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THE 



PHILOSOPHICAL TRANSACTIONS 

OF THE 

ROYAL SOCIETY OF LONDON, 

FROM THEIR COMMENCEMENT, IN 1665, TO THE YEAR 1800; 

WITH NOTES AND BIOGRAPHIC ILLUSTRATIONS, 

BY 

CHARLES HUTTON, LL.D. F.R.S. 
GEORGE SHAW, M.D. F.R.S. F.L.S. 
RICHARD PEARSON, M.D. F.S.A. 



VOL. XV 

from 1781 to 1785. 



LONDON: 
PRINTED BY AND FOR C. AND R. BALDWIN, NEW BRIDGE-STREET, BLACK.FRIARS. 

1809- 



5 o 4 

\\SI2L 



' - £ tff. 



LOAN STACK 



CONTENTS OF VOLUME FIFTEENTH. 



CHI 



Page 

Forster on the Tyger-Cat of the Cape .... 1 

Kirwan, on various Saline Substances .... 3 

Brereton, on a Storm of Lightning 21 

Dobson, on the African Harmattan 23 

Hunter, New Method of the Screw 28 

Pennant, Account of the Turkey 32 

E. Pigott, on a Nebula in Coma Berenices. 37 

N. Pigott, on some Double Stars 38 

Rennell, on the Ganges and Burrampooter. 39 

Herschel, Rotation of the Earth and Planets. 50 

Smeathman, on the Termites of Africa, &c. 60 

Pennant, on Earthquakes in Wales 85 

Stanhope, Earl, on the Roots of Equations. 86 

De La Trobe, Meteor. Journ. at Labrador. . 87 

Royal Society, at London. 87, 277 

Thompson, Experiments on Gunpowder. . . 88 

Cavallo, Luminous Appearance in the Sky. 114 

J. Lloyd, Earthquake near Denbigh 115 

Blagden, Heat of the Gulf-Stream ibid 

Englefield, the Soil at opening a Well 117 

N. Pigott, Astronomical Observations ibid 

Barker, Meteorolog. Journ. 118, 277, 396*, 543 

Bland, Deaths, &c. from Parturition 118 

Wright, a Child born with the Small-pox. . 123 

Kerr, on the Gum Lacca Insect 1 24 

Marsden, a Phenomenon at Sumatra 127 

P. Wilson, Exper. on Cold at Glasgow .... 129 

Atwood, on the Mensuration of Angles. . . 133 

Broussonet, on the Ophidium Barbatum. . . 134 

Marsham, on Washing the Stems of Trees. 138 

Wales, on the Roots of Affected Equations. 139 

Crawford, Power of AnimalstoproduceCold. 147 

Herschel, on a Comet, or the New Planet. . 154 

, Micrometer for Angle of Position. 1 55 

Willard, on the Long, of Camb. in America. 156" 

Cavallo, on Thermometrical Experiments. . 157 

Gioeni, on a New kind of Rain 16~5 

Crell, Experiments on the Acid of Fat . . 168 

White, on Bills of Mortality at York 177 

Torlese, Account of a Monstrous Birth. ... 180 

Fitzgerald, Exper. on Chinese Hemp-seed. . ibid 

More, on Scoria from Iron-Works 182 

Gorsuch, Parish Registers of Holy Cross . . 183 

P. Wilson, Refraction and Velocity of Light. 18+ 

G. Lloyd, Quantity of Rain at Barrowby . . 1<;3 

Six, of an improved Thermometer 195 

Herschel, Parallax of the Fixed Stars 196 

, Catalogue of Double Stars 213 

, of a New Lamp Micrometer . . 229 

, Great Power of his Telescopes. . 234 

Kirwan, Spec. Grav. &c. of Saline Sub. 236", 327 

Volta, on very weak Electricity 26'3 

Wedgewood, Thermom. of Great Heat 278, 571 
vol. xv. a 



Page 
Biog. Notice of Mr. Josiah Wedgewood. . . 278 
Withering, on Rowley-Rag and Toad-stone. 290 

Biog. Notice of Dr. Wm. Withering ibid 

Smeaton, on the Collision of Bodies 295 

Blagden, Effects of Lightning at Heckington. 306 
J. Hunter, Organ of Hearing in Fishes. . . . 308 

Brook, of a New Electrometer ibid 

Vince, on the Sums of Infinite Series. . 309, 638 
Hellins, on the Equal Roots of Equations. . 317 
Ingenhousz, Influence of Veget. on Animals, 319 
Herschel, on the Name of his New Planet. . 324 

, Diam. and Magnitude of the same 325 

Schotte, on a Large Species of Sarcocele . . 345 
Ramsden, New Eye-glasses for Telescopes. 350 

Tunstall, on some Lunar Rainbows 353 

J. Lloyd, account of an Earthquake ibid 

Cavendish, of a new Eudiometer 354 

Edgeworth, the Resistance of the Air .... 362 

Wilson, Alex, on the Solar Spots 366 

Hamilton, Sir W., the Earthquakes in Italy. 373 

Ippolito, on the same Earthquakes 383 

Marshall, on the Turnip Caterpillar 386 

Nairne, Wire shortened by Lightning .... 388 
Schevediawer, Account of Ambergris .... 389 
Herschel, Motion of the Solar System. . . . 397 

Wedgwood, Derbyshire Black Wadd 409 

De Chaulnes, Salt of Urine & Phos. Acid. . 411 

Hutchins, Congelation of Mercury ibid 

Cavendish, on the same subject 420 

Blagden, on the same 431 

Priestley, on Phlogiston, Air, and Water . . 453 

Cavallo, on an improved Air-Pump ibid 

Landerbeck, Variations of Curvature . 456, 627 
Goodricke, Variation of the Star Algol. 456, 544 

Englefield, on the same subject 460 

Palitcb, on the same ibid 

Page, the Wells at Sheerness, Harwich, &c. 46l 

Pigott, Edw. on a New Comet 464 

Hulton, a New Division of the Quadrant. . ibid 
Michell, Distance and Mag. of the Stars. . . 465 

Atkins, Meteorological Journal 477 

Cavallo, on the Meteor of Aug. 18, 1783. ibid 

Aubert, on the same subject 479 

Cooper, on the same 480 

Edgeworth, on the same 481 

Cavendish, Experiments on Air 4S1 , 510 

Kirwan, Remarks on the same 502, 514 

Wollaston, Astronomical Observations ... . 516 
Blagden, Observations on Fiery Meteors . . 520 
Herschel, on the Polar Regions of Mars . . 531 

Andre, on the Teeth of some Fishes 538 

Withering, on the Terra Ponderosa, &c. . . 544 
Wallot, on a Transit of Mercury 553 



r- n r> 



11 



CONTENTS. 



Page 
Watt, Comp. of Water and Deph. Air. 555, 569 

Waring, on the Summation of Series 586 

Cullum, Remarkable Frost in Summer .... 604 
Watt, Test Liquor for Acids and Alkalis. . . <>05 
Woodward, New Plant of the Fungi order. 607 

Six, on the Variation of Local Heat o'O.Q. 

Herschel, Construction of the Heavens. 6ll, 680 

Davidson, Bark Tree in St. Lucia 619 

Pigott, N. on the Meteor of Aug. 18, 1783. 620 

Pigott, Edw. on the Comet of 17S3 621 

Alchome, on Mixing Gold with Tin 622 

Galvez, on Directing Air Balloons 625 

Martineau, Dropsy of the Ovarium ibid 

Darwin, an Artificial Spring of Water .... 627 
Lightfoot, an undescribed Bird 630 



Pa K c 

Biog. Notice of the Rev. John Lightfoot . . 630 

Anderson, a Mountain on St. Vincent's . . . 634 

Hope, on a Plant yielding Asafoetida 640 

Biog. Notice of Dr. John Hope ibid. 

Pigott, Edw. on a New Variable Star .... 64.9 

Zach, Astronomical Observations 651 

Goodricke, on a New Variable Star 653 

Vince, on the Friction of Bodies 654 

Morgan, Geo. the Light of Bodies in Com- 
bustion 668 

Kirwan, Spec. Grav. at dif. Temperatures. . 696* 
Morgan, Wra. Non-conducting Power of a 

Perfect Vacuum 699 

Priestley, Experiments on Air and Water. . 703 

Landen, on Rotatory Motion ibid. 



THE CONTENTS CLASSED UNDER GENERAL HEADS. 



Class I. Mathematics. 

1. Arithmetic, Annuities, Political Arithmetic. 
Bills of Mortality at York White 177 Parish Registers of Holy Cross. . Gorsuch . . 183 

2. Algebra, Analysis, Fluxions, Series. 

Roots of Equations, E. Stanhope 86 The Equal Roots of Equations, Hellins . . . 317 

Roots of Affected Equations, .. Wales ... . 139 Variations of Curvature, . . Landerbeck 456, 627 
Sums of Infinite Series, Vince 309, 638 Summation of Series, Waring. . . 586 

3. Geometry, Trigonometry, Land-surveying. 
New Division of the Quadrant, Hutton. . . . 464 

Class II. Mechanical Philosophy. 



1. Dy 



namics. 



The Collision of Bodies, Smeaton . . 295 

Resistance of the Air, Edgeworth 36'2 



Friction of Bodies, Vince . 

Rotatory Motion Landen 



654 

703 



1. Astronomy, Chronology, Navigation. 



Nebula in Coma Berenices,. . . . Ed. Pigott 37 

On sonic Double Stars, N. Pigott 38 

Rotation of the Earth and Planets, Herschel 50 

Astronomical Observations, . . N. Pigott 117 

Mensuration of Angles Atwood .. 133 

Discovery of the New Planet, Herschel.. 154 

Microra for Angle of Position, Herschel.. 155 

Longit. ol Cambr. in America, Willard .. 156 

Parallax ol the Stars Herschel. . 196 

Catalogue of Double Stars .. Herschel 213,642 

New Lamp Micrometer .Herschel.. 229 

Great Powers of his Telescopes, Herschel. . 234 



Name of his New Planet, .... Herschel . . 324 

Diameter and Mag of the same, Herschel . . 325 

On the Solar Spots, A. Wilson 366 

Motion of the Solar System, ..Herschel.. 3^7 
Variation of the Star Algol, Goodricke 456', 514 

On the same subject, Englefield 460 

On the same Palitch. . . . ibid. 

On a i\e\\ Comet, F, Pigott . . 464 

Distance and Mag. of the Stars, Michell . . 46'5 

Astrononuc.il Observations .... Wollaston. . 5 16 

The Polar Region.-, ot Mars, .-.Herschel.. 531 

Transit of Mercury, Walloi 553 



CONTENTS. Ill 

Page Page 

Construction of the Heavens, Herschel 6 II, 680 Astronomical Observations, .... Zach .... 651 

On the Comet of 1783, E. Pigott . . 621 A New Variable Star, Goodricke 653 

A New Variable Star, E. Pigott . 649 

3. Gunnery, Projectiles. 
Experiments on Gunpowder, . .Thompson 88 

4. Mechanics. 
New Method of the Screw, . . Hunter ... 28 On the Friction of Bodies, .... Vince .... 654 

5. Pneumatics. 

Of a New Eudiometer, Cavendish 354 On Directing Air Balloons, .... Galvez . . . 625 

An Improved Air-Pump, Cavallo. . . . 453 

6. Optics. 

Micrometer for Angle of Posit. . Herschel . . 155 Great Powers of his Telescopes, Herschel . . 234 
Refract, and Velocity of Light, P. Wilson. . 1 84 New Eye-glasses for Telescopes, Ramsden. . 350 
New Lamp Micrometer, Herschel . 229 Light of Bodies in Combustion, G. Morgan 668 

7- Electricity, Magnetism, Thermometry. 

Heat of the Gulph Stream, . . . Blagden . . 115 A New Electrometer, Brook .... 308 

Exper. on Cold at Glasgow, .. P Wilson. . 129 Congelation of Mercury, . . . . Hutchins. . 411 

Thermometrical Experiments, Cavallo. ... 1 57 On the same subject, Cavendish 420 

An Improved Thermometer, . . Six 195 On the same, Blagden . . 431 

On very weak Electricity, .... Volta .... 263 Variation of Local Heat, Six 609 

Thermom. for Great Heat, Wedgewood 278, 57 1 Vacuum, Non-conducting, .... W. Morgan 699 

Class III. Natural History. 
1. Zoology. 

On the Tyger Cat of the Cape, Forster. . . . 1 The Ophidium Barbarum, . . . . Broussonet 134 

Account of the Turkey, ...... Pennant . . 32 The Turnip Caterpillar, Marshall . . 386 

The Termites of Africa, &c. . . Smeathman 60 An undescribed Bird, Lightfoot . . 630 

The Gum Lacca Insect, Kerr 124 

1. Botany. 
New Plant of the Fungi Order, Woodward 607 Bark Tree in St. Lucia, Davidson. . 619 

3. Mineralogy, Fossilogy, &c. 

On Scoria from Iron Work, . . .More .... 182 The Terra Ponderosa, &c Withering 544 

Rowley- rag and Toad-stone, . . Withering 290 On Mixing Gold with Tin, .... Alchorne. . 622 

Account of Ambergris, .... Schwediawer 3S9 On a Mountain in St Vincent's, Anderson 634 

Derbyshire Black Wadd, Wedgwood 409 Spec. Grav. at Dif. Temperatures, Kirwan 696 

Wells at Sheerness, Harwich, &c.Page .... i6l 

4. Geography and Topography. 
The Ganges and Burrampooter, Rennell . . 39 

5. Hydrology. 
Artificial Spring of Water, .... Darwin. . . 627 



IV 



CONTENTS. 



Class IV. Chemical Philosophy. 
J . Chemistry. 



Page 
On various Saline Substances, . Kirwan . . 3 

On the Acid of Fat, Crell 168 

Spec. Grav. of Saline Subst., . . Kirwan 236, 327 
Salt of Urine and Phos. Acid, De Chaulnes 411 

Congelation of Mercury, Hutchins. . ibid. 

On the same subject, Cavendish 420 

On the same, Blagden . . 43 1 



Page 

Experiments on Air, Cavendish 481 , 510 

Remarks on the same, .... Kirwan. . 502, 514 
Comp. of Water and Deph. Air. . "Watt 555, 569 
Test Liquor for Acids and Alkalis, Watt . . 605 

On Mixing Gold with Tin, Alchorne 622 

Light of Bodies in Combustion, G. Morgan 668 
Experiments on Air and Water, Priestley . . 703 



1. Meteorology. 



On a Storm of Lightning, Brereton . . 21 

On the African Harmattan, .... Dobson . . 23 
Meteorol. Journ. at Labrador, . . De La Trobe 87 

London, . . R. Soc. 87, 277 

Luminous Appearance in the Sky, Cavallo 
Meteorol. Journal, Barker 118, 277. 396, 

Phenomenon at Sumatra, Marsden . . 

Experim. on Cold at Glasgow, P. Wilson 

A New kind of Rain, Gioeni. . . . 

The Rain at Barrowby, G. Lloyd 



114 

543 
127 
129 
16'5 
193 



Effects of Lightning at Heckington, Blagden 306 



Account of an Earthquake, . . . 
Wire Shortened by Lightning, 

Meteorological Journal, 

On the Meteor, of Aug. 18, 1783 

On the same subject, 

On the same, 

On the same, 

Observations on Fiery Meteors, 
Remarkable Frost in Summer, 
On the Meteor of Aug. 18,1783, 



. J. Lloyd 


. 353 


Nairne. . 


. 388 


Atkins. . 


. 477 


, Cavallo 


. ibid 


. Aubert . 


. 479 


Cooper . 


. 480 


Edgeworth 481 


Blagden 


. 520 


Cullum . 


. 604 


N. Pigott 


. 620 



3. Geology. 



On Earthquakes in Wales, .... Pennant . . 
Earthquake near Denbigh, .... J . Lloyd . . 
Soil at Opening a Well, Englefield 



85 Account of an Earthquake, 
1 15 The Earthquakes in Italy, 
1 1 7 On the same Earthquakes, 



.J. Lloyd .. 353 
. . Hamilton 373 
, . Ippolito . . 383 



Class V. Physiology. 

1 . Physiology of Animals. 

Power of Anim. to produce Cold, Crawford 147 On the Teeth of some Fishes, .. Andre ... . 538 
Organ of Hearing in Fishes, . . Hunter. . . . 308 

2. Physiology of Plants. 

On Washing Stems of Plants, Marsham. . 138 Influence of Vegetab. on Anim. . Ingenhousz 319 
On Chinese Hemp-seed, Fitzgerald 180 A Plant yielding Asafcetida, .... Hope .... 640 

3. Surgery, Midwifery, Physic. 

Deaths, &c. from Parturition, Bland .... 118 A large kind of Sarcocele, .... Schotte .. . 345 

Child born with the Small-Pox, Wright . . 123 Dropsy of the Ovarium, Martineau 625 

On a Monstrous Birth, Torlese ... 1 80 

Class VI. Biography ; or, Account of Authors. 

Dr. John Hope, 6+0 Josiah Wedgwood, 278 

Rev. John Lightfoot, 650 Dr. Win. Withering, 2y0 



THE 

PHILOSOPHICAL TRANSACTIONS 



OF THE 



ROYAL SOCIETY OF LONDON; 

ABRIDGED. 



/. Natural History and Description of the Tyger-cat of the Cape of Good Hope. 

By John Reinhold Forster, LL. D., F. R. and A. S. Vol. LXXI. Anno 

1781. p. I. 

Few tribes of quadrupeds have in Africa more representatives of their different 
species than that of the Cat. The genus of Antelopes may perhaps be excepted, 
since, to my knowledge, says Dr. F., about 20 different Ghazels and Antelopes 
are to be met with in Africa ; but no more than about 8 or 9 of the cat tribe 
have hitherto been discovered on that continent. However, I know about 21 
different species of this great class ; and I suppose these by no means exhaust it. 

The greater and more numerous the different genera of animals are, the more 
difficult it must be to the natural historian properly to arrange the whole of such 
an extensive division of animals, especially if they are not equally well known. 
To form new genera, in order to arrange them, is a remedy which increases the 
evil, instead of curing it. The best method therefore is to make great divisions 
in each genus, comprehending those species which, on account of some common 
relation or character, have a greater affinity to each other. The genus of cat 
offers 3 very easy and natural subdivisions. The first comprehends animals re- 
lated to the cat tribe, with long hair or manes on their necks ; secondly, such 
as have remarkable long tails without any marks of a mane on their necks ; 
lastly, such as have a brush of hair on the tips of their ears, and shorter tails 
than the second subdivision. I shall confine myself to that species which has 
been hitherto imperfectly known to naturalists. 

The first notice we had of the Cape Cat is to be met with in Labat's Relation 
Historique de l'Ethiopie occidentale, torn. 1, p. 177, taken as is supposed from 
Father Carazzi. Labat mentions there the 'Nsussi, a kind of wild cat of the 
size of a dog, with a coat as much striped and varied as that of a tyger. Its ap- 
pearance bespeaks cruelty, and its eyes fierceness ; but it is cowardly, and gets 
its prey only by cunning and insidious arts. All these characters are perfectly 

vol. xv. B 



2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

applicable to the Cape Cat, and it seems the animal is found in all parts of 
Africa, from Congo to the Cape of Good Hope, in an extent of country of 
about 11° of latitude. Kolbe, in his Present State of the Cape of Good Hope, 
vol. '2, p. 127, of the English edition, speaks of a Tyger Bush-cat, which he 
describes as the largest of all the wild cats of the Cape-countries, and is spotted 
something like a Tyger. A skin of this animal was seen by Mr. Pennant, in a 
furrier's shop in London, who thought it came from the Cape of Good Hope. ; 
from this skin Mr. Pennant gave the first description which could be of any 
utility to ;i natural historian.* All the other authors mention this animal in a 
vague manner. 

When I touched the 2d time at the Cape of Good Hope in the year 1775, an 
animal of this species was offered me to purchase; but I refused buying it be- 
cause it had a broken leg, which made me apprehensive of losing it by death 
during the passage from the Cape to London. It was very gentle and tame. 
It was brought in a basket to my apartment, where 1 kept it above 24 hours, 
which gave me the opportunity of describing it, and of observing its manners 
and economy. These I found perfectly analogous to those of our domestic cats. 
It ate fresh raw meat, and was much attached to its feeders and benefactors : 
though it had broken the fore-leg by accident, it nevertheless was very easy. 
After it had been several times fed by me, it soon followed me like a tame 
favourite cat. It liked to be stroked and caressed ; it rubbed its head and back 
always against the person's clothes who fed it, and desired to be made much of. 
It purred as our domestic cats do when they are pleased. It had been taken when 
quite young in the woods, and was not above 8 or Q months old ; I can however 
positively aver, having seen many skins of full-grown Tyger-cats, that it had 
already very nearly, if not quite, attained its full growth. I was told that the 
Tyger-cats live in mountainous and woody tracts, and that in their wild state 
they are very great destroyers of hares, rabbits, yerbuas, young antelopes, lambs, 
and of all the feathered tribe. 

Description of the Cape Tyger-Cat. — Cat with subelongated, annulated tail, and fulvous body, 
marked above by lengthened and beneath by orbicular spots, with black ears marked by a white 
lunated spot. 

The body is ovate, and elegant : on the neck, rising between the bases of the ears, are four longi- 
tudinal deep-black lines or stripes, which on the back are broken or interrupted : the upper parts of 
the sides are marked by oblong, linear, oblique spots : the lower parts of the sides are marked by 
round scattered spots : the abdomen is of a cinereous white, with small, round, scattere d , black 
spots. 

This animal is the 'Num. I,abat Ethiop. Occident, torn. I . p. 177. 

Tyger-Botek-Katten. Kolbe Cape of Good Hope, vol. 2. p. 127. Engl. edit. 

Cape-Cat. Pennant Synops. Quadr. p. 181. — Measure, from the nose to the base of the tail IS 
inches; the tail 8 inches. See fig. 1, pi. 1. 

* Pennant's Synopsis of Quadrupeds, p. 181, first edit. — Orig. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 3 

II. Experiments and Observations on the Specific Gravities and Attractive Powers 
of various Saline Substances. By Richard Kirwan, Esq., F.R.S. p. 7- 

The doctrine of" chymical affinities has received great improvements from the 
labours of Mr. Bergman of Upsal, and the still later researches of Mr. Wentzel ; 
but the order of these attractions has hitherto been the only point attended to 
by these philosophers, as well as by most preceding chymists ; for I know of 
none (says Mr. K.) except Mr. Morveau of Dijon, who has thought of ascer- 
taining the various degrees of force of chemical attraction, by which one body 
acts on various other bodies, or even on the same body in various circumstances. 
He has however so ably shown the advantages arising from such an inquiry, that 
I have made it the object of my attention, and bestowed much pains on it for 
s.ome time past ; and have thence been enabled to determine pretty exactly the 
proportion of the ingredients of many neutral salts, and the specific gravity of 
the mineral acids in their purest state, and free from all water. The principles 
on which these determinations are founded are the following. 

1st. That the specific gravity of bodies is as their weight, divided by the 
weight of an equal bulk of rain or distilled water, this being at present the 
standard with which every other body is compared. 

2dly. That if bodies, specifically heavier than water, be weighed in air and in 
water, they lose in water part of the weight they were found to have in air ; 
and that the weight so lost is just the same as that of an equal bulk of water, 
and consequently that their specific gravity is equal to their weight in air, or ab- 
solute weight, divided by their loss of weight in water. 

3dly. That if a solid, specifically heavier than a liquid, be weighed first in air, 
and then in that liquid, the weight it loses is equal to the weight of an equal vo- 
lume of that liquid; and consequently if such solid be weighed first in air, then 
in water, and afterwards in any other liquid, the specific gravity of this liquid 
will be as the weight lost in it by such solid, divided by the loss of weight of the 
same solid in water. This method of finding the specific gravity of liquids I 
have found much more exact than that by the areometer, or the comparison of 
weights of equal measures of such liquids and water, both of which are subject 
to several inaccuracies. 

4thly. That where the specific gravity of bodies is already known, the weight 
of an equal bulk of water may also be found, it being as the quotient of their 
absolute weight divided by their specific gravity. This I shall call their loss of 
weight in water. 

Hence, where the specific gravity and absolute weight of the ingredients of 
any compound are known, the specific gravity of such compound may easily be 
calculated, as it ought to be intermediate between that of the lighter and that of 
the heavier, according to their several proportions: this I call the mathematical 

b 2 



4 PHILOSOPHICAL TRANSACTIONS. [ANNO J 7 8 J . 

specific gravity. But, in fact, the specific gravity of compounds, found by 
actual experiment, seldom agrees with that found by calculation, but is often 
greater without any diminution of the lighter ingredient. This increase of 
density must then arise from a closer union of the component parts to each 
other than either had separately with its own integrant parts ; and this more inti- 
mate union must proceed from the attraction or affinity of these parts to each 
other : I therefore imagined that this attraction might be estimated by the in- 
crease of density or specific gravity, and that it 
was proportionable to it, but was soon undeceived. Cubic inch „f common air .... 0.385 

I must also premise, that the absolute weights Fixed air 0.570 

r r ■ , , . , , . Marine Air 0.65+ 

or many sorts 01 air nave been accurately deter- jsjitrous air 300 

mined by Mr. Fontana, the thermometer being Vitriolic air 0.77s 

o , ,, , , Alkaline air 0.2 

at 55 , and the barometer at 2Q-' T inches, or Inflammab le air 0.035 

nearly so. Their weights were as annexed : 

Of' spirit of salt. — From the time I first read in Dr Priestley's Experiments 
on Air (that inexhaustible source of future discoveries) of the exhibition of 
marine acid in the form of air, free from water ; and that this air, reunited with 
water, formed an acid liquor in all respects the same as common spirit of salt ; I 
conceived the possibility of discovering the exact quantity of acid in spirit of salt 
of any given specific gravity, and by means of this the exact proportion of acid 
in all other acid liquors ; for if a given quantity of pure fixed alkali were satu- 
rated, first by a certain quantity of spirit of salt, and then by determined quan- 
tities of the other acids, I concluded, that each of these quantities of acid liquor 
must contain the same quantity of acid ; and this being known, the remainder 
being the aqueous part, this also must be known ; but this conclusion entirely 
rested on the supposition that the same quantity of all the acids was requisite for 
the saturation of a given quantity of fixed alkali ; for if such given quantity of 
fixed alkali might be saturated by a smaller quantity of one acid than of another, 
the conclusion fell to the ground. This point might indeed be in some measure 
determined by weighing the neutral salts, formed by these acids, when thoroughly 
dry ; but still a source of inaccuracy remained : for if they were exposed to a 
considerable heat, part of the acid would necessarily be expelled, and more of 
one acid than of another; and if the heat were not considerable, much of the 
water of crystallization would remain ; so that, if the weights were found to be 
equal, this equality could not be ascribed to equal quantities of acid, but might 
perhaps arise from a smaller proportion of acid in one of them, and a larger 
proportion of water, and in another from a larger proportion of acid and a 
smaller proportion of water ; and if the weights were unequal, no certain con- 
clusion could he drawn. To obviate this difficulty, I used the following expe- 
dient. 1st. I supposed the quantities of nitrous and vitriolic acids, necessary to 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 5 

saturate a given quantity of fixed alkali, exactly the same as that of marine acid 
whose quantity I determined ; and to prove the truth of this supposition, I ob 
served the specific gravity of the spirit of nitre and oil of vitriol I made use of, 
and in which I supposed, from the trial with alkalis, a certain proportion of acid 
and water ; to these I then added more acid and water, and calculated what their 
specific gravities should be on the above supposition ; and finding the result to 
accord with the supposition, I concluded the latter to be exact. 

The experiments made on the marine acid were as follow : I took 2 bottles, 
which I filled nearly to the top with distilled water, of which they contained in 
all 1399.9 gr. and introduced them successively into 2 cylinders filled with ma- 
rine air, which I had obtained from common salt by means of diluted oil of 
vitriol and heat, in a mercurial apparatus; and this process I renewed till the 
water had imbibed, in 18 days, about 794 cubic inches of the marine air. The 
thermometer did not rise all this time above 55°, nor sink, unless perhaps at 
night, under 50°, and the barometer was between 29 and 30 inches. This 
water, or rather spirit of salt, I then found to weigh 1920 gr. that is 520.1 
more than before. The quantity of marine air absorbed amounted then to 
520.3 °t. I then examined the specific gravity of this spirit of salt, and found 
it to be 1.225. Its loss of weight in water (that is, the weight of an equal bulk 
of water) should then be 1567.346 gr. nearly ; but it contained only, as we have 
seen, 1399-9 gr. of water : therefore, subtracting this from 1567.346, the re- 
mainder (that is, 167.446) must be the loss of 520.1 gr. of marine acid; and 

consequently the specific gravity of the pure marine acid, in such a condensed 

520 1 
state as it is in when united to water, must be [ fi ' . = .3100. But still it might 

be suspected, that the density of this spirit did not entirely proceed from the 
mere density of the marine acid, but in part also from the attraction of this acid 
to water, and though the length of time requisite to make water imbibe this 
quantity of acid made me judge that the attraction was not very considerable, 
yet the following experiment was more satisfactory. 

I exposed 1440 gr. of this spirit to marine air for 5 days, the thermometer 
being at 50° or under ; it then weighed 1562 gr. and consequently imbibed 122 
gr. of marine air; its specific gravity was then 1.253, which agrees exactly with 
what it should be by calculation Being now satisfied I had discovered the pro- 
portion of acid and water in spirit of salt, I was impatient to find it in other 
acids also ; and for that purpose I took 180 gr. of very strong oil of tartar per 
deliquium, but of whose specific gravity I can find no note, and found it to be 
saturated by 180 gr. of spirit of salt, whose specific gravity was 1.225. Now, 
by calculation it appears, that 180 gr. of this spirit contains 48.7 gr. of acid, 
and 131.3 of water; and hence I drew up the following table. 



PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

The specific gravity of the strongest spirit of 
salt, made in the usual way, is, according to 
Mr. Baume, 1.18', and according to Mr. Berg- 
man, I.19O ; but we read in the Paris Memoirs 
for the year 1700, p. 19 1, that Mr. Homberg 
passed a spirit whose specific gravity was 1.300 ; 
and that made by Dr. Priestley (vol. 3, p. 275) 
must have been about 1.500. Hence we see 
that spirit of salt, whose specific gravity is I.261 
or less, has little or no attraction with water, and 
therefore attracts none from air, and on that ac- 
count does not heat a thermometer whose ball is 
dipped in it as spirit of vitriol and spirit of nitre 
do, as has lately been observed by the Friendly 
Society of Berlin. 

This table is not exactly accurate, as I had 
not in this first experiment found the point of 
saturation so nicely as was requisite. However 
I have not corrected it, as the error is but 
small, and the proportion may at any time be 
found by calculation ; at least when the specific 
gravity of this spirit does not exceed 1.253. 
Whether the mathematical specific gravity and 
that by observation differ in the higher degrees 
of specific gravity, I have not examined ; but 
the table is formed on the supposition that they 
do not. 



Common spirit of salt is always adulterated with vitriolic acid, and therefore 
not fit for these trials. Intending to determine by this experiment the propor- 
tion of acid, water, and fixed alkali in digestive salt, as it is called, I took 100 
gr. of a solution of a tolerably pure vegetable alkali that had been 3 times cal- 
cined to whiteness, the specific gravity of which solution was I.O97. I also 
diluted the spirit of salt with different portions of water ; the specific gravity of 
one sort was 1.1 15, and of another I.O98. I then found that the above quan- 
tity of the solution of a vegetable alkali required for its saturation 27 gr. of that 
spirit of salt whose specific gravity was I.O98, and 23.35 gr. of that spirit of 
salt whose specific gravity was 1.115. Now, 27 gr. of spirit of salt, whose 
specific gravity is I.098, contain 3.55 gr. of marine acid, as appears by calcula- 
tion. As the principle on which this calculation, by which the proportion of 



Marine 1 


Water. 


Specific 


acid. 




Gravity. 


Parts. 


Parts. 






50 


1.497 




60 


1.431 




70 


1.381 




SO 


1.341 




90 


1.308 




100 


1.282 




no 


1.259 




120 


1 .246 




130 


1.223 




no 


1 .205 




150 


1.196 




160 


1.185 




170 


1.175 




180 


1.166 




190 


1.158 




200 


1.151 




210 


1.144 




220 


1.138 


48.7 


230 


1.132 




240 


1.127 




250 


1.122 




260 


1.118 




270 


1.114 




280 


1.110 




290 


1.106 




300 


1.103 




310 


1.100 




320 


1.097 




330 


1.091 




340 


1.089 




350 


1.086 




360 


1.084 




370 


1.082 




380 


1.080 




390 


1.078 




400 


1.076 




410 


1.074 



VOL. LXXI.J PHILOSOPHICAL TRANSACTIONS. 7 

substances in alloy is found, may not be generally known, I shall here mention 
them in the words of Mr. Cotes. 

" The data requisite are the specific gravities of the mixture and of the two 
ingredients. . . . Then, as the difference of the specific gravities of the mixture 
and the lighter ingredient is to the difference of the specific gravities of the mix- 
ture and the heavier ingredient, so is the magnitude of the heavier to the mag- 
nitude of the lighter ingredient. Then, as the magnitude of the heavier multi- 
plied into its specific gravity, is to the magnitude of the lighter multiplied into 
its specific gravity, so is the weight of the heavier to the weight of the lighter. 
Then, as the sum of these weights is to the given weight of either ingredient, 
so is the weight given, to the weight of the ingredient sought." Thus, in this 
case, I.O98— 1.000= .098 is the magnitude of the heavier ingredient, viz- 
the marine acid ; and .098 X 3.100 = 0.3038 the weight of the marine acid ; 
and, on the other hand, 3.100 — I.O98 = 2.002 the magnitude of the water, 
also 2.002 X 1.000 = 2.002 its weight ; the sum of these weights is 2.3058 : 
then, if 2.3058 parts of spirit of salt contain 0.3038 parts acid, 17 gr. of this 
spirit of salt will contain 3.55 acid. In the same manner it will be found, that 
23.35 gr. of spirit of salt, whose specific gravity was 1.115, contained 3.55 gr. 
acid. 

The point of saturation was pretty accurately found by putting the glass 
cylinder which contained the alkaline solution on the scale of a very sensible 
balance, and at the same time weighing the acid liquor in another pair of scales, 
when the loss of weight indicated the escape of nearly equal quantities of the 
fixed air contained in the solution ; then the acid was gradually added, by dipping 
a glass rod into it, to the top of which a small drop of acid adhered : with this 
the solution was stirred, and very small drops taken up and laid on bits of paper 
stained blue with radish juice. As soon as the paper was in the least reddened, 
the operation was completed, so that there was always a very small excess of 
acid, for which half a grain was constantly allowed ; but no allowance was made 
for the fixed air, which always remains in the solution ; but as, on this account, 
only a small quantity of the alkaline solution was used, this proportion of fixed 
air must have been inconsiderable. If an ounce of the solution had been em- 
ployed, this inappreciable portion of fixed air would be sufficient to cause a sen- 
sible error : for I judged of the quantity of fixed air lost by the difference be- 
tween the weight added to the 100 gr. and the actual weight of the compound. 
When this difference amounted to 2.2 gr. I then judged the whole of the fixed 
air expelled, and found it to be so, as 100 gr. of this alkaline solution, being 
evaporated to dryness in a heat of 300°, left a residuum which amounted to lO-i- 
gr. ; which 104 gr. contained 2.2 gr. of fixed air, as will hereafter be seen. 

Hence 8.3 gr. of pure vegetable fixed alkali, free from fixed air and water, or 



8 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781 . 

10.5 of mild fixed alkali, were saturated by 3.55 gr. of pure marine acid, and 
consequently the resulting neutral salt should, if it contained no water, weigh 
J 1.85 gr. ; but the salts resulting from this union (the solution being evaporated 
to perfect dryness in a heat of l6o° kept up for 4 hours) weighed at a medium 
1 2.66 gr. Of this weight, 11.85 gr. were acid and alkali ; therefore the remainder, 
viz. 0.81 gr. were water; therefore 100 gr. of perfectly dry digestive salt contain 
28 gr. acid, 6.55 water, and 65.4 of fixed alkali. 

I was then curious to compare my experiments with those made by others, 
but could not find any made with sufficient precision except those of Mr. Hom- 
berg in the Paris Memoirs for 1699. However, as to spirit of salt I did not 
think proper to compare them, as he mentions that his could dissolve gold, and 
therefore was probably impure. 

Of spirit of nitre. — The common reddish brown or greenish spirit of nitre 
containing, besides acid and water, a certain portion ot phlogiston; and being 
also mixed with some portion of the acid of sea salt, I judged it unfit for these 
trials; and therefore used only the dephlogisticated sort, which is quite colour- 
less, and resembles pure water in its appearance. This pure acid cannot be made 
to exist in the form of air, as Dr. Priestley has shown; for when it is deprived 
of water and phlogiston, and furnished with a due proportion of elementary fire, 
it ceases to have the properties of an acid, and becomes dephlogisticated air: I 
could not therefore determine its proportion in spirit of nitre, as I had done that 
of the marine acid, but was obliged to use another method. 1st. To 1 963 .25 
gr. of this spirit of nitre, whose specific gravity was 1.419, I gradually added 
1795 gr. of distilled water: and when it cooled I found the specific gravity of 
this mixture I.389. 2dly. To 1984.5 gr. of this I again added 178.75 gr. of 
water; its specific gravity was then 1.362. 

I then took 100 gr. of a solution of fixed vegetable alkali, whose specific gra- 
vity was 1 .097, the same as I had before used in the trials with spirit of salt, and 
found this quantity of alkali to be saturated by 1 1 gr. of the spirit of nitre, 
whose specific gravity was 1.41 9; and by 12 gr. of the spirit, whose specific 
gravity was 1.389; an d ty 13.08 of that whose specific gravity was 1.30'2. The 
quantities here mentioned were the mediums of 5 experiments. I found it neces- 
sary to dilute the nitrous acid with a small proportion of water, of which 1 kept 
an account. When I neglected this precaution, I found that part of the acid 
was phlogisticated, and went off with the fixed air. Note also, that after each 
affusion of acid, 10 minutes were allowed for the matters to unite; a precaution 
which I also found absolutely necessary. 

Hence, on the supposition that a given quantity of fixed vegetable alkali is sa- 
turated by the same weight of both acids, we see that 1 1 gr. of spirit of nitre, 
whose specific gravity is 1.41 9, contain the same quantity of acid as 27 gr. of 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 9 

spirit of salt, whose specific gravity is I.O98, that is, 3.55 gr.; the remainder of 
11 gr. is therefore mere water, viz. 7-45 gr.; consequently, if the density of the 
acid and water had not been increased by their union, the specific gravity of the 
pure and mere nitrous acid should be 1 1.8729; for the specific gravity of this 
acid should be as its absolute weight divided by its loss of weight in water, and 
this loss should be as the total loss of these 1 1 gr. minus the loss of the aqueous 

part. Now the total loss = — — = 7-749, and the loss of the aqueous part 
= 7.45, consequently the loss of the acid part is 7-749 — 7-45 = O.299, and 
therefore the specific gravity of the acid part, that is, of the pure nitrous acid, 

j s _3. _ j 1,8720. But it is well known, that the density of the nitrous acid, 

0.296 - J 

as well as that of the vitriolic, is increased by its union with water; and there- 
fore the loss above found is not the whole of its real loss in its natural state (if 
it could be so found) but partly the loss that arises from the density that accrues 
to it from its union with water; for since its density is increased by this union, 
its loss is less than it would be if the nitrous acid had only its own proper den- 
sity, and consequently the specific gravity above found is greater than its real 
specific gravity. 

To determine therefore the real specific gravity of this acid in its natural state, 
the quantity of accrued density must be found, and subtracted from the specific 
gravity of the spirit of nitre, whose true mathematical specific gravity will then 
appear. I endeavoured to effect this by mixing different portions of spirit of nitre 
and water, remarking the diminution of their joint volume below the sum of 
the spaces occupied by their separate volumes; but could never attain a sufficient 
degree of precision. The following method, though not exactly accurate, I 
found more satisfactory ; 1 2 gr. of the spirit of nitre, whose specific gravity by 
observation was 1.389, contained, as I supposed from the former experiment, 
3.55 gr. of acid, and 8.45 of water; then if the specific gravity of the pure 
nitrous acid were 11.872, the specific gravity of this compound of acid and 
water should be 1.371; for the loss of 3.55 gr. acid should be O.299, and the 

12 

loss of the water 8.45; the sum of the losses 8.749; — — - = 1.371 ; but, asal- 
ready said, the specific gravity by observation was 1.389, therefore the accrued 
density in this case was at least .018, the difference between 1.38g and 1.37 1. I 
say at least, for as the specific gravity 11.872 was certainly too high, the loss 
of 3.55 gr. acid was certainly too small; and if it were greater, the mathema- 
tical specific gravity 1.371 would have been still lower. However, .018 is cer- 
tainly a near approximation to the degree of density that accrues to 3.55 gr. acid 
by their union with 7.45 gr. of .water, and differs inconsiderably from the truth, 
as will appear by the sequel; therefore, subtracting this quantity from 1.419, we 
have nearly the mathematical specific gravity of that proportion of acid and water, 

VOL. XV. C 



10 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

namely, 1.401. And since 11 gr. of this spirit of nitre contain 3.55 gr. of acid 
and 7.45 of water, its loss of weight should be — — = 7-855; and. subtracting 
the loss of the aqueous part from this, the remainder 0.405 is the loss of the 
3.55 gr. acid, and consequently the true specific gravity of the pure and mere 
nitrous acid is — -— = 8.7654. This being settled, the mathematical specific 
gravity, and true increase of density of the above mixtures, will be found. Thus 
the mathematical specific gravity of 1 2 gr. of that spirit of nitre, whose specific 
gravity by observation was 1.389, must be 1.355, supposing it to contain 3.55 

3 55 
sr. acid and 8.45 of water; for the loss of 3.55 gr. acid is -'—^ = o.405, and 
o ° 8./03 

the loss of water 8.45; the sum of these losses is 8.855. Then — ~—= 1.355, 
and consequently the accrued density is 1.389 — 1-355 = .034. In the same 
manner it will be found, that the mathematical specific gravity of 13.08 gr. of 
that spirit of nitre whose specific gravity by observation was 1.362, must be 
1.315, and consequently its accrued density .047- 

But the whole still rests on the supposition that each of these portions of spirit 
of nitre contain 3.55 gr. of acid. To verify this supposition, I could think of 
no better method than that of examining the mathematical specific gravities of 
the first mixture I had made of spirit of nitre and water in large quantities; for 
if the mathematical specific gravities of these agreed exactly with those of the 
quantities I had supposed in smaller portions of each, I could not but conclude, 
that the supposition of such proportions of acid and water, as I had determined 
in each, was just; and that this was the case will appear by the following calcu- 
lations. 1st. When to 1963.25 gr. of spirit of nitre, whose specific gravity was 
1.419, were added 179-5 gr. of water, the quantity of acid on the above suppo- 
sition should be 634.53 gr.; for 11 : 3.55 :: 1 963.25 : 634.53; the quantity of 
water in those 1 963. 25 gr. of spirit of nitre should then be 1328.72, and after 
adding 179-5 gr. of water, the whole quantity of acid and water should be 

2142-75 ; the loss of acid was ' =71 .24, and the sum of the losses 1580.46: 

8.7054 

then the mathematical specific gravity should be tt^tt = 1.355, which is ex- 
actly the same as that which was found in 12 gr. of this spirit of nitre, on the 
supposition that they contained 3.55 gr. of acid. 

Again: when to 1984.5 gr. of this mixture I added 1 78.75 gr. of water, the 
whole quantity of diluted spirit of nitre was 21 63.25 gr. and the quantity of acid 
in 1984.5 gr. was 587.081 gr. for 12:3.55 :: 1984.5 : 587.081 ; the loss of this 
quantity of acid is 66.96 gr. and the sum of the losses of acid and water is 
1643.129 gr.; and consequently the mathematical specific gravity should be 

2i63.75 _ _ j which is the same as that determined in 13.08 gr. of the same 

1643.125 ° 

mixture. 



VOL 



lxxl] 



PHILOSOPHICAL TRANSACTIONS. 



11 



By continuing these mixtures till I found the mathematical specific gravity and 
that by observation nearly to coincide, I was enabled to draw up the following 
table, in which if any errors be found, I hope they will be excused, from the 
impossibility of avoiding them where the weights must be found with such ex- 
treme precision: the two first series were only found by analogy. 



Spirit of 


Acid. 


Water. 


Accrued 
density. 


Mathem. 
specific 


Spec, gra- 
vity by 


Attract, 
of the acid 


Attract, 
of wat. to 


nitre. 






gravity. 


observat. 


to water. 


the acid. 


Grs. 


Grs. 


Grs. 












9 





5.45 


.000 


1.537 


1.537 


— — 


— — 


10 


_ — 


6.45 


.009 


1.458 


1.467 


.009 


.054 


11 


_ — 


7.45 


.018 


1.401 


1.419 


.018 


.045 


12 


_ — 


8.45 


.034 


1.355 


1 .389 


.027 


.036 


13.08 


_ 


9-53 


.047 


1.315 


1.362 


.036 


.027 


14.15 





10.6 


.051 


1.286 


1.337 


.045 


.018 


15.23 


— — 


11.68 


.054 


1.260 


1.314 


.054 


.009 


16.305 


— — 


12.755 


.054 


1.238 


1.292 


.054 


.009 


17.38 


— — 


13.83 


.051 


1.220 


1.271 






18.445 


— — 


14.9 


.047 


1.205 


1.252 






19.53 


— — 


15.98 


.044 


1.191 


1.235 






20.605 


— — 


17.055 


.042 


1.1S0 


1.222 






21.68 ' 


— — 


18.13 


.040 


l.)77 


1.217 






22.755 


— — 


19.205 


.038 


I.160 


1.193 






23.83 


— — 


20.2S 


.036 


1.152 


1.188 






24.905 


— — 


21.45 


.033 


1.144 


1.177 






26.17 


— — 


22.62 


.030 


1.132 


1.162 






27.34 


3.55 


23.79 


.027 


1.130 


1.157 






28.51 


— — 


24.96 


.026 


1.124 


1.150 






29-68 


__ — 


26.13 


.024 


1.114 


1.138 






30.85 


— — 


27.30 


.022 


1.113 


1.135 






32.02 


— — 


28.47 


.020 


1.109 


1.129 






33.09 


— — 


29.54 


.018 


1.102 


1.120 






34.26 


— — 


30.71 


.016 


1.101 


1.117 






35.43 


— — 


31.88 


.014 


1.097 


1.111 






36.60 


— — 


33.05 


.012 


1.094 


1.106 






37.77 


— — 


34.22 


.010 


1.090 


1.100 






38.94 


— — 


35.3.') 


.008 


1.08S 


1 .096 






40.11 


— — 


36.56 


.006 


1.085 


1.091 






41.28 


— — 


37.73 


.004 


1.082 


1.086 






42.45 


— — 


38.90 


.002 


1.080 


1.082 







The intermediate specific gravities may be found by taking an arithmetical 
mean among the specific gravities by observation between which that sought lies, 
and noting how much it exceeds or falls short of such arithmetical mean; and 
then taking also an arithmetical mean among the mathematical specific gravities 
between which that sought for must lie, and a proportionate excess or defect. I 
have added a column of attraction of the nitrous acid to water, as far as it keeps 
pace with the increase of density, but no further, as I am unacquainted with 
the law of its further increase. The specific gravity of the strongest spirit of 
nitre yet made is, according to Mr. Baume, 1.500; and according to Mr. Berg- 

c 1 



12 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

man, 1.586. I next proceeded to examine the proportion of acid, water, and 
fixed alkali, in nitre, in the same manner as I had before done that in digestive 
salt, and found that 100 gr. of perfectly dry nitre, contain 28.48 gr. of acid, 5.2 
of water, and 66.32 of fixed alkali. 

I shall now compare the result of these experiments with those of Mr. Hom- 
berg. The specific gravity of the spirit of nitre which Mr. Homberg made use 
of, was 1.349; an d of this, he says, 1 oz. 2 dr. and 36 gr., that is, 62 1 Troy, 
are requisite to saturate 1 French oz. (472.5 Troy) of dry salt of tartar; accord- 
ing to my computation, 6l3 gr. are sufficient; for this specific gravity lies be- 
tween the tabular specific gravities by observation, 1.362 and 1.337, and is nearly 
an arithmetical mean between them. The corresponding mathematical specific 
gravity lies between the tabular quantities 1.315 and 1.286, and is nearly 1.300. 
Now the proportion of acid and water in this is 2.629 °f ac 'd> ar >d 7-465 of 
water; for 8.765 — 1.300 = 7.465 water, and 8.765 X .300 = 2.629 of acid; 
and the sum of both is 10.044. Now, since 10.5 gr. mild vegetable fixed alkali 
require 3.55 gr. of acid for their saturation, 472.5 will require 159.7; therefore 
if 10.044 gr. of nitre contain 2.629 gr. acid, the quantity of this spirit of nitre 
requisite to give 159.7, will be 6l3.2 nearly; and hence the difference between 
us is only about 8 gr. 

2dly. Mr. Homberg says, he found his salt, when evaporated to dryness, to 
weigh 186 gr. more than before; whereas, by my experiment, it should weigh 
but 92.8 gr. more than at first. I shall mention the cause of this difference in 
treating of tartar vitriolate, for it cannot be entirely attributed to the difference 
of evaporation. 3dly. Mr. Homberg infers, that 1 oz. (that is, 472.5 Troy gr.) 
of this spirit of nitre contains 141 gr. Troy of real acid: by my computation 
it contains but 123.08 gr. of real acid. This difference evidently proceeds from 
his neglecting the quantity of water that certainly enters into the composition of 
nitre; for he proceeds on this analogy, 62 1 : 186.6 :: 472.5 : 141. 

The proportion of fixed alkali I have assigned to nitre is fully confirmed by a 
very curious experiment of Mr. Fontana's, inserted in Rozier's Journal for No- 
vember 1 778. This ingenious philosopher decomposed 2 oz. of nitre by distilling 
it in a strong heat for 18 hours. After the distillation there remained in the 
retort a substance purely alkaline, amounting to 10 French dr. and 12gr. Now 
1 French oz. = 944 gr. Troy, and the alkaline matter amounts to 607 gr. Troy; 
and, according to my computation, 944 gr. of nitre should contain 625 of alkali. 
So small a difference may fairly be attributed to the loss in transferring from one 
vessel to another, weighing, filtering, evaporating, &c. 

Mr. Lavoisier, in the Paris Memoirs for the year 1776, has given us, after 
Dr. Priestley, the analysis of the nitrous acid. In 2 oz. French measure 
(=945gr. troy) of spirit of nitre, whose specific gravity was 1.3 160, he dis- 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 13 

solved 2 oz. and 1 dr. of mercury ; the quantity of air obtained during the solu- 
tion was igo cubic inches French (= 202.55 English). This air was all nitrous. 
There remained a white mercurial salt, which, being distilled, afforded 12 cubic 
inches (= 12.785 English) of air mixed with red vapours, and which differed 
little from common air. There afterwards arose 224 cubic inches (= 238.56 
English) of dephlogisticated air, during the production of which, the mercury 
was almost revivified, there remaining but a few grains of a yellow sublimate. 
The 12 inches of air mixed with red vapours arose, he says, from a mixture of 
36 cubic inches of nitrous air (=38.34 English) and 14 of dephlogisticated 
air (M.91 English) ; and as the mercury was almost wholly revived, he concludes, 
that these airs arose from the nitrous acid, and formed it; and hence infers, that 
16 oz. of this spirit of nitre (= 7560 gr. troy) contained 13 oz. 7 dr. 36fgr. 
(that is, 6589 gr. troy) of water, and consequently only Q7 1 gr. troy of real 
acid, and therefore 2oz. of this spirit of nitre contained but 120 gr. troy of real 
acid: but, by my calculation, 2oz. of this spirit of nitre contained 213 gr. acid; 
for its mathematical specific gravity is I.265. The same weight of acid will 
also be found in it by computing the weight of the volumes of the different airs 
he himself found it consist of, or at least to afford by its decomposition ; for 
202.55 cubic inches of nitrous air weigh, by Mr. Fontana's experiment, 80.8174 
gr. troy, and 238.56 inches of dephlogisticated air weigh 100.ig52gr. troy, and 
adding to these the weight of 38.34 inches of nitrous air, and of 14.91 of 
dephlogisticated air, which made the 12 cubic inches of air mixed with red 
vapours, we shall find the whole weight of these airs to be 202.181 gr. the few 
grains wanting of 213 gr. may be accounted for from the absorption of the water 
in which he received the airs, and by allowing for that still remaining in the 
yellow sublimate. 

Of oil of vitriol. — The oil of vitriol I made use of was not perfectly dephlo- 
gisticated; but though pale, yet a little inclined to red. It contained some 
whitish matter, as I perceived by its becoming milky on the affusion of pure 
distilled water. How far this may alter the result of the following experiments 
1 have not tried; but believe it to be as pure as that which is commonly used in 
experiments, and therefore the fittest for my purpose. 

To 2519.75 gr. of this oil of vitriol, whose specific gravity was 1.81Q, I 
gradually added lSOgr. of distilled water, and 6 hours after found its specific 
gravity to be 1.77 1. To this mixture I again added 1 78.75 gr. of water, and 
found its specific gravity, when cooled to the temperature of the atmosphere, 
to be I.719: it was then milky, t then saturated the same quantity of the oil 
of tartar abovementioned, with each of these sorts of oil of vitriol in the manner 
already mentioned, and found the saturation to be effected (taking the medium 
of 5 experiments) by 6.5 gr. of that whose specific gravity was 1.819; by 6.96 



14 PHILOSOPHICAL TRANSACTIONS. [aNN0 1781. 

gr. of that whose specific gravity was 1-77 I ; and by 7.41 of that whose specific 
gravity was 1 .7 J 9. 

I was obliged to add a certain proportion of water to each of these sorts of 
oil of vitriol; for when they were not diluted, I perceived that part of the acid 
was phlogisticated, and went off with the fixed air; but knowing the quantity of 
water that was added, it was easy to find, by the rule of proportion, the quantity 
of each sort of oil of vitriol that was taken up by the alkali. Hence I supposed that 
each of these quantities of oil of vitriol, of different densities, contained 3.55 
gr. of acid, as they saturated the same quantity of vegetable fixed alkali as 1 1 gr. 
of spirit of nitre, which contained that quantity of acid. 

I then endeavoured to find the specific gravity of the pure vitriolic acid, in 
the same manner as I before had that of the nitrous, as it cannot be had in the 
shape of air unless united to such a quantity of phlogiston as quite alters its 
properties. The loss of 6.5 gr. of oil of vitriol, whose specific gravity is 1.81 9, 

is — '- — = 3.572; but as these 6.5 gr. contained, besides 3.55 gr. acid, 2.Q5 of 

1.819 
water, the loss of this must be subtracted from the entire loss, and then the 

remainder 0.622 is the loss of the pure acid part, in that state of density to 

which it is reduced by its union with water. The specific gravity therefore of the 

3 55 

pure vitriolic acid, in this state of density, is -^.- = 5.707. But to find its 
natural specific gravity, we must find how much its density is increased by its 
anion with this quantity of water: and in order to observe this, I proceeded as 
before with the nitrous acid. Thus, 6.96 gr. of oil of vitriol, whose specific 
gravity was 1-771, contained 3.55 gr. acid, and 3.41 of water; then its specific 
gravity by calculation should be I.726, for the loss of 3.55 gr. acid is — '— - = 
.0622; the loss of 3.41 gr. water is 3.41 ; the sum of the losses 4.032. Then 
~-s= 17.261 ; therefore the accrued density is I.771 — I.726 = .045. 
Taking this therefore from 1.81 9, its mathematical specific gravity will be 
1.774; then the loss of 6.5 gr. of oil of vitriol, whose specific gravity, 

by observation, is 1.819, will be found to be — —^ = 3.664; but of this, 

* 1.7/4? 

2.95 gr. are the loss of the water it contains, and the remainder 0.7 14* the loss 

3 55 
of the mere acid part. Then — '— = 4.9649 is nearly the true specific gravity 

of the pure vitriolic acid. I then found the true increase of density arising from 
the union of the vitriolic acid and water in the foregoing mixtures, and observed, 
that in oil of vitriol, whose specific gravity was 1.77 1 3 it was 0.84, and in that 
whose specific gravity was 1 .7 19, it was 0.100. 

* By mistake, the following calculations were made on the supposition dial the loss was 0.715; 
the difference being immaterial, die calculations were not repeated. — Orig. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 15 

To obtain a synthetical proof of these deductions, I compared them with the 
specific gravities of the first mixtures I had made: for if these deductions were 
true, the mathematical specific gravities, and the accrued densities, added to 
each other, should amount to the same quantity, as the specific gravities by 
observation; and this I found to happen very nearly: for in the first 
experiment, where 251 9.7 5 gr. of oil of vitriol, whose specific gravity was 
1.8 19, were mixed with 180 gr. of water, that oil of vitriol contained 
by my calculation 1376.171 gr. of acid and 1143.597 gr. of water, 
besides the 180 gr. of water that were added to it, the loss of the acid was 

■ ° ' ' = 277.22. The whole quantity of oil of vitriol was 2699.75 gr.; then 

the sum of the losses was 1600.8I ; and therefore the mathematical specific 

gravity '" *, = 1.686; to which adding 0.84, the degree of accrued density, 

the specific gravity by observation should be 1 .770, which wants less than 1000th 
part in 2700 of being just. Again: in the mixture whose specific gravity was 
1.719, the sum of the losses was 1779.549, and the weight of the whole 
2878.4; the mathematical specific gravity should be — — '-— - ■== I.617; towhich 

adding O.100, the specific gravity by observation should be J. 7 17, which is 
nearly the truth. 

By continuing these mixtures till the specific gravities by calculation and 
observation nearly coincided, I formed the following table. The extra-tabular 
proportions are to be sought in the manner already shown; the first two series 
were formed by analogy. 



16 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781. 



Oil and 
spirit of 
vitriol. 



Grs. 

5.58 
6.04 
6.5 
6.96 
7.41 
7.87 
8.33 
8 79 
9-'5 
9-71 
10.17 
10.03 
1 1 .09 
11.55 
12.01 
12.47 
12.93 
13.39 
13.85 
14.31 
14.77 
15.23 
15.69 
16.15 
16.61 
17.07 
17.53 
17.99 
18.45 
1891 
19.37 
19-83 
20.29 
20.75 
21.21 
21.67 
22.13 
22.59 
23.05 
23.51 
23.97 
24.43 
24.89 
25.35 
25.81 
26.27 
26.73 
27.19 
27.65 



Acid. 



Water. 



Grs. 



3.35 



Grs. 
2.03 
2.49 
2.95 
3.41 
3.86 
4.32 
4.78 
5.24 
5.70 
6.16 
6.62 
7.08 
7.54 
8.00 
8.46 
8.92 
9-38 
9.84 
'0.30 
10.76 
11.22 
11.68 
12.14 
12.60 
13.06 
13.52 
13.98 
14.44 
1490 
15.36 
15.82 
16.28 
16.74 
17.20 
17.66 
18.12 
18.58 
19-04 
19.50 
19.96 
20.42 
20.88 
21.34 
21.80 
22.26 
22.72 
23.18 
23.64 
24 10 



Acer ed I Mat *" e ~ | Specific lAttract. of Attract, of 
density | mat ' s P e " g rav ' t y bv ^ e acid water to 
' ' ]cific grav. observat. to water, the acid. 



.000 
.005 
.045 
.084 
0.100 
0.112 
0.122 
0.129 
0.137 
0.139 
0.140 
0.139 
0.132 
0.127 
0.120 
0.113 
0.106 
0.100 
0.094 
0.088 
.083 
.078 
.074 
.070 
.066 
.062 
.059 
.056 
.053 
.050 
.047 
.044 
.040 
.038 
.035 
.032 
.029 
.026 
.023 
.020 
.018 
.016 
.014 
.012 
.010 
.008 
.006 
.004 
.002 



2.032 

1.884 

1.774 

1 .687 

I.619 

1.563 

1.515 

1.476 

1.441 

1.412 

1.385 

1.363 

1.343 

1.325 

1.308 

1.294 

1.280 

1.268 

1.257 

1.247 

1.237 

1.228 

1.220 

1.212 

1.205 

1.199 

1.191 

1.187 

1.181 

1.176 

1.167 

1.166 

1.162 

1.158 

1.154 

1.150 

1.146 

1.143 

1.140 

1.137 

1.134 

1.131 

1.128 

1.125 

1.123 

1.120 

1.118 

1.116 

1.114 



2.032 

1.889 

1.819 

1.771 

1.719 

1.675 

1.637 

1 .605 

1.578 

1.551 

1.525 

1.502 

1.475 

1.452 

1.428 

1.407 

1.386 

1.36S 

1.351 

1335 

1.320 

1 .306 

1-294 

1.282 

1271 

1.261 

1.250 

1.243 

1.234 

1.226 

1.214 

1.210 

1.203 

1.196 

1.189 

1.182 

1.175 

1.169 

1.163 

1.157 

1.152 

1.147 

1.142 

1.137 

1.133 

1.128 

1.124 

1.120 

1.116* 



.005 
.045 
.084 
0.100 
0.112 
0.122 
0.129 
0.137 
0.139 
0.149 
0.140 



0.140 

0.149 

0.139 

0.137 

0.129 

0.122 

0.U2 

0.100 

.084 

.045 

.005 



The specific gravity of the most concentrated oil of vitriol yet made is, 
according to Mr. Beaume and Bergman, 2.125. 

I ascertained the proportion of acid water and fixed alkali in tartar vitriolate, as 



TOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. \J 

before, in nitre and digestive salt. I found the salts, resulting from the satura- 
tion of the same oil of tartar, with portions of oil of vitriol of different specific 
gravities, to weigh, at a medium, 12.45 gr. Of this weight, only 11.85gr. 
were alkali and acid, the remainder therefore was water, viz. 0.6 of a grain; 
consequently 100 gr. of perfectly dry tartar vitriolate contain 28.51 gr. acid, 4.82 
of water, and 6667 of fixed vegetable alkali. In drying this salt I used a heat 
of 240° to expel the adhering acid more thoroughly, and I kept it in that heat a 
quarter of an hour. 

According to Mr. Homberg, 1 French oz. (or 472.5 gr. troy) of dry salt of 
tartar required 297.5 gr. troy of oil of vitriol, whose specific gravity was I.674, 
to saturate it; but, by my calculation, this quantity of fixed alkali would require 
325 gr. : a difference which, considering our different methods of determining 
the specific gravity of liquids (his method, viz. that by mensuration, giving it 
always less than mine) the different desiccation of our alkalis, &c. may pass 
for inconsiderable. 

The resulting salt weighed, according to Mr. Homberg, 182 gr. Troy above 

the original weight of the fixed alkali ; but by my experiment it should weigh 

but 87.7 gr. more; for 10.5 : 12.45 :: 472.5 : 560.2. It is bard to say how 

Mr. Homberg could find this great excess of weight both in nitre and tartar 

vitriolate, unless he meant by the original weight of the salt of tartar the weight 

of the mere alkaline part, distinct from the fixed air it contained : and indeed 

one would be apt to think he did make this distinction ; for in that case the 

excess of weight will be very nearly such as he determined it : for 10.5 : 8.3 :: 

472.5 : 373.3. Now the whole weight of his nitre was 56o.2,as above shown; 

then 560.2 — 373.3 = 11 6.9, which is only 4 gr. more than he determined it. 

Hence he inferred, that 1 oz. (472.5 gr. Troy) of this oil of vitriol contains 

291.7 gr. of acid. By my computation it contains but 213.3 ; but it must be 

considered that he made no allowance for the water contained in tartar vitriolate, 

and imagined the whole of tne increase of weight proceeded from the acid that 

is united in it to the fixed alkali. Now the aqueous part in o6o gr. of tartar 

vitriolate amounts to 37 gr. the remaining difference may be attributed to the 

different degrees of desiccation, &c. 

Of the acetous acid. — I have made no experiment on this acid ; but, by 
calculating from the experiment of Mr. Homberg, I find the specific gravity of 
the pure acetous acid, free from superfluous water, should be 2.130. It is pro- 
bable that its affinity to water is not strong enough to cause any irregular increase 
in its density, at least that can be expressed by 3 decimals ; and hence its pro- 
portion of acid and water may always be calculated from its specific gravity and 
absolute weight. 100 parts of foliated tartar, or, as it should rather be called, 
acetous tartar, contain well dried 32 of fixed alkali, .19 of acid, and 49 parts of 
vol xv. D 



18 l'HILOSOl'HICAL TRANSACTIONS. [ANNO 1781. 

water. The specific gravity of the strongest concentrated vinegar yet made, is 
1 .o6g. It is more difficult to find the point of saturation with the vegetable 
than with the mineral acids ; because they contain a mucilage that prevents their 
immediate union with alkalis ; and hence they are commonly used in too great 
quantity. They should be used moderately hot, and sufficient time should be 
allowed them to unite. 

From these experiments it follows : 1st. That fixed vegetable alkalis take up 
an equal quantity of the 3 mineral acids, and probably of all pure acids ; for 
we have seen that 8.3 grains of pure vegetable alkali, that is, free from fixed air, 
take up 3.55 gr. of each of these acids; and consequently 100 parts of caustic 
fixed alkali would require 42.4 parts of acid to saturate them. Now Mr. Berg- 
man has found, that 100 parts of caustic fixed vegetable alkali take up 47 parts 
of the aerial acid, which, considering his alkali might contain some water, differs 
but little from my calculation. It should therefore seem, that alkalis have a cer- 
tain determinate capacity of uniting to acids, that is, to a given weight of acids ; 
and that this capacity is equally satiated by that given weight of any pure acid 
indiscriminately. This weight is about 2.35 of the weight of the vegetable 
alkali. 2dly. That the three mineral acids, and probably all pure acids, take up 
2.253 times their own weight of pure vegetable alkali, that is, are saturated by 
that quantity. 

3dly. That the density accruing to compound substances, from the union of 
their component parts, and exceeding its mathematical ratio, increases from a 
minimum, when the quantity of one of them is very small in proportion to that 
of the other ; to a maximum, when their quantities differ less ; but that the at- 
traction, on the contrary, of that part which is in the smallest quantity to that 
which is in the greater, is at its maximum when the accrued density is at its 
minimum, but not reciprocally ; and hence the point of saturation is probably 
the maximum of density and the minimum of sensible attraction of one of the 
parts. Hence no decomposition operated by means of a substance that has a 
greater affinity with one part of a compound than with the other, and than these 
parts have to each other, can be complete, unless the minimum affinity of this 
3d substance be greater than the maximum affinity of the parts already united. 
Hence few decompositions are complete unless a double affinity intervenes ; and 
hence the last portion of the separated substance adheres so obstinately to that to 
which it was first united, as all chemists have observed. Thus, though acids 
have a greater affinity to phlogiston than the earths of the different metals have 
to it, yet they can never totally dephlogisticate these earths, but only to a cer- 
tain degree ; so though atmospheric air, and particularly dephlogisticated air, at- 
tracts phlogiston more strongly than the nitrous acid does ; yet not even dephlo- 
gisticated air can deprive the nitrous acid totally of its phlogiston, as is evident 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. ly 

from the red colour of the nitrous acid when nitrous air and dephlogisticated air 
are mixed together. Hence also mercury precipitated from its solution in any 
acid, even by fixed alkalis, constantly retains a portion of the acid to which it 
was originally united, as Mr. Bayen has shown ; so also does the earth of alum, 
when precipitated in the same manner from its solution ; and thus several anoma- 
lous decompositions may be explained. Indeed, I have reason to doubt whether 
mercury does not attract acids more strongly than alkalis attract them. 

4thly. That concentrated acids are, in some measure phlogisticated, and 
evaporate by union with fixed alkalis. 5thly. That knowing the quantity of 
fixed alkali in oil of tartar, we may determine the quantity of real pure acid in 
any other acid substance that is difficultly decomposed, as the sedative acid, and 
those of vegetables and animals; for 10.5 gr. of the mild alkali will always be 
saturated by 3.55 gr. of real acid: and reciprocally, the quantity of acid in any 
acid liquor being known, the quantity of real alkali in any vegetable alkaline 
liquor may be found. 

Of the specific gravity of Jived air in its fixed stale. — Being desirous to 
know the specific gravity of some substances which are difficultly procured, or 
at least preserved for any time, free from fixed air, such as fixed and volatile al- 
kalis, I was induced to seek the specific gravity of the former in its fixed state, 
as of an element necessary to the calculation of the latter ; it being very evident 
that its density, in its fixed state, must be very different from that which it pos- 
sesses in its fluid elastic state. I therefore took a piece of white marble, of the 
purest kind, which weighed 440.25 gr. and weighing it in water, found it to 
losel62gr. ; its specific gravity was therefore 2.7 J 75. Of this marble, reduced 
to a fine powder, I put 1 80 gr. into a phial, and expelling the fixed air by the 
dilute vitriolic acid and heat, I found its quantity amount to 105.28 cubic inches ; 
the thermometer being at 65°, and the barometer between 29 and 30 inches; 
this bulk of air would, at 55° of Fahrenheit, occupy but 102.4 cubic inches; at 
which temperature, accordir o to the experiment of Mr. Fontana, a cubic inch 
of fixed air, the barometer being at 29°^-, would weigh 0.57 of a grain ; there- 
fore the weight of the whole quantity of fixed air amounted to 58.368 gr. which 
is nearly -i- of the weight of the marble. At this rate, 100 gr. of the marble 
contained 32.4 2 of fixed air. 

To determine the proportion of water and calcareous earth, and also the 
specific gravity of this latter, I put 300g.25 gr. of the same marble finely 
powdered into a crucible, loosely covered ; the crucible and its contents, before 
calcination, weighed 83Q4 gr. and after remaining 14 hours in a white heat I 
found it to weigh 7067-5 gr. The weight of the crucible alone was 5384.75 
gr. ; therefore the weight of the lime singly was 1 682.75 gr. The marble then 
lost by calcination 1326.5 gr.; 180 gr. of the marble should then lose 79.343 

d 2 



20 PHILOSOPHICAL TRANSACTIONS. [ANNO J 781. 

gr. and 100 gr. should lose 44.08 ; but of these 44.08, 32.42 were fixed air, as 

is already seen, therefore the remainder, that is, 1 1 .66 gr. were water, and the 

quantity of pure calcareous earth in lOOgr, of the marble was 55.Q2 gr. 

I next proceeded to discover the specific gravity of the lime. Into a brass 

box, which weighed 607-65 gr. and in the bottom of which a small hole was 

drilled, I stuffed as much as possible of the _ . 

drains. 
finely powdered lime, and then screwed the Weight of the box in air . . o'o7.6'5 

cover on, and weighed it both in air and water. Ill l "Z° f f w ,u Sl u m *??• " 73 ' 75 

, T . . Weight of the box and lime 

When immersed in this latter, a considerable in air 1013.3 

quantity of common air was expelled; when Weight of lime singly in air. 135.85 

. . , .... „. . ,. Loss ot weight of the box and 

this ceased, 1 weighed it. Ihe result of tins lime in water 256.5 

experiment was as annexed : Loss of wei S ht of lime s ™E l y ' S2.3 

Hence, dividing the absolute weight of the lime by its loss in water, its specific 
gravity was found to be 2.3Q08. 

From these data I deduced the specific gravity of fixed air in its fixed state ; 
for 100 gr. of marble consist of 55. 02 of earth, 32.42 of fixed air, and 1 1.66 
of water; and the specific gravity of the marble is 2.717- Now the specific 
gravity of the fixed air, in its fixed state, is as its absolute weight divided by its 
loss of weight in water ; and its loss of weight in water is as the loss of 100 gr. 
of marble minus the losses of the pure calcareous earth and of the water. 

Loss of 100 gr. of marble = = is6.8 gr. 

6 2.7 17 

55 9'2 
Loss of 55.92 gr. calcareous earth = • — — = 23.39 gr. 

2.390 6 

Loss of 1 1 .66 gr. water = 1 1 .66 

Sum 35.05 

Then the loss of the fixed air 36.8 — 35.05 = 1.75 ; consequently, its spe- 
cific gravity is — '■=-? = 18.52 ; by which it appears to be the heaviest of all acids, 
or even of all bodies yet known, gold and platina excepted. 

Of fixed vegetable alkali. — As the manner of conducting the experiments 
made on this salt was nearly the same as that used in the foregoing, except that 
to find its specific gravity I weighed it in aether instead of water, I shall content 
myself, to avoid the repetition of tedious calculation, with relating the result of 
these experiments. 1st. I found that lOOgr. of this alkali contain about 6.7 gr. 
of earth, which, according to Mr. Bergman, is siliceous : this earth passes the 
filter with it when the alkali is not saturated with fixed air, so that it seems to 
be held in solution as in liquor silicum. 2uMy. I found, that the quantity of 
fixed air in oil of tartar and dry vegetable fixed alkali, is various at various times 
and in various parcels of the same salt ; but that at a medium in the purer alkalis 
it maybe rated at 21 gr. in 100 ; and hence the quantity of this alkali in any 
solution of it may be very nearly guessed at, by adding a known weight of a 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 21 

dilute acid to a given weight of such solution, and then weighing it again ; for 
as 21 is to 100, so is the weight lost, to the weight of mild alkali in such 
solution. 

The specific gravity of mild and perfectly dry 4 times calcined fixed alkali, free 
from siliceous earth, and containing 21 per cent, of fixed air, I found to be 
5.0527. When it contains more fixed air, its specific gravity is probably higher, 
except it were not perfectly dry : whence I inferred the specific gravity of this 
alkali, when caustic and free from water, to be 4.234. 

From the weight of the aerial acid, in its fixed state, it happens, that fixed 
alkalis, when united to it, are specifically heavier than when united either to the 
vitriolic or nitrous acids. Thus Mr. R. Watson, in the Phil. Trans, for the 
year 1770, p. 337, found the specific gravity of dry salt of tartar, including 
siliceous earth, to be 2.761 : whereas the specific gravity of tartar vitriolate was 
only 2.636, and that of nitre l.y33. The reason why nitre is so much lighter 
than tartar vitriolate, is, because it contains much more water, and its union 
with the alkali is less intimate. 

Impure vegetable fixed alkalis, such as pearl ash, pot ashes, &c. contain more 
fixed air, as appears by the experiments of Dr. Lewis. Pearl ash, according to 
Mr. Cavendish, contains 28.4 or 28.7 per cent, of fixed air. Hence, in lyes of 
equal specific gravity with those of a purer alkali, the quantity of saline matter 
will be more probably in the ratio of 28.4 or 2S.7 to 21 : but this surplus weight 
is only fixed air. 

III. Account of the violent Storm of Lightning at East-Bourn, in Sussex, 
Sept. ^7, 1780. Communicated by Owen Salusbury Brereton, Esq., F. R., 
and A. S. p. 42. 

I am desired by my friend and neighbour James Adair, Esq., of Soho-square, 
to communicate an account of Icie dreadful accident which happened to him and 
his family at East-Bourn, in the county of Sussex, at Q o'clock in the morning, 
on Sunday the 17th of September last, (1780). He rented a house which 
stood by itself, built of various sorts of stone, 3 stories high, and facing the 
sea, which was nearly south-east of it. The morning was very stormy, with 
rain, thunder, and lightning; and just at 9 o'clock a horrid black cloud ap- 
peared, out of which Mr. Adair saw several balls of fire drop into the sea 
successively, as he was approaching the window in a one-pair of stairs room; 
and very soon after, as he was standing at it with his hands clasped, and extended 
open against the middle of the frame, a most violent flash of fire forced his 
hands asunder, and threw him several yards on the floor on his back, with both 
his legs upright in the air, which remained long so fixed. He was very sensible 
of his situation all the time, but could not open his eyes nor speak; nor had he 



22 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

the least power of motion of any of his limhs for a long time. On help coming 
in, and examining his clothes, which were blue cloth, his right sleeve, both of 
coat and waistcoat, and also shirt, were all torn on the inside of the arm entirely 
open, as if by a dog, from the shoulder to the wrist; the right side of the 
breeches was tern in the same manner, and part of each of the brass buttons 
melted. 

He had in his fob a gold watch with a steel chain; the button which opens it, 
and 3 other places of the case were melted. The pendant to which the chain is 
fixed was almost melted through, and much of the steel chain is incorporated with 
it, as is reciprocally some gold on that part of the steel which was within the fob. 
The going of the watch had stopped instantaneously, occasioned as at first appeared 
by the small pendulum spiral steel spring having been lengthened; not that it was 
absolutely so, but relatively, respecting the scapement of the watch, the several 
inner turns being brought closer together. His right arm, right side, and thigh, 
were miserably scorched, and the flesh torn: the foot of the stocking of his right 
leg and his shoe were torn in several places between the buckle and the toe-end 
of the shoe, and one of his toes split almost to the bone; but the buckle, which 
was a broad silver one, was not the least hurt nor even marked, and remained 
buckled as before. His sleeve-button of gold, in which was plaited hair covered 
with crystal, was broken from its link, and neither hair nor crystal have been 
found. A key and a penknife in his right-side breeches pocket have several 
marks of fusion on them. 

The frame of the window, on which Mr. Adair was leaning, was little 
damaged; but every pane of glass so completely smashed, it could scarcely be 
perceived it had ever any glass in it. The room was stuccoed and papered, and 
between the windows hung a large pier glass, which, with much of the stucco, 
was shivered to pieces, and strewed over the floor. A door opposite the window 
was shattered to pieces, and the posts of a bed in a room behind, and all the 
bell-wires were destroyed. Under the dining-room Mr. Adair was in, on the 
parlour floor, were his coachman, butler, and footman. The coachman was 
going to open a glass-door to go towards the sea, and was struck dead. His 
body was totally black. His clothes, and the caul of his wig, and cravat, were 
much torn; but no particular flesh wound was found. The enamelled face of 
his silver watch was broken to pieces, and the links of its steel chain fastened 
together. 

The footman was dressing his hair near a window, when he was thrown dead 
on the ground. He appeared much scorched, bruised, and black. He had a 
very large wound in his side, which penetrated near his heart; but very little, if 
any, blood came from it. His buck-skin breeches were much torn, and the 
steel of a metal knee-buckle driven through them. The window sash was driven 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 23 

into the room, and a stone, about 8 inches square, forced out of the wall into 
the middle of the room, not far from the body. The butler was a yard or two 
behind the coachman, and going out with a telescope in his hand, which was 
forced in pieces from him, his hat and wig were thrown to some distance, and 
he perceived a violent pressure on his skull and on his back, but was no other- 
wise hurt. He had a silver watch with a silver chain, which received no damage. 
In the room over Mr. Adair's, a young lady was dressing, and her maid attend- 
ing. They were both driven to a distant part of the room, and rendered insen- 
sible for some time, but not hurt. The posts of the bed she had just left were 
all shivered to pieces, and the bell wires destroyed, and the chimney thrown 
down on the roof. 

Though the bodies of the two servants lay unburied from Sunday till Tues- 
day, all their limbs were as entirely flexible as those of a living person. Multi- 
tudes on the shore before the house saw the meteor dart in a right line over their 
heads, and break against the front of the house in different directions, and all 
agreed that the form and flame was exactly like that of an immense sky-rocket. 

IF. An Account of the Harmattan, a singular African Wind. By Matthew 

Dobson, M. D., F. R. S. p. 46. 

The harmattan is a periodical wind, which blows from the interior parts of 
Africa towards the Atlantic Ocean, and possesses such extraordinary properties, 
as to merit the attention of the naturalist, making a curious and important 
article in the history and theory of the winds. It is from the materials furnished 
by Mr. Norris, that the following account is drawn up. 

On that part of the coast of Africa which lies between Cape Verd and Cape 
Lopez, an easterly wind prevails during December, January, and February, 
which by the Fantees, a nation on the Gold Coast, is called the harmattan. 
Cape Verd is in 15° n. latitude, ind Cape Lopez in 1° s. latitude, and the coast 
between these two capes runs, in an oblique direction, nearly w. s. w. to e. s. e. 
forming a range of upwards of 2100 miles. At the Isles de Los, which are a 
little to the northward of Sierra Leone, and to the southward of Cape Verd, it 
blows from the e. s. e. on the Gold Coast from the n. e. and at Cape Lopez and 
the river Gabon, from the n. n. e.. This wind is, by the French and Portugueze 
who frequent the Gold Coast, called the n. e. wind, the quarter from which it 
blows. The English, who sometimes borrow words and phrases from the 
Fantee language, which is less guttural and more harmonious than that of their 
neighbours, adopt the Fantee word harmattan. The harmattan comes on 
indiscriminately, at any hour of the day, at any time of the tide, or at any 
period of the moon, and continues sometimes only a day or two, sometimes 5 
or 6 days, and it has been known to last 15 or l6 days. There are generally 3 



24 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

or 4 returns of it every season. It blows with a moderate force, not quite so 
strong as the sea breeze, which every clay sets in during the fair season from the 
w. w. s. w. and s. w.; but somewhat stronger than the land wind at night from 
the n. and n. n. w. 

1. A fog or haze is one of the peculiarities which always accompanies the 
harmattan. The gloom occasioned by this fog is so great, as sometimes to 
make even near objects obscure. The English fort at Whydah stands about the 
midway between the French and Portuguese forts, and not quite a quarter of a 
mile from either, yet very often from it neither of the other forts can be dis- 
covered. The sun, concealed the greatest part of the day, appears only for a 
few hours about noon, and is then of a mild red, exciting no painful sensation 
on the eye. The particles which constitute the fog are deposited on the grass, 
the leaves of trees, and even on the skin of the negroes, so as to make them 
appear whitish. They do not flow far over the surface of the sea: at 2 or 3 
miles distance from the shore the fog is not so thick as on the beach; and at 4 
or 5 leagues distance it is entirely lost, though the harmattan itself is plainly 
felt for 10 or 12 leagues, and blows fresh enough to alter the course of 
the current. 

2. Extreme dryness makes another extraordinary property of this wind. No 
dew falls during the continuance of the harmattan; nor is there the least 
appearance of moisture in the atmosphere. Vegetables of every kind are very 
much injured, all tender plants, and most of the productions of the garden, are 
destroved; the grass withers, and becomes dry like hay; vigorous ever-greens 
likewise feel its pernicious influence; the branches of the lemon, orange, and 
lime trees droop, the leaves become flaccid, wither, and, if the harmattan con- 
tinues to blow for 10 or 12 days, are so parched as to be easily rubbed to dust 
between the fingers: the fruit of these trees, deprived of its nourishment, and 
stinted in its growth, only appears to ripen, for it becomes yellow and dry, 
without acquiring half the usual size. The natives take this opportunity, of 
the extreme dryness of the grass and young trees, to set fire to them, especially 
near their roads, not only to keep the roads open to travellers, but to destroy 
the shelter which long grass, and thickets of young trees, would afford to skulk- 
ing parties of their enemies. A fire thus lighted flies with such rapidity as to 
endanger those who travel: in that situation a common method of escape is, 
on discovering a fire to windward, to set the grass on fire to leeward, and then 
follow your own fire. There are other extraordinary effects produced by the 
extreme dryness of the harmattan. The covers of books, even closely shut up 
in a trunk, and lying among clothes, are bent as if they had been exposed to 
the fire. Household furniture is also much damaged: the pannels of doors and 
of wainscot split, and any veneered work flies to pieces. The joints of a well- 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 25 

laid floor of seasoned wood opened sufficiently to lay one's finger in them ; but 
become as close as before on the ceasing of the harmattan. The seams also in 
the sides and decks of ships are much injured, and the ships become very leaky, 
though the planks are 2 or 3 inches in thickness. Iron-bound casks require the 
hoops to be frequently driven tighter; and a cask of rum or brandy, with 
wooden hoops, can scarcely be preserved ; for, unless a person attends to keep 
it moistened, the hoops fly off. 

The parching effects of this wind are likewise evident on the external parts of 
the body. The eyes, nostrils, lips, and palate, are rendered dry and uneasy, 
and drink is often required, not so much to quench thirst, as to remove a painful 
aridity in the fauces. The lips and nose become sore, and even chapped; and 
though the air be cool, yet there is a troublesome sensation of prickling heat on 
the skin. If the harmattan continues 4 or 5 days, the scarf skin peels off", first 
from the hands and face, and afterwards from the other parts of the body, if it 
continues a day or two longer. Mr. Norris, who frequently visited the coast of 
Africa, observed, that when sweat was excited by exercise on those parts which 
were covered by his clothes from the weather, it was peculiarly acrid, and tasted, 
on applying his tongue to his arm, something like spirit of hart's-horn diluted with 
water. 

As the state of salt of tartar placed in the open air, and the quantity evapo- 
rated from a given surface of water, are obvious proofs of the comparative mois- 
ture or dryness of the atmosphere, Mr. Norris put the harmattan to each of 
these tests; and particularly to moisten salt of tartar ad deliquium, and exposed 
it to the night air during the time that the harmattan was blowing. The follow- 
ing is the account of the result of these experiments. Salt of tartar will not 
only remain dry during the night as well as in the day; but, when liquefied so 
as to run on a tile, and exposed to tie harmattan, becomes perfectly dry in 2 or 
3 hours; and, exposed in like manner to the night air, will be dry before 
morning. 

It appears, from experiments made by Mr. Norris, that if the evaporation of 
the whole year be supposed to go on in the same proportion with what occurred 
during a short and very moderate return of the harmattan, the annual harmattan 
evaporation would be 133 inches; and if the calculation was made in proportion 
to the evaporation which occurs during a longer visit from the harmattan, and a 
more forcible breeze, the annual harmattan evaporation would be much more 
considerable. If the annual evaporation be in like manner calculated, in pro- 
portion to the evaporation which took place subsequent to and preceding the 
harmattan, the annual evaporation at Whydah on the Gold Coast, would be 64 
inches, and he had found the annual evaporation at Liverpool to be 36 inches. 

VOL. xv. E 



26 PHILOSOPHICAL TRANSACTIONS. [ANNO I78I. 

These three therefore are in the following proportion; harmattan 133 inches, 
Whydah 64 inches, and Liverpool 36 inches. 

3. Salubrity forms a third peculiarity of the harmattan. Though this wind is 
so very prejudicial to vegetable life, and occasions such disagreeable parching 
effects on the human species, yet it is Highly conducive to health. Those 
labouring under fluxes and intermitting fevers generally recover in an harmattan. 
Those weakened by fevers, and sinking under evacuations for the cure of them, 
particularly bleeding, which is often injudiciously repeated, have their lives 
saved, and vigour restored, in spite of the doctor. It stops the progress- of 
epidemics: the small-pox, remittent fevers, &c. not only disappear, but those 
labouring under these diseases, when an harmattan comes on, are almost certain 
of a speedy recovery. Infection appears not then to be easily communicated 
even by art. In the year 1770 there were on board the Unity, at Whydah, 
above 300 slaves; the small-pox broke out among them, and it was determined 
to inoculate; those who were inoculated before the harmattan came on, got very 
well through the disease. About 70 were inoculated a day or two after the har- 
mattan set in; but not one of them had either sickness or eruption. It was 
imagined, that the infection was effectually dispersed, and the ship clear of the 
disorder; but in a very few weeks it began to appear among these 70. About 50 
of them were inoculated the second time; the others had the disease in the 
natural way: an harmattan came on, and they all recovered, except one girl, 
who had an ugly ulcer on the inoculated part, and died some time afterwards of 
a locked jaw. Mr. Norris dissents from Dr. Lind, who speaks of the harmattan 
as " fatal and malignant; that its noxious vapours are destructive to blacks as 
well as whites; and that the mortality which it occasions is in proportion to the 
density and duration of the fog." The baneful effects here pointed out proceed 
from the periodical rains which fall in March, April, &c. and which are ushered 
in by the tornados, or strong gusts of wind from the n. e. and e. n. e. accom- 
panied with violent thunder and lightning, and very heavy showers. The earth, 
drenched by these showers and acted on with an intense solar heat as soon as 
the storm is over, sends forth such noisome vapours as strike the nostrils with 
a most offensive stench, and occasion bilious vomitings, fluxes, and putrid fevers. 
Besides these vapours, which are annual, there appears to be a collection of still 
more pestiferous matter, confined for a longer time, and issuing from the earth 
after an interval of 5, 6, or 7 years. There may indeed be instances in which 
the harmattan comes loaded with the effluvia of a putrid marsh; and if there are 
any such situations, the nature of the wind may be so changed as to become 
even noxious. 

It appears that, except a few rivers and some lakes, the country about and 






VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 2? 

beyond Whydah is covered for 400 miles back, with verdure, open plains of 
grass, clumps of trees, and some woods of no considerable extent. The surface 
is sandy, and below that a rich reddish earth; it rises with a gentle ascent for 
1 50 miles from the sea before there is the appearance of a hill, without afford- 
ing a stone of the size of a walnut. Beyond these hills there is no account of 
any great ranges of mountains. With respect to the origin of this wind, 
Mr. Norris says, " the harmattan, according to Dr. Lind, arises from the con- 
flux of several rivers about Benin; but when I was on a visit to the King of 
Dahomey, 120 miles north, or inland from the fort at Whydah, I there felt the 
harmattan blowing from the n. e. stronger than I have at any other time, though 
Benin then bore from me s. e." On this head Mr. Norris makes the following 
conjecture: " The intersection of 3 lines, viz. an east line drawn from Cape 
Verd, a north-east one from the centre of the Gold Coast, and a north line 
from Cape Lopez, would point out a probable source of this extraordinary wind." 
Three lines, drawn according to the direction of Mr. Norris, towards the points 
of the compass from which the harmattan blows on Cape Verd, the Gold Coast, 
and Cape Lopez, converge to a part of Africa about the 15th degree of n. lati- 
tude, and the 25th degree of e. longitude, which is that part of Africa where, 
according to Ptolemy, the mountains of Caphas are situated. From these 
mountains, according to the same authority, the river Daradus arose, supposed 
by some to be now the river Senegal. It may be conjectured, that the dis- 
agreeable Levant wind of the Mediterranean proceeds from the same part of 
the continent of Africa; for it prevails during the same season of the year, and 
may derive its qualities from the surface over which it passes. 

The last article of information with which I have been favoured by 
Mr. Norris, is an account of the manner in which the Fantee nation divide 
their year. Aherramantah, or the harmattan, from the 1st of December to the 
middle of February, about 10 weeks. Quakorah, a wind up the coast, from 
s. s. w. to s. s. e. from the middle of February to the first week in March, about 
3 weeks. Pempina, or tornado season, part of March, all April, and the 
greatest part of May, about 12 weeks. Abrenama, or the old man's and 
woman's children, that is, the Pleiades, the rainy season, the latter end of May, 
all June, and to about the 20th of July, 8 weeks. Atukogan, or 5 stars, that 
is, Orion, high wind and squally, the rains very heavy, to the middle of August, 
3 weeks. Worrobakorou, or one star, the ceasing of the rains, about 3 weeks. 
Mawurrah, the name of a certain star ; close, foggy weather and no breeze, the 
first 3 weeks in September. Boutch, no land breeze in this season, the wind 
blows fresh down the coast, about 6 weeks. Autiophi, or the croziers; tornados 
and southerly wind, with some rain, generally called the latter rains, about 4 

e 2 



28 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

weeks, to the beginning of December, when the Aherramantah season again 
commences. 

V. A New Method of applying the Screw. By Mr. IVm. Hunter, Surg. p. 58. 
The method is somewhat similar to Nonius's division of the circle. In cer- 
tain cases it may be attended with some advantages to a greater degree than by 
those commonly practised. Let ab (rig. 2, pi. 1) be a plate of metal in which 
the screw cd plays, having a number of threads in an inch equal to a. Within 
the screw cd there is a female screw, by which is received the smaller screw de 
of a + 1 threads in an inch. This screw is retained from moving round along 
with the screw cd by means of the apparatus at afgb. Now, if the handle ckl 
be turned a times round the screw, cd will advance upwards an inch, and if we 
suppose the screw de to move round along with cd, the point e will also advance 
an inch. If we now turn the screw de a times backward, the point e will move 



a 



downwards of an inch, and the result of both motions will be to lift the 

a + i 

point e upward (1 =) of an inch. But if, while the screw cd is 

1 a + 1 ' a + I 

turned a times round, de be kept from moving, the effect will be the same as if 
it had moved a times round with cd and been a times turned back, that is, it 

will advance of an inch. At one turn therefore of the handle ckl it will 

a + I 

move upwards ( X =) -; of an inch. If then we suppose the handle 

r v a + 1 a ' a- + a rr 

ckl to be b inches long, the power gained by the machine will be as (a 2 -|- a) 
X 6.2832 b to unity. 

To illustrate this by a particular example, let the screw cd have 10 threads in 
an inch, and de 1 1 ; then, while the handle ckl is turned 10 times round, the 
point d will rise 1 inch above its former situation. But at 10 turns it can only 
pass over 10 threads of the screw de, and consequently it will advance on that 
screw 4-f of an inch. The point e therefore must rise V4- of an inch, that the 
point d may have room to rise a complete inch above its former place: therefore, 
at one turn of the handle, the point e will rise -H-o of an inch; and if the handle 
be supposed half a foot long, the power, to produce an equilibrium, must be to 
the weight, as 1 to 110 X 6.2832 X 6 = 4146. 012, which is the very number 
expressed by the general theorem, viz. (c a + a) X 6.2832 b, calling a = 10 
and b = 6. 

Now let us compare, according to the rules before laid down, this method of 
using the screw with the common one. And first, in order to have the same 
power by means of the common screw that is exerted by this machine, it must 
have a number of threads in an inch equal to a 1 + a, which would render it too 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 29 

weak to resist any considerable violence. For example, if DC have 5 threads in 
an inch, and de 6, and if the handle ckl be afoot in length, the power gained 
by the engine will be nearly as (a 2 + a) X 6b = 2l60 to 1; whereas, to have 
the same force by means of the common screw, it must have 30 threads in an 
inch, and so must yield under a resistance which the other screw would overcome 
without any difficulty. On this principle, the screw may be applied with advan- 
tage in presses of different kinds, by fixing one of the plates of the press to the 
end of the screw at e. 

If the screw de be intended to carry an index which must turn round at the 
same time that it rises upwards, the common screw is preferable; for though I 
can see a method by which the machine before described may be made to answer 
this purpose, I am almost afraid to propose it. I mean, that within the screw 
de another still smaller should be made to play, and be connected with the 
screw cd, so as to move round along with it. It must have a 2 + a -f- 1 threads 
in an inch, and they must be in the contrary direction to those of cd, so that 
when they are both turned together, and cd moves upward, this other one 
may move downward. At one turn of the handle this will move upward 

— - — X -3 -7 = 4 , o 3 ~, a i i — °f an mcn J a "d at the same time will move 

a* + a a 2 + a + I a* + 2a 3 + 2u* + a 

round in a circular direction. For example, let cd have 5 threads (= a) in an 
inch, de 6 (= a + l), and a third screw within de, but connected with cd so 
as to partake of its motion, 31 (= a' -f « + 0- At one turn of the handle, 
this screw will rise upwards j X{ X -rr = mhr of an inch ; but this appears too 
complicated for use, and the least inaccuracy in the construction would hinder it 
from moving. 

But, on the other hand, if while the point e rises it is of consequence that 
it be kept from going round, the machine under consideration will best answer 
this purpose. On this principle it may be useful in several respects: for instance, 
let a (fig. 3) represent a magnifying lens, and let it be moveable on the screw bc 
of l6 threads in an inch, which turns within the larger screw cd of 15 threads 
in an inch, and that again moves within the plate ef in the end of the cylinder 
gf.* To use the instrument, fix the object to be magnified on the pin gl, and 
then turn the lens A on the screw bc, till it be nearly at the proper distance from 
the pin, and opposite to it. You may then adjust the distance more accurately 
by turning the screw dc, at each turn of which the lens will recede from, or 
approach to, the pin -^-^ of an inch. This it will do and not turn aside, but 
still remain opposite to the pin lg. A double microscope might be fitted on in 

* The screw bc is restrained from moving along with cd by the small pillar uk, which slides back- 
wards and forwards in a groove in the cylinder gf.— Orig. 



30 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

the place of the lens a. The whole instrument may be furnished with a handle, 
as at m ; or, if larger, it may have 3 feet to stand on a table. 

On the last principle it must be owned, the common screw has the advantage, 
as 2 screws will produce more friction than one; and besides, in the compound 
engine there is an additional friction from the piece fg (fig. 2) on the pillars be- 
tween which it moves. 

Another case in which this machine may be employed, is in the micrometer. 
Thus, let the screw ab (fig. 4) of 50 threads in an inch be turned round by the 
index c, which moves on the graduated circle ecd in the direction cd. Within 
the screw ab is the smaller one ap of 51 threads in an inch, retained from moving 
round by the bar gfh. The piece af is continued to k, where it forms a fine 
point. To use the instrument, let it be adjusted to the telescope or microscope 
by which you are to view a star, or some small object, and let the point k appear 
just to touch one edge of the object. Then turn the index c, and the point k 
will advance upwards till it appears to cover the other edge of the object, and 
thus you can determine its size. The point k will advance at each complete 
turn of the index ^Vo- °* an nicn 5 anc * '*" tlie circle be divided into 80 equal 
parts, 1 of which, if it is an inch in diameter, will be very observable, while the 
index moves over one of these, the point k will advance ,, „ ,'„ „ „ of an inch. 

Thus, for example, suppose I am to measure the diameter of a nervous fibre 
in the medullary substance of the brain, I make the point k appear close to one 
edge, and turn the index till the same point pass over the fibre, and appear to 
touch the other edge: I then look on the graduated circle ecd, and perceive that 
the index c has passed over, suppose, 23.2 divisions. Hence I conclude the dia- 
meter of the fibre to be 23.2 X wAinr = Trnnr °f an » n ch, which is nearly the 
size as found by the accurate observations of Dr. Monro. There should be a 
Nonius's scale on the index which will measure to -fc of a division. 

As the index c must continue close to the plate ecd, while at the same time 
it turns round the screw ab, which is continually rising, it must be made as in 
fig. 5, where a, b, are 2 small pieces which play in a groove in the screw ab (fig. 
4) while the groove cd (fig. 5) in the index is filled up by a protuberance of the 
plate ecd (fig. 4); the piece below the groove cd (fig. 5) being sunk into that 
plate. The whole machinery may be inclosed in a cylinder of brass reaching 
from b to l (fig. 4), so that the point of the screw kl may be without it, and 
the sides of the cylinder may be open at ecd. 

It is further to be observed, that what has been said goes on the supposition 
that the point k, in the micrometer, is equally magnified with the object we are 
to measure. But, if this point be placed in the focus of the eye-glass of a double 
microscope; when it moves it will pass over, not the object itself, but its image, 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 31 

magnified by the object-glass. In this case, if the object-glass magnify the dia- 
meter 10 times, while the index passes over 1 division, the point k will pass over 
the image of an object, the diameter of which is -^ 4 ; of an inch. As in 
this mode of application the point k must fall between the object and eye-glass, 
the screws may be contained within the fulcrum by which the microscope is 
supported. 

The machine (fig. 2) may be applied as a jack to raise great weights a little 
way from the ground, by substituting 2 cross hand-spikes for the handle ckl; 
or a vertical handle may be employed in the following manner. Let a (fig. 6) be 
a pinion turned by the handle ab, which suppose a foot in length. Let the pinion 
a have 4 teeth, and move the wheel cd of l6 teeth. The screw ef of 4 threads 
in an inch is fixed in this wheel, and turns round along with it. Within it 
plays the screw fg of 5 threads in an inch, and which we suppose prevented 
from following the motion of ef: it terminates in such a shoulder as that repre- 
sented at g, and being continued to h ends in a foot as in the figure. The 
whole is inclosed in a strong frame. The pinion a must be connected in such a 
manner with the wheel cd, as to rise within the frame along with it, which may 
easily be done by making its axis play in a piece of wood or metal, which is con- 
nected by the end to the screw ef. Or, if this should be deemed inconvenient, 
as the rising of the pinion must raise the handle ab, the wheel cd may be hin- 
dered from rising, and at the same time turn the screw ef, by a contrivance 
similar to that used with the index c (fig. 4) in the micrometer. In either case, 
the axis of the pinion should be continued through the opposite side of the 
frame, and armed with a heavy fly to regulate the motion. When the machine 
is to be applied to use, the bottom of the frame resting on the ground, if the 
body to be lifted be already as high as the top g, that top is applied below it; 
but if it be close to the ground, we put below it the foot h; then, if the handle 
ab be turned once round, the wheel cd and screw ef will turn \ part round 
and the point f will rise (4- X \ =) tV of an inch. The point g or h will 
therefore be lifted upwards ( T ' T X \ =) -jV of an inch. But the end b of the 
handle ab has described above 6 feet; therefore the velocity of the point g is to 
that of the point b, as 1 to (72 X 80 =) 5760. Therefore, if we suppose a 
man to act at the handle with a force equal to 30 lbs. he may keep in equilibrio 
a weight of 172800 lbs. But a subduction of perhaps more than \ of this must 
be made, that he may raise the weight, as the friction of the engine will be con- 
siderable. Suppose it to be -J-, the effect still remains equal to 57600 lbs. or 25 
tons, 14 cwts. and 32 lbs. 

It will easily appear, that this method of applying the screw may take place in 
many other engines, particularly where great accuracy is required; or where we 
want a motion to be performed with great power, while at the same time it need 



32 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

not have any large compass. The few examples given above may serve as a 
specimen. 

VI. An Account of the Turkey. By Thomas Pennant, Esq., F. R. S. p. 67. 

TURKEY. — Bill convex, short and strong. Head and neck covered with a 
naked tuberose flesh, with a long fleshy appendage hanging from the base of 
the upper mandible. On the breast a long tuft of coarse black hairs. 

Wild Turkey. — Josselyn's Voy. Qy. Rarities 8. Clayton's Virgin. Lawson, 
149. Catesby Topp. 44. — Le coque d'Inde, Belon 248. — Gallo-pavo, Gesner. 
Av. 481. Icon. 56. — Gallo-pavo, Aldrov. Av. II. 18. — Gallo-pavo, the Turkey, 
A. 3. — Gallo-pavo sylvestris Novae Angliaa, a New England wild Turkey, Raii 
Synopsis Avium 5 1 . — Meleagris Gallo-pavo. M. capite caruncula frontali gula- 
rique, maris pectore barbato, Lin. Syst. 268. — Le Dindon de BufFon III. 
Brisson. 1, 158, tab. 16. PI. Enl. Q7 ■ 

Description. — T. with the characters described in the definition of the genus. 
The plumage, dark glossed with variable copper colour, and green. Coverts of 
the wings and the quill feathers barred with black and white. Tail consists of 
2 orders. The upper or shorter very elegant, the ground colour a bright bay; 
the middle feather marked with numerous bars of shining black and green. 
The greatest part of the exterior feathers of the same ground with the others 
marked with 3 broad bands of mallard green, placed remote from each other. 
The two next are coloured like those of the middle; but the end is plain and 
crossed with a single bar, like the exterior. The longer or lower order are of a 
rusty white colour, mottled with black; and crossed with numerous narrow- 
waved lines of the same colour, and near the end with a broad band. 

Wild turkeys preserve a sameness of colouring; the tame, as usual with 
domestic animals, vary. It is needless to point out the differences in so well 
known a bird: the black approaches nearest to the original stock. This variety 
I have seen nearly in a state of nature in Richmond and other parks. A most 
beautiful kind has of late been introduced into England, of a snowy whiteness, 
finely contrasting with its red head. These, I think, came out of Holland, 
probably bred from an accidental white pair; and from them preserved pure from 
any dark or variegated birds. 

The sizes of the wild turkeys have been differently represented. Some wri- 
ters assert that there have been instances of their weighing 60 pounds; but I 
find none who, speaking from their own knowledge, can prove their weight to 
be above 40. Josselyn says, that he has eaten part of a cock, which after it 
was plucked, and the entrails taken out, weighed 30. Lawson, whose authority 
is unquestionable, saw half a turkey serve 8 hungry men for 2 meals; and says, 
that he had seen others which he believed weighed 40 pounds. Catesby tells us, 



VOL. LXXI.J PHILOSOPHICAL TRANSACTIONS. 33 

that out of the many hundreds which he had handled, very few exceeded 30 
pounds; each of these speak of their being double that size merely from the 
reports of others. 

The manners of these birds are as singular as their figure. Their attitudes in 
the season of courtship are very striking. The males fling their heads and neck 
backwards, bristle up their feathers, drop their wings to the ground, strut and 
pace most ridiculously; wheel round the females with their wings rustling along 
the earth, at the same time emitting a strange sound through their nostrils not 
unlike the grurr of a great spinning wheel. On being interrupted they fly into 
great rages, and change their notes into a loud and guttural gobble, and then 
return to dalliance. The sound of the female is plaintive and melancholy. The 
passions of the males are very strongly expressed by the change of colours in 
the fleshy substance of the head and neck, which alters to red, white, blue, and 
yellowish, as they happen to be affected. The sight of any thing red excites 
their choler greatly. They are polygamous, one cock serving many hens. 
They lay in the spring, and produce a great number of eggs. They will persist 
in laying for a great while. They retire to some obscure place to sit, the cock 
through rage at the loss of his mate being very apt to break the eggs. The 
females are very affectionate to their young, and make great moan on the loss of 
them. They sit on their eggs with such perseverance, that if they are not taken 
away when addle, the hens will almost perish with hunger before they will quit 
the nest. Turkies greatly delight in the seeds of nettles; but those of the 
purple-fox glove prove fatal to them. Turkies are very stupid birds, quarrel- 
some, and cowardly. It is diverting to see a whole flock attack the common 
cock, who will, for a long time, keep a great number at bay. They are very 
swift runners in the tame as well as the wild state: they are but indifferent flyers. 
They love to perch on trees, and gain the height they wish by rising from bough 
to bough. In a wild state they get to the very summit of the loftiest trees, even 
so high as to be beyond the reach of the musquet. 

In the state of nature they go in flocks even of 500, feed much on the small 
red acorns, and grow so fat in March that they cannot fly more than 3 or 4 
hundred yards, and are soon run down by a horseman. In the unfrequented 
parts bordering on the Mississippi, they are so tame as to be shot with even a 
pistol. They frequent the great swamps of their native country, and leave them 
at sun-rising to repair to the dry woods in search of acorns and berries; and 
before sun-set retire to the swamps to roost. 

The flesh of the wild turkey is said to be superior in goodness to the tame, 

but redder. Eggs of the former have been taken from the nest, and hatched 

under tame turkies. The young will still prove wild, perch separate, yet mix 

and breed together in the season. The Indians sometimes use the breed pro- 

vol. xv. F 



34 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

duced from the wild as decoy birds to seduce those in a state of nature within 
their reach. When disturbed, they do not take wing, but run out of sight. 
It is usual to chace them with dogs, when they will fly and perch on the next 
tree. They are so stupid or so insensible of danger, as not to fly on being shot 
at; but the survivors remain unmoved at the death of their companions. Wild 
turkies are now become most excessively rare in the inhabited parts of America, 
and are only found in numbers in the distant and most unfrequented spots. 
The Indians make a most elegant clothing of the feathers. They twist the 
inner webs into a strong double thread of hemp, or inner bark of the mulberry 
tree, and work it like matting; it appears very rich and glossy, and as fine as 
a silk shag. They also make fans of the tail; and the French of Louisiana were 
wont to make umbrellas by the junction of A of the tails. 

Turkies are natives only of America, or the New World, and of course 
unknown to the ancients. Since both these positions have been denied by some 
of the most eminent naturalists of the J 6th century, I beg leave to lay open, 
in as few words as possible, the cause of their error. Belon, the earliest of 
those writers who are of opinion that these birds were natives of the old world, 
founds his notion on the description of the Guinea fowl, the Meleagrides of 
Strabo, Athenaeus, Pliny, and others of the ancients. I rest the refutation on 
the excellent account given by Athenaeus, taken from Clytus Milesius, a disciple 
of Aristotle, which can suit no other than that fowl. " They want," says he, 
" natural affection towards their young; their head is naked, and on the top is a 
hard round body like a peg or nail: from their cheeks hangs a red piece of flesh 
like a beard. It has no wattles like the common poultry. The feathers are 
black, spotted with white. They have no spurs; and both sexes are so like as 
not to be distinguished by the sight." Varro and Pliny take notice of the 
spotted plumage and the gibbous substance on the head. Athenaeus is more 
minute, and contradicts every character of the turkey, whose females are re- 
markable for their natural affection, and differ materially in form from the males, 
whose heads are destitute of the callous substance and whose heels, in the males, 
are armed with spurs. Aldrovandus, who died in 1(305, draws his arguments 
from the same source as Belon; I therefore pass him by, and take notice of the 
greatest of our naturalists Gesner, who falls into a mistake of another kind, 
and wishes the turkey to be thought a native of India. He quotes yElian for 
that purpose, who tells us, " That in India are very large poultry not with 
combs, but with various coloured crests interwoven like flowers, with broad 
tails neither bending nor displayed in a circular form, which they draw along 
the ground as peacocks do when they do not erect them; and that the 
feathers are partly of a gold colour, partly blue, and of an emerald colour." 
This in all probability was the same bird with the peacock pheasant of 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 35 

Mr. Edwards, Le Paon de Tibet of M. Brisson, and the Pavo bicalcaratus 
of Linneus. I have seen this bird living. It has a crest, but not so con- 
spicuous as that described by ^Elian; but it has those striking colours in form of 
eyes, neither does it erect its tail like the peacock, but trails it like the phea- 
sant. The catreus of Strabo seems to be the same bird. He describes it as 
uncommonly beautiful and spotted, and very like a peacock. The former author 
gives a more minute account of this species, and under the same name. He 
borrows it from Clitarchus, an attendant of Alexander the Great in all his con- 
quests. It is evident from his description, that it was of this kind; and it is 
likewise probable, that it was the same with his large Indian poultry before cited. 
He celebrates it also for its fine note; but allowance -must be made for the 
credulity of iElian. The catreus, or peacock pheasant, is a native of Tibet, 
and in all probability of the north of India, where Clitarchus might have 
observed it; for the march of Alexander was through that part which borders on 
Tibet, and is now known by the name of Penj-ab, or five rivers. 

I shall now collect from authors the several parts of the world where turkies 
are unknown in the state of nature. Europe has no share in the question; it 
being generally agreed that they are exotic in respect to that continent. Neither 
are they found in any part of Asia Minor, or the Asiatic Turkey, notwithstand- 
ing ignorance of their true origin first caused them to be named from that 
empire. About Aleppo, capital of Syria, they are only met with, domesticated 
like other poultry. In Armenia they are unknown, as well as in Persia; having 
been brought from Venice by some Armenian merchants into that empire, where 
they are still so scarce as to be preserved among other rare fowl in the royal 
menagery. Du Hakie acquaints us, that they are not natives of China; but 
were introduced there from other countries. He errs from misinformation in 
saying that they are common in India. I will not quote Gemelli Careri, to 
prove that they are not found in the Philippine Islands, because that gentleman, 
with his pen travelled rounr 1 the world in his easy chair, during a very long indis- 
position and confinement in his native country. But Dampier bears witness 
that none are found in Mindanao. 

The hot climate of Africa barely suffers these birds to exist in that vast con- 
tinent, except under the care of mankind. Very few are found in Guinea, 
except in the hands of the Europeans, the negroes declining to breed any on 
account of the great heats. Prosper Alpinus satisfies us, that they are not found 
either in Nubia or in Egypt. He describes the Meleagrides of the ancients, and 
only proves that the Guinea hens were brought out of Nubia, and sold at a 
great price at Cairo; but is totally silent about the turkey of the moderns. 

Let me here observe, that the Guinea hens have long been imported 
into Britain. They were cultivated in our farm-yards; fori discover in 1277, 

K 1 



36 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

in the Grainge of Clifton, in the parish of Amhrosden, in Buckinghamshire, 
among other articles, 6 Mutilones and 6 Afrieanae foeminae, for this fowl was 
familiarly known by the names of Afra Avis and Gallina Africana and Numida. 
It was introduced into Italy from Africa, and from Rome into our country. 
They were neglected here by reason of their tenderness and difficulty of rearing. 
We do not find them in the bills of fare of our ancient feasts; neither do we 
find the turkey: which last argument amounts to almost a certainty, that such a 
hardy and princely bird had not found its way to us. The other likewise 
was then known by its classical name; for that judicious writer Doctor Cains 
describes, in the beginning of the reign of Elizabeth, the Guinea fowl, for the 
benefit of his friend Gesner, under the name of Meleagris, bestowed on it by 
Aristotle. 

