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Full text of "A budget of paradoxes. Reprinted, with the author's additions, from the 'Athenaeum"

BUDGET OF PAEADOXES. 



LONDOM : PRINTED BY 

SPOTTISWOODE AND CO., STEW-STREET iQtJAEH 
A.VU PARLIAMENT fcTUKKT 




BUDGET OF PARADOXES, 



BT 



AUGUSTUS DE MORGAN, 

F.R.A.S. & C.P.S. 

OF TRINITY COLLEGE, CAMB1UDGB. 



[REPRINTED, WITH THE AUTHOR'S ADDITIONS, FROM THE ' 



' Ut agendo snrgamus arguendo gustamus.' 
PTOCHODOKIAKCHUS 




LONDON : 
LONGMANS, GREEN, AND CO. 

1872. 



A/I rujhtt referred. 



AC 



EDITOR'S PREFACE. 



IT is not without hesitation that I have taken upon myself 
the editorship of a work left avowedly imperfect by the 
author, and, from its miscellaneous and discursive character, 
difficult of completion with due regard to editorial limita- 
tions by a less able hand. 

Had the author lived to carry out his purpose he would 
have looked through his Budget again, amplifying and 
probably rearranging some of its contents. He had collected 
materials for further illustration of Paradox of the kind 
treated of in this book ; and he meant to write a second 
part, in which the contradictions and inconsistencies of 
orthodox learning would have been subjected to the same 
scrutiny and castigation as heterodox ignorance had already 
received. 

It will be seen that the present volume contains more 
than the Athenaeum Budget. Some of the additions formed 
a Supplement to the original articles. These supplementary 
paragraphs were, by the author, placed after those to which 
they respectively referred, being distinguished from the rest 
of the text by brackets. I have omitted these brackets as 
useless, except where they were needed to indicate sub- 
sequent writing. 



Vl EDITOR'S PREFACE. 

Another and a larger portion of the work consists of 
discussion of matters of contemporary interest, for the 
Budget was in some degree a receptacle for the author's 
thoughts on any literary, scientific, or social question. 
Having grown thus gradually to its present size, the book 
as it was left was not quite in a fit condition for publication, 
but the alterations which have been made are slight and 
few, being in most cases verbal and such as the sense 
absolutely required, or transpositions of sentences to secure 
coherence with the rest, in places where the author, in his 
more recent insertion of them, had overlooked the connexion 
in which they stood. In no case has the meaning been in 
any degree modified or interfered with. 

One rather large omission must be mentioned here. It 
is an account of the quarrel between Sir James South and 
Mr. Troughton on the mounting, &c. of the equatorial 
telescope at Campden Hill. At some future time when the 
affair has passed entirely out of the memory of living 
Astronomers, the appreciative sketch, which is omitted in 
this edition of the Budget, will be an interesting piece of 
history and study of character. 

A very small portion of Mr. James Smith's circle-squaring 
has been left out, with a still smaller portion of Mr. De 
Morgan's answers to that Cyclometrical Paradoxer. 

In more than one place repetitions, which would have 
disappeared under the author's revision, have been allowed 
to remain, because they could not have been taken away 
without leaving a hiatus, not easy to fill up without damage 
to the author's meaning. 



EDITOR'S PREFACE. vii 

I give these explanations in obedience to the rules laid 
down for the guidance of editors at page 11. If any apology 
for the fragmentary character of the book be thought 
necessary, it may be found in the author's own words 
at page 438. 

The publication of the Budget could not have been 
delayed without lessening the interest attaching to the 
writer's thoughts upon questions of our own day. I trust 
that, incomplete as the work is compared with what it 
might have been, I shall not be held mistaken in giving it 
to the world. Bather let me hope that it will be welcomed 
as an old friend returning under great disadvantages, but 
bringing a pleasant remembrance of the amusement which 
its weekly appearance in the Athenceum gave to both writer 
and reader. 

The Paradoxes are dealt with in chronological order. 
This will be a guide to the reader, and with the alphabetical 
Index of Names, &c., will, I trust, obviate all difficulty of 
reference. 

SOPHIA DE MORGAN. 

6 MERTON ROID, PRIMROSE HILL. 



Erratum. 
Page 40, line 27, for Litchfield read Liehfield. 



A BUDGET 

OP 



PARADOXES 



INTKODUCTOKY. 

IF I had before me a fly and an elephant, having rever seen 
more than one such magnitude of either kind ; and if the fly 
were to endeavour to persuade me that he was larger than the 
elephan^ I might by possibility be placed in a difficulty. The 
apparently little creature might use such arguments about the 
effect of distance, and might appeal to such laws of sight and 
hearing as I, if unlearned in those things, might be unable 
wholly to reject. But if there were a thousand flies, all buzzing, 
to appearance, about the great creature ; and, to a fly, declaring, 
each one for himself, that he was bigger than the quadruped ; 
and all giving different and frequently contradictory reasons ; and 
each one despising and opposing the reasons of the others I 
should feel quite at my ease. I should certainly say, My little 
friends, the case of each one of you is destroyed by the rest. I 
intend to show flies in the swarm, with a few larger animals, for 
reasons to be given. 

In every age of the world there has been an established system, 
which has been opposed from time to time by isolated and dis- 
sentient reformers. The established -system has sometimes fallen, 
slowly and gradually : it has either been upset by the rising in- 
fluence of some one man, or it has been sapped by gradual change 
of opinion in the many. 

I have insisted on the isolated character of the dissentients, as 
an element of the a priori probabilities of the case. Show me a 
schism, especially a growing schism, and it is another thing. The 
homceopathists, for instance, shall be, if any one so think, as 



2 A BUDGET OF PARADOXES. 

wrong as St. John Long ; but an organised opposition, supported 
by the efforts of many acting in concert, appealing to common 
arguments and experience, with perpetual succession and a com- 
mon seal, as the Queen says in the charter, is, be the merit of the 
schism what it may, a thing wholly different from the case of the 
isolated opponent in the mode of opposition to it which reason 
points out. 

During the last two centuries and a half, physical knowledge 
has been gradually made to rest upon a basis which it had not 
before. It has become mathematical. The question now is, not 
whether this or that hypothesis is better or worse to the pure 
thought, but whether it accords with observed phenomena in 
those consequences which can be shown necessarily to follow from 
it, if it be true. Even in those sciences which are not yet under 
the dominion of mathematics, and perhaps never will be, a 
working copy of the mathematical process has been made. This 
is not known to the followers of those sciences who are not them- 
selves mathematicians, and who very often exalt their horns against 
the mathematics in consequence. They might as well be squaring 
the circle, for any sense they show in this particular. 

A great many individuals, ever since the rise of the mathematical 
method, have, each for himself, attacked its direct and indirect 
consequences. I shall not here stop to point out how the very 
accuracy of exact science gives better aim than the preceding 
state of things could give. I shall call each of these persons a 
paradoxer, and his system a paradox. I use the word in the old 
sense : a paradox is something which is apart from general 
opinion, either in subject-matter, method, or conclusion. 

Many of the things brought forward would now be called 
crotchets, which is the nearest word we have to old paradox. But 
there is this difference, that by calling a thing a crotchet we mean 
to speak lightly of it ; which was not the necessary sense of para- 
dox. Thus in the sixteenth century many spoke of the earth's 
motion as the paradox of Copernicus, who held the ingenuity of 
that theory in very high esteem, and some, I think, who even in- 
clined towards it. In the seventeenth century, the depravation 
of meaning took place, in England at least. Phillips says paradox 
is ' a thing which seemeth strange ' here is the old meaning : 
after a colon, he proceeds ' and absurd, and is contrary to common 
opinion,' which is an addition due to his own time. 

Some of my readers are hardly inclined to think that the word 
paradox could once have had no disparagement in its meaning ; 
still less that persons could have applied it to themselves. I 



INTRODUCTORY. 3 

chance to have met with a case in point against them. It is 
Spinoza's ' Pbilosophia ScripturaB Interpres, Exercitatio Paradoxa,' 
printed anonymously at Eleutheropolis, in 1666. This place 
was one of several cities in the clouds, to which the cuckoos re- 
sorted who were driven away by the other birds ; that is, a feigned 
place of printing, adopted by those who would have caught it if 
orthodoxy could have caught them. Thus, in 1656, the works of 
Socinus could only be printed at Irenopolis. The author deserves 
his self-imposed title, as in the following : 

Quanto sane satius fuissefc illam [Trinitatem] pro mysterio non 
habuisse, et Philosophiae ope, antequam quod esset statuerent, secun- 
dum verse logices praecepta quid esset cum Cl. Keckermanno inves- 
tigasse ; tanto fervore ac labore in profundissimas speluncas et 
obscurissimos metaphysicarum speculationum atque fictionum recessus 
se recipere ut ab adversariorum. telis sententiam suam in tuto collo- 
carent. Profecto magnus ille vir . . . dogma illud, quamvis apud 
theologos eo nomine non multum gratiee iniverit, ita ex immotis 
Philosophies fundamentis explicat ac demonstrat, ut paucis tantum 
immutatis, atque additis, nihil amplius animus veritate sincere deditus 
desiderare possit. 

This is properly paradox, though also heterodox. It supposes, 
contrary to all opinion, orthodox and heterodox, that philosophy 
can, with slight changes, explain the Athanasiau doctrine so as to 
be at -least compatible with orthodoxy. The author would stand 
almost alone, if not quite ; and this is what he meant. I have 
met with the counter-paradox. I have heard it maintained that 
the doctrine as it stands, in all its mystery, is a priori more 
likely than any other to have been Revelation, if such a thing 
were to be ; and that it might almost have been predicted. 

After looking into books of paradoxes for more than thirty 
years, and holding conversation with many persons who have 
written them, and many who might have done so, there is one 
point on which my mind is fully made up. The manner in 
which a paradoxer will show himself, as to sense or nonsense, will 
not depend upon what he maintains, but upon whether he has or 
lias not made a sufficient knowledge of what has been done by 
others, especially as to the mode of doing it, a preliminary to in-, 
venting knowledge for himself. That a little knowledge is a 
dangerous thing is one of the most fallacious of proverbs. A 
person of small knowledge is in danger of trying to make his 
little do the work of more ; but a person without any is in more 
danger of making his no knowledge do the work of some. . Take 
the speculations on the tides as an instance. Persons with nothing 

" 2 



4 A BUDGET OF PAKADOXES. 

but a little geometry have certainly exposed themselves in their 
modes of objecting to results which require the higher mathe- 
matics to be known before an independent opinion can be formed 
on sufficient grounds. But persons with no geometry at all have 
done the same thing much more completely. 

There is a line to be drawn which is constantly put aside in the 
arguments held by parodoxers in favour of their right to instruct 
the world. Most persons must, or at least will, like the lady in 
Cadogan Place, 1 form and express an immense variety of opinions 
on an immense variety of subjects ; and all persons must be their 
own guides in many things. So far all is well. But there are 
many who, in carrying the expression of their own opinions beyond 
the usual tone of private conversation, whether they go no fur- 
ther than attempts at oral proselytism, or whether they commit 
themselves to the press, do not reflect that they have ceased to 
stand upon the ground on which their process is defensible. As- 
piring to lead others, they have never given themselves the fair 
chance of being first led by other others into something better 
than they can start for themselves ; and that they should first 
do this is what both those classes of others have a fair right to 
expect. New knowledge, when to any purpose, must come by 
contemplation of old knowledge, in every matter which concerns 
thought ; mechanical contrivance sometimes, not very often, 
escapes this rule. All the men who are now called discoverers, in 
every matter ruled by thought, have been men versed in the minds 
of their predecessors, and learned in what had been before them. 
There is not one exception. I do not say that every man has 
made direct acquaintance with the whole of his mental ancestry ; 
many have, as I may say, only known their grandfathers by the 
report of their fathers. But even on ;this point it is remarkable 
how many of the greatest names in all departments of knowledge 
have been real antiquaries in their several subjects. ., 

I may cite, among those who have wrought strongly upon 
opinion or practice in science, Aristotle, Plato, Ptolemy, Euclid, 
Archimedes, Eoger Bacon, Copernicus, Francis Bacon, Ramus, 
Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, Newton, 
Locke. I take none but names known out of their fields of work ; 
and all were learned as well as sagacious. I have chosen my 
instances : if any one will undertake to show a person of little or 
no knowledge who has established himself in a great matter ot 
pure thought, let him bring forward his man, and we shall see. 

This is the true way of putting off those who plague others 

1 Mrs. Wititterly, in Nicholas Nickleby. 



INTRODUCTORY. 5 

with their great discoveries. The first demand made should be 
Mr. Moses, before I allow you to lead me over the Eed Sea, I 
must have you show that you are learned in all the wisdom of the 
Egyptians upon your own subject. The plea that it is unlikely 
that this or that unknown person should succeed where Newton, 
&c. have failed, or should show Newton, &c. to be wrong, is utterly 
null and void. It was worthily versified by Sylvanus Morgan 
(the great herald who in his ' Sphere of Gentry ' gave coat armour 
to ' Gentleman Jesus,' as he said), who sang of Copernicus as 
follows (1652): 

If Tellus winged be, 
The earth a motion round ; 
Then much deceived are they 
Who nere before it found. 
Solomon was the wisest, 
His wit nere this attained ; 
Cease, then, Copernicus, 
Thy hypothesis vain. 

Newton, &c. were once unknown ; but they made themselves 
known by what they knew, and then brought forward what they 
could do ; which I see is as good verse as that of Herald Sylvanus. 
The demand for previous knowledge disposes of twenty-nine cases 
out of thirty, and the thirtieth is worth listening to. 

I have not set down Copernicus, Galileo, &c. among the para- 
doxers, merely because everybody knows them ; if my list were 
quite complete, they would have been in it. But the reader will 
find Gilbert, the great precursor of sound magnetical theory ; and 
several others on whom no censure can be cast, though some of 
their paradoxes are inadmissible, some unproved, and some capital 
jokes, true or false : the author of the 'Vestiges of Creation' is an 
instance. I expect that my old correspondent, General Perronet 
Thompson, will admit that his geometry is part and parcel of my 
plan ; and also that, if that plan embraced politics, he would 
claim a place for his ' Catechism on the Corn Laws,' a work at one 
time paradoxical, but which had more to do with the abolition of 
the bread-tax than Sir Robert Peel. 

My intention in publishing this Budget in the Athenceum is 
to enable those who have been puzzled by one or two discoverers 
to see hoiv they look in the lump. The only question is, has the 
selection been fairly made ? To this my answer is, that no selec- 
tion at all has been made. The books are, without exception, 
those which I have in my own library ; and I have taken all I 
mean all of the kind : Heaven forbid that I should be supposed 



6 A BUDGET OF PARADOXES. 

to have no other books ! But I may have been a collector, in- 
fluenced in choice by bias ? I answer that I never have collected 
books of this sort that is, I have never searched for them, never 
made up my mind to look out for this book or that. I have 
bought what happened to come in my way at shop or auction ; I 
have retained what came in as part of the undescribed portion of 
miscellaneous auction lots ; I have received a few from friends 
who found them among what they called their rubbish ; and I 
have preserved books sent to me for review. In not a few in- 
stances the books have been bound up with others, unmentioned 
at the back ; and for years I knew no more I had them than I 
knew I had Lord Macclesfield's speech on moving the change of 
Style, which, after I had searched shops, &c. for it in vain, I 
found had been reposing on my own shelves for many years, at 
the end of a summary of Leibnitz's philosophy. Consequently, I 
may positively affirm that the following list is formed by accident 
and circumstance alone, and that it truly represents the casualties 
of about a third of a century. For instance, the large proportion 
of works on the quadrature of the circle is not my doing : it is 
the natural share of this subject in the actual run of events. 

[I keep to my plan of inserting only such books as I possessed 
in 1863, except by casual notice in aid of my remarks. I have 
found several books on my shelves which ought to have been 
inserted. These have their titles set out at the commencement 
of their articles, in leading paragraphs ; the casuals are without 
this formality. 1 ] 

Before proceeding to open the Budget, I say something on niy 
personal knowledge of the class of discoverers who square the 
circle, upset Newton, &c. I suspect I know more of the English 
class than any man in Britain. I never kept any reckoning ; but 
I know that one year with another and less of late years than in 
earlier time I have talked to more than rive in each year, giving 
more than a hundred and fifty specimens. Of this I am sure, 
that it is my own fault if they have not been a thousand. Nobody 
knows how they swarm, except those to whom they naturally 
resort. They are in all ranks and occupations, of all ages and 
characters. They are very earnest people, and their purpose is 
bonafide the dissemination of their paradoxes. A great many 
the mass, indeed are illiterate, and a great many waste their 
means, and are in or approaching penury. But I must say that 
never, in any one instance, has the quadrature of the circle, of 

1 The brackets mean that the paragraph is substantially from some one of the 
Athenceitm Supplements. (En.) 



INTRODUCTORY. 7 

the like, been made a pretext for begging ; even to be asked to 
purchase a book is of the very rarest occurrence it has happened, 
and that is all. 

These discoverers despise one another : if there were the concert 
among them which there is among foreign mendicants, a man 
who admitted one to a conference would be plagued to death. I 
once gave something to a very genteel French applicant, who 
overtook me in the street, at my own door, saying he had picked 
up my handkerchief : whether he picked it up in my pocket for 
an introduction, I know not. But that day week came another 
Frenchman to my house, and that day fortnight a French lady ; 
both failed, and I had no more trouble. The same thing hap- 
pened with Poles. It is not so with circle-squarers, &c. : they 
know nothing of each other. Some will read this list, and will 
say I am right enough, generally speaking, but that there is an 
" exception, if I could but see it. 

I do not mean, by my confession of the manner in which I 
have sinned against the twenty-four hours, to hold myself out as 
accessible to personal explanation of new plans. Quite the con- 
trary : I consider myself as having made my report, and being 
discharged from further attendance on the subject. I will not, 
from henceforward, talk to any squarer of the circle, trisector of 
the angle, duplicator of the cube, constructor of perpetual motion, 
subverter of gravitation, stagnator of the earth, builder of the 
universe, &c. I will receive any writings or books which require 
no answer, and read them when I please : I will certainly preserve 
them this list may be enlarged at some future time. 

There are three subjects which I have hardly anything upon; 
astrology, mechanism, and the infallible way of winning at play. 
I have never cared to preserve astrology. The mechanists make 
models, and not books. The infallible winners though I have 
seen a few think their secret too valuable, and prefer mutare 
qu<tdrata rotundis to turn dice into coin at the gaming-house : 
verily they have their reward. 

I shall now select, to the mystic number sev jn, instances of my 
personal knowledge of those who think they have discovered, in 
illustration of as many misconceptions. 

1. Attempt by help of the old philosophy, the discoverer not 
being in possession of modern knowledge. A poor schoolmaster, 
in rags, introduced himself to a scientific friend with whom I was 
talking, and announced that he had found out the composition of 
the sun. ' How was that done ? ' ' By consideration of the four 
elements.' ' What are they ? ' ' Of course, fire, air, earth, and 



A BUDGET OF PARADOXES. 



water -'Did you not know that air, earth, and water, have Ion, 
been known to be no elements at all, but compounds V_< Wh 
do you mean, sir ? Who ever heard of such a thing ? '' 

2. The noUonthat difficulties are enigmas, to be overcome in 
a moment by a lucky thought. A nobleman of very hETfc 
now long dead, read an article by me on the quadrature in 
early number of the Penny Magazine. He had, I suppose sc 
recollections of geometry. He put pencil to paper, dTw a rcle 
and constructed what seemed likely to answer, and indeed, wa - 
as he said- certain, if only this bit were equal to that ; wiTh of 
course it was not He forwarded his diagram to the Secreta y 
the Diffusion Society, to be handed to the author of the art Lie 
case the difficulty should happen to be therein overcome 

3. Discovery at all hazards, to get on in the world. Thirty 
years ago, an officer of rank, just come from foreign service and 
trying for a decoration from the Crown, found that his claim 'were 
of doubtful amount and was told by a friend that so and To who 

ttn^owt^ 6 ^ ^.f d f nal Cklm f S 

but that if some clever fellow would mi* f,o *i 
light he thought his a ffair m 



e a poper 



. th , ' > 

, that though perhaps they were wrong, the advisers 



^ H1S r6SUIt WaS abou ' 



He came to In 7 ? ^ H1S r6SUIt WaS about 

ame to London, and somebody sent him to me. Like manv 

ht mind PUrSUU ' h6 Seemed t0 ha t"* > whole fo^ of 



LO rfMiiriTirm TT l. i i "WH.LU. uc UfJtJlJ. 



INTRODUCTORY. 9 

Memoirs, in which were a large number of observed places of the 
planets compared with prediction, and asked him whether it could 
be possible that persons who did not know the circle better than 
he had found it could make the calculations, of which I gave him 
a notion, so accurately ? He was perfectly astonished, and took 
the titles of some books which he said he would read. 

5. Application for the reward from abroad. Many years ago, 
about twenty-eight, I think, a Jesuit came from South America, 
with a quadrature, and a cutting from a newspaper, announcing 
that a reward was ready for the discovery in England. On this 
evidence he came over. After satisfying him that nothing had 
ever been offered here, I discussed his quadrature, which was of 
no use. I succeeded better when I told him of Richard White, 
also a Jesuit, and author of a quadrature published before 1648, 
under the name of Chryscespis,-of which I can give no account, 
having never seen it. This White (Albius) is the only quad- 
rator who was ever convinced of his error. My Jesuit was struck 
by the instance, and promised to read more geometry he was 
no Clavius before he published his book. He relapsed, how- 
ever, for I saw his book advertised in a few days. I may say, as 
sufficient proof of my being no collector, that I had not the 
curiosity to buy this book ; and my friend the Jesuit did not 
send me a copy, which he ought to have done, after the hour I 
had given him. 

6. Application for the reward at home. An agricultural 
labourer squared the circle, and brought the proceeds to London. 
He left his papers with me, one of which was the copy of a letter 
to the Lord Chancellor, desiring his Lordship to hand over 
forthwith 100,000^., the amount of the alleged offer of reward. 
He did not go quite so far as M. de Vausenville, who, I think 
in 1778, brought an action against the Academy of Sciences to 
recover a reward to which he held himself entitled. I returned 
the papers, with a note, stating that he had not the knowledge 
requisite to see in what the problem consisted. I got for answer 
a letter in which I was told that a person who could not see that 
he had done the thing should ' change his business, and appro- 
priate his time and attention to a Sunday-school, to learn what 
he could, and keep the litle children from durting their close.' 
I also received a letter from a friend of the quadrator, informing 
me that I knew his friend had succeeded, and had been heard to 
say so. These letters were printed without the names of the 
writers for the amusement of the readers of Notes and Queries, 
First Series, xii. 57, and they will appear again in the sequel. 



10 A BUDGET OF PAKADOXES. 

[There are many who have such a deep respect for any attempt 
at thought that they are shocked at ridicule even of those who 
have made themselves conspicuous by pretending to lead the 
world in matters which they have not studied. Among my 
anonymes is a gentleman who is angry at my treatment of 
the ' poor but thoughtful ' man who is described in my intro- 
duction as recommending me to go to a Sunday-school because I 
informed him that he did not know in what the difficulty of 
quadrature consisted. My impugner quite forgets that this 
man's ' thoughtfulness ' chiefly consisted in his demanding a 
hundred thousand pounds from the Lord Chancellor for his dis- 
covery; and I may add, that his greatest stretch of invention 
was finding out that ' the clergy ' were the means of his modest 
request being unnoticed. I mention this letter because it affords 
occasion to note a very common error, namely, that men unread 
in their subjects have, by natural wisdom, been great benefactors 
of mankind. My critic says, ' Shakspeare, whom the Pro r (sic) 
may admit to be a wisish man, though an object of contempt as 
to learning. . . .' Shakspeare an object of contempt as to 
learning ! Though not myself a thoroughgoing Shakspearean 
and adopting the first half of the opinion given by George III., 
'What! is there not sad stuff? only one must not say so' I 
am strongly of opinion that he throws out the masonic signs of 
learning in almost every scene, to all who know what they are. 
And this over and above every kind of direct evidence. First, 
foremost, and enough, the evidence of Ben Jonson that he had 
'little Latin and less Greek;' then Shakspeare had as much 
Greek as Jonson would call some, even when he was depreciating. 
To have any Greek at all was in those days exceptional. In 
Shakspeare's youth St. Paul's and Merchant Taylors' schools were 
to have masters learned in good and clean Latin literature, and 
also in Greek if such may be gotten. When Jonson spoke as 
above, he intended to put Shakspeare low among the learned, 
but not out of their pale ; and he spoke as a rival dramatist, who 
was proud of his own learned sock ; and it may be a subject of 
inquiry how much Latin he would call little. If Shakspeare's 
learning on certain points be very much less visible than Jonson's, 
it is partly because Shakspeare's writings hold it in chemical 
combination, Jonson's in mechanical aggregation.] 

7. An elderly man came to me, to show me how the universe 
was created. There was one molecule, which by vibration became 
Heaven knows how ! the Sun. Further vibration produced 
Mercury, and so on. I suspect the nebular hypothesis had got 



INTRODUCTORY. 1 1 

into the poor man's head by reading, in some singular mixture 
with what it found there. Some modifications of vibration gave 
heat, electricity, &c. I listened until my informant ceased to 
vibrate which is always the shortest way and then said, ' Our 
knowledge of elastic fluids is imperfect.' ' Sir ! ' said he, ' I 
see you perceive the truth of what I have said, and I will 
reward your attention by telling you what I seldom disclose, 
never, except to those who can receive my theory the little 
molecule whose vibrations have given rise to our solar system is 
the Logos of St. John's Gospel ! ' He went away to Dr. Lardner, 
who would not go into the solar system at all the first molecule 
settled the question. So hard upon poor discoverers are men of 
science who are not antiquaries in their subject ! On leaving, 
he said, ' Sir, Mr. De Morgan received me in a very different 
way ; he heard me attentively, and I left him perfectly satisfied 
of the truth of my system.' I have had much reason to think 
that many discoverers, of all classes, believe they have convinced 
every one who is not peremptory to the verge of incivility. 

My list is given in chronological order. My readers will 
understand that my general expressions, where slighting or 
contemptuous, refer to the ignorant, who teach before they 
have learnt. In every instance, those of whom I am able to 
speak with respect, whether as right or wrong, have sought 
knowledge in the subject they were to handle before they com- 
pleted their speculations. I shall further illustrate this at the 
conclusion of my list. 

Before I begin the list, I give prominence to the following 
letter, addressed by me to the Correspondent of October 28, 1865. 
Some of my paradoxers attribute to me articles in this or that 
journal ; and others may think I know some do think they 
know me as the writer of reviews of some of the very books 
noticed here. The following remarks will explain the way iu 
which they may be right, and in whicli they may be wrong : 

THE, EDITORIAL SYSTEM. 

SIR, I have reason to think that many persons Lave a very in- 
accurate notion of the Editorial system. What 1 call by this name has 
grown up in the last centenary a word I may use to signify the 
hundred years now ending, arid to avoid the ambiguity of century. It 
cannot conveniently be explained by editors themselves, and edited 
journals generally do not like to say much about it. In your paper 
parhaps, in which editorial duties differ somewhat from those of 
ordinary journals, the common system may be freely spoken of. 



12 A BUDGET OF PARADOXES. 

When a reviewed author, as very often happens, writes to the 
editor of the reviewing journal to complain of what has been said of 
him, he frequently even more often than not complains of 'your 
reviewer.' He sometimes presumes that ' you ' have, ' through 
inadvertence ' in this instance, ' allowed some incompetent person to 
lower the character of your usually accurate pages.' Sometimes he 
talks of 'your scribe,' and, in extreme cases, even of ' your hack.' All 
this shows perfect ignorance of the journal system, except where it is 
done under the notion of letting the editor down easy. But the editor 
never accepts the mercy. 

All that is in a journal, except what is marked as from a corre- 
spondent, either by the editor himself or by the correspondent's real 
or fictitious signature, is published entirely on editorial responsibility, 
as much as if the editor had written it himself. The editor, therefore, 
may claim, and does claim and exercise, unlimited right of omission, 
addition, and alteration. This is so well understood that the editor 
performs his last function on the last revise without the ' contributor ' 
knowing what is done. The word contributor is the proper one : it 
implies that he furnishes materials without stating what he furnishes 
or how much of it is accepted, or whether he be the only contributor. 
All this applies both to political and literary journals. No editor 
acknowledges the right of a contributor to withdraw an article, if he 
should find alterations in the proof sent to him for correction which 
would make him wish that the article should not appear. If the 
demand for suppression were made I say nothing about what might 
be granted to request the answer would be, ' It is not your article, 
but mine ; I have all the responsibility ; if it should contain a libel, I 
could not give you up, even at your own desire. You have furnished 
me with materials, on the known and common understanding that I 
was to use them at my discretion, and you have no right to impede my 
operations by making the appearance of the article depend on your 
approbation of my use of your materials.' 

There is something to be said for this system, and something against 
it I mean simply on its own merits. But the all-conquering argu- 
ment in its favour is, that the only practicable alternative is the 
modern French plan of no articles without the signature of the writers. 
I need not discuss this plan ; there is no collective party in favour of 
it. Some may think it is not the only alternative ; they have not pro- 
duced any intermediate proposal in which any dozen of persons have 
concurred. Many will say, Is not all this, though perfectly correct, 
well known to be matter of form ? Is it not practically the course of 
events that an engaged contributor writes the article, and sends it to 
the editor, who admits it as written substantially, at least ? And is 
it not often very well known, by style and in other ways, who it was 
wrote the article ? This system is matter of form just as much as 
loaded pistols are matter of form so long as the wearer is not assailed ; 
but matter of form takes the form of matter in the pulling of a trigger, 



INTRODUCTORY. 13 

so soon as the need arises. Editors aud contributors who can work 
together find each other out by elective affinity, so that the common 
run of events settles down into most articles appearing much as they 
are written. And there are two safety-valves ; that is, when judicious 
persons come together. In the first place, the editor himself, when he 
has selected his contributor, feels that the contributor is likely to know 
his business better than an editor can teach him ; in fact, it is on 
that principle that the selection is made. But he feels that he is more 
competent than the writer to judge questions of strength and of tone, 
especially when the general purpose of the journal is considered, of 
which the editor is the judge without appeal. An editor who meddles 
with substantive matter is likely to be wrong, even when he knows the 
subject ; but one who prunes what he deems excess, is likely to be 
right, even when he does not know the subject. In the second place, 
a contributor knows that he is supplying an editor, and learns, without 
suppressing truth or suggesting falsehood, to make the tone of his com- 
munications suit the periodical in which they are to appear. Hence 
it very often arises that a reviewed author, who thinks he knows the 
name of his reviewer, and proclaims it with expressions of dissatis- 
faction, is only wrong in supposing that his critic has given all his 
mind. It has happened to myself, more than once, to be announced as 
the author of articles which I could not have signed, because they did 
not go far enough to warrant my affixing my name to them as to a 
sufficient expression of my own opinion. 

There are two other ways in which a reviewed author may be wrong 
about his critic. At editor frequently makes slight insertions or 
omissions I mean slight in quantity of type as he goes over the last 
proof; this he does in a comparative hurry, and it may chance that he 
does not know the full sting of his little alteration. The very bit which 
the writer of the book most complains of may not have been seen by the 
person who is called the writer of the article until after the appearance 
of the journal ; nay, if he be one of those few, I daresay who do not 
read their own articles, may never have been seen by him at all. Pos- 
sibly, the insertion or omission would not have been made if the editor 
could have had one minute's conversation with his contributor. Some- 
times it actually contradicts something which is allowed to remain in 
another part of the article ; and sometimes, especially in the case of 
omission, it renders other parts of the article unintelligible. These are 
disadvantages of the system,' and a judicious editor is not very free 
with his nuns et alter pannus. Next, readers in general, when they 
see the pages of a journal with the articles so nicely fitting, and so 
many ending with the page or column, have very little notion of the 
cutting and carving which goes to the process. At the very last 
moment arises the necessity of some trimming of this kind ; and the 
editor, who would gladly call the writer to counsel if he could, is 
obliged to strike out ten or twenty lines. He must do his best, but it 
ma v chance that the omission selected would take from the writer the 



14 A BUDGET OF PARADOXES. 

power of owning the article. A few years ago, an able opponent of 
mine wrote to a journal some criticisms upon an article which he 
expressly attributed to me. I replied as if I were the writer, which, in 
a sense, I was. But if any one had required of me an unmodified 'Yes ' 
or ' No ' to the question whether I wrote the article, I must, of two 
falsehoods, have chosen ' No : ' for certain omissions, dictated by the 
necessities of space and time, would have amounted, had my signature 
been affixed, to a silent surrender of points which, in my own cha- 
racter, I must have strongly insisted on, unless I had chosen to admit 
certain inferences against what I had previously published in my own 
name. I may here add that the forms of journalism obliged me in this 
case to remind my opponent that it could not be permitted to me, in 
that journal, either to acknowledge or deny the authorship of the articles. 
The cautions derived from the above remarks are particularly wanted 
with reference to the editorial comments upon letters of complaint. 
There is often no time to send these letters to the contributor, 
and even when this can be done, an editor is and very properly 
never of so editorial a mind as when he is revising the comments of 
a contributor upon an assailant of the article. He is then in a better 
position as to information, and a more critical position as to responsi- 
bility. Of course, an editor never meddles, except under notice, with 
the letter of a Correspondent, whether of a complainant, of a casual in- 
formant, or of a contributor who sees reason to become a correspondent. 
Omissions must sometimes be made when a grievance is too highly 
spiced. It did once happen to me that a waggish editor made an inser- 
tion without notice in a letter signed by me with some fiction, which 
insertion contained the name of a friend of mine, with a satire which I 
did not believe, and should not have written if I had. To my strong 
rebuke, he replied ' I know it was very wrong ; but human nature 
could not resist.' But this was the only occasion on which such a 
thing ever happened to me. 

I daresay what I have written may give some of your readers to under- 
stand some of the pericula et commoda of modern journalism. I have 
known men of deep learning and science as ignorant of the prevailing 
system as any uneducated reader of a newspaper in a country town. I 
may, perhaps, induce some writers not to be too sure about this, that, 
or the other person. They may detect their reviewer, and they may be 
safe in attributing to him the general matter and tone of the article. 
But about one and another point, especially if it be a short and sting- 
ing point, they may very easily chance to be wrong. It has happened 
to myself, and within a few weeks to publication, to be wrong in two 
ways in reading a past article to attribute to editorial insertion what 
was really my own, and to attribute to myself what was really editorial 
insertion. 

What is a man to do who is asked whether he wrote an article. 
He may, of course, refuse to answer ; which, is regarded as an 



INTRODUCTORY. 15 

admission. He may say, as Swift did to Serjeant Bettesworth, 
' Sir, when I was a young man, a friend of mine advised me, 
whenever I was asked whether I had written a certain paper, to 
deny it ; and I accordingly tell you that I did not write it.' He 
may say, as I often do, when charged wit.li having invented a joke, 
story, or epigram, ' I wa*nt all the credit I can get, and therefore 
I always acknowledge all that is attributed to me, truly or not ; 
the story, c. is mine. But for serious earnest, in the matter of 
imputed criticism, the answer may be, ' That article was of my 
material, but the editor has not let it stand as I gave it ; I cannot 
own it as a whole.' He may then refuse to be particular as to 
the amount of the editor's interference. Of this there are two 
extreme cases. The editor may have expunged nothing but a 
qualifying adverb. Or he may have done as follows. We all 
remember the account of Adam which satirizes woman, but 
eulogizes her if every second and third line be transposed. As 
in 

Adam could find no solid peace 

When Eve was given him for a mate, 

Till lie beheld a woman's face, 
Adam was in a happy state. 

If this had been the article, and a gallant editor had made the 
transpositions, the author could not with truth acknowledge. If 
the alteration were only an omitted adverb, or a few things of the 
sort, the author could not with truth deny. In all that comes 
between, eveiy man must be his own casuist. I stared, when I 
was a boy, to hear grave persons approve of Sir Walter Scott's 
downright denial that he was the author of Waverley, in answer 
to the Prince Regent's downright question. If I remember 
rightly, Samuel Johnson would have approved of the same course. 
It is known that, whatever the law gives, it also gives all that 
is necessary to full possession ; thus a man whose land is environed 
by the land of others has a right of way over the land of these 
others. By analogy, it is argued that when a man has a right to 
his secret, he has a right to all that is necessary to keep it, and 
that is not unlawful. If, then, he can only keep his secret by 
denial, he has a right to denial. This I admit to be an answer as 
against all men except the denier himself; if conscience and self- 
respect will allow it, no one can impeach it. But the question 
cannot be solved on a case. That question is, A lie, is it malum in 
se, without reference to meaning and circumstances ? This is a 
question with two sides to it. Cases may be invented in which a 



16 A BUDGET OF PARADOXES. 

lie is the only way of preventing a murder, or in which a lie may 
otherwise save a life. In these cases it is difficult to acquit, and 
almost impossible to blame ; discretion introduced, the line be- 
comes very hard to draw. 

I know but one work which has precisely as at first appears 
the character and object of my Budget. It is the ' Eeview of the 
Works of the Eoyal Society of London,' by Sir John Hill, M.D. 
(1751 and 1780, 4to.) This man offended many: the Eoyal 
Society, by his work ; the medical profession, by inventing and 
selling extra-pharmacopceian doses ; Grarrick, by resenting the 
rejection of a play. So Grarrick wrote: 

For physic and farces his equal there scarce is ; 
His farces are physic ; his physic a farce is. 

I have fired at the Eoyal Society and at the medical profession, 
but I have given a wide berth to the drama and its wits ; so 
there is no epigram out against me, as yet. He was very able 
and very eccentric. Dr. Thomson (Hist. Roy. Soc.~) says he has 
no humour, but Dr. Thomson was a man who never would have 
discovered humour. 

Mr. Weld (Hist. Roy. Soc.} backs Dr. Thomson, but with a re- 
markable addition. Having followed his predecessor in observing 
that the Transactions in Martin Folkes's time have an unusual 
proportion of trifling and puerile papers, he says that Hill's book 
is a poor attempt at humour, and glaringly exhibits the feelings 
of a disappointed man. It is probable, he adds, that the points 
told with some effect on the Society ; for shortly after its publica- 
tion the Transactions possess a much higher scientific value. 

I copy an account which I gave elsewhere. 

When the Eoyal Society was founded, the Fellows set to work 
to prove all things, that they might hold fast that which was 
good. They bent themselves to the question whether sprats were 
young herrings. They made a circle of the powder of a unicorn's 
horn, and set a spider in the middle of it ; ' but it immediately 
ran out.' They tried several times, and the spider ' once made 
some stay in the powder.' They enquired into Kenelm Digby's 
sympathetic powder. ' Magnetical cures being discoursed of, Sir 
Gilbert Talbot promised to communicate what he knew of sym- 
pathetical cures ; and those members who had any of the powder 
of sympathy, were desired to bring some of it at the next meeting.' 

June 21, 1661, certain gentlemen were appointed ' curators of 
the proposal of tormenting a man with the sympathetic powder ; ' 
I cannot find any record of the result. And so they went on 



INTRODUCTORY. 1 7 

until the time of Sir John Hill's satire, in 1751. This once well- 
known work is, in my. judgment, the greatest compliment the 
Royal Society ever received. It brought forward a number of 
what are now feeble and childish researches in the Philosophical 
Transactions. It showed that the inquirers had actually been 
inquiring; and that they did not pronounce decision about 
'natural knowledge' by help of ' natural knowledge.' But for 
this, Hill would neither have known what to assail, nor how. 
Matters are now entirely changed. The scientific bodies are far 
too well established to risk themselves. Iblt qui zonam perdidit 

Let him take castles who lias ne'er a gi-oafc. 

These great institutions are now without any collective purpose, 
except that of promoting individual energy ; they print for their 
contributors, and guard themselves by a general declaration that 
they will not be answerable for the things they print. Of course 
they will not put forward anything for everybody ; but a writer of 
a certain reputation, or matter of a certain look of plausibility and 
safety, will find admission. This is as it should be ; the pas- 
turer of flocks and herds and the hunters of wild beasts are two 
very different bodies, with very different policies. The scientific 
academies are what a spiritualist might call 'publishing mediums,' 
and their spirits fall occasionally into writing which looks as if 
minds in the higher state were not always impervious to nonsense. 

The following joke is attributed to Sir John Hill. I cannot 
honestly say I believe it ; but it shows that his contemporaries did 
not believe he had no humour. Good stories are always in some 
sort of keeping with the characters on which they are fastened. 
Sir John Hill contrived a communication to the Royal Society 
from Portsmouth, to the effect that a sailor had broken his leg in 
a fall from the mast-head ; that bandages and a plentiful applica- 
tion of tarwater had made him, in three days, able to use his leg 
as well as ever. While this communication was under grave 
discussion it must be remembered that many then thought tar- 
water had extraordinary remedial properties the joker contrived 
that a second letter should be delivered, which stated that the 
writer had forgotten, in his previous communication, to mention 
that the leg was a wooden leg ! Horace Walpole told this story, 
I suppose for the first time ; he is good authority for the fact of 
circulation, but for nothing more. 

Sir John Hill's book is droll and cutting satire. Dr. Maty, 
(Sec. Royal Society) wrote thus of it in the Journal Britannique 
(Feb. 1751), of which he was editor: 

c 



18 A BUDGET OF PAEADOXES. 

H est facheux que cet ingenieux Naturaliste, qui nous a deja donne 
et qui nous prepare encore des ouvrages plus utiles, empioie a cette 
odieuse tache une plume qu'il trempe dans le fiel et dans 1' absinthe. II 
est vrai que plusieurs de ses remarques sont fondees, et qu'a 1'erreur 
qu'il indique, il joint en meme terns la correction. Mais il n'est pas tou- 
jours equitable, et ne manque jamais d'insulter. Que peut apres tout 
prouver son livre, si ce n'est que la quarante-cinquieme partie d'un 
tres-ample et tres-utile Becueil n'est pas exempte d'erreurs ? Devoit- 
il confondre avec des Ecrivains superficiels, dont la Liberte du Corps ne 
permet pas de restreindre la fertilite, cette foule de savans du Premier 
ordre, dont les Merits ont orne et ornent encore les Transactions ? A-t-il 
oublie qu'on j a vu frequemment les noms des Boyle, des Newton, 
des Halley, des De Moivres, des Hans Sloane, etc. ? Et qu'on y trouve 
encore ceux des Ward, des Bradley, des Graham, des Ellicot, des Watson, 
et d'un Auteur que Mr. Hill prefere a tous les autres, je veux dire de 
Mr. Hill lui-meme ? 

This was the only answer ; but it was no answer at all. Hill's 
object was to expose the absurdities ; he therefore collected the 
absurdities. I feel sure that Hill was a benefactor of the Royal 
Society ; and much more than he would have been if he had 
softened their errors and enhanced their praises. No reviewer 
will object to me that I have omitted Young, Laplace, &c. But 
then my book has a true title. Hill should not have called his 
a review of the ' Works.' 

It was charged against Sir John Hill that he had tried to 
become a Fellow of the Royal Society and had failed. This he 
denied, and challenged the production of the certificate which a 
candidate always sends in, and which is preserved. But perhaps 
he could not get so far as a certificate that is, could not find any 
one to recommend him ; he was a likely man to be in such a 
predicament. As I have myself run foul of the Society on some 
little points, I conceive it possible that I may fall under a like 
suspicion. Whether I could have been a Fellow, I cannot know ; 
as the gentleman said who was asked if he could play the violin, 
I never tried. I have always had a high opinion of the Society 
upon its whole history. A person used to historical inquiry 
learns to look at wholes ; the Universities of Oxford and 
Cambridge, the College of Physicians, &c. are taken in all their 
duration. But those who are not historians I mean not 
possessed of the habit of history hold a mass of opinions about 
current things which lead them into all kinds of confusion when 
they try to look back. SN"ot to give an instance which will offend 
any set of existing men this merely because I can do without 
it let us take the country at large. Magna Charta for ever ! 



INTRODUCTORY. 19 

glorious safeguard of our liberties ! Nullus liber homo capiatur 
aut imprisonetur,. . . . aut aliquo modo destruatur, nisi per 
judicium parium. . . . Liber homo; frank home; a capital 
thing for him but how about the villeins ? Oh, there are none 
noiv ! But there were. Who cares for villains, or barbarians, or 
helots ? And so England, and Athens, and Sparta, were free 
States : all the freemen in them were free. Long after Magna 
Charta, villains were sold with their * chattels and offspring,' 
named in that order. Long after Magna Charta, it was law that 
' Le Seigniour poit rob, naufrer, et chastiser son villein a son 
volunt, salve que il ne poit luy maim.' 

The Eoyal Society was founded as a co-operative body, and co- 
operation was its purpose. The early charters, &c. do not contain 
a trace of the intention to create a scientific distinction, a kind 
of Legion of Honour. It is clear that the qualification was ability 
and willingness to do good work for the promotion of natural 
knowledge, no matter in how many persons, nor of what position 
in society. Charles II. gave a smart rebuke for exclusiveness, as 
elsewhere mentioned. In time arose, almost of course, the idea 
of distinction attaching to the title ; and when I first began 
to know the Society, it was in this state. Gentlemen of good 
social position were freely elected if they were really educated 
men ; but the moment a claimant was announced as resting on 
his science, there was a disposition to inquire whether he was 
scientific enough. The maxim of the poet was adopted ; and 
the Fellows were practically jdivided into Drink-deeps and 
Taste-nots. 

I was, in early life, much repelled by the tone taken by the 
Fellows of the Society with respect to their very mixed body. A 
man high in science some thirty-seven years ago (about 1830) 
gave me some encouragement, as he thought. ' We shall have you a 
Fellow of the Royal Society in time,' said he. Umph ! thought I : 
for I had thatday heard of some recent elections, the united science 
of which would not have demonstrated I. 1, nor explained the action 
of a pump. Truly an elevation to look up at ! It came, further, to 
my knowledge that the Royal Society if I might judge by the 
claims made by very influential Fellows considered itself as 
entitled to the best of everything : second-best being left for the 
newer bodies. A secretary, in returning thanks for the Royal 
at an anniversary of the Astronomical, gave rather a lecture to 
the company on the positive duty of all present to send the very 
best to the old body, and the absolute right of the old body to 
expect it. An old friend of mine, on a similar occasion, stated as 

c 2 



20 A BUDGET OF PAEADOXES. 

a fact that the thing was always done, as well as that it ought to 
be done. 

Of late years this pretension has been made by a President 
of the Society. In 1855, Lord Eosse presented a confidential 
memorandum to the Council on the expediency of enlarging 
their number. He says, ' In a Council so small it is impossible 
to secure a satisfactory representation of the leading scientific 
Societies, and it is scarcely to be expected that, under such cir- 
cumstances, they will continue to publish inferior papers while 
they send the best to our Transactio'iis.' 1 

And, again, with all the Societies represented on the Council, 
1 even if every Science had its Society, and if they published every- 
thing, withholding their best papers [i.e. from the Eoyal Society], 
which they would not be likely to do, still there would remain to 
the Eoyal Society . . .' Lord Eosse seems to imagine that the 
minor Societies themselves transfer their best papers to the 
Eoyal Society ; that if, for instance, the Astronomical Society 
were to receive from A. B. a paper of unusual merit, the Society 
would transfer it to the Eoyal Society. This is quite wrong : any 
preference of the Eoyal to another Society is the work of the 
contributor himself. But it shows how well hafted is the Eoyal 
Society's claim, that a President should acquire the notion that 
it is acknowledged and acted upon by the other Societies, in their 
joint and corporate capacities. To the pretension thus made I 
never could give any sympathy. When I first heard Mr. Christie, 
Sec. E. S., set it forth at the anniversary dinner of the Astro- 
nomical Society, I remembered the Baron in Walter Scott 

Of Gilbert the Galliard a heriot lie sought, 
Saying, Give thy best steed as a vassal ought. 

And I remembered the answer 

Lord and Earl though thou be, I trow 
I can rein Buck's-foot better than thou. 

Fully conceding that the Eoyal Society is entitled to pre- 
eminent rank and all the respect due to age and services, I 
could not, nor can I now, see any more obligation in a contributor 
to send his best to that Society than he can make out to be due 
to himself. This pretension, in my mind, was hooked on, by 
my historical mode of viewing things already mentioned, to my 
knowledge of the fact that the Eoyal Society the chief fault, 
perhaps, lying with its President, Sir Joseph Banks had sternly 
set itself against the formation of other societies ; the Geological 



INTRODUCTORY. 21 

and Astronomical, for instance, though it must be added that 
the chief rebels came out of the Society itself. And so a certain 
not very defined dislike was generated in my mind an anti- 
aristocratic affair to the body which seemed to me a little too 
uplifted. This would, I daresay, have worn off; but a more 
formidable objection arose. My views of physical science gradu- 
ally arranged themselves into a form which would have rendered 
F.R.S., as attached to my name, a false representation symbol. 
The Royal Society is the great fortress of general physics : and in 
the philosophy of our day, as to general physics, there is some- 
thing which makes the banner of the R.S. one under which I 
cannot march. Everybody who saw the three letters after my 
name would infer certain things as to my mode of thought which 
would not be true inference. It would take much space to explain 
this in full. I may hereafter, perhaps, write a budget of collected 
results of the a priori philosophy, the nibbling at the small 
end of omniscience, and the effect it has had on common life, 
from the family parlour to the jury-box, from the girls'-school 
to the vestry -meeting. There are in the Society those who 
would, were there no others, prevent my criticism, be its con- 
clusions true or false, from having any basis ; but they are in the 
minority. 

There is no objection to be made to the principles of philosophy 
in vogue at the Society, when they are stated as principles ; but 
there is an omniscience in daily practice which the principles 
repudiate. In like manner, the most retaliatory Christians have 
a perfect form of round words about behaviour to those who 
injure them : none of them are as candid as a little boy I knew, 
who, to his mother's admonition, You should love your enemies, 
answered Catch me at it ! 

Years ago, a change took place which would alone have put a 
sufficient difficulty in the way. The co-operative body got tired 
of getting funds from and lending name to persons who had little 
or no science, and wanted F.R.S. to be in every case a Fellow 
Really Scientific. Accordingly, the number of yearly elections was 
limited to fifteen recommended by the Council, unless the general 
body should choose to elect more ; which it does not do. The 
election is now a competitive examination : it is no longer Are you 
able and willing to promote natural knowledge ; it is Are you one 
of the upper fifteen of those who make such claim. In the list of 
candidates a list rapidly growing in number each year shows 
from thirty to forty of those whom Newton and Boyle would have 
gladly welcomed as fellow-labourers. And though the rejected 



22 A BUDGET OF PAKADOXES. 

of one year may be the accepted of the next or of the next but 
one, or but two, if self-respect will permit the candidate to hang 
on yet the time is clearly coming when many of those who 
ought to be welcomed will be excluded for life, or else shelved at 
last, when past work, with a scientific peerage. Coupled with 
this attempt to create a kind of order of knighthood is 'an ab- 
surdity so glaring that it should always be kept before the general 
eye. This distinction, this mark set by science upon successful 
investigation, is of necessity a class-distinction. Rowan Hamilton, 
one of the greatest names of our day in mathematical science, 
never could attach F.R.S. to his name he could not afford it. 
There is a condition precedent Four Red Sovereigns. It is 
four pounds a year, or to those who have contributed to the 
Transactions forty pounds down. This is as it should be : the 
Society must be supported. But it is not as it should be that a 
kind of title of honour should be forged, that a body should take 
upon itself to confer distinctions for science, when it is in the 
background and kept there when the distinction is trumpeted 
that the wearer is a man who can spare four pounds a year. I 
am well aware that in England a person who is not gifted, either 
by nature or art, with this amount of money power, is, with the 
mass, a very second-rate sort of Newton, whatever he may be in 
the field of investigation. Even men of science, so called, have 
this feeling. I know that the scientific advisers of the Admiralty, 
who, years ago, received 100. a year each for his trouble, were 
sneered at by a wealthy pretender as ' fellows to whom a hundred 
a year is an object.' Dr. Thomas Young was one of them. To 
a bookish man I mean a man who can manage to collect books 
there is no tax. To myself, for example, 40L worth of books 
deducted from my shelves, and the life-use of the Society's 
splendid library instead, would have been a capital exchange. 
But there may be, and are, men who want books, and cannot pay 
the Society's price. The Council would be very liberal in allow- 
ing their books to be consulted. I have no doubt that if a known 
investigator were to call and ask to look at certain books, the 
Assistant-Secretary would forthwith seat him with the books 
before him, absence of F.R.S. not in any wise withstanding. But 
this is not like having the right to consult any book on any day, 
and to take it away, if farther wanted. 

