1.6546 


0.21870 


37 II 




•71 


•77117 


.88715 


.26282 


.10134 


.61068 


.78 58 1 


■6375 


.21419 


37 38 




.72 


.78384 


.89423 


.27059 


.10401 


.61691 


.79022 


.6210 


.2097S 


3805 




•73 


•79659 


.90123 


.27S49 


.10670 


.62307 


•79453 


.6050 


•20547 


38 32 




•74 


.80941 


.90817 


.2S652 


.10942 


.62915 


•79875 


•5895 


.20125 


38 59 




0-75 


0.S2232 


9.91504 


1.29468 


O.II216 


0.63515 


9.80288 


1-5744 


C.19712 


39 26 




•76 


•83530 


.92185 


■30297 


•I 1493 


.64108 


.80691 


•5599 


-19309 


39 52 i 




•77 


.84838 


•92S59 


•31 139 


•II773 


.64693 


.81086 


■5458 


.18914 


40 19 




.78 


.86153 


•93527 


•31994 


.12055 


.65271 


.81472 


■5321 


.18528 


40 45 




•79 


.87478 


.94190 


.32862 


.12340 


•65841 


.81850 


.5188 


.18150 


41 II 




0.80 


0.8881 1 


9.94846 


^•33743 


0.12627 


0.66404 


9.82219 


'•5059 


O.17781 


41 37 




.81 


.90152 


•95498 


•34638 


.12917 


.66959 


.82581 


■4935 


.17419 


42 02 




.82 


•91503 


.96144 


•35547 


.13209 


.67507 


-82935 


.48 13 


.17065 


42 28 1 




•83 


•9-863 


.96784 


.36468 


•13503 


.68048 


.832S1 


.4696 


.16719 


42 53 




.84 


•94233 


.97420 


•37404 


.13800 


.68581 


.83620 


.4581 


.163S0 


43 18 




0.85 


0.95612 


9.98051 


1-38353 


0,14099 


0.69107 


9-S3952 


1.4470 


0.16048 


43 43 




.86 


.97000 


.98677 


■39316 


.14400 


.69626 


.84277 


.4362 


-15723 


44 08 




.87 


.98398 


•99299 


.40293 


.14704 


.70137 


•84595 


.4258 


.15405 


44 32 




.88 


.99S06 


.99916 


.41284 


. 1 5009 


.70642 


.84906 


.4156 


.15094 


44 57 




.89 


1.01224 


0.00528 


.42289 


•I5317 


•71139 


.85211 


.4057 


.14789 


45 21 




0.90 


1.02652 


O.OII37 


i^43309 


0.15627 


0.71630 


9-85509 


1.3961 


O.I 4491 


45 45 




.91 


.04090 


.01741 


.44342 


•15939 


.72113 


.85801 


.3867 


.14199 


46 09 




.92 


•05539 


.02341 


.45190 


.16254 


.72590 


.860S8 


•3776 


.13912 


4^ ^i 




•93 


.06998 


.02937 


.46453 


.16570 


.73059 


.86368 


.3687 


.13632 


46 56 




•94 


.08468 


•03530 


.47530 


. 1 6888 


■73522 


.86642 


■3601 


•13358 


47 20 




1 
0.95 


1.09948 


0.041 19 


1.48623 


0.17208 


0.73978 


9.86910 


i^35i7 


0.13090 


47 43 




.96 


.11440 


.04704 


.49729 


•17531 


.74428 


-87173 


■3436 


.12827 


48 06 




•97 


.12943 


.05286 


■50S51 


•'7855 


.74870 


•87431 


•3356 


.12569 


48 29 




.98 


•M457 


.05S64 


.51988 


.18181 


.75307 


.87683 


-3279 


.12317 


48 51 




•99 


•15983 


.06439 


•53141 


.18509 


•75736 


.87930 


.3204 


.12070 


49 14 




1. 00 


1. 17520 


0.0701 1 


1.54308 


0.18839 


0.76159 


9.88172 


13130 


O.I1828 


49 36 


> 



Smithsonian Tables. 



Table 1 6 (continued). 
HYPERBOLIC FUNCTIONS. 



43 





sinh. u 


cosh, u 


tanh. u 


coth u 


gd u 


a 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


i,oo 


1. 17520 


0.0701 1 


1.54308 


0.18839 


0.76159 


9.8S172 


13130 


O.I 1828 


49O36' 1 


.OI 


.19069 


.075S0 


-55491 


.19171 


.76576 


.88409 


■3059 


.11591 


49 58 


.02 


.20630 


.08146 


.56689 


.19504 


.76987 


.88642 


.2989 


•I 1 358 


5021 j 


•03 


.22203 


.08708 


.57904 


.19839 


•77391 


.88869 


.2921 


.11131 


50 42 


.04 


.23788 


.09268 


.59134 


.20176 


•77789 


.89092 


.2855 


.10908 


51 04 } 


1.05 


1.25386 


0.09825 


1.60379 


0.20515 


O.78181 


9.89310 


I.2791 


0.10690 


51 26 


.06 


.26996 


•10379 


.61641 


.20855 


.78566 


-89524 


.2728 


.10476 


51 47 


.07 


.28619 


.10930 


.62919 


.21197 


.7S946 


-89733 


.2667 


.10267 


52 08 


.08 


•30254 


.11479 


.64214 


.21541 


•79320 


.89938 


.2607 


.10062 


52 29 


.09 


•31903 


.12025 


.65525 


.21886 


.79688 


.90139 


.2549 


.09861 


52 50 


1. 10 


1-33565 


0. 1 2 569 


I.66S52 


0.22233 


0.80050 


9.90336 


1.2492 


0.09664 


53 " 


.11 


•35240 


.I3IU 


.68196 


.22582 


.80406 


.90529 


■2437 


.09471 


53 31 


.12 


.36929 


.13649 


.69557 


.22931 


.80757 


.90718 


•2383 


.09282 


53 52 


•13 


•38631 


.14186 


•70934 


.23283 


.81102 


-90903 


■2330 


.09097 


54 12 


.14 


•40347 


.14720 


•72329 


•23636 


.81441 


.91085 


.2279 


.08915 


54 32 


i.iS 


1.42078 


0-15253 


1.73741 


0.23990 


0.81775 


9.91262 


1.2229 


O.0S73S 


54 52 


.16 


.43822 


.15783 


•75171 


.24346 


.82104 


.91436 


.2180 


.08564 


55 II 


.17 


•455S1 


.16311 


.76618 


.24703 


.82427 


.91607 


.2132 


•08393 


55 31 


.18 


•47355 


.16836 


.78083 


.25062 


•82745 


-91774 


.2085 


.08226 


55 50 


.19 


.49143 


.17360 


.79565 


.25422 


.83058 


.91938 


.2040 


.08062 


56 09 


1.20 


1.50946 


0.17882 


1. 8 1 066 


0.25784 


0.83365 


9.92099 


1.1995 


0.07901 


56 29 


.21 


.52764 


.18402 


.825S4 


.26146 


.83668 


.92256 


.1952 


.07744 


56 47 


.22 


•54598 


.18920 


.84121 


.26510 


.83965 


.92410 


.1910 


.07590 


57 06 


•23 


•56447 


•19437 


.85676 


.26876 


.84258 


.92561 


.1868 


.07439 


57 25 


.24 


.5S311 


.19951 


.87250 


.27242 


.84546 


.92709 


.1828 


.07291 


57 43 


1.25 


1. 60192 


0.20464 


1.88S42 


0.27610 


O.84S28 


9.92854 


1. 1789 


0.07146 


5802 


.26 


.62088 


.20975 


■90454 


.27979 


.85106 


.92996 


.1750 


.07004 


58 20 


•27 


.64001 


.21485 


.92084 


•28349 


.85380 


.93135 


.1712 


.06865 


58 38 


.28 


•65930 


.21993 


.93734 


.28721 


.85648 


•93272 


.1676 


.06728 


58 55 


.29 


.67876 


.22499 


•95403 


.29093 


-85913 


.93406 


.1640 


.06594 


59 13 


i 1-30 


1.69838 


0.23004 


1.97 091 


0.29467 


0.86172 


9-93537 


1. 1605 


0.06463 


59 31 


1 -31 


.71818 


.23507 


.9S800 


.29842 


.8642S 


■93665 


.1570 


.06335 


59 48 


•32 


■73S14 


.24009 


2.00528 


.30217 


.86678 


•93791 


■1537 


.06209 


60 05 


•33 


.75828 


.24509 


.02276 


•30594 


.86925 


•93914 


.1504 


.060S6 


60 22 


•34 


.77S60 


.25008 


.04044 


.30972 


.87167 


■94035 


.1472 


.05965 


60 39 


1 '-3^ 


1.79909 


0.25505 


2.05833 


0.31352 


0.87405 


9.94154 


I.1441 


0.05846 


60 56 


•36 


.81977 


.26002 


.07643 


.31732 


.87639 


.94270 


.1410 


.05730 


61 13 


1 -37 


.84062 


.26496 


.09473 


.32113 


.87869 


.94384 


.1381 


.05616 


61 29 


•38 


.86166 


.26990 


.11324 


•32495 


.88095 


.94495 


•I351 


■05505 


61 45 


•39 


.88289 


.27482 


.13196 


.32878 


-88317 


.94604 


.1323 


•05396 


62 02 


1.40 


1.90430 


0.27974 


2.15090 


0.33262 


0.88535 


9.94712 


1. 1295 


0.05288 


62 18 


.41 


.92591 


.28464 


.17005 


•33647 


.88749 


.94817 


.1268 


.05183 


62 34 


1 .42 


.94770 


.28952 


.18942 


•34033 


.88960 


.94919 


.1241 


.05081 


62 49 


•43 


.96970 


.29440 


.20900 


.34420 


.89167 


.95020 


.1215 


.04980 


63 OS 


■44 


.99188 


.29926 


.22881 


•34807 


.89370 


.95119 


.1189 


.048S I 


63 20 


1.45 


2.01427 


0.30412 


2.24884 


0.35196 


0.89569 


9.95216 


1.1165 


0.04784 


6336 


.46 


.03686 


.30896 


.26910 


•355S5 


.89765 


.953" 


.1140 


.046S9 


63 51 


■"^l 


•05965 


•31379 


-28958 


.35976 


•89958 


.95404 


.1116 


.04596 


64 06 


1 .48 


.08265 


.31862 


.31029 


•36367 


-90147 


.95495 


.1093 


.04505 


64 21 


•49 


.10586 


.32343 


-33123 


•36759 


.90332 


•95584 


.1070 


.04416 


64 36 


1.50 


2.12928 


0.32823 


2.35241 


0.37 1 51 


0.90515 


9.95672 


1.1048 


0.04328 


64 51 



Smithsonian Tables. 



44 



Table 1 6 {continuea). 

HYPERBOLIC FUNCTIONS. 





siuh. u 


cosh. u 


tanh. u 


coth. u 






u 


















gd. u 




Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 




1.50 


2.12928 


0.32823 


2.35241 


O.37151 


0.90515 


9.95672 


1. 1048 


0.04328 


64° 51' 




•51 


.15291 


■2,-i2PZ 


-37382 


.37545 


.90694 


■95758 


.1026 


.04242 


65 05 




•52 


.17676 


•33781 


-39547 


.37939 


.90870 


.95842 


.1005 


.04 1 58 


65 20 




•53 


.20082 


.34258 


-41736 


.38334 


.91042 


.95924 


.09S4 


.04076 


65 34 




•54 


.22510 


•34735 


-43949 


•38730 


.91212 


.96005 


.0963 


•03995 


65 48 




^•55 


2.24961 


0.3521 1 


2.46186 


0.39126 


0.91379 


9 960S4 


1.0943 


0.03916 


66 02 




•56 


•27434 


.356S6 


.4S44S 


•39524 


.91 542 


.96162 


.0924 


■03838 


66 16 




•57 


.29930 


.36160 


•50735 


•39921 


•91703 


.96238 


.0905 


.03762 


66 30 




.58 


•3-449 


•36633 


-53047 


.40320 


.91860 


■96313 


.0SS6 


.03687 


66 43 




•59 


.34991 


•37105 


•55384 


.40719 


.92015 


.96386 


.0868 


.03614 


66 57 




1.60 


2-37557 


0-37577 


2.57746 


0.41 1 19 


0.92167 


9.96457 


1.0850 


0-03543 


67 10 




.61 


40146 


.38048 


•60135 


.41520 


.92316 


-96528 


.0832 


.03472 


67 24 




.62 


.42760 


.38518 


.62549 


.41921 


.92462 


.96597 


.0815 


•03403 


67 37 




■63 


•45397 


.38987 


.64990 


•42323 


.92606 


.96664 


.0798 


•03336 


67 50 




.64 


.48059 


•39456 


•67457 


•42725 


•92747 


.96730 


.0782 


.03270 


68 03 




1.65 


2.50746 


0.39923 


2.69951 


0.43129 


0.92886 


9-96795 


1.0766 


0.03205 


68 15 




.66 


•53459 


.40391 


.72472 


.43532 


•93022 


.96858 


.0750 


.03142 


68 28 




.67 


.56196 


.40857 


.75021 


•43937 


-93155 


.96921 


•0735 


•03079 


68 41 




.68 


•58959 


•41323 


.77596 


•44341 


-93286 


.96082 


.0720 


.03018 


68 53 




.69 


.61748 


.41788 


.80200 


•44747 


■93415 


.97042 


.0705 


.02958 


69 05 




1.70 


2.64563 


0.42253 


2.82832 


0-45153 


0.93541 


9.97100 


1. 0691 


0.02900 


69 18 




•71 


.67405 


.42717 


.85491 


•45559 


.93665 


-97158 


.0676 


.02S42 


69 30 




.72 


•70273 


.43180 


.88 180 


•45966 


•93786 


.97214 


.0663 


.02786 


69 42 




•73 


.73168 


•43643 


.90897 


•46374 


•93906 


.97269 


.0649 


.02731 


69 54 




•74 


.76091 


.44105 


•93643 


.46782 


.94023 


-97323 


.0636 


.02677 


70 05 




1-75 


2.79041 


0.44567 


2.96419 


0.47191 


0.94138 


9-97376 


1.0623 


0.02624 


70 17 




.76 


.S2020 


.45028 


.99224 


.47600 


.94250 


.97428 


.0610 


•02572 


70 29 




■11 


.85026 


.45488 


3.02059 


.48009 


.94361 


•97479 


.0598 


.02521 


70 40 




.78 


.88061 


.45948 


.04925 


.48419 


•94470 


■97529 


.0585 


.02471 


70 51 




•79 


.91125 


.46408 


.07821 


.48830 


•94576 


•97578 


.0574 


.02422 


71 03 




1.80 


2.94217 


0.46867 


3.10747 


0.49341 


0.94681 


9.97626 


1.0562 


0.02374 


71 14 




.81 


•97340 


•47325 


•13705 


.49652 


•94783 


•97673 


.0550 


■02327 


71 25 




.82 


3.00492 


•47783 


. 1 6694 


.50064 


.948S4 


.97719 


■0539 


.02281 


71 36 




•83 


.03674 


.48241 


.19715 


.50476 


•94983 


.97764 


.0528 


.02236 


71 46 




.84 


.06S86 


.48698 


.22768 


.508S9 


.950S0 


.97809 


.0518 


.02191 


71 57 




1.85 


3.10129 


0.49154 


3-25853 


0.51302 


0.95175 


9.97852 


1.0507 


0.02148 


72 08 




.86 


•13403 


.49610 


.28970 


.51716 


.95268 


•97895 


■0497 


.02105 


72 18 




•87 


.16709 


.50066 


.32121 


•52130 


•95359 


■97936 


.0487 


.02064 


72 29 




.88 


.20046 


.50521 


•35305 


•52544 


•95449 


-97977 


.0477 


.02023 


1^ 39 




.89 


•23415 


.50976 


.38522 


.52959 


•95537 


.98017 


.0467 


■01983 


72 49 




1.90 


3.26816 


0.51430 


3-41773 


0.53374 


0.95624 


9.98057 


1.0458 


0.01943 


72 59 




.91 


.30250 


.51884 


.45058 


.53789 


•95709 


.98095 


.0448 


.01905 


73 09 1 




.92 


•33718 


•5233S 


.48378 


.54205 


•95792 


•98133 


■0439 


.01867 


73 19 




•93 


.37218 


-52791 


.5'733 


.54621 


•95873 


.98170 


.0430 


.01830 


IZ 29 




.94 


•40752 


•53244 


•55123 


•55038 


-95953 


.98206 


.0422 


.01794 


11 39 




1.95 


3-44321 


0.53696 


3.58548 


0-55455 


0.96032 


9.98242 


I.0413 


0.01758 


73 48 




.96 


•47923 


.54148 


.62009 


•55S72 


.96109 


.98276 


.0405 


.01724 


73 58 




•97 


•51561 


.54600 


.65507 


.56290 


.96185 


.98311 


■0397 


.0 1 689 


74 07 




.98 


•55234 


•55051 


.69041 


•56707 


.96259 


.98344 


.0389 


.01656 


74 17 




•99 


.58942 


•55502 


.72611 


.57126 


-96331 


■'^'iyii 


•0381 


.01623 


74 26 1 




2.00 


3.62686 


0-55953 


3.76220 


0.57544 


0.96403 


9.98409 


1-0373 


O.O1591 


74 35 





Smithsonian Tables. 



Table 1 6 {continued). 
HYPERBOLIC FUNCTIONS. 



45 





sin 


h.u 


cosh, u 


tanh. u 


coth. u. 






u 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


gd. u 




j 2.00 


3.626S6 


0-55953 


3.76220 


0.57544 


0.96403 


9.98409 


10373 


O.OI591 


74°35' 




.01 


.66466 


.56403 


.79865 


•57963 


•96473 


.98440 


.0366 


.01560 


74 44 




.02 


.702S3 


•56853 


-83549 


.58382 


.96541 


.98471 


.0358 


.01529 


74 53 




i -03 


•7413^ 


•57303 


.87271 


.5S802 


.96609 


.98502 


•0351 


.0149S 


75 02 




.04 


.78029 


•57753 


.91032 


.59221 


•96675 


•98531 


•0344 


.01469 


75 II 




' 2.05 


3.81958 


0.58202 


3-94832 


0.59641 


0.96740 


9.98560 


1^0337 


0.01440 


75 20 




! .06 


.S5926 


.58650 


.9S67 1 


.60061 


.96S03 


.98589 


-0330 


.01411 


75 28 




.07 


.89932 


.59099 


4.02550 


.604S2 


.96S65 


.98617 


•0324 


•01383 


75 37 




.08 


•93977 


•59547 


.06470 


.60903 


.96926 


.9S644 


•0317 


.01356 


75 45 




.09 


.9S061 


•59995 


.10430 


.61324 


.969S6 


.98671 


.0311 


.01329 


75 54 




2.10 


4.02186 


0.60443 


4.I443I 


0.61745 


0.97045 


9.98697 


1.0304 


0.01303 


76 02 




.11 


.06350 


.60890 


.18474 


.62167 


-97103 


•98723 


.0298 


.01277 


76 10 




! .12 


•1055s 


•61337 


.22558 


.625S9 


•97159 


.9S748 


.0292 


.01252 


76 19 




■13 


.14S01 


.61784 


.26685 


.63011 


.97215 


•9S773 


.0286 


.01227 


76 27 




.14 


.190S9 


.62231 


•30855 


•63433 


.97269 


.9S798 


.0281 


.01202 


76 35 




2-IS 


4-23419 


0.62677 


4.35067 


0.63856 


0-97323 


9.98821 


1.0275 


O.OII79 


76 43 




.16 


.27791 


•63123 


•39323 


.64278 


•97375 


.98845 


.0270 


.01155 


76 51 






.32205 


.63569 


•43623 


.64701 


.97426 


.98868 


.0264 


.01132 


76 58 




.18 


.36663 


.64015 


.47967 


•65125 


•97477 


.98890 


.0259 


.OHIO 


77 06 




.19 


.41165 


.64460 


■52356 


.65548 


.97526 


.98912 


-0254 


.OIOS8 


77 14 




2.20 


4.457 1 1 


0.64905 


4.56791 


0.65972 


0.97574 


9.98934 


1.0249 


0.01066 


77 21 




.21 


.50301 


•65350 


.61271 


.66396 


.97622 


•9S955 


.0244 


.01045 


77 29 




.22 


•54936 


•65795 


.65797 


.66820 


.97668 


.98975 


.0239 


.01025 


77 36 




•23 


.59617 


.66240 


-70370 


.67244 


•97714 


.98996 


.0234 


.01004 


77 44 




.24 


•64344 


.66684 


.74989 


.67668 


•97759 


.99016 


.0229 


.009S4 


77 51 




2.25 


4.691 17 


0.67128 


4.79657 


0.68093 


0.97803 


9-99035 


1.0225 


0.00965 


77 58 




.26 


•73937 


•67572 


.84372 


.68518 


.97846 


•99054 


.0220 


.00946 


7805 




.27 


.78804 


.68016 


.89136 


.68943 


.97888 


•99073 


.0216 


.00927 


78 12 




.28 


.83720 


.68459 


.93948 


.69368 


.97929 


.99091 


.0211 


.00909 


78 19 




.29 


.88684 


.68903 


.9S81O 


.69794 


.97970 


.99109 


.0207 


.00S9I 


78 26 




2.30 


4.93696 


0.69346 


5-03722 


0.70219 


0.98010 


9.99127 


1.0203 


0.00873 


78 33 




•31 


.9S758 


.69789 


.08684 


•70645 


.9S049 


.99144 


.0199 


.00856 


78 40 




•32 


5-03870 


.70232 


-13697 


.71071 


.9S087 


.99161 


.0195 


.00839 


78 46 




•33 


.09032 


•70675 


.1S762 


•71497 


.98124 


•99178 


.0191 


.00S22 


78 53 




•34 


.14245 


.71117 


-23S78 


•71923 


.98161 


.99194 


.0187 


.00806 


79 00 




2-35 


5.19510 


0-71559 


5.29047 


0.72349 


0.98197 


9.99210 


1.0184 


0.00790 


79 06 




•36 


.24S27 


.72002 


.34269 


.72776 


•98233 


.99226 


.0180 


.00774 


79 13 




•37 


.30196 


•72444 


•39544 


-73203 


.98267 


.99241 


.0176 


.00759 


79 19 




•3S 


.35618 


.72885 


•44873 


-73630 


.98301 


.99256 


.0173 


.00744 


79 25 




•39 


.41093 


•73327 


.50256 


.74056 


•9833s 


.99271 


.0169 


.00729 


79 32 




2.40 


5.46623 


0.73769 


5-55695 


0.74484 


0.98367 


9.99285 


1. 0166 


0.007 1 5 


7938 




.41 


.52207 


.74210 


.61189 


.74911 


.98400 


.99299 


.0163 


.00701 


79 44 




.42 


-57S47 


•74652 


.66739 


•75338 


.98431 


•99313 


.0159 


.00687 


79 50 




•43 


•63542 


•75093 


•72346 


.75766 


.9S462 


•99327 


.0156 


.00673 


79 56 




•44 


.69294 


•75534 


.78010 


.76194 


.98492 


.99340 


•0153 


.00660 


80 02 




2.45 


5^7 5103 


0.75975 


5^83732 


0.76621 


0.98522 


9^99353 


1.0150 


0.00647 


80 oS 




.46 


.S0969 


•76415 


.89512 


.77049 


•98551 


•99366 


.0147 


.00634 


80 14 




•47 


.86893 


.76S56 


•95352 


-77477 


•98579 


•99379 


.0144 


.0062 1 


80 20 




.48 


.92876 


.77296 


6.01250 


.77906 


.98607 


•99391 


.0141 


.00609 


80 26 




•49 


.98918 


■77737 


.07209 


-78334 


.98635 


•99403 


.0138 


.00597 


80 31 




2.50 


6.05020 


0.78177 


6.13229 


0.78762 


0.9S661 


9.99415 


1.0136 


0.00585 


80 37 





SiMiTHsoNfAN Tables. 



46 



Table 1 6 {continued). 

HYPERBOLIC FUNCTIONS. 





sinh. u 


cosh. u 


tanh. u 


coth. u 




u 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


gd. u 


2.50 


6.05020 


0.78177 


6.13229 


0.78762 


0.98661 


9-99415 


1. 01 36 


0.00585 


80° 37' 


•51 


.11183 


.78617 


.19310 


.79191 


.98688 


.99426 


•0133 


.00574 


80 42 


•52 


.17407 


.79057 


•25453 


.79619 


.98714 


.99438 


.0130 


.00562 


80 48 


•53 


.23692 


.79497 


.31658 


.8004S 


•98739 


.99449 


.0128 


.00551 


80 53 


•54 


.30040 


•79937 


•37927 


.80477 


.98764 


.99460 


.0125 


.00540 


80 59 


2.55 


6.36451 


0.80377 


6.44259 


0.80906 


0.98788 


9.99470 


I.OI23 


0.00530 


81 04 


.56 


.42926 


.80816 


.50656 


•81335 


.98812 


.99481 


.0120 


.00519 


81 10 


•57 


.49464 


.81256 


.57118 


.81764 


•98835 


.99491 


.0118 


.00509 


81 15 


.58 


.56068 


.81695 


.63646 


.82194 


.9S858 


.99501 


.0115 


.00499 


81 20 


•59 


.62738 


.82134 


.70240 


.82623 


.98881 


.99511 


.0113 


.00489 


81 25 


2.60 


6.69473 


0.82573 


6.76901 


0.83052 


0.98903 


9.99521 


I.OIII 


0.00479 


81 30 


.61 


.76276 


.83012 


.83629 


.83482 


.98924 


-99530 


.0109 


.00470 


81 35 


.62 


.83146 


•83451 


.90426 


.83912 


.98946 


.99540 


.0107 


.00460 


81 40 


•63 


.900S 5 


.83890 


.97292 


.84341 


.98966 


.99549 


.0104 


.00451 


81 45 


.64 


.97092 


.84329 


7.04228 


.84771 


.98987 


•99558 


.0102 


.00442 


81 50 


2.65 


7.04169 


0.84768 


7.11234 


0.85201 


0.99007 


9.99566 


1. 0100 


0.00434 


81 55 


.66 


•ii3>7 


.85206 


.18312 


.85631 


.99026 


-99575 


.0098 


.00425 


82 CO 


.67 


•18536 


.85645 


.25461 


.86061 


.99045 


.99583 


.0096 


.00417 


82 05 


.68 


.25827 


.86083 


.32683 


.86492 


.99064 


.99592 


.0094 


.0040S 


82 09 


.69 


•33190 


.86522 


.39978 


.86922 


.99083 


.99600 


.0093 


.00400 


82 14 


2.70 


7.40626 


0.86960 


7.47347 


0.87352 


O.99101 


9.99608 


1. 009 1 


0.00392 


82 19 


•71 


•4S137 


.87398 


•54791 


.87783 


.99118 


.99615 


.0089 


.003S5 


82 23 


.72 


•55722 


.87836 


.62310 


.88213 


.99136 


.99623 


.0087 


.00377 


82 28 


•73 


•633S3 


.88274 


.69905 


.8S644 


•99153 


.99631 


.0085 


.00369 


82 32 


•74 


.71121 


.88712 


.77578 


.89074 


.99170 


.99638 


.0084 


.00362 


82 37 


2-75 


7-78935 


0.89150 


7.85328 


0.89505 


0.99186 


9.99645 


1.0082 


0.00355 


82 41 


.76 


.86S28 


.89588 


•93157 


.89936 


.99202 


.99652 


.0080 


.0034S 


82 45 


•77 


.94799 


.90026 


8.01065 


.90367 


.99218 


.99659 


.0079 


.00341 


82 50 1 


.78 


8.02S49 


.90463 


.09053 


.90798 


■99233 


.99666 


.0077 


■00334 


82 54 , 


•79 


.10980 


.90901 


.17122 


.91229 


.99248 


.99672 


.0076 


.00328 


82 58 1 


2.80 


8.19192 


0.91339 


8.25273 


0.91660 


0.99263 


9.99679 


1.0074 


0.00321 


83 02 


.81 


.27486 


.91776 


•33506 


.92091 


.99278 


.996S5 


.0073 


.00315 


83 07 


.82 


.35862 


.92213 


.41823 


.92522 


.99292 


.99691 


.0071 


.00309 


83 II 


•83 


.44322 


.92651 


.50224 


•92953 


.99306 


.99698 


.0070 


.00302 


83 15 


.84 


.52867 


.93088 


.58710 


•93385 


.99320 


.99704 


.0069 


.00296 


83 19 


2.85 


8.61497 


0.93525 


8.67281 


0.93816 


0.99333 


9.99709 


1.0067 


0.00291 


83 23 


.86 


.70213 


•93963 


.75940 


.94247 


.99346 


-99715 


.0066 


.00285 


83 27 


.87 


.79016 


.94400 


.84686 


.94679 


•99359 


.99721 


.0065 


.00279 


83 31 


.88 


.87907 


.94837 


•93520 


.95110 


.99372 


.99726 


.0063 


.00274 


83 34 


.89 


.96S87 


.95274 


9.02444 


.95542 


.99384 


.99732 


.0062 


.00268 


83 38 


2.90 


9.05956 


0.957 1 1 


9.11458 


0.95974 


0.99396 


9-99737 


1. 006 1 


0.00263 


83 42 


•91 


.15116 


.96148 


.20564 


.96405 


.99408 


.99742 


.0060 


.00258 


83 46 


.92 


.24368 


.96584 


.29761 


.96837 


.99420 


-99747 


.0058 


.00253 


83 50 


•93 


.33712 


.97021 


.39051 


.97269 


•99531 


-99752 


.0057 


.00248 


83 53 


•94 


.43149 


■97458 


•48436 


.97701 


.99443 


-99757 


.0056 


.00243 


83 57 


2.95 


9.52681 


0.9789s 


9-57915 


0.98133 


0.99454 


9.99762 


1.0055 


0.00238 


84 00 


.96 


.62308 


•98331 


.67490 


.98565 


.99464 


.99767 


-0054 


.00233 


84 04 


•97 


.72031 


.98768 


.77161 


.98997 


.99475 


.99771 


-0053 


.00229 


84 08 


.98 


.81851 


.99205 


.86930 


.99429 


•99485 


.99776 


.0052 


.00224 


84 II 


•99 


.91770 


.99641 


.96798 


.99861 


.99496 


.99780 


.0051 


.00220 


84 15 


3.00 


10.01787 


1 .00078 


10.06766 


1.00293 


0-99505 


9.99785 


1.0050 


0.00215 


84 18 



Smithsonian Tables. 



Table 1 6 {conlinued). 
HYPERBOLIC FUNCTIONS. 



47 





sin 


h. u 


cosh, u 


tanh. u 


coth 


. u 








Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


Nat. 


Log. 


gd. u 




3-0 
.1 

.2 

•3 

•4 


10.0179 
11.0765 
12.2459 

13^5379 
14.9654 


1.00078 
.04440 
.08799 

•i3f55 
•17509 


10.0677 
II.1215 
12.2866 
13-5748 
14.9987 


1.00293 
.04616 
•08943 
•13273 
.17605 


0-99505 
•99595 
.99668 
.99728 
.99777 


9-99785 
.99824 
.99856 
.99882 
•99903 


1.0050 
.0041 

•0033 
.0027 
.0022 


0.00215 
.00176 
.00144 
.00118 
.00097 


84° 1 8' 

84 50 

85 20 

85 47 

86 II 




•7 
.8 

•9 


16.5426 
18.2855 
20.2113 

22.3394 
24.6911 


1.21860 
.26211 
•30559 
•34907 
•39254 


16.5728 
18.3128 
20.2360 
22.361S 
24.7113 


1. 21940 
.26275 
.30612 

•34951 
•39290 


0.99818 
.99851 
.99878 
.99900 
.99918 


9.99921 
•99935 
•99947 
•99957 
.99964 


I.OO18 
.0015 
.0012 
.0010 
.0008 


0.00079 
.00065 
.00053 
.00043 
.00036 


8632 

86 52 

87 10 
87 26 
87 41 




4.0 
.1 
.2 
•3 
•4 


27.2899 
30.1619 

33-3357 
36.8431 
40.7193 


1.43600 
•47946 
.52291 
.56636 
.60980 


27.3082 
30.1784 

33-3507 
36.8567 
40.7316 


1.43629 
.47970 
■52310 
.56652 
.60993 


0^99933 
•99945 
•99955 
.99963 
.99970 


9.99971 

•99976 
.99980 

•99984 
.99987 


1.0007 

.0005 
.0004 
.0004 
.0003 


0.00029 
.00024 
.00020 
.00016 
.00013 


87 54 

88 06 
88 17 
88 27 
88 36 




4^5 
.6 

•7 
.8 

•9 


45.0030 

49-7371 
54.9690 
60.7511 
67.1412 


1.65324 
.69668 
.74012 

•78355 
.82699 


45.0141 
49.7472 
54.9781 

60.7593 
67.1486 


1-65335 
.69677 
.74019 
.78361 
.82704 


0^99975 
.99980 

•99983 
.99986 

•99989 


9-99989 
.99991 

•99993 
•99994 
•99995 


1.0002 
.0002 
.0002 
.0001 
.0001 


0.000 1 1 
.00009 
.00007 
.00006 
.00005 


88 44 
88 51 

88 57 

89 03 
89 09 




50 


74.2032 


1.87042 


74.2099 


1.87046 


0.99991 


9.99996 


1. 0001 


0.00004 


89 14 





Table 17. Factorials. 

See table 15 for logarithms of the products 1.2.3. ■ ■ ■ ft from i to 100. 
See table 31 for log. («+/) for values of « between i.ooo and 2.000. 



n 


I 
n : 


«.• = I. 2. 3. 4 . . , « 


n 


I 


I. 


I 


I 


2 


0.5 


2 


2 


3 


.16666 66666 66666 66666 66667 


6 


3 


4 


.04166 66666 66666 66666 66667 


24 


4 


5 


-00833 33333 33333 33333 33333 


120 


5 


6 


0.00138 88888 88888 88S88 88889 


720 


6 


7 


.00019 84126 98412 69841 26984 


5040 


7 


8 


.00002 48015 87301 58730 15873 


40320 


8 


9 


.00000 27557 31922 39858 90653 


3 62880 


9 


10 


.00000 02755 73192 23985 89065 


36 28S00 


10 


II 


0.00000 00250 52108 38544 17 188 


399 16S00 


II 


12 


.00000 00020 87675 69878 6S099 


4790 01600 


12 


13 


.00000 ooooi 60590 43836 82161 


62270 20S00 


13 


14 


.00000 00000 1 1470 74559 77297 


8 71782 91200 


14 


15 


.00000 00000 00764 71637 31820 


130 76743 68000 


15 


16 


0.00000 00000 00047 79477 33239 


2092 27898 8S000 


16 


17 


.00000 00000 00002 81 145 72543 


35568 74280 96000 


17 


18 


.00000 00000 00000 1 5619 20697 


6 40237 37057 28000 


18 


19 


.00000 00000 00000 00822 06352 


121 64510 O40S8 32000 


19 


20 


.00000 00000 00000 00041 I 03 I 8 


2432 90200 81766 40000 


20 



Smithsonian Tables. 



48 



Table 18. 
EXPONENTIAL FUNCTION. 



X 


logioC^^) 


e3^ 


e—x 


X 


logio(^^) 


ex 


e-x 




o.oo 


0.00000 


1. 0000 


1 .000000 


0.50 


0.21715 


1.6487 


0.606531 




.01 


.00434 


.0101 


0.990050 


•51 


.22149 


•6653 


.600496 




.02 


.00869 


.0202 


.980199 


•52 


.22583 


.6820 


.594521 




•03 


.01303 


.0305 


.970446 


.53 


.23018 


.6989 


.58S605 




.04 


•01737 


.0408 


.960789 


•54 


.23452 


.7160 


■582748 




0.05 


0.02I7I 


I.0513 


0.951229 


0-55 


0.23886 


^•7333 


0.576950 




.06 


.02606 


.0618 


.941765 


.56 


.24320 


.7507 


.571209 




.07 


.03040 


.0725 


•932394 


•57 


.24755 


.76S3 


•565525 




.oS 


•03474 


•0833 


.923116 


.58 


.25189 


.7860 


•559S98 




.09 


.03909 


.0942 


•9 1 393 1 


•59 


•25623 


.8040 


•554327 




O.IO 


0.04343 


1.1052 


0.904837 


0.60 


0.26058 


1.8221 


O.548S12 




.11 


.04777 


.1163 


.895834 


.61 


.26492 


.8404 


•543351 




.12 


.05212 


•1275 


.886920 


.62 


.26926 


.8589 


•537944 




•13 


.05646 


.1388 


•878095 


•63 


.27361 


.8776 


•53-592 




.14 


.060S0 


•1503 


.869358 


.64 


•27795 


.8965 


.527292 




0.15 


0.06514 


1.1618 


0.860708 


0.65 


0.28229 


1-9155 


0.522046 




.16 


.06949 


•1735 


.852144 


.66 


.28663 


•9348 


.516S51 




•17 


•07383 


•1853 


•843665 


.67 


.29098 


•9542 


.511709 




.18 


.07817 


.1972 


.835270 


.68 


•29532 


•9739 


.506617 




•19 


.08252 


.2092 


.826959 


.69 


.29966 


•9937 


•501576 




0.20 


0.08686 


1.2214 


0.818731 


0.70 


0.30401 


2.0138 


0.496585 




.21 


.09120 


•2337 


.810584 


•71 


•3083s 


.0340 


.491644 




.22 


•09554 


.2461 


.802519 


.72 


.31269 


.0544 


.486752 




•23 


.09989 


.2586 


•794534 


•73 


.31703 


•0751 


.481909 




.24 


.10423 


.2712 


.786628 


•74 


.32138 


•0959 


.477114 




0.25 


0.10857 


1.2840 


0.778801 


075 


0.32572 


2.1170 


0.472367 




.26 


.11292 


.2969 


.771052 


.76 


.33006 


.1383 


.467666 




.27 


.11726 


.3100 


.763379 


•77 


•33441 


.1598 


.463013 




.28 


.12160 


•3231 


.755784 


.78 


•33875 


.1815 


.458406 




.29 


•1259s 


•3364 


.748264 


•79 


•34309 


.2034 


•453845 




0.30 


0.13029 


1-3499 


0.740818 


0.80 


0.34744 


2.2255 


0.449329 




•31 


•13463 


•3634 


•733447 


.81 


•35178 


.2479 


■444858 




•32 


•13897 


•3771 


.726149 


.82 


•35612 


•2705 


.440432 




•33 


.14332 


•3910 


.718924 


•83 


.36046 


•2933 


.436049 




•34 


.14766 


•4049 


.711770 


.84 


.36481 


.3164 


•4317H 




0-35 


0.15200 


1.4191 


0.704688 


0.85 


0.36915 


2.3396 


0.427415 




.36 


•15635 


.4333 


.697676 


.86 


•37349 


•3632 


.423162 




•37 


,16069 


•4477 


.690734 


.87 


•37784 


.3869 


.418952 




•38 


•16503 


.4623 


.683861 


.88 


.38218 


.4109 


.414783 




•39 


.16937 


.4770 


.677057 


.89 


•38652 


•4351 


.410656 




0.40 


0.17372 


1.4918 


0.670320 


0.90 


0.39087 


2.4596 


C.406570 




.41 


.17806 


.5068 


.663650 


.91 


•39521 


.4843 


.402524 




.42 


.18240 


.5220 


.657047 


.92 


•39955 


.5093 


•398519 




•43 


.18675 


•5373 


.650509 


•93 


.40389 


'5345 


•394554 




•44 


.19109 


•5527 


.644036 


•94 


.40S24 


.5600 


.390628 




045 


0.19543 


1.5683 


0.637628 


0-95 


0.41258 


2.5857 


0.386741 




.46 


.19978 


.5841 


.631284 


.96 


.41692 


.6117 


.382893 




•47 


.20412 


.6000 


.625002 


•97 


.42127 


.6379 


.379083 




.48 


.20846 


.6161 


.618783 


.98 


.42561 


.6645 


.3753" 




•49 


.21280 


•6323 


.612626 


•99 


.42995 


.6912 


•371577 




0.50 


0.21715 


1.6487 


0.606531 


1. 00 


0.43429 


2.7183 


0.367879 





Smithsonian Tables. 



Table 1 8 (continued). 
EXPONENTIAL FUNCTION. 



49 



X 


logio(^^) 


ex 


e-x 


X 


logio {e^ ) 


ex 


e-x 


I.OO 


0.43429 


2.71S3 


0.367879 


1.50 


0.65144 


4.4817 


0.223130 


.OI 


.43864 


•7456 


.364219 


•5' 


•65578 


.5267 


.220910 j 


.02 


.44298 


•7732 


•360595 


•52 


.60013 


■5722 


.218712 1 


■03 


•44732 


.8011 


•357007 


•53 


.66447 


.6182 


■216536 I 


.04 


.45167 


.8292 


•353455 


•54 


.66881 


.6646 


.214381 1 


1.05 


0.45601 


2.8577 


0.349938 


I-S5 


0.67316 


4-7"5 


0.212248 


.06 


.46035 


.8864 


•346456 


.56 


.67750 


■75S8 


.210136 


.07 


.46470 


.9154 


•343009 


•57 


.68184 


.8066 


.208045 


.oS 


.46904 


.9447 


•339596 


•58 


.68619 


.8550 


.205975 


.09 


•47338 


■9743 


.336216 


•59 


•69053 


.9037 


.203926 


MO 


0.47772 


3.0042 


0.332871 


1.60 


0.69487 


4^9530 


0.201897 


! .11 


.4S207 


•0344 


•329559 


.61 


.69921 


5.0028 


.199888 


.12 


.48641 


.0649 


.326280 


.62 


•70356 


■0531 


.197899 


■13 


.49075 


•0957 


.323033 


i^ 


.70790 


.1039 


.195930 


.14 


.49510 


.1268 


.319819 


.64 


.71224 


•1552 


.193980 


1. 15 


0.49944 


3.1582 


0.316637 


1.65 


0.71659 


5.2070 


0.192050 


.16 


•50378 


.1899 


.313486 


.66 


.72093 


•2593 


.T90139 


■ 17 


.50SI2 


.2220 


.310367 


.67 


■72527 


.3122 


.188247 


.18 


.51247 


•2544 


.307279 


.68 


.72961 


.3656 


.186374 


.19 


.5I6SI 


.2871 


.304221 


.69 


■73396 


•4195 


.184520 


1.20 


0.52115 


3-3201 


0.301 194 


1.70 


0.73830 


5^4739 


0.182684 


.21 


•52550 


•3535 


.298197 


•71 


.74264 


.5290 


.180866 


.22 


.529S4 


.3872 


.295230 


.72 


■74699 


.5845 


.179066 


■23 


.53418 


.4212 


.292293 


•73 


•75'33 


.6407 


.177284 


.24 


•53853 


•4556 


.289384 


•74 


■75567 


•6973 


•175520 


1.25 


0.54287 


3-4903 


0.286505 


1-75 


0.76002 


5^7546 


0.173774 


.26 


.54721 


•5254 


.283654 


.76 


.76436 


.8124 


.172045 


•27 


•55155 


.5609 


.280832 


■77 


.76870 


.8709 


•170333 


.28 


•55590 


.5966 


.278037 


.78 


■77304 


•9299 


.168638 


.29 


.56024 


.6328 


.275271 


•79 


■77739 


.9895 


.166960 


1.30 


0.56458 


3-6693 


0.272532 


1.80 


0.78173 


6.0496 


0.165299 


•31 


•56893 


.7062 


.269820 


.81 


.78607 


.1104 


.163654 


•32 


•57327 


•7434 


•267135 


.82 


•79042 


.1719 


.162026 


•33 


•57761 


.7810 


.264477 


■83 


.79476 


•2339 


.160414 


•34 


•58195 


.8190 


.261846 


.84 


.79910 


.2965 


.158817 


1-35 


0.5S630 


3-8574 


0.259240 


1.85 


0.S0344 


6.3598 


0.157237 


•36 


.59064 


.8962 


.256661 


.86 


.80779 


•4237 


•155673 


•37 


•59498 


•9354 


.254107 


.87 


.81213 


•48S3 


.154124 1 


•38 


•59933 


•9749 


•251579 


.88 


.81647 


•5535 


.152590 


•39 


.60367 


4.0149 


.249075 


.89 


.82082 


.6194 


.151072 


1.40 


0.60801 


4.0552 


0.246597 


1.90 


0.82516 


6.6859 


0.149569 


.41 


.61236 


.0960 


.244143 


.91 


.8 29 50 


•7531 


.148080 


.42 


.61670 


-1371 


.241714 


■92 


■833S5 


.8210 


.146607 


•43 


.62104 


.1787 


.239309 


•93 


•S3S19 


.8895 


.145148 


•44 


•62538 


.2207 


.236928 


•94 


•84253 


.9588 


.143704 


1.45 


0.62973 


4.2631 


0.234570 


1-95 


0.84687 


7.02S7 


0.142274 


.46 


•63407 


.3060 


.232236 


.96 


.85122 


•0993 


.140858 


•47 


.63841 


•3492 


.229925 


•97 


•85556 


.1707 


•139457 


.48 


.64276 


•3929 


.227638 


.98 


.85990 


.2427 


.138069 


•49 


.64710 


•4371 


■225373 


•99 


•86425 


•315s 


.136695 


1.50 


0.65144 


4.4817 


0.223130 


2.00 


0.86859 


7^389i 


0-I3533S 



Smithsonian Tables. 



50 



Table 18 {continued). 
EXPONENTIAL FUNCTION. 



X 


logio {ex-) 


ex 


e-x 


■*• 


logio {ex) 


ex 


e — X 


2.00 


0.86859 


7-3891 


O.I3533S 


2.50 


1.08574 


12.182 


0.082085 


.01 


•87293 


•4633 


•133989 


•51 


.09008 


•305 


.081268 


.02 


.87727 


•5383 


•132655 


•52 


.09442 


.429 


.0S0460 


•03 


.88162 


.6141 


•I3I336 


•53 


•09877 


•554 


.079659 


.04 


.88596 


.6906 


.130029 


•54 


.10311 


.680 


.078S66 


2.01; 


0.89030 


7.7679 


0.128735 


2-55 


1.10745 


12.807 


0.078082 


.06 


.89465 


.8460 


.127454 


•56 


.11179 


•936 


•077305 


.07 


.89899 


.9248 


.126186 


•57 


.11614 


13.066 


.076536 


.08 


•90333 


8.0045 


.124930 


•58 


.12048 


.197 


■075774 


.09 


.90768 


.0S49 


.123687 


•59 


.12482 


•330 


.075020 


2.10 


0.91202 


8.1662 


0.122456 


2.60 


1. 12917 


13.464 


0.074274 


.11 


.91636 


.2482 


.121238 


.61 


•I335I 


•599 


•073535 


.12 


.92070 


•33" 


.120032 


.62 


•13785 


•736 


.072803 


•13 


•92505 


.4149 


.118837 


•63 


.14219 


•874 


.072078 


•14 


•92939 


•4994 


•117655 


.64 


.14654 


14.013 


.071361 


2.15 


0-93373 


8.5849 


0.116484 


2-65 


1. 1 5088 


14-154 


0.070651 


.16 


.93808 


.6711 


.115325 


.66 


.15522 


.296 


.069948 


•17 


.94242 


•7583 


.114178 


.67 


•15957 


•440 


.069252 


.18 


.94676 


.8463 


.113042 


.68 


.16391 


•585 


.068563 


.19 


.95110 


•9352 


.111917 


.69 


.16825 


•732 


.067881 


2.20 


0-95545 


9.0250 


0.110803 


2.70 


1. 17260 


14.880 


0.067206 


.21 


•95979 


.1157 


.109701 


•71 


.17694 


15.029 


.066537 


.22 


.96413 


•2073 


.108609 


.72 


.18128 


.180 


•065S75 


•23 


.96848 


•2999 


.107528 


-73 


.18562 


•333 


.065219 


.24 


.97282 


•3933 


.106459 


-74 


.18997 


.487 


.064570 


2.25 


0.97716 


9.4877 


0.105399 


2.75 


1. 19431 


15-643 


0.063928 


.20 


.9S151 


■5831 


.104350 


.76 


.19865 


.800 


.063292 


.27 


.98585 


.6794 


.103312 


•77 


.20300 


•959 


.062662 


.28 


.99019 


.7767 


.102284 


.78 


•20734 


16.119 


.062039 


.29 


•99453 


.8749 


.101266 


■79 


.21168 


.281 


.061421 


2.30 


0.99888 


9-9742 


0.100259 


2.80 


1. 2 1 602 


16.445 


0.060810 


•31 


1.00322 


10.074 


.099261 


.81 


.22037 


.610 


.060205 


•32 


.00756 


.176 


.098274 


.82 


.22471 


.777 


.059606 


•33 


.01191 


.278 


.097 296 


•83 


.22905 


•945 


.059013 


•34 


.01625 


.381 


.096328 


.84 


.23340 


17.116 


.058426 


2-35 


1.02059 


10.486 


0.095369 


2.85 


i^23774 


17.2S8 


0.057844 


•36 


.02493 


•591 


.094420 


.86 


.24208 


.462 


.057269 


•37 


.02928 


.697 


.093481 


.87 


.24643 


.637 


.056699 


•38 


.03362 


.805 


.092551 


.88 


•25077 


.814 


•056135 


•39 


.03796 


•913 


.091630 


.89 


•25511 


■993 


.055576 


2.40 


1.04231 


11.023 


0.090718 


2.90 


1-25945 


18.174 


0.055023 


.41 


.04665 


• 134 


.089815 


.91 


.26380 


•357 


.054476 


.42 


.05099 


.246 


.088922 


.92 


.26814 


.541 


•053934 


•43 


•05534 


•359 


.08S037 


•93 


.27248 


.728 


•053397 


•44 


.05968 


•473 


.087161 


•94 


.27683 


.916 


.052866 


2-45 


1.06402 


11.588 


0.086294 


2-95 


1.28117 


19.106 


0.052340 


.^6 


.06836 


•705 


.085435 


.96 


'"■W 


.298 


.051819 


•47 


.07271 


.822 


.084585 


•97 


.28985 


-492 


•051303 


.48 


.07705 


.941 


.083743 


.98 


.29420 


.688 


.050793 


.49 


.08139 


12.061 


.082910 


•99 


.29854 


.886 


.050287 


2.50 


1.08574 


12.182 


0.082085 


3.00 


1.30288 


20.086 


0.049787 



Smithsonian Tables- 



Table 1 8 {continued). 

EXPONENTIAL FUNCTION. 



51 



X 


logioC'^-^') 


ex 


e-x 


X 


logio(^^) 


ex 


e-x 


3.00 


I.3028S 


20.086 


0.049787 


3-50 


1.52003 


33.115 


0.030197 


.01 


•30723 


.287 


.049292 


.51 


-52437 


.448 


.029S97 


.02 


•3"57 


-491 


,048801 


.52 


.52872 


-784 


.029599 


•03 


•3'59i 


.697 


.048316 


-53 


-53306 


34-124 


.029305 


.04 


.32026 


.905 


•047835 


•54 


-53740 


-467 


.029013 


3-05 


1.32460 


21-115 


0.047359 


3-55 


I-54I75 


34-813 


0.028725 


.06 


.32894 


.328 


.046888 


-56 


.54609 


35-163 


-028439 


.07 


•33328 


-542 


.04642 1 


•57 


.55043 


•517 


.028156 


.08 


•33763 


.758 


•045959 


-58 


•55477 


-874 


.027876 


.09 


•34197 


•977 


.045502 


•59 


.55912 


36234 


.027598 


3.10 


1-34631 


22.19S 


0.045049 


3.60 


1.56346 


36-598 


0-027324 


.11 


.35066 


.421 


.044601 


.61 


.56780 


.966 


.027052 


.12 


•35500 


.646 


•044157 


.62 


.57215 


37-338 


.026783 


•13 


■35934 


.874 


.043718 


.63 


.57649 


o-7'3 


.026516 


.14 


•3636S 


23.104 


•043283 


.64 


.58083 


38.092 


.026252 


3.15 


1-36803 


23-336 


0.042852 


3-65 


1.58517 


38-475 


0.025991 


.16 


•37237 


•571 


.042426 


.66 


.58952 


.861 


-025733 


•17 


•37671 


.807 


.042004 


.67 


.59386 


39.252 


.025476 


.i8 


.38(06 


24.047 


.041586 


.68 


.59820 


.646 


.025223 


.19 


•3S540 


.28S 


.041172 


.69 


.60255 


40.045 


.024972 


3.20 


1-38974 


24-533 


0.040762 


3-70 


1.60689 


40.447 


0.024724 


.21 


•39409 


•779 


.040357 


•71 


.61123 


-854 


.024478 


.22 


-39843 


25.028 


•039955 


•72 


.61558 


41.264 


.024234 1 


•23 


.40277 


.280 


•039557 


•73 


.61992 


.679 


•023993 


.24 


.40711 


•534 


.039164 


•74 


.62426 


42.098 


•023754 


3-25 


1.41146 


25.790 


0.038774 


3-75 


1.62860 


42,521 


0.023518 1 


.26 


.41580 


26.050 


.038388 


•76 


•63295 


.948 


.023284 


.27 


.42014 


.311 


.038006 


■77 


.63729 


43-380 


.023052 


.28 


-42449 


.576 


.037628 


.78 


.64163 


.816 


.022823 


.29 


.42883 


•843 


•037254 


•79 


.64598 


44.256 


.022596 


3-3° 


1-43317 


27.113 


0.036S83 


3.80 


1.65032 


44.701 


0.022371 


•31 


-43751 


.385 


.036516 


.81 


.65466 


45-150 


.022148 


•32 


.44186 


.660 


.036153 


.82 


.65900 


.604 


.021928 


•33 


.44620 


•938 


.035793 


i^ 


•66335 


46.063 


.021710 


•34 


•45054 


28.219 


•035437 


.84 


.66769 


•525 


.021494 


3-35 


1.454S9 


28.503 


0.035084 


385 


1.67203 


46.993 


0.021280 '. 