Having denied, on the very best authorities, that the turkey ever existed as a 
native of the old world, I must now bring my proofs of its being only a native 
of the new, and of the period in which it first made its appearance in Europe. 
The first precise description of these birds is given by Oviedo, who in 1525 drew 
up a summary of his greater work, the History of the Indies, for the use of 
his monarch Charles v. This learned man had visited the West Indies and its 
islands in person, and payed particular regard to the natural history. It appears 
from him, that the turkey was in his days an inhabitant of the greater islands, 
and of the main-land. He speaks of them as peacocks; for being a new bird 
to him, he adopts that name from the resemblance he thought they bore to the 
former. " But," says he, " the neck is bare of feathers, but covered with a skin 
which they change after their phantasie into diverse colours. They have a horn 
as it were on their front, and hairs on the breast." He describes other birds 
which he also calls peacocks. They are of the gallinaceous genus, and known 
by the name of Curassao birds, the male of which is black, the female ferrugi- 
nous. The next who speaks of them as natives of the main-land of the warmer 
parts of America, is Francisco Fernandez, sent there by Philip n., to whom he 
was physician. This naturalist observed them in Mexico. We find by him, 
that the Indian name of the male was huexolotl, of the female cihuatotolin. 
He gives them the title of Gallus Indicus and Gallo pavo. The Indians as well 
as Spaniards, domesticated these useful birds. He speaks of the size by com- 
parison, saying, that the wild were twice the magnitude of the tame; and that 
they were shot with arrows or guns. I cannot learn the time when Fernandez 
wrote. It must be between the years 1555 and 1598, the period of Philip's 
reign. Pedro de Ciesa mentions turkies on the Isthmus of Darien. Lery, a 
Portugueze author, asserts, that they are found in Brazil, and gives them an Indian 
name; but since I can discover no traces of them in that diligent and excellent 
naturalist Marcgrave, who resided long in that country, I must deny my assent. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 37 

Bat the former is confirmed by that able and honest navigator Dampier, who 
saw them frequently, as well wild as tame, in the province of Yucatan, now 
reckoned part of the kingdom of Mexico. 

In North America they were observed by the very first discovered. When 
Rene de Laudonniere, patronized by Admiral Coligni, attempted to form a 
settlement near the place where Charlestown now stands, he met with them on 
his first landing in 1564, and by his historian has represented them with 
great fidelity in the 5th plate of the recital of his voyage: from his time the 
witnesses to their being natives of the continent are innumerable. They have 
been seen in flocks of hundreds in all parts from Louisiana even to Canada; but 
at this time are extremely rare in a wild state, except in the more distant parts, 
where they are still found in vast abundance. 

It was from Mexico or Yucatan that they were first introduced into Europe; 
for it is certain, that they were imported into England as early as the year 
1524, the 15th of Henry vm. We probably received them from Spain, 
with which we had great intercourse till about that time. They were most 
successfully cultivated in our kingdom from that period; insomuch, that they 
became common in every farm-yard, and became even a dish in our rural feasts 
by the year 1585; for we may certainly depend on the word of old Tusser, in 
his Account of the Christmas Husbandlie Fare, in the Five Hundred Points of 
good Husbandrie, p. 57- 

Beefe, mutton, and porke, shred pies of the best, 
Pig, veale, goose, and capon, and turkie well drest, 
Cheese, apples, and nuts, jolie carols to heare, 
As then in the countrie, is counted good cheare. 

But at this very time they were so rare in France, that we are told, that the very 
first which was eaten in that kingdom appeared at the nuptial feast of Charles ix., 
in 1750. 

To this account I beg lervj to mention the very extraordinary appearance on 
the thigh of a turkey, bred in my poultry-yard, and which was killed a few 
years ago for the table. The servant in plucking it was very unexpectedly 
wounded in the hand. On examination, the cause appeared so singular, that 
the bird was brought to me. I discovered, that from the thigh-bone issued a 
short upright process, and to that grew a large and strong toe, with a sharp and 
crooked claw, exactly resembling that of a rapacious bird. 

VII. Of a Nebula in Coma Berenices. By Edward Bigot, Esq. p. 82. 
On the 23d of March, 17 79, Mr. P. discovered a nebula in the constellation of 
Coma Berenices, previously he presumes unnoticed; at least not mentioned in 
M. de Lalande's Astronomy, nor in M. Messier's ample Catalogue of nebulous 



38 i'HILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

Stars. He observed it in an achromatic transit instrument, 3 feet long, and 
deduced its mean r. a., by comparing it to several stars, having made the neces- 
sary corrections for aberration and nutation, the result of all being igi° 28' 3S' 7 . 
Its declination north was 22° 53'4- The diameter of this nebula about 2' of a 
degree. 

Fill. Double Stars discovered in 1779> ot Frampton-house, Glamorganshire. 

By Nathan. Pigott, Esq., F. R. S., Foreign Member of the Academies of 

Brussels and Caen, and Correspondent of the Royal Academy of Sciences at 

Paris, p. 84. 

Inclosed are the determinations of the places of 3 double stars, which I dis- 
covered this summer (1779)'- at ^ east I presume they have not been observed 
before, because I do not find them inserted in Dr. Bradley's catalogue, published 
in the Nautical Almanac 1773, or in the Connoisance des Terns, or in other cata- 
logues in my possession, y Delphini indeed, is in M. de la Caille's catalogue; 
but not as a double star. The instrument he used was not probably powerful 
enough for that purpose. In the two-feet telescope of my quadrant it appears 
only as a single star. These stars were observed by me in a three-feet achro- 
matic telescope of a transit instrument, with an object-glass near 2 inches 
diameter. The r. a. are nicely determined by several observations, which 
always agree with each to a fraction of a second in time. The declinations were 
deduced from the difference of altitudes between the double stars and the known 
stars to which they were compared. 

September 5, 1 779- 

App. r. a. App. declination. 

307° 21' b" . .«■ Delphini, 3d mag 15° 8' 53"n. 

309 6 3<> . . 2d or brightest of y Delphini 4 15 20 40 n. 

9 J. . diff. r. a. of the 2 stars in y Delphini. 

Note, both the stars in y Delphini have the same, or nearly the same, decli- 
nation. The 1st is of the 6th, the 2d of the 4th mag. 

September 1Q. 

319 59 27 + /3 Aquarii, 3dmag 6' 31 34 s. 

3 IS 3 21.. preceding double star, 5th mag 7 40 34 s. 

11 — dirt". R. a. between 1st and 2d of the double stars. 

Note, the 1st seemed of the 5th, the 2d of the 7th mag. The 1st is perhaps 
6" or 8" s. of the following one. 

337 36 55 4- £ Pegasi, 3d mag 9 41 24 n. 

346 53 361. . double star, 8th, 9th mag 3 5() 17 y. 

Note, both the stars of this double star have the same, or nearly the same r. a.; 
their difference in declination is 15" or perhaps 20". 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 39 

IX. An Account of the Ganges and Burrampooter Rivers. By James Rennell, 

Esq., F.R.S. p. 87. 

The * Ganges and -f- Burrampooter rivers, with their numerous branches and 
adjuncts, intersect the country of Bengal in such a variety of directions, as to 
form the most complete and easy inland navigation that can be conceived. So 
equally and admirably diffused are those natural canals, over a country that 
approaches nearly to a perfect plane, that, after excepting the lands contiguous 
to Burdwan, Birboom, &c. which altogether do not constitute a 6th part of 
Bengal, we may fairly pronounce, that every other part of the country has, even 
in the dry season, some navigable stream within 25 miles at farthest, and more 
commonly within a 3d part of that distance. It is supposed, that this inland 
navigation gives constant employment to 30,000 boatmen ; for all the salt, and 
a large proportion of the food consumed by 10 millions of people, are conveyed 
by water within the kingdom of Bengal and its dependencies. To these must 
be added, the transport of the commercial exports and imports, probably to the 
amount of 2 millions sterling per ann.; the interchange of manufactures and 
products throughout the whole country; the fisheries; and the article of travelling 

These rivers exactly resemble each other in length of course; in bulk, till they ap- 
proach the sea; in the smoothness and colour of their waters; in the appearance of 
their borders and islands; and finally, in the height to which their floods rise with 
the periodical rains. Of the two, the Burrampooter is the larger; but the difference 
is not obvious to the eye. It is now well known that they derive their sources 
from the vast mountains of Thibet*; whence they proceed in opposite directions; 
the Ganges seeking the plains of Hindostan, by the west; and the Burrampooter by 
the east; both pursuing the early part of their course through rugged vallies and 
defiles. The Ganges, after wandering about 750 miles through these moun- 
tainous regions, issues forth a deity to the superstitious, yet gladdened, inhabi- 
tant of Hindostan. From riurdwar, or Hurdoar, in latitude 30°, where it 
gushes through an opening in the mountains, it flows with a smooth navigable 
stream through delightful plains during the remainder of its course to the sea, 
which is about 1350 miles, diffusing plenty immediately by means of its living 

* The proper name of this river in the language of Hindostan, is Pudda or Padda. It is also 
named Burra-Gonga, or the Great River; and Gonga, the river, by way of eminence; and from 
this doubtless the European names of the river are derived. — Orig. 

+ The orthography of this word, as given here, is according to the common pronunciation in 
Bengal ; but it is said to be written in the Sancrit language, Brahma-pootar, which signifies the son 
of Brahma. — Orig. 

+ These are among the highest of the mountains of the old hemisphere. Their height may in 
some measure be guessed, by the circumstance of their rising considerably above the horizon, when 
viewed from the plains of Bengal, at the distance of 150 miles. — Orig. 



40 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

productions; and secondarily by enriching the adjacent lands, and affording an 
easy means of transport for the productions of its borders. 

In its course through the plains, it receives eleven rivers, some of which are 
equal to the Rhine, and none smaller than the Thames, besides as many others 
of less note. It is owing to this vast influx of streams, that the Ganges exceeds 
the Nile so greatly in point of magnitude, while the latter exceeds it in length 
of course by one-third. Indeed the Ganges is inferior, in this last respect, to 
many of the northern rivers of Asia; though probably it discharges as much or 
more water than any of them, because those rivers do not lie within the limits 
of the periodical rains.* 

The bed of the Ganges is very unequal in point of width. From its first 
arrival in the plains at Hurdvvar, to the conflux of the Jumnah, the first river of 
note that joins it, its bed is generally from a mile to a mile and a quarter wide; 
and, compared with the latter part of its course, tolerably straight. Hence, 
downward, its course becomes more winding, and its bed consequently wider, 
till, having alternately received the waters of the Gogra, Soane, and Gunduck, 
besides many smaller streams, its bed has attained its full width ; though, during 
the remaining 600 miles of its course, it receives many other principal streams. 
Within this space it is, in the narrowest parts of its bed, half a mile wide, and 
in the widest, 3 miles; and that, in places where no islands intervene. The 
stream within this bed is always either increasing or decreasing, according to the 
season. When at its lowest, which happens in April, the principal channel 
varies from 400 yards to a mile and a quarter; but is commonly about 3 quarters 
of a mile. It is fordable in some places above the conflux of the Jumnah, but 
the navigation is never interrupted. Below that, the channel is of considerable 
depth, for the additional streams bring a greater accession of depth than width. 
At 500 miles from the sea, the channel is 30 feet deep when the river is at its 
lowest; and it continues at least this depth to the sea, where the sudden expan- 
sion of the stream deprives it of the force necessary to sweep away the bars of 
sand and mud thrown across it by the strong southerly winds; so that the prin- 
cipal branch of the Ganges cannot be entered by large vessels. About 220 miles 
from the sea, but 300 reckoning the windings of the river, commences the head 
of the Delta of the Ganges, which is considerably more than twice the area of 
that of the Nile. The two westernmost branches, named the Cossimbuzar and 

* The proportional lengths of course of some of the most noted rivers in die world are shown 
nearly in the following numbers: 

European rivers: Thames 1; Rhine 5l; Danube?; Wolga 9j- — Asiatic rivers: Indus :>',■ 
Euphrates 8h; Ganges yi ; Burrampooter y J ; Nou Kian, or Ava river S £ J Jennisea 10 3 Oby 10£; 
Amoor I 1 ; Lena I I .J ; Hoanho (of China) I3j ; Kian Keu (of ditto) 15J. — African river: Nile 12 J. 
American rivers: Mississippi 8; Amazons 15|. — Orig. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 41 

Jellinghy rivers, unite and form what is afterwards named the Hoogly river, 
which is the port of Calcutta, and the only branch of the Ganges that is com- 
monly navigated by ships. The Cossimbuzar river is almost dry from October 
to May ; and the Jellinghy river is in some years unnavigable during 2 or 3 of 
the driest months; so that the only subordinate branch of the Ganges, that is 
at all times navigable, is the Chundnah river, which separates at Moddapour, 
and terminates in the Hooringotta. 

That part of the Delta bordering on the sea, is composed of a labyrinth of 
rivers and creeks, all of which are salt, except those that immediately communi- 
cate with the principal arm of the Ganges. This tract, known by the name of 
the Woods, or Sunderbunds, is in extent equal to the principality of Wales; 
and is so completely enveloped in woods, and infested with tigers, that if any 
attempts have ever been made to clear it, they have hitherto miscarried. Its 
numerous canals are so disposed as to form a complete inland navigation through- 
out and across the lower part of the Delta, without either the delay of going- 
round the head of it, or the hazard of putting to sea. Here salt, in quantities 
equal to the whole consumption of Bengal, and its dependencies, is made and 
transported with equal facility: and here also is found an inexhaustible store of 
timber for boat-building. The breadth of the lower part of this Delta is upwards 
of 180 miles; to which, if we add that of the two branches of the river that 
bound it, we shall have about 200 miles for the distance to which the Ganges 
expands its branches at its junction with the sea. 

It has been observed before, that the course of this river, from Hurdwar to 
the sea, is through a uniform plain, or at least what appears such to the eye: 
for, the declivity is much too small to be perceptible. A section of the ground, 
parallel to one of its branches, 60 miles in length, was taken by order of 
Mr. Hastings; and it was found to have about Q inches descent in each mile, 
reckoning in a straight line, and making allowance for the curvature of the earth. 
But the windings of the river •;. jre so great, as to reduce the declivity on which 
the water ran, to less than 4 inches per mile.* The medium rate of motion of 
the Ganges is less than 3 miles an hour in the dry months. In the wet season, 
and during the draining oft' of the waters from the inundated lands, the current 
runs from 5 to 6 miles an hour; but there are instances of its running 7, and 
even 8 miles, in particular situations, and under certain circumstances. 

Commonly there is found on one side of the river an almost perpendicular 
bank, more or less elevated above the stream, according to the season, and with 

* M. de Condamine found the descent of the river Amazons, in a straight course of about I860 
miles, to be 1020 English feet, or 6-j- inches in a mile. If we allow for the windings, it comes out 
nearly the same as the Ganges (which winds about I A mile in 3, taking its whole course through the 
plains), namely, about -1 inches in a mile. — Orig. 

VOL. XV. G 



42 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

deep water near it: and on the opposite side a bank, shelving away so gradually 
as to occasion shallow water at some distance from the margin. This is more 
particularly the case in the most winding parts of the river, because the very 
operation of winding produces the steep and shelving banks: for the current is 
always strongest on the external side of the curve formed by the serpentine 
course of the river; and its continual action on the banks either undermines 
them, or washes them down. In places where the current is remarkably rapid, 
or the soil uncommonly loose, such tracts of land are swept away in the course 
of one season, as would astonish those who have not been eye-witnesses to the 
magnitude and force of the mighty streams occasioned by the periodical rains of 
the tropical regions. This necessarily produces a gradual change in the course 
of the river; what is lost on one side being gained on the other, by the mere 
operation of the stream: for the fallen pieces of the bank dissolve quickly into 
muddy sand, which is hurried away by the current along the border of the 
channel to the point whence the river turns off to form the next reach, where 
the stream becoming weak, it finds a resting place, and helps to form a shelving- 
bank, which commences at the point, and extends downwards, along the side 
of the succeeding reach. 

It is evident that the repeated additions made to the shelving bank above- 
mentioned, become in time an encroachment on the channel of the river; and 
this is again counterbalanced by the depredations made on the opposite steep 
bank, the fragments of which, either bring about a repetition of the circum- 
stances above recited, or form a bank or shallow in the midst of the channel. 
Thus a steep and a shelving bank are alternately formed in the crooked parts of 
the river (the steep one being the indented side, and the shelving one the pro- 
jecting) ; and thus a continual fluctuation of course is induced in all the wind- 
ing parts of the river ; each meander having a perpetual tendency to deviate 
more and more from the line of the general course of the river, by eating deeper 
in the bays, and at the same time adding to the points, till either the opposite 
bays meet, or the stream breaks through the narrow isthmus, and restores a 
temporary straightness to the channel. 

Several of the windings of the Ganges and its branches are fast approaching 
to this state ; and in others, it actually exists at present. The experience of 
these changes should operate against attempting canals of any length, in the 
higher parts of the country ; and I much doubt, if any in the lower parts would 
long continue navigable. During 1 1 years of my residence in Bengal, the out- 
let or head of the Jellinghy river was gradually removed 4 of a mile farther 
down : and by 2 surveys of a part of the adjacent bank of the Ganges, taken 
about the distance of Q years from each other, it appeared that the breadth of an 
English mile and a half had been taken away. This is however the most rapid 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 43 

change that I have noticed ; a mile in 10 or. 12 years being the usual rate of en- 
croachment, in places where the current strikes with the greatest force, namely, 
where 2 adjoining reaches approach nearest to a right angle. In such situations 
it not unfrequently excavates gulfs of considerable length within the bank. 
These gulfs are in the direction of the strongest parts of the stream ; and are, 
in fact, the young shoots, as it were, which in time strike out and become 
branches of the river ; for we generally find them at those turnings that have 
the smallest angles. 

There are not wanting instances of a total change of course in some of the 
Bengal rivers. The Cosa River, equal to the Rhine, once ran by Purneah, and 
joined the Ganges opposite Rajemal. Its junction is now 45 miles higher up. 
Gour, the ancient capital of Bengal, stood on the banks of the Ganges. Ap- 
pearances favour very strongly the opinion, that the Ganges had its former bed 
in the tract now occupied by the lakes and morasses between Nattore and Jaffier- 
gunge, striking out of its present course at Bauleah, and passing by Pootyah. 
With an equal degree of probability, favoured by tradition, we may trace its 
supposed course by Dacca, to a junction with the Burrampooter or Megna near 
Fringybazar; where the accumulation of two such mighty streams probably 
scooped out the present amazing bed of the Megna.* 

In tracing the sea coast of the Delta, we find no less than 8 openings ; each 
of which, without hesitation, one pronounces to have been in its time the prin- 
cipal mouth of the Ganges. Nor is the occasional deviation of the principal 
branch, probably the only cause of fluctuation in the dimensions of the Delta. 
One observes that the Deltas of capital rivers, the tropical ones particularly, en- 
croach on the sea. Now, is not this owing to the mud and sand brought down 
by the rivers, and gradually deposited, from the remotest ages down to the pre- 
sent time ? The rivers are loaded with mud and sand at their entrance into the 
sea ; and the sea recovers its transparency at the distance of 20 leagues from the 
coast ; which can only arise from che waters having precipitated their earthy par- 
ticles within that space. The sand and mud banks at this time, extend 20 miles 
off some of the islands in the mouths of the Ganges and Burrampooter ; and 
in many places rise within a tew feet of the surface. Some future generation 
will probably see these banks rise above water, and succeeding ones possess and 
cultivate them ! Next to earthquakes, perhaps the floods of the tropical rivers 
produce the quickest alterations in the face of our globe. Extensive islands are 
formed in the channel of the Ganges, during a period far short of that of a 

man's life ; so that the whole process lies within the compass of his observation. 

« 

* Megna and Burrampooter are names belonging to the same river in different parts of its course. 
The Megna falls into the Burrampooter ; and, though a much smaller river, communicates its name 
to the other during the rest of its course. — Orig. 

G 2 



44 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

Some of these islands, 4 or 5 miles in extent, are formed at the angular turnings 
of the river, and were originally large sand banks thrown up round the points, 
but afterwards insulated by breaches of the river. Others are formed in the 
straight parts of the river, and in the middle of the stream ; and owe their origin 
to some obstruction lurking at the bottom. Whether this be the fragments of 
the river bank ; or a large tree swept down from it ; or a sunken boat ; it is 
sufficient for a foundation ; and a heap of sand is quickly collected below it. 
This accumulates amazingly fast : in the course of a few years it peeps above 
water, and having now usurped a considerable portion of the channel, the river 
borrows on each side to supply the deficiency in its bed ; and in such parts of the 
river we always find steep banks on both sides.* Each periodical flood brings an 
addition of matter to this growing island ; increasing it in height as well as ex- 
tension, until its top is perfectly on a level with the banks that include it : and 
at that period of its growth it has mould enough on it for the purposes of culti- 
vation, which is owing to the mud left on it when the waters subside, and is in- 
deed a part of the economy which nature observes in fertilizing the lands in 
general. 

While the river is forming new islands in one part, it is sweeping away old 
ones in other parts. In the progress of this destructive operation, we have op- 
portunities of observing, by means of the sections of the falling bank, the 
regular distribution of the several strata of sand and earths, l)ing above each 
other in the order in which they decrease in gravity. As they can only owe this 
disposition to the agency of the stream that deposited them, it would appear that 
these substances are suspended at different heights in the stream, according to 
their respective gravities. We never find a stratum of earth under one of sand ; 
for the muddy particles float nearest the surface.-j- I have counted 7 distinct 
strata in a section of one of these islands. Indeed, not only the islands, but 
most of the river banks wear the same appearance : for as the river is always 
changing its present bed, and verging towards the site of some former one now 
obliterated, this must necessarily be the case. Asa strong presumptive proof of 
the wanderings of the Ganges from the one side of the Delta to the other, there 
is no appearance of virgin earth between the Tiperah hills on the east, and the 
province of Bardwan on the west; nor on the north till we arrive at Dacca and 
Bauleah. In all the sections of the numerous creeks and rivers in the Delta, 
nothing appears but sand and black mould in regular strata, till we arrive at the 

* This evidently points out the means for preventing encroachments on a river bank in the straight 
parts of its course, viz. to remove the shallows in the middle of its channel — Orig. 

■f A glass of water taken out of the Ganges, when at its height, yields about 1 part in 4 of mud- 
No wonder then that the subsiding waters should quickly form a stratum of earth ; or that the Delta 
should encroach on the sea ! — Orig. 



VOL. LXXI.J PHILOSOPHICAL TRANSACTIONS. 45 

clay that forms the lower part of their beds. There is not any substance so 
coarse as gravel either in the Delta or nearer the sea than 400 miles, where a 
rocky point, a part of the base of the neighbouring hills, projects into the 
river : but out of the vicinity of the great rivers the soil is either red, yellow, 
or of a deep brown. 

The annual swelling and overflowing of the Ganges appears to owe its increase 
as much to the rain water that falls in the mountains contiguous to its source, 
and to the sources of the great northern rivers that fall into it, as to that which 
falls in the plains of Hindoostan ; for it rises 15-l feet out of 32, the sum total 
of its rising, by the latter end of June: and it is well known, that the rainy 
season does not begin in most of the flat countries till about that time. In the 
mountains it begins early in April ; and by the latter end of that month, when 
the rain-water has reached Bengal, the rivers begin to rise, but by very slow de- 
grees ; for the increase is only about an inch per day for the first fortnight. It 
then gradually augments to 2 and 3 inches before any quantity of rain falls in the 
flat countries ; and when the rain becomes general, the increase on a medium is 
5 -nches per day. By the latter end of July all the lower parts of Bengal, con- 
tiguous to the Ganges and Burrampocter, are overflowed, and form an inunda- 
tion of more than 100 miles in width ; nothing appearing but villages and trees, 
excepting very rarely the top of an elevated spot, the artificial mound of some 
deserted village, appearing like an island. 

The inundations in Bengal differ from those in Egypt in this particular, that 
the Nile owes its floods entirely to the rain-water that falls in the mountains 
near its source ; but the inundations in Bengal are as much occasioned by the rain 
that falls there, as by the waters of the Ganges ; and as a proof of it, the lands 
in general are overflowed to a considerable height long before the bed of the 
river is filled. It must be remarked, that the ground adjacent to the river bank, 
to the extent of some miles, is considerably higher than the rest of the country,* 
and serves to separate the waters ot the inundation from those of the river till it 
overflows. This high ground is in some seasons covered a foot or more ; but the 
height of the inundation within varies of course according to the irregularities of 
the ground, and is in some places 1 2 feet. Even when the inundation becomes 
general, the river still shows itself, as well by the grass and reeds on its banks, 
as by its rapid and muddy stream ; for the water of the inundation acquires a 
blackish hue, by having been so long stagnant among grass and other vegetables : 
nor does it ever lose this tinge, which is a proof of the predominancy of the 

* This property of die bank is well accounted for by Count Buffbn, who imputes it to the precipi- 
tation of mud made by the waters of the river, when it overflows. The inundation, says he, puri- 
fies itself as it flows over the plain ; so that the precipitation must be greatest on the parts nearest to 
the margin of the river. — Orig. 



4(5 l'HTLOSOPHICAL TRANSACTIONS. [ANN0 1781. 

rain water over that of the river ; as the slow rate of motion of the inundation, 
which does not exceed half a mile per hour, is of the remarkahle flatness of the 
country. 

There are particular tracts of land, which, from the nature of their culture, 
and species of productions, require less moisture than others ; and yet, by the 
lowness of their situation, would remain too long inundated, were they not 
guarded by dikes or dams, from so copious an inundation as would otherwise 
happen from the great elevation of the surface of the river above them. These 
dikes are kept up at an enormous expense ; and yet do not always succeed, for 
want of tenacity in the soil of which they are composed. 

During the swoln state of the river, the tide totally loses its effect of counter- 
acting the stream; and in a great measure that of ebbing and flowing, except 
very near the sea. It is not uncommon for a strong wind, that blows up the 
river for any continuance, to swell the waters 1 feet above the ordinary level at 
that season : and such accidents have occasioned the loss of whole crops of rice.* 
A very tragical event happened at Luckipour in 1763, situated above 50 miles 
from the sea, by a strong gale of wind conspiring with a high spring tide, at a 
season when the periodical flood was within a foot and half of its highest pitch. 
It is said that the waters rose 6 feet above the ordinary level. Certain it is, that 
the inhabitants of a considerable district, with their houses and cattle, were 
totally swept away; and, to aggravate their distress, it happened in a part of the 
country which scarce produces a single tree for a drowning man to escape to. 

Embarkations of every kind traverse the inundation : those bound upwards, 
availing themselves of a direct course and still water, at a season when every 
stream rushes like a torrent. The wind too, which at this season blows regu- 
larly from the south-east, favours their progress ; insomuch that a voyage which 
takes up 9 or 10 days by the course of the river when confined within its banks, 
is now effected in 6. Husbandry and grazing are both suspended ; and the pea- 
sant traverses in his boat, those fields which in another season he was wont to 
plow; happy that the elevated site of the river banks place the herbage they 
contain, within his reach, otherwise his cattle must perish. 

The following is a table of the gradual increase of the Ganges and its branches, 
according to observations made at Jellinghy and Dacca. 

In May it rose, at Jellinghy. . 6 ft. inc. At Dacca C ft. 4 inc. 

June 9 ') 4 <)" 

July 12 (>' 5 6 

In the first half of August. ... 4 1 11 

In all 32 U 3 

* The rice I speak of is of a particular kind ; for the growth of its stalk keeps pace with the in- 
crease of the flood at ordinary times, but is destroyed by a too sudden rise of the water. The har- 
vest is often reaped in boats. There is also a kind of grass which overtops the flood in the same 
manner, and at a small distance has the appearance of a field of the richest verdure. — Orig, 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. ^7 

These observations were made in a season, when the waters rose rather higher 
than usual ; so that we may take 3 1 feet for the medium of the increase. 

The inundation is nearly at a stand for some days preceding the middle of 
August, when it begins to run off; for though great quantities of rain fall in 
the flat countries, during August and September, yet, by a partial cessation of 
the rains in the mountains, there happens a deficiency in the supplies necessary 
to keep up the inundation. The quantity of the daily decrease of the river is 
nearly in the following proportion : during the latter half of August, and all 
September, from 3 to 4 inches ; from September to the end of November it 
Gradually lessens from 3 inches to an inch and a half; and from November to 
the latter end of April, it is only half an inch per day at a medium. These pro- 
portions must be understood to relate to such parts of the river as are removed 
from the influence of the tides ; of which more will be said by and by. The 
decrease of the inundation does not always keep pace with that of the river, by 
reason of the height of the banks ; but after the beginning of October, when 
the rain has nearly ceased, the remainder of the inundation goes off quickly by 
evaporation, leaving the lands highly manured, and in a state fit to receive the 
seed, after the simple operation of plowing. 

There is a circumstance attending the increase of the Ganges, little known or 
attended to ; because few people have made experiments on the heights to which 
the periodical flood rises in different places. The circumstance alluded to, is, the 
difference of the quantity of the increase, as expressed in the foregoing tables, 
in places more or less remote from the sea. It is a fact, confirmed by repeated 
experiments, that from about the place where the tide commences, to the sea, 
the height of the periodical increase diminishes gradually, till it totally disappears 
at the point of confluence. Indeed, this is perfectly conformable to the known 
laws of fluids : the ocean preserves the same level at all seasons, under similar 
circumstances of tide, and necessarily influences the level of all the waters that 
communicate with it, unless precipitated in the form of a cataract. Could we 
suppose, for a moment, that the increased column of water, of 3 1 feet perpen- 
dicular, was continued all the way to the sea, by some preternatural agency : 
whenever that agency was removed, the head of the column would diffuse itself 
over the ocean, and the remaining parts would follow, from as far back as the 
influence of the ocean extended ; forming a slope, whose perpendicular height 
would be 31 feet. This is the precise state in which we find it. At the point of 
junction with the sea, the height is the same in both seasons at equal times of 
the tides. At Luckipour there is a difference of about 6 feet between the 
heights in the different seasons; at Dacca, and places adjacent, 14; and near 
Custee, 31 feet. Here then is a regular slope; for the distances between 
the places bear a proportion to the respective heights. This slope must add to 



48 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

the rapidity of the stream ; for, supposing the descent to have been originally 4 
inches per mile, this will increase it to about 5-|-. Custee is about "240 miles 
from the sea, by the course of the river ; and the surface of the river there, 
during the dry season, is about 80 feet above the level of the sea at high water. 
Thus far does the ocean manifest its dominion in both seasons : in the one by 
the ebbing and flowing of its tides ; and in the other by depressing the periodical 
flood, till its surface coincides as nearly with its own, as the descent of the 
channel of the river will admit. 

Similar circumstances take place in the Jeilinghy, Hoogly, and Burrampooter 
rivers ; and probably in all others that are subject either to periodical or occa- 
sional swellings. Not only does the flood diminish near the sea, but the river 
banks diminish in the same proportion ; so that in the dry season the height of 
the periodical flood may be known by that of the bank. If it be objected to 
the above solution, that the lowness of the banks in places near the sea, is the 
true reason why the floods do not attain so considerable a height, as in places 
farther removed from it, and where the banks are high ; for that the river, want- 
ing a bank to confine it, diffuses itself over the surface of the country : in an- 
swer to this, it may be observed, that it is proved by experiment, that at any 
given time, the quantity of the increase in different places bears a just propor- 
tion to the sum total of the increase in each place respectively : or, in other 
words, that when the river has risen 3 feet at Dacca, where the whole rising is 
about 14 feet ; it will have risen upwards of 64- feet at Custee, where it rises 31 
feet in all. 

The quantity of water discharged by the Ganges, in one second of time, 
during the drv season, is 80,000 cubic feet ; but in the place where the experi- 
ment was made, the river, when full, has thrice the volume of water in it ; 
and its motion is also accelerated in the proportion of 5 to 3 : so that the quan- 
tity discharged in a second at that season is 405,000 cubic feet. If we take the 
medium the whole year through, it will be nearly 80,000 cubic feet in a second. 

The Burrampooter, which has its source from the opposite side of the same 
mountains that give rise to the Ganges, first takes its course eastward, or directly 
opposite to that of the Ganges, through the country of Thibet, where it is 
named Sanpoo or Zanciu, which bears the same interpretation as the Gonga of 
Hindoostan, namely, the River. Its course through Thibet, as given by Father 
Du Halde, and formed into a map by Mr. D'Anville, though sufficiently exact 
for the purposes of general geography, is not particular enough to ascertain the 
precise length of its course. After winding with a rapid current through Thibet, 
it washes the border of the territory of Lassa, in which is the residence of the 
grand Lama, and then deviating from an east to a south-east course, it ap- 
proaches within *2'20 miles of Yunan, the westernmost province of China. Here 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 4g 

it appears, as if" undetermined whether to attempt a passage to the sea by the 
Gulf of Siam, or by that of Bengal ; but seemingly determining on the latter, 
it turns suddenly to the west through Assam, and enters Bengal on the north- 
east. I have not been able to learn the exact place where it changes its name ; 
but as the people of Assam call it Burrampoot, it would appear that it takes this 
name on its entering Assam. After its entry into Bengal, it makes a circuit 
round the western point of the Garrow Mountains ; and then, altering its course 
to south, it meets the Ganges about 40 miles from the sea. 

Father Du Halde expresses his doubts concerning the course that the Sanpoo 
takes after leaving Thibet, and only supposes generally that it falls into the gulf 
of Bengal. M. D'Anville, his geographer, with great reason supposed the 
Sanpoo and Ava River to be the same : and in this he was justified by the in- 
formation which his materials afforded him : for the Burrampooter was repre- 
sented to him, as one of the inferior streams that contributed its waters to the 
Ganges, and not as its equal or superior ; and this was sufficient to direct his re- 
searches, after the mouth of the Sanpoo River, to some other quarter. The 
Ava River, as well from its bulk, as the bent of its course for some hundred 
miles above its mouth, appeared to him to be a continuation of the river in 
question : and it was accordingly described as such in his maps, the authority of 
which was justly esteemed as decisive ; and till the year 17^5, the Burrampooter, 
as a capital river, was unknown in Europe. 

On tracing this river in 1 7^5, I was no less surprized, at finding it rather 
larger than the Ganges, than at its course previous to its entering Bengal. This 
I found to be from the east ; though all the former accounts represented it as 
from the north : and this unexpected discovery soon led to inquiries, which fur- 
nished an account of its general course to within 100 miles of the place where 
Du Halde left the Sanpoo. I could no longer doubt that the Burrampooter and 
Sanpoo were one and the same river: :...d to this was added the positive assurances 
of the Assamers, " That their river came from the north-west, through the 
Bootan mountains." And to place it beyond a doubt, that the Sanpoo River is 
not the same with the river of Ava, but that this last is the great Nou Kian of 
Yunan ; I have in my possession a manuscript draught of the Ava River, to 
within 150 miles of the place where Du Halde leaves the Nou Kian, in its 
course towards Ava ; together with very authentic information that this river 
(named Irabattey by the people of Ava) is navigable from the city of Ava into 
the province of Yunan in China. 

The Burrampooter, during a course of 400 miles through Bengal, bears so 
intimate a resemblance to the Ganges, except in one particular, that one descrip- 
tion may serve for both. The exception I mean is, that during the last 60 miles 
before its junction with the Ganges, it forms a stream which is regularly from 4 

VOL. xv. H 



50 PHILOSOPHICAL TRANSACTIONS. [aNNO]78I. 

to 5 miles wide, and but for its freshness might pass for an arm of the sea. 
Common description fails in an attempt to convey an adequate idea of the gran- 
deur of this magnificent object. 

I have already endeavoured to account for the singular breadth of the Megna, 
by supposing that the Ganges once joined it where the Issamutty now does; and 
that their joint waters scooped out its present bed. The present junction of these 
two mighty rivers below Luckipour, produces a body of running fresh water, 
hardly to be equalled in the old hemisphere, and, perhaps, not exceeded in the 
new. It now forms a gulf interspersed with islands, some of which rival, in 
size and fertility, our Isle of Wight. The water at ordinary times is hardly 
brackish at the extremities of these islands ; and, in the rainy season, the sea, 
or at least the surface of it, is perfectly fresh to the distance of many leagues 
out. 

The Bore (which is known to be a sudden and abrupt influx of the tide into 
a river or narrow strait) prevails in the principal branches of the Ganges, and in 
the Megna ; but the Hoogly River, and the passages between the islands and 
sands situated in the gulf, formed by the confluence of the Ganges and Megna, 
are more subject to it than the other rivers. This may be owing partly to their 
having greater embouchures in proportion to their channels, than the others 
have, by which means a larger proportion of tide is forced through a passage 
comparatively smaller ; and partly to there being no capital openings near them, 
to draw off any considerable portion of the accumulating tide. In the Hoogly 
or Calcutta River, the Bore commences at Hoogly Point, the place where the 
river first contracts itself, and is perceptible above Hoogly Town ; and so quick 
is its motion, that it hardly employs 4 hours in travelling from one to the other, 
though the distance is near 70 miles. At Calcutta it sometimes occasions an 
instantaneous rise of 5 feet : and both here, and in every other part of its track, 
the boats, on its approach, immediately quit the shore, and make for safety to 
the middle of the river. 

In the channels, between the islands in the mouth of the Megna, &c. the 
height of the Bore is said to exceed 12 feet ; and is so terrific in its appearance, 
and dangerous in its consequences, that no boat will venture to pass at spring 
tide. After the tide is fairly past the islands, no vestige of a Bore is seen, which 
may be owing to the great width of the Megna, in comparison with the passages 
between the islands ; but its effects are visible enough by the sudden rising of the 
tides. 

X. Astronomical Observations on the Rotation of the Planets round their Axes, 
made ivith a View to determine whether the Earth's Diurnal Motion is perfectly 
Equable. By Mr. William Her schel, of Bath. p. 115. 
The various motions of the planet we inhabit; the annual revolution in its 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 51 

orbit; the diurnal rotation round its axis; the menstrual motion round the com- 
mon centre of gravity of the moon and earth; the precession of the equinoctial 
points; the diminution of the obliquity of the ecliptic; the nutation of the 
earth's axis: in short, every one of the motions that arise from the actions of 
the sun, moon, and planets, combined with the spheroidical figure of the earth, 
and the projectile and rotatory motions first impressed on it, have all been con- 
sidered by astronomers, and their real and apparent inequalities investigated. 
Aud to the great honour of modern astronomers it must be confessed, that no 
science has ever made such considerable strides towards perfection in so short a 
time as astronomy has done since the invention of the telescope. 

There is one of the motions of the earth however which, it seems, has hitherto 
escaped the scrutiny of observers: viz. the diurnal rotation round its axis. The 
principal reason why this has not been looked into, is probably the difficulty of 
finding a proper standard to measure it by ; since it is itself used as the standard 
by which we measure all the other motions. We have indeed no cause to sus- 
pect any very material periodical irregularity, either diurnal, menstrual, or an- 
nual; for the great perfection of our present time-pieces would have discovered 
any considerable deviation from that equability which we have hitherto ascribed to 
the diurnal motion of the earth. And yet, it is not perhaps altogether impos- 
sible but that inequalities may exist in this motion, which, in an age when obser- 
vations are carried to such a degree of refinement, may be of some consequence. 

To show how far time-keepers, though ever so perfect, are from being a 
proper, or at least a sufficient standard, to examine the diurnal motion of the 
earth by, it may be asked, whether it is probable, that any clock would have dis- 
covered to us the aberration of the fixed stars? And yet that aberration produces 
a change in longitude, and of consequence in right ascension, which causes an 
annual irregularity in a star's coming to the meridian, which a time-piece, were 
it a sufficient standard, would soon have discovered, and which we might have 
attributed to an inequality of the earth's diurnal motion, had we not been ac- 
quainted with its real cause. And if we were to find out any apparent irregu- 
larity, acceleration, or retardation, should we not much rather suspect the clock 
than the diurnal motion ? We may therefore venture to say, that the aberration 
of the fixed stars, though attended with the above-mentioned consequence, 
would for ever have remained a secret to us, had it not been found out by other 
methods than time-keepers. 

Now, if time-pieces fail us in this critical case, where we stand in the greatest 
need of their assistance, it is almost in vain to expect any help from another 
quarter; for what mechanical movement on earth, or motion of the heavens, is 
there that can measure out such equal portions of time as we require to compare 
the diurnal motion of the earth to? However, to proceed, since we have 

h 2 



bl PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

already great proofs that the diurnal motion of the earth is, if not perfectly equa- 
ble, at least more so than any other motion we are acquainted with, it will not 
appear absurd to suppose the diurnal rotation of the other planets to be so like- 
wise. This suggested the thoughts of estimating the diurnal motion of one 
planet very exactly by that of another, making each the standard of the other. 
In this manner we may obtain a comparative view, by which future astronomers, 
if they shall hereafter be inclined to pursue the subject, may be enabled to make 
some estimate of the general equability of the rotatory motions of the planets. 
For if in length of time they should perceive some small retardation in the diurnal 
motion of a planet, occasioned by some resistance of a very subtle medium in 
which the heavenly bodies perhaps move ; or, on the other hand, if there should 
be found an acceleration from some cause or other, they might then ascribe the 
alteration either to the diurnal motion of the earth, or to the gyration of the 
other planet, according as circumstances, or observed phenomena, should make 
one or the other of these opinions most probable. 

Now, this method of comparing together different rotations of several planets, 
simple as it may appear, was not without some difficulties. In the first place it 
was evident, that the common account of their diurnal motions, (Keill, Ast. 
Lect. 5) which makes that of Jupiter 9 h 56 m , of Mars 24 h 40 m , how true soever 
it may be in a general way, was much too inaccurate for this critical purpose. 
The gyration of Venus was still less to be depended on, being only noted to the 
hour, without the minutes : it became therefore necessary to proceed to observa- 
tions of a more determinate kind. From what had already been seen of the rota- 
tion of the planets, Mr. H. concluded, that Mars on several accounts would be 
the most eligible planet for his purpose: for the spots on Jupiter change so 
often, that it is not easy, if at all possible, to ascertain the identity of the same 
appearance, for any considerable length of time. Nor do the dark spots only 
change their place, which may be supposed to be large black congeries of vapours 
and clouds swimming in the atmosphere of Jupiter; but also the bright spots, 
though they may adhere firmly to the body of Jupiter, may undergo some appa- 
rent change of situation, by being differently covered or uncovered on one side 
or the other, by alterations in the belts. For Mr. H. had observed the revolu- 
tion of a very bright spot, not suspected of any change of situation, to be first, 
by one set of observations, at the rate of 9 h 51 m 45 s .6; and afterwards, by an- 
other set immediately following, at the rate of 9 h 50 m 48 s . 

As the principal belts on Jupiter are equatorial, and as we have certain con- 
stant winds on our planet, especially near the equator, that regularly, for certain 
periods, blow the same way, it is easily supposed, that they may form equatorial 
belts by gathering together the vapours which swim in our atmosphere, and car- 
rying them about in the same direction. This will, by analogy, account for all 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 53 

the irregularities of Jupiter's revolutions, deduced from spots on his disc that 
may have changed their situation; for if we suppose the rotation of Jupiter, ac- 
cording to Cassini, to be 9 h 56 m , then some spots that Mr. H. had observed 
must have been carried through about 60° of Jupiter's equator in 22 of his revo- 
lutions or days. This would certainly be a very great velocity in the clouds, 
which is however not unparalleled by what has happened in our own atmosphere. 
But to return: on the planet Mars we see spots of a different nature; their 
constant and determined shape, as well as remarkable colour, show them to be 
permanent and fastened to the body of the planet. These will give the revolu- 
tion of his equator to a great certainty, and by a great number of revolutions, 
to a very great exactness also. Supposing then, that by a method hereafter de- 
scribed, we can determine whether a spot on the disc of Mars is, or is not, in 
the line which joins the centre of the earth and the centre of that planet, to half 
an hour's time with certainty, probably 10 or 12 minutes will be found sufficient 
for that purpose, in this case we shall in 30 days have the revolution true to a 
minute; and, by continuing these observations for 3 months, we shall have it to 
20 s . When we are so far certain, we can easily arrive to a much greater degree 
of exactness; for as we now can no longer mistake a whole revolution, if we take 
the time of any particular spot being in the line which joins the centres of the 
planets during one opposition of Mars, and take the same again at or near the 
next opposition, we shall have an interval of about 780 days, which will give the 
diurnal motion of that planet true to about 2 s . The next opposition will give it 
to 1, and so forth; by which means, and by taking a proper number of such 
periods, we may determine the rotation of Mars to as great an exactness as we 
shall think necessary for the purpose of our comparative view. Had such obser- 
vations as these been made 2000, or perhaps only so many hundred years ago, 
we might now, by repeating them, most probably become acquainted with some 
curious minute changes of the solar system that have hitherto passed unnoticed. 
There is a certain circumstance which would almost create a suspicion that 
there has been some retardation in the diurnal motion of the earth. The differ- 
ence between the equatorial and polar diameters of the earth, by actual measure- 
ment, has been found to be about 36 English miles and -^-; but, by a calcula- 
tion wherein the present rotation is made use of, it will only amount to about 33 
miles and -V; from which it should seem probable, that when the earth assumed 
the present form, the diurnal rotation was somewhat quicker than it is at present, 
by which means the centrifugal force bore a greater proportion to the force of 
gravity, to which it is contrary, and thus occasioned a higher elevation of the 
equatorial parts. But Mr. H. would not lay much stress on this argument; for, 
in the calculation it has been supposed, that the earth is nearly of an equal den- 
sity at the surface and towards the centre, which it seems is not agreeable to 



54 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

some late curious experiments and calculations that have heen made on the at- 
traction of a mountain,* the result of which ought now to be taken into consi- 
deration, and the calculation repeated. If all the data could be exactly depended 
on, it would be practicable enough from the laws of gravity, and the present 
rotation and given form of the earth, to find the centrifugal force required to 
produce that form, and thence to show what must have been its diurnal motion 
when it assumed the same. However, these are researches that in the present 
situation Mr. H. neither had opportunity nor perhaps ability enough to investi- 
gate properly; and which therefore he hoped some of our excellent mathema- 
ticians will think worth while to look into. 

Mr. H. now relates his observations on Jupiter and Mars. The telescopes 
used were of his own construction; and were, a 20-feet Newtonian reflector, a 
10-feet reflector of the same form, and a 7-feet reflector, already mentioned in 
his paper on the mountains of the moon. His time he gained by equal altitudes 
taken with a brass quadrant of 2-feet radius, carrying a telescope which magnifies 
about 40 times: for the correction of altitudes taken of the sun, he used De 
Lalande's tables. He kept the time by two very good pieces; one having a deal 
pendulum-rod, the other a compounded one of brass and iron, both having a 
proper contrivance not to stop when winding up. The rate of going of his 
clocks he determined by the transit of stars. 

Observations on Jupiter in the year 1778. — Feb. 24, clock l m 10 s too soon. 
About 9 o'clock saw a bright belt on one part of Jupiter's disc. About 10 
o'clock it was advanced as far as the centre. At 1 l h the white belt still more 
advanced. At ll h 25 m it approached towards the edge of the disc; and at 12 h 
was extended all over it. 

Feb. 25, 8 h , the same bright belt observed yesterday extended all over. At 
8 h 45 m it was divided by a darkish spot, situated at some distance from the centre. 
At Q h 5 m the small dark division was advanced a little farther than the centre. 
At 9 h 23 m the spot visibly advanced a considerable deal farther. 

March 2, 8 h 2 m , the darkish spot, with some alteration in its shape, was in 
the middle of the disc. 

March 3, 10 h 34 m , the bright belt on the south of the equator was in the 
middle: that is, if a line be drawn perpendicular to the equatorial belt, and 
through the centre, the end of the equatorial belt touches it. At 13 h 49 m the 
darkish spot, in which there had been some alteration, seemed to be in the 
centre. 

March 14, the clock altered to true equated time; but the rate of going not 

* See Mr. Hutton's Account of the Calculations made from the Survey and Measures taken at 
Schihallien, in order to ascertain the mean Density of the Earth. Phil. Trans., 1 7 7 S, Abridg. vol. 

xiv. p. 420. — Orig. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 55 

changed, being well regulated. At 7 h 35 m the spot was in the centre, but did 
not seem quite to fill the white belt ; nor was it so large and distinct as it was 
before. 

April 7, 9 h 31 m , 3 dark, spots in the equatorial belt nearly in the centre. 
April 12, 7 h 50 m , the 3 dark spots in the centre. The southernmost of the 
3 is nearly quite vanished ; the other 2 are also much fainter. They are, how- 
ever, distinct enough to be known. 

Observations on Jupiter in 1/79- — April 14, clock 52 s too late. At 8 h 48 m a 
remarkable bright spot in the equatorial belt towards the north is in the centre. 
At 8 h 58 ra , the spot a little past the centre. 

April 19, clock true mean time. At 7 h 10 m , a bright spot just in the centre, 
which, from its shape, seems to be the same that was there April 14th. At 
7 h 20 m , the spot visibly past the centre. 

April 23, clock shows true time. At 9 h 38 m , the same bright spot in the 
centre. At 9 h 43 m , it was past the centre. 

Comparing together the observations made in the year 1778, Feb. 24 and 
March 3, we obtain an interval of 7 days 34 minutes, which being divided by 
17 revolutions made by Jupiter on his axis, we have the time of 1 synodical 
revolution equal to 9 h 54 m 56 s .4. 

The dark spot on Feb. 25 was observed some time before, and also just after 
it was past the centre; therefore supposing it to be in the centre about 8 h 58 m , 
we have 

1°. From Feb. 25 d 8 h 58 m to March 2 d 8 h 2 m = 4 d 23 h 4 m , which divided by 
12 rev. gives 1 revol. = 9 h 55 m 20 s . 

2°. From Feb. 25 d 8 h 58 m to March 3 d 13 h 49 m = 6 d 4 h 51 m = 15 revol. 
which gives 1 rev. = 9 h 55 m 24 s . 

3°. From Feb. 25 d 8 h 58 m O s to March 14 d 7 h 36 m 10 s , allowing l m 10 s for 
the alt. of the clock, = l6 d 22 h 38 m 10 s = 41 revol. which gives 1 revol. = 
9 h 55 m 4 S .6. 

4°. From March 2 d 8 h 2 m to March 3 d 1 3 h 49 m = l d 5 h 47 m = 3 revol. which 
gives 1 revol. = 9 h 55 m 40 s . 

5°. From March 2 d 8 h 2 m s to March 14 d 7 h 36 m 10 s = J l 23 h 34 m 10 s =s 
29 revol. hence 1 revol. = 9 h 54™ 58 s .2. 

6°. From March 3 d 13 h 49 m s to 14 d 7 h 36 m *T> S = 10 d I7 h 47 m 10 s == 26 
revol. hence 1 revol. = 9 h 54 m 53 5 .4. 

7°. From April 7 d 9 h 31 m to I2 d 7 h 50 m = 4 d 22 h 29 m = 12 revol. hence 1 
revol. = 9 h 5l m 35 s . 

Again, comparing together the observations of 1779? which were made with 
the utmost attention to time, we have, 



56 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

1°. From April 14 d 8 h 48 m 52 s to April 19 d 7 h K> m s = 4 d 22 h 21 m 8 s = 12 
revol. hence 1 revol. = Q h 5 1 m 45\6. 

2°. From April ig d 7 h 40 m to April 23 d 9 h 38 m = 4 d 2 h 28 m = 10 revol. 
hence 1 revol. = g h 50 m 48 s . 

And taking both together, from April 14 d 8 h 48 m 52 s to April 23 d g h 38 m s 
= Q A O h 4g m 8 s = 22 revol. hence 1 revol. = g h 51™ ig s .4. 

These several results are so exceedingly various, that it is evident Jupiter is not 
a proper planet for the critical purpose of a comparative view of the diurnal mo- 
tions ; nor can this great variety proceed from any inaccuracy in the observations; 
for, Mr. H. thinks it is hardly possible to make a mistake in the situation of a 
spot that shall amount to so much as 5 minutes of time. The observation of 
April 23, 1 779, was made with a view to ascertain this point, when it was 
found that 5 minutes of time made a sensible difference in the situation of a spot 
when near the centre. 

By a comparison of the different periods it appears, that a spot which is carried 
about in the atmosphere of Jupiter generally suffers an acceleration, or, which is 
the same thing, performs its revolutions by degrees in less time than it did at 
first ; which is agreeable enough to the theory of equatorial winds, since it may 
probablv take up some time before a spot can acquire a sufficient velocity to go 
as fast as those winds may blow. And, by the bye, if Jupiter's spots should be 
observed in different parts of his year, and be found in some to be accelerated, 
in others to be retarded, it would almost amount to a demonstration of his mon- 
soons and their periodical changes ; but if his axis should not be inclined enough 
to his orbit, to occasion such a change, they may probably always blow in the 
same direction. 

Observations on Mars in the year \777- — Twenty-feet Newtonian reflector; 
poiver 300. April 8, 7 h 30 m , observed 2 spots on Mars, with a bright belt or 
partition between them. The belt not very well defined. At g h 30 m , the spots 
were advanced, and more spotted parts visible. At 10 h the revolution of Mars 
on his axis very evident. 

April 17, ten-feet Newtonian reflector ; power about 2 1 1 . At 7 h 50 m , two 
bright spots, so luminous that they seemed to project beyond the disc. 

April 26, ten-feet reflector; power 211. At g h 5'", the spots on the planet 
very taint. 

Observations on Mars in the year 1 779- — May gth, clock 15 s too fast; by 
equal altitudes on the 14th of April, and by the transit of a star, it was found 
to lose l m .45 per day. At 1 l h l m by the clock, a very remarkable dark spot not 
far from the centre. At 1 l h 30 m the figures gone from the centre. 

May 1 1, clock 12' too fast. At 10 h I8 m , the same spot that was visible May 
g, is on the disc, the darkest place being entirely south-east of the centre. At 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 57 

1 l h 43 m , the darkest part is almost arrived at the centre. At 12 h 17 m , the dark 
spot is with its edge just near the centre. 

May 13. Seven-feet reflector ; power 222. Clock g 5 too fast. At 1 l h 26 m , 
Mars seems now to be in the same situation he was the 1 1th, at 10 h 8 m . 

May 22, clock 4 s too slow. At 12 h 5 m , the figure of May 1 1th not on the 
disc ; but some other fainter spots are visible. 

June 6, the clock loses V.Q per day. At 10 h 10 m , the same figure is on the 
disc of Mars which was there April 8, 1777, at 7 h 30 m . 

June 15, clock I7 m too slow. At g 1 ' 45 m , the same figure is on Mars that 
was there May g, at U h l m ; but it is more advanced. Mr. H. supposed it to 
be the same, and in the same situation, as April 17, 1777, at 7 h 50 m . 

June 17, clock 20 s slow. At g" 12 m , the dark spot on Mars is rather more 
advanced than it was May 11th, at 10 h 18 m . At 10" the spot visibly advanced. 

June ig, clock 22 s too slow by the transit of 2 Scorpii observed this evening. 
At 8 h 40 m , the figure on the disc of Mars appears now to be as it was April 26, 
1777. At 1 l h 47 m , the state of the air near the horizon is very unfavourable. 
With much difficulty it can but just be seen that the figure is not quite so far ad- 
vanced as it was May 11th, at 1 l h 43 m , but can certainly not be above 2 or 3 
minutes from it. 

Now to examine the result of the above-mentioned observations : comparing 
together the 2 following short intervals of the year 1 779, we have, 

From May g d 1 l h O m 45 s to May 1 l d 12 h l6 m 48 s = 2 d l h l6 m 3 s = 2 revol. 
hence 1 revol. = 24 h 38 m T.5 

A 2d small interval. From May ll d 10 17 m 48s to 13 d ll h 25 m 51 s = 
2 d 1 8 m 3 s = 2 revol. hence 4 revol. = 24 h 34 m P.5. 

Here we have 2 very short intervals that agree to 4 m , which is more than we 
could have expected in such short peiiods of time. Comparing together obser- 
vations that were made at a greater distance, we find, first monthly period, from 
May 1 l d 10 h 17 m 48 s to June 17 d g h g m 20 s allowing 3 m , because the observation 
says the spot was rather more advanced, = 36 d 22 h 51 m 32 s = 36 revol. hence 1 
revol. = 24 h 38 m 5 s .g. 

Second monthly period, from May ll d ll h 42 m 48 s to June ig d 1 l h 50 m 22*, 
allowing 3 m for the time the spot would have taken to come to the place men- 
tioned, = 3g d h 7 m 34 s = 38 revol. hence 1 revol. = 24 h 38 m 5 S .4. 

Third monthly period, from May 13 d ll h 25 m 51 s to June )7 d g h 9 m 20 s = 
34 d 21 h 43 m 2g 8 = 34 revol. hence 1 revol. = 24 h 38 m 20 5 .3. 

This last is perhaps as likely to be near the truth as any, since the same spot 
was here observed for the 3d time, and therefore its motion become more 
familiar. 

Here we have 3 longer periods that agree to 15 seconds, which is quite suf- 

vol. xv. I 



58 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

ficient for extending the interval of time to those observations that were made in 
the year 1777- But as these are the synodical revolutions, it will be necessary 
first to reduce them to sydereal rotations. In fig. 7, pi. 1, let us suppose the 
orbit of Mars, mabc, to be in the same plane with the orbit of the earth, edfg; 
and the axis of Mars to be perpendicular to his orbit. Let m, e, m, e, be the 
situations of Mars and the earth on the 13th of May and 17th of June ; then 
will the line em, that connects the centres of Mars and the earth, point out the 
geocentric place of Mars on the 13th of May ; and the line em, the geocentric 
place of the same planet on the 17th of June. Draw er and ms parallel to er ; 
then will er point out the geocentric place of Mars on the 13th of May ; and 
the angle sme is equal to the angle mer. Now, by an ephemeris the geocentric 
place of Mars, May 13, at ll h 20 m , was 7 s 20° 59' 21"; and on the 17th of 
June, at g h Q m , it was 7 s 12° 27' 22", by which we obtain the difference or angle 
rem = ems = 8° 31' 59". 

Now a spot on Mars, situated in the direction me, will have made a sydereal 
revolution when it returns to the same, or a parallel direction ms. From which 
we gather, that the spot on the 17th of June, after coming to the line me, 
where it finishes the synodical revolution, will have to go through an arch of 
8° 3l' 59", in order to arrive into the direction of the line ms, where it finishes 
the sydereal rotation. The time it will take to go through this arch, at the syde- 
real rate of 24 h 39 m 20 s to 360 degrees, or 4MO9 per minute of a degree, will 
be 35 m 3\8 ; this being divided by the number of revolutions 34, gives l m l s -8 ; 
which, added to 24 h 38 m 20 s .3, gives 24 h 3g m 22 .1 for the sydereal revolution 
of Mars, as found by the 3d of the monthly periods. This quantity will help 
us to find a proper divisor for the 3 following long biennial periods. 

It is to be observed, that Mars has been retrograde in the above example, for 
which reason the measure of the angle ems was to be added to the synodical 
revolution when we wanted to find the sydereal rotation ; but if he had been 
direct, or if his place had been more advanced in the ecliptic than that to which 
we compared it, as at p, then the line juct parallel to em would be the direction 
to which the spot should return, in order to accomplish a sydereal revolution, 
and therefore the quantity of the angle a^e = ^er, or difference of the geocen- 
tric places ought to be subtracted from the synodical revolution to obtain the 
sydereal one. 

First biennial period from 1777, April 8 d 7 h 30 m to 1779, June 6 d I0 h 10 = 
789 d 2 h 40 m . 

The geocentric places of Mars at those times were, 6* 6° 3l' 26* and 7 s 13° 
48' 30", their diff. I s 7° 17' &", turned into time, at 4MO9 per minute of a de- 
gree, and subtracted, because Mars is more advanced in the ecliptic, is 78()'' 2 h 
40- o 9 - 2 h 33 m 11\8 = 789 d h 6 m 48\2 = 768 revol. hence 1 revol. = 
24 h 39 m 23'.03. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 5Q 

Second biennial period, 1777, April 17 d 7 h 50 m s to 1779, J »ne 15 d g h 45 m 
17 s = 78g d l h 55 m 17 s . The geocentric places 6 s 3 d si' 27" and 7 s 12 d 40' '23' ', 
the diff. Is Q d 8' 56", turned into time 789 d l h 55 m 17 s , and subtracting 
2 h 40 m 52 s , leaves 788 d 23 h 14 m 25 s = 768 revol. hence 1 revol. = 24 h 39™ 18 s .94. 

Third biennial period, 1777, April 26 d 9 h 5 m O s to 1779, June 19 d 8 h 40 m 22 s = 
783 d 23 h 35 m 22'. The geocentric places 6 s 1° 24' 36" and 7 s 12° 31' 48", the 
diff. I s 11° 7' 12" turned into time gives 783 d 23 h 35 m 22 s , and subtracted 
2 h 45 m 1 5 s .61eaves 783 d 20 h 50 ra 6 3 .4 = 763 revol. hence 1 revol. = 24 h 39 m 23 5 .04. 

As these 3 periods are supported by observations of equal validity, Mr. H. 
takes a mean of them all for the nearest approximation to the true sydereal re- 
volution of Mars on his axis, which therefore is 24 h 39 m 21 '.67. 

It remains now only to see how far we may depend on this determination of 
Mars's diurnal rotation as coming near the truth ; and looking over those causes 
which may possibly produce any errors, we find, first of all, that in the long 
biennial periods a mistake in the number of revolutions would produce a con- 
siderable deviation from truth. Secondly, in the observations of a spot which 
moves so slow, we are also liable to some considerable mistake in estimating the 
time when it comes to a certain place ; and the more so, if that place is not the 
centre. Lastly, the time itself is liable to inaccuracy. 

As to the 1st, it appears from the 3 monthly periods observed in the year 
1779, when the proper allowances for the geocentric places are made, that the 
sydereal revolution of Mars cannot well be less than 24 h 39 m 5 s , nor more than 
24 h 39™ 22 s ; but if we should divide any one of the 3 biennial periods by a sup- 
posed number of revolutions, only one more or one less than we have done, the 
difference would be so considerable, that nothing but a mistake in every one of 
the 3 monthly periods, of at least one whole hour, could justify such a suppo- 
sition ; and that such a mistake in the situation of a spot on Mars cannot have 
been made in those observations, is evident enough from the exactness with 
which they were made, and from their agreement with each other. 

The 2d cause of error, which is the uncertainty in assigning the exact time 
when a spot comes to the centre, is of some force/ But it seems highly proba- 
ble, from the manner in which the spots on Mars pass over the disc of that 
planet, that there can hardly be so great an error as 10 m in an observation of 
any remarkable spot's coming to the centre. However, not being willing to 
trust more to the eye than ought to be done, Mr. H. had recourse to the fol- 
lowing experiment. He drew several circles of 1 inch radius, taking care to 
make no visible impression of a centre ; and placed in each a fine point at the 
several distances of .0424, .0636, .0848, in ten thousands of an inch from the 
real centre ; some to the right, others to the left. These measures are the sines 
to radius l, of 2° 26', 3° 39', and 4° 52'; which are the arches a spot on 

1 2 



dO PHILOSOPHICAL TRANSACTIONS. [ANNO 178], 

Mars passes over in K), 15, 20 m minutes respectively. He exposed them to 
several persons unacquainted with his designs, and found, that not one of them 
made a single mistake in saying whether the point was, or was not, in the centre 
of the circle, and which way it deviated from it. As the direction of the mo- 
tion of a spot on Mars is known, he thought the persons who were to judge of 
the place of the points were entitled to be acquainted with the line in which they 
were placed, which for that reason was always to the right and left only. The 
points that answer to the excentricity of 15' and 20' are indeed so visibly out of 
the centre, that we may safely say, that any mistake, in estimating the time of a 
spot on Mars coming to the centre, cannot well exceed a quarter of an hour at 
the outside. 

As for the 3d and last occasion of error, the time itself, he thinks may be 
depended on to a few seconds; but the observations of the year J 777, indeed, 
are far from having the same advantage. He was not then provided with an al- 
titude instrument, therefore set his clock by a good sun-dial, with the equation 
of time contained in the Nautical Almanac, and found it to agree generally to a 
minute or 1 with the time calculated for the eclipses of Jupiter's first satellite, as 
he deduced it for Bath from the Nautical Almanac. However, it was certainly 
liable to an error of several minutes; therefore, allowing no less than 10 m for the 
clock in 1777, and 20 m for an error in estimating the situation of a spot in 1779, 
it will both amount to half an hour; then, if we take a mean of the 3 numbers, 
by which we have divided the 3 biennial periods, we have 766*^; an( l half an hour 
divided by 766-^, will therefore give us the quantity to which, it seems, can 
amount, all the uncertainty in the sydereal diurnal rotation of Mars, which 
is 2 S .34. 

XI. Of the Termites in Africa and other Hot Climates. By Mr. Henry 
Smeathman, of Clement's Inn. p. 139. 

The size and figure of the buildings of these insects have attracted the notice 
of many travellers, and yet the world has not hitherto been furnished with a 
tolerable description of them, though their contrivance and execution scarcely 
fall short of human ingenuity and prudence ; but when we come to consider the 
wonderful economy of these insects, with the good order of their subterraneous 
cities, they will appear foremost on the list of the wonders of the creation, as 
most closely imitating mankind in provident industry and regular government. 

These insects are known by various names: they belong to the termes of Lin- 
neus, and other systematical naturalists: by the English, in the windward parts 
of Africa, they are called Bugga Bugs ; in the West Indies, Wood Lice, Wood 
Ants, or White Ants. By the French, at Senegal, Vague- Vagues ; in the West 
Indies, Poux de Bois, or Fourmis Blanches. By the Bohns, or Sherbro people, 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 6l 

in Africa, Scantz. By the Portuguese in the Brazils, Coupee or Cutters, from 
their cutting things in pieces. By this latter name and that of Piercers or Eaters, 
and similar terms, they are distinguished in various parts of the tropical regions. 

The termites are represented by Linneus as the greatest plagues of both Indies, 
and are indeed every way between the tropics so deemed, from the vast damages 
they cause, and the losses which are experienced in consequence of their eating 
and perforating wooden buildings, utensils, and furniture, with all kinds of 
household-stuff and merchandize, which are totally destroyed by them, if not 
timely prevented ; for nothing less hard than metal or stone can escape their de- 
structive jaws. 

These insects have generally obtained the name of ants, it may be presumed, 
from the similarity in their manner of living, which is, in large communities 
which erect very extraordinary nests, for the most part on the surface of the 
ground, whence their excursions are made through subterraneous passages or 
covered galleries, which they build whenever necessity obliges, or plunder in- 
duces, them to march above ground, and at a great distance from their habita- 
tions carry on a business of depredation and destruction, scarcely credible but to 
those who have seen it. But though they live in communities, and are like the 
ants omnivorous; though like them at a certain period they are furnished with 4 
wings, and emigrate or colonize at the same season; they are by no means the 
same kind of insects, nor does their form correspond with that of ants in any 
one state of their existence, which, like most other insects, is changed several 

times. 

The termites resemble the ants also in their provident and diligent labour, but 
surpass them as well as the bees, wasps, beavers, and all other animals, in the 
arts of building, as much as the Europeans excel the least cultivated savages. 
It is more than probable they excel them as much in sagacity and the arts of 
government; it is certain that they show more substantial instances of their in- 
genuity and industry than any other animals; and do in fact lay up vast maga- 
zines of provisions and other stores; a degree of prudence which has of late 
years been denied, perhaps without reason, to the ants. Such however are the 
extraordinary circumstances attending their economy and sagacity, that it is diffi- 
cult to determine, whether they are more worthy of the attention of the curious 
and intelligent part of mankind on these accounts, or from the ruinous conse- 
quences of their depredations, which have deservedly procured them the name of 
Fatalis or Destructor. 

These communities consist of one male and one female, who are generally the 
common parents of the whole, or greater part, of the rest, and of 3 orders of 
insects, apparently of very different species, but really the same, which together 
compose great commonwealths, or rather monarchies, if we may be allowed the 



62 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

term. Linneus, having seen or heard ot" only 2 of these orders, has classed the 
genus erroneously: for he has placed it among the aptera, or insects without 
wings ; whereas the chief order, that is, the insect in its perfect state, having 4 
wings without any sting, it belongs to the neuroptera ; in which class it will con- 
stitute a new genus of many species. 

The different species of this genus resemble each other in form, in their 
manner of living, and in their good and bad qualities; but differ as much as 
birds in the manner of building their habitations or -nests, and in the choice of 
the materials of which they compose them. There are some species which build 
on the surface of the ground, or part above and part beneath, and 1 or 2 species, 
perhaps more, that build on the stems or branches of trees, sometimes aloft at a 
vast height. 

Of every species there are 3 orders: 1st, the working insects, which Mr. S. 
calls labourers; next the fighting ones, or soldiers, which do no kind of labour; 
and lastly, the winged ones, or perfect insects, which are male and female, and 
capable of propagation. These might very appositely be called the nobility or 
gentry, for they neither labour, nor toil, nor fight, being quite incapable of 
either, and almost of self-defence. These only are capable of being elected 
kings or queens; and nature has so ordered it, that they emigrate within a few 
weeks after they are elevated to this state, and either establish new kingdoms, 
or perish within a day or two. 

The termes bellicosus, being the largest species, is most remarkable and best 
known on the coast of Africa. It erects immense buildings of well-tempered 
clay or earth, which are contrived and finished with such art and ingenuity, that 
we are at a loss to say, whether they are most to be admired on that account, or 
for their enormous magnitude and solidity. It is from the two lower orders of 
this, or a similar species, that Linneus seems to have taken his description of the 
termes fatalis; and most of the accounts brought home from Africa or Asia, of 
the white ants, are also taken from a species that are so much alike in external 
habit and size, and build so much in their manner, that one may almost venture 
to pronounce them mere variations of the same species. The reason that the 
larger termites have been most remarked, is obvious; they not only build larger 
and more curious nests, but are also more numerous, and do infinitely more mis- 
chief to mankind. When these insects attack such things as we would not wish 
to have injured, we must consider them as most pernicious; but when they are 
employed in destroying decayed trees and substances which only encumber the 
surface of the earth, they may be justly supposed very useful. In this respect 
they resemble very much the common flies, which are regarded by mankind in 
general as noxious, and at best as useless beings in the creation; but this is cer- 
tainly for want of consideration. There are not probably in all nature animals 



VOL. LXXI.J PHILOSOPHICAL TRANSACTIONS. 63 

of more importance, and it would not be difficult to prove, that we should feel 
the want of one or two species of large quadrupeds, much less than of one or two 
species of these despicable looking insects. Mankind in general are sensible that 
nothing is more disagreeable, or more pestiferous, than putrid substances; and 
it is apparent to all who have made observation, that those little insects contribute 
more to the quick dissolution and dispersion of putrescent matter than any other. 
They are so necessary in all hot climates, that even in the open fields a dead ani- 
mal or small putrid substance cannot be laid on the ground 2 minutes before it 
will be covered with flies and their maggots, which instantly entering quickly 
devour one part, and perforating the rest in various directions, expose the whole 
to be much sooner dissipated by the elements. Thus it is with the termites; 
the rapid vegetation in hot climates, of which no idea can be formed by any thing 
to be seen in this, is equalled by as great a degree of destruction from natural as 
well as accidental causes.* It seems, that when any thing whatever is arrived at 
its last degree of perfection, the Creator has decreed it shall be totally destroyed 
as soon as possible, that the face of nature may be speedily adorned with fresh 
productions in the bloom of spring or the pride of summer: so when trees, and 
even woods, are in part destroyed by tornados or fire, it is wonderful to observe, 
how many agents are employed in hastening the total dissolution of the rest; 
but in the hot climates there are none so expert, or who do their business so ex- 
peditiously and effectually, as these insects, which in a few weeks destroy and 
carry away the bodies of large trees, without leaving a particle behind, thus 
clearing the place for other vegetables, which soon fill up every vacancy ; and in 
places, where 2 or 3 years before there has been a populous town, if the inha- 
bitants, as is frequently the case, have chosen to abandon it, there shall be a very 
thick wood, and not the vestige of a post to be seen, unless the wood has been 
of a species which, from its hardness, is called iron wood. 

The nests of this species, the termes bellicosus, are so numerous all over the 
island of Bananas, and the adjacent continent of Africa, that it is scarcely pos- 
sible to stand on any open place, such as a rice plantation, or other clear spot, 
where one of these buildings is not to be seen within 50 paces, and frequently 2 
or 3 are to be seen almost close to each other. In some parts near Senegal, as 
mentioned by Mons. Adanson, their number, magnitude, and closeness of situa- 
tion, make them appear like the villages of the natives. These buildings are 
usually termed hills, by natives as well as strangers, from their outward appear- 
ance, which is that of little hills more or less conical, generally pretty much in 
the form of sugar loaves, and about 10 or 12 feet in perpendicular height above 

* The Guinea grass, which is so well known and so much esteemed by our planters in the West 
Indies, grows in Africa 13 feet high on an average, which height it attains in about 5 or 6 months; 
and the growth of many other plants is as quick. — Orig. 



64 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

the common surface of the ground. These hills continue quite bare till they 
are 6 or 8 feet high; but in time the dead barren clay, of which they are com- 
posed, becomes fertilized by the genial power of the elements in these prolific 
climates, and the addition of vegetable salts and other matters brought by the 
wind; and in the 2d or 3d year, the hillock, if not over-shaded by trees, becomes, 
like the rest of the earth, almost covered with grass and other plants; and in 
the dry season, when the herbage is burnt up by the rays of the sun, it is not 
much unlike a very large hay-cock. 

Every one of these buildings consists of 2 distinct parts, the exterior and the 
interior. The exterior is one large shell in the manner of a dome, large and 
strong enough to inclose and shelter the interior from the vicissitudes of the 
weather, and the inhabitants from the attacks of natural or accidental enemies. 
It is always therefore much stronger than the interior building, which is the 
habitable part, divided, with a wonderful kind of regularity and contrivance, into 
an amazing number of apartments for the residence of the king and queen, and 
the nursing of their numerous progeny; or for magazines, which are always 
found well filled with stores and provisions. 

These hills make their first appearance above ground by a little turret or two 
in the shape of sugar loaves, which are run a foot high or more. Soon after, 
at some little distance, while the former are increasing in height and size, they 
raise others, and so go on increasing the number and widening them at the base, 
till their works below are covered with these turrets, which they always raise the 
highest and largest in the middle, and, by filling up the intervals between each 
turret, collect them as it were into one dome. They are not very curious or 
exact about these turrets, except in making them very solid and strong; and 
when by the junction of them the dome is completed, for which purpose the 
turrets answer as scaffolds, they take away the middle ones entirely, except the 
tops, which joined together make the crown of the cupola, and apply the clay 
to the building of the works within, or to erecting fresh turrets for the purpose 
of raising the hillock still higher; so that doubtless some part of the clay is used 
several times, like the boards and posts of a mason's scaffold. 

When these hills are little more than half their height, it is always the practice 
of the wild bulls to stand as centinels on them, while the rest of the herd is 
ruminating below. They are sufficiently strong for that purpose, and at their 
full height answer excellently well as places to look out. Mr. S. has been with 
4 men on the top of one of these hillocks. Whenever word was brought of a 
vessel in sight, they immediately ran to some bugga bug hill, as they are called, 
and clambered up to get a good view; for on the common surface it was seldom 
possible to see over the grass or plants, which, in spite of monthly brushings, 
generally prevented all horizontal views at any distance. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 65 

The outward shell or dome is not only of use to protect and support the in- 
terior buildings from external violence and the heavy rains, but to collect and 
preserve a regular degree of genial warmth and moisture, which seems very ne- 
cessary for hatching the eggs and cherishing the young ones. The royal chamber, 
which Mr. S. so calls on account of its being adapted for, and occupied by, the 
king and queen, appears to be in the opinion of this little people of the most 
consequence, being always situated as near the centre of the interior building as 
possible, and generally about the height of the common surface of the ground, 
at a pace or two from the hillock. It is always nearly in the shape of half an 
egg or an obtuse oval within, and may be supposed to represent a long oven. In 
the infant state of the colony, it is but about an inch in length; but in time 
will be increased to 6 or 8 inches or more in the clear, being always in propor- 
tion to the size of the queen, who, increasing in bulk as in age, at length re- 
quires a chamber of such dimensions. Its floor is perfectly horizontal; and in 
large hillocks, sometimes more than an inch thick of solid clay. The roof also, 
which is one solid and well-turned oval arch, is generally of about the same so- 
lidity, but in some places it is not a quarter of an inch thick, viz. on the sides 
where it joins the floor, and where the doors or entrances are made level with it 
at nearly equal distances from each other. These entrances will not admit any 
animal larejer than the soldiers or labourers; so that the king, and the queen, 
who is, at full size, a thousand times the weight of a king, can never possibly 

go out. 

The royal chamber, if in a large hillock, is surrounded by an innumerable 
quantity of others of different sizes, shapes, and dimensions; but all of them 
arched in one way <" r another, sometimes circular, and sometimes elliptical or 
oval. These either open into each other, or communicate by passages as wide; 
and, being always empty, are evidently made for the soldiers and attendants, of 
whom it will soon appear great numbers are necessary, and of course always in 
waiting. These apartments are joined by the magazines and nurseries. The 
former are chambers of clay, and are always well filled with provisions, which to 
the naked eye seem to consist of the raspings of wood and plants which the ter- 
mites destroy, but are found in the microscope to be principally the gums or in- 
spissated juices of plants. These are thrown together in little masses, some of 
which are finer than others, and resemble the sugar about preserved fruits, others 
are like tears of gum, one quite transparent, another like amber, a 3d brown, 
and a 4th quite opaque, as we see often in parcels of ordinary gums. These 
magazines are intermixed with the nurseries, which are buildings totally different 
from the rest of the apartments: for these are composed entirely of wooden 
materials, seemingly joined together with gums. Mr. S. calls them the nurseries 
because they are invariably occupied by the eggs, and young ones, which appear 

vol. xv. K 



66 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/8) 

at first in the shape of labourers, but white as snow. These buildings are ex- 
ceedingly compact, and divided into many very small irregular-shaped chambers, 
not one of which is to be found of half an inch in width. They are placed all 
round the royal apartments, and as near as possible to them. 

When the nest is in the infant state, the nurseries are close to the royal 
chamber; but as in process of time the queen enlarges, it is necessary to enlarge 
the chamber for her accommodation ; and as she then lays a greater number of 
eggs, and requires a greater number of attendants, so it is necessary to enlarge 
and increase the number of the adjacent apartments; for which purpose the 
small nurseries which are first built are taken to pieces, rebuilt a little farther ofF 
a size larger, and the number of them increased at the same time. Thus they 
continually enlarge their apartments, pull down, repair, or rebuild, according to 
their wants, with a degree of sagacity, regularity, and foresight, not even imi- 
tated by any other kind of animals or insects yet heard of. 

There is one remarkable circumstance attending the nurseries. They are 
always slightly overgrown with mould, and plentifully sprinkled with small white 
globules about the size of a small pin's head. These at first Mr. S. took to be 
the eggs; but, on bringing them to the microscope, they evidently appeared to 
be a species of mushroom, in shape like our eatable mushroom in the young 
state in which it is pickled. They appear, when whole, white like snow a little 
thawed and then frozen again, and when bruised seem composed of an infinite 
number of pellucid particles, approaching to oval forms and difficult to separate; 
the mouldiness seems likewise to be the same kind of substance. The nurseries 
are inclosed in chambers of clay, like those which contain the provisions, but 
much larger. In the early state of the nest they are not larger than a hazel- 
nut, but in great hills are often as large as a child's head of a year old. 

The disposition of the interior parts of these hills is pretty much alike, except 
when some insurmountable obstacle prevents; for instance, when the king and 
queen have been first lodged near the foot of a rock or of a tree, they are cer- 
tainly built out of the usual form, otherwise pretty nearly according to the fol- 
lowing plan. The royal chamber is situated at about a level with the surface of 
the ground, at an equal distance from all the sides of the building, and directly 
under the apex of the hill. It is on all sides, both above and below, surrounded 
by what Mr. S. calls the royal apartments, which have only labourers and sol- 
diers in them, and can be intended for no other purpose than for these to wait 
in, either to guard or serve their common father and mother, on whose safety 
depends the happiness, and, according to the negroes, even the existence of the 
whole community. 

These apartments compose an intricate labyrinth, which extends a foot or more 
in diameter from the royal chamber on every side. Here the nurseries and ma- 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 6/ 

gazines of provisions begin, and, being separated by small empty chambers and 
galleries, which go round them or communicate from one to the other, are con- 
tinued on all sides to the outer shell, and reach up within it -§- or 4 of its height, 
leaving an open area in the middle under the dome, which very much resembles 
the nave of an old cathedral : this is surrounded by 3 or 4 very large gothic-shaped 
arches, which are sometimes 1 or 3 feet high next the front of the area, but 
diminish very rapidly as they recede from it, like the arches of aisles in perspec- 
tives, and are soon lost among the innumerable chambers and nurseries behind 
them. All these chambers, and the passages leading to and from them, being 
arched, they help to support each other; and while the interior large arches pre- 
vent them falling into the centre, and keep the area open, the exterior building 
supports them on the outside. There are, comparatively speaking, few openings 
into the great area, and they for the most part seem intended only to admit that 
genial warmth into the nurseries which the dome collects. The interior build- 
ing or assemblage of nurseries, chambers, &c. has a flattish top or roof, without 
any perforation, which would keep the apartments below dry, in case through 
accident the dome should receive any injury and let in water; and it is never ex- 
actly flat and uniform, because the insects are always adding to it by building 
more chambers and nurseries: so that the divisions or columns between the future 
arched apartments resemble the pinnacles on the fronts of some old buildings, 
and demand particular notice, as affording one proof that for the most part the 
insects project their arches, and do not make them by evacuation. 

The area has also a flattish floor, which lies over the royal chamber, but 
sometimes a good height above it, having nurseries and magazines between. It 
is likewise water-proof, and contrived, as far as we may guess, to let the water 
off, if it should get in, and run over by some short way into the subterraneous 
passages, which run under the lowest apartments in the hill in various directions, 
and are of an astonishing size, being wider than the bore of a great cannon. 
One, that Mr. S. measured, was perfectly cylindrical, and 13 inches in diameter. 
These subterraneous passages or galleries are lined very thick with the same kind 
of clay of which the hill is composed, and ascend the inside of the outward 
shell in a spiral manner, and winding round the whole building up to the top, 
intersect each other at different heights, opening either immediately in the dome 
in various places, and into the interior building, the new turrets, &c. or com- 
municating with them by other galleries of different bores or diameters, either 
circular or oval. 

From every part of these large galleries are various small pipes or galleries 
leading to different parts of the building. Under ground there are a great many 
that lead downward by sloping descents, 3 and 4 feet perpendicular among the 
gravel, whence the labouring termites cull the finer parts, which, being worked 

k 1 



68 1'HILOSOl'HICAL TRANSACTIONS. [ANNO 1781. 

up in their mouths to the consistence of mortar, becomes that solid clay or 
stone of which their hills and all their buildings, except their nurseries, are 
composed. Other galleries again ascend, and lead out horizontally on every 
side, and are carried underground near to the surface a vast distance: for if you 
destroy all the nests within 100 yards of your house, the inhabitants of those 
which are left unmolested farther off, will still carry on their subterraneous galle- 
ries, and invade the goods and merchandizes contained in it by sap and mine, and 
do great mischief, if you are not very circumspect. 

But to return to the cities whence these extraordinary expeditions and opera- 
tions originate: it seems there is a degree of necessity for the galleries under the 
hills being thus large, being the great thoroughfares for all the labourers and 
soldiers, going forth or returning on any business whatever, whether fetching 
clay, wood, water, or provisions ; and they are certainly well calculated for the 
purposes to which they are applied, by the spiral slope which is given them; for 
if they were perpendicular, the labourers would not be able to carry on their 
building with so much facility, as they ascend a perpendicular with great diffi- 
culty, and the soldiers can scarcely do it at all. It is on this account that some- 
times a road like a ledge is made on the perpendicular side of any part of the 
building within their hill, which is flat on the upper surface, and half an inch 
wide, and ascends gradually like a staircase, or like those roads which are cut on 
the sides of hills and mountains, that would otherwise be inaccessible: by which, 
and similar contrivances, they travel with great facility to every interior part. 

This too is probably the cause of their building a kind of bridge of one vast 
arch, which answers the purpose of a flight of stairs from the floor of the area 
to some opening on the side of one of the columns which support the great 
arches, which must shorten the distance exceedingly to those labourers who have 
the eggs to carry from the royal chamber to some of the upper nurseries, which 
in some hills would be 4 or 5 feet in the straightest line, and much more if car- 
ried through all the winding passages which lead through the inner chambers 
and apartments. Mr. S. had a memorandum of one of these bridges, half an 
inch broad, a quarter of an inch thick, and 10 inches long, making the side of 
an elliptic arch of proportionable size; so that it is wonderful it did not fall over 
or break by its own weight before they got it joined to the side of the column 
above. It was strengthened by a small arch at the bottom, and had a hollow or 
groove all the length of the upper surface, either made purposely for the inhabi- 
tants to travel over with more safety, or else, which is not improbable, worn so 
by frequent treading. 

The nests before described are so remarkable on account of their size, that 
travellers have seldom, where they were to be seen, taken notice of any other; 
and have generally, when speaking of white ants, described them as inhabitants 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 69 

of those hills. Those however which are built by the smaller species of those 
insects, are very numerous, and some of them exceedingly well worth our 
attention; one sort in particular, which from their form Mr. S. has named turret 
nests. These are a great deal less than the foregoing, and indeed much less in 
proportion to the size of the buildings; but their external form is more curious, 
and, their solidity considered, they are prodigious buildings for so small an 
animal.* 

These buildings are upright cylinders composed of a well-tempered black earth 
or clay, about -f- of a yard high, and covered with a roof of the same material in 
the shape of a cone, whose base extends over and hangs down 3 or 4 inches 
wider than the perpendicular sides of the cylinder; so that most of them 
resemble in shape the body of a round windmill; but some of the roofs have so 
little elevation in the middle, that they are pretty much in the shape of a full- 
grown mushroom. 

After one of these turrets is finished, it is not altered or enlarged ; but when 
no longer capable of containing the community, the foundation of another is 
laid within a few inches of it. Sometimes, though but rarely, the 2d is begun 
before the first is finished, and a 3d before they have completed the 2d: thus 
they will run up 5 or 6 of these turrets at the foot of a tree in the thick woods, 
and make a most singular group of buildings. The turrets are so strongly built, 
that in case of violence they will much sooner overset from the foundation, and 
tear up the gravel and solid earth, than break in the middle; and in that case the 
insects will frequently begin another turret and build it, as it were, through that 
which is fallen ; for they will connect the cylinder below with the ground, and 
run up a new turret from its uppet side, so that it will seem to rest on the hori- 
zontal cylinder only. 

Mr. S. did not observe any thing else about these nests that was remarkable, 
except the quantity of the black brown clay, which is as dark coloured as rich 
vegetable mould, but burns to an exceeding fine and clear red brick. Within, 
the whole building is pretty equally divided into innumerable cells of irregular 
shapes; sometimes they are quadrangular or cubical, and sometimes pentagonal; 
but often the angles are so ill defined, that each half of a cell will be shaped like 
the inside of that shell which is called the sea-ear. Each shell has two or more 
entrances, and as there are no pipes or galleries, no variety of apartments, no 
well-turned arches, wooden nurseries, &c. &c. they do not by any means excite 
our admiration so much as the hill nests, which are indeed collections of won- 
ders. There are two sizes of these turret nests, built by two different species of 

* If their height be estimated and computed by the size of the builders, and compared with ours 
on the like scale ; each of them is 4 or 5 times the height of the monument, and a great many times 
its solid contents. — Orig. 



70 PHILOSOPHICAL TRANSACTIONS. [aNNO 1781. 

termites. The larger species, the termes atrox, En its perfect state measures 
1 inch and -^ from the extremities of the wings on the one side to the extremi- 
ties on the other. The lesser species, termes mordax, measures only -Jl of an 
inch from tip to tip. 

The next kind of nests, built by another species of this genus, the termes arbo- 
rum, have very little resemblance to the former in shape or substance. These are 
generally spherical or oval, and built in trees. Sometimes they are seated between 
the arms and the stems of trees, and very frequently may be seen surrounding 
the branch of a tree at the height of 70 or 80 feet; and, though but rarely, as 
large as a very great sugar cask. They are composed of small particles of wood 
and the various gums and juices of trees, perhaps combined with those of the 
animals, and worked by those little industrious creatures into a paste, and so 
moulded into innumerable little cells of very different and irregular forms, which 
afford no amusing variety and nothing curious, but the immense quantity of 
inhabitants, young and old, with which they are at all times crowded; on which 
account they are sought for in order to feed young fowls, and especially for the 
treating of turkies. These nests are very compact, and so strongly attached to 
the boughs on which they are fixed, that there is no detaching them but by 
cutting them in pieces, or sawing off' the branch: and they will sustain the force 
of a tornado as long as the tree on which they are fixed. This species has the 
external habit, size, and almost the colour, of the termes atrox. 

Some nests are built in those sandy plains called, after the Spaniards, 
Savannas, that resemble the hill nests first described. They are composed of a 
black mud, brought from a few inches below the white sand, and are built in the 
form of an imperfect cone, or bell-shaped, having their tops rounded. These 
nests are generally about 4 or 5 feet high. They seemed to be inhabited by 
nearly as large insects, differing very little except in colour, which is lighter than 
that of the termites bellicosi. 

It has been before observed, that there are of every species of termites 3 
orders; of these orders the working insects or labourers are always the most 
numerous; in the termes bellicosus there seems to be at the least 100 labourers 
to one of the fighting insects or soldiers. They are in this state about J- of an 
inch long, and 25 of them weigh about a grain; so that they are not so large as 
some of our ants. From their external habit and fondness for wood, they have 
been very expressively called wood-lice by some people, and the whole genus has 
been known by that name, particularly among the French. They resemble 
them, it is true, very much at a distance, but they run as fast or faster than any 
other insects of their size, and are incessantly bustling about their affairs. The 2d 
order, or soldiers, have a very different form from the labourers, and have been 
by some authors supposed to be the males, and the former neuters; but they are, 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. "J \ 

in fact, the same insects as the foregoing, only they have undergone a change of 
form, and approached one degree nearer to the perfect state. They are now 
much larger, being half an inch long, and equal in bulk to 15 of the labourers. 
There is now likewise a most remarkable circumstance in the form of the head 
and mouth; for in the former state the mouth is evidently calculated for gnawing 
and holding bodies; but in this state, the jaws being shaped just like 2 very 
sharp awls a little jagged, they are incapable of any thing but piercing or wound- 
ing, for which purposes they are very effectual, being as hard as a crab's claw, 
and placed in a strong horny head, which is of a nut-brown colour, which seems 
to labour under great difficulty in carrying it : on which account perhaps the 
animal is incapable of climbing up in perpendicular surfaces. 

The 3d order, or the insect in its perfect state, varies its form still more than 
ever. The head, thorax, and abdomen, differ almost entirely from the same 
parts in the labourers and soldiers ; and, besides, the animal is now furnished with 
4 fine large brownish, transparent, wings, with which it is at the time of emigra- 
tion to wing its way in search of a new settlement. In short, it differs so much 
from its form and appearance in the other 2 states, that it has never been sup- 
posed to be the same animal, but by those who have seen it in the same nest ; 
and some of these have distrusted the evidence of their senses. It was so long 
before Mr. S. met with them in the nests himself, that he doubted the informa- 
tion which was given by the natives, that they belonged to the same family. 
Indeed 20 nests may be opened without finding one winged ant ; for those are 
to be found only just before the commencement of the rainy season, when they 
undergo the last change, which is preparative to their colonization. Add to this, 
they sometimes abandon an outward part of their building, the community 
being diminished by some accident. Sometimes, too, different species of the real 
ant (formica) possess themselves by force of a lodgement, and so are frequently 
dislodged from the same nest, and taken for the same kind of insects. This is 
often the case with the nests of the smaller species, which are often totally 
abandoned by the termites, and completely inhabited by different species of ants, 
cockroaches, scolopendrae, scorpions, and other vermin, fond of obscure retreats, 
that occupy different parts of their roomy buildings. 

In the winged state they have also much altered their size as well as form. 
Their bodies now measure between 6 and 7 tenths of an inch in length, their 
wings being above 2-l inches from tip to tip, and they are equal in bulk to about 
30 labourers, or 2 soldiers. They are now also furnished with 2 large eyes, one 
on each side of the head, and very conspicuous ; if they have any before, they 
are not easily to be distinguished. Probably in the ]st 2 states, their eyes, if 
they have any, may be small like those of moles ; for as they live like these 
animals always under-ground, they have as little occasion for these organs, and 



72 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

it is not to be wondered at that we do not discover them ; but the case is much 
altered when they arrive at the winged state, in which they are to roam, though 
but for a few hours, through the wide air, and explore new and distant regions. 
In this form the animal Gomes' abroad during or soon after the first tornado, 
which at the latter end of the dry season proclaims the approach of the ensuing 
rains, seldom waiting for a 2d or 3d shower, if the 1st, as is generally the case, 
happens in the night, and brings much wet after it. 

The quantities that are to be found the next morning all over the surface of 
the earth, but particularly on the waters, is astonishing ; for their wings are 
only calculated to carry them a few hours, and after the rising of the sun not 
one in 1000 is to be found with 4 wings, unless the morning continues rainy, 
when here and there a solitary being is seen winging its way from one place to 
another, as if solicitous only to avoid its numerous enemies, particularly various 
species of ants, which are hunting on every spray, on every leaf, and in every 
possible place, for this unhappy race, of which probably not a pair in many 
millions get into a place of safety, to fulfil the great law of nature, and lay the 
foundation of a new community. Not only all kinds of ants, birds, and car- 
nivorous reptiles, as well as insects, are on the hunt for them, but the inhabi- 
tants of many countries, and particularly of that part of Africa where Mr. S. 
was, eat them.* On the following morning however they are to be seen 

* Mr. Konig, in an Essay on these Insects, read before the Society of Naturalists of Berlin, says, 
that, in some parts of the East Indies, the queens are given alive to old men for strengthening the 
back, and that the natives have a method of catching the winged insects, which he calls females, 
before the time of emigration. They make two holes in the nest; the one to windward, and the 
other to leeward. At the leeward opening they place the mouth of a pot, previously rubbed within 
with an aromatic herb calk-d bergera, which is more valued there than the laurel in Europe. On the 
windward side they make a fire of stinking materials, which not only drives these insects into the 
pots, but frequently the hooded snakes also, on which account they are obliged to be cautious in 
removing them. By this method they catch great quantities, of which they make with flour a 
variety of pastry, which they can afford to sell very cheap to the poorer ranks of people. Mr. Konig 
adds, that this kind of food is very plentiful ; the too great use of it brings on an epidemic colic and 
dysentery, which kills in two or three hours. 

I have not, says Mr. S., found the Africans so ingenious in procuring or dressing them. They are 
content with a very small part of those which, at the time of swarming, or rather of emigration, 
fall into the neighbouring waters, which they skim off with calabashes, bring large kettles full of 
them to their habitations, and parch them in iron pots over a gentle fire, stirring them about as is 
usually done in roasting coffee. In that state, without sauce or any other addition, they serve them 
as delicious food ; and they put them by hands-full into their mouths, as we do comfits. 1 have eaten 
them dressed this way several times, and think them both delicate, nourishing, and wholesome; they 
are something sweeter, but not so fat and cloying, as the caterpillar or maggot of the palm-tree 
snout-beetle, curculio palmarum, which is served up at all the luxurious tables of West Indian 
epicures, particularly of the French, as the greatest dainty of the western world. 

According to the Baron de Geer, Mr. Sparrman s;iys, that the Hottuntots eat these insects, and 



VOL. LXXI.] PHILOSOPHICAL TBANSACTIONS. 73 

running on the ground in chace of each other ; sometimes with a wing or 1 still 
hanging to their bodies, which are not only' useless, but seem rather cumber- 
some. The greater part have no wings, but they run exceedingly fast, the males 
after the females ; Mr. S. sometimes remarked 2 males after one female, con- 
tending with great eagerness who should win the prize, regardless of the 
innumerable dangers that surrounded them. 

They are now become, from being one of the most active, industrious, and 
rapacious, from one of the most fierce and implacable little animals in the world, 
the most innocent, helpless, and cowardly ; never making the least resistance to 
the smallest ant. The ants are to be seen on every side in infinite numbers, of 
various species and sizes, dragging these annual victims of the laws of nature to 
their different nests. It is wonderful that a pair should ever escape so many 
dangers, and get into a place of security. Some however are so fortunate ; and 
being found by some of the labouring insects that are continually running about 
the surface of the ground under their covered galleries, are elected kings and 
queens of new states ; all those who are not so elected and preserved, certainly 
perish, and most probably in the course of the following day. The manner in 
which these labourers protect the happy pair from their innumerable enemies, 
not only on the day of the massacre of almost all their race, but for a long time 
after, will, Mr. S. hopes, justify him in the use of the term election. The little 
industrious creatures immediately inclose them in a small chamber of clay suit- 
able to their size, into which at first they leave but one small entrance, large 
enough for themselves and the soldiers to go in and out, but much too little for 
either of the royal pair to make use of ; and when necessity obliges them to 
make more entrances, they are never larger ; so that, of course, the voluntary 
subjects charge themselves with the task of providing for the offspring of their 
sovereigns, as well as to work and to fight for them, till they shall have raised a 
progeny capable at least of dividing the task with them. 

About this time a most extraordinary change begins to take place in the queen, 
to which Mr. S. knows nothing similar, except in the pulex penetrans of 
Linneus, the jigger of the West Indies, and in the different species of coccus, 
cochineal. The abdomen of this female begins gradually to distend and enlarge 

even grow fat on them ; but he does not say what methods they take to procure or dress them. And 
other writers mention their being an article of diet in different parts of South America. 

Sir Hans Sloane says, the silk-cotton tree worm is esteemed by the Indians and negroes beyond 
marrow. This worm is no more than a large maggot, being the caterpillar of a large Capricorn 
beetle, or goat chafer : the larva of a pretty large cerambix, which is also brought from Africa, 
where I have eaten those worms roasted. This insect is most probably to be found in all countries 
where the silk-cotton tree (bombax) is indigenous. I have discoursed with several gentlemen on the 
taste of the white ants ; and we have always agreed, that they are most delicious. One gentleman 
compared them to sugared marrow, another to sugared cream and a paste of sweet almonds. — Orig. 
VOL. XV. L 



74 PHILOSOPHICAL TRANSACTIONS. [ANNO 1JS1. 

to such an enormous size, that an old queen will have it increased so as to be 
1500 or 2000 times the bulk of the rest of her body, and 20 or 30 thousand 
times the bulk of a labourer, as Mr. S. has found by carefully weighing and 
computing the different states. The skin between the segments of the abdomen 
distends in every direction ; and at last the segments are removed to half an inch 
distance from each other, though at first the length of the whole abdomen is 
not half an inch. They preserve their dark brown colour, and the upper part 
of the abdomen is marked with a regular series of brown bars, from the thorax 
to the posterior part of the abdomen, while the intervals between them are 
covered with a thin, delicate, transparent skin, and appear of a fine cream 
colour, a little shaded by the dark colour of the intestines and watery fluid, seen 
here and there beneath. Mr. S. conjectures the animal is upward of 2 years 
old when the abdomen is increased to 3 inches in length ; he had sometimes 
found them of near twice that size. The abdomen is now of an irregular 
oblong shape, being contracted by the muscles of every segment, and is become 
one vast matrix full of eggs, which make long circumvolutions through an 
innumerable quantity of very minute vessels, that circulate round the inside in a 
serpentine manner, which would exercise the ingenuity of a skilful anatomist to 
dissect and develope. This singular matrix is not more remarkable for its 
amazing extension and size, than for its peristaltic motion, which resembles the 
undulating of waves, and continues incessantly without any apparent effort of 
the animal; so that one part or other alternately is rising and sinking in perpetual 
succession, and the matrix seems never at rest, but is always protruding eggs to 
the amount, as he had frequently counted in old queens, of 60 in a minute, or 
80 thousand and upward in 1 day of 24 hours.* 

These eggs are instantly taken from her body by her attendants, of whom 
there always are, in the royal chamber and the galleries adjacent, a sufficient 
number in waiting, and carried to the nurseries, which in a great nest may some 
of them be 4 or 5 feet distant in a straight line, and consequently much farther by 
their winding galleries. Here, after they are hatched, the young are attended and 
provided with every thing necessary, till they are able to shift for themselves, 
and take their share in the labours of the community. This then is an accurate 
description and account of the termes bellicosus, or species that builds the large 
nests in its different states. 

* Since the reading of this paper, Mr. Jolin Hunter, so celebrated for his great skill and experi- 
ence in comparative anatomy, has' dissected 'I young queens. He hnds the abdomen contains 2 
ovaria, in each ot which are many hundred ova-ducts, and in each of these ova-ducts a vast many 
eggs; so that there seems no doubt of the fact, as the matrix of a full-grown queen must be calcu- 
lated for tlie production and yielding of a prodigious number of eggs. He lias also dissected the 
kings; the ret>ult ol these dissections, with some further particulars, will be related in another paper. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 75 

Those which build either the roofed turrets or the nests in the trees, seem in 
most instances to have a strong resemblance to them, both in their form and 
economy, going through the same changes from the egg to the winged state. 
The queens also increase to a great size when compared with the labourers; but 
very short of those queens before described. The largest are from about an inch 
to an inch and a half long, and not much thicker than a common quill. There 
is the same kind of peristaltic motion in the abdomen, but in a much smaller 
degree ; and, as the animal is incapable of moving from her place, the eggs 
are doubtless carried to the different cells by the labourers, and reared with a 
care similar to that which is practised in the larger nests. 

It is remarkable of all these different species, that the working and the fight- 
ing insects never expose themselves to the open air ; but either travel under 
ground, or within such trees and substances as they destroy ; except indeed when 
they cannot proceed by their latent passages, and find it convenient or necessary 
to search for plunder above ground. In that case they make pipes of that 
material with which they build their nests. The larger sort use the red clay ; 
the turret builders use the black clay ; and those which build in the trees employ 
the same ligneous substances of which their nests are composed. With the ma- 
terials they completely line most of the roads leading from their nests into the 
various parts of the country, and travel out and home with the utmost security 
in all kinds of weather. If they meet a rock or any other obstruction, they 
will make their way over the surface ; and for that purpose erect a covered way or, 
arch, still of the same materials, continuing it with many windings and ramifica- 
tions through large groves ; having, where it is possible, subterranean pipes 
running parallel with them, into which they sink and save themselves, if their 
galleries above ground be destroyed by any violence, or the tread of men or ani- 
mals alarms them. When we chance by accident to enter any solitary grove, 
where the ground is pretty well covered with their arched galleries, they give the 
alarm by loud hissings, which are heard distinctly at every step we take ; soon 
after which we may examine their galleries in vain for the insects ; we find only 
small holes, just large enough for them, by which they have made their escape 
into their subterraneous roads. These galleries are large enough for them to 
pass and repass so as to prevent any stoppages, though there are always nume- 
rous passengers, and shelter them equally from light and air, as well as from their 
enemies, of which the ants, being the most numerous, are the most formidable. 

The termites, except their heads, are exceeding soft, and covered with a very 
thin and delicate skin ; being blind, they are no match on open ground for the 
ants, who can see, and are all of them covered with a strong horny shell not 
easily pierced, and are of dispositions bold, active, and rapacious. Whenever 
the termites are dislodged from their covered ways, the various species of the 

L 2 



76 PHILOSOPHICAL TRANSACTIONS. [aNNO 1781. 

former, who probably are as numerous above ground as the latter are in their 
subterraneous passages, instantly seize and drag them away to their nests, to 
feed the young brood. The termites are therefore exceeding solicitous to pre- 
serve their covered ways in good repair ; and if one of them be demolished, for 
a few inches in length, it is wonderful how soon they rebuild it. At first in 
their hurry they get into the open part an inch or two, but stop so suddenly that 
it is very evident they are surprized ; for though some run straight on, and get 
under the arch as speedily as possible in the farther part, most of them run as 
fast back, and very few will venture through that part of the track which is left 
uncovered. In a few minutes they are seen rebuilding the arch, and by the next 
morning they will have restored their gallery for 3 or 4 yards in length, if so 
much has been ruined ; and, on opening it again, will be found as numerous as 
ever, under it, passing both ways, li you continue to destroy it several times, 
they will at length seem to give up the point, and build another in a different 
direction ; but, if the old one led to some favourite plunder, in a few days they 
will rebuild it again ; and, unless you destroy their nest, never totally abandon 
their gallery. 

The termites arborum, those which build in trees, frequently establish their 
nests within the roofs and other parts of houses, to which they do considerable 
damage, if not timely extirpated. The large species are not only much more 
destructive, but more difficult to be guarded against, since they make their ap- 
proaches chiefly under ground, descending below the foundations of houses and 
stores at several feet from the surface, and rising again either in the floors, or 
entering at the bottoms of the posts, of which the sides of the buildings are 
composed, and bore quite through them, following the course of the fibres to 
the top, or making lateral perforations and cavities here and there as they pro- 
ceed. While some are employed in gutting the posts, others ascend from them, 
entering a rafter or some other part of the roof. If they once find the thatch, 
which seems to be a favourite food, they soon bring up wet clay, and build their 
pipes or galleries through the roof in various directions, as long as it will sup- 
port them ; sometimes eating the palm-tree leaves and branches of which it is 
composed, and perhaps (for variety seems very pleasing to them) the rattan or 
other running plant which is used as a cord to tye the various parts of the roof 
together, and that to the posts which support it : thus, with the assistance of 
the rats, who during the rainy season are apt to shelter themselves there, and to 
burrow through it, they very soon ruin the house, by weakening the fastenings 
and exposing it to the wet. In the mean time the posts will be perforated in 
every direction as full of holes as that timber in the bottoms of ships which has 
been bored by the worms ; the fibrous and knotty parts, which are the hardest, 
being left to the last. 



VOL. JLXXI.] PHILOSOPHICAL TRANSACTIONS. 77 

In carrying on this business, they sometimes find, it seems, that the post has 
some weight to support ; and then, if it is a convenient track to the roof, or is 
itself a kind of wood agreeable to them, they bring their mortar, and fill all or 
most of the cavities, leaving the necessary roads through it, and, as fast as they 
take away the wood, replace the vacancy with that material ; which being 
worked together by them closer and more compactly than human strength or art 
could ram it, when the house is pulled to pieces, in order to examine if any of 
the posts are fit to be used again, those of the softer kinds are often found re- 
duced almost to a shell, and all or a greater part transformed from wood to clay, 
as solid and as hard as many kinds of free-stone used for building in England. 
It is much the same when the termites bellicosi get into a chest or trunk con- 
taining clothes and other things ; if the weight above is great, or they are afraid 
of ants or other enemies, and have time, they carry their pipes through, and 
replace a great part with clay, running their galleries in various directions. The 
tree termites indeed, when they get within a box, often make a nest there, and 
being once in possession destroy it at their leisure. They did so to the pyramidal 
box which contained Mr. S.'s compound microscope. It was of mahogany, and 
he had left it in the store of Governor Campbell, of Tobago, for a few months, 
while he made the tour of the Leeward Islands. On his return he found these 
insects had done much mischief in the store, and, among other things, had 
taken possession of the microscope, and eaten every thing about it except the 
glass or metal, and the board on which the pedestal is fixed, with the drawers 
under it, and the things inclosed. The cells were built all round the pedestal 
and the tube, and attached to it on every side. All the glasses which were 
covered with the wooden substance of their nests retained a cloud, of a gummy 
nature, on them, that was not easily got off, and the lacquer or burnish with 
which the brass work was covered was totally spoiled. Another party had taken 
a liking to the staves of a Madeira cask, and had let out almost a pipe of fine old 
wine. If the large species of Africa (the termites bellicosi) had been so long in 
the uninterrupted possession of such a store, they would not have left 20 pounds 
weight of wood remaining of the whole building, and all that it contained.* 

* Captain Phillip of the navy, who was some time at the Brazils in the service of Portugal, gave 
Mr. S. the .following relation. " An engineer, returned from surveying the country, left his trunk on 
a table : the next morning, not only all his clothes were destroyed by White Ants or Cutters, but his 
papers also ; and the latter in such a manner, that there was not a bit left of an inch square. The 
black lead pencils were likewise so completely destroyed, that the smallest piece, even of the black 
lead, could not be found. The clothes were not entirely cut to pieces and carried away, but appeared 
as if moth-eaten, there being scarce a piece as large as a shilling that was free from small holes ; and 
it was further remarkable, that some silver coin, which was in the trunk, had a number of black 
specks on it, caused by something so corrosive that they could not easily be rubbed off even with 
sand." — Orig. 



78 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

These insects are not less expeditious in destroying the shelves, wainscotting, 
and other fixtures of a house, than the house itself. They are for ever piercing 
and boring in all directions, and sometimes go out of the broadside of one post 
into that of another joining to it ; but they prefer and always destroy the softer 
substances the first, and are particularly fond of pine and fir boards, which they 
excavate and carry away with wonderful dispatch and astonishing cunning : for, 
except a shelf has something standing on it, as a book, or any thing else which 
may tempt them, they will not perforate the surface, but artfully preserve it quite 
whole, and eat away all the inside, except a few fibres which barely keep the two 
sides connected together ; so that a piece of an inch board, which appears solid 
to the eye, will not weigh much more than two sheets of pasteboard of equal 
dimensions, after these animals have been a little while in possession of it.* In 
short, the termites are so insidious in their attacks, that we cannot be too much 
on our guard against them : they will sometimes begin and raise their works, 
especially in new houses, through the floor. If you destroy the work so begun, 
and make a fire on the spot, the next night they will attempt to rise through 
another part ; and, if they happen to emerge under a chest or trunk early in the 
night, will pierce the bottom, and destroy or spoil every thing in it before the 
morning. On these accounts we are careful to set all our chests and boxes on 
stones or bricks, so as to leave the bottoms of such furniture some inches above 
the ground ; which not only prevents these insects finding them out so readily, 
but preserves the bottoms from a corrosive damp which would strike from the 
earth through, and rot every thing in them : a vast deal of vermin also would 
harbour under, such as cock-roaches, centipedes, millepedes, scorpions, ants, 
and various other noisome insects. 

When the termites attack trees and branches in the open air, they sometimes 
vary their manner of doing it. If a stake in a hedge has not taken root and 
vegetated, it becomes their business to destroy it. If it has a good sound bark 
round it, they will enter at the bottom, and eat all but the bark, which will re- 
main, and exhibit the appearance of a solid stick, which some vagrant colony of 
ants or other insects often shelter in till the winds disperse it ; but if they cannot 
trust the bark, they cover the whole stick with their mortar, and it then looks 
as if it had been dipped into thick mud that had been dried on. Under this 
covering they work, leaving no more of the stick and bark than is barely suffi- 
cient to support it, and frequently not the smallest particle, so that on a very 
small tap with your walking stick, the whole stake, though apparently as thick 
as your arm, and 5 or (i feet long, loses its form, and disappearing like a shadow, 

* " The white ants arc transparent as glass, and bite so forcibly, that in the space of one night 
alone they can eat their way through a thick wooden chest of goods, and make it as full of holes, a* 
if it had been shot through with hail-shot," Bosnian's Guinea, p. 270", 277, 493. — Orig. 



VOL. LXXI.j PHILOSOPHICAL TRANSACTIONS. JQ 

falls in small fragments at yonr feet. They generally enter the body of a large 
tree which has fallen through age, or been thrown down by violence, on the side 
next the ground, and eat away at their leisure within the bark, without giving 
themselves the trouble either to cover it on the outside, or to replace the wood 
which they have removed from within, being somehow sensible that there is no 
necessity for it. These excavated trees deceived Mr. S. some times in running : 
for, attempting to step 2 or 3 feet high, he might as well have attempted to step 
upon a cloud, and has come down with such unexpected violence, that, besides 
shaking his teeth and bones almost to dislocation, he has been precipitated, head 
foremost, among the neighbouring trees and bushes. Sometimes, though 
seldom, the animals are known to attack living trees ; though probably not be- 
fore symptoms of mortification have appeared at the roots, since it is evident that 
these insects are intended in the order of nature to hasten the dissolution of such 
trees and vegetables as have arrived at their greatest maturity and perfection, and 
which would, by a tedious decay, serve only to encumber the face of the earth. 
This purpose they answer so effectually, that nothing perishable escapes them, 
and it is almost impossible to leave any thing penetrable on the ground a long 
time in safety ; for the odds are, that put it where you will abroad, they will find 
it out before the following morning, and its destruction follows very soon of 
course. In consequence of this disposition, the woods never remain long en- 
cumbered with the fallen trunks of trees or their branches ; and thus it is that 
the total destruction of deserted towns is so effectually completed, that in 2 or 3 
years a thick wood fills the space ; and, unless iron-wood posts have been made 
use of, not the least vestige of a house is to be discovered. 