So much for the Royal Society as concerns myself. I must add, 
that there is not a spark of party feeling against those who 
wilfully remain outside. The better minds of course know better; 
and the smaller savants look complacently on the idea of an 



INTRODUCTORY. 23 

outer world which makes elite of them. I have done such a 
thing as serve on a committee of the Society, and report on a 
paper : they had the sense to ask, and I had the sense to see that 
none of my opinions were compromised by compliance. And I 
will be of any use which does not involve the status of homo trium 
tiierarum ; as I have elsewhere explained, I would gladly be 
Fautor Realis Scientice, but I would not be taken for Falsce 
Ra'ioiiis Sacerdos. 

Nothing worse will ever happen to me than the smile which 
individuals bestow on a man who does not groove. Wisdom, like 
religion, belongs to majorities ; who can wonder that it should be 
so thought, when it is so clearly pictured in the New Testament 
from one end to the other ? 

The counterpart of paradox, the isolated opinion of one or of 
few, is the general opinion held by all the rest ; and the counter- 
part of false and absurd paradox is what is called the ' vulgar 
error,' the pseudodox. There is one great work on this last subject, 
the Pseudodoxia Epidemica of Sir Thomas Browne, the famous 
author of the Religio Medici:, it usually goes by the name of 
Browne ' On Vulgar Errors ' (1st ed. 1646 ; 6th, 1672). A careful 
analysis of this work would show that vulgar errors are frequently 
opposed by scientific errors ; but good sense is always good sense, 
and Browne's book has a vast quantity of it. 

As an example of bad philosophy brought against bad observa- 
tion. The Amphisbsena serpent was supposed to have two heads, 
one at each end ; partly from its shape, partly because it runs 
backwards as well as forwards. On this Sir Thomas Browne makes 
the following remarks : 

And were there any such species or natural kind of animal, it would 
be hard to make good those six positions of body which, according to 
the three dimensions, are ascribed unto every Animal ; that is, infra, 
supra, ante, retro, dextrosum, sinistrosum : for if (as it is determined) 
that be the anterior and upper part wherein the senses are placed, and 
that the posterior and lower part which is opposite thereunto, there is 
no inferior or former part in this Animal ; for the senses, being placed 
at both extreams, doth make both ends anterior, which is impossible ; 
the terms being Relative, which mutually subsist, and are not without 
each other. And therefore this duplicity was ill contrived to place one 
head at both extreams, and had been more tolerable to Lave settled 
three or four at one. And therefore also Poets have been more reason- 
able than Philosophers, and Geryon or Cerberus less monstrous than 
Amphitbcentk 

There may be paradox upon paradox : and there is a good 
instance in the eighth century in the case of Virgil, an Irishman, 



24 A BUDGET OF PARADOXES. 

Bishop of Salzburg and afterwards Saint, and his quarrels with 
Boniface, an Englishman, Archbishop of Mentz, also afterwards 
Saint. All we know about the matter is, that there exists a 
letter of 748 from Pope Zachary, citing Virgil then, it seems, at 
most a simple priest, though the Pope was not sure even of that 
to Eome to answer the charge of maintaining that there is 
another world (mundus) under our earth (terra), with another 
sun and another moon. Nothing more is known : the letter 
contains threats in the event of the charge being true ; and there 
history drops the matter. Since Virgil was afterwards a Bishop 
and a Saint, we may fairly conclude that he died in the full 
flower of orthodox reputation. It has been supposed and it 
seems probable that Virgil maintained that the earth is peopled 
all the way round, so that under some spots there are antipodes ; 
that his contemporaries, with very dim ideas about the roundness 
of the earth, and most of them with none at all, interpreted him 
as putting another earth under ours turned the other way, 
probably, like the second piece of bread-and-butter in a sandwich, 
with a sun and moon of its own. In the eighth century this 
would infallibly have led to an underground Gospel, an under- 
ground Pope, and an underground Avignon for him to live in. 
When, in later times, the idea of inhabitants for the planets 
was started, it was immediately asked whether they had sinned, 
whether Jesus Christ died for them, whether their wine and their 
water could be lawfully used in the sacraments, &c. 

On so small a basis as the above has been constructed a com- 
panion case to the persecution of Galileo. On one side the 
positive assertion, with indignant comment, that Virgil was 
deposed for antipodal heresy, on the other, serious attempts at 
justification, palliation, or mystification. Some writers say that 
Virgil was found guilty ; others that he gave satisfactory expla- 
nation, and became very good friends with Boniface : for all 
which see Bayle. Some have maintained that the antipodist was 
a different person from the canonised bishop : there is a second 
Virgil, made to order. When your shoes pinch, and will not 
stretch, always throw them away and get another pair : the same 
with your facts. Baronius was not up to the plan of a substitute : 
his commentator Pagi (probably writing about 1690) argues for 
it in a manner which I think Baronius would not have approved. 
This Virgil was perhaps a slippery fellow. The Pope says he 
hears that Virgil pretended licence from him to claim one of 
some new bishoprics : this he declares is totally false. It is part 
of the argument that such a man as this could not have been 



INTRODUCTOKY. 25 

created a Bishop and a Saint: on this point there will be opinions 
and opinions. 1 

Lactantius, four centuries before, had laughed at the antipodes 
in a manner which seems to be ridicule thrown on the idea of the 
earth's roundness. Ptolemy, without reference to the antipodes, 
describes the extent of the inhabited part of the globe in a way 
which shows that he could have had no objection to men turned 
opposite ways. Probably, in the eighth century, the roundness of 
the earth was matter of thought only to astronomers. It should 
always be remembered, especially by those who affirm persecution 
of a true opinion, that but for our knowing from Lactantius that 
the antipodal notion had been matter of assertion and denial 
among theologians, we could never have had any great confidence 
in Virgil really having maintained the simple theory of the exist- 
ence of antipodes. And even now we are not entitled to affirm it 
as having historical proof: the evidence goes to Virgil having 
been charged with very absurd notions, which it seems more 
likely than not were the absurd constructions which ignorant 
contemporaries put upon sensible opinions of his. 

One curious part of this discussion is, that neither side has 
allowed Pope Zachary to produce evidence to character. He 
shall have been an Urban, say the astronomers ; an Urban he 
ought to have been, say the theologians. What sort of man was 
Zachary ? He was eminently sensible and conciliatory ; he con- 
trived to make northern barbarians hear reason in a way which 
puts him high among that section of the early popes who had 
the knack of managing uneducated swordsmen. He kept the 
peace in Italy to an extent which historians mention with ad- 
miration. Even Bale, that .Maharajah of pope-haters, allows 
himself to quote in favour of Zachary, that 'multa Papalem 
dignitatem decentia, eademque pra3clara (scilicet) opera confecit.' 
And this, though so willing to find fault that, speaking of 
Zachary putting a little geographical description of the earth 
on the portico of the Lateran Church, he insinuates that it was 
intended to affirm that the Pope was lord of the whole. Nor 
can he say how long Zachary held the see, except by announcing 
his death in 752, ' cum decem annis pestilentia? sedi praefuisset.' 

1 An Irish antiquary informs me that Virgil is mentioned in annals, at A.I/. 781, as 
1 Verghil, i.e. the geometer, Abbot of Achadhbo [and Bishop of Saltzburg], died in 
Germany in the thirteenth year of his bishoprick.' No allusion is made to his 
opinions ; but it seems he was, by tradition, a mathematician. The Abbot of Aghabo 
(Queen's County) was canonised by Gregory IX., in 1233. The story of the second, 
or scapegoat, Virgil would be much damaged by the character given to the real 
bishop, if there were anything in it to dilapidate. 



26 A BUDGET OF PARADOXES. 

There was another quarrel between Virgil and Boniface which 
is an illustration. An ignorant priest had baptised ' in^nomine 
Patriot, et Filia, et Spiritua Sancta.' Boniface declared the 
rite null and void ; Virgil maintained the contrary ; and Zachary 
decided in favour of Virgil, on the ground that the absurd form 
was only ignorance of Latin, and not heresy. It is hard to believe 
that this man deposed a priest for asserting the whole globe to 
be inhabited. To me the little information that we have seems 
to indicate but not with certainty that Virgil maintained the 
antipodes : that his ignorant contemporaries travestied his theory 
into that of an underground cosmos ; that the Pope cited him 
to Eome to explain his system, which, as reported, looked like 
what all would then have affirmed to be heresy ; that he gave 
satisfactory explanations, and was dismissed with honour. It 
may be that the educated Greek monk, Zachary, knew his 
Ptolemy well enough to guess what the asserted heretic would 
say ; we have seen that he seems to have patronised geography. 
The description of the earth, according to historians, was a map ; 
this Pope may have been more ready than another to prick up his 
ears at any rumour of geographical heresy, from hope of informa- 
tion. And Virgil, who may have entered the sacred presence as 
frightened as Jacquard, when Napoleon I. sent for him and said, 
with a stern voice and threatening gesture, ' You are the man who 
can tie a knot in a stretched string,' may have departed as well 
pleased as Jacquard with the riband and pension which the inter- 
view was worth to him. 

A word more about Baronius. If he had been pope, as he 
would have been but for the opposition of the Spaniards, and if 
he had lived ten years longer than he did, and if Clavius, who 
would have been his astronomical adviser, had lived five years 
longer than he did, it is probable, nay almost certain, that the 
great exhibition, the proceeding against Galileo, would not have 
furnished a joke against theology in all time to come. For 
Baronius was sensible and witty enough to say that in the Scrip- 
tures the Holy Spirit intended to teach how to go to Heaven, 
not how Heaven goes ; and Clavius, in his last years, confessed 
that the whole system of the heavens had broken down, and 
must be mended. 

The manner in which the Galileo case, a reality, and the 
Virgil case, a fiction, have been hawked against the Eoman see 
are enough to show that the Pope and his adherents have not 
cared much about physical philosophy. In truth, orthodoxy has 



INTRODUCTORY. 27 

always had other fish to fry. Physics, which in modern times 
has almost usurped the name philosophy, in England at least, 
has felt a little disposed to clothe herself with all the honours 
of persecution which belong to the real owner of the name. 
But the bishops, &c. of the middle ages knew that the contest 
between nominalism and realism, for instance, had a hundred 
times more bearing upon orthodoxy than anything in astronomy, 
&c. A wrong notion about substance might play the mischief 
with transubstantiation. 

The question of the earth's motion was the single point in 
which orthodoxy came into real contact with science. Many 
students of physics were suspected of magic, many of atheism : but, 
stupid as the mistake may have been, it was bond fide the magic or 
the atheism, not the physics, which was assailed. In the astro- 
nomical case it was the very doctrine, as a doctrine, indepen- 
dently of consequences, which was the corpus delicti : and this 
because it contradicted the Bible. And so it did ; for the stability 
of the earth is as clearly assumed from one end of the Old Testa- 
ment to the other as the solidity of iron. Those who take the 
Bible to be totidem, verbis dictated by the God of Truth can 
refuse to believe it; and they make strange reasons. They 
undertake, a prioi*i, to settle Divine intentions. The Holy Spirit 
did not mean to teach natural philosophy : this they know before- 
hand ; or else they infer it from finding that the earth does move, 
and the Bible says it does not. Of course, ignorance apart, every 
word is truth, or the writer did not mean truth. But this puts 
the whole book on its trial : for we never can find out what the 
writer meant, until we otherwise find out what is true. Those 
who like may, of course, declare for an inspiration over which 
they are to be viceroys ; but common sense will either accept 
verbal meaning or deny verbal inspiration. 



28 A BUDGET OF PARADOXES. 



Questiones Morales, folio, 1489 [Paris]. By T. Buridan. 

This is the title from the Hartwell Catalogue of Law Books. I 
suppose it is what is elsewhere called the ' Commentary on the 
Ethics of Aristotle,' printed in 1489. Buridan (died about 1358) 
is the creator of the famous ass which, as Burdin's ass, was cur- 
rent in Burgundy, perhaps is, as a vulgar proverb. Spinoza says 
it was a jenny ass, and that a man would not have been so foolish ; 
but whether the compliment is paid to human or to masculine 
character does not appear perhaps to both in one. The story 
told about the famous paradox is very curious. The Queen of 
France, Joanna or Jeanne, was in the habit of sewing her lovers 
up in sacks, and throwing them into the Seine ; not for blab- 
bing, but that they might not blab certainly the safer plan. 
Buridan was exempted, and, in gratitude, invented the sophism. 
What it has to do with the matter has never been explained. 
Assuredly qui facit per alium facit per se will convict Buridan 
of prating. The argument is as follows, and is seldom told in 
full. Buridan was for free-will that is, will which determines 
conduct, let motives be ever so evenly balanced. An ass is equally 
pressed by hunger and by thirst ; a bundle of hay is on one side, 
a pail of water on the other. Surely, you will say, he will not be 
ass enough to die for want of food or drink ; he will then make 
a choice that is, will choose between alternatives of equal force. 
The problem became famous in the schools ; some allowed the 
poor donkey to die of indecision ; some denied the possibility of 
the balance, which was no answer at all. 

The following question is more difficult, and involves free-will 
to all who answer ' Which you please.' If the northern hemisphere 
were land, and all the southern hemisphere water, ought we to 
call the northern hemisphere an island, or the southern hemisphere 
a lake ? Both the questions would be good exercises for paradoxers 
who must be kept employed, like Michael Scott's devils. The 
wizard knew nothing about squaring the circle, &c., so he set 
them to make ropes out of sea sand, which puzzled them. Stupid 
devils ! much of our glass is sea sand, and it makes beautiful 
thread. Had Michael set them to square the circle or to find 
a perpetual motion, he would have done his work much better. 
But all this is conjecture : who knows that I have not hit on the 
very plan he adopted ? Perhaps the whole race of paradoxers 
on hopeless subjects are Michael's subordinates, condemned to 
transmigration after transmigration, until their task is done. 



THE BUDGET OPENED BURIDAN. 29 

The above was not a bad guess. A little after the time when 
the famous Pascal papers were produced, I came into possession 
of a correspondence which, but for these papers, I should have 
held too incredible to be put before the world. But when one 
sheep leaps the ditch, another will follow : so I gave the following- 
account in the Athenceum of October 5, 1867 : 

The recorded story is that Michael Scott, being bound by contract 
to procure perpetual employment for a number of young demons, was 
worried out of his life in inventing jobs for them, until at last he set 
them to make ropes out of sea sand, which they never could do. We 
have obtained a very curious correspondence between the wizard 
Michael and his demon-slaves ; but we do not feel at liberty to say how 
it came into our hands. We much regret that we did not receive it 
in time for the British Association. It appears that the story, true as 
far as it goes, was never finished. The demons easily conquered the 
rope difficulty, by the simple process of making the sand into glass, 
and spinning the glass into thread, which they twisted. Michael, 
thoroughly disconcerted, hit upon the plan of setting some to square 
the circle, others to find the perpetual motion, &c. He commanded 
each of them to transmigrate from one human body into another, until 
their tasks were done. This explains the whole succession of cyclo- 
meters, and all the heroes of the Budget. Some of this correspondence 
is very recent ; it is much blotted, and we are not quite sure of its 
meaning : it is full of figurative allusions to driving something illegible 
down a steep into the sea. It looks like a humble petition to be 
allowed some diversion iu the intervals of transmigration ; and the 

answer is 

Rumpat et serpens iter institutum, 

a line of Horace, which the demons interpret as a direction to come 
athwart the proceedings of the Institute by a sly trick. Until we saw 
this, we were suspicious of M. Libri : the unvarying blunders of the 
correspondence look like knowledge. To be always out of the road 
requires a map : genuine ignorance occasionally lapses into truth. We 
thought it possible M. Libri might have played the trick to show how 
easily the French are deceived ; but with our present information, our 
minds are at rest on the subject. We see M. Chasles does not like to 
avow the real source of information : lie will not confess himself a 
spiritualist. 



30 A BUDGET OF PARADOXES. 

Philo of Gradara is asserted by Montucla, on the authority of 
Eutocius, the commentator on Archimedes, to have squared the 
circle within the ten-thousandth part of a unit, that is, to four 
places of decimals. A modern classical dictionary represents it as 
done by Philo to ten thousand places of decimals. Lacroix com- 
ments on Montucla to the effect that myriad (in Greek ten thou- 
sand] is here used as we use it, vaguely, for an immense number. 
On looking into Eutocius, I find that not one definite word is 
said about the extent to which Philo carried the matter. I give 
a translation of the passage : 

We ought to know that Apollonius Pergseus, in his Ocytocium [this 
work is lost], demonstrated the same by other numbers, and came 
nearer, which seems more accurate, but has nothing to do with 
Archimedes ; for, as before said, he aimed only at going near enough 
for the wants of life. Neither is Porus of Nicaea fair when he takes 
Archimedes to task for not giving a line accurately equal to the 
circumference. He says in his Cerii that his teacher, Philo of Gadara, 
had given a more accurate approximation (etc tucpifiemipove opiflyuovg 
ayayetv) than that of Archimedes, or than 7 to 22. But all these [the 
rest as well as Philo] miss the intention. They multiply and divide by 
tens of thousands, which no one can easily do, unless he be versed in 
the logistics [fractional computation] of Magnus [now unknown]. 

Montucla, or his source, ought not to have made this mistake. 
He had been at the Greek to correct Philo Gadetanus, as he had 
often been called, and he had brought away and quoted airo 
TaSapwv. Had he read two sentences further, he would have 
found the mistake. 

We here detect a person quite unnoticed hitherto by the 
moderns, Magnus the arithmetician. The phrase is ironical ; it 
is as if we should say, ' To do this a man must be deep in Cocker.' 
Accordingly, Magnus, Baveme, and Cocker, are three personifica- 
tions of arithmetic ; and there may be more. 

Aristotle, treating of the category of relation, denies that the 
quadrature has been found, but appears to assume that it can be 
done. Boethius, in his comment on the passage, says that it has 
been done since Aristotle, but that the demonstration is too long 
for him to give. Those who have no notion of the quadrature 
question may look at the English Cyclopaedia, art. 'Quadrature 
of the Circle.' 



EAKLY CIRCLE SQUARERS. 31 



Tetragonismus. Id est circuli quadratura per Campanula, 
Archimedem Syracusanum, atque Boetium mathematicse per- 
spicacissimos adinventa. At the end, Impressum Venetiis per 
loan. Bapti. Sessa. Anno ab incarnatione Domini, 1503. Die 
28 Augusti. 

This book has never been noticed in the history of the subject, 
and I cannot find any mention of it. The quadrature of Campanus 
takes the ratio of Archimedes, 7 to 22, to be absolutely correct ; 
the account given of Archimedes is not a translation of his book ; 
and that of Boetius has more than is in BoetAius. This book 
must stand, with the next, as the earliest in print on the subject, 
until further showing : Murhard and Kastner have nothing so 
early. It is edited by Lucas Gauricus, who has given a short 
preface. Luca Gaurico, Bishop of Civita Ducale, an astrologer 
of astrologers, published this work at about thirty years of age, 
and lived to eighty-two. His works are collected in folios, but I 
do not know whether they contain this production. The poor fellow 
could never tell his own fortune, because his father neglected to 
note the hour and minute of his birth. But if there had been 
anything in astrology, he could have worked back, as Adams and 
Leverrier did when they caught Neptune : at sixty he could have 
examined every minute of his day of birth, by the events of his 
life, and so would have found the right minute. He could then 
have gone on, by rules of prophecy. Gauricus was the mathe- 
matical teacher of Joseph Scaliger, who did him no credit, as we 
shall see. 

In hoc opere contenta Epitome Liber de quadratura 

Circuli Paris, 1503, folio. 

The quadrator is Charles Bovillus, who adopted the views of 
Cardinal Cusa, presently mentioned. Montucla is hard on his 
compatriot, who, he says, was only saved from the laughter of 
geometers by his obscurity. Persons must guard against most 
historians of mathematics in one point : they frequently attribute 
to Jns oivn age the obscurity which a writer has in their own time. 
This tract was printed by Henry Stephens, at the instigation of 
Faber Stapulensis, and is recorded by Dechales, &c. It was also 
introduced into the 'Margarita Philosophica' of 1815, in the 
same appendix with the new perspective from Viator. This is not 
extreme obscurity, by any means. The quadrature deserved it ; 
but that is another point. 



32 A BUDGET OF PARADOXES. 

It is stated by Montucla that Bovillus makes TT VW. But 
Montucla cites a work of 1507, Introductorium Geometricum., 
which I have never seen. He finds in it an account which 
Bovillus gives of the quadrature of the peasant labourer, and 
describes it as agreeing with his own. But the description makes 
TT = 3, which it thus appears Bovillus could not distinguish 
from V 10. It seems also that this 3, about which we shall see 
so much in the sequel, takes its rise in the thoughtful head of a 
poor labourer. It does him great honour, being so near the truth, 
and he having no means of instruction. In our day, when an 
ignorant person chooses to bring his fancy forward in opposition 
to demonstration which he will not study, he is deservedly 
laughed at. 

Mr. James Smith, of Liverpool hereinafter notorified attri- 
butes the first announcement of 3^ to M. Joseph Lacornme, a 
French well-sinker, of whom he gives the following account : 

In the year 1836, at which time Lacomme could neither read nor 
write, he had constructed a circular reservoir and wished to know the 
quantity of stone that would be required to pave the bottom, and for 
this purpose called on a professor of mathematics. On putting his 
question and giving the diameter, he was surprised at getting the 
following answer from the Professor ' Qu'il lui e'ait impossible de le lid 
dire au juste, attendu quepersonne n'avait encore pu trouver d'une maniere 
exacte le rapport de la circonference au diametre.' From this he was 
led to attempt the solution of the problem. His first process was 
purely mechanical, and he was so far convinced he had made the dis- 
covery that he took to educating himself, and became an expert 
arithmetician, and then found that arithmetical results agreed with his 
mechanical experiments. He appears to have eked out a bare existence 
for many years by teaching arithmetic, all the time struggling to get a 
hearing from some of the learned societies, but without success. In 
the year 1855 he found his way to Paris, where, as if by accident, he 
made the acquaintance of a young gentleman, son of M. Winter, a 
commissioner of police, and taught him his peculiar methods of calcu- 
lation. The young man was so enchanted that he strongly recom- 
mended Lacomme to his father, and subsequently through M. Winter 
he obtained an introduction to the President of the Society of Arts and 
Sciences of Paris. A committee of the society was appointed to 
examine and report upon his discovery, and the society at its seance 
of March 17, 1856, awarded a silver medal of the first class to 
M. Joseph Lacomme for his discovery of the true ratio of diameter 
to circumference in a circle. He subsequently received three other 
medals from other societies. While writing this I have his likeness 
before me, with his medals on his breast, which stands as a frontispiece 



NICHOLAS OF CUSA AGRIPPA. 33 

to a short biography of this extraordinary man, for which I am in- 
debted to the gentleman who did me the honour to publish a French 
translation of the pamphlet I distributed at the meeting of the British 
Association for the Advancement of Science, at Oxford, in 1860. 
Correspo-ndent, May 3, 1866. 

My inquiries show that the story of the medals is not incredible. 
There are at Paris little private societies which have not so much 
claim to be exponents of scientific opinion as our own Mechanics' 
Institutes. Some of them were intended to give a false lustre : as 
the * Institut Historique,' the members of which are ' Membre de 
1'Institut Historique.' That M. Lacomme should have got four 
medals from societies of tbis class is very possible : that be should 
have received one from any society at Paris wbicb bas tbe least 
claim to give one is as yet simply incredible. 

Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio. 

The real title is 'Haec accurata recognitio trium voluminum 
operum clariss. P. Nicolai Cusse . , . proximo sequens pagina 
monstrat.' Cardinal Cusa, wbo died in 1464, is one of tbe earliest 
modern attempters. His quadrature is found in tbe second 
volume, and is now quite unreadable. In these early days every 
quadrator found a geometrical opponent, wbo finished him. 
Eegiomontanus did tbis office for tbe Cardinal. 

De Occulta Philosophia libri III. By Henry Cornelius Agrippa. 

Lyons, 1550, 8vo. 
De incertitudine et vanitate scientiarum. By the same. Cologne, 

1531, 8vo. 

Tbe first editions of these works were of 1530, as well as I can 
make out; but tbe first was in progress in 1510. In the second 
work Agrippa repents of having wasted time on the magic of tbe 
first ; but all those who actually deal witb demons are destined 
to eternal fire witb Jamnes and Mambres and Simon Magus. 
This means, as is tbe fact, that his occult philosophy did not actu- 
ally enter upon black magic, but confined itself to the power of 
tbe stars, of numbers, &c. The fourth book, which appeared after 
tbe deatb of Agrippa, and really concerns dealing witb evil spirits, 
is undoubtedly spurious. It is very difficult to make out what 
Agrippa really believed on tbe subject. I have introduced his 
books as the most marked specimens of treatises on magic, a 
paradox of our day, though not far from orthodoxy in bis ; and 
bere I should have ended my notice, if I had not casually found 
something more interesting to tbe reader of our day. 

D 



34 A BUDGET OF PARADOXES. 

Walter Scott, it is well known, was curious on all matters 
connected with magic, and has used them very widely. But it is 
hardly known how much pains he has taken to be correct, and to 
give the real thing. The most decided detail of a magical pro- 
cess which is found in his writings is that of Dousterswivel in 
' The Antiquary ' ; and it is obvious, by his accuracy of process, 
that he does not intend the adept for a mere impostor, but for 
one who had a lurking belief in the efficacy of his own processes, 
coupled with intent to make a fradulent use of them. The 
materials for the process are taken from Agrippa. I first quote 
Mr. Dousterswivel : 

... I take a silver plate when she [the moon] is in her fifteenth 
mansion, which mansion is in de head of Libra, and I engrave upon one 
side de worts Schedbarschemoth Schartachan \_ch should be t~\ dat is, 
de Intelligence of de Intelligence of de moon and I make his picture 
like a flying serpent with a turkey-cock's head vary well Then upon 
this side I make de table of de moon, which is a square of nine, 
multiplied into itself, with eighty-one numbers [nine] on every side, 
and diameter nine. . . . 

In the'De Occulta Philosophia,' p. 290, we find that the 
fifteenth mansion of the moon incipit capite Librae, and is good 
pro extrahendis thesauris, the object being to discover hidden 
treasure. In p. 246, we learn that a silver plate must be used 
with the moon. In p. 248, we have the words which denote the 
Intelligence, &c. But, owing to the falling of a number into a 
wrong line, or the misplacement of a line, one or other which 
takes place in all the editions I have examined Scott has, sad 
to say, got hold of the wrong words ; he has written down the 
demon of the demons of the moon. Instead of the gibberish 
above, it should have been Malcha betharsisim hed beruah sche- 
hakim. In p. 253, we have the magic square of the moon, with 
eighty-one numbers, and the symbol for the Intelligence, which 
Scott likens to a flying serpent with a turkey-cock's head. He 
was obliged to say something ; but I will stake my character 
and so save a woodcut on the scratches being more like a pair 
of legs, one shorter than the other, without a body, jumping over 
a six-barred gate placed side uppermost. Those who thought 
that Scott forged his own nonsense, will henceforth stand corrected. 
As to the spirit Peolphan, &c., no doubt Scott got it from the 
authors he elsewhere mentions, Nicolaus Remigius and Petrus 
Thyracus ; but this last word should be Thyraeus. 

The tendency of Scott's mind towards prophecy is very marked, 



OEONTIUS FINAEUS-URSUS. 35 

and it is always fulfilled. Hyder, in his disguise, calls out to 
Tippoo ' Cursed is the prince who barters justice for lust ; he 
shall die in the gate by the sword of the stranger.' Tippoo was 
killed in a gateway at Seringapatam. 

Orontii Finaei. . . Quadrature Circuli. Paris, 1544, 4to. 

Orontius squared the circle out of all comprehension ; but he 
was killed by a feather from his own wing. His former pupil, 
John Buteo, the same who I believe for the first time calculated 
the question of Noah's ark, as to its power to hold all the animals 
and stores, unsquared him completely. Orontius was the author 
of very many works, and died in 1555. Among the laudatory 
verses which, as was usual, precede this work, there is one of a 
rare character : a congratulatory ode to the wife of the author. 
The French now call this writer Oronce Finee ; but there is much 
difficulty about delatinisation. Is this more correct than Oronce 
Fine, which the translator of De Thou uses ? Or than Horonce 
Phine, which older writers give ? I cannot understand why M. 
de Viette should be called Viete, because his Latin name is Vieta. 
It is difficult to restore Buteo ; for not only now is butor a block- 
head as well as a bird, but we really cannot know what kind of 
bird Buteo stood for. We may be sure that Madame Fine was 
Denise Blanche ; for Dionysia Candida can mean nothing else. 
Let her shade rejoice in the fame which Hubertus Sussannaeus 
has given her. 

I ought to add that the quadrature of Orontius, and solutions 
of all the other difficulties, were first published in * De Kebus 
Mathematicis Hactenus Desideratis,' of which I have not the date. 

Nicolai Baymari Ursi Dithmarsi Fundamentum Astronomicum, 
id est, nova doctrina sinuum et triangulorum. . . . Strasburg, 
1588, 4to. 

People choose the name of this astronomer for themselves : I 
take Ursus, because he was a bear. This book gave the quadra- 
ture of Simon Duchesne, or a Quercu, which excited Peter Metius, 
as presently noticed. It also gave that unintelligible reference to 
Justus Byrgius which has been used in the discussion about the 
invention of logarithms. 

The real name of Duchesne is Van der Eycke. I have met 
with a tract in Dutch, Letterkundige Aanteekeningen, upon Van 
Eycke, Van Ceulen, &c., by J. J. Dodt van Flensburg, which I 
make out to be since 1841 in date. I should much like a trans- 

2 



36 A BUDGET OF PARADOXES. 

lation of this tract to be printed, say in the Phil. Mag. Dutch 
would be clear English if it were properly spelt. For example, 
learn-master would be seen at once to be teacher ; but they will 
spell it leermeester. Of these they write as van deze; widow 
they make weduwe. All this is plain to me, who never saw a 
Dutch dictionary in my life ; but many of their mispellings are 
quite unconquerable. 

Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli 
quadraturam invenit. Antwerp, 1589, 4to. 

The attempt is more than commonly worthless ; but as Mon- 
tucla and others have referred to the verses at the end, and as the 
tract is of the rarest, I will quote them : 

Circulus loquitur. 

Vocabar ante circulus 
Eramque curvus undique 
Ut alta solis orbita 
Et arcus ille nubium. 
Eram figura nobilis 
Carensque sola origine 
Carensque sola termino. 
Modo indecora prodeo 
Novisque foedor angulis. 
Nee hoc peregit Archytas 
Neque Icari pater neque 
THUS lapete filius. 
Quis ergo casus aut Deus 
Meam quadravit aream ? 

Hespondet auctor. 

Ad alta Turiee ostia 
Lacumque limpidissimum 
Sita est beata ci vitas 
Parum Saguntus abfuit 
Abestque Sucro plusculum. 
Hie est poeta quispiam 
Libenter astra consulens 
Sibique semper arrogans 
Negata doctioribus. 
Senex ubique cogitans 
Sui frequenter immemor 
Nee explicare circinum 



PETER BUNGUS. 37 

Nee exarare lineas 
Sciens ut ipse praedicat. 
Hie ergo bellus artifex 
Tuam quadra vit aream. 

Falco's verses are pretty, if the w ~ mysteries be correct ; but of 
these things I have forgotten what I knew. [One mistake has 
been pointed out to me : it is Archytas]. 

As a specimen of the way in which history is written, I copy 
the account which Montucla who is accurate when he writes 
about what he has seen gives of these verses. He gives the date 
1587 ; he places the verses at the beginning instead of the end; 
he says the circle thanks its quadrator affectionately ; and he 
says the good and modest chevalier gives all the glory to the 
patron saint of his order. All of little consequence, as it happens ; 
but writing at second-hand makes as complete mistakes about 
more important matters. 

Petri Biingi Bergomatis Numeronim mysteria. Bergomi [Ber- 
gamo], 1591, 4to. Second Edition. 

The first edition is said to be of 1585 ; the third, Paris, 1618. 
Bungus is not for my purpose on his own score, but those who 
gave the numbers their mysterious characters : he is but a collector. 
He quotes or uses 402 authors, as we are informed by his list : 
this just beats Warburton, whom some eulogist or satirist, I forget 
which, holds up as having used 400 authors in some one work. 
Bungus goes through 1, 2, 3, &c., and gives the account of every- 
thing remarkable in which each number occurs ; his accounts not 
being always mysterious. The numbers which have nothing to 
say for themselves are omitted : thus there is a gap between 50 
and 60. In treating 666, Bungus, a good Catholic, could not 
compliment the Pope with it, but he fixes it on Martin Luther 
with a little forcing. If from A to I represent 1-10, from K to 
S 10-90, and from T to Z 100-500, we see 

MARTIN LU TERA 

30 1 80 100 9 40 20 200 100 5 80 1 

which gives 666. Again, in Hebrew, Lulter does the same : 

i n h 1 *> 
200 400 30 6 30 

And thus two can play at any game. The second is better 
than the first : to Latinise the surname and not the Christian 
name is very unscholarlike. The last number mentioned is a 



38 A BUDGET OF PARADOXES. 

thousand millions ; all greater numbers are dismissed in half a 
page. Then follows an accurate distinction between number 
and multitude a thing much wanted both in arithmetic and 
logic. 

What may be the use of such a book as this ? The last occa- 
sion on which it was used was the following. Fifteen or sixteen 
years ago the Koyal Society determined to restrict the number of 
yearly admissions to fifteen men of science, and noblemen ad 
libitum ; the men of science being selected and recommended by 
the Council, with a power, since practically surrendered, to the 
Society to elect more. This plan appears to me to be directly 
against the spirit of their charter, the true intent of which is, 
that all who are fit should be allowed to promote natural know- 
ledge in association, from and after the time at which they are 
both fit and willing. It is also working more absurdly from year 
to year ; the tariff of fifteen per annum will soon amoirnt to the 
practical exclusion of many who would be very useful. This 
begins to be felt already, I suspect. But, as appears above, the 
body of the Society has the remedy in its own hands. When the 
alteration was discussed by the Council, my friend the late Mr. 
Gralloway, then one of the body, opposed it strongly, and in- 
quired particularly into the reason why fifteen, of all numbers, 
was the one to be selected. Was it because fifteen is seven and 
eight, typifying the Old Testament Sabbath, and the New Testa- 
ment day of the resurrection following ? Was it because Paul 
strove fifteen days against Peter, proving that he was a doctor 
both of the Old and New Testament ? Was it because the prophet 
Hosea bought a lady for fifteen pieces of silver ? Was it because, 
according to Micah, seven shepherds and eight chiefs should 
waste the Assyrians? Was it because Ecclesiastes commands 
equal reverence to be given to both Testaments such was the 
interpretation in the words ' Give a portion to seven, and also 
to eight ' ? Was it because the waters of the Deluge rose fifteen 
cubits above the mountains ? or because they lasted fifteen 
decades of days ? Was it because Ezekiel's temple had fifteen 
steps ? Was it because Jacob's ladder has been supposed to have 
had fifteen steps ? Was it because fifteen years were added to 
the life of Hezekiah ? Was it because the feast of unleavened 
bread was on the fifteenth day of the month ? Was it because 
the scene of the Ascension was fifteen stadia from Jerusalem ? 
Was it because the stone-masons and porters employed in 
Solomon's temple amounted to fifteen myriads ? &c. The Council 
were amused and astounded by the volley of fifteens which was 



THE FIFTEENS OF BUNGUS. 39 

fired at them ; they knowing nothing about Bungus, of which 
Mr. Gralloway who did not, as the French say, indicate his 
sources possessed the copy now before me. In giving this 
anecdote I give a specimen of the book, which is exceedingly rare. 
Should another edition ever appear, which is not very probable, 
he would be but a bungling Bungus who should forget the fifteen 
of the Royal Society. 

[I make a remark on the different colours which the same 
person gives to one story, according to the bias under which he 
tells it. My friend Galloway told me how he had quizzed the 
Council of the Royal Society, to my great amusement. When- 
ever I am struck by the words of any one, I carry away a vivid 
recollection of position, gestures, tones, &c. I do not know 
whether this be common or uncommon. I never recall this joke 
without seeing before me my friend, leaning against his book- 
case, with Bungus open in his hand, and a certain half-deprecia- 
tory tone which he often used when speaking of himself. Long 
after his death, an F.E.S. who was present at the discussion, told 
me the story. I did not say I had heard it, but I watched him, 
with Gralloway at the bookcase before me. I wanted to see 
whether the two would agree as to the fact of an enormous 
budget of fifteens having been fired at the Council, and they 
did agree perfectly. But when the paragraph of the Budget 
appeared in the Athenaeum, my friend, who seemed rather to 
object to the shewing-up, assured me that the thing was grossly 
exaggerated ; there was indeed a fifteen or two, but nothing like 
the number I had given. I had, however, taken sharp note of 
the previous narration. 

I will give another instance. An Indian officer gave me an 
account of an elephant, as follows. A detachment was on the 
march, and one of the gun-carriages got a wheel off the track, 
so that it was also off the ground, and hanging over a precipice. 
If the bullocks had moved a step, carriages, bullocks, and all 
must have been precipitated. No one knew what could be done 
until some one proposed to bring up an elephant, and let him 
manage it his own way. The elephant took a moment's survey of 
the fix, put his trunk under the axle of the free wheel, and waited. 
The surrounders, who saw what he meant, moved the bullocks 
gently forward, the elephant followed, supporting the axle, until 
there was ground under the wheel, when he let it quietly down. 
From all I had heard of the elephant, this was not too much 
to believe. But when, years afterwards, I reminded my friend 



40 A BUDGET OF PARADOXES. 

of his story, he assured me that I had misunderstood him, that 
the elephant was directed to put his trunk under the wheel, and 
saw in a moment why. This is reasonable sagacity, and very 
likely the correct account ; but I am quite sure that, in the fit 
of elephant-worship under which the story was first told, it was 
told as I have first stated it.] 

[Jordani Bruni Nolani de Monade, Numero et Figura . . . item de 
Innumerabilibus, Immense, et Infigurabili. . . Frankfort, 1591, 
8vo. 

I cannot imagine how I came to omit a writer whom I have 
known so many years, unless the following story will explain it. 
The officer reproved the boatswain for perpetual swearing ; the 
boatswain answered that he heard the officers swear. ' Only in 
an emergency,' said the officer. 'That's just it,' replied the 
other ; ' a boatswain's life is a life of 'mergency.' OKordano 
Bruno was all paradox ; and my mind was not alive to his 
paradoxes, just as my ears might have become dead to the boat- 
swain's oaths. He was, as has been said, a vorticist before 
Descartes, an optimist before Leibnitz, a Copernican before 
Gralileo. It would be easy to collect a hundred strange opinions 
of his. He was born about 1550, and was roasted alive at Rome, 
February 17, 1600, for the maintenance and defence of the holy 
Church, and the rights and liberties of the same. These last 
words are from the writ of our own good James I., under which 
Leggatt was roasted at Smithfield, in March 1612 ; and if I had a 
.copy of the instrument under which Wightman was roasted at 
Litchfield, a month afterwards, I daresay I should find something 
quite as edifying. 1 extract an account which I gave of Bruno 
in the Comp. Aim. for 1855 : 

He was first a Dominican priest, then a Calvinist ; and was roasted 
alive "at Rome, in 1600, for as many heresies of opinion, religious and 
philosophical, as ever lit one fire. Some defenders of the papal cause 
Lave at least worded their accusations so to be understood as imputing 
to him villainous actions. But it is positively certain that his death 
was due to opinions alone, and that retractation, even after sentence, 
would have saved him. There exists a remarkable letter, written from 
Home on the very clay of the murder, by Scioppius (the celebrated 
scholar, a waspish convert from Lutheranism, known by his hatred to 
Protestants and Jesuits) to Rittershusius, a well-known Lutheran 
writer on civil and cation law, whose works are in the index of prohi- 
bited books. This letter has been reprinted by Libri (vol. iv. p. 407). 
The writer informs his friend (whom he wished to convince that even a 
Lutheran would have burnt Bruno) that all Rome would tell him that 



GIOKDANO BBUNO. 41 

Bruno died for Lutheranism ; but this is because the Italians do not 
know the difference between one heresy and another, in which simpli- 
city (says the writei*) may God preserve them. That is to say, they 
knew the difference between a live heretic and a roasted one by actual 
inspection, but had no idea of the difference between a Lutheran and a 
Calvinist. The countrymen of Boccaccio would have smiled at the idea 
which the German scholar entertained of them. They said Bruno was 
burnt for Lutheranism, a name under which they classed all Protestants : 
and they are better witnesses than Schopp, or Scioppius. He then 
proceeds to describe to big Protestant friend (to whom he would 
certainly not have omitted any act which both their Churches would 
have condemned) the mass of opinions with which Bruno was charged ; 
as that there are innumerable worlds, that souls migrate, that Moses 
was a magician, that the Scriptures are a dream, that only the Hebrews 
descended from Adam and Eve, that the devils would be saved, that 
Christ was a magician and deservedly put to death, &c. In fact, says 
he, Bruno has advanced all that was ever brought forward by all 
heathen philosophers, and by all heretics, ancient and modern. A time 
for retractation was given, both before sentence and after, which should 
be noted, as well for the wretched palliation which it may afford, as for 
the additional proof it gives that opinions, and opinions only, brought 
him to the stake. In this medley of charges the Scriptures are a dream, 
while Adam, Eve, devils, and salvation are truths, and the Saviour a 
deceiver. We have examined no work of Bruno except the De Monade, 
8fc., mentioned in the text. A strong though strange theism runs 
through the whole, and Moses, Christ, the Fathers, &c., are cited in a 
manner which excites no remark either way. Among the versions of 
the cause of Bruno's death is atheism : but this word was very often 
used to denote rejection of revelation, not merely in the common course 
of dispute, but by such writers, for instance, as Brucker and Morhof. 
Thus Morhof says of the De Monade, 8fc., that it exhibits no manifest 
signs of atheism. What he means by the word is clear enough, when 
he thus speaks of a work which acknowledges God in hundreds of 
places, and rejects opinions as blasphemous in several. The work of 
Bruno in which his astronomical opinions are contained is De Monade, 
8fc. (Frankfort, 1591, 8vo). He is the most thorough-going Copernican 
possible, and throws out almost every opinion, true or false, which has 
ever been discussed by astronomers, from the theory of innumerable 
inhabited worlds and systems to that of the planetary nature of comets. 
Libri (vol. iv.) has reprinted the most striking part of his expressions 
of Coperuican opinion. 

The Satanic doctrine that a Church may employ force in aid 
of its dogma is supposed to be obsolete in England, except as an 
individual paradox ; but this is difficult to settle. Opinions 
are much divided as to what the Roman Church would do in 



42 A BUDGET OE PAKADOXES. 

England, if she could : any one who doubts that she claims the 
right does not deserve an answer. When the hopes of the 
Tractarian section of the High Church were in bloom, before the 
most conspicuous intellects among them had transgressed their 
ministry, that they might goto their own place, I had the curiosity 
to see how far it could be ascertained whether they held the 
only doctrine which makes me the personal enemy of a sect. I 
found in one of their tracts the assumption of a right to per- 
secute, modified by an asserted conviction that force was not 
efficient. I cannot now say that this tract was one of the 
celebrated ninety ; and on looking at the collection I find it so 
poorly furnished with contents, &c., that nothing but searching 
through three thick volumes would decide. In these volumes I 
find, augmenting as we go on, declarations about the character 
and power of ' the Church ' which have a suspicious appearance. 
The suspicion is increased by that curious piece of sophistry, 
No. 87, on religious reserve. The queer paradoxes of that tract 
leave iis in doubt as to everything but t^his, that the church(man) 
is not bound to give his whole counsel in all things, and not 
bound to say what the things are in which he does not give it. 
It is likely enough that some of the ' rights and liberties ' are 
but scantily described. There is now no fear ; but the time was 
when, if not fear, there might be a looking for of fear to come ; 
nobody could then be so sure as we now are that the lion was 
only asleep. There was every appearance of a harder fight at 
hand than was really found needful. 

Among other exquisite quirks of interpretation in the No. 87 
above mentioned is the following. GTod himself employs re- 
serve ; he is said to be decked with light as with a garment (the 
old or prayer-book version of Psalm civ. 2). To an ordinary 
apprehension this would be a strong image of display, manifesta- 
tion, revelation ; but there is something more. ' Does not a 
garment veil in some measure that which it clothes ? Is not 
that very light concealment ? ' 

This No. 87, admitted into a series, fixes upon the managers 
of the series, who permitted its introduction, a strong presump- 
tion of that underhand intent with which they were charged. 
At the same time it is honourable to our liberty that this series 
could be published : though its promoters were greatly shocked 
when the Essayists and Bishop Colenso took a swing on the 
other side. When No. 90 was under discussion, Dr. Maitland, 
the librarian at Lambeth, asked Archbishop Howley a question 
about No. 89. * I did not so much as know there was a No. 89^ 



RITUALISM. I-! 

was the answer. I am almost sure I have seen this in print, 
and quite sure that Dr. Maitland told it to me. It is creditable 
that there was so much freedom ; but No. 90 was too bad, and 
was stopped. 

The Tractarian mania has now (October 1866) settled down 
into a chronic vestment disease, complicated with fits of tran- 
substantiation, which has taken the name of Ritualism. The 
common sense of "our national character will not put up with a 
continuance of this grotesque folly ; millinery in all its branches 
will at last be advertised only over the proper shops. I am told 
that the Eitualists give short and practical sermons ; if so, they 
may do good in the end. The English Establishment has always 
contained those who want an excitement ; the New Testament, 
in its plain meaning, can do little for them. Since the Ee volu- 
tion, Jacobitism, Wesleyanism, Evangelicism, Puseyism, and 
Eitualism, have come on in turn, and have furnished hot water 
for those who could not wash without it. If the Eitualists should 
succeed in substituting short and practical teaching for the 
high-spiced lectures of the doctrinalists, they will be remembered 
with praise. John the Baptist would perhaps not have brought 
all Jerusalem out into the wilderness by his plain and good 
sermons : it was the camel's hair and the locusts which got him 
a congregation, and which, perhaps, added force to his precepts. 
When at school I heard a dialogue, between an usher and the 

man who cleaned the shoes, about Mr. , a minister, a very 

corporate body with due area of waistcoat. ' He is a man of 
great erudition,' said the first. ' Ah, yes, sir,' said Joe ; ' any- 
one can see that who looks at that silk waistcoat.'] 

[When I said at the outset that I had only taken books 
from my own store, I should have added that I did not make any 
search for information given as part of a work. Had I looked 
through all my books, I might have made some curious additions. 
For instance, in Schott's Magia Naturalis (vol. iii. pp. 756-778) 
is an account of the quadrature of Gephyrauder, as he is mis- 
printed in Montucla. He was Thomas Gephyrander Salicetus; 
and he published two editions, in 1608 and 1609 : I never even 
heard of a copy of either. His work is of the extreme of absurdity : 
he makes a distinction between geometrical and arithmetical frac- 
tions, and evolves theorems from it. More curious than his quad- 
rature is his name ; what are we to make of it ? If a German, he is 
probably a German form of Bridgeman, and Salicetus refers him to 
Weiden. But Thomas was hardly a German Christian name of his 



44 A BUDGET OF PAEADOXES. 

time ; of 526 German philosophers, physicians, lawyers, and theolo- 
gians who were biographed by Melchior Adam, only two are of this 
name. Of these one is Thomas Erastus, the physician whose theolo- 
gical writings against the Church as a separate power have given the 
name of Erastians to those who follow his doctrine, whether they 
have heard of him or not. Erastus is little known ; accordingly, 
some have supposed that he must be Erastus, the friend of St. 
Paul and Timothy (Acts xix. 22 ; 2 Tim. iv. 20 ; Kom. xvi. 23), 
but what this gentleman did to earn the character is not hinted 
at. P^ew words would have done : Grains (Eom. xvi. 23) has an 
immortality which many more noted men have missed, given by 
John Bunyan, out of seven words of St. Paul. I was once told 
that the Erastians got their name from Blastus, and I could not 
solve bl = er : at last I remembered that Blastus was a chamber- 
lain as well as Erastus ; hence the association which caused the 
mistake. The real heresiarch was a physician who died in 1583 ; 
his heresy was promulgated in a work, published immediately 
after his death by his widow, De Excommunicatione Ecclesiastica. 
He denied the power of excommunication on the principle above 
stated ; and was answered by Beza. The work was translated by 
Dr. R. Lee (Edinb. 1844, 8vo). The other is Thomas Grynseus, 
a theologian, nephew of Simon, who first printed Euclid in Greek ; 
of him Adam says that of works he published none, of learned 
sons four. If Gephyrander were a Frenchman, his name is not so 
easily guessed at ; but he must have been of La Saussaye. The 
account given by Schott is taken from a certain Father Philip 
Colbinus, who wrote against him. 

In some manuscripts lately given to the Eoyal Society, 
David Gregory, who seems to have seen Gephyrander's work, calls 
him Salicetus Westphalus, which is probably on the title-page. 
But the only Weiden I can find is in Bavaria. Murhard has both 
editions in his Catalogue, but had plainly never seen the books : 
he gives the author as Thomas Gep. Hyandrus, Salicettus West- 
phalus. Murhard is a very old referee of mine ; but who the 
non nominandus was to see Montucla's Gephyrauder in Murhard's 
Gep. Hyandrus, both writers being usually accurate ?] 



NAPIEK GILBERT BAPTIST A PORTA. 45 



A plain discoverie of the whole Revelation of St. John . . . 
whereunto are annexed certain oracles of Sibylla . . . Set Foorth 
by John Napeir L. of Marchiston. London, 1611, 4to. 

The first edition was Edinburgh, 1593, 4to. Napier always 
believed that his great mission was to upset the Pope, and that 
logarithms, and such things, were merely episodes and relaxations. 
It is a pity that so many books have been written about this 
matter, while Napier, as good as any, is forgotten and unread. 
He is one of the first who gave us the six thousand years. ' There 
is a sentence of the house of Elias reserved in all ages, bearing 
these words : The world shall stand six thousand years, and then 
it shall be consumed by fire : two thousand yeares voide or without 
lawe, two thousand yeares under the law, and two thousand 
yeares shall be the daies of the Messias. . . .' 

I give Napier's parting salute : it is a killing dilemma : 

In summar conclusion, if thou o Borne aledges thyselfe reformed, and 
to beleeue true Christianisme, then beleeue Saint John the Disciple, 
whome Christ loued, publikely here in this Reuelation proclaiming thy 
wracke, but if thou remain Ethnick in thy priuate thoghts, beleeuing 
the old Oracles of the Sibyls reuerently keeped somtime in thy Capitol : 
then doth here this Sibyll proclame also thy wracke. Repent therefore 
alwayes, in this thy latter breath, as thou louest thine Eternall salvation. 
Amen. 

Strange that Napier should not have seen that this appeal could 
not succeed, unless the prophecies of the Apocalypse were no true 
prophecies at all. 

De Magnete magneticisque corporibus, et de magno magnete 
tellure. By William Gilbert. London, 1600, folio. There is 
a second edition ; and a third, according to Watt. 

Of the great work on the magnet there is no need to speak, 
though it was a paradox in its day. The posthumous work of 
Gilbert, 'De Mundo nostro sublunari philosophia nova' (Ams- 
terdam, 1651, 4to) is, as the title indicates, confined to the 
physics of the globe and its atmosphere. It has never excited 
attention : I should hope it would be examined with our present 
lights. 

Elementorum Curvilineorium Libri tres. By John Baptista Porta. 

Rome, 1610, 4to. 

This is a ridiculous attempt, which defies description, except 
that it is all about lunules. Porta was a voluminous writer. 



46 A BUDGET OF PARADOXES. 

His printer announces fourteen works printed, and four to come, 
besides thirteen plays printed, and eleven waiting. His name is, 
and will be, current in treatises on physics for more reasons than 
one. 

Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi. 
Bologna, 1612, folio. 