•36 


-45923 


.789 


•034735 


.86 


.67638 


47-465 


.021068 


•37 


•46357 


29.079 


•034390 


.87 


.6S07 2 


942 


.020S58 


•38 


-46792 


-371 


.034047 


.88 


.68 506 


48.424 


.020651 


•39 


.47226 


.666 


-033709 


.89 


.68941 


.911 


.020445 


3-4° 


1.47660 


29.964 


0.033373 


390 


1-69375 


49.402 


0.020242 


.41 


.48094 


30.265 


.033041 


.91 


.69809 


.899 


.020041 


.42 


-48529 


■569 


.032712 


.92 


.70243 
.70678 


50.400 


.019841 


•43 


.48963 


.877 


.032387 


.93 


-907 


.019644 


•44 


-49397 


31.187 


.032065 


.94 


.71112 


51-419 


.01944S 


3-45 


1-49832 


31-500 


0.031746 


3-95 


1.71546 


51-935 


0.019255 


.46 


.50266 


.817 


.031430 


.96 


.71981 


52-457 


.019063 


•47 


.50700 


32-137 


.031117 


•97 


.72415 


-985 


.018873 


.48 


•5"34 


.460 


.030807 


.98 


.72849 


53-517 


.0186S6 


•49 


-51569 


.786 


.030501 


.99 


.73283 


54-055 


.018500 


3-50 


1.52003 


33-"S 


0.030197 


4.00 


1.73718 


54.598 


0.018316 



Smithsonian Tables. 



52 



Table 1 8 (continued). 

EXPONENTIAL FUNCTION. 



X 


logio(«^) 


cx 


e-x 


X 


logio(^^) 


e* 


e-x 




4.00 


I737I8 


54-598 


O.O18316 


4.50 


1-95433 


90.017 


0.011109 




.01 


.74152 


55-147 


.018133 


•51 


•95S67 


.922 


.010998 




.02 


.74586 


.701 


•017953 


•52 


.96301 


91.836 


.010889 




•03 


.75021 


56.261 


.017774 


•53 


-96735 


92-759 


.010781 




.04 


•75455 


.826 


,017597 


•54 


.97170 


93.691 


■010673 




4.05 


1.75889 


57-397 


0.017422 


4-55 


1.97604 


94.632 


0.010567 




1 .06 


•7(3324 


•974 


.017249 


•56 


.98038 


95-583 


.010462 i 




1 .07 


.76758 


58-557 


.017077 


•57 


-98473 


96.544 


.010358 




.08 


.77192 


59-145 


.016907 


•58 


.98907 


97-5'4 


.010255 i 




.09 


.77626 


.740 


.016739 


•59 


•99341 


98.494 


•010153 ; 




4.10 


1. 78061 


60.340 


0.016573 


4.60 


1-99775 


99-484 


0.010052 




.11 


•78495 


•947 


.016408 


.61 


2.00210 I 


00.48 


.009952 




.12 


.78929 


61-559 


.016245 


.62 


.00644 I 


01.49 


•009853 




•13 


•79364 


62.178 


.0160S3 


•63 


.01078 I 


02.51 


•009755 i 




.14 


•79798 


.803 


.015923 


.64 


•01513 I 


03-54 


.009658 




4-15 


1.80232 


63^434 


0.015764 


4.65 


2.01947 I 


04.58 


0.009562 




.16 


.80667 


64.072 


.015608 


.66 


.02381 1 


05.64 


.009466 




•17 


.81101 


•715 


.015452 


.67 


.02S16 I 


06.70 


.009372 




.18 


•81535 


65.366 


.015299 


.68 


.03250 1 


07.77 


.009279 




1 .19 


.81969 


66.023 


.015146 


.69 


.036S4 I 


08.85 


.009187 




4.20 


1.82404 


66.686 


0.014996 


4.70 


2.04118 1 


09.95 


0.009095 




1 .21 


.82838 


67^357 


.014S46 


•71 


•04553 I 


11.05 


.009005 




.22 


.83272 


68.033 


.014699 


•72 


.04987 I 


12.17 


.008915 




•-3 


•83707 


.717 


.014552 


•73 


.05421 1 


1330 


.00S826 




.24 


.84141 


69.408 


.01440S 


•74 


.05S56 1 


14-43 


.008739 




4-^5 


1-84575 


70.105 


0.014264 


4-75 


2.06290 1 


15.58 


0.008652 




.26 


.85009 


.810 


.014122 


.76 


.06724 I 


16.75 


.008566 




.^7 


.85444 


71.522 


.013982 


•77 


.07158 1 


17.92 


.008480 ! 




.28 


•85S78 


72.240 


.013843 


.78 


-07593 > 


19.10 


.008396 




.29 


.86312 


.966 


■013705 


•79 


.08027 1 


20.30 


.008312 1 




4-30 


1.86747 


73-700 


0.013569 


4.80 


2.0S461 1 


21.51 


0.008230 




•31 


.87181 


74.440 


•013434 


.81 


.0SS96 


22.73 


.008148 ' 




•32 


.87615 


75-189 


.013300 


.82 


.09330 1 


23-97 


.00S067 ' 




•33 


.88050 
.88484 


•944 


.OI316S 


•83 


.09764 


25.21 


.007987 




•34 


76.708 


.013037 


.84 


.10199 


26.47 


.007907 




4-35 


1. 88918 


77-478 


0.012907 


4-85 


2.10633 


27-74 


0.007S2S 




•36 


•89352 
•89787 


78.257 


.012778 


.86 


.11067 


29.02 


.007750 




•37 


79.044 


.012651 


.87 


.11501 


30.32 


.007673 1 




.38 


.90221 


79.838 


.012525 


,88 


.11936 


31-63 


•007597 i 




•39 


.90655 


80.640 


.012401 


.89 


.12370 


32-95 


.007521 




4.40 


1.91090 


81.451 


0.012277 


4.90 


2.12804 


r 34.29 


0.007447 i 




.41 


.91524 


82.269 


.012155 


.91 


•13239 


135-64 


.007372 




.42 


.91958 


83.096 


.012034 


.92 


•13673 


[37.00 


.007299 




•43 


.92392 


•931 


.011914 


•93 


.14107 


138-38 


.007227 




•44 


.92827 


84^775 


.011796 


•94 


•14541 


139-77 


.007155 




4-45 


1.93261 


85.627 


0.0 1 1679 


4-95 


2.14976 


141. 17 


0.007083 




.46 


•9369s 


86.488 


.011562 


.96 


.15410 


142.59 


.007013 




•47 


.94130 


87-357 


.011447 


.97 


.15844 


144-03 


,006943 




.48 


•94564 


88.235 


•01 1333 


.98 


.16279 


145-47 


,006874 




•49 


•94998 


89.121 


.011221 


•99 


.16713 


146.94 


,006806 




4-5° 


^•95433 


90.017 


O.OIIIO9 


5.00 


2-17147 


148.41 


0.006738 





Smithsonian Tables. 



Table 1 8 {conHnued). 
EXPONENTIAL FUNCTION. 



53 



X 


logio(<r^) 


e^ 


e-x 


X 


log,o(^') 


ex 


e—x 


5.00 


2.I7147 


148.41 


0.006738 


5-0 


2.17147 


148.41 


0.006738 


.01 


.17582 


149.90 


.00667 1 


.1 


.21490 


164.02 


.000097 


.02 


.18016 


151.41 


.006605 


.2 


•25833 


181.27 


.005517 


•03 


.1S45O 


152-93 


.006539 


•3 


.30176 


200.34 


.004992 


.04 


.18884 


15447 


.006474 


•4 


•34559 


221.41 


.004517 


5.05 


2.19319 


1 56.02 


0.006409 


5-5 


2.38862 


244.69 


O.OO40S7 


.06 


•19753 


i57'59 


.006346 


.6 


.43205 


270.43 


.003698 


.07 


.20187 


159.17 


.006282 


•7 


•47548 


298.87 


.003346 


.oS 


.20622 


160.77 


.006220 


.8 


.51891 


330-30 


.003028 


.09 


.21056 


162.39 


.006158 


•9 


•56234 


365.04 


.002739 

1 


5.10 


2.21490 


164.02 


0.006097 


6.0 


2-60577 


403.43 


0.002479 


.11 


.21924 


165.67 


.006036 


.1 


.64920 


445.86 


.002243 


.12 


.22359 


167.34 


.005976 


.2 


.69263 


492-75 


.002029 


•13 


.22793 


169.02 


.005917 


•3 


.73606 


544-57 


.001836 


.14 


.23227 


170.72 


.005858 


•4 


.77948 


601.85 


.001662 


515 


2.23662 


172.43 


0.005799 


H 


2.82291 


665.14 


0.001503 


.16 


.24096 


174.16 


.005742 


.6 


.86634 


735^io 


.001360 


•17 


•24530 


175-91 


.005685 


•7 


.90977 


812.41 


.001231 


.18 


.24965 


177-68 


.005628 


.8 


-95320 


897.85 


.001114 


•19 


•25399 


179-47 


.005572 


•9 


.99663 


992.27 


.001008 


5.20 


2^25833 


181.27 


0.005517 


7.0 


3.04006 


1096.6 


0.000912 


.21 


.26267 


183.09 


.005462 


.1 


.08349 


1212.0 


.OOOS25 


.22 


.26702 


184-93 


.005407 


.2 


.12692 


1339-4 


.000747 


■23 


.27136 


186.79 


.005354 


•3 


•17035 


1480.3 


.000676 


•24 


.27570 


188.67 


.005300 


-4 


.21378 


1636.0 


.000611 


5-25 


2.28005 


190.57 


0.005248 


7-5 


3.25721 


1808.0 


0.000553 


.26 


.28439 


192.48 


,005195 


.6 


.30064 


1998.2 


.000500 


.27 


.28873 


194.42 


.005144 


.7 


-34407 


2208.3 


.000453 


.28 


.29307 


196-37 


.005092 


.8 


•3S750 


2440.6 


.000410 


•29 


.29742 


198.34 


.005042 


•9 


-43093 


2697.3 


.000371 


5-30 


2.30176 


200.34 


0.004992 


8.0 


3^47436 


2981.0 


0.000335 


•31 


.30610 


202.35 


.004942 


.1 


•51779 


3294-S 


.000304 


•32 


•3' 045 


204.38 


.004893 


.2 


.56121 


3641.0 


.000275 


•33 


•31479 


206.44 


.004844 


-3 


.60464 


4023.9 


.000249 


■34 


•31913 


20S.51 


.004796 


-4 


.64807 


4447.1 


.000225 


5-35 


2.32348 


210.61 


0.004748 


H 


3.69150 


4914.8 


0.000203 j 


•36 


.32782 


212.72 


.004701 


.6 


-73493 


5431-7 


.000184 


•37 


•33216 


214.86 


.004654 


•7 


.77S36 


6002.9 


.000167 


•38 


•33650 


217.02 


.004608 


.8 


.82179 


6634.2 


.000151 


1 -39 


.34085 


219.20 


.004562 


•9 


.86522 


7332-0 


.000136 


1 

i 5-40 


2.34519 


221.41 


0.004517 


9.0 


3.90865 


8103.1 


0.000123 


.41 


•34953 


223.63 


.004472 


.1 


.95208 


8955-3 


.000112 


42 


•35388 


225.88 


.004427 


.2 


.99551 


9897.1 


.000101 


•43 


.35822 


228.15 


.004383 


■3 


4.03894 


10938. 


.000091 


44 


.36256 


230.44 


.004339 


•4 


.08237 


12088. 


.000083 


5-45 


2.36690 


232.76 


0.004296 


9-5 


4.12580 


13360. 


0.000075 


i 46 


•37125 


235-10 


.004254 


.6 


.16923 


14765. 


.000068 


•47 


•37559 


237-46 


.004211 


-7 


.21266 


16318. 


.000061 


48 


•37993 


239-85 


.004169 


.8 


.25609 


18034. 


.000055 


1 ^49 


.38428 


242.26 


.004128 


•9 


•29952 


19930. 


.000050 


5.50 

! 


2.38862 


244.69 


0.004087 


1 0.0 


434294 


22026. 


0.000045 



Smithsonian Tables. 



54 



Table 19. 
EXPONENTIAL FUNCTIONS. 

Value ot ejc' and e-x' and their logarithms. 



X 


* 


log «r*' 


.-• 


log e-'* 




0.1 


I.OIOI 


0.00434 


0.99005 


r.99566 




2 


1 .0408 


01737 


96079 


98263 




3 


1.0942 


03909 


91393 


96091 




4 


I-I735 


06949 


85214 


93051 




5 


1.2840 


10857 


77880 


89143 




0.6 


1-4333 


0.15635 


0.69768 


1.84365 




7 


1-6323 


21280 


61263 


78720 




8 


1 .8965 


27795 


52729 


72205 




9 


2.2479 


35178 


444S6 


64S22 




I.O 


2.7183 


43429 


36788 


56571 




1.1 


3-3535 


0.52550 


0.29820 


1.47450 




2 


4.2207 


62538 


23693 


37462 




3 


5-4195 


73396 


18452 


26604 




4 


7-0993 


85122 


14086 


14878 




5 


9-4877 


97716 


10540 


02284 




1.6 


1.2936 X 10 


I.III79 


0.77305 X lo-i 


2.88821 




7 


1.7993 


255'i 


55576 " 


744S9 




8 


2-5534 


40711 


39164 


592S9 




9 


3.6966 " 


56780 


27052 '* 


43220 




2.0 


5-4598 " 


73718 


18316 " 


26282 




2.1 


8.2269 " 


1.91524 


0.12155 " 


2.08476 




2 


1.2647 X io2 


2.10199 


79071 X 10-2 


3.89801 




3 


1.9S34 


29742 


50418 


70258 




4 


3->73S 


50154 


31511 " 


49S46 




5 


5.1801 " 


71434 


19305 " 


28566 




2.6 


8.6264 " 


2-93583 


0.11592 " 


2-06417 




7 


1.4656 X io3 


3. 1 6601 


68233 X 10-8 


4-83399 




8 


2.5402 


40487 


39367 " 


59513 




9 


4.4918 


65242 


22263 " 


34758 




3-0 


8.1031 


90S65 


12341 


09135 




3.1 


1.4913 X 10* 


4-17357 


0.67055 X 10-* 


5.82643 




2 


2.8001 " 


44718 


35713 " 


55282 




3 


5-3637 


72947 


18644 " 


_ 27053 




4 


1.04S2 X 10* 


5.02044 


95402 X 10-5 


6.97956 




5 


2.089S 


32011 


47851 


67989 




3.6 


4.2507 


5.62846 


0.23526 " 


6.37154 




7 


8.8205 


94549 


1 1337 " , 


05451 




8 


1.8673 X 106 


6.27121 


53553 X 10-6 


7.72879 




9 


4.0329 


60562 


24796 " 


39438 




4.0 


8.8861 


94871 


11254 " 


05129 




4.1 


1.9975 X io7 


7.30049 


0.50062 X 10—' 


g.69951 




2 


4.5809 " 


66095 


21830 " 


33905 




3 


1.0718 X 108 


8.03010 


93303 X 10-8 


9.96990 




4 


2.5582 


40794 


39089 " 


59206 




5 


6.2296 " 


79446 


16052 " 


20554 




4.6 


1.^476 X I09 


9.18967 


0.64614 X 10—8 


r6.8i033 




7 


3.9225 " 


59357 


25494 " „ 


40643 




8 


1. 01 42 X loi'' 


10.00614 


98595 X 10-10 


i 1.99386 




9 


2.6755 " 


42741 


37376 " 


57259 




5-0 


7.2005 " 


85736 


13888 


14264 





Smithsonian Tables. 



Table 20. 
EXPONENTIAL FUNCTIONS. 



55 





Values ol ^*' and ^ * 


and their logarithms. 




X 




log^*" 


n 

e ^ 


log^~*' 


1 


2-1933 




0.34109 


0.45594 


T.65891 


-^ 


4.S105 




.68219 


.20788 


.31781 


3 


1.0551 X 


10 


1.02328 


.94780 X 1 0-1 


2.97672 


4 


2.3141 


" 


•36438 


.43214 


.63562 


5 


5-0754 


" 


•70547 


•19703 " 


•29453 


6 


1.1132 X 


I02 


2.04656 


0.89833 X 10-2 


3-95344 


7 


2.4415 


" 


.38766 


.40958 


.61234 


8 


5-3549 


" 


•72875 


.18674 " 


^.27125 


9 


1-1745 X 


10^ 


3.06985 


.85144 X 10-3 


4.9301 5 


10 


2.5760 


" 


.41094 


.38820 " 


.58906 


11 


5.6498 


« 


3-75203 


0.17700 " 


4.24797 


12 


1.2392 X 


10* 


4-09313 


.80700 X IO-* 


5.90687 


13 


2.7178 


" 


•43422 


•36794 '; 


-56578 


14 


5.9610 


" 


•77532 


.16776 


.22468 


IS 


1 .3074 X 


10^ 


5.11641 


.764S7 X 10-5 


6.88359 


16 


2.867s 


« 


5-45751 


0.34873 


6.54249 


17 


6.2S93 


" 


.79860 


.15900 " 


.20140 


18 


1.3794 X 


lO^ 


6.13969 


.72495 X 10-6 


7.86031 


19 


3-0254 


" 


.48079 


•33053 " 


.51921 


20 


6.6356 




.82188 


.15070 


.17812 



Table 21 o 
EXPONENTIAL FUNCTIONS. 

Values otS *' and 6 * and their logarithms. 



X 


e * 






log ^ * ' 


1 

2 

3 

4 
5 

6 

7 
8 

9 
10 

11 

12 
13 
14 
15 

16 

17 
18 

19 
20 


1.5576 
2.4260 
3-7786 

9. 1 666 

14.277 
22.238 
34-636 
53-948 
84.027 

130.88 
203.85 
317.50 
494.52 
770.24 

1 199.7 
186S.6 
2910.4 

4533-1 
7060.5 


0.19244 
.38488 

•57733 
.76977 
.96221 

I.I 5465 
•34709 
•53953 
•73198 
.92442 

2.1 1686 
•30930 
.50174 
.69418 
.88663 

3.07907 
.27151 
•46395 
•65639 
.84883 


0.64203 
.41221 
.26465 
.16992 
.10909 

0.070041 
.044968 
.028871 
.018536 
.011901 

0.0076408 
.0049057 
.0031496 
.0020222 
.0012983 

0.000S3355 
.00053517 
.00034360 
.00022060 
.00014163 


T.80756 
.61512 

.42267 
.23023 
•03779 

2.84535 
.65291 
.46047 
.26802 
•07558 

3.88314 

.69070 

.49S26 
.30582 
•I 1337 

4.92093 
.72849 
•53605 
•34361 
•I5II7 



Smithsonian Tables. 



56 Tables 22 AND 23. EXPONENTIAL FUNCTIONS AND LEAST SQUARES. 

TABLE 22. — Exponential Functions. 

Value of e" and <f"^ and their logarithms. 



X 


^ 


log.f' 


e-' 


X 


^■^ 


log^^ 


e'" 


1/64 


1.0157 


0.00679 


0.98450 


1/3 


1-3956 


0.14476 


0.71653 


1/32 


•0317 


•01357 


.96923 


1/2 


.6487 


.21715 


•60653 


I/I6 


.0645 


.02714 


•93941 


3/4 


2.1170 


•32572 


•47237 


i/io 


.1052 


•04343 


.90484 


I 


■7183 


.43429 


•3678S 


1/9 


•1175 


.04825 


.89484 


5/4 


3-4903 


.54287 


.28650 


1/8 


^•m>^ 


0.05429 


0.88250 


3/2 


4.4817 


0.65144 


0.22313 


1/7 


■1536 


.ob204 


.86688 


7/4 


5-7546 


.76002 


•17377 


1/6 


.1814 


.07238 


.84648 


2 


7-3891 


.86859 


•13534 


i/S 


.2214 


.08686 


.81873 


9/4 


9-4877 


.97716 


.10540 


1/4 


.2840 


.10857 


.77880 


5/2 


12.1S25 


1.08574 


.08208 



TABLE 23. — Least Squares. 

Values of P = ^^f^ *^ ^(*^>' d {hx). 

This table gives the value of P, the probability of an observational error having a value posi 

five or negative equal to or less than x when h is the measure of precision, P = / 

■\I-kJ " 



ihxyi 



d{/ix). 


For values of the inverse 


function see the 


table on 


Diffusion. 








hx 





1 


2 


3 


4 


6 


6 


7 


8 


9 




0.0 




.01128 


.02256 


•033S4 


.04511 


•05637 


.06762 


.07886 


.09008 


.10128 




.1 


.11246 


.12362 


•13476 


•14587 


-15695 


.16800 


.17901 


.18999 


.20094 


.211S4 




.2 


.22270 


•23352 


.24430 


.25502 


.26570 


•27633 


.28690 


.29742 


.30788 


.31828 




•3 


.32863 


•33891 


•34913 


•3592S 


■36936 


•37938 


•38933 


.39921 


.40901 


.41874 




•4 


.42839 


-43797 


•44747 


.45689 


.46623 


.47548 


.48466 


•49375 


•50275 


.51167 




0.5 


.52050 


-52924 


•53790 


■54646 


-55494 


•56332 


.57162 


•57982 


.58792 


•59594 




.6 


.60386 


.61168 


.61941 


•62705 


•63459 


.64203 


.64938 


.65663 


•66378 


.670S4 




•7 


.67780 


.68467 


.69143 


.69810 


.70468 


.71116 


•71754 


•72382 


.73001 


.73610 




.8 


.74210 


.74S00 


■75381 


•75952 


•76514 


.77067 


.77610 


.78144 


.78669 


.79184 




•9 


.79691 


.80188 


.80677 


.81156 


.81627 


.82089 


.82542 


.S2987 


•83423 


.83851 




1.0 


.84270 


.84681 


.85084 


.85478 


.85865 


.86244 


.86614 


•86977 


•87333 


.876S0 




.1 


.8S021 


-88353 


.88679 


.88997 


.89308 


.89612 


.89910 


.90200 


.904S4 


.90761 




.2 


.91031 


.91296 


•91553 


.91805 


.92051 


.92290 


•92524 


.92751 


•92973 


.93190 




•3 


.93401 


.93606 


.93807 


.94002 


.94191 


•94376 


•94556 


-94731 


.94902 


■95067 




•4 


.95229 


•95385 


■95538 


.95686 


.95S30 


•95970 


.96105- 


-96237 


•96365 


.96490 




1.5 


.96611 


.9672S 


.96841 


•96952 


•97059 


.97162 


•97263 


.97360 


•97455 


■97546 




.6 


•97635 


.97721 


■97804 


.97884 


.97962 


.98038 


.98110 


.9S181 


.98249 


■98315 




•7 


-98379 


.98441 


.98500 


•98558 


.98613 


.9S667 


.98719 


.98769 


.98817 


.98S64 




.8 


.98909 


.98952 


■9S994 


•99035 


.99074 


.991 u 


.99147 


.99182 


.99216 


.99248 




-9 


.99279 


.99309 


-99338 


•99366 


.99392 


.99418 


•99443 


.99466 


•994S9 


.99511 




2.0 


-99532 


-99552 


-99572 


.99591 


.99609 


.99626 


.99642 


.99658 


•99673 


.996S8 




.1 


.99702 


-99715 


.99728 


.99741 


•99753 


-99764 


•99775 


-99785 


-99795 


.99805 




.2 


.99814 


.99822 


.99831 


•99839 


.99846 


•99854 


.99861 


.99867 


•99874 


.99S80 




•3 


.99886 


.99891 


•99S97 


.99902 


.99906 


.99911 


-99915 


.99920 


•99924 


•99928 




•4 


-99931 


-99935 


.99938 


.99941 


•99944 


•99947 


.99950 


•99952 


•99955 


•99957 




2.5 


•99959 


.99961 


•99963 


.99965 


•99967 


•99969 


.99971 


.99972 


•99974 


•99975 




.6 


•99976 


•99978 


.99979 


.99980 


.99981 


.99982 


.99983 


.99984 


-999S5 


.99986 




•7 


.99987 


-99987 


.99988 


.99989 


.99989 


.99990 


.99991 


.99991 


.99992 


.99992 




.8 


.99992 


•99993 


•99993 


•99994 


.99994 


.99994 


•99995 


.99995 


-99995 


-99996 




-9 


•99996 


.99996 


•99996 


•99997 


.99997 


•99997 


•99997 


-99997 


•99997 


,99998 




3.0 


.99998 


-99999 


•99999 


1. 00000 

















2 /'' 

Taken from a paper by Dr. James Burgess 'on the Definite Integral r^y ^ ^~'^ dt, with Ex. 
tended Tables of Values.' Trans. Roy. See. of Edinburgh, vol. xxxix, 1900, p. 257. 
Smithsonian Tables. 



Table 24. 
LEAST SQUARES. 



57 



Thi 


s table gives the values of the probability P 


, as definec 


in last table, correspondine to 


different values of 




-r/ 


r where r is the " probable error." The probable error r is equal to 0.47694/ h. 




r 





1 


2 


3 


4 


5 


6 


7 


8 


9 


0.0 


.00000 


.00538 


.01076 


.01614 


.02152 


.02690 


.03228 


.03766 


•04303 


.04840 


O.I 


•0537S 


.05914 


.06451 


.06987 


•07523 


.0S059 


.08594 


.09129 


.09663 


.10197 


0.2 


.10731 


. 1 1 264 


.11796 


.12328 


.12860 


13391 


.13921 


•14451 


.14980 


.15508 


0-3 


•16035 


.16562 


.17088 


.17614 


.18138 


.18662 


.19185 


•19707 


.20229 


.20749 


0.4 


.21268 


.21787 


.22304 


.22821 


•23336 


.23851 


.24364 


.24876 


•25388 


.25898 


0.5 


.26407 


.26915 


.27421 


.27927 


.28431 


•28934 


.29436 


.29936 


•30435 


■30933 


0.6 


•31430 


•31925 


•32419 


•32911 


•33402 


•33892 


•34380 


.34866 


•35352 


■35835 


0-7 


•36317 


.36798 


•37277 


•37755 


•38231 


•38705 


•39178 


•39649 


.40118 


.40586 


0.8 


.41052 


•41517 


.41979 


.42440 


.42S99 


•43357 


•43813 


•44267 


•44719 


•45169 


0.9 


.45618 


.46064 


.46509 


.46952 


•47393 


•47832 


.48270 


.48705 


•49139 


•49570 


1.0 


.50000 


.50428 


•50S53 


•51277 


.51699 


.52119 


•52537 


•52952 


•53366 


•53778 


I.I 


.541SS 


•54595 


.55001 


.55404 


•55806 


• 56205 


.56602 


.56998 


•57391 


.57782 


1.2 


.5S171 


•58558 


.58942 


•59325 


•59705 


.60083 


.60460 


•60S33 


.61205 


■61575 


1-3 


.61942 


.62308 


.62671 


.63032 


•63391 


■63747 


.64102 


•64454 


.64804 


.65152 


1.4 


.6549S 


.65S41 


.66182 


.66521 


.66858 


•67193 


.67526 


.67S56 


.68184 


.68510 


1.5 


•6SS33 


•69155 


•69474 


.69791 


.70106 


.70419 


.70729 


.71038 


•71344 


.71648 


1.6 


.71949 


.72249 


•72546 


.72841 


•73134 


■73425 


•73714 


.74000 


■74285 


■74567 


1-7 


.74847 


•75124 


.75400 


•75674 


■75945 


.76214 


.764S1 


•76746 


.77009 


.77270 


1.8 


•77528 


•77785 


.78039 


.78291 


.78542 


.78790 


.79036 


.79280 


•79522 


.79761 


1.9 


.79999 


.80235 


.80469 


.80700 


.80930 


.81158 


•81383 


.81607 


.81828 


.82048 


2.0 


.82266 


.824S1 


.82695 


.82907 


.83117 


•83324 


•83530 


•83734 


•83936 


■84137 


2.1 


i9^^. 


•84531 


.84726 


.84919 


.85109 


•85298 


.85486 


.85671 


•85854 


.86036 


2.2 


.S6216 


.86394 


.86570 


.86745 


.86917 


.870S8 


•87258 


.87425 


•87591 


•S7755 


2-3 


.S791S 


.S807S 


.88237 


•88395 


.88 5 50 


.8S705 


.S8857 


.89008 


•89157 


.89304 


2.4 


.S9450 


.89595 


.89738 


.89879 


.90019 


.90157 


■90293 


.90428 


.90562 


.90694 


2.5 


.90825 


.90954 


.91082 


.91208 


•91332 


•91456 


•91578 


.91698 


.91817 


•91935 


2.6 


.92051 


.92166 


.92280 


.92392 


.92503 


•92613 


.92721 


.92828 


■92934 


•93038 


2.7 


•93141 


•93243 


•93344 


•93443 


•93541 


•93638 


•93734 


•93828 


•93922 


.94014 


2.8 


.94105 


•94195 


.94284 


•94371 


.94458 


•94543 


.94627 


.94711 


■94793 


•94S74 


2.9 


•94954 


•95033 


.95111 


•95187 


•95263 


•95338 


•95412 


.95484 


•95557 


.95628 







1 


2 


3 


4 


5 


6 


7 


8 


9 


3 


.95698 


.96346 


.96910 


•97397 


.97817 


.98176 


.98482 


•98743 


.98962 


•99147 


4 


.99302 


•99431 


•99539 


99627 


.99700 


.99760 


.99808 


.99848 


•99879 


.99905 


5 


.99926 


•99943 


.99956 .99966 


•99974 


.99980 


.99985 


.99988 


.99991 


•99993 



Table 25. 
LEAST SQUARES. 

Values of the factor 0.6745-%/-^^. 
\ n— 1 

This factor occurs in the equation r^ =r o.674S\/ for the probable error of a single observation, and other 

\n—i 
similar equations. 



n == 


1 


2 


3 


4 


5 


6 


7 


8 


9 


00 






0.6745 


0.4769 


0.3894 


0.3372 


0.3016 


0.2754 


0.2549 


0.2385 


10 


0.2248 


0.2133 


•2034 


.1947 


.1871 


•1803 


.1742 


.1686 


.1636 


•1590 


20 


•1547 


.1508 


.1472 


.1438 


.1406 


•1377 


•1349 


•1323 


.1298 


•1275 


30 


.1252 


.1231 


.1211 


.1192 


•1174 


•1157 


.1140 


.1124 


.1109 


.1094 


40 


.1080 


.1066 


•1053 


.1041 


.1029 


.1017 


.1005 


.0994 


.0984 


.0974 


50 


0.0964 


0.0954 


0.0944 


0-0935 


0.0926 


0.0918 


0.0909 


0.0901 


0.0893 


0.0SS6 


6o 


.087S 


.0871 


.0864 


•0857 


.0850 


.0843 


.0837 


.0830 


.0824 


.0818 


70 


.0812 


.0806 


.oSoo 


■0795 


.0789 


.0784 


.0779 


.0774 


.0769 


.0764 


80 


■0759 


•0754 


•0749 


.0745 


.0740 


•0736 


.07'!-' 


.0727 


■0723 


.0719 


90 


•0715 


.0711 


.0707 


.0703 


.0699 


.0696 


.0692 


.0688 


.0685 


.06S1 



Smithsonian Tables. 



58 



Table 26.- LEAST SQUARES. 

Values ol tlie factor 0.6746'< 



'\n(M-l)" 



. _ . for the probable error of the arithmetic i 



n 


= 


1 


2 


3 


4 


6 


6 


7 


8 


9 


00 






0.4769 


0.2754 


0.1947 


0.1508 


0.1 23 1 


0.1041 


0.0901 


0.0795 


lO 


0.071 1 


0.0643 


.0587 


.0540 


.0500 


.0465 


•0435 


.0409 


.0386 


.0365 


20 


.0346 


.0329 


.0314 


.0300 


.02S7 


.0275 


.0265 


•0255 


.0245 


.0237 


3° 


.0229 


.0221 


.0214 


.0208 


.0201 


.0196 


.0190 


.0185 


.0180 


.0175 


40 


.0171 


.0167 


.0163 


.0159 


.0155 


.0152 


.0148 


.0145 


.0142 


.0139 


50 


0.0136 


0.0134 


O.0131 


0.0128 


0.0126 


0.0124 


0.0122 


0.0119 


0.0117 


0.0115 


60 


■01 1 3 


.0111 


.0110 


.0108 


.0106 


.0105 


.0103 


.0101 


.0100 


.0098 


70 


.0097 


.0096 


.0094 


.0093 


.0092 


.0091 


.0089 


.ooSS 


.0087 


.0086 


80 


.0085 


.0084 


.0083 


.00S2 


.0081 


.0080 


.0079 


.0078 


.0077 


.0076 


90 


.0075 


.0075 


.0074 


.0073 


.0072 


.0071 


.0071 


.0070 


.0069 


.0068 



Table 27. -LEAST SQUARES. 

Values of the factor 0.8453'* 



\ ti(n-l) 



This factor occurs in the approximate equation r =:o.8453 



>l;c{n—l) 



for the probable error of a single observation. 



TO 


= 


1 


2 


3 


4 


6 


6 


7 


8 


9 


00 






0.5978 


0.3451 


0.2440 


0.1890 


0.1543 


0.1304 


0.1130 


0.0996 


10 


0.0891 


0.0806 


.0736 


.0677 


.0627 


•0583 


.0546 


•0513 


.0483 


•0457 


20 


•0434 


.0412 


■0393 


.0376 


.0360 


•0345 


•0332 


.0319 


.0307 


.0297 


.30 


.0287 


.0277 


.0268 


.0260 


.0252 


.0245 


.0238 


.0232 


.0225 


.0220 


40 


.0214 


.0209 


.0204 


.0199 


.0194 


.0190 


.0186 


.0182 


.0178 


.0174 


50 


0.0171 


0.0167 


0.0164 


0.0161 


0.0158 


0.0155 


0.0152 


0.0150 


0.0147 


0.0145 


60 


.0142 


.0140 


•0137 


•0135 


•0133 


.0131 


.0129 


.0127 


.0125 


.0123 


70 


.0122 


.0120 


.01 iS 


.0117 


.0115 


.0113 


.0112 


.0111 


.0109 


.0108 


80 


.0106 


.0105 


.0104 


.0102 


.0101 


.0100 


.0099 


.009S 


.0097 


.0096 


90 


.0094 


.0093 


.0092 


.0091 


.0090 


.0089 


.0089 


.0088 


.0087 


.0086 



Table 28. -LEAST SQUARES. 

Values of 0.8453 — . — - • 
nyn— 1 



This factor occurs in the approximate equation >-q= 0.8453 



"\ln~> 



for the probable error of the arithmetical mean. 



n 


= 


1 


2 


3 


4 


6 


6 


7 


8 


9 




00 






0.4227 


0.1993 


0.1220 


0.0845 


0.0630 


0.0493 


0.0399 


0.0332 




10 


0.0282 


0.0243 


.0212 


.0188 


.0167 


.0151 


.0136 


.0124 


.0114 


.0105 




20 


.0097 


.0090 


.0084 


.0078 


.0073 


.0069 


.0065 


.0061 


.0058 


•0055 




30 


.0052 


.0050 


.0047 


.0045 


.0043 


.0041 


.0040 


.003S 


.0037 


•0035 




40 


.0034 


•0033 


.0031 


.0030 


.0029 


.0028 


.0027 


.0027 


.0026 


.0025 




50 


0.0024 


0.0023 


0.0023 


0.0022 


0.0022 


0.0021 


0.0020 


0.0020 


0.0019 


0.0019 




60 


.0018 


.0018 


.0017 


.0017 


.0017 


.0016 


.0016 


.0016 


.0015 


•001 5 




70 


•00 1 5 


.0014 


.0014 


.0014 


■00 1 3 


•00 1 3 


.0013 


.0013 


.0012 


.0012 




80 


.0012 


.0012 


.00 u 


.0011 


.0011 


.0011 


.0011 


.0010 


.0010 


.0010 




90 


.0010 


.0010 


.0010 


.0009 


.0009 


.0009 


.0009 


.0009 


.0009 


.0009 





Smithsonian Tables. 



Table 29. 
LEAST SQUARES. 



59 



Observation equations : 

aizi + biZ2 + . . . IiZq =Mi, weight pi 
a2Zi + b2Z2 + . . . l2Zq = Mj. weight p2 



Auxiliary equations : 



Normal equations : 



anZi + biiZo + . . . InZq = Mn, weight pn. 

[paa] =piar +P2a| + . . • pna^. 
[pab] = piaibi + P2a2b2 + . . . pna„bn. 

[paM] = piaiMi + paagMa + . . . pnanMn. 

[paa]zi+ [pab]z2 + . . . [pal]zq = [paM] 
[pabjzi + [pbbjzo + . . . [pbl]zq = [pbM] 

[pla]zi + iplb]z2 + . . . [plljzq = [plM]. 

Solution of normal equations in the form, 

zi = Ai[paM] + Bi[pbM] + • • • Li[plM] 
Z2 = A2[paM] + B2[pbM] + . . . L2[plM] 

zq = An[paM] + Bn[pbMi + •"• ■ Ln[plM]. 



gives 



wherein 



weight of zi = pzi = (Ai)— ' ; probable error of zi = — — 

VPZl 

r 

weight of Z2 = pz2 = (62)"^ ; probable error of Z2 = 

V/Pig 

weight of Zq = pz = (Ln)~^; probable error of Zq = — — 

VPz^ 

r = probable error of observation of weight unity 
= 0.6745 -%/ — !— . (q unknowns.) 



-q 

Arithmetical mean, n observations : 



= 0.6745 a/ — — = - ' (approx.) =probable error of ob- 

' "~^ V^n(n— i)' servation of weight unity. 

, / S v2 _ 0.845 3 2 V , 

ro = 0.6745-1/ — : ' /i • (approx.) = probable error 

\n(n-i) nVn-i of mean. 

Weighted mean, n observations: 

, /Spv2 r ^ / Spv2 

r = 0.6745 V ^^: ^o =^^=0.6745 ^^^ 



i)Sp 

Probable error (R) of a function (Z) of several observed quantities zi, Z2, . . . whose 
probable errors are respectively, r^, r2, . . . . 

Z = f (zr, Z2, . . .) 

Examples : 

Z = zi ± Z2 + . . . Ri = rl + tI+ . . . 

Z = Azi ± Az2 ± . . . R2 =A2 rl + Bhl+ . ."". 

Z = zi Z2. R* =zi r^ + Zi r\. 



Smithsonian Tables. 



6o 



V,. 



Table 30. 
DIFFUSION. 

Inverse * values of z'/c= i — —7— / 

log X == log (2^) + logv''^^- ^ expressed in seconds. 
= log 5 + log-v//^^. / expressed in days. 
= log 7 + log \/^. " " years. 

. i = coefficient of diffusion.t 
c = initial concentration. 
V = concentration at distance x, time /. 



v/c 


log 2? 


2g 


log S 


5 


logy 


7 


0.00 


+ CO 


+ 00 


+ « 


+ 00 


00 


00 


.01 


0.56143 


3.6428 


3.02970 


1070.78 


4.31098 


20463. 


.02 


•5I7I9 


3.2900 


2.98545 


967.04 


.26674 


18481. 


•03 


.48699 


3.0690 


•95525 


902.90 


•23654 


17240. 


.04 


.46306 


2.9044 


•93132 


853-73 


.21261 


16316. 


0.05 


0.44276 


2.7718 


2.91 102 


814.74 


4.I9231 


15571. 


.06 


.42486 


2.6598 


.89311 


781.83 


.17440 


14942. 


.07 


.40865 


2.5624 


.87691 


753^20 


.15820 


14395- 


.08 


•39372 


2.4758 


.86198 


727.75 


•14327 


13908. 


.09 


•37979 


2-3977 


.84804 


704.76 


•12933 


13469^ 


0.10 


0.36664 


2.3262 


2.S3490 


683-75 


4.I1619 


13067. 


.11 


•35414 


2.2602 


.82240 


664.36 


.10369 


12697. 


.12 


.34218 


2.1988 


.81044 


646.31 


•09173 


12352. 


■13 


•33067 


2.1413 


-79893 


629.40 


.08022 


12029. 


.14 


•31954 


2.0871 


.78780 


613-47 


.06909 


1 1 724. 


0.15 


0.30874 


2.0358 


2.77699 


598.40 


4.05828 


1 1436. 


.16 


.29821 


1.987 1 


.76647 


584.08 


.04776 


1 1 162. 


•17 


.28793 


1.9406 


.75619 


570.41 


.03748 


10901. 


.18 


.27786 


1. 896 1 


.74612 


557-34 


.02741 


10652. 


.19 


.2679S 


I.S534 


-73624 


544-80 


•01753 


10412. 


0.20 


0.25S25 


1.8124 


2.72651 


532-73 


4.00780 


10181. 


.21 


.24866 


1.7728 


.71692 


521.10 


3.99821 


9958.9 


.22 


.23919 


1^7346 


•70745 


509.86 


.98874 


9744.1 


•23 


.22983 


1.6976 


.69808 


498.98 


•97937 


9536.2 


.24 


.22055 


1. 661 7 


.6S880 


488.43 


.97010 


9334.6 


0.25 


0.21134 


1.6268 


2.67960 


478.19 


3.96089 


9138.9 


.26 


.20220 


I • 5930 


.67046 


468.23 


•95175 


8948.5 


.27 


.19312 


1.5600 


.66137 


458-53 


.94266 


^763-2 


.28 


.18407 


1.5278 


.65232 


449.08 


•93361 


8582.5 


.29 


•17505 


1.4964 


■64331 


439-85 


.92460 


8406.2 


0.30 


0.16606 


1-4657 


2.63431 


430.84 


3.91560 


8233-9 


■31 


.15708 


1^4357 


•62533 


422.02 


.90662 


8065.4 


•32 


.14810 


1 .4064 


.61636 


413-39 


.89765 


7900.4 


•33 


.13912 


1-3776 


.60738 


404.93 


.88867 


7738.S 


•34 


.13014 


i^3494 


.59840 


396.64 


.87969 


7580.3 


0.35 


0.12114 


1.3217 


2.58939 


3S8.50 


3.87068 


7424.8 


•36 


.11211 


1.2945 


■58037 


380.51 


.86166 


7272.0 


■37 


.10305 


1.2678 


■57131 


372.66 


.85260 


7122.0 


•38 


.09396 


1.2415 


.56222 


364-93 


■8435' 


6974.4 


•39 


.08482 


1. 2157 


•55308 


357-34 


•83437 


6829.2 


0.40 


0.07563 


1. 1902 


2-54389 


349-86 


3.82518 


6686.2 


.41 


.06639 


1. 1652 


.53464 


342.49 


•81593 


6545-4 


.42 


.05708 


1-1405 


•52533 


335-22 


.80662 


6406.6 


•43 


.04770 


1.1161 


•51595 


328.06 


•79724 


6269.7 


•44 


.03824 


1.0920 


.50650 


320.99 


•78779 


6134.6 


0.45 


0.02870 


1.0683 


2.49696 


314.02 


3-77825 


6001.3 


.46 


.01907 


1.0449 


-48733 


307-13 


.76862 


5S69-7 


•47 


.00934 


1.0217 


.47760 


300.33 


•758S9 


5739-7 


.48 


9.99951 


0.99886 


.46776 


293.60 


•74905 


561 1.2 


•49 


.98956 


0.97624 


.45782 


286.96 


•7391 1 


5484.1 


0.50 


9-97949 


0.95387 


2-44775 


280.38 


3.72904 


5358.4 



• Kelvin, Mathematical and Physical Papers, vol. III. p. 428 ; Becker, Am. Jour, 
of Sci. vol. III. 1897, p. 2S0. t For direct values see table 23. 

SviTHSONiAN Tables. 



Table 30 (continued). 
DIFFUSION. 



6l 



vie 


log 2q 


iq 


log 5 


5 


logy 


V 


0.50 


9-97949 


0.95387 


2.44775 


280.38 


3.72904 


5358-4 


•51 


.96929 


-93 '74 


•43755 


273-87 


.71884 


5234-1 


.52 


.95896 


.90983 


.42722 


267.43 


.70851 


51 1 1.0 


•53 


.94848 


.88813 


.41674 


261.06 


.69803 


4989.1 


•54 


•93784 


.86665 


.40610 


254-74 


.68739 


4868.4 


0.55 


9.92704 


0.84536 


2-39530 


248.48 


3.67659 


4748.9 


.56 


.91607 


.82426 


.38432 


242.28 


.66561 


4630-3 


•57 


.90490 


•80335 


•37316 


236-13 


.65445 


4512.8 


.58 


•S9354 


.78260 


.361S0 


230.04 


.64309 


4396-3 


•59 


.88197 


.76203 


•35023 


223.99 


.63152 


4280.7 


0.60 


9.8701S 


0.74161 


2-33843 


217-99 


3-61973 


4166.1 


.61 


.85S15 


•72135 


.32640 


212.03 


.60770 


4052.2 


.62 


•S45S7 


.70124 


.31412 


206. 1 2 


•59541 


3939-2 


•63 


•83332 


.68126 


.30157 


200.25 


.58286 


3827.0 


.64 


.82048 


.66143 


.28874 


194.42 


•57003 


3715-6 


0.65 


9.80734 


0.64172 


2.27560 


188.63 


3-556S9 


3604.9 


.66 


•7938S 


.62213 


.26214 


182.87 


•54343 


3494-9 


.67 


.78008 


.60266 


•24833 


177.15 


.52962 


3385-4 


.68 


.76590 


-58331 


.23416 


171.46 


•51545 


3276.8 


.69 


•75133 


.56407 


•21959 


165.80 


.500S8 


3168.7 


0.70 


9-73634 


0.54493 


2.20459 


160.17 


3.48588 


3061. 1 


•71 


.72089 


.52588 


.18915 


154-58 


.47044 


2954.2 


.72 


.70495 


•50694 


.17321 


149.01 


•45450 


2847.7 


•73 


.68S49 


.4SS08 


-15675 


143-47 


.43804 


2741.8 


•74 


.67146 


.46931 


.13972 


137-95 


.42101 


2636.4 


075 


9.65381 


0.45062 


2.12207 


132.46 


3-40336 


2531-4 


.76 


•63550 


.43202 


.10376 


126.99 


-38505 


2426.9 


•77 


.61646 


.41348 


.08471 


121.54 


.36600 


2322.7 


.78 


.59662 


.39502 


.06487 


II 6. 1 1 


.34616 


2219.0 


.79 


•57590 


.37662 


.04416 


110.70 


•32545 


2115.7 


0.80 


9-55423 


0.35829 


2.02249 


105.31 


3-30378 


2012.7 


.81 


•53150 


•34001 


1^99975 


99-943 


.28104 


1910.0 


.82 


-507 58 


.32180 


•97584 


94-589 


•25713 


1807.7 


•83 


•48235 


•30363 


-95061 


89.250 


.23190 


1705-7 


.84 


.45564 


.28552 


-92389 


83.926 


.20518 


1603.9 


0.85 


9-42725 


0.26745 


1-89551 


78.615 


3.17680 


1502.4 


.86 


-39695 


■24943 


.86521 


IZ-Z^l 


.14650 


1401.2 


•87 


-36445 


•23145 


.83271 


68.032 


.11400 


1300.2 


.88 


.32940 


•21350 


.79766 


62.757 


.07895 


1 199.4 


.89 


•29'35 


•19559 


.75961 


57-492 


3.04090 


1098.7 


0.90 


9.24972 


0.17771 


1-71797 


52.236 


2.99926 


998.31 


.91 


.20374 


.15986 


.67200 


46.989 


•95329 


898.03 


.92 


•15239 


.14203 


.62065 


41-750 


.90194 


797.89 


•93 


.09423 


.12423 


.56249 


36-5'6 


•84378 


697.88 


•94 


9.02714 


.10645 


•49539 


31.2S9 


.77668 


597-98 


0.95 


8.94783 


0.08868 


1. 41609 


26.067 


2.69738 


498.17 


.96 


.850S2 


.07093 1 


-31907 


20.848 


.60036 


39S.44 


•97 


•72580 


■05319 


.19406 


15-633 


•47535 


298.78 


.98 


•54965 


•03545 


.01791 


10.421 


.29920 


199.16 


•99 


.24859 


■01773 


9.71684 


5.21007 


I •99813 


99^571 


1.00 


— CO 


0.00000 

1 


— 00 


0.00000 


— 00 


0.000 



SurTHSONiAN Tables. 



62 



Table 31 . 
GAMMA FUNCTION. 



Value 



of log I e~'x" 

Jo 



^<to + 10. 



Values of the logarithms + lo of the " Second Eulerian Integral " (Gamma function) I e—*x'*—^dx or log r(«)+io 

Jq 

for values of n between i and 2. When « has values not lying between i and 2 the value of the function can be 
readily calculated from the equation r(«-)-i) ^ nV(n) =: «(« — i) . . . (« — r)r{« — r). 



r 

Jo 



n 





1 


2 


3 


4 


5 


6 


7 


8 


9 


1.00 




97497 


95001 


92512 


90030 


87555 


85087 


82627 


80173 


77727 


yyy 


1. 01 


752S7 


72S55 


70430 


68011 


65600 


63196 


60798 


58408 


56025 


53648 


1.02 


51279 


48916 


46561 


44212 


41870 


39535 


37207 


34886 


32572 


30265 


1.03 


27964 


25671 


23384 


21104 


1 883 1 


16S64 


14305 


I20S2 


09806 


07S67 


1.04 


05334 


03108 


00889 


9S677 


96471 


94273 


92080 


89895 


S7716 


85544 


1.05 


9-9883379 


81220 


79068 


76922 


74783 


72651 


70525 


68406 


66294 


64 1 88 


1.06 


62089 


59996 


57910 


55830 


53757 


51690 


49630 


47577 


45530 


434S9 


1.07 


4145s 


39428 


37407 


35392 


33384 


31382 


29387 


27398 


25415 


23439 


1.08 


21469 


19506 


17549 


ISS99 


13655 


11717 


09785 


07860 


OS94I 


04029 


1.09 


02123 


00223 


9S329 


96442 


94561 


92686 


90818 


88956 


87100 


85250 


1.10 


9.9783407 


81570 


79738 


77914 


76095 


74283 


72476 


70676 


68882 


67095 


I. II 


65313 


63538 


61768 


60005 


58248 


56497 


54753 


53014 


51281 


49555 


1. 12 


47834 


46120 


4441 1 


42709 


41013 


39323 


37638 


35960 


34288 


32622 


I-I3 


30962 


29308 


27659 


26017 


24381 


22751 


21126 


19508 


17896 


16289 


1. 14 


146S9 


13094 


1 1 505 


09922 


08345 


06774 


05209 


03650 


02096 


00549 


1.15 


9.9699007 


97471 


95941 


94417 


92898 


91386 


89879 


8S378 


86883 


85393 


1. 16 


83910 


82432 


80960 


79493 


78033 


76578 


75129 


736S6 


72248 


70S 1 6 


1. 17 


69390 


67969 


66554 


65145 


63742 


62344 


60952 


59566 


581S5 


56810 


1. 18 


55440 


54076 


52718 


51366 


5?°'9 


48677 


47341 


460 II 


446S7 


43368 


1. 19 


42054 


40746 


39444 


38147 


36856 


35570 


34290 


33016 


31747 


30483 


1.20 


9.9629225 


27973 


26725 


25484 


24248 


23017 


21792 


20573 


19358 


18150 


1. 21 


16946 


15748 


14556 


13369 


12188 


HOT I 


09841 


08675 


0751 s 


06361 


1.22 


05212 


04068 


02930 


01796 


00669 


99546 


98430 


97318 


96212 


951 1 1 


1.23 


594015 


92925 


91840 


90760 


89685 


88616 


S7553 


86494 


85441 


84393 


1.24 


83350 


82313 


81280 


80253 


79232 


78215 


77204 


76198 


75197 


74201 


1.25 


9-957321 1 


72226 


71246 


70271 


69301 


68337 


^7377 


66423 


65474 


64530 


1.26 


63592 


62658 


61730 


60806 


59888 


58975 


58067 


57165 


56267 


55374 


1.27 


54487 


53604 


52727 


51855 


50988 


50126 


49268 


4S416 


47570 


46728 


1.28 


45891 


45059 


44232 


43410 


42593 


41782 


40975 


40173 


39376 


38585 


1.29 


37798 


37016 


36239 


35467 


34700 


33938 


33181 


32429 


316S2 


30940 


1.30 


9-9530203 


29470 


28743 


28021 


27303 


26590 


25883 


25180 


24482 


237S9 


I-3I 


23100 


22417 


21739 


21065 


20396 


19732 


19073 


18419 


17770 


17125 


1.32 


16485 


15850 


15220 


14595 


13975 


13359 


12748 


12142 


11541 


10944 


1-33 


10353 


09766 


09184 


08606 


08034 


07466 


06903 


06344 


05791 


05242 


1-34 


04698 


04158 


03624 


03094 


02568 


02048 


01532 


01021 


00514 


00012 


1.35 


9-9499515 


99023 


98535 


98052 


97573 


97100 


96630 


96166 


95706 


95251 


1.36 


94800 


94355 


93913 


93477 


93044 


92617 


92194 


91776 


91362 


90953 


1-37 


90549 


90149 


89754 


89363 


88977 


88595 


88218 


87846 


87478 


87115 


1.38 


86756 


86402 


86052 


85707 


85366 


85030 


84698 


84371 


84049 


83731 


1-39 


83417 


83108 


82803 


82503 


82208 


81916 


81630 


81348 


81070 


80797 


1.40 


9.9480528 


80263 


80003 


79748 


79497 


79250 


79008 


78770 


78537 


78308 


1.41 


78084 


77864 


77648 


77437 


77230 


77027 


76829 


76636 


76446 


76261 


1.42 


76081 


75905 


75733 


75565 


75402 


75243 


75089 


74939 


74793 


74652 


1-43 


74515 


74382 


74254 


74130 


74010 


73894 


73783 


73676 


73574 


73476 


1.44 


73382 


73292 


73207 


73125 


73049 


72976 


72908 


72844 


72784 


72728 



Legendre's "Exercises de Calcul Integral," tome ii. 



Smitheon'an Tables. 



i 



Table 31 {continued). 

GAMMA FUNCTION. 