The first object of admiration which strikes one, on opening their hills, is the 
behaviour of the soldiers. If you make a breach in a slight part of the building, 
and do it quickly with a strong hoe or pick-axe, in the space of a few seconds a 
soldier will run out, and walk about the breach, as if to try whether the enemy 
is gone, or to examine what is the cause of the attack. He will sometimes go 
in again, as if to give the alarm : but most frequently, in a short time, is fol- 
lowed by 2 or 3 others, who run as fast as- they can, straggling after each other, 
and are soon followed by a large body, who rush out as fast as the breach will 
permit them, and so they proceed, the number increasing, as long as any person 
continues battering their building.* It is not easy to describe the rage and fury 

* " They throw up little hills of 7 or 8 feet high, so very full of holes that they rather seem like 
honey-combs than burrows. These ant-hills are of a very small circumference in proportion to their 
height, being sharp at top, so that to judge by the looks of them one would think die wind could 
blow them down. I one day attempted to knock oft" the top of one of them with my cane, but the 
stroke had no other effect than to bring some thousands of the animals out of doors, to learn what was 
the matter •. on which I took to my heels and ran away as fast as I could." Smith's Voyage to 
Guinea.— Orig. 



80 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 78 1 . 

they show. In their hurry they frequently miss their hold, and tumble down 
the sides of the hill, but recover themselves as quickly as possible ; and, being 
blind, bite every thing they run against, and thus make a crackling noise, while 
some of them beat repeatedly with their forceps on the building, and make a 
small vibrating noise, something shriller and quicker than the ticking of a watch: 
Mr. S. could distinguish this noise at 3 or 4 feet distance, and it continued for a 
minute at a time, with short intervals. While the attack proceeds they are in 
the most violent bustle and agitation. If they get hold of any one, they will in 
an instant let out blood enough to weigh against their whole body ; and if it 
be the leg they wound, you will see the stain on the stocking extend an inch in 
width. They make their hooked jaws meet at the first stroke, and never quit 
their hold, but suffer themselves to be pulled away leg by leg, and piece after 
piece, without the least attempt to escape. On the other hand, keep out of 
their way, and give them no interruption, and they will in less than halfan hour 
retire into the nest, as if they supposed the wonderful monster that damaged 
their castle was gone beyond their reach. Before they are all got in you will see 
the labourers in motion, and hastening in various directions towards the breach : 
every one with a burthen of mortar in his mouth ready tempered. This they 
stick upon the breach as fast as they come up, and do it with so much dispatch 
and facility, that though there are thousands, and even millions of them, they 
never stop or embarrass each other ; and you are most agreeably deceived when, 
after an apparent scene of hurry and confusion, a regular wall arises, gradually 
filling up the chasm. While they are thus employed, almost all the soldiers 
are retired quite out of sight, except here and there one, who saunters about 
among 6 hundred or a thousand of the labourers, but never touches the mortar 
either to lift or carry it ; one, in particular, places himself close to the wall they 
are building. This soldier will turn himself leisurely on all sides, and every now 
and then, at intervals of a minute or two, lift up his head, and with his forceps 
beat upon the building, and make the vibrating noise before-mentioned; on 
which immediately a loud hiss, which appears to come from all the labourers,, 
issues from within side the dome and all the subterraneous caverns and passages : 
that it does come from the labourers is very evident, for you will see them all 
hasten at every such signal, redouble their pace, and work as fast again. 

As the most interesting experiments become dull by repetition or continuance, 
so the uniformity with which this business is carried on, though so very wonder- 
ful, at last satiates the mind. A renewal of the attack however instantly 
changes the scene, and gratifies our curiosity still more. At every stroke we 
hear a loud hiss ; and on the first the labourers run into the many pipes and 
galleries with which the building is perforated, which they do so quickly that 
they seem to vanish, for in a few seconds all are gone, and the soldiers rush out 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 81 

as numerous and as vindictive as before.* On finding no enemy, they return 
again, leisurely into the hill, and very soon after, the labourers appear loaded as 
at first, as active and as sedulous, with soldiers here and there among them, 
who act just in the same manner, one or other of them giving the signal to 
hasten the business. Thus the pleasure of seeing them come out to fight or to 
work alternately may be obtained as often as curiosity excites or time permits: 
and it will certainly be found, that the one order never attempts to fight, or the 
other to work, let the emergency be ever so great. 

We meet great obstacles in examining the interior parts of these tumuli. In 
the first place, the works, for instance the apartments which surround the royal 
chamber and the nurseries, and indeed the whole internal fabric, are moist, and 
consequently the clay is very brittle: they have also so close a connexion, that 
they can only be seen as it were by piece-meal; for having a kind of geometrical 
dependance or abutment against each other, the breaking of one arch pulls down 
2 or 3. To these obstacles must be added the obstinacy of the soldiers, who 
fight to the very last, disputing every inch of ground so well as often to drive 
away the negroes who are without shoes, and make white people bleed plentifully 
through their stockings. Neither can we let a building stand so as to get a view 
of the interior parts without interruption; for while the soldiers are defending 
the out-works, the labourers keep barricadoing all the way against us, stopping 
up the different galleries and passages which lead to the various apartments, par- 
ticularly the royal chamber, all the entrances to which they fill up so artfully, as 
not to let it be distinguishable while it remains moist; and externally it has no 
other appearance than that of a shapeless lump of clay. It is however easily 
found, from its situation with respect to the other parts of the building, and by 
the crouds of labourers and soldiers which surround it, who show their loyalty 
and fidelity by dying under its walls. The royal chamber in a large nest is capa- 
cious enough to hold many hundreds of the attendants, besides the royal pair, 
and it is always found as full of them as it can hold. These faithful subjects 
never abandon their charge, even in the last distress; for whenever Mr. S. took 
out the royal chamber, and, as he often did, preserved it for some time in a large 
glass bowl, all the attendants continued running in one direction round the king 
and queen with the utmost solicitude, some of them stopping on every circuit at 
the head of the latter, as if to give her something. When they came to the 
extremity of the abdomen, they took the eggs from her, and carried them away, 
and piled them carefully together in some part of the chamber, or in the 

* By die soldiers being so ready to run out, on the repetition of the attack, it appears that they but 
just withdraw out of sight, to leave room for the labourers to proceed without interruption in repairing 
the breach. The sudden retreat of the labourers, in case of an alarm, is also a wonderful instance 
of good order and discipline. — Orig. 

VOL XV. M 



82 PHILOSOPHICAL TRANSACTIONS. [ANNO I J8 1. 

bowl under, or behind any pieces of broken clay which lay most convenient for 
the purpose. 

Some of these little unhappy creatures would ramble from the chamber, as if 
to explore the cause of such a horrid ruin and catastrophe to their immense 
building, as it must appear to them; and, after fruitless endeavours to get over 
the side of the bowl, return and mix with the croud, that continue running 
round their common parents to the last. Others, placing themselves along her 
side, get hold of the queen's vast matrix with their jaws, and pull with all their 
strength, so as visibly to lift up the part which they fix at; but, as Mr. S. never 
saw any effect from these attempts, he never could determine whether this pulling 
was with an intention to remove her body, or to stimulate her to move herself, 
or for any other purpose; but, after many ineffectual tugs, they would desist, 
and join in the croud running round, or assist some of those whc are cutting off 
clay from the external parts of the chamber or some of the fragments, and 
moistening it with the juices of their bodies, to begin to work a thin arched shell 
over the body of the queen, as if to exclude the air, or to hide her from the 
observation of some enemy. These, if not interrupted, before the next morn- 
ing, completely cover her, leaving room enough within for great numbers to run 
about her. Mr. S. does not mention the king in this case, because he is very 
small in proportion to the queen, not being larger than 30 of the labourers, so 
that he generally conceals himself under one side of the abdomen, except when 
he goes up to the queen's head, which he does now and then, but not so fre- 
quently as the rest. 

If in your attack on the hill you stop short of the royal chamber, and cut 
down about half of the building, and leave open some thousands of galleries and 
chambers, they will all be shut up with thin sheets of clay before the next morn- 
ing. If even the whole is pulled down, and the different buildings are thrown 
in a confused heap of ruins, provided the king and queen are not destroyed or 
taken away, every interstice between the ruins, at which either cold or wet can 
possibly enter, will be so covered as to exclude both, and, if the animals are 
left undisturbed, in about a year they will raise the building to near its pristine 
size and grandeur. 

The marching termites are not less curious in their order, than those described 
before. This species seems much scarcer and larger than the termes bellicosus. 
Mr. S. could get no information relative to them from the black people, from 
which he conjectures they are little known to them: his seeing them was very 
accidental. One day having made an excursion with his gun up the river Came- 
rankoes, on his return through the thick forest, while he was sauntering very 
silently in hopes of finding some sport, on a sudden he heard a loud hiss, which, 
on account of the many serpents in those countries, is a most alarming sound. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 83 

The next step caused a repetition of the noise, which he soon recognized, and 
was rather surprised at not seeing any covered ways or hills. The noise however 
led him a few paces from the path, where, to his great astonishment, he saw an 
army of termites coming out of a hole in the ground, which could not be above 
4 or 5 inches wide. They came out in vast numbers, moving forward as fast 
seemingly as it was possible for them to march. In less than a yard from this 
place they divided into 2 streams or columns, composed chiefly of the first 
order, which he calls labourers, 12 or 15 a-breast, and crouded as close after 
each other as sheep in a drove, going straight forward without deviating to the 
right or left. Among these, here and there, one of the soldiers was to be seen, 
trudging along with them, in the same manner, neither stopping nor turning; 
and as he carried his enormous large head with apparent difficulty, he put Mr. 
S. in mind of a very large ox among a flock of sheep. While these were bustling 
along, a great many soldiers were to be seen spread about on both sides of the 
2 lines of march, some a foot or two distant, standing still or sauntering about, 
as if on the look out lest some enemy should suddenly come on the labourers. 
But the most extraordinary part of this march was the conduct of some others 
of the soldiers, who having mounted the plants which grow thinly here and there 
in the thick shade, had placed themselves on the points of the leaves, which 
were elevated 10 or 15 inches above the ground, and hung over the army march- 
ing below. Every now and then one or other of them beat with his forceps on 
the leaf, and made the same sort of ticking noise so frequently observed to be 
made by the soldier who acts the part of a surveyor or super-intendant, when 
the labourers are at work repairing a breach made in one of the common hills of 
the termites bellicosi. This signal among the inarching white ants produced a 
similar effect; for, whenever it was made, the whole army returned a hiss, and 
obeyed the signal by increasing their pace with the utmost hurry. The soldiers 
who had mounted aloft, and gave these signals, sat quite still during the intervals, 
except making now and then a slight turn of the head, and seemed as solicitous 
to keep their posts as regular centinels. The 2 columns of the army joined into 
one, about 12 or 15 paces from their separation, having in no part been above 3 
yards asunder, and then descended into the earth by 2 or 3 holes. They conti- 
nued marching by Mr. S. for above an hour that he stood admiring them, and 
seemed neither to increase nor diminish their numbers, the soldiers only excepted, 
who quitted the line of march, and placed themselves at different distances on 
each side of the 2 columns; for they appeared much more numerous before he 
quitted the spot. Not expecting to see any change in their march, and being 
pinched for time, the tide being nearly up, and his departure fixed at high water, 
he quitted the scene with some regret, as the observation of a day or two might 
have afforded him the opportunity of exploring the reason and necessity of their 

M 2 



84 PHILOSOPHICAL TRANSACTIONS. [ANNOJ78J. 

marching with such expedition, as well as of discovering their chief settlement, 
which is probably built in the same manner as the large hills before described. 
If so, it may be larger and more curious, as these insects were at least one-third 
larger than the other species, and consequently their buildings must be more 
wonderful, if possible: thus much is certain, there must be some fixed place for 
their king and queen, and the young ones. 

The economy of nature is wonderfully displayed in a comparative observation 
on the different species who are calculated to live under ground until they have 
wings, and this species which marches in great bodies in open day. The former, 
in the first 2 states, that is, of labourers and soldiers, have no eyes that Mr. S. 
could ever discover; but when they arrive at the winged or perfect state in which 
they are to appear abroad, though only for a few hours, and that chiefly in the 
night, they are furnished with 2 conspicuous and fine eyes: so the termes viaruin, 
or marching bugga bugs, being intended to walk in the open air and light, are 
even in the first state furnished with eyes proportionably as fine as those which 
are given to the winged or perfect insects of the other species. 

Explanation of the Figures to Mr. Smeathman's Account of' the Termites of Africa, Sj-c. 

PI. 1, fig. 8, the hill-nest raised by the termites bellicosi ; aaa, turrets by which their hills are raised 
and enlarged. 

Fig. 9, a section of fig. 8, as it would appear on being cut down through the middle from the top 
a foot lower than the surface of the ground; a a, a horizontal line from a on the left, and a perpen- 
dicular line from a at the bottom, will intersect each other at the royal chamber ; the darker shades 
near it are the empty apartments and passages, which it seems are left so for the attendants on the king 
and queen, who, when old, may require near 100,000 to attend them every day; the parts which 
are the least shaded and dotted are the nurseries, surrounded, like the royal chamber, by empty pas- 
sages on all sides for the more easy access to them with the eggs from the queen, the provision for the 
young, &c. The magazines of provisions are situated without any seeming order among the vacant 
passages which surround the nurseries ; b, the top of the interior building, which often seems, from 
the arches carrying upward, to be adorned on the sides with pinnacles; c, the floor of the area or 
nave; odd, the large galleries which ascend from under all the buildings spirally to the top; e, a 
bridge. 

Fig. 10, the first appearance of a hill-nest by two turrets. 

Fig. 11, a tree, with the nest of the termites arborum, and their covered way; ffff, covered 
ways of the termites arborum. 

Fig. 12, a section of the nest of the termites arborum. 

Fig. 13, a nest of the termites bellicosi, with Europeans on it, seemingly observing a vessel atsea. 

Fig. H, a bull standing centinel on one of these nests, while the rest of the herd are ruminating 
below; gcg, the African palm-trees, from the nuts of which is made the oleum palmae. 

Fig. 1 5, a transverse section of a royal chamber; aa, the thin sides in which the entrances are made. 

Fig. 16, a longitudinal section of a royal chamber; b, the entrances; a, the door shut up, as left 
by the labourers. 

Fig 17, a royal chamber fore-shortened. 

Fig. 18, the same royal chamber represented as just opened, and discovering b, the queen, and 
her attendants running round her; bb, a line drawn from b to b will run along the range of doors 
or entrances; aaa, a line run from a to a a will cross the door, which remains closed as it was found. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 85 

The rest are represented as they appear since the mortar, with which they were stopped up, has been 
in part, or wholly picked out with a small instrument. 

Fig. 19, a nursery. Fig. 20, a little nursery, with the eggs, the young ones, the mushrooms, 
mouldiness, &c. as just taken from the hill. 

Fig. 21, the mushrooms magnified by a lens. 

PI. 2, fig. 1 and 2, the turret nests, with roofs of the termes mordax and a termes atrox as finished. 

Fig. 3, a turret, with the roof begun. Fig. 4, a turret, raised only about half its height. Fig. 5, 
a turret, building on one which had been thrown down. Fig. 6, 6, a turret broken in two. 

Fig. 7, a termes bellicosus. Fig. 8, a king. Fig. 9, a queen. Fig. 10, the head of a perfect in- 
sect magnified. Fig. 11, a face, with stemmata magnified. Fig. 12, a labourer. Fig. 13, a la- 
bourer magnified. Fig. 14, a soldier. Fig 15, a soldier's forceps and part of his head magnified. 
Fig. 16, the termes mordax. Fig. 17, the face with the stemmata magnified. Fig. IS, a labourer. 
Fig- 1 9, a soldier. Fig. 20, the termes atrox. Fig. 21, the face and stemmata magnified. Fig. 22, 
a labourer. Fig. 23, a soldier. Fig. 24, idem. Fig. 25, the termes destructor. Fig. 26", the facff 
and stemmata magnified. Fig. 27, the termes arborum. Fig. 28, the face and stemmata magnified. 
Fig. 29, a labourer. Fig. 30, a soldier. Fig. 31, a queen. 

n. b. In the figures II, 17, 21, 26", and 28, the two white spots between the edges are the 
stemmata. 

XII. An Account of several Earthquakes felt in JVales. By T. Pennant, Esq., 

F.R.S. p. 193. 

On Dec. 8, between 4 and 5 in the evening, we were alarmed with 1 
shocks of an earthquake; a slight one, immediately followed by another very 
violent. It seemed to come from the north-east, and was preceded by the usual 
noise. Mr. P. could not trace it farther than Holywell. The earthquake pre- 
ceding this was on the 29th of August last, about a quarter before 9 in the 
morning. Mr. P. was aware of it by a rumbling noise, not unlike the coming 
of a great waggon into the court-yard. Two shocks immediately followed, which 
were strong enough to terrify the people. They came from the north-east; were 
felt in Anglesea, at Caernarvon, Llanrwst, in the isle of Clwyd south of Den- 
bigh, at his house, and in Holywell. 

The next, in this retrograde way of enumerating these phenomena, was on 
Sept. 8, 1775, about a quarter before 10 at night: the noise was such as pre- 
ceded the former, and the shock so violent as to shake the bottles and glasses on 
the table round which Mr. P. and some company were sitting. This seemed to 
come from the east. In the Gentleman's Magazine of that year, this shock, it 
was said, extended to Shropshire, and quite to Bath, and to Swansea in South 
Wales. The earliest earthquake Mr. P. remembered here was on the 10th of 
April 1750. It is recorded in the Philos. Trans. 

Mr. P. resided near a mineral country, in a situation between lead mines and 
coal mines; in a sort of neutral tract, about a mile distant from the first, and 
half a mile from the last. On the strictest inquiry he could not discover that 
the miners or colliers were ever sensible of the shocks under ground; nor have 



86 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

they ever perceived, when the shocks in question have happened, any falls of the 
loose and shattery strata, in which the last especially work ; yet the earthquakes 
have had violence sufficient to terrify the inhabitants of the surface. Neither 
were these local ; for, excepting the first, all may be traced to very remote parts. 
The weather was remarkably still at the time of every earthquake Mr. P. 
had felt. 

XIII. On the Roots of Equations, in an Extract of a Letter from the Rt. Hon. 

Philip Earl Stanhope, F. R. S., to Mr. Jas. Clow, Prof, of Philos., Glasgow. 

Dated Chevening, Feb. ]6, 1777- p- 195. 

I have lately made some curious observations concerning the roots of adfected 
equations, part of which have occurred to Messieurs Daniel Bernoulli, Euler, De 
La Grange, Lambert, and others ; but some of them, I believe, are quite new. 
I will give you one instance of a quadratic equation, as the simplest. 

Let the quadratic equation lixx — 15a - -f- 5=0, be proposed. I say then, 

l_l_ Or O _1_ *%■? 

that if two recurring series be formed from the fractions — , *" — — 

1 — Z — ZZ 1 — Z — ZZ 

which have a common denominator, and each series of co-efficients, continued 
both ways (that is, as well before, as after the first term), the fractions formed 
by dividing each term of the 1st series by the corresponding term of the 2d series, 

j, -U +7 -4 +3 -1 -3 2 _l I 3 4 _7 11 18 29 » .„ 

viz. sc. _ i4 , + g , _ 5 , +4 , _ 1? _ 4 , -, -, i 5 , 7 , i2 , -, — , — , &c. Will 

converge in the simplest manner possible ; those before the bar, in a retrograde 

" + - "" 

22 



order to the greater root — — — ; and those after the bar, in a direct order to 



the smallest root — — — ; where it is to be observed, that the greater root is 
affirmative, notwithstanding the sign — being prefixed to some of the terms, 
because in each fraction the numerator and the denominator are affected by the 
same sign, whether + or — . 

The chief improvement I have made, consists in approximating to two roots 
at once, by one and the same series, continued backwards as well as forwards. 
I have not time to enlarge on this subject at present ; but the little I have said 
will be a specimen of the method to be used in higher equations. 



PHILOSOPHICAL TRANSACTIONS. 



87 



VOL. LXXI.] 

XIV. Extract of Two Meteorological Journals of the Weather, observed at Nain 
in 57° N. Lat. and at Okak in 57° 20' N. Lat. both on the Coast of Labrador. 
Communicated by Mr. De La Trobe. p. 197. 





Thermometer at Okak. 


Therm 


ometer a 


. Nain. 


Baror 


neter at ', 


''Jain. 


1779 


High. 


Lowest 


Mean. 


High. 


Lowest 


Mean. 


High. 


Lowest 


Mean. 


August. . 


78.0 


37.0 


52.0 


78.0 


38.0 


52.0 


2S.5 


27.8 


28 1.5 


Septemb. 


74.0 


32.0 


45.0 


74.0 


35.0 


45.4 


28.6 


27.5 


28 1.4 


October 


45.0 


11.0 


32.3 


47.0 


14.0 


33.6 


28.6 


27.4J 


28 2.5 


Novemb. 


36.0 


15.0 


273 


36.0 


9-0 


27.3 


28.5 


27.2 


28 6.1 


Decernb. 


31.0 


-12.0 


12.7 


32.0 


— 13.0 


11.1 


28.3J 


27. lj 


28 3.0 


1780 




















January 


35.0 


-13.0 


15.3 


35.0 


-16.0 


13.4 


28.2 


26.6 


27 6.8 


February 


33.0 


— 17.0 


13.1 


32.0 


— 23.0 


9J 


28.5J 


26.10 


27 9.5 


March. . 


45.0 


— 14.0 


10.0 


39.0 


— 18.0 


10.0 


28.8 


27.3 


2S 1.9 


April . . . 


57.0 


9.0 


20.5 


45.0 


4.0 


28.2 


28.8J 


27.7 


28 3.7 


May 


55.0 


23.0 


39.0 


53.0 


23.0 


37.6 


2S.6J 


27.9 


28 3.1 


June. . . . 


68.0 


33.0 


43.6 


61.0 


32.0 


43.1 


28.3 


26.11 


28 0.5 


July ... . 


84.0 


38.0 


52.0 


84.0 


39.0 


52.2 


28.11 


27.5 


28 1.3 


Mean of a 


11 




31.0 






30.3 


French Inches . . 


28 1.5 



Meteorological Journal kept at the House of the Royal Society, 
the President and Council, p. 1 99. 

The abstract of the whole of the year 1780 is as follows. 



By Order of 





Thermometer without. 


Thermometer within. 


Barometer 




Rain. 


1780. 


jreatest 
Height. 


Least 
Height. 


Mean 
Height. 


Greatest 
Height. 


Least 
Height. 


Mean 
Height. 


Greatest 
Height. 


Least 
Height. 


Mean 
Height. 

29-77 
29.91 
29.91 
29.65 
29.94 
30.01 
30.05 
30.05 
29.83 
29.69 
29.85 
30.29 


Inches. 


January . . . 
February . . 
March .... 
April 

June 

July . .. 
August .... 
September 
October . . . 
November 
December 


47.0 
53.5 
59.0 
65.5 
84.5 
84.5 
82.0 
83.5 
84.0 
66.0 
52.0 
50.0 


20.0 
20.0 
34.5 
33.0 
45.0 
48.0 
54.0 
58.5 
48.0 
41.5 
26.0 
34.0 


31.9 
37.8 
51.4 
46.7 
59.7 
62.9 
66.4 
69.2 

61.3 

52.3 
42.0 
38.5 


40.5 
49.0 
56.5 
65.0 
74.5 
76.0 
78.5 
76.5 
79-0 
65.0 
53.0 
46.5 


24.5 
31.0 
36.0 
S8.0 
51.0 
50.0 
61.0 
62.0 
56.0 
46.0 
36.0 
32.0 


33.6 
38.4 
49-9 
48.0 
60.4 
63.2 
69.4 
68.3 
65.2 
53.9 
43.6 
39.8 


30.35 
30.52 
30.45 
30.17 
30.28 
30.37 
30.34 
30.20 
30.20 
30.29 
30.47 
30.55 


28.59 
29.08 
29.38 
28.81 
29.38 
29.79 
29.59 
29.85 
29.14 
28.66 
28.94 
29.69 


0.692 
0.858 
1.189 
2.739 
0.822 
0.852 
1.602 
0.485 
2.903 
2.356 
2.505 
0.310 


Whole Year 






51.7 






52.8 






29.91 


17.313 



Mean variation of the needle, 22° 4 1'. 
Mean dip for the month of June, 72° 1 7 '• 



88 I'HILOSOrHICAL TRANSACTIONS. [ANNO 1781. 

XV. New Experiments on Gunpowder, &c. By Benjamin Thompson,* Esq., 

F. R. S. p. 220. 

These experiments were undertaken principally with a view to determine the 
most advantageous situation for the vent in fire-arms, and to measure the veloci- 
ties of bullets, and the recoil under various circumstances. Mr. T. hoped also 
to find out the velocity of the inflammation of gunpowder, and to measure its 
force more accurately than had hitherto been done. 

These experiments, on the force of fired gunpowder, on the same principle of 
those of Mr. Robins and Dr. Hutton, appear to have been made with great care 
and accuracy, but on a small scale, being performed only with a musket barrel. 
This and the other parts of the machinery were very nicely made, and contrived 
to answer the several purposes ; which were, to determine the velocity of the 
bullets, the recoil of the barrel, the effect of firing the charge in different parts 
of it, the most advantageous situation for the vent, &c. Mr. T. had a contriv- 
ance for shutting the vent as soon as the fire was communicated to the charge ; 
and it is very certain, that no part of the elastic fluid made its escape by this 
vent ; for, on firing the piece, there was only a simple flash from the explosion 
of the priming, and no stream of fire was to be seen issuing from the vent, as 
is always to be observed when a common vent is made use of, and in all other 
cases where this fluid finds a passage. So that no part of the charge was lost by 
the vent. The velocities of the bullets were determined by means of a pendulum, 
into which they were discharged, according to the method invented by Mr. 
Robins, and pursued by Dr. Hutton with cannon-balls, as described at p. 282, 
&c. vol. 14. The chord of the arc, through which the pendulum ascended in 
each experiment, was measured by a ribbon, according to the method invented 
and described by Mr. Robins. 

The recoil was measured in the following manner. The barrel was suspended 
in a horizontal position, and nearly in a line with the centre of the target, by 
two small pendulous rods, 64 inches in length, and 25.6 inches asunder; which 
being parallel to each other, and moving freely on polished pivots about the axes 
of their suspension, and on two pair of trunnions that were fixed to the barrel, 
formed, together with the barrel, a compound pendulum ; and from the lengths 
of the vibrations of this pendulum, the velocity with which the barrel began to 
recoil, or rather its greatest velocity, was determined. But in order that the 
velocity of the recoil might not be too great, so as to endanger the apparatus 
when large charges were made use of, it was found necessary to load the barrel 
with an additional weight of more than 40 lbs. of iron. The chord of the arc 
through which the barrel ascended in its recoil, was measured by a ribbon also; and 

Now Count ol' lUunf'ord. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 8Q 

the lengths of those chords, expressed in inches and decimal parts of an inch, 
are set down in the tables. The method of computing the velocity of the re- 
coil from the chord of the arc through which the barrel ascended, is too well 
known to require an explanation : .and it is also well known, that the velocities 
are to each other as the chords of those arcs. The lengths of those chords, 
therefore, as they are set down in the tables, are, in all cases, as the velocities 
of the recoil. 

The powder made use of in these experiments was of the best kind, such as is 
used in proving great guns at Woolwich. A cartridge, containing 12 lbs. of 
this powder, was given to Mr. T. by the late general Desaguliers of the Royal 
Artillery. This powder was immediately taken out of the cartridge, and put 
into glass bottles, which were previously made very clean and dry ; and in these 
it was very carefully sealed up till it was opened for use. When it was wanted 
for the experiments, it was weighed out in a very exact balance, with so much 
attention, that there could hardly be an error in any instance greater than a 
quarter part of a grain. The bottles were never opened but in fine weather, and 
in a room that was free from damp, and no more charges of powder than were 
necessary for the experiments of the day were weighed out at a time. Each 
charge was carefully put up in a cartridge of very fine paper, and these filled car- 
tridges were kept in a turned wooden box, that was varnished on the inside as 
well as the outside, to prevent its imbibing moisture from the air. The paper of 
which these cartridges were made, was so fine and thin, that 1280 sheets of it 
made no more than an inch in thickness, and a cartridge capable of containing 
half an ounce of powder weighed only 4 of a grain. The cartridges were 
formed on a wooden cylinder, and accurately fitted to the bore of the piece, and 
the edges of the paper were fastened together with paste made of flour and 
water. 

When a cartridge was filled, the powder was gently shaken together, and its 
mouth was tied up and secured with a piece of fine thread ; and when it was 
used it was put entire into the piece, and gently pushed down into its place with 
the ramrod, and afterwards it was pricked with a priming-wire thrust through 
the vent, and the piece was primed ; so that no part of the powder of the charge 
was lost in the act of loading, as is often the case when the powder is put loose 
into the barrel : nor was any part of it expended in priming ; but the whole 
quantity was safely lodged in the bottom of the bore or chamber of the piece, 
and the bullet was put down immediately upon it, without any wadding either 
between the cartridge and the bullet, or over the bullet. 

The bullets were all cast in the same mould, and consequently could not vary 
in their weights above 2 or 3 grains at most, especially as care was taken to bring 
the mould to a proper temperature as to heat before the casting ; and when 

vol. xv. N 



00 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781 



leather was put about them, or otherbullets than those of lead were used, the weight 
was determined very exactly before they were put into the piece. The diameter 
of the bullet was determined by measurement and also by computation from its 
weight, and the specific gravity of the metal of which it was formed ; and both 
these methods gave the same dimensions very nearly. 

A Table showing the weights and dimensions of the principal parts of the apparatus. 

Of the barrel. 

Inches. 

Length 44,7 

Length of the bore from the muzzle to the breech- pin 43.45 

Diameter of the bore 0.78 

Thickness of metal at the lower vent 0.36" 

Thickness of metal at the muzzle 0. 1 

Weight of the barrel, with the breech pin, the vent-screws, and vent 
tube, 6 lbs. 6 oz. 

Of the gun carriage. 

Length 28.4 

Distance between the two pair of trunnions 25.6 

Diameter of each trunnion 0.25 

Weight 40 lbs. 14 oz. 

Of the rods by which the carriage was suspended. 

Length from the axis of suspension, or centre of the pivots, to the centre of the trunnions of the 
gun carriage, 6'4 inches. 

Weight of each rod, 1 lb. 4 oz. 

Total weight of the barrel and its carriage, with the allowance made for the weight of the 
rods by which it was suspended, 48 lbs. This was its weight from experiment N g 3, to experiment 
N° 123 inclusive. 

Of the bullet. 

Diameter 0.75 inch. Weight when of lead, 5S0 grains. 

Of the pendulum. 

Total length of the pendulum from the axis of suspension to the bottom of the circular plate. . 69. 5 

Diameter of the circular plate to which the targets were fastened 13. 

Distance between the shoulders of the pivots 3.8 

Diameter of the pivots 27 

Weight of the iron part of the pendulum 47 lb. 4 oz. 

Of the pendulum with the targets fixed to it, as it was prepared for making the experiments, and 

numbered. 





Total 
length to 

the 
ribbon. 


Distance from the axis of 
suspension. 


Total 
weight of 




To the centre 
of gravity. 


To the centre 
of oscillation. 


iron and 
wood. 




Inches. 


Inches. 


Inches. 


lbs. oz. 


Pendulum N° 1 




69.25 

69.5 


50.25 
54.4 
55.62 
54.6 


58.45 
59-15 
60.23 
59. 18 


57 
82 4 




100 IS 


4 


88 4 



VOL. LXXI.] 



HI 

■e o 



The 
charge of 
powder. 



Grs. 



N°l 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

l6 

17 

18 

19 
20 
21 
22 
23 
24 
25 
26 
27 
2S 
29 
30 
31 

32 
33 

34 
35 
36 

37 
38 

39 
40 
41 
42 



208 



4l6 
208 
104 
310 



330 



330 



165 



165 



330 



165 



165 



-a 

bo 



B S 
£•= 

*-. o 

c 

o 

> 



fa. 



290 



218 



3.6 
1.8 

■9 
2.7 



2-9 



2.7 
2.9 

1.45 



1.45 



2-9 

3.2 
1.45 

1.45 



-3 3 



In. 




.5 


.5 


.5 






1.22 
2.65 



2.65 



2.65 






1.32 



2.6 

1.3 





o 

o O J 

^ 3 

■S * 3 

o M' ■ 

3 - 
O 



Grs. 



Inches. 



2.6 



1-9 



1.3 

2.6 



PHILOSOPHICAL TRANSACTIONS. 



General table of the experiments. 



c a 

in ^ 

CD "S 
-3 , 






<u 



ff^ 




'^ ^ c 

3 .£3 Oh 

pq 



Inches. 



13.2 
14.5 
12.6 



8.5 

5.2 

9-6 

10.1 

11.85 

10.9 
10.9 

13.25 
10.4 

6.8' 

6.85 
6.7 
6.3 
7.5 
6.8 
7.8 
8.05 
10.2 

5.9 

6.65 

5.45 



7.9 
7 ■ 
7.4 



2:5 § 



64.5 
65. 



65. 

65.25 

64.6 

65. 

64.75 

65.25 

61.5 

63.5 

63.5 

63. 

62.2 



60.6 
6l,5 
65. 



63. 
64. 
62.4 
62.6 

63. 



60.25 
62. 
6i. 
58.6 



6.45 
6.31 
6.45 



64.6 

65. 

65. 



Inches. 



to o 

J3 <D 

.-> <d 



c 
XI 



33.5 
36.5 
17.8 
18.5 
38.68 
38.48 
6.1 
16.5 
17.69 
10.18 
24.69 
24.95 
24.9 

26.2 

12.7 

26.3 

26.4 

14.73 

14.2 

14.8 

14.58 

14.68 

14.95 

15.6 

16.15 

26. 

28.1 

13.2 

15.15 

15.45 
12.65 

15.45 

15.25 

16.3 

17.9 

23.5 

24.8 

18. 

17.71 

17.91 



Ft. in 
sec 



P 



1267 
1399 
1213 



Remarks. 



1281 
782 
1459 
1527 
IS01 
1646 
1748 
2060 

1619 
1633 
1084 
1093 
1071 
1035 
1142 
1004 
1153 
1192 
1559 
1536 
914 
1027 

839 
839 

1217 
1129 
1161 
1277 
1497 

1236 
1197 
1230 



First day. 

Second day. 

The pendulum gave way. 

4 bullets fired at once. 

Ditto. 

Without any bullet. 

Ditto. 

Pen. N° 2j very fair; 3d day. 



'.The powder was lighted by the long vent- 
r tube. 



The barrel very much heated.. 



> The short vent-tube was made use of. 
Fourth day. 



f Not leathered; weight of the bullet and 
) wad 603 grs. In exp. N° 32 no less than 
\ 40 large grs. of unfired powder were driven 
(_ through the screen. 

~) In these 6 experts, the bullets were 
I leathered, and the powder was lighted by 
I the valve-vent. 



! 



The pend. N° 2 ruined. 

5th day ; medium velocity in these expe- 
riments and N°47, 1225. 



N 2 



9'2 



■c 
o 

X 

■5 a 

o c 
I* 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781. 



N°43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 

59 
60 
6i 
62 
63 
64 
65 
66 
67 
68 

69 
70 

71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 

82 

83 
84 
85 
86 
87 



The 
charge of 
powder. 



J3 

so 



Grs 



90 
290 



330 



18 



45 



145 



In. 



E 
o 

2 <o 
EJg 



a a 



111. 



1.3 



1.3 



2.6 




1.3 
1.3 



2.6 





1.3 




1.3 




Grs, 



90 
251 
354 



eg a 
a 

.5 -o 



Inches, 



6.5 

6.75 

6.6 

6.4 

6.3 

7.2 

7.4 

7.3 

7.4 

7.6 

7.25 

7.5 

7.4 

7-1 

7.4 

131 

1.2 

1.16 

0.6 

8. 

8.5 

7.2 

7.7 

8.4 

8. 

6.82 

6.6 

6.85 

5.5 



5.3 



3.2 
4.35 
3.3 
4.2 



1.33 
2.82 
3.32 



S a 

.2 a 

wra 



Inches, 



64.0 

64.5 

64.9 

6 1.6 

62. 

63.5 

64.6 

63. 

64. 

6l. 

62.3 

64. 

62.2 

6'4. 



63. 
65. 
59-5 
65. 



6*. 
64.6 



65. 
0'4.6 



63.6 
63.4 



62.2 
63.2 

61.2 



o 
-a 
O 



Inches. 



18.3 
1 8.3.5 



18.1 

22.58 

22.92 

22.38 

23.21 

23.76 

23.0" 

23.26 

23.56 
11.12 
1 1 .62 
9.6'2 
11.33 
26.4 

25.3 

26.35 

25.8 

19.56 

18.2 

19.12 

16.33 

S.72 

8. 44 

8.17 

9-3 

13.25 

13.25 

8.92 

1 1 .68 

9.83 
11.45 

15.25 

14.35 
4.5 
7.16 
.9.62 

11.3 



o j-> 

.. n 

£>a= 

P 



Ft in 
sec, 



1248 
1299 
1265 
1 293 
1266 
141-1 
1455 
1412 
1476 
152P, 
1483 
1502 
1450 
1433 
1454 



1599 
1652 
156'2 
1495 
|633 
1556 
1349 
1291 
1345 
1 080 



103? 
1044 



1763 
1317 
1130 



Remarks. 



► Medium velocity 1276. 

> Medium velocity 1427. 

> Medium velocity 1493. 

> Medium velocity 1460. 



In these 4 experts, the piece was fired 

■ with powder alone, and the screen was 
I taken away from before the pendulum. 

■ 6th day; medium velocity 1625. 

■ Medium velocity 1328. 

• Medium velocity 1 594. 

The powder was rammed very hard. 
Ditto much harder. 
Ditto as hard as in N° 68. 
Ditto ditto. 

Government powder, no bullet. 
Best double Battle powder. 
Government powder. 
Double Battle powder. 

> 7 tli day; medium velocity 1040. 

20 grs. best alkaline salt of tartar. 
20 grs. asthiops mineral. 
20 grs. sal ammoniac 
20 grs. fine brass dust. 

. The screws which held the hooks by which the 
J pendulum was suspended gave way, and the pen- 

t dulum came down. 

"1 8 Uj day; in each of these 4 experiments, 
( from 50 to 70 granula- or particles of un- 
( fired powder were driven through the 
J screen. 



VOL. LXXI.J 



PHILOSOPHICAL TRANSACTIONS. 



93 



cu 
x 



N° 



Grs. 



88 
89 
90 
91 
92 
93 
9* 
95 
96 
97 

98 

99 

100 
101 

102 



145 
165 

290 

437 £ 



103 

104 

105 

106 

107 

108 

109 

110 

111 

112 

11 

114 

115 

116 

117 

118 

119 

120 

121 

122 

123 



The 

charge of 

powder. 



165 



104 
145 



-a 



In. 



1.3 

1.45 

2.6 

3.9 



1.45 



21S 
290 



.9 
1.3 



In. 



Grs. 



a 3 



Inches. 



6'00 

603 

US4 

1754 

2352 



i.14 

1.8 
2.6 



4371 



2.28 
3.9 



2.6 



a 
a, 



bp-g 
.5 -a 



6.5 

6.34 

10.12 

13.65 

16.55 



1.68 
6.7 



.65 
.43 

.86' 



4.51 

5.4 
5.6 

6.18 

8.48 

9-45 

8.73 
93 



4h 



to "3 



Inches. 



Inches 



65.4 

64.6" 

65. 

63.4 

63.3 



2.6 



60.5 

uncert. 

63. 



65. 



6'5.8 

65. 

65.6 

65.2 
65.6 



•3 '5 



■3 
° S 

o 



Ft.in 
sec. 



8.85 

8.65 

8.5 

8.4 

9-15 
10.56 
11. 
J0.5 
10.3 5 
10.65 

10.6 



15.22 

15.13 

21.92 

27. 18 

32.25 

4.3 

5.5 

5.6 

11.70 

17.5 

15.88 

17.9 

4.9 
4.8 
5.6 



10.6 

12.92 
13.2S 

14.3 

19.68 

23.9 

22.8 
23.4 



65.5 

64. 

63.6 

65. 

64. 

64.9 
64.5 

65. 



63.6 



22.94 

23.7 

24.1 

23.8 

24.6 

33. 

33.3 

33.6' 

32.5 

33.2 

32.9 

17.9 



1229 
1229 

978 
916 

833 



Remarks. 



138 

92 

180 



732 

877 
910 

990 

1380 

1526 



I Very few unfired grains of powder struck 
) the screen. 

( There were no marks of any unfired 
( powder having reached the screen. 



The screen was taken away. 
( The whole surface of the target was 
( bespattered with unfired grains of powder. 

The pendulum was not observed. 
1 In each of these experiments near J^ part 
j of the substance of the bullet was melted 
\ and blown away by the impulse of the 
(.flame. 

9th day. 

{About 40 grs. of powder were driven 
through the screen, 
j About 40 unfired grs. of powder. Medium 
\ velocity 894. 40 unfired grains. 

{Double proof Battle powder; no unfired 
grains. 
Ditto, ditto. 

Government powder: bullet leathered; 

weight 602 grains. 
Bullet naked; very few unfired grains. 



1419 

1460 

1462 

1436 

1438 

1423 

1378 

152 

1738 

1824 

1729 

17061 ) 

1757 [-Medium velocity 1751 

1789) 

Without any bullet 



■ Medium velocity 1444. 



-Medium velocity 1413. 

Double proof Battle powder. 

Gov. pow. ] No unfired grs. through the sci . 



"} 



Medium velocity 1764. 



In the 1 first experiments the barrel was fixed to a carriage, that has not been 
described, which, together with the barrel and rods by which it was suspended, 
weighed only 234- lb. Length of the bore of the piece 43.5 inches. Weight 



94 l'HILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

of the bullet 580 grains. This gun carriage being found to be too light, another 
was substituted in the room of it. 

To determine how much of the force of the powder was lost by windage and 
by the vent, oiled leather was fastened round the bullet, so that it now accu- 
rately fitted the bore of the piece; and in the 5 experiments, from N° 35 to N° 
3Q inclusive, the valve-vent was made use of. Weight of the bullet, in the ex- 
per. 3 to 24, with the leather in which it was enveloped, 603 grains. 

Finding that the blast of the powder always reached as far as the pendulum, 
when large charges were used, and suspecting that this circumstance, with the 
impulse of the unfired grains, might in a great measure occasion the apparent 
irregularity in the velocities of the bullets; to remedy these inconveniences, a 
large sheet of paper of a moderate thickness was stretched on a square frame of 
wood, and interposed as a screen before the pendulum at the distance of 2 feet 
from the surface of the target, in the exper. 25, 31. The screen was found to 
answer perfectly well the purpose for which it was designed, and it was continued 
during the remainder of the experiments, the paper being replaced every 3d or 
4th experiment. 

The bullets were now put naked into the piece, exper. 32, 39, and the powder 
was lighted by the short vent-tube, and some little improvement was made in the 
steel edges between which the ribbons passed that served to measure the ascend- 
ing arcs of the pendulum and of the recoil, by which means the friction was 
lessened, and the ribbon was prevented from twisting or entangling itself as it 
was drawn out. 

The apparatus, commencing exper. 40, the barrel with its carriage as before; 
the pendulum, N° 3, and leaden bullets, weighing 580 grains each. 

The experiments N° 78, 79' 80, an d 81, were made in hopes of being able to 
discover a method of adding to the force of gunpowder. Twenty grains of the 
substances mentioned in the remarks on each experiment were intimately mixed 
with the powder of the charge. In the experiment N° 82, a large wad of tow 
well soaked in etherial spirit of turpentine, was put into the piece immediately 
on the bullet: and in the experiment N° 83 a wad, soaked in alkohol, was put 
into the piece in like manner. 

In the 9 experiments, viz. from N° 84 to N° 92 inclusive, the valve-vent was 
used, and the bullets were made to fit the bore of the piece very exactly by means 
of oiled leather, which was so firmly fastened about them that in each experiment 
it entered the target with the bullet. 1'he bullet used in experiment N°85, was 
of wood. Those used in the experiments N° 86 and N° 87, were formed in the 
following manner: a small bullet was cast of plaistcr of Paris, which beino- 
thoroughly dried, and well heated at the fire, was fixed in the centre of the 
mould that served for casting all the leaden bullets used in these experiments; 



VOL. LXXI.] PHILOSOPHICAL TEANSACTIONS. 95 

and melted lead being poured into this mould, the cavity that surrounded the 
small plaister bullet was entirely filled up, and a bullet was produced, which to 
the eye had every appearance of solidity, but was as much lighter than a solid 
leaden bullet of the same diameter, as the plaister bullet was lighter than a leaden 
bullet of the same size. In the experiments N° 88 and N° 89, solid leaden 
bullets were used. In the experiment N° 90, 2 bullets were discharged at once; 
in the experiment N° 91, 3; and in the experiment N° 92, 4 were used. In 
each of these experiments a fresh sheet of paper was used as a screen to the pen- 
dulum, that the velocities of the bullets might be measured more accurately; 
and also, that the quantity of unfired powder might be estimated with greater 
precision. 

In the experiments N° 93 to 99 the piece was fired with powder only. 

In the experiments N° IOO and N° 101, the bullets were not put down into 
the bore, but were supported by 3 wires, which being fastened to the end of the 
barrel projected beyond it, and confined the bullet in such a situation that its 
centre was in a line with the axis of the bore, and its hinder part was -fa of an 
inch without or beyond the mouth of the piece. In experiment N° 102, the 
bullet was just stuck, into the barrel in such a manner that near 4- of it was with- 
out the bore. All that part of the bullet which lay towards the bore of the piece 
appeared to be quite flat from the loss of substance it had sustained ; and its sur- 
face was full of small indents, which probably were occasioned by the unfired 
grains of powder that struck, against it. 

The experiments N° 103 to 123 were made with the pendulum N° 4. The 
rest of the apparatus as before. 

Of the method used in computing the velocities of the bullets. — As the method 
of computing the velocity of a bullet from the arc of the vibration of a pendu- 
lum into which it is fired is so well known, Mr. T. does not enlarge on it, but 
just gives the theorems that have been proposed by different authors, and refers 
those who wish to see more on the subject to Mr. Robins's New Principles of 
Gunnery; to Mr. Euler's Observations on Mr. Robins's book; and lastly to Dr. 
Hutton's paper on the initial Velocities of Cannon Balls, published in the Philos. 
Trans, for the year 1778. 

If a denote the length of the axis of the pendulum to the ribbon which mea- 
sures the chord of the arc of its vibration ; 

g, the distance of the centre of gravity below the axis; 

/, the distance of the centre of oscillation ; 

h, the distance of the point struck by the bullet; 

c, the chord of the ascending arc of the pendulum ; 
p, the weight of the pendulum ; 
b, the weight of the bullet, and 



9« 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781. 



v, the original velocity of the bullet: Then 

is a theorem for finding the velocity on Mr. 



v = X 
a 



— 4- - V 

bh ~ f * </Zh 



Robins's principles. 

v = - X TT +'~57 r - X v/'-j is the theorem proposed by Mr. Eider, who has 
corrected a small error in Mr. Robins's method; and 

v = 5.672 eg s/f X —,-, — - is Dr. Hutton's theorem, which is sufficiently accu- 
rate, and far more simple and expeditious than either of the preceding. It is to 
be remembered, that g, h, and c, may be expressed in any measure; butf must 
be English feet, and v will be the velocity of the bullet in English feet in a 
second. 

The velocities of the bullets in most of the foregoing experiments were first 
computed by Eider's method; but in going over the calculations a 2d time, Mr. 
T. used Dr. Hutton's theorem. Both these methods gave the same velocity very 
nearly, but the Doctor's method is by much the easiest in practice. In these 
computations care was taken to make a proper allowance for the bullets that 
were lodged in the pendulum, and also for the velocity lost by the bullet in pass- 
ing through the screen. 

The corrections necessary on account of the bullets lodged in the pendulum 
were made in the following manner. 

/; was continually added to the value of p, 

X b to the value of g, and 

f h 

- x b to the value of f 

Of the spaces occupied by the different charges of powder. — The heights of the 
charges of powder, or the lengths of the spaces which they occupied in the bore, 
were determined by measurement; and in order 
that this might be done with greater accuracy, 
inches and tenths of inches were marked on the 
ram-rod, and the charge was gently forced down 
till it occupied the same space in each experi- 
ment. The annexed table shows the heights of 
the charges as they were determined by mea- 
surement, and also their heights computed from 
the diameter of the bore of the piece, and the 
specific gravity of the powder that was used. 

In the experiment N° 30, the powder was put into a cartridge so much 
smaller than the bore of the piece, that the charge, instead of occupying I.45 
inches, extended 3.2 inches. By this disposition of the powder, its action on 
the bullet appears to have been very much diminished. 



h-> 



Weight 
of the 


Height of the charge. 


powder. 


Measured. 


Computed. 


Grs. 


Inches. 


Inches. 


104 


.9 


0.8957 


1+5 


1.3 


1 .2490 


l6o 


1.45 


1 .42 1 1 


208 


1.8 


1.7914 


21S 


1.9 


I.S775 


290 


2.6 


J. 4980 


310 


2.7 


2.6700 


33i) 


2.9 


2.8422 


410' 


3.6 


3.5s:s 


437 .', 


3.9 


3.70'so 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. QJ 

Of the effect that the heat which pieces acquire in firing produces on the force 
of powder. — It is very probable, that the excess of the velocity of the bullet in 
the 2d experiment, over that of the first, was occasioned more by the heat the 
barrel had acquired in the first experiment than by the position of the vent, or 
any other circumstance; for Mr. T. found, on repeated trials, that the force of 
any given charge of powder is considerably greater when it is fired in a piece that 
has been previously heated by firing, or by any other means, than when the 
piece has not been heated. Every body that is acquainted with artillery knows, 
that the recoil of great guns is much more violent after the 2d or 3d discharge, 
than it is at first; and on ship-board, where it is necessary to attend to the recoil 
of the guns, in order to prevent dangerous accidents that might be occasioned 
by it, the constant practice has been on board of ships, to lessen the quantity of 
powder after the first 4 or 5 rounds. By the recoil it should seem that the 
powder exerted a greater force also in the 4th experiment, being the 2d on the 
Qd day, than it did on the 3d, or the 1st of that day; but the pendulum giving 
way, it was not possible to compare the velocities of the bullets in the manner 
we did in the 2 experiments above-mentioned. 

Concluding from the result of the experiments mentioned above, as well as 
from other reasons, that the temperature of the piece has a considerable effect on 
the force of the powder, Mr. T. afterwards took care to bring the barrel to a 
proper degree of heat, by firing it once or oftener with powder each time he 
recommenced the experiments after the piece had been left to cool. 

Of the manner in ivhich pieces acquire heat in firing. — Mr. T. was much sur- 
prised, on taking hold of the barrel immediately after the experiment N° 17, 
when it was fired with 330 gr. of powder without any bullet, to find it so very 
hot that he could scarcely bear it in his hand, evidently much hotter than he had 
ever observed it before, though the same charge of powder had been used in the 
two preceding experiments, and in both these experiments the piece was loaded 
with a bullet, which one would naturally imagine, by confining the flame, and 
prolonging the time of its action, would heat the barrel much more than when 
it was fired with powder alone. This, Mr. T. remarks, cannot happen from the 
heat of the inflamed powder, but from the rapidity of its action on the piece, by 
which the particles of the metal are put into a very quick vibratory motion, 
which soon produces a great heat through its whole substance; like as when any 
body is struck with a rapid blow by another hard body, even when cold ; and as 
a bullet becomes hot when striking against any hard obstacle. This Mr. T. 
illustrates in various instances, and then adds : 

Now the effort of any given charge of powder on the gun is very nearly the 
same, whether it be fired with a bullet or without; but the velocity with which 
the generated elastic fluid makes its escape, is much greater when the powder is 
fired alone, than when it is made to impel one or more bullets; the heat ought 

vol. xv. O 



08 philosophical transactions. [anno 178 1. 

therefore to be greater in the former case than in the latter, as I found by expe- 
riment. But to make this matter still plainer, we will suppose any given quan- 
tity of powder to be confined in a space that is just capable of containing it, 
and that in this situation it is by any means set on fire. Let us suppose this 
space to be the chamber of a piece of ordnance of any kind, and that a bullet, 
or any solid body, is so firmly fixed in the bore immediately on the charge, that 
the whole effort of the powder shall not be able to remove it. As the powder 
goes on to be inflamed, and the elastic fluid is generated, the pressure on the 
inside of the chamber will be increased, till at length, all the powder being burnt, 
the strain on the metal will be at its greatest height, and in this situation things 
will remain, the cohesion or elasticity of the particles of metal counterbalancing 
the pressure of the fluid. Under these circumstances very little heat would be 
generated; for the continued effort of the elastic fluid would approach to the 
nature of the pressure of a weight ; and that concussion, vibration, and friction, 
among the particles of the metal, which in the collision of elastic bodies is the 
cause of the heat that is produced, would scarcely take effect. 

But instead of being firmly fixed in its place, let the bullet now be moveable, 
but let it give way with great difficulty, and by slow degrees. In this case, the 
elastic fluid will be generated as before, and will exert its whole force on the 
chamber of the piece; but as the bullet gives way to the pressure, and moves on 
in the bore, the fluid will expand itself and become weaker, and the particles of 
the metal will gradually return to their former situations; but the velocity with 
which the metal restores itself being but small, the vibration that remains in the 
metal, after the elastic fluid has made its escape, will be very languid, as will be 
the heat that is generated by it. But if, instead of giving way with so much 
difficulty, the bullet is much lighter, so as to afford but little resistance to the 
elastic fluid in making its escape, or if the powder is fired without any bullet at 
all; then, there being little or nothing to oppose the flame in its passage through 
the bore, it will expand itself with an amazing velocity, and its action on the 
gun will cease almost in an instant, the strained metal will restore itself with a 
very rapid motion, and a sharp vibration will ensue, by which the piece will be 
much heated. 

Of the effect of ramming the poivder in the chamber of the piece. — The charge, 
consisting of 218 gr. of powder, being put gently into the bore of the piece in 
a cartridge of very fine paper, without being rammed, the velocity of the bullets 
at a mean of the 40th, 41st, 42d, and 47th exper., was at the rate of 1225 feet 
in a second; but in the 68th, 69th, and 70th exper., when the same quantity of 
powder was rammed down with 5 or 6 hard strokes of the ram-rod, the mean 
velocity was 132Q. feet in a second. Now the total force or pressure exerted by 
the charge on the bullet is as the square of its velocity, and 1329* is to 1225' 2 as 
1.1776 is to 1 ; or nearly as 6 is to 5; and in that proportion was the force of 
the given charge of powder increased by being rammed. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. QQ 

In the 71st experiment the powder was also rammed, but the vent, instead 
of being at the bottom of the bore, was at 1.3, and the velocity of the bullet 
was very considerably diminished, being only at the rate of 1080 feet in a 
second, instead of 127 6 feet in a second, which was the mean velocity with this 
charge, and with the vent in this situation when the powder was rammed. See 
experiments N° 43, 44, 45, and 46. 

When, instead of ramming the powder, or pressing it gently together in the 
bore, it is put into a space larger than it is capable of filling, the force of the 
charge is thereby sensibly lessened, as Mr. Robins and others have found by re- 
peated trials. In the 30th experiment the charge, consisting of no more than 
l65 grains of powder, was made to occupy 3.2 inches of the bore, instead of 
1.45 inches, which space it just filled when it was gently pushed into its place 
without being rammed ; the consequence was, the velocity of the bullet, instead 
of being 1 100 feet in a second or upwards, was only at the rate of 914 feet in 
a second, and the recoil was lessened in proportion. 

And hence we may draw this practical inference, that the powder, with which 
a piece of ordnance or a fire-arm is charged, ought always to be pressed together 
in the bore ; and if it is rammed to a certain degree, the velocity of the bullet 
will be still further increased. It is well known, that the recoil of a musket is 
greater when its charge is rammed than when it is not ; and there cannot be a 
stronger proof that ramming increases the force of the powder. 

Of the relation of the velocities of bullets to the charges of powder by ivhich 
they are impelled. — It appears by all the experiments that have hitherto been made 
on the initial velocities of bullets, that when the weights and dimensions of the 
bullets are the same, and they are discharged from the same piece by different 
quantities of powder, the velocities are in the sub-duplicate ratio of the weights 
of the charges very nearly. 

The following table will shew how accurately this law obtained in the fore- 
going experiments. 





Velocities. 












A , , 








Charges. 


1 
Computed. 




1 

Actual. 


Difference. 


N° of exp. 


437 h 


1/64 




1764 




3 


330 


1533 




15^4 


+ 61 


2 


310 


1486 




1459 


- 27 


1 


2.90 


14-36 




1436 





7 


218 


1232 




1225 


— 7 


4 


20S 


1216 




1256 


4- 40 


3 


165 


1083 




1087 


+ 4 


2 


liD 


101S 




1040 


+ 22 


2 


104 


860 




757 


— 103 


2 



The computed velocities, as they are set down in this table, were determined 
from the ratio of the square root of 4374 (the weight in grains of the largest 
charge of powder) to the mean velocity of the bullet with that charge and the 

o 2 



100 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

vent atO, viz. 1764 feet in a second, and the square root of the other charges 
expressed in grains. And the actual velocities are means of all experiments that 
were made under similar circumstances. The 4th column shows the difference 
of the computed and actual velocities, or the number of feet in a second by 
which the actual velocity exceeds or falls short of the computed : and in the 5th 
column is set down the number of experiments with each charge, from the 
mean of which the actual velocity was determined. 

The agreement of the computed and actual velocities will appear more striking, 
if we take the sum and difference of those velocities with all the charges except 
the first : thus, 

Sum of the velocities, — 1764. 

, ^ , 

Computed. Actual. Difference. N°ofexp. 

SS6i 9S5i — 10 13 

So that it appears, that the difference, or the actual velocity, was smaller than 
the computed by -54-5- P art on ly at a mean of 23 experiments. 

But as by far the greater number of the experiments were made with the fol- 
lowing charges, viz. 2Q0, 218, 208, 165, and 145 grains of powder, let us 
take the sum and difference of the computed and actual velocities of those 
charges : thus, 

Sum of the velocities. 

. A. 



1 

Computed. Actual. Difference. N° of exp. 

5y85 6044 +59 IS 

Here the agreement of the theory with the experiments is so very remarkable, 
that we must suppose it was in some measure accidental ; for the difference of 
the velocities in repeating the same experiment, is in general much greater than 
the difference of the computed and actual velocities in this instance ; but we 
may fairly conclude, from the result of all these trials, that the velocities of like 
musket bullets, when they are discharged from the same piece by different quan- 
tities of the same kind of powder, are very nearly in the sub-duplicate ratio of 
the weights of the charges. 

On the effect of placing the vent in different parts of the charge. — There have 
been 2 opinions with respect to the manner in which gunpowder takes fire. Mr. 
Robins supposes that the progress of its inflammation is so extremely rapid, 
" that all the powder of the charge is fired and converted into an elastic fluid, 
before the bullet is sensibly moved from its place ;" while others have been of 
opinion that the progress of the inflammation is much slower, and that the 
charge is seldom or never completely inflamed before the bullet is out of the 
gun. The large quantities of powder that are frequently blown out of lire-arms 
uninflamed, seem to favour the opinion of the advocates for the gradual firing ; 



VOL. LXXI.] 



PHILOSOPHICAL TRANSACTIONS. 



101 



but Mr. Robins endeavours to account for that circumstance on different prin- 
ciples, and supports his opinion by showing that every increase of the charge 
within the limits of practice produces a proportional increase of the velocity of 
the bullet, and that when the powder is confined by a great additional weight, 
by firing 2 or more bullets at a time instead of 1, the velocity is not sensibly 
greater than it ought to be according to his theory. 

If this were a question merely speculative, it might not be worth while to 
spend much time in the discussion of it ; but as it is a matter upon the know- 
ledge of which depends the determination of many important points respecting 
artillery, and from which many useful improvements may be derived, too much 
pains cannot be taken to come at the truth. Till the manner in which powder 
takes fire, and the velocity with which the inflammation is propagated, are 
known, nothing can with certainty be determined with respect to the best form 
for the chambers of pieces of ordnance, or the most advantageous situation for 
the vent ; nor can the force of powder, or the strength that is required in dif- 
ferent parts of the gun, be ascertained with any degree of precision. 

As it would be easy to determine the best situation for the vent from the 
velocity of the inflammation of powder being known, so on the other hand I 
had hopes of being able to come at that velocity by determining the effect of 
placing the vent in different parts of the charge ; for which purpose the follow- 
ing experiments were made. 

By the annexed experiments 
it appears, 1st, that the differ- 
ence in the force of any given 
charge of powder which arises 
from the particular situation of 
the vent is extremely small. 

2dly. From the result of all 
these experiments it appears, that 
the effect of placing the vent in 
different positions with respect to 
the bottom of the chamber is dif- 
ferent, in different charges; thus, 
with \6d grains of powder, the 
velocity of the bullet was rather 
diminished by removing the vent 
from 0, or the bottom of the 
bore, to 1.32; but with 218 
grains of powder the velocity was 
a little increased, as was also the 
recoil. With 290 grains of pow- 
der the velocity was greatest 



Experiments showing the effect of placing the vent in differ- 
ent parts of the charge. 



Weight of the 
charge of pow- 
der. 


'5. ~o 
3 £ 

a. >, 

C/3 J3 


Vent from the 
bottom of the 
bore. 


Velocity of the 
bullet at a me- 
dium. 


I Recoil mea- 
| sured upon the 
ribbon at a me- 
dium. 


1 

X 

O £ 

B.§ 

3 M 
1^ ID 


Grains. 


Inches. 


Inches. 


Ft.inasec. 


Inches. 




lo'5 


1.45 





1087 


14.465 


a 


• . . . 


.... 


1.32 


1082 


14.31 


3 


218 


'•9 





1225 


17.93 


4 


.... 


.... 


1.3 


1276 


18.34 


4 


290 


2.6 





1427 


22.626 


3 


• . . . 




1.3 


1493 


23.34 


3 




.... 


2.6 


1 4b'0 


23.286 


4 


.... 


.... 





1444 


23.135 


4 


.... 




2.6 


1413 


24.5 


3 


310 


2.7 








24.69 


1 


.... 


.... 


1.32 





24.95 


I 


.... 




2.65 





24.9 


1 


330 


2.9 





15 94 


26.075 


2 


.... 




1.3 


1625 


26.4 


2 


.... 


.... 


2.6" 


1525 


25.3 


2 


437 £ 


3.9 





1764 


J3.3 


3 


.... 


.... 


2.6 


1751 


32.866 


3 



102 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

when the powder was lighted at the vent 1.3, which was near the middle of the 
charge, and rather greater when it was lighted at the top, or immediately behind 
the bullet, than when it was lighted at the bottom. And by the recoil it would 
seem, that the velocities of the bullets varied nearly in the same manner when 
the charge consisted of 310 grains of powder. With 330 grains of powder, 
both the velocity and the recoil were greater when the powder was lighted at the 
middle of the charge, than when it was lighted at the bottom ; but they were 
least of all when it was lighted near the top. And when an ounce of powder 
was made use of for the charge, its force was greatest when it was lighted at the 
bottom. But the difference in the force exerted by the powder which arose from 
the particular position of the vent was in all cases so inconsiderable, being less 
than what frequently occurred in repeating the same experiment, that no conclu- 
sion can be drawn from the experiments, except only this, that any given charge 
of powder exerts nearly the same force, whatever is the position of the vent. 

And hence the following practical inference naturally occurs, viz. that in the 
formation of fire-arms, no regard need be had to any supposed advantages that 
gun-smiths and others have hitherto imagined were to be derived from particular 
situations for the vent, such as diminishing the recoil, increasing the force of 
the charge, &c. ; but the vent may be indifferently in any part of the chamber 
where it will best answer on other accounts : and there is little doubt but the 
same thing will hold good in great guns, and all kinds of heavy artillery. The 
form Mr. T. recommends for the bottom of the bore, is that of a hemisphere ; 
and the vent to be brought out directly through the side of the barrel, in a line 
perpendicular to its axis, and pointing to the centre of the hemispherical con- 
cavity of the chamber. In this case the vent would be the shortest possible ; it 
would be the least liable to be obstructed, and the piece would be more easily 
cleaned, than if the bottom of the bore was of any other form. All these ad- 
vantages, and several others not less important, would be gained by making the 
bottom of the bore and vent of great guns in the same manner. 

A new* method of determining the velocities of bullets. — From the equality of 
action and re-action it appears that the momentum of a gun must be precisely 
equal to the momentum of its charge ; or that the weight of the gun, multiplied 
into the velocity of its recoil, is just equal to the weight of the bullet and of the 
powder (or the elastic fluid that is generated from it) multiplied into their res- 
pective velocities : for every particle of matter, whether solid or fluid, that issues 
out of the mouth of a piece, must be impelled by the action of some power, 
which power must re-act with equal force against the bottom of the bore. Even 

* This method is not new ; as a specimen of it was given by Robins, in his New Principles of 
Gunnery, prop. 1 1, p. 10*). Nor is the method generally true, as is proved in Dr. Hutton's Tracts, 
p. 262. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 103 

the fine invisible elastic fluid, generated from the powder in its inflammation, 
cannot put itself in motion without re-acting against the gun at the same time. 
Thus we see pieces when they are fired with powder alone, recoil as well as when 
their charges are made to impel a weight of shot, though the recoil is not in 
the same degree in both cases. 

It is easy to determine the velocity of the recoil in any given case, by sus- 
pending the gun in a horizontal position by two pendulous rods, and measuring 
the arc of its ascent, by means of a ribbon according to the method already des- 
cribed, and this will give the momentum of the gun, its weight being known, 
and consequently the momentum of its charge. But in order to determine the 
velocity of the bullet from the recoil, it will be necessary to find out how much 
the weight and velocity of the elastic fluid contributes to it. That part of the 
recoil which arises from the expansion of this fluid is always very nearly the same, 
whether the powder is fired alone, or whether the charge is made to impel one 
or more bullets ; which Mr. T. says he has found by a great variety of experi- 
ments.* If therefore a gun, suspended according to the method prescribed, be 
fired with any given charge of powder, but without any bullet or wad, and the 
recoil be observed ; and if the same piece be afterwards fired with the same quan- 
tity of powder, and a bullet of a known weight, the excess of the velocity of 
the recoil in the latter case, over that in the former, will be proportional to the 
velocity of the bullet ; for the difference of these velocities, multiplied into the 
weight of the gun, will be equal to the weight of the bullet multiplied into its 
velocity. 

Thus if w be put equal to the weight of the gun, 

u = the velocity of its recoil when fired without a bullet, 

v = the velocity of the recoil when the same charge impels a bullet, 

b = the weight of the bullet, and 

v = its velocity ; then it will be 

V — u 

v = X w. 

B 

Let us see how this method of determining the velocities of bullets will an- 
swer in practice. In the 94th exper. the recoil, with l65 gr. of powder, without 
a bullet, was 5.5 inches, and in the 95th exper. with the same charge, the recoil 
was 5.6 inches. The mean is 5.55 inches; and the length of the rods by which 
the barrel was suspended being 64 inches, the velocity of the recoil u, answering 
to 5.55 inches measured on the ribbon, is that of 1.1358 feet in a second. Now 
in 5 experiments, viz. exper. -20, 21, 22, 23, 24, with the same charge of 
powder, and a bullet weighing 580 gr., the medium recoil was 14.6 inches. 

* Remarked in Robins's New Principles of Gunnery, prop. 11, p. 111. But it is not generally 
true. 



104 l'HJLOSOPHICAL TRANSACTIONS. [ANNO 1781. 

And the velocity of the recoil (= v) answering to this length is that of 2.Q880 
feet in a second: consequently v — u, or 2.988O — 1.1358 is equal to 1.8522 
feet in a second. 

But as the velocities of recoil are known to be as the chords of the arcs through 
which the barrel ascends, it is not necessary, in order to determine the velocity of 
the bullet, to compute the velocities v and u ; but the quantity v — u, or the 
difference of the velocities of the recoil when the given charge is fired with and 
without a bullet, may be computed from the value of the difference of the chords, 
by one operation. Thus the velocity answering to the chord g.05 is that of 
1.8522 feet in a second, which is just equal to v — u, as was before found. 

The weight of the barrel, together with its carriage, was 47-j- pounds, to 
which three quarters of a pound is to be added on account of the weight of the 
rods by which it was suspended, which makes w = 48 pounds, or 336,000 grains, 
and the weight of the bullet was 580 grains, b is therefore to w as 580 is to 
336,000, that is, as 1 is to 579-31, very nearly; and v = X w is equal 

to (v — u) X 579.31. 

The value of v — u answering to the experiments before-mentioned was found 
to be 1.8522; consequently the velocity of the bullets, = v, was 1.8522 X 
579.31 = 1073 feet in a second, which is extremely near 1083 feet in a second, 
the mean of the velocities, as they were determined by the pendulum. 

But the computation for determining the velocity of a bullet on these prin- 
ciples may be rendered still more simple and easy in practice; for the velocities of 
the recoil being as the chords measured on the ribbon, if 

c be put equal to the chord of the recoil when the piece is fired with powder 
only, and 
c = the chord when a bullet is discharged by the same charge, 

then c — c will be as v — u ; and consequently as ■ X w, which measures 

the velocity of the bullet, the ratio of w to b remaining the same. 

If therefore we suppose a case in which c — c is equal to 1 inch, and the velo- 
city of the bullet be computed from that chord, the velocity in any other case, 
when c — c is greater or less than 1 inch, will be found by multiplying the dif- 
ference of the chords c and c by the velocity that answers to a difference of ] 
inch. The length of the parallel rods by which the barrel was suspended being 
64 inches, the velocity of the recoil answering to c — c = 1 inch measured on 
the ribbon is 0.204655 parts of a foot in a second; and this is also, in this case 
the value of v — u; the velocity of the bullet is therefore v = 0.204655 X 
579.31 = 118.35 feet in a second. Consequently the velocity of the bullet, ex- 
pressed in feet per second, may in all eases lie found by multiplying the difference 
of the chords c and c, by 118.35, the weight of the barrel, the length of the 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 105 

rods by which it is suspended, and the weight of the bullet remaining the same, 
and this whatever the charge of powder may be that is made use of, and how- 
ever it may differ in strength and goodness. 

According to this rule the velocities of the bullets in the several experi- 
ments have been computed from the recoil; and by comparing them with the 
velocities shown by the pendulum, we shall be enabled to judge of the accuracy 
of this new method of determining the velocities of bullets. The consequence 
of this comparison is, that several of the velocities, as determined by the two 
methods, agree nearly together; and that several, on the contrary, disagree 
very much, and that by differences which Mr. T. cannot account for. Hence 
it ought to be inferred, that the new method is not generally to be relied on. 

Of a very accurate method of proving gunpowder. — All the eprouvettes, or 
powder-triers, in common use are defective in many respects. Neither the abso- 
lute force of gunpowder can be determined by means of them, nor the compa- 
rative force of different kinds of it, but under circumstances very different from 
those in which the powder is made use of in service. As the force of powder 
arises from the action of an elastic fluid, generated from it in its inflammation, 
the quicker the charge takes fire, the more of this fluid will be generated in any 
given short space of time, and the greater of course will be its effect on the 
bullet. But in the common method of proving gunpowder, the weight by which 
the powder is confined is so great in proportion to the quantity of the charge, 
that there is time quite sufficient for the charge to be all inflamed, even when 
the powder is of the slowest composition, before the body to be put in motion 
can be sensibly moved from its place. The experiment therefore may show which 
of two kinds of powder is the stronger when equal quantities of both are con- 
fined in equal spaces, and completely inflamed; but the degree of the inflamma- 
bility, which is a property essential to the goodness of the powder, cannot by 
these means be ascertained. » 

Hence it appears how powder may answer to the proof, such as is commonly 
required, and may yet turn out very indifferent when it comes to be used in ser- 
vice. And this, Mr. T. believes, frequently happens; at least he knows com- 
plaints from officers of the badness of our powder are very common ; and he 
would suppose that no powder is ever received by the Board of Ordnance but 
such as has gone through the established examination, and has answered to the 
usual test of its being of the standard degree of strength. But though the 
common powder triers may show powder to be better than it really is, they 
never can make it appear to be worse than it is; it will therefore always be the 
interest of those who manufacture that commodity to adhere to the old method 
of proving it. But the purchaser will find his account in having it examined in 
a method by which its goodness may be ascertained with greater precision. 

vol. xv. P 



106 PHILOSOPHICAL TRANSACTIONS. [aNNO 1781. 

The method Mr. T. would recommend, is as follows. A quantity of powder 
being provided, which, from any previous examination or trial, is known to be 
of a proper degree of strength to serve as a standard for the proof of other 
powder, a given charge of it is to be fired, with a fit bullet, in a barrel sus- 
pended by 2 pendulous rods, and the recoil is to be carefully measured on the 
ribbon. And this experiment being repeated 3 or 4 times, or oftener if there be 
any difference in the recoil, the mean and the extremes of the chords may be 
marked on the ribbon by black lines drawn across it, and the word proof may be 
written on the middle line; or if the recoil be uniform (which it will be to a suf- 
ficient degree of accuracy, if care be taken to make the experiments under the 
same circumstances) then the proof mark is to be made in that part of the ribbon 
to which it was constantly drawn out by the recoil in the different trials. 

The recoil, with a known charge of standard powder, being thus ascertained 
and marked on the ribbon, let an equal quantity of any other powder, that is to 
be proved, be fired in the same barrel, with a bullet of the same weight, and 
every other circumstance alike ; then if the ribbon is drawn out as far or farther 
than the proof mark, the powder is as good or better than the standard ; but if 
it falls short of that distance, it is worse than the standard, and is to be rejected. 
For the greater the velocity is with which the bullet is impelled, the greater will 
be the recoil ; and when the recoil is the same, the velocities of the bullets are 
equal, and the powder is of the same degree of strength, if the quantity of the 
charge be the same. And if care be taken in proportioning the charge to the 
weight of the bullet, to come as near as possible to the medium proportion that 
obtains in practice, the determination of the goodness of gunpowder, from the 
result of this experiment, cannot fail to hold good in actual service. 

The length of the bore recommended, is 30 inches, and its diameter 1 inch, 
consequently it is just 30 calibres in length, and will carry a leaden bullet of 
about 3 ounces. The barrel may be made of gun metal, or of cast iron as that 
is a cheaper commodity ; but great care must be taken in boring it, to make the 
cylinder perfectly straight and smooth, as well as to preserve the proper dimen- 
sions. Of whatever metal the barrel is made, it ought to weigh at least 50 lbs. 
in order that the velocity of the recoil may not be too great ; and the rods by 
which it is suspended should be 5 feet in length. The vent may be about ~ of 
an inch in diameter ; and it should be bouched or lined with gold, in the same 
manner as the touch-hole is made in the better kind of fowling-pieces, in order 
that its dimensions may not be increased by repeated firing. 

The bullets should be made to fit the bore with very little windage ; and it 
would be better if they were all cast in the same mould, and of the same parcel 
of lead, as in that case their weights and dimensions would be more accurately 
the same, and the experiments would of course be more conclusive. The stated 






VOL. LXXI.j PHILOSOPHICAL TRANSACTIONS. 107 

charge of powder may be half an ounce, and it should always be put up in a 
cartridge of very fine paper ; and after the piece is loaded it should be primed 
with other powder, first taking care to prick the cartridge by thrusting a priming 
wire down the vent. The machine for the tape to slide through may be the 
same as is described by Dr. Hutton in his account of his experiments on the 
initial velocities of cannon balls; as his method is much better calculated to 
answer the purpose than that proposed and made use of by Mr. Robins. It will 
also be better for the axis of the pendulous rods to rest on level pieces of wood 
or iron, than for them to move in circular grooves : only care must be taken to 
confine them by staples or some other contrivance, to prevent their slipping 
out of their places. The trunnions, by means of which the barrel is connected 
with the pendulous rods, and on which it is supported, should be as small as 
possible, in order to lessen the friction ; and for the same reason they should be 
well polished, as well as the grooves that receive them. They need not be cast 
on the barrel, but may be screwed into it after it is finished. 

In making the experiments, regard must be had to the heat of the barrel, as 
well as to the temperature of the atmosphere ; for heat and cold, dryness and 
moisture, have a very sensible effect on gunpowder to increase or diminish its 
force. If therefore a very great degree of accuracy is at any time required, it 
will be best to begin by firing the piece 2 or 3 times merely to warm it ; after 
which 3 or 4 experiments may be made with standard powder, to determine anew 
the proof mark, as the strength of the same powder is different on different 
days ; and when this is done, the experiments with the powder that is to be 
proved are to be made, taking care to preserve the same interval of time between 
the firings, that the heat of the piece may be the same in each trial. If all 
these precautions are taken, and if the bullets are of the same weight and di- 
mensions, powder may be proved by this method with much greater accuracy 
than has hitherto been done by any of the common methods made use of for 
that purpose.* 

Of the comparative goodness, or value, of powder of different degrees of 
strength. — Estimating the strength of powder by the square of the velocity a 
given charge gives to a bullet, by experiment Mr. T. finds that double proof 
Battle powder is stronger than the same weight of government powder, in the 
proportion of 6 to 5. But as the former was sold at 2 shillings the lb. and the 

* The foregoing method for an eprouvette, appears to be the same as a new one hinted and recom- 
mended by Mr. Robins, at p. 123 of his New Principles of Gunnery. And from the same remark 
of Mr. Robins's also, Dr. Hutton made one with a small brass cannon, and several other improved 
contrivances, which was much used at Woolwich, and found to be a very regular and accurate eprou- 
vette, and most ready and convenient when used with powder only, without balls. 

p 2 



108 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

latter at is. Ofd. Mr. T. infers that Battle powder is therefore sold at the rate 
of lOd. a pound, or4l-i percent dearer than in proportion it ought to be. 

Of the relation of the velocities of bullets to their weights. — According to Mr. 
Robins's theory, when bullets of the same diameter, but different weights, are 
discharged from the same piece by the same quantity of powder, their velocities 
should be in the reciprocal sub-duplicate ratio of their weights. But as this 
theory is founded on a supposition that the action of the elastic fluid, generated 
from the powder, is always the same in any and every given part of the bore 
when the charge is the same, whatever may be the weight of the bullet ; and as 
no allowance is made for the expenditure of force required to put the fluid itself 
in motion, or for the loss of it by the vent ; it is plain that the theory is defec- 
tive. It is true that Dr. Hutton, in his experiments, found this law to obtain 
without any great error, and possibly it may hold good with sufficient accuracy in 
many cases ; for it sometimes happens that a number of errors or actions, whose 
operations have a contrary tendency, so compensate each other, that their 
effects when united are not sensible. But when this is the case, if any one of 
the causes of error is removed, those which remain will be detected. 

When any given charge is loaded with a heavy bullet, more of the powder is 
inflamed in a very short space of time than when the bullet is lighter, and the 
action of the powder ought of course to be greater on that account ; but then a 
heavy bullet takes up more time in passing through the bore than a light one, 
and consequently more of the elastic fluid, generated from the powder, escapes 
by the vent and by windage. It may happen then, that the augmentation of the 
force, on account of one of these circumstances, may exactly counterbalance 
the diminution of it arising from the other ; and if it should be found on trial 
that this is the case in general, in pieces as they are now constructed, and with 
all the variety of shot that are used in practice, it would be of great use to know 
the fact : and possibly it might answer as well, as far as it relates to the art of 
gunnery, as if we were perfectly acquainted with, and were able to appreciate, 
the effect of each varying circumstance under which an experiment can be made. 
But when, concluding too hastily from the result of a partial experiment, we 
suppose with Mr. Robins, that because the sum total of the action or pressure 
of the elastic fluid on the bullet, during the time of its passage through the 
bore, happens to be the same when bullets of different weights are used (which 
collective pressure is in all cases proportional to, and is accurately measured by, 
the velocity, or rather motion, communicated to the bullet) that therefore the 
pressure in any given part is always exactly the same, when the quantity of 
powder is the same with which the piece is fired ; and thence endeavour to prove, 
that the inflammation of gunpowder is instantaneous, or that the whole charge 
is in all cases inflamed, and " converted into an elastic fluid before the bullet is 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. IOQ 

sensibly moved from its place ;" such reasonings and conclusions may lead to 
very dangerous errors. 

It is undoubtedly true, that if the principles assumed by Mr. Robins with 
respect to the manner in which gunpowder takes fire, and the relation of the 
elasticity of the generated fluid to its density, or the intensity of its pressure on 
the bullet as it expands in the barrel, were just ; and if the loss of force by the 
vent and windage was in all cases inconsiderable, or if it was prevented, the de- 
ductions from the theory respecting the velocities of bullets of different weights 
would always hold good. But if, on the contrary, it should be found, on 
making the experiments carefully, and in such a manner as entirely to prevent 
inaccuracies arising from adventitious circumstances, that the velocities observe a 
law different from that which the theory supposes, we may fairly conclude that 
the principles, on which the theory is founded, are erroneous. 

Mr. T. now makes a comparison of this relation, by means of the experiments 
from N° 84 to U2 inclusive, and finds that the ratio above-mentioned does not 
generally hold good. But it may be justly objected to this comparison, that 
those very experiments were very bad ones, being condemned as such by Mr. T. 
himself in several parts of his paper ; and that besides, he makes the calculation 
from the velocities as deduced from the recoil of the gun, instead of those from 
the pendulum, which have in this instance a very different relation. 

Mr. T. proceeds. There are many reasons to suppose, that the diminution 
of the action of the powder on the bullet, when it is lighter, is not so much 
owing to the smallness of the quantity of powder that takes fire in that case, as 
to the vis inertias of the generated fluid. It is true, that a greater portion of 
the charge takes fire when the bullet is heavy than when it is light ; but then the 
quantity of unfired powder in any case was much too small to account for the 
apparent diminution of the force when light bullets were used. If the elastic 
fluid, in the action of which the force of powder consists, were infinitely fine, 
or if its weight bore no proportion to that of the powder that generated it ; and 
if the gross matter, or caput mortuum, of the powder remained in the bottom 
of the bore after the explosion, then, and on no other supposition, would the 
pressure on the bullet be inversely as the space occupied by the fluid : but it is 
evident that this can never be the case. 

A curious subject for speculation here occurs : how far would it be advan- 
tageous, were it possible, to diminish the specific gravity of gunpowder, and 
the fluid generated from it, without lessening its elastic force ? It would cer- 
tainly act on very light bullets with greater force ; but when heavy ones came to 
be used, there is reason to think that, except extraordinary precaution was taken 
to prevent it, the greatest part of the force would be lost by the vent and by 
windage. The velocity with which elastic fluids rush into a void space, is as the 



110 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

elasticity of the fluid directly, and inversely as its density ; if therefore the den- 
sity of the fluid generated from powder was 4 times less than it is, its elasticity 
remaining the same, it would issue out at the vent, and escape by the side of 
the bullet in the bore, with nearly 4 times as great a velocity as it does at pre- 
sent ; but we know from experiment that the loss of force on these accounts is 
now very considerable. 

An elastic bow, made of very light wood, will throw an arrow, and especially 
a light one, with greater velocity than a bow of steel of the same degree of 
stiffness : but, for practice, gunpowder may be supposed to be so light as to be 
rendered entirely useless : and for some purposes it seems probable, that it would 
not be the worse for being even heavier than it is now made. Vents are abso- 
lutely necessary in fire-arms, and in large pieces the windage must be consider- 
able, in order that the bullets, which are not always so round as they should be, 
may not stick in the bore ; and those who have been present at the firing of 
heavy artillery and large mortars with shot and shells, must have observed, that 
there is a sensible space of time elapses between the lighting of the prime and the 
explosion ; and that, during that interval, the flame is continually issuing out at 
the vent with a hissing noise, and with a prodigious velocity, as appears by the 
height to which the stream of fire mounts up in the air. 

As it appears from these experiments, says Mr. T. that the relation of the 
velocities of bullets to their weights is different from that which Mr. Robins's 
theory supposes, it remains to inquire what the law is which actually obtains. 
And first, as the velocities bear a greater proportion to each other than the re- 
ciprocal sub-duplicate ratio of the weights of the bullets, Mr. T. examines how 
near they come to the reciprocal sub-triplicate ratio of their weights: and here 
the velocities computed on the last supposition appear to agree rather better with 
the experiments than those computed on Mr. Robins's principles ; but still there 
is a considerable difference between the actual and the computed velocities in the 
3 last experiments in the table, which it has been observed were the erroneous 
ones. 

As the powder itself is heavy, it may be considered as a weight that is put in 
motion along with the bullet ; and if we suppose the density of the generated 
fluid is always uniform from the bullet to the breech, the velocity of the centre 
of gravity of the powder, or, which amounts to the same thing, of the elastic 
fluid, and the gross matter generated from it, will be just half as great as the 
velocity of the bullet. If therefore we put p to denote the weight of the pow- 
der, b the weight of the bullet, and u its initial velocity ; then bv + -Ipv = 
(b + ip) X v will express the momentum of the charge at the instant when the 
bullet quits the bore. If now, instead of ascertaining the relation of the velo- 
cities to the weights of the bullets, we add halt the weight of the powder to the 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. Ill 

weight of the bullet, and compute the velocities from the reciprocal sub-tripli- 
cate ratio of the quantity (b -+■ ip) in each experiment, there then results a 
pretty near agreement between the actual and computed velocities in 5 out of the 
8 experiments compared ; but in the other same 3 faulty ones, as before, the dif- 
ference is still very great. 

Of an attempt to determine the explosive force of aurum fulminans, or a com- 
parison between its force and that of gunpowder. — Mr. T. having provided him- 
self with a small quantity of this wonderful powder, he endeavoured to asser- 
tain its explosive force by making use of it instead of gunpowder for discharging 
a bullet, and measuring, by means of the pendulum, the velocity which the 
bullet acquired ; and concluding, from the tremendous report with which this 
substance explodes, that its elastic force was vastly greater than that of gun- 
powder, he took care to have a barrel provided of uncommon strength, on pur- 
pose for the experiment. Its length in the bore was 13.25 inches, the diameter 
of the bore 0.55 of an inch, and its weight 7 lbs. 2 oz. This barrel being 
charged with -fa of an ounce (= 27-34 grains) of aurum fulminans and 2 leaden 
bullets, which, together with the leather that was put about them to make them 
fit the bore without windage, weighed 427 grains ; it was laid upon a chafing- 
dish of live-coals, at the distance of about 10 feet from the pendulum, and 
against the centre of the target of the pendulum the piece was directed. After 
some minutes the powder exploded, but with a report infinitely less than what 
was expected, the noise not greatly exceeding the repoi t of a well-charged wind- 
gun. The bullets struck the pendulum nearly in the centre of the target, and 
both of them remained in the wood : and Mr. T. found, on making the calcu- 
lation, that they had impinged against it with a velocity of 428 feet in a 
second. 

If we now suppose that the force of aurum fulminans arises from the action 
of an elastic fluid generated from it in the moment of its explosion, and that the 
elasticity of this fluid, or rather the force it exerts on the bullet as it goes on to 
expand, is always as its density, or inversely as the space it occupies ; then, from 
the known dimensions of the barrel, the length of the space occupied by the 
charge (which in this experiment was 0.47 of an inch), and the weight and 
velocity of the bullets, the elastic force of this fluid at the instant of its genera- 
tion may be determined : and on making the calculation on these principles, Mr. 
T. found that its force was 307 times greater than the mean elastic force of 
common air ; and consequently was but about the 5 th or Oth of the strength of 
gunpowder. 

Of the specific gravity of gunpoiuder. — To determine the specific gravity of 
gunpowder, Mr. T. used the following method. A large glass bucket, with a 
narrow mouth, being suspended to one of the arms of a very nice balance, and 



112 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

exactly counterpoised by weights put in the opposite scale, it was filled first with 
government powder poured in lightly, then with the same powder shaken well 
together, afterwards with powder and water together, and lastly with water alone, 
and in each case the contents of the bucket were very exactly weighed. The 
specific gravity of gunpowder, as determined from these experiments, is as 
follows : 

Specific gravity of rain water 1 .000 

Government powder, as it lies light in a heap, mixed with air. . 0.836 

Government powder well shaken together O.937 

The solid substance of the powder 1 .745 

Hence it appears, that a cubic inch of government powder, shaken well 
together, weighs just 243 grains ; that a cubic inch of solid powder would 
weigh 442 grains ; and consequently that the interstices between the particles of 
the powder, as it is grained for use, are nearly as great as the spaces which those 

particles occupy. 

MISCELLANEOUS EXPERIMENTS. 

Of some unsuccessful attempts to increase the force of gunpowder. — It has 
been supposed by many, that the force of steam is even greater than that of gun- 
powder ; and that if a quantity of water, confined in the chamber of a gun, 
could at once be rarefied into steam, it would impel a bullet with prodigious 
velocity. Several attempts have been made to shoot bullets in this manner ; but 
Mr. T. knew of none that had succeeded ; at least so far as to render it probable 
that water can ever be substituted instead of gunpowder for military purposes, as 
some have imagined. The great difficulty that attends making these experiments 
lies in finding out a method by which the water can at once be rarefied, and 
converted into elastic steam. Mr. T. contrived a method for this purpose, which 
was by filling with water the thin air-bladders of very small fishes, and inclosing 
them in the middle of cartridges of gunpowder, and then firing them ; but he 
constantly found, that the force of the charge was very sensibly diminished by 
the addition of the globule of water, and the larger the quantity of water was 
that was thus confined, the less was the effect of the charge ; neither the recoil 
of the pistol, nor the penetration of the bullet, being near equal to what they 
were when the given quantity of powder was fired without the water ; and the 
report of the explosion appeared to be lessened in a still greater proportion than 
the recoil or penetration. 

Concluding that this diminution of the force of the charge arose from the 
bursting of the little bladder, and the dispersion of the water among the powder 
before it was all inflamed, by which a great part of it was prevented from taking 
fire, Mr. T. repeated the experiments with highly rectified spirits of wine instead 
of water ; but the result was nearly the same as before: the force of the charge 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 113 

was constantly and very sensibly diminished. He afterwards made use of aetherial 
oil of turpentine ; and then of small quantities of quicksilver ; but still with no 
better success. Every thing he mixed with the powder, instead of increasing, 
served to lessen the force of the charge. Common pulvis fulminans is made of 
1 part of sulphur, 1 parts of salt of tartar, and 3 parts of nitre ; and if we may 
judge by the report of the explosion, the elastic force of this compound is con- 
siderably greater than that of gunpowder. Mr. T. tried the. effect of mixing 
salt of tartar with gunpowder ; having provided some of this alkaline salt in its 
purest state, thoroughly dry, and in a fine powder, he mixed n O grains of it 
with 145 grains of gunpowder; and on discharging a bullet with the mixture, 
he found that the alkaline salt had considerably lessened the force of the powder. 
Mr. T. next made use of sal ammoniacum. That salt has been found to pro- 
duce a very large quantity of elastic air, or vapour, when exposed to heat under 
certain circumstances ; but when 20 grains of it were mixed with a charge of 
gunpowder, instead of adding to its force, it diminished it very sensibly. 

Most, if not all, the metals, are thought to produce large quantities of air 
when they are dissolved in proper menstrua, and particularly brass, when it is 
dissolved in spirit of nitre. Desirous of seeing if this could be done by the 
flame, or acid vapour of fired powder, Mr. T. mixed 20 grains of brass in a 
very fine powder, commonly called brass dust, with 145 grains of powder, and 
with this compound and a fit bullet he loaded the barrel and discharged it ; but 
the experiment showed, that the force of the powder was not increased by the 
addition of the brass dust, but the contrary. It seems probable however, that 
neither brass dust nor sethiops mineral are of themselves capable of diminishing 
the force of gunpowder in any considerable degree, otherwise than by filling up 
the interstices between the grains, and obstructing the passage of the flame, and 
so impeding the progress of the inflammation. And hence it appears, how 
earthy particles and impurities of all kinds are so very detrimental to gunpowder. 
It is not that they destroy or alter the properties of any of the bodies of which 
the powder is composed, but simply, that by obstructing the progress of the in- 
flammation, they lessen its force, and render it of little or no value. Too much 
care therefore cannot be taken, in manufacturing powder, to free the materials 
from all heterogeneous matter. 

Of an attempt to shoot flame instead of bullets. — Having often observed paper 
and other light bodies to come out of great guns and small arms inflamed, Mr. 
T. was led to try if other inflammable bodies might not be set on fire in like 
manner, and particularly inflammable fluids ; and he thought if this could be 
effected, it might be possible to project such ignited bodies by the force of the 
explosion, and by that means communicate the fire to other bodies at some con- 
siderable distance -. but in this attempt he failed totally. Mr. T. never could set 

VOL. XV. Q 



114 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

dry tow on fire at the distance of 5 yards from the muzzle of the barrel. He 
repeatedly discharged large wads of tow and paper, thoroughly soaked in the 
most inflammable fluids, such as alkohol, setherial spirit of turpentine, balsam 
of sulphur, &c. : but. none of them were ever set on fire by the explosion. 
Sometimes he discharged 3 or 4 spoonfuls of the inflammable fluid, by interpos- 
ing a very thin wad of cork over the powder, and another over the fluid ; but 
still with no better success. The fluid was projected against the wall as before, 
and left a mark where it hit ; but it never could be made to take fire ; so he 
gave up the attempt. If it had succeeded, probably it would have turned out 
one of the most important discoveries in the art of war that have been made 
since the invention of gunpowder. 

XFI. A Luminous appearance in (he Heavens. Bi/ T. Cavallo, F.R.S. p. 32Q 
At about half past Q, March 27, 1781, a white light began to be seen in the 
sky, which became gradually more and more dense till 10 o'clock, at which time 
it formed a complete luminous arch from east to west. At that time it appeared 
to be an arch of about 7 or 8 degrees in breadth, extended nearly from east to 
west. Its western part quite reached the horizon ; but the eastern part of the 
arch seemed to begin at about 50° or 60° above the horizon. It did not pass 
through the zenith, but at about 8° or 10° southward of it, and it was nearly 
perpendicular to the horizon. 

The whiteness of this arch was much denser than that of any aurora borealis, 
though it did not cast so much light on terrestrial objects. Towards the middle 
it was so dense, that the stars over which it passed were eclipsed ; but the sides 
of this luminous arch were more faint and transparent. At about f past 10 it 
began to lose its brightness, and then vanished gradually, so that at 1 1 o'clock 
none of it could be perceived. As soon as any part of this arch lost its dense 
whiteness, the stars appeared through it quite distinct ; so that it could not be a 
cloud. The light also seemed to vanish without change of place ; for it did not 
appear to be dispersed through the sky, or to be driven in any direction. This 
extraordinary appearance seemed quite distinct from the aurora borealis, for the 
following reasons; viz. because it eclipsed the stars over which it passed; be- 
cause its light, or rather its white appearance, was stationary and not lambent ; 
and because its direction was from east to west. The atmosphere was in other 
respects very serene, the stars shining very bright, and no cloud appearing. The 
northern light was exceedingly faint, and very low about the northern point of 
the horizon. The wind was nearly north-east, and it could be just felt in the 
streets. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 115 

XVII. Account of an Earthquake at Hafodunos near Detibigh. By John Lloyd, 

Esq., F.R.S. p. 331. 
August 29, 1781, at 8 h 37 m 30', as Mr. L. was sitting on his bed-side, he 
heard a rumbling noise, as if at a distance : the sound seemed to approach, and 
whenvit was greatest the bed rocked and shook so much that he could scarcely 
keep his seat. The barometer had been stationary nearly for the 3 preceding 
days, and did not seem to be affected with the shock. The morning was re- 
markably fine, and not a single cloud to be seen. Two of his sisters and a gen- 
tleman were walking on the terrace in the garden by the side of a wall : they all 
perceived the noise, at first as if at a great distance ; but when it was greatest 
they perceived the wall to shake, though they did not observe any agitation 
under their feet. It continued from 15 to 18 minutes; and its course was 
nearly from south-east to north-west. Some other persons in the house per- 
ceived a double shock ; and this was observed by many who felt it in other 
places. It was felt at most other parts in Wales. And 2 other shocks were 
afterwards felt the same year in Wales. 

XVIII. On the Heat of the Water in the Gulf-Stream. By Chas. Blagden, 

M. D., F. R. S. p. 334. 

One of the most remarkable facts observed in navigating the ocean, is that 
constant and rapid current which sets along the coast of North America to the 
northward and eastward, and is commonly known to seamen by the name of the 
gulf-stream. It seems justly attributed to the effect of the trade-winds, which, 
blowing from the eastern quarter into the great Gulf of Mexico, cause there an 
accumulation above the common level of the sea; in consequence of which, it is 
constantly running out by the channel where it finds least resistance, that is, 
through the Gulf of Florida, with such force as to continue a distinct stream to 
a very great distance. Since all ships going from Europe to any of the southern 
provinces of North America must cross this current, and are materially affected 
by it in their course, every circumstance of its motion becomes an object highly 
interesting to the seaman, as well as of great curiosity to the philosopher. 

During a voyage to America in the spring of the year 1776, Dr. B. used 
frequently to examine the heat of sea-water newly drawn, in order to compare it 
with that of the air. The passage was made far to the southward. In this 
situation, the greatest heat of the water which he observed was such as raised 
the quicksilver in Fahrenheit's thermometer to 774. This happened twice ; the 
first time on the 10th of April, in latitude 21° 10' n. and longitude by reckon- 
ing 52° w. ; and the 2d time, 3 days afterwards, in latitude 22° ^' and longitude 
55°; but in general the heat of the sea near the tropic of Cancer about the 
middle of April was from 76" to 77°. 

a 2 



Il6 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

The rendezvous appointed for the fleet being off Cape Fear, their course, on 
approaching the American coast, became north-westward. On the '23d of 
April the heat of the sea was 74°, the latitude at noon '28° 7' n. Next day the 
heat was only 71°, then in latitude 29 12'; the heat of the water, therefore, 
was now lessening very fast in proportion to the change of latitude. The 25th 
the latitude was 31° 3'; but though they had thus gone almost 2° farther to the 
northward, the heat of the sea was this day rather increased, it being 72° in the 
morning, and 72% in the evening. Next day, the 26th of April, at half after 
8 in the morning, the thermometer rose to 78°; higher than he had ever ob- 
served it, even within the tropic. As the difference was too great to be imputed 
to any accidental variation, Dr. B. immediately conceived that they must have 
come into the gulf-stream, the water of which still retained great part of the 
heat that it had acquired in the torrid zone. This idea was confirmed by the 
subsequent regular and quick diminution of the heat : the ship's run for a quarter 
of an hour had lessened it 2° ; the thermometer at 8A h being raised by sea- 
water fresh drawn only to 7 6° ; by 9 the heat was reduced to 73°, and in J- of an 
hour more, to 7 1° nearly : all this time the wind blew fresh, and they were going 
7 knots an hour on a north-western course. The water now began to lose the 
fine transparent blue colour of the ocean, and to assume something of a greenish 
olive tinge, a well-known indication of soundings. Accordingly, between 4 and 
5 in the afternoon ground was struck with the lead at the depth of 80 fathoms, 
the heat of the sea being then reduced to 6g°. In the course of the following 
night and next day, as they came into shallower water and nearer the land, the 
temperature of the sea gradually sunk to 65°, which was nearly that of the air 
at the time. 

Bad weather on the 26th prevented them from taking an observation of the 
sun ; but on the 27th, though it was then cloudy at noon, they calculated the lati- 
tude from 2 altitudes, and found it to be 33° 2& n. The difference of this 
latitude from that which was observed-on the 25th, being 2° 23', was so much 
greater than could be deduced from the ship's run marked in the log-book, as to 
convince the seamen that they had been set many miles to the northward by the 
current. 

From these observations, Dr. B. thinks it may be concluded, that the gulf- 
stream, about the 33d degree of north latitude, and the 76th degree of longi- 
tude west of Greenwich, is, in the month of April, at least () degrees hotter 
than the water of the sea through which it runs. As the heat of the sea-water 
evidently began to increase in the evening of the 25th, and as the observations 
show that they were getting out of the current when he first tried the heat in 
the morning of the 26th, it is most probable that the ship's run during the night 
is nearly the breadth of the stream measured obliquely across ; that, as it blew a 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 117 

fresh breeze, could not be much less than 25 leagues in 15 hours, the distance 
of time between the two observations of the heat, and hence the breadth of the 
stream may be estimated at 20 leagues. The breadth of the Gulf of Florida, 
which evidently bounds the stream at its origin, appears by the charts to be 2 or 
3 miles less than this, excluding the rocks and sand-banks which surround the 
Bahama Islands, and the shallow water that extends to a considerable distance 
from the coast of Florida ; and the correspondence of these measures is very re- 
markable, since the stream, from well-known principles of hydraulics, must 
gradually become wider as it gets to a greater distance from the channel by which 
it issues. 

XIX. On the Appearance of the Soil at opening a Well at Hanby, Lincolnshire. 
By Sir Henry C. Englefield, Bart., F. R. and A. S. p. 345. 

The spot on which the well was sunk is nearly on a level with Lincoln Heath? 
and of course high ground compared with the fen, which is distant from it above 
6 miles. The soil was uniformly a blue clay, in parts rather inclining to a shaly 
structure, and contained many casts of tellinse, a very little pyrites, and some 
few small, but very elegant belemnites. These are all the usual fossils of clay ; 
but what Sir H. thinks without example is, that through the whole mass of clay 
were interspersed nodules of pure chalk, evidently rounded by long attrition, and 
of all sizes from that of a pea to a child's head. They lay in no sort of order 
that he could find. How deep this appearance might have continued he 
could not determine, but no water having been found at the depth of 30 feet, 
the trial was given up, as the expense would have exceeded the advantage 
proposed. In all the environs there is not the least trace of chalk in any form 
whatever that he could discover or hear of. 

XX. Astronomical Observations, by Nath. Pigott, Esq., F. R. S. p. 347- 
In 1778 and \77Q Mr. P. observed in Glamorganshire; and by 35 meridian 
observations of the sun and stars, all agreeing within 12 s from the mean, he de- 
termined the latitude of his observatory at Frampton House 51° 25' I" n. And 
its longitude, by comparison of many observations of the eclipses of Jupiter's 
satellites, was 3° 29' 30* west of Greenwich. Frampton House lies between 
Cowbridge and Lantwit ; about 4 miles south' of the former, and 1 mile north of 
the latter, and about 2 miles from the Bristol channel ; and is nearly under the 
same meridian as Watchet, a market town in Somersetshire. 

In the beginning of 1778, the declination west of a magnetic needle of 4 
inches, made by Mr. Dollond, appeared to be 22° 1 1'. 



118 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781, 



XXI. Abstract of a Register of the Barometer, Thermometer, and Rain, at 
Lyndon, in Rutland, 1780. By Thomas Barker, Esq. p. 351. 



Jan. 

Feb. 

Mar, 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 



Mom. 

Aftern 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 

Morn. 

Aftern. 



Barometer. 



Highest. 



29-S9 
30.06 
29-94 
2977 
29.33 
29.89 
29.87 
29.81 
29.79 
29.87 
30.00 
30.0S 



Lowest. 



28.16 

28.72 

28.99 

28.40 

28.80 

29.26 

29.21 

29.43 

28.70 

2S.20 

28.62 

29.22 



Mean. 



29.39 

29.49 

29.47 

29.21 

29.4S 

29.55 

29.61 

29.65 

29.3S 

29-23 

29.41 

29-83 



Mean of all 



Thermometer. 



In the House. 



Hia;. Low 



29.48 



39 


28 


40 


29 


44 


33 


44 J, 


34 


51* 


4-1 * 


53 h 


43* 


53 


40 


55 


41* 


67 


51 


72 


52* 


65 h 


52 


7H 


52* 


69$ 


58* 


7H 


5.9* 


68 


6l 1 


72 


63 


70 


53 


73* 


53 A 


58i 


461 


59 


48 


50 


38* 


50* 


381 


45 


35 


45* 


35 



Mean 



34 
35 
37 
38 
46 

*7h 

46 

46 

55 

57 

57 £ 

59 

63 

64 

64 

66 

61 

63 

51 

52 

43 

43 * 

40 

40 * 



Abroad. 
Hig. Low Mean 



36* 15* 27 
43 



50 



41 

46" 

49 

61 

52 

60 

65 

80* 

62 1 

SO 

65 

83 

63 

81 i 

61 

82 

56 

64 

48* 

48 

46* 

50 



22* 32 
22 I 31 

30.1 ■ 3 y 
40 



30 

45 



51 



29* 38 
38 i 48 
40* 50* 
53 I 6l 
43 i 53* 



51 

51* 

61 

52 

63 

43 

53* 

33* 

45* 

19 

31 

26 



64 

57 h 

69 h 

58 

70 

52 

65 

44 

53 

36" 

40 

35 

38* 



Rain. 



48 



1.013 
1.572 
1.175 
2.727 
1.201 
1.920 
1.566 
0.432 
3.427 
3.080 
1.461 
0.534 



Mean rain. 



10 yrs 
71—80 



20.108 



1.677 

1.871 

1.355 

1.314 

2 081 

2.374 

2.507 

2.468 

3.1 42 

2.975 

2.372 

1.889 



26.U24 



45 yrs. 
36—80 



1.573 
1.378 
1.315 
1.465 
1.610 
2.249 
2.516 
2.247 
2.016 
2.158 
1.943 
1.740 



22.210 



XXII. Some Calculations of the Number of Accidents or Deaths which happen 
in consequence of Parturition ; and of the Proportion of Male to Female Chil- 
dren, as well as of Twins, monstrous Productions, and Children dead- born ; 
taken Jrom the Midwifery Reports of the Westminster General Dispensary: 
with an Attempt to ascertain the Chance of Life at different Periods, from 
Infancy to Twenty-six Years of Age ; also the Proportion of Natives to the 
rest of the Inhabitants of London. By Robt. Bland, M. D., of the West- 
minster General Dispensary, p. 355. 
As Dr. B.'s first view was to find the proportion of difficult labours, and of the 

accidents or deaths that happen in consequence of child-birth, he began as 

follows : 

Of I897 women delivered under the care of the Dispensary, 63, or 1 in 30, 

had unnatural labours: in 18 of these, or 1 in 105, the children presented by 

their feet; in 36, or l in 52, the breech presented; in 8 the arms presented ; 

and in 1 the funis. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 11Q 

Again, 17 women, or 1 in 111, had laborious labours: in 8 of these, or I 
in 236, the heads of the children were lessened ; in 4 a single blade of a forceps 
was used , and in the remaining 5, in which the faces of the children were 
turned to the pubes, the delivery was at length accomplished by the pains. 

3dly. 1 woman had convulsions about the 7th month of her pregnancy, and 
was delivered a month after of a dead child, and recovered. 1 woman had con- 
vulsions during labour; brought forth a live child, and recovered: 9 women, or 
1 in 210, had uterine haemorrhage before and during labour. Of these 1 died 
undelivered; 1 died a few hours, and 1 ten days, after delivery, and 6 recovered. 

4thly. 5 women had the puerperal fever, of whom 4 died. In one of these 
the placenta was undelivered, and continued so to her death: 2 women were 
seized with mania, but recovered in about 3 months. In 1 woman a suppuration 
took place, soon after labour, from the vagina into the bladder and rectum. 
This patient recovered, but the urine and stools continue to pass through the 
wounds. Of 1 woman the perinaeum was lacerated to the sphincter ani. A 
suture was attempted, but without effect; she recovered, but is troubled with 
prolapsus uteri: 5 had large and painful swellings of the legs and thighs, but 
recovered. 

105 therefore of the?e, or 1 in 18, had preternatural or laborious births, or 
suffered in consequence of labour. Of this number of cases, 43, or 1 in 44, 
were attended with particular difficulty or danger; and ? only, or 1 in 270, died. 
The remaining 62 wefe delivered and recovered with little more than the common 
assistance: and 1792 had natural labours, not attended with any particular 
accidents. 

The proportion of male to female children, of the number of twins, and of 
the children that were deficient or monstrous, and of those that were dead-born, 
is as follows: 

I897 women were delivered of 1923 children; 972 boys, and 951 girls, or as 
46 boys to 45 girls. — 23 of the women, or 1 in 80, were delivered of twins, 1(3 
of whom were boys and 30 girls, — 1 woman was delivered of 3 girls. Of the 
twins and triplets therefore, the males were only half the number of the females. 
— 8 of the children, or 1 in 241, were deficient or monstrous. Of these, 1 
was web-fingered; 1 had a hare-lip; 1 had a dropsical head and distorted spine; 
1 a dropsical head ; in 1 a part of the palate, and in 2 a considerable portion of 
the cranium was wanting; one of these lived an hour after it was born; and 1 
had 2 heads;* 1 woman was delivered of a monstrous twin.-f- — 84 of the children, 

* It had 2 heads and necks, 4 hands and arms, 2 spines, uniting at the sacrum, and terminating 
in one pelvis, whence the lower extremities proceeded single ; there was one navel-string, and one 
male organ of generation. On opening the body there were found, 2 thoracic cavities, tire right 
moie complete than the left; the heart also, and the lungs on the right side, were more perfect than 



120 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

or 1 in 23 of the whole number, were dead-born.* Of these, 49, or nearly £, 
were boys, and 35 were girls. 

Of 1400 women who returned their letters, or of whom a certain account 
could be obtained, 85, or nearly 1 in 16, had buried their children before the 
end of 2 months. Of this number 53, or 5 in 8, were boys, and 32 girls. 
This singular circumstance of there being a greater number of males than females, 
among the still-born children, and of a greater number of male children dying 
in infancy than of females, has been remarked by Dr. Price and other writers on 
calculations; and Dr. Haygarth has shown, that at Chester more husbands die 
in a given period than wives. This naturally suggests an inquiry, whether the 
lives of males are at all ages more precarious than those of females. 

To be enabled to assist in answering this question, I add, says Dr. B., the 
following article to my register, viz. of the children that shall be living when 
the women apply for their letters, how many will be boys, and how many girls? 
Table of the ages at which women begin and cease to be capable of bearing children, and of the inter- 
mediate periods at which they are most so. 
Of 'J 102 pregnant women, Years of age. 



36 or 1 in 5S were from 15 to iy 1 S5, or 1 in 25, from 

4y or 1 in 43 were 20 J 15 to 20 inclusive. 

578 or 5 in 19 were from 21 to 25 "| l6S4, or four-fifths 

6'yy nearly 1 in 3 were from 26' to 30 > were from 21 to 

407 nearly 1 in 5 were from 31 to 35 J 35 inclusive. 

291 or 3 in 22 were from 36' to 40 



36 or 1 in 58 were from 41 to 45 \ 42, or 1 in 50, from 

6 or 1 in 350 were from 46 to 4.9 J 4 1 to 49. 

2T02 
those on the left, which latter were very small. There were 2 stomachs, 2 sets of intestines, which, 
at length uniting, terminated in one rectum and anus. There was but one urinary bladder. — Orig. 

+ Of this singular production, to which Dr. B. had not ventured to give a name, die following is the 
history and description. The woman who produced it was about 27 years of age ; this was her first 
pregnancy. She was, after a natural labour, delivered of a female foetus, and its placenta, in which 
nothing uncommon was observed; and though the uterus remained of an unusual size, yet the pains, 
not recommencing, there was no suspicion entertained but that its bulk was occasioned by coagulated 
blood. On the 3d day the pains became violent, and this monster was born. Its shape was spherical, 
but somewhat flattened. It measured in its largest diameter 5 inches, and weighed about 1 8 ounces. 
It received its nourishment by an umbilical chord, to which was attached a portion of membranes, 
and though no placenta was found, it is probable it had a small one, and that it was inclosed in its 
own involucrum. It was completely covered with a cuticula, and a little above the part where the 
navel-string terminated, there was a hairy scalp covering a bony prominence, somewhat resembling 
the arch of the cranium. On dissection it was found to be plentifully supplied with blood-vessels, 
proceeding from the navel-string, and branching through every part of it. It had a small brain and 
medulla spinalis continued into a bony theca, with nerves passing from thence through die foramina 
of the bones; but no resemblance of any thoracic or abdominal viscera. The rest of its bulk was 
made up of fat. — Orig. 