Eheticus, Vieta, and Cataldi are the three untiring computers 
of Germany, France, and Italy ; Napier in Scotland, and Briggs in 
England, come just after them. This work claims a place as 
beginning with the quadrature of Pellegrino Borello of Reggio, 
who will have the circle to be exactly 3 diameters and -^^ of a 
diameter. Cataldi, taking Van Ceulen's approximation, works 
hard at the finding of integers which nearly represent the ratio. 
He had not then the continued fraction, a mode of representation 
which he gave the next year in his work on the square root. He 
\has but twenty of Van Ceulen's thirty places, which he takes from 
Clavius : and anyone might be puzzled to know whence the Italians 
got the result ; Van Ceulen, in 1612, not having been translated 
from Dutch. But Clavius names his comrade Grruenberger, and 
attributes the approximation to them jointly ; * Lud. a Collen et 
Chr. Grruenbergerus invenerunt,' which he had no right to do, 
unless, to his private knowledge, Grruenberger had verified Van 
Ceulen. And Grruenberger only handed over twenty of the places. 
But here is one instance, out of many, of the polyglot character 
of the Jesuit body, and its advantages in literature. 

Philippi Lausbergii Cyclometrise Novsa Libri Duo. Middleburg, 
1616, 4to. 

This is one of the legitimate quadratures, on which I shall 
here only remark that by candlelight it is quadrature under 
difficulties, for all the diagrams are in red ink. 

Recherches Curieuses des Mesures du Monde. By S. C. de V. 
Paris, 1626, 8vo. (pp. 48). 

It is written by some Count for his son ; and if all the French 
nobility would have given their sons the same kind of instruction 
about rank, the old French aristocracy would have been as pros- 
perous at this moment as the English peerage and squireage. I 
sent the tract to Capt. Speke, shortly after his arrival in England, 
thinking he might like to see the old names of the Ethiopian pro- 
vinces. But I first made a copy of all that relates to Prester John, 
himself a paradox. The tract contains, inter alia, an account of 



PRESTER JOHN. 47 

the four empires ; of the great Turk, the great Tartar, the great 
Sophy, and the great Prester John. This word great (grand), 
which was long used in the phrase ' the great Turk,' is a generic 
adjunct to an emperor. Of the Tartars it is said that ' c'est vne 
nation prophane et barbaresque, sale et vilaine, qui mangent la 
chair demie crue, qui boiuent du laict de jument, et qui n'vsent 
de nappes et seruiettes que pour essuyer leurs bouches et leurs 
mains.' Many persons have heard of Prester John, and have 
a very indistinct idea of him. I give all that is said about him, 
since the recent discussions about the Nile may give an interest 
to the old notions of geography. 

Le grand Prestre Jean qui est le quatriesme en rang, est Empereur 
d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid, 
comme estant descendu de la Boyne de Saba, Boyne d'Ethiopie, laqu?lle 
estant venue en Hierusalem pour voir la sagesse de Salomou, enuiron 
1'an du monde 2952, s'en retourna grosse d'vn fils qu'ils nomment 
Moylech, duquel ils disent estre descendus en ligne directe. Et ainsi 
il se glorifie d'estre le plus ancien Monarque de la terre, disant que son 
Empire a dure plus de trois mil ans, ce que nul autre Empire ne pent 
dire. Aussi met-il en ses tiltres ce qui s'ensuit : Nous, N. Souuerain 
en mes Royaumes, vniquement ayme de Dieu, colomne de la foy, sorty 
de la race de luda, &c. Les limites de cet Empire touchent a la mer 
Ronge, et aux montagnes d'Azuma vers 1'Orient, et du coste de 
1' Occident, il est borne du fleuue du Nil, qui le separe de la Nubie, vers 
le Septentrion il a 1'^Egypte, et au Midy les Royaumes de Congo, et de 
Mozambique, sa longueur contenant quarante degre, qui font mille 
vingt cinq lieues, et ce depuis Congo on Mozambique qui sont au Midy, 
iusqu'en ^-Egypte qui est au Septentrion, et sa largeur contenant depuis 
le Nil qui est a 1' Occident, iusqu'aux montagnes d'Azuma, qui sont a 
1'Orient, sept cens vingt cinq lieues, qui font vingt neuf degrez. Get 
empire a sous soy trente grandes Prouinces, scavoir, Medra, Gaga, 
Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy, 
Angote, Cigremaon, Gorga Cafatez, Zastanla, Zeth, Barly, Belangana, 
Tygra, Gorgany, Barganaza, d'Ancut, Dargaly Ambiacatina, Cara- 
cogly, Amara . Maon (sic), Guegiera, Bally, Dobora et Macheda. 
Toutes ces Prouinces cy dessus sont situees iustement sous la ligne 
equinoxiale, entres les Tropiques de Capricorne, et de Cancer. Mais 
elles s'approchent de nostre Tropiqne, de deux cens cinquante lieues 
plus qu' elles ne font de I'autre Tropique. Ce mot de Prestre Jean 
signifie grand Seigneur, et n'est pas Prestre comme plusieurs pense, il a 
este tousiours Chrestien, mais souuent Schismatique : maintenant il est 
Catholique, et reconnaist le Pape pour Sounerain Pontife. I'ay veu 
quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ay 
confere souuent par le moyen de nostre trucheman : il estoit d'vn port 
graue et serieux, succiur (sic) en son parler, mais subtil a merueilles 
en tout ce qu'il disoit. II prenoit grand plaisir au recit (me je luy 



48 A BUDGET OF PARADOXES. 

faisais de nos belles ceremonies, et de la granite de nos Prelats enleurs 
habits Pontificaux, et autres choses que je laisse pour dire, que 1'Ethi- 
opien est ioyoux et gaillard, ne ressemblant en rien a la salete du Tar- 
tare, ny a 1'affreux regard du miserable Arabe, mais ils sont fins et 
cauteleux, et ne se fient en personne, soup9onneux a merueilles, et fort 
devotieux, ils ne sont du tout noirs comme 1'on croit, i'entens parler de 
ceux qui ne sont pas sous la ligne Equinoxiale, ny trop proches d'icelle, 
car ceux qui sont dessous sont les Mores que nous voyons. 

It will be observed that the author speaks of his conversation 
with an Ethiopian bishop, about that bishop's sovereign. Some- 
thing must have passed between the two which satisfied the 
writer that the bishop acknowledged his own sovereign under 
some title answering to Prester John. 

De Cometa anni 1618 dissertationes Thomae Fieni et Liberti 
Fromondi. . . Equidem Thomee Fieni epistolica queBstio, An 
verum sit Coelum moveri et Terram quiescere ? London, 1670, 
8vo. 

This tract of Fienus against the motion of the earth is a reprint 
of one published in 1619. I have given an account of it as a 
good summary of arguments of the time, in the Companion to the 
Almanac for 1836. 

Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to. 

This is a celebrated work on the approximative quadrature, 
which, having the suspicious word oyclometricus, must be noticed 
here for distinction. 

1620. In this year, Francis Bacon published his 'Novum 
Organum,' which was long held in England but not until the 
last century to be the work which taught Newton and all his 
successors how to philosophise. That Newton never mentions 
Bacon, nor alludes in any way to his works, passed for nothing. 
Here and there a parodoxer ventured not to find all this teaching 
in Bacon, but he was pronounced blind. In our day it begins 
to be seen that, great as Bacon was, and great as his book really 
is, he is not the philosophical father of modern discovery. 

But old prepossession will find reason for anything. A learned 
friend of mine wrote to me that he had discovered proof that 
Newton owned Bacon for his master : the proof was that Newton, 
in some of his earlier writings, used the phrase experimentum 
crucis, which is Bacon's. Newton may have read some of Bacon, 
though no proof of it appears. I have a dim idea that I once 
saw the two words attributed to the alchemists : if so, there is 



FRANCIS BACON. 49 

another explanation ; for Newton was deeply read in the al- 
chemists. 

I subjoin a review which I wrote of the splendid edition of 
Bacon by Spedding, Ellis, and Heath. All the opinions therein 
expressed had been formed by me long before : most of the 
materials were collected for another purpose. 

The Works of Francis Bacon. Edited by James Spedding, 
R. Leslie Ellis, and Douglas D. Heath. 5 vols. 

No knowledge of nature without experiment and observation : 
so said Aristotle, so said Bacon, so acted Copernicus, Tycho Brahe, 
Gilbert, Kepler, Galileo, Harvey, &c., before Bacon wrote. No 
derived knowledge until experiment and observation are con- 
cluded : so said Bacon, and no one else. We do not mean to say 
that he laid down his principle in these words, or that he carried 
it to the utmost extreme : we mean that Bacon's ruling idea was 
the collection of enormous masses of facts, and then digested 
processes of arrangement and elimination, so artistically contrived, 
that a man of common intelligence, without any unusual sagacity, 
should be able to announce the truth sought for. Let Bacon 
speak for himself, in his editor's English : 

But the course I propose for the discovery of sciences is such as 
leaves but little to the acuteness and strength of wits, but places all wits 
and understandings nearly on a level. For, as in the drawing of a straight 
line or a perfect circle, much depends on the steadiness and practice of 
the hand, if it be done by aim of hand only, but if with the aid of rule 
or compass little or nothing, so it is exactly with my plan. . . For 
my way of discovering sciences goes far to level men's wits, and leaves 
but little to individual excellence ; because it performs everything by 
the surest rules and demonstrations. 

To show that we do not strain Bacon's meaning, we add what 
is said by Hooke, whom we have already mentioned as his pro- 
fessed disciple, and, we believe, his only disciple of the day of 
Newton. We must, however, remind the reader that Hooke was 
very little of a mathematician, and spoke of algebra from his own 
idea of what others had tol'd him : 

The intellect is not to be suffered to act without its helps, but is 
continually to be assisted by some method or engine, which shall 
be as a guide to regulate its actions, so as that it shall not be able to 
act amiss. Of this engine, no man except the incomparable Verulam 
hath had any thoughts, and he indeed hath promoted it to a very good 
pitch ; but there is yet somewhat more to be added, which lie seemed 
to want time to complete. By this, as by that art of algebra in geo- 





50 A BUDGET OF PARADOXES. 

metry, 'twill be very easy to proceed in any natural inquiry, regularly 
and certainly. . . For as 'tis very hard for the most acute wit to find 
out any difficult problem in geometry without the help of algebra . . . 
and altogether as easy for the meanest capacity acting by that method 
to complete and perfect it, so will it be in the inquiry after natural 
. knowledge. 

Bacon did not live to mature the whole of this plan. Are we 
really to believe that if he had completed the ' Instauratio ' we 
who write this and who feel ourselves growing bigger as we 
write it should have been on a level with Newton in physical 
discovery? Bacon asks this belief of us, and does not get it. 
But it may be said, Your business is with what he did leave, 
and with its consequences. Be it so. Mr. Ellis says : l That his 
method is impracticable cannot, I think, be denied, if we reflect 
not only that it never has produced any result, but also that the 
process by which scientific truths have been established cannot 
be so presented as even to appear to be in accordance with it.' 
That this is very true is well known to all who have studied the 
history of discovery : those who deny it are bound to establish 
either that some great discovery has been made by Bacon's 
method we mean by the part peculiar -to Bacon or, better still, 
to show that some new discovery can be made, by actually making- 
it. No general talk about induction : no reliance upon the 
mere fact that certain experiments or observations have been 
made ; let us see where Bacon's induction has been actually 
used or can be used. Mere induction, enumeratio simplex, is 
spoken of by himself with contempt, as utterly incompetent. 
For Bacon knew well that a thousand instances may be contra- 
dicted by the thousand and first : so that no enumeration of 
instances, however large, is ' sure demonstration,' so long as any 
are left. 

The immortal Harvey, who was inventing we use the word 
in its old sense the circulation of the blood, while Bacon was in 
, the full flow of thought upon his system, may be trusted to say 
whether, when the system appeared, he found any likeness in it 
to his own processes, or what would have been any help to him, 
if he had waited for the ' Novum Organum.' He said of Bacon, 
* He writes philosophy like a Lord Chancellor.' This has been 
generally supposed to be only a sneer at the sutor ultra crepidam ; 
but we cannot help suspecting that there was more intended by 
it. To us, Bacon is eminently the philosopher of error prevented, 
not of progress facilitated. When we throw off the idea of being 
led right, and betake ourselves to that of being kept from going 



FRANCIS BACON. 51 

wrong, we read his writings with a sense of their usefulness, his 
genius, and their probable effect upon purely experimental science, 
which we can be conscious of upon no other supposition. It 
amuses us to have to add that the part of Aristotle's logic of 
which he saw the value was the book on refutation of fallacies. 
Now is this not the notion of things to which the bias of a 
practised lawyer might lead him ? In the case which is before 
the Court, generally speaking, truth lurks somewhere about the 
facts, and the elimination of all error will show it in the residuum. 
The two senses of the word law come in so as to look almost like 
a play upon words. The judge can apply the law so soon as the 
facts are settled : the physical philosopher has to deduce the law 
from the facts. Wait, says the judge, until the facts are deter- 
mined : did the prisoner take the goods with felonious intent ? 
did the defendant give what amounts to a warranty ? or the like. 
Wait, says Bacon, until all the facts, or all the obtainable facts, 
are brought in : apply my rules of separation to the facts, and the 
result shall come out as easily as by ruler and compasses. We think 
it possible that Harvey might allude to the legal character of 
Bacon's notions : we can hardly conceive so acute a man, after 
seeing what manner of writer Bacon was, meaning only that he 
was a lawyer and had better stick to his business. We do our- 
selves believe that Bacon's philosophy more resembles the action 
of mind of a common-law judge not a Chancellor than that of 
the physical inquirers who have been supposed to follow in his 
steps. It seems to us that Bacon's argument is, there can be 
nothing of law but what must be either perceptible, or mechani- 
cally deducible, when all the results of law, as exhibited in 
phenomena, are before us. Now the truth is, that the physical 
philosopher has frequently to conceive law which never was in his 
previous thought to educe the unknown, not to choose among 
the known. Physical discovery would be very easy work if the 
inquirer could lay down his this, his that, and his t'other, and say, 
' Now, one of these it must be ; let us proceed to try which.' 
Often has he done this, and failed ; often has the truth turned 
out to be neither this, that, nor t'other. Bacon seems to us to 
think that the philosopher is a judge who has to choose, upon 
ascertained facts, which of known statutes is to rule the decision : 
he appears to us more like a person who is to write the statute- 
book, with no guide except cases and decisions presented in all 
their confusion and all their conflict. 

Let us take the well-known first aphorism of the ' Novum 
Organum : ' 

B 2 



52 A BUDGET OF PAEA BOXES. 

Man being the servant and interpreter of nature, can do and under- 
stand so much, and so much only, as he has observed in fact or in 
thought of the course of nature : beyond this he neither knows anything 
nor can do anything. 

This aphorism is placed by Sir John Herschel at the head of 
his ' Discourse on the Study of Natural Philosophy : ' a book con- 
taining notions of discovery far beyond any of which Bacon ever 
dreamed ; and this because it was written after discovery, instead 
of before. Sir John Herschel, in his version, has avoided the 
translation of re vel mente observaverit, and gives us only ' by his 
observation of the order of nature.' In making this the opening 
of an excellent sermon, he has imitated the theologians, who 
often employ the whole time of the discourse in stuffing matter 
into the text, instead of drawing matter out of it. By observation 
he (Herschel) means the whole course of discovery, observation, 
hypothesis, deduction, comparison, &c. The type of the Baconian 
philosopher, as it stood in his mind, had been derived from a 
noble example, his own father, William Herschel, an inquirer 
whose processes would have been held by Bacon to have been 
vague, insufficient, compounded of chance work and sagacity, and 
too meagre of facts to deserve the name of induction. In another 
work, his treatise on Astronomy, Sir John Herschel, after noting 
that a popular account can only place the reader on the threshold, 
proceeds to speak as follows of all the higher departments of 
science. The italics are his own : 

Admission to its sanctuary, and to the privileges and feelings of 
a votary, is only to be gained by one means sound and sufficient 
knowledge of mathematics, tJte great instrument of all exact inquiry, 
without which no man can ever make such advances in this or any other 
of the higher departments of science as can entitle him. to form an inde- 
pendent opinion on any subject of discussion within their range. 

How is this? Man can know no more than he gets from 
observation, and yet mathematics is the great instrument of all 
exact inquiry. Are the results of mathematical deduction results 
of observation ? We think it likely that Sir John Herschel 
would reply that Bacon, in coupling together observare re and 
observare mente, has done what some wags said Newton afterwards 
did in his study-door cut a large hole of exit for the large cat, 
and a little hole for the little cat. But Bacon did no such thing : 
he never included any deduction under observation. To mathe- 
matics he had a dislike. He averred that logic and mathematics 
should be the handmaids, not the mistresses, of philosophy. He 
ineant that they should play a subordinate and subsequent part 



FRANCIS BACON. 53 

in the dressing of the vast mass of facts by which discovery was 
to be rendered equally accessible to Newton and to us. Bacon 
himself was very ignorant of all that had been done by mathe- 
matics ; and, strange to say, he especially objected to astronomy 
being handed over to the mathematicians. Leverrier and Adams, 
calculating an unknown planet into visible existence by .enormous 
heaps of algebra, furnish the last comment of note on this 
specimen of the goodness of Bacon's views. The following 
account of his knowledge of what had been done in his own day 
or before it, is Mr. Spedding's collection of casual remarks in 
Mr. Ellis's several prefaces : 

Though he paid great attention to astronomy, discussed carefully the 
methods in which it ought to be studied, constructed for the sati? fac- 
tion of his own mind an elaborate theory of the heavens, and listened 
eagerly for the news from the stars brought by Galileo's telescope, he 
appears to have been utterly ignorant of the discoveries which had 
just been made by Kepler's calculations. Though, he complained in 
1623 of the want of compendious methods for facilitating arithmetical 
computations, especially with regard to the doctrine of Series, and 
fully recognized the importance of them as an aid to physical inquiries 
he does not say a word about Napier's Logarithms, which had been 
published only nine years before and reprinted more than once in the 
interval. He complained that no considerable advance had been made 
in geometry beyond Euclid, without taking any notice of what Lad 
been done by Archimedes and Apollonius. He saw the importance of 
determining accurately the specific gravities of different substances, and 
himself attempted to form a table of them by a rude process of his own, 
without knowing of the more scientific though still imperfect methods 
previously employed by Archimedes, Ghetaldus, and Porta. He speaks 
of the tvpijxa of Archimedes in a manner which implies that he did not 
clearly apprehend either the nature of the problem to be solved or the 
principles upon which the solution depended. In reviewing the pro- 
gress of mechanics, he makes no mention of Archimedes himself, or of 
Stevinus, Galileo. Guldinus, or Ghetaldus. He makes no allusion to 
the theory of equilibrium. He observes that a ball of one pound weight 
will fall nearly as fast through the air as a ball of two, without alluding 
to the theory of the acceleration of falling bodies, which had been 
made known by Galileo more than thirty years before. He proposes an 
inquiry with regard to the lever namely, whether in a balance with 
arms of different length but equal weight the distance from the fulcrum 
has any effect upon the inclination, though the theory of the lever was 
as well understood in his own time as it is now. In making an experi- 
ment of his own to ascertain the cause of the motion of a windmill, he 
overlooks an obvious circumstance which makes the experiment incon- 
clusive, and an equally obvious variation of the same experiment which 
would Lave sLown Lim that Lis tLeory was false. He speaks of the 



54 A BUDGET OF PARADOXES. 

poles of the earth as fixed, in a manner which seems to imply that he 
was not acquainted with the precession of the equinoxes ; and in 
another place, of the north pole being above and the south pole below, 
as a reason why in our hemisphere the north winds predominate over 
the south. 

Much of this was known before, but such a summary of Bacon's 
want of knowledge of the science of his own time was never yet 
collected in one place. We may add, that Bacon seems to have 
been as ignorant of Wright's memorable addition to the resources 
of navigation as of Napier's addition to the means of calculation. 
Mathematics was beginning to be the great instrument of exact 
inquiry : Bacon threw the science aside, from ignorance, just at 
the time when his enormous sagacity, applied to knowledge, 
would have made him see the part it was to play. If Newton 
had taken Bacon for his master, not he, but somebody else, would 
have been Newton. 

There is an attempt at induction going on, which has yielded 
little or no fruit, the observations made in the meteorological 
observatories. This attempt is carried on in a manner which 
would have caused Bacon to dance for joy ; for he lived in times 
when Chancellors did dance. Eussia, says M. Biot, is covered by 
an army of meteorographs, with generals, high officers, subalterns, 
and privates with fixed and defined duties of observation. Other 
countries have also their systematic observations. And what has 
come of it ? Nothing, says M. Biot, and nothing will ever come 
of it : the veteran mathematician and experimental philosopher 
declares, as does Mr. Ellis, that no single branch of science has 
ever been fruitfully explored in this way. There is no special 
object, he says. Any one would suppose that M. Biot's opinion, 
given to the French Government upon the proposal to construct 
meteorological observatories in Algeria (Comptes Rendue,vol. xli, 
Dec. 31, 1855), was written to support the mythical Bacon, modern 
physics, against the real Bacon of the ' Novum Organum.' There 
is no special object. In these words lies the difference between 
the two methods. 

[In the report to the Greenwich Board of Visitors for 1867, 
Mr. Airy, speaking of the increase of meteorological observatories, 
remarks ' Whether the effect of this movement will be that 
millions of useless observations will be added to the millions that 
already exist, or whether something may be expected to result 
which will lead to a meteorological theory, I cannot hazard a 
conjecture.' This is a conjecture, and a very obvious one : if 



i'RANCIS BACON. 55 

Mr. Airy would have given 2f cZ. for the chance of a meteorological 
theory formed by masses of observations, he would never have 
said what I have quoted.] 

Modern discoveries have not been made by large collections of 
facts, with subsequent discussion, separation, and resulting de- 
duction of a truth thus rendered perceptible. A few facts have 
suggested an hypothesis, which means a supposition, proper to 
explain them. The necessary results of this supposition are 
worked out, and then, and not till then, other facts are examined 
to see if these ulterior results are found in nature. The trial of 
the hypothesis is the special object: prior to which, hypothesis 
must have been started, not by rule, but by that sagacity of 
which no description can be given, precisely because the very 
owners of it do not act under laws perceptible to themselves. 
The inventor of hypothesis, if pressed to explain his method, must 
answer as did Zerah Colburn, when asked for his mode of instan- 
taneous calculation. When the poor boy had been bothered for 
some time in this manner, he cried out in a huff, ' God put it 
into my head, and I can't put it into yours.' Wrong hypotheses, 
rightly worked from, have produced more useful results than 
unguided observation. But this is not the Baconian plan. 
Charles the Second, when informed of the state of navigation, 
founded a Baconian observatory at Greenwich, to observe, observe, 
observe away at the moon, until her motions were known suf- 
ficiently well to render her useful in guiding the seaman. And 
no doubt Flamsteed's observations, twenty or thirty of them 
at least, were of signal use. But how? A somewhat fanciful 
thinker, one Kepler, had hit upon the approximate orbits of the 
planets by trying one hypothesis after another : he found the 
ellipse, which the Platonists, well despised of Bacon, and who 
would have despised him as heartily if they had known him, had 
investigated and put ready to hand nearly 2,000 years before. 
The sun in the focus, the motions of the planet more and more 
rapid as they approach the sun, led Kepler and Bacon would 
have reproved him for his rashness to imagine that a force re- 
siding in the sun might move the planets, a force inversely as the 
distance. Bouillaud, upon a fanciful analogy, rejected the inverse 
distance, and, rejecting the force altogether, declared that if such 
a thing there were, it would be as the inverse square of the 
distance. Newton, ready prepared with the mathematics of the 
subject, tried the fall of the moon towards the earth, away from 
her tangent, and found that, as compared with the fall of a stone, 



56 A BUDGET OF PARADOXES. 

the law of the inverse square did hold for the moon. He deduced 
the ellipse, he proceeded to deduce the effect of the disturbance 
of the sun upon the moon, upon the assumed theory of universal 
gravitation. He found result after result of his theory in con- 
formity with observed fact : and, by aid of Flamsteed's obser- 
vations, which amended what mathematicians call his constants, 
he constructed his lunar theory. Had it not been for Newton, 
the whole dynasty of Greenwich astronomers, from Flamsteed of 
happy memory, to Airy whom Heaven preserve, might have 
worked away at nightly observation and daily reduction, without 
any remarkable result : looking forward, as to a millennium, to 
the time when any man of moderate intelligence was to see 
the whole explanation. What are large collections of facts for ? 
To make theories from., says Bacon : to try ready-made theories 
by, says the history of discovery : it's all the same, says the 
idolater : nonsense, say we ! 

Time and space run short : how odd it is that of the three 
leading ideas of mechanics, time, space, and matter, the first two 
should always fail a reviewer before the third. We might dwell 
upon many points, especially if we attempted a more descriptive 
account of the valuable edition before us. No one need imagine 
that the editors, by their uncompromising attack upon the notion 
of Bacon's influence common even among mathematicians and 
experimental philosophers, have lowered the glory of the great 
man whom it was, many will think, their business to defend 
through thick and thin. They have given a clearer notion of his 
excellencies, and a better idea of the power of his mind, than ever 
we saw given before. Such a correction as theirs must have come, 
and soon, for as Hallam says after noting that the 'Novum 
Organum' was never published separately in England, Bacon has 
probably been more read in the last thirty years now forty than 
in the two hundred years which preceded. He will now be more 
read than ever he was. The history of the intellectual world is 
the history of the worship of one idol after another. No sooner 
is it clear that a Hercules has appeared among men, than all 
that imagination can conceive of strength is attributed to him, 
and his labours are recorded in the heavens. The time arrives 
when, as in the case of Aristotle, a new deity is found, and the 
old one is consigned to shame and reproach. A reaction may 
afterwards take place, and this is now happening in the case of 
the Greek philosopher. The end of the process is, that the oppo- 
sing deities take their places, side by side, in a Pantheon dedicated 
pot to gods, but to heroes. 



COPERNICUS AND THE POPE. 57 

Passing over the success of Bacon's own endeavours to improve 
the details of physical science, which was next to nothing, and of 
his method as a whole, which has never been practised, we might 
say much of the good influence of his writings. Sound wisdom, 
set in sparkling wit, must instruct and amuse to the end of time : 
and, as against error, we repeat that Bacon is soundly wise, so far 
as he goes. There is hardly a form of human error within his 
scope which he did not detect, expose, and attach to a satirical 
metaphor which never ceases to sting. He is largely indebted to 
a very extensive reading ; but the thoughts of others fall into his 
text with such a close-fitting compactness that he can make even 
the words of the Sacred Writers pass for his own. A saying of 
the prophet Daniel, rather a hackneyed quotation in our day, 
Multi pertransibunt, et augebitur scientia, stands in the title-page 
of the first edition of Montucla's ' History of Mathematics ' as a 
quotation from Bacon and it is not the only place in which this 
mistake occurs. When the truth of the matter, as to Bacon's 
system, is fully recognized, we have little fear that there will be 
a reaction against the man. First, because Bacon will always 
live to speak for himself, for he will not cease to be read : 
secondly, because those who seek the truth will find it in the 
best edition of his works, and will be most ably led to know what 
Bacon was, in the very books which first showed at large what he 
was not. 

In this year (1620) appeared the corrections under which the 
Congregation of the Index i.e. the Committee of Cardinals 
which superintended the Index of forbidden books proposed to 
allow the work of Copernicus to be read. I insert these con- 
ditions in full, because they are often alluded to, and I know of 
no source of reference accessible to a twentieth part of those who 
take interest in the question. 

By a decree of the Congregation of the Index, dated March 5, 
1616, the work of Copernicus, and another of Didacus Astunica, 
are suspended donee coirigantur, as teaching : 

' Falsam iilam doctrinam Pythagoricam,divinae que Scripturje omnino 
adversantem, de mobilitate Terras et immobilitate Solis.' 

But a work of the Carmelite Foscarini is : 

' Omnino prohibendura atque damnandum,' because 'ostendere conatur 
prasfatani doctrinam .... consonam esse veritati et non adversari 
Sacra3 Sci - iptura3.' 

Works which teach the false doctrine of the earth's motion 



58 A BUDGET OF PARADOXES. 

are to be corrected ; those which declare the doctrine conformable 
to Scripture are to be utterly prohibited. 

In a ; Monitum ad Nicolai Copernici lectorem, ej usque emen- 
datio, permissio, et correctio,' dated 1620 without the month or 
day, permission is given to reprint the work of Copernicus with 
certain alterations ; and, by implication, to read existing copies 
after correction in writing. In the preamble the author is called 
nobilia astrologua ; not a compliment to his birth, which was 
humble, but to his fame. The suspension was because : 

' Sacree Scriptures, ejusque verro et CatLolices interpretation! repug- 
nantia (quod in horaine Christiano minime tolerandum) non per hypo- 
thesin tractare, sed ut verissima adatruere noa dubitat ! 

And the corrections relate : 

' Locis in quibus^non ex hypothesi, sed asserendo de situ et motu Terras 
disputat.' 

That is, the earth's motion may be an hypothesis for eluci- 
dation of the heavenly motions, but must not be asserted as a 
fact. 



(In Pref. circa finem.) ' Copernicus. Si fortasse erunt 
qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi 
summunt, propter aliquem locum scriptures, male ad suum propositum 
detortum, ausi fuerint meum hoc institutum reprehendere ac insec- 
tari : illos nihil moror adeo ut etiam illorum judicium tanquam 
temerarium contemnam. Non enim obscurum est Lactantium, celebrem 
alioqui scriptorem, sed Mathematicum pai*um, admodum pueriliter de 
forma terree loqui, cum deridet eos, qui terrain globi formam habere 
prodiderunt. Itaque non debet mirum videri stndiosis, si qui tales nos 
etiam videbunt. Mathemata Mathematicis scribuntur, quibus et hi 
nostri labores, si me non fallit opinio, videbuntur etiam Beipub. eccle- 
siasticee conducere aliquid . . . Emend. Ibi si fortasse dele omnia, 
usque ad verbum hi nostri labores et sic accommoda Cceterum hi nostri 
labores. 1 

All the allusion to Lactantius, who laughed at the notion of the 
earth being round, which was afterwards found true, is to be 
struck out. 

(Cap. 5. lib. i. p. 8.) ' Copernicus. Si tamen attentius rem consider- 
emus, videbitur heec queestio nondum absoluta, et idcirco minime 
contemnenda. Emend. Si tamen attentius rem consideremus, nihil 
refert an Terrain in medio Mundi, an extra Medium existere, quoad sol- 
yendas coelestium motuum apparentias existimemus.' 

We must not say the question is not yet settled, but only that 



COPERNICUS AND THE POPE. 59 

it may be settled either way, so far as mere explanation of the 
celestial motions is concerned. 

(Cap. 8. lib. i.) ' Totum hoc caput potest expungi, quia ex professo 
tractat de veritate motus Terree, dum solvit veterum rationes probantes 
ejus quietem. Cam tamen problematice videatur loqui ; ut studiosis 
satisfiat, seriesque et ordo libri integer maneat ; emendetur ut infra.' 

A chapter which seems to assert the motion should perhaps be 
expunged ; but it may perhaps be problematical ; and, not to 
break up the book, must be amended as below. 

(p. 6.) ' Ooperniciis. Cui ergo hesitamus adhuc, nobilitatem illi formes 
sues a natura congruentem concedere, magisquam quod totus labatur 
mundus, cujus finis ignoratur, soirique nequit, neque fateamur ipsius 
cotidian revolutionis in coelo apparentiam esse, et in terra veritatem ? 
Efc heec perinde se habere, ac si diceret Virgilianus ^Eneas : Provehimur 
portu .... Emend. Cur ergo non possum mobilitatem illi formsa 
sues concedere, magisque quod totus labatur mundus, cujus finis 
ignoratur scirique nequit, et quse apparent in coelo, perinde se habere, 
ao si . . . .' 

' Why should we hesitate to allow the earth's motion,' must be 
altered into ' I cannot concede the earth's motion.' 

(p. 7.) ' Copernicus. Addo etiam, quod satis absurdum videretur, 
continent! sive locanti motnm adscribi, et non potius contento et 
locato, quod est terra. Emend. Addo etiam difficilius non esse 
contento et locato, quod est Terra, motum adscribere, quam continenti.' 

We must not say it is absurd to refuse motion to the contained 
and located, and to give it to the containing and locating ; say 
that neither is more difficult than the other. 

(p. 7.) ' Copernicus. Vides ergo quod ex his omnibus probabilior sit 
mobilitas Terras, quam ejus quies, preesertim in cotidiana revolutione, 
tanquam terne maxime propria. EincmL Vides . . . delendus est 
usque ad finem capitis.' 

Strike out the whole of the chapter from this to the end ; it 
says that the motion of the earth is the most probable hypothesis. 

(Cap. 9. lib. i. p. 7.) ' Copernicus. Cum igitur nihil prohibeat mobili- 
tatem Teme, videndum nunc arbitror, an etiam plures illi motua 
conveniant, ut possit una errantium syderum existimari. Emend. Cum 
igitur Terram moveri assumpserim, videndum nunc arbitror, an etiam 
illi plures possint convenire motus.' 

We must not say that nothing prohibits the motion of the 
earth, only that having assumed it, we may inquire whether our 
explanations require several motions. 



60 A BUDGET OF PARADOXES. 

(Cap. 10. lib. 1. p. 9.) ' Copernicus. Non pudet nosfateri .... hoc 
potius in mobilitate terra? verificari. Emend. ISTon pudet nos assumere 
.... hoc consequent er in mobilitate verificari.' 

(Cap. 10. lib. i. p. 10.) ' Copernicus. Tanta nimiruni. est divina ha3C 
Opt. Max. fabrica. Emend. Dele ilia verba postrema.' 

(Cap. ii. lib. i.) ' Copernicus. De triplici motu telluris demonstratio. 
Emend. De hypothesi triplicis motus Terree, ejusque demonstratioiie.' 

(Cap. 10. lib. iv. p. 122.) ' Copernicus. De magnitudine horum trium 
siderum, Solis, Lunee, et Terrse. Emend. Dele verba horum trium 
sidcrum, quia terra non est sidus, ut facit earn Copernicus. ' 

We must not say we are not ashamed to acknowledge ; assume 
is the word. We must not call this assumption a Divine work. 
A chapter must not be headed demonstration, but hypothesis. 
The earth must not be called a star ; the word implies motion. 

It will be seen that it does not take much to reduce Copernicus 
to pure hypothesis. No personal injury being done to the author 
who indeed had been 1 7 years out of reach the treatment of 
his book is now an excellent joke. It is obvious that the Car- 
dinals of the Index were a little ashamed of their position, and 
made a mere excuse of a few corrections. Their mode of deal- 
ing with chap. 8, this problematice videtur loqui,ut studiosis satis- 
fiat, is an excuse to avoid corrections. But they struck out the 
stinging allusion to Lactantius in the preface, little thinking, 
honest men, for they really believed what they said that the 
light of Lactantius would grow dark before the brightness of 
their own. 

1622. I make no reference to the case of Galileo, except this. 
I have pointed out (Penny Cycl. Suppl. ' Gralileo ; ' Engl. Cycl. 
' Motion of the Earth ') that it is clear the absurdity was the act 
of the Italian Inquisition for the private and personal pleasure 
of the Pope, who knew that the course he took would not commit 
him as Pope and not of the body which calls itself the Church. 
Let the dirty proceeding have its right name. The Jesuit 
Riccioli, the stoutest and most learned Anti-Copernican in 
Europe, and the Puritan Wilkins, a strong Copernican and 
Pope-hater, are equally positive that the Eoman Church never 
pronounced any decision : and this in the time immediately fol- 
lowing the ridiculous proceeding of the Inquisition. In like 
manner a decision of the Convocation of Oxford is not a law of 
the English Church ; which is fortunate, for that Convocation, 
in 1622, came to a decision quite as absurd, and a great deal 
more wicked than the declaration against the motion of the earth. 
The second was a foolish mistake : the first was a disgusting 



KNIGHT AND THE OXFORD CONVOCATION. 61 

surrender of right feeling. Tbe story is told without disappro- 
bation by Anthony Wood, who never exaggerated anything 
against the university of which he is writing eulogistic history. 

In 1622, one William Knight put forward in a sermon preached 
before the University certain theses which, looking at the state 
of the times, may have been improper and possibly of seditious 
intent. One of them was that the bishop might excommunicate 
the civil magistrate : this proposition the clerical body could not 
approve, and designated it by the term erronea, the mildest 
going. But Knight also declared as follows 

Stibditis mere privatis, si Tyrannus tanquarn latro aut stuprator 
in ipsos faciat impetum, et ipsi nee potestatem ordinariam 
implorare, nee alia ratione effugere periculum possint, in preserti 
periculo se et suos contra tyrannum, sicut contra privatum gras- 
satorem, defendere licet. 

That is, a man may defend his purse or a woman her honour, 
against the personal attack of a king, as against that of a private 
person, if no other means of safety can be found. The Convoca- 
tion sent Knight to prison, declared the proposition 'falsa, 
periculosa, et impiaj and enacted that all applicants for degrees 
should subscribe this censure, and make oath that they would 
neither hold, teach, nor defend Knight's opinions. 

The thesis, in the form given, was unnecessary and improper. 
Though strong opinions of the king's rights were advanced at the 
time, yet no one ventured to say that, ministers and advisers 
apart, the king might personally break the law ; and we know 
that the first and only attempt which his successor made brought 
on the crisis which cost him his throne and his head. But the 
declaration that the proposition was false far exceeds in all that 
is disreputable the decision of the Inquisition against the earth's 
motion. We do not mention this little matter in England. 
Knight was a Puritan, and Neal gives a short account of his ser- 
mon. From comparison with Wood, I judge that the theses, as 
given, were not Knight's words, but the digest which it was 
customary to make in criminal proceedings against opinion. 
This heightens the joke, for it appears that the qualifiers of the 
Convocation took pains to present their condemnation of Knight 
in the terms which would most unequivocally make their censure 
condemn themselves. This proceeding took place in the interval 
between the two proceedings against Gralileo : it is left undeter- 
mined whether we must say pot-kettle-pot or kettle-pot-kettle. 



62 A BUDGET OF PARADOXES. 

Liberti Fromondi . . '. Ant-Aristarchus, sive orbis terras immo- 
bilis. Antwerp, 1631, 8vo. 

This book contains the evidence of an ardent opponent of 
Galileo to the fact, that Eoman Catholics of the day did not con- 
sider the decree of the Index or of the Inquisition as a declara- 
tion of their Church. Fromond would have been glad to say as 
much, and tries to come near it, but confesses he must abstain. 
See Penny Cyclop. Suppl. 'Galileo,' and Eng. Cycl. 'Motion 
of the Earth.' The author of a celebrated article in the Dublin 
Review, in defence of the Church of Eome, seeing that Drink- 
water Bethune makes use of the authority of Fromondus, but for 
another purpose, sneers at him for bringing up a ' musty old Pro- 
fessor.' If he had known Fromondus, and used him he would have 
helped his own case, which is very meagre for want of knowledge. 1 

Advis a Monseigneur 1'eminentissime Cardinal Due de Richelieu, 
siir la Proposition faicte par le Sieur Morin pour 1'invention des 
longitudes. Paris, 1634, 8vo. 

This is the Official Eeport of the Commissioners appointed by 
the Cardinal, of whom Pascal is the one now best known, to consider 
Morin's plan. See the full account in Delambre, Hist. Astr. 
Mod. ii. 236, &c. 

Arithmetica et Greometria practica. By Adrian Metius. Ley- 
den, 1640, 4to. 

This book contains the celebrated approximation guessed at by 
his father, Peter Metius, namely, that the diameter is to the 
circumference as 113 to 355. The error is at the rate of about a 
foot in 2,000 miles. Peter Metius, having his attention called 
to the subject by the false quadrature of Duchesne, found that 
the ratio lay between ^-5- and f|. He then took the liberty of 
taking the mean of both numerators and denominators, giving 
44JJ- He had no right to presume that this mean was better than 
either of the extremes ; nor does it appear positively that he did so. 
He published nothing : but his son Adrian, when Van Ceulen's work 
showed how near his father's result came to the truth, first made 
it known in the work above. (See Eng. Cyclop, art. ' Quadrature.') 

A discourse concerning a new world and another planet, in two 

books. London, 1640, 8vo. 
Cosmotheoros : or conjectures concerning the planetary worlds 

1 The article referred to is about thirty years old : since it appeared another has 
been given (Dubl. Rev. Sept. 1865) which is of much greater depth. In it will also bo 
found the Roman view of Bishop Virgil (ante, p. 24). 



PLUEALITY OF WORLDS. 63 

and their inhabitants. Written in Latin, by Christianus Huy- 
ghens. This translation was first published in 1698. Glasgow 
1757, 8vo. [The original is also of 1698.] 

The first work is by Bishop Wilkins, being the third edition, [first 
in 1638] of the first book, 'That the Moon maybe a Planet;' and the 
first edition of the second work, ' That the Earth may be a Planet.' 
[See more under the reprint of 1802.] Whether other planets be 
inhabited or not, that is, crowded with organisations, some of 
them having consciousness, is not for me to decide ; but I should 
be much surprised if, on going to one of them, I should find it 
otherwise. The whole dispute tacitly assumes that, if the stars 
and planets be inhabited, it must be by things of which we can 
form some idea. But for aught we know, what number of such 
bodies there are, so many organisms may there be, of which we 
have no way of thinking nor of speaking. This is seldom re- 
membered. In like manner it is usually forgotten that the matter 
of other planets may be of different chemistry from ours. There 
may be no oxygen and hydrogen in Jupiter, which may have gens 
of its own. But this must not be said : it would limit the omni- 
science of the a priori school of physical inquirers, the larger half 
of the whole, and would be very unphilosophical. Nine-tenths 
of my best paradoxers come out from among this larger half, 
because they are just a lit/tie more than of it at their entrance. 

There was a discussion on the subject some years ago, which 
began with 

The plurality of worlds : an Essay. London, 1853, 8vo. [By Dr. 
Wm. Whewell, Master of Trinity College, Cambridge]. A 
dialogue on the plurality of worlds, being a supplement to the 
Essay on that subject. [First found in the second edition, 1854 ; 
removed to the end in subsequent editions, and separate copies 
issued.] 

A work of sceptical character, insisting on analogies which pro- 
hibit the positive conclusion that the planets, stars, &c., are what 
we should call inhabited worlds. It produced several works and 
a large amount of controversy in reviews. The last predecessor 
of whom I know was 

Plurality of Worlds. . . . By Alexander Maxwell. Second Edition. 

London, 1820, 8vo. 

This work is directed against the plurality by an author who 
does not admit modern astronomy. It was occasioned by Dr. Chal- 
mers's celebrated discourses on religion in connexion with astro- 
nomy. The notes contain many citations on the gravity controversy, 



64 A BUDGET OF PAEADOXES. 

from authors now very little read : and this is its present value. I 
find no mention of Maxwell, not even in Watt. He communicated 
with mankind without the medium of a publisher ; and, from Vieta 
till now, this method has always been favourable to loss of books. 

A correspondent informs me that Alex. Maxwell, who wrote on 
the plurality of worlds, in 1820, was a law-bookseller and pub- 
lisher (probably his own publisher) in Bell Yard. He had pecu- 
liar notions, which he was fond of discussing with his customers. 
He was a bit of a Swedenborgian. 

There is a class of hypothetical creations which do not belong 
to my subject, because they are acknowledged to be fictions, as 
those of Lucian, Eabelais, Swift, Francis Godwin, Voltaire, &c. 
All who have more positive notions as to either the composition 
or organisation of other worlds, than the reasonable conclusion 
that our Architect must be quite able to construct millions of 
other buildings on millions of other plans, ought to rank with 
the writers just mentioned, in all but self-knowledge. Of every 
one of their systems I say, as the Irish Bishop said of Gulliver's 
book, I don't believe half of it. Huyghens had been preceded 
by Fontenelle, who attracted more attention. Huyghens is very 
fanciful and very positive ; but he gives a true account of his 
method. ' But since there's no hopes of a Mercury to carry us 
such a journey, we shall e'en be contented with what's in our 
power : we shall suppose ourselves there. . . .' And yet he says, 
'We have proved that they live in societies, have hands and 
feet. . . .' Kircher had gone to the stars before him, but would 
not find any life in them, either animal or vegetable. 

The question of the inhabitants of a particular planet is one 
which has truth on one side or the other : either there are some 
inhabitants, or there are none. Fortunately, it is of no conse- 
quence which is true. But there are many cases, where the 
balance is equally one of truth and falsehood, in which the choice 
is a matter of importance. My work selects, for the most part, 
sins against demonstration : but the world is full of questions of 
fact or opinion, in which a struggling minority will become a 
majority, or else will be gradually annihilated : and each of the 
cases subdivides into results of good, and results of evil. What is 
to be done ? 

Periculosum est credere et non credere ; 
Hippolitus obiit quia novercee creditum est ; 
Cassandrse quia non creditum ruit Ilium : 
Ergo exploranda est veritas multum prius 
Quam stulta prove judicet sententia. 



VENETIAN PAKADOXERS. LONGOMONTANUS. 65 



Nova Demonstratio immobilitatis terraB petita ex virtute mag- 
netica. Bj Jacobus Grandamicus. Flcxiae (La Fleche), 1645, 
4*o. 

No magnetic body can move about its poles : the earth is a 
magnetic body, therefore, &c. The iron and its magnetism are 
typical of two natures in one person ; so it is said, ' Si exaltatus 
fuero a terra, omnia traham ad me ipsum.' 

Le glorie degli incogniti, o vero gli huomini illustri dell' ac- 
cademia de' signer! incogniti di Venetia. Venice, 1 647, 4to. 

This work is somewhat like a part of my own : it is a budget 
of Venetian nobodies who wished to be somebodies ; but paradox 
is not the only means employed. It is of a serio-comic character, 
gives genuine portraits in copper-plate, and grave lists of works ; 
but satirical accounts. The astrologer Andrew Argoli is there, 
and his son ; both of whom, with some of the others, have place in 
modern works on biography. Argoli's discovery that logarithms 
facilitate easy processes, but increase the labour of difficult ones, 
is worth recording. 

Controversiae de vera circuli mensura . . . inter 

C. S. Longomontanum et Jo. Pellium. Amsterdam, 1647, 4to. 

Longomontanus, a Danish astronomer of merit, squared the 
circle in 1644 : he found out that the diameter 43 gives the square 
root of 18252 for the circumference; which gives 3*14185 . . . 
for the ratio. Pell answered him, and being a kind of circulating 
medium, managed to engage in the controversy names known and 
unknown, as Koberval, Hobbes, Carcavi, Lord Charles Cavendish, 
Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri 
and Grolius. Among them, of course, Longomontanus was made 
mincemeat : but he is said to have insisted on the discovery in his 
epitaph. 

The great circulating mediums, who wrote to everybody, heard 
from everybody, and sent extracts to everybody else, have been 
Father Mersenne, John Collins, and the late Prof. Schumacher : 
all 'late' no doubt, but only the last recent enough to be so 
styled. If M.C.S. should ever again stand for ' Member of the 
Corresponding Society,' it should raise an acrostic thought of the 
three. There is an allusion to Mersenne's occupation in Hobbes's 
reply to him. He wanted to give Hobbes, who was very ill at 
Paris, the Roman Eucharist : but Hobbes said, 'I have settled all 

F 



QQ A BUDGET OF PARADOXES. 

that long ago ; when did you hear from Grassendi ?' We are re- 
minded of William's answer to Burnet. John Collins disseminated 
Newton, among others. Schumacher ought to have been called 
the postmaster-general of astromony, as Collins was called the 
attorney-general of mathematics. 

A late discourse. ... by Sir Kenelme Digby . . . Rendered into 
English by R. White. London, 1658, 12mo. 

On this work see Notes and Queries, 2nd series, vii. 231, 299, 
445, viii. 190. It contains the celebrated sympathetic powder. I 
am still in much doubt as to the connexion of Digby with this 
tract. Without entering on the subject here, I observe that in 
Birch's 'History of the Royal Society,' to which both Digby and 
White belonged, Digby, though he brought many things before 
the Society, never mentioned the powder, which is connected only 
with the names of Evelyn and Sir Gilbert Talbot. The sym- 
pathetic powder was that which cured by anointing the weapon 
with its salve instead of the wound. I have long been convinced 
that it was efficacious. The directions were to keep the wound 
clean and cool, and to take care of diet, rubbing the salve on the 
knife or sword. If we remember the dreadful notions upon drugs 
which prevailed, both as to quantity and quality, we shall readily 
see that any way of not dressing the wound would have been use- 
ful. If the physicians had taken the hint, had been careful of 
diet, &c. , and had poured the little barrels of medicine down the 
throat of a practicable doll, they would have had their magical 
cures as well as the surgeons. Matters are much improved now ; 
the quantity of medicine given, even by orthodox physicians, 
would have been called infinitesimal by their professional ances- 
tors. Accordingly, the College of Physicians has a right to 
abandon its motto, which is Ars longa, vita brevis, meaning 
Practice is long, so life is short. 

Examinatio et emendatio Mathematics Hodiernse. By Thomas 
Hobbes. London. 1666, 4to. 

In six dialogues : the sixth contains a quadrature of the circle. 
But there is another edition of this work, without place or date 
on the title-page, in which the quadrature is omitted. This 
seems to be connected with the publication of another quadra- 
ture, without date, but about 1670, as may be judged from its 
professing to answer a tract of Wallis, printed in 1669. The 
title is ' Quadratura circuli, cubatio sphaBroe, duplicatio cubi,' 4to . 



THOMAS HOBBES. SCALIGER. 67 

Hobbes, who began in 1655, was very wrong in his quadrature ; 
but, though not a Gregory St. Vincent, he was not the ignoramus 
in geometry that he is sometimes supposed. His writings, erro- 
neous as they are in many things, contain acute remarks on points 
of principle. He is wronged by being coupled with Joseph 
Scaliger, as the two great instances of men of letters who have 
come into geometry to help the mathematicians out of their diffi- 
culty. I have never seen Scaliger's quadrature, except in the 
answers of Adrianus Eomanus, Vieta and Clavius, and in the 
extracts of Kastner. Scaliger had no right to such strong oppo- 
nents : Erasmus or Bentley might just as well have tried the 
problem, and either would have done much better in any twenty 
minutes of his life. 

Scaliger inspired some mathematicians with great respect for 
his geometrical knowledge. Vieta, the first man of his time, who 
answered him, had such regard for his opponent as made him 
conceal Scaliger's name. Not that he is very respectful in his 
manner of proceeding : the following dry quiz on his opponent's 
logic must have been very cutting, being true. ' In grammaticis, 
dare navibus Austros, et dare naves Austris, sunt aeque significantia. 
Sed in Geometricis, aliud est adsumpsisse circulum BCD non esse 
majorem triginta sex segmentis BCDF, aliud circulo BCD non esse 
majora trigiuta sex segmenta BCDF. Ilia adsumptiuncula vera est^ 
hoec falsa.' Isaac Casaubon, in one of his letters to De Thou, 
relates that, he and another paying a visit to Vieta, the conversa- 
tion fell upon Scaliger, of whom the host said that he believed 
Scaliger was the only man who perfectly understood mathematical 
writers, especially the Greek ones : and that he thought more of 
Scaliger when wrong than of many others when right ; pluris se 
Scaligerum vel errantem facere quam multos KaropSovvras. This 
must have been before Scaliger's quadrature (1594). There is an 
old story of some one saying, ' Mallem cum Scaligero errare, quam 
cum Clavio recte sapere.' This I cannot help suspecting to have 
been a version of Vieta's speech with Clavius satirically inserted, 
on account of the great hostility which Vieta showed towards 
Clavius in the latter years of his life. 

Montucla could not have read with care either Scaliger's quadra- 
ture or Clavius's refutation. He gives the first a wrong date : he 
assures the world that there is no question about Scaliger's quad- 
rature being wrong, in the eyes of geometers at least : and he 
states that Clavius mortified him extremely by showing that it 
made the circle less than its inscribed dodecagon, which is, of 
course, equivalent to asserting that a straight line is not always 

F 2 



68 A BUDGET OF PARADOXES. 

the shortest distance between two points. Did Clavius show 
this ? No, it was Scaliger himself who showed it, boasted 
of it, and declared it to be a ' noble paradox ' that a theorem 
false in geometry is true in arithmetic ; a thing, he says with 
great triumph, not noticed by Archimedes himself! He says in 
so many words that the periphery of the dodecagon is greater 
than that of the circle ; and that the more sides there are to the 
inscribed figure, the more does it exceed the circle in which it is. 
And here are the words, on the independent testimonies of Clavius 
and Kastner : 

Ambitus dodecagon! circulo inscribendi plus potest quam circuli am- 
bitus. Et quanto deinceps pluriuin laterum fuerit polygonum circulo 
inscribendum, tanto plus poterit ambitus polygoni quam ambitus 
circuli. 