63 



n 





1 


2 


3 


4 


5 


6 


7 


8 


9 




1.45 


9.9472677 


72630 


725S7 


72549 


72514 


72484 


72459 


72437 


72419 


72406 




1.46 


72397 


72393 


72392 


72396 


72404 


72416 


72432 


72452 


72477 


72506 




1.47 


7^539 


72576 


72617 


72662 


72712 


72766 


72824 


72886 


72952 


73022 




1.48 


73097 


73175 


73258 


73345 


73436 


73531 


73630 


7373-\ 


73841 


73953 




1.49 


74068 


74188 


74312 


74440 


74572 


74708 


74848 


74992 


75141 


75293 




1.50 


9-9475449 


75610 


75774 


75943 


76116 


76292 


76473 


76658 


76S47 


77040 




1. 51 


77^37 


774^-7 


77642 


77851 


78064 


78281 


78502 


78727 


78956 


79189 




1-5^ 


79426 


79667 


79912 


80161 


80414 


80671 


80932 


81196 


81465 


81738 




1-53 


82015 


82295 


82580 


82868 


83161 


83457 


S3758 


84062 


84370 


84682 




1-54 


84998 


8531S 


85642 


85970 


86302 


86638 


86977 


87321 


87668 


88019 




1.55 


9.94S8374 


88733 


89096 


89463 


89834 


90208 


905S7 


90969 


91355 


91745 




1.56 


92139 


92537 


92938 


93344 


93753 


94166 


94583 


95004 


95429 


95857 




'•57 


96289 


96725 


97165 


97609 


98056 


98508 


98963 


99422 


99885 


00351 




1.58 


500822 


01296 


01774 


02255 


02741 


03230 


03723 


04220 


04720 


05225 




1-59 


05733 


06245 


06760 


07280 


07803 


08330 


08860 


09395 


09933 


10475 




1.60 


9.9511020 


1 1 569 


12122 


12679 


13240 


13804 


14372 


14943 


15519 


16098 




i.6i 


16680 


17267 


17857 


18451 


19048 


19649 


20254 


20862 


21475 


22091 




1.62 


22710 


23333 


23960 


24591 


25225 


25863 


26504 


27149 


27798 


28451 




1.63 


29107 


29766 


30430 


31097 


31767 


32442 


33120 


33801 


34486 


35175 




1.64 


35867 


36563 


37263 


37966 


38673 


39383 


40097 


40815 


41536 


42260 




1.65 


9.95429S9 


43721 


44456 


45195 


4593S 


46684 


47434 


48 1 87 


48944 


49704 




1.66 


50468 


51236 


52007 


52782 


53560 


54342 


55127 


55916 


56708 


57504 




1.67 


58303 


59106 


59913 


60723 


61536 


62353 


63174 


63998 


64825 


65656 




1.68 


66491 


67329 


68170 


69015 


69864 


70716 


71571 


72430 


73293 


74159 




1.69 


75028 


75901 


76777 


77657 


78540 


79427 


80317 


81211 


82108 


83008 




1.70 


9-9583912 


84820 


85731 


86645 


87563 


884S4 


89409 


90337 


91268 


92203 




1.71 


93141 


94083 


95028 


95977 


96929 


97884 


98843 


99S05 


00771 


01740 




1.72 


602712 


03688 


04667 


05650 


06636 


07625 


0S618 


09614 


10613 


11616 




1-73 


12622 


13632 


14645 


1 5661 


1 668 1 


17704 


18730 


19760 


20793 


21830 




1.74 


22869 


23912 


24959 


26009 


27062 


28118 


29178 


30241 


31308 


32377 




1.75 


9-9633451 


34527 


35607 


36690 


37776 


3S866 


39959 


41055 


42155 


43258 




1.76 


44364 


45473 


46586 


47702 


48821 


49944 


51070 


52199 


53331 


54467 




1.77 


55606 


56749 


57894 


59043 


60195 


61350 


62509 


63671 


64836 


66004 




1.78 


67176 


68351 


69529 


70710 


71895 


73082 


74274 


75468 


76665 


77866 




1.79 
1.80 


79070 
9.9691287 


80277 
92526 


81488 
93768 


82701 
95014 


83918 
96263 


85138 

97515 


86361 

98770 


87588 


88818 


90051 




00029 


01 291 


02555 




1.81 


703823 


05095 


06369 


07646 


08927 


10211 


1 1498 


12788 


140S2 


15378 




1.82 


16678 


1 7981 


19287 


20596 


21908 


23224 


24542 


25864 


27189 


28517 




1.83 


29848 


31182 


32520 


33860 


35204 


36551 


37900 


39254 


40610 


41969 




1.84 


43331 


44697 


46065 


47437 


48812 


50190 


51571 


52955 


54342 


55733 




1.85 


9.9757126 


58522 


59922 


61325 


62730 


64139 


65551 


66966 


68384 


69805 




1.86 


71230 


72657 


74087 


75521 


76957 


78397 


79839 


81285 


82734 


84186 




1.S7 


85640 


87098 


88559 


90023 


91490 


92960 


94433 


95909 


97389 


98871 




1.88 


800356 


01844 


03335 


04830 


06327 


07827 


09331 


10837 


12346 


13S59 




1.89 


15374 


16893 


18414 


19939 


21466 


22996 


24530 


26066 


27606 


29148 




1.90 


9.9830693 


32242 


33793 


35348 


36905 


38465 


40028 


41595 


43164 


44736 




1.91 


4631 1 


47890 


49471 


51055 


52642 


54232 


55S25 


57421 


59020 


60621 




1.92 


62226 


63834 


65445 


67058 


68675 


70294 


71917 


73542 


75170 


76S02 




1-93 


78436 


80073 


81713 


83356 


8 5002 


86651 


88302 


S9957 


91614 


23215 




1.94 


94938 


96605 


98274 


99946 


01621 


03299 


04980 


06663 


08350 


10039 




1.95 


9.9911732 


13427 


15125 


16826 


18530 


20237 


21947 


23659 


25375 


27093 




1.96 


2S815 


30539 


32266 


33995 


35728 


37464 


39202 


40943 


426S8 


44435 




1.97 


461S5 


47937 


49693 


51451 


53213 


54977 


56744 


58513 


60286 


62062 




1.98 


63S40 


65621 


67405 


69192 


70982 


72774 


74570 


76368 


78169 


79972 




1.99 


81779 


83588 


85401 


87216 


89034 


90S 54 


9267S 


94504 


96333 


98165 





Smithsonian Tables. 



64 



Table 32. 
ZONAL SPHERICAL HARMONICS.* 



Degrees 


Pi 


P2 


P3 


P4 


Ps 


Pe 


P7 i 


O 


+ 1. 0000 


+ 1. 0000 


+ 1. 0000 


+ 1. 0000 


+ 1. 0000 


+ 1. 0000 


+ 1. 0000 


I 


.999S 


•9995 


.9991 


•9985 


•9977 


.9968 


•9957 


2 


•9994 


.99S2 


•9963 


•9939 


•9909 


.9872 


•9830 


3 


.99S6 


•9959 


.9918 


.9863 


•9795 


.9714 


.9620 


4 


.9976 


.9927 


.9854 


•9758 


.9638 


•9495 


•9329 


! 5 


+ 0.9962 


+ 0.9886 


+ 0.9773 


+ 0.9623 


+ 0.9437 


+ 0.9216 


+ 0.8962 


6 


•9945 


.9836 


.9674 


•9459 


.9194 


.8881 


.8522 


1 7 


•9925 


•9777 


•9557 


.9267 


.8911 


.8492 


.8016 


! 8 


•9903 


.9709 


•9423 


.9048 


.8589 


.8054 


•7449 


9 


.9S77 


•9633 


•9273 


.8803 


.8232 


•7570 


.6830 


10 


+ 0.9S48 


+ 0.9548 


+ 0.9106 


+ 0.8532 


+ 0.7840 


+ 0.7045 


+ 0.6164 


II 


.98 1 6 


•9454 


.8923 


.8238 


•7417 


.6483 


.5462 


12 


.9781 


•9352 


■8724 


•7920 


.6966 


.5891 


•4731 


13 


•9744 


.9241 


.8511 


.7582 


.64S9 


•5273 


.3980 


14 


•9703 


.9122 


.82S3 


.7224 


•5990 


•4635 


.3218 


15 


+ 0.9659 


+ 0.8995 


+ 0.8042 


+ 0.6847 


+ 0.5471 


+ 0.3983 


+ 0.2455 ! 


16 


.9613 


.8860 


•7787 


•6454 


•4937 


•3323 


+ .1700 


17 


•9563 


.8718 


•7519 


.6046 


•4391 


.2661 


+ .0961 


18 


•95" 


.8568 


.7240 


.5624 


•3836 


.2002 


+ .0248 


19 


•9455 


.8410 


.6950 


.5192 


.3276 


•1353 


— ^0433 


20 


+ 0.9397 


+ 0.8245 


+ 0.6649 


+ 0.4750 


+ 0.2715 


+ 0.0719 


— 0.1072 


21 


•9336 


.8074 


•6338 


.4300 


.2156 


+ .0106 


.1664 


22 


.9272 


•7895 


.6019 


•3845 


.1602 


— .0481 


.2202 


23 


.9205 


.7710 


.5692 


•3386 


.1057 


- ^1038 


.2680 


24 


•9135 


•7518 


•5357 


.2926 


•0525 


- -1558 


•3094 


^^ 


+ 0.9063 


+ 0.7321 


+ 0.5016 


+ 0.2465 


+ 0.0009 


— 0.2040 


— 0.3441 


26 


.89S8 


.7117 


.4670 


.2007 


— .0489 


.2478 


•3717 


27 


.8910 


.6908 


•4319 


•1553 


— .0964 


.2869 


.3922 


28 


.8829 


.6694 


•3964 


.1105 


— •1415 


.3212 


•4053 


29 


.8746 


.6474 


.3607 


.0665 


- •1839 


•3502 


•41*3 


30 


+ 0.8660 


+ 0.6250 


+ 0.3248 


+ 0.0234 


— 0.2233 


— 0.3740 


— 0.4102 


31 


•^57^ 


.6021 


.2887 


— •01S5 


•2595 


•3924 


.4022 


32 


.S480 


.5788 


•2527 


— -0591 


.2923 


•4053 


•3877 


33 


.8387 


■5551 


.2167 


— .0982 


.3216 


.4127 


•3671 j 


34 


.8290 


•5310 


.1809 


— -1357 


•3473 


.4147 


•3409 


35 


+ 0.8192 


+ 0.5065 


+ 0.1454 


— 0.1714 


— 0.3691 


— 0.4114 


— 0.3096 


36 


.8090 


.4818 


.1102 


.2052 


•3871 


.4031 


.2738 


37 


.7986 


•4567 


•0755 


.2370 


.4011 


.3898 


.2343 


38 


.78S0 


•4314 


.0413 


.2666 


.4112 


•3719 


.1918 


39 


•7771 


.4059 


.0077 


.2940 


.4174 


•3497 


.1470 


40 


+ 0.7660 


+ 0.3802 


— 0.0252 


— 0.3190 


— 0.4197 


— 0.3236 


— 0.1006 


41 


•7547 


•3544 


•0574 


.3416 


.4181 


•2939 


— ^0535 


42 


•7431 


.3284 


.0887 


.3616 


.4128 


.2610 


— .0064 


43 


•7314 


•3023 


.'IIQI 


•3791 


.4038 


.2255 


+ ^0398 


44 


•7193 


.2762 


.I4S5 


•3940 


•3914 


.1878 


+ .0846 


45 


+ 0.7071 


+ 0.2500 


— 0.1768 


— 0.4063 


— 0.3757 


— 0.1484 


+ 0.1271 


46 


.6947 


.2238 


.2040 


.4158 


.3568 


— .1078 


.1667 


47 


.6S20 


•1977 


.2300 


.4227 


•3350 


— .0665 


.2028 


48 


.6691 


.1716 


•2547 


.4270 


•3105 


— ^0251 


•2350 


49 


.6561 


.1456 


.2781 


.4286 


.2836 


+ .0161 


.2626 


50 


+ 0.6428 


+ 0. 1 1 98 


— 0.3002 


— 0.4275 


— 0.2545 


+ 0.0564 


+ 0.2854 



Smithsonian Tables. 



* Calculated by Mr. C. E. Van Orstrand for this publication. 



Table 32 {.continued). 
ZONAL SPHERICAL HARMONICS. 



65 



i Degrees 


Pi 


P2 


Ps 


P4 


P5 


Pe 


P7 


50 


+ 0.6428 


+ O.I 198 


— 0.3002 


— 0.4275 


— 0.2545 


+ 0.0564 


+ 0.2854 j 


51 


.6293 


.0941 


•3209 


•4239 


•2235 


.0954 


•3031 1 


52 


•6157 


.06S6 


.3401 


.4178 


.1910 


.1326 


•3154 I 


53 


.6018 


•0433 


•3578 


.4093 


•1571 


.1677 


.3221 1 


54 


.5878 


.0182 


•3740 


•3984 


.1223 


.2002 


•3234 ; 


55 


+ 0-5736 


— 0.C065 


— 0.3886 


-0.3852 


— 0.0868 


+ 0.2297 


+ 0.3191 


56 


•5592 


.0310 


.4016 


•3698 


— .0509 


.2560 


•3095 


57 


•5446 


•0551 


•4I3I 


•3524 


— .0150 


•2787 


•2947 i 


58 


•5299 


.078S 


.4229 


•3331 


+ .0206 


.2976 


.2752 j 


59 


•5150 


.1021 


.4310 


•31 19 


+ -0557 


•3125 


.2512 


60 


+ 0. 5000 


— 0.1250 


— 0.4375 


— 0.2891 


+ 0.0898 


-1- 0.3232 


+ 0.2231 


61 


.4S48 


.1474 


•4423 


.2647 


.1229 


.3298 


.1916 


62 


•4695 


.1694 


•4455 


.2390 


■1545 


•3321 


.1572 


63 


•4540 


.1908 


.4471 


.2121 


.1844 


■3302 


.1203 


64 


•4384 


.2117 


.4470 


.1841 


.2123 


•3240 


.0818 


^1 


-1- 0.4226 


— 0.2321 


— 0.4452 


— 0.1552 


+ 0.2381 


+ 0.3138 


+ 0.0422 


66 


.4067 


.2518 


.4419 


.1256 


.2615 


.2997 


+ .0022 


67 


•3907 


.2710 


•4370 


•0955 


.2824 


.2S19 


— ^037 5 


68 


•3746 


.2895 


•4305 


.0651 


•3005 


.2606 


— ^0763 


69 


■3584 


■3074 


.4225 


•0344 


•3158 


.2362 


— •i'35 


70 


+ 0.3420 


— 0.3245 


— 0.4130 


— 0.0038 


-1- 0.3281 


+ 0.2089 


— 0.1485 


71 


•3256 


■3410 


.4021 


+ .0267 


•3373 


.1791 


.1808 


72 


.3090 


.3568 


.3898 


.0568 


•3434 


.1472 


.2099 


73 


.2924 


•3718 


•3761 


.0864 


•3463 


.1136 


•2352 


74 


•2756 


.3860 


.3611 


•"53 


.3461 


.0788 


•2563 


75 


+ 0.2588 


— 0.3995 


— 0.3449 


+ 0.1434 


+ 0.3427 


+ 0.0431 


— 0.2730 


76 


.2419 


.4122 


•3275 


•1705 


•3362 


+ .0070 


.2850 


77 


•2250 


.4241 


.3090 


.1964 


.3267 


— .0290 


.2921 


78 


.2079 


■4352 


.2894 


.2211 


•3143 


— .0644 


.2942 


79 


.1908 


•4454 


.2688 


.2443 


.2990 


— .0990 


.2913 


80 


+ 0.1736 


— 0.4548 


— 0.2474 


+ 0.2659 


-|- 0.2810 


— O.1321 


-0.2835 


81 


.1564 


•4633 


.2251 


■2859 


.2606 


•1635 


.2708 


82 


.1392 


.4709 


.2020 


.3040 


.2378 


.1927 


•2536 


83 


.1219 


•4777 


•1783 


•3203 


.2129 


.2193 


.2321 


84 


.1045 


.4836 


•1539 


•3345 


.1861 


.2431 


.2067 


85 


+ 0.0872 


— 0.4886 


— 0.1 291 


+ 0.3468 


+ 0.1577 


— 0.2638 


— 0.1778 


86 


.0698 


■4927 


.1038 


•3569 


.1278 


.2810 


.1460 


87 


•0523 


■4959 


.0781 


.3648 


.0969 


•2947 


.1117 


88 


•0349 


.4982 


.0522 


•3704 


.0651 


■3045 


•0755 


89 


■0175 


•4995 


.0262 


•3739 


.0327 


•3105 


.0381 


90 


+ 0.0000 


— 0.5000 


— 0.0000 


+ 0.3750 


+ 0.0000 


— 0.3125 


— 0.0000 



Smithsonian Tables. 



66 








Table 33. 














ELLIPTIC INTEGRALS. 












Values ot M(l- 


siii''esiB.^<t>)^^d<t>. 








This table 


gives the values of the integrals between o and >i 


r/2 of the function 


I— sin'flsin^ 


<^) d4> for different val- 






ues of the modulus corresponding to each degree of 6 between and 


90. 




e 


p d* 


1 ^(i—sm'0sin''<^)' ii<j> 

Jo 


e 


Jq (i-sin=esin2,/))i Jq 


Number. 


Log. 


Number. 


Log. 


Number. 


Log. 


Number. 


Log. 


0° 


1.5708 


O.196120 


1.5708 


O.196120 


45° 


1.8541 


O.26S127 


1.3506 


O.130541 


I 


5709 


196153 


5707 


196087 


6 


8691 


271644 


3418 


127690 


2 


5713 


196252 


5703 


195988 


7 


8S48 


275267 


3329 


1247S8 


3 


5719 


196418 


5697 


195822 


8 


9011 


279001 


3238 


121836 


4 


5727 


196649 


5689 


19559I 


9 


9180 


282848 


3147 


118836 


5° 


1-5738 


0.196947 


1.5678 


0.195293 


50° 


1-9356 


0.286811 


1-3055 


0.115790 


6 


5751 


197312 


5665 


194930 


I 


9539 


290895 


2963 


1 1 2698 


7 


5767 


197743 


5649 


194500 


2 


9729 


295101 


2870 


109563 


8 


5785 


198241 


5632 


194004 


3 


9927 


299435 


2776 


106386 


9 


5805 


198S06 


561 1 


193442 


4 


2.0133 


303901 


26S1 


103169 


10° 


1.5828 


0.199438 


1-5589 


O.192S15 


55° 


2.0347 


0.308504 


1.2587 


0.099915 


I 


5S54 


200137 


5564 


192121 


6 


0571 


313247 


2492 


096626 


2 


5882 


200904 


5537 


191362 


7 


0804 


318138 


2397 


093303 


3 


5913 


201740 


5507 


190537 


8 


1047 


323182 


2301 


089950 


4 


5946 


202643 


5476 


189646 


9 


1300 


328384 


2206 


0S6569 


15° 


1. 598 1 


0.203615 


1.5442 


0.188690 


60° 


2.1565 


0.333753 


I.2II1 


0.083164 


6 


6020 


204657 


5405 


187668 


1 


1842 


339295 


2015 


079738 


7 


6061 


205768 


5367 


1865S1 


2 


2132 


345020 


1920 


076293 


8 


6105 


20694S 


5326 


185428 


3 


2435 


350936 


1826 


072834 


9 


615I 


208200 


52S3 


184210 


4 


2754 


357053 


1732 


069364 


20° 


1.6200 


0.209522 


1-5238 


0.182928 


65° 


2.3088 


0.363384 


1.1638 


0.065889 


I 


6252 


210916 


5191 


1815S0 


6 


3439 


369940 


1545 


062412 


2 


6307 


212382 


5141 


180168 


7 


3809 


376736 


1453 


05S937 


3 


6365 


2 1 392 1 


5090 


17S691 


8 


4198 


383787 


1362 


055472 


4 


6426 


215533 


5037 


177150 


9 


4610 


391112 


1272 


052020 


25° 


1 .6490 


O.2I72I9 


1. 498 1 


0.175545 


70° 


2.5046 


0.398730 


1. 1184 


0.048589 


6 


6557 


21898I 


4924 


173876 


I 


5507 


406665 


1096 


045183 


7 


6627 


22081S 


4864 


172144 


2 


5998 


414943 


lOII 


041812 


8 


6701 


222732 


4803 


170348 


3 


6521 


423596 


0927 


038481 


9 


6777 


224723 


4740 


168489 


4 


7081 


432660 


0844 


035200 


30° 


1.6858 


0.226793 


1.4675 


0.166567 


750 


2.7681 


0.442176 


1.0764 


0.031976 


I 


6941 


228943 


4608 


164583 


6 


8327 


452196 


06S6 


02S819 


2 


7028 


23II73 


4539 


162537 


7 


9026 


462782 


0611 


025740 


3 


7119 


233485 


4469 


160429 


8 


9786 


474008 


0538 


022749 


4 


7214 


235880 


4397 


158261 


9 


3.0617 


485967 


0468 


019858 


35° 


I.7312 


0.238359 


1.4323 


0.156031 


80° 


3-1534 


0.498777 


1. 0401 


0.017081 


6 


7415 


240923 


4248 


153742 


1 


2553 


51259I 


0338 


014432 


7 


75-2 


243575 


4171 


151393 


2 


3699 


527613 


0278 


OII927 


8 


7633 


246315 


4092 


148985 


3 


5004 


544120 


0223 


009584 


9 


7748 


249146 


4013 


146519 


4 


6519 


562514 


0172 


007422 


40° 


1.7868 


0.252068 


I -393 1 


0.143995 


85° 


3-8317 


0.583396 


1.0127 


0.005465 


I 


7992 


255085 


3S49 


141414 


6 


4.0528 


607751 


O0S6 


003740 


2 


8122 


258197 


3765 


138778 


7 


3387 


637355 


0053 


002278 


3 


8256 


261406 


3680 


136086 


8 


7427 


676027 


0026 


OOI12I 


4 
45° 


8396 
1.8541 


264716 
0.268127 


3594 
1.3506 


133340 


9 
90° 


5-4349 


735192 


oooS 


GOO326 


0.130541 


CO 


00 


1 .0000 





Smithsonian Tables. 



67 



Table 34. 

MOMENTS OF INERTIA, RADII OF GYRATION, AND WEIGHTS. 

In each case the axis is supposed to traverse the centre of gravity of the body. The axis is 
one of symmetry. The mass of a unit of volume is w. 



Body. 



Sphere of radius r 

Spheroid of revolution, po- 
lar axis 2a, equatorial di- 
ameter 2r 

Ellipsoid, axes za, 2b, 2c 

Spherical shell, external ra- 
dius r, internal r' 

Ditto, insensibly thin, ra- 
dius r, thickness dr 

Circular cylinder, length 2a, 
radius r 

Elliptic cylinder, length 2a, 
transverse axes 2b, 2c 

Hollow circular cylinder, 
length 2a, external ra- 
dius r, internal r' 

Ditto, insensibly thin, thick- 
ness dr 

Circular cylinder, length 2a, 
radius r 

Elliptic cylinder, length 2a, 
transverse axes 2a, 2b 

Hollow circular cylinder, 
length 2a, external ra- 
dius r, internal r' 

Ditto, insensibly thin, thick- 
ness dr 

Rectangular prism, dimen- 
sions 2a, 2b, 2c 

Rhombic prism, length 2a, 
diagonals 2b, 2c 

Ditto 



Diameter 

Polar axis 

Axis 2a 
Diameter 

Diameter 

Longitudinal 
axis 2a 

Longitudinal 
axis 2a 

Longitudinal 
axis 2a 

Longitudinal 
axis 2a 

Transverse 
diameter 

Transverse 
axis 2b 

Transverse 
diameter 

Transverse 
diameter 

Axis 2a 
Axis 2a 
Diagonal zb 



Weieht. 



3 

i^-Kwar"^ 

\Trwabc 




2inva{7-'^—r'-) 

^irwardr 

2Tr2var^ 
2irwabc 

2irwa{r^ — r'^) 

4trwardr 
Swabc 
\wabc 
A^wabc 



Moment of Inertia lo 



Square of Ra- 
dius of Gyra- 
tion (?. 




15 

i^irwabc(P-\-fi ) 

IS 
8ir7v{r^ — r'5) 

IS 

Sinvr^dr 

3 

invar* 

irwabc{b^-\-<:^) 
2 

nwa[r*—r'^) 

4irwar^dr 

'K7uar^(T)r'^-\-4a'^) 

6 
irwabc(y'^-\-jfi'^) 

6 

■mua < 2{r* — r'^) ) 



6 \ +4^2(^2 



irwa (2r^-\ — a'^r)dr 

?,wabc(b'^-\-fi) 

3 

2wabc{b''-\-c'^) 

3 

2wabc(c'^-\-2a'^) 



2f^ 

5 

S 
<^2.ff2 

5 

2(r5— r ^S) 
2r2 

3 

y2 

2 

^2-fr2 
4 

y2_l_^'2 



r^ cfi 

^2_j_^'2 (fi 
"4 '"3 



^2 /z2 
2 +^ 
^2-1-^2 

3 

6 

^2 a2 



(Taken from Rankine.) 



Smithsonian Tables. 



68 



Table 35. 
STRENGTH OF MATERIALS. 



The strength of most materials varies so that the following figures serve only as a rough indication of the strength of a 

particular sample. 



TABLE 36 (a). — Metals. 



TABLE 35(b). — Stones.* 



Name of Metal. 


Tensile strength in 
pounds per sq. in. 


Aluminum wire 


30000-40000 


Brass wire 


50000-150000 


Bronze wire, phosphor, hard- 




drawn 


1 1 0000- 1 40000 


Bronze wire, silicon, hard- 




drawn 


95000-1 1 5000 


Bronze : Cu, 58.54 parts ; Zn, 




38.70; A), 0.21; with 2.55 




parts of the allov, Sn, 29.03, 




wrought iron, 58.06, ferro- 




manganese, I2.gi 


60000-75000 


Copper wire, hard-drawn 


60000-70000 


Gold wire 


20000 


Iron, cast 


1 3000-33000 


" wire, hard-drawn 


S0OOO-120OOO 


" " annealed 


50000-60000 


Lead, cast or drawn 


2600-3300 


Palladium * 


39000 


Platinum * wire 


50000 


Silver* wire 


42000 


Steel 


80000-330000 


" wire, maximum 


460000 


" Specially treated nickel- 




steel, approx. comp. 0.40 




C; 3.25 Ni ; treatment 




secret 


250000 


" piano wire, 0.033 i"- 




diam. 


357000-390000 


" piano wire, 0.051 in. diam. 


325000-337000 


Tin, cast or drawn 


4000-5000 


Zinc, cast 


7000-13000 


" drawn 


22000-30000 


According to Boys, quartz 


fibres have a 


tensile strength of between ii( 


)000and 167000 


pounds per square inch. 





Material. 


Size of test 
piece. 


Resistance to 

crushing in 

pds. per sq. in. 


Marble 
Tufa 

Brownstone 
Sandstone 
Granite 
Limestone 
1 


4 in. cubes 

2 " " 

4 in. cubes 
4 " " 
4 " " 


7600-20700 
7700-1 1600 
7300-23600 
2400-29300 
9700-34000 
6000-25000 





* Data furnished by the U. S. Geological Survey. 



TABLE 35(c). -Brick. 





Kind of Brick. 


Resistance to crushing in pds. 
per sq. in. 


Tested 
flatwise. 


Tested 
on edge. 


Soft burned 
Medium burned 
Hard burned 
Vitrified 
Sand-lime 


1800-4000 

4000-6000 

6000-8500 

8500-25000 

1800-4000 


I 600-3000 
3000-4500 
4500-6500 
(5500-20000 


Brick piers laid up in i part Portland 
cement, 3 of sand, have from 20 to 40 per 
cent the crushing strength of the brick. 





Authority of Wertheim. 



* Data furnished by the U. S. Geological Survey. 



TABLE 35 (d). — Concretes.* 



Coarse 
Aggregate. 


Proportions by volume. 
Cement : sand : aggregate. 


Size of test piece. 


Resistance to 

crushing in pds. 

per sq. in. 


Sandstone 

Cinders 

Limestone 

Conglomerate 

Trap 




5 : 14 to 1:1:5 
3:6 "1:1:3 
4:8 "1:2:4 
6:12 " 1:2:4 
2:9 "1:2:4 


12 in. cube 
12 " " 
12 " " 
12 " " 
12 " " 


1550-3860 
790-2050 
1200-2840 
1080-3830 
820-2960 



* Data furnished by the U. S. Geological Survey. 
Smithsonian Tables. 



Table 36. 
STRENGTH OF MATERIALS. 

Average Results of Timber Tests. 

The test pieces were small and selected. Endwise compression tests of 
some of the first lot, made when green and containing over 40 per cent moisture, 
showed a diminishing in strength of 50 to 75 per cent. 

See also Table yj. A particular sample inay vary greatly from these data, 
which can indicate only in a general way the relative values of a kind of timber. 
Note that the data below are from selected samples and therefore probably high. 

The upper lot are from the U. S. Forestry circular No. 15 ; the lower from the 
tests made for the loth U. S. Census. 



69 



NAME OF SPECIES. 


TRANSVERSE 
TESTS. 


COMPRESSION. 


SHEAR- 
ING. 














Modulus 
of rupture. 
Ib./sq. in. 


Modulus of 
elasticity. 
Ibs./sq. in. 


II to grain. 
Ibs./sq. in. 


X to grain. 
Ibs./sq. in. 


Along the 

grain. 
Ibs./sq. in. 


Long-leaf pine 


12,600 


2,070,000 


8,000 


1260 


835 


Cuban pine 


13,600 


2,370,000 


8,700 


1200 


770 


Short-leaf pine 


10,100 


1, 680,000 


6,500 


1050 


770 


Loblolly pine 


11,300 


2,050,000 


7,400 


1 1 50 


800 


White pine 


7,900 


1,390,000 


5,400 


700 


400 


Red pine 


9,100 


1 ,620,000 


6,700 


1000 


500 


Spruce pine 


10,000 


1,640,000 


7,300 


1200 


800 


Bald cypress 


7,900 


1,290,000 


6,000 


800 


500 


White cedar 


6,300 


910,000 


5,200 


700 


400 


Douglass spruce 


7,900 


1, 680,000 


5,700 


Soo 


500 


White oak 


13,100 


2,090,000 


8,500 


2200 


1000 


Overcup oak 


11,300 


1,620,000 


7,300 


1900 


1000 


Post oak 


12,300 


2,030,000 


7,100 


3000 


1 1 00 


Cow oak 


11,500 


1,610,000 


7,400 


1900 


900 


Red oak 


11,400 


1,970,000 


7,200 


2300 


1 1 00 


Texan oak 


13,100 


1,860,000 


8,100 


2000 


900 


Yellow oak 


10,800 


1.740,000 


7,300 


1800 


1 1 00 


Water oak 


12,400 


2,000,000 


7,800 


2000 


1 100 


Willow oak 


10,400 


1,750,000 


7,200 


1600 


900 


Spanish oak 


12,000 


1,930,000 


7,700 


1800 


900 


Shagbark hickory 


1 6,000 


2,390,000 


9,500 


2700 


1 1 00 


Mockernut hickory 


15,200 


2.320,000 


10,100 


3100 


1 100 


Water hickory 


12,500 


2,080,000 


8,400 


2400 


1000 


Bitternut hickory 


15,000 


2,280,000 


9,600 


2200 


1000 


Nutmeg hickory 


12,500 


1,940,000 


8,800 


2700 


1 100 


Pecan hickory 


1 5' 300 


2,530,000 


9,100 


2800 


1200 


Pignut hickory 


18,700 


2,730,000 


10,900 


3200 


1200 


White elm 


10,300 


1,540,000 


6,500 


1200 


800 


Cedar elm 


13-500 


1,700,000 


8,000 


2100 


1300 


White ash 


10,800 


1,640,000 


7,200 


1900 


1 100 


Green ash 


11,600 


2,050,000 


8,000 


1700 


1000 


Sweet gum 


9,500 


1,700,000 


7,100 


1400 


800 


Poplar 


9,400 


1,330,000 


5,000 


1 1 20 




Basswood 


8,340 


1,172,000 


5,190 


8S0 




Ironwood 


7.540 


1,158,000 


5-275 


2000 




Sugar maple 


16,500 


2,250,000 


8.800 


3600 




White maple 


14,640 


1,800,000 


6,850 


2580 




Box elder 


7,580 


873,000 


4,580 


1580 




Black walnut 


11,900 


1,560,000 


8,000 


2680 




Sycamore • 


7,000 


790,000 


6,400 


2700 




Hemlock 


9,480 


1,138,000 


5,400 


1 100 




Red fir 


13,270 


1,870,000 


7,780 


1750 




Tamarack 


13,150 


1,917,000 


7,400 


1480 




Red cedar 


1 1 ,800 


938,000 


6.300 


2000 




Cottonwood 


10,440 


1,450,000 


5,000 


1 100 




Beech 


16,200 


1,730,000 


6,770 


2840 





Smithsonian Tables. 



70 Table 37. 

UNIT STRESSES FOR STRUCTURAL TIMBER 
POUNDS PER SQUARE INCH. 



EXPRESSED IN 



Recommended by the Committee on Wooden Bridges and Trestles, American Railway 
Engineering Association, 1909. 



KIND OF TIMBER. 


BENDING. 


SHEARING. 


Extreme fibre 
stress. 


Modulus of 
elasticity. 


Parallel to grain. 


Longitudinal 
shear in beams. 


Average 


Safe 


Average. 


Average 


Safe 


Average 


Safe 




ultimate. 


stress. 


ultimate 


stress. 


ultimate. 


stress. 


Douglass fir 


6100 


1200 


1,510,000 


690 


170 


270 


110 


Long-leaf pine 


6500 


1300 


1,610,000 


720 


180 


300 


120 


Short-leaf pine 


5600 


HOC 


1,480,000 


710 


170 


330 


130 


White pine 


4400 


900 


1,130,000 


400 


100 


180 


70 


Spruce 


4800 


1000 


1,310,000 


600 


ISO 


170 


70 


Norway pine 


4200 


800 


1,190,000 


590 


130 


250 


100 


Tamarack 


4600 


900 


1,220,000 


670 


170 


260 


100 


Western hemlock 


5800 


HOC 


1,480,000 


630 


160 


270* 


100 


Redwood 


5000 


900 


800,000 


300 


80 


- 


- 


Bald cypress 


4800 


900 


1,150,000 


500 


120 


- 


- 


Red cedar 


4200 


800 


860,000 


- 


- 


- 


- 


White oak 


5700 


1 100 


1,150,000 


840 


210 


270 


IXO 


KIND OF TIMBER. 


COMPRESSION 


'0 j: 

X. a 

Z 


Perpendicular 
to grain. 


Parallel to grain. 


c E ij 

S.2S 


Formulas for safe 








8^:; 


stress in long 
columns over 15 


u 












Elastic 


Safe 


Average 


Safe 


i; re 


diameters. t 


C3 ^ 




limit. 


stress. 


ultimate. 


stress. 


9 




Oi M 


Douglass fir 


630 


,310 


3600 


1200 


900 


I200{l-L/6o.D) 


10 


Long-leaf pine 


S20 


260 


3800 


1300 


980 


i30o(i-L/6o.D) 


10 


Short-leaf pine 


340 


170 


3400 


1 100 


830 


iioo(i-L/6o.D) 


10 


White pine 


290 


ISO 


3000 


1000 


7 so 


iooo(i-L/6o.D) 


10 


Spruce 


,370 


180 


3200 


1100 


830 


iioo(i-L/6o.D) 


- 


Norway pine 




150 


2600* 


800 


600 


8oo(i-L/6o.D) 


- 


Tamarack 


- 


220 


3200* 


1000 


7 SO 


iooo(i-L/6o.D) 


- 


Western hemlock 


440 


220 


3500 


1200 


900 


i2oo(i-L/6o.D) 


- 


Redwood 


400 


I, SO 


3300 


900 


680 


9oo(i-L/6o.D) 


- 


Bald cypress 


340 


170 


3900 


1 100 


8^0 


iioo(i-L/6o.D) 


- 


Red cedar 


470 


230 


2800 


900 


680 


90o(i-L/6o.D) 


- 


White oak 


920 


450 


3500 


1300 


980 


i30o(i-L/6o.D) 


12 



These unit stresses are for a green condition of the timber and are to be used without increasing the live- 
load stresses for impact. 
* Partially air-dry. 
t L = length in inches. D = least side in inches. 

Smithsonian Tables. 



Tables 38-39. 
ELASTIC MODULI. 



71 



TABLE 38. — Rigidity Modulus. 

If to the four consecutive faces of a cube a tangential stress is applied, opposite in direction on 
adjacent sides, the modulus of rigidity is obtained by dividing the numerical value of the tangential 
stress per unit area (kg. per sq. mm.) by the number representing the change of angles on the 
non-stressed faces, measured in radians. 



Substance. 



Aluminum 

" cast .... 
Brass 

" cast, 60 Cu+ 12 Sn 
Bismuth, slowly cooled . 
Bronze, cast, 86 Cu + 1 2 Sn 
Cadmium, cast .... 
Copper, cast 

it 
Gold ...'.'.*.*.! 

Iron, cast 

Magnesium, cast . . . 

Nickel 

Phosphor bronze . . . 



Rigidity 
Modulus. 



3350 
2580 

3550 
3715 
3700 
1240 
4060 
2450 
4780 

4213 
4450 
4664 
2850 
3950 
5210 
6706 

7975 
6940 
8108 

7505 
1710 
7820 
4359 



Refer- 



14 

5 

10 
II 

5 
5 
5 
5 



19 

5 
14 

5 

IS 
10 

7 
16 

14 
5 
5 

II 



Substance. 



Quartz fibre . . . 
(( t( 

Silver 

" hard-drawn . 
Steel 

" cast . . . . 

" cast, coarse gr. 

" silver- . . . 
Tin, cast . . . . 

Zinc 

Platinum . . . . 

Glass 

Clay rock . . . . 

Granite 

Marble 

Slate 



Rigidity 
Modulus. 



2S88 
2380 
2960 
2650 
2566 
2816 
8290 

7458 
8070 
7872 
1730 
1543 
3880 
3820 
6630 
6220 

2350 
2730 
1770 
1280 
II90 
2290 



Refer- 
ence. 



20 
21 

s 

10 

16 

II 

16 
15 

5 
II 

5 
19 

5 

19 
16 
22 



23 

23 
23 
23 



References 1-16, see Table 48. 
17 Gratz, Wied. Ann. 28, 18S6. 
iS Savart, Fogg. Ann. 16, 1829. 

19 Kiewiet, Diss. Gottingen, 1886. 

20 Threlfall, Philos. Mag. (5) 30, i{ 



21 Boys, Philos. Mag. (5) 30, 1890. 

22 Thomson, Lord Kelvin. 

23 Gray and Milne. 

24 Adams-Coker, Carnegie Publ. No. 46, 

1906. 



TABLE 39. — VarlaUon of the Rigidity Modulus with the Temperature. 

n, = fi„ (i — af — fif^ — yi^), where ^ = temperature Centigrade. 



Substance. 



Brass . 

Copper . 

Iron . . 

Platinum 
Silver . 
Steel . 



2652 
3200 
3972 
3900 
8108 
6940 
6632 
2566 
8290 



2158 

2716 

572 
206 

483 
III 

187 



(3io8 



36 



19 
12 

38 
59 



yio" 



32 

47 
— II 



II 
—9 



Authority. 



Pisati, Nuovo Cimento, 5, 34, 1879. 

Kohlrausch-Loomis, Pogg. Ann. 141. 

Pisati, loc. cit. 

K and L, loc. cit. 

Pisati, loc. cit. 

K and L, loc. cit. 

Pisati, loc. cit. 



nt*z=nv> [i — o (/— 15)]; Horton, Philos. Trans. 204 A, 1905. 



Copper 
Copper (com- 
mercial) 
Iron 

Steel 



4-37^ 

3.80 
8.26 

S.45 



=.00039 

.00038 
.00029 
.00026 



Platinum 


6.46* 


Gold 


2.45 


Silver 


2.67 


Aluminum 


2-55 



a = .00012 
.00031 
.00048 
.00148 



Tin 
Lead 
Cadmium 
Quartz 



1.50^ 
C.80 
2.31 
3.00 



a =.00416 
.00164 
.0058 

.00012 



Smithsonian Tables. 



* Modulus of rigidity in lo" dynes per sq. cm. 



72 



Young's Modulus 



Table 40. 
ELASTIC MODULI. 

Young's Modulus. 
Intensity of longitudinal stress (kg. per sq. mm.) ^ 
Elongation per unit length 



Substance. 


Temp. 

°C 


u 


V c 


Substance. 


Temp. 

°C. 


§■3 


V- • 









X " 









^ 5 






>-s 








>^ 




Aluminum .... 


20 


7200 


t 


Nickel-Steel, 5-^% ni. . 


_ 


19900 


13 


" . . 




12.3 


7462 


2 


1 . 25/, 




- 


18600 


13 


Lead, drawn . . 




15 


1803 


3 


Palladium, annealed 




15 


9709 


3 


" annealed . 




15 


1727 


3 


Phosphor-bronze 






I20IO 


II 


Bronze .... 






9194 


4 


Platinum, drawn 




15 


17044 


3 


Cadmium . . . 




- 


7070 


5 


" annealed 




IS 


I5518 


3 


Delta metal . . 




- 


1 1697 


6 


" .... 




13-2 


16020 


2 


Iron, drawn . . 




15 


20869 


3 


" drawn 




10 


15989 


I 


" annealed . 




15 


20794 


3 


Silver, drawn . . . 




15 


7357 


3 


" 







20310 


7 


" annealed 




15 


7140 


3 


" 




- 


21740 


8 


Steel wire, drawn . 




15 


18S10 


3 


" cast . . . 




- 


11713 


4 


" " annealed 




15 


17280 


3 


" soft . . . 




15-6 


15750 


9 


Steel, cast, drawn . 




15 


19550 


3 


" drawn . . 




20 


19385 


I 


" " annealed 




15 


19560 


3 


" drawn . . 




- 


20500 


10 


" Bessemer . . 






21136 


4 


Gold, drawn . . 




15 


8I3I 


3 


" puddle . 






- 


21112 


4 


" annealed . 




15 


5585 


3 


" mild . . 






15-5 


21700 


9 


" drawn . . 




12.9 


8630 


2 


" very soft 








20705 


13 


Copper, drawn . 




15 


12450 


3 


" half soft 






- 


20910 


13 


" annealed 




15 


10520 


3 


" hard 






- 


20600 


13 


" drawn . 







I2I40 


7 


Bismuth . . 






- 


3190 


5 


" drawn . 




20 


12550 


I 


Zinc, drawn . 






15 


8734 


3 


" electr. h'd 


i'n 


19-5 


13220 


9 


Tin, drawn 






15 


414S 


3 


Brass, drawn . . 




15 


8543 


3 


" cast . . 








1700 


13 


" .... 







9810 


7 






( 6000 




" drawn . . 




~ 


10220 

9930 


II 

10 


Glass 






( 8000 


" 




" .... 




- 


10450 


9 






( 1500 




German silver 




— 


12094 


4 


Carbon 


_ 


1 '° 


— 


h'd 


d'n 


- 


1 1550 


II 






( 2500 




(( U 




20 


13300 
20300 

22790 


9 

5 

12 


Marbles 


_ 


6-, 1 6 


24 
24 


Nickel .... 






Granites 




^0 ^ 

5159 
8985 






- 


Basic intrusives . . . 


- 


24 


" hard drawn . 




"•5 


23950 

21680 


II 

2 


Rocks : See Nagaoka, 
Philos. Mag. 1900. 








I Slotte, Acta Soc. Fenn. 26, 1899; 29, 1906. 


10 Baumeister, Wied. Ann. 18, i 


583. 




2 Meyer, Wied. Ann. 59, 1S96. 


II Searle, Philos. Mag. (5) 49, 1$ 


00. 




3 Wertheim, Ann. chim. phys. (3) 12, 1844. 


12 Cantone, Wied. Beibl. 14, 189 


0. 




4 PscheidI, Wien. Ber. II, 79, 1879. 


13 Mercadier, C. R. 113, 1891. 






5 Voigt, Wied. Ann. 48, 1893. 


14 Katzenelsohn, Diss. Berlin, if 


587. 




6 Amagat, C. R. 108, 1889. 


15 Wertheim, Pogg. Ann. 78, 18. 


19- 




7 Kohlrausch, Loomis, Fogg. Ann. 141, 1S71. 


16 Pisati, Nuovo Cimento, 5, 34, 


1879. 




8 Thomas, Drude Ann. i, 1900. 


References 17-19,866 Table 47. 






9 Gray, etc., Proc. Roy. Soc. 67, 1900. 









Compiled partly from Landolt-Bornstein's Physikalisch-Chemische Tabellen. 
Smithsonian Tables. 



Tables 41-44. * 73 

COMPRESSIBILITY, HARDNESS, CONTRACTION OF ELEMENTS. 

TABLB 41. — Compressibility of the More Important Solid Elements. 

Arranged in order of the increasing atomic weigiits. Tiie numbers give tlie mean elastic change 
of volume for one megabar (0.987 atm.) between 100 and 500 megabars, multiplied by 10''. 



Lithium 


8.8 


Potassium 


31-5 


Selenium 


1 1.8 


Iodine 


»3- 


Carbon 


0-5 


Calcium 


S-5 


Bromine 


51.8 


Caesium 


61. 


Sodium 


15.4 


Chromium 


0.7 


Rubidium 


40. 


Platinum 


0.21 


Magnesium 


2.7 


Manganese 


0.7 


Molybdium 


0.26 


Gold 


0.47 


Aluminum 


1-3 


Iron 


0.40 


Palladium 


0.3S 


Mercury 


3-71 


Silicon 


0.16 


Nickel 


0.27 


Silver 


0.84 


Thallium 


2.6 


Red phosphorus 


9.0 


Copper 


0.54 


Caduiium 


I 9 


Lead 


2.2 


Sulphur 


12.5 


Zinc 


1-5 


Tin 


1.6 


Bismuth 


2.8 


Chlorine 


95- 


Arsenic 


4-3 


Antimony 


2.2 







StuU, Zeitschr. Phys Chem 6i, 1907. 
TABLE 42.— Hardness. 



Agate 


7- 


Brass 


3-4- 


Iridosmium 


7- 


Sulphur 


1-5-2-5 


Alabaster 


I 


7 


Calimine 


5- 


Iron 


4-5- 


Stibnite 




Alum 


2-2 


S 


Calcite 


3- 


Kaolin 


I. 


Serpentine 


3-4- 


Aluminum 


2 




Copper 


2-5-3- 


Loess (0°) 


0-3 


Silver 


2-5-3- 


Amber 


2-2 


S 


Corundum 


9- 


Magnetite 


6. 


Steel 


5-8. 5 


Andalusite 


7 


s 


Diamond 


ID. 


Marble 


3-4. 


Talc 


I. 


.\nthracite 


'> 




Dolomite 


3-5-4- 


Meerschaum 


2-3- 


Tin 


1-5 


Antimony 


3 


1 


Feldspar 


6. 


Mica 


2.8 


Topaz 


S. 


Apatite 


S 




Flint 


7- 


Upal 


4-6. 


Tourmaline 


7-3 


Aragonite 


3 




Fluorite 


4- 


Orthoclase 


6. 


Wax (0°) 


0.2 


Arsenic 




s 


Galena 


2-5 


Palladium 


4.8 


Wood's metal 


3- 


Asbestos 


S 




Garnet 


7- 


Phosphorbronze 


4- 






Asphalt 


1-2 




Glass 


4-5-6.5 


Platinum 


4-3 






Augite 


6 




Gold 


2-5-3- 


Plat-iridium 


6-5 






Barite 


3 


3 


Graphite 


0.5-1. 


Pyrite 


6-3 






Beryl 


7 


8 


Gypsum 


1.6-2. 


Quartz 


7- 






Bell-metal 


4 




Hematite 


6. 


Rock-salt 


2. 






Bismuth 


2 


S 


Hornblende 


5-5 


Ross' metal 


2.5-3.0 






Boric acid 


3 




Iridium 


6. 


Silver chloride 


1-3 







From Landolt-Bornstein-Meyerhoffer Tables : Auerbachs, Winklemann, Handb. der Phys. i? 
TABLE 43. — Relative Hardness 0! the Elements, 



c 


lO.O 


Ru 


6.5 


Cu 


30 


Au 


2-5 


Sn 


1.8 


Li 


0.6 


B 


9 5 


Mn 


5-0 


Sb 


3-0 


Te 


2-3 


Sr 


1.8 


P 


0-5 


Cr 


9.0 


Pd 


4.8 


Al 


2.9 


Cd 


2.0 


Ca 


i-S 


K 


0-5 


Os 


7.0 


Fe 


4-5 


Ag 


2-7 


S 


2.0 


Ga 


1-5 


Na 


0.4 


Si 


7.0 


Pt 


43 


Bi 


2-S 


Se 


2.0 


Pb 


1-5 


Rb 


0-3 


Ir 


6-5 


As 


3-5 


Zn 


2-5 


Mg 


2.0 


In 


1.2 


Cs 


0.2 



Rydberg, Zeitschr. Phys Chem 33, igcxj 

TABLE 44. — Ratio, p, ol Transverse Contraction to Longitudinal Extension under Tensile Stress. 

(Poissnn's Ratio.) 



Metal 


Pb 


Au 


Pd 


Pt 


Ag 


Cu 


Al 


Bi 


Sn 


Ni 


Cd 


Fe 


P 


0-45 


0.42 


0-39 


0-39 


0.38 


0-35 


0-34 


0-33 


0.33 


0.31 


0.30 


0.28 


Smithson 

1 


p for -. n 
AN Tab 


F 
larbles, 
LES. 


rom data 
.27;grai 


from P 
lites, 0.2 


hysikalis 
4 ; basic 


ch-Techn 
intrusive 


ischen R 
s, 0.26 ; § 


eichsans 
lass, 0.2 


talt, IQ07 
3. Adan 


is-Coker 


1906. 





74 • Table 45. 

ELASTICITY OF CRYSTALS.* 

The formulae were deduced from experiments made on rectangular prismatic bars cut from the crystal. These bars 
were subjected to cross bending and twisting and the corresponding Elastic Moduli deduced. The symbols 
a /3 7) «i Pi 71 and a, /So fo represent tlie direction cosines of the length, the greater and the less transverse 
dimensions of the prism wuh reference to the principal axis of the crystal. E is the modulus for extension or 
compression, and T is the modulus for torsional rigidity. 1 he moduli are in grams per square centimeter. 



Barite. 

-^ = 16.130^+ i8.5i;3'+ 10.427* +2(38.79i3V' 4 15.217V +8.SSa"/3') 

loi" 

-Tp- = 69.520''+ 1 1 7.663' +116.467* + 2(20.16)3-7- + S5. 297V + ^-7-35"'''^') 

Beryl (Emerald). 

^" == 4.325 sin'^ + 4.619 cos*0+ 13.328 sm2^cos2^ [ ^^f ^ ^^^K^'^'^^ ^"?^u^ Y^'^''^' 
L ^-^ ^ r \ ^ J rijj r rj the length, breadth, and thickness 

10**' , ., ^ oj .T 1 of the specimen make with the 

^j^= 15.00 -3.675 C0SV2- 17-536 cos-^cos^?>i [ principal axis of the crystal. 

Fluorspar. 



i^=l3.o5-6.26(a*+;3' + 7*) 

loi" 

= 5S.04 — 50.0S (/3 '7- + 7'-a- + «-)8-) 



T 

Pyrite. 

i^"-5.o8-2.24(a* + /3' + 7*) 

-^ — 18.60 — 17.95 (/3V + rofi + a^/32) 

Rock salt. 

^ = 33.48-9.66(a* + /3* + 7*) 

loW 

i^ = 1 54. 58 - 77-28 (3 7- + 7-a- +«-^-) 

Sylvine. 

ig-'3=75.i-48.2(a* + )3' + 7*) 

loio 

-^ = 306.0 — 192.8 ()3-7- + 7-a- + a-j3-) 

Topaz. 
loW 
-^ =4.34ia* + 3.46018* + 3.7717*+ 2 (3.8790V + 2.8567V + 2.39a^i3^) 

loi* 

-^ = 14.8S0* + 16.5^/3* + 16.457* + 30.89/3V + 40-S97-a2 + 43.5ia-j82 

Quartz. 

-^ = 12.734 (1—72)24. 16.693 (i — 7-)7^ + 9-7057* — 8-460/37 (3a2 — ;3-) 

loio 

— = 19.665 + 9.060702 + 22.98472712 — 16.920 [(7)81+ 371) (3001 — )83i) — 3272)] 



* These formulae are taken from Voigt's papers (Wied. Ann. vols. 31, 34, and 35). 
Smithsonian Tables. 



Table 46. 
ELASTICITY OF CRYSTALS. 



75 



Some particular values of the Elastic Moduli are here given. Under E are given moduli for extension or compression 
in the directions indicated by the subscripts and explained in the notes, and under T the moduli for torsional 
rigidities round the axes similarly indicated. Moduli in grams per sq. cm. 



(a) Isometric System.* 



Authority. 



Fluorspar 
Pyrite . 
Ruck salt 

Sylvine . 



Sodium chlorate 
Potassium alum . 
Chromium alum 
Iron alum . . . 



1473 X 106 
3530 X 10'^ 
419 X 106 
403 X 10^ 
401 X lo^ 
372 X io« 
405 X io<5 
iSi X 106 
161 X 10*' 
186 X iqS 



1008 X 10^ 
2530 X 10'' 
349 X io« 
339 X 106 
209 X 10" 
196 X 10^ 
319 X io« 
199 X iqi* 
177 X 10^ 



910 X lo^ 
2310 X 10^ 
303 X 106 



345 X 106 

1075 X 108 

129 X lo^ 



655 X io'5 



Voigt.t 



Koch.t 

Voigt. 
Koch. 
Beckenkamp.§ 



(l>) Orthorhombic System. 



Substance. 



Barite 
Topaz 



E, 



620 X lo^ 
2304 X lo^ 



E, 



540 X 106 
2890 X 106 



959 X 106 
2652 X 10^ 



376 X iqO 
2670 X 10^ 



702 X 106 
2893 X 10" 



740 X lo^ 
3180 X 106 



Authority. 



Voigt. 



Substance. 



Barite 
Topaz 



T,, = T,, 



283 X 10*5 

1336 X lo^ 



Ti 3 — T3 



293 X 10^ 
1353 X 106 



T.., = T,„ 



121 X lO^ 

1 104 X 10^ 



Authority. 



Voigt. 



In the MoNOCLiNic System, Coromilas (Zeit. fiir Kryst. vol. i) gives 
Emax = 887 X 106 at 21.9° to the principal axis. 
E„i„=: 313X106 at 75.4° 
Emai^ 2213 X 10^ in the principal axis. 
Emin = 1554 X 106 at 45° to the principal axis. 



Gypsum 
Mica 



In the Hexagonal System, Voigt gives measurements on a beryl crystal (emerald). 
The subscripts indicate inclination in degrees of the axis of stress to the principal axis of 
the crystal. 

Eo= 2165X106, E45 = 1796 X 106, E9o=23i2X io«. 

To = 667X106, T9o= 883X106. The smallest cross dimension of the 
prism experimented on (see Table 82), was in the principal axis for this last case. 