* By dead-born children Dr. B. means those that die after they have been perceived to move, thatis, 
generally after 4 months. Abortions, or deaths before that period, may reasonably be estimated at 
double this number; so that perhaps 1 child in 8 dies in the womb, or in the act oi (Mining into the 
world. — Orig. 



VOL. LXXI.] 



PHILOSOPHICAL TRANSACTIONS. 



121 



Tables of the number of children born by 1389* women, with the number that were living at the time of 

their applying to the Dispensary . 



Women. 


No. of children 
born by each 
woman. 


Total of child 
born. 


Total of child, 
living. 


'No. of women 
J who had pre- 
served their 
children. 


No. of children 
preserved by 
each woman. 


Total of child, 
preserved. 


1 


24 


24 


5 


.... 






1 


\7 


17 


3 


.... 


. . 


. 


. . 




3 


16 


48 


5 


.... 




. 






2 


14 


28 


11 


.... 






. . 




11 


J3 


155 


46 


.... 


. . 


, 


. . 




U 


12 


168 


44 


.... 


. . . 


. 






15 


11 


165 


45 


1 


I 








22 


10 


220 


84 




. . . 


# 






33 


9 


297 


93 


.... 










56 


8 


448 


151 


4 


8 


1 


52 


74 


7 


518 


213 


3 


7 


21 


89 


6 


534 


214 


11 


6 


66 


138 


5 


690 


288 


32 


5 


160 


169 


4 


676 


293 


84 


4 


336 


208 


3 


624 


299 


174 


3 


522 


254 


2 


508 


259 


306 


2 


612 


299 


1 


299 


171 


464 


1 


464 


1389 | 




t5419 


2224 


1079 




2224 


and 370 we 


re in their first pregnancy 




and 310 had lost all their 


children. 


13S9 








13S9 











I have placed (says Dr. B.) these 2 tables together, thac we might have an oppor- 
tunity of observing how exceedingly fertile the women of the poorer classes in this 
country are; and at the same time how unable to rear any considerable number 
of children; for, though 321 of the women had borne 6 children and upwards 
each, and were all again pregnant, 1 9 only of them had been able to rear 6 or 
more children; and though 102 of the women had borne 9 children and upwards 
each, only 1 of them had been able to preserve that number living. I am in- 
clined to believe, that this great mortality among the children does not arise 
from any natural imbecility or a constitution vitiated from the birth, many of 
those victims being born with all the appearances of health and vigour; but that 
we ought rather to search for the cause of it in the poverty of the parents, 

* In order to account for the difference between the number of the women in these and the pre- 
ceding tables, it is proper to mention, that this account was not begun until some months after the 
former one. In these also care has been taken that no woman is reckoned more than once, though 
many of them had been assisted by the midwives to the Dispensary 2, 3, or 4 times; 370, as noted in 
the table, were in their first pregnancy. — Orig. 

+ Of these 5419 children, 2747 were boys, and 26'72 girls, or nearly as 36 boys to 35 girls. This 
proportion of the boys to the girls will be found a little different from what is given in a former table . 
-Orig. 

VOL. XV. R 



122 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781. 

which prevents their taking the necessary care of, or even affording sufficient 
clothing and nourishment to, their offspring. 

I shall now from these tables attempt to collect what the chance of life is at 
different periods, from infancy to 26 years of age; but, that I may be under- 
stood, it will be necessary to premise some account of the method I have fol- 
lowed. I have supposed each of the women to bear a child every 2 years; this, 
from the account of those who returned to the Dispensary a 2d, 3d, or 4th time, 
appearing to be the mean term. On this principle, when I find that a woman 
applied at the Dispensary who had had 1 child before, I conclude, that that 
child would be 2 years old, if living; but if the woman had borne 2 children, 
I suppose that the first would be 4, the second 2 years old, and so on. And 
finding, that of 299 children born by as many women, who were now advanced 
in their 2d pregnancy, 17 1, or -^ only were living, I conclude, that on an ave- 
rage 5 out of 12 die under 2 years of age: and observing that of 508 children 
born by 254 women, who were now advanced in their 3d pregnancy, 259 only 
were living, I first deduct 210, which is T V of the whole number, who died 
under 2 years of age; and then find that 39, which is nearly -^ of the whole 
number, or 4- of the survivors, died between 2 and 4 years of age. 

Table of the Chance of Life from Infancy to 26 Years of Age. 



Age. 



Persons 

living. 



Decrease 
of life. 



5 in 12 

6 in 12, or 1 in 7 of the survivors 
8 in 15, or 1 in 1 5 of the survivors 
4 in 7, or 1 in 12j of the survivors 

6 in 10, or 1 in 15 of the survivors 

7 in 10, or 1 in 4 of the survivors 



5400 2250 

2 3150 450 

4 2700 1 80 

6 2520 204 

8 2313 156 

18 2160 540 

26 1620 

3780 or -*3 would die. 

1620 or -jL would be living at the end of 26" years. 

5400 

A comparative table of the population of London, with a view to show the 
proportion of natives to persons born in the different counties of England and 
Wales, in Scotland, Ireland, or foreign countries. 

Of 3236 married persons, 824, or ■{-, were born in London; 1870, or 4-, in 
the different counties of England and Wales; 209, or 1 in 15, in Scotland; 280, 
or 1 in 11, in Ireland; 53, or 1 in 60, were foreigners. 

Of the above number the males and females were in the following pro- 
portions. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 1'23 

Men. Women. 

329 "ere born in London, and . . 495 or 166 more than men. 

952 in different counties 917 or 35 fewer than men. 

135 in Scotland 74 or 6"l fewer than men. 

l6"2 in Ireland 1 19 or 43 fewer than men. 

40 were foreigners .. 13 or 27 fewer than men. 

1618 16"18 166 

Thus, of 824 married persons born in London, there were J- more women 
than men. This may be accounted for either by supposing a greater number of 
males to die or to migrate before they attain a marriageable age than women. It 
is also to be observed, that of the Scotch and of the foreigners, the women are 
in proportion to the men as about 1 to 3; but of the Irish they are as 3 to 7 . 

By this table we find at how great an expense to the country this city is main- 
tained; and as we may suppose that the bulk, of the Scotch, Irish, and foreigners, 
who come into the kingdom, reside in the metropolis, we hence may also learn 
in what proportion they contribute to repair the waste which is incurred by its 
excessive populousness. A more complete knowledge of these facts may give 
rise to regulations which, if the calculations of Dr. Price shall be found to be 
just, are but too necessary. 

XXIII. Account of a Child who had the Small-pox in the IVomb. In a Letter 
from Wm. Wright, M. D., F. R. S., to John Hunter, Esq., F. R. S. p. 372. 

I have read with much pleasure and information Mrs. Ford's case, which you 
published in Philos. Trans., vol. 70, p. 1'28. From the facts you have adduced 
it amounts to a certainty, that her foetus had received the variolous infection in 
the womb. This induces me to lay before you a singular case, that fell under 
my care some years ago. 

In 1768 the small-pox was so general in Jamaica that very few people escaped 
the contagion. About the middle of June Mr. Peterkin, merchant at Martha- 
brae, in the parish of Trelawney, got about 50 new negroes out of a ship; soon 
after they landed, several were taken ill of a fever, and the small-pox appeared; 
the others were immediately inoculated. Among the number of those who had 
the disease in the natural way, was a woman of about 22 years of age, and big 
with child. The eruptive fever was slight, and the small-pox had appeared before 
I saw her. They were few, distinct, and large, and she went through the disease 
with very little trouble, till on the 14th day from the eruption she was attacked 
with the fever, which lasted only a few hours. She was however the same day 
taken in labour, and delivered of a female child with the small-pox on her whole 
body, head, and extremities. They were distinct and very large, such as they 
commonly appear on the 8th or gth day in favourable cases. The child was 
small and weakly; she could suck but little; a wet nurse was procured, and 

R 2 



124 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/81. 

every possible care taken of this infant, but she died the 3d da)' after she was 
born. The mother recovered. In the course of many years practice in Jamaica, 
I have remarked, that where pregnant women had been seized with the natural 
small-pox, or been by mistake inoculated, that they generally miscarried in the 
time of, or soon after, the eruptive fever; but I never saw any signs of small- 
pox on any of their bodies, except on the child's above-mentioned. 

XXIV. Natural History of the Insect which produces the Gum Lacca. By Mr. 

James Kerr, of Patna. p. 374. 

Coccus Lacca. — The head and trunk form one uniform, oval, compressed, 
red body, of the shape and magnitude of a very small louse, consisting of 12 
transverse rings. The back is carinate ; the belly flat ; the antennas half the 
length of the body, filiform, truncated and diverging, sending off 2 often 3 deli- 
cate, diverging hairs, longer than the antennas. The mouth and eyes could not 
be seen with the naked eye. 

The tail is a little white point, sending off 2 horizontal hairs as long as the 
body. It has 3 pair of limbs, half the length of the insect. 

I have often observed the birth of these insects, but never could see any with 
wino-s ; nor could I find any distinction of sexes, nor observe their connubial 
rites : nature and analogy seem to point out a deficiency in my observations, 
possibly owing to the minuteness of the object, and want of proper glasses. 

This insect is described in that state in which it sallies forth from the womb of 
the parent, in the months of November and December. They traverse the 
branches of the trees on which they are produced for some time, and then fix 
themselves on the succulent extremities of the young branches. By the middle 
of January they are all fixed in their proper situations, they appear as plump as 
before, but show no other marks of life. The limbs, antennas, and setae of the 
tail are no longer to be seen. Around their edges they are environed with a 
spissid sub-pellucid liquid, which seems to glue them to the branch : it is the 
gradual accumulation of this liquid, which forms a complete cell for each insect, 
and is what is called gum lacca. About the middle of March the cells are 
completely formed, and the insect is in appearance an oval, smooth, red bag, 
without life, about the size of a small cochineal insect, emarginated at the ob- 
tuse end, full of a beautiful red liquid. In October and November are found 
about 20 or 30 oval eggs, or rather young grubs, within the red fluid of the 
mother. When this fluid is all expended, the young insects pierce a hole 
through the back of their mother, and walk off one by one, leaving their 
exuviae behind, which is that white membranous substance found in the empty 
cells of the stick lac. 

The insects are the inhabitants of four trees. 1. Ficus Keligiosa, Linnaei. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 125 

In Hindostan, Pipul. Banyan tree. 2. Ficus Indica, Linnaei. In Hindostan, 
Bhur. Banyan tree. 3. Plaso, Horti Malabarici. By the natives, Praso. 
4. Rhamnus Jujuba, Linnaei. In Hindostanic, Beyr. 

The insects generally fix themselves so close together, and in such numbers, 
that I imagine only I in 6 can have room to complete her cell : the others die, 
and are eaten up by various insects. The extreme branches appear as if they 
were covered with a red dust, and their sap is so much exhausted, that they 
wither and produce no fruit, the leaves drop off, or turn to a dirty black, colour. 
These insects are transplanted by birds : if they perch on these branches, they 
must carry off a number of the insects on their feet to the next tree they rest 
on. It is worth observing, that these fig trees when wounded drop a milky 
juice, which instantly coagulates into a viscid ropy substance, which, hardened 
in the open air, is similar to the cell of the coccus lacca. The natives boil this 
milk with oils into a bird-lime, which will catch peacocks or the largest birds. 

A red medicinal gum is procured by incision from the plaso tree, so similar 
to the gum lacca that it may readily be taken for the same substance. Hence it 
is probable, that those insects have little trouble in animalizing the sap of these 
trees in the formation of their cells. The gum lacca is rarely seen on the Rhamnus 
Jujuba; and it is inferior to what is found on the other trees. The gum lacca 
of this country is principally found on the uncultivated mountains on both sides 
the Ganges, where nature has produced it in such abundance, that were the 
consumption 10 times greater, the markets might be supplied by this minute 
insect. The only trouble in procuring the lac is in breaking down the branches, 
and carrying them to market. The present price in Dacca is about 12 shillings 
the 100 pounds weight, though it is brought from the distant country of Assam. 
The best lac is of a deep red colour. If it is pale, and pierced at top, the value 
diminishes, because the insects have left their cells, and consequently they can 
be of no use as a dye or colour, but probably they are better for varnishes. 

This insect and its cell have gone under the various names of Gum Lacca, Lack, 
Loc Tree. In Bengal, La; and by the English it is distinguished into 4 kinds. 
1st. Stick lac, which is the natural state from which all the others are formed. 
2d. Seed lac is the cells separated from the sticks. 3d. Lump lac is seed lac 
liquified by fire, and formed into cakes. 4th. Shell lac is the cells liquified, 
strained, and formed into thin transparent laminae in the following manner. 
Separate the cells from the branches, break them into small pieces, throw them 
into a tub of water for one day, wash off the red water and dry the cells, and 
with them fill a cylindrical tube of cotton cloth, 2 feet long, and 1 or 2 inches 
in diameter; tie both ends, turn the bag above a charcoal fire; as the lac liquifies 
twist the bag, and when a sufficient quantity has transuded the pores of the 
cloth, lay it on a smooth junk of the plantain tree (Musa Paradisiaca, Linn.), 



]'i6 1'HILOSOPHTCAL TRANSACTIONS. [ANNO 1781. 

and with a slip of the plantain leaf draw it into a thin lamella; take it off while 
flexible, for in a minute it will be hard and brittle. The value of shell lac is 
according to its transparency. 

This is one of the most useful insects yet discovered. The natives consume a 
great quantity of shell lac in making ornamental rings, painted and gilded in 
various tastes, to decorate the arms of the ladies; and it is formed into beads, 
spiral and linked chains for necklaces, and other female ornaments. 

Fur sealing-wax, take a stick, and heat one end of it on a charcoal fire; put 
on it a few leaves of the shell lac softened above the fire; keep alternately heat- 
ing and adding more shell lac, till you have got a mass of 3 or 4 pounds of 
liquified shell lac on the end of the stick.* Knead this on a wetted board with 3 
ounces of levigated cinnabar, form it into cylindrical pieces; and, to give them 
a polish, rub them while hot with a cotton cloth. 

For japanning, take a lump of shell lac, prepared in the manner of sealing- 
wax, with whatever colour you please, fix it on the end of a stick, heat the 
polished wood over a charcoal fire, and rub it over with the half-melted lac, and 
polish, by rubbing it even with a piece of folded plantain leaf held in the hand; 
heating the lacquer, and adding more lac as occasion requires. Their figures are 
formed by lac, charged with various colours in the same manner. 

Famish. — In ornamenting their images and religious houses, Sec. they make 
use of very thin beaten lead, which they cover with various varnishes, made of 
lac charged with colours. The preparation of them is kept a secret. The leaf 
of lead is laid on a smooth iron heated by fire below, while they spread the 
varnish on it. 

Grindstones. — Take of river sand 3 parts, of seed lac washed 1 part, mix them 
over the fire in a pot, and form the mass into the shape of a grindstone, having 
a square hole in the centre ; fix it on an axis with liquified lac, heat the stone 
moderately, and by turning the axis it may easily be formed into an exact orbi- 
cular shape. Polishing grindstones are made only of such sand as will pass easily 
through fine muslin, in the proportion of 1 parts sand to 1 of lac. This sand 
is found at Ragimaul. It is composed of small angular crystalline particles, 
tinged red with iron, '2 parts to ] of black magnetic sand. The stone-cutters, 
instead of sand, use the powder of a very hard granite called corune. These 
grindstones cut very fast. When they want to increase their power they throw 
sand on them, or let them occasionally touch the edge of a vitrified brick. The 
same composition is formed on sticks, for cutting stones, shells, &c. by the 
hand. 

Painting. — Take one gallon of the red liquid from the first washing for shell 

* In this manner lump lac is formed from seed lac. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 127 

lac, strain it through a cloth, and let it boil for a short time, then add half an 
ounce of soap earth (fossil alkali); boil an hour more, and add 3 ounces of 
powdered load (bark of a tree) ; boil a short time, let it stand all night, and 
strain next day. Evaporate 3 quarts of milk, without cream, to 1 quarts, on a 
slow fire, curdle it with sour milk, and let it stand for a day or two; then mix 
it with the red liquid abovementioned ; strain them through a cloth, add to the 
mixture 1 ounce and a half of alum, and the juice of 8 or 10 lemons: mix the 
whole, and throw it into a cloth-bag strainer. The blood of the insect forms a 
coagulum with the caseous part of the milk, and remains in the bag, while a 
limpid acid water drains from it. The coagulum is dried in the shade, and is 
used as a red colour in painting and colouring. 

Dyeing. — Take 1 gallon of the red liquid prepared as before without milk, to 
which add 3 ounces of alum. Boil 3 or 4 ounces of tamarinds in a gallon of 
water, and strain the liquor. Mix equal parts of the red liquid and tamarind 
water over a brisk fire. In this mixture dip and wring the silk alternately till it 
has received a proper quantity of the dye. To increase the colour, increase the 
proportion of the red liquid, and let the silk boil a few minutes in the mixture. 
To make the silk hold the colour, they boil a handful of the bark called load in 
water, strain the decoction, and add cold water to it; dip the dyed silk into this 
liquor several times, and then dry it. Cotton cloths are dyed in this manner; 
but the dye is not so lasting as in silk. 

Spanish wool. — The lac colour is preserved by the natives on flakes of cotton 
dipped repeatedly into a strong solution of the lac insect in water, and then 
dried. 

XXV. Account of a Phenomenon observed on the Island of Sumatra. By 

William Marsden, Esq. p. 383. 
In the year 1775 the s. e. or dry monsoon, set in about the middle of June, 
and continued with very little intermission till the month of March in the fol- 
lowing year. So long and severe a drought had not been experienced there in 
the memory of the oldest man. The verdure of the ground was burnt up, the 
trees were stripped of their leaves, the springs of water failed, and the earth 
every where gaped in fissures. For some time a copious dew falling in the night 
supplied the deficiency of rain; but this did not last long: yet a thick fog, 
which rendered the neighbouring hills invisible for months together, and nearly 
obscured the sun, never ceased to hang over the land, and add a gloom to the 
prospect already but too melancholy. The Europeans on the coast suffered 
extremely by sickness; about a 4th part of the whole number being carried off by 
fevers and other bilious distempers, the depression of spirits which they laboured 



128 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

under, not a little contributing to hasten the fatal effects. The natives also 
died in great numbers. 

In the month of November that year, the dry season having then exceeded its 
usual period, and the s. e. winds continuing with unremitting violence, the sea 
was observed to be covered, to the distance of a mile, and in some places a 
league from shore, with fish floating on the surface. Great quantities of them 
were at the same time driven on the beach or left there by the tide, some quite 
alive, others dying, but the greatest part quite dead. The fish thus found were 
not of one but various species, both large and small, flat and round, the cat-fish 
and mullet being generally the most prevalent. The numbers were prodigious, 
and overspread the shore to the extent of some degrees; of this I had ocular 
proof or certain information, and probably they extended a considerable way 
farther than I had opportunity of making inquiry. Their first appearance was 
sudden; but though the numbers diminished, they continued to be thrown up, 
in some parts of the coast, for at least a month, furnishing the inhabitants with 
food, which, though attended with no immediate ill consequence, probably con- 
tributed to the unhealthiness so severely felt. No alteration in the weather had 
been remarked for many days previous to their appearance. The thermometer 
stood as usual at the time of year at about 85°. 

Various were the conjectures formed as to the cause of this extraordinary phe- 
nomenon, and almost as various and contradictory were the consequences 
deduced by the natives from an omen so portentous; some inferring the con- 
tinuance, and others, with equal plausibility, a relief from the drought. With 
respect to the cause, I must confess myself much at a loss to account for it satis- 
factorily. If I might hazard a conjecture, and it is not offered as any thing 
more, I would suppose, that the sea requires the mixture of a due proportion of 
fresh water to temper its saline quality, and enable certain species of fish to 
subsist in it. Of this salubrious correction it was deprived for an unusual space 
of time, not only by the want of rain, but by the ceasing of many rivers to flow 
into it, whose sources were dried up. I rode across the mouths of several per- 
fectly dry, which I had often before passed in boats. The fish no longer 
experiencing this refreshment, necessary as it would seem to their existence, 
sickened and perished as in a corrupted element. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 1 2Q 

XXVL Further Experiments on Cold, made at the Macfarlane Observatory 
belonging to Glasgow College. By Patrick Wilson, M. A. p. 386. 

Monday morning, Jan 22, 1781. 

Some days of very cold weather, lately in this fa Therm. Therm, 

country, afforded an opportunity of prose- y ' . . in t'. . . '-T^' 

cuting a little further the experiments and i 30..!! !!!! +2.1 ."..! -12 

observations begun in the course of last year. 1 * 5 - _» -8 

The frost set in on Sunday the 2 1 st of Jan. 3 -0. ...!!- 4 

after a considerable fall of snow on the pre- ^ 45 ~° -8 

ceding evening, and about midnight the ther- 4 30. 1 . . . ! ! 1 -3. ! . 1 11- 8 

mometers were exposed near the observatory in ^ ^ -2 -»2 

the situations mentioned in my former letter. 6 45 .' .' .' \ .'.'!! —2. .!!!.- 10 

The annexed register shows the difference of 7 -3 - 13 

temperature between the snow and the air, till 8 \ \ \ \ \ ' \ \ _ 4 [ ' ' " " _ u 

8 o'clock on Monday morning, to which are 8 30 -2 -10 

subjoined some facts which prove very consonant to those described in the former 
paper. The sign — prefixed, denotes degrees below O. The sign + degrees 
above O, of Fahrenheit's thermometer. 

From 1 o'clock till 3 in the morning, the thermometer in air, at the 
balustrade of the east wing of the observatory, pointed from + 4 to -f 6, and 
on the snow there from — 1 to 0. At half an hour after I the thermometer in 
air, 24 feet from the ground, and to the windward of the house, pointed to 
-j- 7, and at 8 o'clock to + 1. At 3 o'clock the snow in the park, 3 inches 
below the surface, raised the thermometer to -f 14, and at 6 inches below, near 
the ground, to + 24. The barometer stood at 29.8 inches, and there was a 
perceptible motion of the air from the east and J point south. This night was a 
very general and lively aurora borealis, most part of it of a bright red, which 
formed a crown near the zenith; Monday evening. Therm. Therm, 

but it mostly vanished about 3 h - m - in air. in snow, 

o'clock, after which time the air 8 3o!!!!.'.'.!!!!l!J!!!l!! +14 +3 

became more still. During the 9 + 8 +1 

whole of this night, as well as l0 "!!!!!!!! !*! .' \\\\ .* .' .' J 7 \\ 

of the succeeding times of ob- ' 30 ........+ 6 + 

. , 11 Ball of therm. ', an inch 
serving, the air was not nearly above the surf, of the sn. + 5 +3 

so much disposed to give out W Ditto + 5 +3 

'. . luesday morning, 

hoar-frost as it was last year. l Ball oftherm. as formerly 

On Monday evening the dif- half immersed in the sn.+ 6 +3 

J e , 2 + 8 -1-5 

terenceot temperature was found 2 30 +]0 _rg 

to be as in the annexed register. 

vol. xv. S 



130 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

No aurora this evening; the air very still and serene till about 2 o'clock. Tues- 
day morning, when the wind rose remarkably, and clouds formed in the north- 
east. 

On Thursday, January '25, the difference of _ 

P , , , , Thurs. morning. Therm. Therm, 

temperature was found to be as here set down h. m. " in air. in snow. 

in the margin. 9 43 + 10 + 3 

, . 10 . . . . + 10 +3 

From 10 till 11 o'clock this forenoon the 10 30...'.".!+ 14." '. + i 

thermometer on the ballustrade in air, 6 inches n + 1+ + 8 

. . , 11 30 + 17 + ') 

above the snow, pointed to + 14, and when 12 + 2 o . . + 12 

tried on the snow to + 10. About noon this '2 30 + 22 + 20 

. , , r 1 1 • 1 u ' aftern. +2.5 + 2fj 

day some clouds were formed, which became 1 30. ..... + 27. . -+- °7 

quite general by 1 o'clock. 

During the last 2 times of observing, 3 experiments were made with a view 
of discovering whether the snow without doors was gaining any thing from the 
air; or if any of it was carried off in the way of evaporation. For this purpose, 
a shallow dish, made of sheet brass, 4 inches in diameter, was exactly filled with 
snow, and carefully weighed. In order to defend the outside of the dish from 
the air, that no hoar-frost might attach itself to the metal, a circular hole was 
cut in the lid of a paste-board box, so wide, as just to let in the dish to the very brim, 
so that nothing communicated with the external air but the snow itself. The 
apparatus, in this state, was set without doors for 3 hours each time, and then 
brought in to the lobby of the observatory, where the dish was again weighed : 
but in none of these trials did it ever appear that any weight was lost. On the 
contrary, at the first weighing, which was on Monday night, 12 o'clock, it had 
gained 5 grains. In the other 2 trials the increase of weight was scarcely 
perceivable. 

The temperature of the air in the west room of the observatory remaining 
very constantly for nearly 2 days at -+- 27°, a dish of snow, similar to the other 
exposed there, was found to lose weight very sensibly, and for the most part 
at the rate of 2 grains in an hour. Notwithstanding this, the snow thus wasting 
or evaporating had no power of sinking the thermometer below -f 27, the tem- 
perature of the surrounding air; though at one time it was fanned for 4 minutes 
by a piece of paper fastened to the end of a long stick. Not to disturb the 
uniform temperature of this room during these experiments, care was taken to 
stay in it a very short time at every visit, and to keep the door and the window- 
shutters close. 

On Christmas-day there was a frost, which in the morning made the thermo- 
meter in air point to -(- 21 ; and during the preceding night there had been a 
profuse deposition of hoar-frost. A pound of this was collected, and ils capacity 
for heat compared with that of ice, and found equal as nearly as could be judged. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. ]31 

Before making the 2 mixtures necessary for this experiment, the ice was reduced 
to a powder, and spread out on a paper beside the hoar-frost till both had acquired 
the same temperature. 

On Monday night, January 22, about 12 o'clock, having occasion to take up 
a little snow, there was observed a cohesion among its parts rather greater than 
what might have been expected in a substance, at that time, so much frozen. 
This circumstance was further examined by the following experiment. A pane 
of glass was laid on the surface of the snow till it had acquired the temperature 
of _|_ 3 ) after which, with a bit of parchment equally cold, some snow was 
scraped from the very surface, and shaken all over the pane, so as to cover it in 
most parts lightly. On now lifting the pane, and holding it with the snow 
undermost, the whole of it adhered, and it required some smart raps before the 
greater part fell away. What remained cleaved to the glass with still a greater 
adhesion. 

The experiments related above afford further reasons against the opinion of 
the difference of temperature between the snow or hoar-frost and the air 
depending on evaporation. It would also appear, that neither does this pheno- 
menon depend on the deposition of hoar-frost. What renders this the more 
probable is, that last year there was a much more copious deposition at times 
when the difference of temperature was not more remarKable. But allowing 
that a deposition had been found a necessary circumstance, and always in pro- 
portion to that difference, the experiments on the capacities of hoar-frost and 
ice seem to show, that the sensible heat which disappears enters not into the 
composition of the hoar-frost; otherwise the capacity of this substance for heat, 
compared to that of ice or common snow, should be very different. It must be 
confessed however, that the abovementioned experiment would have been more 
applicable to this reasoning, had it been made with hoar-frost given out in colder 
states of the air. 

If the air, at low temperatures, had any power of acting on the snow or hoar- 
frost, so as to produce a gradual melting, this circumstance, according to the 
known laws of heat, might occasion the difference of temperature under con- 
sideration. And what renders this idea not altogether improbable, is the peculiar 
cohesion among the parts of the snow above described. Perhaps a gentle 
melting might take place without much altering the appearance of the snow or 
hoar-frost at the surface, as the parts, when dissolved, might be gradually 
sucked downwards, and be afterwards distributed through the whole drier mass. 
It may also be worthy of an experimental inquiry to determine, how far that 
sort of concretion, observable all over the surface of snow which has been 
long frozen, bears any marks of a slow process of this kind. From a hill, a 
little way to the n. e. of the town, and which was to windward during the frost, 

s 2 



132 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 78 1 . 

there were gathered 2 portions of snow, the one from the surface, and the other 
7 inches below it. The water produced from the 2 kinds was preserved in very 
clean phials, in order to be compared together by some chemical trials, which 
perhaps might throw some light on the whole of this matter. 

One other fact was new to me ; namely, the power of ardent spirits of dis- 
solving snow, and consequently of producing with it a freezing mixture. The 
alcohol and snow separately were at 8 degrees below the freezing point, and when 
mixed suddenly and intimately, the temperature became in the space of 20 
seconds 28° below O. This is a cold only 12° short of that which Fahrenheit 
first produced by using spirit of nitre for the experiment ; and it is not improba- 
ble, had the present experiment been tried with more precaution and address, 
that the result would have been still more remarkable. There was employed 
only about a pint of alcohol, but the proportion of snow was not then attended 
to, and the thaw coming soon afterwards prevented a repetition of the 
experiment. 

Postscript. — The water mentioned as produced from the superficial snow has 
been examined by several chemical trials, with a view of discovering if it dif- 
fered in any respect from the water obtained from snow gathered at considerable 
depths, and near the ground. Had the atmosphere, when the thermometers 
pointed so low, been disposed to furnish any saline principle, the union of such 
an ingredient with the snow would have tended to produce an excess of cold at 
the surface, similar to what was then observed. Or if the snow at these low 
temperatures had acquired any remarkable power of dephlogisticating the air in 
contact with it, a cooling process at and near the confines of the snow and air 
might thereby have been maintained. In either of these cases, some very sen- 
sible indications of a saline, or of a phlogistic principle, might be expected on 
the water given by the snow collected from the surface. But in opposition to 
both these views it remains now to be mentioned, that nothing of this kind did 
appear in the course of the experiments, which indeed were contrived chiefly to 
detect such circumstances. If therefore the arguments produced in both papers 
on this subject will not allow us to account for so remarkable a cooling process 
by an evaporation at the surface of the snow, it would appear, that there remains 
still something unknown with respect to the cause. A proper investigation of 
this matter, in climates favourable to such experiments, may possibly unfold some 
further properties of beat with which at present we may be wholly unacquainted.* 

* This interesting subject was further prosecuted by the author during the winter of 1783- I , by a 
variety of other experiments, of which he transmitted an account to Dr. Black, of Edinburgh, who 
communicated the paper to the Royal Society, which hail been very recently instituted there ; and 
which paper was afterwards published in the first volume of their Transactions, in 17.NN. We there 
find that, from a careful review of all the experiments stated in that and the two former accounts, 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 133 

XXV 11. A General Theory for the Mensuration of the Angle subtended by Two 
Objects, of which One is observed by Rays after Two Refections from Plane 
Surfaces, and the other by Rays coming Directly to the Spectator's Eye. By 
George Atwood, M. A., F. R. S. p. 3Q5. 

The actual determination of an angle implies 2 observations, one taken at each 
extremity of the arc by which that angle is measured. When fixed astronomical 
quadrants or other sectors are used for the practical estimation of angles, one of 
these observations is previously made by directing the axis of the telescope or 
line of collimation to some fixed point in the heavens, the index being then 
coincident with the initial point on the arc of the sector: after this adjustment, 
one observation only is necessary to ascertain the angular distance between that 
point and any other celestial object in the plane of the sector. This method 
however is evidently impracticable, unless the instrument can be steadily fixed ; 
for which reason astronomical quadrants become useless at sea ; and from the 
difficulties which attend placing them in their due position and adjustment on 
firm ground, they are almost wholly confined to regular observatories. 

Mr. Hadley, by an ingenious application of optical principles, contrived to 
bring both extremities of the arc measured into the field of the spectator's view 
at the same time ; by which improvement, angles are taken at sea, as well as on 
land, with an unfixed instrument, to a degree of accuracy sufficient for nautical 
and other purposes, when the utmost exactness is not required. Mr. Hadley's 
invention is a particular case of a very extensive theory, as yet but little attended 
to. According to his method, which is well known, the 2 reflecting surfaces 
used in the observation are perpendicular to the plane of motion ; the direction 

the author was convinced that evaporation had no share whatever in producing the remarkable cold 
which was observed. The title of the paper is thus expressed : " Experiments and Observations on 
a remarkable Cold which accompanies the separation of Hoar-frost from a Clear Air ;" and the fol- 
lowing are the general conclusions which, in die author's opinion, the experiments establish : — 
" That when bodies attract hoar-frost from a clear air, there is a cold produced at their surfaces ; and 
that this cold does not originate from any peculiar qualities of bodies on which the hoar-frost settles, 
any further than as some bodies are capable of attracting from die air more or less of it in a given 
time.'' And again, " That the disposition of the air of thus parting with hoar-frost, and the cold 
which accompanies that separation, has a constant dependance on die general serenity of the atmos- 
phere, and is always interrupted on the sky being overcast with clouds or fogginess, especially near 
the place of observation." 

After stating these conclusions, the audior observes : " That the nature or essence of the thing we 
call heat is so far removed beyond die immediate reach of our senses, that we need not wonder, 
though new facts relating to it come into view, and even though they cannot immediately be traced 
up to any general laws hidierto established. That if, on mature consideration, the present phenomena 
cannot be accounted for in this way, they ought, on that very account, to challenge our attention the 
more, as opening to us die necessity of enlarging our stock of principles, and inviting us forward to 
so desirable a work." 



J 34 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

of the telescope, and of the rays passing between the reflectors, being parallel to 
that plane; whereas the inclination of the telescope, and of the intermediate 
rays, as well as of the reflectors themselves to the plane of motion, admit of 
unlimited variety. A general theory to determine the angle observed by 1 re- 
flections, from the data on which its magnitude depends, without limitation or 
restriction, seems applicable to several useful purposes in practical astronomy. 
Having never seen any geometrical construction or analysis of this curious pro- 
blem, Mr. A. was induced to bestow some consideration on the subject. And it 
must be acknowledged that his labours have produced a long and elaborate 
essay, more fit for a separate volume, than for a paper in the Philos. Trans, or 
these Abridgments; and of which the intricate constructions and analytical 
calculations could be of little or no use to the mere practical optician and 
astronomer. 

XXF1II. On the Ophidium Barbatum Linnei. By P. M. Augustus Broussonet, 

M. D. p. 436. 

This species of fish seems not to have been unknown to the ancients, though 
probably they confounded it with the Conger, to which it bears some resem- 
blance. Perhaps the early Greek and Latin writers on natural history have men- 
tioned it under the name of Tragus, or Callarias ; but, for want of descriptions, 
they left us much in the dark concerning it. Pliny indeed speaks of a fish 
which appears to be of this species : he calls it Ophidion, and as that is the 
name given to it by all the modern writers, we are obliged to accept his synonymy 
without further inquiry. 

The first author to whom we are indebted for a description and figure of the 
ophidium, is Bcllonius ; yet it appears, that he was not certain of the name of 
this fish, since he calls it gryllus, falso congrus, tragus, aselli species: nor was 
he less doubtful of the class to which he should refer it, and therefore placed it 
among the aselli, or gadi, though very different from the species of that family. 
Rondeletius, who wrote soon after Bellonius, has given a better description, and 
a more accurate figure of this fish, which he calls ophidion, with a reference to 
Pliny. In the figure of Bellonius the cirri are very ill represented, and the 
whole fish appears without any spots, whereas in the plate of Rondeletius it is 
covered with oblong spots. This remarkable difference between the figures of 
these authors was sufficient to determine Gesnerus, and others who have written 
since their time, and who are to be considered rather as compilers than authors, 
to take the fish described by Bellonius to be a different species from that of 
Rondeletius. 

Willoughby, who is the first ichthyologist who has given any good descrip- 
tion of fish, treats largely of the ophidium ; and in his account describes the 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 135 

scales, which are, as we shall hereafter explain, oblong, distinct, and disposed 
without any regular order. This description was sufficient to ascertain, that the 
difference between the figures arose from Rondeletius having drawn the scales 
omitted by Bellonius : yet the authors who wrote immediately after Willoughby, 
and particularly Ray in his Synopsis, follow Gesnerus, in maintaining two dif- 
ferent species of cirrata ophidia, one with, the other without, spots. 

Artedi did not take notice of the spots ; he decribes the fish in a genus to 
which he gives the name of ophidion, and places that genus among the Mala- 
copterygii. After him Kleinius once more took notice of the spots ; but at the 
same time introduced another confusion concerning this fish, arising from Ron- 
deletius having said, that it has 2 cirri, while Willoughby asserts it has 4 ; but it 
is easy to reconcile these authors ; for though the ophidium has only 2 cirri, yet 
each of these being divided in 1, they appear as 4 ; so that Willoughby might 
justly say, that it is quadri-cirratus. The same author places the ophidium in a 
genus which he calls enchelyopus, which is indeed not a good family, since it 
comprehends the genera of gymnotus, anarrhichas, cepola, blennius, cobitis, &c. 

Linne, in his description of the ophidium barbatum, says that its whole body 
is covered with oblong spots, without any regular direction. Dr. Gouan, in his 
description of the genus of the ophidium, does not mention the scales ; but 
gives the spots as a generic character. The last author who has mentioned these 
spots, and given a description of this fish, is Mr. Brunniche in his Ichthyologia 
Massiliensis. The genus of ophidium has the following principal characters, 
viz. the body long ; the fins of the back, tail, and anus, confounded in one ; no 
fin on the under part of the body ; and the eyes covered by the common skin. 

Abridged Description of Ophidium Barbatum. — Head compressed, sub-acute, naked, loosely 
covered by the common skin. 

Gape wide ; upper mandible doubled, and rather longer than the lower : lips skinny, thin. 

Teeth, on the margin of both jaws, disposed into a narrow area, wider in front ; minute, sharp, 
thick set, the anterior ones rather larger. 

Tongue sub-obtuse, smooth. 

Palate smooth in the middle, but in front roughened by three areoe of teeth ; the two lateral areae 
of a linear, and die middle of a sub-triangular, form. 

Eyes large, near each other ; situated on the upper part of the head, covered by the common 
skin ; iris silvery, pupil yellowish. 

Cirri or beards two, at the tip of the lower jaw, bipartite, one part longer than the other. Before 
the eyes a covered, recumbent, bony tubercle. 

Body compressed, attenuated towards the tail. 

Lateral line high, smooth, parallel with the back, adorned beneath with a silvery line. 

Scales obovate, covered, umbonated, separate. 

Colour of the head and body silvery flesh-colour. 

Dorsal Jin long, longer but narrower than the anal fin, continued into the tail-fin, dingy white 
at the base, but black at the margin, owing to numerous black points. 

Pectorutjins obovate, pellucid, the membrane freckled or marked by extremely minute spots. 



13(5 PHILOSOPHICAL TUANS ACTIONS. [ANXO 1/81. 

Anal Jin united with the caudal, whitish at the base, black on the margin, furnished with simple 
rays. 

Caudal Jin black, with obtuse tip. 

The scales of the ophidium, which have been figured by Rondeletius, but 
overlooked by many other writers, have been mentioned by Willoughby, but 
without any particular description. They are very different from those on the 
skin of the ophidium imberbe, which are shortly described by Gronovius. Their 
position, as may be seen in the figure, is irregular. They are dispersed over the 
whole body. Their form is sometimes round, sometimes nearly oval. They are 
larger near the head, and in the lower part of the body ; but are hardly to be 
distinguished near the tail. They adhere to the body by means of a particular 
transparent skin, which is in general very thin, but somewhat thicker near the 
neck, and extended loosely over the whole head : this skin is very easily des- 
troyed, after which the scales falling, the body appears spotted (fig. l, pi. 3.) 
These scales are of the same sort as those that Leeuwenhoek has described on 
the eel, like those I have seen on the anarrhichas lupus, the blennius viviparus, 
and many other fishes, which are commonly thought to be without scales. When 
you look at them with the naked eye (fig. 1,) they appear as covered with very 
small grains; but viewed through a microscope (fig. 3,) the middle of them ap- 
pears more elevated than the margin ; and from the centre to the margin, close 
by each other, there are many lines or rays, formed by small scales, placed one 
upon another, like tiles on a roof, the superior being always the nearer to the 
centre. This sort of scales, which may be called umbonatae, are fastened to the 
body by very small vessels inserted in their middle ; they are to be seen on the 
body only, not on the head nor the fins. 

I shall now proceed to the anatomy of this fish, which certainly comprehends 
some very remarkable circumstances, which, I believe, have not yet been ob- 
served in any other species. When we have drawn off" the skin, there appears 
a thin membrane of a silver colour, which covers the muscles. The muscles 
being removed, we find the peritoneum, which lines the abdominal cavity, and 
is adherent to the swimming bladder by some elongations. It is of a silver hue, 
with some very small black points. The ventricle is not to be distinguished from 
the intestines by any other mark but by its size: its form is oblong; it is ex- 
tended almost to the anus, whence the intestinal duct has a retrograde course, 
and then descends again, having a little dilatation near the anus. On the verte- 
bras next the anus, on the outside of the peritoneum, is a kind of cavity of an 
oblong form, containing a reddish viscus, which I take to be the kidney. 

The first vertebra from the head has nothing very remarkable in its structure. 
The 2c\ has on each side an elongated and sharp apophysis, to the apex of which 
is annexed a small ligament. The 3d is very flat, and has on each side a kind of 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 137 

triangular and sharp apophysis, to which adheres a ligament as to the 2d. The 
4th is remarkable in having a sharp apophysis on each side, articulated with the 
body of the vertebra, and under each of them is another articulated apophysis, 
flattish, thick, roundish at its extremities, and forked at its basis (fig. 5.) The 
5th, which is strongly adherent to the former, has in its middle a bifid process. 
The 6th has in its middle a flattish elevation, sharp on each side. Between the 
extremity of the larger apophysis of the 4th vertebra, is a bone, or rather a hard 
cartilage, which bears the figure of a kidney (fig. 6) ; its convexity being turned 
towards the body of the vertebra : its position is parallel to the bodies of the 
vertebrae ; its motion is half circular ; one of its parts, viz. the lowest, being in 
the cavity of the swimming bladder, to which it adheres by a thin membrane, so 
that no air can escape at that part. It is covered by membranes, which adhere 
strongly to its middle ; in this part are fastened the 2 ligaments of the apophy- 
sis of the 2d and 3d vertebrae, of which we spoke before, and which are of a 
greater tenuity. In the same point are fastened also 2 ligaments; each of which 
belongs to an oblong muscle parallel to each other, and fixed to the bones of the 
lowest and posterior part of the head (fig. 4.) 

All this apparatus is certainly subservient to the purpose of swimming, I sup- 
pose, by the cavity of the bladder being made larger or less by the motions of 
the cartilaginous bone; but it is very remarkable, that if these parts are neces- 
sary to some animal function, they should not be found in all the individuals ; for 
I have seen 2, of which the vertebrae were not different from the vertebrae of 
the other species : which difference depends perhaps on the difference of sex. I 
am inclined to believe so ; but the generation in this fish seems to be no less 
mysterious than that of the eel : I could never distinguish a male from a female 
in this species. I do not know if the other species of ophidium have the same 
structure ; I could not perceive it in some specimens of mastacembelus. Wil- 
loughby mentions that singular structure, but without any particular description. 

This fish commonly grows to the size of 8 or 9 inches. It is to be found in 
all the Mediterranean Sea, and in great plenty in the Adriatic. It is taken by 
nets in Provence and Languedoc, with many other small species, which are not 
esteemed, that is, what they call ravailla. It is often confounded with the cepola 
by the fishermen, though they have different names for each species. In Lan- 
guedoc the ophidium is called donzella, and the cepola, flamma. In Provence 
the former has the name of corrudgiao, and the latter that of rougeolla. But 
the name of donzelli, very common on all the coast of the Mediterranean, is 
also applied to the cepola, and the sparus julisLinn. which however is commonly 
called girella. In summer the ophidium is more common : its flesh is not of a 
good taste, rather coarse, as that of all the species of fishes, which having no 
ventral fins, are obliged to make great efforts in swimming, and have conse- 

vol. xv. T 



J38 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

quently the muscles harder. The want of ventral fins induces me to believe, 
that it is not a migratory species. It feeds on small crabs and fishes. 

XXIX. A Further Account of the Usefulness of Washing the Stems of Trees. 
By Mr. Robert Marsham, of Stratton, F. R. S. p. 44Q. 

In the former account, Mr. M. showed how much a beech increased on it s 
stem being cleaned and washed; and in this he shows that the benefit of clean- 
ing the stem continues several years: for the beech which he washed in 1775 
increased in the 5 years after the washing 8-^ inches, or above an inch and 
T V yearly; and the aggregate of 9 unwashed beeches of the same age does not 
amount to 1 inch and T v yearly to each tree. In 1776 Mr. M. washed another 
beech of the same age, viz. seed in 1741; and the increase in 4 years after the 
washing was Q-^- inches, or 2 inches and -^ yearly, when the aggregate of 9 
unwashed beeches amounted to but 1 inch and T \ and a half. In 1770" he 
washed an oak which he planted in 1720, which increased in the 4 years after 
washing 7-^ inches, and the aggregate of 3 oaks planted the same year (viz. all 
he measured) amounted to but 1 inch yearly to each tree. In 177Q Mr. M. 
washed another beech of the same age, and the increase in 178O was 3 inches, 
when the aggregate of 1 5 unwashed beeches was not full 1 5-^v inches, or not 1 
inch and half a tenth to each tree; yet most of these trees grew on better land 
than that which was washed. But Mr. M. apprehends the whole of the extraor- 
dinary increase in the 2 last experiments should not be attributed to washing: 
for in the autumn of 1778 he had greasy pond-mud spread round some favourite 
trees, as far as he supposed their roots extended, and though some trees did not 
show to have received any benefit from the mud, yet others did, that is, an oak 
increased half an inch, and a beech -^, above their ordinary growth. Now 
though the beech gained but -^, yet perhaps that may not be enough 
to allow for the mud; for the summer of 1779 was the most ungenial 
to the growth of trees of any since he had measured them, some not gaining 
half their ordinary growth, and the aggregate increase of all the unwashed and 
unmudded treees that he measured (93 trees in number of various kinds) was in 
1779 but 6 feet 5-j^j- inches, or 77-^ inches, which gives but W and about -J- to 
each tree; when in 1778 (a very dry summer in Norfolk) they increased near 85 
inches, which gives above -^ to each tree: and this summer of 1780 being also 
very dry, yet the aggregate increase was above half an inch more than in 1778. 
But the best increase of these 3 years was low, as there were but 20 of the 93 
trees that there were not planted by Mr. M., and greater increase is reasonably 
expected in young than old trees; yet he had an oak '200 years old in 1780, 
which was 16 feet and 5 inches in circumference, or 197 inches in 200 years. 
But this oak cannot properly be called old. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 13y 

Mr. M, observes, that all the ingredients of vegetation united, which are 
received from the roots, stem, branches, and leaves of a mossy and dirty tree, 
do not produce half the increase that another gains whose stem is clean to the 
head only, and that not 10 feet in height. Is it not clear that this greater share of 
nourishment cannot come from rain ? for the dirty stem will retain the moisture 
longer than when clean, and the nourishment drawn from the roots, and imbibed 
by the branches and leaves, must be the same to both trees. Then must not 
the great share of vegetative ingredients be conveyed in dew ? May not the moss 
and dirt absorb the finest parts of the dew ? and may they not act as a kind of 
screen, and deprive the tree of that share of air and sun which it requires ? 

XXX. On the Use which may be made of the Tables of Natural and Loga- 
rithmic Sines, Tangents, &c. in the Numerical Resolution of Effected Equa- 
tions. By Wm. Wales, F. R. S. p. 454. 

The first intimation met with relating to the use which may be made of the 
tables of sines ? tangents, and secants, in resolving affected equations, is in the latter 
part of the 2d vol. of Prof. Saunderson's Elements of Algebra, printed in 1741, 
after his decease. The professor there shows how to resolve those 2 cases which 
make the 1st and 2d of the following examples, by means of the tables; but it 
appears, from many circumstances, he was not aware that the 3d case could be 
resolved in the same manner. All the 3 forms however were resolved by the late 
Mr. Anthony Thacker, a very ingenious man, who died in the beginning of the 
year 1744, by the help of a set of tables, of his own invention; different from, 
but in some measure analogous to, the tables of sines and tangents. These 
tables were computed and published, with several papers concerning them, after 
his death, by a Mr. Brown, of Cleobury. In these papers, besides explaining 
fully the use of the tables in resolving cubic equations, Mr. Thacker shows that 
his method comprehends the resolution of all biquadratic equations, if they be 
first reduced to cubic ones in the manner which has been explained by Descartes 
and others, and the 2d term then taken away. 

Since that time M. Mauduit has shown how to find the roots of all the 3 
forms of cubic equations, by means of the tables of sines, &c. in his excellent 
Treatise of Trigonometry. But none of these authors have attempted to resolve 
equations of more dimensions than 3, by these means, without first reducing 
them to that number; nor even these, till after the 2d term is taken away: whereas 
such reductions will generally take up more time than is required to bring out 
the value of the unknown quantity by the following method; and, after all, 
frequently serve no other purpose but that of rendering the operation more in- 
tricate and troublesome. 

Mr. Landen, in his lucubrations, published in 1755, has given a general 

T 2 



140 PHILOSOPHICAL TRANSACTIONS. |_ANNO 1/81. 

method of resolving that case of cubic equations, by means of the tables of 
sines, where all the roots are real, without the trouble of taking away the 2d 
term of the equation; and Mr. Simpson has shown how to resolve equations of 
any dimensions, by the same means, provided those equations involve only the 
odd powers of the unknown quantity, and that the co-efficients observe such a 
law as will restrain the equation to that form which is expressive of the cosine of 
the multiple of an arc, of which the unknown quantity is the cosine. This 
was first done, it seems, by John Bernoulli, and afterwards by Mr. Euler, in 
his Introduct. ad Analyt. Infinit. and Mr. de Moivre, in his Miscell. Analyt. ; 
but the resolution of all equations of this form, as well as many others, is com- 
prehended in the first of the following observations. 

The first thought of extending the use of the tables of sines, tangents, and 
secants, beyond the cases which have been already mentioned, occurred while I 
was considering the problem which produced the equation given in this paper as 
the 4th example. And it is remarkable, that the very same thought occurred to 
Dr. Hutton about the same time, and in the resolution of the same problem ; 
and we were not a little surprized, on comparing our solutions together, to find 
that our ideas had taken so exactly the same turn ; and that both should have 
stumbled on a thought, which, as far as either of us knew, had never presented 
itself to any one before. Having since examined further into the matter, I have 
the satisfaction to find, that the principle is very extensive, and that a great 
number of equations, especially such as arise in the practice of geometry, 
astronomy, and optics, may be resolved by it with great ease and expedition. 

But besides the facility with which the value of the unknown quantity is 
brought out by means of the tables of sines, tangents, and secants, this method 
of resolution has another considerable advantage over most others which have 
been proposed, inasmuch as the first state of the equation, without any previous 
reduction, is generally the best it can be in for resolution; and from which it 
may most readily be discovered, how to separate it into such parts as express the 
sine, or the tangent, or the secant of the arc of a circle; or into the sine, tan- 
gent, or secant of some multiple of that arc, or of a part of it: and in the 
doing of which consists the principal part of the business in question. It will 
also be of some advantage to preserve the original substitutions as distinct as 
possible, by using only the signs of the several operations which it may be neces- 
sary to go through in bringing the solution of a problem to an equation, instead 
of performing the operations themselves. 

Besides the advantages which this method of procedure affords to the mode of 
solution now more particularly under consideration, it has so many others over 
that which is commonly used, that I am much surprized the latter should ever 
have been adopted. By preserving thus the original substitutions distinct, all 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 141 

the way through an operation, every expression, even to the final equation, will 
exhibit the whole process up to that step; and it will appear as clearly, how every 
expression has been derived, as it does in that mode of analysis which was used 
by the ancient geometricians; whereas, when the several original expressions 
are melted down as it were into one mass, by the multitude Of actual addi- 
tions, subtractions, multiplications, and divisions, which they generally undergo, 
in a long algebraical process, conducted in the usual manner, it is impossible to 
trace the smallest vsstige of the original quantities in the final equation, except 
such as are represented by a single letter. Of course, however obvious the 
several steps might be at the time when they were taken, every idea of them 
must be totally lost in the result; and it will be utterly impossible to trace them 
back again, in the manner they are done in the composition of a problem, the 
solution of which has been investigated by the geometrical analysis. Let me 
add, that it is to this cause we must attribute all that obscurity which the algebraic 
mode of investigation has been so frequently charged with. 

Mr. W. then sets down, in 6 tables, the analytical expressions or forms of 
the correspondent sines, tangents, and secants of arcs, and their multiples, as 
far as the 6th, each of those being expressed in terms of the others; which tables 
are to serve as formulae or theorems, with which to compare the forms of equa- 
tions, when these occur in practice. 

Observations on the tables. — Each of the formulas in these tables may be con- 
sidered as one side of an equation, involving the unknown quantity x to different 
dimensions. In some of the formulae the odd powers of x are only found, in 
others the even ones alone, and in others both; but they are all equally useful in 
finding the value of the unknown quantity in affected equations which contain all 
the powers of that quantity, as will plainly appear from the following considerations. 

1 . If, on bringing the solution of any problem to an equation with some 
known quantity, it be found to correspond with any of the formulae in these 
tables; or, if by any means it can be reduced to any of them; it is manifest, 
that nothing remains to be done but to divide the known side of the equation by 
the value of the quantity which is here denoted by r, and to seek for the quo- 
tient in the tables of sines, cosines, or tangents, as the case may require, and 
the value of the unknown quantity will be the sine, tangent, secant, or versed 
sine, of a given part of that arc (according as the expression is found in the I st, 
2d, 3d, or 4th table) multiplied by the value of r. 

2. If, as will more frequently happen, the final equation of an operation be 
found equivalent to the sum, difference, product, or quotient, of some 2 or 
more of these formulae; or to the sum, difference, product, or quotient, of some 
2 or more of them multiplied or divided, increased or lessened, by some known 



142 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

quantity or quantities; then, having taken away the known quantities by the 
common algebraic rules, observe the following ones. 

1st. When the equation is found to correspond with the sum or difference of 
2 formulae in these tables, which are the sine and tangent, sine and cosine, or 
cosine and tangent, of the same arc, by running the eye along the tables of 
natural sines and tangents, find these 2 arcs, immediately following each other, 
the sum or difference of the sine and tangent, sine and cosine, or cosine and 
tangent, of which are one of them greater, and the other less, than the number 
which constitutes the known side of the equation. Take the excess of one of 
these sums or differences above, and what the other sum or difference wants of 
the said given number, add these two errors together, and say, as the sum of 
them is to 60", so is that error which belongs to the less arc to a number of 
seconds; which being added to the less arc will give one, the sum or difference of 
whose sine and tangent, sine and cosine, or cosine and tangent, is exactly equal 
to the number which constitutes the known side of the equation. Of the arc, 
thus found, let such a part be taken as the table in which the formula? are found 
directs, and the natural sine, tangent, secant, or versed sine (as the case may 
require) of this part, being multiplied by the value of r, if r be found in the 
equation, will be the value of x sought. 

2d. When the equation happens to be the product or quotient of 2 formulas 
which express the sine and cosine, sine and tangent, or cosine and tangent, of 
the same arc, take the logarithm of the number which constitutes the known 
side of the equation, and then follow exactly the directions given in the first 
case, using the tables of logarithmic sines and tangents, instead of the tables of 
natural ones. 

3d. If the equation, finally resulting from the resolution of any problem, 
present itself in an expression which is composed of the sum or difference of 
the sine, cosine, or tangent, of an arc, of which the unknown quantity is the 
sine, cosine, tangent, or versed sine, and the sine, cosine, or tangent, of some 
multiple of that arc, it will then be convenient to have 2 tables of sines and 
tangents; and in running the eye along them to find the 2 arcs immediately 
following each other, of which the sum or difference of the sine, cosine, or 
tangent, of one of them, and the sine, cosine, or tangent, of some multiple 
of it, may be less, and the sum or difference of the sine, cosine, or tangent, 
of the other, and the sine, cosine, or tangent, of the same multiple of it, may 
be greater than the number which constitutes the known side of the equation, 
for every minute of a degree that the finger is moved over in one, it must be 
moved over a number of minutes in the other, which is equal to the number of 
times that the single arc is contained in the multiple one. When these 2 arcs 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 143 

are found, the operation will not differ so materially from that which is pointed 
out in the first rule as to merit repetition. 

4th. If instead of the sum or difference of the sine, cosine, or tangent, of an 
arc, and the sine, cosine, or tangent, of some multiple of it, the form of 
the equation be such as to be constituted of the product of them, or the quo- 
tient of one divided by the other, the last rule will still hold good, using only 
the logarithmic sines and tangents instead of the natural ones, and comparing 
the sum or difference of them, according as the equation is composed of the 
product or quotient of the 2 factors, with the logarithm of the number which 
constitutes the known side of the equation, instead of that number itself. 

5th. Sometimes the final equation will come out in expressions which are 
constituted of the sum, difference, product, or quotient, of the sine, cosine, 
or tangent, of some multiple of an arc, of which the unknown quantity is the 
sine, tangent, secant, or versed sine, and the sine, cosine, or tangent, of some 
other multiple of the same arc. And in any of these cases it is manifest, that 
the method of proceeding, in order to obtain one of the multiple arcs, and from 
thence the single one, of which the unknown quantity is the sine, tangent, &c. 
will not be greatly different from those which have been described in the 3d and 
4th rules. The most material difference consists in this, that instead of pro- 
ceeding minute by minute, according to the directions in the 3d rule to find the 
single arc, it will now be most convenient to proceed in each table by as many 
minutes at each step as are equal in number to the number of times which the 
single arc is contained in the multiple ones respectively. 

6th. Equations will frequently occur in formulae which express the square, 
cube, &c. of the sine, cosine, or tangent, of the multiple of some arc, of 
which the unknown quantity is the sine, tangent, secant, or versed sine; or in 
formula? which are expressive of the sum, difference, product, &c. of the sine, 
cosine, or tangent, of an arc, and some power of the sine, cosine, or tangent, 
of the same arc; or of some multiple of it, the unknown quantity being some 
other trigonometrical line belonging to that arc. Or the equation may be 
compounded of the sum, difference, product, &c. of the same, or different 
powers of the sines, tangents, or cosines, of different multiples of an arc, the 
unknown quantity being the sine, tangent, secant, or versed sine, of that arc. 
In every one of these cases the tables will give the value of the unknown quan- 
tity, and in most of them with great ease and expedition. The method which 
is to be pursued in each case will readily present itself to a skilful analyst, who 
attends carefully to what has been already said, and to the examples which 
follow. 

4. The formulae in the 4 tables may be greatly varied by supposing x, 
the unknown quantity, to be some part or parts of the sine, tangent, &c. as 



144 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

.i., ^ .»., *., &c. or some multiple of it, as twice, thrice, &c. Or x may be the 
square, or the square root, or any other power of the sine, tangent, secant, or 
versed sine, of an arc; in every one of which cases the formulae will put on dif- 
ferent appearances, either with respect to the powers or co-efficients of the un- 
known quantity, and yet admit ot the same kind of application. 

5. The tables may be rendered yet more extensively useful by inserting ex- 
pressions for the sines, cosines, and tangents, of half the arc which has x for its 
sine, tangent, secant, or versed sine; and also for the sines, cosines, and tan- 
gents, of the odd multiples of this half arc, which expressions, together with 
those already inserted, may be considered as the sines, cosines, and tangents, of 
the multiples of an arc, the unknown quantity being the sine, tangent, &c. of 
twice that arc. And this consideration may sometimes be applied to very useful 
purposes. 

6. In order to render the formulae in the tables more general, I have put r for 
the radius of the circle; whereas it will frequently happen, that the equation, 
finally resulting from the resolution of a problem, especially those which relate 
to the docrine of the sphere, will present itself in a form where the radius must 
be taken equal to unity: what these forms are will readily appear by substituting 
unity for r and its powers every where in the expression. 

Exam- 1 . — Required to find the value of x in an equation of the form x 3 — 
r*x = a. 

If r 2 be expounded by 50, and a by 1 20, the equation may be reduced to 
\/x X "/ (x~ — 50) = ^/ \20; and, consequently, by the tables, if x be consi- 
dered as the secant of an arc, of which the radius is */50, then \/(x 2 — 50) 
will be its tangent, and we shall have to find an arc, such that the tangent mul- 
tiplied by the square root of the secant may be equal to \/l20; or, which 
amounts to the same thing, such an arc that the log. tang, together with half 
the log. secant may be equal to half the log. of 120. But because the tangent 
and secant, here required, are to the radius of the >/ 50, the log. tangents and 
secants in the tables must be increased by the logarithm of that number, and 
therefore log. tang. + + log. 50 + x log. secant -f- J- log. 50 = 4- log. 120: or 
log. tang. + i log. secant = ± log. 120 — f log. of 50. Hence, having taken 
-J- the log. of 50 from i the log. of 120, run the eye along the tables of loga- 
rithmic tangents and secants till an arc be found of which the sum of the log. 
tangent and -i- the log. secant is equal to ig. 7053631, the remainder. In this 
manner it will be readily found, that the sum of the log. tangent and 4. the log. 
secant of 28° 37' is less than that difference by 2012, and that the sum of the 
log. tangent and ~ the log. secant of 28° 38' is greater than it by 1337 : there- 
fore 3349 (2012 + 1337) : 60" :: 2012 : 36". The exact arc therefore, of which 
the sum of the log. tangent and 4 the log. secant is equal to 1 9.765363 1 is 28° 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 145 

37' 36', and the log. secant of it is 10.0566242, which being increased by 
0.8494850, the log. of -/50, gives O.9061092, which is the logarithm of 
8.055810, the value of x sought, and which is true to 7 places of figures. 

Exam. 2. — To find the value of x in the equation x 3 — r 2 x = — a. 

If r be expounded by 3, and a by 10, the equation will be x 3 — Qx = — 10, 
and may be transformed to Vx X V (9 — x~) = V 10; and therefore by the 
tables, the square root of the sine into the cosine of an arc, of which the radius 
is 3, is equal to the square root of 10. Consequently an arc must be found, 
such that the sum of the log. cosine and half the log. sine is equal to half the 
log. of 10. But because the radius of this arc must be 3, the log. sines and 
cosines must be increased by the log. of 3; and therefore log. cos. -f- log. of 3 
+ 4- log. sine + 4- log. of 3 must be equal to half the log. of 10; or, an arc 
must be found of which the sum of the tabular log. cosine and half the log. sine 
is equal to the difference between half the log. of 10 and 14 the log. of 3. 
Hence, having subtracted 14 log. of 3 from half the log. of 10, run the eye 
along Gardiner's tables of logarithmic sines, by which means it will be readily 
found, that the sum of the log. cosine and half the log. sine of 28° 53' 30" is 
less than 197843181, the excess of half the log. of 10 above 14 log. 3, by 15, 
and that the sum of the log. cosine and half the log. sine of 28° 53' 40' / is 
greater than that difference by 60. Consequently 75(15 + 60) : 10" :: 15 : 1", 
The exact arc therefore, of which the sum of the log. cosine and half the log. 
sine is equal to 19.7843181, is 28° 53' 32"; and the log. sine of this arc, in- 
creased by the log. of 3, is 0.1 6 121 53, the logarithm of 1. 44949, the value of 
x required, true to the last place. 

But many equations of this form, and this example among the rest, admit of 
two positive values of the unknown quantity; and by carrying the eye farther 
along the tables it will be found also, that the sum of the log. cosine and half 
the log. sine of 41° 48' 30" is greater than 197843181 by 50, and that the sum 
of the log. cosine and half the log. sine of 41° 48' 40" is too little by 21. Con- 
sequently, 71 (50 + 21) : 10" :: 50 : 7" : of course, 41° 48' 37" is another arc, 
of which the sum of the log. cosine and half the log. sine is equal to 197843181, 
and the log. sine of this arc, increased by the log. of 3, is the logarithm of 
I.999999, another value of x, and which errs but by unity in the 7th place. 

The 3d root, as it is generally called, of this equation, which is necessarily 
negative, and equal to the sum of the other two, belongs properly to the equa- 
tion which is given as the first example, of which it is the affirmative root, and 
may be found by the directions there given. 

Exam. 3. — To find the value of x in the equation a? -\- r*x = a. 

Let us take as examples of this equation x 3 -f 3.r = .04, x 3 -f- 3x = .08, and 
a 3 + 3x = .12, which are 3 of the instances given by Dr. Halley, in his Synopsis 

vol. xv. U 



146 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

of the Astronomy of Comets, to illustrate the mode of computation that he 
pursued in constructing his general table for calculating the place of a comet in 
a parabolic orbit; and it is obvious, a being put for the known side of the equa- 
tion, that it may be transformed to \/ x X \/(3 + x 2 ) = \/ a: where, if x be 
considered as the tangent of an arc, the radius of which is \/3, then \/(3 -\- x 2 ) 
will be the secant of that arc; and consequently, by what is shown in the 1st 
example, an arc must be found such, that the sum of the tabular log. secant and 
half the tabular log. tangent may be equal to the excess of half the log. of a 
above f of the log. of 3. In the first of the above 3 instances this excess will 
be found, 18.943 1891, in the 2d 19.0937041, and in the 3d, 19.1817497; and 
by running the eye along Gardiner's tables of logarithmic sines and tangents, it 
will be found, that the first falls between 0° 26' 20" and 0° 26' 30'', the 2d be- 
tween 0° 52' 50" and 0° 53' 0", and the 3d between 1° 19' 20" and 1° \g' 30"; 
and, by pursuing the mode described in the former 2 examples, the exact arcs 
will be found 0° 26 27"7, 0° 54' 5l"7, and 1° 19' 20".l, and their respective 
tangents, to the radius y/3, .01333248, .02666 1 1, and .0399787, the 3 values 
of x sought. And in this manner Dr. Halley's table may be extended to any 
length with the utmost ease, expedition, and accuracy. 

Thus far this matter has been carried by former writers; but those who may 
be at the trouble of consulting them will find that I have not copied their me- 
thods: on the contrary, these which are given here are more plain and obvious 
than theirs are, and the operations considerably shorter. What follows has not, 
I believe, been adverted to by any before me. 

Exam. 4. — Let the equation arising from the proportion a :b -f- x (l — c 2 ) :: 
c </ (l — x~) "• c^x be taken, which is the result of an inquiry into the situation 
of that place on the surface of the earth, considered as a spheroid, which is at 
the greatest distance from a given one, suppose London. In this inquiry a and 
b were put to represent the sine and cosine of the latitude of the given place, in 
the spheroid; c for •£-§-§-, the ratio of the axes; and x for the sine of the dis- 
tance of the required place from the opposite pole, in the spheroid also. The 
equation, which is of 4 dimensions with all the terms, is manifestly acx = 
[b +x(l — c'")] X V {\ — x 2 ), or — — — - — x . — ^— = -; in which it is 
evident from the tables that the difference between the tangent and the product 
of the sine into a given quantity is known. In order therefore to find the value 
of x, compute — , and , and find the logarithm of the latter. Now because 

the elliptic meridian differs but little from a circle, the place sought will not be 
far from the antipodes of the given one, and its distance from the opposite pole 
may therefore be estimated at 39° 5 ; and, having taken out the natural tangent, 
and logarithmic sine of this arc, add the logarithm of ■ ~ ' ■ to the latter, and find 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 147 

the number corresponding to the sum, which will be less than the natural tan- 
gent of 3Q° 5' by 286p. As this assumption is so near, take 39' 6" for the next, 
repeat the operation, and the result will be 1Q35 too great. Then 4804 (2869 
+ 1935) : 60' 7 :: 2869 : 36'; which being added to 39 5', gives 39 b' 36", for 
the co-latitude of the place sought, and the natural sine of this arc, or .6305856 
is the value of x in this equation. 

To the foregoing Mr. W. adds three other similar examples. 

XXXI. Experiments on the Power that Animals, when placed in certain Cir- 
cumsta?ices, possess of producing Cold. By Adair Craivfbrd, M. D. p. 479. 
The opinions of the ancients, respecting the nature and properties of fire, 
consisted of bold conjectures, which seem rather to have been the offspring of a 
lively and vigorous imagination, than of a just and correct judgment; their ideas 
on this subject being evidently derived, not so much from an accurate observa- 
tion of facts, as from those sentiments of admiration and awe which many of the 
phenomena of fire are calculated to excite. Thus, this element was supposed, 
on the original formation of the universe, to have ascended to the highest place, 
and to have occupied the region of the heavens: it was conceived to be the prin- 
ciple which first communicated life and activity to the animal kingdom: it was 
considered as constituting the essence of inferior intellectual beings; and, by 
many of the ancient nations, it was reverenced as the supreme Deity. Indeed 
the profound veneration with which the element of fire was contemplated, for a 
long succession of ages, by a great part of mankind, appears to be one of the 
most curious circumstances in the history of ancient opinions. To account for 
this we may observe, that there is no principle in nature, obvious to the senses, 
which produces such important effects in the material system, and which, at the 
same time, in the mode of its operation, is so obscure and incomprehensible. 

It appears to be accumulated in an immense quantity in the sun and fixed 
stars, whence its beneficial influence seems to be continually diffused over the 
universe; it is the great instrument by means of which the changes of the sea- 
sons are effected; the diversity of climates is chiefly owing to the various propor- 
tions in which it is distributed throughout the earth. If we add to this the 
mighty alterations which have been produced in human affairs by the introduction 
of artificial fire, by its employment in the separation of metals from their ores, 
and in the various arts which are subservient to the comfort, the ornament, and 
the preservation of the species, it will not appear surprising, that in a rude and 
ignorant age, this wonderful principle should have been considered as endued 
with life and intelligence, and that it should have become the object of religious 
veneration. 

In the dark ages the alchy mists regarded pure fire as the residence of the 

o 2 



148 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

Deity: they conceived it to be uncreated and immense, and attributed to its in- 
fluence most of* the phenomena of* nature. Indeed, it is not wonderful that they 
should have assigned it a high rank in the scale of being, as it was the great 
agent which they employed in the chemical analysis of bodies, and was the in- 
strument of those discoveries that attracted such universal admiration, and that 
enabled them so successfully to impose on the ignorance and credulity of the 
times. 

On the revival of literature, the importance of this branch of science began 
very soon to engage the attention of philosophers. It could not escape the genera, 
observation, in a penetrating and inquisitive age, when the powers of the human 
mind were employed with so much ardour and success in exploring the opera- 
tions of nature, that the element of fire acts a principal part in the system of 
the world; that by the influence of this element those motions are begun and 
supported in the animal and vegetable kingdoms, which are essential to the pro- 
duction and preservation of life; and that it is the great agent in those successive 
combinations and decompositions, by which all things on the surface of the 
earth, and probably throughout the universe, are kept in a continual fluctuation. 

But though the utility of this branch of science was perceived, yet the pro- 
gress that was made in the cultivation of it did not keep pace with the opinion 
which men entertained of its importance. Our senses inform us, that heat has 
a real existence, but they give us no direct information with regard to its nature 
and properties: it is endowed with such infinite subtilty, that it has been called, 
by a very eminent philosopher, an occult quality: by some it has even been con- 
sidered as an immaterial being. It is therefore with great difficulty that it can 
be made the subject of philosophical investigation; and hence the opinions of 
men concerning it have been fluctuating and various, and the words which ex- 
press it vague and ambiguous. The first step that was taken, with a view to the 
cultivation of this branch of* science, was the construction of a machine for 
measuring the variations of sensible heat; observing, that heat has the power of 
expanding bodies, and considering the degree of expansion as proportional to the 
increase of heat, philosophers have endeavoured by means of the former to 
render the latter obvious to the senses. 

To this important invention, the author of which cannot be distinctly traced, 
we are indebted for all the succeeding improvements in the philosophy of heat. 
By means of it men were enabled to establish a variety of interesting facts, and 
to bring some of the most obscure and intricate phenomena of" nature to the 
test of experiment. The opinion, that the heats inherent in various heteroge- 
neous substances differed from each other in kind, as well as in degree, was now 
exploded, since all were found to produce similar effects on the thermometer. 
The increase and diminution of temperature in the different seasons and cli- 



VOL. LXXI.J PHILOSOPHICAL TRANSACTIONS. 1^9 

mates, the laws which nature observes in the heating and cooling of bodies, the 
melting, the vaporific, and shining points, and the degrees of heat in the 
animal, the mineral, and the vegetable kingdoms, were accurately determined. 
In consequence of the attention that was paid to this subject, many curious 
questions arose, which have long exercised the ingenuity of philosophers. That 
property of heat by which it is capable of expanding the densest and hardest 
bodies ; its power in producing fluidity ; its tendency to an equilibrium ; and the 
causes of its various distribution throughout the different substances in nature, 
have become the objects of philosophical inquiry. It was observed, that some 
bodies on exposure to heat, become red and luminous, but are incapable of pro- 
ducing flame, or of maintaining fire : that, on the contrary, others, by the ap- 
lication of fire, and the contact of fresh air, kindle into flame, and continue to 
emit light and heat, apparently from a source within themselves, till they are 
consumed. Hence arose the questions concerning the pabulum of fire, the use 
of the air in inflammation, and the distinction of bodies into combustible and 
incombustible. 

From the first dawnings of philosophy it must have been perceived, that most 
animals have a higher temperature than the medium in which they live ; and that 
a constant succession of fresh air is necessary to the support of animal life. The 
causes of these phenomena have afforded matter for much speculation in ancient 
as well as modern times : but the discovery that animals have, in certain circum- 
stances, the power of keeping themselves at a lower temperature than the sur- 
rounding medium, was reserved for the industry of the present age. This dis- 
covery seems originally to have arisen from observations on the heat of the 
human body in warm climates. It was mentioned by governor Ellis in 1758; 
it was taught by Dr. Cullen before the year 17(35 ; and at length it was com- 
pletely established by the experiments of Dr. Fordyce in heated rooms, which 
were laid before the Society in 1774. 

In the course of these experiments the doctor remained in a moist air heated 
to 130° for the space of 15 minutes, during which time the thermometer under 
his tongue stood at 100°, his pulse made 139 beats in a minute, his respiration 
was but little affected, and streams of water ran down over his whole body, pro- 
ceeding from the condensation of vapour, as evidently appeared from a similar 
condensation on the side of a Florentine flask that had been filled with water at 
100°. He found however, that he could bear a much greater degree of heat 
when the air was dry. In this situation, he frequently supported, naked, for a 
considerable time, without much inconvenience, the heat of 260°, his body pre- 
serving very nearly its proper temperature, being never raised more than 2° 
above the natural standard. 

Various opinions have been entertained with regard to the causes of the facts 



150 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

which were established by these experiments. Some have attributed the cold 
solely to evaporation, and have conceived that the same degree of refrigeration 
would have been produced by an equal mass of dead matter, containing an equal 
quantity of moisture. Others have affirmed, that the cold did not arise solely 
from this cause; but have maintained, that it depended partly on the energy of 
the vital principle, being greater than what would have been produced by an 
equal mass of inanimate matter. The ingenious Dr. Munro, of Edinburgh, 
ascribes the cold in the above-mentioned experiments to the circulation of the 
blood, in consequence of which the warmer fluids are continually propelled from 
the surface towards the centre, where they are mixed with blood at a lower tem- 
perature, and hence the animal is slowly heated, in the same manner as the 
water in a deep lake, during the winter, is slowly cooled, and not without a long 
continuance of frost congealed, no part of it becoming solid till the whole is 
brought down to the freezing point. 

The following experiments were made with a view to determine with greater 
certainty the causes of the refrigeration in the above instances. To discover 
whether the cold produced by a living animal, placed in air hotter than its 
body, be not greater than what would be produced by an equal mass of in- 
animate matter, Dr. C. took a living and a dead frog, equally moist, and of 
nearly the same bulk, the former of which was 
at 67°, the latter at 68°, and laid them on In \ 
flannel in air which had been raised to 106°. 
In the course of 25 minutes the order of heat- 
ing was as annexed.* 

The thermometer being introduced into the stomach, the internal heat of the 
animals was found to be the same with that at the surface. Hence it appears, 
that the living frog acquired heat more slowly than the dead one. Its vital 
powers must therefore have been active in the generation of cold. 

To determine whether the cold produced in 
this instance depended solely on the evapora- 
tion from the surface, increased by the energy 
of the vital principle, a living and dead frog 
were taken at 75°, and were immersed in water 
at Q3°, the living frog being placed in such a 
situation as not to interrupt respiration. -j~ 

These experiments prove, that living frogs have the faculty of resisting heat, 

* In the two following experiments the thermometers were placed in contact with the skin of the 
animals under the axillae. — Orig. 

-j- In the above experiment the water, by the cold frogs and by the agitation which it suffered during 
their immersion, was reduced nearly to yi"j. — Orig. 



Min. 


Air. 


Dead frog. 


Living frog. 


1 





70i° 


67 J 


2 


102 


72 


68 


3 


100 


m 


691 


4 


100 


73 


70 


25 


95 


8l£ 


7S| 



Min. 


Dead Prog. 


laving frog. 


1 


85 u 


81° 


2 


88* 


85 


3 


90£ 


87 


5 


91* 


sy 


6 


91J 


89 


8 


9U 


89 



VOL. LX.XI.] PHILOSOPHICAL TRANSACTIONS. 151 

or producing cold, when immersed in warm water : and the experiments of Dr. 
Fordyce prove, that the human body has the same power in a moist as well as in 
a dry air : it is therefore highly probable, that this power does not depend solely 
on evaporation. 

It may not be improper here to observe, that healthy frogs, in an atmosphere 
above 70°, keep themselves at a lower temperature than the external air, but are 
warmer internally than at the surface of their bodies : for when the air was 77°, 
a frog was found to be 68°, the thermometer being placed in contact with the 
skin ; but when the thermometer was introduced into the stomach, it rose to 
70°4-. It mav also be proper to mention, that an animal of the same species 
placed in water at 6l°, was found to be nearly 6l°J- at the surface, and internally 
it was 66°-±-. These observations are meant to extend only to frogs living in air 
or water at the common temperature of the atmosphere in summer. They do 
not hold with respect to those animals, when plunged suddenly into a warm 
medium, as in the preceding experiments. 

To determine whether other animals also have the power of producing cold, 

when surrounded with water above the standard of their natural heat, a dog at 

102° was immersed in water at 1 14°, the thermometer being closely applied to 

the skin under the axilla, and so much of his head being uncovered as to allow 

him a free respiration. 

In 5 minutes the dog was 108°, water 112° 

6 10.9 112 

11 1 OS 112 the respiration having become very rapid. 

13 108 112 the respiration being still more rapid. 

30 109 112 the animal then in a very languid state. 

Small quantities of blood being drawn from the femoral artery, and from a 
contiguous vein, the temperature did not seem to be much increased above the 
natural standard, and the sensible heat of the former appeared to be nearly the 
same with that of the latter. 

In this experiment a remarkable change was produced in the appearance of 
the venous blood : for it is well known, that in the natural state, the colour of 
the venous blood is a dark red, that of the arterial being light and florid ; but 
after the animal, in the experiment in question, had been immersed in warm 
water for half an hour, the venous blood assumed very nearly the hue of the 
arterial, and resembled it so much in appearance, that it was difficult to distin- 
guish between them. It is proper to observe, that the animal which was the 
subject of this experiment, had been previously weakened by losing a consider- 
able quantity of blood a few days before. When the experiment was repeated 
with dogs which had not suffered a similar evacuation, the change in the colour 
of the venous blood was more gradual ; but in every instance in which the trial 
was made, and it was repeated 6 times, the alteration was so remarkable, that 



152 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 

the blood which was taken in the warm bath could readily be distinguished from 
that which had been taken from the same vein before immersion, by those who 
were unacquainted with the motives or circumstances of the experiment. 

To discover whether a similar change would be produced in the colour of the 
venous blood in hot air, a dog at 102° was placed in air at 134°. In 10 minutes 
the temperature of the dog was 104% that of the air being 130°. In 15 mi- 
nutes the dog was 106°, the air 130°. A small quantity of blood was then 
taken from the jugular vein, the colour of which was sensibly altered, being 
much lighter than in the natural state. The effect produced by external heat on 
the colour of the venous blood, seems to confirm the following opinion, which 
was first suggested by my worthy and ingenious friend Mr. Wilson, of Glasgow. 
Admitting that the sensible heat of animals depends on the separation of abso- 
lute heat from the blood by means of its union with the phlogistic principle in 
the minute vessels, may there not be a certain temperature at which that fluid is 
no longer capable of combining with phlogiston, and at which it must of course 
cease to give off heat ? It was partly with a view to investigate the truth of this 
opinion that Dr. C. was led to make the experiments recited above. 

I shall now endeavour, (says Dr. C.) from the preceding facts, to explain what ap- 
pear to me to be the true causes of the cold produced by animals when placed in a 
medium, the temperature of which is above the standard of their natural heat. 
In a work which I some time since laid before the public, having attempted to 
prove, that animal heat depends on the separation of elementary fire from the 
air in the process of respiration, I observed, thaf when an animal is placed in a 
warm medium, if the evaporation from the lungs be increased to a certain de- 
gree, the whole of the heat separated from the air will be absorbed by the 
aqueous vapour. From the experiments on venous and arterial blood, recited in 
the 3d section of that work, it appears, that the capacity of the blood for con- 
taining heat is so much augmented in the lungs, that, if its temperature were 
not supported by the heat which is separated from the air, in the process of res- 
piration, it would sink 30°. Hence, if the evaporation from the lungs be so 
much increased as to carry off the whole of the heat that is detached from the 
air the arterial blood when it returns by the pulmonary vein will have its sensible 
heat greatly diminished, and will consequently absorb heat from the vessels 
which are in contact with it, and from the parts adjacent. The heat which is 
thus absorbed in the greater vessels will again be extricated in the capillaries, 
where the blood receives a fresh addition of phlogiston. If, in these circum- 
stances, the blood during each revolution were to be equally impregnated with 
this latter principle, it is manifest, that the whole effect of the above process 
would be to cool the system at the centre, and to heat it at the surface ; or to 
convey the heat to that part of the body where it is capable of being instantly 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 153 

carried off by evaporation. But it appears, from the experiments which have 
been last recited, that when an animal is placed in a heated medium, the san- 
guineous mass, during each revolution, is less impregnated with phlogiston ; for 
we have seen, that the venous blood, in these circumstances, becomes gradually 
paler and paler in its colour, till at length it acquires very nearly the appearance 
of the arterial : and it is rendered highly probable by the experiments of Dr. 
Priestley, that the dark, and livid colour of the blood in the veins depends on 
its combination with phlogiston in the minute vessels. Since therefore, in a 
heated medium, this fluid does not assume the same livid hue, we may conclude, 
that it does not attract an equal quantity of the phlogistic principle.* 

It follows, that the quantity of heat given off by the blood in the capillaries 
will not be equal to that which it had absorbed in the greater vessels, or positive 
cold will be produced. If the blood, for example, in its passage to the capil- 
laries, absorb from the greater vessels, a quantity of heat as 30°, and if, incon- 
sequence of its receiving a less impregnation of phlogiston than formerly, it give 
off at the extreme vessels a quantity of heat only as 20°, it is manifest, that on 
the whole a degree of refrigeration will be produced as 10°, and this cause of re- 
frigeration will continue to act while the venous blood is gradually assuming the 
hue of the arterial, till the difference between them is obliterated ; after which it 
will cease to operate. Thus it appears, that when animals are placed in a warm 
medium, the same process which formerly supplied them with heat becomes for 
a time the instrument of producing cold, and probably preserves them from 
such rapid alterations of temperature as might be fatal to life. 

On the whole, the increased evaporation, the diminution of that power by 
which the blood in the natural state is impregnated with phlogiston, and the 
constant reflux of the heated fluids towards the internal parts, seem to be the 
great causes on which the refrigeration depends. Having found that the attrac- 
tion of the blood to phlogiston was diminished by heat, it appeared probable, on 
the other hand, that it would be increased by cold. To determine this, a dog at 
100° was immersed in water nearly at 45°. In about a quarter of an hour a 
small quantity of blood was taken from the jugular vein, which was evidently 
much deeper in its colour than that which had been taken in the warm bath, and 

* It is of no consequence in the above argument, whether we suppose, with Dr. Priestley, that 
the alteration of colour in the blood depends on its combination witli phlogiston in the capillary arte- 
ries, or maintain with some other philosophers that this alteration arises from a change produced in 
the blood itself by the action of the vessels ; it is sufficient for our purpose to assume it as a fact, 
which, I think, has been proved by direct experiment, that, in the natural state of the animal, the 
blood undergoes a change in the capillaries, by which its capacity for containing heat is diminished ; 
and that in a heated medium it does not undergo a similar change. — Orig. 

VOL. XV. X 



154 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/8 1 . 

appeared to me, as well as to several other gentlemen, to be the darkest venous 
blood we had ever seen. 

From this experiment, compared with those which have been recited before, 
we may perceive the reason why animals preserve an equal temperature, notwith- 
standing the great variations in the heat of the atmosphere, arising from the 
vicissitudes of the weather, and the difference of season and climate : for, as 
soon as, by exposure to external cold, an unusual dissipation of the vital heat is 
produce!, the blood, in the course of the circulation, begins to be more deeply 
impregnated with the phlogistic principle. It will therefore furnish a more 
copious supply of this principle to the air in the lungs, and will imbibe a greater 
quantity of fire in return. In summer, on the contrary, the reverse of this will 
take place, less phlogiston will be attracted in the minute vessels, and less fire 
will be absorbed from the air. And hence the power of generating heat is in all 
cases proportioned to the demand. It is increased by the winter colds, dimi- 
nished by the summer heats : it is totally suspended or converted into a contrary 
power, as the exigencies of the animal may require. From the changes which 
are produced in the colour of the venous blood by heat and cold, we may also 
perceive the reason why the temperature of the body is frequently increased by 
plunging suddenly into cold water, and why the warm bath has such powerful 
effects in cooling the system, and in removing a general or partial tendency to 
inflammation. 

XXXII. Account of a Comet. By Mr. Herschel, F. R. S. p. 492. 
On Tuesday the 13th of March, 1781, between 10 and 11 in the evening, 
while examining the small stars in the neighbourhood of H Geminorum, I per- 
ceived one that appeared visibly larger than the rest : being struck with its un- 
common magnitude, I compared it to H Geminorum and the small star in the 
quartile between Auriga and Gemini, and finding it so much larger than either 
of them, suspected it to be a comet. I was then engaged in a series of obser- 
vations on the parallax of the fixed stars, which I hope soon to have the honour 
of laying before the r. s. ; and those observations requiring very high powers, I 
had ready at hand the several magnifiers of 227, 400, 932, 1530, 2010, &c. all 
which I have successfully used on that occasion. The power I had on when 1 
first saw the comQt was 227. From experience I knew that the diameters of the 
fixed stars are not proportionally magnified with higher powers, as the planets 
are ; I therefore now put on the.powers of^46o and y32, and found the diameter 
of the comet increased in proportion to the power, as it ought to be, on a sup- 
position of its not being a fixed star, while the diameters of the stars to which I 
compared it, were not increased in the same ratio. Also, the comet being mag- 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 155 

nified much beyond what its light would admit of, appeared hazy and ill-defined 
with these great powers, while the stars preserved that lustre and distinctness 
which from many thousand observations I knew they would retain. The sequel 
has shown that my surmises were well founded, this proving to be the comet we 
have lately observed. 

Mr. H. reduced all his observations on this comet to 3 tables. The first con- 
tains the measures of the gradual increase of the comet's diameter. The mi- 
crometers he used, when every circumstance is favourable, will measure ex- 
tremely small angles, such as do not exceed a few seconds, true to 6, 8, or 10 
thirds at most ; and in the worst situations true to 20 or 30 thirds : he therefore 
gave the measures of the comet's diameter in seconds and thirds. The first 
table, containing the measures of the comet's diameter, shows that, from March 
17 till April 18, the apparent diameter increased from 1" 53'" to 5" 20'". 

The 2d table contains the comet's distances from several telescopic fixed stars, 
from March 1 3 till April 1 g, and those distances expressed in minutes, seconds, 
and thirds. And the 3d table contains the comet's angle of position with regard 
to the parallel of declination of the same stars measured by a micrometer ; by 
which means its places and apparent path might be determined. 

Description of a Micrometer for taking the Angle of Position. By Mr. JVm. 

Herschel,' of Bath. p. 500. 

Fig. 7, pi. 3, represents the micrometer inclosed in a turned case of wood, as 
it is put together, ready to be used with the telescope, a is a little box which 
holds the eye-glass, b is the piece which covers the inside work, and the box a 
is screwed into it. c is the body of the micrometer containing the brass work, 
showing the index plate a projecting at one side, where the case is cut away to 
receive it. d is a piece, having a screw b at the bottom, by means of which the 
micrometer is fastened to the telescope. To the piece c is given a circular mo- 
tion, in the manner the horizontal motion is generally given to Gregorian re- 
flectors, by the lower part going through the piece d, where it is held by the 
screw e, which keeps the two pieces c and d together, but leaves them at liberty 
to turn on each other. 

Fig. 8, is a section of the case containing the brass work, where may be ob- 
served the piece b hollowed out to receive the box a, which consists of 2 parts 
inclosing the eye lens. This figure also shows how the piece c passes through d, 
and is held by the ring e : the brass work, consisting of a hollow cylinder, a 
wheel and pinion, and index plate, is there represented in its place, f is the 
body of the brass work, being a hollow cylinder with a broad rim c at the upper 
end ; this rim is partly turned away to make a bed for the- wheel d. The pinion 
e turns the wheel d, and carries the index plate a. One of its pivots moves in 

x 2 



156 PHILOSOPHICAL TRANSACTIONS. [_ANNO 1781. 

the arm f, screwed on the upper part of c, which arm serves also to confine the 
wheel d to its place on c. The other pivot is held by the arm g fastened to f. 

Fig. g, is a plan of the brass work. The wheel d, which is in the form of a 
ring, is laid on the upper part of p or c, and held by 2 small arms f and h, 
screwed down to e with the screws i, i. 

Fig. 10 is a plan of the brass work ; d, d, is the wheel placed on the bed or 
socket of the rim of the cylinder c, c, and is held down by the two pieces f, h, 
which are screwed on c, c. The piece f projects over the centre of the index 
plate to receive the upper pivot of the pinion ra, n, the fixed wire fastened to 
c, c. o, p, the moveable wire fastened to the annular wheel d, d. The index 
plate a is divided into 60 parts, each sub-divided into 2, and milled on the edge. 
When the finger is drawn over the milled edge of the index plate from q to- 
wards r, the angle mso, will open, and if drawn from r towards q, it will shut 
again. The case c, c, must have a sharp corner t, which serves as a hand to 
point out the division on the index plate. 

XXXIII. Concerning the Longitude of Cambridge in New Engkmd. By Mr. 

Joseph Hit lard. p. 502. 
The difference of meridians between Greenwich and Cambridge has been 
generally reckoned 4 h 44 m . This was what the late Dr. Winthrop made use of; 
but I do not find that he determined it by actual observations, made by him at 
Cambridge, compared with corresponding ones, made at the Royal Observatory 
at Greenwich. It appears, that in 176Q, at the time of the transit of Venus, 
the doctor was not quite certain of the longitude of Cambridge. He mentioned 
4 h 44 m as near the truth ; but for better fixing it, he gave several of his obser- 
vations of the eclipses of Jupiter's satellites to be compared with those made at 
Greenwich ; but there were too few corresponding ones to determine the point 
with precision ; and as modern astronomers do not place absolute dependence on 
the difference of meridians deduced from the eclipses of Jupiter's satellites, 
unless there has been a series of observations, both of immersions and emer- 
sions, I have wished to find some observations of solar eclipses and occultations 
of fixed stars by the moon, made at Cambridge, of which corresponding ones 
were made at Greenwich. I have met with no observations of occultations made 
by Dr. Winthrop ; but a solar eclipse was observed by him and several other 
gentlemen, at his house, August 5, 176Q, at which I was present and assisting, 
being then a resident graduate at Harvard College : this eclipse I find was ob- 
served at Greenwich, where the beginning of the eclipse was seen at 5 h 2Q m 56 s 
p. m. and the end at 7 h ll m 27 s p. m. apparent time. At Dr. Winthrop's house 
at Cambridge, lat. 42° 25' n. the beginning of this eclipse was observed at 
ll h 39 m 23 s A. M. and the end at 2 h 45 m 9 s P. m. apparent time. Allowing for 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 157 

the spheroidal figure of the earth, and going through the parallactic calculations 
and deductions, I find the difference of meridians between Greenwich and Cam- 
bridge, by the observations of this eclipse, to be 4 h 44 m 22 s . 

In the transit of Venus, in 1769, the internal contact was observed by Dr. 
Winthrop at 2 h 47 m 30 s apparent • time, and at the Royal Observatory, at 
7 h 28 m 57 s apparent time. Allowing the sun's parallax on the day of the transit 
to be 8".38, I find by calculation from these observations, that the difference of 
meridians between Greenwich and Cambridge is 4 1 ' 44 m 1 2 s . Taking the mean 
between the deduction made from the observations of the internal contact of 
Venus, and of the beginning and ending of the above solar eclipse, the differ- 
ence of meridians between Greenwich and Cambridge is 4 h 44 m 17 s . This is 
the difference that I at present take, when I make use of tables fitted to the 
meridian of Greenwich ; but I should be still glad of more corresponding obser- 
vations to ascertain this point. 

Some Thermometrical Experiments ; containing, 1 . Experiments relating to the 
Cold produced by the Evaporation of various Fluids, ivith a Method of Purify- 
ing jEther. 2. Experiments relating to the Expansion of Mercury. 3. Des- 
cription of a Thermometrical Barometer. By Tiberius Cavallo, F. R. S. 
Nominated to prosecute Discoveries in Nat. Hist, pursuant to the Will of the 
late H. Baker, Esq., F. R. S. p. 500. 

] . On the cold produced by the evaporation of fluids, with a method of purify- 
ing cether. — It is at present well known, that by the evaporation of various fluids 
a sensible * degree of cold is produced; and that by the evaporation of aether, 
which is the most volatile fluid we are acquainted with, water may be congealed, 
and the thermometer may be brought several degrees below the freezing point. 
But as various thermometrical experiments, which I lately made, have exhibited 
some new phenomena, and as I have contrived an easy and pleasing method of 
freezing a small quantity of water in a short time, and in every climate ; I think 
it not improper to give an account of these things in the first part of this 
lecture. 

My first experiments were intended to discover, if possible, a fluid cheaper 
than aether, by the evaporation of which a degree of cold sufficient for some 
useful purpose might be generated. B„ut in this my expectation was disappointed, 
as I found that aether was incomparably superior to any other fluid, as the cold 
it produced was several degrees greater than that occasioned by any other of the 
most volatile fluids whatever. Being therefore obliged to use aether, I endea- 
voured to contrive a method, by which the least possible quantity of it might be 
wasted in the production of a degree of cold sufficient to freeze water, and in 
this I met with success. But before we come to the description of this method 



158 PHILOSOPHICAL TRANSACTIONS. [ANN0 1781. 

I shall briefly relate some observations made on the cold produced by the evapo- 
ration of other fluids besides asther. 

In a room, the temperature of which was 64° according to Fahrenheit's ther- 
mometer, and in which the air was gently ventilated, I observed the effects pro- 
duced by various fluids when thrown upon the ball of a thermometer. The ball 
of this thermometer was quite detached from the ivory piece on which the scale 
was engraved. The various fluids were thrown on the thermometer through the 
capillary aperture of a small glass vessel, shaped like a funnel, and care was 
taken to throw them so slowly upon the bulb of the thermometer, that a drop 
might now and then fall from the under part of it ; except when those fluids 
were used, which evaporate very slowly, in which case it was sufficient to keep 
the ball of the thermometer only moist, without any drop falling from it. 
During the experiment the thermometer was kept turning very gently round its 
axis, in order that the fluid used might fall on every part of its bulb. This 
method I find to answer much better than that of dipping the ball of the ther- 
mometer into the fluid and removing it immediately after, or that of wetting the 
thermometer with a feather. The evaporation, and consequently the cold pro- 
duced by it, may be increased by ventilation, viz. by blowing with a pair of 
bellows on the thermometer ; but this was not used in the following experiments, 
because it is not easily performed by one person, and also because it occasions 
very uncertain results. 

With the above described method I began to examine the effects of water, 
and found, that the thermometer was brought down to 56°, viz, 8° below the 
temperature of the room in which the experiment was made, and of the water 
employed. This effect was produced in about 1 minutes time, after which a 
longer continuation did not bring the mercury lower. By means of spirit of 
wine the thermometer was brought down to 48°, which is only l6° below the 
temperature of the room, and of the spirit employed. When the spirit of wine 
is highly rectified, the cold produced by its evaporation is certainly greater than 
when it is of the common sort ; but the difference is not so great as one, who 
never tried the experiment, might expect. The. purer spirit produces the effect 
much quicker. Using various other fluids, which were either compounds of 
water and spirituous substances, or pure essences, I found that the* cold pro- 
duced by their evaporation was generally in some intermediate degree between 
the cold produced by the water and that produced by the spirit of wine. Spirit 
of turpentine brought the thermometer only 3° lower than the temperature of 
the room ; but olive oil and other oils, which evaporate either very slowly or not 
at all, did not sensibly affect the thermometer. 

Wishing to observe how much electrization could increase the evaporation of 
spirit of wine, and consequently the cold produced by it, I put the tube contain- 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 159 

ing the spirit into an insulating handle, and connected it with the conductor of 
an electrical machine, which was kept in action while the experiment was per- 
formed ; by these means the thermometer was brought down to 47°. Having 
tried the 3 mineral acids, I found that instead of cooling they heated the ther- 
mometer, which effect I expected ; since it is well known, that those acids at- 
tract the water from the atmosphere, and that heat is produced by the combina- 
tion of water and any of them. The vitriolic acid, which was very strong and 
transparent, raised the thermometer to 102°; the smoking nitrous acid raised it 
to 72°; and the marine acid raised it to 66°; the temperature of the room, as 
well as of the acids, being 64°, as mentioned above. 

The apparatus which I contrived for the purpose of using the least possible 
quantity of aether in freezing water, &c. consists in a glass tube, terminating in 
a capillary aperture, which tube is to be fixed on the bottle that contains the 
aether. Fig. 11, pi. 3, exhibits such a tube, round the lower part of which, at 
a, some thread is wound, to make it fit the neck of the bottle. When the ex- 
periment is to be made, the stopper of the bottle containing the aether is re- 
moved, and the above-mentioned tube is fixed on it. The thread round this 
tube should be moistened a little with water or spittle before it is fixed on the 
bottle, to prevent more effectually any escape of aether between the neck of the 
bottle and the tube. Then holding the bottle by its bottom fg, fig. 12, and 
keeping it inclined as in the figure, the small stream of aether issuing out of the 
aperture d of the tube de, is directed on the ball of the thermometer, or on a 
tube containing water or other liquor required to be congealed. 

^Ether being very volatile, and having the remarkable property of increasing 
the bulk of air, does not require any aperture, through which the air might 
enter the bottle, in proportion as the aether goes out : the heat of the hand is 
more than sufficient to force the aether in a stream from the aperture d. After 
this manner, throwing the stream of aether on the ball of a thermometer in such 
quantity as that a drop of aether might now and then, for instance every 10 
seconds, fall from the under part of the thermometer, I have brought the mer- 
cury down to 3°, viz. 2Q° below the freezing point, when the atmosphere was 
somewhat hotter than temperate, and that without blowing on the thermome- 
ter. When the aether is very good, viz. is capable of dissolving elastic gum, 
and the thermometer has a small bulb, not above 20 drops of aether are required 
to produce this effect, and about 2 minutes of time ; but when the aether is of 
the common sort, a greater quantity of it, and a longer time, are necessary to be 
employed, though at last the thermometer is brought down very nearly as low 
by this as by the best sort of aether. 

To freeze water by the evaporation of aether, I take a thin glass tube about 4 
inches long, and about -i- of an inch in diameter, hermetically closed at one end,, 



l60 PHILOSOPHICAL TKANS ACTIONS. [ANNO 1781. 

and put a little water in it, so as to fill about half an inch length of it, as is 
shown at cb in the figure. Into this tube a slender wire h is also introduced, 
the lower extremity of which is twisted in a spiral manner, and serves to draw 
up the ice, when formed. Things being thus prepared, I hold the glass tube by 
its upper part a with the fingers of the left hand, and keep it continually and 
gently turning round its axis, first one way, and then the contrary; while with 
the right hand I hold the phial containing the tether in such a manner as to direct 
the stream of aether on the outside of the tube, and a little above the surface of 
the water in it. The capillary aperture d should be kept almost in contact with 
the surface of the tube that contains the water. Continuing this operation for 2 
or 3 minutes, the water will be frozen as it were in an instant ; since it will ap- 
pear to become opaque at the bottom b, and the opacity will ascend to c in less 
than half a second of time, which exhibits a beautiful appearance. This con- 
gelation, however, is only superficial, and in order to congeal the whole quan- 
tity of water, the operation must be continued a minute or 2 longer; after 
which the wire h will be found to be kept very tight by the ice. Now the 
bottle with the aether is left on a table or other place, and to the outside of the 
glass tube the hand must be applied for a moment, to soften the surface of the 
ice, which adheres very firmly to the glass, and then pulling the wire h out of 
the tube, a solid and hard piece of ice will come out, fastened to its spiral 
extremity. 

Instead of the wire h sometimes I put a small thermometer into this tube, so 
as to have its bulb immersed in the water. With this thermometer I have ob- 
served a very remarkable phenomenon, which seems to be not explicable in the 
present state of knowledge concerning heat and cold. This is, that water will 
freeze in the winter with a less degree of cold than it will in the summer, or 
when the weather is hotter : for instance, in the winter the water in the tube ab 
will freeze when the thermometer is about 30° ; but in the summer, or even 
when the temperature of the atmosphere is about 6o°, the quicksilver in the 
thermometer must be brought 10 or 15, or even more, degrees below the freez- 
ing point, before the water which surrounds the said thermometer will be con- 
verted into ice, even superficially ; hence it appears, that in the summer time a 
greater quantity of aether and longer time are required to freeze a given quantity 
of water, than in the winter ; not only because then a greater degree of heat is 
to be overcome, but principally because in the summer a much greater degree of 
cold must be actually produced before the water that is kept in it will assume a 
solid form. When the temperature of the atmosphere has been about 40°, I 
have frozen a quantity of water with an equal weight of good tether, but at pre- 
sent, being summer, between 2 and 3 times the quantity of the same tether must 
be used to produce the same effect. 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. J 6 1 

The proportion between the quantity of the ether and of the water that ma)' 
be frozen by it, seems to vary according to the quantity of water; for a larger 
quantity of water seems to require a proportionably less quantity of ether than a 
smaller quantity of water, supposing that the water is contained in cylindrical 
glass vessels; for I have not tried whether a metal vessel instead of a glass one, 
and whether some other shape besides the cylindrical, might not facilitate the 
congelation. In the beginning of the spring I froze about a quarter of an ounce 
of water with nearly half an ounce weight of ether, the apparatus being larger, 
though similar to that described above. Now as the price of ether, sufficiently 
good for the purpose, is generally between 18 pence and 2 shillings per ounce, 
it is plain, that with less than 2 shillings a quarter of an ounce of ice, or ice 
cream, may be made in every climate, and at any time; which may afford great 
satisfaction to those persons who, living in places where no natural ice is to be 
had, never saw or tasted any such delicious refreshments. 

When a small piece of ice, for instance, of about 10 grains in weight, is 
wanted, the necessary apparatus is very small, and the expense of the ether not 
worth mentioning. I have a small box, which is 4-L inches long, 2 inches 
broad, and 1-^ inch deep, which contains all the apparatus necessary for this pur- 
pose, viz. a bottle capable of containing about 1 ounce of ether, 2 pointed tubes, 
in case that one should break, a tube in which the water is to be frozen, and 
the wire. With the quantity of ether contained in this small and very portable 
apparatus, the experiment, when carefully performed, may be repeated about 10 
times. A person who wishes to perform such experiments in hot climates, and 
in places where ice is not easily procured, requires only a large bottle of ether, 
besides the small apparatus described above. 

It is a known fact, that the moment a quantity of water becomes ice, a ther- 
mometer kept immersed in it, rises a few degrees, and accordingly this is observed 
in our experiment, viz. the mercury of the thermometer, which is immersed in 
the water of the tube ab, will suddenly rise, sometimes as much as 10 degrees, 
when the water becomes first opaque. Electrization increases very little the de- 
gree of cold produced by the evaporation of ether. Having thrown the electri- 
fied and also the unelectrified steam of ether on the bulb of a thermometer, 
the mercury in it was brought down 2 degrees lower in the former than in the 

latter case. 

As various persons may, perhaps, be induced by this paper to repeat such ex- 
periments, and as ether is a fluid which can with difficulty be preserved, it may 
be useful to mention, that a cork confines ether in a glass bottle much better 
than a glass stopple, which it is almost impossible to grind so well as entirely to 
prevent the evaporation of ether. When a stopple, made very nicely out of a 
uniform and close piece of cork, which goes rather tight, is put on a bottle of 

vol xv. Tt 



\Ql PHILOSOPHICAL TRANSACTIONS. [ANNOI78I. 

ether, the smell of that fluid cannot be perceived through it ; but I never saw a 
glass stopple that could produce the same effect. By opening the bottle very 
often, or by long keeping, the cork becomes loose, in which case it must be 
changed; and thus ether, spirit of wine, or any fluid, excepting those which 
corrode cork, may be preserved. 

I shall now describe a method of purifying vitriolic ether, which is very easy 
and expeditious, though not very profitable: this method I learned of Mr. 
Winch, Chemist, in the Haymarket. Fill about a quarter of a strong bottle 
with common ether, and on it pour about twice as much water, then stop the 
bottle, and give it a shake, so as to mix for a time the ether with the water. 
This done, keep the bottle without motion, and with the mouth downwards, till 
the ether is separated from the water and swims over it, which requires not above 
3 or 4 minutes of time; then open the bottle, and keeping it still inverted, let 
the greatest part of the water come out very gently; after this the bottle being 
turned with the mouth upwards, more water must be poured in it, and in short 
the same operation must be repeated 3 or 4 times. Lastly, all the water being 
separated from the ether by decanting it with dexterity, the ether will be found 
to be exceedingly pure. By this means I have purified common vitriolic ether, 
which could not affect elastic gum, and have reduced it into such a state as that 
elastic gum was easily dissolved by it. Indeed this purified ether appeared by 
every trial to be purer than I ever saw it, even when made after the best usual 
method, and in the most careful manner. The only inconvenience attending 
the process is, that a vast quantity of ether is lost. Not above 3 or 4 ounces of 
a pound of common ether remain after the purification. As the greatest part of 
the ether is certainly mixed with the water that is used in the process, it may 
perhaps be worth while to put that water into a retort, and to distil the ether 
from it, which must come sufficiently pure for common use. It is commonly 
believed, that water combines with the purest part of ether, when those 2 fluids 
are kept together; whereas, by the above described process, the contrary is esta- 
blished; perhaps when ether is kept in contact with water for a long time, the 
purest part of it may appear to be lost, because the ether may be combined with, 
and may retain some water in itself, at the same time that the water combines 
with and retains some ether; whereas the case may be different when the ether 
is quickly washed in water, and is immediately after separated from it: but in 
respect to this I have not yet made any experiments, so as to be able to decide 
the matter. 

1. Experiments relating to the expansion of mercury. — The difficulty and un- 
certainty attending the various methods hitherto proDosed for investigating the 
expansion ot quicksilver, or its increase of bulk when rarefied by a given degree 
of heat, determined me to contrive some method by which this purpose might be 



VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. l63 

effected with more certainty and precision. After various experiments I hit on 
the following method, which seems both new and capable of great accuracy, 
though in this I may be deceived. 

First, having blown a ball to a capillary tube, such as are commonly used for 
thermometers, I weighed it, and found that this empty thermometer was equal 
to 79-25 grains. This empty glass, previous to its being weighed, was rendered 
as perfectly clean as possible, which is a necessary precaution in this experiment, 
which depends on a very great accuracy of weight. I then introduced some 
mercury into the stem of this thermometer, taking care that none of it entered 
the ball, and, by adapting a scale of inches to the tube, observed that 4.3 inches 
length of the tube was filled with the mercury. The thermometer was now 
weighed again, and from this weight, the weight of the glass found before being 
subtracted, the remainder, viz. 0.24 gr. showed the weight of so much quick- 
silver as filled 4.3 inches of the tube. Now the ball of the thermometer, and 
also part of the tube, were entirely filled with quicksilver; then, to find out the 
weight of the mercury contained in it, the thermometer was weighed for the last 
time, and from this weight the weight of the glass being subtracted, the re- 
mainder, viz. 32.05 gr. showed the weight of the whole quantity of quicksilver 
contained in the thermometer. 

By comparison with a graduated thermometer in hot and cold water, I made 
a scale to the new thermometer according to Fahrenheit's, and by applying a 
scale of inches found, that the length of 20° in this scale was equal to 1.33 
inch. But 0.24 gr. was the weight of so much mercury as filled 4.3 inches 
length of the tube; therefore, by the rule of proportion it will be found, that 
the weight of so much quicksilver as fills J .33 inch of the tube, viz. the length 
of 20°, is equal to 0.0742 gr. nearly, and that the weight of so much quicksilver 
as fills the length of the tube that is equivalent to 1°, is equal to 0.00371 gr. 
Now it is clear, that the weight of the whole quantity of quicksilver contained 
in the thermometer, is to the weight of so much quicksilver as fills the length 
of 1° in the tube, as the bulk of the whole quantity of quicksilver in a given 
degree of heat, to the increase of bulk that the same whole quantity of quick- 
silver acquires when heated of but 1°, viz. 32.05 gr. is to 0.00371 gr. as 1 is to 
0.001 1 + ; so that by this experiment it appears, that 1° of Fahrenheit's ther- 
mometer increases the bulk of mercury not above T i) l' 00o parts. In this process 
a small deviation from mathematical exactness is occasioned by the small difference 
of weight between the quicksilver of the tube when first weighed and when 11 is 
afterwards heated to 1°; but by an easy calculation it will be found, that this dif- 
ference is so exceedingly small as not to be perceived by our exactest weighing 
and measuring instruments. 

For clearness sake I shall subjoin ihe calculation of the above related experi- 

y 2 



l64 PHILOSOPHICAL TRANSACTIONS. [aNN0 1781. 

ments, disencumbered from words. Here the decimals are not computed to a 
very large number, that being unnecessary for this purpose. 

Weight of the glass 79-25 grs. 

Weight of so much quicksilver as filled 4.3 inches length of the tube, 0.24 
Weight, of the whole quantity of quicksilver contained in the therm. 32.05 

Length of the tube equal to 20° 1 .33 inch. 

4.3 : 0.24 :: 1 .33 : 0.0742 = 20° 

20°: 0.0742:: 1 -.0.00371 

32.05 : 0.00371 :: 1 : 0.0001 1 + = to the expansion occasioned by 1° of heat. 

Having repeated this experiment with other thermometers, and by similar 
calculations, each process gave a result little different from the others, which 
irregularity is certainly owing to the imperfection of my scales, which are not of 
the nicest sort: but taking a mean of various experiments it appears, that 1° of 
heat, according to Fahrenheit's thermometer, increases the bulk of a quantity of 
quicksilver by T o 9 u ir parts, viz. if the bulk of a quantity of quicksilver in the 
temperature of 50° is equal to 100,000 cubic inches, the bulk of the same 
quantity of quicksilver in the temperature of 51° will be equal to 100,009 
cubic inches. 

From these observations the method of graduating, or of determining the 
length of a degree in a new thermometer, is easily deduced, the only requisites 
for the calculation being the weight of a quantity of quicksilver, which fills a 
known length of the tube, and the weight of the whole quantity of quicksilver 
contained in the thermometer when filled. Suppose, for instance, that in 
making a new thermometer it be found, that the weight of so much quicksilver 
as fills 5 inches length of the tube is equal to 10 grs., and that the weight of 
the whole quantity of quicksilver contained in the thermometer weighs 300 grs. 
It is plain, that if the whole quantity of quicksilver weighs 300 grs., then 
___9___ parts of it must weigh 0.027 grs. But the weight of so much mercury 
as fills 5 inches of the tube is equal to 10 grs.; therefore, 0.027 grs. weight of 
quicksilver must fill 0.0133 inch of the tube, and this is equal to the length of 
1°, or the double, treble, &c. of it is equal to 2, 3, &c. degrees. 