There is much resemblance between Joseph Scaliger and 
William Hamilton, in a certain impetuosity of character, and in- 
aptitude to think of quantity. Scaliger maintained that the arc 
of a circle is less than its chord in arithmetic, though greater in 
geometry ; Hamilton arrived at two quantities which are identi- 
cal, but the greater the one the less the other. But, on the whole, 
I liken Hamilton rather to Julius than to Joseph. On this last 
hero of literature I repeat Thomas Edwards, who says that a man 
is unlearned who, be his other knowledge what it may, does not 
understand the subject he writes about. And now one of many 
instances in which literature gives to literature character in 
science. Anthony Teissier, the learned annotator of De Thou's 
biographies, says of Finseus, ' II se vanta sans raison avoir trouve 
la quadrature du cercle ; la gloire de cette admirable decouverte 
etait reservee a Joseph Scaliger, comme 1'a ecrit Scevole de 
St. Marthe.' 

Natural and Political Observations . . . npon the Bills of 
Mortality. By John Graunt, citizen of London. London, 1662, 
4to. 

This is a celebrated book, the first great work upon mortality. 
But the author, going ultra crepidam, has attributed to the 
motion of the moon in her orbit all the tremors which she gets 
from a shaky telescope. But there is another paradox about this 
book : the above absurd opinion is attributed to that excellent 
mechanist, Sir William Petty, who passed his days among the 
astronomers. Orraunt did not write his own book I Anthony Wood 
hints that Petty ' assisted, or put into a way ' his old benefactor : 
no doubt the two friends talked the matter over many a time. 



JOHN GEAUNT. GADBURY ON COMETS. 69 

Burnet and Pepys state that Petty wrote the book. It is enough 
for me that Graunt, whose honesty was never impeached, uses the 
plainest incidental professions of authorship throughout ; that he 
was elected into the Eoyal Society because he was the author ; 
that Petty refers to him as author in scores of places, and published 
an edition, as editor, after Graunt's death, with Graunt's name of 
course. The note on Graunt in the ' Biographia Britannica ' may 
be consulted ; it seems to me decisive. Mr. C. B. Hodge, an able 
actuary, has done the best that can be done on the other side in the 
Assurance Magazine, viii. 234. If I may say what is in my mind, 
without imputation of disrespect, I suspect some actuaries have 
a bias : they would rather have Petty the greater for their Cory- 
pha3us than Graunt the less. 

Pepys is an ordinary gossip : but Burnet's account has an ani- 
mus which is of a worse kind. He talks of ' one Grraunt, a Papist, 
under whose name Sir William Petty published his observations 
on the bills of mortality.' He then gives the cock without a bull 
story of Graunt being a trustee of the New River Company, and 
shutting up the cocks and carrying off their keys, just before the 
fire of London, by which a supply of water was delayed. It was 
one of the first objections made to Burnet's work, that Graunt was 
not a trustee at the time ; and Maitland, the historian of London, 
ascertained from the books of the Company that he was not 
admitted until twenty-three days after the breaking out of the 
fire. Graunt's first admission to the Company took place on the 
very day on which a committee was appointed to inquire into the 
cause of the fire. So much for Burnet. I incline to the view that 
Graunt's setting London on fire strongly corroborates his having 
written on the bills of mortality : every practical man takes stock 
before he commences a grand operation in business. 

De Cometis : or a discourse of the natures and effects of 
Comets, as they are philosophically, historically, and astrologi- 
cal^ considered. With a brief (yet full) account of the III late 
Comets, or blazing stars, visible to all Europe. And what (in a 
natural way of judicature) they portend. Together with some 
observations on the nativity of the Grand Seignior. By John 
Gadbury, ^iXo^a^qyuartk-o'c. London, 1665, 4to. 

Gadbury, though his name descends only in astrology, was a well- 
informed astronomer. D'Israeli sets down Gadbury, Lilly, Wharton, 
Booker, &c., as rank rogues : I think him quite wrong. The easy 
belief in roguery and intentional imposture which prevails in 
edueated society is, to my mind, a greater presumption against the 



70 A BUDGET OF PARADOXES. 

honesty of mankind than all the roguery and imposture itself. 
Putting aside mere swindling for the sake of gain, and looking at 
speculation and paradox, I find very little reason to suspect wilful 
deceit. My opinion of mankind is founded upon the mournful fact 
that, so far as I can see, they find within themselves the means of 
believing in a thousand times as much as there is to believe in, 
judging by experience. I do not say anything against Isaac 
D'Israeli for talking his time. We are all in the team, and we all 
go the road, but we do not all draw. 

An essay towards a real character and a philosophical language. 
By John Wilkins [Dean of Ripon, afterwards Bishop of 
Chester]. London, 1668, folio. 

This work is celebrated, but little known. Its object gives it 
a right to a place among paradoxes. It proposes a language if 
that be the proper name in which things and their relations 
shall be denoted by signs, not words : so that any person, what- 
ever may be his mother tongue, may read it in his own words. 
This is an obvious possibility, and, I am afraid, an obvious im- 
practicability. One man may construct such a system Bishop 
Wilkins has done it but where is the man who will learn it ? 
The second tongue makes a language, as the second blow makes a 
fray. There has been very little curiosity about his performance, 
the work is scarce ; and I do not know where to refer the reader for 
any account of its details, except to the partial reprint of Wilkins 
presently mentioned under 1802, in which there is an unsatisfac- 
tory abstract. There is nothing in the ' Biographia Britannica,' 
except discussion of Anthony Wood's statement that the hint was 
derived from Dalgarno's book, ' De Signis,' 1661. Hamilton 
(' Discussions,' Art. 5,' Dalgarno ') does not say a word on this point, 
beyond quoting Wood ; and Hamilton, though he did now and 
then write about his countrymen with a rough-nibbed pen, knew 
perfectly well how to protect their priorities. 

Problema Austriacum. Plus ultra Quadratura Circuli. Auctore 
- P. Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, 
folio. Opus Geometricum posthumum ad Mesolabium. By the 
same. Gandavi [Ghent], 1668, folio. 

The first book has more than 1200 pages, on all kinds of 
geometry. Gregory St. Vincent is the greatest of circle-squarers, 
and his investigations led him into many truths : he found the 
property of the area of the hyperbola which led to Napier's loga- 
rithms being called hyperbolic. Montucla says of him, with sly 



THE MESOLABUM. GEOMETRICAL QUADRATURE. 71 

truth, that no one has ever squared the circle with so much genius, 
or, excepting his principal object, with so much success. His 
reputation, and the many merits of his work, led to a sharp con- 
troversy on his quadrature, which ended in its complete exposure 
by Huyghens and others. He had a small school of followers, 
who defended him in print. 

Renati Francisci Slusii Hesolabum. Leodii Eburonum [Liege], 
1668, 4to. 

The Mesolabum is the solution of the problem of finding two 
mean proportionals, which Euclid's geometry does not attain. 
Slusius is a true geometer, and uses the ellipse, &c.: but he is 
sometimes ranked with the trisectors, for which reason I place him 
here, with this explanation. 

The finding of two mean proportionals is the preliminary to the 
famous old problem of the duplication of the cube, proposed by 
Apollo (not Apollonius) himself. D'Israeli speaks of the ' six 
follies of science,' the quadrature, the duplication, the perpetual 
motion, the philosopher's stone, magic, and astrology. He might 
as well have added the trisection, to make the mystic number seven : 
but had he done so, he would still have been very lenient ; only 
seven follies in all science, from mathematics to chemistry ! 
Science might have said to such a judge as convicts used to say 
who got seven years, expecting it for life, ' Thank you, my Lord, 
and may you sit there till they are over,' may the Curiosities of 
Literature outlive the Follies of Science ! 

1668. In this year James Gregory, in his Vera Circuli et 
Hyperbolce Quadratura, held himself to have proved that the 
geometrical quadrature of the circle is impossible. Few mathe- 
maticians read this very abstruse speculation, and opinion is 
somewhat divided. The regular circle-squarers attempt the 
arithmetical quadrature, which has long been proved to be impos- 
sible. Very few attempt the geometrical quadrature. One of 
the last is Malacarne, an Italian, who published his Solution 
Geometrique, at Paris, in 1825. His method would make the 
circumference less than three times the diameter. 

La Geomeh-ie Frai^oise, ou la Pratique aisee ... La quadracture 
du cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe du 
Boi . . . Paris, 1676, 8vo. [not Poutault de Beaulieu, the cele- 
brated topographer ; he died in 1674]. 

If this book had been a fair specimen, I might have pointed 
to it in connection with contemporary English works, and made 



72 A BUDGET OF PAKADOXES. 

a scornful comparison. But it is not a fair specimen. Beaulieu 
was attached to the Eoyal Household, and throughout the century 
it may be suspected that the household forced a royal road to 
geometry. Fifty years before, Beaugrand, the king's secretary, 
made a fool of himself, and [so ?] contrived to pass for a geometer. 
He had interest enough to get Desargues, the most powerful 
geometer of his time, the teacher and friend of Pascal, prohibited 
from lecturing. See some letters on the History of Perspective, 
which I wrote in the Athenceum, in October and November, 
1861. Montucla, who does not seem to know the true secret of 
Beaugrand's greatness, describes him as ' un certain M. de Beau- 
grand, mathematicien, fort mal traite par Descartes, et a ce qu'il 
paroit avec justice.' 

Beaulieu's quadrature amounts to a geometrical construction 
which gives ?r= V'lO. His depth may be ascertained from the 
following extracts. First, on Copernicus : 

Copernic, Allenaand, ne s'esfc pas moins rendu illustre par ses doctes 
ecrits ; et nous pourrions dire de luy, qu'il seroit le seul et unique en 
la force de ses Problemes, si sa trop grande presomption ne 1'avoit 
porte a avancer en cette Science une proposition aussi absurde, qu'elle 
est centre la Foy et raison, en faisant la circonference d'un Cercle fixe, 
immobile, et le centre mobile, sur lequel principe Geometrique, il a 
avance en son Traitte Astrologique le Soleil fixe, et la Terre mobile. 

I digress here to point out that though our quadrators, &c., 
very often, and our historians sometimes, assert that men of the 
character of Copernicus, &c. were treated with contempt and 
abuse until their day of ascendancy came, nothing can be more 
incorrect. From Tycho Brahe to Beaulieu, there is but one 
expression of admiration for the genius of Copernicus. There is 
an exception, which, I believe, has been quite misunderstood. 
Maurolycus, in his 'De Sphaera,' written many years before its 
posthumous publication in 1575, and which it is not certain he 
would have published, speaking of the safety with which various 
authors may be read after his cautions, says, ' Toleratur et 
Nicolaus Copernicus qui Solem fixum et Terrain in girum 
circumverti posuit : et scutica potius, aut flagello, quam repre- 
hensione dignus est.' Maurolycus was a mild and somewhat 
contemptuous satirist, when expressing disapproval : as we should 
now say, he pooh-poohed his opponents ; but, unless the above 
be an instance, he was never savage nor impetuous. I am fully 
satisfied that the meaning of the sentence is, that Copernicus, 
who turned the earth like a boy's top, ought rather to have a whip 
given him wherewith to keep up his plaything than a serious 



BEAULIEU'S ALGEBRA. SIR M. HALE. 73 

refutation. To speak of tolerating a person as being more worthy 
of a flogging than an argument, is almost a contradiction. 
I will now extract Beaulieu's treatise on algebra, entire. 

L'Algebre est la science curieuse des S9avans et specialement d'un 
General d'Armee on Capitaine, pour promptement ranger une Armee 
en bataille, et nombre de Mousquetaires et Piquiers qui composent les 
bataillons d'icelle, outre les figures de I'Arithmetique. Cette science a 
5 figures particulieres en cette sorte. P signifie plus au commerce, et 
a 1'Armee Piquiers. M signifie moins, et Mousquetaire en 1'Art dcs 
bataillons. [It is quite true that P and M were used for plus and minus 
in a great many old works.] R signifie ratine en la mesure du Cube, 
et en 1'Armee rang. Q signifie quare en Tun et 1'autre usage. C 
signifie cube en la mesure, et Cavallerie en la composition des bataillons 
et escadrons. Quant a 1'operation de cette science, c'est d'additionner 
un plus d'avec plus, la somme sera plus, et moins d'avec plus, on 
soustrait le moindre du plus, etlareste est la somme requise ou nombre 
trouve. Je dis seulement cecy en passant pour ceux qui n'en S9avent 
rien du tout. 

This is the algebra of the Koyal Household, seventy-three years 
after the death of Vieta. Quaere, is it possible that the fame of 
Vieta, who himself held very high stations in the household all 
his life, could have given people the notion that when such an 
officer chose to declare himself an algebraist, he must be one 
indeed ? This would explain Beaugrand, Beaulieu, and all the 
beaux. Beaugrand not only secretary to the king, but ' mathe- 
matician ' to the Duke of Orleans I wonder what his 'fool 'could 
have been like, if indeed he kept the offices separate, would 
have been in my list if I had possessed his Geostatique, pub- 
lished about 1638. He makes bodies diminish in weight as they 
approach the earth, because the effect of a weight on a lever is 
less as it approaches the fulcrum. 

Remarks upon two late ingenious discourses . . . By Dr. Henry 
More. London, 1676, 8vo. 

In 1673 and 1675, Matthew Hale, then Chief Justice, published 
two tracts, an ' Essay touching Gravitation,' and ' Difficiles Nuga?' 
on the Torricellian experiment. Here are the answers by the 
learned and voluminous Henry More. The whole would be 
useful to any one engaged in research about ante-Newtonian 
notions of gravitation. 



74 A BUDGET OF PABADOXES. 



Observations touching the principles of natural motions ; and 
especially touching rarefaction and condensation . . . By the 
author of Difficiles Nugce. London, 1677, 8vo. 

This is another tract of Chief Justice Hale, published the year 
after his death. The reader will remember that motion, in old 
philosophy, meant any change from state to state : what we now 
describe as motion was local motion. This is a very philosophical 
book, about flux and materia prima, virtus activa and essentialis, 
and other fundamentals. I think Stephen Hales, the author of 
the ' Vegetable Statics,' has the writings of the Chief Justice 
sometimes attributed to him, which is very puny justice indeed. 
Matthew Hale died in 1676, and from his devotion to science it 
probably arose that his famous Pleas of the Crown and other law 
works did not appear until after his death. One of his con- 
temporaries was the astronomer Thomas Street, whose Caroline 
Tables were several times printed : another contemporary was 
his brother judge, Sir Thomas Street. But of the astronomer 
absolutely nothing is known : it is very unlikely that he and the 
judge were the same person, but there is not a bit of positive evi- 
dence either for or against, so far as can be ascertained. Halley 
no less a person published two editions of the 'Caroline Tables,' no 
doubt after the death of the author : strange indeed that neither 
Halley nor any one else should leave evidence that Street was 
born or died. 

Matthew Hale gave rise to an instance of the lengths a lawyer 
will go when before a jury who cannot detect him. Sir Samuel 
Shepherd, the Attorney General, in opening Hone's first trial, 
calls him ' one who was the most learned man that ever adorned 
the Bench, the most even man that ever blessed domestic life, the 
most eminent man that ever advanced the progress of science, 
and one of the [very moderate] best and most purely religious 
men that ever lived. 

Basil Valentine his triumphant Chariot of Antimony, with 
annotations of Theodore Kirkringius, M.D. With the true book 
of the learned Synesius, a Greek abbot, taken out of the 
Emperour's library, concerning the Philosopher's Stone. 
London, 1678, 8vo. 

There are said to be three Hamburg editions of the collected 
works of Valentine, who discovered the common antimony, and 
is said to have given the name antimoine, in a curious way. 
Finding that the pigs of his convent throve upon it, he gave it 



BASIL VALENTINE. THE ALCHEMISTS. 75 

to his brethren, who died of it. The impulse given to chemistry 
by E. Boyle seems to have brought out a vast number of transla- 
tions, as in the following tract : 

Collectanea Chymica : A collection of ten several treatises in 
chymistry, concerning the liquor Alkehest, the Mercury of 
Philosophers, and other curiosities worthy the perusal. Written 
by Eir. Philaletha, Anonymus, J. B. Van-Helmont, Dr. Fr. 
Antonie, Bernhard Earl of Trevisan, Sir Geo. Bipley, Rog. 
Bacon, Geo. Starkie, Sir Hugh Platt, and the Tomb of Semira- 
mis. See more in the contents. London, 1684, 8vo. 

In- the advertisements at the ends of these tracts there are 
upwards of a hundred English tracts, nearly all of the per:od, 
and most of them translations. Alchemy looks up since the 
chemists have found perfectly different substances composed of 
the same elements and proportions. It is true the chemists 
cannot yet transmute ; but they may in time : they poke about 
most assiduously. It seems, then, that the conviction that 
alchemy must be impossible was a delusion: but we do not 
mention it. 

The astrologers and the alchemists caught it in company in 
the following, of which I have an unreferenced note. 

Mendacem et futilem hominem nominare qui volunt, calenda- 
riographum. dicunt ; at qui sceleratum simul ac impostorem, 
chimicum. 

Credo ratem rentis, corpus ne crede chimistis ; 
Est qusevis chimica tutior aura fide. 

Among the smaller paradoxes of the day is that of the Times 
newspaper, which always spells it chymistry : but so, I believe, 
do Johnson, Walker, and others. The Arabic word is very likely 
formed from the Greek : but it may be connected either with 
or with 



Lettre d'un gentil-homme de province a une dame de qualite, 
sur le sujet de la Comete. Paris, 1681, 4to. 

An opponent of astrology, whom I strongly suspect to have 
been one of the members of the Academy of Sciences under the 
name of a country gentleman, writes very good sense on the 
tremors excited by comets. 



76 A BUDGET OF PARADOXES. 



The Petitioning- Comet : or, a brief Chronology of all the famous 
Comets and their events, that have happened from the birth of 
Christ to this very day. Together with a modest enquiry into 
this present comet, London, 1681, 4to. 

A satirical tract against cometic prophecy : 

' This present comet (it's true) is of a menacing aspect, but if the 
neiv parliament (for whose convention so many good men pray) continue 
long to sit, I fear not but the star will lose its virulence and malignancy, 
or at least its portent be averted from this our nation ; which being 
the humble request to God of all good men, makes me thus entitle it, 
a Petitioning-Comet. 

The following anecdote is new to me : 

Queen Elizabeth (1558) being then at Richmond, and being 
disswaded from looking on a comet which did then appear, made 
answer, jacta est alea, the dice are thrown ; thereby intimating that 
the pre-order'd providence of God was above the influence of any star 
or comet. 

The argument was worth nothing : for the comet might have 
been on the dice with the event ; the astrologers said no more, 
at least the more rational ones, who were about half of the 
whole. 

An astrological and theological discourse upon this present 
great conjunction (the like whereof hath not (likely) been in 
some ages) ushered in by a great comet. London, 1682, 4to. 
By C. ST. 

The author foretells the approaching ' sabbatical jubilee,' but 
will not fix the date : he recounts the failures of his predeces- 
sors. 

A judgment of the comet which became first generally visible 
to us in Dublin, December 13, about 15 minutes before 5 in the 
evening, A.D. 1680. By a person of quah'ty. Dublin, 1682, 
4to. 

The author argues against cometic astrology with great ability. 

A prophecy on the conjunction of Saturn and Jupiter in this 
present year 1682. With some prophetical predictions of what 
is likely to ensue therefrom in the year 1684. By John Case, 
Student in physic and astrology. London, 1682, 4to. 

According to this writer, great conjunctions of Jupiter and 
Saturn occur 'in the fiery trigon,' about once in 800 years. Of 



MARCELIS. MATHEMATICAL THEOLOGY. 77 

these there are to be seven : six happened in the several times 
of Enoch, Noah, Moses, Solomon, Christ, Charlemagne. The 
seventh, which is to happen at ' the lamb's marriage with the 
bride,' seems to be that of 1682 ; but this is only vaguely hinted. 

De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 

1698, 4to. 
Ampliatie en demonstratie wegens de Quadrature . . . By Jacob 

Marcelis. Amsterdam, 1699, 4to. 
Eenvoudig vertoog briev-wys geschrevem am J. Marcelis . . 

Amsterdam, 1702, 4to. 
De sleutel en openinge van de quadrature. . . . Amsterdam, 

1704, 4to. 

Who shall contradict Jacob Marcelis ? He says the circum- 
ference contains the diameter exactly times 

0100844908737754167989428218489J4 
6997183037540819440035239271702 

But he does not come very near, as the young arithmetician will 
rind. 

Theologiffi Christianas Principia Mathematica. Auctore Johanne 
Craig. London, 1699, 4to. 

This is a celebrated speculation, and has been reprinted abroad, 
and seriously answered. Craig is known in the early history of 
fluxions, and was a good mathematician. He professed to calcu- 
late, on the hypothesis that the suspicions against historical 
evidence increase with the square of the time, how long it will 
take the evidence of Christianity to die out. He finds, by 
formulae, that had it been oral only, it would have gone out 
A.D. 800 ; but, by aid of the written evidence, it will last till 
A.D. 3150. At this period he places the second coming, which is 
deferred until the extinction of evidence, on the authority of the 
question ' When the Son of Man cometh, shall he find faith on 
the earth ? ' It is a pity that Craig's theory was not adopted : it 
would have spared a hundred treatises on the end of the world, 
founded on no better knowledge than his, and many of them 
falsified by the event. The most recent (October, 1863) is a 
tract in proof of Louis Napoleon being Antichrist, the Beast, the 
eighth Head, &c.; and the present dispensation is to close soon 
after 1864. 

In order rightly to judge Craig, who added speculations on the 
variations of pleasure and pain treated as functions of time, it is 



78 A BUDGET OF PAEADOXES. 

necessary to remember that in Newton's day the idea of force, as a 
quantity to be measured, and as following a law of variation, was 
very new : so likewise was that of probability, or belief, as an object 
of measurement. The success of the ' Principia ' of Newton put it 
into many heads to speculate about applying notions of quantity 
to other things not then brought under measurement. Craig 
imitated Newton's title, and evidently thought he was making 
a step in advance : but it is not every one who can plough with 
Samson's heifer. 

It is likely enough that Craig took a hint, directly or in- 
directly, from Mahometan writers, who make a reply to the 
argument that the Koran has not the evidence derived from 
miracles. They say that, as evidence of Christian miracles is 
daily becoming weaker, a time must at last arrive when it will 
fail of affording assurance that they were miracles at all : 
whence would arise the necessity of another prophet and other 
miracles. Lee, the Cambridge orientalist, from whom the above 
words are taken, almost certainly never heard of Craig or his 
theory. 

Copernicans of all sorts convicted ... to which is added a Treatise 
of the Magnet. By the Hon. Bdw. Howard, of Berks. London, 
1705, 8vo. 

Not all the blood of all the Howards will gain respect for a 
writer who maintains that eclipses admit no possible explanation 
under the Copernican hypothesis, and who asks how a man can 
' go 200 yards to any place if the moving superficies of the earth 
does carry it from him ? ' Horace Walpole, at the beginning of 
his ' Eoyal and Noble Authors,' has mottoed his book with the 
Cardinal's address to Ariosto, 'Dove diavolo, Messer Ludovico, 
avete pigliato tante coglionerie ? ' Walter Scott says you could 
hardly pick out, on any principle of selection except badness 
itself, he means of course the same number of plebeian authors 
whose works are so bad. But his implied satire on aristocratic 
writing forgets two points. First, during a large period of our 
history, when persons of rank condescended to write, they veiled 
themselves under 'a person of honour,' ' a person of quality,' and 
the like, when not wholly undescribed. Not one of these has 
Walpole got ; he omits, for instance, Lord Brounker's translation 
of Descartes on Music. Secondly, Walpole only takes the heads 
of houses : this cuts both ways ; he equally eliminates the Hon. 
Robert Boyle and the precious Edward Howard. This last writer 
is hardly out of the time in which aristocracy suppressed its 



WHISTON, DITTOS, AND SWIFT. 79 

names ; the avowal was then usually meant to make the author's 
greatness useful to the book. In our day, literary peers and 
honourables are very favourably known, and contain an eminent 
class. They rough it like others, and if such a specimen as Edw. 
Howard were now to appear, he would be greeted with 

Hereditary noodle ! knowest thou not, 

Who would be wise, himself must make him so ? 

A new and easy method to find the longitude at land or sea. 
London, 1710, 4to. 

This tract is a little earlier than the great epoch of such publi- 
cations (1714), and professes to find the longitude by the observed 
altitudes of the moon and two stars. 

A new method for discovering the longitude both at sea and 
land, humbly proposed to the consideration of the public. By 
Wm. Whiston and Humphry Ditton. London, 1714, 8vo. 

This is the celebrated tract, written by the two Arian heretics. 
Swift, whose orthodoxy was as undoubted as his meekness, wrote 
upon it the epigram if, indeed, that be epigram of which the 
point is pious wish which has been so often recited for the 
purity of its style, a purity which transcends modern printing. 
Perhaps some readers may think that Swift cared little for Whiston 
and Ditton, except as a chance hearing of their plan pointed them 
out as good marks. But it was not so : the clique had their eye 
on the guilty pair before the publication of the tract. The pre- 
face is dated July 7 ; and ten days afterwards Arbuthnot writes 
as follows to Swift : 

Whiston has at last published his project of the longitude ; the most 
ridiculous thing that ever was thought on. But a pox on him ! lie has 
spoiled one of my papers of Scriblerus, which was a proposition for the 
longitude not very unlike his, to this purpose ; that since there was no 
pole for east and west, that all the princes of Europe should join and 
build two prodigious poles, upon high mountains, with a vast lighthouse 
to serve for a polestar. I was thinking of a calculation of the time, 
charges, and dimensions. Now you must understand his project is by 
lighthouses, and explosion of bombs at a certain hour. 

The plan was certainly impracticable ; but Whiston and Ditton 
might have retorted that they were nearer to the longitude than 
their satirist to the kingdom of heaven, or even to a bishopric. 
Arbuthnot, I think, here and elsewhere, reveals himself as the 
calculator who kept Swift right in his proportions in the matter 



80 A BUDGET OF PARADOXES. 

of the Lilliputians, Brobdingnagians, &c. Swift was very ignorant 
about things connected with number. He writes to Stella that 
he has discovered that leap-year comes every four years, and that 
all his life he had thought it came every three years. Did he 
begin with the mistake of Caesar's priests ? Whether or no, when 
I find the person who did not understand leap-year inventing 
satellites of Mars in correct accordance with Kepler's third law, 
I feel sure he must have had help. 



An essay concerning the late apparition in the heavens on the 
6th of March. Proving by mathematical, logical, and moral 
arguments, that it cou'd not have been produced meerly by the 
ordinary course of nature, but must of necessity be a prodigy. 
Humbly offered to the consideration of the Royal Society. 
London, 1716, 8vo. 

The prodigy, as described, was what we should call a very 
decided and unusual aurora borealis. The inference was, that 
men's sins were bringing on the end of the world. The author 
thinks that if one of the old ' threatening prophets ' were then 
alive, he would give ' something like the following.' I quote a 
few sentences of the notion which the author had of the way in 
which Ezekiel, for instance, would have addressed his Maker in 
the reign of George the First : 

Begin ! Begin ! Sovereign, for once, with an effectual clap of 
thunder. ... Deity ! either thunder to us no more, or when you 
thunder, do it home, and strike with vengeance to the mark. . . . 'Tis 
not enough to raise a storm, unless you follow it with a blow, and the 
thunder without the bolt, signifies just nothing at all. . . . Are then 
your lightnings of so short a sight, that they don't know how to hit, 
unless a mountain stands like a barrier in their way ? Or perhaps so 
many eyes open in the firmament make you lose your aim when you 
shoot the arrow ? Is it this ? No ! but, my dear Lord, it is your 
custom never to take hold of your arms till you have first bound round 
your majestic countenance with gathered mists and clouds. 

The principles of the Philosophy of the Expansive and Con- 
tractive Forces. ... By Robert Greene, M.A., Fellow of Clare 
Hall. Cambridge, 1727, folio. 

Sanderson writes to Jones : 'The gentleman has been reputed 
mad for these two years last past, but never gave the world such 
ample testimony of it before.' This was said of a former work of 
Greene's, on solid geometry, published in 1712, in which he gives 



NEWTON'S APPLE. 81 

a quadrature. He gives the same or another, I do not know 
which, in the present work, in which the circle is 3^- diameters. 
This volume is of 981 good folio pages, and treats of all thino-s, 
mental and material. The author is not at all mad, only wrong 
on many points. It is the weakness of the orthodox follower of 
any received system to impute insanity to the solitary dissentient : 
which is voted (in due time) a very wrong opinion about Coper- 
nicus, Columbus, or Galileo, but quite right about Robert Greene. 
If misconceptions, acted on by too much self-opinion, b$ sufficient 
evidence of madness, it would be a curious inquiry what is the 
least per-centage of the reigning school which has been insane at 
any one time. Greene is one of the sources for Newton being led 
to think of gravitation by the fall of an apple : his authorit" 7 is 
the gossip of Martin Folkes. Probably Folkes had it from 
Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as 
//'"> authority. It is in the draft found among Conduitt's papers 
of memoranda to be sent to Fontenelle. But Fontenelle, though 
a great retailer of anecdote, does not mention it in his eloge of 
Newton ; whence it may be suspected that it was left out in the 
copy forwarded to France. D'Israeli has got an improvement on 
the story : the apple * struck him a smart blow on the head : ' no 
doubt taking him just on the organ of causality. He was ' surprised 
at the force of the stroke ' from so small an apple : but then the 
apple had a mission ; Homer would have said it was Minerva in 
the form of an apple. ' This led him to consider the accelerating 
motion of falling bodies,' which Galileo had settled long before : 
' from whence he deduced the principle of gravity,' which many 
had considered before him, but no one had deduced anything from 
it. I cannot imagine whence D'Israeli got the rap on the head, 
I mean got it for Newton : this is very unlike his usual accounts 
of things. The story is pleasant and possible : its only defect is 
that various writings, well known to Newton, a very learned 
mathematician, had given more suggestion than a whole sack of 
apples could have done, if they had tumbled on that mighty head 
all at once. And Pemberton, speaking from Newton himself, 
says nothing more than that the idea of the moon being retained 
by the same force which causes the fall of bodies struck him for 
the first time while meditating in a garden. One particular tree 
at. Woolsthorpe has been selected as the gallows of the apple- 
shaped goddess: it died in 1820, and Mr. Tumor kept the wood ; 
but Sir D. Brewster brought away a bit of root in 1814, and must 
have had it on his conscience for 43 years that he may have killed 
the tree. Kepler's suggestion of gravitation with the inverse 

G 



82 A BUDGET QF PARADOXES. 

distance, and Bouillaud's proposed substitution of the inverse 
square of the distance, are things which Newton knew better than 
his modern readers. I discovered two anagrams on his name, 
which are quite conclusive : the notion of gravitation was not 
new ; but Newton vuent on. Some wandering spirit, probably, 
whose business it was to resent any liberty taken with Newton's 
name, put into the head of a friend of mine eighty-one anagrams 
on my own pair, some of which hit harder than any apple. 

This friend, whom I must not name, has since made it up to 
about 800 anagrams on my name, of which I have seen about 
650. Two of them I have joined in the title-page : the reader 
may find the sense. A few of the others are personal remarks. 

Great gun ! do us a sum ! 
is a sneer at my pursuits : but, 

Go ! great sum ! fa u du 

is more dignified. 

Sunt agro ! gaudemus, 

is happy as applied to one of whom it may be said : 

Ne'er out of town ; 'tis such a horrid life : 
But duly sends his family and wife. 

Adsum, nugator, suge ! 

is addressed to a student who continues talking after the lecture 
has commenced : oh ! the rascal ! 

Graduatus sum ! nego 
applies to one who declined to subscribe for an M.A. degree. 

Usage mounts guard 
symbolises a person of very fixed habits. 

Gus ! Gus ! a mature don ! 

August man ! sure, god ! 
And Gus must argue, ! 

Snug as mud to argue, 
Must argue on gauds. 

A mad rogue stung us. 
Gag a numerous stud. 

Go ! turn us ! damage us ! 
Tug us ! O drag us ! Amen. 

Grudge us ! moan at us ! 
Daunt us ! gag us more ! 

TJog-ear us, man ! gut us ! 
D us ! a ro^ue tuers ! 



TREATISE ASCRIBED TO NEWTON. 83 

are addressed to me by the circle-squarers ; and, 
O ! Gus ! tug a mean surd ! 

is smart upon my preference of an incommensurable value of TT 
to 3^, or some such simple substitute. While, 
Gus ! Gus ! at 'em a' round ! 

ought to be the backing of the scientific world to the author of 
the c Budget of Paradoxes.' 

The whole collection commenced existence in the head of a 
powerful mathematician during some sleepless nights. Seeing 
how large a number was practicable, he amused himself by in- 
venting a digested plan of finding more. 

Is there any one whose name cannot be twisted into either 
praise or satire ? I have had given to me, 

Thomas Babington Macaulay 
Mouths big : a Cantab anomaly. 

A treatise of the system of the world. By Sir Isaac Newton. 
Translated into English. London, 1728, 8vo. 

I think I have a right to one little paradox of my own : I 
greatly doubt that Newton wrote this book. Castiglione, in his 
'Newtoni Opuscula,' gives it in the Latin which appeared in 1731, 
not for the first time ; he says Angli omnes Newtono trihuunt. It 
appeared just after Newton's death, without the name of any 
editor, or any allusion to Newton's recent departure, purporting 
to be that popular treatise which Newton, at the beginning of 
the third book of the * Principia,' says he wrote, intending it to 
be the third book. It is very possible that some observant turn- 
penny might construct such a treatise as this from the third book, 
that it might be ready for publication the moment Newton could 
not disown it. It has been treated with singular silence : the 
name of the editor has never been given. Riband mentions it 
without a word : I cannot find it in Brewster's Newton, nor in the 
' Biographia Britannica.' There is no copy in the Catalogue of 
the Royal Society's Library, either in English or Latin, except in 
Castiglione. I am open to correction ; but I think nothing from 
Newton's acknowledged works will prove as laid down in the 
suspected work that he took Numa's temple of Vesta, with a 
central fire, to be intended to symbolise the sun as the centre of 
our system, in the Copernican sense. 

Mr.Edleston gives an account of the lectures ' de motu corporum,* 
and gives the corresponding pages of the Latin ' De 

o 2 



84 A BUDGET OF PAEADOXES. 

Mundi' of 1731. But no one mentions the English of 1728. 
This English seems to agree with the Latin ; but there is a mystery 
about it. The preface says, ' That this work as here published is 
genuine will so clearly appear by the intrinsic marks it bears, that 
it will be but losing words and the reader's time to take pains in 
giving him any other satisfaction.' Surely fewer words would 
have been lost if the prefator had said at once that the work was 
from the manuscript preserved at Cambridge. Perhaps it was a 
mangled copy clandestinely taken and interpolated. 

Lord Bacon not the author of 'The Christian Paradoxes,' being 
a reprint of ' Memorials of Godliness and Christianity,' by 
Herbert Palmer, B.D. With Introduction, Memoir, and Notes, 
by the Rev. Alexander B. Grosart, Kenross. (Private circulation, 
1864). 

I insert the above in this place on account of a slight con- 
nexion with the last. Bacon's Paradoxes, so attributed were 
first published as his in some asserted ' Kemains,' 1648. They 
were admitted into his works in 1730, and remain there to this 
day. The title is 'The Character of a believing Christian, set 
forth in paradoxes and seeming contradictions.' The following is 
a specimen : 

He believes three to be one and one to be three ; a father not to be 
older than his son ; a son to be equal with his father ; and one pro- 
ceeding from both to be equal with both : he believes three persons in 

one nature, and two natures in one person He believes the God 

of all grace to have been angry with one that never offended Him ; and 
that God that hates sin to be reconciled to himself though sinning con- 
tinually, and never making or being able to make Him any satisfaction. 
He believes a most just God to have punished a most just person, and 
to have justified himself, though a most ungodly sinner. He believes 
himself freely pardoned, and yet a sufficient satisfaction was made for 
Mm. 

Who can doubt that if Bacon had written this, it must have 
been wrong? Many writers, especially on the Continent, have 
taken him as sneering at (Athanasian) Christianity right and left. 
Many Englishmen have taken him to be quite in earnest, and to 
have produced a body of edifying doctrine. More than a century 
ago the Paradoxes were published as a penny tract ; and, again, at 
the same price, in the 'Penny Sunday Eeader,' vol. vi. No. 148, a 
few passages were omitted, as too strong. But all did not agree : 
in my copy of Peter Shaw's edition (vol. ii. p. 283) the Paradoxes 
have been cut out by the binder, who has left the backs of the 
leaves. I never had the curiosity to see whether other copies of 



BACON'S PARADOXES. SOCINIANS AND UNITARIANS. 85 

the edition have been served in the same way. The Keligious 
Tract Society republished them recently in ' Selections from the 
Writings of Lord Bacon,' (no date; bad plan; about 1863, I 
suppose). No omissions were made, so far as I find. 

I never believed that Bacon wrote this paper ; it has neither his 
sparkle nor his idiom. I stated my doubts even before I heard 
that Mr. Spedding, one of Bacon's editors, was of the same mind. 
(Athenceum, July 16, 1864). I was little moved by the wide con- 
sent of orthodox men : for I knew how Bacon, Milton, Newton, 
Locke, &c., were always claimed as orthodox until almost the 
present day. Of this there is a remarkable instance. 

Among the books which in my younger day were in some 
orthodox publication lists I think in the list of the Christian 
Knowledge Society, but I am not sure was Locke's ' Eeason- 
ableness of Christianity.' It seems to have come down from the 
eighteenth century, when the battle was belief in Christ against 
unbelief, simplicite)^ as the logicians say. Now, if ever there 
were a Socinian 1 book in the world, it is this work of Locke. 
' These two,' says Locke, ' faith and repentance, i.e. believing 
Jesus to be the Messiah, and a good life, are the indispensable 
conditions of the new covenant, to be performed by all those who 
would obtain eternal life.' AIL the book is amplification of this 
doctrine. Locke, in this and many other things, followed Hobbes, 
whose doctrine, in the Leviathan, is fidem, quanta ad salutem 
necessaria est, contineri in hoc articulo, Jesus est Christus. For 
this Hobbes was called an atheist, which many still believe him 
to have been : some of his contemporaries called him, rightly, 

1 I use the word Socinian because it was so much used in Locke's time ; it is used 
in our own day by the small fry, the unlearned clergy and their immediate followers, 
as a term of reproach for all Unitarians. I suspect they have a kind of liking for the 
word ; it sounds like so sinful. The learned clergy and the higher laity know better : 
they know that the bulk of the modern Unitarians go farther than Socinus, and are 
not correctly named as his followers. The Unitarians themselves neither desire nor 
deserve a name which puts them one point nearer to orthodoxy than they put 
themselves. That point is the doctrine that direct prayer to Jesus Christ is lawful 
and desirable : this Socinus held, and the modern Unitarians do not hold. Socinus, 
in treating the subject in his own Insdtutio, an imperfect catechism which he left, lays 
much more stress on John xiv. 13 than on XT. 16 and xvi. 23. He is not disinclined to 
think that Patrem should be in the first citation, where some put it ; but he says 
that to ask the Father in the name of the Son is nothing but praying to the Son in 
prayer to the Father. He labours the point with obvious wish to secure a conclusive 
sanction. In the Racovian Catechism, of which Faustus Socinus probably drew the 
first sketch, a clearer light is arrived at. The translation says : ' But wherein con- 
sists the divine honour due to Christ? In adoration likewise and invocation. For 
we ought at all times to adore Christ, and may in our necessities address our pray* ia 
to him as often as we please; and there are many reasons to induce us to do this 
freely.' There are some who like accuracy, even in aspersion. 



86 A BUDGET OF PARADOXES. 

a Socinian. Locke was known for a Socinian as soon as his work 
appeared : Dr. John Edwards, his assailant, says he is ' Socin- 
ianized all over.' Locke, in his reply, says 'there is not one 
word of Socinianism in it : ' and he was right : the positive 
Socinian doctrine has not one word of Socinianism in it; So- 
cinianism consists in omissions. Locke and Hobbes did not dare 
deny the Trinity : for such a thing Hobbes might have been 
roasted, and Locke might have been strangled. Accordingly, the 
well known way of teaching Unitarian doctrine was the collection 
of the asserted essentials of Christianity, without naming the 
Trinity, &c. This is the plan Newton followed, in the papers which 
have at last been published. 

So I, for one, thought little about the general tendency of 
orthodox writers to claim Bacon by means of the Paradoxes. I 
knew that, in his ' Confession of Faith ' he is a Trinitarian of a 
heterodox stamp. His second Person takes human nature before 
he took flesh, not for redemption, but as a condition precedent of 
creation. ' God is so holy, pure, and jealous, that it is impossible 
for him to be pleased in any creature, though the work of his 

own hands [Genesis i. 10, 12, 18, 21, 25, 31, freely 

rendered]. But purposing to become a Creator, and to commu- 
nicate to his creatures, he ordained in his eternal counsel that 
one person of the Godhead should be united to one nature, and 
to one particular of his creatures ; that so, in the person of 
the Mediator, the true ladder might be fixed, whereby God 
might descend to his creatures and his creatures might ascend 
to God ' 

This is republished by the Eeligious Tract Society, and seems 
to suit their theology, for they confess to having omitted some 
things of which they disapprove. 

In 1864, Mr. Grosart published his discovery that the Paradoxes 
are by Herbert Palmer ; that they were first published surrep- 
titiously, and immediately afterwards by himself, both in 1645 ; 
that the * Eemains ' of Bacon did not appear until 1 648 ; that 
from 1645 to 1708, thirteen editions of the 'Memorials' were 
published, all containing the Paradoxes. In spite of this, the 
Paradoxes were introduced into Bacon's works in 1730, where they 
have remained. 

Herbert Palmer was of good descent, and educated as a Puri- 
tan. He was an accomplished man, one of the few of his day who 
could speak French as well as English. He went into the Church, 
and was beneficed by Laud, in spite of his puritanism ; he sat in 
the Assembly of Divines, and was finally President of Queens' 



CIRCLE SQUARERS. WHISTON ON THE LONGITUDE. 87 

College, Cambridge, in which post he died, August 13, 1647, in the 
46th year of his age. 

Mr. Grosart says, speaking of Bacon's ' Eemains,' ' All who have 
had occasion to examine our early literature are aware that it was 
a common trick to issue imperfect, false, and unauthorised writings 
under any recently deceased .name that might be expected to take. 
The Puritans, down to John Bunyan, were perpetually expos- 
tulating and protesting against such procedure.' I have met with 
instances of all this ; but I did not know that there was so much 
of it : a good collection would be very useful. The work of 1728, 
attributed to Newton, is likely enough to be one of the class. 

Demonstration de 1'immobilitez de la Terre. . . . Par M. de la 
Jonehere, Ingenieur Fran9ais. Londres, 1728, 8vo. 

A synopsis which is of a line of argument belonging to the 
beginning of the preceding century. 

The Circle squared; together with the Ellipsis and several re- 
flections on it. The finding two geometrical mean proportionals, 

or doubling the cube geometrically. By Richard Locke 

London, no date, probably about 1730, 8vo. 

According to Mr. Locke, the circumference is three diameters, 
three-fourths the difference of the diameter and the side of the 
inscribed equilateral triangle, and three- fourths the difference 
between seven-eighths of the diameter and the side of the same 
triangle. This gives, he says, 3-18897. There is an addition to 
this tract, being an appendix to a book on the longitude. 

The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, 
Yorkshire. London, 1732, 8vo. 

Here TT = 3-0625. No proof is offered. 

The longitude discovered by the Eclipses, Occultations, and Con- 
junctions of Jupiter's planets. By William Whiston. London, 
1738. 

This tract has, in some copies, the celebrated preface contain- 
ing the account of Newton's appearance before the Parliamentary 
Committee on the longitude question, in 1714 (Brewster, ii. 257- 
266). This * historical preface,' is an insertion, and is dated April 
28, 1741, with four additional pages dated August 10, 1741. The 
short ' preface ' is by the publisher, John Whiston, the author's 
son. 



88 A BUDGET OF PAEADOXES. 



A- description and draught, of a new-invented machine for carrying 
vessels or ships out of, or into any harbour, port, or river, 
against wind and ti le, or in a calm. For which, His Majesty 
has granted letters patent, for the sole benefit of the author, for 
the space of fourteen years. By Jonathan Hulls. London : 
printed for the author, 1737. Price sixpence (folding plate and 
pp. 48, beginning from title). 

(I ought to have entered this tract in its place. It is so rare 
that its existence was once doubted. It is the earliest description 
of steam-power applied to navigation. The plate shows a barge, 
with smoking funnel, and paddles at the stem, towing a ship of 
war. The engine, as described, is Newcomen's. 

In 1855, John Sheepshanks, so well known as a friend of Art 
and a public donor, reprinted this tract, in fac-simile, from his own 
copy; twenty-seven copies of the original 12mo. size, and twelve 
on old paper, small 4to. I have an original copy, wanting the 
plate, and with ' Price sixpence ' carefully erased, to the honour of 
the book. 

It is not known whether Hulls actually constructed a boat. In 
all probability his tract suggested to Symington, as Symington did 
to Fulton.) 

Le vrai systeme de physique generale de M. Isaac Newton ex- 
pose et analyse en parallele avec celui de Descartes. By 
Louis Castel [Jesuit and F.R.S.]. Paris, 1743, 4to. 

This is an elaborate correction of Newton's followers, and of 
Newton himself, who it seems did not give his own views with 
perfect fidelity. Father Castel, for instance, assures us that New- 
ton placed the sun at rest in the centre of the system. Newton left 
the sun to arrange that matter with the planets and the rest of the 
universe. In this volume of 500 pages there is right and wrong, 
both clever. 

A dissertation on the ^Ether of Sir Isaac Newton. By Bryan 
Robinson, M.D. Dublin, 1743,. 8 vo. 

A mathematical work, professing to prove that the assumed 
ether causes gravitation. 

Mathematical principles of theology, or the existence of God 
geometrically demonstrated. By Richard Jack, teacher of 
Mathematics. London, 1747, 8vo. 

Propositions arranged after the manner of Euclid, with beings 
represented jay circles and squares. But these circles and squares 



JOHN BERNOULLI AND DE FAURE. 89 

are logical symbols, not geometrical ones. I brought this book 
forward to the Eoyal Commission on the British Museum as an 
instance of the absurdity of attempting a classed catalogue from 
the titles of books. The title of this book sends it either to theo- 
logy or geometry : when, in fact, it is a logical vagary. Some of 
the houses which Jack built were destroyed by the fortune of war 
in 1745, at Edinburgh : who will say the rebels did no good what- 
ever ? I suspect that Jack copied the ideas of J. B. Morinus, 
' Quod Deus sit,' Paris, 1636, 4to., containing an attempt of the 
same kind, but not stultified with diagrams. 

Dissertation, decouverte, et demonstrations de la quadrature 
mathematique du cercle. Par M. de Faure, geometre. [.<?. I., 
probably Geneva] 1747, 8vo. 

Analyse de la Quadrature du Cercle. Par M. de Faure, 
Gentilhomme Snisse. Hague, 1749, 4to. 

According to this octavo geometer and quarto gentleman, a 
diameter of 81 gives a circumference of 256. There is an amusing 
circumstance about the quarto which has been overlooked, if 
indeed the book has ever been examined. John Bernoulli (the 
one of the day) and Koenig have both given an attestation : my 
mathematical readers may stare as they please, such is the fact. 
But, on examination, there will be reason to think the two sly 
Swiss played their countryman the same trick as the medical man 
played Miss Pickle, in the novel of that name. The lady only 
wanted to get his authority against sousing her little nephew, and 
said, ' Pray, doctor, is it not both dangerous and cruel to be the 
means of letting a poor tender infant perish by sousing it in water 
as cold as ice ? ' ' Downright murder, I affirm,' said the doctor ; 
and certified accordingly. De Faure had built a tremendous 
scaffolding of equations, quite out of place, and feeling cock-sure 
that his solutions, if correct, would square the circle, applied to 
Bernoulli and Koenig who after his tract of two years before, 
must have known what he was at for their approbation of the 
solutions. And he got it, as follows, well guarded : 

Suivant les suppositions posees dans ce Memoire, il est si evident 
que t doit etre = 84, y = 1, et z = 1, que cela n'a besoin ni de preuve 
ni d'autorite pour etre reconnu par tout le monde. 

a Basle le 7e Mai 1749. JEAN BERNOULLI. 

Je souscris au jugement de Mr. Bernoulli, en consequence de ces 
suppositions. 

a la Haye le 21 Juin 17 I'.'. S. KOEXIG. 

On which de Faure remarks with triumph as I have no doubt 



90 . A BUDGET OF PARADOXES. 

it was intended he should do ' il conste clairement par ma 
presente Analyse et Demonstration, qu'ils y ont deja reconnu et 
approuve parfaitement que la quadrature du cercle est mathema- 
tiquement demontree.' It should seem that it is easier to square 
the circle than to get round a mathematician. 

An attempt to demonstrate that all the Phenomena in Nature 
may be explained by two simple active principles, Attraction 
and Repulsion, wherein the attractions of Cohesion, Gravity 
and Magnetism are shown to be one and the same. By Go win 
Knight. London, 1748, 4to. 

Dr. Knight was Mr. Panizzi's archetype, the first Principal 
Librarian of the British Museum. He was celebrated for his 
magnetical experiments. This work was long neglected ; but is 
now recognised as of remarkable resemblance to modern specula- 
tions. 

An original theory or Hypothesis of the Universe. By Thomas 
Wright of Durham. London, 4to. 1750. 

Wright is a speculator whose thoughts are now part of our 
current astronomy. He took that view or most of it of the 
milky way which afterwards suggested itself to William Herschel. 
I have given an account of him and his work in the Philosophi- 
cal Magazine for April, 1848. 

Wright was mathematical instrument maker to the King ; and 
kept a shop in Fleet Street. Is the celebrated business of Trough- 
ton & Simms, also in Fleet Street, a lineal descendant of that of 
Wright ? It is likely enough, more likely than that as I find 
him reported to have affirmed Prester John was the descendant 
of Solomon and the Queen of Sheba. Having settled it thus, it 
struck me that I might apply to Mr. Simms, and he informs me 
that it is as I thought, the line of descent being Wright, Cole, 
John Troughton, Edward Troughton, Troughton & Simms. 

The theology and philosophy in Cicero's Somnium Scipionis 
explained. Or, a brief attempt to demonstrate, that the 
Newtonian system is perfectly agreeable to the notions of the 
wisest ancients : and that mathematical principles are the only 
sure ones. [By Bishop Home, at the age of nineteen.] 
London, 1751, 8vo. 

This tract, which was not printed in the collected works, and is 
now excessively rare, is mentioned in Notes and Queries, 1st S., 



BISHOP HORNE AND OLD BEN MARTIN. 91 

v. 490, 573 ; 2nd S., ix. 15. The boyish satire on Newton is 
amusing. Speaking of old Benjamin Martin, he goes on as 
follows : 

But the most elegant account of the matter [attraction] is by that 
hominiform animal, Mr. Benjamin Martin, who having attended 
Dr. Desaguliers' fine, raree, gallanty shew for some years [Desa- 
guliers was one of the first who gave public experimental lectures, 
before the saucy boy was born] in the capacity of a turnspit, has, it 
seems, taken it into his head to set up for a philosopher. 

Thus is preserved the fact, unknown to his biographers, that 
Benj. Martin was an assistant to Desaguliers in his lectures. 
Hutton says of him, that ' he was well skilled in the whole circle 
of the mathematical and philosophical sciences, and wrote useful 
books on every one of them' : this is quite true ; and even at this 
day he is read by twenty where Home is read by one ; see the 
stalls, passim,. All that I say of him, indeed my knowledge of 
the tract, is due to this contemptuous mention of a more durable 
man than himself. My assistant secretary at the AstronomicaJ 
Society, the late Mr. Epps, bought the copy at a stall because his 
eye was caught by the notice of ' Old Ben Martin,' of whom he 
was a great reader. Old Ben could not be a Fellow of the Royal 
Society, because he kept a shop : even though the shop sold 
nothing but philosophical instruments. Thomas Wright, similarly 
situated as to shop and goods, never was a Fellow. The Society 
of our day bas greatly degenerated : those of the old time would 
be pleased, no doubt, that the glories of their day should be 
commemorated. In the early days of the Society, there was a 
similar difficulty about Graunt, the author of the celebrated work 
on mortality. But their royal patron, 'who never said a foolish 
thing,' sent them a sharp message, and charged them if they 
found any more such tradesmen, they should 'elect them without 
more ado.' 