In the RhombohedRAL System, Voigt has measured quartz. The subscripts have the 
same meaning as in the hexagonal system. 

£0=1030X106, E_45 = 1305X106, E+45 = S5oXio6, £90 = 785X106, 

To = 508 X 1 06, T90 = 348 X 106. 
Baumgarten 1[ gives for calcite 

Eo= 501X106, E_45 = 44i X106, E + 45 = 772Xio6, £90 = 790X106. 



* In this system the subscript a indicates that compression or extension takes place along the crystalline axis, and 
distortion round the axis. The subscripts i and c correspond to directions equally inclined to two and normal to the 
third and equally inclined to all three axes respectively. 

T Voigt, " Wied. Ann." 31, p. 474, p. 701. '»»? i 34i P- Q^i, 1888 ; 36, p. 642, 1888. 

t Koch, " Wied. Ann." i!S, p. 325, 1882. 

§ Heckenkamp, "Zeit. fiir Krvst." vol. 10. ^ u . .u , f ..t,.^^., 

II The subscripts i, 2, 3 indicaie that the three principal axes are the axes of stress; 4, 5. 6 inal the axes ot stress 
are in the three principal planes at angles of 45° to the corresponding axes. 

H Baumgarten, " Pof;g. Ann." 152, p. 369, 1879. 

Smithsonian Tables. 



76 



Tables 47-49. 
COMPRESSIBILITY OF CASES. 



TABLE 47. —Relative Volumes at Various Pressures and Temperatures, the volume at 0°G and at 1 atmo- 
sphere being taken as 1 000 000. 



Atm. 


Oxygen. 


Air. 


Nitrogen. 


Hydrogen. 


0° 


99°-5 


•99°-S 


0° 


99°-4 


20o°.4 


0° 


99°- 5 


I99°.6 


0° 


99°.3 


200°. 5 


lOO 
200 

300 

400 
500 
600 
700 
800 
900 
1000 


9265 
4570 
3208 

2312 
2115 
1979 
1879 
1800 
1735 


7000 

4843 
3830 
3244 
2867 
2610 
2417 
2268 
2151 


9095 
6283 
4900 
4100 
3570 
3202 
2929 
2718 


9730 

3658 

3036 

2680 

2450 
2288 
2168 

2070 

1992 


7360 
5170 
4170 
3565 

3'So 
2904 
2699 
2544 
2415 


9430 
6622 
5240 
4422 

3883 
3502 
3219 

3000 
2828 


9910 

519s 

3786 

3142 
2780 

2543 
2374 
2240 
2149 
2068 


7445 
5301 
4265 

3655 
3258 
2980 
2775 
2616 


9532 
6715 

5331 
4515 

3973 
3589 
3300 
3085 


5690 
4030 
3207 
2713 
2387 
2149 
1972 
1832 
1720 


7567 
5286 

4147 

3006 
2680 
2444 

2244 
2093 


9420 

6520 

5075 
4210 
3627 
3212 
2900 
2657 



Amagat: C. R. m, p- 871, 1890; Ann. chim. phys. (6) 29, pp. 68 and 505, 1893. 

TABLE 48. — Ethylene. 

fv at 0° C and i atm. = i. 



Araagat, C. R. m, p- 871, 1890; 116, p. 946, 1893. 
TABLE 49. — Ethylene. 



Amagat, Ann. chim. phys. (5) 22, p. 353, iSSi. 



Atm. 


0° 


10° 


20° 


30° 


40° 


60° 


80° 


100° 


i37°-5 


i98°.s 


46 


_ 


0.562 


0.684 


_ 


_ 


_ 


_ 


- 


- 


- 


48 


- 


0.508 


- 


- 


- 


- 


- 


— 


— 


~ 


50 


0.176 


0.420 


0.629 


0.731 


0.8 1 4 


0.954 


1.077 


1. 192 


1-374 


1.652 


52 


- 


0.240 


0.598 


- 


- 


- 


- 


- 


— 


"~ 


54 


- 


0.229 


0.561 


- 


— 


— 


~ 


~ 


- 




56 


— 


0.227 


0.524 


— 


— 


— 


— 


~ 


~ 


"* 


100 


0.310 


0-331 


0.360 


0.403 


0.471 


0.668 


0.847 


1.005 


1.247 


I.5S0 


150 


0.441 


0.459 


0.485 


0.515 


0.551 


0.649 


0.776 


0.924 


1. 178 


1.540 


200 


0.565 


0.585 


0.610 


0.638 


0.669 


0.744 


0.838 


0.946 


1. 174 


1-537 


300 


0.806 


0.827 


0.852 


0.878 


0.908 


0.972 


1.048 


I.I33 


1. 310 


1.628 


500 


1.256 


1.280 


1.308 


1-337 


1.367 


1-431 


1.500 


1.578 


1.721 


1.985 


1000 


2.289 


2.321 


2-354 


2.387 


2.422 


2.493 


2.566 


2.643 


2.798 





Pressure in 
meters o£ 
mercury. 


Relative values of pv at — 


i6°.3 


20°.3 


30°. 


40°.o 


5o°.o 


6o°.o 


70O.0 


79°.9 


89°-9 


ioo°.o 


60 

90 

120 

150 
180 
210 
240 
270 
300 
320 


1950 

810 

1065 

1325 
1590 

1855 
2IIO 
2360 
2610 
2860 
3035 


2055 

900 

III5 
1370 

1625 

1890 
2145 
2395 

2640 
2890 

3065 


2220 
1 190 
I 195 
1440 
1690 

1945 
2200 

2450 
2710 
2960 

3'25 


2410 

153s 
1325 
1540 
1785 
2035 
2285 
2540 
2790 
3040 
3200 


2580 

1875 
15IO 
1660 
1880 
2130 

2375 
2625 

2875 
3125 
3285 


2715 
2100 
I710 
1780 
1990 
2225 
2470 
2720 
2965 
3215 

3375 


2865 
2310 
1930 

1950 
2125 
2340 

2565 
2810 
3060 
3300 
3470 


2970 
2500 
2160 
2II5 
2250 
2450 
2680 
2910 
3150 
3380 

3545 


3090 
2680 

2375 
2305 
2390 
2565 
2790 

3015 
3240 

3470 

3625 


3225 
2860 

2565 

2470 
2540 

2700 
2910 

3125 

3345 
3560 
3710 



Smithsonian Tables, 



Tables 50-52. 
COMPRESSIBILITY OF GASES. 

TABLE 60. — Carbon Dioxide. 



77 











Relative values of pv at — 






Pressure in 


































mercury. 


180.2 


35°-' 


40°.2 


So°.o 


6o°.o 


70°.o 


80O.0 


go°.o 


30 


liquid 


2360 


2460 


2590 


2730 


2S70 


2995 


3120 


50 


- 


1725 


1900 


2145 


2330 


2525 


2685 


2845 


80 


625 


750 


825 


1200 


1650 


1975 


2225 


2440 


no 


825 


930 


980 


1090 


1275 


1550 


1845 


2105 


140 


1020 


II20 


i'75 


1250 


1360 


1525 


i7>5 


1950 


170 


1210 


I3IO 


1360 


1430 


1520 


1645 


1780 


1975 


200 


1405 


1500 


1550 


16.5 


1705 


1810 


1930 


2075 


230 


1590 


1690 


1730 


1800 


1890 


1990 


2090 


2210 


260 


1770 


1870 


1920 


1985 


2070 


2166 


2265 


2375 


290 


1950 


2060 


2100 


2170 


2260 


2340 


2440 


2550 


320 


2135 


2240 


2280 


2360 


2440 


2525 


2620 


2725 



3225 

2980 

2635 
2325 

2160 

2'3S 
2215 
2340 
2490 

265s 
2830 



50 
100 
150 
300 

500 
1000 



Relative values of pv ; pv a.t o'' C. and i atm. = i. 



0.105 
0.202 
0.295 

0-559 
0.891 
1.656 



10^ 20" 



O.I 14 

0.213 
0.309 
0.578 
0.913 

1.685 



0.680 

0.229 
0.326 

0.599 
0.938 

1. 716 



30- 40' 



0-77S 
0.255 
0.346 
0.623 
0.963 
1.748 



0.750 
0.309 

0-377 
0.649 
0.990 
1.780 



60° 80° 100° 137° 198° 258° 



0.984 
0.661 
0.485 
0.710 
1.054 
1.848 



1.096 
0.873 
0.681 
0.790 
1. 124 
1. 92 1 



1.206 
1.030 
0.878 
0.890 
1. 201 
1.999 



.380 

•259 
.159 
.108 
.362 



1-530 
1-493 
1.678 



1.847 
1.818 
1.820 



Amagat, C. R. iii, p. 871, i8go; Ann. chim. phys. (5) 22, p. 353, 18S1; (6) 29, pp. 68 and 405, 1893. 



TABLE 51. — Compressibility of Oases. 



Gas. 


p.v. (i atm.) 


I dip.v.) 




a 


Density. 
= 32,o°C 

P — 76""' 


Density. 

Very small 

pressure. 


poVo (i atm.). 






t = o 


O2 


1 .00038 


— .00076 


11.2° 


.00094 


32- 


32- 


H2 


0.99974 


+ .00052 


10.7 


+ -00053 


2.015 (16°) 


2.0173 


No 


1. 000 1 5 


— .00030 


14.9 


.00056 


28.005 


28.016 


CO 


1.00026 


— .00052 


13.8 


.0008 I 


2S.OOO 


28.003 


CO2 


1.00279 


— .00558 


15.0 


— .00668 


44-268 


44.014 


N.,0 


1.00327 


— .00654 


II.O 


— -00747 


44.285 


43.996 


Air 


1.00026 


— .00046 


II.4 


- 


- 


- 


NH3 


1 .00632 


" 


" 


" 







Rayleigh, Zeitschr. Phys. Chem. 32, p. 705, 1905. 



TABLE 52. — Compressibility of Air and Oxygen between 18° and 22° C. 

Pressures in metres of mercury, pv, relative. 



Air 
O2 


pv 


24.07 
26968 


34-90 
26908 


45-24 
26791 


55-30 
26789 


64.00 
26778 


72.16 
26792 


84.22 
26840 


101.47 
27041 


214-54 

: 29585 


304.04 
32488 


P 

pv 


24.07 
26843 


26614 


- 


55-50 
26185 


64.07 
26050 


72-15 
25858 


84.19 

25745 


101.06 
25639 


214.52 

26536 


303-03 
28756 



Amagat, C. R. 1879. 



Smithsonian Tables. 



78 Tables 53-54. 

RELATION BETWEEN PRESSURE, TEMPERATURE AND 
VOLUME OF SULPHUR DIOXIDE AND AMMONIA.* 

TABLE 63. — Sulphur Dlozlde. 

Original volume looooo under one atmosphere of pressure and the temperature of the experi- 
ments as indicated at the top of the different columns. 



c 


Corresponding Volume for Ex- 




Pressure 


ll 

in Atmospheres for 1 


a s 


periments at Temperature — 




Experiments at Temperature — 1 1 


1 E 








Volume. 








58°.o 


99°.6 


i83°.2 


S8°.o 


99°.6 


i83°.2 


10 


8560 


9440 


_ 










12 


6360 


7800 


- 


1 0000 


- 


9.60 


, - 


14 
16 
18 


4040 


6420 
5310 
4405 


- 


9000 
8000 


9.60 
10.40 


10.35 
11-85 


- 


20 


- 


4030 


- 


7000 


"•55 


13-05 


- 


24 
28 


: 


3345 
2780 


3180 


6000 


12.30 


14.70 


- 


32 


- 


2305 


2640 


5000 


1315 


16.70 


- 


3b 


- 


1935 


2260 


4000 


14.00 


20.15 


- 


40 
50 


~ 


1450 


2040 
1640 


3500 


14.40 


23.00 


- 


60 


- 


- 


1375 


3000 


- 


26.40 


29.10 


70 


- 


- 


1 130 


2500 


- 


30-15 


33-25 


80 
90 


: 


: 


930 
790 


2000 


- 


35-20 


40-95 


100 


- 


- 


6S0 


1500 


- 


39.60 


55-20 


120 


- 


- 


545 


1000 


- 


- 


76.00 


140 
160 


- 


- 


430 
325 


500 


- 


- 


117.20 



TABLE 64. — Ammonia. 

Original volume looooo under one atmosphere of pressure and the temperature of the experiments as 
indicated at the top of the different columns. 



_c 


Correspoi 


ding Volume for Ex- 




Pressure 


in Atmosph 


eres for Experiments 1 


b 
5 S 

CL, 


periments at lemperature — 


Volume. 




at Temperature — 




46='.6 


gg^6 


i83°.6 


3o°.2 


46°.6 


99°. 6 


183^.0 


10 


9500 


_ 


_ 


1 0000 


8.85 


9-50 


• 


_ 


12.5 

15 
20 


7245 
5880 


7635 
6305 
4645 


4875 


9000 
8000 


9.60 
10.40 


10.45 
11.50 


12.00 


\ 


25 


- 


3560 


3835 


7000 


11.05 


13.00 


13.60 


— 


30 


- 


2S75 


3185 


6000 


11.80 


14-75 


15-55 


- 


35 
40 

45 


- 


2440 
2080 
1795 


2680 
2345 
2035 


5000 
4000 


12.00 


16.60 
18-35 


18.60 
22.70 


19.50 
24.00 


50 


- 


1490 


1775 


3500 


~ 


18.30 


25.40 


27.20 


P 


- 


1250 


1590 


3000 


- 


- 


29.20 


31-50 


60 


- 


975 


1450 


2500 


- 


- 


34-25 


37-35 


70 
80 


I 


I 


1245 
II25 


2000 


- 


- 


41.45 


45-50 


90 


- 


- 


1035 


1500 


- 


- 


49.70 


58.00 


100 






950 


1000 






59-65 


93.60 



* From the experiments of Roth, " Wied. Ann." vol. 11, 1880. 
Smithsonian Tables. 



Table 55. 
COMPRESSIBILITY OF LIQUIDS. 



79 



If Fi is the volume under pressure /i atmospheres at PC, and Vi is volume at pressure pi and the 
same temperature, then the compressibility coefficient may be defined at that temperature as ; 



j8t=- 



In absolute units (referred to megadynes) the coefficient is 



1.0137 



-fit. 



Substance. 


t. 


Pressures. 


/3.106 


Is 


Substance. 


t. 


Pressures. 


/3.I08 


c2£ 
























Acetone 


0.00 


1-500 


82 


I 


jMethyl alcohol 


100. 


8.68-37.3 


221 


3 


" 


0.00 


500-1000 


59 


i< 


II II 


18.10 


8 


120 


2 


" 


0.00 


1 000- 1 500 


47 


11 


Nitric acid 


20.3 


1-32 


338 


II 


" 


99-5 


8.94-36.5 


276 


3 


lOils : Almond 


17- 




P 


8 


Benzole 


5-95 


8 


83 


2 


Olive 


20.5 


- 


63 


ii 


" 


17.9 


8 




" 


Paraffin 


14.8 


- 


63 


6 


" 


15-4 
78.8 


1-4 


87 


4 


Petroleum 


16.5 


- 


70 


12 


" 


1-4 


126 




Rock 


19.4 


- 


l^ 


8 


Carbon bisulphide 


0.00 


1-500 


66 


I 


Rape -seed 


20.3 


- 


60 


" 


11 « 


0.00 


500-1000 


53 


" 


Turpentin 


19.7 


- 


79 


" 


<l u 


0.00 


1 000- 1 500 


43 


" 


Toluene 


10. 


- 


79 


13 


" " 


49.2 


1 000- 1 500 


51 


" 


" 


100. 


- 


150 


(( 


Chloroform 


0. 


- 


lOI 


5 


Xylene 


10. 


- 


74 


15 


" 


20. 


- 


128 




" 


100. 


- 


132 


" 


" 


40. 


- 


162 


" 


Paraffins: CeH^ 


23- 


O-I 


159 


14 


" 


60. 


- 


204 


" 


C7H16 






" 


134 


II 


" 


100. 


8-9 


211 


3 


CsHis 


' 




a 


121 


" 


(1 


100. 


19-34 


206 




C9H20 


' 




" 


"3 


" 


Collodium 


14.8 




97 


6 


C10H.22 


' 




" 


105 


" 


Ethyl alcohol 


28. 


1 50-200 


86 


7 


C12H.26 


' 




11 


92 


<■ 


" " 


28. 


1 50-400 


81 


" 


C14H30 


' 




" 


83 


<i 


« « 


65. 


1 50-200 


no 


" 


C16H34 


" 


" 


75 


a 


« (( 


65- 


1 50-400 


100 


" 


Water 


0. 


1-25 


52-5 


I 


(1 (( 


100. 


1 50-200 


168 


" 


u 


10. 


" 


50.0 


{< 


" " 


ICO. 


1 50-400 


132 


" 


" 


20. 


II 


49.1 


** 


(1 «< 


185. 


150-200 


320 


" 


tl 


0. 


25-50 


51.6 


** 


" " 


185. 


1 50-400 


245 


" 


II 


10. 


" 


49.2 


II 


II II 


310. 


1 50-200 


4200 


i< 


II 


20. 


" 


47.6 


II 


" " 


310. 


1 50-400 


1530 


" 


<l 


0. 


I-IOO 


511 


" 


" '♦ 


0. 


1-50 


96 


I 


II 


10. 


" 


48.3 


" 


« «< 


20. 


1-50 


112 


" 


<l 


20. 


II 


46.8 


" 


II « 


40. 


1-50 


^o5 


" 


" 


50- 


" 


44.9 


" 


II <i 


0. 


100-200 


85 


" 


" 


100. 


" 


47-8 


IC 


II II 


0. 


300-400 


73 


" 


l< 


0. 


100-200 


49.2 


" 


II ii 


20. 


300-400 


78 


" 


l< 


10. 


" 


46.1 


It 


II <i 


40. 


300-400 


87 


" 


l< 


20. 


" 


44.2 


a 


11 II 


0. 


500-600 


64 


" 


" 


50- 


" 


42-5 


11 


<i « 


0. 


700-800 


56 


II 


" 


100. 


i< 


46.8 


<i 


II u 


20. 


700-800 


62 


" 


" 


0. 


1-500 


47-5 


<i 


II II 


40. 


700-800 


65 


<i 


« 


20.4 


" 


43-4 


" 


II II 


0. 


900-1000 


52 


i< 


l< 


48.85 


" 


41.6 


« 


Ethyl chloride 


II. 


8.5-34.2 


138 


3 


« 


0. 


500-1000 


41.6 


II 


II 11 


15.2 


8.7-37.2 


153 


" 


<• 


0, 


1 000- 1 500 


35-8 


<i 


11 II 


61.S 


12.6-34.4 


256 


" 


l< 


20.4 


" 


33-8 


(( 


11 II 


99.0 


12.8-34.5 


495 


" 


" 


48.85 


" 


32-5 


" 


Glycerine 


20.5 


- 


25 


8 


(1 


0. 


I 500-2000 


32-4 


<i 


" 


14.8 


— 


22 


6 


« 


0. 


2000-2500 


29.2 


<i 


Mercury 


0. 


- 


3-92 


9 


« 


0. 


2500-3000 


26.1 


" 


" 


0. 


- 


3-90 


10 


i< 


48.85 


Ii 


25-4 


« 


Methyl alcohol 


14.7 


8.50-37.1 


104 


3 













For references see page 80. 



Smithsonian Tables. 



8o Table 56. 

COMPRESSIBILITY AND BULK MODULI OF SOLIDS. 



SoUd. 



Crystals : Barite . . 
Beryl . . 
Fluorspar 
Pyrites 
Quartz 
Rock salt 
Sylvine . 
Topaz . . 
Tourmaline 

Brass 

Copper 

Delta metal ... 

Lead 

Steel 

Glass 



Compression 

per unit 
volume per 
atmo. X lo^. 



1-93 

0.747 

1.20 

1. 14 

2.67 

4.20* 

7-45* 
0.61 
0.1 13 

0-95 
0.86 
1.02 
2.76 
0.68 
;.2-2.9 



Authority. 



Voigt 



Amagat 

Buchanan 

Amagat 



Calculated values of bulk 
modulus in — 



Grams per 

sq. cm. 



535 X 106 

1384 " 

860 " 

906 " 

387 " 

246 " 

138 " 

1694 " 

9140 " 

1090 " 

1202 " 

1012 " 

374 " 

1518 " 

405 " 



Pounds per 
sq. in. 



7.61 X I0« 

19.68 " 

12.24 " 

12.89 " 

5-5° " 

3.50 " 

1.97 " 

24.11 " 

130.10 " 

15.48 " 

17.10 " 

14.41 " 

5-32 " 

21.61 " 

5-76 " 



Note: Winklemann, Schott, and Straulel (Wied Ann. 6i, 63, 1897; 68, 1899) give the following coefficients (among 
others) for various Jena glasses in terras of the volume decrease divided by the increase of pressure expressed in kilo- 
grams per square millimeter: 

The following values in cm' / Kg of io« X Compressibility are given for the corresponding temperatures by Griineisen 
Ann. der Phys. 33, p. 65, 1910. 

Al. — 191°, 1.32; 17°, 1.46; 125°, 1.70. Fe. — 190°, 0.61 ; iS°, 0.63 ; 165°, 0.67. 

Cu. —191°, 0.72; 17°, 0.77; 165°, 0.83. Ag.— 191°, 0.71; 16°, 0.76; 166°, 0.86. 

Pt. — 189°, 0.37 ; 17°. 0-39 ; 164°, 0.40. Pb. — 191°, (2.5) ; 14°, (3.2) 



No. 


Glass. 


Compres- 
sibility. 


No. 


Glass. 


Compres- 
sibility 


66s 

1299 

16 

278 




7520 
5800 
4S30 
3790 


2IS4 
S 20S 
500 
S 196 


Kalibleisilicat 

Heaviest Bleisilicat 

Very Heavy " 

Tonerdborat with sodium, baryte 


3660 
3550 
3510 
3470 


Barj'tborosilicat 

Natronkalkzinksilicat .... 





* Rontgen and Schneider by piezometric experiments obtained 5.0 X 10-^ for rock salt, and 5.6 X io-« for sylvine 
(Wied. Ann., vol. 31). 



References to Tables 55 and 56. 



Liquids (Table 55) : 

1 Amagat, Ann. chlm. phys. (6) 29, 1893. 

2 Rontgen, Wied. Ann. 44, p. i, 1891. 

3 Amagat, C. R. 68, p. 1170, 1S69; Ann. 

chim. phys. (5) 28, 1883. 

4 Pagliani- Palazzo, Mem. Acad. Lin. (3) 19, 

1883. 

5 Grimaldi, Zeitschr. Phys. Chem. i, 1887. 

6 de Metz, Wied. Ann. 41, p. 663, 1890; 47, 

p. 706, 1892. 

7 Barus, Sill. Journ. 39, p. 478, 1890; 41, 1891 ; 

Bull. U.S. Geol. Surv. 1892. 
Solids (Table 56) : 
Amagat, C. R. 108, p. 228, 1889 ; J. de Phys. (2) 

8, p.197, 18S9. 



8 Quincke, Wied. Ann. 19, p. 401, 1883. 

9 Amagat, Ann. chim. phys. (6) 22, p. 95, 1891. 

10 Aime, Ann. chim. phys. (3) 8, p. 268, 1843. 

11 Colladon-Sturm, Pogg. Ann. 12, p. 39, 1828. 

12 Martini. 

13 de Heen, Bull. Acad. Roy. Belg. (3) 9, 1885. 

14 Bartoli, Rend Lomb. (2) 28, 29, 1896. 

15 Protz, Ann. der Phys. (4) 31, p. 127, 1910. 
See also Bridgman, Proc. Ann. Acad. 48, p. 309, 

191 2 (HjO) 49, p. 3, 1913 (alcohols, etc.) ; 
49, p. 627, 1914 (high pressure technique). 

Buchanan, Proc. Roy. Soc. Edinb. 10, 1880. 
Voigt, Wied. Ann. 31, 1887; 34, 1888, 36, 
1888. 



Smithsonian Tables. 



Table 57. gl 

SPECIFIC GRAVITIES CORRESPONDING TO THE BAUNIE SCALE. 

The specific gravities are for i5.56°C (6o°F) referred to water at the same temperature as unity. 
For specific gravities less than unity the values are calculated from the formula : 

140 



Degrees Baume = 



For specific gravities greater than unity from: 

Degrees Baume = 145 



Specific Gravity 
MS 



-130. 



Specific Gravity 



Specific Gravities less than i. 




0.00 


O.OI 


0.02 


0.03 


0.04 


0.05 


0.06 


0.07 


0.08 


0.09 


Specific 
Gravity. 


















































Degrees Baum6. 










0.60 


103-33 


99-51 


95.81 


92.22 


88.75 


85-38 


82.12 


78.95 


75.88 


72.90 


.70 


70.00 


67.18 


64.44 


61.78 


59-19 


56.67 


54.21 


51.82 


49-49 


47.22 


.80 


45.00 


42.84 


40.73 


38.68 


36.67 


34-71 


32-79 


30.92 


29.09 


27.30 


.90 


25-56 


23-85 


22.17 


20.54 


18.94 


^7-2,7 


15-83 


14-33 


12.86 


11.41 


1. 00 


10.00 




















Specific Gravities greater than i. 




0.00 


O.OI 


0.02 


0.03 


0.04 


0.05 


0.06 


0.07 


0.08 


0.09 


Specific 
Gravity. 


















































Degrees Baum^. 










I. GO 


0.00 


1.44 


2.84 


^•11 


.5-.S8 


6.91 


8.21 


9.49 


10.74 


11.97 


1. 10 


13.18 


14-37 


15-54 


16.68 


17.81 


18.91 


20.00 


21.07 


22.12 


23-15 


1.20 


24.17 


25.16 


26.15 


27.11 


28.06 


29.00 


29.92 


30-83 


31-72 


32.60 


1.30 


33-46 


34.31 


35-15 


35-98 


36.79 


37-59 


38.38 


39.16 


39-93 


40.68 


1.40 


41-43 


42.16 


42.S9 


43.60 


44.31 


45.00 


45-68 


46.36 


47-03 


47-68 


1.50 


48.33 


48.97 


49.60 


50-23 


50.84 


51-45 


52.05 


52.64 


53-23 


53.80 


1.60 


54.38 


54-94 


55-49 


56.04 


56.58 


57-12 


57-65 


58.17 


58.69 


59-20 


1.70 


5971 


60.20 


60.70 


61.18 


61.67 


62.14 


62.61 


63.08 


63-54 


63-99 


1.80 


64.44 


64.89 


65-33 


65.76 


1 66.20 


66.62 











Smithsonian Tables. 



82 



Tables 58-59. 

REDUCTIONS OF WEIGHINGS IN AIR TO VACUO. 

TABLE 68. 



When the weight M in grams of a body is determined in air, a correction is necessary for the 
buoyancy of the air equal to M S (i/d — i/dj) where 5 = the density (wt. of i ccm in grams 
= 0.0012) of the air during the weighing, d the density of the body, dj that of the weights. 
5 for various barometric values and humidities may be determined from Tables 153 to 155. The 
following table is computed for 5 = 0.0012. The corrected weight = M + kM/'ooo- 



Density 
of body 
weighed 


Correction factor 


, k. 


Density 
of body 


Correction factor 


, k. 


Pt. Ir. 


Brass 


Quartz or 


Pt. Ir. 


Brass 


Quartz or 
Al. weights 




weights 


weights 


Al. weights 




weights 


weights 




di = 2i.5. 


8.4. 


2.65. 




di = 2i.5. 


8.4. 


2.65. 


.5 


+ 2.34 


+ 2.26 


+ I-9S 


1.6 


+ 0.69 


+ 0.61 


+ 0.30 


.6 


+ I.9d 


+ 1.86 


+ 1-55 


1-7 


+ .65 


+ .56 


- .25 


•7 


+ 1.66 


+ 1-57 


+ 1.26 


1.8 


+ .62 


+ .52 


- .21 


•P 


+ 1-55 


+ 1.46 


+ I.IS 


1.9 


+ .58 


+ 49 


- .18 


.80 


+ 144 


+ 1.36 


+ 1-05 


2.0 


+ -54 


+ 46 


-- -15 


.8s 


+ 1.36 


+ 1.27 


+ 0.96 


2-5 


+ 43 


+ .34 


-- .03 


.90 


+ 1.28 


+ 1.19 


+ .88 


3-0 


+ -34 


+ .26 


— .05 


•95 


+ 1.21 


+ 1.12 


+ .81 


4.0 


+ .24 


+ .16 


— -15 


1.00 


+ 1.14 


+ 1.06 


-- -75 


6.0 


+ .14 


+ .06 


— -25 


I.I 


+ 1.04 


+ 0-9S 


- .64 


8.0 


+ -09 


+ .01 


— -30 


1.2 


+ 0.94 


+ .86 


+ -55 


1 0.0 


+ .06 


— .02 


— -33 


1-3 


+ -87 


+ 78 


-f- -47 


15.0 


+ .03 


— .06 


— -37 


1.4 


+ .80 


+ -71 


+ 40 


20.0 


+ .004 


— .08 


— -39 


1-5 


+ -75 


+ .66 


+ -35 


22.0 


— .001 


— .09 


— .40 



TABLE 68. — Reductions of Densities In All to Vacuo. 

(This correction may be accomplished through the use of the above table for each separate 
weighing.) 

If s is the density of the substance as calculated from the uncorrected weights, S its true den- 
sity, and L the true density of the liquid used, then the vacuum correction to be applied to the 
uncorrected density, s, is 0.0012 (i — s/L). 

Let Ws = uncorrected weight of substance, Wi = uncorrected weight of the liquid displaced 
by the substance, then by definition, s=:LWs/Wi. Assuming D to be the density of the 
balance of weights, Ws {i +0.0012 (i/S — i/D)}and Wi {i +0.0012 (i/L— i/D)}are the 
true weights of the substance and liquid respectively (assuming that the weighings are made 
under normal atmospheric corrections, so that the weight of i cc. of air is 0.0012 gram). 

Ws{i + 0.0012 (i/S — i/D)) 
Then the true density S — *■ ' ' f -^ 



But from above Ws/Wi : 



Wi{i + 0.0012 (i/L—i/U)} 

: s/L, and since L is always large compared with 0.0012, 
S — S = O.OOI2 (i — s/L). 
The values of 0.0012 (i — s/L) for densities up to 20 and for liquids of density i (water), 
0.852 (xylene) and 13.55 (mercury) follow : 

(See reference below for discussion of density determinations). 



Density of 

substance 

s. 


Corrections. 


Density of 

substance 

s 


Corrections. 




Water. 


Lr= 0.852 
Xylene. 


Mercury. 


L=i 

Water. 


Mercury. 




0.8 
0.9 
I. 

2. 

3- 
4- 

7. 
8. 

9- 
10. 


+ 0.00024 

+ .00012 

0.0000 

— .0012 

— .0024 

— .0036 

— .004S 

— .0060 

— .0072 

— .0084 

— .0096 

— .0108 


— 0.0002 

— .0016 

— .0030 

— .0044 

— .0058 

— .0073 

— .0087 

— .0101 

— .0115 

— .0129 


+ O.OOII 
+ .0010 
+ .0009 
+ .0008 
+ .0008 
+ .0007 
+ .0006 
+ .0005 
+ .0004 
+ -0003 


II. 
12, 

13- 
14. 

IS- 

16. 

17- 

18. 
19. 
20. 


— 0.0120 

— -0132 

— .0144 

— .oit;6 

— .0168 

— .0180 

— .0192 

— .0204 

— .0216 

— .0228 


+ 0.0002 

+ .0001 

0.0000 

0.0000 

— .0001 

— .0002 

— .0003 

— .0004 

— .0005 

— .0006 





Smithsonian Tables. 



Johnston and Adams, J. Am. Chem. Soc. 34, p. 563, tgiz. 



Table 60. 83 

DENSITY OR MASS IN CRAMS PER CUBIC CENTIMETER OF THE 
ELEMENTS, LIQUID OR SOLID. 

N. B. The density of a specimen may depend considerably on its state and previous treatment. 



Element. 


Physical State. 


Grams per 
cu. cm.* 


Tempera- 
ture.! 


Authority. 


Aluminum 


cast 
wrought 


2.56-2.58 
2.65-2.80 






'' 


pure 


2.58 


4 


Mallet, 1882. 


Antimony 


vacuo-distilled 


6.6i8 


20 


Kahlbaum, 1902. 


" 


ditto-compressed 


6.691 


20 


<» 


" 


amorphous 


6.22 




Herard. 


Argon 


liquid 


1.3845 


-183 


Baly-Donnan. 


*' 


" 


14233 


— 189 


i( 11 


Arsenic 


crystallized 


5-73 


14 




" 


amorph. br.-black 


3-70 




Geuther. 


" 


yellow 


3.88 




Linck. 


Barium 




378 




Guntz. 


Bismuth 


solid 


9.70-9.90 






u 


electrolytic 


9-747 




Classen, 1890. 


" 


vacuo-distilled 


9.781 


20 


Kahlbaum, 1902. 


" 


liquid 


10.00 


271 


Vincentini-Omodei. • 


" 


solid 


9.67 


271 


" " 


Boron 


crystal 


2-535 




Wigand. 


t( 


amorph. pure 


2.45 




Moissan. 


Bromine 


liquid 


3.12 




Richards-Stull. 


Cadmium 


cast 
wrought 


8.54-8.57 
8.67 






" 


vacuo-distilled 


8.648 


20 


Kahlbaum, 1902. 


« 


solid 


8.37 


318 


Vincentini-Omodei. 


" 


liquid 


7-99 


318 


" " 


Caesium 




1-873 


20 


Richards-Brink. 


Calcium 




1-54 




Brink. 


Carbon 


diamond 


3-52 




Wigand. 


" 


graphite 


2.25 




" 


Cerium 


electrolytic 
pure 


6.79 

7.02 




Muthmann- Weiss. 


Chlorine 


liquid 


1.507 


-33-6 


Drugman-Ramsay. 


Chromium 




6.52-6.73 






" 


pure 


6.92 


20 


Moissan. 


Cobalt 




8.71 


21 


Tilden, Ch. C. 1898. 


Columbium 




8.4 


15 


Muthmann- Weiss. 


Copper 


cast 

drawn 

wrought 


8.3c^8.95 
8.93-8.95 
8.85-8.95 






" 


electrolytic 


8.88-8.95 






" 


vacuo-distilled 


8.9326 


20 


Kahlbaum, 1902. 


" 


ditto-compressed 


8.9376 


20 


it u 1 


« 


liquid 


8.217 




Roberts- Wrightson. 


Erbium 




4-77 




St. Meyer, Z. Ph. Ch. 37. 


Fluorine 


liquid 


1. 14 


— 200 


Moissan-Dewar. 


Gallium 




5-93 


23 


de Boisbaudran. 


Germanium 




5-46 


20 


Winkler. 


Glucinum 




1.85 




Humpidge. 


Gold 


cast 
wrought 


19.3 
19-33 






" 


vacuo-distilled 


18.88 


20 


Kahlbaum, 1902. 


i( 


ditto-compressed 


19.27 


20 


" 


Helium 


liquid 


0.15 


-269 


Onnes, 1908. 


Hydrogen 


liquid 


0.070 


— 252 


Dewar, Ch. News, 1904. 


Indium 




7.2S 




Richards. 



*To reduce to pounds per cu. ft. multiply by 62 4. 

t Where the temperature is not given, ordinary atmospheric temperature is understood. 
Compiled from Clarke's Constants of Nature, Landolt-Bornstein-Meyerhoffer's Tables, and other sources. Where 
no authority is stated, the values are mostly means from various sources. 

Smithsonian Tables. 



Sd. Table 60 {continued). 

DENSITY OR MASS IN CRAMS PER CUBIC CENTIMETER OF THE 
ELEMENTS, LIQUID OR SOLID. 



Element. 



Iridium 

Iodine 

Iron 



Krypton 

Lanthanum 

Lead 



Lithium 

Magnesium 

Manganese 



Sodium 



Strontium 
Sulphur 



Physical State 



pure 

gray cast 

white cast 

wrought 

liquid 

steel 

liquid 

cast 

wrought 

solid 

liquid 

vacuo-distilled 

ditto-compressed 



Mercury 


liquid 


" 


solid 


Molybdenum 




Neodvmium 




Nickel 




Nitrogen 


liquid 


Osmium 




Oxygen 


liquid 


Palladium 




Phosphorus 


white 


" 


red 


" 


metallic 


Platinum 




Potassium 




" 


solid 


u 


liquid 


Praesodymium 




Rhodium 




Rubidium 




Ruthenium 




Samarium 




Selenium 




Silicon 


cryst. 




amorph. 


Silver 


cast 


" 


wrought 


" 


vacuo-distilled 


" 


ditto-compressed 




liquid 



solid 
liquid 



liquid 



Grams per 
cu. cm.* 



Temper- 
ature.t 



22.42 


17 


4.940 


20 


7.85-7.88 




7-03-7-I3 




7-5^-7-73 




7.80-7.90 




6.88 




7.60-7.80 




2.16 


—146 


6.15 




"•37 


24 


11.36 


24 


11.005 


325 


10.645 


325 


11.342 


20 


"•347 


20 


0-534 


20 


1.741 




7.42 




13-596 





13-546 


20 


13.690 


-3S.8 


14-193 


— 3S.8 


1 4^383 


—188 


9.01 




6.96 




8.60-8.90 




0.810 


—195 


0.854 


—205 


22.5 






1. 14 


—184 


12.16 




1.83 




2.20 




2^34 


15 


21.37 


20 


0.870 


20 


0.851 


62.1 


0.830 


62.1 


6-475 




12.44 




1^532 


20 


12.06 





7.7-7-8 




4.3-4.8 




2.42 


20 


2-35 


15 


10.42-10.53 




10.6 




10.492 


20 


10.503 


20 


9.51 




0.9712 


20 


0.9519 


97-6 


0.9287 


97-6 


1 .0066 


—188 


2.50-2.58 




2.0-2.1 




1.811 


113 



Authority. 



Deville-Debray 
Richards-Stull 



Roberts-Austen 

Ramsay-Travers 

Muthmann-Weiss 

Reich 

Vincentini-Omodei 

Kahlbaum, 1902 

Richards-Brink, '07 

Voigt 

Prelinger 

Regnault, Volkmann 

Vincentini-Omodei 

Mallet 

Dewar, 1902 

Moissan 

Muthmann-Weiss 

Baly-Donnan, 1902 

Deville-Debray 

Richards-Stull 



Hittorf 

Richards-Stull 
Richards-Brink, '07 
Vincentini-Omodei 

Muthmann-Weiss 
Holborn Henning 
Richards-Brink, '07 
Toby 
Muthmann-Weiss 

Richards-Stull-Brink 
Vigoroux 



Kahlbaum, 1902 

Wrightson 
Richards-Brink, '07 
Vincentini-Omodei 

Dewar 
Matthiessen 

Vincentini-Omodei 



*To reduce to pounds per cubic ft. multiply by 62.4. 
t Where the temperature is not given, ordinary atmo: 



nary atmosphere temperature is understood. 



Smithsonian Tables. 



Tables 60 {comtKueJ) and 61. MASS OF VARIOUS SUBSTANCES. 



85 



TABLE 60 (continued). 



■ Density or Mass In grains per cubic centimeter and pounds per cubic loot of tlie 
elements, llduld or solid. 



Element. 


Physical State. 


Grams per 
cu. cm. 


Tempera- 
ture. 


Authority. 


Tantalum 




16.6 






Tellurium 


crystallized 


6.25 






" 


amorphous 


6.02 


20 


Beljankin. 


Thallium 




11.86 




Richards-Stull. 


Thorium 




12.16 


17 


Bolton. 


Tin 


white, cast 


7.29 




Matthiessen. 


" 


" wrought 


7-30 






it 


" crystallized 


6.97-7.18 






" 


" solid 


7.184 


226 


Vincentini-Omodei 


« 


" liquid 


6.99 


226 


Vincentini-Omodei 




gray 


5-8 






Titanium 




4-5 


18 


Mixter. 


Tungsten 




18.6-19.1 






Uranium 




18.7 


13 


Zimmermann. 


Vanadium 




5-69 




Ruff-Martin. 


Xenon 


liquid 


3-52 


109 


Ramsay-Travers. 


Yttrium 




3.80 




St. Meyer. 


Zinc 


cast 


7.04-7.16 






(( 


wrought 


7.19 






" 


vacuo-distilled 


6.92 


20 


Kahlbaum, 1902. 


a 


ditto-compressed 


7-13 


20 


" " 


" 


liquid 


6.48 




Roberts-Wrightson. 


Zirconium 




6.44 







TABLE 61.— Mass In grams per cubic centimeter and in pounds per cubic foot of different kinds of wood. 

The wood is supposed to be seasoned and of average dryness. 





Grams 


Pounds 




Grams 


Pounds 


Wood. 


per cubic 


per cubic 


Wood. 


per cubic 


per cubic 




centimeter. 


foot. 




centimeter. 


foot. 


Alder 


C.42-0.68 


26-42 


Hazel 


0.60-0.80 


37-49 


Apple 


0.66-0.84 


41-52 


Hickory 


0.60-0.93 


37-58 


Ash 


0.65-0.85 


40-53 


Holly 


0.76 


47 


Bamboo 


0.31-0.40 


19-25 


Iron-bark 


1.03 


64 


Basswood. See Linden. 






Juniper 


0.56 


35 


Beech 


0.70-0.90 


43-56 


Laburnum 


0.92 


57 


Blue gum 


1. 00 


62 


Lancewood 


0.68-1.00 


42-62 


Birch 


0.51-0.77 


32-48 


Lignum vitae 


I-I7-I-33 


73-83 


Box 


0.95-1. 16 


59-72 


Linden or Lime-tree 


0.32-0.59 


20-37 


Bullet-tree 


1.05 


65 


Locust 


0.67-0.71 


42-44 


Butternut 


0.38 


24 


Logwood 


.91 


57 


Cedar 


0.49-0.57 


30-35 


Mahogany, Honduras 


0.66 


41 


Cherry 


0.70-0.90 


43-56 


" Spanish 


0.85 


53 


Cork 


0.22-0.26 


14-16 


Maple 


062-0.75 


39-47 


Dogwood 


0.76 


47 


Oak 


0.60-0.90 


37-56 


Ebony 


I-II-I-33 


69-83 


Pear-tree 


0.61-0.73 


38-45 


Elm 


0.54-0.60 


34-37 


Plum-tree 


0.66-0.78 


41-49 


Fir or Pine, American 






Poplar 


0-35-0-5 


22-31 


White 


0.35-0.50 


22-31 


Satinwood 


0-95 


59 


" Larch 


0.50-0.56 


31-35 


Sycamore 


0.40-0.60 


24-37 


" Pitch 


0.83-0.85 


52-53 


Teak, Indian 


0.66-0.88 


41-55 


" Red 


0.48-0.70 


30-44 


" African 


0.98 


61 


" Scotch 


0.43-0.53 


27-33 


Walnut 


0.64-0.70 


40-43 


" Spruce 


0.48-0.70 


30-44 


Water gum 


1.00 


62 


*• Yellow 


0.37-0.60 


23-37 


Willow 


0.40-0.60 


24-37 


Greenheart 


0.93-1.04 


58-65 









* Where the temperature is not given, ordinary atmospheric temperature is understood. 
Smithsonian Tables. 



86 Table 62. 

DENSITY OR MASS IN GRAMS PER CUBIC CENTIMETER AND POUNDS 

PER CUBIC FOOT OF VARIOUS SOLIDS. 

N. B. The density of a specimen depends considerably on its state and previous treatment ; especially is this the 
case with porous materials. 



Material. 


Grams per 
cu. cm. 


Pounds per 
cu. foot. 


Material. 


Grams per 
cu. cm. 


Pounds per 
cu. foot. 




Agate 


2.5-2.7 


156-168 


Gum arable 


I.3-I.4 


80-85 1 


Alabaster : 






Gypsum 


2-3I-2-33 


144-145 1 




Carbonate 


2.69-2.78 


168-173 


Hematite 


4-9-5-3 


306-330 




Sulphate 


2.26-2.32 


141-145 


Hornblende 


3-0 


187 




Albite 


2.62-2.65 


163-165 


Ice 


0.917 


57.2 




Amber 


I.06-I.II 


66- 69 


Ilmenite 


4.5-5- 


280-310 




Amphiboles 


2.9-3.2 


180-200 


Ivory 


1. 83- 1. 92 


1 14-120 




Anorthite 


2.74-2.76 


171-172 


Labradorite 


2.7-2.72 


168-170 




Anthracite 


I.4-I.8 


87-112 


Lava : basaltic 


2.8-3.0 


175-185 




Asbestos 


2.0-2.8 


125-175 


trachytic 


2.0-2.7 


125-168 




Asphalt 


I.I-I.5 


69- 94 


Leather : dry 


0.86 


54 




Basalt 


2.4-3.1 


150-190 


greased 


1.02 


64 




Beeswax 


0.96-0.97 


60- 61 


Lime : mortar 


1. 65-1.78 


103-111 




Beryl 


2.69-2.7 


168-168 


slaked 


1. 3-1. 4 


81- 87 




Biotite 


2.7-3.1 


170-190 


Limestone 


2.68-2.76 


167-171 




Bone 


1.7-2.0 


106-125 


Litharge : 








Brick 


1.4-2.2 


87-137 


Artificial 


9-3-9-4 


580-585 




Butter 


0.86-0.87 


53- 54 


Natural 


7.8-8.0 


490-500 




Calamine 


4- 1 -4- 5 


255-280 


Magnetite 


4.9-5-2 


306-324 




Caoutchouc 


0.92-0.99 


57-62 


Malachite 


3-7-4-I 


231-256 




Celluloid 


1.4 


87 


Marble 


2.6-2.84 


160-177 




Cement, set 


2.7-3.0 


170-190 


Meerschaum 


099-1.28 


62- 80 




Chalk 


1.9-2.8 


118-175 


Mica 


2.6-3.2 


165-200 




Charcoal: oak 


0.57 


35 


Muscovite 


2.76-3.00 


172-225 




pine 


0.28-0.44 


18- 28 


Ochre 


3-5 


218 




Chrome yellow 


6.00 


374 „ 


Oligoclase 


2.65-2.67 


165-167 




Chromite 


4-32-4-57 


270-285 


Olivine 


3-27-3-37 


204-210 




Cinnabar 


8.12 


507 


Opal 


2.2 


137 ^ 




Clay 


1.8-2.6 


122-162 


Orthoclase 


2.58-2.61 


161-163 




Coal, soft 


1. 2-1. 5 


75- 94 


Paper 


0.7-1. 15 


44- 72 




Cocoa butter 


0.S9-0.91 


56- 57 


Paraffin 


0.87-0.91 


54- 57 




Coke 


1.0-1.7 


62-105 


Peat 


0.84 


52 




Copal 


1.04-1.14 


65- 71 


Pitch 


1.07 


^7 ^ 




Corundum 


3.9-4.0 


245-250 


Porcelain 


2-3-2.5 


143-156 




Diamond : 






Porphyry 


2.6-2.9 


162-181 




Anthracitic 


1.66 


104 


Pyrite 


4-95-5-I 


309-318 




Carbonado 


3.01-3.25 


188-203 


Quartz 


2.65 


165 




Diorite 


2.52 


157 


Quartzite 


2-73 


170 




Dolomite 


2.84 


177 


Resin 


1.07 


67 




Ebonite 


115 


72 


Rock salt 


2.18 


136 ^ 




Emery 


4.0 


250 


Rutile 


6.00-6.5 


374-406 




Epidote 


3-2 5-3- 5 


203-218- 


Sandstone 


2.14-2.36 


134-147 




Feldspar 


2-55-27S 


159-172 


Serpentine 


2.50-2.65 


156-165 




Flint 


2.63 


164 


Slag, furnace 


2.0-3.9 


125-240 




Fluorite 


3.18 


198 


Slate 


2.6-3.3 


162-205 




Gamboge 


1.2 


75 ,„ 


Soapstone 


2.6-2.8 


162-175 




Garnet 


3- 1 5-4-3 


197-268 


Starch 


^■P 


95 




Gas carbon 


1.88 


117 


Sugar 


1. 61 


100 




Gelatine 


1.27 


180 


Talc 


2.7-2.8 


168-174 




Glass : common 


2.4-2.8 


150-175 


Tallow 


0.91-0.97 


57- 60 




flint 


2-9-5-9 


180-370 


Topaz 


3-5-3-6 


219-223 




Glue 


1.27 


80 


Tourmaline 


3-0-3-2 


190-200 




Granite 


2.64-2.76 


165-172 


Zircon 


4.68-4.70 


292-293 




Graphite 


2.30-2.72 


144-170 











Smithsonian Tables. 



Table 63. 

DENSITY OR MASS IN CRAMS PER CUBIC CENTIMETER 

AND POUNDS PER CUBIC FOOT OF VARIOUS 

ALLOYS (BRASSES AND BRONZES). 



87 





Grams 


! 
Pounds 1 


Alloy. 


per cubic 


per cubic i 




centimeter. 


foot. 


Brasses : Yellow, 70CU + 3oZn, cast 


8.44 


527 


rolled 














8.56 


534 


" " " drawn 














8.70 


542 


" Red, 90CU 4- loZn 














8.60 


536 


White, 50CU + 5oZn . 














8.20 


511 


Bronzes: 9oCu-|- loSn 














8.78 


548 


" 85CU -j- iS^n 














8.S9 


555 


" 8oCu -|- 2oSn 














8.74 


545 


75Cu+25Sn . 














8.83 


551 


German Silver: Chinese, 26.3CU + 36.6Zn+ 36.8N 










8.30 


518 


Berlin (I ) 52CU + 26Zn + 22Ni 










8.45 


527 


" (2) 59Cu + 3oZn+ iiNi 










8.34 


520 


" (3) 63CU + 3oZn + 6N 


i 










8.30 


518 


Nickelin .... 












8.77 


547 


LeadandTin: 87.sPb+ i2.5Sn 














10.60 


661 


" " " 84Pb + i6Sn . 














IO-33 


644 


" " " 77.SPb+22.2Sn 














10.05 


627 


" " " 63.7Pb4-36.3Sn 














9-43 


588 


" " " 46.7Pb+S3-3Sn . 














8.73 


545 


" " " 3o.5Pb + 69.5.Sn 














8.24 


514 


Bismuth, Lead, and Tin : 53Bi + 4oPb + 7Cd 










10.56 


659 


Wood's Metal : 5oBi -f 25Pb + i2.sCd + i2.5Sn . 










9.70 


605 


Cadmium and Tin : 32Cd + 68Sn 










7.70 


480 


Gold and Copper : 98AU -|- ^Cu 














18.84 


1 176 


" " " 96AU + 4CU 














18.36 


"45 


" " " 94AU + 6CU 














17-95 


1 120 


" " « 92AU + 8CU 














17-52 


1093 


" " " 90AU -j- loCu . 














17.16 


I07I 


" " " 88AU+12CU . 














16.81 


1049 


" " " 86Au + 14CU . 














16.47 


1027 


Aluminum and Copper: loAl + 90CU 














7.69 


480 


5AI + 95CU . 














8.37 


522 


3AI + 97CU . 














8.69 


542 


Aluminum and Zinc : 91 Al -f 9Zn 














2.80 


175 


Platinum and Iridium: 9oPt + loir . 














21.62 


1348 


85Pt+i5lr. 














21.62 


1348 


66.67Pt4-33-33ir 














21.87 


1364 


5Pt + 9sIr . . 














22.38 


1396 


Constantin : 6oCu 4" 4oNi 














8.88 


554 


Magnalium : 70AI -|- 3oMg 














2.0 


125 


Manganin : 84CU 4- i2Mn 4- 4Ni 














8.5 


530 


Platinoid: German silver 4- little Tungsten 










9.0 


560 



Smithsonian Tables. 



88 Tables 64-65. 

Table 64.-DENSITIES OF VARIOUS NATURAL AND ARTIFICIAL 

MINERALS. 

(See also Table 62.) 



Name and Formula. 



Pure compounds, all at 
25°C 

Magnesia, MgO 

Lime, CaO 

Forms of SiOj: 

Quartz, natural 
" artificial 

Cristobalite, artificial 

Silica glass 

Forms of AUSiOj : 

Sillimanite glass 

Sillimanite cryst. 

Forms of MgSiOj : 

j8 Monoclinic pyroxene 

a Orthorhombic pyroxene 

/3' Monoclinic amphibole 

7' Orthorhombic amphi- 
bole 

Glass 

Forms of CaSiOj : 

a (Pseudo-wollastonite) 

j3 (Wollastonite) 

Glass 
Fonns of Ca^SiO^ : 

a — calcium-orthosilicate 

3 — " 

y — " 
^.'— " 

Lime-alumina compounds : 
3CaO • AI2O3 
5CaO-3Al,C), 
CaO • Al,03 
3CaO • 5AI2O3 
3CaO • 5AI2O3, unstable 

form 
Forms of MgSiOg • CaSiOj : 
Diopside, natural, cryst. 
" artificial, " 

" glass 



Density 
grams 
per cc. 



3603 
3-306 

2.646 
2.642 
2.319 
2.206 

2-53 
3.022 

3-183 
3.166 



2.849 
2-735 

2.904 
2.906 
2.895 

3-26 
3-27 
2.965 



3.029 
2.820 
2.972 



3-04 

3-258 
3.265 
2.846 



Sp.Vol. 
cc. per 
gram. 



•2775 I 
•3025 



•3779 
•3785 
.4312 

•4533 

•395 
•3309 

.3142 
•3 '59 



•3510 
.3656 

-3444 
•3441 
•3454 



•307 


« 


.306 


" 


■337 




•3301 


3 


-3S46 




•3365 




329 


" 


3069 


4 


3063 




3514 


I 



Name and Formula. 



Feldspars : 
Albite glass, NaAlSijOg, 

art. 
Albite cryst., NaAlSijOj 

art. 
Anorthite glass, 

CaAljSijOg, art. 
Anorthite cryst., 

CaAl2Si208, art. 
Soda anorthite, 

NaAlSi04, art. 
Borax, glass, NajB^O, 

" cryst. " 
Fluorite, natural, CaF2 

(20°) 
(NH,)2SO, (30°) 

K3SO, (30°) 

KCl, fine powder (30°) 
Forms of ZnS : 
Sphalerite, natural* 
Wurtzite, artificial! 
Greenockite, artificial 
Forms of HgS : 
Cinnabar, artificial 
Metacinnabar, artifi- 
cial 

Minerals : 

Gehlenite, from Velar- 
dena 

Spurrite, from Velardena, 
2Ca2Si04 • CaCOa 

Hillebrandite, from Vel- 
ardena, 

CaSi03-Ca(OH)2 

Pyrite, natural, FeS^ 

Marcasite, natural, FeSj 

* Only 0.15% Fe total impurity, 
t Same composition as Sphaler- 
ite. 