By this means the scale may be made; that is, it may be divided into degrees, 
but the numbers cannot be added to them without finding which of those degrees 
corresponds with the freezing point or boiling point. Either the point of boiling 
or freezing may be found by experiment, or any other point may be ascertained 
by comparison with another thermometer, and then the other degrees are nomi- 
nated accordingly. 

3. Description of a thermometrical barometer. — The determination of the 
various degrees of heat shown by boiling water, under different pressures of the 
atmosphere, has been attempted by various persons, but it was lately completed 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 1 65 

by the accurate and numerous experiments of Sir George Shuckburgh. His 
valuable paper is inserted in the 69th vol. of the Philos. Trans. On considering 
this paper, I thought it possible to construct a thermometer with proper apparatus, 
which, by means of boiling water, might indicate the various gravity of the at- 
mosphere, viz. the height of the barometer. This thermometer, with the suit- 
able apparatus, might, I thought, be packed into a small and very portable box, 
and I even flattered myself, that with such an instrument the heights of moun- 
tains, &c. might perhaps be determined with greater facility than with the com- 
mon portable barometer. My expectations are far from having been disappointed, 
and though the instrument which I have hitherto constructed has various defects, 
I have however thought of some expedients which will undoubtedly render it 
much more perfect ; I shall then present to this Society a more particular account 
of it, and also of the experiments which I intend to make with it. The instru- 
ment in its present state consists of a cylindrical tin vessel, about 2 inches in 
diameter and 5 inches high, in which vessel the water is contained, which may 
be made to boil by the flame of a large wax candle. The thermometer is fastened 
to the tin vessel in such a manner, as that its bulb may be about 1 inch above 
the bottom. The scale of this thermometer, which is of brass, exhibits on one 
side of the glass tube a few degrees of Fahrenheit's scale, viz. from 200° to 
21 6°. On the other side of the tube are marked the various barometrical 
heights, at which the boiling water shows those particular degrees of heat which 
are set down in Sir G. Shuckburgh's table. With this instrument the barome- 
trical height is shown within -V of an inch. The degrees of this thermometer 
are somewhat longer than ~ of an inch, and consequently may be subdivided into 
many parts, especially if a nonius is used. But the greatest imperfection of this 
instrument arises from the smallness of the tin vessel, which does not admit a 
sufficient quantity of water: and I find, that when a thermometer is kept in a 
small quantity of boiling water, the quicksilver in its stem does not stand very 
steady, sometimes rising or falling even half a degree; but when the quantity 
of water is sufficiently large, for instance is 10 or 12 ounces, and is kept boiling 
in a proper vessel, its degree of heat under the same pressure of the atmosphere 
is very settled. 

END OF THE SEVENTY-FIRST VOLUME OF THE ORIGINAL. 



/. On a new Kind of Rain. By the Count de Gioeni, an Inhabitant of the 3d 
Region of Mount Etna. From the Italian. Vol. LXXIl, Anno 1782. p. 1. 
The morning of r«»J 24th inst. (April 1781) exhibited here a most singular 
phenomenon. Every place exposed to the air was found wet with a coloured 



l66 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

cretaceous grey water, which, after evaporating and filtrating away, left every 
place covered with it to the height of 1 or 3 lines; and all the iron-work that 
was touched by it became rusty. The shower extended from n. \ n. e. to s. -J- 
s. w. over the fields, about 70 miles in a right line from the vertex of Etna. 
There is nothing new in volcanos having thrown up sand, and also stones, by the 
violent expansive force generated within them, which sand has been carried by 
the wind to distant regions. But the colour and subtilty of the matter occasioned 
doubts concerning its origin ; which increased from the remarkable circumstance 
of the water in which it came incorporated; for which reasons some other prin- 
ciple or origin was suspected. 

It became therefore necessary by all means to ascertain the nature of this 
matter, in order to be convinced of its origin, and of the effects it might pro- 
duce. This could not be done without the help of a chemical analysis. To do 
this then with certainty, I endeavoured to collect this rain from places where it 
was most probable no heterogeneous matter would be mixed with it. I therefore 
chose the plant called Brassica Capitata, which having large and turned up leaves, 
they contained enough of this coloured water; many of these I emptied into a 
vessel, and left the contents to settle till the water became clear. This being 
separated into another vessel, I tried it with vegetable alkaline liquors and mineral 
acids; but could observe no decomposition by either. I then evaporated the 
water, to reunite the substances that might be in solution: and touching it again 
with the aforesaid liquors, it showed a slight effervescence with the acids. When 
tried with the syrup of violets, this became a pale green ; so that I was persuaded 
it contained a calcareous salt. With the decoction of galls no precipitation was 
produced. The matter being afterwards dried in the shade, it appeared a very 
subtile, fine earth, of a cretaceous colour, but inert, from having been diluted 
by the rain. 

I next thought of calcining it with a slow fire, and it assumed the colour of 
a brick. A portion of this being put into a crucible, I applied to it a stronger 
heat, by which it lost almost all its acquired colour. Again, I exposed a portion 
of this for a longer time to a very violent heat, from which a vitrification might 
be expected; it remained however quite soft, and was easily bruised, but returned 
to its original dusky colour. From the most accurate observations of the smoke 
frum the 3 calcinations, I could not discover either colour or smell that indicated 
any arsenical or sulphureous mixture. Having therefore calcined this matter in 
3 portions, with 3 different degrees of fire, I presented a good magnet to eacl ; 
it did not act either on the first or second; a slight attraction was visible in many 
places on the third; this persuaded me, that this earth contains a martial prin- 
ciple in a metallic form, and not in a vitriolic substance. 

The nature of these substances then being discovered, their volcanic origin 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. it)/ 

appears; for iron, the more it is exposed to violent calcination, the more it is 
divided, by the loss of its phlogistic principle; which cannot naturally happen 
but in the great chimney of a volcano. Calcareous salt, being a marine salt 
combined with a calcareous substance by means of violent heat, cannot be other- 
wise composed than in a volcano. As to their dreaded effects on animals and 
vegetables, every one knows the advantageous use, in medicine, both of the one 
and the other, and this in the same form as they are thus prepared in the great 
laboratory of nature. Vegetables, even in flower, do not appear in the least 
macerated, which has formerly happened from only showers of sand. 

How this volcanic production came to be mixed with water may be conceived 
in various ways. Etna, about its middle regions, is generally surrounded with 
clouds that do not always rise above its summit, which is 2900 paces above the 
level of the sea. This matter being thrown out, and descending on the clouds 
below it, may happen to mix and fall in rain with them in the usual way. It 
may also be conjectured, that the thick smoke which the volcanic matter con- 
tained might, by its rarefaction, be carried in the atmosphere by the winds, over 
that tract of country; and then, cooling so as to condense and become specifi- 
cally heavier than the air, might descend in that coloured rain. I must, how- 
ever, leave to philosophers, to whom the knowledge of natural agents belongs, 
the examination and explanation of such phenomena, confining myself to obser- 
vation and chemical experiments. 

p. s. On Friday the 4th of May, about a quarter past 3 in the afternoon, a 
slight shock of an earthquake was felt in the country about Etna, which became 
more sensible at some distance from the mountain; its direction was from north 
to south. The volcano had continued its flames and explosions; and the night 
before, a column of smoke, composed of globes as it were piled on each other, 
had ascended over the crater to double the height of the mountain, as far at least 
as one could judge at the distance of 22 miles, which the vertex is in a right line 
from this city. This remained the whole night perpendicular, only one of the 
globes had separated and lengthened out to the westward from the summit. Now 
and then all the inside of the column, and of the lengthened outpart, became 
illuminated by electric tire, which was of a deep red colour, and gradually went 
out again, beginning at the bottom, in about *2 seconds. The fire has continued 
on the crater till this day, May 8th, ejecting red-hot masses or stones, which 
rolling beautifully down the cone, have illuminated this region; some lava has 
run over from the crater towards the w. n. w. but without having force enough 
to burst the sides or walls of the volcano. 



l68 PHILOSOPHICAL TKANSACTIONS. [AN.VO 1782. 

//. New Chemical Experiments relative to the Acid extracted from Fat. By 
Dr. Crell. An Abstract from the Latin, p. 8.* 

To obviate the objection that in the mode of obtaining the concentrated acid 
of fat by the action of the vitriolic acid on Segner's salt, some of the vitriolic 
acid might be volatilized with it; Dr C. 

Exper. 56, put 3 oz. of Segner's salt (i. e. of the salt compounded of the 
vegetable alkali and the acid of fat) into a coated glass retort, and subjected the 
same to the open fire, gradually increased. A small quantity of water first came 
over, viz. the water of crystallization. When the heat was increased to such a 
degree that the retort began to be red-hot, there immediately rose up an abun- 
dance of grey vapour, indicative, as Dr. C. thought, of a strong acid; but on 
opening the vessels, after they had become cold, he perceived no fumes nor any 
of the smell peculiar to the acid; but rather the smell of spirit of tartar, with 
which the obtained fluid, weighing 11 dr., agreed in other respects, viz. in taste 
and colour; it effervesced slightly with salt of tartar. The residuum was an al- 
kaline salt, with an admixture of carbonaceous matter, but without any trace of 
volatile alkali. 

The method of obtaining the smoking acid of fat, acidum pinguedinis fumans, 
had been hitherto extremely tedious, 9 distillations, exper. I-9, being required, 
besides rectification, exper. 46; after which the acid was to be saturated with an 
alkali, the solution to be evaporated, the salt thus obtained to be calcined, and 
then again to be dissolved and the solution to be evaporated, before the oil of 
vitriol could expel a pure acid from it, exper. 53. He was therefore anxious to 
obtain a pure acid of fat by a shorter process. Accordingly 

Exper. 57, he distilled some purified suet in copper vessels lined with tin. 
On applying a gentle heat nothing rose up but water; but when the heat was in- 
creased, there followed a greenish fluid. At the same time the tin in various 
parts of the alembic, and especially in the tube adapted to it, was melted, and 
had penetrated to the outside. When the distillation was over, he found in the 
receiver the acid and oil, not as in the former experiments congealed, but in a 
fluid state, though the residuum was almost wholly converted into a coally matter. 
Thus he had discovered a shorter process; not only however was the acid conta- 
minated with copper, but the vessels were so much damaged by the great degree 
of heat to which they had been subjected, that they would hardly serve for any 
other operations afterwards. 

Abandoning therefore this method, which was not attended with the desired 
success, he thought of having recourse to a solution of suet in an alkaline salt, 
j. e. to soap. For it appeared to him highly probable, that the alkaline salt, at 

* See vol. xiv. p. 666, of these Abridgments. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. l(3Q 

the same time that it dissolved the fat, combined with its acid ; so that if the oil 
of the soap could be separated from Segner's salt, he should then immediately 
get to that stage of the process, to arrive at which had cost him so much time 
and trouble in exper. 46. Now the separation of the oil appeared to him to be 
no difficult matter, seeing that soap is readily decompounded by every acid, as 
well as by some neutral salts; and that when decompounded, the oil might be 
separated by filtration from the watery fluid, and to the residuum left by the eva- 
poration of this last, vitriolic acid might be added. Being aware, however, that 
common soap would not be proper, both because the lixivium with which it is 
prepared is not pure, and because common salt is added to separate the soap from 
the water, and in part unites with it, he made a soap for the occasion. 

Exper. 58. With lb. ss. quicklime, lb. j- salt of tartar, and lb. vj. hot water, he 
prepared a caustic lixivium, which he afterwards strained through a thick linen 
cloth. Of this lixivium he took a 4th part, diluted it with a little water, and 
boiled it with lb.j. of suet, until most of the aqueous part being evaporated, the 
alkali and suet began to unite. The remainder of the lixivium was then added, 
and the boiling was continued with a gentle heat, the mixture being constantly 
stirred, until a transparent, and as it were mucilaginous compound was formed, 
which gelatinized as it became cold, and was exactly like common soap before 
common salt is added to it. 

Having thus prepared a soap suited to his purpose, his next object was to sepa- 
rate the oil from the alkali, so as to leave the latter combined with the acid of 
fat, i. e. under the form of Segner's salt. And this he thought he could effect 
by means of alum. Accordingly, 

Exper. 59, he dissolved the gelatinous compound obtained in the preceding 
exper. in water, and added some pulverized alum, which immediately caused the 
oil to rise up to the surface in a coagulated state. This being skimmed off, some 
more alum was added; and this was repeated 9 times, till no more oil rose up to 
the surface.* The filtrated liquor was then evaporated to dryness.-f- 

Exper. 60. It occurred to Dr. C. that alum would be the best chemical agent 
he could employ, for expelling the acid, unmixed with vitriolic acid, from Segner's 
salt. Accordingly, to 1 parts of Segner's salt he added 1 part of burnt alum, 
and subjected the mixture to distillation in a sand bath, with a strong heat. 
When the distillation was over, he found in the receiver a smoking acid, of the 
same nature with that which was obtained in exper. 53, and he was therefore 

* The proportions should be as follow: to 10 lb. of the soap-jelly dissolved in water add at dif- 
ferent times 2:oz. of alum. This mixture being filtrated and evaporated, yields 21^ oz of saline 
matter, consisting of vitriolated tartar, Segner's salt, and a portion of undecompounded alum. 

+ If this liquor be set by to crystallize, the vitriolated tartar and superabundant alum may for the 
most part be separated} and the remaining liquor may be afterwards evaporated. 

VOL. XV. Z 



170 PHILOSOPHICAL TRANSACTIONS. [ANN O 1782. 

pleased to see he had thus succeeded in shortening the process. Nevertheless he 
perceived that the acid thus obtained had somewhat of a sulphureous smell 
whence he suspected that (contrary to Beaume's assertion, Chym. Exper. 1, p. 
365) by the strong degree of heat employed in the process, some of the vitriolic 
acid had been expelled from the alum. He therefore resolved to employ the ol. 
vitrioli, as in that case a less degree of heat would be required. 

Exper, 61. On 3 parts of the saline mass * pour 1 part of oil of vitriol; an 
extrication of grey fumes, with the smell of the acid of fat, will immediately 
follow: a gentle heat is sufficient for disengaging all the acid; for when a greater 
degree of heat is applied nothing is forced over into the receiver except a few drops 
of a reddish brown oil. 

To ascertain whether the acid of fat thus procured was contaminated with vi- 
triolic acid, Dr. C. added some of it (the acid of fat) to a solution of saccharum 
saturni; it threw down a precipitate which was not redissolved on adding wine- 
vinegar, even when boiled and digested therewith. Having thus detected an ad- 
mixture of vitriolic acid, he thought it might be separated from the acid of fat, 
by distillation with a fresh quantity of the saline mass; in which case the vitriolic 
acid uniting with the alkali, would disengage the acid of fat.-}- 

Exper. 62. Accordingly, to 4 oz. of the obtained acid he added a fresh portion 
(amounting to 1 oz.) of the saline mass, and distilled with a gentle heat. There 
passed over into the receiver a colourless smoking acid, some of which being added 
to a solution of saccharum saturni, it did indeed throw down a sediment, but 
this sediment was redissolved on adding wine-vinegar. 

Exper. 63. Wishing to see how this concentrated acid would act on metals, 
he digested 4 gr. of gold, precipitated from its solution in aqua regis by vitriol of 
iron, in 1 oz. of the acid. — Another quantity of the acid was digested with gold- 
leaf; a third quantity with 4 gr. of platina; and a fourth quantity with silver leaf. 
In these exper. the acid which was before colourless, acquired a gold-colour. 
This he at first supposed to be owing to the actual solution of some particles of 
gold; but when he observed the same phenomenon to occur when the acid was 
digested with silver, he was then led to suspect that this change of colour was 
produced in the acid by the degree of heat alone. 

Exper. 64-74. He distilled the colourless acid perse 8 different times. That 
portion which rose up into the receiver was pellucid, but the other portion in 

* The following are the best proportions: to $ of the saline mass, exper. 59, note*, add 4 J oz. of 
oil of vitriol; to the remaining \ of the saline mass add the distilled acid, in order to rectifj it. 
In this manner about 5 oz. of colourless smoking acid may be obtained. 

+ If this method be adopted, even pearl ashes may be used for making the soap; for by distilling 
the obtained acid over a fresh quantity of the saline mass, every kind of mineral acid mixed with the 
acid of fat, will be left behind in the said mass. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 17 1 

the retort was of a gold-colour, and a brown matter was deposited in circles at 
the bottom of the retort. The strength of the acid was impaired by these re- 
peated distillations. 

Being thus convinced that in exper. 63 the gold-colour which the acid acquired 
was no proof of any of the gold having been dissolved by it, he resolved to make 
other trials. Accordingly, 

Exper. 75. He attempted to dissolve gold leaf and some grains of platina by 
digesting them in this acid for 6 weeks. On adding salt of tartar, no precipi- 
tation at first took place; but after subjecting the mixture to digestion, a preci- 
pitate was thrown down, which being edulcorated and dried was of a white co- 
lour.* This precipitate he suspected to be of an earthy nature; but the quan- 
tity was too small to allow him to ascertain to which species of earth it belonged. 
He supposes it to have been volatilized by the acid of fat. — The solution showed no 
signs of any metallic impregnation on adding Beguin's volatile tincture of sulphur. 

Exper. 76. He digested for the space of a month 8 gr. of gold calx, obtained 
by salt of tartar, with 4 oz. of the acid of fat. The greater part of the calx 
remained undissolved at the bottom of the vessel. But on adding to the filtrated 
liquor, some of the volatile tincture of sulphur, a bluish grey-colour was imme- 
diately produced. The liquor being strained and the sediment on the filtre being 
dried, it appeared of a dirty yellow-colour, denoting the presence of gold. This 
however was more clearly proved, by evaporating a part of the solution, which 
then yielded some yellowish brown crystals, of an indeterminate figure. 

Exper. 77. To promote the action of the acid of fat upon gold, he thought 
of mixing other acids with it. Accordingly to the same quantity of gold calx, 
he added 40 drops of acid of fat, with which in one vessel were mixed 20 drops 
of pure nitrous acid, in another 20 drops of spirit of salt. In the first vessel, 
bubbles of air were immediately extricated, denoting an incipient solution; in 
the second vessel no change took place. Both vessels were then subjected to a 
digesting heat, by which the solution in the first vessel was promoted, but in the 
second no traces of a solution appeared. Of each of these liquors 8 drops were 
added to 2 separate portions of a diluted solution of tin; the first instantly depo- 
sited a purple precipitate, the other only became a little turbid, without under- 
going any change of colour. 

Exper. 78. He was encouraged by this experiment to try whether this acid 
could not be made to dissolve gold in its metallic state. Accordingly to a bit of 
gold leaf he added 80 drops of the acid of fat and 20 drops of pure nitrous acid. 
Its surface was almost immediately covered with air-bubbles, and the solution 

* The same phenomenon was observed when salt of tartar was mixed and digested with acid of fat 
previously digested with silver and bismuth. 

Z 2 



172 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

went on gently and gradually; but on adding 20 drops more of nitrous acid, the 
solution was greatly promoted, and by subjecting it to a proper degree of heat, 
the whole portion of gold leaf was dissolved. This shows, he thinks, the dif- 
ference between this acid and the muriatic acid; for 2 parts of smoking muriatic- 
acid and 1 part of aqua-fortis will not, he says, dissolve gold, especially if a di- 
gesting heat be not applied. Hence he infers that the acid of fat is entitled to 
be classed with the stronger acids. 

Exper. 79- Calx of platina, precipitated by salt of tartar from its solution in 
aqua regis, being treated in the same manner (exper. 76) was dissolved. One 
portion of the filtrated solution gave a dark coloured precipitate with Beguin's 
tincture, which when collected on a filtre and dried, was of a yellowish brown 
colour. The other portion of the solution being evaporated, yielded oblong yel- 
lowish brown crystals, in much greater quantity than the solution of gold 
had done. 

Exper. 80. Silver leaf was slightly corroded by the acid of fat. By continued 
digestion the calx of silver was dissolved by it. 

Exper. 81. It exerted but little solvent power over quicksilver in its metallic 
state; but 

Exper. 82. Calx of quicksilver, obtained by means of salt of tartar from cor- 
rosive sublimate, was read''}' dissolved by the acid of fat, even without the assist- 
ance of heat. The solution being subjected to distillation, towards the end of 
the operation, when the heat was increased, a white sublimate attached itself to 
the neck of the retort. Dr. C. remarks that the acid of fat is the only acid, ex- 
cepting the muriatic acid, which gives a dry sublimate with quicksilver; and what 
is singular, this sublimate is volatilized at a lower degree of heat than the muri- 
atic sublimate of quicksilver. 

Exp. 83. It dissolved copper, even when not assisted by heat ; but more 
readily when subjected to digestion. The solution yielded crystals which deli- 
quesced in the air. 

Exp. 84. The solution of iron had an astringent taste ; it yielded needle-like 
crystals, which scarcely attracted moisture from the air. 

Exp. 85. Lead, in its metallic state, was rather corroded than dissolved by 
this acid ; but it readily dissolved minium, and the solution yielded crystals, 
which had a sweetish taste. 

Exp. 86. It dissolved regulus of antimony with the assistance of heat. The 
evaporated solution yielded crystals which did not deliquesce in the air. 

Exp. 87. Zinc was readily dissolved. The solution had a strong metallic taste, 
and on adding salt of tartar, it let fall a white sediment, which (like the flowers 
of zinc) turned yellow on exposure to flame. 

Exp. 88. Tin-tilings were readily acted upon by this acid, and were converted 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. • I7S 

into a yellow powder. Half an oz. of the acid was sufficient to corrode 2 scr. 
of tin, with the assistance of heat. It emitted a very disagreeable smell, like 
that which is produced by the action of the muriatic acid upon zinc. The small 
quantity of turbid supernatant liquor could not be rendered clear by filtration 
through many folds of blotting paper. But after standing at rest for a short 
time, a yellowish powder was deposited, while the supernatant liquor, now be- 
come clear, appeared of a beautiful rose-colour. — This corroded calx of tin being 
digested in distilled water, and the water being afterwards filtrated and evaporated, 
a white deliquescent salt was obtained; and on adding to this salt a fresh quantity 
of the acid, the rose-colour was again produced, without any diminution of the 
quantity of sediment. 

Exp. 89. Bismuth, in its metallic state, was not dissolved by this acid ; but 
its calx was. When the solution was diluted with water, it became milky and de- 
posited a white sediment ; but it underwent no change on adding either the 
vitriolic or muriatic acid. 

Exp. go. Regulus of cobalt was not dissolved by it ; but its calx was. From 
the solution distilled with nitre a salt was obtained, which being dissolved in 
water gave a sympathetic ink. 

* Exp. 91. It had very little action upon regulus of nickel ; but it dissolved the 
calx of this metal, even without the assistance of heat. The solution was of a 
greenish colour, and suffered no precipitation on adding the vitriolic and nitrous 
acids. 

Exp. 92. White arsenic was dissolved with difficulty, even when assisted by heat. 

Exp. 93. The Ilfeld ore of manganese was dissolved by this acid. It first 
separated a black powder from the ore, and afterwards dissolved the ore itself, 
in considerable quantity. The acid, which acquired a brown colour by digestion 
with other metals, suffered no change by digestion with the manganese. The 
solution, which emitted a smell like that which is given out from a solution of 
tin, had a metallic taste, and was rendered somewhat turbid by the addition of 
water. When Beguin's tincture was added to the solution, it acquired a red 
colour, and the precipitate which it threw down very abundantly, being dried, 
was of the same colour. 

Precipitations of metals, dissolved in other acids, produced by commixtion with 
the acid of fat. — Exp. 94. Gold. Having obtained some beautiful yellow crys- 
tals (not unlike in figure to the crystals of common salt) from a solution of gold 
in aqua regis, which solution had been exposed to the open air, Dr. C. dissolved 
them in distilled water and added the acid of fat to the solution, whereupon a 
yellow precipitate was thrown down. This precipitate being edulcorated and 
dried, it afterwards attracted moisture from the air. 

Exp. 95. Plalina. This acid being added to a solution of platina in aqua 



\J4 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

regis, an orange-coloured precipitate was thrown down. This precipitate heing 
edulcorated and exsiccated, it became of a yellowish grey colour, and was much 
less deliquescent than the precipitate from gold. 

Exp. Q6. Silver. The acid of fat being added to a solution of silver in nitrous 
acid, a grey-coloured precipitate, inclining somewhat to red, was obtained. 

Exp. Q7- Quicksilver. This metal was precipitated from its solution in 
nitrous acid by the acid of fat. But, what is very remarkable, when this acid 
was added to a solution of corrosive sublimate; in a short time the solution be- 
came milky, and deposited a white powder. This effect takes place sooner if 
the mixture be subjected to a digesting heat. Dr. C. thinks that this may serve 
as a test by which the acid of fat may be distinguished from other acids, and 
particularly from the muriatic acid. This white precipitate being washed and 
afterwards dissolved with the assistance of a digesting heat, in water, a piece of 
copper was whitened on being thrown into it. The evaporated solution gave a 
white residuum, which did not deliquesce in the air. 

Exp. 98. Lead. The precipitate from a nitrous solution of lead, had the 
appearance of small needle-like crystals, which being edulcorated, were readily 
dissolved in water, subjected to a digesting heat. The evaporated solution gave 
a powder which was but little deliquescent. 

Exp. 99. Bismuth. The nitrous acid used for dissolving this metal, had 
been so much diluted, that when the solution was ended, a fresh addition of 
water occasioned no precipitation. But as soon as some drops of the acid of fat 
were added to the solution, a white powder was- thrown down. This being 
washed and dissolved in water with a digesting heat, and the solution being after- 
wards filtrated and evaporated, a white residuum was obtained, which was very 
deliquescent. 

Exp. 100. Regulus of sfntimony. To a saturated solution of this metal in 
aqua regis, distilled water being added, it became turbid ; after this was filtrated 
a fresh addition of water produced no further change in it ; but when some of 
the acid of fat was poured into it, a white precipitate was immediately let fall, 
which was for the most part soluble in water; from which, by evaporation was 
obtained a residuum which attracted moisture from the air, and shot into small 
crystals. 

Exp. 101. Tin, was precipitated from its solution in aqua regis by this acid. 
The precipitate was of a yellowish brown colour. Being washed and digested 
with water, it yielded a white salt, which was very deliquescent. 

Exp. 102. Copper. No precipitate was obtained either from vitriolated copper 
or nitrated copper, by admixtion with the acid of fat. 

Exp. 103. Iron. Nor from nitrated or vitriolated iron. 

Exp. 104. Zinc. Nor from nitrated or vitriolated zinc. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 175 

Exp. 105. Regulus of Cobalt. Nor from this metal dissolved in the nitrous 
acid. 

Exp. 106. Regulus of Nickel. Nor from this metal whether dissolved in the 
nitrous or muriatic acid. 

Exp. 107. Arsenic dissolved in the nitrous acid, gave no precipitate on com- 
mixtion with the acid of fat. 

Exp. 108. Manganese dissolved in the nitrous acid exhibited no change on 
admixtion with this acid. 

The action of different acids upon Segner s salt* It has been already shown 
that the vitriolic acid expels the acid from Segner's salt. 

Exp. 10Q. Nitrous acid. Upon 2 drs. of Segner's salt, Dr. C. poured an equal 
quantity of double aqua fortis. No effervescence ensued. After subjecting the 
mixture to distillation, the fluid in the receiver had the taste peculiar to the acid 
of fat, but had somewhat of the smell of aqua f >rtis. But that the salt was de- 
compounded and its acid let loose, was evident from the precipitation which took 
place on adding some of the distilled fluid to a solution of lead in nitrous acid. 

Exp. 110. Muriatic acid. Equal quantities by weight of Segner's salt and 
muriatic acid being mixed together, and subjected to distillation ; 2 drs. of acid 
of fat were obtained, which possessed its peculiar smell, and precipitated a white 
powder from corrosive sublimate. 

Exp. 111. Wine-Vinegar. Of this, 6 drs. were poured upon 2 drs. of Seg- 
ner's salt, and the mixture was subjected to distillation. The distilled fluid had 
the smell of vinegar, and produced no change in corrosive sublimate. 

Exp. 112. Fluoric acid being added in equal weight to this salt, it very 
quickly united with it, and the compound appeared almost dry ; being afterwards 
subjected to distillation with a strong heat, the fluid which passed over consisted of 
fluoric acid unchanged. 

Exp. 113. Salt of phosphorus. Half an ounce of the sal phosphori dissolved 
in water, was added to 2 drs. of Segner's salt. At the beginning of the distilla- 

* Relative to the figure of this salt, Dr. C. remarks that, on the authority of Segner, he had as- 
serted in the preceding paper, that it resembled the terra foliata tartari ; but having afterwards pre- 
pared it in larger quantity, and examined it more attentively, he found that the saline mass was 
covered with a firm crust, to which, on removing it, there adhered many dagger-like Crystals 
(pugionis quadrangularis forma) of which the 2 opposite sides were narrower than the others. These 
crystals were for the most part 3 lines in length. If there be no excess of alkaline salt and the crys- 
tals be dried on blotting paper, they do not deliquesce in the air : in which circumstance, as well as 
in the form of the crystals, this salt differs remarkably from the terra foliata tartari. Dr. C. thinks 
that Segner prepared so small a quantity of his salt, that he could not have an opportunity of ob- 
serving the crystals concealed under the saline crust. Perhaps, too, his acid was not sufficiently freed 
from the oily particles, and he might not have used for saturating the acid any other alkaline salt 
than pearl ashes. 



176 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

tion what passed over was merely water ; this being poured out of the receiver, 
the fire was increased ; but what rose up in distillation was not acid, nor did it 
decompound saccharum saturni. 

Exp. 114. White Arsenic. Equal quantities of white arsenic and Segner's 
salt of rather a yellowish colour, were triturated together into a powder, and in 
order to promote their action on each other, 2 drs. of distilled water were added, 
and the mixture was digested with a gentle heat. In about a quarter of an 
hour, part of the powder or mass turned black, and adhered strongly to the 
sides of the vessel in the form of a black, circle. Being afterwards subjected to 
distillation, only a small quantity of fluid was obtained, and that had no acid 
taste, nor did it give a precipitate when added to sugar of lead. 

Exp. 1 15. Nitrated Cobalt. One drachm of Segner's salt was added to 4- oz. 
of a nitrous solution of cobalt, and the mixture was subjected to distillation, 
till all the fluid part was drawn off. The exsiccated salt in the retort was of a 
green colour, and when cold turned white; -being dissolved in distilled water, it 
exhibited a new species of sympathetic ink, not unlike the common sympathetic 
ink from cobalt, but inclining more to a yellow colour. 

Exp. 11 6. Sal ammoniacum animale. Of the animal sal ammoniac (com- 
pounded of acid of fat and volatile alkali) 1 drs. were mixed with 15 grs. of the 
lapis haematites, and the mixture was subjected to sublimation ; when the opera- 
tion was over, it was found that the sal-ammoniacum animale had sublimed un- 
changed, while the lapis haematites remained at the bottom of the retort. The 
result was the same when the operation was repeated with the addition of a 
small quantity of water. 

The action of the acid of fat on neutral salts. — Exper. 117. Nitre. Two dr. 
of the acid of fat being poured upon 1 dr. of purified nitre, the latter was dis- 
solved with some degree of effervescence or commotion. No sooner was the 
retort piaced in the sand bath, than it was seen to be rilled with a yellow vapour, 
the colour of which grew darker and darker till at length it turned red. The 
fluid in the receiver had the taste of the nitrous acid, with some admixture of 
the taste of the acid of fat; and its action on silver showed that it did not consist 
of pure nitrous acid. 

Exp. 118. Common Salt. Two drachms of this salt were dissolved in an 
equal weight of the acid of fat. Towards the end of the distillation, grey 
vapours were distinctly seen ; and when the distillation was finished, the smell of 
the fluid in the receiver was the same as the smell of the muriatic acid ; and he 
was induced io believe, by subjecting it to other tests, that the fluid in the re- 
ceiver was the muriatic acid. 

Exp. 110. Terra foliata tartari. The acid of fat being added in equal quan- 
tity to the terra foliata tartarj, a slight effervescence ensued ; being subjected to 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 177 

distillation, the fluid collected in the receiver was found to be vinegar. 

Exf}. 120. Sal Mirabile Glauberi. The acid of fat and this salt were mixed 
together in equal weights, and were afterwards subjected to distillation. The 
fluid collected in the receiver, in addition to the smell of the acid of fat, had 
something of a sulphureous smell mixed with it. On adding some of this 
distilled fluid to a solution of lead in acid fat, a white precipitate was thrown 
down; a proof that a small quantity of the vitriolic acid had been disengaged 
from the alkali with which it was before united. This Dr. C. attributes to the 
phlogiston still adhering to the acid of fat, by which phlogiston (according to 
his explanation) a portion of the vitriolic acid is rendered more volatile. 

Exp. 121. Tartarus tartarisalus. The acid of fat being added to a solution 
of this salt in water, a copious precipitation took place. On pouring off the 
liquor, the sediment had the taste and other properties of cream of tartar. 

Dr. C. concludes with some remarks on the relationship or affinity between the 
acid of fat and the muriatic acid. Both acids yield a dry ammoniacal salt with 
the volatile alkali, and with magnesia alba a deliquescent salt. Both precipitate 
silver and mercury from their solutions in other acids; and when water is added 
to a solution of regulus of antimony in either of these acids, a precipitation 
takes place. And further, when muriatic acid is added to a solution of silver or 
mercury in the acid of fat, nothing is precipitated. But there is a remarkable 
difference between them in other respects. For instance, the acid of fat com- 
bines intimately with oily substances; the salt which it forms with calcareous 
earth is not deliquescent; ether is easily prepared from it; and it throws down a 
precipitate from a solution of corrosive sublimate. 

///. Observations on the Bills of Mortality at York. By William White, M. D., 

F. A. S. p. 35. 

Mr. Drake, p. r. s., in his Antiquities of York, has given the number of 
births and burials for 7 years; from Aug. 5, 1728, to Aug. 5, 1735, 
inclusive. This gave a favourable opportunity of comparing our present state 
after an elapse of 45 years. In order to this, the different parish registers were 
carefully examined from Jan. 1, 1770, to Dec. 31, 1776, inclusive. 

Table 1 shows the number of births and burials in York from Aug. 5, 1728, 
to Aug. 5, 1735, for all the several parishes, which collected together are, 2803 
births, and burials 3488. The burials therefore exceeded the births by 685 in 
7 years, or 98 annually. 

Table 2 shows the number of births and burials from Jan. 1, 1770, to Dec. 
31, I776, inclusive: and these are, in like manner, 3323 births, and 3175 
burials. Therefore decreased in burials 313, or 44f annually; births increased 
520, or 743- ditto; births exceed the burials 148, or 21 4- ditto. 

The 3d table shows the number of births and burials, with the proportion of 
males and females, annually, from Jan. 1, 1770, to Dec. 3 J, 1776. The 
result of all is as follows : 

VOL. XV. A A 



178 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

Number of males born in 7 years 1666, or 238 annually. 
Number of males buried in 7 years 1476, or 21Qf annually. 
Number of females born in 7 years 1657, or 236a annually. 
Number of females buried in 7 years 1699, or 2424- annually. 

The 4th table shows the mortality of the seasons: being for winter 9 18, 
spring 8 16, summer 682, autumn 759. 

In order to find the number of inhabitants in any place, where, either from 
its bulk, or other reasons, a numerical survey cannot be obtained, 2 methods 
may be used. The 1st is, multiplying the number of houses by the medium 
of inhabitants in each. The 2d is, one recommended by Mons. Mohean, in a 
work, entitled, Recherches et Considerations sur la Population de la France. 
He found, by very laborious calculations, that the number of inhabitants may 
be known by the births, the latter being to the former nearly as 1 to 27. 

By an account given into the House of Commons in March 178 J, the number 
of houses in York subject to the new house-tax was 2285: if to those be added 
such as were too small to come under the tax, which may probably amount to 
one-third more, the total of the houses in York will be about 3000. This 
number multiplied by A\, which is nearly the medium of people in a house, 
gives 12,750 for the number of inhabitants. By the 2d rule we have 12,798 
for the number of inhabitants, being the result of 474, the average annual 
births, multiplied by 27. The remarkable coincidence of these methods of 
calculation makes it very probable, that if we estimate the number of inhabitants 
at 12,800, we shall not be far from the truth. 

However this may be as to the exact number of inhabitants, it affects not the 
principal end of the present inquiry, which is to show how we are improved in 
population and healthfulness within 40 years past. To prove this, we must 
find the number of inhabitants in the year 1735, from tab. 1. We there find 
the average annual births to be 400; this multiplied by 27 gives 10,800 for the 
number at that time. This number divided by the average annual deaths 498, 
gives the proportion of deaths 1 in 2 If. Such was the state of this city as to 
mortality 46 years ago. 

Very different from this is our present situa- Vienna 1 in 194 

tion, the proportion of deaths being now London 1 in 20J 

, . r . ' „ i-i-^i • r Edinburgh 1 in 204 

decreased to 1 in 28J-, which is the quotient ol Berlin.. . i in 21 

12,800, the number of inhabitants, divided by Rome ' in 22 

. _„ ., r i i ,1 Amsterdam I in 22 

453, the present average ot annual deaths. Dublin.. . l in 22 

This is certainly a great rise in the scale of heal- Leeds l in 22 

., • t? i ■ c i t j Northampton. . . 1 in 26' 

thiness. b rom being near as fatal as London Shrewsbury . l in 26 

we have become less sothan many country places, Liverpool 1 in >"fa 

•11 r i.u j . • Manchester.. .1 in 28 

as will appear from the annexed comparative Y ork. 1 in 281 

view of the proportion of deaths in different 
places: viz. there dies every year, at 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. Ijy 

Hence in J 735, at York it would require 21 4. years to bury a number equal 
to that of its inhabitants; but in 1776, 28J- years would be required for the 
same. One-third less die yearly now than in the former period; and we are 
certainly advancing still higher, for in 1777 the births were more than in any 
former year, being 5 1 6, the burials 464. As there is no settled manufactory 
here, there is little increase or decrease of the people by acquisition or emigra- 
tion, and probably what may happen in either case is nearly balanced by the other. 
It appears from tab. 4, that the summer season is by much the healthiest at 
York; autumn the next; then the spring; winter being by far the most fatal. 
Dr. Percival found much the same to be the case at Manchester. At Chester 
Dr. Haygarth says November was the most sickly month. It appears that our 
diseases are chiefly of the inflammatory kind, which physicians know to be the 
general attendants of the winter and spring months. The disorders of the 
summer and autumn are more particularly such as arise from putrescency and 
acrimony, such as slow and remitting fevers, dysenteries, choleras, and the like; 
those then, being with us the healthiest seasons, show, that we are not subject 
to putrid diseases. Dr. Wintringham has given an account of the weather and 
the corresponding diseases at York for sixteen years successively, in his Com- 
mentarium Nosologicum, to which learned work the curious reader is referred 
for further satisfaction on this subject. 

Among the general causes of our increasing population and healthiness, we 
may enumerate the introduction of inoculation, which has been the means of 
saving a number of lives; improvements in the treatment and cure of several 
disorders, the cool regimen in fevers, the admission of fresh air, the general 
use of antiseptic medicines and diet, have doubtless had a salutary and extensive 
influence on the health of mankind, and have much obviated the malignity of 
some of our most dangerous diseases. To these may be added a general 
improvement and greater attention to nature in the management of infants. 

After the general causes of healthiness, such as are particular, or of a more 
local nature, come under consideration. In this respect the city of York has 
been much improved within a few years past. The streets have been widened in 
many places, by taking down a number of old houses built in such a manner as 
almost to meet in the upper stories, by which the sun and air were almost ex- 
cluded in the streets and inferior apartments. They have also been new paved, 
additional drains made, and, by the present method of conducting the rain from 
the houses, are become much drier and cleaner than formerly. The erection of 
the locks, about 4 miles below the city, has been a great advantage to it: for, 
before this, the river was frequently very low, leaving quantities of sludge and 
dirt in the very heart of the city, also the filth of the common sewers which it 

A A 2 



180 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

was unable to wash away. The lock has effectually prevented this for the future, 
by the river being kept always high, broad, and spacious; and has thus con- 
tributed to the salubrity as well as beauty of York. 

IV. Account of a monstrous Birth. In a Letter from John Torlese, Esq., 
Chief of Anjingo, to the Hon. William Hornbey, Governor of Bombay. 
Dated April 5, 1780. p. 44. 

As I know you are curious with respect to the productions of nature, I have 
taken the liberty to inclose you a drawing of a child which a Nair woman was 
delivered of the 28th of March at midnight, and which lived till the 1st of April 
in the morning. In the afternoon I went to see it in company with Mr. Hut- 
chenson and Dr. Crozier. It had but 1 body, at the extremity of which were 
2 heads, 1 larger than the other. It had 4 hands and arms perfect, 2 legs on 1 
side its body, and 1 on the other, which began on the middle of its back, 
and appeared by nature intended for 2 by its size and from the appearance of the 
foot, which looked as if 2 had been squeezed or rather mashed together. It had 
but 1 navel, and 1 anus, but 2 genitals of the female. It was fed during its 
short existence by hand with goat's milk. It is remarkable, that 1 head would 
sleep while the other was awake; or 1 would cry and the other not. They both 
died at the same instant. 

V. Experiments with Chinese Hemp-Seed. By Keane Fitzgerald, Esq. p. 46. 
A few grains of Chinese hemp-seed had been given to me by the late 

Mr. Elliot, brother to Gen. Elliot, who had formerly resided for some time in 
China. He told me, the hemp in that country was deemed superior to that of 
any other, both for fineness and strength, and wished I would try whether it 
would come to maturity in this kingdom. He gave me between 30 and 40grs. 
of seed for the purpose, which I laid by, as I thought, carefully, with intent of 
sowing them the spring following, which is the usual time of sowing hemp in 
this country; but I had unluckily forgotten where I laid them, and did not find 
them till the beginning of last June, by which time I imagined them to be very 
unfit for vegetation; but as I concluded they would be still more so by keeping 
them till the succeeding April, I had them sowed the 4th day of that month, 
and was much surprized to find that 32 of the seeds had vegetated strongly, and 
grown to an amazing size, several of the plants measuring in height more than 
14 feet, and nearly 7 inches in circumference, by the middle of October follow- 
ing, at which time they came into bloom. There were from 30 to 40 lateral 
branches on a plant; these were set oft" in pairs, one on each side of the stem 
pointing horizontally; the others at about 5 or inches distance from them, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 181 

pointing in different directions, and so on to the top, the bottom branches of 
some measuring more than 5 feet, the others decreasing gradually in length 
towards the top, so as to form a beautiful cone when in flower, which were 
unluckily nipped by a few nights frost that happened to be pretty sharp towards 
the end of the month; and the plants began to droop at the beginning of 
November, at which time I had them pulled up by the roots. 

As I was but little acquainted either with the cultivation of the seed, or pre- 
paring the plants afterwards for the production of hemp, and as these plants 
were very different in their size from any I had ever seen, the best method that 
occurred to me was, that of steeping them in water, where I let them remain 
for a fortnight, and then placed them in an upright position against a south wall 
to dry and bleach. On trying whether the hemp could be easily separated from 
the woody part, I was agreeably surprized to find, that on peeling a few inches 
longitudinally from the root, the whole rind, from the bottom to the top, not 
only of the stem but also of all the lateral branches, stripped off" cleanly, with- 
out breaking any one of them. The toughness of the hemp seemed to be 
extraordinary, and on drying and beating divides into an infinity of tough fibres. 
The plants when stripped are quite white, and when the lateral branches are cut 
off, appear like handsome young poles. They are perforated in the middle, but 
the perforation is not larger than that of a goose quill, in a stem of more than 
2 inches diameter. The woody part seems pretty substantial, and if they should 
be found of any duration, might be applied to many useful purposes; or if not, 
I should imagine they would produce plenty of good ashes by burning. The 
rough hemp that has been pealed from the 32 plants, when thoroughly dried, 
weighed 3 pounds and a quarter; but I do not think it had come to full matu- 
rity, though I can hardly doubt but the plants would have come to perfection if 
the seed had been sown in the proper season. The summer was remarkably 
dry, notwithstanding which, though the situation they were placed in was 
very warm, and the ground not rich, I found, on measuring the plants at dif- 
ferent times, that they had grown nearly 1 1 inches per week. 

As the culture of so valuable a kind of hemp, as this promises to produce, 
appears to be of consequence to a maritime and commercial kingdom, 1 have 
applied to the directors of the East-India Company, to give proper orders to 
their factors and super-cargoes in China, to procure some of the best seed that 
can be obtained; and send even a small parcel, by each of their returning ships, 
which they have very obligingly promised; and from what has already appeared, 
there can be no doubt of its continuing in a state fit for vegetation for a much 
longer time than is usually required for that voyage. 

If the seed should arrive in safety, I can hardly doubt of obtaining the 
assistance of the society established for the encouragement of arts, manufactures, 



182 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

commerce; and should expect from their wonted assiduity and liberal disposi- 
tion of proper rewards for the culture and manufacture of so valuable a com- 
modity, to see it as successfully carried to perfection as several other branches 
have happily attained by their care and protection; and shall think myself very 
happy in being any ways instrumental in forwarding so good a purpose. 

VI. On some Scoria from Iron JVorks, which resemble the Vitrified Filaments 
described by Sir William Hamilton. By Samuel More, Esq. p. 50. 

In the account given of the eruption of Mount Vesuvius in August, 1/7Q, 
by Sir Wm. Hamilton, printed in the Philos. Trans., vol. 70, p. 42, et seq. 
among many other equally curious informations, it is said, " Long filaments of 
vitrified matter, like spun-glass, were mixed with and fell with the ashes." And 
in a note annexed it is also said, that " during an eruption of the volcano in the 
isle of Bourbon in 1766, some miles of country, at the distance of 6 leagues 
from the volcano, were covered with a flexible capillary yellow glass, some of 
which were 2 or 3 feet long, with small vitreous globules at a little distance one 
from the other." 

There appeared to me, on reading these passages, an exact similarity between 
these productions of the 2 volcanos and some scoria I had received from a worthy 
friend, who is master of one of the largest works in England for smelting, iron. 
In a letter accompanying the specimen, he writes, " I have sent a specimen of some 
slag, or vitrified cinder, which has by the reverberation of the blast from the 
Tweer,* been drawn out while fluid into long cobweb-like threads, sometimes 10 
or 12 feet in length, and affixed itself to the beams, &c. of the bellows room." 

Whoever has attentively viewed the large furnaces where iron ore is smelted 
by coke, will readily allow, that they present the most striking resemblance, 
however diminished, of that most tremendous of all appearances, the eruption 
of a volcano ; and that the most exact pictures hitherto seen of the flowing of the 
lava from the one, is shown by the running of the slag from the other : this has 
induced me to send, for the inspection of the r. s., some of the scoria in its 
capillary state, and with all due deference to the acknowledged abilities of Sir 
William Hamilton, to submit, whether the fine filaments may not be produced 
in the eruption of the great furnaces of nature, by means similar to those by 
which we see them formed in the furnaces of art. Sir William seems to think, 
" That what he calls the natural spun glass which fell at Ottaiano, as well as 
that which fell in the Isle of Bourbon in 176O, must have been formed, most 
probably, by the operation of such a sort of lava as has been just described 
(that is, perfectly vitrified) cracking, and separating in the air at the time of its 

* The Tweer is that opening through which the air is driven by the bellows into the body of the 
furnace. 



VOL. LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



183 



emission from the volcanos, and by that means spinning out the pure vitrified 
matter from its pores or cells, the wind at the same time carrying off those fila- 
ments of glass as fast as they were produced." 

That some of the fine filaments found after the eruptions of the volcanos 
were formed in this manner is not unlikely : but as we see about the iron fur- 
naces the vitrified scoria drawn into fine threads, of very considerable length, by 
the simple action of the wind from the bellows, is it not very probable, that the 
far greater part at least of those filaments scattered over the land, and which 
were found 2 or 3 feet long, were drawn out before the ejection of the lava from 
the crater by the force of those violent torrents of wind which must be required 
to support and actuate so intense a fire as at those times fills the body of the 
mountain ? The extreme fineness to which these filaments are reduced, and 
their brittleness, render it almost impossible to convey them to any distance, 
preserving at the same time any considerable length of the fibres ; these now 
sent resemble cotton in appearance, but if examined with a microscope will be 
found in all respects similar to those described by Sir W. Hamilton. 



VII. An Extract of the Register of the Parish of Holy Cross, Salop, being a 
Third Decade of Years from Michaelmas 1770 to Michaelmas 1780, carefully 
digested in the following Table. By the Rev. Mr. William Gorsuch, Vicar 
p. 53. 



_ .. , f Males 
Baptized | Females 

„ . , S Males 
Buned i Females 



Under a month 
From mo. to 1 yr. 

1 to 2 .. 

2 .. 5 .. 



VI 


•si 

vi 


vi 
vi 

w 


VI 


vi 

V| 


vi 

-v? 


vi 

vi 


V| 
VI 

00 


vi 


VI 

00 

o 




23 


20 


19 


20 


18 


31 


16 


18 


20 


18 


£}"■ 


16 


18 


16 


12 


23 


14 


17 


27 


22 


17 


16 


1.9 


12 


11 


13 


28 


13 


12 


23 


13 


!!?}- 


13 


20 


17 


10 


6" 


21 


14 


15 


13 


22 



Died in the 10 years. 
Male. Fem. Total. 



5 
10 
15 
20 
25 
30 
35 



10 .. 

15 .. 
20 

25 ... 

30 ... 

35 ... 

40 ... 



11 

15 
11 
17 

7 
1 

1 
4 
8 
3 
8 



11 

23 

11 

15 

7 

2 

2 

2 

4 

4 

3 



22 

38 

22 

32 

14 

3 

3 

6 

12 

7 

11 



Increase 



40 to 45 
45 . . 50 . . . 



74 



Died in the 10 yean. 
Male. Pem. Total. 



50 

55 

60 
65 
70 
75 
80 
85 
90 



55 .. 
60 ... 

65 .., 
70 ... 
75 ... 
80 ... 
85 ... 
90 ... 

95 ... 



7 

3 

11 

5 

13 
3 



11 15 
9 7 

12 7 
1 1 

4 



11 

8 

19 
9 

22 

6 

26 

16 

19 

2 

4 



An actual survey was made in 1775, when the number of the inhabitants was 
found to be 105" : of which there were under ten 287, and above seventy 57, 
viz. from 70 to 75, males 12 females 10 = 22. From 75 to 80, males 8 fe- 
males 11 = 19. From 80 to 85, males 8 females 6 = 14. From 85 to 90, 
males 1 females 1 = 2. 



184 PHILOSOPHICAL TRANSACTIONS. [aNNO 1782. 

An actual survey was made in the year 17SO, when the number of inhabitants 
were 1113. There remains alive in 1780, under 10 years of age, males 155 
females 138 = 293. From 70 to 75, males 6, females 11 = 17. From 75 to 
80, males 5, females 8=13. From 80 to 85, males 2, females 4=6. From 
85 to 89, males 2, females 1 = 3. 

The number of inhabitants actually surveyed 
every 5 years for 30 years, as annexed. The n ]7 ^ ' 104 g 

increase of 48 persons in the year 1765 was 1765 1090' 

1 ■ r r •!■ 1770 1046 

owing to the ingress 01 4 numerous families 1775 K)5 _ 

into large houses, which were almost unin- 1780 1113 

habited for many years before. 

The decrease of 50 persons in the year 1770, was occasioned by the demo- 
lishing of 9 houses, in order to open a way to the-new stone bridge built over 
the river Severn. 

Vlll. An Experiment proposed for determining, by the Aberration of the Fixed 
Stars, ivhether the Rays of Light, in pervading different Media, change thei 
Velocity according to the Law which results from Sir Isaac Neivtons Ideas con- 
cerning the Cause of Refraction ; and for ascertaining their Velocity in every 
Medium whose refractive Density is known. By Patrick Wilson, A. M., As- 
sistant to Alex. Wilson, M. D., Professor of Practical Astronomy in the Uni- 
versity of Glasgow, p. 58. 

On the supposition that the refraction of light is caused by a certain action of 
gross and sensible bodies on it, Sir Isaac Newton has demonstrated, that the 
sines of incidence and refraction, when the rays pass out of one medium into 
another of different density, must always be in a constant ratio. This con- 
stancy of the ratio of the sines is agreeable to universal experience, and has been 
called the law of refraction. On the same grounds he has also demonstrated, 
that the velocity of the rays must be greater in the more refracting medium in 
the inverse ratio of the sines. Ot this property of refraction however, we have 
hitherto had no evidence in the way of experiment. The ideas entertained by Sir 
Isaac from which this property has been deduced, though they confess their great 
author, by a most beautiful simplicity, and by a very striking agreement with 
fact, have yet been deemed by some persons as not perfectly authentic. His 
contemporary Leibnitz and others have attempted demonstrations of the law of 
refraction from principles very different, and which do not lead to the opinion of 
the acceleration of light in the more refracting medium. At present it is pro- 
posed to point out a method of determining experimentally the law of the 
variation of the velocity of light, according to the change of the medium. If 
observations shall shew this law to be agreeable to Sir Isaac's conclusions, we 
shall then have a very strong additional evidence in favour of his principles. If, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. ]85 

contrary to the most probable issue of the experiment, some unsuspected law 
should be discovered, we must, according to the rules of induction laid down 
by that great master in philosophy, so far restrict our general conclusions, and 
accommodate our ideas to the real condition of things. 

The method of experiment at present alluded to, is that of observing the 
aberration of the fixed stars with a telescope filled with a dense fluid, such as 
water, or any other equally limpid and of greater refraction, fitted to bring the 
rays to a focus by the surface of the medium opposed to the object having a 
proper degree of convexity. Suffice it at this time to suggest a general notion 
of the instrument ; and proceed we now to explain in what manner it can assist 
us in the present inquiry. 

Since aberration, taken in its enlarged sense, depends on the relative velocities 
of light and of the telescope, if the rays were really to move much faster or 
much slower in an unusual telescope of this kind, it seems to follow, that the 
quantity of aberration given in these circumstances, compared with Dr. Bradley's 
angle, would certainly indicate the new rate of velocity. Such an inference 
would certainly be just, and it is on these grounds that we propose to inquire into 
the velocity of the rays, as they move forward in dense media so applied to teles- 
copes. Granting however, for the sake of argument, that light moves down 
through such an unusual telescope with an increased velocity, suited to the re- 
fractive density of the medium, it will by no means happen, that the aberration 
will be changed on that account. This proposition, which at first view may ap- 
pear paradoxical, and even contradictory to what has been affirmed above, is 
however not the less certain, and may serve to show what caution is sometimes 
requisite in applying general principles to particular cases : for it will be proved, 
that the aberration in such a telescope will precisely agree with that of Dr. Brad- 
ley's only in the case of the rays moving swifter in the watery medium than in air, 
in the ratio assigned by Sir Isaac Newton, and that this sameness of aberration 
will itself be a proof of light being so accelerated within the telescope. In the 
illustrations which follow, the reader is supposed not to be wholly unaccustomed 
to the distinctions between absolute and relative motion, as this will prevent repe- 
titions and all unnecessary prolixity. 

Let abc (fig. 13, pi. 3,) be the spherical refracting surface of such a telescope 
as has been described, and let the telescope be supposed to be at rest, or the 
velocity of light to be infinite with respect to that of the earth, and let gbmf be 
a line drawn from a star at g, in the pole of the ecliptic, through the centre m 
of the refracting surface ; the image of the star will be formed somewhere, as at 
f, in the line bf ; and here the intersection of the cross wires used in observing 
must be placed. It is evident, that the star will be seen in its true direction fg ; 
and we must conclude that to be its true direction, because we know that the 

vol. xv. B R 



J86 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

ray gbf passes into the medium without being refracted by it, and bmf would be 
considered as the axis of the telescope. 

Now let the spherical refracting surface with its wires, or the unusual telescope, 
be carried laterally with the motion of the earth towards a. Conceive gbf to be 
a line not partaking of this lateral motion, which at any particular moment 
passes through m, the centre of convexity. Along this line suppose one of 
many rays to pass from a star situated in the pole of the ecliptic. Then will all 
the contemporary light of this pencil of parallel rays be made to converge, so as 
to meet in a focus somewhere in the unrefracted ray bf. Let f therefore be the 
point in absolute space where the image of the star is so formed. Let the paral- 
lel motion of the telescope, whose refracting spherical surface is abc, be in the 
direction of hf, and take fd to fb as the lateral velocity of the telescope to the 
velocity of light in air, and join bd : then it is manifest that bd will be the po- 
sition of a telescope such as Dr. Bradley's, when the image of the star is formed 
in the axis bd, and that ibg, or its equal fbd, will be the angle of greatest 
aberration. 

Also, the velocity of the rays, as they proceed to the focus f, after refraction 
at the surface abc, being supposed the same as in air, it is evident, that the line 
dml drawn through d and the centre of convexity m, must give the position of 
the axis of this kind of telescope, when the image of the star is formed there : 
for, by the hypothesis, the image is formed at f in absolute space ; and since bf 
is supposed to be to fd, as the velocity of light within the medium, to the 
lateral velocity of the telescope, the point d of the axis dl will arrive at f, when 
the rays arrive there to form the image. And the observer not knowing, or at 
present not taking account of, the lateral motion of the telescope, will suppose, 
that the line lmd, joining the image of the star and the centre of convexity m, 
is the true direction of the star ; just as before he concluded, that fmbg would 
be the direction of the star when the lateral motion of the telescope was sup- 
posed to be nothing. Hence it is evident, that the intersection of the cross 
wires, used in observing, must now be placed at d ; or else, if those be still used 
that were before supposed to be at f, the refracting surface abc, with the line 
or axis bf, must revolve about the centre m, till the vertex b comes to l, and 
the cross wires f to d. 

In like manner, if the velocity of the rays were increased after refraction at 
the spherical surface in any ratio, as that of df to ef, the refraction continuing 
the same, then emo, drawn through the centre of convexity, would now give 
the position of the axis of the telescope necessary for receiving the image 
formed at f. For the space described by the rays in passing downwards to the 
focus, in this case and the former being equal, the times of their converging at 
f will be reciprocally as the velocities, or as ef to df. But, on account of the 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. ]87 

equable lateral motion of the telescope, df and ef will be as the times of the 
points d and e arriving at f : therefore, in the last case, the intersection of the 
cross wires, supposed at e, will meet the image at f, and accordingly the star 
will be seen in the axis. 

From what has been said it will appear, that if df, fig. 14, be taken to ef, 
as the sine of incidence to the sine of refraction peculiar to the medium which 
fills the telescope ; then, from the property of the focus, we shall have this pro- 
portion, viz. bf : fm :: df : ef. Hence the line emo, passing through m, must 
be parallel to db ; but db, as before, denotes the position of Dr. Bradley's teles- 
cope, when the aberration of the star is at its maximum, and emo, parallel to 
it, denotes the position of the water telescope, at the same time, on the suppo- 
sition that the velocity of the rays without and within are as ef to df, or in- 
versely as the sines of incidence and refraction peculiar to water. Here then we 
discover what must be the law of variation as to the velocity of the rays, pro- 
vided that the aberration given by such a telescope shall come out the same with 
that found by Dr. Bradley. It is the very same which follows from the New- 
tonian principles : for from the manner of observing, the angle of aberration is 
always determined by the position of the telescope necessary for having the image 
formed somewhere in the axis. 

But supposing that in the course of observing with such a telescope, the 
aberration should come out different from what has already been ascertained by 
Dr. Bradley, it may next be inquired how, from the difference given, the ve- 
locity of light within the telescope is to be deduced. (Fig. 15,) Imagine then 
such a telescope actually to give fmd as the greatest angle of aberration, and let 
this be supposed greater than that of Dr. Bradley's, which, for example, let be 
fme. From what has been already said, the velocity of light corresponding to 
this last mentioned angle, is deducible from the known refraction of the medium 
which fills the telescope ; and, by construction, the velocity corresponding to 
fmd, the angle given, must be to the former, inversely as the tangents of these 
angles. From this consideration we have the following analogy, for finding the 
velocity corresponding to whatever difference there may be observed between the 
two aberrations at present alluded to. The rule in all cases must be ; " as the 
tangent of the observed angle is to the tangent of the Bradleyan angle, so is the 
velocity of light deducible from the hypothesis of the observed angle being the 
same with that of Dr. Bradley, to the velocity sought." It has already been 
shown, how the former of these velocities can be universally ascertained, from 
the known refraction of the medium which is taken to fill the telescope, and 
therefore the last term of the above proportion, which is the velocity sought, is 
thereby given. 

In a telescope of this kind will not have escaped notice, that the ray bf, 

b b '2 



188 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

fig. 14, which, on account of its passing to the focus unrefracted, maybe called 
the axis of the pencil, can never be found in the axis of the telescope eo, except 
at the focus f, where d and p meet. That ray however op, parallel to bg, 
which falls obliquely on the axis of the telescope eo, will continue to pass along 
it after refraction, and for that reason it may be called the relative axis of the 
pencil. This will appear, by considering that the particle of light, which at any 
moment is refracted at the vertex o of the spherical surface, is found by hypo- 
thesis in the axis a second time, when it meets the contemporary light at the 
focus. But since the motion both of the axis and of the particle is uniform and 
rectilinear, the former cannot be found in the latter at 2 different times, without 
being found in it continually during the whole interval. In like manner, a part 
of every other ray from the star, which successively falls on the vertex, must 
move relatively along the axis after refraction : and thus a constant succession of 
these particles constitute a visual refracted ray, whose relative path must always 
be in the axis oe. 

All that has been shown concerning the telescope already considered, will re- 
ceive still further illustration, by tracing the motion of this particular refracted 
ray till it arrives at the focus. This way of viewing the subject will also render 
the reasoning more general, and make it apply to telescopes when the dense 
fluid within is supposed to be confined by object-glasses of any figure. But in 
order to this, it will be convenient to premise, and briefly to demonstrate, what 
shall afterwards be referred to by the name of 

Prop. A. — If any very small body or particle of light, as it moves uniformly 
in the absolute path sb, fig. l6, has passed relatively along a part of the line cd, 
which advances equably and parallel to itself in the direction dk ; and if at any 
instant the absolute path of the particle be changed into any other, as br ; then 
it will still pass relatively along the moving line, provided its velocity now be to 
its former velocity, as the sine of the angle dbf to the sine of the angle dbr ; 
these being the angles which the moving line bd makes with bf and br, the ab- 
solute path or direction of the particle in the two cases. 

The construction of this figure is so simple, that it is unnecessary formally to 
point it out. Since, by hypothesis, the velocity of the particle along br is to its 
former along bf, as the sine fz to the sine rt ; or, on account of similar tri- 
angles, as df to ir, and, on account of parallels, as df to dw, it follows, that 
the time of its describing br now, is to the time of formerly describing its equal 
bf, as dw to df. But the line bd advancing with a uniform motion, the time 
of its arriving at w is to the time of its arriving at f, also as dw to df. There- 
fore, when the particle arrives at r, the point d of the moving line will have ar- 
rived at w, and wrp will be its position. Hence the particle at that moment 
must be found in the intersection r of this line, with its absolute path br. In 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 18Q 

the same manner it may be shown, that at any other time the particle will be 
found in the intersection : therefore, from the time of its direction being 
changed at e, it must pass relatively along the moving line as before. By a 
small alteration in the construction it may be shown, that if the absolute path 
had been so changed at b as to have augmented the angle fbd, still the particle 
would have moved relatively along db, provided its velocity after had been to its 
velocity before, as the sine of fbd the first angle, to the sine of the increased 
angle. 

To apply therefore this proposition to the present investigation, let db be 
conceived as the axis of a telescope perpendicular to the spherical surface of a 
refracting medium which accompanies it in its lateral motion, sb the absolute 
path of a particle of light which had passed relatively along db produced, till its 
arrival at b, and br its absolute path within the medium of the telescope. Then 
it is evident that fbd, or its equal cbs, will be universally the angle of incidence, 
and rbd the angle of refraction. Hence, by prop. A, that ray of the parallel 
pencil which is refracted at o, the vertex of the spherical surface in fig. 14, must 
still pass relatively along the axis, provided the velocity within the telescope be to 
its former in air, as the sine of incidence to the sine of refraction. But the 
image of the star being produced by the meeting of all the contemporary light, 
will consequently be found in the axis, which, by hypothesis, deviates frum (he 
true place of the star by the same quantity as Dr. Bradley's angle ; so that in this 
way of considering the matter, the same thing results which was formerly shown 
in regard to a telescope so constructed. 

By prop, a it is also manifest, that whatever number of refractions that ray 
which falls on the extremity of the axis suffers, in pervading object-glasses of 
any figure, or even dense media beyond the object-glass, if bounded by trans- 
parent planes to which the axis produced is perpendicular, yet if the velocities 
and refractions so correspond, still the ray in question will pass relatively along 
the axis till it meet the rest at the focus : for here the refracted ray in the first 
medium becomes the incident ray in relation to its path in the 2d, and this in its 
turn becomes an incident ray in relation to its path in the 3d medium, &c. and 
therefore, by the prop, a, can never deviate from the moving axis, whatever be 
the refractive density of the media, or however these are disposed in the order of 
succession. And since, by Sir Isaac Newton's theorem, the ratio of the sine of 
incidence to the sine of refraction, in the passage of a ray out of one medium 
into another, is compounded of the ratio which the former has to the latter, in 
the passage of that ray out of the first medium into any third, and of the ratio 
of the former to the latter in the passage of the same ray out of the 3d medium 
into the 2d, &c. it follows, that if the velocities be related to the degree of re- 
fraction as before-mentioned, the ray in the last dense medium will, notvuth- 



igO . PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

standing any number of previous refractions by glasses, &c. have the same final 
velocity that would have been acquired on its passing immediately out of air into 
that medium. This being the case, it appears, that though the intervention of 
an object-glass may shorten the focal distance of such a telescope, yet it will not 
displace the image nor alter the rule of inferring the final velocity of the rays in 
the dense medium from the aberration given ; at least when this is supposed to 
be the same with Dr. Bradley's. 

But further, if the aberration of such a telescope should differ from the Brad- 
leyan one, and give, for example, the angle omb, fig. 15, still the ray po, 
which falls on o the vertex, must be considered as an incident ray, which, after 
refraction, passes along the axis. By prop, a therefore, the velocity of the ray, 
whatever this may be after refraction, must be to that velocity by which it would 
have moved relatively in the axis, so inclined to its path, previous to the refrac- 
tion, inversely as the sines of incidence and refraction. Now this being duly 
considered, it will be found that the velocity within the medium, corresponding 
to this supposed aberration, or the absolute velocity within the medium, must 
be to the velocity within the medium corresponding to the Bradleyan aberration, 
inversely as the tangents of these two angles : for let v and v express the veloci- 
ties before and after refraction corresponding to the Bradleyan angle, and x and 
x the velocities before and after corresponding to the supposed uncommon angle, 
x being the actual velocity after refraction ; then, because by prop, a the ante- 
cedent is to the consequent, in both cases, in the same ratio, viz. as the sine of 
refraction to the sine of incidence, it will be v : v :: x : x, and therefore v : x :: 
v : x. But from the nature of the aberration v must be to x (this supposititious 
velocity before incidence) inversely as the tangents of the angles of the two aber- 
rations. This therefore must be the ratio of v to x. But v is given, as before 
shown ; therefore x the velocity within the medium corresponding to the sup- 
posed observed aberration is also given, and by the same rule as was found for- 
merly in the case of the first telescope. 

What has been at present advanced is unconnected with any hypothetical 
notions concerning the rays or the cause of refraction. Light has been con- 
sidered only as something which moves uniformly from one place to another, 
and which is always refracted according to a known law. The first of these pro- 
perties has been put beyond all doubt by the observations of Dr. Bradley and 
Mr. Molyneux ; and it has been long known that the last is quite agreeable to 
experience. 

It has indeed always been taken for granted, that the velocity of the ray 
whicn passes through the centre of convexity, represents the common velocity 
of all the contemporary light of the converging pencil. This may perhaps be 
reckoned a circumstance of which we have no proof. But it must be considered, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 1Q1 

that if the rays of light, after being variously bent towards the focus, were no 
longer to move with the same common velocity, the image formed at the focus 
of Dr. Bradley's telescope, would be elongated in the direction of the aberra- 
tion. Those who have attended to this subject will be at no loss in discerning 
the reason of this. The extent of that lengthened image would depend on the 
difference of velocity which would obtain among the converging rays, and would 
probably increase according to the magnitude of the aperture of the object-glass. 
But such a phenomenon being contrary to experience, it follows, that the un- 
equal bending of the rays does not give them unequal velocities, while moving 
in the same medium. This is another property with regard to the motion of 
light which may be considered as proved experimentally by Dr. Bradley's obser- 
vations, and which doubtless would have occurred to him if he had had occasion 
to trace the refraction of a pencil of parallel rays at the object-glass of his 
telescope. 

To conclude : in bringing this question concerning the velocity of light to the 
issue of an experiment, that fluid would doubtless be most proper for the teles- 
cope which absorbs the fewest rays, and possesses the greatest refractive density, 
and which at the same time is not liable to generate air-bubbles. To compensate 
for the unavoidable loss of light, which by Mr. Canton's and Dr. Priestley's ex- 
periments is found to be considerable in such cases, it perhaps may be necessary 
to use an achromatic object-glass for the sake of a large aperture, and of such a 
figure as to shorten the focal distance as much as the observations of such a small 
angle can admit of. Some contrivance too will be requisite to keep the whole 
space between the object-glass and the eye-glass always full, notwithstanding the 
expansions and contractions of the confined fluid by heat and cold, or its waste 
by evaporation. 

It might prove a very considerable abridgment of the necessary apparatus, if 
this kind of telescope could be connected with the common telescope of a mural 
quadrant, or zenith sector, and their axes made perfectly parallel by previous ob- 
servations of a proper terrestrial object. But as there would be some room for 
apprehending that the exact adjustment of the axes might be affected in raising 
the telescopes afterwards for celestial observations, this might be examined into 
by directing them to some star situated in, or very near, the ecliptic, and taking 
its meridian altitudes at a time of the year when it is in quadrature with the sun, 
in which case it would have no aberration. But either in this way, or with two 
separate instruments, the experiment miqjht be made in a few nights, by taking 
the zenith distance of a proper star, the plane of the instruments being alter- 
nately turned different ways in observing, to get the true zenith distance inde- 
pendent of the error of the line of collimation ; or the meridian altitude of the 
pole star may be observed in December above and below the pole, which will 



1Q'2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

give the apparent distance of the star from the pole at that time as affected by 
aberration. The error of the line of collimation would not affect the result in 
this way, being the same in the observation both above and below the pole* 

* Though Mr. Wilson did not bring forward this interesting tract till the year 1782, yet it is well 
known that, so long ago as 1770, his attention was drawn to this subject by a particular view 
which had occurred to him when reading over Dr. Bradley's admirable paper on aberration, in the 
Phil. Trans. It then struck Mr. Wilson that, in reasoning concerning the relative motion of the 
ray from the star, no account had been taken of its having finally to pass through the aqueous and 
vitreous humours of the eye on its way to the retina, in order to produce vision This unavoidable 
and ultimate motion of the ray seemed to him to have some relation to the subject. 

His idea was, that when looking into Dr. Bradley's sector, we perceived the image of the star in 
the centre of the field, at that instant a straight line, joining that centre at the centre of the retina, 
must coincide with the axis of the eye produced: because, by the laws of vision, an object must 
always appear in the direction of the optical axis and the eye which beholds it. But, as the image 
could not be seen in this direction unless the ray, when moving in the aqueous and vitreous humours, 
passed relatively along the axis of the eye, he was led to think that the velocity of the ray, in those 
dense fluids, was that which was justly deducible from the angle of aberration, shown by Dr. 
Bradley's sector ; and not its velocity in air; as had been hitherto imagined. 

Considering now that as the celebrated Romer, by a method wholly different from aberration, had 
nearly ascertained the velocity of light in the ethereal spaces, it now occurred to Mr. Wilson, that, 
by comparing the results afforded by these two different methods, it might be determined whether 
light was accelerated or not in the denser medium according to the ratio resulting from the New- 
tonian doctrine of refraction. This view, of resorting to the principles of aberration, for deciding 
experimentally in a question of such high moment to optics and to general physics, arose in Mr. 
Wilson's mind in the way now stated, and so long ago ; as appears by the outlines of it published in 
the London Chronicle of the 4th December 1770, under the signature X. 

Not long after this however, on further consideration, he found that some conclusions had been 
too hastily adopted ; a circumstance the less surprising, as it will appear in the sequel that the very 
same were fallen into, without ever having been corrected, by philosophers and geometricians of 
the first eminence ; though now known to be entirely false. On this account it may be both instruc- 
tive and entertaining to trace a little the history of this intricate subject, and to shew the steps by 
which Mr. Wilson was led to a just comprehension of it. This we have been enabled to do by se- 
veral late communications with him, during his present residence at Hampstead. 

While he took it for granted, that the aberration of the axis of the eye must differ from that 
of Doctor Bradley's sector, yet he became soon sensible that the consequent displacement of the 
image of the star, as perceived by the eye looking in, would be much more minute than at first he 
imagined, by reason of the near proximity of the eye to the field of the sector. Still however this 
displacement seemed sufficient to give rise to phenomena of a very peculiar kind, some symptoms 
of which might be detected by a very close attention to the image. He supposed the case when tne 
aberration of a star, near the pole of the ecliptic, lay at right angles to a horizontal wire passing 
through the centre of the field, when the telescope turned in a vertical circle. Then by making the 
wire gradually to approach the image, this he concluded ought to disappear when at some small 
distance from the wire; and, when brought to coincide with the wire, it ought to appear visible 
upon it, instead of being hid behind it. Such indeed would be the necessary consequences of the 
premises he now went on, by reason of the displacement of the image that would be occasioned 
by the eye. 

But as Dr. Bradley has never mentioned any symptoms of phenomena so very peculiar, Mr. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 1 Q3 

IX. Quantity of Rain which fell at Barrowby near Leeds. By George Lloyd, 

Esq., F. R. S. p. 71- 
This table of rain contains the quantity fallen in each month of 4 successive 
years, the sums of which for those years are, in 1778, 28 inches; in 1779, 

Wilson was led to suspect some fallacy in his present grounds ; and that, in reality, the aberration 
of the axes of the eye and of the sector might not at all differ, and that the ray passed relatively 
along both, when they lay in the same straight line. For, according to this, the image of the star 
would appear in its true place in the field, and of course the above phenomena could not exist. 
He, on further consideration, found his suspicion was just, by the detection of a most material 
circumstance, soon to be explained, which from the beginning had entirely escaped him. By taking 
in this circumstance, and tracing its consequences, the whole discussion, at once, received a new 
form ; and he was enabled fully to demonstrate, by the arguments stated in the present paper, that 
the aberration of the axis of the eye and that of the telescope must precisely agree, notwithstanding 
the acceleration of the ray on entering the eye, as resulting from Newton's doctrine of refraction. 

Having arrived at this important conclusion, at first so little apprehended, it could not but occur 
that the same theory would hold true whatever magnitude or deepness was imputed to the eye. 
Still the aberration of its axis would precisely agree with that of Dr Bradley's sector, when the ray 
from the star passed relatively over both. From this it followed immediately, as an identical propo- 
sition, that a telescope of any length filled with water, or any dense clear fluid, between the object 
glass and the wires at the focus, would shew the very same aberration with Dr. Bradley's sector, or 
any other telescope, having air only within it. 

This bein<r demonstrable, according to the Newtonian doctrine of refraction, Mr. Wilson saw that 
it was immediately applicable to the purpose he had originally in view : because such an agreement 
between a water and an air telescope, if actually found by observation, would constitute a proof of 
the acceleration of light in the dense medium, in the ratio assigned by Newton. The reader 
will perceive that this is the very thing which Mr. Wilson illustrates and proves by his present 

paper. 

In endeavouring to trace the circumstances of the displacement of the image necessarily arising 
from his former premises, it comes to be considered how far the eye beheld the illumined wires in 
the field of Doctor Bradley's sector, in their true places, notwithstanding the motion of the earth in 
its orbit. This opened a question entirely new, namely, whether a terrestrial object, once seen in 
the axis of a water telescope, steadily and immutably pointed, could ever appear to depart from die 
axis by any new lateral motion given to both, by the orbitual motion, or otherwise. In this inquiiy, 
the same circumstances he had formerly detected clearly pointed out that such a terrestrial aberra- 
tion was an impossible tiling, according to the Newtonian doctrine of refraction ; and that the ob- 
ject, once seen in the axis of the water telescope when immutably pointed, would still continue to 
be seen in the axis, notwithstanding the direction of the orbitual motion, relative to the axis, con- 
stantly varying according to the time of the day. 

The illustration and proofs of the various points now detailed, Mr. Wilson had fully made out before 
the end of 1772, as can be shown by original letters in his possession, especially from one gentleman,* 
of die first eminence as an astronomer and mathematician, who with the greatest liberality and can- 
dour honoured, and warmly encouraged him in these researches by his correspondence. It was not 
till he had arrived at a full understanding of the subject he learned that the late excellent and emi- 
nent geometer Abbe Boscovich had proposed a similar experiment to him, and with the same view, 
but concerning which he had not then made any publication. Afterwprds Lalande, in the 4th vol. of 
his Astronomy, published in 1781, pages 687, 688, gave an account of Boscovich's ideas from his own 

* Dr. Maskelyne. 

VOL. XV. C c 



1Q4 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

2Q.05 inches; in 1780, 22.Q inches; in 1781, 25.6 inches; and the mean of 
the 4 years is 26.4 nearly per year. 

letter, said to be dated in 176~6'. This account is quite conformable to what Boscovich himself o-ives 
in his Opuscula, first publishe 1 at Bassano in 1785. In these volumes there is another tract on ter- 
restrial aberration, which topic appears to have come under his attention only a little time before 
publishing his Opuscula, and many years after the same subject had been considered by Mr. Wilson. 
It is very remarkable however, by the account given by Lalande, and by Boscovich's own account 
in the two tracts of his Opuscula, that this excellent person proceeds entirely on a radical and con- 
firmed mistake on both points, which overthrows all his conclusions ; though many of them, parti- 
cularly those relating to terrestrial aberration, are very extraordinary, and justly and beautifully de- 
duced from his erroneous principles ; and had they been true, would have led to most wonderful and 
important discoveries. 

In regard to the first point, Boscovich asserts, and in this Lalande joins him, that the aberration 
of the axes of the water and air telescope, when the star is seen in the axes of each, must neces- 
sarily be different, and that the former would give only 15" aberration of a star in the pole of the 
ecliptic, instead of 20" the well known aberration of Dr. Bradley's sector, in that case. He then 
concludes that, were this difference actually found by observation, it would constitute the proof of 
the acceleration of light in the dense medium. In showing how the aberration of the water telescope 
should so differ, Boscovich considers the ray at entering, at the axis, as still proceeding down 
in the water in its former absolute direction, though much accelerated. But by Mr. Wilson's papei 
it is evident that this cannot possibly happen, on the hypotheses admitted. He has shown that the 
real or absolute path of the ray, before entering, is inclined to the moving axis, and consequently 
to the surface of the water. On that account its absolute direction, at the moment of entrance, 
must be changed by refraction, so as to make a less absolute angle than it did before with the moving 
axis and the water telescope. 

This unavoidable change of the absolute direction of the ray, at entering, is the very important 
circumstance which Mr. Wilson at last detected, and which delivered him from all his previous mis- 
conceptions, and on which the whole reasoning on this subject entirely hinges. It appears however 
from the year 177<>, till 17^5, when Mr. Boscovich published his Opuscula, that this important 
circumstance had never once occurred to him; in consequence of which it is now well known that 
all his conclusions, in the two tracts abovementioned, concerning the water telescope, anil terrestrial 
aberration, are quite erroneous. Boscovich there considers only one effect produced on the ray a^ 
entering the water telescope, namely the acceleration of its velocity. But Mr. Wilson considers a 
second and simultaneous effect produced on the ray by refraction in consequence of its known 
oblique incidences, namely the unavoidable change of its former absolute direction. Accordingly 
the scope of his paper is to show how these two different but concomitant effects must, according to 
the Newtonian doctrine of refraction, precisely counteract one another, so as to make the aberration 
of the water and air telescopes to agree, when the star is seen in the axis of both. This conclusion 
is the very reverse of that of Boscovich. From never having attended to this second effect produced 
in the ray, as changing its former absolute direction, Boscovich necessarily concluded the possibility 
of terrestrial aberration ; and so deduced many curious things from it in his opuscula, all of which 
are illusions. But whoever reasons about this point, and takes into account this second effect on die 
ray, must immediately perceive that a terrestrial aberration, in the case of the water telescope, is an 
impossible thing. 

In the 2d vol. of the Philos. Trans., of the Edinburgh Royal Society, there is a most ingenious 
paper, on the Motion of Light, by a philosopher and geometer of great eminence, which points out 
Boscovich's delusion concerning this terrestrial aberration. This he does solely by taking in this 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. ] C)5 

X. Of an improved Thermometer. By Mr. James Six. p. 72. 
Attempting some time before to ascertain the greatest degree of heat and cold 
that happened in the atmosphere each day and night, or during the course of 24 
hours, Mr. S. experienced the inconvenience which attends thermometers 
commonly used for that purpose ; viz. the necessity of the observer's eye being 
on the instrument the very instant the mercury stands at the highest or lowest 
degree : for, since the time when that may happen is utterly uncertain, tf it be 
not immediately noticed, it can never after be known. The sultry heat of the 
summer's days, and freezing cold of the winter's nights, which is commonly 
most severe at a late unseasonable hour, render it very unpleasant to be abroad 
in the open air, though it is absolutely necessary for the thermometer to be 
placed in such a situation. Ingenious men of our own country, as well as 
foreigners, have, it seems, long ago, endeavoured to remedy this inconvenience ; 
and several thermometers of different constructions have been invented for that 
purpose. Van Swinden describes one, which he says was the first of the kind, 
made on a plan communicated by Mr. Bernoulli to Mr. Leibnitz. Mr. Kraft, 
he also tells us, made one nearly like it. A description of those by Lord 
Charles Cavendish and Mr. Fitzgerald may be seen in the Philos. Trans, vol. 50, 
p. 501, and vol. 51, p. 820. Though much ingenuity appears in the invention 
of those curious instruments, Mr. S. thought that a thermometer might be 
constructed more conveniently to answer the purpose, and show accurately the 
greatest degree of heat and cold which happened in the observer's absence. Mr. 
S. then gives a description of another thermometer, rather of a complex form ; 
and then adds, thus far our thermometer resembles in some respects those of 
Mr. Bernoulli and Lord Charles Cavendish ; but the method of showing how 
high the mercury had risen in the observer's absence, the essential property of 
an instrument of this kind, is wholly different from theirs, and effected in the 
following manner. Within the small tube of the thermometer, above the sur- 
face of the mercury on either side, immersed in the spirit of wine, is placed a 
small index, so fitted as to pass up and down as occasion may require : that sur- 
face of the mercury which rises carries up the index with it, which index does 
not return with the mercury when it descends ; but, by remaining fixed, shows 
distinctly, and very accurately, how high the mercury had risen, and conse- 
quently what degree of heat or cold had happened. Towards evening, says Mr. 
S. I usually visit my thermometer, and see at one view, by the index on the left 

circumstance of tbe unavoidable change of the absolute direction of the ray at entering the water 
telescope. The author there thinks that he was the first who ever detected that important circum- 
stance ; not then adverting that the same was fully pointed out, and reasoned from as the leading 
principle of Mr. Wilson's present paper, published in the London Philos. Trans., 5 years before the 
time the paper in question was read at Edinburgh in 1788. 

c c 2 



iy6 1'HILOSOPHICAL TRANSACTIONS. [aNNO 1/82. 

.side, the cold of the preceding night ; and by that on the right, the heat of the 
day. These I minute down, and then apply a small magnet to that part of the 
tube against which the indexes rest, and move each of them down to the surface 
of the mercury : thus, without heating, cooling, separating, or at all disturbing 
the mercury, or moving the instrument, may this thermometer, without a touch, 
be immediately rectified for another observation. When I wish to put the ther- 
mometer out of my hand, without hanging it up, I have a stand to place it on ; 
for if the mercury presses against the index, while the instrument lies in an hori- 
zontal position, it is in danger of passing by it, which is avoided by keeping the 
thermometer in a position nearly vertical. 

XI. On the Parallax of the Fixed Stars. By Mr. Herschel. F. R. S. p. 82. 

To find the distance of the fixed stars has been a problem which many eminent 
astronomers have attempted to solve ; but about which, after all, we remain in a 
great measure still in the dark. Various methods have been pursued without 
success, and the result of the finest observations has hardly given us more than 
a distant approximation, from which we may conclude, that the nearest of the 
fixed stars cannot be less than 40 thousand diameters of the whole annual orbit 
of the earth distant from us. Trigonometry, by whose powerful assistance the 
mathematician has boldly ascended into the planetary regions, and measured 
the diameters and orbits of the heavenly bodies, for want of a proper base, can 
here be but of little service ; for the whole diameter of the annual orbit of the 
earth is a mere point when compared to the immense distance of the stars. 
Now, as it is not in our power to enlarge this base, we can only endeavour to 
improve the instruments by which we measure its parallax. 

There are two things requisite for measuring extremely small angles with 
accuracy. First, that the instrument we use for this purpose, be it quadrant, 
sector, or micrometer, should be divided and executed with sufficient exactness ; 
and, secondly, that the telescope, by which the observations are to be made, 
should have an adequate power and distinctness. On the first head, the great 
improvements by instrument-makers have hardly left us any thing to desire : we 
can now measure seconds with almost as much facility and truth as former ob- 
servers could measure minutes ; nor does it seem impossible to go still further, 
and divide instruments that would show thirds with sufficient accuracy. It is in 
the latter, or optical part, we find the greatest difficulty. To see a single second 
of a degree with precision, requires a telescope of very great perfection ; there- 
fore, supposing the mechanical part of an apparatus well executed, it will still be 
necessary to try how far the power of our telescope will enable us to ascertain 
with confidence the division or number of seconds it points out. If on trial we 
find that our instrument will give us the same measure within the second, every 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 197 

time the experiment is repeated, we may pronounce it capable of measuring 
seconds ; if otherwise, it will remain to be examined, whether the fault lies in 
the mechanical or optical part. 

Let us now suppose that the parallax of the fixed stars does not amount to a 
single second, yet still the case is by no means desperate ; and though the diffi- 
culty of measuring seconds will soon suggest to us what extraordinary powers 
and distinctness of the telescope, and accuracy of the micrometer, are required 
to measure thirds ; this ought by no means to discourage us in the attempt. 
Could we measure angles, much smaller than seconds, might we not hope to 
find the parallax of some of the fixed stars at least to amount to several thirds ? 
On the other hand, if it should appear indeed that, even with such improved 
methods of measurement, we could not reach the remote situation of such 
almost infinitely distant suns, we might still derive a valuable approximation to- 
wards truth from such repeated observations, even though they should not be 
attended with all the success we expected from them. On this assurance, Mr. 
H. endeavoured to take such a method for attempting the investigation of the 
parallax of the stars as to avail himself of the improvements he had already 
made, and was still in hopes of making, in his telescopes. 

The next thing necessary to be considered in this undertaking was, the 
manner of putting it into execution. The method pointed out by Galileo, and 
attempted by Hook, Flamsteed, Molineux, and Bradley, of taking distances of 
stars from the zenith that pass very near it, though it failed with regard to 
parallax, has been productive of the most noble discoveries of another nature. 
At the same time it has given us a much juster idea o( the immense distance of 
the stars, and furnished us with an approximation to the knowledge of their 
parallax that is much nearer the truth than we ever had before. Dr. Bradley, 
in a letter to Dr. Halley on the subject of a new discovered motion of the fixed 
stars, says, " I believe I may venture to say, that in either of the two stars last 
mentioned (y Draconis and n Ursae majoris) it (the annual parallax) does not 
amount to 2". I am of opinion, that if it were l" I should have perceived it in 
the great number of observations that I made, especially on y Draconis ; which 
agreeing with the hypothesis (without allowing any thing for parallax) nearly as 
well when the sun was in conjunction with, as in opposition to, this star, it 
seems very probable, that the parallax of it is not so great as one single second." 
Phil. Trans, n. 406. As it is not known that any thing more decisive has been 
done on the subject, it will not he amiss to see how far this method of finding the 
parallax has really been successful. The instrument that was used on this occa- 
sion, was the same as the present zenith sectors, which can hardly be allowed 
sufficient to show an angle of 1 or even 2 seconds with accuracy ; yet, on ac- 
count of the great number of observations, and above all the great sagacity of 



108 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

the observer, we will admit that if the parallax had amounted to 2 seconds he 
would have perceived it. The star on which these observations were made, is 
marked of the 3d magnitude in the catalogue of Ptolemy ; in Tycho Brahe's of 
the 3d ; in the Prince of Hesse's of the 3d ; in Hevelius's between the 3d and 
2d ; in Flamsteed's of the 2d ; and now appears as a very bright star of the 3d, 
or a small star of the 2d magnitude ; therefore its parallax is probably consider- 
ably less than that of a star of the first magnitude. Several authors, who have 
touched on this subject, seem to have overlooked this distinction ; and from Dr. 
Bradley's account of the parallax of y Draconis. have concluded the parallax of 
the stars in general not to exceed 1 " ; but this appears by no means to follow from 
the doctor's observations. It is rather evident that, for aught we know to the 
contrary, the stars of the first magnitude may still have a parallax of several 
seconds ; and probably this is as accurate a result as that method is capable of 
giving, at least in latitudes where there is not a star of the first magnitude that 
passes directly through the zenith.* 

* De La Lande, in his excellent book of Astronomy, says, that the parallax of the fixed stars has 

been proved to be absolutely insensible (liv. 16", § 2782.) He reports the observations of Tycho 

Brahe, Picard, Hook, and Flamsteed, and concludes (§ '27~>i) from die discovery of die aberration 

by Dr. Bradley (which it seems he also allows to be the most decisive on the subject) that now die 

question about parallax is resolved. In giving us the opinion which the doctor had of the result of 

his own observations with regard to the annual parallax, De La Lande only mentions " M. Bradley 

pense que si elle (la parallaxe) eut ete seulement de 1", il l'auroit appercue dans le grand nombre 

d'observations qu'il avoit faites, surtout de y du Dragon." But if we also take in those lines on which 

Dr. Bradley seems to lay the greatest stress, viz. " I believe 1 may venture to say, that in either of 

the two stars last mentioned it does not amount to 2 seconds ;" and if we allow for the magnitude of 

the stars on which die observations were made, I think I have fairly stated the full amount of all the 

actual proofs we have of the smallness of die annual parallax. Now, since it has escaped the finest 

observations of Bradley, it is not likely diat it should come up to the full quantity to which it might 

amount without being perceived ; and therefore the doctor might think it highly probable, " that it 

is not so great as one single second ;" and his opinion, as well as De La Lande's, who believes it to 

be absolutely insensible, are perfectly consistent with all the observations diat have hitherto been 

made ; though the actual proofs, which are die subject of our present inquiry, do not extend so far. 

Against die parallax of Sirius, De La Lande (§ 2731) mentions " forty-five meridian altitudes taken 

by Dr. Bevis,* with the eight-feet mural quadrant of the Royal Observatory at Greenwich, none of 

which differed 3 or 4 ' from the mean altitude." Now if they differed 3 or +" from die mean, we 

may suppose diey differed 6 or 8" from each other ; and that observations, subject to so many causes 

of error as I shall presently enumerate, and which differed so much from each other, cannot give the 

least evidence either for or against a parallax, will need no proof. Refraction alone, which is liable 

to such changes at the meridian altitude of Sirius, notwithstanding the most careful observations oi 

the barometer and diermometer should be made to ascertain its quantity, would, widi me, remain an 

unanswerable argument against die validity of such observations in a subject of this critical nicety. — 

Orig. 

« These observations were not made by Dr. Bevis, but extracted from the registers of the Royal Obs< rvatorj at my de- 
sire and calculated by myselt, and sent in a letter by Dr. Bevis to Paris. — Ne\ il Maskelyne. 



VOL. LXX1I.] PHILOSOPHICAL TRANSACTIONS. \QQ 

In general, the method of zenith distances lahours under the following con- 
siderable difficulties. In the first place, all these distances, though they should 
not exceed a few degrees, are liable to refractions ; and I hope to be pardoned, 
says Mr. H. when I say that the real quantities of these refractions, and their 
differences, are very far from being perfectly known. Secondly, the change of 
position of the earth's axis arising from nutation, precession of the equinoxes, 
and other causes, is so far from being completely settled, that it would not be 
verv easy to say what it exactly is at any given time. In the third place, the 
aberration of light, though best known of all, may also be liable to some small 
errors, since the observations from which it was deduced laboured under all the 
foregoing difficulties. I do not mean to say, that our theories of all these 
causes of error are defective ; on the contrary, I grant that we are for most 
astronomical purposes sufficiently furnished with excellent tables to correct our 
observations from the above-mentioned errors. But when we are on so delicate 
a point as the parallax of the stars ; when we are investigating angles that may 
perhaps not amount to a single second, we must endeavour to keep clear of every 
possibility of being involved in uncertainties ; even the 1 OOth part of a second 
becomes a quantity to be taken into consideration. 

I shall now deliver the method I have taken, and show that it is free from 
every error to which the former is liable, and is still capable of every improve- 
ment the telescope and mechanism of micrometers can furnish. Let oe (fig. I, 
pi. 4,) be two opposite points of the annual orbit, taken in the same plane with 
two stars a, k, of unequal magnitudes. Let the angle aob be observed when 
the earth is at o : and let the angle cie6 be also- observed when the earth is at e. 
From the difference of these angles, if any should be found, we may calculate 
the parallax of the stars, according to a theory that will be delivered hereafter. 
These two stars, for reasons that will soon appear, ought to be as near each 
other as possible, and also to differ as much in magnitude as we can find them. 

Galileo, I believe, was the first who suggested this method ; but in the 
manner he mentions it in his 3d dialogue of the Systema Cosmicum, it would 
be exposed to all the difficulties we have enumerated, and would wish to avoid ; 
for he does not observe that the two stars should be so near each other as thus to 
preclude the influence of every cause of error. This method has also been 
mentioned by other authors ; and we find that Dr. Long observed the double 
star which is the first of Aries in Ptolemy's catalogue ; that in the head of 
Castor ; the middle one in the sword of Orion ; and that in the breast of Virgo, 
with telescopes of 14 and 17 feet, and " was persuaded they would be found 
always to appear the same." Bat when the theory of parallax snail be explained, 
it will be seen that every one of these stars are totally improper for the purpose; 
for the stars of y Arietis are near 10" distant from each other, and are also equal 



200 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

in magnitude. In a Geminorum the stars, though near enough, do not suffi- 
ciently differ in magnitude to show any parallax. The stars in the Nebula of 
Orion, on account of their extreme smallness or distance, are still more im- 
proper than any; and those of y Virginis are equal in magnitude. 

I do not find that any thing else has been done on the subject. Galileo 
justly remarks, that such observations ought to be made with the best telescopes, 
and on this occasion he mentions the power of his own, which enlarged the disc 
of the sun a thousand times, from which we find it magnified about 32 times ; 
but we can hardly think his or even Dr. Long's, whose power might probably be 
60 or 70, sufficient for that purpose. What would Galileo say, if he were told 
that our present opticians make instruments that enlarge the disc of the sun 
above 40,000 times ? What would even Cassini say, if he were to view the first 
star of Aries, which, appeared to him as split in two, through a telescope that 
will show n Coronae borealis and // Draconis to be double stars ? 

But to proceed, I shall now prove that this method, if stars properly situated, 
such as I have found, are taken, is free from all the errors occasioned by refrac- 
tion, nutation, precession of the equinoxes, changes of the obliquity of the 
ecliptic, and aberration of light; and that the annual parallax, if it even should 
not exceed the 10th part of a second, may still become visible, and be ascer- 
tained at least to a much greater degree of approximation than it ever has been 
done. It will also appear, from the great number of observations I have already- 
made on several double stars, especially 1 Bootis, that we can now with much 
greater certainty affirm the annual parallax to be exceedingly small indeed ; and 
that there is a great probability of succeeding still further in this laborious but 
delightful research, so as to be able at last to say, not only how much the 
annual parallax is not, but how much it really is. 

Let there be 2 stars at a distance from each other, not exceeding 5 seconds ; 
suppose them to be observed at an altitude of 20° ; and let them be so situated 
with respect to each other, that one of them may be 20°, and the other 20° and 
5" high : then the whole effect of mean refraction at that altitude, by Dr. Mas- 
kelyne's excellent tables, will be 2' 35".5 for 20°, and 2' 35 y/ .4888 for '20° 5". 
The difference is O'.Ol 1 1 . Now, in the first place, we have nothing to do with 
the refraction itself, since the real altitude of the stars is not in question. In 
the next place, we also have no concern with the difference of refraction between 
the two stars, though no more than the .01 1 1th part of a second, because the 
real distance between the two stars is not required. It follows then, that these 
observations can only be affected by the difference of the difference; that is, by 
an alteration in the quantity of refraction occasioned by the change of heat and 
cold, or weight of the atmosphere, and pointed out to us by the rise and fall of 
the barometer and thermometer. Let us then see what this difference of the 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 201 

difference may amount to. Suppose a change of 22° of Fahrenheit's ther- 
mometer, that is, from the freezing point to the moderate air of a summer's 
night, and a difference of an inch in the height of the barometer ; these two 
causes both conspiring, which does not often happen, may occasion an alteration 
of .00096th part of a second in 5, at an altitude of 20° ; but this, being less 
than the thousandth part of a second, may safely be rejected as a quantity alto- 
gether insensible. 

Since it may not be always convenient to view those stars at the altitude of 
20°, it remains to see what effect different altitudes may have : let us then 
make the most unfavourable supposition, that they may one time be seen in a 
horizontal position, having before been seen vertical. In this case, as the 
whole difference of refraction in a difference of 5" of altitude is no more than 
.0111, provided they are observed not lower than 20°, and the whole difference of 
the difference of refraction is only .0000 ; the sum .012, when both conspire, 
not exceeding much the 100th part of a second, may still be rejected as insen- 
sible. Let us also examine how near the horizon it may be safe to observe such 
stars. At 10°, for instance, the refraction is 5' 14". 6; the difference for 5" is 
.0388 ; the joint effect of the changes in the barometer and thermometer is 
.0034 ; the sum of the whole together amounts to .0422, which is less than 
half the 10th of a second : now this may either be taken into consideration, -or 
such low observations may be avoided, as being by no means necessary, and but 
ill suiting the high powers a telescope proper for this purpose ought to bear. 

The change of position of the earth's axis I consider as an unsurmountable 
obstacle to taking the parallax of stars by the method of zenith distances : for 
though refraction is much reduced in the zenith, this change is there no less 
sensible than in other parts of the heavens ; but as this will always affect our 
two stars exactly alike, we are entirely freed from this embarrassment. The 
aberration of light can have no influence of the least consideration on our two 
stars, as a mere inspection of the tables will show. In a whole degree, its 
effects, when greatest, amount but to -^ of a second, and consequently in 5" 
to no more than .0005, or the 2000th part of a second. 

Observations of the relative distance of the two stars that make up a double 
star being thus cleared of every impediment, are capable of being continually 
improved by every degree of perfection the telescope may acquire: we can chuse 
stars that may be viewed sufficiently high to be clear of the vapours that swim 
near the horizon, and consequently employ the greatest powers our instruments 
are capable of. From experience I can also affirm, that the stars will bear a 
much higher degree of magnifying than other celestial objects. Too much has 
hitherto been taken for granted in optics: every natural philosopher is ready 
enough to allow the necessity of making experiments, and tracing out the steps 

vol. xv. D D 



202 PHILOSOPHICAL TRANSACTIONS. |_ANNO 1/82. 

of nature; why this method should not be more pursued in the art of seeing 
does not appear. Theories are only to be used when proper data are assigned; 
but the data are carefully to be re-examined, when new improvements may widely 
alter the result of former experiments. Thus, we are told, that we gain nothing 
by magnifying too much. I grant it; but shall never believe I magnify too 
much till by experience I find, that I can see better with a lower power. Nor 
is even that sufficient: a lower power may show more of the object; it may show 
it brighter, nay even distincter, and therefore on the whole belter; and yet the 
greater power may, in a particular case, be preferable: for if the object is so 
small as not to be at all visible with the lower power, and I can, by magnifying 
more, obtain a view of it, though neither so bright nor distinct as I could wish, 
is it not evident, that here this power is preferable to the former ? 

The naturalist does not think himself obliged to account for all the phenomena 
he may observe; the astronomer and optician may claim the same privilege. 
When we increase the power we lessen the light in the inverse ratio of the square 
of the power; and telescopes will, in general, discover more small stars, the 
more light they collect; yet with a power of 227 I cannot see the small star 
near the star following o Aquilae, when, by the same telescope, it appears very 
plainly with the power of 460: now, in the latter case, the power being more 
than double, the light is less than the fourth part of the former. In such par- 
ticular cases I generally suspect my own eyes, and have recourse to those of my 
friends. I had the pleasure of showing this star to Dr. Watson, junior, who 
soon discovered the small star, which accompanies the other, with the power of 
460 ; but saw nothing of it with 227, though the place where to look for it had 
been pointed out to him by the higher power. The experiment has been too 
often repeated to be doubtful, and has also been confirmed by others of nearly 
the same nature: for instance, the smallest of the 2 that accompany the star 
near h Aquilae, the small star near ^ Herculis, and the small star near « Lyrae, 
are invisible with my power of 227, but visible with the same aperture when 
the power is 460. Also the small stars near Flamsteed's 24th of Aquila, the 
smaller of 2 near 0- Coronas, the small star near the star south of t Aquilas, the 
small star near the second o Persei, the small star near the star which accom- 
panies Flamsteed's 10th sub pede et scapula dextra Tauri, the small star near |3 
Delphini, and the small star near the pole star, are all much brighter and 
stronger, and therefore much sooner seen with 4fjo, than with 227. 

Great power may also, in particular circumstances, be favourable, even with 
an excess of aberration. When two stars are so close together as to make the 
scale for measuring the distance of their centres too small, if, by magnifying 
much, we can enlarge that distance, we may gain a considerable advantage, pro- 
vided the centres, or apparent bodies of the stars, remain distinct enough for the 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 203 

purpose of these measures. The appearance of a Lyrae in my Newtonian re- 
flector with a power of 460 is represented in fig. 2; with 2011) in fig. 3; with 
3l68 in fig. 4; and with 6450 in fig. 5. Now in all these figures we see, that 
the centres are still distinct enough to measure their distances with sufficient 
truth; or if any little error should be introduced by the magnitude of the central 
point, it will be more than sufficiently balanced by the largeness of the scale. 
In this manner, with a power of 3l68, I have obtained a scale of no less than 
10 inches -fig- for the distance of the centres of the two stars of « Geminorum; 
and as we know these centres to be but a few seconds distant, it is plain how 
great an advantage we gain by such an enlarged scale. 

These experiments have but very lately pointed out to me a method of making 
a new micrometer, on a construction entirely different from any that are now in 
use, which I have been successful enough to put in practice, and by which I 
have already begun to determine the distance of the centres of some of the most 
remarkable double stars to a very great degree of accuracy.* 

The powers that may be used on various double stars are different, according 
to their relative magnitudes: e Bootis, for instance, will not bear the same power 
as a, Geminorum, nor would it be difficult to assign a reason for it; but as I 
here shall merely confine myself to facts, it will be sufficient in general to men- 
tion, that two stars, which are equal, or nearly so, will bear a very high power: 
with a Geminorum I have gone as far as 31 68; but with the former only to 
2010. The difficulty of using high powers is exceedingly great; for the field of 
view takes in less than the diameter of the hair or wire in the finder, and the effect 
of the earth's diurnal motion is so great, that it requires a great deal of practice 
to find the object, and manage the instrument. It appears to me very probable, 
that the diurnal motion of the earth will be the greatest obstacle to our progress 
in magnifying, unless we can introduce a proper mechanism to carry our tele- 
scopes in a contrary motion. 

Though opticians have proved that 2 eye-glasses will give a more correct image 
than one, I have always, from experience, persisted in refusing the assistance of 
a 2d glass, which is sure to introduce errors greater than those we would correct. 
Let us resign the double eye-glass to those who view objects merely for entertain- 
ment, and must have an exorbitant field of view. To a philosopher this is an 
unpardonable indulgence. I have tried both the single and double eye-glass of 
equal powers, and always found that the single eye-glass had much the supe- 
riority in point of light and distinctness. With the double eye-glass I could not 
see the belts on Saturn, which I very plainly saw with the single one, I would 
however except all those cases where a large field is absolutely necessary, and 
where power joined to distinctness is not the sole object of our view. 

* For a description of this micrometer see a subsequent paper. 

D n 2 



204 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

The application of the different powers of a telescope in general is of some 
consequence; and in answer to those who may think I have strained or over- 
charged mine, I must observe, that a single glance at the subsequent h Draconis, 
n Coronas, and the star near y. Bootis, with a power of 460, showed them to me 
as double stars; when, in 2 former reviews of the heavens, I had twice set them 
down in my journal as single stars, where I used only the power of 222 and 227, 
and in all probability should never have found them double, had I not looked 
with a higher power. 

We are to remember, that it is much easier to see an object when it is pointed 
out to us, than when it falls in our way unexpectedly, especially if of such a 
nature as to require some attention to be seen at all ; but to say no more of other 
advantages of high powers, it is evident, that in the research of the parallax of 
the fixed stars they are absolutely necessary. If we would distinctly perceive 
and measure or estimate extremely small quantities, such as a 10th of a second, 
it appears, that when we use a power of 460, this 10th of a second will be no 
more in appearance than 46", and even with a power of 1500 will be but 2' 30", 
which is a quantity not much more than sufficient to judge well of objects and 
distinguish them from each other, such as a circle from a square, triangle, or 
polygon.* 

It has been observed, that objects become indistinct when the principal optic 
pencil at the eye becomes less than the 40th or 50th part of an inch in diameter. 
In the experiments that have been made on this subject it appears to me, that 
the indistinctness which is ascribed to the smallness of the optical pencil may be 
owing to very different causes: at least it will be easy to bring contrary experi- 
ments of extremely small pencils, not at all affected by this inconvenience; for 
instance, it is well known, that microscopes, consisting of a single lens or 
globule, are remarkable for distinctness. We also know, that they have been 
made so small as to magnify above 10,000 times.-f- From this we may infer 
that their apertures, and consequently the diameters of the optic pencil at the 
eye, could not exceed the 2500th part of an inch. I am therefore inclined to 
believe, that we must look for distinctness in the perfection of the object-spe- 
culum or object-glass of a telescope; and if we can make the first image in the 
focus of a speculum almost as perfect as the real object, what should hinder our 
magnifying but the want of light ? Now, if the object has light sufficient, as 
the stars most undoubtedly have, I see no reason why we should limit the powers 
of our instruments by any theory. Is it not best to have recourse to experiments 

* By a set of experiments, made in the year 1 774, I found, that I could discover or perceive a 
bright object, such as white paper, against the sky-light, when it subtended an angle of 35" ; but 
could only distinguish it to be a circle, and no other figure, when it appeared under an angle of 2' 24". 

+ See Padre Delia Torre's Method, &c. Scelta di Opusculi. 



VOL. LXX1I.] PHILOSOPHICAL TRANSACTIONS. 205 

to find how far our endeavours, to render the first image perfect, have been 
successful. 

As soon as I was fully satisfied that, in the investigation of parallax, the 
method of double stars would have many advantages above any other, it became 
necessary to look out for proper stars. This introduced a new series of observa- 
tions. I resolved to examine every star in the heavens with the utmost attention 
and a very high power, that I might collect such materials for this research as 
would enable me to fix my observations on those that would best answer my end. 
The subject has already proved so extensive, and still promises so rich a harvest, 
to those who are inclined to be diligent in the pursuit, that I cannot help inviting 
every lover of astronomy to join with me in observations that must inevitably 
lead to new discoveries. I took some pains to find out what double stars had 
been recorded by astronomers; but my situation permitted me not to consult 
extensive libraries, nor indeed was it very material : for as I intended to view the 
heavens myself, Nature, that great volume, appeared to me to contain the best 
catalogue on this occasion. However, I remembered that the star in the head 
of Castor, that in the breast of the Virgin, and the first star in Aries, had been 
mentioned by Cassini as double stars. I also found the Nebula in Orion was 
marked in Huygens' Systema Saturnium as containing 7 stars, 3 of which (now 
known to be 4) are very near together. With this small stock 1 began, and in 
the course of a few years' observations have collected the stars contained in my 
catalogue. I find, with great pleasure, that a very excellent observer, whom I 
have the honour to call my friend,* has also, though unknown to me, met with 
3 of those stars that will be found in my catalogue: and on this occasion I also 
beg leave to observe, that the Astronomer Royal, when I was at Greenwich last 
May, with his usual politeness, showed me, among other objects, a. Herculis as 
a double star, which he had discovered some years ago. The Rev. Mr. Hornsby 
also, when I had the pleasure of seeing him at Oxford, in a conversation on the 
subject of the stars of the first magnitude that have a proper motion, mentioned 
7r Bootis as a double star. It is a little hard on young astronomers to be obliged 
to discover over-again what has already been discovered; however, the pleasure 
that attended the view when I first saw these stars has made some amends for not 
knowing they had been seen before. 

If I should mention, in my list of observations, a few that may be found 
difficult to be verified by other telescopes, I must beg the indulgence of the 
observers. I hope it will sufficiently appear, that I have guarded against optical 
delusions; and every astronomer, I make no doubt, will find, by those observa- 

* Phil. Trans., for the year 1781, double stars discovered in 1779, at Frampton-house, Glamor- 
ganshire, by Nat. Pigott, Esq., f. r.s., &c. 



•20C) PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

tions that fall within the compass of his instruments, and attention to circum- 
stances necessary to the right management of them, that I have had all along 
truth and reality in view, as the sole object of my endeavours; and therefore he 
will be inclined to give some credit to what he does not immediately perceive, 
when he finds himself successful where he takes the proper precautions so neces- 
sary in delicate observations, even with the best instruments. I have been in 
some doubt in what manner to communicate these observations. My first view 
was to have methodized them properly; but I find them so extensive that there 
is but little probability that one person should be able to bring them to a con- 
clusion, for which reason I have now resolved to give them unfinished as they 
are, that every person who is inclined to engage in this pursuit may become a 
fellow-labourer. 

In settling the distances of double stars I have occasionally used 2 different 
ways. Those that are extremely near each other may be estimated by the eye, 
in measures of their own apparent diameters. For this purpose their distance 
should not much exceed 2 diameters of the larger, as the eye cannot so well 
make a good estimation when the interval between them is greater. This 
method has often the preference to that of the micrometer: for instance, when 
the diameter of a small star, perhaps not equal to half a second, is double the 
vacancy between the two stars. Here a micrometer ought to measure lOths of 
seconds at least, otherwise we could not, with any degree of confidence, rely on 
its measures; nay, even then, if the stars are situated in the same parallel of 
declination and near the equator, their quick motion across the micrometer 
makes it extremely difficult to measure them, and in that case an estimation by 
the eye is preferable to any other measure ; but this requires not a little practice, 
precaution, and time, and yet with proper care it will be found that this method 
is capable of great exactness. Let 2 small circles be drawn, either equal or un- 
equal, at a distance not exceeding twice the diameter of the larger: let these be 
shown to several persons in the same light and point of view. Then, if every 
one of them will separately and carefully write down his estimation of the 
interval between them, in the proportion of either of their diameters, it will be 
found on a comparison, that there will seldom be so much as a quarter of a 
diameter difference among all the estimations. If this agreement takes place 
with so many different eyes, much more may we expect it in the estimations of 
the same eye, when accustomed to this kind of judgment. 