Home's first pamphlet was published when he was but twenty- 
one years old. Two years afterwards, being then a Fellow of bis 
college, and having seen more of the world, he seems to have felt 
that his manner was a little too pert. He endeavoured, it is said, 
to suppress his first tract : and copies are certainly of extreme 
rarity. He published the following as his maturer view : 



92 A BUDGET OF PAEADOXES. 



A fair, candid, and impartial state of the case between Sir 
Isaac Newton and Mr. HutcLinson. In which is shown how 
for a system of physics is capable of mathematical demonstra- 
tion; how far Sir Isaac's, as such a system, has that demon- 
stration ; and consequently, what regard Mr. Hutchinson's claim 
may deserve to have paid to it. By George Home, M.A. 
Oxford, 1753, 8vo. 

It must be remembered that the successors of Newton were 
very apt to declare that Newton had demonstrated attraction as a 
physical cause : he had taken reasonable pains to show that he 
did not pretend to this. If any one had said to Newton, I hold 
that every particle of matter is a responsible being of vast intel- 
lect, ordered by the Creator to move as it would do if every other 
particle attracted it, and gifted with power to make its way in 
true accordance with that law, as easily as a lady picks her way 
across the street ; what have you to say against it ? Newton 
must have replied, Sir ! if you really undertake to maintain this 
as demonstrable, your soul had better borrow a little power from 
the particles of which your body is made : if you merely ask me 
to refute it, I tell you that I neither can nor need do it; for 
whether attraction comes in this way or in any other, it comes, 
and that is all I have to do with it. 

The reader should remember that the word attraction, as used 
by Newton and the best of his followers, only meant a drawing 
towards, without any implication as to the cause. Thus whether 
they said that matter attracts matter, or that young lady attracts 
young gentleman, they were using one word in one sense. Newton 
found that the law of the first is the inverse square of the dis- 
tance : I am not aware that the law of the second has been 
discovered ; if there be any chance, we shall see it at the year 
1856 in this list. 

In this point young Home made a hit. He justly censures 
those who fixed upon Newton a more positive knowledge of what 
attraction is than he pretended to have. 'He has owned over 
and over he did not know what he meant by it it might be this, 
or it might be that, or it might be anything, or it might be 
nothing.' With the exception of the nothing clause, this is true, 
though Newton might have answered Home by ' Thou hast said 
it,' 

(I,thought everybody knew the meaning of ' Thou hast said it :' 
but I was mistaken. In three of the evangelists 2v \systs is the 



HOKNE ON NEWTON. WEYMAN LEE. 93 

answer to ' Art thou a king ?' The force of this answer, as always 
understood, is ' That is your way of putting it.' The Puritans, 
who lived in Bible phrases, so understood it: and Walter Scott, 
who caught all peculiarities of language with great effect, makes 
a marked instance, ' Were you armed ? I was not I went in my 
calling, as a preacher of (rod's word, to encourage them that drew 
the sword in His cause. In other words, to aid and abet the 
rebels, said the Duke. Thou hast spoken it, replied the prisoner.') 

Again, Home quotes Eowning as follows : 

Mr. Rowning, pt. 2 p. 5 in a nobe, has a very pretty conceit upon 
this same subject -of attraction, about every particle of a fluid being 1 
intrenched in three spheres of attraction and repulsion, one within 
another, ' the innermost of which (he says) is a sphere of repulsion, 
which keeps them from approaching into contact ; the next, a sphere 
of attraction, diffused around this of repulsion, by which the particles 
are disposed to run together into drops ; and the outermost of all, a 
sphere of repulsion, whereby they repel each other, when removed out 
of the attraction.' So that between the urginys, and suUicitations, of 
one and t'other, a poor unhappy particle must ever be at his wit's end, 
not knowing which way to turn, or whom to obey first. 

Rowning has here started the notion which Boscovich afterwards 
developed. 

I may add to what precedes that it cannot be settled that, as 
Granger says, Desaguliers was the first who gave experimental 
lectures in London. William Whiston gave some, and Francis 
Hauksbee made the experiments. The prospectus, as we should 
now call it, is extant, a quarto tract of plates and descriptions, 
without date. Whiston, in his life, gives 1714 as the first date 
of publication, and therefore, no doubt, of the lectures. Desagu- 
liers removed to London soon after 1712, and commenced his 
lectures soon after that. It will be rather a nice point to settle 
which lectured first; probabilities seem to go in favour or 
Whiston. 

An Essay to ascertain the value of leases, and annuities for 
years and lives. By W[eyman] L[ee]. London, 1737, 8vo. 

A valuation of Annuities and Leases certain, for a single life. 
By Weyman Lee, Esq. of the Inner Temple. London, 1751, 
8vo. Third edition, 177:!. 

Every branch of exact science has its paradoxer. The world at 
large cannot tell with certainty who is right in such questions as 
squaring the circle, &c. Mr. Weyrnan Lee was the assailant of 



94 A BUDGET OF PARADOXES. 

what all who had studied called demonstration in the question of 
annuities. He can be exposed to the world : for his error arose 
out of his not being able to see that the whole is the sum of all 
its parts. 

By an annuity, say of 100., now bought, is meant that the 
buyer is to have for his money lOQl. in a year, if he be then 
alive, 100L at the end of two years, if then alive, and so 
on. It is clear that he would buy a life annuity if he 
should buy the first 100. in one office, the second in another, 
and so on. All the difference between buying the whole from 
one office, and buying all the separate contingent payments at 
different offices, is immaterial to calculation. Mr. Lee would 
have agreed with the rest of the world about the payments to be 
made to the several different offices, in consideration of their several 
contracts : but he differed from every one else about the sum to 
be paid to one, office. He contended that the way to value an 
annuity is to find out the term of years which the individual has 
an even chance of surviving, and to charge for the life annuity 
the value of an annuity certain for that term. 

It is very common to say that Lee took the average life, or ex- 
pectation, as it is wrongly called, for his term : and this I have 
done myself, taking the common story. Having exposed the 
absurdity of this second supposition, taking it for Lee's, in my 
'Formal Logic,' I will now do the same with the first. 

A mathematical truth is true in its extreme cases. Lee's prin- 
ciple is that an annuity on a life is the annuity made certain for 
the term within which it is an even chance the life drops. If, 
then, of a thousand persons, 500 be sure to die within a year, and 
the other 500 be immortal, Lee's price of an annuity to any one 
of these persons is the present value of one payment : for one year 
is the term which each one has an even chance of surviving and 
not surviving. But the true value is obviously half that of a 
perpetual annuity : so that at 5 per cent. Lee's rule would give 
less than the tenth of the true value. It must be said for the 
poor circle-squarers, that they never err so much as this. 

Lee would have said, if alive, that I have put an extreme case : 
but any universal truth is true in its extreme cases. It is not 
fair to bring forward an extreme case against a person who is 
speaking as of usual occurrences : but it is quite fair when, as 
frequently happens, the proposer insists upon a perfectly general 
acceptance of his assertion. And yet many who go the whole hog 
protest against being tickled with the tail. Counsel in court are 
good instances: they are paradoxers by trade. June 13, 1849, at 



MONTUCLA'S HISTORY OF CIRCLE SQUARING. 95 

Hertford, there was an action about a ship, insured against a total 
loss : some planks were saved, and the underwriters refused to pay. 
Mr. Z. (for deft.) 'There can be no degrees of totality; and some 
timbers were saved.' L. C. B. 'Then if the vessel were burned to 
the water's edge, and some rope saved in the boat, there would be 
no total loss.' Mr. Z. 'This is putting a very extreme case.' 
L. C. B. 'The argument would go that length.' What would 
Judge Z. as he now is say to the extreme case beginning some- 
where between six planks and a bit of rope ? 

Histoire des recherches sur la quadrature du cercle. . . . avec 
une addition concernant les problemes de la duplication du 
cube et de la trisection de 1'anglo. Paris, 1754, 12mo. [By 
Montucla.] 

This is the history of the subject. It was a little episode to 
the great history of mathematics by Montucla, of which the first 
edition appeared in 1758. There was much addition at the end 
of the fourth volume of the second edition ; this is clearly by 
Montucla, though the bulk of the volume is put together, with 
help from Montucla's papers, by Lalande. There is also a second 
edition of the history of the quadrature, Paris, 1831, 8vo, 
edited, I think, by Lacroix ; of which it is the great fault that it 
makes hardly any use of the additional matter just mentioned. 

Montucla is an admirable historian when he is writing from his 
own direct knowledge : it is a sad pity that he did not tell us 
when he was depending on others. We are not to trust a quarter 
of his book, and we must read many other books to know which 
quarter. The fault is common enough, but Montucla's good 
three-quarters is so good that the fault is greater in him than in 
most others : I mean the fault of not acknowledging ; for an 
historian cannot read everything. But it must be said that 
mankind give little encouragement to candour on this point. 
Hallam, in his ' History of Literature,' states with his own usual 
instinct of honesty every case in which he depends upon others : 
Montucla does not. And what is the consequence? Montucla is 
trusted, and believed in, and cried up in the bulk ; while the 
smallest talker can lament that Hallam should be so unequal and 
apt to depend on others, without remembering to mention that 
Hallam himself gives the information. As to a universal history 
of any great subject being written entirely upon primary know- 
ledge, it is a thing of which the possibility is not yet proved by 
an example. Delambre attempted it with astronomy, and was 
removed by death before it was finished, to say nothing of the 
gaps he left. 



96 A BUDGET OF PARADOXES. 

Montucla was nothing of a bibliographer, and his descriptions 
of books in the first edition were insufficient. The Abbe Rive 
fell foul of him, and as the phrase is, gave it him. Montucla 
took it with great good humour, tried to mend, and, in his second 
edition, wished his critic had lived to see the vernis de biblio- 
graphe which he had given himself. 

I have seen Montucla set down as an esprit fort, more than 
once : wrongly, I think. When he mentions Barrow's address to 
the Almighty, he adds, ' On voit, au reste, par la, que Barrow 
etoit un pauvre philosophe ; car il croyait en 1'immortalite de 
1'ame, et en une Divinite autre que la nature universelle.' This 
is irony, not an expression of opinion. In the book of mathe- 
matical recreations which Montucla constructed upon that of 
Ozanam, and Ozanam upon that of Van Etten, now best known in 
England by Mutton's similar treatment of Montucla, there is an 
amusing chapter on the quadrators. Montucla refers to his own 
anonymous book of 1754 as a curious book published by Jombert. 
He seems to have been a little ashamed of writing about circle- 
squarers : what a slap on the face for an unborn Budgeteer I 

Montucla says, speaking of France, that he finds three notions 
prevalent among the cyclometers : 1. that there is a large reward 
offered for success; 2. that the longitude problem depends on 
that success ; 3. that the solution is the great end and object of 
geometry. The same three notions are equally prevalent among 
the same class in England. No reward has ever been offered by 
the government of either country. The longitude problem in 
no way depends upon perfect solution : existing approximations 
are sufficient to a point of accuracy far beyond what can be 
wanted. And geometry, content with what exists, has long passed 
on to other matters. Sometimes a cyclometer persuades a skipper 
who has made land in the wrong place that the astronomers are in 
fault, for using a wrong measure of the circle ; and the skipper 
thinks it a very comfortable solution S And this is the utmost 
that the proble.ni ever has to do with longitude. 

Antinewtoniamsmus. By Cielestino Cominale, M.D. Naples, 
1754 and 1756, 2 vols. 4to. 

The first volume upsets the theory of light; the second 
vacuum, vis inertise, gravitation, and attraction. I confess I 
never attempted these big Latin volumes, numbering 450 closely- 
printed quarto pages. The man who slays Newton in a pamphlet 
is the man for me. But I will lend them to anybody who will 



REWARD FOR QUADRATURE. 97 

give security, himself in 500., and two sureties in 2501. each, that 
he will read them through, and give a full abstract ; and I will 
not exact security for their return. I have never seen any 
mention of this book : it has a printer, but not a publisher, as 
happens with so many unrecorded books. 

1755. The French Academy of Sciences came to the deter- 
mination not to examine any more quadratures or kindred 
problems. This was the consequence, no doubt, of the publication 
of Montucla's book : the time was well chosen ; for that book was 
a full justification of the resolution. The Eoyal Society followed 
the same course, I believe, a few years afterwards. When our 
Board of Longitude was in existence, most of its time was con- 
sumed in listening to schemes, many of which included the 
quadrature of the circle. It is certain that many quadrators have 
imagined the longitude problem to be connected with theirs : and 
no doubt the notion of a reward being offered by Government for 
a true quadrature is a result of the reward offered for the longi- 
tude. Let it also be noted that this longitude reward was not 
a premium upon excogitation of a mysterious difficulty. The 
legislature was made to know that the rational hopes of the 
problem were centred in the improvement of the lunar tables and 
the improvement of chronometers. To these objects alone, and 
by name, the offer was directed : several persons gained rewards 
for both ; and the offer was finally repealed. 

Fundamentals Figura Georaetrica, primas tantum lineas circuli 
quadrature possibilitatis ostendens. By Niels Erichsen 
(Nicolaus Ericius), shipbuilder, of Copenhagen. Copenhagen, 
1755, 12mo. 

This was a gift from my oldest friend who was not a relative, 
Dr. Samuel Maitland of the ' Dark Ages.' He found it among 
his books, and could not imagine how he came by it : I could 
have told him. He once collected interpretations of the Apo- 
calypse : and auction lots of such books often contain quadratures. 
The wonder is he never found more than one. 

The quadrature is not worth notice. Erichsen is the only 
squarer I have met with who has distinctly asserted the particulars 
of that reward which has been so frequently thought to have been 
offered in England. He says that, in 1747, the Eoyal Society, on 
the 2nd of June, offered to give a large reward for the quadrature of 
the circle and a true explanation of magnetism, in addition to 
30,000^. previously promised for the same. I need hardly say that 

ir 



98 A BUDGET OE PARADOXES. 

the Royal Society had not 30,000. at that time, and would not, if 
it had had such a sum, have spent it on the circle, nor on magnetic 
theory ; nor would it have coupled the two things. On this book, 
see Notes and Queries, 1st S. xii. 306. Perhaps Erichsen meant 
that the 30,000. had been promised by the Government, and the 
addition by the Eoyal Society. 

October 8, 1866. I receive a letter from a cyclometer who 
understands that a reward is offered to any one who will square 
the circle, and that all competitors are to send their plans to me. 
The hoaxers have not yet failed out of the land. 

Theoria Philosophise Naturalis redacta ad unicam legem virium 
in natura existentium. Editio Veneta prima. By Roger Joseph 
Boscovich. Venice, 1763, 4to. 

The first edition is said to be of Vienna, 1758. This is a 
celebrated work on the molecular theory of matter, grounded on 
the hypothesis of spheres of alternate attraction and repulsion. 
Boscovich was a Jesuit of varied pursuit. During his measure- 
ment of a degree of the meridian, while on horseback or waiting 
for his observations, he composed a Latin poem of about five 
thousand verses on eclipses, with notes, which he dedicated to the 
Eoyal Society : ' De Solis et Lunse defectibus,' London, Millar 
and Dodsley, 1760, 4to. 

Traite de paix entre DCS Cartes et Newton, precede des vies 
littcraires de ces deux chefs de la physique moderne. . . . By 
Aime Henri Paulian. Avignon, 1763, 12mo. 

I have had these books for many a year without feeling the 
least desire to see how a lettered Jesuit would atone Descartes 
and Newton. On looking at my two volumes, I find that one 
contains nothing but the literary life of Des Cartes ; the other 
nothing but the literary life of Newton. The preface indicates 
more : and Watt mentions three volumes. I dare say the first 
two contain all that is valuable. On looking more attentively at 
the two volumes, I find them both readable and instructive ; the 
account of Newton is far above that of Voltaire, but not so 
popular. But he should not have said that Newton's family 
came from Newton in Ireland. Sir Rowland Hill gives fourteen 
Newtons in Ireland : twice the number of the cities that con- 
tended for the birth of Homer may now contend for the origin of 
Newton, on the word of Father Paulian. 



BAILLY'S LETTERS TO VOLTAIRE. 99 



Philosophical Essays, in three parts. By B. Lovett, Lay 
Clerk of the Cathedral Church of Worcester. Worcester, 1766, 
8vo. 

The Electrical Philosopher: containing a new system of 
physics founded upon the principle of an universal Plenum 
of elementary fire . . . By R. Lovett. Worcester, 1774, 8vo. 

Mr. Lovett was one of those ether philosophers who bring in 
elastic fluid as an explanation by imposition of words, without 
deducing any one phenomenon from what we know of it. And 
yet he says that attraction has received no support from geome- 
try ; though geometry, applied to a particular law of attraction, 
had shown how to predict the motions of the bodies of the t^olar 
system. He, and many of his stamp, have not the least idea of 
the confirmation of a theory by accordance of deduced results 
with observation posterior to the theory. 

Lettres sur 1'Atlantide de Platon, et sur 1'ancien Histoire de 
1' Asie, pour servir de suite aux lettres sur 1'origine des Sciences, 
adressees a M. de Voltaire, par M. Bailly. London and Paris, 
'1779, 8vo. 

I might enter here all Bailly's histories of astronomy. The 
paradox which runs through them all more or less, is the doctrine 
that astronomy is of immense antiquity, coming from some 
forgotten source, probably the drowned island of Plato, peopled 
by a race whom Bailly makes, as has been said, to teach us 
everything except their existence and their name. These books, 
the first scientific histories which belong to readable literature, 
made a great impression by power of style : Delambre created a 
strong reaction, of injurious amount, in favour of history founded 
on contemporary documents, which early astronomy cannot 
furnish. These letters are addressed to Voltaire, and continue 
the discussion. There is one letter of Voltaire, being the fourth, 
dated Feb. 27, 1777, and signed ' le vieux malade de Ferney, V. 
puer centum annorum.' Then begin Bailly's letters, from 
January 16 to May 12, 1778. From some ambiguous expressions 
in the Preface, it would seem that these are fictitious letters, sup- 
posed to be addressed to Voltaire at their dates. Voltaire went 
to Paris February 10, 1778, and died there May 30. Nearly all 
this interval was his closing scene, and it is very unlikely that 
Bailly would have troubled him with these letters. 



H a 



100 A BUDGET OF PAEADOXES. 

An inquiry into the cause of motion, or a general theory of 
physics. By S. Miller. London, 1781, 4to. 

Newton all wrong : matter consists of two kinds of particles, 
one inert, the other elastic and capable of expanding themselves 
ad infinitum. 

Des Erreurs et de la Verite, ou les hommes rappeles au prin- 
cipe universel de la science ; ouvrage dans lequel, en faisant 
remarquer aux observateurs 1'incertitude de leurs recherches, 
et leurs meprises continuelles, on leur indique la route qu'ils 
auroient du. suivre, pour acquerir 1'evidence physique sur 
1'origine du bien et du mal, sur l'homme, sur la nature matcrielle, 
et la nature sacree ; sur la base des gouvernements politiques, 
sur 1'autorite des souverains, sur la justice civile et criininellc, 
sur les sciences, les langues, et les arts. Par un Ph. . . . 
Inc. ... A Edimbourg. 1782. Two vols. 8vo. 

This is the famous work of Louis Claude de Saint-Martin 
(1743-1803), for whose other works, vagaries included, the reader 
must look elsewhere : among other things, he was a translator of 
Jacob Behrnen. The title promises much, and the writer has 
smart thoughts now and then ; but the whole is the wearisome 
omniscience of the author's day and country, which no reader of 
our time can tolerate. Not that we dislike omniscience ; but 
we have it of our own country, both home-made and imported ; 
and fashions vary. But surely there can be but one omniscience ? 
Must a man have but one wife ? Nay, may not a man have a 
new wife while the old one is living ? There was a famous 
instrumental professor forty years ago, who presented a friend to 

Madame . The friend started, and looked surprised ; for, 

not many weeks before, he had been presented to another lady, 
with the same title, at Paris. The musician observed his 

surprise, and quietly said, ' Celle-ci est Madame de Lon- 

dres.' In like manner we have a London omniscience now 
current, which would make any one start who only knew the old 
French article. 

The book was printed at Lyon, but it was a trick of French 
authors to pretend to be afraid of prosecution : it made a book 
look wicked-like to have a feigned place of printing, and stimu- 
lated readers. A Government which had undergone Voltaire 
would never have drawn its sword upon quiet Saint-Martin. To 
make himself look still worse, he was only ph[ilosophe] Inc. . . , 
which is generally read Inconnu, but sometimes Incredule : 



SAINT-MARTIN. 101 

most likely the ambiguity was intended. There is an awful 
paradox about the book, which explains, in part, its leaden same- 
ness. It is all about Vhomme, Vhomme, Vhomme, except as much 
as treats of les homines, les hommes, les hommes ; but not one 
single man is mentioned by name in its 500 pages. It reminds 
one of 

Water, water, everywhere, 

And not a drop to drink. 

Not one opinion of any other man is referred to, in the way of 
agn-emcnt or of opposition. Not even a town is mentioned : 
there is nothing which brings a capital letter into the middle of a 
sentence, except, by the rarest accident, siich a personification as 
Justice. A likely book to want an Edimbourg godfather ! 

Saint-Martin is great in mathematics. The number four 
essentially belongs to straight lines, and nine to curves. The 
object of a straight line is to perpetuate ad infinitum the pro- 
duction of a point from which it emanates. A circle O bounds 
the production of all its radii, tends to destroy them, and is in 
some sort their enemy. How is it possible that things so distinct 
should not be distinguished in their number as well as in their 
action ? If this important observation had been made earlier, 
immense trouble would have been saved to the mathematicians, 
who would have been prevented from searching for a common 
measure to lines which have nothing in common. But, though 
all straight lines have the number four, it must not be supposed 
that they are all equal, for a line is the result of its law and its 
number ; but though both are the same for all lines of a sort, 
they act differently, as to force, energy, and duration, in different 
individuals ; which explains all differences of length, &c. I 
congratulate the reader who understands this ; and I do not pity 
the one who does not. 

Saint-Martin and his works are now as completely forgotten as 
if they had never been born, except so far as this, that some one 
may take up one of the works as of heretical character, and lay it 
down in disappointment, with the reflection that it is as dull as 
orthodoxy. For a person who was once in some vogue, it would 
be difficult to pick out a more fossil writer, from Aa to Zypoeus, 
except, though it is unusual for (, ) to represent an interval of 
more than a year his unknown opponent. This opponent, in the 
very year of the ' Des Erreurs . . . .' published a book in two 
parts with the same fictitious place of printing ; 



102 A BUDGET OF PARADOXES. 



Tableau Naturel des Rapports qui existent entre Dieu, 1'Horame, 
et 1'Univers. A Edimbourg, 1782, 8vo. 

There is a motto from the Des Erreurs itself, ' Expliquer les 
choses par I'homme, et non 1'homme par les choses. Des Erreurs 
et de la Verite, par un PH. . . . INC. . . ., p. 9.' This work is set 
down in various catalogues and biographies as written by the 
PH. . . . INC. . . . himself. But it is not usual for a writer to 
publish two works in the same year, one of which takes a motto 
from the other. And the second work is profuse in capitals and 
italics, and uses Hebrew learning : its style differs much from the 
first work. The first work sets out from man, and has nothing 
to do with Grod : the second is religious and raps the knuckles of 
the first as follows : ' Si nous voulons nous preserver de toutes 
les illusions, et surtout des amorces de 1'orgueil par lesquelles 
1'homme est si souvent seduit, ne prenons jamais les homines, 
mais toujours Dieu pour notre terme de comparaison.' The first 
uses four and nine in various ways, of which I have quoted one : 
the second says, ' Et ici se trouve deja ime explication des 
nombres quatre et neuf, qui ont peu embarrasse dans 1'ouvrage deja 
cite. L'homme s'est egare en allant de quatre a neuf . . . .' 
The work cited is the Erreurs, &c., and the citation is in the 
motto, which is the text of the opposition sermon. 

Method to discover the difference of the earth's diameters ; 
proving its true ratio to be not less variable than as 45 is to 46, 
and shortest in its pole's axis 174 miles . . . likewise a method 
for fixing an universal standard for weights and measures. By 
Thomas Williams. London, 1788, 8vo. 

Mr. Williams was a paradoxer in his day, and proposed what 
was, no doubt, laughed at by some. He proposed the sort of plan 
which the French independently of course carried into effect a 
few years after. He would have the 52nd degree of latitude 
divided into 100,000 parts and each part a geographical yard. 
The geographical tun was to be the cube of the geographical 
yard filled with sea-water taken some leagues from land. All 
multiples and subdivisions were to be decimal. 

I was beginning to look up those who had made similar 
proposals, when a learned article .on the proposal of a metrical 
system came under my eye in the Times of Sept. 15, 1863. The 
author cites Mouton, who would have the minute of a degree 
divided into 10,000 virgulce; James Cassini, whose foot was to be 



PAINE WOLLSTONECE AFT PAKR. 103 

six thousandths of a minute ; and Paucton, whose foot was the 
400,000th of a degree. I have verified the first and third state- 
ments ; surely the second ought to be the six-thousandth. 

An inquiry into the Copernican system . . . wherein it is 
proved, in the clearest manner, that the earth has only her 
diurnal motion . . . with an attempt to point out the only true 
way whereby mankind can receive any real benefit from the 
study of the heavenly bodies. By John Cunningham. London, 
] 789, 8vo. 

The ' true way ' appears to be the treatment of heaven and 
earth as emblematical of the Trinity. 

Cosmology. An inquiry into the cause of what is called gra- 
vitation or attraction, in which the motions of the heavenly 
bodies, and the preservation and operations of all nature, are 
deduced from an universal principle of efflux and reflux. By 
T. Vivian, vicar of Corn wood, Devon. Bath, 1792, 12mo. 

Attraction, an influx of matter to the sun ; centrifugal force, 
the solar rays ; cohesion, the pressure of the atmosphere. The 
confusion about centrifugal force, so called, as demanding an 
external agent, is very common. 

The rights of MAN, being an answer to Mr. Burke's attack on 

the French Revolution. By Thomas Paine. In two parts. 

1791-1792. 8vo. (Various editions.) 
A vindication of the rights of WOMAN, with strictures on 

political and moral subjects. By Mary Wollstonecraft. 1792. 

8vo. 
A sketch of the rights of BOYS and GIRLS. By Launcelot 

Light, of Westminster School ; and Laetitia Lookabout, of 

Queen's Square, Bloomsbury. [By the Rev. Samuel Parr, 

LL.D.] 1792. 8vo. (pp. 64). 

When did we three meet before ? The first work has sunk into 
oblivion : had it merited its title, it might have lived. It is what 
the French call a piece de circonstance ; it belongs in time to the 
French Revolution, and in matter to Burke's opinion of that 
movement. Those who only know its name think it was really 
an attempt to write a philosophical treatise on what we now call 
socialism. Silly government prosecutions gave it what it never 
could have got for itself. 

Mary Wollstonecraft seldom has her name spelt right. I 
suppose the ! O ! character she got made her Woolstonecraft. 



104 A BUDGET OF PARADOXES. 

Watt gives double insinuation, for his cross-reference sends us to 
Goodwin. No doubt the title of the book was an act of disciple- 
ship to Paine's ' Rights of Man ' ; but this title is very badly 
chosen. The book was marred by it, especially when the authoress 
and her husband assumed the right of dispensing with legal 
sanction until the appfoach of offspring brought them to a sense 
of their child's interest. Not a hint of such a claim is found in 
the book, which is mostly about female education. The right 
claimed for woman is to have the education of a rational human 
being, and not to be considered as nothing but woman throughout 
youthful training. The maxims of Mary Wollstonecraft are now, 
though not derived from her, largely followed in the education of 
girls, especially in home education : just as many of the political 
principles of Tom Paine, again not derived from him, are the 
guides of our actual legislation. I remember, forty years ago, 
an old lady who used to declare that she disliked girls from the 
age of sixteen to five-and-twenty. ' They are full,' said she, ' of 
femalities.' She spoke of their behaviour to women as well as to 
men. She would have been shocked to know that she was a 
follower of Mary Wollstonecraft, and had packed half her book 
into one sentence. 

The third work is a satirical attack on Mary Wollstonecraft and 
Tom Paine. The details of the attack would convince any one 
that neither has anything which would now excite reprobation. 
It is utterly unworthy of Dr. Parr, and has quite disappeared 
from lists of his works, if it were ever there. That it was written 
by him I take to be evident, as follows. Nichols, who could not 
fail to know, says (Anecd., vol. ix. p. 120): 'This is a playful 
essay by a first-rate scholar, who is elsewhere noticed in this 
volume, but whose name I shall not bring forward on so trifling 
an occasion.' Who the scholar was is made obvious by Master 
Launcelot being made to talk of Bellendenus. Further, the 
same boy is made to say, ' Let Dr. Parr lay his hand upon his 
heart, if his conscience will let him, and ask himself how many 
thousands of waggon-loads of this article [birch] he has cruelly 
misapplied.' How could this apply to Parr, with his handful of 
private pupils, and no reputation for severity ? Any one except 
himself would have called on the head-master of Westminster or 
Eton. I doubt whether the name of Parr could be connected 
with the rod by anything in print, except the above and an 
anecdote of his pupil, Tom Sheridan. The Doctor had dressed 
for a dinner visit, and was ready a quarter of an hour too soon to 
set off. Tom,' said he, I think I had better whip you now ; 



SAMUEL PARR. 105 

you are sure to do something while I am out.' ' I wish you would, 
sir ! ' said the boy ; ' it would be a letter of licence for the whole 
evening-.' The Doctor saw the force of the retort : my two 
tutelaries will see it by this time. They paid in advance ; and I 
have given liberal interpretation to the order. 

The following story of Dr. Parr was told me and others, about 
1829, by the late Leonard Homer, who knew him intimately. 
Parr was staying in a house full of company, I think in the 
north of England. Some gentlemen from America were among 
the guests, and after dinner they disputed some of Parr's asser- 
tions or arguments. So the Doctor broke out with ' Do you 
know what country you come from ? You come from the place 
to which we used to send our thieves ! ' This made the host 
angry, and he gave Parr such a severe rebuke as sent him irom 
the room in ill-humour. The rest walked on the lawn, amusing 
the Americans with sketches of the Doctor. There was a dark 
cloud overhead, and from that cloud presently came a voice 
which called Tham (Parr-lisp for Sam). The company were 
astonished for a moment, but thought the Doctor was calling his 
servant in the house, and that the apparent direction was an 
illusion arising out of inattention. But presently the sound was 
repeated, certainly from the cloud, 

And nearer, clearer, deadlier than before. 

There was now a little alarm : where could the Doctor have got 
to ? They ran to his bedroom, and there they discovered a 
sufficient rather than satisfactory explanation. The Doctor had 
taken his pipe into his bedroom, and had seated himself, in sulky 
mood, upon the higher bar of a large and deep old-fashioned 
grate with a high mantelshelf. Here he had tumbled backwards, 
and doubled himself up between the bars and the back of the 
grate. He was fixed tight, and when he called for help, he could 
only throw his voice up the chimney. The echo from the cloud 
was the warning which brought his friends to the rescue. 

Days of political paradox were coming, at which we now stare. 
Cobbett said, about 1830, in earnest, that in the country every 
man who did not take off his hat to the clergyman was suspected, 
and ran a fair chance of having something brought against him. 
I heard this assertion canvassed, when it was made, in a party of 
elderly persons. The Radicals backed it, the old Tories rather 
denied it, but in a way which satisfied me they ought to have 
denied it less if they could not deny it more. But it must be 
said that the Governments stopped far short of what their 



106 A BUDGET OF PARADOXES. 

partisans would have had them do. All who know Robert 
Robinson's very quiet assault on church-made festivals in hi 
' History and Mystery of Good Friday ' (1777) will hear or 
remember with surprise that the British Critic pronounced it 
a direct, unprovoked, and malicious libel on the most sacred 
institutions of the national Church. It was reprinted again and 
again: in 1811 it was in a cheap form at 6s 6^. a hundred. 
When the Jacobin day came, the State was really in a fright : 
people thought twice before they published what would now be 
quite disregarded. I examined a quantity of letters addressed to 
George Dyer (Charles Lamb's G.D.) and what between the auto- 
graphs of Thelwall, Hardy, Home Tooke, and all the rebels, 
put together a packet which produced five guineas, or there- 
abouts, for the widow. Among them were the following verses, 
sent by the author who would not put his name, even in a 
private letter, for fear of accidents for consultation whether they 
could safely be sent to an editor : and they were not sent. The 
occasion was the public thanksgiving at St. Paul's for the naval 
victories, December 19, 1797. 

God bless me ! what a thing ! 
Have you heard that the King 

Goes to St. Paul's ? 
Good Lord ! and when he's there, 
He'll roll his eyes in prayer, 
To make poor Johnny stare 

At this fine thing. 

No doubt the plan is wise 
To blind poor Johnny's eyes 

By this grand show ; 
For should he once suppose 
That he's led by the nose, 
Down the whole fabric goes, 

Church, lords, and king. 

As he shouts Duncan's praise, 
Mind how supplies they'll raise 

In wondrous haste. 
For while upon the sea 
We gain one victory, 
John still a dupe will be 

And taxes pay. 

Till from his little store 
Three-fourths or even more 
Goes to the Crown. 



WILLIAM HONE'S TRIALS, 107 

Ah, John ! you little think 
How fast we downward sink 
And touch the fatal brink 
At which we're slaves. 

I would have indicted the author for not making his thirds 
and sevenths rhyme. As to the rhythm, it is not much better 
than what the French sang in the Calais theatre, when the Duke 
of Clarence took over Louis XVIII. in 1814. 

God save noble Clarence, 

Who brings our king to France ; 

God save Clarence ! 
He maintains the glory 
Of the British navy. 
&c. &c. 

Perhaps had this been published, the Government would have 
assailed it as a libel on the church service. They got into the 
way of defending themselves by making libels on the Church, of 
what were libels, if on anything, on the rulers of the State ; until 
the celebrated trials of Hone settled the point for ever, and 
established that juries will not convict for one offence, even 
though it have been committed, when they know the prosecution 
is directed at another offence and another intent. 

The results of Hone's trials (William Hone, 1779-1842) are 
among the important constitutional victories of our century. He 
published parodies on the Creeds, the Lord's Prayer, the Cate- 
chism, &c., with intent to bring the Ministry into contempt : 
everybody knew that was his purpose. The Government indicted 
him for impious, profane, blasphemous intent, but not for 
seditious intent. They hoped to wear him out by proceeding day 
by day. December 18, 1817, they hid themselves under the 
Lord's Prayer, the Creed, and the Commandments ; December 1 9, 
under the Litany ; December 20, under the Athanasian Creed, 
an odd place for shelter when they could not find it in the previous 
places. Hone defended himself for six, seven, and eight hours on 
the several days: and the jury acquitted him in 15, 105, and 20 
minutes. In the second trial the offence was laid both as pro- 
fanity and as sedition, which seems to have made the jury hesitate. 
And they probably came to think that the second count was false 
pretence : but the length of their deliberation is a satisfactory 
addition to the value of the whole. In the first trial the Attorney- 
General (Shepherd) had the impudence to say that the libel 
had nothing of a political tendency about it, but was avowedly 



108 A BUDGET OF PAEADOXES 

set off against the religion and worship of the Church of England. 
The whole is political in every sentence ; neither more nor less 
political than the following, which is part of the parody on the 
Catechism. ' What is thy duty towards the Minister ? My duty 
towards the Minister is, to trust him as much as I can ; to honour 
him with all my words, with all my bows, with all my scrapes, 
and with all my cringes ; to flatter him ; to give him thanks ; to 
give up my whole soul to him ; to idolize his name, and obey his 
word, and serve him blindly all the days of his political life.' 
And the parody on the Creed begins, ' I believe in George, the 
Regent almighty, maker of new streets and Knights of the Bath.' 
This is what the Attorney- General said had nothing of a political 
tendency about it. But this was on the first trial : Hone 
was not known. The first day's trial was under Justice Abbott 
(afterwards C. J. Tenterden). It was perfectly understood, when 
Chief Justice Ellenborough appeared in Court on the second day, 
that he was very angry at the first result, and put his junior aside 
to try his own rougher dealing. But Hone tamed the lion. An 
eye-witness told me that when he implored of Hone not to detail 
his own father Bishop Law's views on the Athanasian Creed, which 
humble petition Hone kindly granted, he held by the desk for 
support. And the same when which is not reported the 
Attorney-General appealed to the Court for protection against a 
stinging attack which Hone made on the Bar : he held on, and 
said, ' Mr. Attorney, what can I do ! ' I was a boy of twelve years 
old, but so strong was the feeling of exultation at the verdicts 
that boys at school were not prohibited from seeing the parodies, 
which would have been held at any other time quite unfit to 
meet their eyes. I was not able to comprehend all about the 
Lord Chief Justice until I read and heard again in after years. 
In the meantime, Joe Miller had given me the story of the 
leopard which was sent home on board a ship of war, and was in 
two days made as docile as a cat by the sailors. ' You have got 
that fellow well under,' said an officer. 'Lord bless your honour !' 
said Jack, ' if the Emperor of Marocky would send us a cock 
rhinoceros, we'd bring him to his bearings in no time ! ' When I 
came to the subject again, it pleased me to entertain the question 
whether, if the Emperor had sent a cock rhinoceros to preside on 
the third day in the King's Bench, Hone would have mastered 
him : I forget how I settled it. There grew up a story that Hone 
caused Lord Ellenborough's death, but this could not have been 
true. Lord Ellenborough resigned his seat in a few months, and 



SUBSCRIPTIONS FOR HONE. 109 

died just a year after the trials ; but sixty-eight years may have 
had more to do with it than his defeat. 

A large subscription was raised for Hone, headed by the Duke 
of Bedford for 105Z. Many of the leading ante-ministerialists 
joined : but there were many of the other side who avowed their 
disapprobation of the false pretence. Many could not venture 
their names. In the list I find : A member of the House of Lords, 
an enemy to persecution, and especially to religious persecution 
employed for political purposes No parodist, but an enemy to 
persecution A juryman on the third day's trial Ellen Borough 
My name would ruin me Oh ! minions of Pitt Oil for the 
Hone The Ghosts of Jeffries and Sir William Roy [Ghosts of 
Jeffries in abundance] A conscientious Jury and a conscientious 
Attorney, ll. 6s. Sd. To Mr. Hone, for defending in his own 
person the freedom of the press, attacked for a political object, 
under the old pretence of supporting Eeligion A cut at corruption 
An Earldom for myself and a translation for my brother One 
who disapproves of parodies, but abhors persecution From a 
schoolboy who wishes Mr. Hone to have a very grand subscription 
* For delicacy's sake forbear,' and ' Felix trembled ' 'I will go 
myself to-morrow ' Judge Jeffries' works rebound in calf by Law 
Keep us from Law, and from the Shepherd's paw I must not 
give you my name, but God bless you ! As much like Judge 
Jeffries as the present times will permit May Jeffries' fame 
and Jeffries' fate on every modern Jeffries wait No parodist, 
but an admirer of the man who has proved the fallacy of the 
Lawyer's Law, that when a man is his own advocate he has a fool 
for his client A Mussulman who thinks it would not be an impious 
libel to parody the Koran May the suspenders of the Habeas 
Corpus Act be speedily suspended Three times twelve for thrice- 
tried Hone, who cleared the cases himself alone, and won three 
heats by twelve to one, \l. 16s. A conscientious attorney, 
11. 6s. Sd. Rev. T. B. Morris, rector of Shelfanger, who dis- 
approves of the parodies, but abhors the making an affected zeal 
for religion the pretext for political persecution A Lawyer 
opposed in principle to Law For the Hone that set the razor 
that shaved the rats Rev. Dr. Samuel Parr, who most seriously 
disapproves of all parodies upon the hallowed language of Scripture 
and the contents of the Prayer-book, but acquits Mr. Hone of 
intentional impiety, admires his talents and fortitude, and 
applauds the good sense and integrity of his juries Religion 
without hypocrisy, and Law without partiality Law ! Law ? 
Law ! 



110 A BUDGET OF PARADOXES. 

These are specimens of a great many allusive mottoes. The 
subscription was very large, and would have bought a handsome 
annuity, but Hone employed it in the bookselling trade, and did 
not thrive. His ' Everyday Book ' and his ' Apocryphal New 
Testament ' are useful books. On an annuity he would have 
thriven as an antiquarian writer and collector. It is well that 
the attack upon the right to ridicule Ministers roused a dormant 
power which was equal to the occasion. Hone declared, on his 
honour, that he had never addressed a meeting in his life, nor 
spoken a word before more than twelve persons. Had he which 
however could not then be done employed counsel, and had a 
guilty defence made for him, he would very likely have been 
convicted, and the work would have been left to be done by 
another. No question that the parodies disgusted all who 
reverenced Christianity, and who could not separate the serious and 
the ludicrous, and prevent their existence in combination. 

My extracts, &c., are from the nineteenth, seventeenth, and six- 
teenth editions of the three trials, which seem to have been con- 
temporaneous (all in 1818) as they are made up into one book, 
with additional title over all, and the motto ' Thrice the brindled 
cat hath mew'd.' They are published by Hone himself, who I 
should -have said was a publisher as well as was to be. And 
though the trials only ended Dec. 20, 1817, the preface attached 
to this common title is dated Jan. 23, 1818. 

The spirit which was roused against the false dealing of 
the Government, i.e. the pretence of prosecuting for impiety 
when all the world knew the real offence was, if anything, sedi- 
tion was not got up at the moment : there had been previous 
exhibitions of it. For example, in the spring of 1 8 1 8 Mr. Russell, 
a little printer in Birmingham, was indicted for publishing the 
Political Litany on which Hone was afterwards tried. He took 
his witnesses to the summer Warwick assizes, and was told that 
the indictment had been removed by certiorari into the King's 
Bench. He had notice of trial for the spring assizes at Warwick: 
he took his witnesses there, and the trial was postponed by the 
Crown. He then had notice for the summer assizes at Warwick ; 
and so on. The policy seems to have been to wear out the ob- 
noxious parties, either by delays or by heaping on trials. The 
Government was odious, and knew it could not get verdicts against 
ridicule, and could get verdicts against impiety. No difficulty 
was found in convicting the sellers of Paine's works, and the like. 
When Hone was held to bail it was seen that a crisis was at hand. 
All parties in politics furnished him with parodies in proof of 



PROFANITY OF LORD BYROX. Ill 

religious persons having made instruments of them. The parodies 
by Addison and Luther were contributed by a Tory lawyer, who 
was afterwards a judge. 

Hone had published, in 1817, tracts of purely political ridicule: 
' official account of the noble lord's bite,' * trial of the dog for 
biting the noble lord,' &c. These were not touched. After the 

o 7 

trials, it is manifest that Hone was to be unassailed, do what he 
might. ' The Political House that Jack built,' in 1 8 1 9 ; The Man 
in the Moon,' 1 820 ; ' The Queen's Matrimonial Ladder,' ' Non mi 
ricordo,' 'The E 1 fowls,' 1 820 ; ' The Political Showman at home,' 
with plates by G. Cruickshank, 1821 [he did all the plates] ; ' The 
Spirit of Despotism,' 1821 would have been legitimate marks 
for prosecution in previous years. The biting caricature of 
several of these works are remembered to this day. ' The Spirit 
of Despotism' was a tract of 1795, of which a few copies had been 
privately circulated with great secrecy. Hone reprinted it, and 
prefixed the following address to ' Robert Stewart, alias Lord 
Castlereagh ' ' It appears to me that if, unhappily, your counsels 
are allowed much longer to prevail in the Brunswick Cabinet, 
they will bring on a crisis, in which the king may be dethroned 
or the people enslaved. Experience has shown that the people 
will not l>e enslaved the alternative is the affair of your em- 
ployers.' Hone might say this without notice. 

In 1819 Mr. Murray published Lord Byron's 'Don Juan,' and 
Hone followed it with ' Don John, or Don Juan unmasked,' a 
little account of what the publisher to the Admiralty was allowed 
to issue without prosecution. The parody on the Commandments 
was a case very much in point : and Hone makes a stinging 
allusion to the use of the ' unutterable Nvme, with a profane 
levity unsurpassed by any other two lines in the English language.* 
The lines are 

'Tis strange the Hebrew noun which means 'I am,' 
The English always use to govern d n. 

Hone ends with : ' Lord Byron's dedication of " Don Juan " to Lord 
Castlereagh was suppressed by Mr. Murray from delicacy to 
Ministers. Q. Why did not Mr. Murray suppress Lord Byron's 
parody on the Ten Commandments? A. Because it contains 
nothing in ridicule of Ministers, and therefore nothing that they 
could suppose would lead to the displeasure of Almighty God.' 

The little matters on which I have dwelt will never appear in 
history from their political importance, except in a few words of 
result. As a mode of thought, silly evasions of all kinds belong 



112 A BUDGET OF PARADOXES. 

to such a work as the present. Ignorance, which seats itself in 
the chair of knowledge, is a mother of revolutions in politics, and 
of unread pamphlets in circle-squaring. From 1815 to 1830 the 
question of revolution or no revolution lurked in all our English 
discussions. The high classes must govern ; the high classes 
shall not govern ; and thereupon issue was to be joined. In 1828- 
1833 the question came to issue; and it was, Eevolution with or 
without civil war ; choose. The choice was wisely made ; and 
the Eeform Bill started a new system so well dovetailed into the 
old that the joinings are hardly visible. And now, in 1867, the 
thing is repeated with a marked subsidence of symptoms ; and the 
party which has taken the place of the extinct Tories is carrying 
through Parliament a wider extension of the franchise than their 
opponents would have ventured. Napoleon used to say that a 
decided nose was a sign of power : on which it has been remarked 
that he had good reason to say so before the play was done. And 
so had our country ; it was saved from a religious war, and from 
a civil war, by the power of that nose over its colleagues. 

The Commentaries of Proclus. Translated by Thomas Taylor. 
London, 1792, 2 vols. 4to. 

The reputation of ' the Platonist ' begins to grow, and will 
continue to grow. The most authentic account is in the Penny 
Cyclopaedia, written by one of the few persons who knew him 
well, and one of the fewer who possess all his works. At page 
Ivi. of the Introduction is Taylor's notion of the way to find the 
circumference. It is not geometrical, for it proceeds on the 
motion of a point: 'the words ' on account of the simplicity of the 
impulsive motion, such a line must be either straight or circular' 
will suffice to show how Platonic it is. Taylor certainly professed 
a kind of heathenism. D'Israeli said, 'Mr. T. Taylor, the Platonic 
philosopher and the modern Plethon, consonant to that philosophy, 
professes polytheism.' Taylor printed this in large type, in a 
page by itself after the dedication, without any disavowal. I 
have seen the following, Greek and translation both, in his hand- 
writing : ' Has dyaQos rj dyaSos sQviKOs' Kai iras ^pia-navos y 
"XpicfTtavos KaKus. Every good man, so far as he is a good man, 
is a heathen ; and every Christian, so far as he is a Christian, is a 
bad man.' Whether Taylor had in his head the Christian of the 
New Testament, or whether he drew from those members of the 
' religious world ' who make manifest the religious flesh and the 
religious devil, cannot be decided by us, and perhaps was not 
known to himself. If a heathen, he was a virtuous one. 



HANNAH MORE -MISS BURNEY. 113 

(1795.) This is the date of a very remarkable paradox. The 
religious world to use a name claimed by a doctrinal sect 
had long set its face against amusing literature, and all works of 
imagination. Bunyan, Milton, and a few others were irresis- 
tible ; but a long face was pulled at every attempt to produce 
something readable for poor people and poor children. In 
1795, a benevolent association began to circulate the works of 
a lady who had been herself a dramatist, and had nourished a 
pleasant vein of satire in the society of Garrick and his friends ; 
all which is carefully suppressed in some biographies. Hannah 
More's Cheap Repository Tracts, which were bought by millions 
of copies, destroyed the vicious publications with which the 
hawkers deluged the country, by the simple process of furnishing 
the hawkers with something more saleable. 

Dramatic fiction, in which the characters are drawn by them- 
selves, was, at the middle of the last century, the monopoly of 
writers who required indecorum, such as Fielding and Smollett. 
All, or nearly all, which could be permitted to the young, was 
dry narrative, written by people who could not make their 
personages talk character ; they all spoke alike. The author 
of the Rambler is ridiculed, because his young ladies talk 
Johnsonese ; but the satirists forget that all the presentable novel- 
writers were equally incompetent ; even the author of ' Zeluco ' 
(1789) is the strongest possible case in point. 

Dr. Moore, the father of the hero of Corunna, with good narra- 
tive power, some sly humour, and much observation of character, 
would have been, in our day, a writer of the Peacock family. 
Nevertheless, to one who is accustomed to our style of things, 
it is comic to read the dialogue of a jealous husband, a suspected 
wife, a faithless maid-servant, a tool of a nurse, a wrong-headed 
pomposity of a priest, and a sensible physician, all talking Dr. 
Moore through their masks. Certainly an Irish soldier does say 
by Jasus, and a cockney footman this here and that there ; and 
this and the like is all the painting of characters which is effected 
out of the mouths of the bearers by a narrator of great power. 
I suspect that some novelists repressed their power under a rule 
that a narrative should narrate, and that the dramatic should be 
confined to the drama. 

I make no exception in favour of Miss Burney ; though she was 
the forerunner of a new era. Suppose a country in which dress 
is always of one colour ; suppose an importer who brings in cargoes 
of blue stuff, red stuff, green stuff, &c., and exhibits dresses of 
these several colours, that person is the similitude of Miss 

i 



114 A BUDGET OF PAKADOXES. 

Burney. It would be a delightful change from a universal dull 
brown, to see one person all red, another all blue, &c. ; but the 
real inventor of pleasant dress would be the one who could mix 
his colours and keep down the bright and gaudy. Miss Burney's 
introduction was so charming, by contrast, that she nailed such men 
as Johnson, Burke, Grarrick, &c., to her books. But when a 
person who has read them with keen pleasure in boyhood, as I 
did, comes back to them after a long period, during which he 
has made acquaintance with the great novelists of our century, 
three-quarters of the pleasure is replaced by wonder that he had 
not seen he was at a puppet-show, not at a drama. Take some 
labelled characters out of our humourists, let them be put 
together into one piece, to speak only as labelled : let there be 
a Dominie with nothing but 'Prodigious ! ' a Dick Swiveller with 
nothing but adapted quotations ; a Dr. Folliott with nothing 
but sneers at Lord Brougham ; and the whole will pack up into 
one of Miss Burney's novels. 

Maria Edgeworth, Sydney Owenson (Lady Morgan), Jane 
Austen, Walter Scott, &c., are all of our century ; as are, I 
believe, all the Minerva Press novels, as they were called, which 
show some of the power in question. Perhaps dramatic talent 
found its best encouragement in the drama itself. But I cannot 
ascertain that any such power was directed at the multitude, 
whether educated or uneducated, with natural mixture of 
character, under the restraints of decorum, until the use of it 
by two religious writers of the school called ' evangelical,' Han- 
nah More and Rowland Hill. The Village Dialogues, though 
not equal to the Repository Tracts, are in many parts an ap- 
proach, and perhaps a copy ; there is frequently humorous satire, 
in that most effective form, self-display. They were published in 
1800, and, partly at least, by the Religious Tract Society, the 
lineal successor of the Repository association, though knowing 
nothing about its predecessor. I think it right to add that 
Rowland Hill here mentioned is not the regenerator of the 
Post Office. Some do not distinguish accurately ; I have heard 
of more than one who took me to have had a logical controversy 
with a diplomatist who died some years before I was born. 