Density 
grams 
per cc. 



2-375 
2.597 
2.692 

2-757 

2-563 

2.36 

2.27 

3.180 
1-765 
2.657 
1.984 

4.090 
4.087 
4.820 

8.176 

7.58 



3-03 
3-005 



2.684 
5.012 
4-873 



Sp. Vol. 
cc. per 
gram. 



.4210 

•3851 
•3715 
.3627 

.3902 

•423 
.440 

•3145 
.5666 

•3764 
.5040 

.2444 

.2447 
.2075 

.1223 

.132 



-330 
.3328 

-3726 

-1995 
.2052 



References: i, Larsen 1909; 2, Day and Shepherd; 3, Shepherd and Rankin, 1909; 4, Allen and 
White, 1909; 5, Allen, Wright and Clement, 1906; 6, Day and Allen, 1905; 7, Washington and 
Wright, 1910; 8, Merwin, 1911 ; 9, Johnston and Adams, 1911; 10, Allen and Crenshaw, 1912; 
II, Wright, 1908. 

All the data of this table are from the Geophysical Laboratory, Washington. 



Table 65. -DENSITIES OF MOLTEN TIN AND TIN-LEAD EUTECTIC. 



Temperature 

Molten tin 

37 pts. Pb, 63, Sn.* 


250°C. 

6.982 

8.011 


300° 

6.943 
7.965 


400° 
6.875 
7-879 


500° 

6.814 

7.800 


600° 
6-755 
7-731 


900° 
6.578 


1200° 
6-399 


1400° 
6.280 


1600° 
6.162 



* Melts at 181. Day and Sosman, Geophysical Laboratory, unpublished. 

For further densities inorganic substances see table 238. 
organic " " " 244. 

Smithsonian Tables. 



Tables 66-67. 
WEIGHT OF SHEET METAL. 



89 



TABLE 66. — Welgbt ol Sheet Metal- (Metric Measure.) 

This table gives the weight in grams of a plate one meter square and of the thickness stated in the 

first column. 



Thickness 
















in thou- 
sandths of 


Iron. 


Copper. 


Brass. 


Aluminum. 


Platinum. 


Gold. 


Silver. 


a cm. 
















1 


7S.0 


89.0 


85.6 


26.7 


215.0 


193.0 


105.0 


2 

3 

4 


156.0 
234.0 
312.0 


178.0 
267.0 
356.0 


I71.2 
256.8 
342.4 


53-4 
80.1 
106.8 


430.0 
6450 
860.0 


386.0 
579.0 
772.0 


210.0 

315-0 
420.0 


5 


390.0 


445.0 


428.0 


133-5 


1075.0 


965.0 


525.0 


6 


468.0 


534-0 


513-6 


160.2 


1290.0 


1158.0 


630.0 


7 
8 


546.0 
624.0 


623.0 
712.0 


684.8 


186.9 
213.6 


1505.0 
1720.0 


1351.0 
1544.0 


735-0 
840.0 


9 
10 


702.0 
7S0.O 


80 1. 
890.0 


770.4 
856.0 


240.3 
267.0 


1935-0 
2150.0 


1737-0 
1930.0 


945.0 
1050.0 



TABLE 67. - Weight of Sheet Metal. (British Measure.) 



Thickness 
in MiU. 


Iron. 


Copper. 


Brass. 


Aluminum. 


Platinum. 


Pounds per 


Pounds per 


Pounds per 


Pounds per 


Ounces per 


Pounds per 


Ounces per 




Sq. Foot. 


Sq. Foot. 


Sq. Foot. 


Sq. Foot. 


Sq. Foot. 


Sq. Foot. 


Sq. Foot. 


1 


.04058 


.04630 


.04454 


.01389 


.2222 


.iiig 


1.790 


2 


.0S116 


.09260 


.08908 


.02778 


•4445 


.2237 


3-579 


3 


.12173 


.13890 


•13363 


.04167 


.6667 


•3356 


5369 


4 


.16231 


.18520 


.17817 


•05556 


.8890 


•4474 


7-158 


5 


.20289 


.23150 


.22271 


.06945 


1.1112 


-5593 


8.948 


6 


•24347 


.27780 


.26725 


•08334 


1-3335 


.6711 


10.738 


7 


.28405 


.32411 


•31 179 


.09723 


1-5557 


-7830 


12.527 


8 


-32463 


•37041 


•35634 


.11112 


1.7780 


.8948 


14-317 


9 


•36520 


.41671 


.40088 


.12501 


2.0002 


1.0067 


16.106 


10 


.40578 


.46301 


.44542 


.13890 


2.2224 


1.1185 


17.896 






Thick 


ness 


Gold. 


Silver. 






















inM 


ils. 


Troy 

Ounces per 

Sq. Foot. 


Grains per 
Sq. Foot. 


Troy 
Ounces per 
Sq. Foot. 


Grains per 
Sq. Foot. 








1 




1.4642 


702.8 


0.7967 


382.4 








2 




2-9285 


1405.7 


I • 5933 


764.8 










3 




4-3927 


2108.5 


2.3900 


"47-2 










4 




5-8570 


281I.3 


3.1867 


1529.6 










5 




7.3212 


3514-2 


39833 


1912.0 










6 




8-7S54 


4217.0 


4.7800 


2294.4 










7 




10.2497 


4919.8 


5-5767 


2676.8 










8 




"■7139 


5622.7 


6-3734 


3059-2 










9 




I3.I7S2 


6325-5 


7.1700 


3441.6 










10 




14.6424 


7028.3 


7.9667 


3824.0 













Smithsonian Tables. 



90 



Table 68. 

DENSITY OF LIQUIDS. 

Density or mass in grams per cubic centimeter and in pounds per cubic foot of various liquids. 



Liquid. 



Grams per 
cubic centimeter. 



Pounds per 
cubic foot. 



Temp. C. 



Acetone . 
Alcohol, ethyl . 
" methyl 

Anilin 
Benzol 
Bromine . 
Carbolic acid (crude) 
Carbon disulphide . 
Chloroform 
Ether 
Gasoline . 
Glycerine . 
Milk 

Naphtha (wood) 
Naphtha (petroleum ether) 
Oils : Amljer . 

Anise-seed 

Camphor 

Castor . 

Cocoanut 

Cotton Seed . 

Creosote 

Lard 

Lavender 

Lemon . 

Linseed (boiled) 

Olive . 

Palm . 

Pine 

Poppy . 

Rapeseed (crude) 
" (refined) 

Resin 

Train or Whale 

Turpentine 

Valerian 
Petroleum 

(light) 
Pyroligneous acid 
Water 



0.792 
0.807 
C.810 

1-035 
0.899 

3-187 
0.950-0.965 

1.293 

1.480 

0.736 
0.66-0.69 

1.260 
1. 028-1. 035 
0.848-0.810 

0.665 

0.800 

0.996 

o.gio 

0.969 

0.925 

0.926 
1.040-1.100 

0.920 

0.877 

0.844 

0.942 

0.918 

0.905 
0.850-0.860 

0.924 

0.915 

0.913 

0-955 
0.918-0.925 

0.873 
0.965 
0.878 
0.795-0.805 
0.800 
1. 000 



49.4 

50-4 
50.5 

64-5 

56.1 

199.0 

59.2-60.2 

80.6 



o 
o 
o 
o 
IS 



923 


18 


45-9 





41.0-43-0 


- 


78.6 





64.2-64.6 


- 


S2-9-50-S 





41-5 


15 


49-9 


15 


62.1 


16 


56.8 


- 


60.5 


15 


57-7 


15 


57.S 


16 


64.9-6S.6 


15 


57-4 


'5 


54-7 


16 


52-7 


16 


58.8 


15 


57-3 


15 


56.5 


15 


S3-0-54-0 


15 


57-7 


- 


57-1 


15 


57 -o 


15 


59-6 


15 


57-3-57-7 


15 


54.2 


16 


60.2 


16 


54-8 





49.6-50.2 


15 


49.9 





62.4 


4 



Smithsonian Tables. 



Table 69. 
DENSITY OF CASES. 



91 



The following table gives the density of the gases at 0° C, 76 cm. pressure, at sea-level and lati- 
tude 45° relative to air as unity and under the same conditions ; also the weight of one liter in 
grams and one cubic foot in pounds. 



Gas. 


Specific 
Gravity. 


Grams 
per liter. 


Pounds 

per cubic 

foot. 


Reference. 


Air 


1. 000 


1.2928 


.0807 1 


Rayleigh; Leduc. 


Acetylene 


0.92 


1. 1620 


-07254 


Berthelot, i860. 


Ammonia 


0-597 


0.7706 


.048 1 1 


Leduc, C. R. 125, 1897. 


Argon 


1-379 


1.782 


.1112 


Ramsey-Travers, Proc. R. Soc. 67, 1900. 


Bromine 


5-524 


7.1388 


-4457 


Jahn, 1882. 


Butane 


2.01 


2-594 


.16194 


P>ankland, Ann. Ch. Pharm. 71. 


Carbon dioxide 


1.5291 


1.976S 


.12341 


Guye, Pintza, 1908. 


" monoxide 


0.9672 


1.2506 


.07S07 


Rayleigh, Proc. R. Soc. 62, 1897. 


Chlorine 


2.491 


3-1674 


-19774 


Leduc, C. R, 125, 1897. 


Coal gas { J™"" 


0.320 


0.414 


.02583 




0.740 


0.957 


•05973 




Cyanogen 


1.S06 


2.3229 


.14522 


Gay-Lussac. 


Ethane 


1.0494 


1-3567 


.08470 


Baume, Perot, J. Ch. et Phys. 1908. 


Fluorine 


1.26 


1.697 


.1059 


Moissan, C. R. 109. 


Helium 


1.368 


0.1787 


.01116 


Ramsay-Travers, Proc. R. Soc. 67, 1900. 


Hydrofluoric acid 


0.7126 


C.894 


.05581 


Thorpe-Hambley, J. Chem. Soc. 53. 


Hydrobromic acid 


2.71 


3-6163 


-2258 


Lowig, Gmelin-Kraut, Org. Chem. 


Hydrochloric acid 


1.2684 


1 .6398 


.10237 


Guye-Gazarian, 1908. 


Hydrogen 


0.0696 


0.09004 


.005621 


Rayleigh, Proc. R. Soc. 53, 1893. 


Hydrogen sulphide 


1.1895 


1-5230 


.09508 


Leduc, C. R. 125, 1897. 


Krypton 


2.868 


3-708 


-2315 


Watson, J. Ch. Soc. 1910. 


Methane 


0-5576 


0.7160 


.04470 


Thomson. 


Neon 


0.6963 


0.9002 


•0558 


Watson, J. Ch. Soc. 1910. 


Nitrogen 


0.9673 


1. 2514 


.07812 


Rayleigh, Proc. R. Soc. 62, 1897. 


Nitric oxide, NO 


1.0367 


1.3402 


.08367 


Guye, Davila, 1908. 


Nitrous oxide, NjO 


1.5298 


1-9777 


•12347 


Guye, Pintza, 1908. 


Oxygen 


1-053 


1.4292 


.08922 


Rayleigh, Proc. R. Soc. 62, 1897. 


Sulphur dioxide 


2.2639 


2.9266 


.18271 


Jaquerod, Pintza, 1908. 


Steam at 100° 


0.469 


0.581 


•0363 




Xenon 


4.526 


S-851 


•3653 


Watson, J. Ch. Soc. 1910. 



Compiled partly from Landolt-Bornstein-Meyerhoffer's Physikalisch-Chemische Tabellen. 
Smithsonian Tables. 



92 



Table 70. 
DENSITY OF AQUEOUS SOLUTIONS. 



The following table gives the density of solutions of various salts in water. The numbers give the weight in 
grams per cubic centimeter. For brevity the substance is indicated by formula only. 







Weight of the dissolved substance in loo parts by weight of 
the solution. 


u 






Substance. 




d 


Authority. 




5 


10 


15 


20 


25 


30 


40 


50 


60 




K2O .... 


1.047 


1.098 


1-153 


1.214 


1.284 


1-354 


1-503 


1.659 


1.809 


IS- 


Schiff. 




KOH . . . 


1.040 


1.082 


1.027 


1.076 


1.229 


1.286 


1.410 


1-53^5 


1.666 


IS- 


" 




NaaO . . . 


I -07 3 


1. 144 


1. 218 


1.2S4 


1-354 


1.421 


1-557 


1.689 


1.829 


'5- 


" 




NaOH . . . 


1.05S 


1. 114 


1. 169 


1.224 


1.279 


1-331 


1.436 


1-539 


1.642 


15- 


" 




NH3 .... 


0.97 8 


0.959 


0.940 


0.924 


0.909 


0.896 


- 




- 


16. 


Carius. 




NH4CI . . . 


1. 01 5 


1.030 


1.044 


1.058 


1.072 


- 


- 


- 


-, 


IS- 


Gerlach. 




KCl . . . . 


1. 03 1 


1.065 


1.099 


1-135 


- 


- 


- 


- 


- 


IS- 


'- 




NaCl. . . . 


1-035 


1.072 


I. no 


1.150 


1. 191 


- 


- 


- 


- 


IS- 


" 




LiCl .... 


1.029 


1-057 


1.085 


1. 116 


1.147 


1. 181 


1-255 


- 


- 


IS- 


'* 




CaClg . . . 


1. 04 1 


1.086 


1. 132 


1. 181 


1.232 


1.286 


1.402 


- 


- 


15- 


" 




CaClz + 6H2O 


1.019 


1.040 


1. 06 1 


1.083 


1. 105 


1. 128 


1. 176 


1.225 


1.276 


18. 


Schiff. 




AICI3 . . . 


1.030 


1.072 


I. Ill 


1-153 


1. 196 


1.241 


1.340 




- 


15- 


Gerlach. 




MgCla . . . 


1. 04 1 


1.085 


1-130 


1. 177 


1.226 


1.278 


- 


- 


- 


15- 


" 




MgCl2+6H20 


1.014 


1.032 


1.049 


1.067 


1.085 


1.103 


1.141 


1.183 


1.222 


24- 


Schiff. 




ZnCl2 . . . 


1.043 


1.089 


1-135 


1. 184 


1.236 


1.289 


1.417 


1-563 


1-737 


19.5 


Kremers. 




CdClz . . . 


1.043 


1.0S7 


1.138 


1-193 


1.254 


1-319 


1.469 


1-653 


1.887 


19-5 


« 




8rCl2. . . . 


1.044 


1.092 


I-I43 


1. 198 


1-257 


1.321 


- 


- 


- 


15- 


Gerlach. 




SrC]2 + 6H20 


1.027 


1-053 


1.082 


i.iii 


1.042 


1.174 


1.242 


1-317 


- 


15- 


'* 




BaCl2 . . . 


1. 04 5 


1.094 


1. 147 


1.205 


1.269 


- 


- 




- 


15- 


" 




BaCl2+2HoO 


1-035 


1-075 


1. 119 


1.166 


1.217 


1-273 


- 


- 


- 


21. 


Schiff. 




CuCl2 . . . 


1.044 


1. 091 


1-155 


1. 221 


1.291 


1.360 


1.527 


- 


- 


17-5 


Franz. 




NiClz . . . 


1.048 


1.09S 


I -1 57 


1.223 


1.299 


- 




- 


- 


17-5 


" 




HgCl2 . . . 


1. 04 1 


1.092 






~ 


- 


- 


- 


- 


20. 


Mendelejeff. 




FesCle . . . 


1. 04 1 


1.086 


1-130 


1. 179 


1.232 


i.2qo 


1-413 


1-545 


1.668 


17-5 


Hager. 




PtCl4. . . . 


1.046 


1.097 


1-153 


1.214 


1.285 


1-362 


1.546 


1-7^5 


- 


- 


Precht. 




SnCl2+2H20 


1.032 


1.067 


1. 104 


1-143 


1. 185 


1.229 


1.329 


1.444 


1.580 


IS- 


Gerlach. 




SnCli+sHaO 


1.029 


1.058 


1.0S9 


1.122 


1-157 


1-193 


1.274 


1-365 


1.467 


IS- 


« 




LiBr .... 


1-033 


1.070 


I. Ill 


1.154 


1.202 


1.252 


1.366 


1.498 


- 


19-5 


Kremers. 




KBr .... 


I -03 s 


1-073 


1.114 


1. 157 


1.205 


1.254 


1.364 


- 


- 


19.5 


" 




NaBr . . . 


1.038 


1.078 


1-123 


1. 172 


1.224 


1.279 


1.408 


1-563 


- 


19.5 


a 




MgBr2 . . . 


1. 04 1 


1.085 


I-135 


1. 189 


1-245 


1.308 


1.449 


1-623 


- 


19.5 


« 




ZnBra . . . 


1.043 


1. 09 1 


1.144 


1.202 


1-263 


1.328 


1-473 


1.648 


1-873 


19.5 


it 




CdBra . . . 


1. 04 1 


1.088 


I -1 39 


1.197 


1.258 


1-324 


1.479 


1.678 


- 


19.5 


" 




CaBr2 . . . 


1.042 


1.087 


1-137 


1. 192 


2.250 


1-313 


1.459 


1.639 


- 


19-5 


it 




BaBrg . . . 


1.043 


1.090 


1. 142 


1.199 


1.260 


1.327 


1.483 


1.683 


— 


19-5 






SrBrz . . . 


1.043 


1.089 


1. 140 


1. 198 


1.260 


1.328 


1.489 


1.693 


1-953 


19-S 


« 




KI . . . . 


1.036 


1.076 


1.118 


1.164 


1.216 


1.269 


1-394 


1.544 


1-732 


19.5 


(( 




Lil . . . . 


1.036 


1.077 


1.122 


1.170 


1.222 


1.278 


1.412 


1-573 


'•775 


19-5 


(( 




Nal . . . . 


1.038 


1.080 


1.126 


1.177 


1.232 


1.292 


1.430 


1.598 


1.808 


19.5 


n 




Znio . . . 


1.043 


1.089 


1.138 


1.194 


1-253 


1.316 


1.467 


1.648 


1-873 


19-S 


(1 




Cdl2 .... 


r.042 


1.086 


1. 136 


1.192 


1. 251 


1-317 


1.474 


1.678 


- 


19-5 


« 




Mgl2. . . . 


1.04 1 


1.086 


1-137 


1.192 


1.252 


1.318 


1.472 


1.666 


1-913 


19-5 


'* 




Cala .... 


1.042 


1.088 


1.138 


1.196 


1.258 


1-319 


1-475 


1.663 


1.908 


19-5 


(( 




Srl2 .... 


1.043 


1.089 


1. 140 


1.198 


1.260 


1.328 


1.489 


1.693 


1-953 


19-5 


tt 




Bal2 .... 


1.043 


1.089 


1. 141 


1.199 


1.263 


1-331 


1-493 


1.702 


1.968 


195 


a 




NaClOa. . . 


1-035 


1.068 


1. 106 


I-I4S 


1.188 


1-233 


1.329 


- 


- 


19-5 


" 




NaBrOs . . . 


1.039 


1. 08 1 


1.127 


1. 176 


1.229 


1.287 




- 


- 


19-5 


(( 




KNO3 . . . 


1. 03 1 


1.064 


1.099 


1-135 


- 




- 


- 


- 


15- 


Gerlach. 




NaNOa . . . 


1.03 1 


1.065 


I.IOI 


1. 140 


1.180 


1.222 


1-313 


1.416 


- 


20.2 


Schiff. 




AgNOs . . . 


1.044 


1.090 


1.140 


1-195 


1-255 


1.322 


1.479 


1.675 


1.918 15. 


Kohlrausch. 



* Compiled from two papers on the subject by Gerlach in the " Zeit. fiir Anal. Chi.n.," vols. 8 and 27. 
Smithsonian Tables. 



Table 70 {continued). 
DENSITY OF AQUEOUS SOLUTIONS. 



93 





Weight of the dissolved substance in loo parts by weight of 








the solution. 







Substance. 




a 


Authority. 




5 


10 


'S 


20 


25 


30 


40 


50 


60 


S 
H 




NH4NO3 . . . 


1.020 


1. 04 1 


1.063 


1.085 


1. 107 


1. 131 


r.178 


1.229 


1.282 


17-5 


Gerlach. 


ZndXOsh . . . 


1.048 


1.095 


1. 146 


1. 201 


1.263 


1-325 


1.456 


1-597 


- 


•7-5 


Franz. 


Zn(N03)2+6H20 


- 


1.054 


- 


1. 113 


- 


1. 178 


1.250 


1.329 


- 


14. 


Oudemans. 


Ca{N03)2 . . . 


1-037 


1-075 


1. 118 


1. 162 


1. 211 


1.260 


1-367 


1.482 


1.604 


17-5 


Gerlach. 


CU(N03)2 . . . 


1.044 


1.093 


I-I43 


1.203 


1.263 


1.328 


I -47 1 


- 


- 


17-5 


P'ranz. 


Sr(N03)2 . . . 


1.039 


1.083 


1. 129 


1. 179 


- 


- 


- 


- 


- 


19-5 


Kremers. 


Pb(N03)o . . . 


1.043 


1. 091 


1-143 


1. 199 


1.262 


1-332 


- 


- 


- 


17-5 


Gerlach. 


Cd{N03)2 . . . 


1.052 


1.097 


1. 1 50 


1. 212 


1.283 


1-355 


1-536 


1-759 


- 


17-5 


Franz. 


C0(N03)2 . . . 


1.045 


1.090 


1-137 


1. 192 


1.252 


1.318 


1.465 


- 


- 


17-S 


" 


Ni(N03)2 . . • 


1.045 


1.090 


I-I37 


1. 192 


1.252 


1.318 


1.465 


- 


- 


17-5 


" 


Fe2(N03)6 . . . 


1.039 


1.076 


1. 117 


1. 160 


1. 210 


1.261 


1-373 


1.496 


1.657 


17-5 


'« 


Mg(N03)o+6HoO 


i.oiS 


1-038 


1.060 


1.082 


1-105 


1. 129 


1. 179 


1.232 




21 


Schiff. 


Mn(N03)-.+6U20 


1.025 


1.052 


1.079 


1. 108 


I.I38 


1. 1 69 


1-235 


1-307 


1.386 


8 


Oudemans. 


K2CO3 .... 


1.044 


1.092 


1.141 


1. 192 


1-245 


1.300 


1.417 


1-543 


- 


15 


Gerlach. 


K2CO3+2H2O . 


1-037 


1.072 


I.IIO 


1. 150 


1. 191 


1-233 


1.320 


1-415 


1. 511 


15- 


" 


NaoCOsioHoO . 


1.019 


1.038 


1.057 


1.077 


I.09S 


1. 118 


- 


- 


- 


15- 


" 


(NH4)2S04 . . 


1.027 


1-055 


1.084 


1-113 


1. 142 


1. 170 


1.226 


1.287 


- 


19. 


Schiff. 


Fe2(b04)3 . . . 


1.045 


1.096 


I.I 50 


1.207 


1.270 


1-336 


1.489 




- 


18. 


Hager. 


FeS04 + 7H20 . 


1.025 


1-053 


1. 08 1 


I. Ill 


1. 141 


1-173 


1.238 


- 


- 


17.2 


-Schiff. 


MgSU4 .... 


1. 05 1 


1. 1 04 


1. 161 


1. 221 


1.284 






- 


- 


15 


Gerlach. 


MgSO + 7H2O . 


1.025 


1.050 


1-075 


I.IOI 


I.I29 


1-155 


1.215 


1.278 


_ 


15- 


" 


Na2So4 4- 10H2O 


1.019 


1.039 


1.059 


1. 08 1 


1. 102 


1. 124 




- 


- 


15- 


" 


CUSO44- 5H0O . 


1. 03 1 


1.064 


1 .098 


I-I34 


I-I73 


1. 213 


- 


- 


- 


18. 


Schiff. 


MnS04 + 4HoO . 


1.03 1 


1.064 


1.099 


1-135 


1. 174 


1.214 


1-303 


1.398 


- 


'5- 


Gerlach. 


ZnS04+7H20 . 


1.027 


1-057 


1.089 


1. 122 


1. 156 


1. 191 


1.269 


I-35I 


1-443 


20.5 


Schiff. 


Fe2(SO)3+K2S04 
























+ 24H2O. . . 


1.026 


1.045 


1.066 


1.088 


1. 112 


1. 141 


- 


- 


_ 


17-5 


Franz. 


Cr2(SO)3+K2S04 
























+ 24H2O . . 


1.016 


1-033 


1-051 


1-073 


1.099 


1. 126 


1. 188 


1.287 


1.454 


17-5 


" 


Mg.S<J4 + K2SO4 
























+ 6H.O . . . 


1.032 


1.066 


I.IOI 


1. 138 


_ 


_ 


_ 


_ 


_ 


15- 


Schiff. 


(NH4)2S04 + 
























FeS04 + 6H2O 


1.02S 


1.058 


1.090 


1. 122 


1. 154 


1. 191 


- 


- 


- 


19. 


" 


K2Cr04 .... 


1.039 


1.082 


1. 127 


1. 174 


1.225 


1.279 


1-397 


- 


- 


195 


" 


K0C10O7 . . . 


1-035 


1.07 1 


1. 108 


- 


- 


- 


- 


_ 


_ 


19-5 


Kremers. 


Fe(Cy)6K4 . . . 


1.028 


1.059 


1.092 


1. 126 


- 


- 


- 


- 


- 


15- 


Schiff. 


Fe(Cy)cK3 . . . 


1.025 


1-053 


1.070 


1. 113 


- 


- 


- 


- 


- 


13 


" 


Pb(CoH302)2 + 
























3H2O .... 


1-031 


1.064 


1. 100 


I-I37 


1. 177 


1.220 


1-315 


1.426 


- 


'5- 


Gerlach. 


2NaOH + AS2O5 
























+ 24H2O . . 
SO3 


1.020 


1.042 


1.066 


1.089 


1. 114 


1. 1 40 


1. 194 


- 


- 


14. 

15- 


Schiff. 
Brineau. 


S 


10 


•s 


20 


30 


40 


60 


80 


ICO 


1.040 


1.084 


1. 132 


1. 170 


1.277 


1.389 


1.564 


1.840 


_ 


SO2 . . . 




I.OI3 


1.028 


1-045 


1.063 


- 




- 


- 


- 


4- 


Schiff. 


N2O5 . . . 




1-033 


1.069 


1. 104 


1. 141 


1. 217 


1.294 


1.422 


1.506 


- 


15- 


Kolb. 


C4H0OG . . 




1. 02 1 


1.047 


1.070 


1.096 


1. 1 50 


1.207 


- 


- 


- 


15- 


Gerlach. 


CeHgOr . . 




I.O18 


1.038 


1.058 


1.079 


1-123 


1. 170 


1-273 


- 


- 


15- 


" 


Cane sugar . 




I.OI9 


1.039 


1.060 


I.0S2 


1. 1 29 


1. 178 


1.289 


- 


_ 


17-5 


" 


HCl . . . 




r.025 


1.050 


1.075 


I.IOI 


1. 151 


1.200 


- 


- 


- 


"5- 


Kolb. 


HBr . . . 




1-035 


1-073 


1. 114 


1. 1 58 


1-257 


1-376 


- 


- 


- 


14. 


Topsoe. 


HI . . . 




1-037 


1.077 


1. 118 


1. 165 


1. 271 


1.400 


- 


- 


- 


13- 


" 


H2SO4 . . 




1.032 


1.069 


1. 106 


I-I45 


1.223 


1-307 


1. 501 


1-732 


1.838 


15- 


Kolb. 


HsSiFle . . 




1.040 


1.082 


1. 127 


1.174 


1-273 


- 


- 


_ 


_ 


17-5 


Stolba. 


P2O5 . . . 




1-035 


1.077 


1. 119 


1. 1 67 


1. 271 


1-385 


1.676 


- 


- 


17-S 


Hager. 


P2O6 + 3H2O 




1.027 


1.057 


1.086 


1. 119 


1.188 


1.264 


1.438 


- 


- 


15- 


Schiff. 


HNO. . . 




1.028 


1.056 


1.088 


1. 119 


I.1S4 


1.250 


1.068 


1-459 


1.528 


15- 


Kolb. 


C2H4U2 . . . . 1 


1.007 


1. 01 4 


I.02I 


1.028 


1. 04 1 


1.052 


1.075 1-055 j 


15- 


Oudemans. 



Smithsonian Tables. 



94 



Table 71 . " 
DENSITY OF PURE WATER FREE FROM AIR. 

[Under standard pressure (76 cm), at every tenth part of a degree of the international hydrogen scale from 0° to 41^^ 

C, in grams per milliliter '] 



De- 






Tenths of Degrees. 






Mean 


grees 














Di«er- 


Centi- 






















ences. 


grade. 





1 


2 


3 


4 


6 


6 


7 


8 


9 







0.999 868 1 


8747 


8812 


8875 


8936 


8996 


9053 


9109 


9163 


9216 


+ 59 


I 


9267 


9315 


9363 


9408 


9452 


9494 


9534 


9573 


9610 


9645 


+ 41 


1 2 


9679 


9711 


9741 


9769 


9796 


9821 


9844 


9866 


9887 


9905 


+ 24 


3 


9922 


9937 


9951 


9962 


9973 


9981 


9988 


9994 


9998 


*oooo 


+ 8 


4 


1. 000 0000 


*9999 


*9996 


*9992 


*9986 


*9979 


*9970 


*996o 


*9947 


*9934 


— 8 


5 


0.999 9919 


9902 


98S4 


9864 


9842 


9819 


9795 


9769 


9742 


9713 


— 24 


6 


9682 


9650 


9617 


9582 


9545 


9507 


9468 


9427 


9385 


9341 


— 39 


7 


9296 


9249 


9201 


9151 


9100 


9048 


8994 


^938 


8881 


8823 


~ P 


8 


8764 


8703 


8641 


8577 


8512 


8445 8377 


8308 


8237 


8165 


— 67 


i ^ 


8091 


8017 


7940 


7863 


7784 


7704 


7622 


7539 


7455 


7369 


— 81 


10 


7282 


7194 


7105 


7014 


6921 


6826 


6729 


6632 


6533 


6432 


-95 


II 


6331 


6228 


6124 


6020 


5913 


5805 


5696 


5586 


5474 


5362 


—108 


12 


5248 


5132 


5016 


4898 


4780 


4660 


4538 


4415 


4291 


4166 


— 121 


\ 13 


4040 


3912 


3784 


3654 


3523 


3391 


3^57 


3122 


2986 


2850 


-133 


i '' 


2712 


2572 


2431 


2289 


2147 


2003 


1858 


1711 


1564 


1416 


—145 


1 

1 IS 


1266 


1114 


0962 


0809 


0655 


0499 


0343 


0185 


0026 


*9865 


-156 


I 16 


0.998 9705 


9542 


9378 


9214 


9048 


8881 


8713 


8544 


8373 


8202 


—168 


! 17 


8029 


7856 


7681 


7505 


7328 


7150 


6971 


6791 


6610 


6427 


—178 


i 18 


6244 


6058 


5873 


56S6 


5498 


5309 


5119 


4927 


4735 


4541 


— 190 


'^ 


4347 


4152 


3955 


3757 


3558 


3358 


3158 


2955 


2752 


2549 


— 200 


1 20 


2343 


2137 


1930 


1722 


1511 


1 301 


1090 


0878 


0663 


0449 


—211 


21 


0233 


0016 


*9799 


*958o 


*9359 


*9i39 


♦8917 


*8694 


*8470 


*8245 


— 221 


i 22 


0.997 8019 


7792 


7564 


7335 


7104 


6873 


6641 


6408 


6173 


5938 


—232 


! 23 


5702 


5466 


5227 


4988 


4747 


4506 


4264 


4021 


3777 


3531 


—242 


24 


3286 


3039 


2790 


2541 


2291 


2040 


1788 


1535 


1280 


1026 


—252 


25 


0770 


G513 


0255 


*9997 


♦9736 


*9476 


*92i4 


*895i 


*8688 


*S423 


—261 


i 26 


0.9968158 


7892 


7624 


7356 


7087 


6817 


6545 


6273 


6000 


5726 


—271 


1 27 


5451 


5176 


4898 


4620 


4342 


4062 


3782 


3500 


3218 


293 s 


—280 


; 28 


2652 


2366 


2080 


1793 


1505 


1217 


0928 


0637 


0346 


0053 


-289 


1 ^9 


0.995 9761 


9466 


9171 


8876 


8579 


8282 


7983 


7684 


7383 


7083 


-298 


! 

1 30 


6780 


6478 


6174 


5869 


5564 


5258 


4950 


4642 


4334 


4024 


—307 


i 31 


3714 


3401 


3089 


2776 


2462 


2147 


1S32 


1515 


1198 


0880 


—3' 5 


32 


0561 


0241 


*9920 


*9599 


*9276 


*8954 


*8630 


♦8304 


*7979 


*7653 


—324 


i 33 


0.994 7325 


6997 


6668 


6338 


6007 


5676 


5345 


501 1 


4678 


4343 


—332 


1 34 


4007 


3671 


3335 


2997 


2659 


2318 


1978 


1638 


1296 


0953 


—340 


',35 


0610 


0267 


*9922 


*9576 


♦9230 


*8883 


*8534 


*8i86 


♦7837 


*7486 


—347 


1 36 


0.9937136 


6784 


6432 


6078 


5725 


5369 


5014 


4658 


4301 


3943 


-355 


37 


3585 


3226 


2866 


2505 


2144 


1782 


1419 


1055 


0691 


0326 


-362 


1 38 


0.992 9960 


9593 


9227 


8859 


8490 


8120 


7751 


7380 


7008 


6636 


—370 


39 


6263 


5890 


5516 


5140 


4765 


4389 


401 1 


3634 


3255 


2876 


—377 


40 


2497 


2116 


1734 


1352 


0971 


0587 


0203 


*98i8 


*9433 


*9047 


-384 


1 41 

1 


0.991 8661 























» According to P. Chappuis, Bureau international des Poids et Mesures, Travaux et M^moires, 13; 1907. 
Smithsonian Tables, 



Table 72. 



95 



VOLUME IN CUBIC CENTIMETERS AT VARIOUS TEMPERATURES OF 

A CUBIC CENTIMETER OF WATER FREE FROM AIR AT THE 

TEMPERATURE OF MAXIMUM DENSITY. 

Hydrogen Thermometer Scale. 



i Temp. 
C. 


.0 


.1 


.2 


•3 


• 4 


•5 


.6 


•7 


.8 


•9 


1 o 


1.000132 


125 


118 


112 


106 


100 


095 


089 


084 


079 


I 


073 


069 


064 


059 


055 


051 


047 


043 


039 


035 ! 


2 


032 


029 


026 


023 


020 


018 


016 


013 


on 


009 


3 


ooS 


006 


005 


004 


003 


002 


001 


001 


000 


000 


4 


000 


000 


000 


001 


001 


002 


003 


004 


005 


007 


! 5 


008 


010 


012 


014 


016 


018 


021 


023 


026 


029 


6 


032 


03s 


039 


042 


046 


050 


054 


058 


062 


066 


7 


070 


075 


080 


0S5 


090 


095 


lOI 


106 


112 


118 


8 


124 


130 


137 


142 


149 


156 


162 


169 


176 


184 


9 


191 


198 


206 


214 


222 


230 


238 


246 


254 


263 


10 


272 


281 


290 


299 


308 


317 


327 


337 


347 


357 


1 II 


367 


377 


388 


398 


409 


420 


430 


441 


453 


464 


12 


476 


487 


499 


5" 


522 


534 


547 


559 


571 


584 


13 


596 


609 


623 


636 


649 


661 


675 


688 


702 


715 


14 


729 


743 


757 


772 


7S6 


800 


815 


830 


844 


859 i 


'5 


873 


890 


905 


920 


935 


951 


967 


983 


998 


015* 


! 16 


1.001031 


047 


063 


080 


097 


113 


130 


147 


164 


1S2 


i '7 


1 98 


216 


233 


252 


269 


287 


305 


323 


341 


358 


! 18 


37^ 


396 


415 


433 


452 


471 


490 


510 


529 


548 


19 


568 


588 


606 


626 


646 


667 


687 


707 


728 


748 


1 20 


769 


790 


811 


832 


853 


874 


895 


916 


938 


960 


' 21 


981 


002* 


024* 


046* 


068* 


091* 


113* 


135* 


158* 


181* 


"" 


1.002203 


226 


249 


271 


295 


319 


342 


364 


389 


412 


-3 


436 


459 


483 


507 


532 


556 


581 


605 


629 


654 


24 


679 


704 


729 


754 


779 


804 


829 


854 


879 


905 


-5 


932 


958 


983 


010* 


036* 


061* 


088* 


115* 


141* 


168* 


26 


1. 003 1 95 


221 


248 


275 


302 


330 


357 


384 


412 


439 i 


27 


467 


495 


523 


550 


579 


607 


635 


663 


692 


720 1 


28 


749 


776 


806 


836 


865 


893 


922 


951 


981 


on* I 


29 


1. 00404 1 


069 


100 


129 


160 


189 


220 


250 


280 


310 


30 


341 


371 


403 


432 


464 


494 


526 


557 • 


588 


619 


31 


651 


682 


713 


744 


777 


808 


840 


872 


904 


936 


1 32 


968 


001* 


033* 


066* 


098* 


132* 


163* 


197* 


229* 


263* 


33 


1.005296 


328 


361 


395 


427 


461 


496 


530 


562 


597 


34 


631 


665 


698 


732 


768 


802 


836 


871 


904 


940 


35 


975 


009* 


044* 


078* 


115* 


150* 


185* 


219* 


255* 


290* 



Reciprocals of the preceding table. 



Smithsonian Tables. 



q6 Table 73. 

DENSITY AND VOLUME OF WATER. 

The mass of one cubic centimeter at 4° C. is taken as unity. 



Temp. C. 


Density. 


Volume. 


Temp. C. 


Density. 


Volume. 


—10° 


0.99815 


1. 00 1 86 


+35° 


0.99406 


1.00598 


—9 


843 


157 


36 


371 


'^J^ 


-8 


869 


131 


37 


336 


669 


—7 


892 


108 


38 


300 


706 


—6 


912 


088 


39 


263 


743 


—5 


0.99930 


1.00070 


40 


0.99225 


1.00782 


—4 


945 


055 


41 


187 


821 


—3 


958 


042 


42 


147 


861 


— 2 


970 


031 


43 


107 


901 


— I 


979 


021 


44 


066 


943 


+0 


0.99987 


1. 000 1 3 


45 


0.99025 


1.00985 


I 


993 


007 


46 


0.98982 


1.01028 


2 


997 


003 


47 


940 


072 


3 


999 


001 


48 


896 


116 


4 


1. 00000 


1. 00000 


49 


852 


162 


5 


0.99999 


1. 0000 1 


50 


0.98807 


1. 01 207 


6 


997 


003 


51 


762 


254 


7 


993 


007 


52 


rj 


301 


8 


988 


012 


53 


669 


349 


9 


981 


019 


54 


621 


398 


10 


0-99973 


1.00027 


55 


0.98573 


1. 01 448 


II 


963 


037 


60 


324 


705 


12 


952 


048 


65 


059 


979 


13 


940 


060 


70 


0.97781 


1.02270 


14 


927 


073 


75 


489 


576 


15 


0.99913 


1.00087 


80 


0.97183 


1.02899 


16 


897 


103 


85 


0.96865 


1.03237 


17 


880 


120 


90 


534 


590 


18 


862 


138 


95 


o^S 


959 


19 


843 


157 


100 


0.95838 


1-04343 


20 


0.99823 


1.00177 


110 


0.9510 


1.0515 


21 


802 


198 


120 


■9434 


1. 060 1 


22 


780 


220 


130 


•9352 


1.0693 


23 


757 


244 


140 


.9264 


1.0794 


24 


733 


268 


150 


•9173 


1.0902 


25 


0.99708 


1.00293 


160 


0.9075 


1.1019 


26 


682 


320 


170 


■^2U 


1.1145 


27 


655 


347 


180 


.8866 


1. 1279 


28 


627 


375 


190 


.8750 


1-1429 


29 


598 


404 


200 


.8628 


1. 1590 


30 


0.99568 


1.00434 


210 


0.S50 


1. 177 


31 


537 


465 


220 


•837 


1. 195 


32 


506 


497 


230 


.823 


1.215 


33 


473 


530 


240 


.809 


1.236 


34 


440 


563 


250 


•794 


1-259 



* From — 10° to o° the values are due to means from Pierre, Weidner, and 
Rosetti; from o° to 41°, to Chappuis, 42° to 100°, to Thiesen ; 110° to 250°, to 
means from the works of Ramsey, Young, Waterston, and Hirn. 



Smithsonian Tables. 



Table 74. 

DENSITY OF MERCURY. 

Density or mass in grams per cubic centimeter, and the volume in cubic 
centimeters of one gram of mercury. 



97 





Mass in 


Volume of 




Mass in 


Volume of 




Temp. C. 


grams per 


I gram in 


Temp. C. 


grams per 


I gram in 






cu. cm. 


cu. cms. 




cu. cm. 


cu. cms. 




—10° 


13.6202 


0.0734205 


30° 


13-5217 


0.0739552 




—9 


6177 


4338 


31 


5193 


9685 




—8 


6152 


4472 


32 


5168 


9819 




—7 


6128 


4606 


33 


5144 


9953 




—6 


6103 


4739 


34 


5119 


40087 




—5 


13.6078 


0.0734873 


35 


13-5095 


0.0740221 




—4 


6053 


5006 


36 


5070 


0354 




—3 


6029 


5140 


37 


5046 


0488 




— 2 


6004 


5273 


38 


5021 


0622 




1 


5979 


5407 


39 


4997 


0756 







13-5955 


0.0735540 


40 


13-4973 


0.0740890 




I 


5930 


5674 


50 


4729 


2230 




2 


59°S 


5808 


60 


4486 


3572 




3 


5880 


5941 


70 


4243 


4916 




4 


5856 


6075 


80 


4001 


6262 




5 


13-5831 


0.0736208 


90 


13-3776 


0.074761 1 




6 


5807 


6342 


100 


3518 


8961 




7 


5782 


6476 


no 


3283 


50285 




8 


5757 


6609 


120 


3044 


1633 




9 


5733 


6743 


130 


2805 


2982 




10 


13-5708 


0.0736877 


140 


13.2567 


0.07S4334 




II 


5683 


7010 


150 


2330 


5688 




12 


5659 


7144 


160 


2093 


7044 




13 


5634 


7278 


170 


1856 


8402 




14 


5610 


7411 


180 


1620 


9764 




15 


13-5585 


0-0737545 


190 


13-1384 


0.0761 1 28 




16 


5560 


7679 


200 


1148 


2495 




17 


5536 


7812 


210 


0913 


386s 




18 


55" 


7946 


220 


0678 


5239 




19 


5487 


8080 


230 


0443 


6616 




20 


13.5462 


0.0738213 


240 


13.0209 


0.0767996 




21 


5438 


^^47 


250 


12.9975 


9381 




22 


5413 


8481 


260 


9741 


70769 




23 


53S9 


8615 


270 


9507 


2161 




24 


5364 


8748 


280 


9273 


3558 




25 


13-5340 


0.0738882 


290 


12.9039 


0.0774958 




26 


5315 


9016 


300 


8806 


6364 




27 


5291 


9150 


310 


8572 


7774 




28 


5266 


9284 


320 


8339 


9189 




29 


5242 


9417 


330 


8105 


80609 




30 


13-5217 


0-0739551 


340 

350 
360 


12.7872 
7638 
7405 


0.0782033 

3464 
4900 





Thiesen und Scheel, Tiitigkeitber. Phys.-Techn. Reichsanstalt, 1897-1898; Chappuis, 
Trav. Bur. Int. 13, 1903. 
Thiesen, Scheel, Sell; Wiss. Abb. Phys.-Techn. Reichsanstalt 2, p. 184, 1895. 

Smithsonian Tables. 



98 



Table 75. 



DENSITIES OF MIXTURES OF ETHYL ALCOHOL AND WATER IN CRAMS 

PER MILLILITER. 

The densities in this table are numerically the same as specific gravities at the various temperatures in terms of water 
at 4° C. as unity. Based upon work done at U. S. Bureau of Standards. See Bulletin Bur. Stds. vol. 9, no. 3 ; con- 
tains extensive bibliography ; also Circular 19, 1913. 











Temperatures. 










Per cent 


















CjHsOH 


















by weight 


10° C. 


is°C. 


20° C. 


25° C. 


30° C. 


3S°C. 


40° C. 







0.99973 


0.99913 


0.99823 


0.99708 


0.99568 


0.99406 


0.99225 




I 


785 


725 


636 


520 


379 


217 


034 




2 


602 


542 


453 


336 


194 


031 


.98S46 




3 


426 


365 


275 


0^57 


014 


.98849 


663 




4 


258 


195 


103 


.98984 


.98839 


672 


485 




5 


098 


032 


.98938 


817 


670 


501 


3" 




6 


.98946 


.98877 


780 


656 


507 


335 


142 




7 


801 


729 


627 


500 


347 


172 


•97975 




8 


660 


584 


478 


346 


189 


009 


808 




9 


524 


442 


331 


193 


031 


.97846 


641 




10 


393 


304 


187 


043 


•9787 s 


685 


475 




II 


267 


171 


047 


•97897 


723 


527 


312 




12 


145 


041 


.97910 


753 


573 


371 


150 




13 


026 


.97914 


775 


611 


424 


216 


.96989 




14 


.97911 


790 


643 


472 


278 


063 


829 




15 


800 


669 


5M 


334 


133 


.96911 


670 




16 


692 


552 


387 


199 


.96990 


760 


512 




17 


583 


433 


259 


062 


844 


607 


352 




18 


473 


313 


129 


.96923 


697 


452 


189 




19 


363 


191 


.96997 


782 


547 


294 


023 




20 


252 


068 


864 


639 


395 


134 


.95856 




21 


139 


.96944 


729 


495 


242 


•95973 


687 




22 


024 


818 


592 


348 


087 


809 


516 




23 


.96907 


689 


453 


199 


•95929 


643 


343 




24 


787 


558 


312 


048 


769 


476 


168 




25 


665 


424 


168 


•95895 


607 


306 


.94991 




26 


539 


287 


020 


738 


442 


133 


810 




27 


406 


144 


.95867 


576 


272 


•94955 


625 




28 


268 


.95996 


710 


410 


098 


774 


438 




29 


125 


844 


548 


241 


.94922 


590 


248 




30 


•95977 


686 


382 


067 


741 


403 


oP 




31 


823 


524 


212 


.94890 


557 


214 


.93860 




32 


665 


357 


038 


709 


370 


021 


662 




33 


502 


186 


.94860 


525 


180 


•93825 


461 




34 


334 


on 


679 


337 


.93986 


626 


257 




35 


162 


.94832 


494 


146 


790 


425 


051 




36 


.94986 


650 


306 


•93952 


591 


221 


.92843 




37 


80s 


464 


114 


756 


390 


016 


634 




38 


620 


273 


•93919 


556 


1 86 


.92808 


422 




39 


431 


079 


720 


353 


.92979 


597 


208 




40 


238 


.93882 


S18 


148 


770 


385 


.91992 




41 


042 


682 


314 


.92940 


558 


170 


774 




42 


.93842 


478 


107 


729 


344 


.91952 


554 




43 


639 


271 


.92897 


516 


128 


733 


332 




44 


433 


062 


685 


301 


,91910 


513 


108 




45 


226 


.92852 


472 


085 


692 


291 


.90884 




46 


017 


640 


257 


.9 1 868 


472 


069 


660 




47 


.92806 


426 


041 


649 


250 


.90845 


434 




48 


593 


211 


.91823 


429 


028 


621 


207 




49 


379 


.91995 


604 


208 


.90805 


396 


.89979 




50 

! 


162 


776 


384 


.90985 


580 


168 


750 





Smithsonian Tables. 



'■%i| i 



Table 75 {continued). 



99 



DENSITY OF MIXTURES 


OF ETHYL ALCOHOL AND WATER l^ 


CRAMS 








PER MILLILITER 








i 






Temperature. 








[ Per cent 














CoHsOH 
















by weight 


10° c. 


.s°C. 


20° C. 


25OC. 


30° c. ■'■ 


35° C. 


40° C. 


50 


0.92162 


0.91776 


0.91384 


0.909S5 


0.90580 


0.90168 


0.89750 


51 


■91943 


555 


160 


760 


353 


.89940 


519 


52 


l-^-Z 


333 


.90936 


534 


125 


710 


288 


51 


502 


no 


711 


307 


.89896 


479 


056 


54 


279 


.90SS5 


485 


079 


667 


248 


.88823 


55 


055 


659 


258 


.898 50 


437 


016 


589 


56 


.90831 


433 


031 


621 


206 


.88784 


356 


57 


607 


207 


.89S03 


392 


.88975 


552 


122 


58 


3S1 


.89980 


574 


162 


744 


319 


.878S8 


59 


154 


752 


344 


•88931 


512 


085 


653 


60 


•89927 


523 


"3 


699 


278 


.87851 


417 


61 


698 


293 


.88S82 


466 


044 


615 


iSo 


62 


468 


062 


650 


233 


.87809 


379 


.86943 


63 


237 


.88830 


417 


.87998 


574 


142 


7<l 


64 


006 


597 


183 


763 


337 


.86905 


466 


65 


•SS774 


364 


.87948 


527 


100 


667 


227 


66 


541 


130 


713 


291 


.86863 


429 


.85987 


67 


308 


■87895 


477 


054 


^^5 


190 


747 


68 


074 


660 


241 


.86817 


387 


.85950 


5^? 


69 


.87839 


424 


004 


579 


148 


710 


266 


70 


602 


187 


.86766 


340 


.85908 


470 


°o5 


71 


365 


.86949 


527 


100 


667 


228 


.84783 


i 72 


127 


710 


287 


.85859 


426 


.84986 


540 


73 


.S6SS8 


470 


047 


618 


184 


743 


297 


74 


648 


229 


.85806 


376 


.84941 


SCO 


053 


i 75 


408 


.85988 


564 


^34 


698 


257 


.83809 


76 


168 


747 


322 


.84S91 


455 


o°'3 


564 


77 


.85927 


505 


079 


647 


211 


.83768 


319 


73 


685 


262 


.84835 


403 


.83966 


523 


074 


79 

1 


442 


018 


590 


158 


720 


277 


.82827 


1 

80 


197 


•84772 


344 


.8391 1 


473 


029 


578 


81 


.84950 


525 


096 


664 


224 


.82780 


329 


82 


702 


277 


.83848 


415 


.82974 


530 


079 


83 


453 


028 


599 


164 


724 


279 


.81828 


84 


203 


•83777 


348 


•82913 


473 


027 


576 


85 


•83951 


525 


095 


660 


220 


.81774 


322 


86 


697 


271 


.82840 


405 


.81965 


519 


067 


87 


441 


014 


583 


148 


708 


262 


.80811 


88 


181 


•82754 


323 


.8 1 888 


448 


003 


552 


89 


.82919 


492 


062 


626 


186 


.80742 


291 


90 


654 


227 


.81797 


362 


.80922 


478 


028 


91 


386 


.81959 


529 


094 


655 


211 


.79761 


92 


114 


.688 


257 


.80823 


384 


.79941 


491 


93 


.81839 


413 


.80983 


549 


III 


669 


220 


94 


561 


134 


705 


272 


•7983s 


393 


.78947 


1 
95 


278 


.80852 


424 


.79991 


555 


114 


670 


96 


.S0991 


566 


138 


706 


J-l"- 


.78831 


388 


97 


698 


274 


.79846 


415 


.78981 


542 


100 


98 


399 


.79975 


547 


oJl'7 


684 


247 


.77806 


99 


094 


670 


243 


.78814 


382 


.77946 


507 


100 


•79784 


360 


•78934 


506 


07S 


641 


203 



Smithsonian Tables. 



lOO Table 76. 

DENSITIES OF AQUEOUS MIXTURES OF METHYL ALCOHOL, 
CANE SUGAR, OR SULPHURIC ACID. 



Per cent 


Methyl 




Sulphuric 


Per cent 


Methyl 




Sulphuric 


by weight 

of 
substance. 


Alcohol. 
D-°C. 


Cane 

Sugar. 

20° 


Acid. 


by weight 

of 
substance. 


Alcohol. 

TCO 


Cane 

Sugar. 

20° 


Acid. 

Dfc. 