I have divided the double stars into several different classes. In the first, I 
have placed all those which require indeed a very superior telescope, the utmost 
clearness of air, and every other favourable circumstance to be seen at all, or 
well enough to judge of them. They seemed to me on that account to deserve a 
separate place, that an observer might not condemn his instrument or his eye if 
he should not be successful in distinguishing them. As these are some of the 



YOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 207 

finest, most minute, and most delicate objects of vision I ever beheld, I shall be 
happy to hear that my observations have been verified by other persons, which 
I make no doubt the curious in astronomy will soon undertake. I should 
observe, that since it will require no common stretch of power and distinctness 
to see these double stars, it will therefore not be amiss to go gradually through a 
few preparatory steps of vision, such as the following: when n Coronas borealis, 
one of the most minute double stars, is proposed to be viewed, let the telescope 
be some time before directed to a Geminorum, or if not in view to either of 
the following stars, £ Aquarii, y. Draconis, g Herculis, a Piscium, or the curious 
double-double star £ Lyrae. These should be kept in view for a considerable 
time, that the eye may acquire the habit of seeing such objects well and dis- 
tinctly. The observer may next proceed to £ Ursas majoris, and the beautiful 
treble star in Monoceros's right fore-foot; after these to i Bootis, which is a fine 
miniature of x Geminorum, to the star preceding a. Orionis, and to n Orionis. 
By this time both the eye and the telescope will be prepared for a still finer 
picture, which is n Coronas borealis. It will be in vain to attempt this latter if all the 
former, at least i Bootis, cannot be distinctly perceived to be fairly separated, 
because it "is almost as fine a miniature of i Bootis as that is of a. Geminorum. 
If the observer has been successful in all these, he may then, at the same time, 
try h Draconis, though I question whether any power less than 4 or 500 will 
show it to be double; but all the former I have seen very well with 227. 

To try the stars of unequal magnitudes it will be expedient to take them in 
some such order as the following: a Herculis, u Aurigae, S Geminorum, k 
Cygni, e Persei, and b Draconis; from these the observer may proeeed to a most 
beautiful object, £ Bootis which I have closely attended these 2 years as very 
proper for the investigation of the parallax of the fixed stars. 

It appears, from what has been said, that these double stars are a most excel- 
lent way of trying a telescope; and as the foregoing remarks have suggested the 
method of seeing how far the power and distinctness of our instruments will 
reach, I shall add the way of finding how much light we have. The observer 
may begin with the pole star and » Lyras ; then go to the star south of i Aquilas, 
the treble star near h Aquilae, and last of all to the star following o Aquilae. 
Now, if his telescope has not a great deal of good distinct light, be will not be 
able to see some of the small stars that accompany them. 

In the 2d class of double stars, I have put all those that are proper for esti- 
mations by the eye or very delicate measures of the micrometer. To compare 
the distances with the apparent diameters, the power of the telescope should not 
be much less than 200, as they will otherwise be too close for the purpose. The 
instrument ought also to be as much as possible free from rays that surround a 
star in common telescopes, and should give the apparent diameters of a double 



208 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

star, perfectly round and well defined, with a deep black division between them, 
as in fig. 6, which represents a Geminorum as I have often seen it with a power 
of 46o. It will be necessary here to take notice, that the estimations made with 
one telescope cannot be applied to those made with another: nor can the estima- 
tions made with different powers, though with the same telescope, be applied to 
each other. Whatever may be the cause of the apparent diameters of the stars, 
they are certainly not of equal magnitude with the same powers in different tele- 
scopes, nor of proportional magnitude with different powers in the same tele- 
scope. In my instruments I have ever found less diameter in proportion the 
higher I was able to go in power, and never have I found so small a proportional 
diameter as when I magnified 6450 times;* therefore if we would wish to com- 
pare any such observations together, with a view to see whether a change in the 
distance has taken place, it should be done with the very same telescope and 
power, even with the very same eye-glass or glasses; for others, though of equal 
power and goodness, would most probably give different proportional diameters 
of the stars. 

In the 3d class I have placed all those double stars that are more than 5 but 
less than 15" asunder; and for that reason, if they should be used for observa- 
tions on the parallax of the fixed stars, they ought to be considered as quite free 
from the effects of refraction, &c. In the same manner that the stars in the 1st 
and 2d classes will serve to try the goodness of the most capital instruments, 
these will afford objects for telescopes of inferior power, such as magnify from 
40 to 100 times. The observer may take them in this or the like order: £ Ursas 
majoris, y Delphini, y Arietis, -w Bootis, y Virginis, i Cassiopeae, ^ Cygni. 
And if he can see all these, he may pass over into the 2d class, and direct his 
instrument to some of those that were pointed out as objects for the very best 
telescopes, where I suppose he will soon find the want of superior power. 

The 4th, 5th, and 6th classes contain double stars that are from 15 to 30'', 
from 30" to l', and from 1' to l' or more asunder. Though these will hardly 
be of any service for the purpose of parallax, I thought it not amiss to give an 
account of such as I have observed; they may perhaps answer another very im- 
portant end, which also requires a great deal of accuracy, though not quite so 
much as the investigation of the parallax of the fixed stars. I will just men- 
tion it, though foreign to my present purpose. Several stars of the first mag- 
nitude have already been observed, and others suspected, to have a proper mo- 
tion of their own; hence we may surmise, that our sun, with all its planets and 
comets, may also have a motion towards some particular part of the heavens, 
on account of a greater quantity of matter collected in a number of stars and 

* See the measures of the diameter of » Lyrce. Catalogue of double stars, 6th class. — Orig. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 20Q 

their surrounding planets there situated, which may perhaps occasion a gravita- 
tion of our whole solar system towards it. If this surmise should have any foun- 
dation, it will show itself in a series of some years; as from that motion will 
arise another kind of hitherto unknown parallax,* the investigation of which 
may account for some part of the motions already observed in some of the prin- 
cipal stars; and for the purpose of determining the direction and quantity of 
such a motion, accurate observations of the distance of stars that are near enough 
to be measured with a micrometer, and a very high power of telescopes, may be 
of considerable use, as they will undoubtedly give us the relative places of those 
stars to a much greater degree of accuracy than they can be had by transit in- 
struments or sectors, and thus much sooner enable us to discover any apparent 
^chano-e in their situation occasioned by this new kind of systematical parallax, if 
I may be allowed to use that expression, for signifying the change arising from 
the motion of the whole solar system. 

I shall now endeavour to deliver a theory of the annual parallax of double 
stars, with the method of computing from it what is generally called the parallax 
of the fixed stars, or of single stars of the first magnitude, such as are nearest 
to us. It may be observed, that the principles on which I have founded the 
following theory are of such a nature, that they cannot be strictly demonstrated, 
in consequence of which they are only proposed as postulata, which have so great 
a probability in their favour, that they will hardly be objected to by those who 
are in the least acquainted with the doctrine of chances. 

General Postulata. — 1. Let the stars be supposed, one with another, to be 
about the size of the sun.-f- 

2. Let the difference of their apparent magnitudes be owing to their different 
distances, so that a star of the 2d, 3d, or 4th magnitude, is 2, 3, or 4 times as 
far off as one of the first. t 

* See the note in the Rev. Mr. Mitchell's paper on the Parallax of the Fixed Stars. Phil. Trans, 
vol. 57, p. 252.— Orig. 

+ See Mr. Mitchell's Inquiry into the probable Parallax and Magnitude of the Fixed Stars, Phil. 
Trans, vol. 57 ; and Dr. Halley on the Number, Order, and Light, of the Fixed Stars, Phil. Trans, 
vol. 31. — Orig. 

t The apparent magnitude is here taken in a stricter sense than is generally used; and by it is rather 
meant the order into which the stars ought to be distinguished than that into which they are commonly 
divided ; for as the order of the magnitudes is here to denote the different relative distances, we are 
to examine carefully the degree of light each star is accurately found to have : a.id considering then 
that light diminishes in the inverse ratio of the squares of the distances, we ought to class the stars 
accordingly. An allowance ought also perhaps to be made for some loss that may happen to the light 
of very remote stars in its passage through immense tracts of space, most probably not quite destitute 
of some very subtle medium. This conjecture is suggested to us by the colour of the very small 
telescopic stars, for 1 have generally found them red, or inclining to red ; which seems to indicate, 
that the more feeble and refrangible rays of the other colours are either stopped by the way, or at 
least diverted from their course by accidental deflections. — Orig. 

VOL XV. E E 



210 PHILOSOPHICAL TRANSACTIONS. [ANNO J 782. 

In fig. 7, let oe be the whole diameter of the earth's annual orbit; and let a, 
A, c, be 3 stars situated in the ecliptic, in such a manner that they may be seen 
all in one line oabc, when the earth is at o. Let the line oabc be perpendicular 
to oe, and draw pe parallel to co. Then, if oa, ab, be, are equal to each other, 
a will be a star of the 1st magnitude, b of the 2d, and c of the 3d. Let us 
now suppose the angle o«e, or parallax of the whole orbit of the earth, to be 
l"of a degree: then we have pea = or/E = \" : and, because very small angles, 
having the same subtense oe, may be taken to be in the inverse ratio of the 
lines oa, ob, oc, &c. we shall have o£e = ■}/, oce = $", &c* Now, when the 
earth is removed to e, we shall have pe6 = e6o = -J-", and pe«. — pe6 = «eZ> 
= ±"; that is, the stars a, b, will appear to be $? distant. We also have pec = 
eco = 4-", and PEa — pec = «ec = •§-"; that is, the stars a, c, will appear to be 
%" distant, when the earth is at e. Now, since we have 6ep = \" , and cep = 
-l", therefore 6ep — cep = bEc = \" — \" = 4"; that is, the stars b, c, will ap- 
pear to be only £.* removed from each other, when the earth is at e. 

From what has been said, we may gather the following general expression, to 
denote the parallax that will become visible in the change of distance between 
the two stars, by the removal of the earth from one extreme of its orbit to the 
other. Let p express the total parallax of a fixed star of the first magnitude, 
M the magnitude of the larger of the two stars, m the magnitude of the smaller, -f- 
and p the partial parallax to be observed by the change in the distance of a double 
star; then will p = — ^— p; and/>, being found by observation, will give us p = 

i " MW . An example or two will explain this sufficiently. Suppose a star of the 
first magnitude should have a small star of the 12th magnitude near it; then will 
the partial parallax we are to expect to see be - p; or -}~±- of the total paral- 

lax of a fixed star of the first magnitude; and if we should, by observation, find 
the partial parallax between 2 such stars to amount to \", we shall have the total 

* This proves what I have before remarked on the parallax of y Draconis ; for that star, (admitting 
it to be a star of between the 2d and 3d magnitude, which ought to be ascertained by experiments, 
as mentioned in the note above) by the postulata, will have its place assigned somewhere between b 
and c, and therefore its parallax will be between \ and ^ of the parallax of a star of the first magni- 
tude. And if Dr. Bradley thought that he should have perceived a parallax in y Draconis, if at most 
it had amounted to 2", it follows, that the angle oue may nearly amount to i or 5" for any thing we 
can conclude to the contrary from those observations. — Orig. 

t Asm and m are here taken to express the relative distances of the stars, in measures whereof 
the distance of the nearer star is taken as unity, those who diink the postulata on which diese esti- 
mations are built cannot be granted, may still use the following formulae, if instead of the magni- 
tudes m, m, they put their own estimations of the relative distances of the stars, according to any 
other mediod whatever they may Uiink it most eligible to adopt; for the apparent magnitude of stars 
is here only proposed as the most probable means we have of forming any conjectures about their rela- 
tive distances. — Orig. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 2 J I 

parallax p = ■ X '_* — = l^OgOQ. If the stars are of the 3d and 24th magni- 

tude, the partial parallax will be - — — = ^~ p = — p; and if by observation, p 

1 x 3 x 24 

is found to be a 10th of a second, the whole parallax will come out ■ — - _ * 

= 0".3428. 

It will be necessary to examine some different situations. Suppose the stars, 
being still in the ecliptic, to appear in one line, when the earth is in any other 
part of its orbit between o and e; then will the parallax still be expressed by 
the same algebraic form, and one of the maxima will still lie at o, the other at 
e; but the whole effect will be divided into 2 parts, which will be in proportion 
to each other as radius — sine to radius + sine of the stars distance from the 
nearest conjunction or opposition. 

When the stars are any where out of the ecliptic, situated so as to appear in 
one line oabc at rectangles to oe, the maximum of parallax will still be expressed 
by '" ~ M p ; but there will arise another additional parallax in the conjunction 

* MM 

and opposition, which will be to that which is found go" before or after the sun., 
as the sine (s) of the latitude of the stars seen at o is to radius (r) ; and the ef- 
fect of this parallax will be divided into 2 parts; half of it lying on one side of 
the large star, the other half on the other side of it. This latter parallax also 
will be compounded with the former, so that the distance of the stars in the con- 
junction and opposition will then be represented by the diagonal of a parallel- 
ogram, of which the two semi-parallaxes are the sides; a general expression for 



ss 



which will be p X V (- h l): for the stars will apparently describe 2 

ellipses in the heavens, whose transverse axes will be to each other in the ratio of 
M to in (fig. 8), and A.a, b£, cc, vd, will be cotemporary situations. Now, if bo. 
be drawn parallel to ac, and the parallelogram bqvo. completed, we shall have 
bo. = ^ca — ±ca = ice = \p 3 or semi-parallax Q0° before or after the sun, and 
bZ> may be resolved into, or is compounded of, bo. and bq; but bq = {bd — \bd 
= the semi-parallax in the conjunction or opposition. We also have R : s :: bo. : 
[,q — p.; therefore the distance bZ> or vd = */ [(|) 2 + (~) 2 ] ; and by substitut- 
ing the value of p into this expression we obtain ~ p X \/( 1- l), as above. 

When the stars are in the pole of the ecliptic, bq will become equal to bo., and 

.... m — m 

hb will be .707 1p — — • 

Hitherto we have supposed the stars to be all in one line oabc; let them now 

be at some distance, suppose 5" from each other, and let them first be both in 

the ecliptic. This case is resolvable into the first; for imagine the star a, fig. 9, 

to stand at x, and in that situation the stars x, b, c, will be in one line, and their 

e e 2 



212 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/62. 



parallax expressed by p. But the angle aEx may be taken to be equal to 

aox; and as the foregoing form gives us the angles xEb, xec. we are to add gei 
or 5" to xEb, and we shall have aEb. In general, let the distance of the stars be 
d, and let the observed distance at e be d ; then will v> = d -{- p, and therefore 
the whole parallax of the annual orbit will be expressed by — — — - — = p. 

Suppose the two stars now to differ only in latitude, one being in the ecliptic, 
the other, for instance, 5" north, when seen at o. This case may also be re- 
solved by the former; for imagine the stars b, c, fig. 7, to be elevated at rect- 
angles above the plane of the figure, so that aob, or aoc, may make an angle 
of 5" at o: then, instead of the lines oabc, eg, Eb, ec, ep, imagine them all 
to be planes at rectangles to the figure; and it will appear, that the parallax of 
the stars in longitude must be the same as if the small star had been without 
latitude. And since the stars b, c, by the motion of the earth from o to e, will 
not change their latitude, we shall have the following construction for finding 
the distance of the stars ab, ac, at e, and from thence the parallax p. Let the 
triangle ab(Z, fig. 10, represent the situation of the stars; ab is the subtense of 
5", that being the angle under which they are supposed to be seen at o. The 

quantity b(Z by the former theorem is found p, which is the partial parallax 

that would have been seen by the earth's moving from o to e, had both stars 
been in the ecliptic; but on account of the difference in latitude it will now be 
represented by «(3, the hypothenuse of the triangle ab@: therefore, in general, 

putting ab = d, and a(3 = d, we have — = p. Hence d being 

taken by observation, and d, m, and m, given, we obtain the total parallax. 

If the situation of the stars differs in longitude as well as latitude, we may- 
resolve this case by the following method. Let the triangle abfi, fig. 1 1, repre- 
sent the situation of the stars, ab = d being their distance seen at o, a(3 = d 
their distance seen at e. That the change Z'|3 which is produced by the earth's 

motion will be truly expressed by p, may be proved as before, by supposing 

the star a to have been placed at a. Now let the angle of position baa, be taken 
by a micrometer,* or by any other method that may be thought sufficiently ex- 
act; then, by solving the triangle aba, we shall have the longitudinal and latitu- 
dinal differences aa and ba of the two stars. Put ax = x, ba = y, and it will 

be x 4- bQ = an. whence d = V \{x -\- p) 2 + mi~\ ; and — — — — — - 

urn = p. 

* The position of a line passing through the two stars, with the parallel of declination of the 
largest of them, may be had by the micrometer I invented for this purpose in the year J 779, of which 
a description has been given in a former paper; whence, by spherical trigonometry, we easily deduce 
their position bax fig. 1 1, with regard to the ecliptic— Orig. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 213 

If neither of the stars should be in the ecliptic, nor have the same longitude 
or latitude, the last theorem will still serve to calculate the total parallax whose 
maximum will lie in e. There will also arise another parallax, whose maximum 
will be in the conjunction and opposition, which will be divided, and lie on dif- 
ferent sides of the large star; but as we know the whole parallax to be exceed- 
ingly small, it will not be necessary to investigate every particular case of this 
kind; for, by reason of the division of the parallax, which renders observations 
taken at any other time, except where it is greatest, very unfavourable, the forms 
would be of little use. 

To finish this theory, I shall only add a general observation on the time and 
place where the maxima of parallax will happen. When 2 unequal stars are 
both in the ecliptic, or, not being in the ecliptic, have equal latitudes, north or 
south, and the larger star has most longitude, the maximum of the apparent 
distance will be when the sun's longitude is gO c more than the stars, or when 
observed in the morning; and the minimum when the longitude of the sun is 
go less than that of the star, or when observed in the evening. When the small 
star has most longitude, the maximum and minimum, as well as the time of 
observation, will be the reverse of the former. When the stars differ in latitudes, 
this makes no alteration in the place of the maximum or minimum, nor in the 
time of observation; that is to say, it is immaterial whether the largest star has 
the least or the most latitude of the two stars. 

XII. Catalogue of Double Stars. By Mr. Herschel, F.R.S. p. 112. 

Introductory Remarks. — The following catalogue contains not only double 
stars, but also those that are treble, double-double, quadruple, double-treble, 
and multiple. The particulars I have given of them are comprehended under the 
following general heads. 1 . The names of the stars and number in Flamsteed's 
catalogue; or, if not contained there, such a description of their situation as 
will be found sufficient to point them out. 2. The comparative size of the stars. 
On this occasion I have used the terms equal, a little unequal, pretty unequal, 
considerably unequal, very unequal, extremely unequal, and excessively unequal, 
as expressing the different gradations to which I have endeavoured to affix always 
the same meaning. 3. The colours of the stars as they appeared to me when I 
viewed them. Here I must remark, that different eyes may perhaps differ a 
little in their estimations. I have, for instance, found, that the little star which 
is near a. Herculis, by some to whom I have showed it has been called green, 
and by others blue. Nor will this appear extraordinary when we recollect that 
there are blues and greens which are very often, particularly by candle-light, mis- 
taken for each other. The situation will also affect the colour a little, making 
a white star appear pale red when the altitude is not sufficient to clear it of the 



214 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/82. 

vapours. It is difficult to find a criterion of the colours of stars, though I might 
in general observe that Aldebaran appears red, Lyra white, and so on ; but when 

1 call the stars garnet, red, pale red, pale rose-colour, white inclining to red, 
white, white inclining to blue, bluish white, blue, greenish, green, dusky, I 
wish rather to refer to the double stars themselves to explain what is meant by 
those terms. 

4. The distances of the stars are given several different ways. Those that are 
estimated by the diameter can hardly be liable to an error of so much as one 
quarter of a second; but here must be remembered what I have before remarked 
on the comparative appearance of the diameters of stars in different instruments. 
Those that are measured by the micrometer, I fear, may be liable to an error of 
almost a whole second: and if not measured with the utmost care, to near 2". 
This is however to be understood only of single measures; for the distance of 
many of them that have been measured very often in the course of 2 years ob- 
servations, can hardly differ so much as half a second from truth, when a proper 
mean of all the measures is taken. As I always make the wires of my micro- 
meter outward tangents to the apparent diameter of the stars, all the measures 
must be understood to include both their diameters; so that we are to deduct the 

2 semi-diameters of the stars if we would have the distance of their centres. 
What I have said concerns only the wire micrometers, for my last new micro- 
meter is of such a construction, that it immediately gives the distance of the 
centres; and its measures, as far as in a few months I have been able to find out, 
may be relied on to about T V of a second, when a mean of 3 observations is 
taken. When I have added inaccurate, we may suspect an error of 3 or 4". 
Exactly estimated may be taken to be true to about £ part of the whole distance; 
but only estimated, or about, &c. is in some respect quite undetermined; for it 
is hardly to be conceived how little we are able to judge of distances when, by 
constantly changing the powers of the instrument, we are as it were left without 
any guide at all. I should not forget to add, that the measure of stars, when 
one is extremely small, must claim a greater indulgence than the rest, on account 
of the difficulty of seeing the wires when the field of view cannot be sufficiently 
enlightened. 

5. The angle of position of the stars I have only given with regard to the 
parallel of declination, to be reduced to that with the ecliptic as occasion may 
require. The measures always suppose the large star to be the standard, and the 
situation of the small one is described accordingly. Thus, in fig. 12, ab repre- 
sents the apparent diurnal motion of a star in the direction of the parallel of de- 
clination ab; and the small star is said to be south preceding at mn, north pre- 
ceding at op, south following at qr, and north following at st. The measure of 
these angles, I believe, may be relied on to 2°, or at most 3°, except when men- 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 215 

tioned inaccurate, where an error amounting to 5° may possibly take, place. In 
mere estimations of the angle, without any wires at all, an error may amount 
to at least 10°, when the stars are near each other. 

6. The dates, when I first perceived the stars to be double, treble, &c. are 
marked in the margin of each star. To shorten the work as much as possible, 
I have put l for the large star; s for the small star; w for white; r for red; d 
for dusky; n for north; s for south; and have also occasionally used other ab- 
breviations that will be easily understood. It may be seen, that this catalogue 
is yet in a very imperfect state, many of the stars not having even the principal 
elements of distance and position determined with any degree of accuracy ; but 
having already mentioned the reason why I give it imperfect as it is, I can only 
add that my endeavours will not be wanting soon to remove those defects. How- 
ever, since this can only be a work of some time, we may hope, in the mean 
while, that many lovers of the science will turn their thoughts to the same 
subject. 



CATALOGUE OF 

First Class. 

1. i Bootis. Flamst. 36. Ad dextrum femur in pe- 
rizomate. 

Sept. 9, 1779- — Double. Very unequal. L red- 
dish ; S blue, or rather a faint lilac. A very beautiful 
object. The vacancy, or black division between them, 
with 227 is | diameter of S; with 460, l\ diameter 
of L; with 932, near 2 diameters of L; with 1159, 
still further; with 2010, extremely distinct, 2j dia- 
meters of L. These quantities are a mean of 2 years 
observations. Position 31° 34' n preceding. 

2. I Ursae majoris. Fl. 53. In dextro posteriore 
pede. 

May 2, 1780. — Double. A little unequal. Both 
w and very bright. The interval with 222 is \ dia- 
meter of L; with 227, 1 diameter of L; with 278, 
near 1| diameter of L. Position 53° 47 ' S following. 

3. <r Coronae borealis, Fl. 17- 

Aug. 7. — Treble. The 2 nearest pretty unequal; 
the 3d very faint with powers lower than 460. The 2 
nearest both w ; the 3d d. Interval of the 2 nearest 
with 227, full l| diameter of L; with 460, 2 dia- 
meters of L. Position 77° 32' n preceding. Distance 
of the 3d from L 24" by exact estimation. Position 
25° n following by estimation. 

4. In constellatione Draconis, Fl. 16. 

Aug. 8. — Double. It is the star to which a line 
drawn from » through fi>, points at nearly the same dis- 
tance from /* as ^ from ». Considerably unequal. L 
w; S w inclining to r. With 222, 1 diameter of L ; 
with 278, U diameter of L. Position 24° 0' s fol- 
lowing. There is a 3d star, at some distance, pre- 
ceding. 

5. <r Cassiopeae, Fl. 8. In dextro cubito. 

Aug. 31 . — Double. It is the star at the vertex of a 
telescopic isosceles triangle turned to the south. Very 
unequal. L w a little inclining to r ; 6 d. With 222, 



DOUBLE STARS. 

near I diameter of L; with 460, 1| diameter of L. 
Position 60° 28' n preceding. 

6". Quae infra oculum Lyncis, Fl. 1 2. 

Oct. 3. — A curious treble star. Two nearest pretty 
unequal. Lw; S w inclining to rose colour. With 
227, about \ diameter; with 460, full f diameter of 
s. Position 88° 37' s preceding. The 1st and 3d con- 
siderably unequal ; 2d and 3d pretty unequal. The 3d 
paler. Distance from the 1st 9" 23"'; too difficult to 
be extremely exact. Position with regard to the 1st 
32° 33' n preceding. 

7. b Draconis, Fl. 39- Trium in recta, in prima 
inflectione colli, borea. 

Oct. 3. — A minute double star. Extremely unequal, 
the small star being a fine lucid point. L w; S in- 
clining to r. With 227, 3 diameter of L ; with 460, 
full lj diameter of L; with 932 (extremely fine) full 
2 diameters of L. Position 77° 8' n following. A 3d 
star at some distance ; dusky r. Position 6'3° 22' n 
following. 

8. i Draconis, Fl. 6"3. In quadrilatero inflexionis 
primae. 

Oct. 3. — A very minute double star. Excessively 
unequal ; the small star can only be seen when the air 
is perfectly clear. Lw; S d. With 227, less than 1 
diameter of L ; with 278, not a diameter of L. Posi- 
tion 63° 14' n preceding. A pretty large 3d star at 
about 3 or 4'. Position of this 3d star with i 88° l& 
n following. 

9. In cauda Lyncis media, Fl. 39- 

Nov. 24. — Double. Very unequal. L w ; S in- 
clining to r. With 227, extremely close; with 460, 
at least § diameter of S. A very fine object. Posi- 
tion 25° 51' s preceding. A proper motion is sus- 
pected in one of the stars. 

10. In sinistra anteriore pede Monocerotis, Fl. 11. 
Feb. 15, 1781. — A curious treble star ; may appear 

double at first sight ; but with some attention we see 



2l6 



1'ilILOSOl'HlCAL. TRANSACTIONS. 



[ANNO 1/82. 



that one of then) again is double. The first, or single 
star, is the largest ; the other two are both smaller, 
and almost equal, but the preceding of them is rather 
larger than the following. They are all w. The two 
nearest with 227, 1 diameter of the preceding, or 
nearly ij of the following; with +(>(>, 1 ' diameter of 
the preceding. Position of the two nearest 1 1° 32' s 
following. For an account of the single star, see the 
2d class. As perfect as I have seen this treble star with 
460, it is one of the most beautiful sights in the hea- 
vens ; but requires a very fine evening. 

11. In constellatione Cancri, Fl. II. 

Mar. 13. — Double. Considerably unequal. Both 
pale r. With 227, 1 full diameter of L; with 4n'0, 
about If diameter of L. Position 86° 10' n preceding. 

12. d Serpentis, Fl. 5.9. In Cauda. 

July 17. —Double. Very unequal. I, reddish w; 
S fine blue. With 227, 1 full diameter of L; with 
278, I i diameter of L. Position 44° 33' n preceding. 

13. In constellatione Aquilae, near Fl. 37- 

July 25. — A curious treble star. It is the last star 
of a telescopic trifolium n following k, similar to that 
in the hand of Aquarius. The two nearest very une- 
qual; the 3d star excessively small, and not visible 
with 227- Tile two nearest with 460, no more than ', 
diameter of L; the farthest about 7 or S". 

14. In constellatione Aquilae, Fl. 24. 

July 30. — Double. In Harris's maps it is the star 
in the elbow of Antinous. Excessively unequal ; the 
small star is but just visible with 2J7 ; but with 400 
it is pretty strong. L pale r; S d. With 2-7, 1 full 
diameter of L; with 460, \\ diameter of L. Posi- 
tion 72° (>' s following. 

15. i Bootis, Fl 4 4. 

Aug. 17. — Double. In Harris's maps it is marked 
i, but has no letter in Fl. Atlas. Considerably unequal. 
Both w. Witli t'l7 they seem almost to touch, or at 
most I diameter of S asunder; with 4d'0, | or J dia- 
meter of S. This is a fine object to try a telescope, 
and a miniature of « Geminorum. Position 29° 54' n 
following. 

16". 1 Coronae borealis, Fl. 2. 

Sept. p. — Double. A little unequal. They are 
whitish stars. They seem in contact with 227, and 
though 1 can see them with this power, I should cer- 
tainly not have discovered them with it; with 460, 
less than | diameter; with 932, fairly separated, and 
the interval a little larger than with 400. I saw them 
also with 2010, but they are so close that this power is 
too much for diem, at least when the altitude of the 
stars is not very considerable; with 460 they are as 
fine a miniature of i Bootis as that is, of « Geminorum. 
Position 59° 19' n following. 

17. In constellatione Bootis, near Fl. 51. 

Sept. 10. — Double. It is a star near «- not marked 
in Flamsteed's catalogue. Considerably unequal. Both 
dusky w inclined to r. The interval with 460 is | 
diameter of S. The position of die small star is turned 
towards y< a little following the line which joins L to 
fij Bootis. See </• Bootis in the 6th cl iss. 

18, In constellatione Coronae borealis. 

Sept. 10. — Double. It is the smallest of 2 tele- 



scopic stars between 6 and S~, not contained in Fl cat. 
Equal. Both d. With 460, about Ig diameters. Posi- 
tion 21° 0' n following. 

19. /; Draconis, near Fl. 20. 

Sept. 1 0. — One of the most minute of all the double 
stars I have hitherto found. It is the small telescopic 
star near the preceding /; Draconis. Considerably un- 
equal. Both dusky w inclining to r. With 460, they 
seem in contact; I ha\ r e however had a very good 
view of a small dark division between them. Position 
(by exact estimation) 25 or 30° s preceding. They 
are too minute for any micrometer I have. It is in vain 
to look for them if every circumstance is not favourable. 
The observer as well as the instrument must have been 
long enough out in the open air to acquire the same 
temperature. In very cold weather, an hour at least 
will be required; but in a moderate temperature, half 
an hour will be sufficient. 

20. In dextro humero Orionis, Fl. 52. 

Oct. 1 — Double. A little unequal. Both w a little 
inclining to pale r. With 227, I diameter; with 460, 
h diameter. Position 6"9° 41' s preceding. 

21. c Trianguli, near Fl 12 and 13. 

Oct. 8. — Double. It is the most north of a small 
telescopic trapezium of unequal stars. Extremely un- 
equal. With 460, I diameter of L. Position (by 
estimation) 55 or 6'o° n preceding. 

22. » Orionis, Fl. 33. Duarum praecedentium 13 im 
(*>) antecedens. 

Oct. 22. — Double. Considerably unequal. Lw: 
S w ; inclining to blue. With 227, they seem almost 
in contact; with 46'0, ^ diameter of S. Position 6" 1° 
23' n following. A very pleasing object and easily 
seen. 

23. In posterioribus femoribus Canis minoris. 
Nov. 21. — A most minute double star. It is the 

small telescopic star following Procyon. A little un- 
equal. Both w. With 278, £ of a diameter of S; 
with 46"0, near | of a diameter of S. They are closer 
than n Coronae, because their diameters, by which 
they are estimated, are smaller. Position 27°21's 
following. To see this very minute double star well, 
Procyon should be near its meridian altitude. There 
is a small telescopic star preceding the double star. 
Distance 1' 59" 39 from centre to centre. 

2). £ Cancri, Fl. 16". 

Nov. 21. — A most minute treble star. It will at 
first sight appear as only a double star, but with proper 
attention, and under favourable circumstances, the pre- 
ceding of them will be found to consist of 2 stars, 
which are considerably unequal. The largest of these 
is larger than the single star; and the least of the 2 is 
less than the single star. The 1st and .'d (in the order 
of magnitude) pretty unequal. The 2d and 3d pretty 
unequal. The 2 nearest both pale r or r. With 278, 
but just separated ; with 46'0, j diameter of S. Po- 
sition 80° 32' n following. For measures relating to 
the 3d or single star, see £ Cancri in the d class of 
double stars. 

Second Class <>t Double Sims. 

I. t « Geminorum. Fl. 66. In capite praece- 
dentis IP. 



VOL. LXXII.J 



PHILOSOPHICAL TRANSACTIONS. 



217 



April 8, 1778. — Double. A little unequal. Both 
w. The vacancy between the 2 stars, with a power 
of 146, is 1 diameter of S; with 222, a little more 
than I diameter of L; with '227, l| diameter of S; 
with 466, near 2 diameters of L ; (see fig. 6") with 
754, 2 diameters of L; with 1)32, full 2 diameters of 
L; with 1 536, very fine and distinct, 3 diameters of 
L; with 3 l6S, the interval extremely large, and still 
pretty distinct. Distance by the micrometer 5". 156. 
Position 32° 47' n preceding. These are all a mean 
of the last 2 years observations, except the first 
with 146. 

2. + * Herculis, Fl. 64. In capite. 

Aug. 2;>, 1779. — A beautiful double star. Very 
unequal. Lr; S blue inclining to green ; the colours 
•with every power the same. The interval with 222, 
lj diameter of L; with 227, above 2 diameters of L; 
with 932, above 3 diameters of L. Distance 4".966. 
All a mean of 2 years observations. A single measure 
with my last new micrometer, from centre to centre, 
4" 34'". Position 3<>° 35' s following. 

3. *£ Herculis, Fl. 75. Trium in sinistro femore, 
tertia. 

Aug. 29. — Double. Pretty unequal. Both w. 
With 227, 1 5 diameter of L ; with46(), 2 diameters 
ofS. Distance 2".969. Position 30° 21' n preceding. 
The measures a mean of 2 years observations. 

4. * p Serpentarii, Fl. 70. Tres has sequitur, quasi 
supra mediam. 

Aug. 29. — Double. Considerably unequal. Lw; 
6 inclining to r. With 227, If diameter of L; with 
460, much above 2 diameters of L. Position y° 14' 
s following. Mean of 2 years observations. 

5 et 6. * t Lyra, Fl. 4 and 5. 

Aug. 29. — A very curious double-double star. At 
first sight it appears double at some considerable dis- 
tance, and by attending a little we see that each of the 
stars is a very delicate double star. The first set con- 
sists of stars that are considerably unequal. The stars 
of the 2d set are equal, or the preceding of them ra- 
ther larger than the following. The colour of the stars 
in the first set L very w; S a little inclining to r. In 
the 2d set both w. The interval between the stars of 
the unequal set, with a power of 227, is full 1 dia- 
meter of L; with 460, near 1 h diameter of L; with 
932, full 1 J diameter; with 2(>]o, 2£ diameters. The 
interval between the equal set with a power of 227 is 
almost lg diameter of either; with 460, full l| dia- 
meter; with 932, 2 diameters; with 2010, 2 2 dia- 
meters. These estimations are a mean of 2 years ob- 
servations. Position of the unequal set 56° 0' n fol- 
lowing. Position of the equal set 72° 57' s following. 

7. * Z, Aquarii, Fl. 55. Trium in manu dextra 
prscedens. 

Sept. 12. — Double. Equal, or the preceding rather 
the larger. Both w. Widi 227, I5 diameter; with 
449, "l^ diameter; with460, 2 diameters; with 910, 
near 2 diameters; with 932, 2 \ diameters; with 2010, 
pretty distinct; but too tremulous to estimate. With 
my 20-feet reflector, power 600, full 2 diameters, 
very distinct. Position 71° 39' n following. Distance 
4".56, mean of 2 years observations. 

VOL. XV. F 



8. £ Coronae borealis, Fl. 7- 

Oct. 1. — Double. Considerably unequal. L fine 
w; S w inclining to r. With 222, almost 3 diameters 
of L. Distance 5".4<>8. Position 25° 51' n preceding, 
mean of 2 years observations. 

9. * Orionis, Fl. 39. In capite nebulosa. 

Oct. 7. — Quadruple, or rather a double star and 2 
more at a small distance. The double star consider- 
ably unequal. Lw; S pale rose colour. With 222, 

1 h diameter of L ; with 44'), above 2 diameters of L. 
Distance 5".8 S3, a mean of all the measures. Posi- 
tion 45° 14' n following. As every one of the 4 stars 
is perfectly distinct, it is evident that the whole ap- 
peared nebulous to Flamsteed for no other reason than 
because his telescope had not sufficient power to distin- 
guish them. 

10 and 11. ir Orionis, Fl. 48. Ultiman cinguli 
praecedit ad austrum. 

Oct. 7 • — A double-treble star, or 2 sets of treble 
stars, almost similarly situated. Preceding set. The 

2 nearest equal; the 3d larger and, compared with 
either of the former 2, pretty unequal. The 2 nearest 
with 222, about 2 diameters. Position of the follow- 
ing star of the 2 nearest with the 3d 6t>° 35' s preced- 
ing. Position of the 2 nearest, by exact estimation, 
2 or 3° n following or s preceding the following set. 
The 2 nearest very unequal. The larger of the 2 and 
the farther considerably unequal. L w; S blueish. 
The 2 nearest with 222, about 2j diameters of L ; the 
2 farthest 43" 1 2'". Position of the 2 nearest 5° 5' n 
following. Position of the 2 farthest 29° 4' n follow- 
ing. A pretty object with 227. 

12. « Piscium, Fl. ultima. In nodo duorum linorum. 
Oct. 19. — Double. Considerably unequal. Both 

w. With 222, not quite 2 diameters of L ; with 460, 
about 3 diameters of L. Distance 5". 123 mean mea- 
sure. Position 67° 23' n preceding. 

13. j«. Draconis, Fl. 21. In lingua. 

Oct. 19. — Double. Equal. Both w. With 227, 
1 5 diameter; with 460, 2| diameters. Distance 
4".354 mean measure. Position 37° 38' s preceding or 
n following. 

14. <•> Aurigae, Fl. 4. 

Oct. 3d. — Double. Very unequal. L w; S r. 
With 227, almost 2 diameters of L ; with 460, full 3 
diameters of L. Position 82° 37' n preceding. 

15. ^ Cygni, Fl. 24. In ala dextra. 

Nov. 2. — Double. Extremely unequal ; the small 
star a mere point. Lw; S r. With 227, near \\ 
diameter of L; with 278, near \\ diameter of L; 
with 460, 2 diameters of L. Position 89° 32' n pre- 
ceding. 

16. I Cephei, Fl. 17. In pectore. 

Nov. 7 . — A fine double star. Considerably unequal. 
L w inclining to r; S dusky grey. With 222, nearly 
2 diameters of L. Single measure 5".00. Position 
20° 1 8' n preceding. 

17. * In sinistro anteriore pede Monocerotis, Fl. 11. 
Dec. 5. — Double. With 222, about 1 \ diameter. 

Position (taken Oct. 20, 178 1 ) with the farther of the 
other 2 stars 31° 38' s following. See the 10th star 
in the first class. 



218 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1782. 



18. i Bootis, Fl. 37. 

April 9, 1780. — Double. Very unequal. L pale 
r, or nearly r. S garnet, or deeper r than the other. 
With 22'?, In diameter of L, with 460, fall 3 dia- 
meters of L. Distance 3" 23'" single measure. Po- 
sition 6 j° 53' n following. 

iii. g Serpentarii, Fl. 5. 

]y] a y <j, — Double. It is a star in the body of 
Cancer, and the double star is at the angular point of 
the 3 telescopic g's making a rectangle. Pretty un- 
equal. Both w. With 227, 1 i diameter of L. Po- 
sition 82° 10' s preceding. 

2ii and 21. I Librae, Fl. ultima. 

May 2.3, i?SU. — Double double. The first set 
very unequal. L fine w. With 227, nearly 2 dia- 
meters of L.* By the micrometer 6" 23'", but too 
large a measure. Position 1° 23' n following. The 
other set both small and obscure. With '227, perhaps 
5 or 6 of their diameters asunder. 

22. i Persei, Fl. 45. In sinistro genu. 

Aug. 2, 1780. — Double. Extremely unequal. L 
w; S d. With 222, 2 J diameters of L. Position 
81° 28' s following, a little inaccurate. A 3d star 
near at about 1 h or 1 f min. 

23. In constellatione Serpentarii, near Fl. 1 1 . 
Aug. 7. — Double. It is the smaller and preceding 

of 2 in the finder. Pretty unequal. L pale r ; S 
dusky r. With 222, about l£ diameter of L; with 
278, about lj diameter of L; with 46u, above 2 
diameters of L. Position 46° 24' n preceding. A 
little inaccurate. 

24. In constellatione Aquarii, Fl. 107. In se- 
quenti flexu 4 a ad a . 

Aug. 23. — Double. In Harris's maps it is marked 
i. Unequal. With 227 , 2 diameters ; with 460, 
about 3 diameters. 

25. k Cygni, Fl. 59. 

Sept. 8. — Double. Extremely unequal. L w in- 
clining to r ; S d. and extremely faint ; with 227, 2j 
diameters of L ; with 46"0, about 4 diameters of L, 
or more. Position 31° 3' n following. 

26. In constellatione Ononis, near Fl. 4 2. In 
longo ensis. 

Oct. 23. — Double. It is the most north of 3 teles- 
copic stars in a line at the end of a cluster near c. 
Extremely unequal. Lw; S d. With 278, l| 
diameter of L. Position 26° 5' n following. 

27. ^Geminomm, Fl. 55. In inguine sinistro se- 
quentis II'. 

March 13, 1781. — Double. Extremely unequal. 
Lw inclining to r; S r. With 227, about .J full 
diameters of L; with 460, 4 or 5 diameters. Posi- 
tion 85° 51' s preceding. 

28. In constellatione Aquilae, near Fl. 54. 

July 23. — Double. It is a star following o. Ex- 
cessively unequal . The small star is not visible with 
227, nor with 278. It is visible with 460 ; but not 
without attention. Distance with 46*0, about 4 or 5 
diameters of L. Position, by very exact estimation, 
36° 28' n preceding. 

* In a future collection this set will be found as a tieble star 
of the fust class, the large white star, with a power of 460 and 
9Si, appearing to be 2 stars — Orig. 



2.9. In constellatione Aquilae, near Fl. 63. In 
medio capite. 

July 31. — Double. It is the star at the vertex of a 
telescopic isosceles triangle near r. Extremely un- 
equal. Both r. With 400, 2 diameters of L. Po- 
sition 75° 4S' n preceding. 

o0. £ Sagittae, Fl. 8. Trium in arundine sequens. 

Aug. 23. — Double. Extremely unequal. The small 
star brighter with -100 than with 227 or with 278; 
with 160, between 4 or 5 diameters of L ; with 278, 
2 1 diameters of L. Distance 5" 27'" inaccurate. 
Position 34° 1 0' n preceding. 

31. In constellatione Draconis, Fl. 56. 

Sept. 6. — Double. A little unequal. Both \v. 
With 40O, near 3 diameters. Distance 5" }"'. 

32. In constellatione Sagittae, near Fl. 4. 

Sept. 7 . — Double. It is the star north following t. 
L pale r ; S d. Distance J' 3'" inaccurate. 

3 1. /3 Orionis, Fl. 19. In sinistro pede splendida. 

Oct. 1. — Double. Extremely unequal. L w; S 
inclining to r. With 2. '7, 2^ or 2\ diameters of 
Bigel. With 400, more than 3 diameters of L. 
Distance 5" 27"'. Position 68° 12' s preceding. The 
small star not wanting apparent magnitude is better to 
be seen with my power of 227 than with 46'u. 

34. Trianguli, Fl. 0. 

Oct. S. — Double. It is marked b in the small tri- 
angle of Harris's maps. Very unequal. L pale r or 
reddish w ; S blueish r. With 227, full I \ diameter 
of L; with 460, full lj diameter of L. Position 
4° 23' n following. A pretty object, somewhat re- 
sembling «. Herculis, but smaller, and not so bright. 

35. In constellatione Trianguli, near Fl. (i. 

Oct 8. — Double. It is the star following t. Equal. 
Both dusky w. With 400, about 2.", diameters. 

3d. In constellatione Eridani, Fl. 32. 

Oct. 22. — Double. Considerably unequal. L red- 
dish w ; S blue. Distance 4" 19'". Position 73° 23' 
n preceding. 

37- In capite Monocerotis. 

Oct. 22. — Double. It is one of a cluster of 6 
telescopic stars, arranged in pairs. 

38. In constellatione Bootis. 

Dec. 24. — Double. It is the most north and 
largest of 3 in a line, s following Fl. 15. Consider- 
ably unequal, L w ; S inclining to r. Distance 5" 10'". 
Position 83° 5' s preceding. 

Third Class of Double Stars. 

1. f Orionis, Fl. 41. Trium contiguarum in 
longo ensis media. 

Nov. 1 1, 1770. — Quadruple. It is the small teles- 
copic Trapezium in the Nebula. Considerably un- 
equal. The most southern star of the following side 
of die Trapezium is the largest ; die star in die oppo- 
site corner is the smallest ; the remaining 2 are nearly 
equal. L pale r; the star preceding I, inclined to 
garnet ; following L inclined to garnet ; opposite to 
L d. With 460, the stars are all full, round, and 
well-defined. The 2 stars in the preceding side dis- 
tance 8". 7 80; in the southern side, 12".812 ; in 
the following side I5".208; in the northern side, 
20". 396. 

2. C, Ursae majoris, Fl. 5i). Trium in cauda media. 



VOL, 



LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



219 



Aug. 17, 1779- — Double. Considerably unequal. 
L w ; Swj inclining to pale rose colour. Distance 
14".5 by 2 years observations, not a mean but that 
which I suppose nearest die truth. Position 50° 40' s 
following. 

3. « Cassiopeae, Fl. 24. In cingulo. 

Aug. 17. — Double. Very unequal. L fine w; 
S fine garnet, both beautiful colours. Distance 
1 1",275 mean measure. Position 27° 56' n following. 

4. In extremitate pedis Cassiopeae, Fl. 55. ' Pto- 
lemaei. 

Aug. 17. — Double. Extremely unequal. Lw; 
S blueish r. Distance 1 ".5 single measure Position 
10° 37' s following. J 

5. * v Andromedae, Fl. 57. Supra pedem sinis- 
trum. 

Aug. 25. — Double. Very unequal. L reddish w; 
S fine light sky-blue, inclining to green. Distance 
9". 254 a mean of 2 years observations. Position 
1°° 37' n. following. A most beautiful object. 

6. /3 Cephei, Fl. 8. In cingulo ad dextrum latus. 
Aug. 31. — Double. Very unequal. L blueish 

wj S garnet. Distance 13". 125. Position 15° 28' s 
preceding. 

7. * /3 Scorpii, Fl. 8. Trium in fronte, lucida- 
rum, borea. 

Sept. 19. — Double. Very unequal. L whitish r ; 
S r. Distance 14". 37 5. Position 6'4° 51' n fol- 
lowing. 

8. * 7s Bootis, Fl 29. 

Sept. 20. — Double. Pretty unequal. L w ; S w, 
inclining to r. Distance o".17l. Position 0° 28' s 
following. 

9. ^ 7 Arietis, Fl. 5. Quae in corau duarum prae- 
cedens. 

Sept. 27- — Double. Equal, or if any difference 
the following is the larger. Distance 10". 172, a 
mean of 2 years observations. L w, inclining a 
little to r ; S w. Position S0° 5' n preceding. 

10. *yDelphini, Fl. 12. Borea sequentis lateris, 
quadrilateri. 

Sept. 27. — Double. Nearly equal, the following 
a little larger. Both w. Distance 11". 822, being a 
mean of the measures taken in Sept. Oct. Nov. and 
Dec. 1779- As I suspect a motion in one of these 
stars, I thought it best not to join other observations 
in that measure. Position 4° 9' n preceding. 

11. x Bootis, Fl. 17. Trium in sinistra manu 
praecedens. 

Sept. 27. — Double. Very unequal. Lw; S d. 
Distance 12". 503, a mean of the observations in 
1779, 80, 8 I . Position about 30° s preceding. 

li. 1 Ononis, Fl. 44. Trium contiguarum in ense 
austrina. 

Oct. 7. — Treble. It is the following or larger of 
the 2 i's. One is L ; the other 2 are extremely small. 
L w ; the other 2 both dusky r. Distance of the 
nearest 12". 5. Distance of the farthest 48" 31'". 
Position of the nearest 43° 5 1' following. Position of 
the farthest 11° 19' s following. 

J In a future collection this will be found as a treble star of 
the first class ; the large star having a small one preceding, easily 
seen with 460 and 932.— Orig. 



13 and 14. 1 Ononis, Fl. 44. Trium contiguarum 
in ense austrina. 

Oct. 7. — Double treble. It is the preceding or 
smallest of the 2 i's. The preceding set, forming a 
triangle, consists of 3 equal stars. All dusky r. 
Distance of the 2 nearer, with 227, about 3 diame- 
ters. The following set, forming an arch, consists of 
3 stars of different sizes. The middle star is the 
largest ; that to the south is also pretty large ; and the 
3d is very small. L w ; 1 w ; S pale r. Distance 
36". 25. 

15. * «. Cjgni, Fl. 78. 

Oct. 19. — Double. Considerably unequal. L w; 
S blueish. Distance b".;)27 mean measure. Posi- 
tion 20° 15' s following. 

16'. * In constellatione Delphini, Fl. 1. 

Nov. 15. — Double. It is the star south preceding 
t. A little unequal. Both w. Distance 12".5. 
Position 9° 42' s preceding. 

17. In extremitate caudae Lacertae, near Fl. I. 
Nov. 20. — Double. Considerably unequal. Lw; 

S d ; inclining to r. Distance 1 3" 43'" inaccurate. 
Position 7b° lti' s preceding. 

18. f 7 Virginis, Fl. 29- De quatuor in ala sinis- 
tra, sequens. 

Jan. 21, 1780. — Double. Equal. Both w. Dis- 
tance 7"-333 mean measure. Position 40° 44' s fol- 
lowing. 

19. f £Cancri, Fl. 16". 

April 5. — Double. Considerably unequal. L pale 
r ; S pale r. Distance 8". 040' mean measure. Posi- 
tion S 8° lti' s preceding. See the 24th in the first 
class, 

20. In constellatione Bootis. 

June 25. — Double. Draw a line through ir and £ 
to die small star under the right foot, and erecting a 
perpendicular towards the left foot of equal length, 
the end of it will mark out this double star. Pretty 
unequal. Bodi r. Distance 7" 3b'" full measure. 
Position 59° 32' n preceding. 

21. In constellatione Equulei, Fl. 1. 

Aug. 2. — Double. Considerably unequal. L w ; 
S much inclining to r. Distance 9"-375 mean mea- 
sure. Position 5° 39' n following. A ;:d small star 
follows at some distance. 

22. Quae infra oculum Lyncis, Fl. 12. 

Aug. 7. — Double. With 22-', about 3 diameters 
of L. Considerably unequal. L w ; S pale r. Dis- 
tance 9" 23'", not extremely accurate. Position 
32° 33' n preceding. See the o'th star in the first 
class. 

23. In constellatione Cassiopeae, Fl. 34. 

Aug. 8. — Double. It is one of 2 telescopic stars, 
and is marked <p in Harris's maps. Extremely un- 
equal. L paler; S d. Distance about 12" or more. 

24. I Sagittae, Fl. 17. 

Aug. 8. — Treble. The 2 nearest extremely un- 
equal. L pale r ; S d. Third star pale r. Distance 
of the 2 nearest I I" 8'". Distance of the 2 largest 
57" 49'". 

25. * In constellatione Serpentarii, Fl. 39- 

Aug. 24 . — Double. It is the more south and 
larger of 2 in the finder. Very unequal. L w ; S 
F 2 



22() 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1782. 



inclining to blue. Distance 10" 2'", a little inaccu- 
rate. Position S7° 14' n preceding. 

26. * In constellatione Cerberi 1 . Hevelii 1*. Fl. 
Herculis 95. 

Sept. 8. — Double. It is the star in the leaf nearest 
to Hercules's face and hand. Equal. Preceding w. 
Following blueish w. Distance 6" 6'". Position 
4° 9' s preceding or n following. 

27. In constellatione Navis, near Fl. 3. 

Feb. 15, 1781. — Double. It is a star between 1 
Canis majoris and % Navis. Equal. Distance about 
15". 

28. In constellatione Navis, near Fl. p. 

Feb. 15. — Double. It is one of 2 telescopic stars 
under Monoceros. Distance about 8". 

29. In naribus Monocerotis, Fl. 8. :: 
Feb. 15. — Double. Distance about 12". 

30. * In constellatione Leonis, Fl. 54-. Duarum 
supra dorsum sequens. 

Feb. 2 1 . — Double. Considerably unequal. L 
brilliant w ; S ash-colour, or greyish w. Distance 
7" 6'" mean measure. Position y° 14' s lollowing. 

31. In constellatione Herculis. 

May 20. — Double. Over » ::. Equal. Both 
very small. Distance about 10". 

32. In constellatione Aquilae, Fl. II. 

July 25. — Double. It is the more south of 2 near 
> and £. Excessively unequal. S hardly visible with 
227, but pretty strong with 460. Distance about 7". 

33. In constellatione Aquilae, near Fl. 7 and 8. 
July 30. — Double. It is a star preceding the 2 

small stars north of k and /. Unequal. L w ; S 
blueish w. Distance I I' 35"' inaccurate, but not 
much. 

34. In constellatione Aquarii, Fl. 94. 

Aug. 20. — Double Between -^ and a towards <£, 
Very unequal. Distance 1 3" 45"'. L pale r ; S d. 

35. In Constellatione Serpentarii, Fl. 54. 

Aug. 21. — Double. It is the preceding of 2 stars 
in the head. Excessively unequal. L reddish w ; S 
d. Distance about 8". 

36. In constellatione Persei. 

Sept. 14. — Double. A little south of y. Con- 
siderably unequal. L w ; S w, inclining to r. Dis- 
tance 1 1" 53", rather full measure. 

37 and 38. In constellatione Persei, near Fl. 38. % 
Sept. 24. — Double-double. South preceding the 
first 0. The equal set with 227, about 4 or 5 diame- 
ters. The unequal set about 5 or diameters. Near 
this last set is also a 3d star forming an obtuse angle 
with the stars of this set. Distance about 10". 

39. Persei, Fl. 40. 

Sept. 21. — Double. It is the 2d or more northern 
•. Extremely unequal. L w ; S d. With 227 , S 
is hardly visible ; with 460, it appears at first sight. 
Distance 14" 59'", inaccurate on account of the ob- 
scurity of S. 

40. In constellatione Herculis, near Fl. 87. 

Oct. 1 0. — Double. Of 3 stars, forming an obtuse 
angle, whereof Fl. 87, (a star south of /«.) is at the 
angular point, that towards Ramus Cereb. Extremely 

J Mr. Bryant o( Bath first observed these stars.— Orig. 



unequal. L w ; S d. Distance 10' 20"'. Position 
19° 37' s following. 

41. * i Herculis, Fl. 43. 

Oct. 10. — Double. Equal. Preceding star w. A 
little inclined to r. Following w. Distance 1 1" 43'". 
Position 88° 2 ■ >' n following. 

42. In constellatione Trianguli. 

Oct. 10. — Double. It is a star north following £ 
Unequal L reddish. S blueish. Both d. Dis- 
tance about 6 or 7". 

43. In sinistra anteriore pede Monocerotis. 

Oct. 2C — Double. It is the more south of 2 tele- 
scopic stars preceding the treble star. Extremely 
unequal. L w ; S d. Position 23° 39' n preceding. 

44. In ore Monocerotis. 

Oct. 20. — Double. Considerably unequal. L w ; 
S r. Distance 12" 30'". Position 6"0° 14' n following. 

4-5. In constellatione Tauri, near Fl. 10. 

Oct. 22. — Double. It is near the star sub pede et 
scapula dextra. Extremely unequal. L pale r ; S d. 
Position 35° 33' s preceding. 

40. In constellatione Monocerotis. 

Oct. 22. — Double. It is the star following the tip 
of the ear. 

Fourth Class of' Double Stars. 

1 . a. Ursae minoris, Fl. I . Stella Polaris. 

Aug. 17, 1779- — Double. Extremely unequal. 
Lw; S r. Distance 17" 15'". Position 66° 42' s 
preceding. 

2. * n Lyrae, Fl. 20. Duarum contiguarum ad 
ortum a testa, borea. 

Aug. 29- — Double. Considerably unequal. L w ; 
S r. Distance 25" 42'". Position 3 1° 5 1' s preceding. 
Three other stars in view. 

3. Fl. b'4. Sagittarii. 

Sept. 19. — Double. It is the preceding star of two. 
Extremely unequal. Distance about 25". 

4. « Persei, 1. Hevelii 9. In dextro brachio. 
Sept. 20. — Double. Very unequal. Lr; S blue. 

Distance 26", very inaccurate. Position 20° 5' n 
preceding. 

5. In constellatione Arietis, Fl. 3'. Quatuor in- 
form, sup. dors, prase. 

Sept. 2/. — Double. It is the first in the head of 
the fly. L w ; S. d. Considerably unequal. Dis- 
tance 25" 32'" inaccurate. Position S7° 14'. 

6. f 6 Serpentis, Fl. 6'3. In extremitate Cauda;. 
Oct. 17- — Double. Equal. Both w. Distance 

J9"-375. 

7. •+ Draconis, Fl. 31. Prima ad i^. 

Oct. 1 9- — Double. Pretty unequal. L w ; s pale r. 
Distance 28" 14'". 

8. * £ Piscium, Fl. So'. Trium in lino lucidarum 
sequens. 

Oct. 19. — Double. Pretty unequal. Lw; Sw 
inclining to blue. Distance S 2". 1H7, not very accu- 
rate. Position 22° 37' n following. 

9. * Prima ad 4- Piscium, Fl. 7 4. Trium in pinna 
costarum prascedens. 

Oct. 30. — Double. Distance 27".5. Position about 
80° s following. An obscure star also within I .} min. 

10. x Tauri, Fl. 59. Australis sequentis lateris 
quadrilateri, in cervice. 



VOL. LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



221 



Oct. 3<>. — Double. Distance 1S"75, very inac- 
curate. 

11. * Cygni, Fl. 17- 

Nov. 20. — Double. Very unequal. L w ; S dusky 
r. Distance 24" 52'". 

12. * 4 1 Aquarii, Fl. 91. 

Nov. 26. — Double. It is the first of 3 4-'s. Un- 
equal. Distance 23" 5'", pretty accurate. 

13. In constellatione Leonis, Fl. S3. 

April 6, 1780. — Double. It is a small star north 
preceding r. A little unequal. Both inclining to r. 
Distance 29" 5'". Position 54° 55' s following. 

14. In constellatione Aquilae, Fl. 57. 

Aug. 2. — Double. It is the preceding of 2, near 
the south end of Antinous's bow. A little unequal. 
Lw; Sw, inclining to r. Distance 29" 28'", pretty 
accurate. Position 81° 55' s preceding. 

15. In dextra aure Camelopardali. I. Hevelii 
ultima. 

Aug. 2. — Double. A little unequal. L reddish w ; 
S reddish w. Distance 20" 5'". 

1 6. In constellatione Cassiopeae, Fl. 3 1 - 

Aug. 2. — Double. It is marked with the letter a 
in Harris's maps. Distance about 2; " or more. 

17. * Cor Caroli, Fl. 12. Canum Venaticorum. 

Aug. 7 — Double. Very unequal. L w ; S in- 
clining to r. Distance 20" 0'", inaccurate. Position 
41° 4/ s preceding. 

18. * In constellatione Cygni, Fl. 61. 

Sept. 20. — Double. It is a star preceding r. Pretty 
unequal. L pale r ; S r ; or L r ; S garnet. Dis- 
tance 16" 7'". Position 30° 28' n following. 

19. In constellatione Aurigae, Fl. 14. 

Sept. 24. — Double. It is the preceding star of a 
cluster of stars that precede <p and x- Very unequal. 
L reddish w ; S d. Distance 16" 8'", a little inaccu- 
rate. Position 37° 3S' s preceding. 

20. a Draconis, Fl. 47- 

Oct. 3. — Double. Very unequal. L pale r ; S 
dusky r. Distance 26" 39'". Position 90° n preced- 
ing or following, by exact estimation. 

21. £Orionis, Fl. 50. Trium in cingulo sequens. 
Oct. 1 0. — Double. Very unequal. L w ; S d. 

Distance about 25". Position 83° 25' n following, 
very inaccurate. 

22. /Cygni, Fl. 63. :: 

Oct, 27. — Double. Extremely unequal. L fine 
wj S d. Distance 18" 11'". 

23. 3 a ad a Cygni, Fl. 46'. In genu dextro. 

Oct. 27. — Double. Considerably unequal. L red- 
dish w; S d. Distance within 30". Position 7° 23' 
n preceding. 

24. 3 ad a Cygni, Fl. 46 adjacens in genu dextro. 
Oct. 27. — Treble. Very unequal, and extremely 

unequal. L fine garnet ; S r ; smallest d. All 
within 30". Position of the brighter of the two small 
stars 44° 19' n preceding. Position of the faintest 
preceding. 

25. In constellatione Ceti, Fl. 66. 

Dec. 23. — Double. It is a star near the place of 
the periodical star 0. Distance l6".875, a little in- 
accurate. 



26. In constellatione Navis, Fl. ip. :: 

Feb. 15, 1781. — Double. It is a star under the 
ham of Monoceros's right-foot. Distance about 25". 

27. In constellatione Comae Berenices, Fl. 24. 
Feb. 28. — Double. Considerably unequal. L 

whitish r ; S blueish r. Mean distance 1 8" 24'". 
Position 3° 28' n preceding. 

28. In constellatione Geminorum. 

March 13. — Double. It is near 7 towards £Tauri. 
A little unequal. Both r. Distance 19" 41"'. Po- 
sition 57° 0' f preceding. 

2Q. h Ursae majoris, Fl. 23. Duarum in. collo 
sequens. 

April 25. — Double. Extremely unequal. L red- 
dish w; S d. Distance with 4bo, 19" 26"'. Posi- 
tion 3° 1 4' n preceding. 

30. In constellatione Lyncis, Fl. 43. Praecedens 
ad boream. 

May 26. — Double. It is the eye or nose of Leo 
minor. Unequal. Distance 24" 53'" inaccurate. 

31. In constellatione Cephei, near Fl. 27. 

May 27. — Treble. It is a star near t. Distance of 
the nearest about 20". 

32. * In constellatione Serpentarii, Fl. 61. 

July 15. — Double. It is a star near y. A little 
unequal. Lw; S grey. Distance 19" 4'", inaccu- 
rate. Position almost directly following. 

33. In constellatione Aquilae. 

July 19. — Treble. It is the first of 2 stars pre- 
ceding v. Distance of the 2 nearest 21" 59"', inac- 
curate. 

3 I. In constellatione Aquilae, near Fl. 64. 

July 25. — Double. It is near a star preceding 6. 
Equal distance about 30". 

35. /3 Delphini, Fl. 6. Austrina praecedentis lateris 
quadrilateri. 

Aug. 1. — Double. Extremely unequal. Hardly 
visible with 227 ; pretty strong with 4b~0. Distance 
25" 54'", rather narrow measure. Position 78° n 
preceding, by exact estimation. 

36. $ Serpentis, Fl. 28. In eductione colli. 

Aug. 13. — Double. Extremely unequal. L w; 
S extremely faint. Distance 24", pretty exactly esti- 
mated. Position 3 or 4° s preceding, too obscure for 
measuring. 

37. ^Equulci, Fl. 7 ■ Duarum in ore sequens. 
Aug. 13. — Double. Excessively unequal. S hardly 

visible with 227 ; but with 460, visible at first sight. 
L w ; S d. Distance 19" 32"'. S, too obscure to 
be very accurate. Position 1 1° 39' n following. 

38. In constellatione Aquarii, Fl. 24. 

Aug. 14. — Double. It is the star in the cheek or 
hair of the neck. Very unequal. L w ; S d. Dis- 
tance 25", very inaccurate. 

39- In constellatione Cygni. 

Oct. 1 . — Double. It is a star north following «-. 
Extremely unequal. L w ; S d. Distance 18" 
exact estimation. Position 30° 2S' s following. 

40. aTrianguli, Fl. 10. 

Oct. 8. — Double. It is the preceding of 3 teles - 
copic stars. Unequal. Distance 17" 19" > pretty 
accurate. 



'222 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1782. 



41. p Herculis, Fl. 86". 

Oct. 10. — Double. Excessively unequal. The 
small star is not visible with 227, nor with 278. I 
saw it very well with 46'0. L inclined to pale r ; 
S d. Distance, by pretty exact estimation, IS". 
Position, by very exact estimation, 30° s preceding. 

42. In constellatione Herculis. 

Oct. 10. — Double. It is a star just by >. Con- 
siderably unequal. L inclined to r ; S inclined to 
blue. Distance IS" 19"'. Position 4° oV n pre- 
ceding. 

43. /i Eridani, Fl. ultima. In origine rluvii. 

Oct. 22. — Double. It is the middle of 3 telescopic- 
stars. Very unequal. L w ; S r. 

44. In constellatione Tauri, near Fl. 4. 

Dec. 22. — Double. It is a small telescopic star 
south following s. Extremely unequal. L w ; S d. 
Fifth Class of Double Stars. 

1. <? Herculis, Fl. 11. In sinistra humero. 
Aug..';, 177.°. — Double. Extremely unequal. Lwj 

S inclining to r. Distance 33".7 5- Position 7 -° '2V 
s following. 

2. * £ Lyra;, Fl. 6". 

Aug. 29- — Double. Pretty unequal. L w ; S w 
inclining to pale rose colour. Distance 41" 58"', 
perhaps a little inaccurate. Position 02° 18' s follow- 
ing, a little inaccurate. 

3. */3Lyrae, Fl. 10. Duarum in jugimento borea. 

Aug. '.'9. — Quadruple. All w. First and 2d con- 
siderably unequal. First and 3d very unequal. First 
and 4th very unequal. The .d a little inclining to r. 
The 3d and 4th more inclining to r. Distance of the 
1st and 2d 43" 57"'. Position 60° 28' s following, a 
little inaccurate. 

4. & Cephei, Fl. 27. Sequitur tiaram. 

Aug. 31. — Double. Considerably unequal. L red- 
dish w ; S blueish w. Distance 38" 18'", a bright 
object. 

5. •(- /3 Cygni, Fl. 6. In ore. 

Sept. 12. — Double. Considerably unequal. L 
pale r ; S a beautiful blue. The estimation of the 
colours the same with 227 and 460. Distance 39" 32'", 
pretty accurate. Position 36° 2S' n following. 

6. * v Scorpii, Fl. 14. Duarum adjacentium 
boreae frontis, borea. 

Sept. 19. — Double. Very unequal. Both w. Dis- 
tance 38" 20"', pretty accurate. Position 6'9° 28' n 
preceding 

7. /* Sagittarii, Fl. 13. In summo arcu, borealis. 
Sept. 19. — Treble. Two small stars near on each 

side. L w ; S both r. Distance of the nearest about 
30". Position — preceding, the other — following. 

8. *■ Herculis, Fl. 7- In dextri brachii ancone. 
Sept. 20. — Double. A little unequal. L r; S 

garnet; or L pale r; S r. When the stars are low the 
first estimation of the colours will take place. Dis- 
tance 39" 59"'- Bosition 79° 37' n following. Has 
a 3d star. 

9. 1 Bootis, Fl. 21. — Trium in sinistra manu, 
media. 

Sept. 27. — Double. Very unequal. I. w; S d. 
Distance 37" 56. This is not a mean of the mea- 



a motion in one of the stars, 
or two may show. Position 



Trium in cingulo pres- 



sures; for I suspect 
which another year 
52° 51' n following. 

10. * <?' Ononis, Fl. 34. 
cedens. 

Oct. 0". — Double. Considerably unequal. L w; 
S blueish r Distance 52".9b"8 full measure. Position 
88° 10' 11 preceding. 

11. f » Dr.Honis, Fl. 24 and 25. In ore duplex. 
Oct. 19. — Double. A little unequal. L pale r; 

S pale r. Distance 54' 48". Position 44° 19' n 
preceding. 

From the right ascension and declination of these 
stars in Flamsteed's catalogue we gather, that in his 
time their distance was 1' II". 418; their position 
44° 23' n preceding ; their magnitude equal or nearly 
so. The difference in the distance of the 2 stars is so 
considerable, that we can hardly account for it other- 
wise than by admitting a proper motion in either one 
or the other of the stars, or in our solar system; most 
probably neither of the 3 is at rest. 

12. * A Arietis, Fl. 9. In vertice. 

Oct. 30.-T-Double. Considerably unequal. L pale 
r; S dusky garnet. Distance 36"' 44'", a little inac- 
curate. Position 42' 0' n following. 

13. <p Tauri, Fl. 52. Borea sequentis lateris 
quadrilaleri in Cervice. 

Oct. 30. — Double. Distance 55".625, inaccurate. 

14. In constellatione Monocerotis. 

Dec. 5. — Multiple. It is a spot over the right fore- 
foot ; 4 or 5 small stars within 1 minute. 

15. c Ursa; majoris, Fl. 16". 

May 2, 1780. — Double. Very unequal. L whitish 
r; S d. Distance with 46'0, 48" 59'". Position 
79° 51' s preceding. 

16". <r Piscium, Fl. 76. Duarum in ore piscis 
sequentis borealior. 

Aug. 3. — Double. Extremely unequal. L pale r ; 
S dusky r. Distance 48". 125, pretty accurate. Posi- 
tion 15° 28' n preceding. 

17. t Andromeda?, Fl. 29- In dextro humero. 
Aug. 25. — Double. Extremely unequal. L w; 

S blueish. Distance 34" 12"', inaccurate. 

18. « Cassiopeae, Fi. 18. In pectore. 
Aug 31. — Double. Extremely unequal. 

r; S d. Distance 52".812. Position 5° 26' 
ceding. 

19- ^ Herculis, Fl. 20. In dextro brachio. 

Sept. 4. Double. Extremely unequal. L reddish 
w; S r distance 41" 49", a little inaccurate. Position 
19° 30' s preceding. 

20. c Pegasi, Fl. 1 
Sept. 8. — Double. 

d ; Distance 37" 5 
n preceding. 

21. t Aurigae, Fl. 29- 

Sept. 26. — Double, about 30". 

22. A Auriga", Fl 15. 

Sept. 30. — Multiple. Two, within about 30". 

23. In constellatione ( Irionis. 

Oct. 10. — Double. It is a star following/. Dis- 
tance about 40". 



L pale 
n pre- 



Very unequal. L pale r; S 
pretty accurate. Position 38° 19' 



VOL. LXXtl 



•] 



PHILOSOPHICAL TRANSACTIONS. 



223 



24. In constellatione Ceti, Fl. 37. 

Oct. 12. Double. It is a star between i and 
towards the north. Distance 42".8 12, inaccurate. 

25. r Ononis, Fl. 20, supra talum in tibia. 

Oct. 23. — Double. Very unequal. Distance 
about 30". 

26. h Leonis, Fl. 6. 

Feb. 21, 1781. — Double. Very unequal. Lr; 
S d. Distance 36" 9'". Position 12° 55' n following. 

27. In constellatione Libras, near Fl. 31. 

May 24-. Double. The most south of 3 small 
stars in the finder. Equal, or the preceding rather 
the larger. Both w inclining to pale r. Distance 
44" 12'", a little inaccurate. Position 40° 17' s 
following. 

28. In constellatione Cephei. 

May 27. — ■ Double. It is a star near S. Ex- 
tremely unequal. Distance about 30". 

29. ' Serpentis, Fl. 53. Post dextrum femur Ser- 
pentarii. 

July 10". — Double. Unequal Distance about 35". 

30. In constellatione Serpentarii, Fl. 53. 

July l.Q. — Double. It is a star between «■ and $ ^ 
of the way from «. Very unequal. L w ; S in- 
clining to r. Distance 32" 21'", narrow measure. 

3 1 . In constellatione Aquilae. 

j u ]y 19, — Double. It is the star next but one pre- 
ceding ^. Very unequal. L r ; S d. Distance 
about 30". 

32. « Andromedae. 

July 21— Double. Extremely unequal The 
small star better with 460 than with 227- L w ; S 
d. Distance 55" 32'", rather narrow measure. 
Position 10° 37' s preceding. 

33. h Aquilae, Fl 15. 

July 25. — Double. Unequal. Both pale r Dis- 
tance 33" 53", inaccurate. 

34. In constellatione Aquilae, A Fl. 28. 

July 25. — Double. It is one of 2 stars near A. 
Distance about 35". 

35. In constellatione Aquilae- 

July 25. — Double. It is a star near that which 
follows C. Very unequal Distance about 40". 

36'. o Scuti, Fl. 2, in constellatione Aquilae. 

July 30. — Double Very unequal. L pale r ; S d. 
Distance 42" 44'", a little inaccurate. 

37. <> Coronae, Fl. IS. 

Sept. 21. — Treble. Very unequal. L w ; S both r. 
Dist. of the nearest about 50" ; the farthest I h min.* 

38. In Constellatione Herculis, Fl. 23. 

Sept. 21. — Double. It is the star between » and % 
Coronae, the largest of a telescopic triangle. Dis- 
tance 36" 27'", rather narrow measure. L w ; S w ; 
inclining to r. 

39. x Lyrae, Fl. 3. In testa fulgida. 

Sept. 24. — Double. Excessively unequal. By 
moonlight I could not see the small star with 278, and 
saw it with great difficulty with 460 ; but in the 
absence of the moon I have seen it very well with 227. 
L fine brilliant w; S dusky. Distance 37" 13'". 
Position 26° 46' s following. 

* In a future collection the small star at the obtuse angular 
point will be found as a double star of the id or 3d class. 



Oct. 22. Having often measured the diameters of 
many of the principal fixed stars, and having always 
found that they measured less and less the more I mag- 
nified, I fixed on this fine star for taking a measure 
with the highest power I have yet been able to apply, 
and on the largest scale of my new micrometer I could 
conveniently use. With a power of 6*450 (determined 
by experiments on a known object at a known distance) 
I looked at this star for at least a quarter of an hour, 
that the eye might adapt itself to the object; having 
experimentally found, that the aberration by this 
means will appear less and less, and, in the telescope 
I used on this occasion with powers from 400 to 1500, 
will often quite vanish, and leave a very well-defined 
circular disc for the apparent diameter of the stars. 
The diameter of « Lyrae, by this attention, appeared 
perfectly round, and occasionally separated from rays 
that were flashing about it. From the very brilliant ap- 
pearance of the star with this great power, and a pretty 
accurate rough calculation founded on its apparent 
brightness, when observed with the naked eye with 
227, with 460, with 6+.">0, I surmise, that it has 
light enough to bear being magnified at least a hun- 
dred thousand times with no more than 6 inches of 
aperture, provided we could have such a power, and 
other considerations would allow us to apply it. When 
I had as good a view as I expected to have, I took its 
diameter with my new micrometer on a scale of 8 
inches and 4428 ten thousandth to 1" of a degree, and 
found it subtended an angle of t)".3553. I had no 
person at the clock ; but suppose the time of its pass- 
ing through the field of my telescope, which in this 
'great power is purposely left undefined, and as large 
as possible, was less than 3 seconds. 

40. » Lyrae, Fl. 8. 

Sept. 24. — Treble. Extremely unequal. L w ; 
S both d. One n preceding, the other s following. 
Distance of the following star 56" 47'", a little inac- 
curate. Position of the same 28° 27' s following. 

41. APersei, Fl. 43. 

Sept. 24. — Double. Unequal. L w. Distance 
about 50". 

42. In constellatione Lyrae. 

Sept. 25. — Double. It is a small star just by 0. A 
little unequal. Both r. Distance 38" 8"'. Position 
26° 18' n following. 

43. In constellatione Cygni, Fl. 76'. 

Oct. 1. — Double. It is the 3d star from f towards 
v. Unequal. Distance 48" by exact estimation. 
Position — preceding. 

44. In constellatione Cygni, Fl. 69. 

Oct. 1. — Treble. Very unequal. L w; S both 
reddish. Position — preceding. 

45. In constellatione Cygni. 

Oct. 1.- Double. It is the more south of 2 teles- 
copic stars following -r. Very unequal. L w ; S d. 
Distance 44" by exact estimation. Position — following. 

46. c Cygni, Fl. 16. l" ad c. 

Oct. 5. — Double. It is the star next following 8. 
Almost equal. Both pale r. Distance 30", by pretty 
exact estimation. 

47. c Cygni, Fl. 26. 2 a ad c. 

Oct 8. — Double. Very unequal. L reddish w ; 



224 



PHILOSOPHICAL TRANSACTIONS. 



[ANNO 1782. 



S dusky r. Distance 3.9" by pretty exact estima- 
tion. 

48. * In constellations Piscium. 

Oct. 8. — Double. It is a telescopic star just by t 
southwards. Both d. Distance about 4-5". 

4p. * In constellatione Arietis, Fl. SO 

Oct. 15. — Double. It is a small star over the 
ram's back. Nearly equal. Distance 31" t>'", in- 
accurate. 

50. v Leporis, Fl. 13. Iu posterioribus pedibus 
austrina. 

Oct. 22. — Double. Considerably unequal. Dis- 
tance about 40". 

51. In constellatione Sagittae. 

Nov. 23. — Double It is a star north following s. 
Extremely unequal. Distance 32" 48'". L r ; S 
blue. 

Sixth Class of Double Stars. 

1. i Ceti, Fl. 6*8. In pectore nova. 

Oct. ','0, 1777. — Double. Very unequal. L gar- 
net. S dusky. Distance mean of some very accu- 
rate measures i'44".2i8; mean of other very accu- 
rate measures 1' 53" .032. As I can hardly doubt the 
motion of this star, I have given the mean of the 
most accurate measures separately ; and hope in a few 
years time to be able to give a better account of it. 

2. o Serpentarii, Fl. 67. 

Aug. 29, J77.°> — Double. Distance about i^ 
min. 

3. J'Lyrae, Fl. 11. 

Aug. 29, 1779. — Double. Extremely unequal. 
L w ; S d. Distance about 4', pretty exact estimation. 

4. « Capricorni, Fl. 5. 

Sept. 19. — Double. Very unequal. L 1; S d. 
Distance about I \ min. Position — s preceding. 

5. In constellatione Arietis, Fl. 41, supra dorsum. 
Sept. 27. — Double. It is the star in the body of 

the fly. Distance 2' 5" 35'". 

6. t Capricorni, Fl. 39. Duarum in eductione 
caudae proeced. 

Sept. 27. — Double. Unequal. L pale r. Dis- 
tance about 1 \ min. 

7. * t Tauri, Fl. 9 k In eductione cornu borei. 
Oct. 6. — Double. Distance 1' 1 1" 25'", pretty 

accurate. 

8. x. Tauri, Fl. 5G and 57. 

Oct. (I. — Double. At a considerable distance. 

9. * C Geniinorum, Fl. 43. In sinistra genu se- 
quentis n 1 . 

Oct. 7. — Double. Very unequal. L reddish w ; 
S dusky r. DistanceV 31" 52'", rather foil measure. 
Position 81° 14' n preceding. 

10. o Cygni, Fl 31. Duarum in dextro pede 
sequens. 

Nov. 2. — Double. Considerably unequal. L pale 
r. S blue. It is the following star of the two o's 
that are close together. Distance 1' 39" 57'". Posi- 
tion 87° 14' s preceding. 

11. * « Leonis, Fl. 32. In corde. 

Nov. 14. — Double. Very unequal. L w ; S d. 
Distance 2' 48" 20'". Position 30° 5' n preceding. 

12. * Leonis, Fl. 84. Quasi in cubilo.. 



April 6. — Double. Considerably unequal. L r; 
S inclining to blue. Distance 1' 22" 42'". Position 
75° 21' s following. 

13. o Leonis, Fl. 95. In extremitate caudae. 
April 6'. — Double. Extremely unequal. L reddish 

w ; S d. Distance about 1 1 min. Position about 
81 )° B following. 

14. » Serpentis, Fl. 5$. In Cauda. 

June 19, 1780. — Double. Extremely unequal. 
L pale r; S d. Distance 1' 21" 2'". Position 9° 7' 
s following. 

15. In constellatione Bootis, near Fl. 6". 

June 25. — Double. It is a telescopic star near that 
which forms a rectangle with «e and 1. Distance 
about 2'. 

10. ^Bootis, Fl. 49. In dextro humero. 

July 23. — Double. Considerably unequal. Dis- 
tance about 24 min. L reddish w. S w. Position 
3° 46'' n following. 

17. f* Bootis, Fl. 51. In baculo recurvo. 

July ;;0, 1780. — Double. Unequal. Distance 
2' 8", exact estimation. Position 80° 25' s following. 
L reddish w. S. pale r. See the 17th star of the 
first class. 

18. ► Coronae, Fl. 21. 

July 30. — Double. Very unequal. L r ; S garnet. 
At some considerable distance. Position about 80° n 
following. 

l c ). x Persei. 

Aug. 2. — Multiple. An astonishing number of 
small stars all within the space of a few minutes. I 
counted not less than 40 within my small held of 
view. 

20. 1* Persei, Fl. 51. Duarum in dextro poplite 
sequens. 

Aug. 2. — Double. Very unequal. L w. Dis- 
tance about l'j. 

21. a Pegasf, Fl. 44. 

Aug. 23. — Double. Distance about 2^ min. 

22. In constellatione Draconis, I. Hevelii 09. 

Aug. 7- — Double. It is the star between * Dra- 
conis and the tail of Ursa major. Distance about 3^ 
min. 

23. In naribus Lyncis. 

Aug. 7. — Double. Distance about 2'. 

24. d Cassiopeae, Fl. 4. 

Aug. 1 2. — Treble. Two are large. Distance 
about 2'. A 3d is obscure. Distance about if min. 
They form almost a right angle. 

25. In constellatione Cassiopeae, Fl. 3. 
Aug. 1 8. — Double. Distance about 2£ min. 
26'. 1 Sagittae, Fl. 11. 

Aug. 19. — Double. Very unequal. L r; S r in- 
clining to blue. Distance 1' 31" 53"'. Position 
8° 32' s following. 

27. In constellatione Aquilae. 

Aug. 21. — Double. A star north of C Distance 
about 1'. 

28. /3 Capricorni, Fl. 0. Trium in sequente cornu 
austrina. 

Aug. 26. — Double. Considerably unequal. Dis- 
tance about 3'. Position — preceding. 



VOL. LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



■225 



29. » Capricorni, Fl. 11. Trium in rostro proe- 
cedens. 

Aug. '-'6. — Double. Distance about 2 J'. 

30. </. Aurigae, Fl. 13. In huraero sinistro. 

Sept. S. — Double. Extremely unequal. L w ; 
S d. Dist. 2' 49" 8"'. Position 6 1 ° 23' s following. 
With a power of 227 > and my common micrometer, the 
diameter of this star measured 2".5 The circum- 
ference was remarkably well defined. 

31. rfTauri, Fl. 88. In sinistro cubito. 

Sept. 24. — Double. Distance 1' 10".6"25. A little 
inaccurate. 

32. A Cygni, Fl. 54. 

Sept. 20. — Double. Extremely unequal. L blueish 
w ; S d. Distance about 1'. Position 12° 42' s 
following. 

33. In constellatione Cygni, Fl. 32. 
Sept. 20. — Double. Distance about 2'. 

34. 6 Aurigae, Fl. 37. In dextro carpo. 
Sept. 26. — Double. Distance about 2'A. 

35. In constellatione Camelopardali, Fl. 13. 

Sept. 26'. — Double. It is the star over the goat's- 
head. Distance about 2'. 

36. In constellatione Camelopardali, Fl. 10. 
Sept. 30. — Double. Distance about l'g. 
37- c Draconis, Fl. 46. In flexura colli. 

Oct. 3. — Double. Distance 3 or 4'. A rich spot. 

38. c Draconis, Fl. 6'4 or 65. 

Oct. 3. — Double. Distance about 2'. 

39- « Ononis, Fl. 58. In dextro humero lucida 
ratilans. 

Oct. 10. — Double. Extremely unequal. L r but 
not deep; S d. Distance 2' 41" 4ti'". Position 
62° 1 8' s following. 

40. y Leporis, Fl. 13. 

Feb. 21, 1 7S I . — Double. Distance about 2'§. 

41. f Cancri 5 ad ?, Fl. 67. 

Feb. 21. Double. Very unequal. L reddish w ; 
Sd. Distance 1' 35" 59'". Position 50° 33' n pre- 
ceding. 

42. S Geminorum, Fl. 78. In capite sequentis n'. 
Mar. 13. — Multiple. Extremely unequal. The 

nearest distance 1' 50" 45"', rather full measure. 
Position 24° 28' n following, not extremely accurate. 
This is the smallest. The next distance 3' 17" iy ", 
pretty accurate. Position 1 5° 56' n following. 

43. C Virginis, Fl. 51. De quatuor ultima et 
sequens. 

May 14. — Double. Extremely unequal. L w; 
S d. Distance 1' 3" 53"', inaccurate. Position 
24° 55' n preceding. 

44. 1 Librae, Fl. 24. 

May 24. — Double. Very "unequal. Lw; S dusky 
r. Distance 59" 4'", not accurate. Position 22° 31' 
s following. 

45. In constellatione Andromedas. 

July 21. — Double. It is a star near 1 towards u. 
L r. Distance about \'h. 

46. «■ Aquilae, Fl. 53T 

July 23. — Double. Extremely unequal. L w ; 

YOL.XV. G 



S d. Dist. 2' 23" 1 S'". Position 64° 44' n preceding. 

47- In constellatione Aquilae, near Fl. 35. 

July 25. — Double. It is one of the preceding stars 
of a small quartile near c, not very near. 

48. In constellatione Aquilae, near Fl. 35. 

July 25. — Double. It is also one of the preceding 
stars of a small quartile near r, not very near. 

40. In constellatione Aquilae. 

July 26. — Double. The following star of a trape- 
zium near 1. 

50. In constellatione Aquilae. 

July 26". — Double. The following star of a trape- 
zium near 1 not near. 

51. In monte Maenali Heveliana. 

Aug. 5. — Double. It is a star near the middle. 
The following of 2, not very near. 

52. In constellatione Bootis 

Aug, 17. — Double It is a star between t andy. 
Distance above 1'. Unequal. 

53. In constellatione Bootis. 

Aug. 17 — Double. It is a star more south than i. 
Distance above I'. 

54. In constellatione Serpentarii. 

Aug. 21. — Double. It is a star more south than 0. 
Distance 75", exact estimation. 

55. In constellatione Cassiopeae, Fl. 2. 
Sept. 6. — Double. It is a star near e. 

tance within 2'j. 

56. 6 Lyrae, Fl. ultima. 
Sept. 25. — Double. Very unequal. 

dining tor. Distance about 1 .J min. 
following. 

57 . In constellatione Cygni, Fl. 79- 
Oct. 1 . — Double It is the 5th star 

Unequal. Lw; S pale r. Dist. 1 ' 40" 

58. In constellatione Aquarii, Fl. 4. 

Oct. 5. — Double. It is the most south of two in 
the arrow of Antinous. Distance above 1'. 

59- In constellatione Cygni, near Fl. 28. 

Oct 5. — Double. It is a star near b. Distance 
73", exact estimation. 

60. In constellatione Cygni. 

Oct. 8. — Double. It is a star near the second c. 
Considerably unequal. L w ; S d. Distance 88", 
exact estimation. 

61. In constellatione Piscium, near Fl. 7 . 
Oct. S.— Treble. It is a star preceding b. 

form a triangle, each side of which is about 1' 

62. x Piscium, Fl. 8. In ventre. 
Oct. 8. — Double. Distance near 2'. 

63. In constellatione Sagittae. 

Oct. 12. — Double. It is near the star north fol- 
lowing s. Extremely unequal. L w inclining to r ; 
S d. Distance 1' 30" 56'". Position 4° <j' s 
preceding. A 3d star in the same direction, at a little 
more than twice the distance. A 4Ui star in view. 

64 In constellatione Eridani. 

Oct. 22. — Double. It is the small star near r. 
Distance about l'|. 

0'5. In capite Monocerotis. 

G 



L r. Dis- 



L w ; S in- 
Position — n 



from j to 1/. 
estimation. 



They 



22t) PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

Oct. 22. — Multiple It is one star with at least 12 star, when on the meridian, measured 1' 4(>' ', a 

around it, all within the field of my telescope mean of 2 very complete observations, they agreed to 

66 aTauri, Fl. 87. Splendida in austrina oculo. 6'"; with 932, it measured 1" Vi" , also a mean of 2 

j)ec. 1<). — Double. Extremely unequal. L r; excellent observal ions ; they agreed to S'". The ap- 

S d. Distance I' 27" 45'", position 52° 58' n fol- parent disc was perfectly well defined with both 

lowincr. With -tn'O, the apparent diameter of this powers. 

Postscript to the Catalogue of Double Stars. — Since having delivered my paper 
on the parallax of the fixed stars, in which I refer to the above catalogue of 
double stars, I have received the 4th volume of the Acta Acadeiniae Theodoro 
Palatinae, which contains a most excellent Memoir of Mr. Mayer's, " De novis 
in Ccelo sidereo Phaenomenis ;" where I see that the idea of ascertaining the 
proper motion of the stars by means of small stars that are situated at no great 
distance from large ones, has induced that gentleman before me to look out for 
such small stars. In the course of that undertaking he has discovered a good 
many double stars, of which he has given us a pretty large list, some of them 
the same with those in my catalogue. My view being the annual parallax, re- 
quired stars much nearer than those that would do for Mr. Mayer's purpose; 
therefore I examined the heavens with much higher powers, and looked out 
chiefly for such as were exceedingly close. 

The above catalogue contains 269 double stars, 227 of which, to my present 
knowledge, have not been noticed by any person. I hope they will prove no in- 
considerable addition to the general stock, especially as in that number there are 
a great many which are out of the reach of Mr. Mayer's and other mural qua- 
drant or transit instruments. It can hardly be expected, that a power of 70 or 
80 would be sufficient to discover those curious stars that are contained in the 
first class of my catalogue ; so that it is not strange they should have entirely 
escaped Mr. Mayer's notice. We see that it is not for want of his looking at 
those stars ; for we find he has frequently observed £ Cancri, the star near 
Procyon, and the star in Monoceros, without perceiving the small stars near 
them, which I have pointed out. Nor is it only in the first class that his tele- 
scope wanted power, light, and distinctness ; for the small stars that are near 
j3 Ononis, (3 Serpentis, ^Ononis, e Pegasi, a. Lyrae, aAndromedae, ju. Sagittarii, 
a Aquilae, n Pegasi, $ Lyrae, i Librae, x Piscium, ?. Tauri, and many more, 
have escaped his discovery, though he has given us the places of other more 
distant small stars not far from them, and therefore must have had them fre- 
quently in the field of view of his telescope. In settling the relative situations 
of very close double stars, neither Mr. Mayer's instruments, nor his method, 
were adequate to the purpose. It is well known, that whenever we employ time 
as a measure, the results cannot be very accurate ; because a mistake of no more 
than a 10th part of a second in time will produce an error of a whole second 
and a half in measure, so that his ar must be extremely defective. Nor could 



VOL. LXXII 



] PHILOSOPHICAL TRANSACTIONS. 22/ 



his micrometer give the declination much better, unless the telescope had borne 
a power of at least 4 or 500. When the angle of position is but small, such 
as 3, 4, 5, or 6 degrees, and the distance of the stars not above a few seconds, 
it is evident that a micrometer must be able to measure lOths of a second at 
least, to give even a tolerable exactness of position. On the contrary, the posi- 
tion being measured with such a micrometer as I have constructed for the pur- 
pose, we may thence deduce the declination, with great confidence, true to a 
quarter of a 10th of a second for every second of the distance of the stars. 

Mr. Mayer's account of a Geminorum, for instance, gives a difference of 
0'.7 of time in ar, of 3". 8 in declination, and of I to 6 in magnitude or degree 
of light of the stars. These quantities reduced to my notation, and compared 
with my measures of the same star, give 

■£ 1 Distance 9".(>35 from centre to centre f a".\ 06 diameters included. 

g ^Position 23° IV n preceding .5^ 32° 47' n preceding. 

u I ^ I 

§ J Magnitude extremely unequal. (_A little unequal. 

To account for this difference, I ascribe Mr. Mayer's error in distance to his 
method of measuring by time. The error of position follows always from an 
observation of the declination taken with the common micrometer, when it is 
deduced from an erroneous ar. In my measures the distance and position are 
independent of each other, which I consider as no small advantage of my cross- 
hair micrometer. The error in the magnitudes of the stars I ascribe to the want 
of power in Mr. Mayer's telescope, which did not separate the stars far enough 
for him to judge accurately of their size ; otherwise he would soon have found, 
that instead of 5, there is hardly so much as 1 single degree of difference in 
their magnitudes. See; fig. 6 for a representation of those stars with my power 
of 460. 

I do not mean to depreciate Mr. Mayer's method, the excellence of which is 
well known ; and with some stars of my 3d, all those of the 4th, 5th, and 6th 
classes, as well as with those still farther distant, to which he has applied it with 
admirable skill, and " magno labore, multisque nocturnis vigiliis," as he very 
justly expresses himself, a better can hardly be wished for; but with stars of the 
2d class which generally differ no more than 1, 2, or 3 tenths of a second of 
time in ar, and can never differ more than 4 tenths, the insufficiency of 
measuring by time is obvious. In regard to the declination, it is also no less 
evident, that it is much more accurate to take an angle, which may be had true 
to 2 or 3° at most, than to measure its tangent, which in stars of the 2d class 
is generally no more than 2, 3, or 4" of a degree, and can never exceed 5. I 
do not so much as mention the stars of the 1st class : they must certainly, as to 

G G 2 



'228 PHILOSOPHICAL TRANSACTIONS. [ANNO I 7 & '2. . 

sense, pass the meridian at the same instant of time. Their distance lias even 
eluded the attacks of my smallest silk-thread micrometer armed with an excellent 
power of 460 ; but I shall soon apply my last new instrument to them, not 
without hopes of success. Now, though I have hitherto not been able to ex- 
press the distance of the stars of the first class, otherwise than by the propor- 
tion it bears to their apparent diameters, I think it a very great point gained, 
that one of my instruments at least (viz. the cross-hair micrometer) has laid hold 
of them : for their angle of position, I think, is within a very small quantity as 
well determined as it is in those of the 2d class. This simple but most useful 
instrument can, by actual measure, discover beyond a doubt a motion in 2 stars 
that are very close together, though it should amount to no more than a 10th 
part of a second of a degree, provided that motion be in such a direction that 
the effect of it be thrown on the angle of position ; wherein, with some of the 
stars of the first class, it would occasion an alteration of 10, 20, 30, or more 
degrees. 

I have marked all those stars in my catalogue which have been observed by 
Mr. Mayer, and other astronomers, with an asterisk (*) affixed to the number, 
that they may be known ; those with the mark of a dagger (-f~) have been ob- 
served by different astronomers before Mr. Mayer. Among the stars which are 
not marked, will be found several that have been observed by Mr. Mayer ; but, 
on comparing them together, it will be seen, that they are observations of dif- 
ferent small stars ; for instance, Mr. Mayer (Act. Acad. vol. 4, p. 296) ob- 
served a small star near Rigel at the distance of l m s . 5 ar in time, and 2' 55".2 
in difference of declination north preceding Rigel. In my 2d class (the 34th 
star) we also find Rigel ; but the small star I have observed is one which has not 
been seen by Mr. Mayer, and is at a distance of no more than 6" 27'". Posi- 
tion 68° 12' south preceding ; and so on with other stars. 

I have used the expression double-star in a few instances of the 6th class in 
rather an extended signification : the example of Flamsteed, however, will suf- 
ficiently authorize my application of the term. I preferred that expression to 
any other, such as comes, companion, or satellite ; because, in my opinion, it 
is much too soon to form any theories of small stars revolving round large ones, 
and therefore I thought it adviseable carefully to avoid any expression that might 
convey that idea. I am very well persuaded that Flamsteed, who first used the 
word comes, meant it only in a figurative sense. I shall not fail to take the first 
opportunity of looking out for those of Mr. Mayer's double-stars which I have 
not in my catalogue, amounting to 31 ; and also for one I find mentioned in 
La Connoissance des Temps for 1783, discovered by Mr. Messier. 



VOL. LXXII.] PHILOSOPHICAL TKANSACTIONS. 22Q 

XIII. Description of a Lamp-Micrometer, and the Method oj using it. By 
Mr. William Herschel, F. R. S. p. 1 63. 

The great difficulty of measuring very small angles, such as hardly amount to 
a few seconds, is well known to astronomers. Since I have been engaged in 
observations on double stars, I have had so much occasion for micrometers that 
would measure exceeding small distances exactly, that I have continually been 
endeavouring to improve these instruments. 

The natural imperfections of the parallel wire micrometer, in taking the dis- 
tance of very close double stars, are the following. When 2 stars are taken 
between the parallels, the diameters must be included. I have in vain attempted 
to find lines sufficiently thin to extend them across the centres of the stars, so 
that their thickness might be neglected. The single threads of the silk-worm, 
with such lenses as I use, are so much magnified, chat their diameter is more 
than that of many of the stars. Besides, if they were much less than they are, 
the power of deflection of light would make the attempt to measure the distance 
of the centres this way fruitless: for I have always found the light of the stars to 
play upon those lines, and separate their apparent diameters into 2 parts. Now 
since the spurious diameters of the stars thus included, to my certain knowledge, 
are continually changing according to the state of the air, and the length of 
time we look at them, we are, in some respect, left at an uncertainty, and our 
measures taken at different times, and with different degrees of attention, will 
vary on that account. Nor can we come at the true distance of the centres of 
any 2 stars, one from another, unless we could tell what to allow for the semi- 
diameters of the stars themselves ; for different stars have different apparent 
diameters, which, with a power of 227, may differ from each other, as I have 
experienced, as far as 2 seconds. The next imperfection, is that which arises 
from a deflection of light on the wires when they approach very near to each 
other ; for if this be owing to a power of repulsion lodged at the surface, it is 
easy to understand that such powers must interfere with each other, and give 
the measures larger in proportion than they would have been, if the repulsive 
power of one wire had not been opposed by a contrary power of the other. 
Another very considerable imperfection of these micrometers is a continual un- 
certainty of the real zero. I have found, that the least alteration in the situa- 
tion and quantity of light will affect the zero, and that a change in the position 
of the wires, when the light and other circumstances remain unaltered, will also 
produce a difference. To obviate this difficulty, whenever I took a measure that 
required the utmost accuracy, my zero was always taken immediately after, 
while the apparatus remained in the same situation it was in when the measure 
was taken ; but this enhances the difficulty, because it introduces an additional 
observation. The next imperfection, which is none of the smallest, is that 



230 I'HILOSOl'HICAL TRANSACTIONS. [ANNO 1782. 

every micrometer hitherto used requires either a screw, or a divided bar and 
pinion, to measure the distance of the wires or divided image. Those who are 
acquainted with works of this kind are but too sensible how difficult it is to have 
screws that shall be perfectly equal in every thread or revolution of each thread ; 
or pinions and bars that shall be so evenly divided as perfectly to be depended on, 
in every leaf and tooth, to perhaps the 2, 3, or 4 thousandth part of an inch ; 
and yet, on account of the small scale of those micrometers, these quantities 
are of the greatest consequence; an error of a single thousandth part inducing 
in most instruments a mistake of several seconds. The last and greatest imper- 
fection of all is, that these wire micrometers require a pretty strong light in the 
field of view : and when I had double stars to measure, one of which was very 
obscure, I was obliged to be content with less light than is necessary to make the 
wires perfectly distinct ; and several stars on this account could not be measured 
at all, though otherwise not too close for the micrometer. 

The instrument I am going to describe, which I call a lamp-micrometer, is 
free from all these defects, and has also to recommend it, the advantage of a 
very enlarged scale. The construction of it is as follows. 

abgcfe (fig. 1, pi. 5,) is a stand 9 feet high, on which a semi-circular board 
qhogp is moveable upward or downward, in the manner of some fire-screens, as 
occasion may require, and is held in its situation by a peg p put into any one of 
the holes of the upright piece ab. This board is a segment of a circle of 14 
inches radius, and is about 3 inches broader than a semi-circle, to give room for 
the handles id, ep, to work. The use of this board is to carry an arm l, 30 
inches long, made to move on a pivot at the centre of the circle, by means of a 
string, which passes in a groove on the edge of the semi-circle pgohq ; the string 
is fastened to a hook at o (not expressed in the figure being at the back of the 
arm l,) and, passing along the groove from oh to q, is turned over a pulley at q, 
and goes down to a small barrel e, within the plane of the circular board, where 
a double-jointed handle ep commands its motion. By this contrivance we see 
the arm l may be lifted up to any altitude from the horizontal position to the 
perpendicular, or be suffered to descend by its own weight below the horizontal 
to the reverse perpendicular situation. The weight of the handle p is sufficient 
to keep the arm in any given position ; but if the motion should be too easy, a 
friction spring applied to the barrel will moderate it at pleasure. 

In front of the arm l a small slider, about 3 inches long, is moveable in a 
rabbet from the end l towards the centre, backward and forward. A string is 
fastened to the left side of the little slider, and goes towards l, where it passes 
round a pulley at m, and returns under the arm from nm, towards the centre, 
where it is led in a groove on the edge of the arm, which is of a circular form, 
upward to a barrel (raised above the plane of the circular board) at r, to which 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 231 

the handle rD is fastened. A second string is fastened to the slider, at the right 
side, and goes towards the centre, where it passes over a pulley n, and the 
weight w, which is suspended by the end of this string, returns the slider to- 
wards the centre, when a contrary turn of the handle permits it to act. 

a and b are 2 small lamps, 2 inches high, 1^ in breadth, by 1-J. in depth. The 
sides, back, and top, are made so as to permit no light to be seen, and the 
front consists of a thin brass sliding door. The flame in the lamp a is placed -^ 
of an inch from the left side, T V * rom tne front, and half an inch from the 
bottom. In the lamp b it is placed at the same height and distance measuring 
from the right side. The wick of the flame consists only of a single very thin 
lamp-cotton thread ; for the smallest flame being sufficient, it is easier to keep it 
burning in so confined a place. In the top of each lamp must be a little slit, 
lengthways, and also a small opening in one side near the upper part, to permit 
air enough to circulate to feed the flame. To prevent every reflection of light, 
the side opening of the lamp a should be to the right, and that of the lamp b to 
the left. In the sliding door of each lamp is made a small hole with the point of 
a very fine needle just opposite the place where the wicks are burning, so that 
when the sliders are shut down, and every thing dark, nothing shall be seen 
but two fine lucid points of the size of 2 stars of the 3d or 4th magnitude. 
The lamp a is placed so, that its lucid point may be in the centre of the circular 
board where it remains fixed. The lamp b is hung to the little slider which 
moves in the rabbet of the arm, so that its lucid point, in a horizontal position 
of the arm, may be on a level with the lucid point in the centre. The move- 
able lamp is suspended on a piece of brass fastened to the slider by a pin exactly 
behind the flame on which it moves as a pivot. The lamp is balanced at the 
bottom by a leaden weight, so as always to remain upright, when the arm is 
either lifted above, or depressed below, the horizontal position. The double- 
jointed handles rD, ep, consist of light deal rods, 10 feet long, and the lowest 
of them may have divisions, marked on it near the end p, expressing exactly 
the distance from the central lucid point, in feet, inches, and tenths. 

From this construction we see, that a person at a distance of 10 feet may 
govern the 2 lucid points, so as to bring them into any required position south 
or north preceding or following, from O to go , by using the handle p, and also 
to any distance from -^ of an inch to 5 or 6 and 20 inches, by means of the 
handle d. If any reflection or appearance of light should be left from the top 
or sides of the lamps, a temporary screen, consisting of a long piece of paste- 
board, or a wire frame covered with black cloth, of the length of the whole arm 
and of any required breadth, with a slit of half an inch broad in the middle, 
may be affixed to the arm by 4 bent wires, projecting an inch or 2 before the 



231 PHILOSOPHICAL. TRANSACTIONS. [aNNO 178'2. 

lamps, situated so that the moveable lucid point may pass along the opening left 
for that purpose. 

Fig. 2 represents part of the arm l, of a larger size ; s the slider ; m the 
pulley, over which the cord xtyz is returned towards the centre ; v trie other 
cord going to the pulley n of fig. ] ; r the brass piece moveable on the pin c, to 
keep the lamp upright. At r is a wire rivetted to the brass piece, on which is 
held the lamp by a nut and screw. Fig. 3, 4, represent the lamps a, b, with 
the sliding doors open, to show the situation of the wicks, w is the leaden 
weight, with a hole d in it, through which the wire r of fig. 2 is to be passed, 
when the lamp is to be fastened to the slider s. Fig. 5 represents the lamp a 
with the sliding door shut ; 1 the lucid point ; and ik the openings at the top, 
and s at the sides for the admission of air. 

Every ingenious artist will soon perceive that the motions of this micrometer 
are capable of great improvement by the application of wheels and pinions, and 
other well known mechanical resources ; but, as the principal object is only to 
be able to adjust the 2 lucid points to the required position and distance, and to 
keep them there for a few minutes, while the observer goes to measure their dis- 
tance, it will not be necessary to say more on the subject. 

I am now to show the application of this instrument. It is well-known to 
opticians, and others, who have been in the habit of using optical instruments, 
that we can with one eye look into a microscope or telescope, and see an object 
much magnified, while the naked eye may see a scale on which the magnified 
picture is thrown. In this manner I have generally determined the power of my 
telescopes ; and any one who has acquired a facility of taking such observations 
will very seldom mistake so much as 1 in 50 in determining the power of an in- 
strument, and that degree of exactness is fully sufficient for the purpose. 

The Newtonian form is admirably adapted to the use of this micrometer ; for 
the observer stands always erect, and looks in a horizontal direction, though the 
telescope should be. elevated to the zenith. Besides, his face being turned away 
from the object to which his telescope is directed, this micrometer may be placed 
very conveniently, without causing the least obstruction to the view : therefore, 
when I use this instrument, I put it at 10 feet distance from the left eye, in a 
line perpendicular to the tube of the telescope, and raise the moveable board to 
such a height, that the lucid point cf the central lamp may be on a level with 
the eye. The handles, lilted up, are passed through 2 loops fastened to the 
tube, just by the observer, so as to be ready for his use. I should observe, that 
the end of the tube is cut away, so as to leave the left eye entirely free to see the 
whole micrometer. 

Having now directed the telescope to a double star, I view it with the right 
eye, and at the same time with the left see it projected on the micrometer : then, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 233 

by the handle p, which commands the position of the arm, I raise or depress it 
so as to bring the 2 lucid points to a similar situation with the 2 stars ; and, by 
the handle d, I approach or remove the moveable lucid point to the same distance 
of the 2 stars, so that the 2 lucid points may be exactly covered by, or coincide 
with the stars. A little practice in this business soon makes it easy, especially to 
one who has already been used to look with both eyes open. 

What remains to be done is very simple. With a proper rule, divided into 
inches and 40th parts, I take the distance of the lucid points, which may 
be done to the greatest nicety, because, as observed before, the little holes are 
made with the point of a very fine needle. The measure thus obtained is the 
tangent of the magnified angle under which the stars are seen, to a radius of 
10 feet ; therefore, the angle being found, and divided by the power of the 
telescope, gives the real angular distance of the centres of a double star. For 
instance, Sept. 25, 1781, I measured aHerculis with this instrument. Having 
caused the 2 lucid points to coincide exactly with the stars centre on centre, I 
found the radius, or distance of the central lamp from the eye, 10 feet 4.15 
inches ; the tangent or distance of the 2 lucid points 50.6 fortieth parts of an 
inch ; this gives the magnified angle 35', and dividing by the power 4<5o, which 
I used we obtain 4" 34'" for the distance of the centres of the 2 stars. The 
scale of the micrometer at this very convenient distance, with the power of 46o 
(which my telescope bears so well on the fixed stars that for near a twelvemonth 
past I have hardly used any other) is above a quarter of an inch to a second ; and 
by putting on my power of 932, which in very fine evenings is extremely distinct, 
I obtain a scale of more than half an inch to a second, without increasing the 
distance of the micrometer ; whereas the most perfect of my former micrometers, 
with the same instrument, had a scale of less than the 2000th part of an inch 
to a second. 

The measures of this micrometer are not confined to double stars only, but 
may be applied to any other objects that require the utmost accuracy, such as 
the diameters of the planets or their satellites, the mountains of the moon, the 
diameters of the fixed stars, &c. For instance, Oct. 22, 1781, I measured the 
apparent diameter of aLyrae ; and judging it of the greatest importance to in- 
crease my scale as much as convenient, I placed the micrometer at the greatest 
convenient distance, and (with some trouble, for want of longer handles, which 
might easily be added) took the diameter of this star by removing the 2 lucid 
points to such a distance as just to inclose the apparent diameter. When I mea- 
sured my radius, it was found to be 22 feet 6 inches. The distance of the 2 
lucid points was about 3 inches ; for I will not pretend to extreme nicety in this 
observation, on account of the very great power I used, which was 6450. 
From these measures we have the magnified angle 38' 10": this divided by the 

vol. xv. H H 



234 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

power gives 0".355 for the apparent diameter of aLyrae. The scale of the mi- 
crometer, on this occasion, was no less than 8.443 inches to a second, as will 
be found by multiplying the natural tangent of a second with the power and 
radius in inches. Nov. 1781, I measured the diameter of the new star ; but the 
air was not very favourable, for this singular star was not so distinct with 227 
that evening as it generally is with 460 : therefore, without laying much stress 
on the exactness of the observation, I shall only report it, to exemplify the use 
of the micrometer. My radius was 35 feet 11 inches. The diameter of the 
star, by the distance of the lucid points, was 2.4 inches, and the power I used 
227 : hence the magnified angle is found to/, and the real diameter of the star 
5 // .022. The scale of this measure .474 millesimals of an inch, or almost half 
an inch to a second. 

XIV. A Paper to obviate some Doubts concerning the Great Magnifying Powers 
used. By Mr. Herschel, F. R. S. Addressed to Sir Joseph Banks, p. 173. 
Sir, I have the honour of laying before you the result of a set of measures I 
have taken in order to ascertain once more the powers of my Newtonian 7-feet 
reflector. The method I have formerly used, and which I still prefer to that 
which I have now been obliged to practise, requires very fine weather and a 
strong sun-shiny day ; but my impatience to answer the requests of Sir Joseph 
Banks would not permit me to wait for so precarious an opportunity at this season 
of the year. The difference in all the powers, as far as 2010, will be found to 
be in favour of those I have mentioned ; and, I believe, a much greater concur- 
rence could not well be expected, where different methods of ascertaining them 
are used. The variation in the 2 highest powers is more considerable than I was 
aware of; but still may easily be shown to be a necessary consequence of the dif- 
ference in the methods. However, if on comparing together the methods, it 
should be thought that the power 5786 is nearer the truth than 6450, I shall 
readily join to correct that number. The manner in which I have now deter- 
mined the powers is as follows: I took one of the eye lenses which magnifies 
least, and measured its solar focus by the sun's rays as exactly as I could 5 times, 
which proved to be 1.01, 1.04, l.OQ, 1.01, 1.05, in half-inch measure, a mean 
of which is 1.04. The sidereal focus of my 7-feet speculum is 170.4 in the 
same measure. Thence, dividing 170.4 by 1.04, we find that the telescope will 
magnify 163.8 times when that lens is used. This power being found, I applied 
the same lens as a single microscope to view with it a certain object, which was 
a drawn brass wire fastened so as not to turn on its axis or change its position ; 
for these wires are seldom perfectly round, or of an even size, and it is there- 
fore necessary to use this caution to prevent errors : then, with a fine pair of 
compasses, I took 4 independent measures of the image of the brass wire, 



VOL, 



LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



235 



which was thrown on a sheet of paper exactly 8± inches from the lens, the eye 
being always as close to the lens as possible. I viewed the same wire, exactly in 
the same manner, with every one of the lenses, and measured the pictures on 
the paper. When I came to the higher powers, the wire was exchanged for 
another, 4.37 times thinner than the former, as determined by comparing the 
proportion of their images 54 to 235-2-, taken by the same lens. 

When the images of these wires are obtained, the power of the telescope, 
with every one of the lenses, becomes known by one plain analogy : viz. as the 
image of the wire by the first lens (77\) is to the power it gives to the telescope 
(l63.8,) so is the image of the wire by the 2d lens (119,) to the power it will 
give to the same telescope (250.7.) The particulars of all the measures are as 
follow : 



Powers as they 
have been called 
in my papers. 