A few years ago, an attempt was made by myself and others 
to collect some information about the Cheap Repository (see 
Notes and Queries, 3rd Series, vi. 241, 290, 353 ; Christian 
Observer, Dec. 1864, pp. 944-49). It appeared that after the 
Religious Tract Society had existed more than fifty years, a friend 
presented it with a copy of the original prospectus of the Rcposi- 



THE EELIGIOUS TEACT SOCIETY. 115 

tory, a thing the existence of which was not known. In this 
prospectus it is announced that from the plan ' will be carefully 
excluded whatever is enthusiastic, absurd, or superstitious.' The 
* evangelical ' party had, from the foundation of the Eeligious 
Tract Society, regretted that the Repository Tracts ' did not 
contain a fuller statement of the great evangelical principles ;' 
while in the prospectus it is also stated that ' no cause of any 
particular party is intended to be served by it, but general 
Christianity will be promoted upon practical principles.' This 
explains what has often been noticed, that the tracts contain a 
mild form of the ' evangelical ' doctrine, free from that more 
fervid dogmitism which appears in the Village Dialogues; and 
such as H. More's friend, Bishop Porteus a great promoter of 
the scheme might approve. The Religious Tract Society (in 
1863) republished some of H. More's tracts, with alterations, 
additions, and omissions ad libitum. This is an improper way 
of dealing with the works of the dead ; especially when the 
reprints are of popular works. A small type addition to the 
preface contains : ' Some alterations and abridgments have been 
made to adapt them to the present times and the aim of the 
Religious Tract Society.' I think every publicity ought to be 
given to the existence of such a practice ; and I reprint what I 
said on the subject in Notes and Queries. 

Alterations in works which the Society republishes are a neces- 
sary part of their plan, though such notes as they should judge 
to be corrective would be the best way of proceeding. But the 
fact of alteration should be very distinctly announced on the title 
of the work itself, not left to a little bit of small type at the end 
of the preface, in the place where trade advertisements, or direc- 
tions to the binder, are often found. And the places in which 
alteration has been made should be pointed out, either by marks 
of omission, when omission is the alteration, or by putting the 
altered sentences in brackets, when change has been made. May 
any one alter the works of the dead at his own discretion ? We 
all know that readers in general will take each sentence to be 
that of the author whose name is on the title; so that a correcting 
republisher makes use of his author's n-ame to teach his own 
variation. The tortuous logic of ' the trade,' which is content 
when ' the world ' is satisfied, is not easily answered, any more 
than an eel is easily caught ; but the Religious Tract Society may 
be convinced [in the old sense] in a sentence. On which course 
would they feel most safe in giving their account to the God of 
truth ? ' In your own conscience, now ? ' 

i -2 



116 A BUDGET OF PAEADOXES. 

I have tracked out a good many of the variations made by the 
Religious Tract Society in the recently published volume of 
Repository Tracts. Most of them are doctrinal insertions or 
amplifications, to the matter of which Hannah More would not 
have objected all that can be brought against them is the want 
of notice. But I have found two which the respect I have for the 
Religious Tract Society, in spite of much difference on various 
points, must not prevent my designating as paltry. In the story 
of Mary Wood, a kind-hearted clergyman converses with the poor 
girl who has ruined herself by lying. In the original, he ' assisted 
her in the great work of repentance ; ' in the reprint it is to be 
shown in some detail how he did this. He is to begin by pointing 
out that ' the heart is deceitful above all things and desperately 
wicked.' Now the clergyman's name is Heartwell : so to prevent 
his name from contradicting his doctrine, he is actually cut down 
to Harwell. Hannah More meant this good man for one of those 
described in Acts xv. 8, 9, and his name was appropriate. 

Again, Mr. Flatterwell, in persuasion of Parley the porter to 
let him into the castle, declares that the worst he will do is to 
' play an innocent game of cards just to keep you awake, or sing 
a cheerful song with the maids.' Oh fie ! Miss Hannah More ! 
and you a single lady too, and a contemporary of the virtuous 
Bowdler ! Though Flatterwell be an allegory of the devil, this 
is really too indecorous, even for him. Out with the three last 
words ! and out it is. 

The Society cuts a poor figure before a literary tribunal. 
Nothing was wanted except an admission that the remarks made by 
me were unanswerable, and this was immediately furnished by the 
Secretary (N. and Q. 3 S. vi. 290). In a reply of which six parts 
out of seven are a very amplified statement that the Society did 
not intend to reprint all Hannah More's tracts, the remaining 
seventh is as follows : 

I am not careful [perhaps this should be careful not~] to notice 
Professor De Morgan's objections to the changes in 'Mary Wood' or 
* Parley the Porter,' but would merely reiterate that the tracts were 
neither designed nor announced to be ' reprints ' of the originals 
[design is only known to the designers ; as to announcement, the title is 
1 'Tis all for the best, The Shepherd of Salisbury Plain, and other 
narratives, by Mrs. Hannah More '] ; and much less [this must be 
careful not; further removed from answer than not careful'] can I 
oncupy your space by a treatise on the Professor's question : ' May 
any one alter the works of the dead at his own discretion ? ' 

To which I say Thanks for help ! 



WILLIAM FREND'S ALGEBRA. 117 

I predict that Hannah More's Cheap Repository Tracts will 
somewhat resemble the Pilgrim's Progress in their fate. Written 
for the cottage, and long remaining in their original position, 
they will become classical works of their kind. Most assuredly 
this will happen if my assertion cannot be upset, namely That 
they contain the first specimens of fiction addressed to the world 
at large, and widely circulated, in which dramatic as distin- 
guished from puppet power is shown, and without indecorum. 

According to some statements I have seen, but which I have 
not verified, other publishing bodies, such as the Christian 
Knowledge Society, have taken the same liberty with the names 
of the dead as the Eeligious Tract Society. If it be so, the 
impropriety is the work of the smaller spirits, who have not been 
sufficiently overlooked. There must be an overwhelming majority 
in the higher councils to feel that, whenever altered works are 
published, the fact of alteration should be made as prominent as 
the name of the author. Everything short of this is suppression 
of truth, and will ultimately destroy the credit of the Society. 
Equally necessary is it that the alterations should be noted. 
When it comes to be known that the author before him is altered, 
he knows not where nor how nor by whom, the lowest reader will 
lose his interest. 



The principles of Algebra. By William Frend. London, 1796, 
8vo. Second Part, 1799. 

This Algebra, says Dr. Peacock, shows ' great distrust of the 
results of algebraical science which were in existence at the time 
when it was written.' Truly it does ; for, as Dr. Peacock had 
shown by full citation, it makes war of extermination upon all 
that distinguishes algebra from arithmetic. Robert Simson and 
Baron Maseres were Mr. Frend's predecessors in this opinion. 

The genuine respect which I entertained for my father-in-law 
did not prevent my canvassing with perfect freedom his anti- 
algebraical and anti-Newtonian opinions, in a long obituary 
memoir read at the Astronomical Society in February 1842, 
which was written by me. It was copied into the Athenceum of 
March 19. It must be said that if the manner in which algebra 
was presented to the learner had been true algebra, he would 
have been right : and if he had confined himself to protesting 
against the imposition of attraction as a fundamental part of the 
existence of matter, he would have been in unity with a great 
many, including Newton himself. I wish he had preferred 



113 A BUDGET OF PARADOXES. 

amendment to rejection when he was a college tutor : he wrote 
and spoke English with a clearness which is seldom equalled. 

His anti-Newtonian discussions are confined to the preliminary 
chapters of his * Evening Amusements,' a series of astronomical 
lessons in nineteen volumes, following the moon through a period 
of the golden numbers. 

There is a mistake about him which can never be destroyed. 
It is constantly said that, at his celebrated trial in 1792, for 
sedition and opposition to the Liturgy, &c., he was expelled the 
University. He was banished. People cannot see the difference; 
but it made all the difference to Mr. Frend. He held his fellow- 
ship and its profits till his marriage in 1808, and was a member 
of the University and of its Senate till his death in 1841, as any 
Cambridge Calendar up to 1841 will show. That they would have 
expelled him if they could, is perfectly true ; and there is a funny 
story also perfectly true about their first proceedings being 
under a statute which would have given the power, had it not been 
discovered during the proceedings that the statute did not exist. 
It had come so near to existence as to be entered into the Vice- 
Chancellor's book for his signature, which it wanted, as was not 
seen till Mr. Frend exposed it : in fact, the statute had never 
actually passed. 

There is an absurd mistake in Gunning's ' Reminiscences of 
Cambridge.' In quoting a passage of Mr. Frend's pamphlet, 
which was very obnoxious to the existing Government, it is 
printed that the poor market-women complained that they were 
to be scotched a quarter of their wages by taxation ; and attention 
is called to the word by its being three times printed in italics. 
In the pamphlet it is ' sconced ' ; that very common old word for 
fined or mulcted. 

Lord Lyndhurst, who has [1863] just passed away under a load 
of years and honours, was Mr. Frend's private pupil at Cambridge. 
At the time of the celebrated trial, he and two others amused 
themselves, and vented the feeling which was very strong among 
the undergraduates, by chalking the walls of Cambridge with 
' Frend for ever!' While thus engaged in what, using the term 
legally, we are probably to call his first publication, he and his 
friends were surprised by the proctors. Flight and chase followed 
of course: Copley and one of the others, Serjeant Rough, 
escaped ; the third, whose name I forget, but who afterwards, I 
have been told, was a bishop, 1 being lame, was captured and 
impositioned. Looking at the Cambridge Calendar to verify the 

1 Herbert Marsh, afterwards Bishop of Peterborough, a relation of my father, (Ed.) 



FRANCIS PLACE WILLIAM COBBETT. 119 

fact that Copley was an undergraduate at the time, I find that 
there are but two other men in the list of honours of his year 
whose names are now widely remembered. And they were both 
celebrated schoolmasters ; Butler of Harrow, and Tate of Eichmond. 

But Mr. Frend had another noted pupil. I once had a con- 
versation with a very remarkable man, who was generally called 
' Place, the tailor,' but who was politician, political economist, 
&c., &c. He sat in the room above his shop he was then a 
thriving master tailor at Charing Cross surrounded by books 
enough for nine, to shame a proverb. The blue books alone, cut 
up into strips, would have measured Great Britain for oh-no-we- 
never-mention-'ems, the Highlands included. I cannot find a 
biography of this worthy and able man. I happened to mention 
William Frend, and he said, ' Ah ! my old master, as I always 
call him. Many and many a time, and year after year, did he 
come in every now and then to give me instruction, while I was 
sitting on the board, working for my living, you know.' 

Place, who really was a sound economist, is joined with 
Cobbett, because they were together at one time, and because he 
was, in 1800, &c., a great Eadical. But for Cobbett he had a 
great contempt. He told me the following story. He and others 
were advising with Cobbett about the defence he was to make on 
a trial for seditious libel which was coming on. Said Place, * You 
must put in the letters you have received from Ministers, 
members of the Commons from the Speaker downwards, &c., 
about your Eegister, and their wish to have subjects noted. You 
must then ask the jury whether a person so addressed must be 
considered as a common sower of sedition, &c. You will be 
acquitted ; nay, if your intention should get about, veiy likely 
they will manage to stop proceedings.' Cobbett was too much 

disturbed to listen ; he walked about the room ejaculating ' D 

the prison ! ' and the like. He had not the sense to follow the 
advice, and was convicted. 

Cobbett, to go on with the chain, was a political acrobat, ready 
for any kind of posture. A friend of mine gave me several times 
an account of a mission to him. A Tory member those who 
know the old Tory world may look for his initials in initials of 
two consecutive words of ' Pay his money with interest ' who 
was, of course, a political opponent, thought Cobbett had been 
hardly used, and determined to subscribe handsomely towards the 
expenses he was incurring as a candidate. My friend was com- 
missioned to hand over the money a bag of sovereigns, that notes 
might not be traced. He went into Cobbett's committee-room, 



120 A BUDGET OF PARADOXES. 

told the patriot his errand, and put the money on the table. 
' And to whom, sir, am I indebted ? ' said Cobbett. ' The donor,' 
was the answer, ' is Mr. Andrew Theophilus Smith,' or some such 
unlikely pair of baptismals. ' Ah ! ' said Cobbett, ' I have known Mr. 
A. T. S. a long time ! he was always a true friend of his country 1 ' 
To return to Place. He is a noted instance of the advantage 
of our jury system, which never asks a man's politics, &c. The 
late King of Hanover, when Duke of Cumberland, being unpopular, 
was brought under unjust suspicions by the suicide of his valet : 
he must have seduced the wife and murdered the husband. The 
charges were as absurd as those brought against the Englishman 
in the Frenchman's attempt at satirical verses upon him : 

The Englishman is a very bad man ; 
He drink the beer and lie steal the can : 
He kiss the wife and he beat the man ; 
And the Englishman is a very G d . 



The charges were revived in a much later day, and the defence 
might have given some trouble. But Place, who had been the 
foreman at the inquest, came forward, and settled the question in 
a few lines. Everyone knew that the old Radical was quite free 
of all disposition to suppress truth from wish to curry favour with 
royalty. 

John Speed, the author of the English History (1632) which 
Bishop Nicolson calls the best chronicle extant, was a man, like 
Place, of no education but what he gave himself. The bishop 
says he would have done better if he had had better training : 
but what, he adds, could have been expected from a tailor ! This 
Speed was, as well as Place. But he was released from manual 
labour by Sir Fulk Grevil, who enabled him to study. 

I have elsewhere noticed that those who oppose the mysteries 
of algebra do not ridicule them ; this I want the cyclometers to 
do. Of the three who wrote against the great point, the negative 
quantity, and the uses of which are connected with it, only 
one could fire a squib. That Robert Simson should do such a 
thing will be judged impossible by all who admit tradition. I 
do not vouch for the following ; I give it as a proof of the 
impression which prevailed about him : 

He used to sit at his open window on the ground floor, as deep 
in geometry as a Robert Simson ought to be. Here he would be 
accosted by beggars, to whom he generally gave a trifle , he 
roused himself to hear a few words of the story, made his dona- 
tion, and instantly dropped down into his depths. Some wags 



MASERES ON THE NEGATIVE SIGN. 121 

one day stopped a mendicant who was on his way to the window, 
with ' Now, my man, do as we tell you, and you will get some- 
thing from that gentleman, and a shilling from us besides. You 
will go and say you are in distress, he will ask you who you are, 
and you will say you are Robert Simson, son of John Simson of 
Kirktonhill.' The man did as he was told ; Simson quietly gave 
him a coin, and dropped off. The wags watched a little, and saw 
him rouse himself again, and exclaim ' Robert Simson, son of 
John Simson of Kirktonhill ! why, that is myself. That man 
must be an impostor.' Lord Brougham tells the same story, with 
some difference of details. 

Baron Maseres was, as a writer, dry ; those who know his 
writings will feel that he seldom could have taken in a joke or 
issued a pun. Maseres was the fourth wrangler of 1752, and 
first Chancellor's medallist (or highest in classics) ; his second 
was Porteus (afterwards Bishop of London). Waring came five 
years after him : he could not get Maseres through the second 
page of his first work on algebra ; a negative quantity stood 
like a lion in the way. In 1758 he published his 'Dissertation 
on the Use of the Negative Sign,' 4to. There are some who care 
little about -f- and , who would give it house-room for the sake 
of the four words ' Printed by Samuel Richardson.' 

Maseres speaks as follows : ' A single quantity can never be 
marked with either of those signs, or considered as either affirma- 
tive or negative ; for if any single quantity, as 6, is marked 
either with the sign -f- or with the sign without assigning 
some other quantity, as a, to which it is to be added, or from 
which it is to be subtracted, the mark will have no meaning or 
signification : thus if it be said that the square of 5, or the 
product of 5 into 5, is equal to +25, such an assertion must 
either signify no more than that 5 times 5 is equal to 25 without 
any regard to the signs, or it must be mere nonsense and unin- 
telligible jargon. I speak according to the foregoing definition, 
by which the affirmativeness or negativeness of any quantity 
implies a relation to another quantity of the same kind to which 
it is added, or from which it is subtracted ; for it may perhaps be 
very clear and intelligible to those who have formed to them- 
selves some other idea of affirmative and negative quantities 
different from that above defined.' 

Nothing can be more correct, or more identically logical : + 5 
and 5, standing alone, are jargon if +5 and 5 are to be 
understood as without reference to another quantity. But those 
who have ' formed to themselves some other idea ' see meaning 



122 A BUDGET OF PARADOXES. 

enough. The great difficulty of the opponents of algebra lay in 
want of power or will to see extension of terms. Maseres is right 
when he implies that extension, accompanied by its refusal, 
makes jargon. One of my paradoxers was present at a meeting 
of the Koyal Society (in 1864, I think) and asked permis- 
sion to make some remarks upon a paper. He rambled into 
other things, and, naming me, said that I had written a 
book in which two sides of a triangle are pronounced equal to 
the third. So they are, in the sense in which the word is used 
in complete algebra; in which A + B = C makes A, B, c, three 
sides of a triangle, and declares that going over A and B, one after 
the other, is equivalent, in change of place, to going over c at 
once. My critic, who might, if he pleased, have objected to 
extension, insisted upon reading me in unextended meaning. 

On the other hand, it must be said that those who wrote on 
the other idea wrote very obscurely about it, and justified Des 
Cartes (De Methodo] when he said : ' Algebram vero, ut solet 
doceri, animadverti certis regulis et numerandi formulis ita esse 
contentam, ut videatur potius ars qua3dam confusa, cujus usu 
ingenium quodam modo turbatur et obscuratur, quam scientia 
qua excolatur et perspicacius reddatur.' Maseres wrote this 
sentence on the title of his own copy of his own work, now before 
me ; he would have made it his motto if he had found it earlier. 
There is, I believe, in Cobbett's ' Annual Kegister,' an account 
of an interview between Maseres and Cobbett when in prison. 

The conversation of Maseres was lively, and full of serious anec- 
dote : but only one attempt at humorous satire is recorded of 
him; it is an instructive one. He was born in 1731 (Dec. 15), 
and his father was a refugee. P'rench was the language of the 
house, with the pronunciation of the time of Louis XIV. He 
lived until 1824 (May 19), and saw the race of refugees who 
were driven out by the first Eevolution. Their pronunciation 
differed greatly from his own ; and he used to amuse himself by 
mimicking them. Those who heard him and them had the two 
schools of pronunciation before them at once; a thing which 
seldom happens. It might even yet be worth while to examine 
the Canadian pronunciation. 

Maseres went as Attorney-General to Quebec; and was ap- 
pointed Cursitor Baron of our Exchequer in 1773. There is a 
curious story about his mission to Canada, which I have heard as 
good tradition, but have never seen in print. The reader shall 
have it as cheap as I ; and I confess I rather believe it. Maseres 
was inveterately honest ; he could not, at the bar, boar to see his 



BARON MASERES. 123 

own client victorious, when be knew his cause was a bad one. 
On a certain occasion he was in a cause which he knew would 
go against him if a certain case were quoted. Neither the judge 
nor the opposite counsel seemed to remember this case, and 
Ma seres could not help dropping an allusion which brought it 
out. His business as a barrister fell off, of course. Some time 
after, Mr. Pitt (Chatham) wanted a lawyer to send to Canada on 
a private mission, and wanted a very honest man. Some one 
mentioned Maseres, and told the above story : Pitt saw that he 
had got the man he wanted. The mission was satisfactorily per- 
formed, and Maseres remained as Attorney-General. 

The 'Doctrine of Life Annuities' (4to. 726 pages, 1783) is a 
strange paradox. Its size, the heavy dissertations on the national 
debt, and the depth of algebra supposed known, put it out of 
the question as an elementary work, and it is unfitted for the 
higher student by its elaborate attempt at elementary character, 
shown in its rejection of forms derived from chances in favour of 
the average, and its exhibition of the separate values of the 
years of an annuity, as arithmetical illustrations. It is a climax 
of unsaleability, unreadability, and inutility. For intrinsic 
nullity of interest, and dilution of little matter with much ink, 
I can compare this book to nothing but that of Claude de St. 
Martin, elsewhere mentioned, or the lectures * On the Nature and 
Properties of Logarithms,' by James Little, Dublin, 1830, 8vo. 
(254 heavy pages of many words and few symbols), a wonderful 
weight of weariness. 

The stock of this work on annuities, very little diminished, 
was given by the author to William Frend, who paid warehouse 
room for it until about 1835, when he consulted me as to its 
disposal. As no publisher could be found who would take it 
as a gift, for any purpose of sale, it was consigned, all but a few 
copies, to a buyer of waste paper. 

Baron Maseres's republications are well known : the Scriptona 
Logarithmici is a set of valuable reprints, mixed with much 
which might better have entered into another collection. It is 
not so well known that . there is a volume of optical reprints, 
Sci^iptores Optici, London, 1823, 4to, edited for the veteran of 
ninety-two by Mr. Babbage at twenty-nine. This excellent 
volume contains James Gregory, Des Cartes, Halley, Barrow, 
and the optical writings of Huyghens, the Principia of the 
undulatory theory. It also contains, by the sort of whim in 
which such men as Maseres, myself, and some others are apt 
to indulge, a reprint of ' The great and new Art of weighing 



124 A BUDGET OF PARADOXES. 

Vanity,' by M. Patrick Mathers, Arch-Bedel to the University of 
St. Andrews, Glasgow, 1672. Professor Sinclair, of Glasgow, a 
good man at clearing mines of the water which they did not 
want, and furnishing cities with the water which they did want, 
seems to have written absurdly about hydrostatics, and to have 
attacked a certain Sanders, M.A. So Sanders, assisted by James 
Gregory, published a heavy bit of jocosity about him. This 
story of the authorship rested on a note made in his copy 
by Kobert Gray, M.D. ; but it has since been fully confirmed by 
a letter of James Gregory to Collins, in the Macclesfield Corre- 
spondence. ' There is one Master Sinclair, who did write the 
Ars Magna et Nova, a pitiful ignorant fellow, who hath lately 
written horrid nonsense in the hydrostatics, and hath abused a 
master in the University, one Mr. Sanders, in print. This Mr. 
Sanders ... is resolved to cause the Bedel of the University 
to write against him. . . . We resolve to make excellent sport 
with him.' 

On this I make two remarks : First, I have learnt from ex- 
perience that old notes, made in books by their possessors, are 
statements of high authority : they are almost always confirmed. 
I do not receive them without hesitation ; but I believe that 
of all the statements about books which rest on one authority, 
there is a larger percentage of truth in the written word than in 
the printed word. Secondly, I mourn to think that when the 
New /Jealander picks up his old copy of this book, and reads it 
by the associations of his own day, he may, in spite of the many 
assurances I have received that my Athenceum Budget was 
amusing, feel me to be as heavy as I feel James Gregory and 
Sanders. But he will see that I knew what was coming, which 
Gregory did not. 

It was left for William Frend to prove that an impugner ol 
algebra could attempt ridicule. He was, in 1803, editor of a 
periodical The Gentleman's Monthly Miscellany, which lasted 
a few months. To this, among other things, he contributed the 
following, in burlesque of the use made of 0, to which he ob- 
jected. The imitation of Eabelais, a writer in whom he de- 
lighted, is good : to those who have never dipped, it may give 
such a notion as they would not easily get elsewhere. The point 
of the satire is not so good. But in truth it is not easy to make 
pungent scoffs upon what is common sense to all mankind. Who 
can laugh with effect at six times nothing is nothing, as false or 
unintelligible? In an article intended for that undistinguishing 
know-0 the ' general reader,' there would have been no force of 



IMITATION OF RABELAIS. 125 

satire, if division by had been separated from multiplication 
by the same. 

I have followed the above by another squib, by the same 
author, on the English language. The satire is covertly aimed at 
theological phraseology; and any one who watches this subject 
will see that it is a very just observation that the Greek words 
are not boiled enough. 



PANTAGRUEL'S DECISION of the QUESTION about NOTHING. 

PANTAGRUEL determined to Lave a snug afternoon with Epistemon and 
Panurge. Dinner was ordered to be set in a small parlour, and a 
particular batch of Hermitage with some choice Burgundy to be drawn 
from a remote corner of the cellar upon the occasion. By way of 
lunch, about an hour before dinner, Pantagruel was composing his 
stomach with German sausages, reindeer's tongues, oysters, brawn, and 
half a dozen different sorts of English beer just come into fashion, when 
a most thundering knocking was heard at the great gate, and from the 
noise they expected it to announce the arrival at least of the First 
Consul, or king Gargantua. Panurge was sent to reconnoitre, and 
after a quarter of an hoar's absence, returned with the news that the 
University of Pontemaca was waiting his highness's leisure in the 
great hall, to propound a question which had turned the brains of 
thirty-nine students, and had flung twenty-seven more into a high 
fever. With all my heart, says Pantagruel, and swallowed down three 
quarts of Burton ale ; but remember, it wants but an hour of dinner 
time, and the question must be asked in as few words as possible ; for 
I cannot deprive myself of the pleasure I expected to enjoy in the 
company of my good friends for a set of mad-headed masters. I wish 
brother John was here to settle these matters with the black gentry. 

Having said or rather growled this, he proceeded to the hall of 
ceremony, and mounted his throne ; Epistemon and Panurge standing 
on each side, but two steps below him. Then advanced to the throne 
the three beadles of the University of Pontemaca with their silver 
staves on their shoulders, and velvet caps on their heads, and they 
were followed by three times three doctors, and thrice three times 
three masters of art ; for everything was done in Pontemaca by the 
number three, and on this account the address was written on parch- 
ment, one foot in breadth, and thrice three times thrice three feet in 
length. The beadles struck the ground with their heads and their 
staves three times in approaching the throne ; the doctors struck the 
ground with their heads thrice three times, and the masters did the 
same thrice each time, beating the ground with their heads thrico 
three times. This was the accustomed form of approaching the throne, 
time out of mind, and it was said to be emblematic of the usual pios- 
tration of science to the throne of greatness. 



12G A BUDGET OF PAKADOXES. 

The mathematical professor, after having spit, and hawked, and 
cleared his throat, and hlown his nose on a handkerchief lent to him, 
for he had forgotten to bring his own, began to read the address. In 
this he was assisted by three masters of arts, one of whom, with a 
silver pen, pointed out the stops ; the second with a small stick rapped 
his knuckles when he was to raise or lower his voice ; and a third 
pulled his hair behind when he was to look Pantagruel in the face. 
Pantagruel began to chafe like a lion : he turned first on one side, then 
on the other : he listened and groaned, and groaned and listened, and 
was in the utmost cogitabundity of cogitation. His countenance 
began to brighten, when, at the end of an hour, the reader stammered 
out these words : 

' It has therefore been most clearly proved, that as all matter may 
be divided into parts infinitely smaller than the infinitely smallest part 
of the infinitesimal of nothing, so nothing has all the properties of 
something, and may become, by just and lawful right, susceptible of 
addition, subtraction, multiplication, division, squaring, and cubing : 
that it is to all intents and purposes as good as anything that has 
been, is, or can be taught in the nine universities of the land, and to 
deprive it of its rights is a most cruel innovation and usurpation, 
tending to destroy all just subordination in the world, making all 
universities superfluous, levelling vice-chancellors, doctors, and proctors, 
masters, bachelors, and scholars, to the mean and contemptible state of 
butchers and tallow-chandlers, bricklayers and chimney-sweepers, who, 
if it were pot for these learned mysteries, might think that they knew 
as much as" their betters. Every one then, who has the good of science 
at heart, must pray for the interference of his highness to put a stop 
to all the disputes about nothing, and by his decision to convince all 
gainsayers that the science of nothing is taught in the best manner in 
the universities, to the great edification and improvement of all the 
youth in the land.' 

Here Pantagruel whispered in the ear of Panurge, who nodded to 
Epistemon, and they two left the assembly, and did not return for an 
hour, till the orator had finished his task. The three beadles had 
thrice struck the ground with their heads and staves, the doctors had 
finished their compliments, and the masters Were making their twenty- 
seven prostrations. Epistemon and Panurge went up to Pantagruel, 
whom they found fast asleep and snoring ; nor could he be roused but 
by as many tugs as there had been bowings from the corps of learning. 
At last he opened his eyes, gave a good stretch, made half a dozen 
yawns, and called for a stoup of wine. I thank you, my masters, says 
be ; so sound a nap I have not had since I came from ' the island of 
Priestfolly. Have you dined, my masters ? They answered the 
question by as many bows as at entrance ; but his highness left them 
to the care of Panurge, and retired to the little parlour with Epistemon, 
where they burst into a fit of laughter, declaring that this learned 
Buragouin about nothing was just as intelligible as the lawyer's 



IMITATION OF RABELAIS. 127 

Galimathias. Panurge conducted the learned body into a large saloon, 
and each in his way hearing a clattering of plates and glasses, con- 
gratulated himself on his approaching good cheer. There they wero 
left by Panurge, who took his chair by Pantagrnel just as the spup 
was removed, but he made up for the want of that part of his dinner 
by a pint of Champagne. The learning of the university had whetted 
their appetites ; what they each ate it is needless to recite ; good wine, 
good stories, and hearty laughs went round, and three hours elapsed 
before one soul of them recollected the hungry students of Pontemaca. 

Epistemon reminded them of the business in hand, and orders were 
given for a fresh dozen of hermitage to be put upon table, and the 
royal attendants to get ready. As soon as the dozen bottles were 
emptied, Pantagruel rose from table, the royal trumpets sounded, and 
he was accompanied by the great officers of his court into the large 
dining hall, where was a table with forty-two covers. Pantagruel sat 
at the head, Epistemon at the bottom, and Panurge in the middle, 
opposite an immense silver tureen, which would hold fifty gallons of 
soup. The wise men of Pontemaca then took their scats according to 
seniority. Every countenance glistened with delight ; the music struck 
up ; the dishes were uncovered. Panurge had enough to do to handle 
the immense silver ladle : Pantagruel and Epistemon had no time for 
eating, they were fully employed in carving. The bill of fare announced 
the names of a hundred different dishes. From Panurge's ladle came 
into the soup plate as much as he took every time out of the tureen ; 
and as it was the rule of the court that every one should appear to eat, 
as long as he sat at table, there was the clattering of nine and thirty 
spoons against the silver soup-plates for a quarter of an hour. They 
were then removed, and knives and forks were in motion for half an 
hour. Glasses were continually handed round in the mean time, and 
then everything was removed, except the great tureen of soup. The 
second course was now served up, in dispatching which half an hour 
was consumed ; and at the conclusion the wise men of Pontemaca had 
just as much in their stomachs as Pantagruel in his head from their 
address : for nothing was cooked up for them in every possible shape 
that Panurge could devise. 

Wine-glasses, large decanters, fruit dishes, and plates were now set 
on. Pantagruel and Epistemon alternately gave bumper toasts : the 
University of Pontemaca, the eye of the world, the mother of taste and 
good sense and universal learning, the patroness of utility, and the 
second only to Pantagruel in wisdom and virtue (for these were her 
titles), was drank standing with thrice three times three, and huzzas 
and clatterings of glasses ; but to such wine the wise men of Pontemaca 
had not been accustomed ; and though Pantagruel did not suffer one 
to rise from table till the eighty-first glass had been emptied, not even 
the weakest headed master of arts felt his head in the least indisposed. 
The decanters indeed were often removed, but they were brought back 
replenished, filled always with nothing. 



128 A BUDGET OF PAKADOXES. 

Silence was now proclaimed, and in a trice Panurge leaped into the 
large silver tureen. Thence he made his bows to Pantagruel and the 
whole company, and commenced an oration of signs, which lasted au. 
hour and a half, and in which he went over all the matter contained 
in the Pontemacan address ; and though the wise men looked very 
serious during the whole time, Pantagruel himself and his whole court 
could not help indulging in repeated bursts of laughter. It was 
universally acknowledged that he excelled himself, and that the ar- 
guments by which he beat the English masters of arts at Paris were 
nothing to the exquisite selection of attitudes which he this day 
assumed. The greatest shouts of applause were excited when he was 
running thrice round the tureen on its rim, with his left hand holding 
his nose, and the other exercising itself nine and thirty times on his 
back. In this attitude he concluded with his back to the pro- 
fessor of mathematics ; and at the instant he gave his last flap, by a 
sudden jump, and turning heels over head in the air, he presented 
himself face to face to the professor, and standing on his left leg, with 
his left hand holding his nose, he presented to him, in a white satin 
bag, Pantagruel's royal decree. Then advancing his right leg, he 
fixed it on the professor's head, and after three turns, in which he 
clapped his sides with both hands thrice three times, down he 
leaped, and Pantagruel, Epistemon, and himself took their leaves of the 
wise men of Pontemaca. 

The wise men now retired, and by royal orders were accompanied 
by a guard, and according to the etiquette of the court, no one having 
a royal order could stop at any public house till it was delivered. The 
procession arrived at Pontemaca at nine o'clock the next morning, and 
the sound of bells from every church and college announced their 
arrival. The congregation was assembled ; the royal decree was 
saluted in the same manner as if his highness had been there in 
person ; and after the proper ceremonies had been performed, the 
satin bag was opened exactly at twelve o'clock. A finely emblazoned 
roll was drawn forth, and the public orator read to the gaping assembly 
the following words : 

' They who can make something out of nothing shall have nothing 
to eat at the court of PANTAGKUEL.' 



ORIGIN of the ENGLISH LANGUAGE, related ly a SWEDE. 

SOME months ago in a party in Holland, consisting of natives of various 
countries, the merit of their respective languages became a topic of 
conversation. A Swede, who had been a great traveller, and could 
converse in most of the modern languages of Europe, laughed very 
heartily at an Englishman, who had ventured to speak in praise of the 
tongue of his dear country. I never had any trouble, says he, in learning 
English. To my very great surprise, the moment I sat foot on shore 



ORIGIN OF ENGLISH; A FABLE. 129 

at Gravesend, I found out, that I could understand, with very little 
trouble, every word that was said. It was a mere jargon, made up of 
German, French, and Italian, with now and then a word from the 
Spanish, Latin, or Greek. I had only to bring my mouth to their 
mode of speaking, which was done with ease in less than a week, and 
I was every where taken for a true-born Englishman ; a privilege by 
the way of no small importance in a country, where each man, God 
knows why, thinks his foggy island superior to any other part of the 
world : and though his door is never free from some dun or other 
coming for a tax, and if he steps out of it he is sure to be knocked 
down or to have his pocket picked, yet he has the insolence to think 
every foreigner a miserable slave, and his country the seat of every 
thing wretched. They may talk of liberty as they please, but Spain 
or Turkey for my money : barring the bowstring and the inquisition, 
they are the most comfortable countries under heaven, and you need 
not be afraid of either, if you do not talk of religion and politics. I do 
not see much difference too in this respect in England, for when I was 
there, one of their most eminent men for learning was put in prison 
for a couple of years, and got his death for translating one of j9Ssop's 
fables into English, which every child in Spain and Turkey is taught, 
as soon as he comes out of his leading strings. Here all the company 
unanimously cried out against the Swede, that it was impossible : for in 
England, the land of liberty, the only thing its worst enemies could 
pay against it, was, that they paid for their liberty a much greater 
price than it was worth. Every man there had a fair trial accord- 
ing to laws, which every body could understand ; and the judges were 
cool, patient, discerning men, who never took the part of the crown 
against the prisoner, but gave him every assistance possible for his 
defence. 

The Swede was borne down, but not convinced ; and he seemed 
determined to spit out all his venom. Well, says he, at any rate you 
will not deny that the English have not got a language of their own, 
and that they came by it in a very odd way. Of this at least I am 
certain, for the whole history was related to me by a witch in Lapland, 
whilst I was bargaining for a wind. Here the company were all in 
unison again for the story. 

In antient times, said the old hag, the English occupied a spot in 
Tartary, where they lived sulkily by themselves, unknowing and un- 
known. By a great convulsion that took place in China, the inhabit- 
ants of that and the adjoining parts of Tartary were driven from their 
seats, and after various wanderings took up their abode in Germany. 
During this time no body could understand the English, for they did 
not talk, but hissed like so many snakes. The poor people felt uneasy 
under this circumstance, and in one of their parliaments, or rather 
hissing meetings, it was determined to seek for a remedy : and an 
embassy was sent to some of our sisterhood then living on Mount 
Hccla. They were put to a nonplus, and summoned the Devil to their 

K 



130 A BUDGET OF PAEADOXE8. 

relief. To him the English presented their petitions, and explained 
their sad case ; and he, upon certain conditions, promised to befriend 
them, and to give them a language. The poor Devil was little aware 
of what he had promised ; but he is, as all the world knows, a man of 
too much honour to break his word. Up and down the world then he 
went in quest of this new language : visited all the universities, and 
all the schools, and all the courts of law, and all the play-houses, and 
all the prisons ; never was poor devil so fagged. It would have made 
your heart bleed to see him. Thrice did he go round the earth in 
every parallel of latitude ; and at last, wearied and jaded out, back 
came he to Hecla in despair, and would have thrown himself into the 
volcano, if he had been made of combustible materials. Luckily at 
that time our sisters were engaged in settling the balance of Europe ; 
and whilst they were looking over projects, and counter-projects, and 
ultimatums, and post ultimatums, the poor Devil, unable to assist them, 
was groaning in a corner and ruminating over his sad condition. 

On a sudden, a hellish joy overspread his countenance; up he 
jumped, and, like Archimedes of old, ran like a madman amongst the 
thi-ong, turning over tables, and papers, and witches, roaring out for a 
full hour together nothing else but 'tis found, 'tis found ! Away were 
sent the sisterhood in every direction, some to traverse all corners of 
the earth, and others to prepare a larger caldron than had ever yet 
been set upon Hecla. The affairs of Europe were at a stand : its 
balance was thrown aside ; prime ministers and ambassadors were 
every where in the utmost confusion ; and, by the way, they have 
never been able to find the balance since that time, and all the fine 
speeches upon the subject, witli which your newspapers are every now 
and then filled, are all mere hocus-pocus and rhodomontade. How- 
ever, the caldron was soon set on, and the air was darkened by witches 
riding on broomsticks, bringing a couple of folios under each arm, and 
across each shoulder. I remember the time exactly: it was just as the 
council of Nice had broken up, so that they got books and papers there 
dog cheap ; but it was a bad thing for the poor English, as these were 
the worst materials that entered into the caldron. Besides, as the 
Devil wanted some amusement, and had not seen an account of the 
transactions of this famous council, he had all the books brought from 
it laid before him, and split his sides almost with laughing, whilst he 
was reading the speeches and decrees of so many of his old friends and 
acquaintance. All this while the witches were depositing their loads 
in the great caldron. There were books from the Dalai Lama, and 
from China : there were books from the Hindoos, and tallies from the 
Caffres : there were paintings from Mexico, and rocks of hieroglyphics 
from Egypt : the last country supplied besides the swathings of two 
thousand mummies, and four-fifths of the famed library of Alexandi-ia. 
Bubble ! bubble ! toil and trouble ! never was a day of more labour 
and anxiety ; and if our good master had but flung in the Greek books 
at the proper time, they would have made a complete job of it. He 



EARLY GENIUS. 131 

was a little too impatient : as the caldron frothed up, he skimmed it 
off with a great ladle, and filled some thousands of our wind-bags 
with the froth, which the English with great joy carried back to their 
own country. These bags were sent to every district : the chiefs first 
took their fill, and then the common people ; hence they now speak 
a language which no foreigner can understand, unless he has learned 
half a dozen other languages ; and the poor people, not one in ten, 
understand a third part of what is said to them. The hissing, how- 
ever, they have not entirely got rid of, and every seven years, when 
the Devil, according to agreement, pays them a visit, they entertain 
him at their common halls and county meetings with their original 
language. 

The good natured old hag told me several other circumstances, 
relative to this curious transaction, which, as there is an Englishman 
in company, it will be prudent to pass over in silence : but I cannot 
help mentioning one thing which she told me as a very great secret. 
You know, says she to me, that the English have more religions among 
them than any other nation in Europe, and that there is more teaching 
and sermonizing with them than in any other country. The fact is 
this ; it matters not who gets up to teach them, the hard words of the 
Greek were not sufficiently boiled, and whenever they get into a 
sentence, the poor people's brains are turned, and they know no more 
what the preacher is talking about, than if he harangued them in 
Arabic. Take my word for it if you please ; but if not, when you get 
to England, desire the bettermost sort of people that you are acquainted 
with to read to you an act of parliament, which of course is written in 
the clearest and plainest stile in which any thing can be written, and 
you will find that not one in ten will be able to make tolerable sense 
of it. The language would have been an excellent language, if it had 
not been for the council of Nice, and the words had been well boiled. 

Here the company burst out into a fit of laughter. The Englishman 
got up and shook hands with the Swede : si non e vero, said he, e ben 
trovato. But, however I may laugh at it here, I would not advise 
you to tell this story on the other side of the water. So here's a 
bumper to Old England for ever, and God save the king.' 



The accounts given of extraordinary children and adolescents 
frequently defy credence. I will give two well-attested instances. 

The celebrated mathematician, Alexis Claude Clairault (now 
Clairaut) was certainly born in May, 1713. His treatise on 
curves of double curvature (printed in 1731) received the appro- 
bation of the Academy of Sciences, August 23, 1729. Fontenelle, 
in his certificate of this, calls the author sixteen years of age, and 

K 2 



A BUDGET OF PARADOXES. 

does not strive to exaggerate the wonder, as he might have done, 
by reminding his readers that this work, of original and sustained 
mathematical investigation, must have been coming from the pen 
at the ages of fourteen and fifteen. The truth was, as attested 
by De Molieres, Clairaut had given public proofs of his power at 
twelve years old. His age being thus publicly certified, all doubt 
is removed : say he had been though great wonder would still 
have been left twenty-one instead of sixteen, his appearance, 
and the remembrances of his friends, schoolfellows, &c., would 
have made it utterly hopeless to knock off five years of that age 
while he was on view in Paris as a young lion. De Molieres, who 
examined the work officially for the Garde des Sceaux, is trans- 
ported beyond the bounds of official gravity, and says that it * ne 
merite pas seulement d'etre imprime, mais d'etre admire comme 
im prodige d'imagination, de conception, et de capacite.' 

That Blaise Pascal was born in June, 1623, is perfectly well 
established and uncontested. That he wrote his conic sections at 
the age of sixteen might be difficult to establish, though tolerably 
well attested, if it were not for one circumstance, for the book 
was not published. The celebrated theorem, Pascal's hexagram, 
makes all the rest come very easy. Now Curabelle, in a work 
published in 1644, sneers at Desargues, whom he quotes, for 
having, in 1642, deferred a discussion until cette grande proposi- 
tion nommee la Pascale vei^ra le jour. That is, by the time 
Pascal was nineteen, the hexagram was circulating under a name 
derived from the author. The common story about Pascal, 
given by his sister, is an absurdity which no doubt has prejudiced 
many against tales of early proficiency. He is made, when quite 
a boy, to invent geometry in the order of Euclid's propositions : 
as if that order were natural sequence of investigation. The 
hexagram at ten years old would be a hundred times less un- 
likely. 

The instances named are painfully astonishing : I give one 
which has fallen out of sight, because it will preserve an imperfect 
biography. John Wilson is Wilson of that Ilk, that is, of 
Wilson's Theorem.-. It is this : If p be a prime number, the 
product of all the numbers up to p -1, increased by 1, is divisible 
without remainder by p. All mathematicians know this as 
Wilson's theorem, but few know who Wilson was. He was born 
August 6, 1741, at the Howe in Applethwaite, and he was heir 
to a small estate at Troutbeck in Westmoreland. He was sent to 
Peterhouse, at Cambridge, and, while an undergraduate was 
considered stronger in algebra than any one in the University, 



JOHN WILSON WILLIAM MORGAN MRS. FRY. 133 

except Professor Waring, one of the most powerful algebraists of 
the century. 1 He was the senior wrangler of 1761, and was then 
for some time a private tutor. When Paley, then in his third 
year, determined to make a push for the senior wranglership, 
which he got, Wilson was recommended to him as a tutor. Both 
were ardent in their work, except that sometimes Paley, when he 
came for his lesson, would find gone a fishing written on his 
tutor's outer door: which was insult added to injury, for Paley 
was very fond of fishing. Wilson soon left Cambridge, and went 
to the bar. He practised on the northern circuit with great 
success ; and, one day, while passing his vacation on his little 
property at Troutbeck, he received information, to his great 
surprise, that Lord Thurlow, with whom he had no acquaintance, 
had recommended him to be a Judge of the Court of Common 
Pleas. He died, Oct. 18, 1793, with a very high reputation 
as a lawyer and a Judge. These facts are partly from Meadley'a 
' Life of Paley,' no doubt from Paley himself, partly from the 
Gentleman's Magazine, and from an epitaph written by Bishop 
Watson. Wilson did not publish anything : the theorem by 
which he has cut his name in the theory of numbers was com- 
municated to Waring, by whom it was published. He married, 
in 1788, a daughter of Serjeant Adair, and left issue. Had a 
family, many will say : but a man and his wife are a family, even 
without children. An actuary may be allowed to be accurate in 
this matter, of which I was reminded by what an actuary wrote 
of another actuary. William Morgan, in the life of his uncle 
Dr. Richard Price, says that the Doctor and his wife were ' never 
blessed with an addition to their family.' I never met "with such 
accuracy elsewhere. Of William Morgan I add that my surname 
and pursuits have sometimes, to my credit be it said, made a 
confusion between him and me. Dates are nothing to the 
xuistaken ; the last three years of Morgan's life were the first 
three years of my actuary-life (1830-33). The mistake was to 
my advantage as well as to my credit. I owe to it the acquaint- 
ance of one of the noblest of the human race, I mean Elizabeth 
Fry, who came to me for advice about a philanthropic design, 
which involved life questions, under a general impression that 
some Morgan had attended to such things. 2 

1 He wrote, in 1760, a tract in defence of Waring, a point of whose algebra had 
been assailed by a Dr. Powell. Waring wrote another tract of the same date. 

2 Mrs. Fry certainly believed that the writer was the old actuary of the Equitable, 
when she first consulted him upon the benevolent Assurance project ; but we were 
introduced to her by our old and dear friend Lady Noel Byron, by whom she had 



134 A BUDGET OF PARADOXES. 



A treatise on the sublime science of heliography, satisfactorily 
demonstrating our great orb of light, the sun, to be absolutely 
no other than a body of ice ! Overturning all the received 
systems of the universe hitherto extant ; proving the celebrated 
and indefatigable Sir Isaac Newton, in his theory of the solar 
system, to be as far distant from the truth, as any of the 
heathen authors of Greece or Borne. By Charles Palmer, Gent. 
London, 1798, 8vo. 

Mr. Palmer burned some tobacco with a burning glass, saw 
that a lens of ice would do as well, and then says 

' If we admit that the sun could be removed, and a terrestrial body 
of ice placed in its stead, it would produce the same effect. The sun 
is a crystaline body receiving the radience of God, and operates on this 
earth in a similar manner as the light of the sun does when applied to 
a convex mirror or glass.' 

Nov. 10, 1801. The Eev. Thomas Cormouls, minister of 
Tettenhall, addressed a letter to Sir Wm. Herschel, from which I 
extract the following : 

Here it may be asked, then, how came the doctrines of Newton to 
solve all astronomic Phenomina, and all problems concerning the same, 
both a parte ante and a parte post. It is answered that he certainly 
wrought the principles he made use of into strickt analogy with the 
real Phenomina of the heavens, and that the rules and results arizing 
from them agree with them and resolve accurately all questions con- 
cerning them. Though they are not fact and true, or nature, but 
analogous to it, in the manner of the artificial numbers of logarithms, 
sines, &c. A very important question arises here, Did Newton mean 
to impose upon the world ? By no means : he received and used the 
doctrines reddy formed ; he did a little extend and contract his prin- 
ciples when wanted, and commit a few oversights of consequences. But 
when he was very much advanced in life, he suspected the fundamental 
nullity of them : but I have from a certain anecdote strong ground to 
believe that he knew it before his decease, and intended to have re- 
tracted his error. But, however, somebody did deceive, if not wilfully, 
neglently at least. That was a man to whom the world has great 
obligations too. It was no less a philosopher than Galileo. 

That Newton wanted to retract before his death, is a notion 
not uncommon among paradoxers. Nevertheless, there is no 

been long known and venerated, and who referred her to Mr. De Morgan for advice. 
An unusual degree of confidence in, and appreciation of each other, arose on their 
first meeting between the two, who had so much that was externally different, and so 
much that was essentially alike, in their natures. (Ed.) 



BISHOP WILKINS'S WORKS, 135 

retraction in the third edition of the ' Principia,' published when 
Newton was eighty-four years old ! The moral of the above is, 
that a gentleman who prefers instructing William Herschel to 
learning how to spell, may find a proper niche in a proper place, 
for warning to others. It seems that gravitation is not truth, 
but only the logarithm of it. 

The mathematical and philosophical works of the Right Rev. 
John Wilkins ... In two volumes. London, 1802, 8vo. 

This work, or at least part of the edition all for aught I know 
is printed on wood ; that is, on paper made from wood-pulp. 
It has a rough surface, and when held before a candle is of very 
unequal transparency. There is in it a reprint of the works on 
the earth and moon. The discourse on the possibility of going 
to the moon, in this and the edition of 1 640, is incorporated : 
but from the account in the life prefixed, and a mention by 
D'Israeli, I should suppose that it had originally a separate title- 
page, and some circulation as a separate tract. Wilkins treats 
this subject half seriously, half jocosely ; he has evidently not 
quite made up his mind. He is clear that ' arts are not yet come 
to their solstice,' and that posterity will bring hidden things to 
light. As to the difficulty of carrying food, he thinks, scoffing 
Puritan that he is, the Papists may be trained to fast the voyage, 
or may find the bread of their Eucharist ' serve well enough for 
their viaticum.' He also puts the case that the story of Do- 
mingo Gonsales may be realized, namely, that wild geese find 
their way to the moon. It will be remembered to use the 
usual substitute for, It has been forgotten that the posthumous 
work of Bishop Francis Godwin of Llandaff was published in 
1638, the very year of Wilkins's first edition, in time for him to 
mention it at the end. Godwin makes Domingo Gronsales get to 
the moon in a chariot drawn by wild geese, and, as old books 
would say, discourses fully on that head. It is not a little 
amusing that Wilkins should have been seriously accused of 
plagiarizing Godwin, Wilkins writing in earnest, or nearly so, 
and Godwin writing fiction. It may serve to show philosophers 
how very near pure speculation comes to fable. From the 
sublime to the ridiculous there is but a step : which is the sub- 
lime, and which the ridiculous, every one must settle for himself. 
With me, good fiction is the sublime, and bad speculation the 
ridiculous. The number of bishops in my list is small. I 
might, had I possessed the book, have opened the list of quad- 
rators with an Archbishop of Canterbury, or at least with a 



136 A BUDGET OF PARADOXES. 

divine who was not wholly not archbishop. Thomas Bradwardine 
(Bragvardinus, Bragadinus) was elected in 1348 ; the Pope put 
in another, who died unconsecrated ; and Bradwardine was again 
elected in 1 349, and lived five weeks longer, dying, I suppose, 
unconfirmed and unconsecrated. Leland says he held the see a 
year, unus tantum annulus, which seems to be a confusion : 
the whole business, from the first election, took about a year. 
He squared the circle, and his performance was printed at Paris 
in 1494. I have never seen it, nor any work of the author, 
except a tract on proportion. 

As Bradwardine's works are very scarce indeed, I give two titles 
from one of the Libri catalogues. 

' ARITHMETIC. BRAUARDINI (Thomas) Ai-ithmetica speculativa revisa 
et correcta a Petro Sanchez Ciruelo Aragonesi, black letter, 
elegant woodcut title-page, YERY RARE, folio. Parisiis, per Thomam 
Anguelast {pro Olivier Senant), s.a. circa 1510. 

' This book, by Thomas Bradwardine, Archbishop of Canterbury, 
must be exceedingly scarce as it has escaped the notice of Pro- 
fessor De Morgan, who, in his Arithmetical Books, speaks of a 
treatise of the same author on proportions, printed at Vienna in 
1515, but does not mention the present work. 

'Bradwardine (Archbp. T.). Brauardini (Thomse) Geometria 
speculativa, cum Tractatu de Quadratura Circuli bene revisa a 
Petro Sanchez Ciruelo, SCARCE, folio. Parisiis, J. Petit, 1511. 

' In this work we find the polygones etoiles, see Chasles (Aperpu,, 
pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of 
this English mathematician, who was Archbishop of Canterbury 
in the xivth Century (tempore Edward III. A.D. 1349) ; and 
who applied geometry to theology. M. Chasles says that the 
present work of Bradwardine contains " Une theorie nouvelle qui 
doit faire honneur au xive Siecle." ' 

The titles do not make it quite sure that Bradwardine is the 
quadrator ; it may be Peter Sanchez after all. 

Nouvelle theorie des paralleles. Par Adolphe Kircher [so signed 
at the end of the appendix]. Paris, 1803, 8vo. 

An alleged emendation of Legendre. The author refers to 
attempts by Hoffman, 1801, by Hauff, 1799, and to a work of 
Karsten, or at least a theory of Karsten, contained in ' Tentamen 
novse parallelarum theorise notione situs fundatae ; auctore Gr. C. 