O 


0.99913 


0.998234 


0.99823 


SO 


0.91852 I 


229567 


1-39505 


I 


.99727 


1. 002 1 20 


1.00506 


51 


.91653 I 


235085 


1.404S7 


2 


•99543 


1. 0060 1 5 


I.OII78 


52 


.91451 I 


240641 


1.41481 


3 


•99370 


1.009934 


1. 01 839 


S3 


.91248 I 


246234 


1.42487 


4 


.99198 


I.OI3881 


1.02500 


54 


.91044 I 


251866 


^•43503 


5 


.99029 


1.017854 


1. 03 1 68 


S5 


.90839 I 


257535 


1^44530 


5 


.9S864 


1. 021855 


1.03843 


56 


.90631 I 


263243 


1.45568 


7 


.98701 


I.O258S5 


1.04527 


57 


.90421 I 


268989 


1. 4661 5 


8 


•9S547 


1.029942 


1.05216 


S8 


.90210 I 


274774 


1-47673 


9 


.98394 


1.034029 


1.05909 


59 


.89996 I 


280595 


1.4S740 


10 


.98241 


1. 038 1 43 


1.06609 


60 


.89781 I 


286456 


1.49818 


II 


■9S093 


1.042288 


1.07314 


61 


.89563 I 


292354 


1.50904 


12 


•97945 


1.046462 


1.08026 


62 


.89341 I 


298291 


1.51999 


13 


.97802 


1.050665 


1.08744 


63 


.89117 I 


304267 


i^53io2 


14 


.97660 


1.054900 


1.09468 


64 


.88890 I 


310282 


i^542i3 


IS 


•97518 


I.O59165 


1.10199 


^5 


.8S662 I 


316334 


1-55333 


16 


•97377 


1 .063460 


1. 1 0936 


66 


.88433 I 


322425 


1.56460 


17 


■97237 


1.067789 


1.11679 


67 


.8S203 I 


328554 


1-57595 


18 


.97096 


I.O72147 


1. 12428 


68 


.87971 I 


334722 


1-58739 


19 


•96955 


1^076537 


i^i3i83 


69 


•87739 I 


34092S 


1.59890 


20 


.96814 


I.0S0959 


M3943 


70 


.87507 I 


347174 


1.61048 


21 


.96673 


I.0854I4 


1. 14709 


71 


.87271 I 


353456 


1.62213 


22 


•96533 


1.089900 


1. 1 5480 


72 


•87033 I 


359778 


1.63384 


23 


.96392 


1.094420 


1. 16258 


73 


.86792 I 


366139 


1.64560 


24 


.96251 


1.09897 I 


1. 1 7041 


74 


.86546 I 


372536 


1-65738 


25 


.96108 


^•i03557 


1. 1 7830 


75 


.86300 I 


378971 


1. 669 1 7 


26 


•95963 


1.108175 


1. 1 8624 


76 


.86051 I 


385446 


1.68095 


27 


■95S17 


1.112828 


1. 19423 


77 


.85801 I 


391956 


1.69268 


28 


.95668 


1.117512 


1.20227 


78 


•85551 I 


398505 


1-70433 


29 


•955'8 


1.122231 


1.21036 


79 


.85300 I 


405091 


1^71585 


30 


.95366 


I.I 26984 


1.21850 


80 


.85048 I 


4II715 


1.72717 


31 


•95213 


i^i3i773 


1.22669 


81 


.84794 I 


418374 


1.73827 


32 


.95056 


1. 1 36596 


1.23492 


82 


•84536 I 


425072 


1.74904 


33 


.94896 


I^i4i453 


1.24320 


83 


.84274 I 


431807 


1-75943 


34 


•94734 


i^i46345 


^25154 


84 


.84009 I 


438579 


1.76932 


35 


•94570 


^•I5i275 


1.25992 


85 


.83742 I 


44538S 


1.77S60 


36 


.94404 


I.I 56238 


1.26836 


86 


.83475 I 


452232 


1.78721 


37 


•94237 


1.161236 


1.27685 


87 


•83207 I 


4591 14 


1.79509 


38 


.94067 


1. 166269 


1.28543 


88 


.82937 I 


466032 


1.S0223 


39 


.93S94 


1.171340 


1.29407 


89 


.82667 I 


4729S6 


1 .80864 


40 


.93720 


1. 176447 


1.30278 


90 


.82396 I 


479976 


1. 8 1 438 


41 


•93543 


1.181592 


1-31157 


91 


.82124 I 


487002 


1.81950 


42 


•93365 


1. 186773 


1.32043 


92 


.81849 I 


494063 


1. 8240 1 


43 


•93185 


1.191993 


1-32938 


93 


.81568 I 


501 1 58 


1.82790 


44 


.93001 


1. 197247 


1-33843 


94 


.81285 I 


5082S9 


1.83115 


45 


.92815 


1.202540 


1-34759 


95 


.80999 I 


515455 


1.83368 


46 


.92627 


1.207870 


1.35686 


96 


.80713 I 


522656 


1.83548 


47 


.92436 


1.213238 


1.36625 


97 


.80428 I 


529891 


1-83637 


48 


.92242 


1. 218643 


^•37574 


98 


.80143 I 


537161 


1. 8360s 


49 


.92048 


1.224086 


1-38533 


99 


.79859 I 


544462 




SO 


.91852 


1.229567 


1-39505 


100 


.79577 I 


551800 





(i) Calculated from the specific gravity determinations of Doroschevski and Rozhdestvenski at 
i5°/i5° C. ; J. Russ., Phys. Chem. Soc, 41, p. 977. 1909^ 

(2) According to Dr. F. Plato; Wiss. Abh. der K. Normal-Eichungs-Kommission, 2, p. 153, 1900. 

(3) Calculated from Dr. Domke's table ; Wiss. Abh. der K. Normal-Eichungs-Kommission, 
5, p. 131, 1900. 

All reprinted from Circular 19, U.S. Bureau of Standards, 1913. 

Smithsonian Tables. 



Table 77. 
VELOCITY OF SOUND IN SOLIDS. 



lOI 



The numbers given in this table refer to the velocity of sound along a bar of the substance, and hence depend on the 
Younji's Modulus of elasticity of the material. The elastic constants of most of the materials given in this table 
vary ilirough a somewhat wide range, and hence the numbers can only be taken as rough approximations to the 
velocity which may be obtained in any particular case. When temperatures are not marked, between lo'^ and 20° 
is to be understood. 







Velocity in 


Velocity in 




Substance. 


Temp. C. 


meters per 
second. 


feet per 
second. 


Authority. 


Metals: Aluminum 





5104 


16740 


Masson. 


Urass 




- 


3500 


1 1 480 


Various. 


Cadmium 






- 


2307 


7570 


Masson. 


Cobalt 






- 


4724 


15500 


" 


Copper 






20 
100 
200 


3560 
3290 
2950 


I 1670 
10800 
9690 


Wertheim. 


Gold (soft) 




20 


1743 


5717 


" 


" (hard) 




- 


2IOO 


6890 


Various. 


Iron and soft steel 




- 


5000 


164IO 


" 


Iron . 




20 


5130 


16S20 


Wertheim. 


"... 




100 


5300 


17390 


u 


"... 




200 


4720 


15480 


tl 


" cast steel 




20 


4990 


16360 


" 


(( a 11 




200 


4790 


I5710 


(( 


Lead . 




20 


1227 


4026 


" 


Magnesium 




- 


4602 


151OO 


Melde. 


Nickel 




- 


4973 


16320 


Masson. 


Palladium 






- 


3150 


10340 


Various. 


Platinum 






20 
100 


2690 
2570 


8815 
8437 


Wertheim. 


" 






200 


2460 


8079 


" 


Silver 






20 
100 


2610 
2640 


8553 
8658 


« 


Tin . 






- 


2500 


8200 


Various. 


Zinc . 






- 


3700 


I214O 


" 


Various : Brick 






- 


3652 


II9S0 


Chladni. 


Clay rock 






- 


3480 


1 1 420 


Gray & Milne. 


Cork 






- 


500 


1640 


Stefan. 


Granite 






- 


3950 


12960 


Gray & Milne. 


Marble 






- 


3810 


12500 


a 


Paraffin 






15 


1304 


4280 


Warburg. 


Slate 






- 


4510 


14800 


Gray & Milne. 


Tallow . 






16 


390 


1280 


Warburg. 


Tuff. 






- 


2850 


9350 


Gray & Milne. 


Glass 


j from 
■ J to 


- 


5000 


164 10 


Various. 




- 


6000 


19690 


" 


Ivory 




- 


3013 


9886 


Ciccone & Campanile. 


Vulcanized rubber ) 
(black) \ 





54 


177 


Exner. 


50 


31 


102 


" 


" (red) . 





69 


226 


" 


" " " 


70 


34 


III 


« 


Wax .... 


17 


880 


2890 


Stefan. 


" .... 


28 


441 


1450 


" 


Woods : Ash, along the fibre . 


- 


4670 


I53IO 


Wertheim. 


" across the rings 


- 


1390 


4570 


It 


" along the rings 


- 


1260 


4140 


" 


Beech, along the fibre 


- 


3340 


10960 


" 


" across the rings . 


- 


1840 


6030 


K 


" along the rings 


- 


1415 


4640 


11 


Elm, along the fibre 


- 


4120 


13516 


" 


" across the rings 


- 


1420 


4665 


'< 


" along the rings 


- 


1013 


3324 


" 


Fir, along the fibre . 


- 


4640 


15220 


" 


Maple " 




- 


4110 


13470 


" 


Oak 




- 


3850 


12620 


" 


Pine " 




- 


3320 


10900 


" 


Poplar " 




- 


4280 


14050 


'« 


Sycamore " 






4460 


14640 





Smithsonian Tables. 



I02 



Table 78. 
VELOCITY OF SOUND IN LIQUIDS AND CASES. 



For gases, the velocity of sound = "^yP/p, where P is the pressure, p the density, and y the ratio of specific heat at 
constant pressure to that at constant volume (see Table 265). 







Velocity in 


Velocity in 




Substance. 


Temp. C. 


meters per 
second. 


feet per 
second. 


Authority. 


Liquids: Alcohol, 95% 



12.5 


1241. 


4072. 


Dorsing, 1908. 


"... 






20.5 


I213. 


3980. 


" 


Ammonia, cone. 






16. 


1663. 


54S6- 


" 


Benzol 






17- 


1 1 66. 


3S26. 


" 


Carbon bisulphide 






15- 


1161. 


3S09. 


" 


Chloroform . 






IS- 


983- 


3225. 


II 


Ether . 






IS- 


1032. 


33S6. 


II 


NaCl, 10% sol. 






IS- 


1470. 


4823. 


II 


" 15% " 






IS- 


1S30- 


5020. 


** 


" 20% " 






iS- 


1650. 


S4I4- 


** 


Turpentine oil 






iS- 


1326. 


43SI- 


" 


Water, air-free 

U « (1 






13- 
19- 
31- 


1441. 
1461. 
ISOS- 


4728. 
4794- 
4938- 


II 


" Lake Geneva 




9- 


I43S- 


4708. 


Colladon-Sturm. 


" Seine river 




iS- 


1437- 


4714. 


Wertheim. 


li " a 




30- 


1528. 


5013- 


" 


" " " 






60. 


1724. 


S657- 


" 


Gases : Air, dry, C02-free 






0. 


331-78 


1088.5 


Rowland. 


» 11 






0. 


331-36 


1087. 1 


Violle, 1900. 


" " C02-free 






0. 


331-92 


1089.0 


Thiesen, 1908. 


" I atmosphere 






0. 


33>-7 


1088. 


Mean. 


" 25 






0. 


33--0 


1089. 


(Witkowski). 


" 50 






0. 


334-7 


1098. 


II II 


" 100 " 






0. 

20. 


350.6 
344- 


1 1 50. 
1 1 29. 


II 11 


<i 
II 






100. 
500. 


386. 
5S3- 


1266. 
1814. 


Stevens. 


" . 






1000. 


700. 


2297. 


** 


Ammonia 






0. 


41 s- 


1361. 


Masson. 


Carbon monoxide 






0. 


337-1 


1 106. 


Wullner. 


" " 






0. 


337-4 


1 107. 


Dulong. 


" dioxide 






0. 


258.0 


846. 


Brockendahl, 1906. 


" disulphide 






0. 


189. 


620. 


Masson. 


Chlorine . 






0. 


206.4 


677. 


Martini. 


" 






0. 


205-3 


674- 


Strecker. 


Ethylene . 






0. 


314- 


1030. 


Dulong. 


Hydrogen 






0. 


1269.5 


4165. 


" 


" 






0. 


1286.4 


4221. 


Zoch. 


Illuminating gas 






0. 


490.4 


1609. 


" 


Methane . 






0. 


432- 


1417. 


Masson. 


Nitric oxide 






0. 


325- 


1066. 


" 


Nitrous oxide . 






0. 


261.8 


859. 


Dulong. 


Oxygen . 






0. 


317-2 


1041. 


" 


Vapors: Alcohol 






0. 


230.6 


7S6. 


Masson. 


Ether . 






0. 


179.2 


588. 


" 


Water . 






0. 


401. 


131s- 


" 


" 






100. 


404.8 


1328. 


Treitz, 1903. 


II 


• 


130. 


424.4 


1392. 





Note : The values from Ammonia to Methane inclusive are for closed tubes. 
Smithsonian Tables. 



Tables 79-80. 
MUSICAL SCALES. 



103 



The pitch relations between two notes may be expressed precisely (i) by the ratio of their vibration frequencies; 
(2) by the number of equally-tempered semitones between them (E. S.); also, less conveniently, (3) by the common 
logarithm of the ratio in (i); (4) by the lengths of the two portions of the tense string which will furnish the notes; 
and (5) in terms of the octave as unity. The ratio in (4) is the reciprocal of that in (i); the number for (5) is 1/12 of 
that for (2); the number for (2) is nearly 40 times that for (3). 

Table 79 gives data for the middle octave, including vibration frequencies for three standards of pitch; a = 435 double 
vibrations per second, is the international standard and was adopted by the American Piano Manufacturers' Associa- 
tion. The "just-diatonic scale "of C-major is usually deduced, following Chladni, from the ratios of the three perfect 
major triads reduced to one octave, thus: 4:5:6 

4:3:6 4:5:6 

F A C E G B D 

16 20 24 30 36 45 54 

24 27 30 32 36 40 45 48 
Other equivalent ratios and their values in E. S. are given in Table 80. By transferring D to the left and using the 
ratio lo : 12 : 15 the scale of A-minor is obtained, which agrees with that of C-major e.\cept that D^ 26 2/3. Nearly the 
same ratios are obtained from a series of harmonics beginning with the eighth; also by taking 12 successive perfect 
or Pythagorean Ufths or fourths and reducing to one octave. Such calculations are most easily made by adding and 
suDtracting intervals expressed in E. S. The notes needed to furnish a just major scale in other keys may be found 
by successive transpositions by fifths or fourths as shown in Table 80. Disregarding the usually negligible difference 
of 0.02 E. S., the table gives the 24 notes to the octave required in the simplest enharmonic organ; the notes fall into 
pairs that differ by a comma, 0.22 E. S. The line "mean tone" is based on Dom Bedos' rule for tuning the organ 
(1746). The tables have been checked by the data in Ellis' Helmholtz's "Sensations of Tone." 













TABLE 


79. 












Note. 


Interval. 


Ratios. 


Logarithms. 


Number of Vibrations per second. 


Beats 
for 0. 1 
























Tem- 
pered. 


Just. 


Just. 


Tem- 
pered. 


Just. 


Tem- 
pered. 


Just. 


Just. 


Just 


Tem- 
pered. 


E. S. 




E. S. 


E. S. 




















c' 




I 


0. 


I.OO 


1. 00000 
1.05926 


0.0000 


0.00000 
.02509 


2j6 


264 


258.7 


258.7 
274.0 


1.50 


d' 


2 

3 


2.04 


1. 125 


1. 12246 
I.1892I 


.05115 


.05017 
.07526 


288 


297 


291.0 


290.3 
307.6 


1.68 


e' 


4 


3.86 


1-25 


1.25992 


.09691 


.10034 


320 


3.30 


323-4 


325-9 


1.89 


f 


1 


4.98 


1-33 


1-33484 
I.4142I 


.12494 


•12543 

.15051 


341.3 


352 


344-9 


345-3 
36S.8 


2.00 


g' 


7 

8 


7.02 


1.50 


1.4983 1 
1.58740 


.17609 


.17560 
.20069 


3«4 


39(5 


3«« 


3«7-5 
410.6 


2.25 


a' 


9 

10 


8.84 


1.67 


1. 68 1 79 
1.781S0 


.22185 


.22577 
.25086 


426.7 


4^0 


431-1 


460.9 


2.52 


b' 


II 


10.88 


1-875 


1.88775 


.27300 


•27594 


480 


495 


485.0 


488.3 


2.83 


c" 


12 


12.00 


2.00 


2.00000 


•30103 


•30103 


512 


528 


517-3 


517-3 


3.00 



TABLE 80. 



Key of 


C 




D 




E 


F 




G 




A 




B 


C 




7 *fs 


Ctf ' 




1. 14 




3.18 




5.00 


6.12 




8.16 




9.98 




12.02 








0.92 




2.96 




4.7S 


5.90 




7-94 




9.76 




11.80 




6 " 


Ftf 




1. 14 

0.92 




2.96 
2.74 




5.00 
4.78 


6.12 
5-9° 




8.16 
7-94 




9-98 
9.76 


II. 10 

10.8S 






5 " 


B 




1. 14 




2.96 


4.08 




6.12 




7-94 




9-98 


II. 10 










0.92 




2.74 


3-86 




5-9° 




7.72 




9.76 


10.88 






4" 


E 




0.92 




2.96 


4.08 




6.12 




7-94 


9.06 




11.10 










0.70 




2-74 


3.86 




5.90 




7.72 


8.84 




10.88 






3" 


A 




0.92 


2.04 




4.08 




5.90 




7-94 


9.06 




II. 10 








0.70 


182 




3-86 




5.68 




7.72 


8.84 




10.88 






2 " 


D 




0.92 


2.04 




4.08 




S-90 


7.02 




9.06 




1 0.88 






i« 


G 


0.00 




2.04 




3.86 




S-90 


7.02 




9.06 




10.88 


12.00 






C 


0.00 




2.04 




3.86 


4-08 




7.02 




8.84 




10.88 


12.00 




i\> 


F 


0.00 




1.82 




3.86 


4-98 




7.02 




8.84 


9.96 




12.00 




2 t>s 


B[> 


0.00 




1.82 


2.94 




4-98 




6.80 




8.84 


9.96 




12.00 




3" 


El> 


-.22 




1.82 


2.94 




4.98 




6.80 


7.92 




9.96 




11.78 




4" 


Ab 


-.22 


0.90 




2.94 




4.76 




6.80 


7.92 




9-96 




11.78 




5" 


Db 


-.22 


0.90 




2.94 




4.76 


S.88 




7.92 




9-74 




11.78 




6" 


G^ 




0.90 




2.72 




4.76 


S.88 




7.92 




9-74 


10.86 






7" 







0.90 




2.72 


3-«4 




5-88 




7.70 




9-74 


10.86 






Harmonic Series 


8 
0.0 


(;::;) 


9 
2.04 


(s'gs) 


10 

3.86 


V4-70/ 


II 

S-51 


12 

7.02 


(25) 


13 

8.41 


14 

g.69 


15 

10.88 


16 
12.00 




Cycle of fifths 


0.0 


1. 14 


2.04 


3.18 


4.08 


5.22 


6,12 


7.02 


8.16 


9.06 


10.20 


II. 10 


12.24 




Cycle of fourths 


0.0 


0.90 


1.80 


2-94 


3-84 


4-98 


5.88 


6.78 


7.92 


8.82 


9.96 


10.86 


11.76 




Mean tone 


0.0 


0.76 


1-93 


3.11 


3,86 


S-03 


5-79 


6.97 


7-72 


8.90 


10.07 


10.83 


12.00 




Equal 7 step 


0.0 




1.71 


343 




5-14 




6.86 




8-57 


10.29 




12.00 





SurTHSONiAN Tables. 



104 



Table 81 . 
ACCELERATION OF GRAVITY. 

For Sea Level and DiUerent Latitudes. 

Calculated from Helmert's formula : 
grrr 911.78030 (i +0.005302 sin. 2 * — 0.000007 sin.'2<I') 



Latitude 
* 




cm. per sec. 


Log. g 


, 

feet per sec. 


Latitude 
4> 




cm. per sec. 


Log. f/ 




feet per sec. 


per sec. 




per sec. 




per sec. 




per sec. 


0° 


978.030 


2.9903522 


32.0875 


50° 


981.066 


2.9916982 


32.1871 


5 


.069 


.9903695 


.0888 


SI 


•"55 


.9917376 


.1901 


10 


.186 


.9904214 


.0927 


52 


.244 


.99.7770 


.1930 


12 


■253 


.9904512 


.0949 


S3 


•331 


.9918156 


•'959 


J4 


•332 


.9904863 


.0974 


54 


.4.8 


.991S540 


..987 


"5 


978.376 


2.9905058 


32.0989 


55 


981.503 


2.9918916 


32.2015 


16 


.422 


.9905262 


.1004 


56 


.588 


.99.9292 


•2043 


17 


.471 


.9905480 


.1020 


57 


.672 


.99.9664 


.2070 


18 


•523 


.9905710 


• 1037 


58 


•754 


.9920027 


•2097 


•9 


■577 


.9905950 


.1055 


59 


•835 


.9920385 


.2124 


20 


978.634 


2.9906203 


32.1074 


60 


981.914 


2.9920735 


32.2.50 


21 


.693 


.9906465 


.1093 


61 


•992 


.99210S0 


.2.75 


22 


•754 


.9906736 


.1113 


62 


982.068 


.9921415 


.2200 


23 


.818 


.9907019 


• I 134 


63 


.142 


•9921743 


.2224 


24 


.884 


.9907313 


.1.56 


64 


.2.5 


.9922066 


.2248 


25 


978.952 


2.9907614 


32. .178 


65 


982.285 


2.9922375 


32.2271 


26 


979.022 


.9907925 


.1201 


66 


•354 


.99226S0 


.2294 


27 


• 094 


.9908244 


.1224 


67 


.420 


•9922972 


• 23.6 


28 


.168 


.990S572 


.1249 


68 


•485 


.9923259 


•2337 


29 


.244 


.9908909 


.1274 


69 


.546 


.9923529 


■2357 


30 


979.321 


2.9909250 


32. .299 


70 


982.606 


2.9923794 


32.2377 


31 


.400 


.9909601 


•'325 


71 


.663 


.9924046 


•2395 


32 


.481 


.9909960 


•1351 


72 


.7.8 


.9924289 


.2413 


33 


.562 


.9910319 


■ 1378 


73 


•770 


.9924519 


•2430 


34 


.646 


.9910691 


..406 


74 


.820 


.9924740 


.2447 


35 


979-730 


2.9911064 


32.14.33 


75 


982.866 


2.9924943 


32.2462 


36 


.8.5 


.9911441 


..461 


76 


.911 


.9925142 


•2477 


37 


.902 


.9911827 


.1490 


77 


•952 


•9925323 


.2490 


38 


.989 


.9912212 


..518 


78 


.990 


.9925491 


•2503 


39 


980 077 


.9912602 


•1547 


79 


9S3.026 


.9925650 


.2514 


40 


980.166 


2.9912996 


32.1576 


80 


983.058 


2.9925791 


32.2523 


4' 


•255 


-99'339i 


.1605 


81 


.088 


.9925924 


•2535 


42 


■345 


.9913789 


•1635 


82 


.115 


.9926043 


•2544 


43 


-435 


.99.4188 


.1664 


83 


.138 


•9926145 


.2551 


44 


.525 


.9914587 


.1694 


84 


.159 


.9926238 


.2558 


45 


980.616 


2.9914989 


32.1724 


85 


983.176 


2.9926312 


32.2564 


46 


.706 


.99.5388 


••753 


86 


.190 


•9926375 


.2568 


47 


.797 


.9915791 


•1783 


87 


.201 


•9926423 


.2572 


48 


.887 


.9916.90 


.1813 


88 


.209 


.9926459 


•2574 


49 


.977 


.99 1 65 88 


.1842 


90 


.216 


.99264S9 


•2S77 



To reduce log. g (cm. per sec. per sec.) to log. g (ft. per sec. per sec.) add log. 0.03280833 =: 8.5159842 — 10. 



CORRECTION FOR ALTITUDE. 

— 0.0003086 cm. per meter when altitude is in meters. 

— 0.000003086 ft. per foot when altitude is in feet. 







Altitude. 


Correction. 


Altitude. 


Correction. 




200 m. 


0.0617 cm./sec.^ 


200 ft. 


0.000617 ft./sec' 




300 


.0926 


300 


.000926 




400 


•'234 


400 


.001234 




500 


•I 543 


500 


.001543 




600 


.1852 


600 


.001852 




700 


.2160 


700 


.002160 




800 


.2469 


800 


.002469 




900 


.2777 


900 


.002777 





Smithsonian Tables. 



105 



Table 82. 
GRAVITY. 

In this table the results of a number of the more recent gravity determinations are bi^ught together. They serve to 
show the degree of accuracy which may be assumed for the numbers in lable Si. In general, gravity is a little 
lower than the calculated value for stations far inland and slightly higher on the coast line. 



Place. 



Singapore 

Georgetown, Ascension . 
Green Mountain, Ascension 
Loanda, Angola . . . 
Caroline Islands . . . 
Bridgetown, Barbadoes 
Jamestown, St. Helena 
Longwood, " 

Pakaoao, Sandwich Islands 
Lahaina, " " 

Haiki, 

Honolulu, " " 

St. Georges, Bermuda 
Sidney, Australia . . 
Cape Town .... 
Tokio, Japan .... 
Auckland, New Zealand 
Mount Hamilton, Gal. (Lick Obs 

" " U II 

San Francisco, Cal. 



Washington, D. C* 
Denver, Colo. . . . 

York, Pa 

Ebensburgh, Pa. . . 
Allegheny, Pa. . . 
Hoboken, N. J. , . 
Salt Lake City, Utah 
Chicago, 111. . . . 
Pampaluna, Spain . 
Montreal, Canada . 
Geneva, Switzerland 



Berne, " 

Zurich, " 

Paris, France .... 
Kew, England . . . 
Berlin, Germany . . . 
Port Simpson, B. C. . 
Burroughs Bay, Alaska 
Wrangell, " 

Sitka. 

St. Paul's Island, " 
Juneau, " 

Pyramid Harbor, " 
Yakutat Bay, " 



Latitude. 

N. +, S. -. 



I" 17' 

-7 56 

— 7 57 

— S 49 
— 10 00 

13 04 

-15 55 

-15 57 

20 43 

20 52 

20 56 

21 18 
3- =3 

-33 52 

-33 56 

35 41 

-36 52 

37 20 

37 20 

37 47 

37 47 

38 53 

39 54 

39 58 

40 27 
40 28 
40 44 

40 46 

41 49 

42 49 

45 31 

46 12 
46 12 

46 57 

47 23 

48 50 

51 28 

52 30 

54 34 

55 59 

56 28 

57 03 

57 07 

58 18 

59 10 
59 32 



Elevation 
in meters. 



14 

5 
686 

46 



10 

533 
3001 

3 
117 

3 
2 

43 

II 

6 

43 

1282 

1282 

114 

114 

10 

1645 

122 

651 

348 

II 

1288 

165 

450 
100 
405 
405 
572 
466 

67 
7 

49 
6 



Gravity, 



Observed. 



978.08 
978.25 
978.10 
978-15 
978.37 
978.18 
978.67 

978.53 
978.28 
978.86 
978.91 
978.97 

979-77 
979.68 
979.62 

979-95 
979.68 
979.66 
979.68 
979.96 
980.02 
980. 1 r 
979-68 
980. 1 2 
980.08 
9S0.09 
9S0.27 
979.82 
980.34 
980.34 
980.73 
980.58 
980.60 
9S0.61 
980.67 
9S0.96 
98 1.20 
981.26 
981.46 
981.51 
981.60 
981.69 
981.67 
981.74 
98 1. 82 
981.83 



Reduced to 
sea level. 



978.08 
978.25 
978.23 
978.16 

978.37 
978.18 
978.67 

978.59 
978.85 
978.86 

978.93 
978.97 

979-77 
979.69 
979-62 

979-95 
979.69 
979.91 
979.92 
979.98 
980.04 
980. 1 1 
979.98 
980.14 
980.20 
980.15 
980.27 
980.05 
980.37 
980.42 
980.75 
980.64 
980.66 
980.69 
980.74 
980.97 
981.20 
981.27 
981.46 
981.51 
98 1 .60 
981.69 
981.67 
981.74 
981.82 
981.83 



Refer- 
ence. 



1 Smith : " United States Coast and Geodetic Survey Report for 1884," App. 14. 

2 Preston : " United States Coast and Geodetic Survey Report for 1890," App. 12. 

3 Preston : Ibid. 1888, App. 14. 

4 Mendenhall : Ibid. 1891, App. 15. 

5 Defforges : " Comptes Rendus," vol. 118, p. 231. 

6 Pierce : " U. S. C. and G. S. Rep. 1883," App. 19. 

7 Cebrian and Los Arcos : " Comptes Rendus des Seances de la Commission Perma- 

nente de I'Association Geodesique International," 1893. 

8 Pierce: " U. S. C. and G. S. Report 1876, App. 15, and 1881, App. 17." 

9 Messerschmidt : Same reference as 7. 



• For references 1-4, values are derived by comparative experiments with invariable pendulums, the value for 
Washington taken as 9S0.111. For the latter see Appendix 5 of the Coast and Geodetic Survey Report for 1901. 

Smithsonian Tables. 



io6 



Table 83. 



SUMMARY OF RESULTS OF THE VALUE OF GRAVITY (gr) AT STATIONS 
IN THE UNITED STATES AND ALASKA.* 



Station. 


Latitude. 


Longitude. 


Elevation. 


observed. 




o t II 


1 II 


Meters. 


cm./sec.2 


Calais, Me 


45 " II 


67 16 54 


38 


980.630 


Boston, Mass. 






42 21 33 


71 03 50 


22 


980.395 


Cambridge, Mass. 






42 22 48 


71 07 45 


14 


980.397 


Worcester, Mass. 






42 16 29 


71 48 28 


170 


980.323 


New York, N. Y. 






40 48 27 


72, 57 43 


38 


980.266 


Princeton, N. J. . 






40 20 57 


74 39 28 


64 


980.177 


Philadelphia, Pa. 






39 57 06 


75 II 40 


16 


980.195 


Ithaca, N. Y. . 






42 27 04 


76 29 00 


247 


9S0.299 


Baltimore, Md. . 






39 17 5° 


76 37 30 


30 


980.096 


Washington, C. & G. S. . 






38 53 13 


77 00 32 


14 


980.111 


Washington, Smithsonian . 






38 53 20 


77 01 32 


10 


980.113 


Charlottesville, Va. 






38 02 01 


78 30 16 


166 


979-937 


Deer Park, Md. . 






39 25 02 


79 19 50 


770 


979-934 


Charleston, S. C. 






32 47 14 


79 56 03 


6 


979-545 


Cleveland, Ohio . 






41 30 22 


81 36 38 


210 


980.240 


Key West, Fla. . 






24 2,1, 33 


81 48 25 


I 


978.969 


Atlanta, Ga. 






33 44 58 


84 23 18 


324 


979523 


Cincinnati, Ohio 






39 08 20 


84 25 20 


245 


980.003 


Terre Haute, Ind. 






39 28 42 


87 23 49 


151 


980.07 1 


Chicago, 111. 






41 47 25 


87 36 03 


182 


980.277 


Madison, Wis. (Univ. of Wis.) 






43 04 35 


89 24 00 


270 


980.364 


New Orleans, La. 






29 56 58 


90 04 14 


2 


979-323 


St. Louis, Mo. 






38 38 03 


90 12 13 


154 


980.000 


Little Rock, Ark. 






34 44 57 


92 16 24 


89 


979.720 


Kansas City, Mo. 






39 05 50 


94 35 21 


278 


979.989 


Galveston, Tex. . 






29 18 12 


94 47 29 


3 


979.271 


Austin, Texas (University) 






30 17 II 


97 44 14 


189 


979.282 


Austin, Texas (Capitol) 






30 16 30 


97 44 16 


170 


979.287 


Ellsworth, Kan. . 






38 43 43 


98 13 32 


469 


979.925 


Laredo, Tex. 






27 30 29 


99 31 12 


129 


979.081 


Wallace, Kan. . 






38 54 44 


loi 35 26 


1005 


979-754 


Colorado Springs, Col. 






38 50 44 


104 49 02 


1841 


979.489 


Denver, Col. 






39 40 36 


104 56 55 


1638 


979.608 


Pike's Peak, Col. 






38 50 20 


105 02 02 


4293 


97S.953 


Gunnison, Col. . 






38 32 ?,2, 


106 56 02 


2340 


979-341 


Grand Junction, Col. . 






39 04 09 


108 33 56 


1398 


979.632 


Green River, Utah 






68 59 23 


no 09 56 


1243 


979-635 


Grand Canyon, Wyo. . 






44 43 16 


no 29 44 


2386 


979.S98 


Norris Geyser Basin, Wyo. 






44 44 09 


no 42 02 


2276 


979-949 


Lower Geyser Basin, Wyo. 






44 33 21 


1 10 48 08 


2200 


979-931 


Pleasant Valley Jet., Utah . 






39 50 47 


in GO 46 


2191 


979-511 


Salt Lake City, Utah . 






40 46 04 


III 53 46 


1322 


979.802 


Ft. Egbert, Eagle, Alaska . 






64 47 22 


141 12 24 


174 


982.182 



* All the values in this table depend on relative determination of gravity and an adopted value for gravity at Wash- 
ington (Coast and Geodetic Survey Office) of gSo.iii. This adopted value was the result of the determination in 
1900 of the relative value of gravity at Potsdam and at Washington. See footnote on previous page. 

Smithsonian Tables. 



J 



Tables 84-85. 
LENGTH OF THE SECONDS PENDULUM. 

TABLE 84. — LengUi of Seconds Pendulum at Sea Level for Different Latitudes.* 



107 



Lati- 
tude. 


Length 
in centi- 
meters. 


Log. 


Length in 
inches. 


Log. 


Lati- 
tude. 


Length 
in centi- 
meters. 


Log. 


Length in 
inches. 


Log. 





99.0950 


1.996052 


39.0131 


I.591218 


50 


99.4027 


1.997398 


39-1348 


1-592563 


5 


.O9S9 


6069 


.0152 


1234 


S5 


.4471 


7592 


.1524 


2758 


10 


.1108 


6I2I 


.0200 


1287 


60 


.4888 


7774 


.1687 


2939 


15 


.1302 


6206 


.0274 


1372 


65 


.5263 


793« 


•1835 


3'03 


20 


.1562 


6320 


.0378 


1485 


70 


•55S7 


8079 


.1962 


3244 


25 


99.1884 


1. 99646 1 


39.0506 


1. 591627 


75 


99.5850 


1. 998 1 94 


39.2067 


1-593360 


30 


•2259 


6625 


.0652 


1790 


80 


.6045 


8279 


.2143 


3444 


35 


.2672 


6S06 


.0S16 


1972 


«5 


.6165 


8331 


.2190 


3496 


40 


.3116 


7000 


.0990 


2166 


90 


.6206 


8349 


.2206 


3514 


45 


•3571 


7199 


.1169 


2364 













* Calculated from force of gravity table by the formula I ^ g /t'. 
centimeters, or 0.000235 inches, or .ooooig6 feet. 



For each 100 feet of elevation subtract 0.000596 



TABLE 85. — Leng:tli of the Seconds Pendulum.* 



Date of 
determi- 
nation. 



1799 
1816 
182I 

1825 
1S27 
1829 
1S30 

1S33 
1869 
1876 
1884 



Number 
of obser- 
vation 
stations. 



IS 
^8 

25 
41 

5 
49 

51 

73 

123 



Range of latitude included by 
the stations. 



From +67^05' to —33° 56' 



+74° 53' 
+38^40' 
+79° 50' 
+79° 50' 
0° o' 

+79^51' 

+79° 50' 
+79° 50' 
+79° 50' 



51 21' 

—60° 4 5' 
-12° 59' 

-5i°35' 
+67^04' 

-5;!° 35' 

-5i°35' 
— 62=56' 
-62° 56' 



Combining the above results 



Length of pendulum in meters, 
for latitude i>. 



0.99063 1 + . 

0-9907 43+- 
0.990880+ . 
O.990977+. 
O.991026-I-. 

0.990555+- 
0.99IOI74-. 
0.990941-}-. 
0.990970-i- , 
0.9910114-. 
0.9909 1 8-f-. 



005637s 
005466s 
005340s 
005142s 
005072s 
005679s 
005087 s 
005142s 
005185s 
005105s 
005262 s 



n> 

n2(|, 
n2<^ 
n2,|) 
n'^ 
n2<^ 

n^</> 



o.9909io-|-.oo5290sin^<^ 



Correspond- 
ing length 
of pendulum 
for lat. 45° 



0-993450 
0.993976 

0.993550 
0.993548 
0.993562 

0-993395 
0.993560 
0.993512 

0-993S54t 

0-993563 
0-993549 

0.993555 



Refer- 
ence. 



3 
4 

5 
6 

7 
8 

9 
10 
II 



1 Laplace : " Traite de Mecanique Celeste," T. 2, livre 3, chap. 5, sect. 42. 

2 Mathieu : " Sur les experiences du pendule;" in " Connaissance des Temps 1816." 
Additions, pp. 314-341, p. 332. 

3 Biot et Arago: " Recueil d'Observations geodesiques, etc." Paris, 1821, p. 575. 

4 Sabine : " An Account of Experiments to determine the Figure of the Earth, etc., by 
Sir Edward Sabine." London, 1S25, p. 352. 

5 Saigey : "Comparaison des Observations du pendule a diverses latitudes; faites par 
MM. Biot, Kater, Sabine, de Freycinet, et Duperry;" in "Bulletin des Sciences Mathe- 
matiques, etc.," T. i, pp. 31-43, and 171-184. Paris, 1827. 

6 Pontecoulant : " Theorie analytique du Systeme du monde," Paris, 1829, T. 2, p. 466. 

7 Airy : " Figure of the Earth ; " in " Encyc. Met." 2d Div. vol. 3, p. 230. 

8 Poisson : "Traite de Mecanique," T. i, p. 377; "Connaissance des Temps," 1834, 
pp. 32-33; and Puissant: "Traite de geodesic," T. 2, p. 464. 

9 Unferdinger : " Das Pendel als geodatisches Instrument j " in Grunert's "Archiv," 1869, 
p. 316. 

10 Fischer: " Die Gestalt der Erde und die Pendelmessungen ;" in " Ast. Nach." 1876, 
col. 87. 

11 Helmert: "Die mathematischen und physikalischen Theorieen der hbheren Geo- 
dasie, von Dr. F. R. Helmert," II. Theil. Leipzig, 1884, p. 241. 

12 Harkness. 



* The data here given with regard to the different determinations which have been made of the length of the 
seconds pendulum are quoted from Harkness (Solar Parallax and its Related Constants, Washington, iSgi). 
t Calculated from a logarithmic expression given by Unferdinger. 

Smithsonian Tables. 



io8 



Tables 86-87. 
MISCELLANEOUS GEODETIC DATA/ 
TABLE 86. 



Length of the seconds pendulum at sea level =/=39.oi2540+o.2o8268 sin^ <p inches. 

=3.251045+0.017356 sin^(^ feet. 
=0.9909910+0.005290 sin^^ meters. 

Acceleration produced by gravity per second 

per second mean solar time . . . =^=32.086528+0.17 1293 sin^^ feet. 

=977.9886 + 5.22 1 o sin^ <p centimeters. 



Equatorial radius 
Polar semi-diameter 



=^^6378206 meters ; 

3963.225 miles. 
=(^=6356584 meters; 

3949.790 miles. 



u 

Reciprocal of flattemng= =295.0 

a—o 

Square of eccentricity =^^= — j— =0.006768658 



6378388+18 meters; ' 
^ 3963-339 miles. 
^ 6356909 meters ; 
? 3949-992 mUes. 

&, 297.0 + 0.5 



S," 0.0067237+0.0000120. 



Co Co 

I ^ 

J 



Difference between geographical and geocentric latitude=(/)— <^'= 

688.2242" sin 2 ^—1.1482" sin 4 ^+0.0026" sin 60. 

Mean density of the Earth = 5. 5247 + 0.0013 (Burgess Phys. Rev. 1902). 

Continental surface density of the Earth = 2.67 \ Harkness 

Mean density outer ten miles of earth's crust = 2.40 J 

Moments of inertia of the Earth; the principal moments being taken as A, B, and C, and 
C the greater: 

— — — =0.0032652 1 = — 7 ; 

C -^ ^ 306.259 

C—.^ =0.001064767 ^£Z*; 

.,4 =^=0.32 5029 Ea^ ; 

C =0.326094 Ea^ ; 

where E is the mass of the Earth and a its equatorial semidiameter. 



TABLE 87. — Lengtb of Degrees on the Earth's Snrlace. 





Miles per degree 


Km. p 


r degree 




Miles per degree 


Km. p 


;r degree 


At 
Lat. 










At 
Lat. 




























of Long. 


of Lat. 


of Long. 


of Lat. 


55° 


of Long. 


of Lat. 


of Long. 


of Lat. 


0° 


69.17 


68.70 


111.32 


110.57 


39-77 


69.17 


64.00 


III-33 


10 


68.13 


68.72 


IO:).64 


110.60 


60 


34-67 


69.23 


5580 


III. 42 


20 


65-03 


6S.79 


104.65 


110.70 


65 


29.32 


69.2S 


47.18 


1 1 1.50 


30 


59-96 


6S.88 


96.49 


110.85 


70 


23-73 


69.32 


38-19 


III.S7 


40 


53.06 


68.99 


85.40 


1 1 1 .03 


75 


17.96 


69.36 


2S.90 


III. 62 


4S 


49.00 


69.05 


78.85 


III. 13 


I 80 


12.05 


69-39 


19-39 


1 1 1.67 


5° 


44-55 


69.11 


71.70 


III. 23 


90 


0.00 


69.41 


0.00 


1 1 1.70 



For more complete table see " Smithsonian Geographical Tables." 



Smithsonian Tables. 



Table 88. 
MISCELLANEOUS ASTRONOMICAL DATA. 



109 



Length of sidereal year=365.2563578 mean solar days; 

= 365 days 6 hours 9 minutes 9.314 seconds. 



Length of tropical year=365.242i9987o — 0.0000062124 5? mean solar days; 

100 

=365 days 5 hours 48 minutes [46.069—0.53675 ^\ seconds. 



100 
Length of sidereal month 



= 27.321661 162 — 0.00000026240 days : 

100 ■' ' 

= 27 days 7 hours 43 minutes ( 11-524 — 0.022671 — ) seconds. 



Length of synodical month 

= 29.530588435 — 0.00000030696 days ; 

= 29 days 12 hours 44 minutes / 2.841 — 0.026522 ^ seconds. 

Length of sidereal day =86164.09965 mean solar seconds. 

N- B. — The factor containing t in the above equations (the year at which the values of the 
quantities are required) may in all ordinary cases be neglected. 

Mean distance from earth to sun ^92900000 miles = 149500000 kilometers. 
Eccentricity of the earth 's orbit = e^ 

0.0 1 67 5 1 04 — 0.0000004180 (t — 1900) — 0.000000126 I — 1 

\ 100 j. 

Solar parallax = 8.7997"-!- 0.003 (Weinberg, A. N. 165, 1904) ; 

8.807 rt 0.0027 (Hinks, Eros, 7) ; 

8.799 (Samson, Jupiter satellites ; Harvard observations). 

Lunar parallax = 3422.68". 

Mean distance from earth to moon = 60.2669 terrestrial radii ; * 

= 238854 miles; 

= 384393 kilometers. 

Lunar inequality of the earth = Z = 6.454". 

Parallactic inequality of the moon = Q= 124.80". ■* 

, //— 1800 

Mean motion of moon's node in 365.25 days = ij. = — 19° 21' 19.6191" + 0.14136" — ioo~ 

Eccentricity and inclination of the moon's orbit = ^2 ^ 0.05490807. 
Delaunay's 7 = sin | 7= 0.044886793. 

7= 5° 08' 43-3546". 
Constant of nutation = 9.2'. 
Constant of aberration =: 20.4962 -j- 0.006 (Weinberg, 1. c.).* 
Time taken by light to traverse the mean radius of the earth's orbit 

= 498.82 J- o.i seconds (Weinberg) ; 
= 498.64 (Samson). 
Velocity of light = 186330 miles per second (Weinberg) ; 
= 299870 -J- 0.03 kilometers per second. 
General precession ^ 50.2564" + 0.000222 {t — 1900). 
Obliquity of the ecliptic = 23° 27' 8.26" — 0.4684 (t — 1900). 

Gravitation constant =: 666.07 X lo-^o cm^/gr. sec^ -^ 0.16 X lO"!". 



* Recent work of Doolittle's and others indicates a value not less than 20.51. 
Smithsonian Tables. 



no 



Tables 89-91 .-ASTRONOMICAL DATA. 

TaWe 89.— Planetary Data. 



Body. 


Reciprocals 


Mean distance 
from the sun. 


Sidereal 
period. 


Equatorial 
diameter. 


Inclination 


Mean 
density. 


Gravity 




of masses. 


Km. 


Mean days 


Km. 


of orbit. 


H^O^i 


at surface, j 

1 


Sun 


I. 








I 391067 





1-39 


27.6 


Mercury 


6000000. 


58 X 106 


87.97 


4842 


7°.oo3 


4.86 


■3 


Venus 


40S0OO. 


108 " 


224.70 


12394 


3-393 


5-2 


7-9 


Earth* 


329390- 


149 " 


365-26 


12756 


— 


5-52 


1. 00 


Mars 


3093500. 


228 " 


686.98 


7320 


1.S50 


3-90 


-4 


Jupiter 


1047-35 


778" 


4332-59 


145250 


1.308 


1.36 


2.6 


Saturn 


3501-6 


1426 " 


10759.20 


123040 


2.492 


■63 


I.OI 


Uranus 


22869. 


2869 " 


30586.29 


4S590 


0-773 


1-34 


•95 


Neptune 


19700. 


4495 " ^ 


60188.71 


56040 


1.778 


1.28 


-97 1 


Moon 


t 81.45 


38 X 10* 


27.32 


3473 


5-147 


3-37 


•17 



* Earth and moon, t Relative to earth. Inclination of axes : Sun 7°. 25 ; Earth 23^.45 ; Mars24°.6; Jupiter 3°.i; 
Saturn 26°. 8; Neptune 27°. 2. Others doubtful. 



Table 90. — Equation of Time. 

The equation of time when + 's to be added to the apparent solar time to give mean time. 
When the place is not on a standard meridian (75'th, etc.) its difference in longitude in time 
from that meridian must be subtracted when east, added when west to get standard time (75'th 
meridian time, etc.). The equation varies from year to year cyclically, and the figure following 
the J- sign gives a rough idea of this variation. 



1 


M. S. 




M. S. 




M. S. 




M. S. 


I Jan. I 

i Feb. I 

15 

1 Mar. I 

1 


+ 3 26- 
+ 9 25- 
+ 13 42r 
+ 14 20- 
+ 12 34r 
+ 9 9zJ 


L14 
I 9 
I 4 

_ 4 

z 6 


Apr. I 

15 
May I 

15 
June I 

15 


+4 2j 
+0 8- 
—2 54: 
—3 49r 
—2 28- 

+0 8: 


z 7 
z 5 

-ID 

- I 

: 3 
: 4 


July I 

Aug. I 

^ 15 
Sept. I 

15 


+3 3i±5 
+ 5 42±3 
+6 9i3 
+4 24i5 
+0 2^7 

—4 4irt9 


Oct. I 

15 

Nov. I 

_ 15 
Dec. I 

15 


—10 12J- 8 
—14 5^ 6 
— 16 i9-[- 2 
-15 22J- 4 
—10 sSJi 8 
— 4 53i 10 



Table 91. — Miscellaneous Astronomical Data. 

Apex of Solar Motion : 

From proper motions, R. A.igio = 17 51"*, Dec.i8io= + 31.4 (Weersma, Gron. Publ. 21.) 

From radial velocities, R. A. 1900 = I7*54"S Dec.1900^-}- 25.1 (Campbell, Lick. Bull. 196.) 
Velocity = 19.5 Km. per sec. (Campbell.) 

Nearest star so far as known: a Centauri, parallax =: 0.759" (Gron. Publ. 24) distance = 4.3 
light years. 

Stars of both greatest proper motion and greatest radial velocity so far as known :* Cordova, 
V243; proper motion = 8.70" in position angle 130° radial velocity + 242 Km. per sec. (Camp- 
bell, Stellar Motions, 1913). Parallax = 0.319" (Gron. Publ. 24, also proper motion). Distance = 
10.2 light years. 

Average velocities with regard to center of gravity of the stellar system, according to Camp- 
bell (Stella'r Motion, 1913) : 

Type B Stars : 6.6 Km. per sec. Type G Stars : 15.0 Km. per sec. 
•' A " 10.9 " " " " K " 16.8 " " " 

" F " 14.4 « " " " M " 17. 1 " " " 

Sun's magnitude =: — 26.5, sending the earth 90,000,000,000 times as much light as the star 
Aldebaran. 

Ratio of total radiation of sun to that of moon about 100,000 to i 



light 



400,000 to I 



Langley. 



* Lalande, 1966, R.A.,gjQ i''3"'.9, Dec.jg,^ 61°. 4' in 1913 was found to have a radial velocity (of approach) of 326 
Km. per sec. (Mount Wilson Solar Observatory.) 

Smithsonian Tables. 



^ 



Table 92. Ill 

TERRESTRIAL MAGNETISM. 

Secular Change of Declination. 

Changes in the magnetic declination between 1810, the date of the earliest available observa- 
tions, and 1910, for one or more places in each state and territory. 



State. 


Station. 


1810 


1820 


1830 


1840 


1850 


i860 


1870 


1880 


1890 


1900 


1910 







































Ala. 


Montgomery 


S.6E 


S.8E 


S.8E 


S.6E 


S.4E 


S.oE 


4.SE 


3.9E 


3.2E 


2.8E 


2.9E 


Alas. 


Sitka 


- 


- 


- 


- 


- 


28.7E 


29.0E 


29.3E 


29.sE 


;29-7E 30.2E 




Kodiak 


- 


- 


- 


- 


- 


26.1E 


2S.6E 


2S.1E 24.7E 


I24.4E 24. lE 




Unalaska 


- 


- 


- 


- 


- 


20.4E 


20. lE 


19.6E 


19.0E 


18.3E }i7.sE 




St. Michael 


- 


- 


- 


- 


- 


- 


- 


24.7E 


23. lE 


22. lE 21.4E 


Ariz. 


Holbrook 


- 


- 


- 


- 


13. 6E 


13.7E 


r3.8E 


13.7E 


13. 4E 


13.sE I3.9E 




Prescott 


- 


- 


- 


- 


I3-3E 


13.sE 


13 .7 E 


13 -eE 


13.sE 


13.7E 14.3E 


Ark. 


Little Rock 


8.6E 


8.8E 


9.0E 


9.0E 


S.SE 


8.6E S.2E 


7.6E 


7.0E 


6.6E. 6.9E 


Cal. 


Los Angeles 


12. lE 12.6E 


I3.2E 


I3-6E 


14.0E 


14. 2E I4-4E 14.6E I14.6E 


14.9E Jis-SE 




San Jose 


iS-oE iis.sE 


16.0E 


16.4E 


16.8E 


17. lE 17.3E [i7.sE 


17.sE 


17.8E 


i8.sE 


Cal. 


Redding 


IS-6E 16. lE 


16.6E 


17.0E 


17.4E 


17.SE '18. lE 18.2E 


18.3E 


18.6E 


19.3E 


Colo. 


Pueblo 


- 


- 


- 


- 


r3.8E 


13.8E 13.8E ji3.sE 


i3-oE 


12.9E 


13.3E 




Glenvvood Sp. 


- 


- 


- 


- 


16.1E 


16.2E 16.3E |i6.iE 


1S.7E 


IS.6E '16.1E 


Conn. 


Hartford 


S-iVV 


S.6W 


6.1W 


6.8W 


7.SW 


8.2W 


8.7W 


9.4W 


9.SW 


10.4W ii.oVV 


Del. 


Dover 


I.6W 


1.9W 


2.3W 


2.8W 


3.4W 


4.0W 


4.7W 


S.3W 


S.9W 


6.4W 7.oW 


D. C. 


Washington 


o.sE 


0.3E 


0.0 


O.sW 


r.oW 


1.7W 


2.4W 


3.0W 


3.6W 


4.2W 4.7W 


Fla. 


Jacksonville 


S.iE 


S.iE 


4.9E 


4.6E 


4.2E 


3.7E 


3.1E 


2.4E 


1.8E 


1.3E 


1.2E 




Pensacola 


7.7E 


7.8E 


7.7E 


7.SE 


7.2E 


6.8E 


6.2E 


5.6E 


5.0E 


4-SE 


4.4E 




Tampa 


6.4E 


6.2E 


5-9E 


S.SE 


S-oE 


4-SE 


3.9E 


3.3E 


2.8E 


2.3E 


2.0E 


Ga. 


Macon 


5.9E 


S-PE 


S.7E 


S.4E 


5-oE 


4-SE 


3.9E 


3.2E 


2.6E 


2.1E 


2.0E 


Haw. 


Honolulu 


- 


_ 


- 


- 


9.4E 


9.4E 


9.SE 


9.8E 


lO.iE 


10.4E 


10.6E 


Idaho 


Pocatello 


- 


- 


- 


- 


17.4E 


I7-7E 


17.8E 


17. 9E 


17.7E 


17.8E 


18.4E 




Boise 


- 


- 


- 


- 


18.0E 


1S.4E 


18.6E 


I8.7E 


18.6E 


18.8E 


19.4E 


111. 


Bloomington 


6.3E 


6.SE 


6.6E 


6.SE 


6.3 E 


S-9E 


5.4E 


4.7E 


4.1E 


3.6E 1 3.4E II 


Ind. 


Indianapolis 


S-oE 


S.iE 


5.0E 


4.7E 


4.4E 


3.8E 


3.2E 


2.6E 


2.0E 


1.4E 


i.iE 


la. 


Des Moines 


_ 


10.2E 


10.4E 


10.5E 


10.4E 


ro.2E 


9.7E 


9.1E 


8.4E 


7.9E 


8.1E 


Kans. 


Emporia 


- 


- 


- 


- 


11.6E 


ii.sE 


11.2E 


10.7E 


lO.iE 


9.8E 


10. lE 




Ness City 


- 


- 


- 


- 


12.4E 


12.4E 


12. 2E 


11.9E 


11.4E 


II. lE 


11.4E 


Ky. 


Lexington 


4-5E 


4-SE 


4.4E 


4.1E 


3.6E 


3. IE 


2.5E 


1.9E 


1.2E 


0.7E 


0.5E 




Princeton 


6.8E 


7.0E 


7.0E 


6.8E 


6.sE 


6.1E 


S.6E 


S-oE 


4-3E 


3.8E 


3.7E 


La. 


Alexandria 


8.4E 


8.7E 


8.8E 


S.SE 


8.7E 


8.4E 


S.oE 


7.4E 


6.9E 


6.6E 


6.8E 


Me. 


Eastport 


13.6W 


14.4W 


IS.2W 


16.0W 


17.0W 


17.7W 


18.2W 18.6W 


18.7W 


19.0W 


19.4W 




Portland 


9.0W 


9.6W 


10.3W 


ii.oW 


11.6W 


12.3W 


12.8W 


13.4W 


I3.9W 


14.4W 


14.8W 


Md. 


Baltimore 


0.9W 


l.iW 


1.4W 


1.9W 


2.4W 


3.1W 


3-8W 


4.4W 


S.oW 


S.6W 


6.1W 


Mass. 


Boston 


7.3W 


7.8W 


8.4W 


9.1W 


9.SW 


lo.sW 


ii.oVV 


11.5W 


12.0W 


12.6W 


I3.IW 


Mass. 


Pittsfield 


5-7W 


6.1W 


6.7W 


7.4W 


8.1W 


8.7W 


9.3W 


lo.oW 


10.4W 


II. oW 


II.SW 


Mich. 