146 



Images of a wire thrown A mean Powers as they 

on a paper in hundredths of of the 4 come out by this 
half inches. measures. method. 



77.. 



78 . . 78 11% 16'3.S6 = 



170.4 
1.0+ 



{;: 



.... 119.. 119.. 119 . 

143.. 143 .. 144 . 

236. . 236' . . 235 . . 

.... Smaller wire. 

53.. 54.. 55.. 

83. . 85 . . 84 .. 

107.. 107 .. 107 .. 

128.. 128 .. 129.. 

1536' An excellent lens, 

2010 236. . 236 . . 238 . 

3168 281.. 283 ..281 

6450 635. . 6".'5 . . 630 . 



227 
27S 

460 

754 

932 

1159 



119 

143^ 

235| 



119.- 
143 .. 

236 . . 

. 54 . . 
. 85 .. 
,108.. 

128 . . 
lost about S months before, 

236' 236 

280 281 

626 629 



54 

8+J 

107J 



P' 



250.7 
,301.8 

496.7 

.775.1 

, 986.7 
H79 9 

2175.8 

2585.5 
57 86.8 



I beg leave, Sir, now to give a short description of the method I have formerly 
used to determine these powers. In the year 1776 I erected a mark of white 
paper, exactly half an inch in diameter, which I viewed with my telescope at the 
greatest convenient distance with one of the least magnifiers. An assistant was 
placed at right angles in a field, at the same distance from my eye as the object 
from the great speculum of the telescope. On a pole erected there I viewed the 
magnified image of the half inch, and the assistant marked it by my direction; 
this being measured, gave the power of the instrument at once. The power 
thus obtained was corrected by theory, to reduce it to what it would be on infi- 
nitely distant objects. The powers of the rest of the lenses I deduced from this, 
by a camera eye-piece, which I made for that purpose, abcd (fig. 17, pi. 3) re- 
presents a perpendicular section of it. The end a screws into the telescope. 
On the end b may be screwed any of the common single lens eye-pieces. Imn 
is a small oval plane speculum, adjusted to an angle of 45° by 3 screws, 2 of 
which appear at o, p. When the observer looks in at b, he may see the object 
projected on a sheet of paper on a table placed under the camera piece, and mea- 

H H 2 



236 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

sure its picture ab, as in fig. 18. The power of one lens therefore being known, 
that of the rest was also found by comparing the measures of the projected 
images. 

It may not be amiss to mention some of the advantages and inconveniencies 
attending each of these methods. When we take the focus of an eye-lens, 
which the first method requires, we are liable to a pretty considerable uncertainty, 
and in very small lenses it is not to be done at all. Also, in calculating the 
power by that focus, no account is made of the aberration which takes place in 
all specula and lenses, and increases the image, so that we rather find out how 
much the telescope should magnify, than how much it really does magnify; but 
in determining the power by an experiment we avoid these difficulties. On the 
other hand, when the power is very great, the latter method becomes inconve- 
nient, both on account of want of light in the object, and a very considerable 
aberration which takes place, and makes the picture too indistinct to be very ac- 
curate in the measure, and of course larger than it ought to be ; and this will 
account for the excess in the measures of my 2 largest powers. However, when 
I employed 6450 on the diameter of a Lyrae, I incline to think the method I had 
used when I determined that power, ought to be preferred, because my lamp- 
micrometer gives the measure of an object as it appears in the telescope, and 
therefore this aberration is included, and should be taken into consideration. 

To prevent any mistakes, I wish to mention again, that I have all along pro- 
ceeded experimentally in the use of my powers, and that I do not mean to say 
I have used 6450, or 5786, on the planets, or even on double stars; every 
power I have mentioned is to be understood as having been used just as it is 
related; but further inferences ought not as yet to be drawn. For instance, my 
observations on £ Bootis mention that I have viewed that star with 2010, or as 
in the above table with 2175, extremely distinct; but on several other celestial 
objects I have found this power of no service. Many plausible suggestions have 
already occurred to account for these appearances; but I wait till further experi- 
ments shall have furnished me with more materials to reason on. The use of 
high powers is a new and untrodden path, and in this attempt variety of new 
phenomena may be expected; I therefore wish not to be in a haste to make general 
conclusions. I shall not fail to pursue this subject, and hope soon to be able to 
attack the celestial bodies with a still stronger armament, which is now preparing. 

XIV. Continuation of the Experiments and Observations on the Specific Gravities 
and Attractive Powers of various Saline Substances. By Rich. Kirwan, Esq., 
F.R.S. p. 179- 
Before entering (says Mr. K.) on a detail of the new experiments I have made 

in the prosecution of this subject, I must beg leave to rectify some mistakes I 
have fallen into in my last paper. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 237 

1. In computing the quantity of acid taken up by 10.5 gr. of mild vegetable 
fixed alkali, I made no allowance for the small quantity of earth it contains, viz. 
0.7035 of a grain; but in large quantities of alkali, this proportion is consider- 
able, and it occasioned a small but sensible error in my subsequent calculations 
of the proportion of ingredients in neutral salts, the quantity of alkali being, by 
that fraction, less than I supposed it in 10.5 gr. This correction being made, it 
will be found, that 1 00 gr. of perfectly dry vegetable fixed alkali, abstracted from 
the quantity of earth, generally contain 22.457 gr. of fixed air, instead of 21, 
as before determined: though the former determination is right, where the earth 
is not separated, yet may well be supposed to exist, as in the alkali of pearl-ash, 
purified by 3 repeated calcinations and solutions. Hence also 100 gr. of such 
alkali, free from earth, water, and fixed air, take up 46.77 gr. of the mineral 
acids, that is, of the mere acid part; and 100 gr. of common mild vegetable 
alkali take up about 36.23 of real acid. 

Now, 100 gr. of perfectly dry tartar vitriolate contain 30.21 of real acid, 64. 61 
of fixed alkali, and 5.18 of water. Crystallized tartar vitriolate loses only 1 per 
cent, of water in a heat in which its acid also is not separated in any degree, and 
therefore contains 6.18 of water. 

Again, 100 gr. of nitre, perfectly dried, contain 30.86 of acid, 66 of alkali, 
and 3.14 of water; but in crystallized nitre the proportion of water is somewhat 
greater; for 100 gr. of these crystals, being exposed to a heat of 180° for 2 hours, 
lost 3 gr. of their weight, without exhaling any acid smell; but when exposed to 
a heat of 200°, the smell of the nitrous acid is distinctly perceived. Hence 100 
gr. of crystallized nitre contain 29.89 of mere acid, 63.97 of alkali, and 6.14 

of water. 

And 100 gr. of digestive salt perfectly dry contain 29.68 of marine acid, 63.47 
of alkali, and 6.85 of water. 100 gr. of crystallized digestive salt lost but 1 gr. 
of their weight before the smell of the marine acid is perceived; and hence they 
contain 7-85 gr. of water. 

But the mistake which cost me most time and pains to correct, was that fallen 
into when I imagined, that the mixtures of oil of vitriol and water, and spirit of 
nitre and water, had attained their maximum of density when they had cooled to 
the temperature of the atmosphere, which at the time of the experiments stood 
between 50 and 60° of Fahrenheit. The former I had even suffered to stand 6 
hours which was much longer than was necessary for its cooling; but when the 
acid was so much diluted as to cause little or no heat, I allowed it to stand but 
for a very little time before I examined its density: yet several months after I 
found many of these mixtures much denser than when I first examined them, 
and that at least 12 hours rest was requisite before concentrated oil of vitriol, to 
which even twice its weight of water is added, attains its utmost density, and still 
more when a less proportion of water is used: thus, when I made the mixture 



'238 



PHILOSOPHICAL TRANSACTIONS. 



[anno 17 82. 

of 251Q.75 gr. of oil of vitriol, whose specific gravity was I.8I9, with 180 of 
water, I found its density 6 hours after 1.77 1 ; hut after 24 hours it was I.798; 
and hence, according to the reasoning in the former paper, the accrued density 
was at least .064, instead of .045, as I had formerly found it. But by using oil 
of vitriol still more concentrated, whose specific gravity was 1 .8846, I was en- 
abled, by a similar train of reasoning, to make a still nearer approximation, and 
found that the accrued density of oil of vitriol, whose specific gravity is 1.81 9, 
amounts to 0.104; and consequently its mathematical specific gravity is 1.715. 
Now 6.5 gr. of this oil of vitriol contained, as I before found, 3.55 of mere acid, 
and the remainder water, and the weight of an equal bulk of water is 3.79 gr. ; 
then subtracting from this the weight of the water that enters into the compo- 
sition of the oil of vitriol, it will be found, that the weight of a bulk of water, 
equal to the acid part, is 0.84, and consequently the specific gravity of the pure 
and mere acid part is 4.226. On this ground, and constantly allowing the mix- 
tures to rest at least 12 hours, till the oil of vitriol was diluted with 4 times its 
weight of water, and then often only 6 hours, before their density was examined, 
I constructed the table hereto annexed; the temperature of the room being con- 
stantly kept between 50 and 6o°; and the column of acid being always 6 12.05. 



Oil of 


Water. 


Accrued ] 


Mathem. 


Physical | 


Oil of 


Water. 


Accrued 


Mathem. 


Physical 


vitriol. 




density. 


sp. grav. 


spec. grav. 


vitriol. 




density. 


spec. grav. 


spec. grav 


Grains. 










Giutfis. 










1000 


387.95 


.07 


1.877 


1.886 


4100 


3487-95 


.070 


1.128 


1.198 


1100 


4-87 .95 


.104 


1.738 


1.844 


4200 


3587-95 


.070 


1.125 


1.195 


1200 


587.95 


.105 


1.6'37 


1.742 


4300 


3687-95 


.070 


1.121 


1.191 


1300 


687 .95 


.144 


1.561 


1.705 


4400 


3787-95 


.070 


1.118 


1.183 


1400 


787.95 


.144 


1.500 


1 .644 


4500 


3887.95 


.070 


1.115 


1.185 


1 500 


887.95 


.137 


1.452 


1.589 ! 


4600 


3987-95 


.070 


1.113 


1 . 1 S3 


16\)0 


987.95 


.137 


1.412 


1.539 


4700 


4087-95 


.070 


1.110 


1.180 


1700 


1087.95 


.130 


1.379 


1.509 


4800 


4187-95 


.070 


1.107 


1.177 


1800 


1187.95 


.124 


1.350 


1.474 


4900 


4287-95 


.070 


1.105 


1.175 


1900 


1287.95 


.116 


1.320' 


1.442 


5000 


4387-95 


.070 


1 . 1 03 


1.172 


2000 


1387-95 


.11(1 


1.304 


1.420 


5100 


4487-95 


■ 069 


1.100 


1.169 


2100 


1487.95 


.112 


1 .286 


1.398 


520(1 


45H7-95 


.06'9 


1 .098 


1.107 


2200 


1587.95 


.112 


1 .-'69 


1.381 


5300 


4687-95 


.06'9 


1 .096' 


1.16'5 


2300 


1 (.87.95 


.108 


1.254 


1.36'2 


5 10 1 


4787-95 


A(^) 


1 ,094 


1.103 


24-00 


1787.95 


.104 


1.241 


1.345 


5500 


4887-95 


.008 


1.092 


l.l60 


2500 


1 887.95 


.104 


1 .229 


1.333 


5600 


4-987-95 


.06'7 


1.091 


1.158 


2600 


1987.95 


.101 


1.219 


1 .320 


5700 


50.s7.95 


.06- 


1.089 


1.156 


2700 


2087-95 


.096' 


1.209 


1.307 


5800 


5187-95 


.007 


1.087 


1.154 


2800 


2187-95 


.091 


1.200 


1.291 


5900 


5287-95 


.005 


1 .1 86 


1.151 


2yoo 


2287.95 


.090 


1.192 


1.282 


600 » 


5387-95 


.' 64 


1 .084 


1.148 


3000 


2.; 87. 05 


.090 


1 184 


1.274 


OHIO 


54 87-9"' 


.1 64 


1 .082 


1 . 1 46 


3100 


2487.95 


.090 


1.1/7 


1.267 


6200 


5587-95 


.063 


1.081 


1 . 1 14 


3200 


2587.95 


.090 


1 170 


1.260 


6300 


5687 .05 


.( 62 


1. :80 


1.11 2 


3300 


2687.95 


.089 


1 1()4 


1.2. 3 


6400 


5787-95 


.(62 


I.(>78 


1.1 10 


3400 


2787.95 


.084 


1 - 1 59 


1.243 


6500 


5S87"> 


.( 01 


1.077 


1.138 


3500 


2887.95 


.083 


1.150 


1.233 


6600 


5987-95 


.060 


i.( 76 


1 . 1 36 


3600 


'-" 87.95 


.(.7;; 


1.149 


1.222 


6700 


6087-9 ■ 


.(-(Ml 


1.1 74 


1 . 1 34 


3?oo 


3087.95 


.073 


1.141 


1.217 


6800 


6 187-95 


.1 Od 


1.0, 2 


1.132 


3800 


3187-95 


.071 


1.140 


1.21 1 


6900 


6287-95 


.060 


1.070 


1 . 1 30 


3900 


3287-95 


.071 


1.136 


1 .2' 8 


7000 


63S7-95 


.059 


1.069 


1 . 1 28 


4000 


3387. 95 


.071 


1.132 


1.204 













•2,39 



VOL. LXXII.J PHILOSOPHICAL TRANSACTIONS. 

With regard to the nitrous acid, I found also I had been a little too precipitate 
as to the time of examining its density, after it had been mixed with water. 
Hence using some whose specific gravity was 1.47 4, I allowed the mixtures to 
rest 12 hours, till it was diluted with twice its weight of water, and the subse- 
quent mixtures 6 hours at least, by the former process of reasoning, I found 
the specific gravity of the mere nitrous acid to be 5.530; the constant number 
in the column of acid being here 3Q3. 



Spirit of 


Water. 


Accrued 


Matheni. 


Physical 


nitre. 




density. 


spec. grav. 


spec. grav. 


Grains. 










9uo 


507 


.... 


1.557 


1.557 


1000 


607 




1.474 


1.474 


1100 


707 


.035 


1.413 


1.448 


1200 


807 


.056 


i .307 


1.423 


1300 


907 


.065 


1 .329 


1.394 


1400 


iou7 


.065 


1.29S 


1 .363 


1500 


1107 


.077 


1.273 


1.350 


1600 


1 207 


.082 


1.251 


1.333 


1700 


1307 


.'.82 


1.233 


1.315 


1800 


1407 


.083 


1.217 


1.300 


lyoo 


1507 


.083 


1.204 


1 .287 


2000 


1607 


.096 


1.191 


1.209 


2100 


1707 


.088 


1.181 


1.254 


2200 


1807 


.071 


1.176 


1.247 


2300 


19' <7 


.068 


1.162 


1.230 


2400 


2007 


.008 


1.154 


1.222 


2500 


2107 


.067 


1.147 


1.214 


2600 


2207 


.065 


1.141 


1.206 


2700 


2307 


.063 


1.135 


1.198 


2800 


2407 


.061 


1.129 


1.190 


2900 


2507 


.058 


1.124 


1.182 


3000 


2607 


.055 


1.120 


1.175 


3100 


2707 


.054 


1.116 


1.170 



Spirit of 


Water. 


Accrued 


Mathem. 


Physical 


nitre. 




density. 


spec. grav. 


spec. grav. 


Grains. 










3200 


2807 


.054 


1.111 


1.105 


3300 


2907 


.053 


1.108 


1.161 


3400 


3007 


.052 


1.104 


1.156 


3500 


3107 


.050 


1.101 


1.151 


3600 


3207 


.048 


1 .098 


1.146 


3700 


3307 


.047 


l.<»95 


1.142 


3800 


3407 


.045 


1.09: 


1.137 


3900 


3^07 


.043 


1.089 


1.132 


4000 


3607 


.040 


1.0S7 


1.127 


4100 


3707 


.037 


1.085 


1.122 


4200 


3807 


.035 


1.0S3 


1.118 


4300 


3907 


.034 


1.080 


1.114 


4400 


4007 


.032 


1.078 


1.110 


4500 


4107 


•029 


1.077 


1.106 


4600 


4207 


.027 


1.075 


1.102 


+700 


4307 


.025 


1.073 


1.098 


4S00 


4407 


.022 


1.072 


1 .094 


4900 


4307 


.020 


1.070 


1.090 


5000 


4607 


.018 


1 .008 


1.086 


5100 


4707 


.015 


1.067 


1.082 


5200 


4807 


.012 


1 .066 


1.078 


5300 


4907 


.008 


I.066 


1.074 



The foregoing experiments were made at the temperature of between 50 and 
60° of Fahrenheit ; but as it may be suspected that the density of the above acids 
is much altered at degrees of temperature considerably different, I endeavoured 
to find the quantity of this alteration, and to calculate what this density would 
be at 55°, that the quantities of acid and water may thence be investigated. To 
this end I took some dephlogisticated spirit of Deg. Sp. gravity, 

nitre, and examined its specific gravity at dif- ^9 i.46'50 

' r ° J 46 1.4587 

ferent degrees of heat, and found it as annexed, §6 ........ U4302 

viz. at 12 ° 1-+123 

Therefore the total expansion of this spirit of nitre from 30 to 120°, that is, 
by 90 of heat, was 0.0527; for 1.4650 — 1.4123 = .0527; by which we see 
that the dilatations are nearly proportional to the degrees of heat; for beginning 
with the first dilatation from 30 to 46°, that is, by l6° of heat, 90 : 0.0527 - 16 



240 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

: O.C093 ; but in reality these ] 6° of heat afforded a dilatation equal only to 
0.0063; for 1.4650— 1.4587 = 0.0063; so that the difference between the 
calculated and observed dilatations is only , „VW, a difference of no consequence 
in the present case; and even that might arise from the immersion of the cold 
glass ball filled with mercury in the liquor, it being the solid I use to try the spe- 
cific gravity of liquids. In the next case the difference is still less; for 90 : 0.0527 
:: 56 : 0.0327; but 56° of heat produced in reality a dilatation of 0.0348, for 
1.4650 — 1.4302 = 0.0348, so that the calculation is deficient only by TrnrW- 

I afterwards tried another, and somewhat Deg. Sp. gravity. 

stronger, spirit of nitre, whose specific gravity 4g ' 1*653 

was, at 150 1.3792 

Here also the expansions are nearly proportional to the degrees of heat; for ] 16 
of heat (the difference between 34 and 150) produce an expansion of O.O958; 
and 15° of heat (the difference between 34 and 49) produce an expansion of 
O.OO97, and by calculation 0.0123, which last differs from the truth only by 
1 » 6 o • By this experiment we see, that the stronger the spirit of nitre is, the 
more it is expanded by the same degree of heat: for if the spirit of nitre of the 
last experiment were expanded in the same proportion as in the first, its dilata- 
tion by 1 l6° of heat should be O 0679, whereas it was found to be O.0958. 

As the dilatation of spirit of nitre is far greater than that of water by the same 
degree of heat, and as it consists only of acid and water, it clearly follows, that 
its superior dilatability must be owing to the acid part; and hence the more acid 
is contained in a given quantity of spirit of nitre, the greater is its dilatability. 
We might therefore suppose, that the dilatation of spirit of nitre was interme- 
diate between that of the quantity of water it contains and that of its quantity 
of acid; but there exists another power also which prevents this simple result, 
namely, the mutual attraction of the acid and water to each other, which makes 
them occupy a less space than the sum of their joint volumes, which condensa- 
tion I have therefore called their accrued density. Taking this into the account, 
we may consider the dilatation of spirit of nitre as equal to those of the quan- 
tities of water and acid it contains, minus the condensation they acquire from 
their mutual attraction, and this rule holds as to all other heterogeneous com- 
pounds. 

To find the quantities of acid and water in spirit of nitre, whose specific gra- 
vity was found in degrees of temperature different from those for which the table 
was constructed, viz. 54, 55, or 56° of Fahrenheit, the surest method is to find 
how much that spirit of nitre is expanded or condensed by a greater or less degree 
of heat, and then, by the rule of proportion, find what its density would be at 
55°; but if this cannot be done, we shall approach pretty near the truth, if we 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 24] 

allow , ■ °-„ for every 15° of heat above or below 55° of Fahrenheit, when the 
specific gravity of spirit is between 1.400 and 1.500; and -p^Vo when the spe- 
cific gravity is between 1 .400 and 1 .300. 

A.s to oil and spirit of vitriol, I found the dilatations exceedingly irregular, 
probably by reason of a white foreign matter, which is more or less suspended or 
dissolved in it, according to its greater or less dilution. This matter I would not 
separate, as I intended trying the density of this substance in the state in which 
it is commonly used. In general I found, that 15° of heat cause a difference of 
about t-jVo- in its specific gravity when it exceeds 1.800; and of T -^ 5 - 5 . when its 
specific gravity is between 1.400 and 1.300: its dilatation is greater than that of 
water, and so much greater as it is stronger. 

The dilatations of spirit of salt are very nearly Deg. Sp. gravity, 

proportional to the degrees of heat, as appears 54 .'!!!"".' u86"o 

by the annexed table. Hence -nrVo should be 66 l 18-20 

added or subtracted for every 21° above or below 128 Kl631 

55°, in order to reduce it to 55°, the degree for which its proportion of acid and 
water was calculated. The dilatability of this acid is much greater than that of 
water, and even than that of the nitrous acid of the same density. 

I now proceed to examine the quantity of pure acids taken up at the point of 
saturation by the various substances they unite with. 

Of the mineral alkali. — That which I made use of was procured from Mr. 
Turner, who by a peculiar and ingenious process extracts it in the greatest purity 
from common salt. Of this alkali I rendered a portion tolerably caustic in the 
usual manner, and evaporating 1 oz. of the caustic solution to perfect dryness, 
I found it to contain 20.25 gr. of solid matter. I was assured that the watery 
part alone exhaled during the evaporation, as the quantity of fixed air contained 
in it was very small, and to dissipate this, a much greater heat would be requisite 
than that which I used. This dry alkali I immediately dissolved in twice its 
weight of water, and saturating it with dilute vitriolic acid, found it to contain 
2.25 gr. of fixed air, that being the weight which the saturated solution wanted 
of being equal to the joint weights of the water, alkali, and spirit of vitriol em- 
ployed. 

The quantity of mere vitriolic acid necessary to saturate 100 gr. of pure 
mineral alkali, I found to be 60 or 6] gr. ; the saturated solution, thus formed, 
being evaporated to perfect dryness, weighed 36.5 gr. but of this weight, only 
28.38 were alkali and acid; therefore the remainder, viz. 8.12 gr. were water. 
Hence lOOgr. of Glauber's salt, perfectly dried, contain 29. 12 of mere vitriolic 
acid, 48.6 of mere alkali, and 22.28 of water; but Glauber's salt crystallized 
contains a much larger proportion of water; for 100 gr. of these crystals, being 
heated red-hot, lost 55 gr. of their weight. This loss I suppose to arise merely 
vol. xv. I I 



242 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

from the evaporation of the watery part, and the remaining 45 contained alkali, 
water, and acid, in the same proportion as the lOOgr. of Glauber's salt, per- 
fectly dried, abovementioned; then these 45 contained 13.iggr. of vitriolic 
acid, 2 1 .87 of fixed alkali, and 9.94 of water; consequently 100 gr. of crystal- 
lized Glauber's salt contain 13.19 of vitriolic acid, 21.87 of alkali, and 64.94 of 
water. 

I also saturated this alkali with the dephlogisticated nitrous acid, and found 
that 100 gr. of the alkali took up 57 of the mere nitrous acid in the experiment 
I most depended on; but this quantity varied in some experiments a ihw grains, 
being sometimes 60, and sometimes 63 gr.; so that I conclude the proportion of 
this acid, taken up by the alkali, is nearly the same as that of the vitriolic acid. 
Supposing this quantity to be 57 gr. then 100 gr. cubic nitre, perfectly dry, 
contain 30 of acid, 52.18 of alkali, and 17.82 of water; but cubic nitre crys- 
tallized contains something more water; for 100 gr. of these crystals lose about 
4 by gentle drying; therefore lOOgr. of the crystallized salt contain 28.8 of 
acid, 50.09 of alkali, and 21.11 of water. 

Of mere marine acid, 100 gr. of this alkali required from 63 to 66 or 67 gr. ; 
perhaps one reason of this variety is, that it is exceeding hard to hit the true 
point of saturation. Allowing it to be 66 gr. then lOOgr. of perfectly dry 
common salt contain nearly 35 of real acid, 53 of alkali, and 13 of water; but 
lOOgr. of the crystallized salt lose 5 by evaporation; then lOOgr. of these 
crystals contain 33.3 of acid, 50 of alkali, and 16.7 of water. 

The proportion of fixed air, alkali, and water, in crystallized mineral alkali, 
I investigated thus: 200 gr. of these crystals were dissolved in 240 of water; 
the solution was saturated by such a quantity of spirit of nitre as contained 40 
of mere nitrous acid; hence I inferred, that these 200 gr. of alkali contained 70 
of real alkali. The saturate solution weighed 40 gr. less than the sum of its 
original weight, and that of the spirit of nitre added to it; therefore it lost 
40 gr. of fixed air. The remainder therefore of the original weight of the 
crystals, must have been water, that is, 90gr.; consequently lOOgr. of these 
crystals contained 35 of alkali, 20 of fixed air, and 45 of water. This propor- 
tion is, particularly with regard to the alkali, very different from that found by 
Mr. Bergman and Lavoisier, which I impute to their having used soda recently 
crystallized. Mine had been made some months, and probably lost much water 
and fixed air by evaporation which altered the proportion of the whole. Accord- 
ing to the calculation of these philosophers 100 gr. of this alkali takes up 80 of 
fixed air. The specific gravity of the crystallized mineral alkali, weighed in 
ether, I found to be 1 .42 1 . 

Of the volatile alkali. — It is not possible, by the old chemical methods, to 
find the proportion of the ingredients in volatile alkalis, whether in a liquid or in 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 243 

a concrete state; seeing that, though it may be separated from fixed air, yet it 
cannot from water, on account of its extreme volatility. Then to find this pro- 
portion we must recur to the experiments of Dr. Priestley, who by his new 
analysis produced this alkali free from the aerial acid and water in the form of 
air; and in the 3d volume of his observations, p. 2Q4, informs us, that 1-^ 
measures of alkaline air take up, and are saturated by, 1 measure of fixed air.* 
Let us suppose the measure to contain 100 cubic inches; then 185 cubic inches 
of alkaline air take up 100 of fixed air; but 185 cubic inches of alkaline air 
weigh, at a medium, 42.55 gr.; and 100 cubic inches of fixed air weigh 57 gr. ; 
then lOOgr. of pure volatile alkali, free from water, take up 134 of fixed air. 

On expelling its aerial acid from a parcel of this alkali in a concrete state, and 
formed by sublimation, I found 100 gr. of it to contain 53 of fixed air, and 
therefore, according to the preceding reasoning, 39-47 of real alkali and 7.53 of 
water per cent. Saturating a solution of this alkali with the vitriolic, nitrous, 
and marine acids, I found, that lOOgr. of the mere alkali take up 106 of mere 
vitriolic acid, 115 of the nitrous, and 30 of the marine. The specific gravity 
of the concrete volatile alkali weighed in ether was 1.4076. 

The proportion of water in the different ammoniacal salts I have not been able 
to find, on account of their volatility; but believe it to be very small, as volatile 
alkali and fixed air crystallize without the help of water, when both are in an 
aerial state. 

Of calcareous earth. — I first dissolved this earth in the nitrous acid, and found 
that, after allowing for the loss of fixed air and the quantity of water I formerly 
mentioned, 100 gr. of the pure earth take up 104 of mere nitrous acid. Instead 
of dissolving this earth immediately in the vitriolic acid, I precipitated its solu- 
tion in the nitrous by the gradual addition of the vitriolic, and found that to 
effect this, Q\ or 92 gr. only of mere vitriolic acid were required. lOOgr. 
of this pure earth demand for their solution 112 of mere marine acid. The 
solution, which is at first colourless, grows greenish on standing. Natural 
gypsum varies in its proportion of acid, earth, and water, 100 gr. of it con- 
taining from 32 to 34 of acid, and also of earth, and from 26 to 32 of water. 
The artificial contains 32 of earth, 29.44 of acid, and 38.56 of water; when 
well dried it loses about 24 of water, and therefore contains 42 of earth, 39 of 
acid, and 19 of water percent. 100 gr. nitrous selenite, carefully dried, con- 
tain 33.28 of acid, 32 of earth, and 34.72 of water. 100 gr. marine selenite, 

* I have lately repeated this experiment, and found that one measure of alkaline air is saturated 
by less than half of one measure of fixed air, but more than | ; conformably to Dr. Priestley's first 
experiment, p. 293 ; by which it appears, that 100 gr. of alkaline air require about \20 of fixed au- 
to saturate them : and hence 100 gr. of concrete volatile alkali contain about 53 of fixed air, 44 of 
mere volatile alkali, and 3 of water. — Orig. 

1 1 1 



244 1-HILOSOPH1CAL TRANSACTIONS. [ANNO 1782. 

well dried, so as to lose no part of the acid, contain 42.56 of acid, 38 of earth, 
and 19.44 of water. 

Of magnesia or muriatic earth. — This earth, perfectly dry and free from fixed 
air, could not be dissolved in any of the acids without heat. In the temperature 
of the atmosphere even the strongest nitrous acid did not act on it in 24 hours; 
but in a heat of 180° these acids, diluted with 4 or 6 times their quantity of 
water, attacked it very sensibly; but as much of the acids dissipated by heat, I 
could not judge of the exact quantity of acid requisite to dissolve a given quan- 
tity of it, any otherwise than by precipitating the solutions by another substance, 
whose capacity for taking up acids was known. The substance used was a 
tolerably caustic vegetable alkali. By this method I found, that 100 gr. of pure 
magnesia take up 125 gr. of mere vitriolic acid, 132 of the nitrous, and 140 of 
the marine. None of these solutions reddened vegetable blues; all of them 
appeared to contain something gelatinous ; that in the marine acid became 
greenish on standing for some time. 

100 gr. of perfectly dry Epsom salt contain 45.67 of mere vitriolic acid, 36.54 
of pure earth, and 17-83 of water; but 100 gr. of crystallized Epsom lose 48 
by drying, and consequently contain 23.75 of acid, 19 of earth, and 57.25 of 
water. Common Epsom salt contains an excess of acid, for its solution reddens 
vegetable blues. 100 gr. of nitrous Epsom, well dried, contain 35.64 of acid, 
27 of pure earth, and 37.36 of water. The solution of marine Epsom cannot 
be tolerably dried without losing much of its acid, together with the water. 
The specific gravity of pure muriatic earth is 2.3296. 

Of earth of alum or argillaceous earth. — This earth I found to contain about 
26 per cent, of fixed air, though I had previously kept it red-hot for half an 
hour: this surprized me much, as most writers say it contains scarcely any. It 
dissolved in acids with a moderate effervescence till the heat was raised to 220°, 
after which I found the solution lighter than the quantities employed in the pro- 
portion I mentioned. 

100 gr. of this earth, exclusive of the fixed air, require 133 of the mere 
vitriolic acid to dissolve them. This solution I made in a very dilute spirit of 
vitriol, whose specific gravity was I.O93, in which the proportion of acid to that 
of water was nearly as 1 to 14. This solution contained a slight excess of acid, 
turning vegetable blues into a brownish red; but it crystallized when cold, and 
the crystals were of the form of alum; so that I believe this to be nearly the 
proper proportion of its acid and earth; but there was not water enough to form 
large crystals. As this solution contained an excess of acid, I added more earth 
to it, but could not prevent its tinging blue paper red, till it formed an insoluble 
salt, that is, one that required an exceeding large quantity of water to dissolve 
it, and while part was thus become insoluble, yet another part would still retain 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 245 

an excess of acid; so that at the same time part would be supersaturated with 
earth, and another with acid, if tinging vegetable blues be a mark of an excess 
of acidity, which indeed in this case seems dubious. 

JOOgr. of alum, perfectly dried, contained 42.74 of acid, 32.14 of earth, 
and 25.02 of water; but crystallized alum loses 44 per cent, by desiccation J 
therefore 100 gr. of it contain 23.Q4 acid, 18 of earth, and 5 8. 06 of water. 

100 gr. of this pure earth take up, as far as I can judge, 153 of the mere 
nitrous acid. Tbe solution still reddened vegetable blues; but after the addition 
of this quantity of pure earth, I think it was, that an insoluble salt came to be 
formed. The solution, when cold, grew turbid, and could not be wholly dis- 
solved by 500 times its weight of water. The same quantity of pure earth 
requires 173.45 of the mere marine acid for its solution; but the solution 
still reddens vegetable blues. After this, an insoluble salt was formed; but the 
beginning of its formation is difficultly discovered both in this and the former 
cases. The specific gravity of argillaceous earth, containing 25 per cent, of 
fixed air, I found to be 1.QQ01. 

Of plrfogistov. — Before proceeding to investigate its proportion in various 
compounds, and particularly in plilogisticated acids, it will be necessary to sav 
something of its nature. It is allowed on all hands, that fixed air, or the aerial 
acid, as it is more properly called, is capable of existing in 2 states; the one 
fixed, concrete, and unelastic, as when it is actually combined with calcareous 
earth, alkalis, or magnesia; the other, fluid, elastic, and aeriform, as when it 
is actually disengaged from all combination. In its concrete and unelastic state 
it can never be produced single and disengaged from other substances; for the 
moment it is separated from them, it assumes its aerial and elastic form. The 
same thing may be said of phlogiston: it can never be produced in a concrete 
state, single and uncombined with other substances; for the instant it is dis- 
engaged from them, it appears in a fluid and elastic form, and is then commonly 
called inflammable air. These different states of the same substance arise, 
according to discoveries of Dr. Black, from the different portions of elementary 
fire contained in such substance, and absorbed by it, while its sensible heat 
remains the same, and hence called its specific fire. For want of attention to 
these different states, the very existence of phlogiston as a distinct principle has 
been frequently called in question, and chemists have been required to exhibit it 
separate in its fixed state, without recollecting, that neither can fixed air be shown 
separate in a concrete state, nor that phlogiston may also be in the same predi- 
cament ; while others have totally mistaken the nature of inflammable air, and 
imagined it to be a combination of acid and phlogiston. The reason why fixed air 
cannot be separated from any substance in a concrete state is, because when it is 
separated, for instance by means of an acid, there is always a double decomposi- 



246 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/82. 

tion, the acid yielding its specific quantity of fire to the concrete fixed air, which 
then assumes an aerial form, while the fixed air yields the substance it was com- 
bined with to the acid. This is so true, that though a solution of lime in the 
nitrous acid yields a considerable quantity of heat, yet a solution of chalk, in 
that acid scarcely yields any ; for all the fire that is set loose, and rendered sen- 
sible in the first case, is absorbed by the fixed air in the 2d case, being precisely 
that which converts it into an aerial form. The separation of phlogiston from a 
metallic earth, in the form of inflammable air, arises from the same cause, the 
dissolving acid yielding its fire to the phlogiston, which then assumes an aerial 
form, while the phlogiston yields the metallic earth to the acid. It is true, that 
much sensible heat is produced on this occasion, for which 3 substantial reasons 
may be assigned ; first, the proportion of fixed air in a given weight of crude 
calcareous earth, is much greater than that of phlogiston in any metal, as will 
hereafter be shown, it being in the former x of the whole, and that of phlo- 
giston in the latter for the most part not even -f . Secondly, much of the phlo- 
giston combines with the acid itself during the solution, and expels part of its 
specific quantity of fire, as Dr. Crawford has shown, and as I have since expe- 
rienced ; and this fire must occasion sensible heat. Thirdly, much of the phlo- 
giston, during solution, unites to the surrounding atmosphere, expelling also 
part of its specific fire, and this also must occasion sensible heat ; anil hence it 
is, that metallic solutions in vacuo are generally attended with less heat, though 
with a more violent effervescence, than in open air. The solution of metallic 
calces is not attended with so much heat as that of their respective metals, not 
only because neither the dissolving acids nor the surrounding air is much phlogisti- 
cated ; but also because they contain an elastic fluid in a concrete state, which ab- 
sorbs much of the fire given out by the dissolving acids, as it acquires an aerial state. 
The origin and formation of inflammable air being thus explained, I now pro- 
ceed to show its identity and homogeneity with phlogiston. By phlogiston is 
generally understood that principle in combustible bodies on which their inflam- 
mability principally depends ; that principle to which metals owe their malleability 
and splendor ; that which combined with vitriolic acid forms sulphur ; that which 
diminishes respirable air. Now inflammable air is that very principle which 
alone is truly inflammable, as Mr. Volta has elegantly shown. In effect, com- 
bustible substances are either animal or vegetable, as horn, hair, grease, 
wood, &c. from all of which Dr. Hales has extracted inflammable air ; or char- 
coal, from which Mr. Fontana has extracted it, as did Dr. Priestley from resin, 
spirit of wine, and ether, in all which it is the only principle that is inflammable, 
and they are inflammable only in proportion as they yield it; or phosphorus, from 
whose acid Dr. Priestley has obtained this air by means of minium, for it was the 
acid, and not the minium, that contained it, as Dr. Priestley rightly conjectured. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. '24/ 

the acid obtained by deliquescence being never thoroughly dephlogisticated till 
heated and vitrified, as Mr. Margraaf has shown ; or they are mineral substances, 
as sulphur, from which inflammable air has been separated by means of fixed 
alkalis, and, according to Dr. Priestley, also by means of marine air, or 
bitumens or bituminous substances, all of which may be made to yield it ; or 
metallic substances, as zinc and regulus of arsenic, both of which are inflam- 
mable ; but neither of them is so when deprived of its inflammable air: this is 
therefore the true and only principle of inflammability in any substance. I ac- 
knowledge that the inflammable air, proceeding from almost all these substances, 
is exceeding impure ; that it contains from some a mixture of aerial acid or of 
oil, and from all some part of the substance which yields it or expels it, and 
hence its smell is different, according to the class of the substances from which 
it is extracted ; but it is equally true, that none of these substances contribute to 
its inflammability ; on the contrary, it is so much the less inflammable (that is, 
requires so much more air to be mixed with it before it flames) as it contains more 
of these heterogeneous substances. Hence inflammable air of the morasses is 
never totally consumed; and, on the contrary, inflammable air, from metals, 
which is the purest of all, is also the most inflammable. 

Secondly, inflammable air is also the principle which reduces metallic earths 
to a metallic state, and gives them their metallic splendour. This has been 
proved analytically and synthetically, and therefore may be said to be as com- 
pletely demonstrated as any thing in natural philosophy : thus Dr. Priestley has 
extracted inflammable air from iron and zinc by heat alone; and the iron, thus 
stripped of its phlogiston, lost its splendour, and was of a black colour, which 
is that which iron, slightly dephlogisticated, always assumes, as appears by mar- 
tial asthiops: so also zinc and regulus of arsenic, when once inflamed, lose their 
metallic appearance: so also a mixture of lead and tin inflames in a moderate 
heat, and then both are converted into a calx destitute of splendour and malle- 
ability. On the other hand, if a current of inflammable air, in the act of com- 
bustion, be directed on the calces of iron, lead, or mercury, they are immedi- 
ately revived and restored to their metallic form, as appears by the experiment 
of Mr. Chaussier. The following experiment is still more conclusive: if a 
polished plate of iron be put into a saturate and dilute solution of copper in the 
vitriolic or marine acids (I mention these because they are commonly used for 
the production of inflammable air, though the result is the same when other acids 
are used), no effervescence will arise, no inflammable air will be caught; but 
the iron will be dissolved, and the copper precipitated in its metallic form. Here 
inflammable air must be produced as usual, for the acid quits the copper and 
dissolves the iron; but this inflammable air instantly loses its aerial form, and 
unites to the copper, just as fixed air leaves alkalis to unite to lime without any 



248 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

effervescence; and, by this same inflammable air is the copper evidently reduced, ac- 
quiring splendour, malleability, and every other metallic property. But if the solu- 
tion of copper be not saturated with copper, a small quantity of inflammable air may 
be caught, as the excess of acid will disengage more of it from the iron than the 
calx of copper can take up. Inflammable air is then the principle that metallizes 
metallic earth; and if metals contain only a specilic earth and phlogiston, in- 
flammable air certainly contains nothing else but phlogiston. If iron and the 
arsenical acid be digested together, no inflammable air is produced; but the 
arsenical acid is, in great measure, converted into white arsenic, as Mr. Berg- 
man has observed, and also Mr. Scheele; what reason can be assigned why inflam- 
mable air is not produced by this as well as by all other acids; but that this 
metallic acid received it, and was by it reduced to a semi-metallic form, as by 
pure phlogiston ? Yet this acid produces inflammable air from zinc, because zinc 
gives out more phlogiston than the regulus of arsenic can take up; but it attracts 
and is metallized by a part of it, and it is only the excess that appears in the 
form of inflammable air, as Mr. Scheele has remarked. This inflammable air 
indeed is not pure, for it holds some of the regulus in solution; but this portion 
of regulus does not enter into its composition, as is very evident. 

Thirdly, inflammable air is the substance which, with vitriolic acid, forms 
sulphur, for it is the very substance which the vitriolic acid separates from 
metals; and this substance, so separated, when in sufficient quantity, and in 
proper circumstances, unites to it in such proportion as to form common sul- 
phur. Thus sulphur is formed by distilling concentrated vitriolic acid with iron 
or bismuth, or by distilling tartar vitriolate with regulus of antimony. It is this 
also that diminishes respirable air, as Dr. Priestley has clearly shown in the 5th 
vol. of his Observations, p. 84; for though in its complete aerial state, after it 
has absorbed that large quantity of fire requisite to its aerial form, it difficultly 
and slowly unites to respirable air in the heat of the atmosphere, their points of 
contact through their difference of density being very small, and there being no 
substance at hand to receive the large portion of elementary lire they both con- 
tain, and of which they must lose a large proportion before they can combine 
together; yet while inflammable air is, as Dr. Priestley elegantly expresses it, in 
its nascent state, before it acquires its whole quantity of specific fire, respirable 
air easily unites to it, and is diminished in proportion to its purity; but if to a mix- 
ture of both, igneous particles of density sufficient to be visible be introduced, a de- 
gree of heat is excited, which, as it rarefies the dephlogisticated part of respirable air 
to a greater degree than it can inflammable air, brings both into nearer contact, 
increases their attraction to each other, and both uniting give out their fire, or 
in other words inflame, when in proper proportion to each other, without any 
decomposition ol either, unless the loss of a gnat part ol their specific fire be 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 24() 

called a decomposition, which loss is not usually called a decomposition; for 
water is never said to be decomposed when it becomes ice, nor metals when they 
become solid on cooling. 

In answer to all this it will be said, that inflammable air undoubtedly contains 
phlogiston, which produces all the beforementioned effects; but that the phlo- 
giston it contains is united to some other substance, which some will have to be 
an acid, some an earth, and others respirable air. To these hypotheses I shall 
oppose one general observation, which is, that since inflammable air, when pure, 
that is, when disengaged from all heterogeneous substances which no way con- 
tribute fo its inflammability, has always the same properties; it must, if it con- 
sists of phlogiston combined with any other substance, be always united to the 
same specific substance; that is, if this be an acid, it must be always the same 
species of acid, or if an earth, it must be always the same species of earth; for 
we find, that substances, which are only generically the same, always produce, 
with any other given substance, compounds whose properties are very different 
from each other. Thus we sec that the different species of alkalis, or earths, or 
metals, produce, with one and the same species of acid compounds essentially 
different. This is a rule which, as far as I know, admits of no exception; and 
if we apply it. to the abovementioned suppositions it will entirely destroy them ; for 
it is impossible to think, that the phlogiston can in every substance, that pro- 
duces inflammable air, meet either the same acid, or earth, or any res- 
pirable air. 

But to be more particular, the following reasons demonstrate that an acid of 
any sort cannot be the basis of inflammable air. 1st. Inflammable air has been, 
by Dr. Priestley, separated from metals by mere heat. Now metals contain no 
acid, except perhaps their dephlogisticated calx, which those eminent chemists, 
Bergman and Scheele, suspect to be of an acid nature; but these calces cannot 
enter into the composition of inflammable air, otherwise the inflammable air of 
each different metal would have different properties, as already shown: nor indeed 
are these the acids that have been supposed to enter into the composition of 
inflammable air; but rather those acids by whose means it is extricated. But as 
this air is extricated from metals, not only by acids, but also by alkalis,* this 
supposition must vanish of course. 

The same reasons militate with equal strength against the supposition that an 
earth of any kind enters into the composition of this air; nor is there an instance 
of any earth rendered permanently fluid by any means, except in sparry air. 
Besides, if it were a metallic earth, it must necessarily be supposed to be in 
a metallic state; and how then could it escape the action of all kind of acids? for 

* Mem. Par. 1776, p. 687- 

VOL. XV K K 



'250 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

no acid is capable of decompounding inflammable air. Lastly, respirable air 
cannot be said to be the basis of inflammable air, unless we suppose that respir- 
able air enters into the composition of metals; for Dr. Priestley has, by solar heat, 
extracted inflammable air from them in a vessel full of mercury, into which 
respirable air had no access, and even in vacuo. Besides respirable air and phlo- 
giston form other compounds very different from inflammable air, viz. fixed and 
phlogisticated airs, as will presently be seen. 

It may also be fairly urged against all these suppositions, that they are not 
founded on any direct experiment, nor any known analogy, but merely gra- 
tuitous, or at least deduced from experiments inadequate to their support; 
whereas the opinion that inflammable air is nothing else than phlogiston thrown 
into a fluid form by elementary fire, is directly founded on that experiment by 
which inflammable air is separated from metals by mere solar heat in the most 
perfect vacuum, just as fixed air united to marble and in a concrete state (in which 
it is nearly of equal density with gold) is separated from the marble, and thrown 
into a permanently fluid form by heat alone. 

In favour of the existence of an acid in inflammable air, it has been said, 
that if this air be passed through water tinged blue by litmus, it reddens 
instantly. I have seen this frequently happen when inflammable air has been 
extracted from iron by spirit of vitriol; but if this air be washed, by passing it 
through lime-water, and then passed through, or agitated in, an infusion of 
litmus, it will not discolour it in the least: this I have seen done by Mr. Fontaua 
in June 1779- It has also been said, that inflammable air and alkaline air, 
mixed together, form a cloud; but this has been fully disproved by 
Dr. Priestley, in the 4th volume of his observations. That an earth of any kind 
is essentially requisite to the constitution of inflammable air, seems to me utterly 
improbable; nor do I know of any experiment whence it can be inferred. That 
metallic substances may be held in solution by inflammable air is certain; but it 
is equally so, that they no way contribute to its inflammability, and are quite 
distinct from it. 

But the opinion, that inflammable air consists of respirable air super saturated 
with phlogiston, is grounded on very specious arguments, drawn from experi- 
ments to be found in various parts of Dr. Priestley'6 works, which deserve so 
much the more attention as the facts mentioned by that excellent philosopher are 
not to be questioned. I shall endeavour to state them with accuracy; but shall 
at the same time accompany them with such remarks as seem to invalidate the 
conclusion that has been drawn from them. 

In the first volume of Dr. Priestley's observations it appears, that a quantity 
of strong inflammable air, having been agitated in a glass jar immersed in a 
trough of water, the surface of which was exposed to the common atmosphere, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 251 

after the operation had continued 10 minutes, near $ of the quantity had dis- 
appeared; the remainder became fit for respiration, and yet was weakly inflam- 
mable. By further agitation it was diminished half, and then admitted a candle 
to burn in it, though feebly; but, on continuing the agitation a little longer, it 
came to extinguish a candle. On this I shall remark, first, that it clearly follows, 
from this experiment, that if the external respirable air had no access to the inside 
of the jar, half nearly of the inflammable air was converted into, or consisted 
of respirable air, since such quantity of air was found in it after the operation. 
Now it is absolutely impossible that either could happen; for inflammable air 
could not be converted into half or even -^ or J- of its volume of respirable air, as 
even ^ of respirable air contains more matter than 4 times its bulk of inflam- 
mable air; it is then evident, that the external air must have had access to it. 
Secondly, I agitated about half a pint of inflammable air, obtained from iron 
and previously passed through lime-water and kept over mercury, in about 12 
times its bulk of water, out of which its air had been boiled in a glass bottle 
closed with a glass-stopper. The agitation continued at several times at least 2 
hours. A large quantity of the air was indeed absorbed, as appeared by opening 
the bottle in water; but the remainder appeared, by the nitrous test, as noxious, 
and was also found to be as inflammable as at first. Even Dr. Priestley attests, 
that inflammable air, which had been united to water for one month, was after- 
wards as inflammable as ever. 3 pr. iQj . 

The true explanation of the first experiment appears, therefore, to be the 
following: first, water easily imbibes inflammable air, but does not combine with 
it; for after it has imbibed -f T of it, its taste is no way altered, as Dr. Priestley 
has observed. 1 pr. J 96. Water also easily imbibes common air: therefore 
when inflammable air is agitated in water, having a communication with the 
atmosphere, the inflammable air must necessarily be diminished by reason of its 
absorption, and the part so absorbed immediately escapes out of the water into 
the atmosphere, as is evident by the smell which is perceived when the quantity 
of inflammable air is considerable. This escape gives room for the further 
absorption of the inflammable air which then escapes in the same manner. In 
the mean time the common air under the jar rises into it, as appears by the 
direct experiments both of Dr. Priestley and Mr. Fontana; and hence the air in 
the jar must appear by the nitrous test slightly phlogisticated and respirable; but 
a further agitation will decompose the common air, as we shall soon see, and 
then a candle will be extinguished. The same process takes place when inflam- 
mable air stands long in water whose surface is exposed to the atmosphere. 

Another experiment of the same tendency, but seemingly more decisive, is to 
be found in the 4th vol. of Dr. Priestley's Observations, p. 368. There it is re- 
lated, that a portion of inflammable air, inclosed in a glass tube hermetically 

k k 2 



'252 l'HILOSOPHICAL TKANSACTIONS. [ANNO 1J62. 

sealed and heated till the glass was softened, stained the glass black, and the tube 
being opened, the air was found reduced to ■£• of its bulk. ; and this residuum was 
found to be mere phlogisticated air, neither precipitating lime-water, nor being 
affected by nitrous air, or in the least inflammable. Yet decisive as this experi- 
ment appears, a little consideration will show the absolute impossibility that in- 
flammable air should consist of ^ phlogisticated air and §■ phlogiston ; for, in 
the first place, one cubic inch of phlogisticated air weighs 0.377 of a grain: 
now let us suppose, that to this phlogisticated air is added ■§. of its bulk of phlo- 
giston ; and to make the supposition still stronger, let us also suppose that 
phlogiston has no weight ; then, by the supposition, this compound of phlogis- 
ticated air and phlogiston will constitute inflammable air, and amount to a bulk 
of 3 cubic inches, and these 3 cubic inches will weigh no more than 0.377 of a 
grain ; but if 3 cubic inches of inflammable air weigh 0.377 of a grain, 1 cubic 
inch should weigh 0.105 of a grain, which cannot be ; for then inflammable air 
would be little more than -i- lighter than common air, contrary to all the experi- 
ments that have been hitherto made, and particularly those of Mr. Cavendish, 
Fontana, and Dr. Priestley himself, which show it to be about 1 1 times lighter 
than common air. Secondly, it is said, that the matter which stained the glass 
black was the true phlogistic part of inflammable air, and was afterwards sepa- 
rated by means of minium. This then contained no phlogisticated air ; but is 
it not certain, that if there had been enough of it, the minium would have been 
reduced and converted into lead ? And might not inflammable air be again se- 
parated from that lead, though no phlogisticated or common air were at hand to 
supply its other supposed constituent part ? Thirdly, in one of Dr. Priestley's 
experiments the inflammable air, contained in the glass tube which was most 
heated, was reduced to so small a bubble, that no experiment could be made on 
it : therefore, in this, at least, the quantity of phlogisticated air did not amount 
to J-, but was quite inconsiderable ; the remainder then, being taken up by the 
calx of lead in the glass, was pure mere phlogiston ; so that this experiment is a 
strong proof of my opinion. Fourthly, if phlogiston could be decomposed by 
heat, and then leave a residuum of phlogisticated air, amounting to -l of its 
bulk, the diminution arising from its inflammation with common or dephlogisti- 
cated air could never be so great as it is found to be by repeated experiments; 
for when inflammable and common air are fired in the proportion of 1 1 of the 
latter to 4 of the former, a bulk equal to the whole of the inflammable air, and 
to J- of the common air, disappears, according to Mr. Volta, and the diminu- 
tion is about 4 of the whole, or more exactly out of 15 measures, only 8.8 
remain ; but if the inflammable air were decomposed, and £ of it, being phlo- 
gisticated air, should remain, then not quite J- the whole would vanish, and the 
residuum should be 10.54 measures. This evidently proves, that pure inflam- 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 253 

mable air is never decomposed, unless the loss of its fire be called a decomposi- 
tion ; but in the act of inflammation is totally transferred on the pure part of 
respirable air to which it unites. Fifthly, to obtain still a clearer insight into 
this matter, I entreated Mr. Cavallo, who is very expert in the management of 
the blow-pipe, as well as in pneumatic experiments, to repeat this experiment in 
my laboratory. We accordingly filled a tube 10.5 inches long, and J- of an inch 
in diameter, with inflammable air from iron received over mercury, and having 
made the tube red-hot throughout and black, and softened it so far as to en- 
danger the escape of the air, we opened it on mercury. The air was diminished 
only -fV, and inflamed with an explosion as loud as an equal quantity of the same 
inflammable air that had not been heated. 

The only question that remains then is, whence the phlogisticated air pro- 
ceeded which Dr. Priestley mentions to have found ? The circumstance of his 
experiment would furnish a plausible answer ; but the doctor has lately informed 
me, that he believes the air was really inflammable, but, being a very small 
quantity, escaped before the flame could be applied. It seems, therefore suffi- 
ciently proved, that inflammable air purified from the acids or other substances 
that expel it from its basisj and also from all particles of the body to which it was 
originally united, such as inflammable air from metals received on mercury, and 
well washed in lime-water, is one and the same substance with phlogiston, differ- 
ing only in quantity of fire, inflammable air containing nearly the same quantity 
of this element as the same bulk of atmospheric air, as Dr. Crawford has found 
by some late experiments, an account of which will soon be laid before the 
public. This does not contradict that most important discovery of this ingeni- 
ous philosopher, that fire and phlogiston repel each other : the meaning of this 
being only, that the addition of phlogiston to any substance, as to respirable 
air, dephlogisticated acids, metallic calces, expels part of the fire already con- 
tained in such substance ; and, on the contrary, by the removal of phlogiston 
from any substance, the quantity of fire absorbed by such substance is increased. 

It may appear extraordinary, supposing inflammable air and phlogiston to be 
the same substance, that inflammable air should mix so easily with water, whereas 
phlogiston constantly repels and is repelled by it ; but this entirely depends on 
the state of this same substance, which, when fixed and concrete, is called 
phlogiston, and, when rarefied and aeriform, inflammable air. In this latter 
state it mixes with water in proportion to its rarefaction, as it even does in the 
less dense forms of its concrete state : thus ether is totally absorbed by ]0 times 
its weight of water. The animal oil of Dippel mixes entirely with water ; so 
does pure Petrol, and essential oils frequently distilled, and the spiritus rector of 
plants. Much more remains to be said of the different states of phlogiston from 
its most rarefied known state, viz. that of inflammable air, to its most condensed 



254 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

state, that in which it is combined with metallic earths, &c. I have already 
distinguished eight intermediate states each differing from the other by the por- 
tion of elementary fire they contain, this quantity being, as far as I can judge 
directly, as the rarefaction of the phlogiston ; but these researches are foreign to 
my present subject. I shall only remark, that phlogiston, in a state perhaps 100 
times rarer than inflammable air, and consequently containing much more fire, 
may possibly constitute the electric fluid. 

p. s. Since the above was written, I have been honoured with a letter from 
Dr. Priestley, in which he informs me, that he has reduced the calces of iron, 
copper, lead, and tin, merely by melting them in inflammable air by means of a 
burning glass. A certain quantity of inflammable air was absorbed by each 
during their reduction ; but the unabsorbed part was equally inflammable, so 
that there was no decomposition ; but the remainder was of the same nature as 
the part absorbed. He also, by the same means, converted nitrous vapour into 
nitrous air, and the phosphoric acid into phosphorus. And since the communi- 
cation of the last-mentioned experiments, which seem to him also a direct proof 
of the identity of inflammable air and phlogiston, he has been so obliging as to 
inform me, that he has revived the calces of metals in* alkaline air as well as in 
inflammable air, and also formed a phosphorus ; and that he has little doubt but 
that he shall be able to produce any thing else in which phlogiston is supposed 
to be concerned. This, he says, agrees with several of his former experiments, 
especially that in which he produces inflammable air from alkaline air, by means 
of the electric spark and volatile alkali from iron, supersaturated with phlogiston 
by means of nitrous air, which he has repeatedly done since the publication of 
his last volume. This observation, he adds, may help to explain some things in 
the theory of chemistry, especially the affinity which all acids have both with 
phlogiston and with alkalis ; but, he says, that alkaline air contains something 
else besides phlogiston ; because when this air is used, there is always a residuum 
of something that is neither alkaline nor inflammable air ; but he wants more 
sun-shine to complete and extend his experiments on this subject.* 

Of the quantity of phlogiston in nitrous air. — 100 gr. of filings of iron being 
dissolved in a sufficient quantity of very dilute vitriolic acid, produced, with the 
assistance of heat gradually applied, 155 cubic inches of inflammable air, the 
barometer at 29.5, and the thermometer between 50 and 6o°. Now inflam- 
mable air and phlogiston being the same thing, this quantity of inflammable 
air amounts to 5.42 gr. of phlogiston. 

Again, 100 gr. of iron, dissolved in dephlogisticated nitrous acid, in a heat 

* Since this paper was committed to the press, I find that Mr. l'ellctier has reduced the arsenical 
acid to a regulus, by merely passing inflammable air through the solution of thai acid in twice its 
weight of water. Roz. Journ. February 1762. — Orig. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 255 

gradually applied and raised to the utmost, afford 83.87 cubic inches of nitrous 
air. And as this nitrous air contains nearly the whole quantity of phlogiston 
which iron will part with (it being more completely dephlogisticated by this acid 
than by any other means) it follows, that 83.87 cubic inches of nitrous air con- 
tain at least 5,42 gr. of phlogiston ; but it may reasonably be thought that the 
whole quantity of phlogiston which iron will part with, is not expelled by the 
vitriolic acid, and that nitrous acid may expel and take up more of it. To try 
whether this was really so, I calcined a certain quantity of green vitriol, till its 
ferruginous basis was quite insipid ; I then extracted from 64 gr. of this ochre 2 
cubic inches of nitrous air, consequently 100 gr. of this ochre would give 3.12 
cubic inches of nitrous air; and if 83.87 cubic inches of nitrous air contain 
5.42 of phlogiston, then 3.12 cubic inches of this air contain 0.2 of a grain of 
phlogiston; consequently, nitrous acid extracts from 100 gr. of iron, -^ of a 
grain more phlogiston than the vitriolic acid does ; therefore 83.87 cubic inches 
of nitrous air, containing nearly all the phlogiston which iron gives out, contain 
5.62 gr. of phlogiston. Then 100 cubic inches of nitrous air contain 6.7 gr. of 
phlogiston, and since 100 cubic inches of nitrous air weigh 39.9 gr. they must 
also contain 33.2 gr. of nitrous acid. Also, 100 gr. of nitrous air contain 
16.792 of phlogiston, and 83.208 of acid. 

When first I made these experiments I imagined, that the nitrous air thus 
expelled contained all the phlogiston of the metals dissolved in the nitrous acid, 
as this acid is well-known to dephlogisticate metals as perfectly as possible ; but 
I soon observed, as did Dr. Priestley and Mr. Fontana, that the greater part of 
this is air resorbed and detained in the solution, the acid and calx having, accord- 
ing to the beautiful remark of Mr. Scheele, a greater attraction to phlogiston 
than either separately ; yet that the calculation is nearly just, will appear clearly 
in my next paper, by its coincidence with the quantity of phlogiston discovered 
in lead by Dr. Priestley and that which is contained very evidently in regulus of 
arsenic, silver, and quicksilver. 

Of the quantity of phlogiston infixed air. — Before I attempt to determine this 
quantity, it will be necessary to prove that it contains any ; and for this purpose 
minutely to examine its nature and origin. Dr. Priestley first discovered, that 
in all processes, in which phlogiston is disengaged from any substance, as in 
combustion, respiration, calcination of metals, putrefaction, decomposition of 
nitrous air by respirable air, &c. fixed air is precipitated from the common or de- 
phlogisticated air in which these processes are performed, and that these last airs 
are diminished both in weight and bulk, and are afterwards less fit, or absolutely 
unfit, for these processes, according to the quantity of phlogiston that was set 
loose. These facts are admitted by all, let their systems be what they may. 
However, Dr. Priestley thinks he has seen one exception to this general rule ; 



256 PHILOSOPHICAL TRANSACTIONS. [ANNO ] 782. 

for, he says, that in the combustion of inflammable and common air, no fixed 
air is precipitated, 5 Pr. 124. He also seems inclined to admit another excep- 
tion in the case of the combustion of sulphur. 

The questions that here arise are, first, whether the fixed air that appears in 
these circumstances proceeded from the respirable air or not ? Secondly, if it 
proceeded from the respirable air, whether it pre-existed in that air ; or whether 
it was generated during the process that exhibits it ? and if so, what are its con- 
stituent parts ? The first question is easily answered ; for in such phlogistic 
processes as are attended with the destruction of the substances that are known 
to contain fixed air, as those of the animal and vegetable kingdom, the fixed air 
may be supposed to proceed in many cases, both from the decomposed substance 
and from the respirable air ; and of this sort are the processes of combustion 
of most animal and vegetable substances, and fermentation ; but the fixed air, 
that appears in such phlogistic processes as are performed on substances that 
contain no fixed air, must be deemed to proceed from the respirable air singly. 
And of this case we have 4 clear instances ; the calcination of metals ; the de- 
composition of nitrous air by respirable air ; the diminution of common air by 
the electric spark ; and, lastly, its diminution by amalgamation. 

And first as to the calcination of metals, Dr. Priestley has observed, that by 
this operation respirable air (and only respirable air) is diminished between J- and 
-L, both in its weight and bulk ; but Mr. Lavoisier has demonstrated, that 
nothing is lost or escapes through the vessels, as Mr. Scheele would have it ; for 
the weight and materials continue undiminished when the operation is performed 
in close vessels. That part, therefore, which the air loses, is taken up by the 
metallic calx, which accordingly is found to gain the very weight which the air 
loses. Now the air contained in the calx is fixed air ; for Mr. Lavoisier also ob- 
served, that by the calcination of lead, by solar heat, over lime-water, the 
water was rendered slightly turbid. It is true, that Dr. Priestley, in a similar 
experiment, did not observe this turbidity ; but he accounts for this circumstance 
very justly, by supposing that the calx of lead absorbed the fixed air preferably to 
the lime. And this supposition is not gratuitous ; for metallic calces, and par- 
ticularly those of lead, are known to attract fixed air as strongly as quick lime, 
or rather more strongly : and what sets this matter beyond all doubt, the calces 
of lead all yield fixed air by heat, and the grey calx of lead, in particular, which 
was that produced by Dr. Priestley, in the experiment to which I allude, affords 
by heat fixed air only. Other calces of lead after fixed air afford also dephlogis- 
ticated air ; but this I shall show also to have been originally fixed air. If filings 
of iron be mixed with water in close vessels, they will be converted into rust, 
and the incumbent air diminished -l, as Mr. Lavoisier attests; but Dr. Priestley 
has shown, that rust of iron yields scarce any other than fixed air, which may 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 257 

be expelled out of it by mere heat. Nay, iron alone, exposed to common air, 
over a vessel of water for 3 months, reduced this air -i- ; and being exposed to 
dephlogisticated air, over a vessel of mercury, it reduced it -^ in 9 months. In 
all these cases the fixed air could surely come from nothing else but the incum- 
bent respirable air and the phlogiston of the metal. 

Secondly, it is well known, that if nitrous air be decomposed by respirable air 
over lime-water, the lime will be precipitated. In this case also, the fixed air 
must proceed from the respirable air and the phlogiston of the nitrous air ; for it 
cannot proceed from the nitrous acid, as this acid is not decomposed, but is taken 
up by the water over which the mixture of both airs is made, as Mr. Bewly has 
undeniably proved : and hence it is, that unless a large quantity of lime-water 
be used, so as to contain enough for both the nitrous and aerial acids to act on, 
there will be no precipitation of lime, as Mr. Fontana has observed ; for the ni- 
trous acid will seize on the lime preferably to the aerial. Dr. Priestley indeed 
observed, that if a bladder, filled with nitrous air, be dipped in lime-water, it 
occasions a precipitation of lime on the surface of the water. 1 Pr. 213. But 
he elsewhere acknowledges, that this proceeds from the inability of the bladder 
to confine nitrous air. 1 Pr. 76 and 128, which Mr. Baume also long ago ob- 
served, without knowing any thing more of this air: Baume sur l'Ether, 285. 
The phlogiston passes through the bladder, and unites to the common air con- 
tiguous to it. Besides, nitrous air acts on the bladder itself, and extracts fixed 
air from it. 1 Pr. 214. Hence also, if rain-water carefully boiled, and freed 
from its own air, be made to absorb a quantity of nitrous air, it will again, on 
boiling, yield it back as pure as at first ; but if common water be made to im- 
bibe nitrous air in the same manner, it will, on boiling, yield also a portion of 
fixed air. 3 Pr. 109. Does not this happen clearly because common water con- 
tains atmospheric air, or air somewhat purer, which is converted into fixed air 
by mixture with the nitrous air ? This experiment also shows, that water itself 
never unites to phlogiston, since it does not take any from nitrous air, where the 
union of phlogiston to the acid is of the laxest kind. 

Thirdly, if the electric spark be taken through common air, this air will be 
diminished J-, and a solution of lime, if contiguous, will be precipitated, and a 
solution of turnsole tinged red. 1 Pr. 184, 186. Whence could the fixed air 
here produced proceed, but from the common air, and the phlogiston of the 
metallic conductors ? This excellent philosopher has even shown it could pro- 
ceed from nothing else ; for after that air had contributed all it could to that 
production, that is, was diminished to the utmost, he changed the liquors, but 
could produce no change in their colour, nor the least sign of fixed air. This 
experiment has also been repeated in France, and the inside of the glass tube, 
in which the common air was contained, was moistened with a solution of caustic 

vol. xv. L 1. 



258 PHILOSOPHICAL TRANSACTIONS. |_ANNO 1782. 

fixed alkali, and the alkali, after the operation, was found crystallized ; but when 
the tube was exhausted of air, and the experiment repeated, no change whatever 
was found in the alkali. Essai sur l'Electricite, par M. Le Comte De La 
Cepede, vol. 1, p. 155. 

Fourthly, if lead and mercury be agitated in a phial, partly filled with 
common air, this air will be diminished i, and the residuum will be found com- 
pletely phlogisticated. The diminution will be still greater if the phial contain 
dephlogisticated air : 4 Pr. 140. The lead is converted into a calx, calcination 
being the known effect of the amalgamation of the base metals ; and this calx 
absorbed the fixed air produced, for Dr. Priestley expelled this air from it : 4 Pr. 
144 ; and hence an amalgama of lead and mercury decrepitates when heated. 
Whence could this fixed air proceed, but from the respirable air ? For surely 
neither lead nor mercury contain any. 

If the above experiments be attended to, the answer to the 2d question will 
be equally obvious. It is certain, that common air does not consist of + of its 
bulk of fixed air; for if it did, the remaining |- must be dephlogisticated air: 
and if so, then the absolute weight of a mixture of 4 dephlogisticated air and i 
fixed air should coincide at least nearly with the absolute weight of an equal bulk 
of common air ; but in fact it is very far from it : for 4 cubic inches of common 
air weighed 1.54 gr. ; but a mixture of 3 cubic inches of dephlogisticated air 
and 1 of fixed air weighs 1 .83 gr. ; neither indeed has so large a portion of 
fixed air been ever supposed to exist in common air. Besides, if fixed air pre- 
existed in common air, it might be separated from it by lime-water, at least in 
some degree. I have mixed 1 part of fixed air with 20 of dephlogisticated air, 
and also with 20 of phlogisticated air in close vessels, and these mixtures did not 
fail to render lime-water turbid. But let common air be agitated in lime-water 
ever so long in close vessels, not the least cloudiness will appear ; nor does 
quick-lime, in these circumstances, in the least affect common air, as Dr. 
Priestley has observed. 2 Pr. 184. The spontaneous precipitation of lime-water 
arises therefore from an accidental diffusion of fixed air through common air 
and the slowness of this precipitation shows its quantity to be very small. The 
inference from the above experiments will be much stronger against the pre- 
existence of fixed air in respirable air, if, instead of common air, dephlogisti- 
cated air be used ; for there the diminution is so great, and the quantity of fixed 
air produced so considerable, that it can by no means be supposed to have pre- 
existed, its properties being so very opposite to those of dephlogisticated air. 

Having synthetically proved the constituent parts of fixed air to be pure 
elementary air and phlogiston, I shall now endeavour to do the same by its 
analysis : and, in the first place, that it contains phlogiston, and even in such 
quantity as to deserve to be classed among the phlogisticated acids, appears by 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 25y 

its action on black manganese. This semi-metallic calx, as has been proved by 
that admirable chemist Mr. Scheele, is completely soluble only in phlogisticated 
acids, and is precipitable from them by fixed alkalis in the form of a white calx. 
He also found, that this manganese is also soluble in water strongly impregnated 
with fixed air, and is also precipitable from it in the form of a white calx. 
35 Mem. Stock, p. 96. 

If fixed air be repeatedly dissolved in, and expelled from water, it leaves each 
time a residuum which is insoluble in water, diminishable by nitrous air, and 
capable of supporting animal life. Hence it is evidently decomposed, the phlo- 
giston separating from it, and gradually uniting to the common atmosphere by 
reason of the repulsive power between it and water. Dr. Priestley indeed found, 
that a candle would not burn in it ; but this arises only from a mixture of a small 
quantity of fixed air not yet decomposed, of which, according to the experi- 
ments of Mr. Cavendish, i is sufficient to extinguish a candle. 

Again, Mr. Achard has converted fixed air into air of nearly the same purity 
as common air by passing it 5 or 6 times through melted nitre. Mem. Berlin. 
1778. Mr. Cavallo passed it but once through melted nitre, and yet found it 
considerably meliorated, for it was diminished by nitrous air. In this case the 
nitrous acid attracted the phlogiston ; for it is known to become phlogisticated 
by the fusion of nitre, so as to be expellable even by the vegetable acids. 2 N. 
Act. Ups. 171. And aqua regia may be made by mixing nitre with marine acid. 

I shall now proceed to investigate the proportion of phlogiston and elementary 
or respirable air in fixed air. Dr. Priestley, in the 4th volume of his Observa- 
tions, p. 380, has satisfactorily proved, that nitrous air parts with as much phlo- 
giston to common air, as an equal bulk of inflammable air does when fired in the 
same proportion of common air. Now, when inflammable air unites with 
common air, its whole weight unites to it, as it contains nothing else but pure 
phlogiston ; since therefore nitrous air phlogisticates common air to the same de- 
gree that inflammable air does, it parts with a quantity of phlogiston equal to the 
weight of a volume of inflammable air similar to that of nitrous air. Now 100 
cubic inches of inflammable air weigh 3.5 gr. ; therefore, 100 cubic inches of 
nitrous air part with 3.5 gr. of phlogiston when they communicate their phlo- 
giston to as much common air as will take it up. I say, that nitrous air parts 
with as much phlogiston, because it is certain, that it does not part with the 
whole of its phlogiston to common or dephlogisticated air, for it contains much 
more, as already shown, and, as appears by the red colour, it constantly assumes 
when mixed with common or dephlogisticated air, which colour belongs to the 
nitrous acid combined with its remaining phlogiston, and not to the fixed air 
then produced, nor to the phlogisticated air remaining, as is very evident. 
Hence the acid, thus formed, is volatile. 4 Pr. 267. 

i. l 1 



2,60 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/8 2. 

One measure of the purest dephlogisticated air and 2 of nitrous air occupy 
only T » T parts of one measure, as Dr. Priestley has observed, vol. 4, p. 245. 
Suppose 1 measure to contain 100 cubic inches, then the whole very nearly of 
the nitrous air will disappear, its acid uniting to the water over which the expe- 
riment is made, and 97 cubic inches of the dephlogisticated air, which is con- 
verted into fixed air by its union with the phlogiston of the nitrous air ; therefore 
97 cubic inches of dephlogisticated air take up all the phlogiston which 200 
cubic inches of nitrous air will part with ; and this we have found to be 7 grains; 
therefore, a weight of fixed air, equal to that of 97 cubic inches of dephlogisti- 
cated air and 7 of phlogiston, will contain 7 gr. of phlogiston. Now, Q7 cubic 
inches of dephlogisticated air weigh 40.74 gr. ; to which adding 7 gr. we have 
the whole weight of the fixed air equal 47.74 gr. = 83.755 cubic inches; and 
consequently 100 cubic inches of fixed air contain 8.357 gr. of phlogiston, and 
the remainder elementary air. 

100 gr. of fixed air contain 14.66 1 of phlogiston and 85.33g of elementary 
air ; which, when stripped of phlogiston, and impregnated with its proper pro- 
portion of elementary fire, becomes again dephlogisticated air. Hence also 100 
cubic inches of dephlogisticated air are converted into fixed air by 7.21 65 gr. of 
phlogiston, and will be then reduced to the bulk of 86.34 cubic inches. And 
reciprocally, 100 cubic inches of fixed air, being decomposed, will afford 
1 15.821 cubic inches of dephlogisticated air, and part with 7.2165 gr. of phlo- 
giston, supposing the decomposition to be complete ; that is, the dephlogisti- 
cated air absolutely pure. 

Of the quantity of phlogiston in vitriolic air. — The method I pursued was this: 
1st. I found the quantity of nitrous air a given weight of copper afforded when 
dissolved in the dephlogisticated nitrous acid, and by that means how much 
phlogiston it parts with. 2dly. I found the quantity of copper which a given 
quantity of the dephlogisticated vitriolic acid could dissolve ; and observed, that 
it could not dissolve the greatest quantity of copper without dephlogisticating a 
further quantity which it does not dissolve. 3dly. 1 found how much it dephlo- 
gisticates what it thoroughly dissolves, and how much it dephlogisticates what it 
barely calcines. 4thly. How much inflammable air a given quantity of copper 
affords when dissolved in the vitriolic acid to the greatest advantage. 5thly. I 
deduct from the whole quantity of phlogiston expelled by the vitriolic acid the 
quantity of it contained in the inflammable air ; the remainder shows the quan- 
tity of it contained in the vitriolic air. 

The particulars were as follow : — 1st. 100 gr. of copper dissolved in the de- 
phlogisticated nitrous acid afforded 67.5 cubic inches of nitrous air, which, 
according to the before-mentioned calculation, contain 4.52 gr. of phlogiston. 
2dly. 100 gr. of real vitriolic acid take up or dissolve 54.73 of copper, and 100 



VOL. LXXII.j PHILOSOPHICAL TRANSACTIONS. 26 1 

gr. of copper require about 182.714 gr. of real vitriolic acid to dissolve them. 
Ao-ain, 100 gr. of copper, when dissolved in the vitriolic acid, retain only as 
much phlogiston as is contained in 3 cubic inches of nitrous air, that is, 0.2 of 
a grain; therefore, since 100 gr. of copper give out 4.52 of phlogiston, the 
vitriolic acid strips it of 4.52 — 0.2, that is, 4.32 gr. of phlogiston. 

3dly. To dissolve 70 gr. of copper in the vitriolic acid, to the greatest advan- 
tage, 20 more must be slightly dephlogisticated ; therefore, to dissolve 100 gr. 
of copper in this acid, 28.6 more must be slightly dephlogisticated. 8 grs. of 
this slightly dephlogisticated calx afforded 4 cubic inches of nitrous air ; there- 
fore, 28.6 would afford 14.3, which contain O.Q58 gr. of phlogiston; but 28.6 
gr. of copper, before any dephlogistication, contain 1.2Q2 gr. of phlogiston ; 
therefore, they lose by this slight dephlogistication 0.344 of a grain of phlogis- 
ton. Hence, when 100 gr. of copper are dissolved in the vitriolic acid, the 
quantity of phlogiston expelled is 4.32 + 0.34 = 4.66 gr. 

4thly. The quantity of inflammable air afforded by the most advantageous 
solution of 100 gr. of copper in the vitriolic acid, is 11 cubic inches, which 
amount to 0.385 of a grain of phlogiston. 5thly. The solution of 100 gr. of 
copper in the vitriolic acid afforded over mercury 75.71 cubic inches of air; but 
of this only 1 1 cubic inches were inflammable air, the remainder therefore was 
vitriolic acid air, amounting to 64.7 1 cubic inches. 6thly. Then the whole 
quantity of phlogiston expelled during the solution of 100 gr. of copper in the 
vitriolic acid, is 4.66 gr. ; of this inflammable air contains but 0.385 of a grain: 
the remainder therefore, which consists of 4.275 gr. must be contained in the 
64.71 cubic inches of vitriolic air ; therefore, 100 cubic inches of vitriolic air 
contain 6.6 gr. of phlogiston, and 71.2 gr. of acid, and 100 cubic inches of this 
air weighing 77.8 gr., 100 gr. of this air contain 8.48 gr. of phlogiston and 
91.52 of acid. 

Of the quantity of phlogiston in sulphur. — This I endeavoured to find by esti- 
mating the quantity of fixed air produced during its combustion. To the top of 
a glass bell, which was open, I firmly tied and cemented a large bladder, destined 
to receive the air expanded by combustion, a quantity of which generally escapes 
when this precaution is not used. Under this bell, which contained about 3O00 
cubic inches of air, I placed a candle of sulphur, weighing 347 gr- ; its wick, 
which was not consumed, weighed half a grain : it was supported by a very thin 
concave plate of tin, to prevent the sulphur from flowing over during the com- 
bustion, and both were supported by an iron wire, fixed on a shelf in a tub of 
water. As soon as the sulphur was fired with a very feeble flame, it was covered 
with the bell, the air being squeezed out of the bladder. The inside of the bell 
was soon filled with white fumes, so that the flame could not be seen. In an 
hour after, the fumes thoroughly subsided, and all was cold. The water rose 



26'2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

within the bell to a height equal to 87.2 cubic inches; whence I deduce that 
87.2 cubic inches of fixed air were produced, which contain 7.287 gr. of phlo- 
giston, which separated from the vitriolic acid, and united to the dephlogisticated 
part of the common air under the bell. The candle of sulphur being weighed, 
was found to have lost 20.75 gr. ; therefore, 20.75 gr. of sulphur contain 7.287 
gr. of phlogiston, besides the quantity of phlogiston which remained in the 
vitriolic air. This air must have amounted to 20.75 — 7.287 = 13.463 gr. 
which contain 1.141 gr. of phlogiston ; therefore the whole quantity of phlo- 
giston in 20.75 gr. of sulphur, is 8.428 gr. ; therefore, 100 gr. of sulphur con- 
tain 40.6l gr. of phlogiston and 59.39 of vitriolic acid. 

Several attempts have hitherto been made to determine the proportion of the 
constituent parts of sulphur ; but all were evidently defective. The first was 
that of Stahl, who calculated the quantity of phlogiston from that of the acid 
remaining after slow combustion ; but as much, both of acid and phlogiston, 
was dissipated, and as the remaining acid was also phlogisticated, and attracted 
much of the moisture of the air, no conclusion whatever could be drawn from 
this experiment. The 2d method was, to form a liver of sulphur, and convert 
this by a gentle long continued heat into a tartar vitriolate, and then calculate 
the weight a given quantity of alkali would gain by this operation. This was 
also devised by Stahl, and followed by Brandt and Newman, and by it they de- 
termined the proportion of phlogiston to that of acid to be nearly as 1 to 16. 
But during the formation of the liver of sulphur, whether in the moist or dry 
way, much of the phlogiston and acid is dissipated, as is evident by the vapour 
and smell that proceed from it, their alkali also contained fixed air, which it lost 
during the operation, and of which they kept no account, as they were ignorant 
of its existence ; and the tartar vitriol formed by them or sal polycreste retained 
much undecomposed sulphur, as always happens when it is not strongly heated ; 
so that this method also was very imperfect : however some subsequent chemists, 
who made the experiment with more care, concluded from it, that sulphur con- 
tained 4- of phlogiston. Exleben, §760. 

By weighing flowers of sulphur in a perforated brass box in water, J found its 
specific gravity to be I.924. It remained in the water a quarter of an hour be- 
fore any air issued from it, and then some bubbles arose ; but when I opened the 
box, I found the middle part of the flowers quite dry, so that I make no doubt 
but some air still remained, and that its specific gravity is still greater. Mr. 
Petit weighed it in oil, aud found its specific gravity 2.344, which I believe to 
be nearly the truth. 

Of the quantity of phlogiston in marine acid air. — 8 gr. of copper dissolved in 
colourless spirit of salt, afforded but 4.9 cubic inches of air, when the air was 
received over water, and this air was inflammable. 8.5 gr. of copper being dis- 



"OL. LXXII.j PHILOSOPHICAL TRANSACTIONS. 263 

solved in the same quantity of the same spirit of salt, and the air received over 
mercury, afforded 9 1. 28 cubic inches of air ; but of these only 4.Q cubic inches 
were inflammable air ; the remainder therefore, viz. 86.38, were marine air, 
which weigh 56.49 gr. 

Now, as spirit of salt certainly does not dephlogisticate copper more than the 
vitriolic acid does, it follows, that these 4.9 cubic inches of inflammable air, and 
86.38 cubic inches of marine air, do not contain more phlogiston than would 
be separated from the same quantity of copper by the vitriolic acid : and since 
100 grains of copper would yield to the vitriolic acid 4.32 gr. of phlogiston, 8.5 
gr. of copper would yield O.367 of a grain of phlogiston ; this then is the whole 
quantity extracted by the marine acid, and contained in Q1.28 cubic inches of air, 
and deducting from this the quantity of phlogiston contained in 4.9 cubic inches 
of inflammable air (= 0.171 of a grain,) the remainder, viz. O.367 — 0.171 = 
0.196, is all the phlogiston that can be found in 80.38 cubic inches of marine 
air. Then 100 cubic inches of marine air can contain but 0.227 nearly of a grain 
of phlogiston, 65.173 of acid. Hence we see why it acts so feebly on oils, spirit 
of wine, &c. having a very small affinity to phlogiston ; and why it is not dis- 
lodged from any basis by uniting with phlogiston, as the vitriolic and nitrous 
acids are, its affinity to it being inconsiderable. 

XVI. Of the Method of rendering very sensible the weakest Natural or Artificial 
Electricity. By Mr. Alexander Volta, Professor of Experimental Philosophy 
in Como, &c. &c. From the Italian, p. 237. 

Whenever, in observing the atmospherical electricity, no degree of it can be 
discovered by the ordinary methods of performing those experiments, it is diffi- 
cult to determine whether any electricity at all does or does not exist in the at- 
mosphere at those times ; since it may exist, and the quantity of it onlv be so 
small as not to affect the electrometers employed. In that case therefore, if we 
rely on the common electrometers, even the most sensible, we must conclude, 
that neither the conductor nor the atmosphere, so high as the conductor reaches, 
contain any electricity ; but by means of the apparatus here described, it will 
be found, that the said conductors are never entirely void of electricity, and 
consequently the air, which surrounds them, is also at all times electrified. This 
method not only shows the existence of electricity, but also ascertains whether it 
is positive or negative, and that when the atmospherical conductor itself is not 
capable of attracting the finest thread ; and if the conductor were to show any 
very small attraction, then, by means of our apparatus, there may be obtained 
even strong sparks. The electrophorus in this case might perhaps better deserve 
the name of electrometer, or micro-electrometer, but Mr. V. rather calls it a 



2(>1 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

condenser of electricity, for the sake of using a word which expresses at once 
the reason and cause of the phenomena to be treated of in this paper. 

The whole method may be reduced to the following few observations. — 1. An 
electrophorus must be procured, the resinous coat of which must be very thin, 
and either not at all electrified, or, if electrified, its electricity be entirely extin- 
guished. 2. Its usual metal plate must be laid on this resinous and unelectrified 
plate, in full and flat contact ; but care must be taken that it does in no point 
touch the lamina of metal on which the resinous stratum is usually fastened. 3. 
Those plates being so conjointly placed, a conducting communication, viz. a 
wire, must be brought from the atmospherical conductor to touch the metal 
plate of the electrophorus, and to touch that only. 4. The apparatus must be 
left in that situation for a certain time, viz. till the metal plate may have acquired 
a sufficient quantity of electricity through the conducting communication, 
which brings it from the atmospherical conductor very slowly. 5. Lastly, the 
conducting communication must be removed from the contact of the metal 
plate : the metal plate is then separated from the resinous one, by lifting it up 
by its insulating handle, after which it is in a state of attracting, of electrifying 
an electrometer, or, if the electricity be sufficiently strong, of giving sparks, 
Sec. at the same time the atmospherical conductor itself shows either no elec- 
tricity at all, or exceeding small signs of it. 

It was mentioned above, that the conducting wire must be left in contact with 
the metal plate for a certain time, the length of which however is not easily de- 
termined, since it depends on variable circumstances. When the conductor 
itself shows no signs of electricity, then it will be necessary to leave the appa- 
ratus during 8, 10, or more minutes. But if the conductor itself be capable of 
just attracting a very small thread, then it will be sufficient to leave the apparatus 
in contact as above-mentioned, for a few seconds only, in order afterwards to 
obtain from it very conspicuous electrical appearances. 

Of the electrophorus to be used, it must be remarked, first, that its being 
very thin is of great importance ; it having been observed, that the thinner the 
resinous stratum is, the greater quantity of electricity can be accumulated into 
the metal plate laid on it ; which is the case whether the electricity is brought to 
it from the atmosphere, or from any other electric power. The thickness of 
-J-5- of an inch, or that of a common coat of varnish, is very proper ; whereas if 
the resin was an inch thick or more, the experiments would answer very badly. 
Also, the surface of the resinous stratum, as well as the under surface of the 
metal plate, must be as plain and as smooth as possible, in order that the two 
surfaces may coincide more perfectly when laid on each other. 

Lastly, it deserves to be repeatedly and particularly observed, that the resinous 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 2(ii 

plate, when it is to be used for our experiment, should be quite free from any the 
least electricity, otherwise the experiments cannot be depended on. If therefore 
the resinous plate has been excited before, so as to remain in some measure elec- 
trified, all possible care should be taken to deprive it of that electricity, which 
however is not easily done. The most effectual method of doing it, is to expose 
the resinous plate to the hot rays of the sun or to a fire, so that its surface may 
be slightly melted, by which means it will entirely lose its electricity.* The 
flame of a candle, or of a piece of paper, will easily deprive the resin of its elec- 
tricity, if its surface be passed over the flame. To observe whether the resinous 
plate is quite free from any electricity, the metal plate must be laid upon it, 
there it must be touched with a finger, and afterwards, being lifted up after the 
usual manner, it must be presented to a fine hair ; for if the hair is not attracted, 
it may be concluded that the resinous plate has no electricity, and consequently 
the apparatus is fit to be used as a condenser of electricity. 

Whenever the atmospherical conductor by itself gives sufficiently strong signs 
of electricity, then there is no occasion to use our condensing apparatus. Besides, 
when the electricity is strong, it often happens that part of the electricity of the 
metal plate is impressed on the resin, in which case the apparatus acts as an elec- 
trophorus, and consequently is unfit for our purpose. To avoid such an incon- 
venience, Mr. V.'s plan is to substitute to the resinous plate a plane, which 
should not be a perfect electric, or quite impervious to electricity, but which 
should be an imperfect conductor, such as might hinder, in a certain degree 
only, the (ree passage of the electric fluid through its substance. There are 
many conductors of this kind ; as, for instance, a clean and dry marble slab, a 
plate of wood, likewise clean and very dry, or covered with a coat of varnish, 
or wax; and the like. The surface of those bodies does not contract any elec- 
tricity ; or if any electricity adhere to them, it vanishes soon, on account of their 
semi-conducting nature ; for which reason they cannot answer the office of an 
electrophorus, and therefore are more fit to be used as condensers of electricity. 
On the other hand, care should be taken, in choosing the above-mentioned 
plane, that it be not too much of a conducting nature, or capable of becoming 

* It has been believed for a long time, that to heat, and especially to melt, sulphur and resins 
was sufficient to excite in them some electricity; but except the tourmalin and some other stones 
which are really excited by heat alone, the resins and sulphur never become electrified by that means 
except when they have by some means or other suffered any friction. The mistake, as Beccaria ob- 
served, was occasioned by this, viz. that even the least friction of the hand, or other body, is suffi- 
cient to excite such substances in those favourable circumstances, without which friction, those sub- 
stances, melted and left to cool by themselves, are so far from acquiring any electricity, that they 
lose every vestige of it in case they were excited before the fusion, as may be easily proved by ex- 
periment : nor ought this to appear wonderful, since fusion or a strong degree of heat renders every 
body a conductor of electricity. — Orig. 

VOL. XV. M M 



20ti PHILOSOPHICAL TRANSACTIONS. [ANNO 1/82. 

so in a very short time, it being quite necessary, that the electricity should find 
a considerable degree of resistance in going through its substance. In choosing, 
or in preparing, such a plane by drying, or otherwise, it is better to render it too 
near to than too far from the nature of a non-conductor. A marble slab, or a 
board properly dried, answers admirably well, and is preferable to any other 
plane : otherwise the resinous plate of an electrophorus is preferable to a common 
table or marble slab not prepared ; for these bodies, having in some measure 
imbibed moisture, conduct much better than is necessary. 

For this purpose it is better to use a flat piece of marble, and to grind it 
against the metal plate, till they coincide so well as to show a sensible cohesion 
between them. Afterwards the piece of marble should be exposed for several 
days to the heat of a warmed place, such as an oven, a chimney, &c. to expe] 
the moisture, and to render it quite fit for our experiments. The marble, thus 
prepared, will continue dry for a considerable time, unless it be long exposed to 
very damp air. As for the small quantity of moisture which the marble may 
accidentally and superficially attract, it may be removed by exposing it to the 
sun, or to a fire, or even by wiping it with a dry and clean cloth, previous to 
the performing of experiments. It is always advantageous to warm the marble 
previous to the experiment. But, instead of preparing the piece of marble by a 
long continued heat, it will be sufficient to give it a coat of copal varnish, or 
amber, or lac varnish : after which it must be kept in an oven for a short time. 
By this means even the worst sort of marble answers very well, even without 
previously warming or keeping it hot during the experiment. By means of the 
varnish even a metal plate may be used instead of the marble. This should be 
first made flat by grinding it against the upper plate, and then it must be var- 
nished, but rather thicker than when the varnish is laid on marble. In this case 
both the plates might be varnished, though it is sufficient to varnish one of 

them. 

The advantages which a varnished plate has above the common electrophorus, 
are 1. That the varnish is always thinner than the common resinous stratum of 
an electrophorus. 2. That the varnish acquires a more smooth and plain sur- 
face ; hence the metal plate may be more easily, and to more advantage adapted 
to it. Instead of the above-mentioned plane of marble or metal varnished, there 
may be substituted, with equal advantage, any sort of plane covered with dry and 
clean oil cloth or oil silk or sattin, or other silk stuff that is not very thick ; 
which will answer very well, without requiring any more than perhaps a slight 
warming. The silk stuffs answer better for this purpose than those made of 
cotton or wool, and these better than linen. However, by a previous drying, 
and keeping them hot during the experiment, paper, leather, wood, ivory, bone, 
and every sort of imperfect conductor, may be made to answer to a certain de- 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 'iti" 

gree. But if those imperfectly conducting substances were dried too much, 
then they would become quite electrics, and consequently useless for our pur- 
pose, excepting when they were used like resins, &c. 

The apparatus may be rendered more simple by applying the silk, or other 
semi-conducting stratum, to the upper, viz. to the metal plate, which is fur- 
nished with a glass handle, instead of the marble or other plate, which in that 
case becomes useless : for in its stead a plane of any kind may be used, such as 
a common wooden or marble table, even not very dry, a piece of metal, a book, 
or other conductor, whether perfect or imperfect, it being only necessary that its 
surface be flat. In fact, nothing more is requisite for the experiment, than that 
the electricity, which tends to pass from one surface to the other, should find 
some resistance or opposition in either of the surfaces. It is immaterial whether 
the non-conducting or semi-conducting stratum be laid on one or the other of 
the planes, it being only necessary that they should coincide very well together, 
which cannot be easily obtained when a common table is used for one of the 
planes, which is the only reason why it is better to use two planes which have 
been worked flat by grinding one upon the other, and one of them varnished, 
&c. A single metal plate, covered with silk, with 3 silk strings fastened to it by 
way of a handle, may be conveniently used for ordinary experiments. 

Hitherto has been considered the use of the condenser in exploring the weak 
atmospherical electricity, which is brought down by the atmospherical conductor.* 
But this, though the principal, is not the only use to which it may be applied. 
It serves likewise to discover the artificial electricity when this is so weak as not 
to be discoverable by any other means, which happens in various cases, as for 
instance : a Leyden phial charged, and then discharged by touching its coated 
sides 3 or 4 times with the discharging rod, or the hand, seems to be quite de- 
prived of electricity ; yet if you touch with the knob of it the metal plate of our 
condenser, when properly situated (viz. on an imperfectly conducting plane, &c.) 
and immediately after take up the said plate, this will be found to give very con- 

* Here it will be proper to mention a remarkable observation which I have made on the atmos- 
pherical electricity with the help of the condenser. The late Mr. Canton and others affirmed that 
they had obtained stronger signs of electricity from their atmospherical apparatus at the time of an 
aurora borealis, than at other times ; but various other philosophers doubted of the influence of 
electricity in that meteor, and some absolutely denied it. I myself was much in doubt about it j 
but at present Mr. Canton's assertion seems to be established beyond a doubt, as I have observed by 
actual experiment. During the strong aurora borealis, which appeared in the night of the 'JSth 
of July, 1780, the light of which rising gradually from the horizon, reached the zenith at near 1 1 
o'clock, and enlightened the heavens with a reddish light, the weather being clear and windy ; our 
condensing apparatus being applied to an atmospherical conductor, gave fine bright sparks ; whereas, 
at other times, that is, in clear weather, and at every hour of the day or night, the same apparatus 
afforded either no sparks at all, or exceedingly small ones ; die reason of which is, because the said 
. onductor was not much elevated. — Orig. 

M M 2 



'2()8 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

spicuous signs of electricity ; which shows that the Leyden phial is not quite de- 
prived of electricity. But if the phial was left so far charged as just to attract a 
light thread, then if the metal plate were to be touched by the knob of it, even 
for a moment, it would afterwards, when lifted up, give a strong spark ; and if 
then it were to be touched again by the knob of the phial, it would afford a 2d 
spark, hardly smaller than the former ; and thus spark after spark may be ob- 
tained for a long time, which is a very surprizing experiment. 2dly. Suppose 
you have an electrical machine in such bad order that its conductor will not 
afford any spark, but will just attract a thread; then if you let this conductor 
touch the metal plate of the condenser, and after suffering it to continue in that 
situation for a few minutes, while the machine is kept in motion, lift up the 
metal plate, you will obtain from it a strong spark. 3dly. In case the electrical 
machine acts very well, but its conductor is so badly insulated, that it will not 
give any sparks, as when the conductor touches the walls of the room, or when 
a chain falls from it on the table ; then if you let the said conductor in that state 
touch the metal plate of the condenser, while the electrical machine is in action, 
the plate will afterwards give sufficiently strong signs of electricity ; which shows 
the great power this apparatus has of drawing and condensing the electricity. 
In short, by either of those methods you will obtain some electricity from such 
bodies as could hardly be expected to give any, even when they are not very dry. 
Indeed, coals and metals excepted, every other body will give some electricity. 

It is now necessary to give an explanation of those phenomena, the theory 
of which will greatly facilitate the practical performance of this kind of experi- 
ments. The whole matter then may be reduced to this, viz. that the metal 
plate has a much greater capacity for holding electricity in one case, viz. when it 
lies on a proper plane, than when it stands quite insulated ; as when it is sus- 
pended in the air by its silk strings or insulating handle, or when it stands on an 
insulating stand, as a thick stratum of resin or the like. It is easy to compre- 
hend, that wherever the capacity of holding electricity is greater, there the 
intensity of electricity is proportionably less, viz. a greater quantity of electricity 
is in that case required, in order to raise its intensity to a given degree ; so-that 
the capacity is inversely as the intensity, or the endeavour by which the electricity 
of an electrified body tends to escape from all the parts of it, to which tendency 
or endeavour the electrical phenomena of attraction, repulsion, and especially 
the degree of elevation of an electrometer, correspond. 

That the intensity of electricity must be inversely proportional to the capacity 
of the body electrified, will be clearly exemplified by the following experiment. 
Take 2 metal rods of equal diameter, but one of them a foot, and the other 5 
feet long; and let the first be electrified so high as that the index of an electro- 
meter annexed to it may be elevated to 60°; then let this electrified rod touch 



VOL. LXXII.J PHILOSOPHICAL TRANSACTIONS . 2(50. 

the other rod ; then it is evident, that the intensity of the electricity, by being 
parted between the 1 rods, will be diminished in proportion as the capacity is in- 
creased ; so that the index of the electrometer, which before was elevated to 6*0°, 
will now fall to 10°, viz. to \ of the former intensity, because now the capacity 
is 6 times greater than when the same quantity of electricity was confined to the 
first rod alone. For the same reason, if the said quantity of electricity was to 
be communicated to a rod 6o times longer, its intensity would be diminished to 
1 degree : and, on the contrary, if the electricity of this long conductor was to 
be contracted into the 6oth part of that capacity, its intensity would be increased 
to 60°. 

Now not only conductors of different bulk have different capacities for holding 
electricity, but also the capacity of the same conductor may be increased or 
diminished by various circumstances, some of which have not yet been properly 
considered. It has been observed, that the capacity of the same conductor is in- 
creased or diminished in proportion as its surface is enlarged or contracted, as is 
shown by Dr. Franklin's experiment of the can and chain, and various other ex- 
periments ; from which it has been concluded, that the capacity of conductors is 
in proportion to their surface, and not to their quantity of matter. This conclu- 
sion is true, but does not comprehend the whole theory, since even the exten- 
sion contributes to increase the capacity ; so that, of 1 conductors, which have 
equal but dissimilar surfaces, that which is the more extended in length has the 
greater capacity. In short, it appears from all the experiments hitherto made, 
that the capacity of conductors is in proportion, not to the surfaces in general, 
but to the surfaces which are free, or uninfluenced by an homologous 
atmosphere. But that which comes nearer to our case is, that the capacity of a 
conductor, which has neither its form nor surface altered, is increased when, in- 
stead of remaining quite insulated, the conductor is presented to another con- 
ductor not insulated ; and this increase is more conspicuous, according as the 
surfaces of those conductors are larger and come nearer to each other. 

When an insulated conductor is opposed or presented to any other conductor 
whatever, Mr. V. calls it a conjugate conductor. The circumstance mentioned 
above, which augments prodigiously the natural capacity of conductors, is that 
which has been hitherto principally overlooked : but let us (says Mr. V.) begin 
with those experiments which show this increased capacity in the simplest manner. 
I take, for example, the metal plate of an electrouhorus, and holding it by its 
insulating handle in the air, electrify it so high that the index of an electrometer 
annexed to it might be elevated to (30° ; then lowering this metal plate by de- 
grees towards a table or other conducting plain surface, I observe that the index 
of the electrometer falls gradually from 60° to 50°, 40°, 30°, &c. Notwith- 
standing this appearance, the quantity of electricity in the plate remains the 



270 THILOSOPHICAL TRANSACTIONS. [ANNO 1/82. 

same, except the plate be brought so near the table as to occasion a transmission 
of the electricity from the former to the latter ; at least the quantity of elec- 
tricity will remain as much the same as the dampness of the air, &c. will permit. 
The decrease therefore of intensity is owing to the increased capacity of the 
plate, which now is not insulated solitary but conjugate. In proof of this pro- 
position, if the plate be removed gradually farther and farther from the table, it 
will be found, that the electrometer rises again to its former station, namely to 
6o°, excepting the loss of that quantity of electricity, which during the experi- 
ment must have been more or less imparted to the air, &c. 

The reason of this phenomenon is easily derived from the action of electric 
atmospheres. The atmosphere of the metal plate, which for the present I shall 
suppose to be electrified positively, acts on the table or other conductor to which 
it is presented ; so that the electric fluid of the table, agreeably to the known 
laws, retiring to the remoter parts of it, becomes more rare in those parts which 
are exposed to the metal plate, and this rarefaction becomes greater the nearer 
the electrified metal plate is brought to the table. If the metal plate is electri- 
fied negatively, then the contrary effects must take place. In short, the parts 
immersed into the sphere of action of the electrified metal plate, contract a con- 
trary electricity, which accidental electricity, making in some manner a com- 
pensation for the real electricity of the metal plate, diminishes its intensity, as 
is shown by the depression of the electrometer. 

The 2 following experiments will throw more light on the reciprocal action of 
the electric atmospheres. First, suppose 2 flat conductors, electrified both posi- 
tively or both negatively, to be presented towards, and to be gradually brought 
near, each other : it will appear, by 2 annexed electrometers, that the nearer 
those 2 conductors come to each other, the more their intensities will increase ; 
which shows, that either of the 2 conjugate conductors has a much less capacity 
now, than when it was singly insulated, and out of the influence of the other. 
This experiment explains the reason why an electrified conductor will show a 
greater intensity when it comes to be contracted into a smaller bulk ; and also 
why a long extended conductor will show a less intensity than a more compact 
one, supposing their quantity of surface and of electricity to be the same ; be- 
cause the homologous atmospheres of their parts interfere less with each other 
in the former than in the latter case. Secondly, Let the preceding experiment 
be repeated with this variation only, viz. that one of the flat conductors be elec- 
trified positively, and the other negatively: the effects then will be just the re- 
verse of the preceding, viz. the intensity of their electricities will be diminished, 
because their capacities are increased the nearer the conductors come to each 
other. 

This matter may be rendered still more clear by insulating the conducting 



VOL. LXX1I.] PHILOSOPHICAL TRANSACTIONS. '27 J 

plane, while the other electrified plate is on it, and afterwards separating them ; 
for then both the metal plate and the conducting plane, which may be called the 
inferior plane, will be found electrified, but possessed of contrary electricities, 
as may be ascertained by electrometers. If the inferior plane be insulated first, 
and then the electrified plate brought over it, then the latter will cause an endea- 
vour in the former to acquire a contrary electricity, which however the insula- 
tion prevents from taking place ; hence the intensity of the electricity of the 
plate is not diminished, at least the electrometer will show a very little and almost 
imperceptible depression, which small depression is owing to the imperfection of 
the insulation of the inferior plane, and to the small rarefaction and condensa- 
tion of the electric fluid, which may take place in different parts of the said in- 
ferior plane. But if in this situation the inferior plane be touched, so as to cut 
off the insulation for a moment, then it will immediately acquire the contrary 
electricity, and the intensity in the metal plate will be diminished. 

If the inferior plane, instead of being insulated, were itself a non-conducting 
substance, then the same phenomena would happen, viz. the intensity of the 
electrified metal plate laid on it would not be diminished. This however is not 
always the case ; for if the inferior non-conducting plane be very thin, and be 
laid on a conductor, then the intensity of the electrified metal plate will be di- 
minished, and its capacity will be increased by being laid on the thin insulating 
stratum ; because in that case the conducting substance, which stands under the 
non-conducting stratum, acquiring an electricity contrary to that of the metal 
plate, will diminish its intensity, &c. and then the insulating stratum will only 
diminish the mutual action of the two atmospheres more or less, according as it 
keeps them more or less asunder. 

The intensity or electric action of the metal plate, which diminishes gradually 
as it is brought nearer and nearer to a conducting plane not insulated, becomes 
almost nothing when the plate is nearly in contact with the plane, the compen- 
sation or accidental balance being then almost perfect. Hence, if the inferior 
plane only opposes a small resistance to the passage of the electricity (whether 
such resistance is occasioned by a thin electric stratum, or by the plane's imper- 
fect conducting nature, as is the case with dry wood, marble, &c.) that resistance 
joined to the interval, however small, that is between the two planes, cannot be 
overcome by the weak intensity of the electricity of the metal plate, which on 
that account will not dart any spark to the inferior plane (except its electricity 
were very powerful, or its edges not well rounded) and will rather retain its elec- 
tricity ; so that, being removed from the inferior plane, its electrometer will 
nearly recover its former height. Besides, the electrified plate may even come 
to touch the imperfectly conducting plane, and may remain in that situation for 



•l~i'l PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

some time; in which case the intensity being reduced almost to nothing, the 
electricity will pass to the inferior plane exceeding slowly. 

But the case will not be the same if, in performing this experiment, the elec- 
trified metal plate be made to touch the inferior plane edgewise ; for then its in- 
tensity being greater than when laid flat, as appears by the electrometer, the 
electricity easily overcomes the small resistance, and passes to the inferior plane, 
even across a thin stratum ;* because the electricity of the one plane is balanced 
by that of the other, only in proportion to the quantity of surface which they 
oppose to each other within a given distance ; and when the metal plate touches 
the other plane in flat and ample contact its electricity is not dissipated. This 
apparent paradox is clearly explained by the theory of electric atmospheres. 

Hitherto we have considered in what manner the action of electric atmos- 
pheres must modify the electricity of the metal plate in its various situations. 
We must now consider the effects which take place when the electricity is com- 
municated to the metal plate while standing on the proper plane. The whole 
business having been proved in the preceding pages, it is easy to deduce the ap- 
lications from it ; yet it will be useful to exemplify it by an experiment. Sup- 
pose that a Leyden phial, or a conductor, were so weakly electrified that the in- 
tensity of its electricity was only of half a degree or even less : if the metal 
plate of our apparatus, when standing on the proper plane, was to be touched 
with that phial or conductor, it is evident, that either of them would impart to 
it a quantity of its electricity, proportional to the plate's capacity, viz. so much 
of it as should make the intensity of the electricity of the plate equal to that of 
the electricity in the conductor or phial, suppose of half a degree ; but the 
plate's capacity, now that it lies on the proper plane, is above 100 times greater 
than if it stood insulated in the air, or, which is the same thing, it requires 100 
times more electricity in order to show the same intensity ; therefore, in this 
case it must require upwards of 100 times more electricity from the phial or 

* This explanation, properly applied, renders evident the actions of points in general. Properly 
speaking, a pointed conductor, not insulated, when presented to an electrified body, has not in itself 
any particular virtue of attracting electricity. It acts only like a conductor not insulated, which does 
not oppose any resistance to the passage of the electric fluid. If the same conductor, instead of 
being pointed, was to present a globular or flat surface, to the electrified body, neither would it in 
that case oppose a greater resistance to the passage of the electricity. But the reason why the elec- 
tricity will not pass nearly so easily from the electrified body to the conductor when it is flat or globu- 
lar, as when it is pointed, is because in the former case the intensity of the electricity in the electri- 
fied body is weakened by the opposed fiat surface, which, acquiring the contrary electricity, com- 
pensates the diminished intensity incomparably more than a point can. It appears, therefore, that 
it is not the particular property of a point or of a flat surface, but the different state of tin- electrified 
body, that makes it part with its electricity easier, and from a greater distance, when a pointed con- 
ducting substance, than when a flat or globular one is presented to it. — Orig. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 273 

conductor. It naturally follows, that when the metal plate is afterwards removed 
from the proper plane, its capacity being lessened so as to remain equal to the 
100th part of what it was before, the intensity of its electricity must become 
of 50° ; since, agreeably to the supposition, the intensity of the electricity in the 
phial or conductor was of half a degree. 

A conductor that is electrified while it stands in full and ample contact with 
another proper conductor, as above specified, and is afterwards separated from it, 
shows the same phenomena that are exhibited by a conductor, which, after 
being electrified, is contracted into a smaller bulk, or contrarywise, like Dr. 
Franklin's experiment of the can and chain. If a small quantity of electricity 
applied to the metal plate of the condenser enables it to give a strong spark, it 
may be asked, what would a great quantity of electricity do ? The answer is, 
that it would do nothing more, because, when the electricity communicated to 
the metal plate is so strong as to overcome the small resistance of the inferior 
plane, it will be dissipated. 

After all that has been said in the preceding pages, it may be easily under- 
stood, that if the metal plate of our condenser can receive a good share of elec- 
tricity from a Leyden phial, or from an ample conductor, however weakly elec- 
trified ; it cannot receive any considerable quantity of it from a conductor of a 
small capacity ; for this conductor cannot give what it has not, except it were 
continually receiving a stream, however small, of electricity, as is the case with 
an atmospherical conductor, or with a prime-conductor of an electrical machine, 
which acts very poorly, but continues in action. In those cases it has been ob- 
served above, that a considerable time is required before the metal plate has ac- 
quired a sufficient quantity of electricity. 

As an ample conductor, weakly electrified, imparts a considerable quantity of 
electricity to the metal plate of our condenser, so that when the said metal plate 
is afterwards separated from its proper plane, the electricity in it appears much 
condensed and vigorous ; so when the same metal plate contains a small quantity 
of electricity, and such as cannot give a spark or affect an electrometer, that 
electricity may be rendered very conspicuous by communicating it to another 
small metal plate or condenser. 

Mr. Cavallo was the first who thought of this improvement, which he de- 
rived by reasoning on my experiments. He actually made a small metal plate 
not exceeding the size of a shilling : this 2d condenser is certainly of great use 
in many cases, in which the electricity is so small as not to be at all, or not 
clearly, observable by my method or a first condenser only, as has been evidently 
proved by some experiments we made together. Sometimes the usual metal 
plate of my condenser acquired so small a quantity of electricity, that being 
afterwards taken up from the inferior plane, and presented to an extremely sen- 

vol xv. N N 



274 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

sible electrometer of Mr. Cavallo's construction, it did not affect it. In this 
case, when the metal plate, thus weakly electrified, was made to touch the 
other small plate properly situated, and that was afterwards brought near an 
electrometer, the electricity was then generally stronger than what would have 
been sufficient to ascertain its quality. Now, if by the help of both condensers 
the intensity of the electricit)' has been augmented J 000 times, which is by no 
means an exaggeration, how weak must then be the electricity of the body 
examined ? how small must that electricity be which is produced by rubbing a 
piece of metal with one's hand, since when this electricity is condensed by both 
condensers, and then is communicated to an electrometer, it can hardly affect 
that instrument ? Yet it is sufficient to afford conviction, that the metal can be 
electrified by the friction of a person's hand. Some years ago, viz. before the 
discovery of our condenser, and of Mr. Cavallo's sensible electrometer, we were 
very far from being able to discover such weak excitations ; whereas at present 
we can observe a quantity of electricity incomparably smaller than the smallest 
observable at those times. 

appendix. — I mentioned, that after various attempts I at last succeeded in 
obtaining undoubted signs of electricity from the simple evaporation of water, 
and from various chemical effervescences; but as this is a fact not less interesting 
than new, it seems proper to subjoin in this place a faithful account of the expe- 
riments made for that purpose. The first set of experiments were made at Paris, 
in company with Mr. Lavoisier and Mr. De la Place, two intelligent philosophers 
and members of the Royal Academy of Sciences. After I had shown them my 
experiments with my condenser, they, as well as myself, began to entertain hopes 
of succeeding in the experiments on the evaporation, &c. Accordingly Mr. 
Lavoisier ordered a larger condenser with a marble plane to be made. The first 
experiment I attempted with this instrument, in company with Mr. De la Place, 
proved unsuccessful ; but the weather at that time was bad, the room was narrow 
and full of vapours, and the apparatus was not quite in proper order. Mr. De 
la Place and Mr. Lavoisier repeated those experiments in the country, and then 
they were attended with success, which incited us to repeat and diversify the ex- 
periments, by which means the discovery was completed ; having obtained une- 
quivocal signs of electricity from the evaporation of water, from the simple com- 
bustion of coals, and from the effervescence of iron filings in diluted vitriolic 
acid. This observation was made the 13th of April of the present year 1782, 
and the experiments were performed in the following manner. In an open gar- 
den a long metal plate was insulated, which, by means of a large iron wire, was 
made to communicate with the metal plate of the condenser laid on the piece of 
marble, which was kept continually warm by some lighted coals set underneath. 
This done, some chafing dishes, containing burning charcoal, were placed on 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 275 

the large insulated plate. The combustion of the coals was helped by a gentle 
wind. Some minutes after, the iron wire, by which the large insulated plate 
was connected with the metal plate of the condenser, was taken off; then the 
metal plate being removed from the marble by its insulated handle, and presented 
to Mr. Cavallo's electrometer, it made the balls of it diverge with negative elec- 
tricity. The experiment was repeated by placing on the large insulated plate 4 
vessels, containing iron filings and water, instead of the chafing dishes: then 
some vitriolic acid was poured into those 4 vessels, sufficient to cause a vigorous 
effervescence, and when the strongest ebullition was going to subside, the metal 
plate of the condenser was removed from over the marble; and being examined, 
not only electrified the electrometer with negative electricity, but gave a sensible 
spark. At this time having tried to obtain electricity from the evaporation of 
water, the effects were equivocal or hardly sensible, the same thing happened a 
few days after, when however we obtained clear signs of electricity from those 
effervescences, which produce fixed and nitrous air. One day the electricity 
arising from the evaporation of water seemed to be positive; but subsequent ex- 
periments, and other circumstances, indicate that such a phenomenon must be 
attributed to a mistake. 