ROSSI W. SPENCE PANICS. 137 

Scliwal, Stuttgardae, 1801, en 8 vohimes.' Surely this is a mis- 
print ; eight volumes on the theory of parallels ? If there be 
such a work, I trust I and it may never meet, though ever so 
far produced. 

Soluzione . . . della quadratura del Circolo. By Gaetano Rossi. 
London, 1804, 8vo. 

The three remarkable points of this book are, that the house- 
hold of the Printfe of Wales took ten copies, Signora Grassini 
sixteen, and that the circumference is 3|- diameters. That is, 
the appetite of Grassini for quadrature exceeded that of the 
whole household (loggia) of the Prince of Wales in the ratio in 
which the semi-circumference exceeds the diameter. And these 
are the first two in the list of subscribers. Did the author see 
this theorem ? 

Britain independent of commerce ; or proofs, deduced from an in- 
vestigation into the true causes of the wealth of nations, that our 
riches, prosperity, and power are derived from sources inherent 
in ourselves, and would not be affected, even though our 
commerce were annihilated. By Wm. Spence. 4th edition, 
1808, 8vo. 

A patriotic paradox, being in alleviation of the Commerce 
panic which the measures of Napoleon I. who felt our Commerce, 
while Mr. Spence only saw it had awakened. In this very 
month (August, 1866), the Pres. Brit. Assoc. has applied a 
similar salve to the coal panic ; it is fit that science, which 
rubbed the sore, should find a plaster. We ought to have an 
iron panic and a timber panic ; and a solemn embassy to the 
Americans, to beg them not to whittle, would be desirable. 
There was a gold panic beginning, before the new fields were 
discovered. For myself, I am the unknown and unpitied victim 
of a chronic gutta-percha panic : I never could get on without 
it; to me, gutta percha and Eowland Hill are the great dis- 
coveries of our day ; and not unconnected either, gutta percha 
being to the submarine post what Eowland Hill is to the super- 
terrene. I should be sorry to lose cow-choke I gave up trying 
to spell it many years ago but if gutta percha go, I go too. 
I think, that perhaps when, five hundred years hence, the people 
say to the Brit. Assoc. (if it then exist) Pray, gentlemen, is it 
not time for the coal to be exhausted ? ' they will be answered out 
of Moliere (who will certainly then exist) : Cela etait autrefois 
ainsi, mais nous avons change taut cela. A great many people 



138 A BUDGET OF PABADOXES. 

think that if the coal be used up, it will be announced some 
unexpected morning by all the yards being shut up and written 
notice outside, ' Coal all gone 1 ' just like the * Please, ma'am, 
there ain't no more sugar,' with which the maid servant damps 
her mistress just at breakfast- time. But these persons should 
be informed that there is every reason to think that there will 
be time, as the city gentleman said, to venienti the occurrite 
morbo. 



An appeal to the republic of letters in behalf of injured science, 
from the opinions and proceedings of some modern authors of 
elements of geometry. By George Douglas. Edinburgh, 
1810, 8vo. 

Mr. Douglas was the author of a very good set of mathematical 
tables, and of other works. He criticizes Simson, Playfair, and 
others, sometimes, I think, very justly. There is a curious 
phrase, which occurs more than once. When he wants to say 
that something or other was done before Simson or another was 
born, he says ' before he existed, at least as an author.' He 
seems to reserve the possibility of Simson's pre-existence, but at 
the same time to assume that he never wrote anything in his 
previous state. Tell me that Simson pre-existed in any other 
way than as editor of some pre-existent Euclid ? Tell Apella ! 

1810. In this year Jean Wood, Professor of Mathematics in 
the University of Virginia (Eichmond), addressed a printed 
circular to 'Dr. Her sch el, Astronomer, Greenwich Observatory.' 
No mistake was more common than the natural one of imagining 
that the Private Astronomer of the king was the Astronomer 
Royal. The letter was on the difference of velocities of the two 
sides of the earth, arising from the composition of the rotation 
and the orbital motion. The paradox is a fair one, and 
deserving of investigation ; but, perhaps it would not be easy to 
deduce from it tides, trade-winds, aerolithes, &c., as Mr. Wood 
thought he had done in a work from which he gives an extract, 
and which he describes as published. The composition of rota- 
tions, &c., is not for the world at large : the paradox of the 
non-rotation of the moon about her axis is an instance. How 
many persons know that when a wheel rolls on the ground, the 
lowest point is moving upwards, the highest point forwards, and 
the intermediate points in all degrees of betwixt and between ? 
This is too short an explanation, with some good difficulties. 



PARADOX WITHOUT STOPPING. 1:J9 



The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson, 
B.D.] Cambridge, 1815. 4to. 

Of this unpunctuating paradoxer I shall give an account in his 
own way : he would not stop for any one ; why should I stop for him ? 
It is worth while to try how unpunctuated sentences will read. 

The reverend J Dobson BD late fellow of saint Johns college 
Cambridge was rector of Brandesburton in Yorkshire he was 
seventh wrangler in 1798 and died in 1847 he was of that sort of 
eccentricity which permits account of his private life if we may 
not rather say that in such cases private life becomes public there 
is a tradition that he was called Death Dobson on account of his 
head and aspect of countenance being not very unlike the 
ordinary pictures of a human skull his mode of life is reported 
to have been very singular whenever he visited Cambridge he was 
never known to go twice to the same inn he never would sleep at 
the rectory with another person in the house some ancient char- 
woman used to attend to the house but never slept in it he has 
been known in the time of coach travelling to have deferred his 
return to Yorkshire on account of his disinclination to travel 
with a lady in the coach he continued his mathematical studies 
until his death and till his executors sold the type all his tracts 
to the number of five were kept in type at the university press 
none of these tracts had any stops except full stops at the end of 
paragraphs only neither had they capitals except one at the 
beginning of a paragraph so that a full stop was generally 
followed by some white as there is not a single proper name in 
the whole of the book I have I am not able to say whether he 
would have used capitals before proper names I have inserted 
them as usual for which I hope his spirit will forgive me if I be 
wrong he also published the elements of geometry in two 
volumes quarto Cambridge 1815 this book had also no stops 
except when a comma was wanted between letters as in the 
straight lines AB, BC I should also say that though the title is 
unpunctuated in the author's part it seems the publishers would 
not stand it in their imprint this imprint is punctuated as usual 
and Deighton and Sons to prove the completeness of their allegi- 
ance have managed that comma semicolon colon and period 
shall all appear in it why could they not have contrived interro- 
gation and exclamation this is a good precedent to establish the 
separate right of the publisher over the imprint it is said that 
only twenty of the tracts were printed and very few indeed of the 
book on geometry it is doubtful whether any were sold there is a 



140 A BUDGET OF PAEADOXES. 

copy of the geometry in the university library at Cambridge and 
I have one myself the matter of the geometry differs entirely 
from Euclid and is so fearfully prolix that I am sure no mortal 
except the author ever read it the man went on without stops 
and without stop save for a period at the end of a paragraph this 
is the unpunctuated account of the unpunctuating geometer 
suum cuique tribuito Mrs Thrale would have been amused at a 
Dobson who managed to come to a full stop without either of the 
three warnings. 

I do not find any difficulty in reading Dobson's geometry ; and 
I have read more of it to try reading without stops than I should 
have done had it been printed in the usual way. Those who dip 
into the middle of my paragraph may be surprised for a moment 
to see that ' on account of his disinclination to travel with a 
lady in the coach he continued his mathematical studies until 
his death and [further, of course] until his executors sold the 
type.' But a person reading straight through would hardly take 
it so. I should add that, in order to give a fair trial, I did not 
compose as I wrote, but copied the words of the correspondent 
who gave me the facts, so far as they went. 

Philosophic/, Sacra, or the principles of natural Philosophy. Ex- 
tracted from Divine Revelation. By the Rev. Samuel Pike. 
Edited by the Rev. Samuel Kittle. Edinburgh, 1815, 8vo. 

This is a work of modified Hutchinsonianism, which I have 
seen cited by several. Though rather dark on the subject, it 
seems not to contradict the motion of the earth, or the doctrine 
of gravitation, Mr. Kittle gives a list of some Hutchinsonians, 
as Bishop Home ; Dr. Stukeley ; the Eev. W. Jones, author of 
' Physiological Disquisitions ; ' Mr. Spearman, author of ' Letters 
on the Septuagint ' and editor of Hutchinson ; Mr. Barker, 
author of ' Eeflexions on Learning ' ; Dr. Catcott, author of a 
work on the creation, &c. ; Dr. Robertson, author of a ' Treatise 
on the Hebrew Language ; ' Dr. Hollo way, author of ' Originals, 
Physical and Theological ; ' Dr. Walter Hodges, author of a work 
on Elohim ; Lord President Forbes (ob. 1747). 

The Eev. William Jones, above mentioned, (1726-1800), the 
friend and biographer of Bishop Home, and his stout defender, 
is best known as William Jones of Nayland, who (1757) pub- 
lished the ' Catholic Doctrine of the Trinity ; ' he was also strong 
for the Hutchinsonian physical trinity of fire, light, and spirit. 
This well-known work was generally recommended, as the de- 
fence of the orthodox system, to those who could not go into the 



TRINITARIAN CONTROVERSY. 

learning of the subject. There is now a work more suited to 
our time : ' The Rock of Ages,' by the Rev. E. H. Bickersteth, 
now published by the Religious Tract Society, without date, 
answered by the Rev. Dr. Sadler, in a work (1859) entitled Gloria 
Patri, in which, says Mr. Bickersteth, 'the author has not 
even attempted to grapple with my main propositions.' I have 
read largely on the controversy, and I think I know what this 
means. Moreover, when I see the note ' There are two other 
passages to which Unitarians sometimes refer, but the deduction 
they draw from them is, in each case, refuted by the context' 
I think I see why the two texts are not named. Nevertheless, 
the author is a little more disposed to yield to criticism than his 
foregoers ; he does not insist on texts and readings which the 
greatest editors have rejected. And he writes with courtesy, both 
direct and oblique, towards his antagonists ; which, on his side 
of this subject, is like letting in fresh air. So that I suspect the 
two books will together make a tolerably good introduction to 
the subject for those who cannot go deep. Mr. Bickersteth's 
book is well arranged and indexed, which is a point of superiority 
to Jones of Nayland. There is a point which I should gravely 
recommend to writers on the orthodox side. The Unitarians in 
England have frequently contended that the method of proving 
the divinity of Jesus Christ from the New Testament would 
equally prove the divinity of Moses. I have not fallen in the 
way of any orthodox answers specially directed at the repeated 
tracts written by Unitarians in proof of their assertion. If there 
be any, they should be more known ; if there be none, some 
should be written. Which ever side may be right, the treatment 
of this point would be indeed coming to close quarters. The 
heterodox assertion was first supported, it is said, by John Bidle 
or Biddle (1615-1662) of Magdalen College, Oxford, the earliest 
of the English Unitarian writers, previously known by a transla- 
tion of part of Virgil and part of Juvenal. But I cannot find 
that he wrote on it. It is the subject of ' aipsa-swu avaaracris^ or a 
new way of deciding old controversies. By Basanistes. Third 
edition, enlarged,' London, 1815, 8vo. It is the appendix to the 
amusing, 'Six more letters to Grranville Sharp, Esq., . . . By 
Gregory Blunt, Esq.' London, 8vo., 1803. This much I can 
confidently say, that the study of these tracts would prevent 
orthodox writers from some curious slips, which are slips obvious 
to all sides of opinion. The lower defenders of orthodoxy fre- 
quently vex the spirits of the higher ones. 

Since writing the above I have procured Dr. Sadler's answer. 



142 A BUDGET OF PARADOXES. 

I thought I knew what the challenger meant when he said the 
respondent had not grappled with his main propositions. I 
should say that he is clung on to from beginning to end. But 
perhaps Mr. B. has his own meaning of logical terms, such as 
proposition : he certainly has his own meaning of cumulative. 
He says his evidence is cumulative ; not a catena, the strength of 
which is in its weakest part, but distinct and independent lines, 
each of which corroborates the other. This is the very opposite 
of cumulative : it is distributive. When different arguments are 
each necessary to a conclusion, the evidence is cumulative ; when 
any one will do, even though they strengthen each other, it is 
distributive. The word cumulative is a synonym of the law word 
constructive ; a whole which will do made out of parts which 
separately will not. Lord Strafford opens his defence with the 
use of both words : ' They have invented a kind of accumulated 
or constructive evidence ; by which many actions, either totally 
innocent in themselves, or criminal in a much inferior degree, 
shall, when united, amount to treason.' The conclusion is, that 
Mr. B. is a Cambridge man ; the Oxford men do not confuse the 
elementary terms of logic. dear old Cambridge ! when the 
New Zealander comes let him find among the relics of your later 
sons some proof of attention to the elementary laws of thought. 
A little-go of logic, please ! 

Mr. B., though apparently not a Hutchinsonian, has a nibble 
at a physical Trinity. * If, as we gaze on the sun shining in the 
firmament, we see any faint adumbration of the doctrine of the 
Trinity in the fontal orb, the light ever generated, and the heat 
proceeding from the sun and its beams threefold and yet one, 
the sun, its light, and its heat, that luminous globe, and the 
radiance ever flowing from it, are both evident to the eye ; but the 
vital warmth is felt, not seen, and is only manifested in the life 
it transfuses through creation. The proof of its real existence is 
self-demonstrating.' 

We shall see how Kevilo 1 illustrates orthodoxy by mathematics. 
It was my duty to have found one of the many illustrations from 
physics ; but perhaps I should have forgotten it if this instance 
had not come in my way. It is very bad physics. The sun, 
apart from its light, evident to the eye ! Heat more self-demon- 
strating than light, because felt ! Heat only manifested by the 
life it diffuses ! Light implied not necessary to life ! But the 
theology is worse than Sabellianism. To adumbrate i.e. make 

1 The name assumed by a "writer who professed to give a mathematical explanation 
of the Trinity, see farther on. (Ed.) 



TRINITARIAN CONTROVERSY SIR RICHARD PHILLIPS. 143 

a picture of the orthodox doctrine, the sun must be heavenly 
body, the light heavenly body, the heat heavenly body : and 
yet, not three heavenly bodies, but one heavenly body. The 
truth is, that this illustration and many others most strik- 
ingly illustrate the Trinity of fundamental doctrine held by the 
Unitarians, in all its differences from the Trinity of persons held 
by the Orthodox. Be right which may, the right or wrong of 
the Unitarians shines out in the comparison. Dr. Sadler confirms 
me by which I mean that I wrote the above before I saw what 
he says in the following words : ' The sun is one object with two 
properties, and these properties have a parallel not in the second 
and third persons of the Trinity, but in the attributes of Deity.' 

The letting light alone, as self-evident, and making heat self- 
demonstrating, because felt i.e. perceptible now and then has 
the character of the Irishman's astronomy : 

Long life to the moon, for a dear noble cratur, 
Which serves us for lamplight all night in the dark, 
While the sun only shines in the day, which, by natur, 
Wants no light at all, as ye all may remark. 

Sir Richard Phillips (born 1768) was conspicuous in 1793, 
when he was sentenced to a year's imprisonment for selling 
Paine's ' Eights of Man ; ' and again when, in 1 807, he was 
knighted as Sheriff of London. As a bookseller, he was able to 
enforce his astronomical opinions in more ways than others. 
For instance, in James Mitchell's 'Dictionary of the Mathe- 
matical and Physical Sciences,' 1823, 12mo., which, though he 
was not technically a publisher, was printed for him a book I 
should recommend to the collector of works of reference there 
is a temperate description of his doctrines, which one may almost 
swear was one of his conditions previous to undertaking the work. 
Phillips himself was not only an anti-Newtonian, but carried to a 
fearful excess the notion that statesmen and Newtonians were 
in league to deceive the world. He saw this plot in Mrs. Airy's 
pension, and in Mrs. Somerville's. In 1836, he did me the 
honour to attempt my conversion. In his first letter he says : 

Sir Richard Phillips has an inveterate abhorrence of all the pre- 
tended wisdom of philosophy derived from the monks and doctors of 
the middle ages, and not less of those of higher name who merely 
sought to make the monkish philosophy more plausible, or so to dis- 
guise it as to mystify the mob of small thinkers. 

So little did his writings show any knowledge of antiquity, 
that I strongly suspect, if required to name one of the monkish 



144 A BUDGET OF PAKADOXES. 

doctors, he would have answered Aristotle. These schoolmen, 
and the ' philosophical trinity of gravitating force, projectile 
force, and void space,' were the bogies of his life. 

I think he began to publish speculations in the Monthly 
Magazine (of which he was editor) in July 1817 : these he 
republished separately in 1818. In the Preface, perhaps judging 
the feelings of others by his own, he says that he ' fully expects 
to be vilified, reviled, and anathematized, for many years to 
come.' Poor man! he was let alone. He appeals with con^ 
fidence to the ' impartial decision of posterity ; ' but posterity 
does not appoint a hearing for one per cent, of the appeals which 
are made ; and it is much to be feared that an article in such a 
work of reference as this will furnish nearly all her materials fifty 
years hence. The following, addressed to M. Arago, in 1835, 
will give posterity as good a notion as she will probably need : 

Even the present year has afforded EVER-MEMORABLE examples, 
paralleled only by that of the Romish Conclave which persecuted 
Galileo. Policy has adopted that maxim of Machiavel which teaches 
that it is more prudent to reward partisans than to persecute opponents. 
Hence, a bigotted party had influence enough with the late short-lived 
administration [I think lie is wrong as to the administration] of 
Wellington, Peel, &c., to confer munificent royal pensions on three 
writers whose sole distinction was their advocacy of the Newtonian 
philosophy. A Cambridge professor last year published an elaborate 
volume in illustration of Gravitation, and on him has been conferred a 
pension of 300Z. per annum. A lady has written a light popular view 
of the Newtonian Dogmas, and she has been complimented by a pension 
of 200Z. per annum. And another writer, who has recently published 
a volume to prove that the only true philosophy is that of Moses, has 
been endowed with a pension of 2007. per annum. Neither of them 
were needy persons, and the political and ecclesiastical bearing of the 
whole was indicated by another pension of 300Z. bestowed on a political 
writer, the advocate of all abuses and prejudices. Whether the con- 
duct of the Romish. Conclave was more base for visiting with legal 
penalties the promulgation of the doctrines that the Earth turns on its 
axis and revolves around the Sun ; or that of the British Court, for its 
craft in conferring pensions on the opponents of the plain corollary, 
that all the motions on the Earth are ' part and parcel ' of these great 
motions, and those again and all like them consecutive displays of 
still greater motions in equality of action and reaction, is A QUESTION 
which must be reserved for the casuists of other generations. . . I 
cannot expect that on a sudden you and your friends will come to my 
conclusion, that the present philosophy of the Schools and Univer- 
sities of Europe, based on faith in witchcraft, magic, &c., is a system 
of execrable nonsense, by which quacks live on the faith of fools ; but I 
desire a free and fair examination of my Aphorisms, and if a few are 



PHILLIPS WOOD- SATIRICAL PARADOX. 145 

admitted to be true, merely as courteous concessions to arithmetic, my 
purpose will be effected, for men will thus be led to think ; and if they 
think, then the fabric of false assumptions, and degrading superstitions 
will soon tumble in ruins. 

This for posterity. For the present time I ground the fame of 
Sir Pt. Phillips on his having squared the circle without knowing 
it, or intending to do it. ' In the Protest presently noted he 
discovered that ' the force taken as 1 is equal to the sum of all 
its fractions .... thus 1 = i + - + T V + aV? & c -j carried to in- 
finity.' This the mathematician instantly sees is equivalent to 
the theorem that the circumference of any circle is double of the 
diagonal of the cube on its diameter. 

I have examined the following works of Sir E. Phillips, and 
heard of many others : 

Essays on the proximate mechanical causes of the general phe- 
nomena of the Universe, 1818, 12mo. 

Protest against the prevailing principles of natural philosophy, 
with the development of a common sense system (no date, 
8vo. pp. 16). 

Four dialogues between an Oxford Tutor and a disciple of the 
common-sense philosophy, relative to the proximate causes of 
material phenomena. 8vo. 1824. 

A century of original aphorisms on the proximate causes of the 
phenomena of nature, 1835, 12mo. 

Sir Richard Phillips had four valuable qualities ; honesty, 
zeal, ability, and courage. He applied them all to teaching 
matters about which he knew nothing ; and gained himself an 
uncomfortable life and a ridiculous memory. 

Astronomy made plain ; or only way the true perpendicular dis- 
tance of the Sun, Moon, or Stars, from this earth, can be 
obtained. By Wm. Wood. Chatham, 1819, 12mo. 

If this theory be true, it will follow, of course, that this earth is the 
only one God made, and that it does not whirl round the sun, but vice 
versa, the sun round it. 

Historic doubts relative to Napoleon Buonaparte. London, ] 819, 

8vo. 

This tract has since been acknowledged by Archbishop 
"\Vhately and reprinted. It is certainly a paradox : but differs 
from most of those in my list as being a joke, and a satire upon 
the reasoning of those who cannot receive narrative, no matter 

L 



146 A BUDGET OF PAKADOXES. 

what the evidence, which is to them utterly improbable a priori. 
But had it been serious earnest, it would not have been so absurd 
as many of those which I have brought forward. The next on 
the list is not a joke. 

The idea of the satire is not new. Dr. King, in the dispute 
on the genuineness of Phalaris, proved with humour that Bentley 
did not write his own dissertation. An attempt has lately been 
made, for the honour of Moses, to prove, without humour, that 
Bishop Colenso did not write his own book. This is intolerable : 
anybody who tries to use such a weapon without banter, plenty 
and good, and of form suited to the subject, should get the 
drubbing which the poor man got in the Oriental tale for striking 
the dervishes with the wrong hand. 

The excellent and distinguished author of this tract has ceased 
to live. I call him the Paley of our day : with more learning, 
and more purpose than his predecessor ; but perhaps they might 
have changed places if they had changed centuries. The clever 
satire above named is not the only work which he published 
without his name. The following was attributed to him, I 
believe rightly : ' Considerations on the Law of Libel, as relating 
to Publications on the subject of Eeligion, by John Search.' 
London, 1833, 8vo. This tract excited little attention: for those 
who should have answered, could not. Moreover, it wanted a 
prosecution to call attention to it : the fear of calling such atten- 
tion may have prevented prosecutions. Those who have read it 
will have seen why. 

The theological review elsewhere mentioned attributes the 
pamphlet of John Search on blasphemous libel to Lord Brougham. 
This is quite absurd : the writer states points of law on credence 
where the judge must have spoken with authority. Besides which, 
a hundred points of style are decisive between the two. I think 
any one who knows Whately's writings will soon arrive at my 
conclusion. Lord Brougham himself informs me that he has no 
knowledge whatever of the pamphlet. 

It is stated in Notes and Queries (3 S. xi. 511) that Search 
was answered by the Bishop of P'erns as S.N., with a rejoinder by 
Blanco White. These circumstances increase the probability that 
Whately was written against and for. 

Voltaire Chretien ; preuves tirees de ses ouvrages. Paris, 1820, 
12mo. 

If Voltaire have not succeeded in proving himself a strong 
theist and a strong anti-revelationist, who is to succeed in proving 



THE WORD CHRISTIAN. 147 

himself one thing or the other in any matter whatsoever ? By 
occasional confusion between theism and Christianity ; by taking 
advantage of the formal phrases of adhesion to the Eoman 
Church, which very often occur, and are often the happiest bits 
of irony in an ironical production ; by citations of his morality, 
which is decidedly Christian, though often attributed to Brah- 
mins ; and so on the author makes a fair case for his paradox, 
in the eyes of those who know no more than he tells them. If 
he had said that Voltaire was a better Christian than himself 
knew of, towards all mankind except men of letters, I for one 
should have agreed with him. 

Christian ! the word has degenerated into a synonym of man, 
in what are called Christian countries. So we have the porrot 
who ' swore for all the world like a Christian,' and the two dogs 
who ' hated each other just like Christians.' When the Irish 
duellist of the last century, whose name may be spared in 
consideration of its historic fame and the worthy people who 
bear it, was (June 12, 1786) about to take the consequence of 
his last brutal murder, the rope broke, and the criminal got up, 

and exclaimed, l By Mr. Sheriff, you ought to be ashamed 

of yourself ! this rope is not strong enough to hang a dog, far 
less a Christian ! ' But such things as this are far from the worst 
depravations. As to a word so defiled by usage, it is well to 
know that there is a way of escape from it, without renouncing 
the New Testament. I suppose any one may assume for himself 
what I have sometimes heard contended for, that no New Testa- 
ment word is to be used in religion in any sense except that of 
the New Testament. This granted, the question is settled. 
The word Christian, which occurs three times, is never recog- 
nised as anything but a term of contempt from those without 
the pale to those within. Thus, Herod Agrippa, who was deep in 
Jewish literature, and a correspondent of Josephus, says to Paul, 
(Acts xxvi. 28) ' Almost thou persuadest me to be (what I and 
other followers of the state religion depise under the name) 
a Christian.' Again,- ( Acts xi. 26) 'The disciples (as they called 
themselves) were called (by the surrounding heathens) Christians 
first in Antioch.' Thirdly, (1 Peter iv. 16) 'Let none of you 
suffer as a murderer. . . . But if as a Christian (as the heathen 
call it by whom the suffering comes), let him not be ashamed.' 
That is to say, no disciple ever called himself a Christian, or 
applied the name, as from himself, to another disciple, from one 
end of the New Testament to the other ; and no disciple need 

L 2 



148 A BUDGET OF PARADOXES. 

apply that name to himself in our day, if he dislike the associa- 
tions with which the conduct of Christians has clothed it. 

Address of M. Hoene Wronski to the British Board of Longitude, 

upon the actual state of the mathematics, their reform, and 

upon the new celestial mechanics, giving the definitive solution 

of the problem of longitude. London, 1820, 8vo. 

M. Wronski was the author of seven quartos on mathematics, 

showing very great power of generalization. He was also deep in 

the transcendental philosophy, and had the Absolute at his 

fingers' ends. All this knowledge was rendered useless by a 

persuasion that he had greatly advanced beyond the whole world, 

with many hints that the Absolute would not be forthcoming, 

unless prepaid. He was a man of the widest extremes. At 

one time he desired people to see all possible mathematics in 

Faj= A O + A 1 fl 1 + A 2 O 2 + A 3 H 3 + &c, 

which he did not explain, though there is meaning to it in the 
quartos. At another time he was proposing the general solution 
of the fifth degree by help of 625 independent equations of one 
form and 125 of another. The first separate memoir from any 
Transactions that t ever possessed was given to me when at 
Cambridge; the refutation (1819) of this asserted solution, 
presented to the Academy of Lisbon by Evangelista Torriano. 
I cannot say I read it. The tract above is an attack on modern 
mathematicians in general, and on the Board of Longitude, and 
Dr. Young. 

1820. In this year died Dr. Isaac Milner, President of Queens' 
College, Cambridge, one of the class of rational paradoxers. 
Under this name I include all who, in private life, and in matters 
which concern themselves, take their own course, and suit their 
own notions, no matter what other people may think of them. 
These men will put things to uses they were never intended for, 
to the great distress and disgust of their gregarious friends. I 
am one of the class, and I could write a little book of cases in 
which I have incurred absolute reproach for not ' doing as other 
people do.' I will name two of my atrocities : I took one of 
those butter-dishes which have for a top a dome with holes in 
it, which is turned inward, out of reach of accident, when not in 
use. Turning the dome inwards, I filled the dish with water, 
and put a sponge in the dome : the holes let it fill with water, 
and I had a penwiper, always moist, and worth its price five 
times over. ' Why ! what do you mean ? It was made to hold 



MILNER'S LAMP. 149 

butter. You are always at some queer thing or other ! ' I 
bought a leaden comb, intended to dye the hair, it being sup- 
posed that the application of lead will have this effect. I did 
not try : but I divided the comb into two, separating the part 
of closed prongs from the other ; and thus I had two ruling 
machines. The lead marks paper, and by drawing the end of 
one of the machines along a ruler, I could rule twenty lines at 
a time, quite fit to write on. I thought I should have killed a 
friend to whom I explained it : he could not for the life of him 
understand how leaden lines on paper would dye the hair. 

But Dr. Milner went beyond me. He wanted a seat suited to 
his shape, and he defied opinion to a fearful point. He spread a 
thick block of putty over a wooden chair and sat in it until it 
had taken a ceroplast copy of the proper seat. This he gave to 
a carpenter to be imitated in wood. One of the few now living 
who knew him my friend, General Perronet Thompson 
answers for the wood, which was shown him by Milner himself ; 
but he does not vouch for the material being putty, which was 
in the story told me at Cambridge ; William Frend also re- 
membered it. Perhaps the Doctor took off his great seal in 
green wax, like the Crown ; but some soft material he certainly 
adopted ; and very comfortable he found the wooden copy. 

The same gentleman vouches for Milner's lamp : but this had 
visible science in it ; the vulgar see 
no science in the construction of the 
chair. A hollow semi-cylinder, but 
not with a circular curve, revolved on 
pivots. The curve was calculated on 
the law that, whatever quantity of oil 
might be in the lamp, the position of 
equilibrium just brought the oil up to 
the edge of the cylinder, at which a 
bit of wick was placed. As the wick 
exhausted the oil, the cylinder slowly 
revolved about the pivots so as to 
keep the oil always touching the wick. 

Great discoveries are always laughed at : but it is very often 
not the laugh of incredulity ; it is a mode of distorting the sense 
of inferiority into a sense of superiority, or a mimicry of supe- 
riority interposed between the laugher and his feeling of in- 
feriority. Two persons in conversation agreed that it was often 




150 A BUDGKET OF PARADOXES. 

a nuisance not to be able to lay hands on a bit of paper to mark 
the place in a book, every bit of paper on the table was sure to 
contain something not to be spared. I very quietly said that I 
always had a stock of bookmarkers ready cut, with a proper place 
for them : my readers owe many of my anecdotes to this absurd 
practice. My two colloquials burst into a fit of laughter ; about 
what ? Incredulity was out of the question ; and there could be 
nothing foolish in my taking measures to avoid what they knew 
was an inconvenience. I was in this matter obviously their 
superior, and so they laughed at me. Much more candid was 
the Eoyal Duke of the last century, who was noted for slow ideas. 
' The rain comes into my mouth,' said he, while riding. ' Had 
not your Royal Highness better shut your mouth ? ' said the 
equerry. The Prince did so, and ought, by rule, to have laughed 
heartily at his adviser ; instead of this, he said quietly, ' It 
doesn't come in now.' 

De Attentionis mensura causisque primariis. By J. F. Herbart. 
Koenigsberg, 1822, 4to. 

This celebrated philosopher maintained that mathematics 
ought to be applied to psychology, in a separate tract, published 
also in 1822 : the one above seems, therefore, to be his challenge 
on the subject. It is on attention, and I think it will hardly 
support Herbart's thesis. As a specimen of his formula, let t be 
the time elapsed since the consideration began, /3 the whole 
perceptive intensity of the individual, (f> the whole of his mental 
force, and z the force given to a notion by attention during the 
time t. Then, 



Now for a test. There is a jactura, v, the meaning of which I 
do not comprehend. If there be anything in it, my mathe- 
matical readers ought to interpret it from the formula 



1-/3 

and to this task I leave them, wishing them better luck than 
mine. The time may come when other manifestations of mind, 
besides belief, shall be submitted to calculation : at that time, 
should it arrive, a final decision may be passed upon Herbart. 



THE WHIZGIG MYTHOLOGICAL ASTRONOMY. 151 



The theory of the Whizgtg considered ; in as much as it mechani- 
cally exemplifies the three working properties of nature ; which 
are now set forth under the guise of this toy, for children of all 
ages. London, 1822, 12mo. (pp. 24, B. McMillan, Bow Street, 
Covent Garden.) 

The toy called the whizgig will be remembered by many. The 
writer is a follower of Jacob Behmen, William Law, Richard 
Clarke, and Eugenius Philaleth.es. Jacob Behmen first an- 
nounced the three working properties of nature, which Newton 
stole, as described in the Gentleman's Magazine, July, 1782, 
p. 329. These laws are illustrated in the whizgig. There is the 
harsh astringent, attractive compression ; the bitter compunction, 
repulsive expansion ; and the stinging anguish, duplex motion. 
The author hints that he has written other works, to which he 
gives no clue. I have heard that Behmen was pillaged by New- 
ton, and Swedenborg by Laplace, and Pythagoras by Copernicus, 
and Epicurus by Dalton, &c. I do not think this mention will 
revive Behmen ; but it may the whizgig, a very pretty toy, and 
philosophical withal, for few of those who used it could ex- 
plain it. 

A Grammar of infinite forms ; or the mathematical elements of 
ancient philosophy and mythology. By Wm. Howison. Edin- 
burgh, 1823, 8vo. 

A curious combination of geometry and mythology. Perseus, 
for instance, is treated under the head, ' the evolution of diminish- 
ing hyperbolic branches.' 

The Mythological Astronomy of the Ancients ; part the second : 
or the key of Urania, the wards of which will unlock all the 
mysteries of antiquity. Norwich, 1823, 12mo. 

A Companion to the. Mythological Astronomy, &c., containing 
remai'ks on recent publications. . . Norwich, 1824, 12mo. 

A new Theory of the Earth and of planetary motion ; in which it 
is demonstrated that the Sun is vicegerent of his own system. 
Norwich, 1825, 12mo. 

The analyzation of the writings of the Jews, so far as they are 
found to have any connection with the sublime science of 
astronomy. [This is pp. 97-180 of some other work, being all 
I have seen.] 

These works are all by Sampson Arnold Mackey, for whom see 
Notes and Queries, 1st S. viii. 468, 565, ix. 89, 179. Had it 



J52 A BUDGET OF PARADOXES. 

not been for actual quotations given by one correspondent only 
(1st S. viii. 565), that journal would have handed him down as 
a man of some real learning. An extraordinary man he certainly 
was : it is not one illiterate shoemaker in a thousand who could work 
upon such a singular mass of Sanscrit and Greek words, without 
showing evidence of being able to read a line in any language 
but his own, or to spell that correctly. He was an uneducated 
Godfrey Higgins. A few extracts will put this in a strong light : 
one for history of science, one for astronomy, and one for philo- 
logy : 
&j v 

' Sir Isaac Newton was of opinion that " the atmosphere of the earth 
was the sensory of God ; by which he was enabled to see quite round 
the earth : " which proves that Sir Isaac had no idea that God could 
see through the earth. 

Sir Richard [Phillips] has given the most rational explanation of 
the cause of the earth's elliptical orbit that I have ever seen in print. 
It is because the earth presents its watery hemisphere to the sun at 
one time and that of solid land the other ; but why has he made his 
Oxonian astonished at the coincidence ? It is what I taught in my 
attic twelve years before. 

Again, admitting that the Eloim were powerful and intelligent beings 
that managed these things, we would accuse them of being the authors 
of all the sufferings of Chrisna. And as they and the constellation of 
Leo were below the horizon, and consequently cut off from the end of 
the zodiac, there were but eleven constellations of the zodiac to be 
seen ; the three at the end were wanted, but those three would be 
accused of bringing Chrisna into the troubles which at last ended in 
his death. All this would be expressed in the Eastern language by 
saying that Chrisna was persecuted by those Judoth Isbcariotb ! ! ! ! ! 
[the five notes of exclamation are the author's]. But the astronomy 
of those distant ages, when the sun was at the south pole in winter, 
would leave five of those Decans cut off from our view, in the latitude 
of twenty-eight degrees; hence Chrisna died of wounds from five 
Decans, but the whole five may be included in Judoth Ishcarioth ! for 
the phrase means the men that are wanted at the extreme parts. Ish- 
carioth is a compound of ish, a man, and carat wanted or taken away, 
and oth the plural termination, more ancient than im. . . ' 

I might show at length how Michael is the sun, and the 
D'-ev-'l, in French Di-ob-al, also 'L-evi-ath-an the evi being the 
radical part both of devil and leviathan is the Nile, which the 
sun dried up for Moses to pass : a battle celebrated by Jude. 
Also how Moses, the same name as Muses, is from mesha, drawn 
out of the water, ' and hence we called our land which is saved 
from the water by the name of marsh.'' But it will be of more use 
to collect the character of S. A. M. from such correspondents of 



A TKANSCENDENTAL PHILOSOPHER. 153 

Notes and Queries as have written after superficial examination. 
Great astronomical and philological attainments ; much ability 
and learning; had evidently read and studied deeply; remark- 
able for the originality of his views upon the very abstruse 
subject of mythological astronomy, in which he exhibited great 
sagacity. Certainly his views were original ; but their sagacity, 
if it be allowable to copy his own mode of etymologizing, is of an 
ori-gin-ale cast, resembling that of a person who puts to his 
mouth liquors both distilled and fermented. 

Principles of the Kantesian, or transcendental philosophy. By 
Thomas Wirgman. London, 1824, 8vo. 

Mr. Wirgman's mind was somewhat attuned to psychology; 
but he was cracky and vagarious. He had been a fashionable 
jeweller in St. James's Street, no doubt the son or grandson of 
Wirgman at 'the well-known toy-shop in St. James's Street,' 
where Sam Johnson smartened himself with silver buckles. 
(Boswell, aet. 69). He would not have the ridiculous large ones 
in fashion ; and he would give no more than a guinea a pair ; 
such, says Boswell, in Italics, were the principles of the business : 
and I think this may be the first place in which the philo- 
sophical word was brought down from heaven to mix with men. 
However this may be, my Wirgman sold snuff-boxes, among 
other things, and fifty years ago a fashionable snuff-boxer would 
be under inducement, if not positively obliged, to have a stock 
with very objectionable pictures. So it happened that Wirgman 
by reason of a trifle too much candour came under the notice 
of the Suppression Society, and ran considerable risk. Mr. 
Brougham was his counsel ; and managed to get him acquitted. 
Years and years after this, when Mr. Brougham was deep in the 
formation of the London University (now University College), 
Mr. Wirgman called on him. ' What now ? ' said Mr. B. with his 
most sarcastic look a very perfect thing of its kind 'you're 
in a scrape again, I suppose ! ' ' No ! indeed ! ' said W., ' my present 
object is to ask your interest for the chair of Moral Philosophy 
in the new University I ' He had taken up Kant ! 

Mr. Wirgman, an itinerant paradoxer, called on me in 1831 : he 
came to convert me. ' I assure you,' said he, ' I am nothing but 
an old brute of a jeweller ; ' and his eye and manner were of the 
extreme of jocosity, as good in their way, as the satire of his 
former counsel. I mention him as one of that class who go away 
quite satisfied that they have wrought conviction. ' Now,' said he, 



154 A BUDGET OF PABADOXES. 

' I'll make it clear to you ! Suppose a number of gold-fishes in a 
glass bowl you understand ? Well ! I come with my cigar, 
and go puff, puff, puff, over the bowl, until there is a little cloud 
of smoke : now, tell me, what will the gold-fishes say to that ? ' 
' I should imagine,' said I, ' that they would not know what to make 
of it.' ' By Jove ! you're a Kantian ; ' said he, and with this and 
the like, he left me, vowing that it was delightful to talk to so 
intelligent a person. The greatest compliment Wirgman ever 
received was from James Mill, who used to say he did not under- 
stand Kant. That such a man as Mill should think this worth 
saying is a feather in the cap of the jocose jeweller. 

Some of my readers will stare at my supposing that Boswell 
may have been the first down-bringer of the word principles into 
common life ; the best answer will be a prior instance of the 
word as true vernacular ; it has never happened to me to notice 
one. Many words have very common uses which are not old. 
Take the following from Nichols (Anecd. ix. 263) : < Lord 
Thurlow presents his best respects to Mr. and Mrs. Thicknesse, 
and assures them that he knows of no cause to complain of any 
part of Mr. Thicknesse's carriage ; least of all the circumstance of 
sending the head to Ormond Street.' Surely Mr. T. had lent 
Lord T. a satisfactory carriage with a moveable head, and the 
above is a polite answer to inquiries. Not a bit of it ! carriage 
is here conduct, and the head is a bust. The vehicles of the 
rich, at the time, were coaches, chariots, chaises, &c., never 
carriages, which were rather carts. Gibbon has the word for 
baggage-waggons. In Jane Austen's novels the word carriage is 
established. 

John Walsh, of Cork (1786-1847). This discoverer has had 
the honour of a biography from Prof. Boole, who, at my request, 
collected information about him on the scene of his labours. 
It is in the Philosophical Magazine for November, 1851, and 
will, I hope, be transferred to some biographical collection where 
it may find a larger class of readers, It is the best biography of 
a single hero of the kind that I know. Mr. Walsh introduced 
himself to me, as he did to many others, in the anterowlandian 
days of the Post-office ; his unpaid letters were double, treble, 
&c. They contained his pamphlets, and cost their weight in 
silver : all have the name of the author, and all are in octavo or 
in quarto letter-form : most are in four pages, and all dated from 
Cork. I have the following by me : 



JOHN WALSH'S DELUSIONS. 155 



The Geometric Base. 1825. The theory of pl&ne angles. 1827. 
Three Letters to Dr. Francis Sadleir. 1838. The invention of 
polar geometry. By Irelandus. 1839. The theory of partial 
functions. Letter to Lord Brougham. 1839. On the invention 
of polar geometry. 1839. Letter to the Editor of the Edin- 
burgh Review. 1840. Irish Manufacture. A new method of 
tangents. 1841. The normal diameter in curves. 1843. 
Letter to Sir R. Peel. 1845. [Hints that Government should 
compel the introduction of Walsh's Geometry into Universities.] 
Solution of Equations of the higher orders. 1845. 

Besides these, there is a ' Metalogia,' and I know not how many 
others. 

Mr. Boole, who has taken the moral and social features of 
Walsh's delusions from the commiserating point of view, which 
makes ridicule out of place, has been obliged to treat Walsh as 
Scott's Alan Fairford treated his client Peter Peebles ; namely, 
keep the scarecrow out of court while his case was argued. My 
plan requires me to bring him in : and when he comes in at the 
door, pity and sympathy fly out at the window. Let the reader 
remember that he was not an ignoramus in mathematics : he 
might have won his spurs if he could have first served as an 
esquire. Though so illiterate that even in Ireland he never 
picked up anything more Latin than Irelandus, he was a very 
pretty mathematician spoiled in the making by intense self- 
opinion. 

This is part of a private letter to me at the back of a page of 
print : I had never addressed a word to him : 

' There are no limits in mathematics, and those that assert there are, 
are infinite ruffians, ignorant, lying blackguards. There is no dif- 
ferential calculus, no Taylor's theorem, no calculus of variations, &c. 
in mathematics. There is no quackery whatever in mathematics ; no 
$ equal to anything. What sheer ignorant blackguardism that ! 

In mechanics the parallelogram of forces is quackery, and is danger- 
ous ; for nothing is at rest, or in uniform, or in rectilinear motion, in 
the universe. Variable motion is an essential property of matter. 
Laplace's demonstration of the parallelogram of forces is a begging of 
the question ; and the attempts of them all to show that the difference 
of twenty minutes between the sidereal and actual revolution of the 
earth round the sun arises from the tugging of the Sun and Moon at 
the pot-belly of the earth, without being sure even that the earth has 
a pot-belly at all, is perfect quackery. The said difference arising 
from and demonstrating the revolution of the Sun itself round some 
distant centre.' 



156 A BUDGET OF PARADOXES. 

In the letter to Lord Brougham we read as follows : 
' I ask the Royal Society of London, I ask the Saxon crew of that 
crazy hulk, where is the dogma of their philosophic god now ? . . . 
When the Royal Society of London, and the Academy of Sciences of 
Paris, shall have read this memorandum, how will they appear ? Like 
two cur dogs in the paws of the noblest beast of the forest . . . Just 
as this note was going to press, a volume lately published by you was 
put into my hands, wherein you attempt to defend the fluxions and 
Principia of Newton. Man ! what are you about ? You come forward 
now with your special pleading, and fraught with national prejudice, 
to defend, like the philosopher Grassi, the persecutor of Galileo, prin- 
ciples and reasoning which, unless you are actually insane, or an 
ignorant quack in mathematics, you know are mathematically false. 
What a moral lesson this for the students of the University of London 
from its head ! Man ! demonstrate corollary 3, in this note, by the 
lying dogma of Newton, or turn your thoughts to something you 
understand.' 

'WALSH IEBLANDUS.' 

Mr. Walsh honour to his memory once had the considera- 
tion to save me postage by addressing a pamphlet under cover to 
a Member of Parliament, with an explanatory letter. In that 
letter he gives a candid opinion of himself : 

(1838.) ' Mr. Walsh takes leave to send the enclosed corrected 
copy to Mr. Hutton as one of the Council of the University of London, 
and to save postage for the Professor of Mathematics there. He will 
find in it geometry more deep and subtle, and at the same time more 
simple and elegant, than it was ever contemplated human genius could 
invent.' 

He then proceeds to set forth that a certain ' tomfoolery 
lemma,' with its ' tomfoolery ' superstructure, * never had exist- 
ence outside the shallow brains of its inventor,' Euclid. He then 
proceeds thus : 

' The same spirit that animated those philosophers who sent Galileo 
to the Inquisition animates all the philosophers of the present day 
without exception. If anything can free them from the yoke of error, 
it is the [Walsh] problem of double tangence. But free them it will, 
how deeply soever they may be sunk into mental slavery and God 
knows that is deeply enough ; and they bear it with an admirable 
grace ; for none bear slavery with a better grace than tyrants. The 
lads must adopt my theory ... It will be a sad reverse for all our 
great professors to be compelled to become schoolboys in their gray 
years. But the sore scratch is to be compelled, as they had before 
been compelled one thousand years ago, to have recourse to Ireland 
for instruction.' 



PROGRESS OF FREE THOUGHT. 157 

The following ' Impromptu ' is no doubt by Walsh himself: he 
was more of a poet than of an astronomer : 

' Through ages unfriended, 

With sophistry blended, 
Deep science in Chaos had slept ; 

Its limits were fettered, 

Its voters unlettered, 
Its students in movements but crept. 

Till, despite of great foes, 

Great WALSH first arose, 
And with logical might did unravel 

Those mazes of knowledge, 

Ne'er known in a college, 
Though sought for with unceasing travail. 

With cheers we now hail him, 

May success never fail him, 
In Polar Geometrical mining ; 

Till his foes be as tamed 

As his works are far-famed 
For true philosophic refining.' 

Walsh's system is, that all mathematics and physics are wrong : 
there is hardly one proposition in Euclid which is demonstrated. 
His example ought to warn all who rely on their own evidence to 
their own success. He was not, properly speaking, insane ; he 
only spoke his mind more freely than many others of his class. 
The poor fellow died in the Cork union, during the famine. He 
had lived a happy life, contemplating his own perfections, like 
Brahma on the lotos-leaf. 

The year 1825 brings me to about the middle of my Athe- 
naeum list : that is, so far as mere number of names mentioned 
is concerned. Freedom of opinion, beyond a doubt, is gaining 
ground, for good or for evil, according to what the speaker 
happens to think : admission of authority is no longer made in 
the old way. If we take soul-cure and body-cure, divinity and 
medicine, it is manifest that a change has come over us. Time 
was when it was enough that dose or dogma should be certified 
by ' II a ete ordonne, Monsieur, il a ete ordonne,' as the apothe- 
cary said when he wanted to operate upon poor de Porceaugnac. 
Very much changed : but whether for good or for evil does not 
now matter ; the question is, whether contempt of demonstration 
such as our paradoxers show has augmented with the rejection of 
dogmatic authority. It ought to be just the other way : for the 



158 A BUDGET OF PARADOXES. 

worship of reason is the system on which, if we trust them, the 
deniers of guidance ground their plan of life. The following 
attempt at an experiment on this point is the best which I can 
make ; and, so far as I know, the first that ever was made. 

Say that my list of paradoxers divides in 1825 : this of itself 
proves nothing, because so many of the earlier books are lost, or 
not likely to be come at. It would be a fearful rate of increase 
which would make the number of paradoxes since 1825 equal to 
the whole number before that date. Let us turn now to another 
collection of mine, arithmetical books, of which I have published 
a list. The two collections are similarly circumstanced as to 
new and old books ; the paradoxes had no care given to the 
collection of either ; the arithmetical books equal care to both. 
The list of arithmetical books, published in 1847, divides at 
1735 ; the paradoxes, up to 1863, divide at 1825. If we take 
the process which is most against the distinction, and allow every 
year from 1847 to 1863 to add a year to 1735, we should say 
that the arithmetical writers divide at 1751. This rough pro- 
cess may serve, with sufficient certainty, to show that the pro- 
portion of paradoxes to books of sober demonstration is on the 
increase ; and probably, quite as much as the proportion of 
heterodoxes to books of orthodox adherence. So that divinity 
and medicine may say to geometry, Don't you sneer : if ration- 
alism, homoeopathy, and their congeners are on the rise among 
us, your enemies are increasing quite as fast. But geometry 
replies Dear friends, content yourselves with the rational in- 
ference that the rise of heterodoxy within your pales is not 
conclusive against you, taken alone ; for it rises at the same 
time within mine. Store within your garners the precious 
argument that you are not proved wrong by increase of dissent ; 
because there is increase of dissent against exact science. But 
do not therefore even yourselves to me : remember that you, 
Dame Divinity, have inflicted every kind of penalty, from the 
stake to the stocks, in aid of your reasoning ; remember that 
you, Mother Medicine, have, not many years ago applied to 
Parliament for increase of forcible hindrance of antipharma- 
copoeal drenches, pills, and powders. Who ever heard of my 
asking the legislature to fine blundering circle-squarers ? Ee- 
member that the D in dogma is the D in decay ; but the D in 
demonstration is the D in durability. 

I have known a medical man a young one who was seriously 
of opinion that the country ought to be divided into medical 
parishes, with a practitioner appointed to each, and a penalty 



MEDICAL REFOKM. 159 

for calling in any but the incumbent curer. How should people 
know how to choose ? The hair-dressers once petitioned Par- 
liament for an act to compel people to wear wigs. My own 
opinion is of the opposite extreme, as in the following letter 
(Examiner ', April 5, 1856) ; which, to my surprise, I saw reprinted 
in a medical journal, as a plan not absolutely to be rejected. 
I am perfectly satisfied that it would greatly promote true 
medical orthodoxy, the predominance of well educated thinkers, 
and the development of their desirable differences. 

SIR. The Medical Bill and the medical question generally is 
one on which experience would teach, if people would be taught. 

The great soul question took three hundred years to settle : the 
little body question might be settled in thirty years, if the deci- 
sions in the former question were studied. 

Time was when the State believed, as honestly as ever it 
believed anything, that it might, could, and should find out 
true doctrine for the poor ignorant community ; to which, like 
a worthy honest state, it added would. Accordingly, by the 
assistance of a Church, which undertook the physic, the surgery, 
and the pharmacy of sound doctrine all by itself, it sent forth 
its legally qualified teachers into every parish, and woe to the 
man who called in any other. They burnt that man, they 
whipped him, they imprisoned him, they did everything but what 
was Christian to him, all for his soul's health and the amendment 
of his excesses. 

But men would not submit. To the argument that the State 
was a father to the ignorant, they replied that it was at best the 
ignorant father of an ignorant son, and that a blind man could 
find his way into a ditch without another blind man to help him. 
And when the State said But here we have the Church, which 
knows all about it, the ignorant community declared that it had 
a right to judge that question, and that it would judge it. It 
also said that the Church was never one thing long, and that it 
progressed, on the whole, rather more slowly than the ignorant 
community. 

The end of it was, in this country, that every one who chose 
taught all who chose to let him teach, on condition only of an open 
and true registration. The State was allowed to patronise one 
particular Church, so that no one need trouble himself to choose 
a pastor from the mere necessity of choosing. But every church 
is allowed its colleges, its studies, its diplomas ; and every man 
is allowed his choice. There is no proof that our souls are 



160 A BUDGET OF PARADOXES. 

worse off than in the sixteenth century ; and, judging by fruits, 
there is much reason to hope they are better off. 

Now the little body question is a perfect parallel to the great 
soul question in all its circumstances. The only things in which 
the parallel fails are the following : Every one who believes in a 
future state sees that the soul question is incomparably more 
important than the body question, and every one can try the 
body question by experiment to a larger extent than the soul 
question. The proverb, which always has a spark of truth at the 
bottom, says that every man of forty is either a fool or a 
physician ; but did even the proverb maker ever dare to say that 
every man is at any age either a fool or a fit teacher of religion ? 