Marquette 


- 


6.7E 


6.7 E 


6.SE 


6.0E 


5.4E 


4.6E 


3.8E 


3-oE 


2.3E 


2.0E 




Lansing 


- 


4.2E 


4.1E 


3.8E 


3.3E 


2.8E 


2.1E 


1.3E 


O.sE 


o.oE 


0.4E 


Minn. 


Northome 


- 


10.4E 


10.7E 


10.8E 


10.7E 


10.4E 


ro.oE 


9.3E 


8.6E 


S.oE 


8.1E 




Mankato 




11.3E 


11.6E 


11.7E 


11.6E 


11.3E 


10.9E 


10.4E 


9-sE 


9.0E 


9.1E 



* Tables have been compiled from United States Magnetic Tables and Magnetic Charts for 1905, published by 
the Coast and Geodetic Survey in 190S. 
SiviiTHSONiAN Tables. 



112 



Table 92 (continued). 

TERRESTRIAL MAGNETISM (.continued). 

Secular Change ol Declination (continued). 



State. 


Station. 


1810 


1820 


1830 


1840 


1850 


i860 


1870 


1880 


1890 


1900 


1910 


i 







































Miss. 


Jackson 


8.2E 


8.4E 


8.5E 


8.4E 


S.2E 


7.9E 


7.SE 


6.9E 


6.4E 


6.0E 


6.2E 




Mo. 


Sedalia 


- 


lo.oE 


[0.2E 


10.2E 


10. lE 


9.8E 


9.4E 


8.7E 


8.0E 


7.6E 


7.9E 




Mont. 


Forsyth 


- 


- 


- 


18.2E 


i8.sE 


18.6E 


[8.6E 


[8.4E 


[7.9E 


[7.8E 


18.3E 






Helena 


- 


- 


- 


18.9E 


I9-3E 


19.6E 


t9.8E 


[9.6E 


C9.4E 


[9.5E 


20.0E 




Nebr. 


Hastings 


- 


11.6E 


12.0E 


12. lE 


12. lE 


12.0E 


[I.7E 


[1.2E 


[0.5E 


[0.2E 


[0.5E 


i 


Nebr. 


Alliance 


_ 


- 


- 


- 


rS-4E 


IS.4E 


IS-3E 


14.8E 


I4-3E 


[4.2E 


I4-5E 




Nev. 


Elko 


- 


- 


- 


- 


I7-3E 


17.6E 


17 ■7E 


17.7E 


17.6E 


17. 8E 


18.3E 






Hawthorne 


- 


- 


- 


- 


16.3E 


16.6E 


16.9E 


17.0E 


17.0E 


17.3E 


17.8E 




N. H. 


Hanover 


7.1W 


7.SW 


8.2W 


8.9W 


9.8W 


10.5W 


ii.iW 


11.6W 


12.0W 


12.5W 


13.0W 




N.J. 


Trenton 


2.8W 


3.1W 


3.SW 


4.1W 


4-7W 


S.4W 


6.0W 


6.7W 


7.2W 


7.8W 


8.4W 




N. M. 


Santa Rosa 


_ 


- 


- 


- 


[2.7E 


12.8E 


12.7E 


12.5E 


12. lE 


12.0E 


12.4E 






Laguna 


- 


- 


- 


- 


[3.4E 


13.6E 


I3.6E 


13.4E 


i3.oE 


13.0E 


13.sE 




N. Y. 


Albany 


S.6W 


S.8W 


6.3W 


6.9W 


7.6W 


8.4W 


9.1W 


9.8W 


10.2W 


10.8W 


11.4W 




Elmira 


2.2W 


2.4W 


2.8W 


3-3W 


4.0W 


4.8W 


S.4W 


6.3W 


7.0W 


7.6W 


8.1W 




N. C. 


Newbem 


1.7E 


1.6E 


1.3E 


0.8E 


0.3E 


0.3W 


i.oW 


1.6W 


2.2W 


2.8W 


3.3W 




N. C. 


Salisbury 


3.9E 


3-8E 


3.6E 


3.2E 


2.7E 


2.1E 


1.5E 


0.8E 


0.2E 


0.4W 


0.7W 




N. Dak. 


Jamestown 


- 


- 


- 


- 


14.5E 


I4-3E 


14.0E 


I3.5E 


12.7E 


12.4E 


12.8E 






Dickinson 


- 


- 


- 


- 


17. 6E 


17.6E 


17. 4E 


17.0E 


16.4E 


16.2E 


16.6E 




Ohio 


Columbus 


3.4E 


3-4E 


3.2E 


2.9E 


2.4E 


1.8E 


1.2E 


0.6E 


0.0 


0.7W 


i.iW 




Okla. 


Okmulgee 


- 


- 


- 


- 


10.2E 


lO.lE 


9.8E 


9.4E 


8.8E 


8.5E 


8.9E 




Okla. 


Enid 


- 


- 


- 


- 


11.2E 


ii.lE 


10.9E 


lO.sE 


9.9E 


9.7E 


lo.iE 


\ 


Oreg. 


Sumpter 


- 


- 


- 


- 


19.3E 


19.7E 


20.0E 


20. 2E 


20. 2E 


20.4E 


21.0E 






Detroit 


16.7E 


17 •4E 


18.0E 


18.6E 


19.2E 


19.7E 


20. lE 


20.4E 


20.5E 


20.8E 


2i.sE 




Pa. 


Philadelphia 


2.2W 


2.4VV 


2.8W 


3.4W 


4.1W 


4.8W 


s.sw 


6.3W 


6.8W 


7.4W 


8.0W 






Altoona 


0.5W 


0.6W 


0.9W 


1.3W 


1.8W 


2.4W 


3.1W 


3.8W 


4-5W 


5.1W 


S.6W 




P. R. 


San Juan 


- 


- 


- 


- 


- 


- 


- 


- 


- 


i.oW 


2.0W 




R. I. 


Newport 


6.6W 


7.1W 


7.7W 


8.4W 


9.1W 


9.8W 


10.3W 


10.8W 


11.3W 


11.9W 


12.4W 




S. C. 


Columbia 


4.4E 


4-3E 


4.1E 


3.7E 


3.2E 


2.7E 


2.1E 


1.4E 


0.8E 


0.2E 


o.iW 




S. D. 


Huron 


- 


- 


- 


13. lE 


13. lE 


12.9E 


12.6E 


12. lE 


11.4E 


II. lE 


11.4E 






Rapid City 


- 


- 


- 


- 


16.4E 


16.4E 


16.3E 


I5.8E 


I5.3E 


iS-iE 


15.4E 




Tenn. 


Chattanooga 


S.3E 


S-3E 


5.1E 


4.8E 


4.4E 


3.9E 


3.3E 


2.6E 


2.0E 


1.5E 


1.3E 






Huntington 


- 


7.4E 


7.4E 


7.3E 


7.0E 


6.6E 


6.1E 


S.5E 


4.9E 


4.4E 


4-3E 




Tex. 


Houston 


- 


8.9E 


9.2E 


9.3E 


9.3E 


9.2E 


8.9E 


8.sE 


7.9E 


7.7E 


8.1E 






San Antonio 


- 


- 


9.6E 


9.8E 


9.9E 


9.8E 


9.6E 


9.3E 


8.9E 


8.7E 


9.1E 




• 


Pecos 


- 


- 


10.8E 


ll.oE 


ii.iE 


II. lE 


ii.oE 


10.8E 


10.4E 


10.3E 


10.7E 




Tex. 


Floydada 


_ 


_ 


_ 


_ 


11.3E 


11.3E 


11.2E 


10.9E 


10.4E 


10.3E 


10.7E 




Utah 


Salt Lake 


- 


- 


- 


- 


16.4E 


16.6E 


16.7E 


i6.sE 


16.3E 


i6.sE 


17. oE 




Vt. 


Rutland 


6.8W 


7.2W 


7.8W 


8.SW 


9.2W 


lO.oW 


10.6W 


11.2W 


11.6W 


12. iW 


12.7W 




Va. 


Richmond 


0.8E 


0.6E 


0.3W 


o.iW 


0.6W 


1.2W 


1.8W 


2.sW 


3.1W 


3.7W 


4.2W 






Lynchburg 


1.9E 


1.8E 


1.6E 


1.2E 


0.8E 


0.2E 


o.sW 


1.2W 


1.8W 


2.4W 


2.8W 




Wash. 


Wilson Creek 










21.3E 


21.6E 


21.9E 


21.9E 


22. lE 


22. 4E 


22. 9E 






Seattle 


19 lE 


19.7E 


20.3E 


20.8E 


21.3E 


21. 8E 


22. lE 


22.3E 


22.6E 


23.0E 


23-5E 




W. Va. 


Charleston 


2.3E 


2.2E 


2.0E 


1.6E 


i.iE 


0.5E 


0.2W 


0.9W 


1.5W 


2.1W 


2.6W 




Wis. 


Madison 


- 


8.6E 


8.7E 


8.6E 


8.3E 


7.8E 


7.2E 


6.4E 


5.6E 


5.0E 


4-9E 




Wyo. 


Douglas 


- 


- 


- 


- 


IS-8E 


16.0E 


16.0E 


IS.8E 


IS.4E 


IS.3E 


IS.7E 






Green River 










16.8E 


17.0E 


17.0E 


16.9E 


16.6E 


16.6E 


17.0E 





Smithsonian Tables. 



Tables 93-94. 
TERRESTRIAL MAGNETISM (continued). 

TABLE 93. — Dip or Inclination. 



113 



This table gives for the epoch January i, 1905, the values of the magnetic dip, I, corresponding 
to the longitudes west of Greenwich in the heading and the north latitudes in the first column. 






65° 


70'^ 


75° 


80° 


85° 


90° 


95° 


100° 


105° 


110° 


ri5° 


120° 


1250 













































19 


- 


- 


48.8 


49.1 


47-5 


46-3 


44.8 


44.2 


43-9 


- 


- 


- 


- 




21 


- 


- 


51.0 


5I-I 


50.0 


49-3 


48.2 


47-0 


46. s 


- 


- 


- 


- 




23 


- 


- 


53-7 


53-0 


524 


51.8 


507 


49.6 


48.8 


48.2 


- 


- 


- 




25 


- 


- 


56-3 


56.0 


55-0 


54-5 


53-2 


524 


51-5 


50.6 


49.8 


48.3 


- 




27 


~ 


- 


5^-9 


58.1 


57-6 


56.8 


55-6 


54-7 


53-9 


53-1 


52.6 


51.0 


- 




29 


- 


60.7 


61.0 


60.2 


59-8 


58.9 


S8.2 


S7.2 


S6.2 


5S-S 


S4.8 


537 


_ 




31 


- 


63.0 


6,1.1 


62.6 


62.0 


61.3 


60.6 


S9-6 


S87 


577 


S6.7 


56.0 


- 




33 


- 


65.0 


65.0 


64.6 


64.0 


63- S 


62.7 


62.0 


61.0 


S9.8 


S8.9 


S8.i 


- 




35 


- 


67.0 


66.9 


66.5 


66.0 


65.6 


64.9 


637 


62.7 


62.3 


61.0 


6c.2 


- 




37 


- 


68.6 


68.9 


68.6 


68.2 


67.7 


66.9 


66.2 


65.1 


64.6 


62.9 


62.2 


- 




39 


- 


70.3 


70.6 


70.4 


70.2 


69.7 


68.8 


68.1 


67.2 


66.1 


65.0 


64.0 


62.8 




41 


- 


71.8 


72.2 


72.2 


71.9 


71.4 


70.8 


69.8 


6S.9 


67.8 


66.8 


65.6 


64.7 




43 


- 


73-5 


73-9 


74.1 


73-^ 


73-3 


72.6 


71.6 


70.7 


69.6 


68.6 


67. S 


66.3 




45 


74-4 


74.8 


7S-6 


75.5 


75-4 


75-0 


74-3 


73-^ 


72.4 


71-5 


70-3 


6q.2 


68.1 




47 


75-7 


76.2 


76.9 


76.8 


76.9 


76.8 


76.0 


75-2 


74.2 


73-0 


71.8 


70.8 


69.9 




49 


76.8 


78.1 


78.2 


78.3 


78.7 


78.1 


77-5 


76.8 


75-8 


74-S 


73-5 


72.3 


71.4 





TABLE 94. — SectQar Change of Dip. 

Values of magnetic dip for places designated by the north latitudes and longitudes west of 
Greenwich in the first two columns for January ist of the years in the heading. The degrees 
are given in the third column and minutes in the succeeding columns. 



Lati- 
tude. 



25 


Longi- 
tude. 




185s 


i860 


i86s 


1870 


187s 


1880 
40 


188s 


1890 


189s 


1900 


190S 


1910 



80 


55+ 


49 


49 


48 


46 


43 


35 


35 


39 


/ 
48 


60 


/ 
77 


25 


no 


49+ 


08 


20 


.30 


39 


46 


55 


61 


68 


76 


86 


q6 


106 


30 


83 


60+ 


66 


70 


73 


74 


73 


67 


57 


51 


53 


63 


78 


q6 


30 


100 


57+ 


44 


49 


58 


67 


70 


65 


60 


61 


68 


77 


90 


105 


30 


"5 


54+ 


53 


62 


69 


71 


70 


72 


75 


79 


85 


91 


96 


lOX 


35 


80 


66+ 


57 


58 


57 


54 


45 


35 


26 


21 


20 


22 


30 


38 


35 


90 


b5+ 


^5 


59 


51 


44 


37 


32 


26 


25 


25 


27 


36 


48 


35 


105 


62+ 


- 


- 


- 


32 


30 


24 


24 


24 


28 


34 


42 


50 


35 


120 


60+ 


03 


06 


c8 


08 


07 


06 


08 


II 


13 


14 


12 


g8 


40 


75 


71+ 


82 


82 


78 


73 


65 


55 


43 


33 


27 


24 


24 


24 


40 


90 


70+ 


.30 


31 


34 


37 


36 


32 


29 


26 


25 


26 


30 


36 


40 


105 


07+ 


- 


- 


- 


5<3 


53 


51 


51 


51 


52 


56 


60 


65 


40 


120 


04+ 


- 


48 


46 


44 


44 


44 


44 


44 


45 


45 


48 


48 


45 


^S 


74+ 


116 


no 


lOI 


92 


80 


68 


57 


46 


35 


28 


24 


20 


45 


75 


75+ 


103 


99 


95 


90 


85 


73 


62 


53 


43 


38 


36 


34 


45 


90 


74+ 


81 


81 


81 


79 


77 


75 


68 


63 


61 


59 


60 


60 


45 


105 


72+ 


- 


- 


- 


- 


- 


22 


20 


20 


21 


22 


24 


27 


45 


122.5 


68+ 


35 


34 


37 


40 


40 


39 


37 


34 


30 


26 


24 


20 


49 


92 


78+ 


26 


25 


24 


22 


20 


20 


15 


12 


II 


09 


06 


04 


49 


120 


72+ 




26 


24 


22 


22 


19 


20 


19 


19 


19 


18 


. 



Smithsonian Tables. 



114 



Tables 95-96. 

TERRESTRIAL MAGNETISM (continued). 

TABLE 9B. — Horizontal Intensity. 



This table gives for the epoch January i, 1905, the horizontal intensity, H, expressed in C. G. S. 
units, corresponding to the longitudes in the heading and the latitudes in the first column. 





65° 


70° 


75° 


80° 


8s° 


90° 


95° 


100° 


105° 


110° 


115° 


120° 


125° 




19 


_ 


_ 


•307 


.314 


•319 


.322 


.328 


•332 


•331 










21 


- 


- 


.301 


•309 


•314 


.31b 


.320 


.324 


•324 










23 


- 


- 


•293 


•303 


•305 


•309 


.312 


•315 


■^'l 


.320 








2S 


- 


- 


.284 


.292 


.295 


.299 


•304 


•307 


.308 


•309 


.312 


.304 




27 


- 


- 


.274 


.280 


.286 


.289 


.296 


.298 


.300 


•303 


.306 


.298 




29 


- 


•257 


.262 


.269 


.276 


.281 


.286 


.289 


.292 


.294 


.297 


.291 




31 


- 


.246 


.251 


.256 


.263 


.269 


.274 


.277 


.282 


.284 


.28s 


.282 




33 


- 


•233 


•239 


■245 


•25' 


•2.S7 


.262 


.266 


.270 


.273 


.274 


.274 




3S 


- 


.220 


.225 


.232 


.240 


.242 


.248 


•253 


.25b 


•259 


.262 


•2b5 




37 


- 


,20S 


.209 


.218 


.222 


.226 


.232 


.238 


.245 


.24b 


.252 


.251 




3Q 


- 


.197 


.198 


•203 


.206 


.212 


.217 


.224 


.229 


•237 


.240 


.242 


.245 


41 


- 


.184 


.i8s 


.186 


.192 


.196 


.202 


.207 


.216 


.223 


.228 


.240 


.236 


43 


- 


.170 


.170 


.169 


•i7,S 


.178 


.187 


.194 


.201 


.210 


•215 


.222 


.226 


4S 


.161 


•157 


•15s 


.156 


•157 


.162 


.169 


.177 


.190 


.192 


.199 


.208 


.215 


47 


•14s 


.144 


.140 


.142 


.142 


.150 


.152 


.161 


.170 


.180 


.188 


.196 


.201 


49 


•131 


.129 


•125 


.126 


.124 


.129 


.i3« 


.146 


•153 


.165 


•175 


.182 


.187 



TABLE 96. —Secular Change of Horizontal Intensity. 

Values of horizontal intensity in C. G. S. units for places designated by the latitude and longi- 
tude in the first two columns for January i of the years in the heading. 



-0 

3 

3 


si 


185s 


i860 


1865 


1870 


1875 


1880 


188s 


1890 


1895 


1900 


1905 


I9I0 



25 



80 


•3099 


.3086 


•3073 


•3057 


.3042 


-.3025 


.3008 


.2990 


.2970 


.2949 


.2920 


.2890 


2.S 


no 


•3229 


•3218 


.3204 


.3189 


•3170 


•3155 


•3143 


•3130 


•3117 


.3104 


.3090 


•3075 


30 


ii^ 


•2S03 


•2795 


.2788 


.2780 


.2772 


.27b3 


.2752 


.2740 


•2725 


.2706 


.2680 


.2644 


30 


100 


- 




.2961 


.2942 


.2924 


.2907 


.2891 


.2877 


.2865 


.2850 


.2830 


.2804 


30 


"5 


.3040 


.3026 


.3011 


.2996 


.2979 


.2964 


.2952 


.2940 


.2929 


.2920 


.2910 


.2898 


3,S 


80 


.2384 


•2379 


•2374 


.2369 


.2367 


•2363 


•2359 


•2352 


•2347 


•2337 


.232c 


.2296 


35 


90 




- 


- 


.24b2 


.2462 


.2461 


.2458 


•2455 


.2447 


•2437 


.2430 


•2399 


3S 


105 


- 


- 


- 


- 


.2620 


.2608 


•2599 


.2590 


•2 5«3 


•2573 


.2560 


•2544 


35 


120 


- 


- 


- 


.2720 


.2707 


.2695 


.2683 


.2672 


.2bb3 


.2656 


.2650 


.2644 


40 


75 


.1880 


.1883 


.1891 


.1902 


.1911 


.1919 


.1925 


.1930 


•I93I 


.1928 


.1920 


.1909 


40 


90 


- 


.2086 


.2082 


.2079 


.2076 


.2075 


.2074 


.2072 


.2068 


.2060 


.2050 


.2036 


40 


105 


- 


- 


- 


.2272 


.2266 


.2261 


.2257 


•2253 


.2248 


.2240 


.2230 


.2217 


40 


120 


- 


- 


- 


.2429 


.2420 


.2412 


.2406 


•2399 


.2392 


.238b 


.2380 


•2379 


4S 


65 


.1504 


.1514 


•1525 


•1537 


•1553 


.1567 


•i57« 


.1589 


.1600 


.1608 


.1610 


.1610 


45 


75 


.1483 


.1485 


.1488 


•1495 


.1506 


.1516 


■1527 


•i53« 


.1546 


.1550 


•1550 


•1554 


45 


90 


_ 


•163s 


•1633 


.1631 


.1628 


.1626 


.1624 


.1623 


.1624 


.1623 


.1620 


.1616 


45 


105 


- 






.1920 


.1919 


.1918 


.1916 


•1913 


.1910 


.1906 


.1900 


.1892 


4S 


122.5 


•2175 


.2170 


.2162 


•2153 


.2145 


•2135 


2127 


.2121 


.2117 


•21 1 5 


.2115 


.2115 


49 


92 


•1332 


•1330 


.1328 


.1324 


.1321 


•1319 


.1318 


.1318 


.1321 


.1324 


•1330 


•1335 


49 


120 


.1841 


.1841 


.1840 


.1839 


.1836 


.1831 


.1826 


.1821 


.1819 


.1820 


.1820 


.1824 



Smithsonian Tables. 



Tables 97-98. ' 
TERRESTRIAL MAGNETISM {continued). 

TABLE 97. — Total Intensity. 



115 



This table gives for the epoch January i, 1905, the values of total intensity, F, expressed in C. G. S. 
units corresponding to the longitudes in the heading and the latitudes in tlie first column. 





19 


65° 


70° 


75° 


80° 


85° 


90° 


95° 


100° 


105° 


110° 


115° 


120° 


125° 






.466 


.480 


•472 


.466 


.462 


•463 


•459 


_ 


_ 


_ 


_ 


21 


- 


- 


•47« 


.492 


.489 


•485 


.480 


•475 


.471 


- 


- 


- 


- 


23 


- 


- 


•495 


.504 


.500 


.500 


•493 


.486 


.481 


.480 


- 


- 


- 


2S 


- 


- 


.512 


.522 


.514 


■515 


.507 


•503 


•495 


•487 


•483 


•457 


- 


27 


- 


- 


.530 


•530 


•534 


•528 


• 524 


.510 


•509 


•505 


•504 


•474 


— 


29 


_ 


•S2S 


•S40 


•541 


•549 


■544 


•543 


•534 


•525 


•519 


•515 


■492 


- 


^I 


- 


•542 


• ss-; 


•5S<3 


.560 


.560 


•558 


.547 


•543 


•531 


.519 


•504 


- 


33 


- 


•551 


.566 


•571 


■ 572 


•57b 


•571 


.5<^7 


•557 


■543 


•530 


.518 


- 


35 


- 


•563 


•574 


.S82 


.590 


.586 


•584 


•571 


.558 


■557 


.540 


■533 


- 


37 


- 


.570 


.581 


■598 


•598 


.596 


•591 


•590 


.582 


•573 


•553 


•538 


- 


39 


_ 


• S84 


•596 


.605 


.608 


.611 


.600 


.600 


.591 


•585 


.568 


•552 


•536 


41 


- 


.5S9 


.605 


.608 


.618 


.614 


.614 


.600 


.600 


•590 


.579 


•581 


•552 


43 


- 


•599 


.6n 


.617 


.627 


.619 


.62 s 


.614 


.608 


.602 


•S89 


• 580 


.562 


45 


•599 


•599 


.62^ 


.621 


.623 


.626 


.624 


.627 


.628 


.605 


•590 


.586 


■576 


47 


.587 


.604 


.618 


.622 


.626 


.6S7 


.628 


.630 


.624 


.616 


.602 


•59(5 


-.585 


49 


•574 


.626 


.611 


.621 


■(^33 


.626 


.638 


•639 


.624 


.617 


.616 


•599 


.588 



TABLE 98. — Secular Change of Total Intensity. 

Values of total intensity in C. G. S. units for places designated by the latitudes and longitudes in the 
first two columns for January i of the years in the heading. (Computed from Tables 92 and 94.) 



Lati- 
tude 


Longi- 
tude. 


ISSS 


i860 


1865 


1870 


1875 


1880 


188s 


1890 


1895 


1900 


190S 


1910 




2S 



80 


■5516 


•5493 


.5467 


■5434 


.5400 


•S364 


■5322 


.5290 


.5264 


■5247 


.5222 


.5206 


2S 


no 


■4935 


■4938 


•4933 


•4925 


.4908 


.4902 


.4891 


■4883 


.4876 


■4873 


.4868 


.4860 


30 


83 


.5800 


•5796 


•5790 


•5777 


•5757 


.5720 


.566S 


•5^25 


.5600 


.5590 


•5581 


■5559 


30 


100 


- 


- 


•5583 


■5570 


•5544 


•5499 


•5456 


•5432 


.5427 


.5421 


.5416 


■5405 


30 


"5 


•5285 


.5280 


.5269 


■5247 


.5215 


■5194 


■5179 


■5167 


.5160 


•5158 


.5151 


.5140 


3S 


80 


.60S9 


.60S0 


.6063 


.6038 


.5996 


.5946 


.5900 


.5863 


•5874 


■5830 


.5818 


•5789 


35 


90 


- 


- 


- 


•5991 


.5964 


■5942 


.5912 


.5901 


■5882 


•5865 


•5858 


•5852 


35 


105 


- 


- 


- 




•5674 


.5629 


.5610 


■5590 


■5588 


•5585 


•5582 


■5572 


35 


120 


- 


- 


- 


.5462 


•5433 


.5406 


■5^88 


•5374 


•536' 


•5350 


•5332 


•5309 


40 


75 


.6206 


.6216 


6220 


.6227 


.6212 


.6182 


.6136 


.6098 


.6070 


.6045 


.6019 


•5985 


40 


90 


_ 


.6254 


.6258 


.6264 


.6250 


.6226 


.6208 


.6187 


.6170 


.6151 


.6141 


•6135 


40 


105 


- 




- 


.6048 


.6019 


■5997 


.S986 


.5976 


.5967 


•5963 


•5953 


•5940 


40 


120 


- 


- 


- 


.5691 


.5670 


■5651 


•5637 


.5620 


.560S 


•5593 


•5590 


•5591 


4S 


65 


.6188 


.6186 


.6167 


.6152 


.6134 


.6107 


.6077 


.6048 


.6019 


.6005 


.5987 


.5962 


45 


75 


.6454 


.6431 


.6413 


.6404 


.6412 


■6363 


•6327 


.6306 


.6266 


.6247 


•(3233 


•6235 


45 


90 


_ 


.6465 


.6457 


•6434 


.640S 


.6386 


■6330 


.6291 


.6382 


.6264 


.6259 


.6244 


45 


105 


- 








- 


•6332 


.6314 


•6303 


.6299 


.6392 


.6284 


.6275 


45 


122.5 


•S9S6 


•5938 


• 5930 


.5918 


.5896 


.5864 


•5834 


.5804 


•5776 


•5754 


•5745 


.5728 


49 


92 


.6643 


.6624 


.6604 


.6566 


•6533 


•6523 


.6472 


•6445 


.6451 


.6447 


.6450 


.6456 


49 


120 




.6100 


.6085 


.6071 


.6061 


.6028 


.6017 


•5995 


.5988 


•5992 


.5986 


•5988 



Smithsonian Tables. 



ii6 



Table 99. 

AGONIC LINE. 

The line of no declination appears to be still mov- 
ing westward in the United States, but the line of no 
annual change is only a short distance to the west of 
it, so that it is probable that the extreme westerly 
position will soon be reached. 





Longitudes of the agonic line for the years — 




Lat. 

N. 




























i8oo 


1850 


187s 


1890 


190S 




o 


o 
















25 


_ 


- 


- 


75-5 


76.1 




3° 


- 


- 


~ 


78.6 


797 




35 


_ 


76.7 


79.0 


79-9 


81.7 




6 


75-2 


77-3 


79-7 


80.5 


82.8 




7 


76.3 


77-7 


80.6 


82.2 


Pi 




8 


76.7 


78.3 


81.3 


82.6 


83.6 




9 


76.9 


78.7 


81.6 


82.2 


83.6 




40 


77.0 


79-3 


81.6 


82.7 


84.0 




I 


77-9 


80.4 


81.8 


82.8 


84.6 




2 


79.1 


81.0 


82.6 


837 


84.8 




3 


794 


81.2 


83.1 


84-3 


85.0 




4 


79.8 


- 


83-3 


84.9 


85-5 




45 


_ 


_ 


83.6 


85.2 


86.0 




6 


_ 


- 


84.2 


84.8 


86.4 




7 


_ 


- 


85.1 


854 


86.4 




8 


_ 


- 


86.0 


85.9 


86.5 




9 


- 


~ 


86.5 


86.3 


87.2 





Smithsonian Tables. 



Table 100. II7 

RECENT VALUES OF THE MAGNETIC ELEMENTS AT MAGNETIC 

OBSERVATORIES. 

(Compiled by the Department of Terrestrial Magnetism, Carnegie Institution of Washington.) 











Magnetic 


Elements. 












Middle 

of 

year. 












Place. 


Latitude. 


Longitude. 




Inclination. 


Intensity (C.G.S 


. units). 












Declination. 






















Horl. 


Ver'l. 


Total. 




Pawlowsk 


/ 
5941N 


/ 
3029E 


1907 


1 
I 09.9E 


/ 
70 37.7N 


.1650 


.4694 


•4975 




Sitka 


5703N 


135 20W 


1910 


30 16.4E 


74 32.2N 


•1559 


•5637 


•5849 




Katharinenburg 


5703N 


6038E 


1907 


I0 35-5E 


70 52.2N 


.1762 


.5081 


•5378 




j Rude Skov 


5551N 


I227E 


1910 


9 28.7W 


68 45.0N 


■1738 


.4468 


•4794 




Eskdalemuir 


55 19N 


312W 


1911 


18 12.4W 


69 37.1 N 


.1685 


•4534 


•4837 




Stonyhurst 


5351N 


2 28 W 


1912 


17 03.6 W 


6841.4N 


.1740 


.4460 


.4787 




Wilhelmshaven 


5332N 


809E 


1910 


II 37.0W 


67 30.5N 


.1812 


•4377 


•4737 




Potsdam 


52 23N 


I304E 


1912 


8 45-9W 


66 20.4N 


.1880 


.4291 


.4685 




Seddin 


5217N 


I3OIE 


1912 


8 47.2W 


66 17.4N 


.1884 


.4290 


.4685 




Irkutsk 


52 16N 


104 16E 


1905 


I 58.1E 


70 25.0N 


.2001 


.5625 


.5970 




De Bilt 


5206N 


5 iiE 


1910 


12 58.2W 


66 46. 5N 


.1854 


•4321 


.4702 




Valencia 


51 56N 


10 15W 


1911 


20 38. 1 W 


68 12. iN 


.1789 


•4473 


.4817 




Clausthal 


51 48N 


10 20E 


1905 


ID 40.3W 












Bochum 


51 29N 


7 14E 


1911 


II 48.3W 












Kew 


51 28N 


19W 


1911 


15 55-3W 


66 57. 2 N 


.18*50 


•4349 


•4726 




Greenwich 


51 28N 


00 


1911 


15 33-oW 


66 52. 1 N 


.1852 


•4337 


.4716 




Uccle 


5048N 


4 21E 


1911 


13 13 9W 


66 oo.iN 


.1902 


•4273 


.4677 




Hermsdorf 


50 46N 


16 14E 


1912 


7 06.9W 


.... 






. . . 




Beuthen 


50 21N 


1855E 


1908 


6 12.3W 








. . . 




Falmouth 


5009N 


505W 


1912 


17 24.2W 


66 26.6N 


.1880 


•4312 


.4704 




Prague 


50 05N 


1425E 


1910 


8 09.6W 












Cracow 


50 04 N 


19 58E 


1911 


5 18.1W 


64 15.5N 


. . . 








St. Helier (Jersey) 


49 12N 


2 05W 


1907 


16 27.4W 


65 34- 5N 










Val Joyeux 


4849N 


2 oiE 


1911 


14 17.6W 


64 4I-6N 


.1974 


.4176 


.4619 




Munich 


4809N 


II 37E 


1910 


931.5W 


63 08.4N 


.2064 


•407s 


.4568 




Kremsmiinster 


48C3N 


14 oSE 


1904 


9 02. 4W 






. . . 


. • . 




O'Gyalla (Pesth) 


4753N 


18 12E 


1911 


6 25.6W 




.2107 




. . . 




Odessa 


4626N 


3046E 


1910 


3 3S-9W 


62 26.9N 


.2171 


.4161 


.4693 




Pola 


4452N 


1351E 


1911 


8 17.5W 


60 03.6N 


.2219 


.3853 


.4446 




Agincourt (Toronto) 


4347N 


79 16W 


1910 


6 03.9W 


74 38-5N 


.1627 


•5923 


.6142 




Perpignan 


4242N 


2 53E 


1910 


12 44.8 W 






. . . 






Tiflis 


41 43N 


' 4448E 


1905 


2 41. 6E 


56 02.8N 


•2545 


.3780 


•4557 




Capodimonte 


40 52N 


14 15E 


191 1 




56 11.7N 




. . . 






Ebro (Tortosa) 


40 49N 


031E 


191I 


13 i'8.'6W 


57 S4-8N 


.2326 


.3709 


•4378 




Coimbra 


40 12N 


825W 


1911 


16 27.4W 


58 46.4N 


.2301 


•3795 


•4438 




Mount Weather 


3904N 


n 53W 


1908 


3 39-2W 


.... 










Baldwin 


3847N 


95 loW 


1908 


8 33.0E 


68 47.8N 


.2171 


•5597 


.6003 




Cheltenham 


3844N 


76 50W 


1910 


541.4W 


70 35.4N 


.1983 


.5626 


.5966 




Athens 


37 59N 


2342E 


1908 


4 53-oW 


52 II. 7N 


.2620 


•3361 


.4262 




San Fernando 


3628N 


6 12W 


191 1 


15 05.2W 


54 3I-5N 


.2489 




. . . 




Tokio 


3541N 


139 45E 


1910 


4 58.2W 


49 07-3N 


.3001 


•3467 


•4585 




Tucson 


32 15N 


no 50 W 


1910 


13 25.8E 


59 19.6N 


.2741 


.4621 


•5372 




Zi-ka-wei 


31 12N 


121 26E 


1907 


2 33.6W 


45 36-6N 


•3306 


•3377 


.4726 




Dehra Dun 


30 19N 


7803E 


191O 


2 31.9E 


43 54-8N 


•3326 


.3202 


.4617 




Helwan 


29 52N 


31 20E 


1912 


2 25.4W 


40 43.7 N 


.3006 


.2588 


•3967 




Barrackpore 


22 46N 


8822E 


191O 


55-5E 


30 42.2N 


•3733 


.2217 


■4341 




Hongkong 


22 18N 


114 loE 


191O 


00.4E 


30 58.8 N 


•37 1 1 


.2228 


.4328 




Honolulu 


21 19N 


158 04 W 


1910 


9 29- 7 E 


39 47-2N 


.2916 


.2428 


•3795 




Toungoo 


18 56N 


9627E 


191O 


24.9P2 


23 02.1N 


.3880 


.1650 


.4216 




Alibag 


1838N 


7252E 


1912 


51. 2E 


23 56- 1 N 


.3687 


.1637 


•4034 




Vieques 


1809N 


65 26W 


1910 


2 20.6W 


49 52-oN 


.2886 


.3424 


•4478 




Antipolo 


1436N 


121 loE 


191I 


40.9E 


16 18. 2N 


.3820 


.1117 


.3981 




Kodaikanal 


10 14N 


7728E 


1910 


55.0W 


3 45-2N 


.3748 


.0246 


•3757 




Batavia-Butenzorg 


6 iiS 


106 49E 


1909 


49. 5E 


31 09.2 S 


.3668 


.2218 


.4286 




St. Paul de Loanda 


848S 


13 13E 


1910 


16 12.3W 


35 32.28 


.2012 


•1437 


•2473 




Samoa (Apia) 


1348S 


171 46W 


1908 


941.9E 


29 21.7S 


•3561 


.2004 


.40S6 




Tananarive 


18558 


4732E 


1907 


9 29.7 W 


54 057S 


•2533 


•3499 


•4319 




Mauritius 


20 06S 


S733E 


I911 


9 18.5W 


53 30.6S 


•2331 


.3151 


.3920 










K 1906 
\ 1910 


8 55-3W 


13 57-28 


.2477 


.0617 


•2553 




Rio de Janeiro 


22558 


4311W 


9 40.0 W 


.... 






. • . 





Smithsonian Tables. 



ii8 



Table 101 . 



PRESSURE OF COLUMNS OF MERCURY AND WATER. 

British and metric measures. Correct at o"^ C. for mercury and at 4° C. for water. 



Metric Measure. 


British Measure. 


Cms. of 
Hg. 


Pressure 

in grams per 

sq. cm. 


Pressure 

in pounds per 

sq. incli. 


Inches of 
Hg. 


Pressure 

in grams per 

sq. cm. 


Pressure 

in pounds per 
sq. inch. 


1 
2 
3 
4 

5 
6 

7 
8 

9 
10 


13-5956 
27.1912 
40.7868 

54-3824 

67.9780 

81.5736 

95.1692 

I08.764S 

122.3604 

135-9560 


0.193376 

0.386752 
0.580128 

0-773504 
O.966SS0 
1. 1 60256 

1-353632 
1.547008 
1.740384 
1.933760 


1 
2 

3 
4 
5 
6 

7 
8 

9 
10 


34-533 

69.066 

103.598 

138-131 
172.664 
207.197 
241.730 
276.262 
310.795 
345-328 


0.491 174 
0.982348 
1.473522 
1.964696 
2.455870 
2.947044 
3.438218 
3-929392 
4.420566 
4.91 1740 


Cms. of 
HoO. 


Pressure 

in grams per 

sq. cm. 


Pressure 

in pounds per 

sq. inch. 


Inches of 
H2O. 


Pressure 

in grams per 

sq. cm. 


Pressure 

in pounds per 

sq. inch. 


1 

2 

3 
4 
5 
6 

7 
8 

9 
10 


I 
2 

3 
4 
5 
6 

7 
8 

9 
10 


0.0142234 
0.0284468 
0.0426702 
0.0568936 
0.071 1 170 
0.0853404 
0.0995638 

O.I 137872 

O.X280I06 
0.1422340 


1 
2 
3 

4 
5 
6 

7 
8 

9 
10 


2.54 
5.08 
7.62 
10.16 
12.70 
1524 
17.78 
20.32 
22.86 

25-40 


0.036127 
0.072255 
0.108382 
O.I445IO 
0.180637 
0.216764 
O.252S92 
O.2S9OI9 
0.325147 
0.361274 



Smithsonian Tables. 



Table 102. II9 

REDUCTION OF BAROMETRIC HEIGHT TO STANDARD TEMPERATURE.* 



Corrections for brass scale and 


Corrections for brass scale and 


Corrections for glass scale and 


English measure. 


metric measure. 


metric measure. 


Height of 


a 


Height of 


a 


Height of 


a 


barometer in 


in inches for 


barometer in 


in mm. for 


barometer in 


in mm. for 


inches. 


temp. F. 


mm. 


temp. C. 


mm. 


temp. C. 


150 


0.00135 


400 


0.0651 


50 


C.00S6 


16.0 


.00145 


410 


.066S 


100 


.0172 


17.0 


.00154 


420 


.06S4 


150 


.0258 


17-5 


.00158 


430 


.0700 


200 


•0345 


18.0 


.00163 


440 


.0716 


250 


.0431 


18.5 


.00167 


450 


.0732 


300 


•0517 


19.0 


.00172 


460 


.0749 


350 


.0603 


19-5 


.00176 


470 


.0765 










4S0 


.O7S1 


400 


C.0689 


200 


o.ooiSi 


490 


.0797 


450 


•0775 


20.5 


.00185 






500 


.0S61 


21.0 


.00190 


500 


0.0813 


520 


.0895 


21.5 


.00194 


510 


.0S30 


540 


.0930 


22.0 


.00199 


520 


.0S46 


560 


.0965 


22.5 


.00203 


530 


.0862 


580 


.0999 


23.0 


.00208 


540 


.0878 






23-5 


.002 1 2 


550 


.0894 


600 


0.1034 






560 


.0911 


610 


.1051 


24.0 


0.00217 


570 


.0927 


620 


.1068 


24.5 


.00221 


580 


•0943 


630 


.I0S5 


25.0 


.00226 


590 


•0959 


640 


.1103 


25-5 


.00231 






650 


.1120 


26.0 


.00236 


600 


0.0975 


660 


•II37 


26.5 


.00240 


610 


.0992 






27.0 


.00245 


620 


.1008 


670 


O.I 1 54 


27-5 


.00249 


630 


.1024 


680 


.1172 






640 


.1040 


690 


.1189 


28.0 


0.00254 


650 


.1056 


700 


.1206 


2S.5 


.00258 


660 


•1073 


710 


.1223 


29.0 


.00263 


670 


.1089 


720 


.1240 


29.2 


.00265 


680 


.1105 


730 


.1258 


29.4 


.00267 


690 


.1121 






29.6 


.00268 






740 


0.1275 


29.8 


.00270 


700 


o.ri37 


750 


.1292 


30.0 


.00272 


710 


.1154 


760 


.1309 






720 


.1170 


770 


•1327 


30.2 


0.00274 


730 


.1186 


7S0 


•1344 


304 


.00276 


740 


.1202 


790 


.1361 


30.6 


.00277 


750 


.1218 


800 


•1378 


30.S 


.00279 


760 


•1235 






31.0 


.00281 


770 


.1251 


850 


0.1464 


31.2 


.00283 


780 


.1267 


900 


•I55I 


31-4 


.00285 


790 


.1283 


950 


.1639 


31.6 


.00287 


800 


.1299 


1000 


•1723 



*The height of the barometer is afTected by the relative thermal expansion of the mercury and 
the glass, iu tlie case of instruments graduated on the glass tube, and by the relative expansion of 
the mercury and the metallic inclosing case, usually of brass, in the case of instruments graduated 
on the brass case. This relative expansion is practically proportional to the first power of the tem- 
perature. The above tables of values of the coefficient of relative expansion will be found to give 
corrections almost identical with those given in the International Meteorological Tables. The 
numbers tabulated under a. are the values of a in the equation //> = ///' — a(t' — /) where //i is the 
height at the standard temperature, ///' the observed height at the temperature/', and a (t' — t) the 
correction for temperature. The standard temperature is o° C. for the metric system and 28°.5 F. 
for the English system. The English barometer is correct for the temperature of melting ice at a 
temperature of approximately 28°.5 F., because of the fact that the brass scale is graduated so as 
to be standard at 62° F., while mercury has the standard density at 32° F. 

Example.— A barometer having a brass scale gave // = 765 mm. at 25° C. ; required, the cor- 
responding reading at 0° C. Here the value of a is the mean of .1235 and .1251, or .1243 ; .' . a{i' — t) 
= .I243X 25 = 3.11. Hence //;, = 765 — 3. 1 1 =761.89 

N. B. — Although a is here given to three and .sometimes to four significant figures, it is seldom 
worth while to use more than the nearest two-fisrure number. In fact, all barometers have not the 
same values for a, and when great accuracy is wanted the proper coefficieuts have to be deter* 
mined by experiment. 

Smithsonian Tablcs< 



I20 



Table 103. 



CORRECTION OF BAROMETER TO STANDARD GRAVITY. 

Altitude term. Correction is to be subtracted. 



Height 


Observed height of barometer in 


nillimeters. 




above sea 
level in 






























meters. 


400 


450 


500 


550 


300 


650 


700 


750 


800 




lOO 












.014 


.015 


.016 


200 








.028 




030 


.032 




300 


Correction in millime- 






.041 




044 


.047 




400 


ters for elevation above 






•055 




059 


.063 




500 
600 


sea level in first column 
and height of barometer 
in top line. 




.064 
.077 


.068 
.082 




073 
088 


.078 






700 






.090 


.096 




102 






800 






.103 


.109 




117 






900 






.115 


.123 




131 






1000 

1 100 








.108 
.118 


118 
130 


.128 
.141 


•137 
.150 




146 








1200 








.129 


142 


•154 


.164 








1300 








.140 


153 


.166 


.178 








1400 








•151 


16s 


.179 


.191 








1500 






.147 


.162 


176 


.191 


.205 








1600 






•157 


.172 


188 


.204 










1700 






.167 


.183 


200 


.217 










iSoo 






•177 


.194 


212 


.230 






1-255 


15000 


1900 






.187 


.204 


224 


.242 






1. 213 


14500 


2000 

2100 




.176 

.185 


.196 
.206 
.216 


•215 
.226 


235 

247 


•255 




1.340 


1. 172 
1. 130 


14000 
13500 






292 


2200 




.194 


•237 


259 








244 


1.088 


13000 


2300 




.203 


.226 


.248 


271 




1-345 




196 


1.046 


12500 


2400 




.212 


.236 


•259 


283 




1. 291 




149 


1.004 


12000 


2500 
2600 


.195 
.203 


.220 
.229 


•245 
■255 


.270 


295 


1-315 


1-237 
1. 184 




lOI 

053 


.962 
.920 


II 500 
I 1000 






2700 


•211 


.238 


.265 






1-255 


1-130 




005 


.879 


10500 


2S0O 


.219 


.247 


•275 






1. 196 


1.076 




957 


■S37 


1 0000 


2900 


.227 


.256 
.265 


.285 


I 


050 


I.I 36 


1.022 




909 


•795 


9500 


3000 


•23s 


.294 




984 


1.076 


.969 




861 


•753 


9000 


3100 


•243 


.274 
.283 






918 


I.016 


•915 




813 




8500 


3200 


.251 






853 


•957 


.861 




•765 




8000 


3300 


i^ 


.292 




1.077 


787 


.897 


.807 






7500 


3400 


.201 




1.005 


721 


•837 


•753 






7000 


3500 
3600 


■:il 


•309 




.862 


655 
789 


•777 
.718 


.700 






6500 
6000 




3700 


.291 






.790 


724 


•658 








5500 


3800 


.299 




•779 


.718 


658 


•598 








5000 


3900 


•307 




.701 


.646 


•592 






4500 


4000 


•3H 




.623 
•545 


•574 
•503 


.526 
.461 






4000 

3500 










•503 


.467 


•431 


•395 


Co 
of an 


rrections in hundredths 
inch for elevation above 


3000 






.419 


•389 


•359 




sea 1 


ivel in last column and 


2500 




•359 


•335 


•311 


.287 




heigh 


t of barometer in bottom 


2000 




.269 


•251 


•233 


.215 




line. 




1500 


.192 


.179 


.167 


•iSS 










1000 


.096 


.090 


.084 


.078 














500 


32 


30 


2S 


26 


24 


22 


20 


18 


16 


•4 


Height 

above sea 

level in 














Observed height of ba 


romet 


;r in inch 


es. 


feet. 



Smithsonian Tables. 



Table 104. 



121 



REDUCTION OF BAROMETER TO STANDARD GRAVITY.* 

Reduction to Latitude 46 ^ — English Scale. 

N. B. From latitude o^ to 44° the correction is to be subtracted. 
From latitude 90'^ to 46*^ the correction is to be added. 





. J„ 




Height of the barometer 


in inches. 




Latituuc. 


'9 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 






Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


Inch. 


0° 


90° 


0.051 


0-053 


0.056 


0.059 


0.061 


0.064 


0.067 


0.069 


0.072 


0.074 


0.077 


0.080 


5 


85 


0.050 


0.052 


0.055 


0.058 


0.060 


0.063 


0.066 


0.068 


0.071 


0-073 


0.076 


0.079 


6 


84 


.049 


.052 


.055 


•057 


.060 


.062 


.065 


.068 


.070 


-073 


.076 


.078 


7 


S3 


.049 


.052 


.054 


.057 


.059 


.062 


.065 


.067 


.070 


.072 


•07 s 


.077 


8 


82 


.049 


.051 


.054 


.056 


•059 


.061 


.064 


.067 


.069 


.072 


•074 


.077 


9 


81 


.048 


.051 


•0S3 


.056 


.058 


.061 


-063 


.066 


.068 


.071 


•073 


.076 


10 


80 


0.048 


0.050 


0.053 


0-055 


0.058 


0.060 


0.063 


0.065 


0.068 


0.070 


0.073 


0.075 


II 


79 


.047 


■049 


.052 


.054 


.057 


-059 


.062 


.064 


.067 


.069 


.072 


•074 


12 


7S 


.046 


•049 


.051 


•054 


.056 


.058 


.061 


.063 


.066 


.068 


.071 


•073 


13 


77 


.045 


.048 


.050 


•053 


•OSS 


.057 


.060 


.062 


.065 


.067 


.069 


.072 


14 


76 


.045 


.047 


.049 


.052 


•054 


.056 


.059 


.061 


-063 


.066 


.068 


.071 


15 


75 


0.044 


0.046 


0.048 


0.051 


0-053 


0.055 


0.058 


0.060 


0.062 


0.065 


0.067 


0.069 


16 


74 


•043 


•045 


.047 


.050 


.052 


.054 


•056 


-059 


.061 


•063 


.065 


.068 


17 


73 


.042 


.044 


.046 


.049 


.051 


•053 


•055 


.057 


.060 


.062 


.064 


.066 


18 


72 


.041 


■043 


•04 S 


.047 


.050 


.052 


,054 


.056 


.058 


.060 


.062 


.065 


19 


71 


.040 


.042 


.044 


.046 


.048 


.050 


.052 


.055 


-057 


•059 


.061 


.063 


20 


70 


0.039 


0.041 


0.043 


0.045 


0.047 


0.049 


0.051 


0-053 


0-055 


0.057 


0.059 


0.061 


21 


69 


.038 


.040 


.042 


.044 


-045 


.047 


.049 


.051 


•053 


•05 s 


-057 


•059 


22 


68 


.036 


.038 


.040 


.042 


-044 


.046 


.048 


.050 


.052 


•054 


.056 


•057 


23 


67 


•03s 


•037 


•039 


.041 


-043 


.044 


.046 


.048 


.050 


.052 


-054 


•055 


24 


66 


•034 


.036 


•037 


•039 


.041 


-043 


.045 


.046 


.048 


.050 


.052 


-053 


25 


65 


0.033 


0.034 


0.036 


0.038 


0.039 


0.041 


0.043 


0.044 


0.046 


0.048 


0.050 


0.051 


26 


64 


.031 


•033 


•034 


.036 


.038 


•039 


.041 


-043 


.044 


.046 


.048 


.049 


27 


63 


.030 


.031 


.033 


•034 


.036 


.038 


•039 


.041 


.042 


.044 


-045 


.047 


28 


62 


.028 


.030 


.031 


-033 


•034 


.036 


•037 


-039 


.040 


.042 


•043 


.045 


29 


61 


.027 


.028 


.030 


.031 


.032 


•034 


-035 


-037 


.038 


•039 


.041 


.042 


30 


60 


0.025 


0.027 


0.028 


0.029 


0-031 


0.032 


0-033 


0.035 


0.036 


0-037 


0-039 


0.040 


31 


59 


.024 


.025 


.026 


.027 


.029 


.030 


.031 


-032 


-034 


•035 


.036 


•037 


32 


58 


.022 


.023 


.025 


.026 


.027 


.028 


.029 


.030 


.032 


-033 


•034 


•035 


33 


57 


.021 


.022 


.023 


.024 


.025 


.026 


.027 


.028 


.029 


.030 


.031 


.032 


34 


56 


.019 


.020 


.021 


.022 


.023 


.024 


.025 


.026 


.027 


.028 


.029 


.030 


35 


55 


0.017 


0.018 


0.019 


0.020 


0.021 


0.022 


0.023 


0.024 


0.025 


0.025 


0.026 


0.027 


36 


54 


.016 


.016 


.017 


.018 


.019 


.020 


.021 


.021 


.022 


.023 


.024 


.025 


37 


S3 


.014 


.015 


•01 s 


.016 


.017 


.018 


.018 


.019 


.020 


.021 


.021 


.022 


38 


52 


.012 


.013 


.014 


.014 


.015 


.015 


.016 


.017 


.017 


.018 


.019 


.019 


39 


SI 


.Oil 


.011 


.012 


.012 


.013 


•013 


.014 


.014 


.015 


.015 


.016 


.017 


40 


50 


0.009 


0.009 


0.0 10 


O.OIO 


0.0 1 1 


O.OII 


0.012 


0.012 


0.012 


0.013 


0.013 


0.014 


41 


49 


.007 


.007 


.008 


.008 


.009 


.009 


.009 


.010 


.010 


.010 


.Oil 


.Oil 


42 


48 


.005 


.006 


.006 


.006 


.006 


.007 


.007 


.007 


.008 


.008 


.008 


.008 


43 


47 


.004 


.004 


.004 


.004 


.004 


.004 


.005 


.005 


.005 


.005 


.005 


.006 


44 


46 


.002 


.002 


.002 


.002 


.002 


.002 


.002 


.002 


•003 


-003 


.003 


•003 



* " Smithsonian Meteorological Tables," p. 58. 



Smithsonian Tables. 



122 Table 105. 

REDUCTION OF BAROMETER TO STANDARD GRAVITY.* 

Reduction to Latitude 45°. —Metric Scale. 

N. B. — From latitude o° to 44° the correction is to be subtracted. 
From latitude 90° to 46° the correction is to be added. 



Latitude. 








Height of the barometer in 


millimeters. 




































520 


560 


600 


620 


640 


660 


680 


700 


720 


740 


760 


7S0 






mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


mm. 