The experiment on the evaporation of water, which did not answer so well at 
Paris, succeeded much better in London, where I bethought me of throwing 
water on the lighted coals, which were kept in an insulated chafing dish. In 
this manner the electricity of the evaporation never fails to electrify the chafing 
dish negatively, and strongly enough for the electricity to be discovered by the 
simple electrometer; it will even afford a spark, if the condenser be used. 
Another time this experiment was repeated with success at Mr. Cavallo's, in the 
following manner. A small crucible, containing 3 or 4 small coals lighted, was 
insulated; then a spoonful of water was thrown on the coals, and immediately 
after an electrometer, which communicated with the coals by means of a wire, 
diverged with negative electricity. 

The experiments hitherto made, though not numerous, yet concur to show, 
that the vapours of water, and in general the parts of all bodies, that are separated 
by volatilization, carry away an additional quantity of electric fluid as well as of 
elementary heat, and consequently that those bodies, from the contact of which 
the volatile particles have been separated, remain both cooled and electrified ne- 
gatively; from which it may be deduced, that whenever bodies are resolved into 
a volatile elastic fluid, their capacity for holding electric fluid is augmented, as 
well as their capacity for holding common fire, or the calorific fluid. This is a 
striking analogy by which the science of electricity throws some light on the theory 
of heat, and alternately derives light from it; I mean on the doctrine of latent 
or specific heat, the first notions of which were suggested by the admirable ex- 

N N 2 



'276 I'HILOSOPHICAL TRANSACTIONS. [ANNO 1J82. 

periments of Dr. Black and Wilke, and which has been afterwards much eluci- 
dated bv Dr. Crawford, who followed the experiments of Dr. Irwin. By follow- 
ing this analogy, it seems that, as the vapours on their condensing lose part of 
their latent heat, on account of their capacity being diminished, so they part 
with some electric fluid. Hence originates the positive electricity, which is al- 
ways more or less predominant in the atmosphere, when the sky is clear, viz. at 
that height where the vapours begin to be condensed. Accordingly, the atmos- 
pherical electricity is stronger in fogs, in which case the vapours are more con- 
densed, so as to be almost reduced into drops, and is still stronger when thick 
fogs become clouds. 

Hitherto we have accounted for the positive atmospherical electricity; but it is 
easy to account for clouds negatively electrified; lor when a cloud, positively 
electrified, has been once formed, its sphere of action is extended a great way 
round, so that if another cloud comes within that sphere, its electric fluid, agree- 
ably to the well known laws of electric atmospheres, must retire to the parts of 
it which are the most remote from the first cloud; and from thence the electric 
fluid may be communicated to other clouds, or vapours, or terrestrial promi- 
nences. Thus a cloud may be electrified negatively, which cloud, after the 
same manner, may occasion a positive electricity in another cloud, &c. This 
explains, not only the negative electricity, which is often obtained from the at- 
mosphere in cloudy weather; and the frequent changes from positive to negative 
electricity, and contrarywise in stormy weather; but also the waving motion often 
observed in the clouds, and the hanging down of them, so as nearly to touch 
the earth. After the fore-mentioned discoveries we need no longer wonder at 
the appearance of lightnings in the eruptions of volcanos, as was particularly 
observed in the late dreadful eruption of Mount Vesuvius. The few experiments 
I have made show, that the quantity of smoke, but much more the rapidity 
with which it is produced, tends to increase the electricity which arises from 
combustion, &c. How great must then be the quantity of electricity that is 
produced in such eruptions ! 



VOL. LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



277 



XVII. Abstract of a Register of the Barometer, Thermometer, and Rain, at 
Lyndon, in Rutland, 1780. By Thomas Barker, Esq. p. 281. 







: 


Barometer. 








Thermometer. 




Rain. 












In the House. 


Abroad. 








Highest. 


Lowest. 


Mean. 


Hig. 


Low 


Mean 


Hig. 


Low Mean 




Jan. 


Morn. 
Aftern. 


30.15 


28.55 


29.45 


461 
46 


32 
33 


38 
38 


47 
50* 


21 32 
25 36 


2.264 


Feb. 


Morn. 
Aftern. 


29.82 


28.32 


29.29 


46 1 
47 


38 
j.9 


421 
43 


45 
52* 


30 37* 
36} 44 


1.664 


Mar. 


Morn. 
Aftern. 


30.01 


29.46 


29.74 


51 

53* 


40 

42 


46 

47* 


44* 
56* 


30 
40 


38 

48 


O.lfO 


Apr. 


Morn. 
Aftern. 


29.S8 


28.92 


29.43 


1 57 
! 58 


41 
43 


50 
51* 


53 
64 


33* 
39 


43 
54 


1.938 


May 


Morn. 
Aftern. 


29-95 


29.20 


29.60 


66 
70 


47 

4S 


54 
55 


64 
76h 


38 
47* 


47 
5.9* 


0.974 


June 


Morn. 
Aftern. 


29.SS 


29.00 


29.40 


69 
73 


58 
5.9 


62 
63* 


69 

79* 


52 | 60 
57 67 


2.958 


July 


Morn. 
Aftern. 


29.96 


29.22 


29.59 


68 
71* 


61 

62 


64 
66 


67 
79* 


49 
62 


58* , 
70.4 ! 


1.683 


Aug. 


Morn. 
Aftern. 


29.89 


29.02 


29.45 


70| 
72* 


60 
61 


65 
66}, 


64 
80 


49* 
61 


57 
71 


1.097 


Sept. 


Morn. 
Aftern. 


29.86 


29-04 


29.45 


65 

67 


50* 
51 


59 

00 


63 
SO 


38 
50* 


52 
63 


4.004 


Oct. 


Morn. 
Aftern. 


30.00 


28.96 


29.67 


59 

61 


44 
44 


52* 
53 


59 

66 


26* 
41 


44 
53* 


0.081 


Nov. 


Morn. 
Aftern. 


29.74 


28.49 


29.22 


51 
51* 


40* 
41 


45 
46 


52 
54 


28 
35 


39 
45 


2.296 


Dec. 


Morn. 
Aftern. 


29.63 


29.00 


29.34 


50 
51 


37| 
37 


43* 
44 


51 
53 


28* 
33* 


39 
42* 


1.703 


Mea 


29-47 1 




52 


50 


20.822 



XVIII. Meteorological Journal kept at the House of the Royal Society 3 for the 
Year 1781. By Order of the President and Council, p. 285. 



A summary of the whole 


is as follows. 














Thermometer without. Thermometer within. 


Barometer. 


Rain. 




Greatest 


Least 


Mean Greatest Least 


Mean 


Greatest 


Least 


Mean 


Inches. 


1781. 


Height. 


Height. 


Height. Height. , Height. 


Height. 


Height. 


Height. 


Height. 


Jan. . 


51.5 


25.0 


38.5 


49.0 


32.0 


35.9 


30.55 


29.04 


29.90 


1.348 


Feb.. 


52.5 


31.0 


42.8 


51.0 


36.0 


45.7 


30.34 


58.95 


29.65 


1.676 


Mar . 


60.5 


32.0 


44.8 


53.5 


35.0 


45.9 


30.47 


29.88 


30.21 


0.292 


April 


66.5 


37.0 


49.2 


67.0 


38.0 


52.8 


30.34 


29.29 


29.88 


0.650 


May. 


80.5 


42.0 


56.8 


76.0 


44.0 


56.8 


30.36 


29 58 


30.05 


O.619 


June. 


84.0 


53.5 


66.2 


79-5 55.0 


66.8 


30.42 


29.42 


29.84 


0.688 


July. 


84.0 


57.0 


68.4 


80.0 


53.5 


6S.7 


30.44 


29.69 


30.05 


1.045 


Aug. 


82.0 


52.0 


67.7 


78.0 


61.0 


69.2 


30.39 


29.54 


29.95 


2.198 


Mean of 
U muntliE. 






53.0 






55.2 






29.95 


8.516 



'278 PHH.OSOPHICAL TRANSACTIONS. [ANNO ]782. 

XIX. An Attempt to make a Thermometer for measuring the Higher Degrees oj 
Heat from a Red Heat up to the Strongest that Vessels made of Clay can sup- 
port. By Josiah Wedgwood.* p. 305. 

A measure for the higher degrees of heat, such as the common thermometers 
afford for the lower ones, would be an important acquisition, both to the philoso- 
pher and the practical artist. The latter must feel the want of such a measure 
on many occasions ; particularly when he attempts to follow, or apply to use, 
the curious experiments of Mr. Pott, related in his Lithogeognosia, and other 
modern writers on similar subjects. When we are told, for instance, that such 
and such materials were changed by fire into a fine white, yellow, green, or 
other coloured glass : and find that these effects do not happen, unless a particular 
degree of fire has fortunately been hit upon, which degree we cannot be sure of 
succeeding in again : — when we are disappointed, by having the result at some 
times an unvitrified mass, and at others an over-vitrified scoria, from a little de- 
ficiency or excess of heat : — when we see colours altered, not only in shade but 

* This ingenious and respectable gentleman died the 3d of Jan. 1795, at Etruria, in Staffordshire, 
at 6"4 years of age. Mr. W. was the younger son of a potter. He derived little or no property from 
his father ; but became, by his elegant manufactories, the maker of his own fortune, and the bene- 
factor of his country to an incalculable extent. His many discoveries of new kinds of earthen wares 
and porcelains ; his studied forms and chaste style of decoration ; and the correctness and judgment 
with which all his works were executed, under his own eye, and mostly by artists of his own form- 
ing, completely turned the current of this branch of commerce in favour of England, which before 
imported the finer earthen wares from the Continent. But by Mr. W.'s ingenious endeavours, and 
through his example, this country has ever since exported such wares to a great annual amount ; the 
whole of which is drawn from the earth, and from the industry of the inhabitants ; while the na- 
tional taste has been improved, and its reputation greatly raised in foreign countries. Mr. W. was 
also commendably known in the walks of philosophy : besides his ingenious mechanical contrivances, 
and philosophical arrangements and operations, through which his private manufactory had the effect 
of a public work of experiments ; his communications to the a. s. (of which learned body he became 
a member about the year 178+,) show a mind enlightened by science, and contributed to procure 
him the esteem of all scientific men. Besides the above paper, other ingenious and useful commu- 
nications of his appear in the Phil. Trans, volumes 73, 7\, 76, and 80. Mr. W. was the proposer 
of the Grand Trunk Canal, and the chief agent in obtaining the act of parliament for making it, 
against the prejudices of the landed interest, then very powerful. That canal, 90 miles in length, 
unites the rivers Trent and Mersey ; branches have been made from it to the Severn, to Oxford, and 
to many other parts ; and it has also a communication with the Grand Junction Canal from Braun- 

ston to Brentford, &c. Mr. W. having very honourably acquired a large fortune, his purse was 

always open to the calls of charity, and to the support of every institution for the public good. To 
his relations, friends, and neighbours, he was endeared by his many private virtues ; and he has 
been deeply regretted by his country, as the able and zealous supporter of her commerce, and the 
steady patron of every valuable interest of society. Mr. W.'s merits have also otherwise contributed 
to the benefit of futurity ; having reared and left behind him a family, whose virtues and useful in- 
genuity do so much honour to his paternal care in their education. Other particulars of Mr. W. s 
life and works may be seen in the Gentleman's Magazine for the year 1795, vol. 6"j, p. 84. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 270 

in kind, and in many cases destroyed, by a small augmentation of the heat 
which had produced them ; insomuch, that in the gradual increase of the fire, a 
precise moment of time must be happily seized, in order to catch them in per- 
fection : — and when inconveniences, similar to these, arise in operations by fire 
on metals and other substances : — how much is it to be wished, that the authors 
had been able to convey to us a measure of the heat made use of in their valu- 
able processes ! 

In a long course of experiments, for the improvement of the manufacture I am 
engaged in, some of my greatest difficulties and perplexities have arisen from not 
being able to ascertain the heat to which the experiment-pieces had been exposed. 
A red, bright red, and white heat, are indeterminate expressions ; and even 
though the 3 stages were sufficiently distinct from each other, they are of too 
great latitude; as the brightness or luminousness of fire increases, with its 
force, through numerous gradations, which can neither be expressed in words, 
nor discriminated by the eye. Having no other resource, I have been obliged 
to content myself with such measures as my own kilns and the different parts of 
them afforded. Thus the kiln in which our glazed ware is fired furnishes 3 
measures, the bottom being of one heat, the middle of a greater, and the top 
still greater : the kiln in which the biscuit ware is fired furnishes 3 or 4 others, 
of higher degrees of heat ; and by these I have marked my registered experi- 
ments. But though these measures had been fully adequate to my own views, 
which they were not, it is plain, that they could not be communicated to others; 
that their use is confined to a particular structure of furnaces, and mode of 
firing ; and that, on any alteration in these, they would become useless and 
unintelligible, even where now they are best known. And indeed, as this part 
of the operation is performed by workmen of the lowest class, we cannot depend 
on any great accuracy even in one and the same furnace. It has accordingly 
often happened, that the pieces fired in the top of the kiln in one experiment, 
have been made no hotter than those fired in the middle in another, and vice 
versd. 

The force of fire, in its higher as well as lower stages, can no otherwise be 
justly ascertained than by its effects on some known body. Its effect in changing 
colours has already been hinted at ; and I have observed compositions of calces 
of iron with clay to assume, from different degrees of fire, such a number of 
distinct colours and shades, as promised to afford useful criteria of the respective 
degrees. With this idea, I prepared a quantity of such a composition, and 
formed it into circular pieces, about an inch in diameter, and a quarter of an 
inch thick. A number of these were placed in a kiln, in which the fire was 
gradually augmented, with as much uniformity and regularity as possible, for 
near 6o hours ; the pieces taken out at equal intervals of time during the succes- 



280 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

sive increase of heat, and piled in their order on each other in a glass tube, ex- 
hibited a regular and pretty extensive series of colours ; from a flesh-colour to a 
deep brownish red, thence to a chocolate, and so on to nearly black, with all 
the intermediate tints between these colours. A back being fixed to the tube, 
like the scale of a thermometer, and the numbers of the pieces marked on it 
respectively opposite to them, it is obvious, that these numbers may be con- 
sidered as so many thermometric divisions or degrees ; and that, if another piece 
of the same composition be fired in any other kiln or furnace, not exceeding the 
utmost heat of the first, it will acquire a colour corresponding to some of the 
pieces in the tube, and thus point out the degree of heat which that piece, and 
consequently such other matters as were in the fire along with it, have 
undergone. 

It must however be confessed, that for general use a thermometer on this 
principle is liable to objection, as ideas of colours are not perfectly communicable 
by words ; nor are all eyes, or all lights, equally adapted for distinguishing them, 
especially the shades which approach near to each other ; and the effects of phlo- 
gistic vapours, in altering the colour, may not in all cases be easily guarded 
against. 

In considering this subject attentively, another property of argillaceous bodies 
occurred to me ; a property which obtains, in a greater or less degree, in every 
kind of them that has come under my examination, so that it may be deemed a 
distinguishing character of this order of earths : I mean, the diminution of 
their bulk by fire ; I have the satisfaction to find, in a course of experiments 
lately made with this view, that it is a more accurate and extensive measure of 
heat than the different shades of colour. I have found, that this diminution 
begins to take place in a low red heat ; and that it proceeds regularly, as the 
heat increases, till the clay becomes vitrified, and consequently to the utmost 
degree that crucibles, or other vessels made of this material, can support. The 
total contraction of some good clays, which I have examined, in the strongest 
of my own fires, is considerably more than i part in every dimension. 

If, therefore, we can procure at all times a clay sufficiently apyrous or un- 
vitrescible, and always of the same quality in regard to contraction by heat ; and 
if we can find means of measuring this contraction with ease and minute accu- 
racy, I flatter myself, that we shall be furnished with a measure of fire sufficient 
for every purpose of experiment or business. We have, in different parts of 
England, immense beds of clay ; each of which, at equal depths, is pretty uni- 
form in quality throughout its whole extent. Of all the sorts I have hitherto 
tried, some of the purest Cornish porcelain clays seem the best adapted, both 
for supporting the intensity, and measuring the degrees, of fire. For preparing 
and applying this material to thennoinetric purposes, the following method is 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 281 

proposed : the clay is first to be washed over, and while in a dilute state passed 
through a fine lawn. Let it then be made dry, and put up in boxes.* 

The dry clay is to be softened, for use, with about ■§. of its weight of water ; 
and formed into small pieces, in little moulds of metal, -^-of an inch in breadth, 
with the sides pretty exactly parallel, this being the dimension intended to be 
measured, about vV of an inch deep, and 1 inch long. To make the clay de- 
liver easily, it will be necessary to oil the mould, and make it warm. These 
pieces, when perfectly dry, are put into another iron mould or gage, consisting 
only of a bottom, with two sides, half an inch deep ; to the dimensions of 
which sides the breadth of the pieces is to be pared down. 

For measuring the diminution which they are to suffer from the action of fire, 
another gage is made, of two pieces of brass, 24 inches long, with the sides 
exactly straight, divided into inches and tenths, fixed half an inch asunder at 
one end, and -£>- at the other, on a brass plate ; so that one of the thermometric 
pieces, when pared down in the iron gage, will just fit to the wider end. Let us 
suppose this piece to have diminished in the fire J- of its bulk, it will then pass 
on to half the length of the gage ; if diminished -f- it will go on to the narrow- 
end ; and in any intermediate degree of contraction, if the piece be slid along 
till it rests against the converging sides, the degree at which it stops will be the 
measure of its contraction, and consequently of the degree of heat it has 
undergone. 

These are the outlines of what appears to me necessary for the making and 
using of this thermometer; and it is hoped, that the whole process will be found 
sufficiently simple, and easy of execution. It may however be proper to take 
notice of a few minuter circumstances, and to mention some observations which 
occurred in the progress of the inquiry. 1 . There ought to be a certainty of 
the clay being easily, and at all times, procurable in sufficient quantity, and on 
' moderate terms. That this is the case with the clay here made choice of, will 
be evident to every one acquainted with the natural history of Cornwall, where 
there are beds ot this clay inexhaustible, and in too many hands to be monopo- 
lized. If this should not prove satisfactory, the author offers to this illustrious 
Society, and will think himself honoured by their acceptance of, a sufficient 
space in a bed of this clay to supply the world with thermometer-pieces for nu- 
merous ages ; and he does not apprehend, that any greater inconveniences can 
arise to foreign artists or philosophers, from their being supplied with clay for 
these thermometers from this spot only, than what we now feel from being sup- 

* While the clay is thus kept dry in boxes, as well as while it continues in its natural bed, it is se- 
cure from alterations in quality, which clays in general are subject to undergo, when exposed, for a 
long course of years, to the joint actions of air and moisture. — In the lawns I made use of, the inter- 
stices were each less than the 100,000 parts of an inch. — Orig. 

VOL. XV. O o 



282 PHILOSOPHICAL TRANSACTIONS. [ANNO 1762. 

plied with mercury for the common thermometers from the Spanish or Hunga- 
rian mines. 

2. We ought to be assured also, that all the clay made use of for these ther- 
mometers, is perfectly similar. For this purpose, it will be best to dig it out of 
the earth in considerable quantity at once, an extent of some square feet or yards 
in area, and to the depth of 6 or 7 yards or more from the surface, and to mix. 
the whole thoroughly together, previous to the further preparation already men- 
tioned. When the first quantity is exhausted, another perpendicular column 
may be dug from the same bed, close to the first, to the same depth, and pre- 
pared in the same manner ; by which means we may be assured of its similarity 
with the former parcel, and that it will diminish equally in the fire. 

3. This clay, dried by the summer heat, or in a moderately warm room, or 
with more heat before a fire, has not been observed to differ in degree of dryness. 
After being so dried, it loses about a 10th part of its weight in the heat of boil- 
ing water, about as much more in that of melted lead, and from thence to a red 
heat J O parts, in all -£fa. Each of these heats soon expels from the clay its de- 
terminate quantity of matter, chiefly air; after which, the same heat, though 
continued for many hours, has no further effect. I had some hopes, that the 
graduation of the common thermometer might be continued, on this principle, 
up to the red heat at which the shrinking of the clay commences, so as to 
connect the 2 thermometers together by one series of numbers ; but the loss of 
weight appears not to be sufficiently uniform, or proportional to the degree of 
heat, to answer that purpose ; for it was found to go on quicker, and bladders 
tied to the mouths of the vessels in which the pieces were heated, became more 
rapidly distended, at the commencement of redness than at any other time. 
From low red heat to a strong one, such as copper melts in, the loss of weight 
was only about 2 parts in 100 ; though the difference between these 2 heats ap- 
pears to be much greater than what the same loss corresponds to in the lower 
stages. After this period, the decrease of weight entirely ceased. The vapours 
expelled from the clay, caught separately in the different degrees of heat, seemed, 
from the few trials made with them, to consist of common air mixed with fixed 
air. They all precipitated lime-water ; that which was first extricated, exceeding 
weakly ; the others more and more considerably ; but the last not near so 
strongly as the air expelled from lime-stone in burning. None of them were 
inflammable. 

The thermometric pieces may be formed much more expeditiously than in the 
single mould, by means of an instrument used for similar purposes by the potters. 
It consists of a cylindrical iron vessel, with holes in the bottom, of the form and 
dimensions required. The soft clay, put in the vessel, is forced by a press down 
through these apertures, in long rods, which may be cut while moist, or broken 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 283 

when dry, into pieces of convenient lengths. It was hoped, that this method 
would of itself have been sufficient, without the addition of the paring gage, 
making proper allowance, in the size of the holes, for the shrinking of the clay 
in drying. But it was found, that a variety of little accidents might happen to 
alter the shape and dimensions of the pieces, in a sensible degree, while in their 
soft state ; so that it will be always safest to have recourse to the paring gage, 
for ascertaining and adjusting their breadth when perfectly dry, this being the 
period at which the pieces are exactly alike with regard to their future diminish- 
ing ; so that if they are now reduced to the same breadth, we may be sure that 
they will suffer equal contractions from equal degrees of heat afterwards, 
whether they have been made in a mould, or by a press, or in any other way ; 
neither is any variation in the length or thickness of these pieces of the least 
consequence, provided one of the dimensions, that by which they are after- 
wards to be measured, is made accurate to the gage. 

5. It will be proper to bake the pieces, when dry, with a low red heat, in 
order to give them some firmness or hardness, that they may, if necessary, be 
able to bear package and carriage ; but more especially to prepare them for being 
put into an immediate heat, along with the matters they are to serve as measures 
to, without bursting or flying, as unburnt clay would do. We need not be 
solicitous about the precise degree of heat employed in this baking, provided only 
that it does not exceed the lowest degree which we shall want to measure in prac- 
tice ; for a piece that has suffered any inferior degrees of heat, answers as well 
for measuring higher ones as a piece which has never been exposed to fire at all. 
In this part of the preparation of the pieces, it may be proper to inform the 
operator of a circumstance, which, though otherwise immaterial, might at first 
disconcert him : if the heat be not in all of them exactly equal, he will probably 
find, that while some have begun to shrink, others are rather enlarged in their 
bulk ; for they all swell a little just on the approach of redness. As this is the 
period of the most rapid produce of air, the extension may perhaps be owing to 
the air having at this moment become elastic to such a degree, as to force the 
particles of the clay a little asunder before it obtains its own enlargement. 

6. Each division of the scale, though so large as a 10th of an inch, answers 
to -g-i-^ part of the breadth of the little piece of clay. We might go to much 
greater nicety, either by making the divisions smaller, or the scale longer ; but 
it is not apprehended that any thing of this kind will be found necessary : and 
indeed, in proceeding much further in either way, we may possibly meet with 
inconveniences sufficient to counter- balance the apparent additional accuracy of 
measurement. 

7. The divisions of this scale, like those of the common thermometers, are 

o o 1 



284 I'HILOSOPHICAL TRANSACTIONS. [ANNO ] 76'2. 

unavoidably arbitrary ; but the method here proposed appears sufficiently com- 
modious and easy of execution, the divisions being adjusted by measures every- 
where known, and at all times obtainable: for however the inches used in dif- 
ferent countries may differ in length, this cannot affect the accuracy of the scale, 
provided the proportions between the wider and narrower end of the gage are 
exactly as -fa of those inches to -fa, and the length 240 of the same lOths; 
and that the pieces in their perfectly dry state, before firing, fit precisely to the 
wider end. When one gage is accurately adjusted to these proportional measures 
2 pieces of brass should be made, one fitting exactly into one end, and the other 
into the other; these will serve as standards for the ready adjustment of other 
gages to the dimensions of the original. By this simple method we may be 
assured that thermometers on this principle, though made by different persons 
and in different countries, will all be equally affected by equal degrees of heat 
and all speak the same language: the utility of this last circumtance is now too 
well known to need being insisted on. 

8. If a scale 2 feet in length should be reckoned inconvenient, it may be 
divided into 2, of 1 foot each, by having 3 pieces of brass fixed on the same 
plate; the 1st and 2d, -fa of an inch apart at one end, and -fa at the other; the 
2d and 3d, -fa at one end, and -fa at the other; so that the first reaches to the 
120th division, and the 2d from thence to the 240th. 

g. As this thermometer, like all others, can express only the heat felt by 
itself, the operator must be careful to expose the pieces to an equal action of the 
fire with the body whose heat he wants to measure by them. In kilns, ovens, 
reverberatories, under a muffle, and wherever the heat is pretty steady and 
uniform, the means of doing this are too obvious to need being mentioned. 
But in a naked fire, where the heat is necessarily more fluctuating, and unequal 
in different parts of the fuel, some precaution will be required. The thermo- 
meter-piece may generally be put into the crucible, along with the subject- 
matter of the experiment. But where the matter is of such a kind as to melt 
and stick to it, the piece may be previously inclosed in a little case made of cru- 
cible clay. The smallness of the pieces will admit of this being done without 
inconvenience, at least in any but the smallest crucibles, as the pieces themselves 
may be diminished to any size that may be found proper, provided only that one 
of the dimensions, -^ u of an inch, be preserved as mentioned in obs. 4. For the 
very smallest sort of crucibles, the case may be put in close to the crucible, so 
as to form as it were an addition to its bulk on the outside. If it be asked, why 
the case is not always thus put in by the side of the crucible? it is answered, 
that in judging of the heat of large crucibles from a thermometer- piece placed 
on the outside of them, we may sometimes be deceived, as the piece in its little 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 285 

case has been found to heat sooner than the matter in the larger vessel; but in 
small ones, as the crucible and case are nearly alike in bulk, there is little danger 
of error from this cause. 

10. These thermometer-pieces possess some singular properties, which we 
could not have expected to find united in any substance whatever, and which 
peculiarly fit them for the purposes they are here applied to. 1st. When 
baked by only moderate degrees of fire, though they are, like other clays, of a 
porous texture, and imbibe water; yet, when saturated with the water, their 
bulk continues exactly the same as in a dry state. 2d. By very strong fire, they 
are changed to a porcelain or semi-vitreous texture; yet their contraction, on 
further augmentations of the heat, proceeds regularly as before, up to the 
highest degree of fire that I have been able to produce. 3d. They bear sudden 
alternatives of heat and cold; may be dropped at once into intense fire, and, 
when they have received its heat, may be plunged as suddenly into cold water, 
without the least injury from either. 4th. Even while saturated with water in 
their porous state, they may be thrown immediately into a white heat, without 
bursting or suffering any injury. 5th. Sudden cooling, which alters both the 
bulk and texture of most bodies, does not at all affect these, at least not in any 
quality subservient to their thermometric uses. 6th. Nor are they affected by 
long continuance in, but solely by, the degree of heat they are exposed to. In 
3 minutes or less, they are perfectly penetrated by the heat which acts on them, 
so as to receive the full contraction which that degree of heat is capable of pro- 
ducing, equally with those which had undergone its action during a gradual 
increase of its force for many hours. Strong degrees of heat are communicated 
to them with more celerity than weak ones: perhaps the heat may be more 
readily transmitted, in proportion as the texture becomes more compact. 

These facts have been ascertained by many experiments, the particulars of 
which are omitted, because they would swell this paper much beyond the bulk 
intended. 

1 1 . The use and accuracy of this thermometer for measuring, after an opera- 
tion, the degree of heat which the matter has undergone, will be apparent. 
The foregoing properties afford means of measuring it also, easily and expedi- 
tiously, during the operation, so that we may know when the fire is increased to 
any degree previously determined on. The piece may be taken out of the fire 
in any period of the process, and dropped immediately into water, so as to be fit 
for measuring by the gage in a few seconds of time. At the same instant, 
another piece may be introduced into the place of the former, to be taken out and 
measured in its turn; and thus alternately, till the desired degree of heat is 
obtained. But as the cold piece will be 2 or 3 minutes in receiving the full heat, 
and corresponding contraction ; to avoid this loss of time it may be proper, on 



'286 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

some occasions, to have 2 or more pieces, according to convenience, put in toge- 
ther at first, that they may be successively cooled in water, and the degrees of 
heat examined at shorter intervals. It will be unnecessary to say any thing fur- 
ther on precautions or procedures which the very idea of a thermometer must 
suggest, and in which it is not apprehended that any difficulty can occur, which 
every experimenter will not readily find means to obviate. 

12. It now only remains, that the language of this new thermometer be 
understood, and that it may be known what the heats meant by its degrees really 
are. For this purpose a great number of experiments has been made, from which 
the following results are selected. The scale commences at a red-heat, fully 
visible in day-light; and the greatest heat that I have hitherto obtained in my 
experiments is l6o°. This degree I have produced in an air-furnace about 8 
inches square. Mr. Alchorne has been so obliging as to try the necessary expe- 
riments with the pure metals at the Tower, to ascertain at what degrees of this 
thermometer they go into fusion; and it appears, that the Swedish copper melts 
at 27, silver at 28, and gold at 32. Brass is in fusion at 21. Yet., in the brass 
and copper foundries, the workmen carry their fires to 140° and upwards: for 
what purpose they so far exceed the melting heat, or whether so great an addi- 
tional heat be really necessary, I have not learnt. The welding heat of iron is 
from QO to 95°; and the greatest heat that could be produced in a common smith's 
forge 125. Cast iron was found to melt at 130°, both in a crucible in my own 
furnace, and at the foundry; but could not be brought into fusion in the smith's 
forge, though that heat is only 5° lower. The heat by which iron is run down 
among the fuel for casting is 1 50°. 

As the welding state of iron is a softening or beginning fusion of the surface, 
it has been generally thought that cast iron would melt with much less heat than 
what is necessary for producing this effect on the forged; whereas, on the con- 
trary, cast iron appears to require, for its fusion, a heat exceeding the welding 
heat 35 or 40°, which is much more than the heat of melted copper exceeds the 
lowest visible redness. Thus we find, that though the heat for melting copper 
is by some called a white heat, it is only 27° of this thermometer. The welding 
heat of iron, or 9O , is likewise a white heat; even 130°, at which cast iron is 
in fusion, is no more than a white heat; and so on to 1(J0° and upwards is all a 
white heat still. This shows abundantly how vague such a denomination must 
be, and how inadequate to the purpose of giving us any clear ideas of the extent 
of what we have been accustomed to consider as one of the 3 divisions of heat 
in ignited bodies. 

A Hessian crucible, in the iron foundry, viz. about 150°, melted into a slag- 
like substance. Soft iron nails, in a Hessian crucible in my own furnace, melted 
into one mass with the bottom of the crucible, at 154°: the part of the crucible 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 287 

above the iron was little injured. The fonding heat of the glass furnaces I 
examined, or that by which the perfect vitrification of the materials is produced, 
was at one of them 1 14° for flint-glass, and 124° for plate-glass; at another it 
was only 70° for the former, which shows the inequality of heat, perhaps un- 
known to the workmen themselves, made use of for the same purpose. After 
complete vitrification, the heat is abated for some hours to 28 or 2Q°, which is 
called the settling heat; and this heat is sufficient for keeping the glass in fusion. 
The fire is afterwards increased, for working the glass, to what is called the 
working heat; and this I found, in plate-glass, to be 57°. Delft ware is fired by 
a heat of 40 or 41°; cream-coloured, or queen's ware, by 86°; and stone ware, 
called by the French pots de gres, by 102°: by this strong heat, it is changed to 
a true porcelain texture. The thermometer-pieces begin to acquire a porcelain 
texture at about 110°. 

-The above degrees of heat were ascertained by thermometer-pieces fired along 
with the ware in the respective kilns. But this thermometer affords means of 
doing much more, and, going further in these measures than I could at first 
even have expected; it will enable us to ascertain the heats by which many of the 
porcelains and earthen wares of distant nations and different ages have been 
fired: for as burnt clay, and compositions in which clay is a prevailing ingredient, 
suffer no diminution of their bulk by being repassed through degrees of heat 
which they have already undergone, but are diminished by any additional heat 
(according to obs. 5), if a fragment of them be made to fit into any part of the 
gage, and then fired along with a thermometer-piece till it begins to diminish, 
the degree at which this happens points out the heat by which it had been fired 
before. Of several pieces of ancient Roman and Etruscan wares, which I have 
examined, none appear to have undergone a greater heat than 32°, and none 
less than 20°; for they all began to diminish at those or the intermediate 
degrees. 

By means of this thermometer some interesting properties of natural bodies 
may likewise be discovered, or more accurately determined, and the genus of 
the bodies ascertained. Jasper, for instance, is found to diminish in the fire, 
like an artificial mixture of clay and siliceous matter; granite, on the contrary, 
has its bulk enlarged by fire, while flint and quartzose stones are neither enlarged 
nor diminished. These experiments were made in fires between 70 and 80° of 
this thermometer. A sufficient number of facts like these, compared with 
each other, and with the properties of such natural or artificial bodies as we wish 
to find out the composition of, may lead to various discoveries, of which I have 
already found some promising appearances ; but many more experiments are 
wanting to enable me to speak with that certainty and precision on these subjects 
which they appear to deserve. 



288 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 782. 

A piece of an Etruscan vase melted completely at 33°; pieces of some other 
vases and Roman ware about 36°; Worcester china vitrified at 94 ; Mr. Spri- 
mont's Chelsea china at 105°; the Derby at 1 12°; and Bow at 121°; but Bristol 
china showed no appearance of vitrification at 135°. The common sort of 
Chinese porcelain does not perfectly vitrify by any fire I could produce; but 
began to soften about 120°, and at 156° became so soft as to sink down, and 
apply itself close on a very irregular surface underneath. The true stone nan- 
keen, by this strong heat, does not soften in the least; nor does it even acquire a 
porcelain texture, the unglazed parts continuing in such a state as to imbibe water 
and stick to the tongue. The Dresden porcelain is more refractory than the 
common Chinese, but not equally so with the stone nankeen. The cream- 
coloured or queen's ware bears the same heat as the Dresden, and the body is as 
little affected by this intense degree of fire. 

Mr. Pott says, that to melt a mixture of chalk and clay in certain proportions, 
which proportions appear from his tables to be equal parts, is " among the 
master-pieces of art." This mixture melts into a perfect glass at 123° of this 
thermometer. The whole of Mr. Pott's or any other experiments may, by 
repeating and accompanying them with these thermometric pieces, have their 
respective degrees of heat ascertained, and thereby be rendered more intelligible 
and useful, to the reader, the experimenter, and the working artist. I flatter 
myself that a field is thus opened for a new kind of thermometrical inquiries; 
and that we shall obtain clearer ideas with regard to the differences of the degrees 
of strong fire, and their corresponding effects on natural and artificial bodies; 
those degrees being now rendered accurately measurable, and comparable with 
each other, equally with the lower degrees of heat which are the province of the 
common mercurial thermometer. 

Appendix. Analysis of the clay of which the thermometric pieces are formed. — 
This clay makes no effervescence with acids. Diluted nitrous and marine acids 
being boiled on it, and afterwards saturated with fixed alkali, no precipitation or 
turbidness appeared. It therefore contains no calcareous earth, as that earth 
would have been dissolved by the acids, and precipitated from them by the 
alkali. Calcined with powdered charcoal, it contracted no sulphureous smell, 
and the acids had no more action on it than before. It therefore contains no 
gypsous matter, or combination of calcareous earth with vitriolic acid; as that 
acid would have formed sulphur with the inflammable principle of the charcoal, 
and left the calcareous earth pure, or in a state of solubility by acids. 

Some of the clay was calcined with an equal weight of salt of tartar, which, 
for the greater certainty in regard to its purity, had been run per deliquium, 
and afterwards evaporated to dryness. The calcined mixture was boiled in water, 
the filtered liquor slowly evaporated, and suffered to cool at intervals. No 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 28p 

crystallization was formed : the dry salt appeared merely alkaline as at first, and 
deliquiated in the air; a further proof that this clay contains no gypseous 
matter; for the vitriolic acid would have been absorbed by the alkali, and formed 
vitriolated tartar, a salt which neither liquefies in the air, nor dissolves easily in 
water, and which therefore would have crystallized long before the alkali became 
dry, or remained after its deliquiation. A 20th part of gypsum, ground with 
clay, was very distinguishable by both the foregoing processes; producing a sul- 
phureous smell; and calcareous earth by calcination with charcoal powder; and 
crystals of vitriolated tartar by calcination with the same alkaline salt. 

To separate the pure argillaceous part, or that matter which in all clays forms 
alum with the vitriolic acid, 240 grains of this clay were thoroughly moistened 
with oil of vitriol, boiled to dryness, and at last made nearly red-hot. The mix- 
ture was then boiled in water; the earth which remained undissolved was treated 
again in the same manner with vitriolic acid, and this operation repeated 5 or 6 
times. The clay was diminished in the first operation about 70 grains; but less 
and less in the succeeding ones, and in the last scarcely 2 grains. The filtered 
liquors yielded crystals of true alum; but its quantity was not examined, as the 
produce of alum from aluminous earth is already sufficiently known, and the 
quantity of aluminous earth itself, or its proportion to the indissoluble earth, 
was here the object. From the 240 grains of clay there remained in one expe- 
riment 98, and in another 95 grains of indissoluble earth; so that 5 parts of 
this clay consist of 3 parts of pure argillaceous or alum earth, and 2 parts of an 
earth of a different kind. 

With respect to the nature of this last earth, it is easier to determine nega- 
tively what it is not, than positively what it is; but ascertaining the former will 
be a great step towards the discovery of the latter. That it is not calcareous, 
gypseous, or argillaceous, is manifest from the experiments. — It is not jasper; 
as this consists, in great part, of argillaceous earth, which would have been 
extracted by the vitriolic acid. — It is not fluof; as this, by the same acid, would 
have been* decomposed, its own acid expelled, and a gypseous earth left. — It is 
not of the micaceous kind; as the peculiar aspect of these earths would readily 
betray them to the eye. — It is not granite; for strong fire, which granite melts 
in, has no effect on this. Nor is there any known kind of earth to which it is 
in any degree similar, except those of the siliceous order; and with these it per- 
fectly agrees in all the properties I am acquainted with, that they possess in a 
state of powder. 

It does not vitrify or soften with pure clay, in the strongest fire I have been 
able to produce. Nor is it disposed to melt with the matter of Hessian cruci- 
bles; for a little of it rubbed on the inside of a crucible, and urged with strong 

vol. xv. P p 



2Q0 PHILOSOPHICAL TRANSACTIONS. [aNNO 1782. 

fire, continued white, powdery, and unaltered. Thirty grains of this earth 
were mixed with an equal weight of dry fossil alkali, and the same quantity of a 
fine white quartzy sand was mixed with the same proportion of the same alkali : 
the two mixtures were put into 2 small crucibles, which were surrounded with 
sand in a larger one, that both might be exposed to an equal heat. They both 
began to melt at the same time; and at about 80° of the thermometer they 
had formed perfect transparent glasses. Though these properties may not, per- 
haps, be thought sufficient of themselves, for determining with certainty that 
this substance is of the siliceous kind, yet, when joined to the negative proofs, 
of its not belonging to any other known order of earthy bodies, they afford the 
fullest evidence which the nature of the subject can admit of, that the indis- 
soluble part of this clay is truly siliceous; and consequently that the clay consists 
of 2 parts of pure siliceous earth, to 3 parts of pure argillaceous or aluminous 
earth. 

XX. An Analysis of Two Mineral Substances, viz. the Roivley-rag-stane, and 
the Toad-stone. By William Withering* M. D. p. 327. 
In a prefatory letter to Dr. Priestley, Dr. W. states that he had sent the 
results of his examination of the toad-stone and the Rowley-rag-stone ; being 
part of a plan which he had long before formed for a chemical analysis of all the 
substances that are known to exist in the earth in large quantity. Some years 
before he transmitted to the r. s. an analysis of the different marles found in 
Staffordshire ; and in the course of experiments which this subject had led him 
to, he found it convenient to form some new tables, and to enlarge some that 

* Dr. Withering practised physic, for a great number of years, with much celebrity, at Birmingham ; 
near which place he died in 17!iy, in the 58th year of his age. He was initiated in the medical 
profession under his father, who was an apothecary at Wellington, in Shropshire, and was after- 
wards sent to Edinburgh, where he took his degree of m. r>. in 1766. In 17 70 he published his 
Arrangement of Plants growing naturally in Great- Britain, in 2 vols., and which has since gone 
through 4 editions, with numerous improvements and additions, so as to make + vols, in 8vo. It is a 
most complete national Flora. In 177*) appeared his Account of the Scarlet Fever and Sore Throat, 
and in 1785 his Account of the Foxglove. In both these publications he appeared to great advan- 
tage as a practical physician. And although he was not the first to point out the diuretic powers of 
the foxglove in hydropic affections (that having been done before by Dr. Darwin) yet he produced a 
great number of cases in which it had been given with success, together with many useful admoni- 
tions concerning its preparations and doses. In 1783 he published a translation of Bergmann's 
Sciagraphia Regni Mineralis, under the title of Outlines of Mineralogy ; before which time he had 
shown that he had bestowed considerable attention on chemical pursuits, by some papers inserted in 
the Philos. Trans. It should be added that, while he was at Lisbon for the benefit of his health in 
17 05, he analyzed the hot mineral waters in the neighbourhood of that city. For other particulars 
concerning the life of this ingenious physician and naturalist, the reader is referred to the Gent. Mag. 
for l7y;;, a "d t0 l^ r - Duncan's Annals of Medicine for die same year. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 2Q I 

were less completely formed before. One of them he subjoined to this 
paper. The facts taken from M. Macquer are marked wjth an m ; those with 
the * are the consequence of his own experiments. 

In order to save much repetition in future, it may not be amiss to mention, 
once for all, a few particulars in the conduct of these processes. 1st. By water, 
is always meant water distilled in glass vessels, or by means of a large tin refri- 
geratory in Mr. Irwin's method. 2d. Only glass or china vessels are used in the 
liquid processes. 3d. By a mortar he means those excellent ones made by 
Mr. Wedgewood; or as will be specified at the time, a steel mortar tempered so 
hard that it will bear the grinding of enamel in it without discolouration. 

4th. Filtres are never employed, it being found impossible to get the quantities 
accurate where they are used. The powdery parts are allowed to subside till the 
supernatant liquor becomes clear. This sometimes requires days or weeks ; but 
he was ignorant of a better method. By giving the vessels a circular motion 
round their axes, he could greatly facilitate the subsiding of the solid contents. 
If the separating vessels are made like a common tart-dish, with a spreading 
border, the liquors may be poured off very near, without disturbing the sedi 
ments. 5th. Phlogisticated alkali, means the vegetable fixed alkali prepared by 
the deflagration of nitre and crystals of tartar dissolved in water, and boiled with 
Prussian blue in such quantity, that it will not any longer precipitate an earth 
from an acid. 

Rowley-Rag. 

The stone which is the subject of the following experiments forms a range of 
hills in the southern part of Staffordshire. The lime-stone rocks at Dudley 
bed up against it, and the coal comes up to the surface against the lime- 
stone. The highest part of the hills is near the village of Rowley. The 
summit has a craggy, broken appearance, and the fields on each side to a con- 
siderable distance are scattered over with large fragments of the rock, many of 
which are sunk in the ground. In a quarry near Dudley, where a pretty large 
opening has been made in order to get materials for mending the roads, the rock 
appears to be composed of masses of irregular rhomboidal figures : some of these 
masses inclose rounded pebbles of the same materials. At the distance of 4, 5, 
or 6 miles from the hills, as at Bilston, Willenhall, and Wednesbury, the rag- 
stone is frequently found some feet below the surface in rhomboidal pieces, form- 
ing an horizontal bed of no great depth, and seldom of more than a few yards 
extent. Over the whole of this tract of country it is used to mend the roads, 
and lately has been carried to Birmingham to pave the streets. Some people sell 
it in powder, as a substitute for emery in cutting and polishing. 

More obvious properties. — Its appearance dark grey, with numerous minute 

P P 2 



2Q2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 782. 

shining crystals. When exposed to the weather, gets an ochry colour on the 
outside ; strikes fire with steel ; cuts glass ; melts, though not easily, under the 
blow-pipe. Heated in an open fire, becomes magnetic, and loses about 3 in 100 
of its weight. 

Exper. — a. after 3 drs. had been broken to small pieces with a hard steel 
hammer, on a plate of the same metal, it was ground to an impalpable powder 
in one of Mr. Wedgevvood's China mortars. The mortar, which had been 
previously weighed, lost only ■£■ of a grain weight during this operation. 

B. This powder was repeatedly washed with pure water, so as to carry oft' all 
the finer parts, and the coarser ground again, till the whole was washed awav. 
The washings were then filtered, and the powder carefully collected and dried. The 
water employed in the washings did not appear to have dissolved any part of the 
stone ; for no precipitate was formed either on the addition of mild fixed alkali, 
or of silver dissolved in the nitrous acid. 

c. 100 parts of this powder were put into a small mattrass, arid covered with 
marine acid: a degree of heat was excited, and a very slight effervescence took 
place. Water was then added, and the mixture kept boiling for half an hour. 
The liquor was decanted off, and more acid added, which was boiled as before. 
This was decanted, and the residuum washed with water till the water came off 
tasteless. These waters were added to the liquors before decanted. The powder 
had now an ash-coloured appearance, and when dried weighed 80|. To the 
liquors (c) phlogisticated fixed alkali was added, till no more Prussian blue was 
precipitated. To effect this, it took I oz. 5 drs. 12grs. of the phlogisticated 
alkali. The precipitate, when washed and dried, weighed 47- 

e. The powder of 80-J- (c) mixed with twice its weight of fossile fixed alkali, 
was put into a black lead crucible, and exposed to a red heat for 2 hours. The 
heat was never sufficient to render the mass fluid, nor to make it adhere firmly 
to the crucible. The saline part was then washed away by repeated effusions of 
hot water. To the remaining powder marine acid was added repeatedly, and 
boiled as before. The powder was now perfectly edulcorated by hot water, and 
when dry weighed 47 \. The above liquors were all added to the liquor (c), and 
phlogisticated fixed alkali was dropped in, till no more Prussian blue was precipi- 
tated. To effect this, \ oz. of the alkali was required. This precipitate weighed 
1Q; so that the whole of the Prussian blue weighed 66. After calcination 
in a crucible it was reduced to 31^, and was then wholly attracted by a magnet. 

f. Mild fixed alkali was now gradually added to the liquors after the sepa- 
ration of the Prussian blue, and a white powder was precipitated. This powder, 
when well washed and dried, weighed 46^. After being exposed to a low red 
heat for lO minutes, it weighed only 32J-. 



VOL. LXXII.J PHILOSOPHICAL TRANSACTIONS. 2g3 

g. The edulcorated powder (e) was now perfectly white; was not acted on 
either by the vitriolic, nitrous, or marine acids, but readily melted into a glass 
with fossile fixed alkali; during the melting an effervescence took, place. 

h. The white powder (p) readily dissolved in diluted vitriolic acid, and 
under a slow evaporation formed crystals which had the appearance and the taste 
of alum. These crystals were then reduced to powder, and boiled in alcohol. 
The alcohol was decanted off, but did not appear to have dissolved any part of 
the powder; nor did it afford any precipitate on the addition of mild fixed alkali. 

Conclusions. — From these experiments it appears, that the Rowley-rag-stone 
consists of siliceous earth, clay, or earth of alum, and calx of iron. From the 
latter must be deducted 1 \\ for the quantity of calciform iron, found by experi- 
ment to be contained in the quantity of phlogisticated alkali made use of, and 
then the proportions in 100 parts of the stone will be these: Pure siliceous 
earth A7±; pure clay, free from fixable air, 324-; iron in a calciform state 20; 
the sum 100. 

From this view of the component parts of this stone, it is not improbable, 
that it might advantageously be used as a flux for calcareous iron ores. The 
makers of iron are acquainted with such ores; but never could work them to 
advantage, for want of a cheap and efficacious flux. 

Toad-Stone, 

From Derbyshire; sent to Dr. W. by Mr. Whitehurst, who has so fully and 
so accurately described the mode of its stratification, that it is needless to enlarge 
on that subject. 

More obvious properties. — Of a dark brownish grey, a granulated texture; 
with several cavities filled with crystallized spar. It does not strike fire with 
steel. It melts to a black glass. 

Exb. A. 100 parts rubbed to an extremely fine powder in a China mortar, 

and boiled in marine acid; the solution was decanted: the undissolved part, after 
proper washing and drying, weighed 7 1 • 

b. The undissolved part was rubbed with twice its weight of mild fossil alkali, 
and then exposed to a red heat in a black lead crucible for 1 hour. 

c. This mixed mass was reduced to powder, and repeatedly boiled, first in 
marine afterwards in strong vitriolic acid: the residuum now weighed 56, and 
was perfectly white. 

D. The liquors of exp. a. and c. being put all together, phlogisticated fixed 
alkali was added till no further precipitation ensued. This precipitate was a 
Prussian blue, which, when washed and dried, weighed 56-V- After exposure 
to a red heat in a crucible for 40 minutes, it weighed only 2Q, and was wholly 
attracted by the magnet. Now the 2 oz. 5 dr. and 32 gr. of phlogisticated fixed 
alkali used in this experiment, contain 13 gr. of calciform iron, as ascertained by 



'294 PHILOSOPHICAL TRANSACTIONS. [ANNO 1/82. 

a separate trial ; therefore, deducting 13 from 22, we have 1 6 for the quantity of 
calciform iron obtained from the stone. 

e. The earthy parts were next precipitated from the liquors by the addition of 
mild fossil alkali. The precipitate, when perfectly edulcorated and dried, weighed 

29tV 

f. Distilled vinegar was added to this powder, and suffered to stand in a cool 

place for 4 hours; the vinegar was poured off, and the residuum repeatedly 
washed with pure water. To these liquors mild fixed alkali was added, and a 
white precipitate subsided, which, when washed and dried, weighed 7-^. 

g To the residuum (f) dilute vitriolic acid was added: a solution took place, 
which solution, by evaporation and crystallization, yielded alum. 

h. The part of the residuum (f) undissolved by the vitriolic acid was boiled in 
nitrous acid, in marine acid, and in aqua regia, without being diminished; the 
weight of it when dried was 7-rV It could not be fused by the greater heat of 
a blow-pipe, but melted into a glass when mixed with calcareous earth. 

i. The undissolved part (exp. c.) was not fusible by itself; nor was it acted on 
by vitriolic, nitrous, or marine acid. It melted into a glass with fossil alkali. 

k. The precipitate of 7 T v (exp. p.) after a sufficient exposure to heat was put 
into 1 oz. of water: the next morning the water had a pellicle on its surface, and 
tasted like lime-water. 

c. Siliceous earth 56 ? .-., 5 

ii . More ditto 7 T » ff ( — "»» 

^ , . TT .1 , , __ d. Calciform iron \6 

Conclusions. — Hence it appears, that 100 F K calcareous earth.. . 

parts of this specimen of toad-stone contained: <*■ h. Earth of alum 14- 



I o 



i 



io'A 



From the addition of \-fc of weight it is probable, that the substances capable of 
uniting with fixnble air were not in the specimen used fully saturated with it, as 
they would be after their precipitation by the mild alkali. On repeating these 
experiments with different portions of the toad-stone, the quantities of the 
calcareous earth were found to differ a little; but nothing further appeared to 
invalidate the general conclusions. 



VOL. LXXII.] 



PHILOSOPHICAL TRANSACTIONS. 



295 



A Table showing tie Solubility or Insolubility of 



Alcohol. 



Substances. 



fNeut. \ 



-g 
'o 

M 

o 



Metal. 



Earthy 



fNeut. 



S < Metal. 

o 



Earthy 



Vitriolated tartar. 
Glauber's salt. 
Vitriolic ammoniac 
Vitriol of silver. 

mercury. 

copper. 



Heavy spar. 
Selenite. 
Alum. 
Epsom salt. 
Nitre. 

Cubic nitre. 
Nitrous ammoniac. 
Nitre of silver. 

-mercury, 
copper. 



-lead. 



Calcareous. 



Results. 



r 



Neut. 



3 



Earthy. 



Insoluble m 

Insoluble m 

Insoluble M.'rS 

Insoluble M.I « 

Insoluble ula < Metal. ) 

Insoluble M 

Insoluble m 

Insoluble.* 

Insoluble.* 

Insoluble m 

Insoluble.* 

Soluble.* 

Soluble m. 

Soluble m. 

Soluble m. 

Soluble m. 

Insoluble M.£§ 

Soluble M. I 

Soluble.* 

Soluble m. 



Neut. 



> 






)Neut. 3 



L Metal. 



Substances. 


Results. 


Digestive salt. 


Soluble m. 


Common salt. 


Insoluble m. 


Sal ammoniac. 


Soluble m. 


Luna cornea. 


Insoluble m. 


Corros. Sublimate. 


Soluble m. 


Muria cupri. 


soluble m. 


ferri. 


Soluble m. 


Muria calcarea. 


Soluble m. 


magnesias. 


Soluble.* 


aluminosa. 


Soluble.* 


Soluble tartar. 


Soluble * 


Rochelle salt. 


Insoluble.* 


Veget. ammoniac. 




Verdigris. 


Soluble.* 


Sugar of lead. 


Soluble.* 


Veg. alkali mild. 


Insoluble. 


Foss. alkali mild. 


Insoluble. 


Vol. alkali mild. 


Soluble.* 


Calcareous spar. 


Soluble.* 



XXI. New Fundamental Experiments on the Collision of Bodies. By Mr. John 

Smeaton, F. R.S. p. 337. 

It is universally acknowledged, that the first simple principles of science 
cannot be too critically examined, in order to their being firmly established ; more 
especially those which relate to the practical and operative parts of mechanics, 
on which much of the active business of mankind depends. A sentiment of 
this kind occasioned my tract on mechanic power, published in the Philos. 
Trans., for 1776 (abridg. vol. 14, p. 71). What I have now to offer was in- 
tended as a supplement to that, and the experiments were then in part tried ; but 
the completion of them was deferred at that time, partly from want of leisure; 
partly to avoid too great a length of the paper itself; and partly to avoid the 
bringing forward too many points at once. My present purpose is to show, that 
the true doctrine of the collision of bodies hangs as it were on the same hook, 
as the doctrine of the gradual generation of motion from rest, considered in that 
paper ; that is, that whether bodies are put into gradual motion, and uniformly 
accelerated from rest to any given velocity; or are put in motion, in an instanta- 
neous manner, when bodies of any kind strike one another ; the motion, or sum 
of the motions produced, has the same relation to mechanic power there defined, 
which is necessary to produce the motion desired. To prove this, and at the 
same time to show some capital mistakes in principle, which have been assumed 
as indisputable truths by men of great learning, is the reason of my now pur- 
suing the same subject. 

I do not mean to point out the particular mistakes which have been made by 



2Cl6 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

particular men, as that would lead me into too great a length : I shall therefore 
content myself with observing, that the laws of collision, which have been 
investigated by mathematical philosophers, are principally of 3 kinds ; viz. those 
relating to bodies perfectly elastic ; to bodies perfectly unelastic, and perfectly 
soft; and to bodies perfectly unelastic, and perfectly hard. To avoid prolixity, I 
shall consider in each, only the simple case of 2 bodies which are equal in weight, 
or quantity of matter, striking each other. Respecting those which are perfectly 
elastic, it is universally agreed that, when 2 such bodies strike each other, no 
motion is lost; but that in all cases, what is lost by one is acquired by the other: 
and hence, that if an elastic body in motion strike another at rest, on the stroke 
the former will be reduced to a state of rest, and the latter will fly oft" with an 
equal velocity. In like manner, if a non-elastic soft body strike another at rest, 
they neither of them remain at rest, but proceed together from the point of 
collision with exactly one half of the velocity that the first had before the stroke ; 
this is also universally allowed to be true, and is fully proved by very good expe- 
riments on the subject. 

Respecting the 3d species of body, that is, those that are non-elastic, 
and yet perfectly hard ; the laws of motion relating to them, as laid down 
by one species of philosophers, have been rejected by another ; the latter alledg- 
ing, that there are no such bodies to be found in nature to try the experiment 
on ; but those who have laid down and assigned the doctrine that would attend 
the collision of bodies of this kind, if they could be found, have universally 
agreed, that if a non-elastic hard body was to strike another of the same kind 
at rest, that, in the same manner as is agreed concerning non-elastic soft bodies, 
they neither of them would remain at rest, but would in like manner proceed 
from the point of collision, with exactly one half of the velocity that the first 
had before the stroke : in short, they lay it down as a rule attending all non- 
elastic bodies, whether hard or soft, that the velocity after the stroke will be 
the same in both, viz. one half of the velocity of the original striking body. 
Here is therefore the assumption of a principle, which in reality is proved by no 
experiment, nor by any fair deduction of reason that I know of, viz. that the 
velocity of non-elastic hard bodies after the stroke must be the same as that 
resulting from the stroke of non-elastic soft bodies; and the question now is, 
whether it is true or not ? 

Here it may be very properly asked, what ill effects can result to practical men, 
if philosophers should reason wrong concerning the effects of what does not exist 
in nature, since the practical men can have no such materials to work on, or 
misjudge of? But it is answered, that they who infer an equality of effects be- 
tween the 2 sorts, may from thence be misled themselves, and in consequence 
mislead practical men in their reasonings and conclusions concerning the sort 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 2Q7 

with which they have abundant concern, to wit, the non-elastic soft bodies, of 
which water is one, which they have much to do with in their daily practice. 

Previous to the trying my experiment on mills I never had doubted the truth 
of the doctrine, that the same velocity resulted from the stroke of both sorts of 
non-elastic bodies; but the trial of those experiments made me clearly see at least 
theinconclusiveness, if not the falsity, of that doctrine: because I found a result 
which I did not expect to have arisen from either sort; and from which, when it 
appeared from experiment, I could see a substantial reason why it should take 
place in one sort, and that it was impossible that it could take place in the other; 
for if it did, the bodies could not have been perfectly hard, which would be con- 
trary to the hypothesis. Of this deduction I have given notice in my said tract 
on mills, published in the Philos. Trans, for 175Q,* [Abridg. vol. ii. p. 338]. 

It may also be said, that since we have no bodies perfectly elastic, or perfectly 
unelastic and soft, why should we expect any bodies perfectly unelastic and hard? 
Why may not the effects be such as should result from a supposition of their 
being imperfectly elastic joined with their being imperfectly hard? But here I 
must observe, that the supposition appears to be a contradiction in terms. We 
have bodies which are so nearly perfectly elastic, that the laws may be very well 
deduced and confirmed by them; and the same obtains with respect to non- 
elastic soft bodies; but concerning bodies of a mixed nature, which are by far 
the greatest number, so far as they are wanting in elasticity, they are soft, and 
bruise, yield, or leave a mark in collision ; and so far as they are not perfectly 
soft they are elastic, and observe a mixture of the law relative to each; but im- 
perfectly elastic bodies, imperfectly hard, come in reality under the same descrip- 
tion as the former mixed bodies: for so far as they are imperfectly hard they are 
soft, and either bruise and yield, or leave a mark in the stroke; and so far as 
they want perfect elasticity, they are non-elastic; that is to say, they are bodies 
imperfectly elastic, and imperfectly soft; and in fact I have never yet seen any 
bodies but what come under this description. It seems therefore, that respecting 
the hardness of bodies, they differ in degrees of it, in proportion as they have 
a greater degree of tenacity or cohesion; that is, are farther removed from per- 
fect softness, at the same time that their elastic springs, so far as they reach, are 
very stiff; and hence we may by the way conclude, that the same mechanic 
power that is required to change the figure in a small degree of those bodies that 
have the popular appellation of hard bodies, would change it in a great degree 
in those bodies that approach towards softness, by having a small degree of tena- 

* " The effect therefore, of overshot wheels, under the same circumstance of quantity and fall, 
is at a medium double to that of the undershot : and as a consequence thereof, that non -elastic bodies, 
when acting by their impulse or collision, communicate only a part of their original power; the 
other part being spent in changing their figure in consequence of the stroke."— Orig. 
VOL. XV. Q Q 



'2QS PHILOSOPHICAL TRANSACTIONS. [ANNO I 78'2. 

city or cohesion. In the former kind we may rank the harder kinds of cast iron, 
and in the latter, soft tempered clay. 

While the philosophical world was divided by the dispute about the old and 
new opinion, as it was called, concerning the powers of bodies in motion, in 
proportion to their different velocities: those who held the old opinion contend- 
ing, that it was as the velocity simply, asked those of the new, How, on their 
principles, they would get rid of the conclusions arising from the doctrine of un- 
elastic perfectly hard bodies? They replied, they found no such bodies in nature, 
and therefore did not concern themselves about them. On the other hand, those 
of the new opinion asked those of the old, How they would account for the case 
of non-elastic soft bodies, where, according to them, the whole motion lost by 
the striking body was retained in the two after the stroke, the two bodies moving 
together with the half velocity, though the two non-elastic bodies had been 
bruised and changed their figure by the stroke; for, if no motion was lost, the 
change of figure must be an effect without a cause? To obviate this, those of the 
old opinion seriously set about proving, that the bodies might change their figure, 
without any loss of motion in either of the striking bodies. 

Neither of these answers have appeared to me satisfactory, especially since my 
mill experiments; for with respect to the first, it is no proper argument to urge 
the impossibility of finding the proper material for an experiment, in answer to 
a conclusion drawn from an abstract idea. On the other hand, if it can be 
shown, that the figure of a body can be changed, without a power, then, by 
the same law, we might be able to make a forge hammer work on a mass of soft 
iron, without any other power than that necessary to overcome the friction, re 
sistance, and original vis inertias, of the parts of the machine to be put in mo- 
tion; for, as no progressive motion is given to the mass of iron by the hammer, 
it being supported by the anvil, no power can be expended that way; and if none 
is lost to the hammer from changing the figure of the iron, which is the only 
effect produced, then the whole power must reside in the hammer, and it would 
jump back again to the place from which it fell, just in the same manner as if it 
fell on a body perfectly elastic, on which, if it did fall, the case would really 
happen: the power therefore to work the hammer would be the same, whether 
it fell on an elastic or non-elastic body ; an idea so very contrary to all experience, 
and even apprehension, of both the philosopher and vulgar artist, that I shall 
here leave it to its own condemnation. 

As nothing however is so convincing to the mind as experiments obvious to 
the senses, I was very desirous of contriving an experiment in point; and as I 
saw no hopes of finding matter to make a direct experiment, I turned my mind 
towards an indirect one; so circumscribed however, as to prove incontestably, 
that the result of the stroke of two non-elastic perfectly hard bodies could not 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 29P 

be the same as would result from the collision of two soft ones; that is, if it can 
be bona fide proved, that one-half of the original power is lost in the stroke of 
soft bodies by the change of figure, as was very strongly suggested by the 
mill experiments; then, since no such loss can happen in the collision of 
bodies perfectly hard, the result and consequence of such a stroke must be 
different. 

The consequence of a stroke of bodies perfectly hard, but void of elasticity, 
must doubtless be different from that of bodies perfectly elastic: for having no 
spring, the body at rest could not be driven off with the velocity of the striking 
body, for that is the consequence of the action of the spring or elastic parts be- 
tween them, as will be shown in the result of the experiments; the striking body 
will therefore not be stopped, and as the motion it loses must be communicated 
to the other, from the equality of action and reaction, they will proceed toge- 
ther, with an equal velocity, as in the case of non-elastic soft bodies: the ques- 
tion therefore that remains is, what that velocity must be? — It must be greater 
than that of the non-elastic soft bodies, because there is no mechanical power 
lost in the stroke. It must be less than that of the striking body, because, if 
equal, instead of a loss of motion by the collision, it will be doubled. If there- 
fore non-elastic soft bodies lose half their motion, or mechanical power, by 
change of figure in collision, and yet proceed together with half the velocity, 
and the non-elastic hard bodies can lose none in any manner whatever; then, as 
they must move together, their velocity must be such as to preserve the equality 
of the mechanic power unimpaired, after the stroke, the same as it was before it. 

For example, let the velocity of the striking body before the stroke be 20, 
and its mass or quantity of matter 8; then, according to the rule deduced from 
the experiments in the tract on Mechanic Power (see exper. 3 and 4) that power 
will be expressed by 20 X 20 = 400, which X 8 = 3200; and if half of it is 
lost in the stroke,* in the case of non-elastic soft bodies, it will be reduced to 
l600; which -7- l6 the double quantity of matter, will give 100 for the square 

* But, it may be said, if half of it is not lost by the stroke, what then becomes of Mr. S.'s rule ? 
And what good reason has he to suppose that the half, or indeed any part, of the power or momentum 
of any body is lost by the stroke? In fact, Mr. S. bewilders and puzzles himself about a thing 
which he calls mechanical power, which is proportional to the height or space that a body falls through 
to acquire its velocity, which is known to be proportional to the square of that velocity. Whereas 
the real force or momentum of a body in motion, or with which it strikes any obstacle, is a quite 
different thing, being proportional to the velocity in a given body, or to the product of die velocity 
and the body, no part of which is lost by the stroke, but remains the same after the stroke as before 
it. And hence, instead of Mr. S.'s complex and unnatural way of computing the common velocity 
of the two bodies after the stroke, the rule is very plain and simple ; viz. divide the momentum, 
20 x 8 = 160, by the sum of the two bodies, 8 + 8 = 16', and the quotient 10, is their common 
velocity after the stroke. 

a Q 2 

1 



300 PHILOSOPHICAL TRANSACTIONS. |_ANNO 17»2. 

of their velocity; the square root of which being 10, will be the velocity of the 
two non-elastic soft bodies after the stroke, being just one-half of the original 
velocity, as it is constantly found to be. But in the non-elastic hard bodies, no 
power being lost in the stroke, the mechanic power will remain after it, as before 
it, = 3200; this, in like manner, being divided by l6, the double quantity of 
matter, will give 200 for the square of the velocity, the square root of which is 
14.14 &c. for their velocity after the stroke, which is to 10, the velocity of the 
non-elastic soft bodies after the stroke, as the square root of 2 to 1 ; or as the 
diagonal of a square to its side.* 

It remains therefore now to be proved, that precisely half of the mechanic 
power is lost in the collision of non-elastic soft bodies; for which purpose my 
mind suggested the following reflections. In the collision of elastic bodies, the 
effect, seemingly instantaneous, is yet performed in time; during which time the 
natural springs residing in elastic bodies, and which constitute them such, are 
bent or forced, till the motion of the striking body is divided between itself and 
the body at rest; and in this state the two bodies would then proceed together, 
as in the case of non-elastic soft bodies; but as the springs will immediately re- 
store themselves in an equal time, and with the same degree of impulsive force 
with which they were bent in this reaction, the motion that remained in the 
striking body will be totally destroyed, and the total exertion of the two springs, 
communicated to the original resting body, will cause it to fly off with the same 
velocity with which it was struck. 

On this idea, if we could construct a couple of bodies in such a way, that 
they should either act as bodies perfectly elastic; or, that their springs should at 
pleasure be hooked up, retained, or prevented from restoring themselves, when 
at their extreme degree of bending; and if the bodies under these circumstances 
observed the laws of collision of non-elastic soft bodies, then it would be proved, 
that one-half of the mechanical power, residing in the striking body, would be 
lost in the action of collision; because the impulsive force or power of the spring 
in its restitution being cut off, or suspended from acting, which is equal to the 
impulsive force or power to bend it, and which alone has been employed to com- 
municate motion from one body to the other, it would make it evident, that one- 
half of the impulsive force is lost in the action, as the other half remains locked 
up in the springs. It also follows, as a collateral circumstance, that be the im- 
pulsive power of the springs what it may from first to last, yet as one-half of the 
time of the action is by this means cutoff, in this sense also it will follow, that 

• This erroneous conclusion is deduced by Mr. S. from his false rule, for finding the velocities of 
bodies after impact. The true rule is the same for all non-elastic bodies, whether hard or soft. If 
die bodies adhere and move together with one common velocity immediately after the stroke, that 
velocity must bj the half of the velocity before the sttoke, as found in the note above ; whatever the 
nature of the bodies may be. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. SOI 

one-half of the mechanic power is destroyed; or rather, in this case, remains 
locked up in the springs, capable of being re-exerted whenever they are set at 
liberty, and of producing a fresh mechanic.d effect, equivalent to the motion or 
mechanical power of the two non-elastic soft bodies after their collision. 

Hence we must infer, that the quantity of mechanical power expended in dis- 
placing the parts of non-elastic soft bodies in collision, is exactly the same as that 
expended in bending the springs of perfectly elastic bodies; but the difference in 
the ultimate effect is, that in the non-elastic soft bodies, the power taken to dis- 
place the parts will be totally lost and destroyed, as it would require an equal 
mechanic power to be raised afresh, and exerted in a contrary direction to restore 
the parts back again to their former places; whereas, in the case of the elastic 
bodies, the operation of half the mechanic power is, as observed already, only 
locked up and suspended, and capable of being re-exerted without a further 
original accession. 

Those ideas arose from the result of the experiments tried on the machine 
described in my said tract on Mechanic Power, and were also communicated to 
my very worthy and ingenious friend Wm. Russel, Esq., f. r. s., at the same 
time that I showed him those experiments in 1759; but the mode of putting this 
matter to a full and fair mechanical trial has since occurred; and though some 
rough trials, sufficient to show the effect, were made on it, prior to offering the 
paper on mechanical power to the Society in 1776, yet the machine itself I had 
not leisure to complete to my satisfaction till lately; which I mention, to apo- 
logize for the length of time that these speculations have taken in bringing 
forward. 

Description of the machine for collision. — Fig. 6, pi. 5, shows the front of the 
machine as it appears at rest when fitted for use. a is the pedestal, and ab the 
pillar, which supports the whole; c, d, are two compound bodies of about a 
pound weight each, but as nearly equal in weight as may be. These bodies are 
alike in construction, which will be more particularly explained by fig. 7. These 
bodies are suspended by 2 white fir rods, of about half an inch diameter, ef and 
gh, being about 4 feet long from the point of suspension to the centre of the 
bodies; and their suspension is on the cross piece 11, which is mortoised through, 
to let the rods pass with perfect freedom; and they hang on 2 small plates filed 
to an edge on the under side, and pass through the upper part of the rods. 
Their centres are at k and 1, and the edges being let into a little notch, on 
each side of the mortoise, the rods are at liberty to vibrate freely on their res- 
pective points, or rather edges, of suspension, and are determined to one plain 
of vibration, mn is a fiat arch of white wood, which may be covered with 
paper, that the marks on it may be the more conspicuous. The cross piece 11 is 
made to project so far before the pillar, that the bodies in their vibrations may 



302 PHILOSOPHICAL TRANSACTIONS. [ANNO ]/82. 

pass clear of it, without danger of striking it; ancT also the arch mn is brought 
so far forward as to leave no more than a clearance, sufficient for the rods to 
vibrate freely without touching it. 

Fi^. 7, shows one of the compound bodies, drawn of a larger size, ab is a 
block of wood, and about as much in breadth as it is represented in height, 
through a hole in which the wooden rod cc passes, and is fixed in it. db repre- 
sents a plate of lead, about ■§ of an inch thick, one on each side, screwed on by 
way of giving it a competent weight, ibefg represents the edge of a springing 
plate of brass, rendered elastic by hard hammering; it is about -§- of an inch in 
breadth, and about ^ of an inch thick. It is fixed down on the wooden block 
dB by means of a bridge plate, whose end is shown at hi, and is screwed down 
on each side the spring plate by a screw which, being relaxed, the spring can be 
taken out at pleasure, and adjusted to its proper situation, kl is a light thin slip 
of a plate, whose under edge is cut into teeth like a fine saw or ratchet, and is at- 
tached to the spring by a pin at k, which passes through it, and also through a 
small stud rivelted into the back part of the spring, and on which pin, as a 
centre, it is freely moveable. 

mn shows a small plate or stud seen edgeways, raised on the bridge plate, 
through a hole in which stud the ratchet passes ; and the lower part of the hole 
is cut to a tooth shaped properly to catch the teeth of the ratchet, and retain it 
together with the spring at any degree to which it may be suddenly bent ; and 
for this purpose it is kept bearing gently downward, by means of a wire-spring 
opq, which is in reality double, the bearing part at o being semi-circular ; from 
which branching off on each side the rod cc, passes to p, and fixes at each end 
into the wood at q. However, to clear the ratchet, which is necessarily in the 
middle as well as the rod, the latter is perforated ; and also the block is cut away, 
so far as to set the main spring at e free of all obstacles that would prevent its 
play from the point b. The part (g is shown thicker than the rest, by being 
covered with thin kid leather tight sewed on, to prevent a certain jarring that 
otherwise takes place on the meeting of the springs in collision. 

In tig. 6, the marks on the arch mn are put on as follows, op is an arch of a 
circle from the centre 1, and qr an arch of a circle from the centre k intersecting 
each other at s. Now the middle line of the marks t, v, are at the same dis- 
tance from the middle line at s that the centres Ik are ; so that when each body 
hangs in its own free position, without bearing against the other, the rodef will 
cover the mark at t, and the rod gh will cover the mark at v. From the point 
s and on the arches sp and sq respectively, set off points at an equal and com- 
petent distance from s each way, which will give the middle of the mark w and 
x: and on the arch sp find a middle point between the mark v and w, which let 
be y ; and on the other side, in like manner, on the arch sq find a middle point 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 303 

for the mark z ; then set off the distance sv or st from y each way, and from z 
each way ; and from these points, drawing lines to the respective centres 1 and k, 
they will give the place and position of the marks a, b, and c, d ; and thus is the 
machine prepared for use. 

For trials on elastic bodies. — For this use, take out the pins and ratchets from 
each respectively, and the springs being then at liberty, with a short bit of stick, 
suppose the same size as the rods, turn aside the rod gh with the right hand, 
carrying the body d upwards till the stick is on the mark w, as suppose at ; 
there hold it, and with the left set the body c perfectly at rest ; in which case the 
rod ef will be over the mark t ; then suddenly withdraw the stick, in the direc- 
tion that the rod gh is to follow it, and the spring of the body d, impinging on 
that of the body c, they will be both bent, and also restored ; and the body c 
will fly off, and mount till its rod ef covers the mark x ; the rod of the striking 
body D remaining at rest on its proper mark of rest v, till the body c returns, 
when the body d will fly off in the same manner ; the two bodies thus rebound- 
ing a number of times, losing a part of their vibration each time ; but so nearly 
is the theory of elastic bodies thus fulfilled, that the single advantage of ori- 
ginally pushing the rod gh beyond the mark w, by the thickness of the stick, 
or its own thickness, is sufficient to carry the rod of the quiescent body c com- 
pletely to its mark x. 

There are several other experiments that may be made with this apparatus, in 
confirmation of the doctrine of the collision of elastic bodies ; which being uni- 
versally agreed on, and well known, it is needless further to dwell on here ; but 
respecting the application to non-elastic soft bodies, it is far more difficult to 
come at a fitness of materials for this kind of experiments, than it is for those 
supposed perfectly elastic. The conclusions however may be attained with equal 
certainty. 

For trials on non-elastic soft bodies. — For this purpose, the ratchet must be 
applied and put in order as before described, and the springs being both set to 
their point of rest, let the body d be put to its mark w in the same manner as 
before described, and the body c to rest. The body d being let go, and striking 
the body c at rest, in consequence of the stroke, the springs being hooked up 
by the ratchets, they both move from their resting marks t, v, respectively to- 
ward M : now if they both moved together, and the rod ef covered the mark c, 
and the rod gh covered the mark d at their utmost limit, then they would truly 
obey the laws of non-elastic soft bodies ; because their medium ascent would be 
to the mark z, which is just half* the angle of ascent to the mark x ; but as in 
this piece of machinery, though the main or principle springs are hooked up, yet 

* It should be said nearly half the angle. 



304 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

every part of them, and all the materials of which they are composed, and to 
which they are attached, have a degree, or more properly speaking, a certain 
compass of elasticity, which, as such, is perfect, and no motion thereby lost. 
We must not therefore expect the two compound bodies after the stroke to stick 
together without separating, as would be the case with bodies truly non-elastic 
and soft ; but that from the elasticity they are posses-ed of, they will by rebound- 
ing be separated ; but that elasticity being perfect, can occasion no loss of mo- 
tion to the sum of the two bodies ; so that if the body c ascends as much above 
its mark c as the body d falls short of its mark d, then it will follow, that their 
medium ascent will still be to the mark z, as it ought to have been, had they 
been truly non-elastic soft bodies ; and this, in reality, is truly the case in the 
experiment, as nearly as it can be discerned. 

After a few vibrations, by the rubbing of the springs against each other, they 
are soon brought to rest ; and here they would always rest had they been truly 
and properlv perfect non-elastic soft bodies ; but here, as in the case of these 
bodies, by a change of the figure and situation of the component parts, there is 
expended one half of the mechanical power of the first mover, yet in this case the 
other half is not lost, but suspended, ready to be re-exerted whenever it is set 
at liberty; and that it is really and bona fide one half and neither more nor less, 
appears from this uncontroverted simple principle, that the power of restitution 
of a perfect spring is exactly equal to the power that bends it. And this may, 
in a certain degree, be shown to be fact by experiment, if there were any need of 
such a proof; for if, when the bodies are at rest after the last experiment, the 
two rods are lashed together near the bottom with a bit of thread, and then the 
ratchets unpinned and removed ; on cutting the thread with a pair of scissars 
they will each of them rebound, c towards m, and d towards n ; and if they re- 
bounded respectively to z and y, the mechanical power exerted would be the 
same as it was after the stroke, when the mean of their two ascents was up to 
the mark z ; but here it is not to be expected, because not only the motion lost 
by the friction of the ratchets is to be deducted, because it had the effect of real 
non-elasticity ; but also the elasticity that separated them in the stroke, which 
was lost in the vibrations that succeeded ; neither of which hindered the mean 
ascent to be to z , but yet, under all these disadvantages in the machine, if not 
unreasonably ill made, the rod ef will ascend to d, and gh to a : and hence I 
infer, as a positive truth, that in the collision of non-elastic soft bodies, one half 
of the mechanic power residing in the striking body is lost in the stroke.* 

* Here Mr. S. puzzles himself again about his mechanical power. There is no real force or mo- 
mentum lost by striking bodies, if they adhere and move together on the stroke ; as he might easily 
and directly have convinced himself of, by discharging a leaden bullet into a pendulous block of 
wood ; being both, in some degree, soft and non-elastic bodies. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 305 

Respecting bodies unelastic and perfectly hard, we must infer, that since we 
are unavoidably led to a conclusion concerning them, which contradicts what is 
esteemed a truth capable of the strictest demonstration ; viz. that the velocity of 
the centre of gravity of no system of bodies can be changed by any collision 
among them, something must, be assumed that involves a contradiction. This 
perfectly holds, according to all the established rules, both of perfectly elastic 
and perfectly non-elastic soft bodies ; rules which must fail in the perfectly non- 
elastic hard bodies, if their velocity after the stroke is to the velocity of the 
striking body, as 1 is to the square root of 2 ; for then the centre of gravity of 
the two bodies will by the stroke acquire a velocity greater than the centre of 
gravity the two bodies had before the stroke in that proportion ; which is proved 
thus. 

At the outset of the striking body, the centre of gravity of the two bodies in 
our case will be exactly in the middle between the two ; and when they meet it 
will have moved from their half distance to their point of contact, so that the 
velocity of the centre of gravity before the bodies meet will be exactly one half 
of the velocity of the striking body ; and therefore, if the velocity of the strik- 
ing body be 2, the velocity of the centre of gravity of both will be ] . After 
the stroke, as both bodies are supposed to move in contact, the velocity of the 
centre of gravity will be the same as that of the bodies ; and as their velocity is 
proved to be the square root of 2, the velocity of their centre of gravity will be 
increased from 1, to the square root of 2 ; that is, from 1 to 1 .414 &c* 

The fair inference from these contradictory conclusions therefore is, that an 
unelastic hard body (perfectly so) is a repugnant idea, and contains in itself a 
contradiction ; for to make it agree with the fair conclusions that may be drawn 
on each side, from clear premises, we shall be obliged to define its properties 
thus : that in the stroke of unelastic hard bodies they cannot possibly lose any 
mechanic power in the stroke ; because no other impression is made than the 
communication of motion ; and yet they must lose a quantity of mechanic 
power in the stroke ; because, if they do not, their common centre of gravity, 
as above shown, will acquire an increase of velocity by their stroke on each 
other. In like manner, the idea of a perpetual motion perhaps, at first sight, 
may not appear to involve a contradiction in terms ; but we shall be obliged to 
confess that it does, when, on examining its requisites for execution, we find we 
shall want bodies having the following properties; that when they are made to 
ascend against gravitation their absolute weight shall be less ; and that when they 
descend by gravitation, through an equal space, their absolute weight shall be 
greater ; which, according to all we know of nature, is a repugnant or contra- 
dictory idea. 

* Here is another false conclusion, drawn in consequence of a former mistake. 

VOL. XV. R R 



306 PHILOSOPHICAL TRANSACTIONS. [ANNO 1762. 

XXII. Proceedings relative to the Accident by Lightning at Heckingham. By 
Dr. Blagden and Mr. Nairne. p. 355. 

The first communication is a letter to the president of the r. s. from the prin- 
cipal officers of the Board of Ordnance, dated Dec. 22, 1781, as follows. 

Sir — Having received information that, last summer, a stroke of lightning 
set fire to the poor-house at Heckingham, near Norwich, notwithstanding it 
was armed with eight pointed conductors, we request you will communicate to 
us such particulars relating to that fact, as may have come to your knowledge. 

(Signed) Amherst; Charles Frederick ; H. Strachey ; J. Kenrick. 

Sir Jos. Banks, Bart. President of the Royal Society. 

It does not appear that any particulars relating to that fact had come to the 
president's knowledge. However, the council of the r. s. appointed a commit- 
tee of their members to inquire into the particulars, as appears by the following 
extracts. 

Extracts from the Minutes of the Council of the Royal Society. 

Jan. lO, 1782. — The president laid before the council a letter to him from 
the Board of Ordnance, acquainting him, that the poor-house at Heckingham, 
near Norwich, had been struck by lightning, notwithstanding it was armed with 
8 pointed conductors ; and requesting him to communicate to them such particu- 
lars relating to that fact as may have come to his knowledge. — Resolved, That 
Dr. Blagden and Mr. Nairne be requested to repair to Heckingham, and examine 
into the circumstances of the accident, and report thereon to the council : that 
they engage a draughtsman, to take such drawings as may be requisite ; and 
that the necessary expenses be defrayed by the Society. 

Feb. 7, 1782. — Dr. Blagden read to the council his and Mr. Nairne's report 
of the survey made by them of the poor-house at Heckingham in Norfolk, in 
consequence of their appointment by a former council. The said report was 
ordered to be read to the Society on Thursday the 14th inst. And the president 
was requested to transmit it immediately afterwards to the Board of Ordnance ; 
and to desire that they would return the drawings as soon as they should have 
taken copies of them, or made such other use of them as they might think 
necessary. 

Report of the Committee. — Read February 14, 1782. — To the President 
and Council of the Royal Society. — Gentlemen, pursuant to your resolution, 
appointing us a committee to examine the House ol Industry at Heckingham in 
Norfolk, which had been struck by lightning though it was armed witli conduc- 
tors, we arrived there on the 21st of January. Seven months had then elapsed 
since the accident, yet we had the satisfaction to learn, that no material changes 
had been made in the conductors or the building in that period ; some laths that 
had been burnt, some bricks and pantiles which had been damaged or thrown 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 307 

down, were replaced ; but we found means to procure distinct information of 
those repairs from the workmen who had been employed to execute them. In 
order to communicate a clear idea of the accident, it will be necessary to premise 
a general account of the building ; then to represent the manner in which the 
conductors were applied ; and, lastly, to describe the stroke of lightning, with 
its effects. 

The general form of the building is that of the Roman letter h consisting of 
a centre range and two flanks. It stands on a gentle rising, which can by no 
means be termed a hill, with its front facing s. 9 w. To the western side of the 
west flank, and eastern side of the east flank, some lower buildings are annexed, 
serving as offices of different kinds ; and there are two courts, one before and 
the other behind the house, with some small gardens and yards on each of the 
flanks, in all of which stand various detached offices. 

A very minute description is then given of all the parts of the building of 
the poor-house, with various low detached and attached offices, as lean-tos, stables, 
yards, privies, pig-houses, &c. &c. the whole illustrated by drawings of plans 
and elevations in 6 engraved plates ; which may well be spared on this occasion. 
To all the 8 chimnies of the building they found iron rods affixed, reaching 
between 4 and 5 feet above the top of the chimney, pointed at the upper end, 
and tapering about 10 inches to that point. Each rod or bar was nearly square, 
measuring, on a mean, about half an inch one way, and -^ of an inch the 
other, with the angles just rounded off. These conductors were continued down 
the building by a succession of similar bars of iron, in general from 6 to 8 feet 
long, joined to each other by 2 hooks and nuts ; that is, the corresponding ends 
of each bar being formed into a hook bent at right angles, the hook of the 
uppermost went into a hole of the lowermost, where it was fastened with a nut, 
and the hook of the lowermost went into a similar hole of the bar above, where 
it was fixed in the same manner ; the length of each of these joints, from nut 
to nut, was about 2 inches. Though there were 8 of these conductors reaching 
above the chimnies, yet they had only 4 terminations below. For the conductors 
to the 2 chimnies, called d and e, being continued toward each other along the 
roof, united in the valley over the lead gutter there, and from that point only 
one conductor was continued down the valley toward the ground. In like 
manner the 2 conductors from the chimnies a and c united in the valley of the 
roof between them, and were carried down toward the ground as a single rod. 
All the 3 conductors from the chimnies f, g, and h, successively joined toge- 
ther, and only a single rod was continued from them down the lower part of the 
building. Lastly, the conductor from the chimney b went down single all the 
way, without having formed a junction with any other. 

The conductors in their passage down the building being thus reduced to 4, 

rk2 



308 1HTLOSOPHICAL TRANSACTIONS. [aNNO 17b2. 

the gentlemen next show their 4 terminations ; which it hence appears were far 
from being so proper or fit as they ought to have been.; being carried but a few 
inches below the surface of the ground, and dry ; instead of being continued to 
many feet in depth, and ending in water, or very moist earth, as is generally directed 
in such cases, to render the conductors safe and effectual. The gentlemen, after 
a minute and careful examination and measurement of all the parts of the build- 
ing, give a very clear and ample description of them, in their report to the So- 
ciety ; but which may well be omitted, being particulars of very little conse- 
quence, and the case itself unimportant. One hip of the extreme corner of the 
building, at the greatest distance from the conductors, was struck and set on 
fire, by a very loud explosion of lightning; but the fire was quickly extinguished, 
and little or no damage was sustained. The gentlemen then conclude their re- 
port as follows. 

Such are the facts we were able to collect from an assiduous examination of 
the poor-house at Heckingham, and of those witnesses in the neighbourhood 
who knew any thing of the accident. We have stated the appearances as they 
presented themselves to us, with all the minuteness that could be preserved 
without too much crowding the narrative, and independently of any opinions. 
Whether the earth or the clouds were positive at the time ; whether the top or 
bottom of the hip was first affected by the stroke ; whether all the lightning took 
its course through the hip, or part went that way, and part through the con- 
ductor ; and how far the conductors were properly constructed, or adequately 
terminated ; are questions which will naturally suggest themselves to your con- 
sideration. (Signed) C. Blagden, and Edw. Nairne. 

XXIII. On the Organ of Hearing in Fishes. By John Hunter, Esq., F. R.S. 

p. 379- 
Reprinted with additions in Mr. J. H.'s Observations on the Animal 
OZconomy, 4to. 1786. 

XXIV. Of a New Electrometer. By Mr. Abraham Brook, p. 384. 
This new electrometer appears to be of very complex structure. It has a 
broad square wooden board, as a foot to stand on. Into this is fixed an upright 
glass rod, to insulate the machine from the table the foot stands on. To this 
upright rod are attached horizontal arms, of brass wire, terminated by large thin 
copper shells ; the electricity being presented to these balls, they are moved and 
turned round the upright rod. The degree or strength of the electricity is mea- 
sured either by an index to a graduated circle, or by different weights that are 
raised at the extremity of another index or lever. 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 30g 

XXF. A New Method of Investigating the Sums of Infinite Series. By the 
Rev. S. Fince, A. M., of Cambridge, p. 38g. 

The subject of this paper is divided into 3 parts : the first, Mr. V. says, con- 
tains a new and general method of finding the sum of those series which De 
Moivre has found in one or two particular cases ; but whose method, though it 
be in appearance general, will on trial be found to be absolutely impracticable. 
The 2d contains the summation of certain series, the last differences of whose 
numerators become equal to nothing. The 3d contains observations on a cor- 
rection which is necessary in investigating the sums of certain series by collecting 
two terms into one, with its application to a variety of cases. 

We must however content ourselves with a very abridged state of this paper ; 
retaining only a few specimens of the several ingenious methods above-men- 
tioned : and besides, altering a little the notation of some of the characters or 
ligatures, for the greater ease and simplicity in printing. 

Part 1. — Lem. 1. Let r be any whole number ; then the fluent of — ~ — can 

1 + X* 

always be exhibited by circular arcs and logarithms ; but when x = 1, the fluent 
of the same fluxion will be expressed by the infinite series 

l — — — + - r ■ — 3 t + &c. the sum of this series therefore can always 
be found by circular arcs and logarithms. 

Lem. 2. To find the sum of the infinite series 
_f 1+A i a + " b _ & c 

1 . r + 1 r + 1 . 2r + 1 ~ 2r + 1 . Sr + 1 

Assume 1 — — - + gp-— — 3-7^— + &c - • = s ; then by several alge- 
braical processes, Mr. V. rinds the sum required to be as follows : viz. — — — 

1 . r + 1 
a + b 1 a 4 26 {Ira— (r + 2) b) x s - ra + (,■ + 1) b 

r + 1 . 2r + 1 ' Qr + 1 . 3r + 1 " 7 " ~* 

Cor. 1. Hence it appears that the sum of this series can never be exhibited in 

finite terms, except a : b as r + 2 : 1r, in which case the sum is equal to — ?- 

^ r + 2 

Hence, if a = 3, b = % then r = 1 ; .-. — - -i- -f -L - & c . . . = 1. 

Ifa=1 , i= 4,thenr4;,. i i ? -- 9 n - r .^-^+&c = '. 

Ifa=i,i=8,tl«r=|;^^- n r Tf + I J^- 5 ^+ &c =±. 



Prop. 1. — To find the sum of 

m . m 4 

T . r 4 1 . 2r 4 1 r + 1 . 3r 4 
Every series of this kind may be resolved into the following series 



m . m 4 n , m 4 2« 

1 . r 4 1 . 2r 4 1 "*" r 4 1 . 3r 4 1 . 4r 4 1 ' Ar 4 1 . or 4 1 . 6r 4 1 t" ^ c - 



310 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

a a + b a+26 a + 3b , . . , P 

HTTi ~ rTTTsT+1 + ,>,• + .,. 3r + , - ,7- + ,,„•+! + &c - for lf we re ' 

duce two terms of this series into one, it will become 

«ar — b . Qra +- (2r — l ) b ra + (4r - 1) b 

l . ;• + 1 . 2r + 1 ~*~ Qr + 1 . 3r + 1.4; + l ' ir + \ . or + 1 . 6r + l ' 
where the denominators being the same as in the given series, and the nume- 
rators also in arithmetic progression, we have only to take a and b such quanti- 
ties that the respective numerators may be also equal ; assume therefore Ira — 
b = m, Ira + {ir — 1 ) b = m + n ; therefore, b = — , a =. " ■ "" ~ \ -\ which 

substituted for a and b in Lem. 2, gives — "' — — - -f- - — — — !!L±_!i 

° l . r + 1 . 1r + I 2r + 1 . 3r + l . 4r + 1 

, m + 2» , » _ 2n» - (r + 1) « , (2r + 1) n - o m 

"r 4r + 1 . br + 1 . 6r + 1 ~ r ~~ Jr 3 AS-)- — . 

Let r = 1 , and we have 

m , m + n m + 2a . , . 3« _ 2w 

If m =], 1.^,^3+^+^+ &C.... = L-2S; 
m =l, n = 0, _L- i + _i-_ + r -i- 7+ &c....= s -i. 
If »=!, „ = i,_J__ + __^_ T+ _ r _^__ + &c..= I l X s + A ; 

m=l, W =0,--i--+ — j^ + 2i . 26 . 31 + &C - * =2l ~To- 
Cor. If 2r : r + 1 :: n : m, the sum of the series can be accurately found, 
and will be equal to - ■- — . Let therefore m = r + 1, and then n = 2r, 

consequently -^—j + 2r + , ? >4r + T + h^Ti + &c = 27 ; 

which is also known from other principles. 
Prop. 2. — To find the sum of 

r + 1 . 2r + 1 • 3c + 1 "" 3; + 1.4; + 1 . 5r + 1 "*" 5r + 1 . 6r + I . 7r + I T &C * 
Proceeding much in the same manner as in prob. 1, Mr. V. finds that the sum 

of this infinite series is equal to 

(2r + I) re — drm , Srm — (.ir + \) n 2rm — (;• — 1) « 

o75 X S "I 4;-* " i SF.T+" l"~ 

Cor. In prop. 1 , substitute a for ra, and 2b for ?j, and we have 

a _ j « + 26 , a + U 

I . r + 1 " 2r + 1 ' 2r + I . 3r + 1 . ir + 1 "*" 4r + 1 . 5r + 1 . 6r +1 ' &C ' - 
ra - (;• + 1) b (^r_+_ 1)6 - ra 
75 X & -f 2H 

Also in this prop, substitute « + /' fur m, and 2i for n, and we have 

a + fe I a+3h U & c = k+ Vb-ra 

r + l . 'ir + 1 . 3r + 1 ~ 3r + 1 . 4r + I . or + 1 ~ r 3 A s -}- 

ra - (2r ± 1) ft . ra + ft 

2r> "*" 2r 2 x (r + l)' 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 311 

Subtract this latter series from the former, and then 

« « + h . _r_ a + 2ft & C = 

1 ' 2r 4- 1 . 3r + 1 . 4r 4- 1 



1 . r 4- I . 2r + 1 r + 1 . 2r + 1 . 3r + I ' 2r 4- 1 . 3r + 1 . 4r 4- 1 

'Ira - (r 4-1) 26 . (:r + 1) 6 - ra /a + 26 

— -75 X S -t- ; , 3 2r , x (r + j). 

Let r = 1 , and we have 
_J! ^il 6 4- a -t-^- - &c... = {la-Ab) X s + iliriS. 

1.2.3 2.3.4^3.4.5 v ' ~ ^ 4 

If«=i, * = o jf7 ^ -rb+jXT- 181 = 2s-^; 

1 3 . 5 c 17 f- 

«=!.* = 2 >T7773 ~ 27775 + 3TT5 ~ &c = T ~ 6s - 

Prop. 3. — To find the sum of the infinite series , r + L 2 ™ + t 3r + L + 

^±^ + m + ' 2n , ^ ■ + &c. By a si- 

2r + 1 . 3r + 1 . 4r + 1 . 5r +. 1 ' 4r + 1 • 5r + 1 . 6r + 1 . Jr + 1 ' -^ 

milar process Mr. V. finds the sum of this infinite series will be generally ex- 

. , irm — (3 4- 2) n (3r + 1) n - inn rm + n 

pressed by - T X 8 + gj bVTFFl? 

Let r = 1 , and we have 

in . »i + 11 . m + 2« |B 4r« — 5ra , 7n—5m 

77273" + 3.4.5.6- + 5.6.7.8 + &C " ' " " = — 6~ X S + ~W~' 

Ifm=i, »= i, r72T 3 —+3T4^ti +6^771 + &c -*-- =l s -iV 
ro = i, n= i, 777.771 + 37737S + TTtfTTs + &c - '• • = L 6~ 1 6 S; 

7 12 17 l 

m = 7, « = 5> nTTs" + J7 7.776 + 7767778 + &c ' * ' * = 1 s ; 

Cor. If ?z : m as 4r : 3r + 2, the sum of the series can be accurately had ; 
let therefore n = 4r and m = 3r + 2, and we shall have 

3'" + 2 , 7r+ 2 , & _ _J_ 

l.r+1.2r+1.9r+1^2r+l.Sr+1.4r+1.5r+l ' ~ 2r . r + I' 

If r _ 1 1 4- ? — + -- ii_ + &c - i • 

11 r — ' ' 1 . 2 . 3 . 4 ' 3 . 4 . 5 . 6 ^ 5 . 6 . 7 . 8 ^ 0CC — 4 ' 

r O ! I 1 .J ? L. Xrp _L . 

r — ^ 1.3.5.7 ~ 5.7-9.11 r 9-11 • 13. 15 ~ — 96' 



,, 5 - H , 17 . . 1 

r ~ ' 1 .7 . 13 . iy "*" 13 . 19 .25 .31 "•" 25. 31. 37. 43 "T" — 336" 

Prop. 4. — To find the sum of the infinite series 



r + 1 . 2r + 1 . 3r + 1 . 4r + 1 

j "' + " I mj-j?n , & 

"T ",. + i . 4r + I . 5r 4- 1 . 6V + 1 ' 5r + 1 . 6> + 1 . 1r + 1 . Sr + 1 ^ 

By a like process also Mr. V. finds that this series is = 
(5 r + 2) n - irm ( , 2m — (4?- + l) n Irm — (r — 2) « , 4rm — (2r — ] ) n 

6T? - X S -r- 6>4 -)- ,2. r s( r+ i) "•" 12r'(r + l).(2r+l) 

Cor. 1 . By a like process also it is found that 

a !±i + &c. = 

1 . r + 1 . 2r + 1 . or + 1 r + 1 . Vr + l . 3r + 1 . 4r + 1 ' 

4ra — (3r + 2) 26 . (3r+ 1)26 — 2m ra + 26 _ 2ro 4- 6 

3H X S -J- 3r4 ^ ^ + x) - - g r * # ^ r + !) _ ( 2r + ,) 



312 PHILOSOPHICAL TP.ANSACTIONS. [ANNO 1/82. 

Let r = 1 , and we have 

_ a _ a + b _j_ a + '2b „ 4a — 10/) 834 - 32a 
1 . 2 : 3 . 4 3.3.4.5 '3.-4.5.6 — 3 X S ^ 36 ' 

If a = 1, b = 0, ! ! u ! 2 - &c. . = - s - - 

' 1.2.3.4 2.3.4.5 '3.4.5.6 3 9 ' 

„ a 7. i ' 1 , X o 2 13 

a = 3, s= l, J- &c. ... = - s — 

'1.2.4 2 . 3 . 5 ~ 3 . 4 . 3 36 

Cor. 2. If a : h as 3r + 2 : 2?-, the sum of the series can be accurately found; 

take .-. a = 3r + 2, and b = 1r, and we shall have 

3r + 2 5r+ 2 , „ 1 



&c....= 



1 . r + 1 . 2r + I . .S/- +1 r + 1 . 2r + 1 . 3r + 1 . 4r 4- 1 ' (»•+•). (2r+ I) 

If r = J ' 1.2.3.4 ~ 2T3 ."4T5 + sTTTST 6 ~ &C = 00 ; 

r — o ': __i? J t frr — • 

' 1.3.5.7 3. 5. 7. 9. 5. 7. 9. 11 — 15' 

_ „ '1 _I7_ , _2J__ _ & _ I 

' 1.4.7.10 4.7.10.13 "*" 7 .10.13.16 °" ' 28' 

Prop. 5. — To find the sum of the infinite series — — - — , ,' — — ■ — ■ + 

1 . r + 1 . 2r 4- 1 . 3r 4- 1 . 4r 4- 1 ' 

m 4- n m 4 2« 

2r + 1 . 3r + 1 . 4r + 1 . 5r + 1 . 0) • + 1 "~ 4r + 1 . br + 1 . 6r + 1 . ?;■ + 1 . Sr 4- 1 
+ &C. 

This series also in like manner is found equal to 

2rm — (2r 4- 1) n (4r + 1) n — 2rm firm + .','» 2/v» + /; 

6r b - X S ■+■ — --— 72. r 4 (r+ I) 24r».(r4- 1). (2r+l)' 
Let r = 1 , and we have 

m m + n , m + 2>i , 2m — 3fl w . 25?i — \6m 



1.2.3.4.5 '3.4.5.6.7' 5.6.7.8.9' -6 ' 72 

Um=>, n = 0, _^__ + _-^_-+_-L ¥ _ } + &c....=I S -| ; 

«. = 1, »= 1, --[-- + ~ 5 -- 7 + -~h-+ kc - ■ ■ ■ =s-) s ' 

m=25, n= 16, --^_ + _-^ + - r ^-— + &e. . . . = I s . 
Co? - . If 7< : m as 2r : 2/ + ] , the sum of the series can be accurately found ; 
assume therefore n = 2r, ?« = 2r -|- 1, and we have 

1 . _J -L&r ' 

1 . »■ 4 1 . .;/• 4 l . ir + 1 2r 4- 1 . 3r + 1 .5/' + 1 .6r + l' "*~6>.(r+l).(2r+l) 

If — 1 _J— J- _1 4- _!— JU — 1 

'1.2.4.5 "*" 3.4.6.7 "^ 5 . 6 . 8 . 9 KC - ' 30' ' 

r — 3 ' _i_ ! j_ . ' _ 4- &c = — 

' 1 . 4 . 10 . 13 ' 7 . 10 . 16 . 19 ' 13. U) - 22 . 25 ' ' ' 504' 

Mr. V. concludes this part with pointing out a remarkable property of those 

series whose sum can be accurately found : viz. that when the number of factors 

in the denominator is even, the numerator is always equal to the sum of the 

two middle factors; and when the number of factors is odd, the numerator is 

equal to the middle factor, and consequently will take it out oi the denominator, 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 313 

and leave a series whose numerators are unity, and whose denominators want the 
middle factor. 

Part ii. Prop. — To find the sum of the infinite series 
I + —1 — + I + &c 

n (» 4- m) n + rm n + m n 4- (; • + 1 ) m ' n + 2m . . . . n + (r + 2) m ' 

when the last differences of the numerators become equal to nothing. 

Assume a + nb -\- n (n + m) . c + n (n + m) . (n -f 2m) . d + &c. to any 
number (?•') of terms; then, if for n we write n + m, n -f- 2m, n + 3m, &c. 
successively, there will result a series of quantities whose r'th difference is = 0; 
substitute therefore this series of quantities for p, q, s, &c. respectively, and the 
given series becomes of a form which manifestly resolves itself into several other 
series, the number of which is r ; and the sum of each of these being taken by 
a well known rule, the sum of the given series becomes 
f I h - I i 

n(n + vi)....(n + (r—i))}i).m.r n + m....(n+ (r—\)7ii).m.(r— \) ' n + 2m....(n+ (r— i)m).m(r— 2) 
■j- &c. where the law of continuation is manifest. 
Exam. To find the sum of the infinite series 

— - -A- -— - -I- 10 i _21— _i_ & 
1.2.3.4 - *" 2.3.4.5 *" 3.4.5.6*" 4.5.6.7 ' ' 

Here n = 1, m = 1, r = 3, and the 3d differences become = 0; therefore 
a + b + 1c = 3, a + lb + 6c = 6, a + 3b + 12c = 10, consequently a = l, 
6=1, c = -i., and therefore the sum sought will be 

FTs .3.3 ~^~ 2.3.2 ~*~ 2T3 — 36* 

This proposition may also be applied to find the sum of all those series whose 
numerators being unity, the denominators shall be deficient by any number of 
corresponding terms, however taken: for as the product of all such factors must 
form a progression, whose differences will become equal to nothing, if such pro- 
ducts be assumed for the numerators of the given series having its factors com- 
pleted, another series will be formed equal to the given series, whose sum can 
be found by this proposition. 

Exam. To find the sum of the infinite series 



1.2.4.6 ' 2.3.5.7 ' 3.4.6.8 

By completing the factors in the denominators, and multiplying the nume- 
rators by the same quantities, the given series becomes 

1.2.3 15 4.5.6 + 2.3.4 24 5.6. l + 3 .4 . /.'ft . 7 ■ 8 + &C ' in W ' lich CESe " = »• 
m = 1, r = 5, and the 3d differences become = 0; therefore a -\- b + 2c = 15, 
a + lb + 6c = 24, a + 3b + 12c = 35, consequently a = 8, b = 5, c = 1, 
and therefore the sum of the series required is 



5 l _ 211 

o Q 1 <; a I Q a. si ~~ 70 



1.2. o. 4. 5. 5 r 2.3.4.5.4 ' 3.4.5.3 7200 

By this proposition we may also investigate the sum of the series when there 
vol xv. S s 



314 PHILOSOPHICAL TRANSACTIONS. [_ANNOl/82. 

are any number of deficient terms in the denominators, and where the last dif- 
ferences of the numerators become equal to nothing; for if the factors in the 
denominators be completed, and the numerators be multiplied by the same quan- 
tities, their differences will still become equal to nothing. 
Exam. To find the sum of the infinite series 

__L_ + -±— + —L- + _J°_ + »i__ 

1.3.4.0'^ 2 . 4 . 5 . 7 n 3 . 5 .6 . 8 ' 4 . 6 .7 .9 ~ 5 . 7 . 8 . 10 ~ 

This series, by completing the factors in the denominators and multiplying 
the numerators by the same quantities, becomes 

•; — , , . + " — , , c , — ; + „,.,--„ + &c. m which case n = 1, 

1.2.3.4.3.0 2.3.4.5.0.7 3 . 4 . o . b . / . S 

m = 1, r = 5, and as the 5th differences are = O, 

Therefore a + b + 2e + 6d -J- 24<? = 10, a + 26 + 6c + 24d -f 120e = 54, 
a + 3/f' + 12c -(- 60(/ + 360e = 1 68, a + 4£ + 20c + 1 20d + 840e = 400, 
a + 5b + 30c + 210d 4- l6sOe = 810; whence a = O, b = O, c = — 1, 
d = 0, e = -i-; consequently the sum of the given series is = — 
_L_ -i ' — 17 

3.4.5.3 ' 5 .2 — 180' 

By a method similar to that made use of in this proposition may any number 
of factors be taken from the denominators of those series delivered in part the 
1st, and also from a great variety of others; but as the examples here given 
must be sufficient to point out the method of proceeding in all other cases, we 
may proceed to the 3d part. 

Part 3. — The sum of every converging infinite series, whose terms ultimately 
become equal to nothing, may always be exhibited by the sum of another series 
formed by collecting 2 or more terms of the former series into one. This is not 
true however where the terms of the infinite series continually diverge, or con- 
verge to any assignable quantity, and are affected with the signs -}-, — , alter- 
nately: for instance, the series 4- — ■§- + -§- — 1+ &c. if we collect 2 terms into 
one, beginning at the 1 st term, will become — — — — — — ^— r + & c . Jf vve 

begin at the 2d term, it becomes - — ■ + — — 4- — -, -f &c; neither of which 

° 1 . Z 3 . 4 o . 

gives the sum of the assumed series; but in this, and every other case of the 
like nature, a correction will be necessary: to determine the value of which, and 
whence the necessity of it arises, is the subject of this 3d part. 

Lemma. — If r be any quantity whatever, then will — = 1 l. 

Jkc. ad infinitum. 

For — = = (by common division) 1 4- &c. ad infi- 

2r r + r v J ' r r r r 

nitum. 

Cor. 1. Hence — — = — 4 1 &c. ad infinitum. 

2r t r >' r r 



VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 315 

Cor. 2. Hence also -f- = - — - + -— - + &c. ad infinitum. 
2o v v v v 

and i == _;_i_!_"'--L.- — &c. ad infinitum. 

2t> o o 

p RO p i — If — * — be the general term of a series formed by writing for n 

rn + m ° 

any series of numbers in arithmetic progression, and whose signs are alternately 
-f and — ; then if a series be formed by collecting two terms into one, begin- 
ning at the first term, the sum of the series thence arising will be less than the 
sum of the given series by — . If a series be formed by beginning at the second 

term, the sum of this will be greater than the sum of the given series by — . 

■p or i e t — " " "I" a — be any two successive terms of the series, which, 

r Ul 1CL r „ + m {n + a) r + m J ' 

if we begin to collect at the 1st term, that term being +, will be two terms to be 
collected into one, and which will therefore give (r „ + m) x ~[™ + a) ,. + „,-, for a 

general term of the resulting series. Let us now make n infinite, and then the 
denominator of this term becomes infinite, and the numerator finite; therefore 
the terms of this latter series at an infinite distance becoming infinitely small, the 
series will there terminate. Now, by making n infinite in the given series, the 

two successive general terms at an infinite distance become ; ; consequently 

this series is still contiuued after the other terminates; and the terms of such a 
continuation will be (as they begin with 

__2 n + a — , making n infinite) 1- -j- &c. which will 

rn + m (n + a) r + m J b ' r r r r 

also be continued ad infin. and whose sum by the lemma is — ; consequently the 
given series exceeds that which is formed by collecting two terms into one, be- 
ginning at the first-, by — ; hence the sum of the latter series + — will be equal 

to the sum of the former. If we begin to collect at the 2d term, then will — 
ii + a 



~ 1 _ - be the two successive general terms of the given series to 

m + m ' (n + a) r + m ° . 

be collected into one; consequently the continuation of the given series, when 

n becomes infinite, will be 1 + - — &c. ad infinitum, whose sum 

by cor. 1 to the lem. is ; in this case therefore, the sum of the given series 

is less than the sum of the series formed by collecting 2 terms into one, begin- 
ning at the 2d term, by ^-; hence the sum of the latter series — — will be equal 
to the sum of the former. 

1 2 3 4* 

Exam. Let the given series be - — - + - — - + &c. 

Here r = 1, n = 1, 2, 3, 4, &c. and m = 1. Now, if we begin to collect 

s s 2 



31(3 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 

at the 1st term, the series resolves itself into — — — — — - — — - — &c. and the 
correction, to be added, being -, we have — — — — — g— — &c. + - for 

the sum of the given series. Now — — — ■ — - — - — -z~ — &c. is well known to 

° 2.34.50.7 

be equal to — 1 + hyp. log. of 2; consequently the sum of the given series is 
= — i + hyp. log. of 2. 

If we begin to collect at the 2d term, the series becomes — — -\- (- - — ■ -f- 

&c. and the correction, to be subtracted, being 

- we have — - + — - -f — r- + &c. — - for the sum of the given series; but 

2 1.23.45.0 2 ° 

1 1- —p + &c. is equal to the hyp. log. of