0° 


90° 


1.38 


1.49 


1.60 


1.65 


1.70 


1.76 


I.81 


1. 86 


1.92 


1.97 


2.02 


2.08 


5 


85 


1.36 


1.47 


1-57 


1.63 


1.68 


1-73 


1.78 


1.84 


1.89 


1.94 


1.99 


2.04 


6 


84 


1-35 


1.46 


1.56 


1. 61 


1.67 


1.72 


1.77 


1.82 


1. 87 


1-93 


1.98 


2.03 


7 


83 


1-34 


1-45 


'•55 


1.60 


1.65 


1.70 


1.76 


1.81 


1.86 


1.91 


1.96 


2.01 


8 


82 


1-33 


1.43 


1-54 


^•59 


1.64 


1.69 


1.74 


1.79 


1.84 


1.89 


1.94 


2.00 


9 


81 


1.32 


1.42 


1-52 


^•57 


1.62 


1.67 


1.72 


1-77 


1.82 


1.87 


1.92 


1.97 


10 


80 


1.30 


1.40 


1.50 


1-55 


1.60 


1.65 


1.70 


^•75 


1.80 


1.8s 


1.90 


1.95 


II 


79 


1.28 


1.38 


1.48 


1-53 


1.58 


1.63 


1.68 


^•73 


1.78 


1.83 


1.88 


1-93 


12 


78 


1.26 


1.36 


1.46 


1.51 


1.56 


1.60 


1.6s 


1.70 


1-75 


1.80 


1.85 


1.90 


13 


77 


1.24 


1^34 


1.44 


1.48 


'•53 


1.58 


1.63 


1.67 


1.72 


1.77 


1.82 


1.87 


14 


76 


1.22 


1.32 


1.41 


1.46 


1.50 


1-55 


1.60 


1.65 


1.69 


1.74 


1.79 


1.83 


15 


75 


1.20 


1.29 


1.38 


^•43 


1.48 


1.52 


1-57 


1.61 


1.66 


1.71 


1-75 


1.80 


16 


74 


1. 17 


1.26 


1-35 


1.40 


1.44 


1.49 


1-54 


1.58 


1.63 


1.67 


1.72 


1.76 


17 


73 


1-15 


1.24 


1.32 


1^37 


1.41 


1-45 


1.50 


1.54 


1-59 


1.63 


1.68 


1.72 


18 


72 


1. 12 


1. 21 


1.29 


1-34 


1.38 


1.42 


1.46 


^•51 


1-55 


1-59 


1.64 


1.68 


19 


71 


1.09 


1. 17 


1.26 


1.30 


1-34 


1.38 


1^43 


1.47 


1.51 


1-55 


1-59 


1.64 


20 


70 


1.06 


1. 14 


1.22 


1.26 


I-3I 


1-35 


1-39 


1-43 


1.47 


1-51 


^•55 


1-59 


21 


69 


1.03 


I. II 


1. 19 


1.23 


1.27 


1.31 


1^35 


1.38 


1.42 


1.46 


1.50 


1.54 


22 


68 


1. 00 


1.07 


1-15 


1. 19 


1.23 


1.26 


1.30 


1^34 


1.38 


1.42 


1.46 


1.49 


23 


67 


0.96 


1.04 


I. II 


1-15 


1. 18 


1.22 


1.26 


1.29 


1-33 


1-37 


1.41 


1.44 


24 


66 


•93 


1. 00 


1.07 


1. 10 


1. 14 


1. 18 


1. 21 


I.2S 


1.28 


1.32 


1^35 


1-39 


25 


65 


0.89 


0.96 


1.03 


1.06 


1. 10 


I-I3 


1. 16 


1.20 


1.23 


1.27 


1.30 


1-33 


26 


64 


•85 


.92 


0.98 


1.02 


1.05 


1.08 


I. II 


1. 15 


1. 18 


1. 21 


1.25 


1.28 


27 


63 


.81 


.88 


•94 


0.97 


1. 00 


1.03 


1.06 


1. 10 


I-I3 


1. 16 


•I. 19 


1.22 


28 


62 


•77 


•83 


.89 


.92 


0-95 


0.98 


I.OI 


1.04 


1.07 


1. 10 


I-I3 


1. 16 


29 


61 


■73 


•79 


.85 


.87 


.90 


•93 


0.96 


0.99 


1.02 


1.04 


1.07 


1. 10 


30 


60 


0.69 


0-75 


0.80 


0.83 


0.85 


0.88 


0.91 


0.94 


0.96 


0.98 


I.OI 


1.04 


31 


59 


.65 


.70 


■75 


•77 


.80 


.82 


•85 


•87 


.90 


.92 


0-95 


0.97 


32 


58 


.61 


•65 


.70 


.72 


•75 


•77 


•79 


.82 


.84 


.86 


.89 


.91 


33 


57 


•56 


.61 


•65 


.67 


.69 


•71 


•74 


.76 


.78 


.80 


.82 


.84 


34 


56 


.52 


•56 


.60 


.62 


.64 


.66 


.68 


.70 


•72 


•74 


.76 


•78 


35 


55 


0.47 


0.51 


0^55 


0.56 


0.58 


0.60 


0.62 


0.64 


0.66 


0.67 


0.69 


0.71 


36 


54 


•43 


.46 


•49 


•51 


•53 


■H 


.56 


•58 


•59 


.61 


•^^ 


.64 


37 


53 


•38 


.41 


•44 


•45 


•47 


.48 


•50 


•51 


■^ 


•^i 


•56 


•57 


38 


52 


•33 


.36 


•39 


.40 


.41 


•43 


•44 


•45 


.46 


.48 


•49 


.50 


39 


51 


.29 


•31 


•33 


•34 


•35 


•37 


•38 


•39 


.40 


.41 


.42 


•43 


40 


50 


0.24 


0.26 


0.28 


0.29 


0.30 


0.31 


0.31 


0.32 


0-33 


0.34 


0.35 


0.36 


41 


49 


.19 


.21 


.22 


•23 


.24 


.24 


•25 


.26 


•27 


•27 


.28 


•29 


42 


48 


.14 


.16 


•17 


•17 


.18 


.18 


.19 


.19 


.20 


.21 


.21 


.22 


43 


47 


.10 


.10 


.11 


.12 


.12 


.12 


•13 


•13 


•13 


.14 


.14 


.14 


44 


46 


•05 


.05 


.06 


.06 


.06 


.06 


.06 


.07 


.07 


.07 


.07 


.07 



* " Smithsonian Meteorological Tables," p. 59. 



Smithsonian Tables. 



Tables 106-t07. 
TABLE 106. — Correction ol the Barometer for Capillarity.* 



123 



I. Metric Measure. 


Diameter 


Height of Meniscus in Millimeters. 


















of tube 


0.4 


0.6 


0.8 


1.0 


1.2 


1.4 


1.6 


1.8 


in mm. 


















Correction to be added in millimeters. 


4 


0.83 


1.22 


1-54 


1.98 


2-37 


_ 


_ 


_ 


5 


•47 


0.65 


0.86 


1.19 


1-45 


1.80 


- 


- 


6 


.27 


.41 


.56 


0.78 


0.98 


1. 21 


1-43 


- 


7 


.18 


.28 


.40 


•53 


.67 


0.82 


0.97 


1-13 


8 


- 


.20 


.29 


•3^ 


.46 


•56 


.65 


0.77 


9 


- 


•15 


.21 


.28 


•33 


.40 


.46 


•52 


10 


- 


- 


•15 


.20 


.25 


.29 


•33 


■37 


II 


- 


- 


.10 


.14 


.18 


.21 


.24 


.27 


12 


~ 


- 


.07 


.10 


•13 


•15 


.18 


.19 


13 






.04 


.07 


.10 


.12 


•13 


.14 


2. British Measure. 


Diameter 


Height of Meniscus in Inches. 


















of tube 


.01 


.02 


.03 


.04 


.05 


.06 


.07 


.08 


in inches. 


















Correction to be added in hundredths of an inch. 


•15 


2.36 


4.70 


6.86 


9-23 


11.56 


_ 


_ 


_ 


.20 


1. 10 


2.20 


3.28 


4-54 


5-94 


7.85 


- 


- 


•25 


0-55 


1.20 


1.92 


2.76 


3.68 


4.72 


5.88 


- 


•30 


•36 


0.79 


1.26 


1.77 


2.30 


2.88 


348 


4.20 


•35 


- 


•51 


0.82 


'•o5 


1.49 


1.85 


2.24 


2.6s 


.40 


- 


.40 


.61 


0.8 1 


1.02 


1.22 


1.42 


1.62 


•45 


- 


- 


•32 


•51 


0.68 


0.83 


0.96 


1-15 


.50 


- 


- 


.20 


•35 


•47 


.=;6 


.64 


0.7 1 


•55 






.08 


.20 


•31 


.40 


•47 


■52 



* The first table is from Kohlrausch (Experimental Physics), and is based on the experiments of Mendelejeff and 
Gutkowski (Jour, de Phys. Chem. Geo. Petersburg, 1877, or Wied. Beib. 1877). The second table has been calcu- 
lated from the same data by conversion into inches and graphic interpolation. 







TABLE 107. - 


- Volume of Mercury Meniscus In Cu. Mm 












Diameter of tube in mm. 








Height of 
meniscus. 




































14 


15 


16 


17 


18 


•9 


20 


21 


Z2 


23 


24 


mm. 
























1.6 


157 


i8s 


214 


245 


2S0 


,3iS 


3S6 


.398 


444 


492 


545 


1.8 


181 


211 


244 


281 


320 


362 


407 


455 


507 


560 


616 


2.0 


206 


240 


278 


3'9 


362 


409 


460 


513 


571 


631 


694 


2.2 


233 


271 


313 


3S8 


406 


459 


515 


574 


637 


704 


776 


2.4 


262 


303 


350 


400 


454 


5'i 


573 


639 


70S 


7S1 


859 


2.6 


291 


33« 


388 


444 


503 


565 


633 


706 


782 


862 


948 






Scheel und Heuse, Aiinalen der Pliysik, 33, p. 291, 1910. 








Smithsonian 


Tables. 























124 



Table 108. 



AERODYNAMICS. 

The pressure on a plane surface normal to the wind is for ordinary wind velocities expressed by 

P =^ kwav^ 
where ^ is a constant depending on the units employed, w the mass of unit volume of the air, 
a the area of the surface and v the velocity of the wind.* Engineers generally use the table of 
values of /'given by Smeaton in 1759. This table was calculated from the formula 

>p== .004922''^ 
and gives the pressure in pounds per square foot when v is expressed in miles per hour. The 
corresponding formula when v is expressed in feet per second is 

/>=. 00228 5^2. 

Later determinations do not agree well together, but give on the average somewhat lower 
values for the coefficient. The value of w depends, of course, on the temperature and the baro- 
metric pressure. Langley's experiments give /67« = .ooi66 at ordinary barometric pressure and 
10° C. temperature. 

For planes inclined at an angle a less than 90° to the direction of the wind the pressure may 
be expressed as /'a = FaP^^- 

Table 108, founded on the experiments of Langley, gives the value of Fa. for different values of 
a. The word aspect, in the headings, is used by him to define the position of the plane relative to 
the direction of motion. The numerical value of the aspect is the ratio of the linear dimension 
transverse to the direction of motion to the linear dimension, a vertical plane through which is 
parallel to the direction of motion. 

TABLE 108. —Values of Fa In Eanatlon Pa = FaP9o. 





Plane 30 in. X 4.8 in. 
Aspect 6 (nearly). 


Plane 12 in. X 12 in. 
Aspect I. 


Plane 6 in. X 24 in. 
Aspect J. 


a 


Fo. 


a 


Fa 


a 


Fa 


0° 

5 
10 

15 

20 

25 

30 
35 
40 

45 
50 


0.00 
0.28 
0.44 
0.55 
0.62 

0.66 
0.69 
0.72 
0.74 
0.76 

0.78 


0° 

5 
10 

15 
20 

25 

30 

35 
40 

45 
50 


0.00 

o.is 

0.30 
0.44 
0.57 

0.69 

0.78 
0.84 
0.88 

0.91 


0° 

5 
10 

15 
20 

25 

30 


0.00 
0.07 
0.17 
0.29 
0.43 

0.58 
0.71 



* The following pressures in pounds per square inch show roughly the influence of the shape and sire of the resist- 
ing surface (Dines' results). The wind velocity was 20.9 miles per hour. The flat plates were | in. thick. 

Square, sides 4 in 1.51 Plate, 6 in. diam. 90° cone at back 1.49 

Circle, same area 1.51 

Rectangle, 16 in. by 1 i 70 

Sguare, 12 in. sides 1.57 

Circle, same area i 55 

Rectangle, 24 in. by 6 1.59 

Square, sides 16 in 1.52 

Plate, 6 in. diam. 4I thick 1.45 

Ditto, curved side to wind 0.92 

Sphere, 6 in. diam 0.67 



Same, cone in front 0.98 

" sharp 30° cone at back 1.54 

" cone in front 0.60 

5 in. Robinson cup on 8J in. of \ in. rod .... 1.68 

Same, with back to wind 0.73 

9 in. cup on 6^ in. of § in. rod 1.75 

Same, with back to wind 0.60 

22 in. cup on 9! in. of \ in. rod 2.60 

Same, with back to wind 1.04 



Smithsonian Tables. 



Table 109. 



125 



AERODYNAMICS. 

On the basis of the results given in Table 108 Langley states the following condition for the 
soaring of an aeroplane 76.2 centimeters long and 12.2 centimeters broad, weighing 500 grams, 
— that is, a plane one square foot in area, weighing i.i pounds. It is supposed to soar in a 
horizontal direction, with aspect 6. 



TABLE 109. — Data lor the Soaring of Planes 76.2 X 12.2 cms. weighing 500 Qrams, Aspect 6. 



Inclination 
to the hori- 
zontal a. 


Soaring speed v. 


Work expended per minute 
(activity). 


Weight of planes of like 
form, capable of soaring 
at speed v with the ex- 
penditure of one horse 
power. 


Meters per 
sec. 


Feet per 
sec. 


Kilogram 
meters. 


Foot 
pounds. 


Kilograms. 


Pounds. 


2° 

5 

ID 

IS 

30 

45 


20.0 
15.2 
12.4 
II. 2 
10.6 
II. 2 


66 

50 
41 

37 
35 
37 


24 
41 
65 
86 

175 
336 


174 
297 

474 

623 

1268 

2434 


95.0 

55-5 
34-8 
26.5 
13.0 
6.8 


209 
122 

77 
58 
29 

15 



In general, if p- 



weight 



Soaring speed ^= \/ 
Activity per unit of weight 



^ Fa cos a 

7/ tan a 



The following data for curved surfaces are due to Wellner (Zeits. flir Luftschifffahrt, x., Oct, 

1893)- 

Let the surface be so curved that its intersection with a vertical plane parallel to the line of 
motion is a parabola whose height is about -^^ the subtending chord, and let the surface be 
bounded by an elliptic outline symmetrical with the line of motion. Also, let the angle of incli- 
nation of the chord of the surface be o, and the angle between the direction of resultant air 
pressure and the normal to the direction of motion be fi. Then y3 < o, and the soaring speed is 



'=^j] 



-, while the activity per unit of weight =2/ tan /3. 



^ Fg. cos 3 

The following series of values were obtained from experiments on moving trains and in the 
wind. 

Angle of inclination a = —3° 0° +3° (P 9° 12° 

Inclination factor Fa= 0.20 0.50 0.75 0.9c i.oo 1.05 

tan/3= o.oi c.02 0.03 0.04 o.io 0.17 

Thus a curved surface shows finite soaring speeds when the angle of inclination o is zero or even 
slightly negative. Above a= 12° curved surfaces rapidly lose any advantage they may have for 
small inclinations. 
Smithsonian Tables. 



126 Tables 1 10-1 12. 

TABLE 110. — Friction. 

The following table of coefficients of friction /and its reciprocal \lf, together with the angle of friction or angle of 
repose (/>, is quoted from Rankine's "Applied Mechanics.'" It was compiled by Rankine from the results of 
General Morin and other authorities, and is sufficient for all ordinary purposes. 



Material. 


/ 


1// 


* 




Wood on wood, dry 


.25-.50 


4.00-2.00 


14.0-26.5 




" " " soapy . 






.20 


5.00 


II. 5 




Metals on oak, dry 






.50-.60 


2.00-1.67 


26.5-31.0 




" " " wet 






.24-26 


4.17-3.85 


I3-5-I4.5 




" " " soapy . 






.20 


5.00 


II. 5 




" " elm, dry 






.20-.25 


5.00-4.00 


1 1. 5-14.0 




Hemp on oak, dry 






■53 


1.89 


28.0 




" " " wet 






•33 „ 


3-°°o. 


18.5 




Leather on oak 






.27-.38 


3.70-2.86 


1 5.0-19.5 




" " metals, dry . 






.56 


1.79 


29-5 




" " " wet . 






•36 


2.78 


20.0 




« « a greasy 






•23 


4-35 


13.0 




oily 






•15 


6.67 


^-5 




Metals on metals, dry . 






.15-20 


6.67-5.00 


8.5-1 i.s 




" " " wet . 






•3 „ 


3-33 


16.5 




Smooth surfaces, occasionally greased . 


.07-.08 


14.3-12.50 


4.0-4.5 




" " continually greased . 


.05 


20.00 


3-0 




" " best results .... 


.03-.036 


33-3-27-6 


1.75-2.0 




Steel on agate, dry * 


.20 


5.00 


1 1.5 




" " " oiled * 


.107 


9-35 


6.1 




Iron on stone 


•30-70 


3-33- 1 -43 


16.7-35.0 




Wood on stone 


About .40 


2.50 


22.0 




Masonry and brick work, dry .... 


.60-.70 


1.67-1.43 


33-f^35-o 




" '• " " damp mortar 


•74 


1-35 


36-5 




" on dry clay 


•51 


1.96 


27.0 




" " moist clay 


•33 


3.00 


18.25 




Earth on earth 


.25-1.00 


4.00-1.00 


14.0-45.0 




" " " dry sand, clay, and mixed earth . 


•38-75 


2.63-1 ^33 


21.0-37.0 




" " " damp clay 


1. 00 


1. 00 


45.0 




" " " wet clay . . . * . 


•31 


3-23 


17.0 




" " " shingle and gravel 


.81-1. II 


1.23-0.9 


39.0-48.0 





* Quoted from a paper by Jenkin and Ewing, " Phil. Trans. R. S." vol. 167. In this paper it is shown that in 
cases wliere " static friction " exceeds " kinetic friction " there is a gradual increase of the coefficient of friction as the 
speed is reduced towards zero. 

TABLE 111. - Lubricants. 

The best lubricants are in general the following: Low temperatures, light mineral lubricating 
oils. Very great pressures, slow speeds, graphite, soapstone and other solid lubricants. Heavy 
pressures, slow speeds, ditto and lard, tallow and other greases. Heavy pressures and high speeds, 
sperm oil, castor oil, heavy mineral oils. Light pressures, high speeds, sperm, refined petroleum 
olive, rape, cottonseed. Ordinary machinery, lard oil, tallow oil, heavy mineral oils and the 
heavier vegetable oils. Steam cylinders, heavy mineral oils, lard, tallow. Watches and delicate 
mechanisms, clarified sperm, neat's-foot, porpoise, olive and light mineral lubricating oils. 





TABLE 112. — Lubricants For Cutting Tools. 






Material. 


Turning. 


Chucking. 


Drilling. 


Tarpiiig 
Milling. 


Reaming. 


Tool Steel, 
Soft Steel, 
Wrought iron 
Cast iron, brass 
Copper 
Glass 


dry or oil 

dry or soda water 

dry or soda water 

dry 

dry 

turpentine or kerosene 


oil or s. w. 
soda water 
soda water 
dry 
dry 


oil 

oil or s. w. 

oil or s. w. 

dry 

dry 


oil 
oil 
oil 
dry 
dry 


lard oil 
lard oil 
lard oil 
dry 
mixture 



Mixture = M crude petroleum, Y^ lard oil. Oil = sperm or lard. 
Tables iii and 112 quoted from "friction and Lost Work in Machinery and Mill Work," Thurston, Wiley and Sons. 
Smithsonian Tables. 



Table 113. 
VISCOSITY. 



127 



The coefficient of viscosity is the tangential force per unit area of one face of a plate of the 
fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured 
in terms of the temporary rigidity which it gives to the fluid. Solids may be included in this 
definition when only that part of the rigidity which is due to varying distortion is considered. 
One of the most satisfactory methods of measuring the viscosity of fluids is by the observation of 
the rate of flow of the fluid through a capillary tube, the length of which is great in comparison 
with its diameter. Poiseuille* gave the following formula for calculating the viscosity coefficient 

in this case : (n = — r-rt where k is the pressure height, r the radius of the tube, s the density of 

the fluid, V the quantity flowing per unit time, and / the length of the capillary part of the tube. 
The liquid is supposed to flow from an upper to a lower reservoir joined by the tube, hence k 
and / are different. The product hs is the pressure under which the flow takes place. Hagen- 
bach t pointed out that this formula is in error if the velocity of flow is sensible, and suggested a 
correction which was used in the calculation of his results. The amount to be subtracted from 

v'^ . ^ . 

h, according to Hagenbach, is -t= — , where ^ is the acceleration due to gravity. Gartenmeister | 

\ 2 .g 

points out an error in this to which his attention had been called by Finkener, and statef that the 

quantity to be subtracted from h should be simply — ; and this formula is used in the reduction 

of his observations. Gartenmeister's formula is the most accurate, but all of them nearly agree 
if the tube be long enough to make the rate of flow very small. None of the formulas take into 
account irregularities in the distortion of the fluid near the ends of the tube, but this is probably 
negligible in all cases here quoted from, although it probably renders the results obtained by the 
" viscosimeter " commonly used for testing oils useless for our purpose. 

The term "specific viscosity" is sometimes used in the headings of the tables; it means the 
ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified tem- 
perature. 

dv 

The friction of a fluid is proportional to the size of the rubbing surface, to —, where v is the 

velocity of motion in a direction perpendicular to the rubbing surface, and to a constant known 
as the viscosity. 







(a) Variation of Viscosity of Water, with Temperature 


. Dynes per sq. cm. 








a. 
9 ■ ; 


Poiseville. 


Sprung. 


SloUe. 


Thorpe-Rogers. 


Hosking. 




Slotte. 


Thorpe-Rogers 


Hosking. 




H 


1846. 


1876. 


1883. 


i894.§ 


1909.11 




1883. 


1894. 


1909.11 




0° 


O.OI716 


0.01778 


0.01808 


C.OI778 


0.01793 


55° 


0.00510 


0.00506 


.00508 




5 


.01515 


.01510 


.01524 


.01510 


.01522! 


60 


.00472 


.00468 


.00469 




10 


.01309 


.01301 


.01314 


•01303 


.013101 


65 


.00438 


.00436 


.00436 




15 


.01146 


.01135 


.01144 


.01134 


.01142 


70 


.00408 


.00406 


.00406 




20 


.oiooS 


.01003 


.01008 


.01002 


.01006 


75 


.00382 


.O03S0 1 .00380 




=5 


.00897 


.00896 


.00806 


.00891 


.C0893 


80 


.00358 


.00356 > .00356 




.lo 


.00S03 


.00S02 


.00S03 


.00798 


.00800 1 


«5 


•00337 


•00335 ' -00335 




^^ 


.00721 


.00723 


.00724 


.00720 


.00724 


90 


.003 1 8 


.00316 .00316 




40 


.00653 


.00657 


.00657 


.00654 


.00657 


95 


.00301 


.00299 .00300 




45 


.00595 


.00602 


.00602 


.00597 


.00600 


100 


.00285 


.00283 .0028411 




50 




•00553 


•00553 


.00548 


.00550 


153 


" 


.0018111 




(b) Variation oi Specific Viscosity of Water with Temperature, u 




0° 


1. 000 


25° 


0.498 


50° 


0.307 


7 5° 


0.212 


100° 


0.158 




,0 
3 


•S49 


30 


.446 


55 


.283 


80 


.199 


124° 


.I241F 




10° 


■730 


35 


.404 


60 


.262 


«5 


.1S7 


153° 


•loiir 




15° 


.637 


40 


•367 


65 


•243 


90 


.176 




- 




20° 


.561 


45 


•335 


70 


.226 


95 


.167 









* " Cotuptes rendus," vol. 15, 1842; "Mem. Serv. Etr." 1846. 

t " Poga;. Ann." vol. log, i860. 

t " Zeitschr. Phys. Chem." vol. 6, 1890. 

§ Thorpe and Rogers, " Philos. Trans." 185A, p. 397, 1894; " Proc. Roy. Sec." 55, p. 14S, 1894. 

II Hosking, Phil. Mag. 17, p. 502, 1909; 18, p. 260, 1909. 

11 de Haas, Diss. Leiden, 1894. 



Smithsonian Tables. 



128 



Tables 114-116. 



VISCOSITY. 

TABLE 114. — Solution of Alcohol In Water.* 

CoeiScients of viscosity, in C. G. S. units, for solution of alcohol in water. 









Percentage by wei 


ght of alcohol in the mixture. 






Temp. 
C. 









































8.21 


16.60 


34- .S8 


43-99 


53-36 


7S-7S 


87-45 


99-72 


0° 


0.0181 


0.0287 


0.0453 


0.0732 


0.0707 


0.0632 


0.0407 


0.0294 


0.0180 


5 


•0152 


.0234 


•0351 


.0558 


.0552 


.0502 


•0344 


.0256 


.0163 


lO 


.0131 


.0195 


.0281 


•0435 


.0438 


.0405 


.0292 


.0223 


.0148 


15 


.0114 


.0165 


.0230 


•0347 


•0353 


•0333 


.0250 


.0195 


.0134 


20 


.0101 


.0142 


.0193 


.0283 


.0286 


.0276 


.0215 


.0172 


.0122 


25 


0.0090 


0.0123 


0.0163 


0.0234 


0.0241 


0.0232 


0.0187 


0.0152 


O.OIIO 


30 


.0081 


.0108 


.0141 


.0196 


.0204 


.0198 


.0163 


•0135 


.0100 


35 


.0073 


.0096 


.0122 


.0167 


.0174 


.0171 


.0144 


.0120 


.0092 


40 


.0067 


.0086 


.0108 


.0143 


.0150 


.0149 


.0127 


.0107 


.0084 


45 


.0061 


.0077 


.0095 


.0125 


.0131 


.0130 


•01 13 


.0097 


.0077 


50 


0.0056 


0.0070 


0.0085 


0.0109 


O.OII5 


0.0115 


0.0102 


0.0088 


0.0070 


55 


.0052 


.0063 


.0076 


.0096 


.0102 


.0102 


.0091 


.0086 


.0065 


60 


.0048 


.0058 


.0069 


.0086 


.0091 


.0092 


.0083 


.0073 


.0060 



The following tables (115-116) contain the results of a number of experiments in the viscosity of mineral oils denved 
from petroleum residues and used for lubricating purposes.! 



TABLE 115. -Mineral Olls.l 



TABLE 116. -Oils. 







M 




Sp. viscosity. Water at 


>. 


'^ c 


.s — 


20° C. = I. 












B 


^^ 


n^«- 








Q 


° c. 


° C. 


20° C. 


50° C. 


100° C. 


■931 


243 


274 


_ 


11.30 


2.9 


.921 


216 


24b 


- 


7-31 


2-5 


.906 


189 


208 


- 


3-45 


1-5 


.921 


163 


190 


_ 


27.80 


2.8 


.917 


132 


168 


- 


- 


2.6 


.904 


170 


207 


8.65 


2.65 


1-7 


.891 


151 


182 


4-77 


1.86 


1-3 


.878 


108 


148 


2.94 


1.48 




.855 


42 


45 


1.65 


- 


- 


.90s 


i6s 


202 


- 


3.10 


1-5 


.894 


1,39 


270 


7.60 


3.60 


1-3 


.866 


90 


224 


2.50 


1.50 





Oil. 


>. 


C ^ 

'£ c 


C .- 

•=.E 


0, ;o 






b 


P3 


oO 0- 




Q 


°c. 


°c. 


> 2-S 


Cylinder oil . . 


.917 


227 


274 


191 


Machine oil . . 


.914 


213 


260 


102 


Wagon oil . . 


.914 


148 


182 


80 


" " . . 


.911 


1^7 


187 


70 


Naphtha residue 


.910 


134 


162 


55 


Oleo-naphtha . 


.910 


219 


2.S7 


121 


" " 


.904 


201 


242 


66 


" " 


.894 


184 




26 


Oleonid . . . 


.884 


i8s 


217 


28 


best 










quality 


.881 


1 88 


224 


20 


Olive oil . . . 


.916 


_ 


_ 


22 


Whale oil . . 


.87Q 


- 


- 


9 




•875 


" 


" 


8 



* This table was calculated from the table of fluidities given by Noack (Wied. Ann. vol. 27, p. 217), and showsa 
maximum for a solution containing about 40 per cent of alcohol. A similar result was obtained for solutions of acetic 
acid. 

t Table 115 is from a paper by Engler in Dingler's " Poly. Jour." vol. 268, p. 76, and Table 116 is from a paper by 
Lamansky in the same journal, vol. 248, p. 2g. The very mixed composition of these oils renders the viscosity a very 
uncertain quantity, neither the density nor the flashing point being a good guide to viscosity. 

t The different groups in this table are from different residues. 

Smithsonian Tables. 



Table 117. 
VISCOSITY. 



129 



This table gives some miscellaneous data as to the viscosity of liquids, mostly referring to oils and paraffins. The 

viscosities are in C. G. S. units. 



Liquid. 


G.% 


Coefficient 
of 

viscosity. 


Temp. 
Cent.° 


Authority. 




Ammonia 




0.0160 
0.0149 


II.9 
14.5 


Poiseuille. 




Anisol 




O.OI 1 1 


20.0 


Gartenmeister. 




Colophonium .... 




3 X 10I6 


15- 


Reiger. 




Di-ethyl ether .... 




0.00276 


6^7 


Thorpe, Roger. 




Glycerine 






42.20 
25.18 

13-87 
8.30 
4.94 


2.8 

8.1 
14-3 
-0-3 
^6.5 


Schottner. 
« 




Glycerine and water 
(1 « 


94.46 
80.31 
64.05 
49-79 


7-437 
1. 02 1 
0.222 
0.092 


8-5 
8.5 

8-5 
8-5 






Glycol 




0.0219 


0.0 


Arrhenius. 




Menthol, solid .... 
" liquid .... 




209 X loio 
0.069 


14.9 
34 9 


Heydweiller. 




Mercury* 




0.0184 
C.0170 
0.0157 
0.0122 
0.0102 
0.0093 


— 20 

0.0 

20.0 

1 00.0 

200.0 

300.0 


Koch. 
« 




Meta-cresol 




0.1878 


20.0 


Gartenmeister. 




1 Olive oil 




0.9S90 


15.0 


Brodmann. 




Paraffins: Decane 

Dodecane 
Heptane 
Hexadecane . 
Hexane 
Nonane 




0.0077 
0.0126 
0.0045 
0.0359 
0.0033 
0.0062 


22.3 

233 

24.0 
22.2 

23-7 
22.3 


Bartolli & Stracciati. 

It K 
« « 

« X 




Octane 
Pentane 
Pentadecane . 
Tetradecane . 
Tridecane 
Undecane 




0.0053 
0.0026 
0.0281 
0.0213 
0.0155 
0.0095 


22.2 
21.0 
22.0 
21.9 

23-3 
22.7 


« « 
« « 
t< i< 




Petroleum (Caucasian) 




0.0190 


17-S 


Petroff. 




Phenol 




0.127 


18.3 


Scarpa. 




Rape oil 




25-3 
3-85 
1.63 
0.96 


0.0 

lO.O 

20.0 
30.0 


0. E. Meyer. 

« 
« 





♦Calculated from the formula ^t = .oi7 — .000066; + . oooooozii^ — .00000000025^ (vide Koch, Wied. Ann. vol. 14, 

r. issi). 

Smithsonian Tables. 



I30 



Table i 18. 
VISCOSITY. 



This table gives the viscosity of a number of liquids together with their temperature variation. 
The headings are temperatures in Centigrade degrees, and the numbers under them the coeffi- 
cients of viscosity in C. G. S. units.* 



Liquid. 


Temperature Centigrade. 




c 
























0° 


10° 


20° 


30° 


40° 


50° 


70° 


90° 


« 


Acetates : Methyl 


_ 


.0046 


.0041 


.0036 


.0032 


.0030 


_ 


_ 


I 


Ethyl 


- 


.0051 


.0044 


.0040 


•0035 


.0032 


- 


- 


I 


Propyl 


- 


.0066 


.0059 


.0052 


.0044 


.0039 


- 


- 


I 


Allyl 


- 


.0068 


.0061 


.0054 


.0049 


.0044 


- 


- 


I 


Amyl 


- 


.0106 


.0089 


.0077 


.0065 


.0058 


- 


- 


I 


Acids: Formic 


- 


.02262 


.01804 


.01465 


.01224 


.01025 


- 


- 


2 


Acetic 


- 


•01 50 


.0126 


.0109 


.0094 


.0082 


- 


- 


I 


Propionic 


- 


.0125 


.0107 


.0092 


.0081 


•0073 


- 


- 


3 


" 


- 


.0139 


.0118 


.0101 


.0091 


.ooSo 


- 


- 


I 


Butyric 


- 


.0196 


.0163 


.0136 


.0118 


.0102 


- 


- 


2 


Valeric 


- 


.0271 


.0220 


.0183 


■0155 


.0127 


- 


- 


3 


Salicylic 


- 


.0320 


.0271 


.0222 


.0181 


.0150 


- 


- 


3 


Alcohol : Methyl 


.00813 


.00686 


.00591 


.00515 


.00450 


.00396 


- 


- 


4 


Ethyl 


.01770 


.01449 


.01192 


.00990 


.O082S 


.00698 


.00504 


- 


4 


Propyl 


.03882 


.02917 


.02255 


.01778 


.01403 


.01128 


.00757 


.00526 


4 


Butyric 


.05185 


.03872 


•02947 


.02266 


.OI7S0 


.01409 


.00926 


.00633 


4 


Allyl 


.02144 


.01703 


.01361 


.01165 


.00911 


.00760 


.00548 


.00407 


4 


Isopropyl 


.04564 


•03245 


.02369 


.01755 


.01329 


.01026 


.00642 


- 


4 


Isobutyl 


.08038 


•05547 


.03906 


.02863 


.02121 


.01609 


.00973 


•00633 


4 


Amyl (op.-inac.) 


.08532 


.06000 


•04341 


.03206 


.02414 


.01849 


.01147 


.00758 


4 


Aldehyde 


.00267 


.00244 


.00222 


- 


- 


- 


- 


- 


3 


Aniline 


- 


- 


.0440 


.0319 


.0241 


.0189 


- 


- 


5 


Benzole 


.00902 


.00759 


.00649 


.00562 


.00492 


.00437 


•00351 


- 


4 


Bromides : Ethyl 


.00478 


.00432 


.00392 


■00357 


- 


- 


- 


- 


4 


Propyl 


.00645 


•00575 


.00517 


.00467 


.00425 


.00388 


.00328 


- 


4 


Allyl 


.00619 


.00552 


.00496 


.00449 


.00410 


•00374 


.00316 


- 


4 


Ethylene 


•0243s 


.02035 


.01716 


.01470 


.01280 


.01124 


.00895 


•00733 


4 


Carbon bisulphide 


.00429 


.00396 


.00367 


.00342 


.00319 


- 


- 


- 


4 


Carbon dioxide (liq.) 


.00099 


.OO0S5 


.0007 I 


- 


- 


- 


- 


- 


6 


Chlorides : Propyl 


.00436 


.00390 


•00352 


•00319 


,00291 


- 


- 


- 


4 


Allyl 


.00402 


.00358 


.00322 


.00292 


- 


- 


- 


- 


4 


Ethylene 


.01128 


.00961 


■00833 


.00730 


.00646 


.00576 


.00470 


- 


4 


Chloroform 


.00700 


.00626 


.00564 


.0051 I 


.00466 


.00390 


- 


- 


4 


Ether 


- 


.0026 


•0023 


.0021 


- 


- 


- 


- 


I 


Ethylbenzole 


.00874 


.00758 


.00666 


.00592 


.00529 


.00477 


.00394 


•00330 


4 


Ethylsulphide 


.00559 


.00496 


.00444 


.00401 


.00363 


•00331 


.00279 


•00237 


4 


Iodides : Methyl 


.00594 


.00536 


.00487 


.00446 


.00409 


- 


- 


-> 




Ethyl 


.00719 


.00645 


•OO5S3 


•00530 


.00484 


.00444 


•00378 


- 




Propyl 


.00938 


.00827 


•00737 


.00662 


.OO59S 


•00544 


.00456 


•00387 


4 


Allyl 


.00930 


.O0S19 


.00726 


.00652 


.OO5S8 


•00534 


.00448 


.00381 


4 


Metaxylol 


.00802 


.00698 


.00615 


•00547 


.00491 


.00444 


.00369 


•00313 


4 


Nitrobenzene 


- 


- 


.0203 


.0170 


.0144 


.0124 


- 


- 


I 


Paraffines : Pentane 


.00283 


.00256 


.00232 


.00212 


- 


- 


- 


- 


4 


Hexane 


.00396 


■00355 


.00320 


.00290 


.00264 


.00241 


.00221 


- 


4 


Heptane 


.00519 


.00460 


.00410 


.00369 


•00334 


.00303 


•00253 


.00214 


4 


Octane 


.00703 


.0061 2 


•OO53S 


.00478 


.00428 


.00386 


.00318 


.00266 


4 


Isopentane 


.00273 


.00246 


.00223 


.00204 


- 


- 


- 


- 


4 


Isohexane 


.00371 


•00332 


.00300 


.00272 


.00247 


.00226 


- 


- 


4 


Isoheptane 


.00477 


.00423 


•00379 


•00342 


.00309 


.00282 


.00235 


.00200 


4 


Propyl aldehyde 


- 


.0047 


.0041 


.0036 


•0033 


- 


- 


- 


I 


Toluene 


.00768 


.00668 


.00586 


.00520 


.00466 


.00420 


.00348 


.00292 


4 


I Pribram-Handl, Wien. Ber. 78 


,1878,80,1879,84, 1897; Proc. Roy. Soc. 55, 1894, 60, 1896; . 


our. 


1881. 


Chem. Soc. 71, 1897; Cham. News, 75, 1897. 




2 Gartenmeister, Zeitschr. Phys 


Chera. 6, 1890. 5 Wijkander, Wied. Beibl. 3, 1879. 




3 Rellstab, Diss. Bonn, 1868. 


6 Warburg-Babo, Wied. Ann. 17, 1S82. 




4 Thorpe-Roger, Philos. Trans. 


18s A, 1894, 189 A, 





* Calculated from the specific viscosities given in Landolt & Bbrnstein's Phys. Chem. Tab. 
For inorganic acids, see Solutions. 
Smithsonian Tables. 



Table 119. 
VISCOSITY OF SOLUTIONS. 



131 



This table is intended to show the effect of change of concentration and change of temperature on the viscosity of 
solutions of salts in water. The specific viscosity X loo is given for two or more densities and for several tem- 
peratures in the case of each solution, fi stands for specific viscosity, and t for temperature Centigrade. 



Salt. 


Percentage 
by weit^ht 
of salt ni 
solution. 


Density. 


^ 


t 


M 


t 


M 


t 


M 


t 


Authority. 


BaCl2 


7.60 
15.40 
24-34 


- 


77-9 

86.4 

100.7 


10 

t( 


44-0 
56.0 
66.2 


30 
« 


35-2 
39-6 
47-7 


5f 


- 


- 


Sprung. 


Ba(N03)2 


2.98 
5.24 


1.027 
1. 05 1 


62.0 
68.1 


15 


51-1 

54-2 


25 


42.4 
44-1 


35 


34-8 
36-9 


45 


Wagner. 


CaCla 
« 


15.17 
31.60 

3975 
44.09 


- 


1 10.9 

272.5 
670.0 


10 


71-3 
177.0 

379-0 

593-1 


■1? 


50-3 
124.0 

245-5 
363-2 


5f 


- 


- 


Sprung. 

(1 


Ca(N03)2 


17-55 
30.10 
40.13 


1. 171 

1.274 
1.386 


93-8 
1 44- 1 
242.6 


IS 


74.6 
112.7 
217.1 


25 


60.0 
90-7 
156-5 


35 


49-9 

75-1 

1 28. 1 


45 


Wagner. 


CdCla 


11.09 
16.30 
24.79 


1. 109 
1. 181 
1.320 


77-5 
88.9 
104.0 


15 


60.5 

70.5 
80.4 


25 


49-1 

57-5 
64.6 


35 


40.7 
47.2 
53-6 


45 

(1 


« 


Cd(N03)2 


7.81 
15.71 
22.36 


1.074 

1-159 
1.241 


61.9 
71.8 
85.1 


15 


50.1 
58.7 
69.0 


25 


41. 1 

48.8 
57-3 


35 


34-0 
41-3 
47-5 


45 


<( 


CdS04 


7.14 
14.66 
22.01 


1.068 
1. 159 
1.268 


78.9 

96.2 

120.8 


15 


61.8 
72.4 
91.8 


25 


49-9 
58.1 

73-S 


35 


41-3 
48.8 
60.1 


45 


« 


C0CI2 


7-97 
14.86 
22.27 


1. 08 1 
1. 161 
1.264 


83.0 
1 1 1.6 
161.6 


IS 


65.1 

85.1 

126.6 


25 


53-6 
1 01 .6 


35 


44-9 
58.8 
85.6 


45 
11 


(1 


C0(N03)2 


8.28 
15.96 
24-53 


1-073 
1. 144 
1.229 


74-7 
87.0 
1 10.4 


IS 


69.2 
88.0 


25 


48.7 

55-4 
71-5 


35 


39-8 
44-9 
59-1 


45 




C0S04 

« 


7.24 
14.16 
21.17 


1.086 

1-159 
1.240 


86.7 
1 17.8 
193.6 


IS 


68.7 

95-5 
146.2 


25 


55-0 

76.0 

1 13-0 


35 


45-1 
61.7 
89-9 


45 


« 

u 


CuCla 


12.01 
21-35 
33-03 


1. 104 
1-215 
1-331 


87.2 
121.5 
178.4 


IS 


67.8 

95-8 

137-2 


25 


SS-i 

77-0 

107.6 


35 


45.6 


45 


t< 


Cu(N03)2 


lis 

46.71 


1. 177 
1.264 
1-536 


97-3 
126.2 
382.9 


IS 


76.0 

98.8 

283.8 


25 


61.S 

80.9 

215-3 


35 


172.2 


45 


" 


CUS04 

it 
(( 


6.79 

12.57 
17.49 


1-055 
1.115 
1. 163 


79-6 
98.2 
124.5 


15 

It 


61.8 
74.0 
96.8 


25 


49-8 
59-7 
75-9 


35 


41.4 
52-0 
61.8 


45 


« 
« 


HCl 

t( 


8.14 
16.12 
23.04 


1-037 
1.084 
1. 114 


71.0 
80.0 
91.8 


15 


57-9 
66.5 

79-9 


25 


48.3 
56-4 
65-9 


35 


40.1 
48.1 
56-4 


45 


« 
« 
« 


HgCl2 


0.23 
3-55 


1.002 
1-033 


76.75 


10 


58-5 
59-2 


20 


46.8 
46.6 


P 


38.3 

38-3 


40 


« 



Smithsonian Tagles. 



132 



Table 119 {coHtinutd). 
VISCOSITY OF SOLUTIONS. 



Salt. 


Percentage 
by weight 
of salt in 
solution. 


Density. 


f* 


t 


!>■ 


/ 


ft 


t 


^ 


/ 


Authority. 


HNO3 

(1 


8.37 
12.20 
28.31 


1.067 
1. 116 
1. 178 


66.4 
69.5 
80.3 


15 


54-8 
57-3 
65-5 


25 


45-4 
47-9 
54-9 


35 


37-6 
40.7 
46.2 


45 


Wagner. 


H2SO4 


7.87 
15.50 
2343 


1.065 
1-130 
1.200 


77-8 
95.1 
122.7 


15 


61.0 
75-0 
95-5 


25 
(1 


50.0 
60.5 

77-5 


35 
11 


41.7 
49.8 
64-3 


45 


"' 


KCl 


10.23 

22.21 


- 


70.0 
70.0 


10 


46.1 
48.6 


3p 


33-1 
36-4 


sp 


- 


- 


Sprung. 


KBr 


14.02 
23.16 
3464 


_ 


67.6 
66.2 
66.6 


10 


44-8 
44-7 
47.0 


2P 
I' 


32.1 

33-2 
35-7 


sp 


_ 


: 


u 


KI 

(1 


8.42 
17.01 
33-03 
45-98 
54.00 


- 


69.5 

65-3 
61.8 
63.0 
68.8 


10 

11 


44.0 

42.9 
42.9 

45-2 
48.5 


3p 


31-3 
31-4 
32-4 
35-3 
37-6 


5p 


- 


- 


n 


KCIO3 


3-51 
5.69 


- 


71.7 


10 


44-7 
45.0 


30 


31-5 
31-4 


5f 


- 


- 


" 


KNO3 


6.32 
12.19 
17.60 


~ 


70.8 
68.7 
68.8 


10 


44-6 
44.8 
46.0 


30 


31.8 
32-3 
33-4 


5p 


~ 


~ 


" 


K2SO4 


5-17 
9-77 


- 


77-4 
81.0 


10 


48.6 

52-0 


3p 


34-3 
36-9 


5p 


- 


- 


'"' 


KaCrOi 


"■93 
19.61 
24.26 
32-78 


1-233 


75-8 
85-3 
97-8 
109.5 


10 


62.5 
68.7 

74-5 
88.9 


30 


41.0 
47-9 


40 


- 


- 


Slotte. 
Sprung. 


KaCroOv 


4.71 
6.97 


1.032 
1.049 


72.6 
73-1 


10 
It 


55-9 
56-4 


20 


45-3 
45-5 


30 


37-5 
37-7 


40 


Slotte. 


LiCl 


7.76 

13-91 
26.93 


- 


96.1 
121.3 
229.4 


10 


59-7 

75-9 

142.1 


3f 


41.2 
52.6 
98.0 


50 


i 


: 


Sprung. 
II 


Mg(N03)2 


18.62 
34-19 
39-77 


1. 102 
1.200 
1.430 


99.8 

213-3 
317-0 


15 


81.3 
164.4 
250.0 


25 


66.5 
132.4 
191.4 


35 


56.2 
109.9 
1 58. 1 


45 


Wagner. 
i< 


MgSOi 


4.98 

9-50 
19.32 


~ 


96.2 
130.9 

302.2 


10 


59-0 

77-7 

166.4 


3f 


40.9 

53-0 
106.0 


5p 


~" 


_ 


Sprung. 


MgCi04 


12.31 
21.86 
27.71 


1.089 
1. 164 
1. 217 


111.3 
1 67. 1 
232.2 


10 


84.8 

125-3 
172.6 


20 


67.4 

99.0 

133-9 


3p 


55-0 

79-4 

106.6 


40 


Slotte. 


MnCl2 
t< 


8.01 
15-65 
30-33 
40.13 


1.096 
1. 196 
1-337 
1-453 


92.8 
130.9 
256.3 
537-3 


15 


71. 1 

104.2 
193.2 
393-4 


25 


57-5 
84.0 

155-0 
300.4 


35 


48.1 

68.7 

123.7 

246.5 


45 


Wagner. 



Smithsonian Tables. 



Table 119 (conUmitd). 
VISCOSITY OF SOLUTIONS. 



133 



Salt. 


Percentage 
by weight 
of salt in 
solution. 


Density. 


M 


i 


ft 


/ 


f* 


t 


(i 


t 


Authority. 


Mn(N03)2 


1S.31 
29.60 

49-31 


1. 148 

1-3-3 
1.506 


96.0 

167.5 
396.8 


15 


76.4 
126.0 
301. 1 


25 


64-5 
104.6 
221.0 


35 


55-6 
88.6 
188.8 


45 


Wagner. 


MnS04 


11-45 
1S.80 
22.08 


1. 147 
I.251 
1.306 


129.4 
228.6 
661.8 


15 


98.6 
172.2 
474-3 


25 


78.3 
1 37- 1 
347-9 


35 


63-4 
107.4 
266.8 


45 


« 


NaCl 


7-95 
14-31 

23.22 


: 


82.4 
94-8 
1-^8.3 


10 


52.0 
60.1 
79-4 


3f 


31-8 
36-9 
47-4 


50 
It 


_ 


_ 


Sprung. 


NaBr 


9-77 
1 8. 58 
27.27 


_ 


75-6 
82.6 

95-9 


10 


48.7 

53-5 
61.7 


3f 


34-4 
38.2 

43-8 


50 


- 


- 


« 
« 
« 


Nal 


8.83 
17-15 
35-69 
55-47 


- 


73-1 
73-8 
86.0 

157-2 


10 


46.0 
47-4 
55-7 
96.4 


30 


32-4 
33-7 
40.6 
66.9 


50 


; 


; 


" 


NaClOs 


11.50 

20.59 
33-54 


_ 


78.7 

88.9 

121.0 


10 


50.0 
56.8 

75-7 


3f 


35-3 
40.4 
53-0 


50 


- 


- 


"' 


NaNOs 


7.25 

12.35 
18.20 

31-55 


- 


75-6 
81.2 
87.0 
121. 2 


10 


47-9 
51.0 

55-9 
76.2 


3f 


33-8 
36.1 

39-3 
53-4 


5f 


- 


- 


« 


Na2S04 


4.98 

9-50 
14.03 
19.32 


- 


96.2 
130.9 
187.9 
302.2 


10 


59.0 

77-7 
107.4 
166.4 


30 


40.9 

53-0 

71. 1 

106.0 




- 


- 


« 


Na2Cr04 
« 


S-76 
10.62 
14.81 


1.058 
1. 112 
1. 164 


85.8 
103-3 
127-5 


10 


66.6 

79-3 
97.1 


20 


53-4 
63-5 
77-3 


3p 


43-8 
63.0 


40 


Slotte. 

ii 


NH4CI 


3-67 

8.67 

15.68 

23-37 


- 


69.1 

67-3 
67.4 


10 


45-0 
45-3 
46.2 

47-7 


3f 


31-9 
32.6 

34-0 
36.1 


SO 


- 


- 


Sprung. 


NHiBr 


15-97 
25-33 
36.88 


- 


65.2 
62.6 
62.4 


10 


43-2 
43-3 
44.6 


3f 


31-5 
32-2 
34-3 


SO 


- 


- 


« 
« 


NH4NO3 


5-97 
12.19 
27.08 
37.22 
49-83 


- 


69.6 
66.8 
67.0 
71.7 
81. 1 


10 
« 

« 


44-3 
44-3 
47-7 
51.2 

63-3 


30 
« 


31.6 
31-9 
34 9 
38.8 
48.9 


SO 
(1 


- 


- 


« 


(NH4)2S04 


8.10 
15-94 

25-51 


- 


107.9 
120.2 
148.4 


10 
« 


52-3 
60.4 
74.8 


30 


37-0 
43-2 
54.1 


5f 


- 


- 


« 
« 



Smithsonian Tables. 



134 



Table 119 {.continued). 
VISCOSITY OF SOLUTIONS. 



Salt. 


Percentage 
by weight 
of salt in 
solution. 


Density. 


M 


t 


f* 


/ 


M 


/ 


M 


t 


Authority. 


(NH4)2Cr04 


10.52 

1975 
28.04 


1.063 
1. 120 
I-I73 


79-3 
88.2 

lOI.I 


10 


62.4 
70.0 
80.7 


20 


57-8 
60.8 


30 


42.4 
48.4 
56-4 


40 


Slotte. 


(NH4)2Cr207 
>< 


6.S5 
13.00 

19-93 


1.039 
1.078 
1. 126 


77-6 


10 


56.3 

57-2 
58.8 


20 


45-8 
46.8 
48.7 


3p 


38-0 

39-1 
40.9 


40 





NiCla 


11.45 
22.69 
30.40 


1. 109 
1.226 
1-337 


90.4 
140.2 
229.5 


15 


70.0 
109.7 
171.8 


25 


57-5 

87.8 

X39.2 


35 


48.2 

72.7 

1 1 1. 9 


45 


Wagner. 


Ni(N03)2 


16.49 
30.01 
40.95 


1. 136 
1.278 
1.388 


90.7 

135-6 
222.6 


15 


70.1 
105.9 
169.7 


25 


57-4 
85-5 
128.2 


35 


48.9 

70.7 

152-4 


45 


<( 


NiSOi 


10.62 
18.19 
25-35 


1.092 
1. 198 
1-314 


94.6 
154-9 
298-5 


15 


73-5 
"9-9 
224.9 


25 

(1 


60.1 

99-5 

173-0 


35 
(1 


49.8 

75-7 
152.4 


45 


u 


Pb(N03)2 


17-93 
32.22 


1. 179 
1.362 


74-0 
91.8 


15 


59-1 
72-S 


25 


48.5 
59-6 


35 


40-3 
50.6 


45 


" 


Sr(N03)2 


10.29 
21.19 
32.61 


1.0S8 
1. 124 
1-307 


69-3 
87.3 
1 1 6.9 


15 


56.0 
69.2 
93-3 


25 


45-9 
57-8 
76.7 


35 


39-1 
48.1 
62.3 


45 


t( 


ZnCla 


15-33 
23-49 
33-78 


1.146 
1.229 
1-343 


93-6 
111.5 
151.7 


IS 


72.7 

86.6 

1x7.9 


25 


57-8 
69.8 
90.0 


35 


48.2 

57-5 
72.6 


45 




Zn(N03)2 


15-95 
30-23 
44-5° 


1. 115 
1.229 
1-437 


80.7 
104.7 
167.9 


15 


64-3 
85.7 
130.6 


25 


52.6 

695 
105.4 


35 


43-8 
57-7 
87.9 


45 




ZnS04 


7.12 
16.64 
23.09 


1. 106 
1. 195 
1. 281 


97-1 
156.0 
232.8 


15 


79-3 
1 18.6 

177-4 


25 


62.7 

94-2 

135-2 


35 


51-5 

73-5 

108. 1 


45 


« 



Smithsonian Tables. 



Tablc 1 20. 
SPECIFIC VISCOSITY.* 



135 



Dissolved salt. 


Normal solution. 


i normal. 


i normal. 


i normal. 


Authority. 




.§- 


^ 


>> 


*l 


>, 




>> 


S'S 






s 
Q 






a ^ 


B 

Q 


■5 


c 










Acids : CI2O3 . . 
HCl . . . 


1.0562 


I.OI2 


1.0283 


1.003 


I.OI43 


1. 000 


1.0074 


0.999 


Reyher. 




I.0177 


1.067 


1.0092 


1.034 


1.0045 


1.017 


1.0025 


1.009 


" 




HCIO3 . . 


I.04S5 


1.052 


1.0244 


1.025 


I.OI26 


1.014 


1.0064 


1 .006 


•( 




HNOs . . 


1.0332 


1.027 


1. 01 68 


I.OI I 


1 .0086 


1.005 


1.0044 


1.003 


" 




II2SO4 . . 


1-0303 


1.090 


1.0154 


1.043 


1.0074 


1.022 


1-0035 


I .008 


Wagner. 




Aluminium sulphate 


1.0550 


1.406 


1.027S 


1. 178 


I.OI38 


1.082 


1.0068 


1.038 


>< 




Barium chloride . . 


1.0884 


I.I23 


1. 044 1 


1.057 


1.0226 


1.026 


I.OII4 


I.OI3 


" 




" nitrate . . 


- 




1.0518 


1.044 


1.0259 


1.021 


1.0130 


1.008 


" 




Calcium chloride 


1.0446 


1. 156 


1. 02 1 8 


1.076 


I.OI05 


1.036 


1.0050 


I.OI7 


" 




" nitrate . . 


1.0596 


1. 117 


1 .0300 


1-053 


I.015I 


1.022 


1.0076 


1.008 


*' 




Cadmium chloride . 


1.0779 


I-I34 


1.0394