Common sense points out the following settlement of the 
medical question : and to this it will come sooner or later. 

Let every man who chooses subject to one common law of 
manslaughter for all the crass cases doctor the bodies of all 
who choose to trust him, and recover payment according to 
agreement in the courts of law. Provided always that every 
person practising should be registered at a moderate fee in a 
register to be republished every six months. 

Let the register give the name, address, and asserted Qualifica- 
tion of each candidate as licentiate, or doctor, or what not, of 
this or that college, hall, university, &c., home or foreign. Let 
it be competent to any man to describe himself as qualified by 
study in public schools without a diploma, or by private study, 
or even by intuition or divine inspiration, if he please. But 
whatever he holds his qualification to be, that let him declare. 
Let all qualification which of its own nature admits of proof be 
proved, as by the diploma or certificate, &c., leaving things which 
cannot be proved, as asserted private study, intuition, inspiration, 
&c., to work their own way. 

Let it be highly penal to assert to the patient any qualification 
which is not in the register, and let the register be sold very 
cheap. Let the registrar give each registered practitioner a copy 
of the register in his own case ; let any patient have power to 
demand a sight of this copy ; and let no money for attendance 
be recoverable in any case in which there has been false repre- 
sentation. 

Let any party in any suit have a right to produce what medi- 
cal testimony he pleases. Let the medical witness produce his 
register, and let his evidence be for the jury, as is that of an 
engineer or a practitioner of any art which is not attested by 
diplomas. 



MEDICAL REFORM REV. R. TAYLOR. 161 

Let any man who practises without venturing to put his name 
on the register be liable to fine and imprisonment. 

The consequence would be that, as now, anybody who pleases 
might practise ; for the medical world is well aware that there 
is no power of preventing what they call quacks from practising. 
But very different from what is now, every man who practises 
would be obliged to tell the whole world what his claim is, and 
would run a great risk if he dared to tell his patient in private 
anything different from what he had told the whole world. 

The consequence would be that a real education in anatomy, 
physiology, chemistry, surgery, and what is known of the thing 
called medicine, would acquire more importance than it now 
has. 

It is curious to see how completely the medical man of the 
nineteenth century squares with the priest of the sixteenth cen- 
tury. The clergy of all sects are now better divines and better 
men than they ever were. They have lost Bacon's reproach that 
they took a smaller measure of things than any other educated 
men ; and the physicians are now in this particular the rear- 
guard of the learned world ; though it may be true that the rear 
in our day is further on in the march than the van of Bacon's 
day. Nor will they ever recover the lost position until medicine 
is as free as religion. 

To this it must come. To this the public, which will decide 
for itself, has determined it shall come. To this the public has, 
in fact, brought it, but on a plan which it is not desirable to 
make permanent. We will be as free to take care of our bodies 
as of our souls and of our goods. This is the profession of all 
who sign as I do, and the practice of most of those who would not 
like the name HETEROPATH.' 



The motion of the Sun in the Ecliptic, proved to be uniform in a 
circular orbit . . . with preliminary observations on the fallacy 
of the Solar System. By Bartholomew Prescott, 1825, 8vo. 

The author had published, in 1803, a 'Defence of the Divine 
System,' which I never saw ; also, ' On the inverted scheme of 
Copernicus.' The above work is clever in its satire. 

Manifesto of the Christian Evidence Society, established Nov. 12, 
1824. Twenty-four plain questions to honest men. 

These are two broadsides of August and November, 1826, 
signed by Robert Taylor, A.B., Orator of the Christian Evidence 



162 A BUDGET OF PARADOXES. 

Society. This gentleman was a clergyman, and was convicted of 
blasphemy in 1827, for which he suffered imprisonment, and got 
the name of the Devil's Chaplain. The following are quota- 
tions : 

' For the book of Revelation, there was no original Greek at all, but 
Erasmus wrote it himself in Switzerland, in the year 1516. Bishop 
Marsh, vol. i. p. 320.'- ' Is not God the author of your reason ? Can he 
then be the author of anything which is contrary to your reason ? If 
reason be a sufficient guide, why should God give you any other ? if it 
be not a sufficient guide, why has he given you that ? ' 

I remember a votary of the Society being asked to substitute for 
reason ' the right leg,' and for guide ' support,' and to answer the 
two last questions : he said there must be a quibble, but he did 
not see what. It is pleasant to reflect that the argumentum a, 
carcere is obsolete. One great defect of it was that it did not go 
far enough : there should have been laws against subscriptions 
for blasphemers, against dealing at their shops, and against rich 
widows marrying them. 

Had I taken in theology, I must have entered books against 
Christianity. I mention the above, and Paine's ' Age of Reason,' 
simply because they are the only English modern works that 
ever came in my way without my asking for them. The three 
parts of the ' Age of Reason ' were published in Paris 1793, Paris 
1795, and New York 1807. Carlile's edition is of London, 
1818, 8vo. It must be republished when the time comes, to show 
what stuff governments and clergy were afraid of at the begin- 
ning of this century. I should never have seen the book, if it 
had not been prohibited : a bookseller put it under my nose with 
a fearful look round him ; and I could do no less, in common 
curiosity, than buy a work which had been so complimented by 
church and state. And when I had read it, I said in my mind to 
church and state, Confound you 1 you have taken me in worse 
than any reviewer I ever met with. I forget what I gave for 
the book, but I ought to have been able to claim compensation 
somewhere. 



Cabbala Algebraica. Auctore Gul. Lud. Christmann. Stuttgard, 
1827, 4to. 

Eighty closely printed pages of an attempt to solve equations 
of every degree, which has a process called by the author cabbala. 
An anonymous correspondent spells cabbala as follows, xaft/3a\\, 
and makes 666 out of its letters. This gentleman has sent me, 



CABBALA ALPHABETICA. 163 

since my Budget commenced, a little heap of satirical communi- 
cations, each having a 666 or two ; for instance, alluding to my 
remarks on the spelling of chemistry, he finds the fated number in 
^i/jLsia. With these are challenges to explain them, and hints about 
the end of the world. All these letters have different fantastic 
seals ; one of them with the legend ' keep your temper,' another 
bearing * bank token five pence.' The only signature is a triangle 
with a little circle in it, which I interpret to mean that the 
writer confesses himself to be the round man stuck in the three- 
cornered hole, to be explained as in Sydney Smith's joke. 

There is a kind of Cabbala Alphabetica which the investigators 
of the numerals in words would do well to take up : it is the 
formation of sentences which contain all the letters of the alphabet, 
and each only once. No one has done it with v and j treated as 
consonants ; but you and I can do it. Dr. "Whewell and I amused 
ourselves, some years ago, with attempts. He could not make 
sense, though he joined words : he gave me 

Phiz, styx, wrong, buck, flame, quid. 

I gave him the following, which he agreed was ' admirable 
sense : ' I certainly think the words would never have come 
together except in this way : 

I, quartz pyx, who fling muck beds. 

I long thought that no human being could say this under any 
circumstances. At last I happened to be reading a religious 
writer as he thought himself who threw aspersions on his 
opponents thick and threefold. Heyday ! came into my head, 
this fellow flings muck beds ; he must be a quartz pyx. And then 
I remembered that a pyx is a sacred vessel, and quartz is a hard 
stone, as hard as the heart of a religious foe-curser. So that the 
line is the motto of the ferocious sectarian, who turns his religious 
vessels into mud-holders, for the benefit of those who will not 
see what he sees. 

I can find no circumstances for the following, which I 
received from another : 

Fritz ! quick ! land ! hew gypsum box. 
From other quarters I have the following : 
Dumpy quiz ! whirl back fogs next. 

This might be said in time of haze to the queer little figure in 



164 A BUDGET OF PAKADOXES. 

the Dutch weather-toy, which comes out or goes in with the 
change in the atmosphere. Again, 

Export my fund ! Quiz black whigs. 

This Squire Western might have said, who was always afraid of 
the whigs sending the sinking-fund over to Hanover. But the 
following is the best : it is good advice to a young man, very well 
expressed under the circumstances : 

Get nymph ; quiz sad brow ; fix luck. 

"Which in more sober English would be, Marry ; be cheerful ; 
watch your business. There is more edification, more religion in 
this than in all the 666-interpretations put together. 

Such things would make excellent writing copies, for they 
secure attention to every letter ; v and j might be placed at the 
end. 

The Celtic Druids. By Godfrey Higgins, Esq. of Skellow Grange, 

near Doncaster. London, 1827, 4to. 
Anacalypsis, or an attempt to draw aside the veil of the Saitic 

Isis : or an inquiry into the origin of languages, nations, and 

religions. By Godfrey Higgins, &c London, 1836, 

2 vols. 4to. 

The first work had an additional preface and a new index in 
1829. Possibly, in future time, will be found bound up with 
copies of the second work two sheets which Mr. Higgins circu- 
lated among his friends in 1831 : the first a ' Eecapitulation,' the 
second ' Book vi. ch. 1.' 

The system of these works is that 

The Buddhists of Upper India (of whom the Phenician Canaanite, 
Melchizedek, was a priest), who built the Pyramids, Stonehenge 
Carnac, &c. will be shown to have founded all the ancient mythologies 
of the world, which, however varied and corrupted in recent times, 
were originally one, and that one founded on principles sublime, 
beautiful, and true. 

These works contain an immense quantity of learning, very 
honestly put together. I presume the enormous number of facts, 
and the goodness of the index, to be the reasons why the Ana- 
calypsis found a permanent place in the old reading-room of the 
British Museum, even before the change which greatly increased 
the number of books left free to the reader in that room. 

Mr. Higgins, whom I knew well in the last six years of his life, 
and respected as a good, learned, and (in his own way) pious man, 



GODFREY HIGOINS. 165 

was thoroughly and completely the man of a system. He had 
that sort of mental connection with his theory that made his 
statements of his authorities trustworthy : for, besides perfect 
integrity, he had no bias towards alteration of facts : he saw his 
system in the way the fact was presented to him by his authority, 
be that what it might. 

He was very sure of a fact which he got from any of his 
authorities : nothing could shake him. Imagine a conversation 
between him and an Indian officer who had paid long attention 
to Hindoo antiquities and their remains : a third person was 
present, ego qui scribo. G. H. 'You know that in the temples 
of I-forget-who the Ceres is always sculptured precisely as in 

Greece.' Col. , ' I really do not remember it, and I have 

seen most of these temples.' G. H. ' It is so, I assure you, 

especially at I-forget-where.' Col. , 'Well, I am sure! I 

was encamped for six weeks at the gate of that very temple, and, 
except a little shooting, had nothing to do but to examine its 
details, which I did, day after day, and I found nothing of the 
kind.' It was of no use at all. 

Godfrey Higgins began life by exposing and conquering, at 
the expense of two years of his studies, some shocking abuses 
which existed in the York Lunatic Asylum. This was a pro- 
ceeding which called much attention to the treatment of the 
insane, and produced much good effect. He was very resolute 
and energetic. The magistracy of his time had scruples about 
using the severity of law to people of such station as well-to-do 
farmers, &c. : they would allow a great deal of resistance, and 
endeavour to mollify the rebels into obedience. A young farmer 
flatly refused to pay under an order of affiliation made upon him 
by Godfrey Higgins. He was duly warned ; and persisted : he 
shortly found himself in gaol. He went there sure to conquer 
the Justice, and the first thing he did was to demand to see his 
lawyer. He was told, to his horror, that as soon as he had been 
cropped and prison-dressed, he might see as many lawyers as he 
pleased, to be looked at, laughed at, and advised that there was 
but one way out of the scrape. Higgins was, in his speculations, 
a regular counterpart of Bailly ; but the celebrated Mayor of Paris 
had not his nerve. It is impossible to say, if their characters had 
been changed, whether the unfortunate crisis in which Bailly was 
not equal to the occasion would have led to very different results 
if Higgins had been in his place : but assuredly constitutional 
liberty would have had one chance more. There are two works 
of his by which he was known, apart from his paradoxes. 



166 A BUDGET OF PARADOXES. 

First, ' An apology for the life and character of the celebrated 
prophet of Arabia, called Mohamed, or the Illustrious.' London, 
8vo. 1829. The reader will look at this writing of our English 
Buddhist with suspicious eye, but he will not be able to avoid 
confessing that the Arabian prophet has some reparation to 
demand at the hands of Christians. Next, ' Horse Sabbaticse ; or 
an attempt to correct certain superstitions and vulgar errors 
respecting the Sabbath. Second edition, with a large appendix.' 
London, 12mo. 1833. This book was very heterodox at the 
time, but it has furnished material for some of the clergy of our 
day. 

I never could quite make out whether Godfrey Higgins took 
that system which he traced to the Buddhists to have a Divine 
origin, or to be the result of good men's meditations. Himself a 
strong theist, and believer in a future state, one would suppose 
that he would refer a universal religion, spread in different forms 
over the whole earth from one source, directly to the universal 
Parent. And this I suspect he did, whether he knew it or not. 
The external evidence is balanced. In his preface he says 

* I cannot help smiling when I consider that the priests Lave objected 
to admit my former book, " the Celtic Druids," into libraries, because 
it was antichristian ; and it has been attacked by Deists, because it 
was superfluously religious. The learned Deist, the Rev. R. Taylor 
[already mentioned], has designated me as tlie religious Mr. Higgins.' 

The time will come when some profound historian of literature 
will make himself much clearer on the point than I am. 

The triumphal Chariot of Friction : or a familiar elucidation of 
the origin of magnetic attraction, &c. &c. By William Pope. 
London, 1829, 4to. 

Part of this work is on a dipping-needle of the author's con- 
struction. It must have been under the impression that a book 
of. naval magnetism was proposed, that a great many officers, the 
Royal Naval Club, &c. lent their names to the subscription list. 
How must they have been surprised to find, right opposite to the 
list of subscribers, the plate presenting ' the three emphatic letters, 
J. A. 0.' And how much more when they saw it set forth that if 
a square be inscribed in a circle, a circle within that, then a 
square again, &c., it is impossible to have more than fourteen 
circles, let the first circle be as large as you please. From this 
the seven attributes of Grod are unfolded ; and further, that all 
matter was moral, until Lucifer churned it into physical ' as far 



JACOTOT TRACT ON PROBABILITY. . 167 

as the third circle in Deity ' : this Lucifer, called Leviathan in 
Job, being thus the moving cause of chaos. I shall say no more, 
except that the friction of the air is the cause of magnetism. 

Remarks on the Architecture, Sculpture, and Zodiac of Palmyra ; 
with a Key to the Inscriptions. By B. Prescot. London, 
1830, 8vo. 

Mr. Prescot gives the signs of the zodiac a Hebrew origin. 

Epitome de matheinatiques. Par F. Jacotot, Avocat. 3ieme edition. 

Paris, 1830, 8vo. (pp. 18). 
Methode Jacotot. Choix de propositions mathematiques. Par 

P. Y. de Sepres. 2nde edition. Paris, 1830, 8vo. (pp. 82). 

Of Jacotot's method, which had some vogue in Paris, the 
principle was Tout est dans tout, and the process Apprendre 
quelque chose, et a y rapporter tout le reste. The first tract has 
a proposition in conic sections and its preliminaries : the second 
has twenty exercises, of which the first is finding the greatest 
common measure of two numbers, and the last is the motion of a 
point on a surface, acted on by given forces. This is topped up 
with the problem of sound in a tube, and a slice of Laplac^s 
theory of the tides. All to be studied until known by heart, and 
all the rest will come, or at least join on easily when it conies. 
There is much truth in the assertion that new knowledge hooks 
on easily to a little of the old, thoroughly mastered. The day is 
coming when it will be found out that crammed erudition, got up 
for examinations, does not cast out any hooks for more. 

Lettre a MM. les Membres de 1'Academie Boyale des Sciences, 
contenant un developpement de la refutation du systeme de la 
gravitation universelle, qui leur a etc presentee le 30 aout, 1830. 
Par Felix Passot. Paris, 1830, 8vo. 

Works of this sort are less common in France than in England. 
In France there is only the Academy of Sciences to go to : in 
England there is a reading public out of the Eoyal Society, &c. 

About 1830 was published, in the Librai^y of Useful Know- 
ledge, the tract on Probability, the joint work of the late Sir 
John Lubbock and Mr. Driukwater (Bethune). It is one of the 
best elementary openings of the subject. A binder put my name 
on the outside (the work was anonymous) and the consequence 
was that nothing could drive out of people's heads that it was 



168 A BUDGET OF PAKADOXES. 

written by me. I do not know how many denials I have made, 
from a passage in one of my own works to a letter in the Times : 
and I am not sure that I have succeeded in establishing the 
truth, even now. I accordingly note the fact once more. But 
as a book has no right here unless it contain a paradox or thing 
counter to general opinion or practice I will produce two small 
ones. Sir John Lubbock, with whom lay the executive arrange- 
ment, had a strong objection to the last word in ' Theory of 
Probabilities,' he maintained that the singular probability, should 
be used ; and I hold him quite right. 

The second case was this : My friend Sir J. L., with a large 
cluster of intellectual qualities, and another of social qualities, 
had one point of character which I will not call bad and cannot 
call good ; he never used a slang expression. To such a length 
did he carry his dislike, that he could not bear head and tail, 
even in a work on games of chance : so he used obverse and reverse. 
I stared when I first saw this : but, to my delight, I found that 
the force of circumstances beat him at last. He was obliged to 
take an example from the race-course, and the name of one of 
the horses was Bessy Bedlam ! And he did not put her down as 
Elizabeth Bethlehem, but forced himself to follow the jockeys. 


[Almanach Remain sur la Loterie Royale de France, ou les 
Utrennes necessaires aux Actionnaires et Receveurs de la dite 
Loterie. Par M. Menut de St.-Mesmin. Paris, 1830. 12mo. 

This book contains all the drawings of the French lottery (two 
or three, each month) from 1758 to 1830. It is intended for 
those who thought they could predict the future drawings from 
the past : and various sets of sympathetic numbers are given to 
help them. The principle is, that anything which has not 
happened for a long time must be soon to come. At rouge et 
noir, for example, when the red has won five times running, 
sagacious gamblers stake on the black, for they think the turn 
which must come at last is nearer than it was. So it is : but 
observation would have shown that if a large number of those 
cases had been registered which show a run of five for the red, 
the next game would just as often have made the run into six 
as have turned in favour of the black. But the gambling 
reasoner is incorrigible : if he would but take to squaring the 
circle, what a load of misery would be saved. A writer of 1823, 
who appeared to be thoroughly acquainted with the gambling of 
Paris and London, says that the gamesters by profession are 
haunted by a secret foreboding of their future destruction, and 



PAKADOXES OF CHANCE. 169 

seem as if they said to the banker at the table, as the gladiators 
said to the emperor, Morituri te salutant. 

In the French lottery, five numbers out of ninety were drawn 
at a time. Any person, in any part of the country, might stake 
any sum upon any event he pleased, as that 27 should be drawn ; 
that 42 and 81 should be drawn ; that 42 and 81 should be 
drawn, and 42 first ; and so on up to a quine determine, if he 
chose, which is betting on five given numbers in a given order. 
Thus, in July, 1821, one of the drawings was 

8 46 16 64 13. 

A gambler had actually predicted the five numbers (but not 
their order), and won 131,350 francs on a trifling stake. M. 
Menut seems to insinuate that the hint what numbers to cnoose 
was given at his own office. Another won 20,852 francs on the 
quaterne 8, 16, 46, 64,. in this very drawing. These gains, of 
course, were widely advertised : of the multitudes who lost 
nothing was said. The enormous number of those who played 
is proved to all who have studied chances arithmetically by the 
numbers of simple quaternes which were gained : in 1 822, four- 
teen ; in 1823, six ; in 1824, sixteen; in 1825, nine, &c. 

The paradoxes of what is called chance, or hazard, might them- 
selves make a small volume. All the world understands that 
there is a long run, a general average ; but great part of the 
world is surprised that this general average should be computed 
and predicted. There are many remarkable cases of verification ; 
and one of them relates to the quadrature of the circle. I give 
some account of this and another. Throw a penny time after 
time until head arrives, which it will do before long : let this 
be called a set. Accordingly, H is the smallest set, TH the next 
smallest, then TTH, &c. For abbreviation, let a set in which 
seven tails occur before head turns up be T 7 H. In an immense 
number of trials of sets, about half will be H ; about a quarter 
TH; about an eighth, T 2 H. Buffon tried 2,048 sets; and 
several have followed him. It will tend to illustrate the prin- 
ciple if I give all the results ; namely, that many trials will 
with moral certainty show an approach and the greater the 
greater the number of trials to that average which sober reason- 
ing predicts. In the first column is the most likely number of 
the theory : the next column gives BufTon's result ; the three 
next are results obtained from trial by correspondents of mine. 
In each case the number of trials is 2,048. 



170 A BUDGET OF PAEADOXES. 



H 


1,024 . 


1,061 . 


1,048 . 1,017 . 


1,039 


TH . 


512 . 


494 . 


507 . 


547 . 


480 


T 2 H . 


256 . 


232 . 


248 . 


235 . 


267 


T'H . 


128 . 


137 . 


99' , 


118 . 


126 


T<H . 


64 . 


56 . 


71 . 


72 -. 


67 


T 5 H . 


32 . 


29 . 


38 . 


32 . 


33 


T 6 H . 


16 . 


. 25 . 


17 . 


30 . 


19 


T 7 H , 


8 . 


8 . 


9 . 


9 . 


10 


T 8 H . 


4 . 


6 . 


, 5 . 


3 . 


3 


T 9 H . 


2 . 




3 . 


2 . 


4 


T l H . 


1 . 




1 . 


1 




T n H 






. 


1 




T 12 H 






. 







T 13 H 


1 . 




1 . 







T u H 






. 







T 15 H 






1 . 


1 




&c. 















2,048 . 2,048 . 2,048 . 2,048 . 2,048 

In very many trials, then, we may depend upon something like 
the predicted average. Conversely, from many trials we may 
form a guess at what the average will be. Thus, in Buffon's 
experiment the 2,048 first throws of the sets gave head in 1,061 
cases : we have a right to infer that in the long run something 
like 1,061 out of 2,048 is the proportion of heads, even before 
we know the reasons for the equality of chance, which tell us that 
1,024 out of 2,048 is the real truth. I now come to the way in 
which such considerations have led to a mode in which mere 
pitch-and-toss has given a more accurate approach to the quadra- 
ture of the circle than has been reached by some of my para- 
doxers. What would my friend 1 in No. 14 have said to this? 
The method is as follows : Suppose a planked floor of the usual 
kind, with thin visible seams between the planks. Let there be 
a thin straight rod, or wire, not so long as the breadth of the 
plank. This rod, being tossed up at hazard, will either fall quite 
clear of the seams, or will lay across one seam. Now BufFon, 
and after him Laplace, proved the following : That in the long 
run the fraction of the whole number of trials in which a seam 
is intersected will be the fraction which twice the length of the 
rod is of the circumference of the circle having the breadth of a 
plank for its diameter. In 1855 Mr. Ambrose Smith, of Aber- 
deen, made 3,204 trials with a rod three-fifths of the distance 
between the planks: there were 1,213 clear intersections, and 
1 1 contacts on which it was difficult to decide. Divide these 

1 See p. 172. This article was a supplement to No. 14 in the Athen&um Budget. 



THE INTERMINABLE FRACTION TT. 171 

contacts equally, and we have 1,218^ to 3,204 for the ratio of 6 
to 5?r, presuming that the greatness of the number of trials gives 
something near to the final average, or result in the long run : 
this gives 7r=3'1553. If all the 11 contacts had been treated as 
intersections, the result would have been 77 = 3' 141 2, exceedingly 
near. A pupil of mine made 600 trials with a rod of the length 
between the seams, and got ?r=3'137. 

This method will hardly be believed until it has been re- 
peated so often that ' there never could have been any doubt 
about it.' 

The first experiment strongly illustrates a truth of the theory, 
well confirmed by practice : whatever can happen will happen if we 
make trials enough. Who would undertake to throw tail eight 
times running? Nevertheless, in the 8,192 sets tail 8 times 
running occurred 17 times ; 9 times running, 9 times ; 10 times 
running, twice; 11 times and 13 times, each once; and 15 times, 
twice.] 

1830. The celebrated interminable fraction 3-14159. . . , which 
the mathematician calls TT, is the ratio of the circumference to 
the diameter. But it is thousands of things besides. It is con- 
stantly turning up in mathematics : and if arithmetic and algebra 
had been studied without geometry, IT must have come in some- 
how, though at what stage or under what name must have 
depended upon the casualties of algebraical invention. This will 
readily be seen when it is stated that TT is nothing but four times 
the series 



ad infinitum. It would be wonderful if so simple a series had 
but one kind of occurrence. As it is, our trigonometry being 
founded on the circle, TT first appears as the ratio stated. If, for 
instance, a deep study of probable fluctuation from the average 
had preceded geometry, TT might have emerged as a number 
perfectly indispensable in such problems as What is the chance 
of the number of aces lying between a million + x and a million 
x, when six million of throws are made with a die ? I have not 
gone into any detail of all those cases in which the paradoxer 
finds out, by his unassisted acumen, that results of mathematical 
investigation cannot be : in fact, this discovery is only an accom- 
paniment, though a necessary one, of his paradoxical statement of 
that which must be. Logicians are beginning to see that the 
notion of horse is inseparably connected with that of non-horse : 
that the first without the second would be no notion at all. And 
it is clear that the positive affirmation of that -which contradicts 



172 A BUDGET OF PAEADOXES. 

mathematical demonstration cannot but be accompanied by a 
declaration, mostly overtly made, that demonstration is false. If 
the mathematician were interested in punishing this indiscretion, 
he could make his denier ridiculous by inventing asserted results 
which would completely take him in. 

More than thirty years ago I had a friend, now long gone, who 
was a mathematician, but not of the higher branches : he was, 
inter alia, thoroughly up in all that relates to mortality, life 
assurance, &c. One day, explaining to him how it should be 
ascertained what the chance is of the survivors of a large number 
of persons now alive lying between given limits of number at the 
end of a certain time, I came, of course, upon the introduction of 
TT, which I could only describe as the ratio of the circumference 
of a circle to its diameter. ' Oh, my dear friend ! that must be 
a delusion ; what can the circle have to do with the numbers 
alive at the end of a given time ? ' ' I cannot demonstrate it to 
you; but it is demonstrated.' 'Oh! stuff! I think you can 
prove anything with your differential calculus : figment, depend 
upon it.' I said no more ; but, a few days afterwards, I went to 
him and very gravely told him that I had discovered the law of 
human mortality in the Carlisle Table, of which he thought very 
highly. I told him that the law was involved in this circum- 
stance. Take the table of expectation of life, choose any age, 
take its expectation and make the nearest integer a new age, do 
the same with that, and so on ; begin at what age you like, you 
are sure to end at the place where the age past is equal, or most 
nearly equal, to the expectation to come. ' You don't mean that 
this always happens ? ' ' Try it.' He did try, again and again ; 
and found it as I said. ' This is, indeed, a curious thing ; this is 
a discovery.' I might have sent him about trumpeting the law 
of life : but I contented myself with informing him that the same 
thing would happen with any table whatsoever in which the first 
column goes up and the second goes down ; and that if a pro- 
ficient in the higher mathematics chose to palm a figment upon 
him, he could do without the circle : a corsaire, corsaire et demi, 
the French proverb says. 'Oh !' it was remarked, 'I see, this was 
Milne ! ' It was not Milne : I remember well showing the formula 
to him some time afterwards. He raised no difficulty about TT ; 
he knew the forms of Laplace's results, and he was much "in- 
terested. Besides, Milne never said stuff ! and figment ! And he 
would not have been taken in : he would have quietly tried it 
with the Northampton and all the other tables, and would have 
grot at the truth. 



EUCLID WITHOUT AXIOMS. 173 

The first book of Euclid's Elements. With alterations and 
familiar notes. Being an attempt to get rid of axioms alto- 
gether ; and to establish the theory of parallel lines, without 
the introduction of any principle not common to other parts of 
the elements. By a member of the University of Cambridge. 
Third edition. In usum serenissimje filiolae. London, 1830. 

The author was Lieut. -Col. (now General) Perronet Thompson, 
the author of the ' Catechism on the Corn Laws.' I reviewed the 
fourth edition which had the name of ' Geometry without 
Axioms,' 1833 in the quarterly Journal of Education for 
January, 1834. Col. Thompson, who then was a contributor to 
if not editor of the Westminster Review, replied in an article 
the authorship of which could not be mistaken. 

Some more attempts upon the problem, by the same author, 
will be found in the sequel. They are all of acute and legitimate 
speculation ; but they do not conquer the difficulty in the manner 
demanded by the conditions of the problem. The paradox of 
parallels does not contribute much to my pages : its cases are to 
be found for the most part in geometrical systems, or in notes to 
them. Most of them consist in the proposal of additional pos- 
tulates ; some are attempts to do without any new postulate. 
Gen. Perronet Thompson, whose paradoxes are always constructed 
on much study of previous writers, has collected in the work 
above-named, a budget of attempts, the heads of which are in the 
Penny and English Cyclopaedias, at ' Parallels.' He has given 
thirty instances, selected from what he had found. 

Lagrange, in one of the later years of his life, imagined that he 
had overcome the difficulty. He went so far as to write a paper, 
which he took with him to the Institute, and began to read it. 
But in the first paragraph something struck him which he had 
not observed : he muttered II faut que fy songe encore, and put 
the paper in his pocket. 



The following paragraph appeared in the Morning Post, 
May 4, 1831 : 

' We understand that although, owing to circumstances with which 
the public are uot concerned, Mr. Groulburn declined becoming a 
candidate for University honours, that his scientific attainments are 
far from inconsiderable. He is well known to be the author of an 
essay in the Philosophical Transactions on the accurate rectification of 
a circular arc, and of an investigation of the equation of a lunar 



174 A BUDGET OF PARADOXES. 

caustic a problem likely to become of great use in nautical as- 
tronomy.' 

This hoax which would probably have succeeded with any 
journal was palmed upon the Morning Post., which supported 
Mr. Goulburn, by some Cambridge wags who supported Mr. 
Lubbock, the other candidate for the University of Cambridge. 
Putting on the usual concealment, I may say that I always sus- 
pected Dr-nkw-t-r B-th-n- of having a share in the matter. The 
skill of the hoax lies in avoiding the words ' quadrature of the 
circle,' which all know, and speaking of ' the accurate rectification 
of a circular arc,' which all do not know for its synonyme. The 
Morning Post next day gave a reproof to hoaxers in general, 
without referring to any particular case. It must be added, 
that although there are caustics in mathematics, there is no 
lunar caustic. 

So far as Mr. Groulburn was concerned, the above was poetic 
justice. He was the minister who, in the old time, told a depu- 
tation from the Astronomical Society that the Government ' did 
not care twopence for all the science in the country.' There may 
be some still alive who remember this : I heard it from more than 
one of those who were present, and are now gone. Matters are 
much changed. I was thirty years in office at the Astronomical 
Society ; and, to my certain knowledge, every Government of that 
period, Whig and Tory, showed itself ready to help with influence 
when wanted, and with money whenever there was an answer for 
the House of Commons. The following correction subsequently 
appeared. Referring to the hoax about Mr. Groulburn, Messrs. C. 
H. and Thompson Cooper have corrected an error, by stating that 
the election which gave rise to the hoax was that in which Messrs. 
Groulburn and Yates Peel defeated Lord Palmerston and Mr. 
Cavendish. They add that Mr. Gunning, the well-known Esquire 
Bedell of the University, attributed the hoax to the late Eev. R. 
Sheepshanks, to whom, they state, are also attributed certain clever 
fictitious biographies of public men, as I understand it which 
were palmed upon the editor of the Cambridge Chronicle, who 
never suspected their genuineness to the day of his death. Being 
in most confidential intercourse with Mr. Sheepshaaks, both at the 
time and all the rest of his life (twenty-five years), and never 
having heard him allude to any such things which were not in 
his line, though he had satirical power of quite another kind I 
feel satisfied he had nothing to do with them. I may add that 
others, his nearest friends, and also members of his family, never 



SCIENTIFIC ELECTION SQUIB. 175 

heard him allude to these hoaxes as their author, and disbelieve 
his authorship as much as I do myself. I say this not as imputing 
any blame to the true author, such hoaxes being fair election 
jokes in all time, but merely to put the saddle off the wrong horse, 
and to give one more instance of the insecurity of imputed 
authorship. Had Mr. Sheepshanks ever told me that he had 
perpetrated the hoax, I should have had no hesitation in giving 
it to him. I consider all clever election squibs, free from bitter- 
ness and personal imputation, as giving the multitude good 
channels for the vent of feelings which but for them would cer- 
tainly find bad ones. 

[ But I now suspect that Mr. Babbage had some hand in the 
hoax. He gives it in his ' Passages, &c.' and is evidently writing 
from memory, for he gives the wrong year. But he has given the 
paragraph, though not accurately, yet with such a recollection of 
the points as brings suspicion of the authorship upon him, perhaps 
in conjunction with D. B. Both were on Cavendish's committee. 
Mr. Babbage adds, that ' late one evening a cab drove up in hot 
haste to the office of the Morning Post, delivered the copy as 
coming from Mr. Gmilburn's committee, and at the same time 
ordered fifty extra copies of the Post to be sent next morning to 
their committee-room. I think the man the only one I ever 
heard of who knew all about the cab and the extra copies must 
have known more.] 

Demonville. A Frenchman's Christian name is his own secret, 
unless there be two of the surname. M. Demonville is a very 
good instance of the difference between a French and English 
discoverer. In England there is a public to listen to discoveries 
in mathematical subjects made without mathematics : a public 
which will hear, and wonder, and think it possible that the pre- 
tensions of the discoverer have some foundation. The unnoticed 
man may possibly be right : and the old country-town reputation 
which I once heard of, attaching to a man who * had written a 
book about the signs of the zodiac which all the philosophers in 
London could not answer,' is fame as far as it goes. Accordingly, 
we have plenty of discoverers who, even in astronomy, pronounce 
the learned in error because of mathematics. In France, beyond 
the sphere of influence of the Academy of Sciences, there is no 
one to cast a thought upon the matter : all who take the least 
interest repose entire faith in the Institute. Hence the French 
discoverer turns all his thoughts to the Institute, and looks for 



176 A BUDGET OF PARADOXES. 

his only hearing in that quarter. He therefore throws no slur 
upon the means of knowledge, but would say, with M. Demon- 
ville ' A 1'egard de M. Poisson, j'envie loyalement la millieme 
partie de ses connaissances mathematiques, pour prouver mon 
systeme d'astronomie aux plus incredules.' This system is that 
the only bodies of our system are the earth, the sun, and the 
moon ; all the others being illusions, caused by reflexion of the 
sun and moon from the ice of the polar regions. In mathematics, 
addition and subtraction are for men ; multiplication and division, 
which are in truth creation and destruction, are prerogatives of 
Deity. But nothing multiplied by nothing is one. M. Demon- 
ville obtained an introduction to William the Fourth, who desired 
the opinion of the Eoyal Society upon his system : the answer 
was very brief. The King was quite right ; so was the Society : 
the fault lay with those who advised His Majesty on a matter 
they knew nothing about. The writings of M. Demonville in my 
possession are as follows. The dates which were only on covers 
torn off in binding were about 1831-34 : 

' Petit cours d'astronomie' followed by ' Sur 1'unite mathematique.' 
Principes de la physique de la creation implicitement admis dans la 
notice sur le tonnerre par M. Arago. Question de longitude sur 
mer. Vrai systeme du monde (pp. 92). Same title, four pages, small 
type. Same title, four pages, addressed to the British Association. 
Same title, four pages, addressed to M. Mathieu. Same title, four 
pages, on M. Bouvard's report. Resume de la physique de la crea- 
tion ; troisieme partie du vrai systeme du monde. 

The quadrature of the circle discovered, by Arthur Parsey, author 
of the 'art of miniature painting.' Submitted to the consider- 
ation of the Royal Society, on whose protection the author 
humbly throws himself. London, 1832, 8vo. 

Mr. .Parsey was an artist, who also made himself conspicuous 
by a new view of perspective. Seeing that the sides of a tower, 
for instance, would appear to meet in a point if the tower were 
high enough, he thought that these sides ought to slope to one 
another in the picture. On this theory he published a small 
work, of which I have not the title, with a Grecian temple in the 
frontispiece, stated, if I remember rightly, to be the first picture 
which had ever been drawn in true perspective. Of course the 
building looked very Egyptian, with its sloping sides. The 
answer to his notion is easy enough. What is called the picture 
is not the picture from which the mind takes its perception ; that 
picture is on the retina. The intermediate picture, as it may be 
called the human artist's work is itself seen perspectively. If 



PERSPECTIVE RITCHIE'S GEOMETRY. 177 

the tower were so high that the sides, though parallel, appeared 
to meet in a point, the picture must also be so high that the 
picture-sides, though parallel, would appear to meet in a point. 
I never saw this answer given, though I have seen and heard the 
remarks of artists on Mr. Parsey's work. I am inclined to think 
it is commonly supposed that the artist's picture is the represen- 
tation which comes before the mind : this is not true ; we might 
as well say the same of the object itself. In July 1831, reading 
an article on squaring the circle, and finding that there was a 
difficulty, he set to work, got a light denied to all the mathe- 
maticians in some would say through a crack, and advertised 
in the Times that he had done the trick. He then prepared this 
work, in which, those who read it will see how, he showed that 

3*14159 should be 3-0625. He might have found out his 

error by stepping a draughtsman's circle with the compasses. 

Perspective has not had many paradoxes. The only other one 
I remember is that of a writer on perspective, whose -name I 
forget, and whose four pages I do not possess. He circulated 
remarks on my notes on the subject, published in the Athencewm*, 
in which he denies that the stereographic projection is' a case of 
perspective, the reason being that the whole hemisphere makes 
too large a picture for the eye conveniently to grasp at once. 
That is to say, it is no perspective because there is too much 
perspective. 

Principles of Geometry familiarly illustrated. By the Rev. W. 

Ritchie, LL.D. London, 1833, 12mo. 
A new Exposition of the system of Euclid's Elements, being an 

attempt to establish his work on a different basis. By Alfred 

Day, LL.D. London, 1839, 12mo. 

These works belong to a small class which have the peculiarity 
of insisting that in the general propositions of geometry a propo- 
sition gives its converse : that 'Every B is A' follows from 'Every 
A is B.' Dr. Ritchie says, ' If it be proved that the equality of 
two of the angles of a triangle depends essentially upon the 
equality of the opposite sides, it follows that the equality of the 
opposite sides depends essentially on the equality of the angles.' 
Dr. Day puts it as follows : 

' That the converses of Euclid, so called, where no particular limit- 
ation is specified or implied in the leading proposition, more than in 
the converse, must be necessarily true ; for as by the nature of the 
reasoning the leading proposition must be universally true, should the 
converse not be so, it cannot be so universally, but has uu lea^t all tho 

N 



178 A BUDGET OF PAKADOXES. 

exceptions conveyed in the leading proposition, and the case is therefore 
unadapted to geometric reasoning ; or, what is the same thing, by the 
very nature of geometric reasoning, the particular exceptions to the 
extended converse must be identical with some one or other of the 
cases under the universal affirmative proposition with which we set 
forth, which is absurd.' 

On this I cannot help transferring to my reader the words of the 
Pacha when he orders the bastinado, May it do you good ! A 
rational study of logic is much wanted to show many mathema- 
ticians, of all degrees of proficiency, that there is nothing in the 
reasoning of mathematics which differs from other reasoning. 
Dr. Day repeated his argument in ' A Treatise on Proportion/ 
London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. 
He published, in 1818, a work on arithmetic, with rational ex- 
planations. This was too early for such an improvement, and 
nearly the whole of this excellent work was sold as waste paper. 
His elementary introduction to the Differential Calculus was 
drawn up while he was learning the subject late in life. Books 
of this sort are often very effective on points of difficulty. 



Letter to the Royal Astronomical Society in refutation of Mistaken 
Notions held in common, by the Society, and by all the New- 
tonian philosophers. By Capt. Forman, R.N. Shepton- Mallet, 
1833, 8vo. 

Capt. Forman wrote against the whole system of gravitation, 
and got no notice. He then wrote to Lord Brougham, Sir J. 
Herschel, and others I suppose, desiring them to procure notice 
of his books in the reviews : this not being acceded to, he wrote 
(in print) to Lord John Russell to complain of their ' dishonest ' 
conduct. He then sent a manuscript letter to the Astronomical 
Society, inviting controversy : he was answered by a recommen- 
dation to study dynamics. The above pamphlet was the con- 
sequence, in which, calling the Council of the Society ' craven 
dunghill cocks,' he set them right about their doctrines. From 
all I can learn, the life of a worthy man and a creditable officer 
was completely embittered by his want of power to see that no 
person is bound in reason to enter into controversy with every 
one who chooses to invite him to the field. This mistake is not 
peculiar to philosophers, whether of orthodoxy or paradoxy; a 
majority of educated persons imply, by their modes of proceeding, 
that no one has a right to any opinion which he is not prepared 
to defend against all comers. 



INSPIRED PARADOXERS. 179 



David and Goliath, or an attempt to prove that the Newtonian 
system of Astronomy is directly opposed to the Scriptures. 
By Wm. Lauder, Sen., Mere, Wilts. Mere, 1833, 12mo. 

Newton is Goliath; Mr. Lauder is David. David took five 
pebbles ; Mr. Lauder takes five arguments. He expects oppo- 
sition ; for Paul and Jesus both met with it. 

Mr. Lauder, in his comparison, seems to put himself in the 
divinely inspired class. This would not be a fair inference in 
every case ; but we know not what to think when we remember 
that a tolerable number of cyclometers have attributed their 
knowledge to direct revelation. The works of this class are very 
scarce ; I can only mention one or two from Montucla. Alphonso 
Cano de Molina, in the last century, upset all Euclid, ani squared 
the circle upon the ruins; he found a follower, Janson, who 
translated him from Spanish into Latin. He declared that he 
believed in Euclid, until God, who humbles the proud, taught 
him better. One Paul Yvon, called from his estate de la Leu, 
a merchant at Eochelle, supported by his book-keeper, M. Pujos, 
and a Scotchman, John Dunbar, solved the problem by divine 
grace, in a manner which was to convert all Jews, Infidels, &c. 
There seem to have been editions of his work in 1619 and 1628, 
and a controversial 'Examen' in 1630, by Eobert Sara. There 
was a noted discussion, in which Mydorge, Hardy, and others 
took part against de la Leu. I cannot find this name either in 
Lipenius or Murhard, and I should not have known the dates if 
it had not been for one of the keenest bibliographers of any time, 
my friend Prince Balthasar Boncompagni, who is trying to find 
copies of the works, and has managed to find copies of the titles. 
In 1750, Henry Sullamar, an Englishman, squared the circle by 
the number of the Beast : he published a pamphlet every two or 
three years ; but I cannot find any mention of him in English 
works. In France, in 1753, M. de Causans, of the Guards, cut a 
circular piece of turf, squared it, and deduced original sin and 
the Trinity. He found out that the circle was equal to the 
square in which it is inscribed ; and he offered a reward for 
detection of any error, and actually deposited 10,000 francs as 
earnest of 300,000. But the courts would not allow any one to 
recover. 

1834. In this year Sir John Herschel set up his telescope at 
Feldhausen, Cape of Good Hope. He did much for astronomy, 

N 2 



180 A BUDGET OF PARADOXES. 

but not much for the Budget of Paradoxes. He gives me, how- 
ever, the following story. He showed a resident a remarkable 
blood-red star, and some little time after he heard of a sermon 
preached in those parts in which it was asserted that the state- 
ments of the Bible must be true, for that Sir J. H. had seen in his 
telescope ' the very place where wicked people go.' 

But red is not always the colour. Sir J. Herschel has in his 
possession a letter written to his father, Sir W. H., dated April 
3, 1787, and signed ' Eliza Cumyns,' begging to know if any of 
the stars be indigo in colour, ' because, if there be, I think it 
may be deemed a strong conjectural illustration of the expression, 
so often used by our Saviour in the Holy Gospels, that " the 
disobedient shall be cast into outer darkness ; " for as the Almighty 
Being can doubtless confine any of his creatures, whether cor- 
poreal or spiritual, to what part of his creation He pleases, if 
therefore any of the stars (which are beyond all doubt so many 
suns to other systems) be of so dark a colour as that above 
mentioned, they may be calculated to give the most insufferable 
heat to those dolorous systems dependent upon them (and to 
reprobate spirits placed there), without one ray of cheerful light ; 
and may therefore be the scenes of future punishments.' This 
letter is addressed to Dr. Heirschel at Slow. Some have placed 
the infernal regions inside the earth, but others have filled this 
internal cavity for cavity they will have with refulgent light, 
and made it the abode of the blessed. It is difficult to build 
without knowing the number to be provided for. A friend of 
mine heard the following (part) dialogue between two strong 
Scotch Calvinists : ' Noo ! hoo manny d'ye thank there are of 
the alact on the arth at this moment ? Eh I mabbee a doozen 
Hoot ! mon ! nae so mony as thot 1 ' 

1834. From 1769 to 1834 the Nautical Almanac was pub- 
lished on a plan which gradually fell behind what was wanted. 
In 1834 the new series began, under a new superintendent (Lieut. 
"W. S. Stratford). There had been a long scientific controversy, 
which would not be generally intelligible. To set some of the 
points before the reader, I reprint a cutting which I have by me. 
It is from the Nautical Magazine, but I did hear that some had 
an idea that it was in the Nautical Almanac itself. It certainly 
was not, and I feel satisfied the Lords of the Admiralty would 
not have permitted the insertion ; they are never in advance of 
their age. The Almanac for 1834 was published in July 1833. 



COUNCIL OF THE SOLAR SYSTEM. 181 



THE NEW NAUTICAL ALMANAC. Extract from the 'Primum Mobile,' 
and ' Milky Way Gazette.' Communicated by AEROLITE. 

A meeting of the different bodies composing the Solar System 
was this day held at the Dragon's Tail, for the purpose of taking 
into consideration the alterations and amendments introduced 
into the New Nautical Almanac. The honourable luminaries 
had been individually summoned by fast-sailing comets, and 
there was a remarkably full attendance. Among the visitors we 
observed several nebulas, and almost all the stars whose proper 
motions would admit of their being present. 

The SUN was unanimously called to the focus. The small 
planets took the oaths, and their places, after a short discussion, 
in which it was decided that the places should be those of the 
Almanac itself, with leave reserved to move for corrections. 

Petitions were presented from a and 8 Ursae Minoris, com- 
plaining of being put on daily duty, and praying for an increase of 
salary. Laid on the plane of the ecliptic. 

The trustees of the eccentricity 1 and inclination funds re- 
ported a balance of '00001 in the former, and a deficit of 0"'009 
in the latter. This announcement caused considerable surprise, 
and a committee was moved for, to ascertain which of the bodies 
had more or less than his share. After some discussion, in 
which the small planets offered to consent to a reduction, if 
necessary, the motion was carried. 

The FOCAL BODY then rose to address the meeting. He re- 
marked that the subject on which they were assembled was one 
of great importance to the routes and revolutions of the heavenly 
bodies. For himself, though a private arrangement between two 
of his honourable neighbours (here he looked hard at the Earth 
and Venus) had prevented his hitherto paying that close atten- 
tion to the predictions of the Nautical Almanac which he de- 
clared he always had wished to do ; yet he felt consoled by 
knowing that the conductors of that work had every disposition 
to take his peculiar circumstances into consideration. He de- 
clared that he had never passed the wires of a transit without 
deeply feeling his inability to adapt himself to the present state 
of his theory ; a feeling which he was afraid had sometimes caused 
a slight tremor in his limb. Before he sat down, he expressed a 
hope that honourable luminaries would refrain as much as 
possible from eclipsing each other, or causing mutual perturba- 

1 See Sir J. Herschel's Astronomy, p. 369. 



182 A BUDGET OF PARADOXES. 

tions. Indeed, he should be very sorry to see any interruption of 
the harmony of the spheres. (Applause.) 

The several articles of the New Nautical Almanac were then 
read over without any comment ; only we observed that Saturn 
shook Ms ring at every novelty, and Jupiter gave his belt a 
hitch, and winked at the satellites at page 21 of each month. 

The MOON rose, to propose a resolution. No one, he said, 
would be surprised at his bringing this matter forward in the 
way he did, when it was considered in how complete and satis- 
factory a manner his motions were now represented. He must 
own he had trembled when the Lords of the Admiralty dissolved 
the Board of Longitude, but his tranquillity was more than re- 
established by the adoption of the new system. He did not 
know but that any little assistance he could give in Nautical 
Astronomy was becoming of less and less value every day, owing 
to the improvement of chronometers. But there was one thing, 
of which nothing could deprive him he meant the regulation of 
the tides. And, perhaps, when his attention was not occupied by 
more than the latter, he should be able to introduce a little 
more regularity into the phenomena. (Here the honourable 
luminary gave a sort of modest libration, which convulsed the 
meeting with laughter.) They might laugh at his natural 
infirmity if they pleased, but he could assure them it arose only 
from the necessity he was under, when young, of watching the 
motions of his worthy primary. He then moved a resolution 
highly laudatory of the alterations which appeared in the New 
Nautical Almanac. 

The EARTH rose, to second the motion. His honourable satel- 
lite had fully expressed his opinions on the subject. He joined 
his honourable friend in the focus in wishing to pay every 
attention to the Nautical Almanac, but, really, when so impor- 
tant an alteration had taken place in his magnetic pole l (hear) 
and there might, for aught he knew, be a successful attempt to 
reach his pole of rotation, he thought he could not answer for 
the preservation of the precession in its present state. (Here 
the hon. luminary, scratching his side, exclaimed, as he sat down, 
4 More steam-boats confound 'em !') 

An honourable satellite (whose name we could not learn) pro- 
posed that the resolution should be immediately despatched, cor- 
rected for refraction, when he was called to order by the Focal 
Body, who reminded him that it was contrary to the moving 

1 Captain Ross had just stuck a bit of brass there. 



COUNCIL OF THE SOLAR SYSTEM. 183 

orders of the system to take cognizance of what passed inside the 
atmosphere of any planet. 

SATURN and PALLAS rose together. (Cries of ' New member ! ' 
and the former gave way.) The latter, in a long and eloquent 
speech, praised the liberality with which he and his colleagues had 
at length been relieved from astronomical disqualifications. He 
thought that it was contrary to the spirit of the laws of gravita- 
tion to exclude any planet from office on account of the eccen- 
tricity or inclination of his orbit. Honourable luminaries need 
not talk of the want of convergency of his series. What had 
they to do with any private arrangements between him and the 
general equations of the system ? (Murmurs from the opposi- 
tion.) So long as he obeyed the laws of motion, to which he had 
that day taken a solemn oath, he would ask, were old planets, 
which were now so well known that nobody trusted them, 
to .... 

The FOCAL BODY said he was sorry to break the continuity of 
the proceedings, but he thought that remarks upon character, 
with a negative sign, would introduce differences of too high an 
order. The honourable luminary must eliminate the expression 
which he had brought out, in finite terms, and use smaller in- 
equalities in future. (Hear, hear.) 

PALLAS explained, that he was far from meaning to reflect upon 
the orbital character of any planet present. He only meant to 
protest against being judged by any laws but those of gravitation, 
and the differential calculus: he thought it most unjust that 
astronomers should prevent the small planets from being ob- 
served, and then reproach them with the imperfections of the 
tables, which were the result of their own narrow-minded policy. 
(Cheers. ) 

SATURN thought that, as an old planet, he had not been 
treated with due respect. (Hear, from his satellites.) He had 
long foretold the wreck of the system from the friends of inno- 
vation. Why, he might ask, were his satellites to be excluded, 
when small planets, trumpery comets, which could not keep their 
mean distances (cries of oh ! oh !), double stars, with graphical 
approximations, and such obscure riff-raff of the heavens (great 
uproar) found room enough. So help him Arithmetic, nothing 
could come of it, but a stoppage of all revolution. His hon. 
friend in the focus might smile, for he would be a gainer by such 
an event ; but as for him (Saturn), he had something to lose, 
and hon. luminaries well knew that, whatever they might think 
under an atmosphere, above it continual revolution was the only 



184 A BUDGET OF PARADOXES. 

way of preventing perpetual anarchy. As to the hon. luminary 
who had risen before him, he was not surprised at his remarks, 
for he had invariably observed that he and bis colleagues allowed 
themselves too much latitude. The stability of the system re- 
quired that they should be brought down, and he, for one, would 
exert all his powers of attraction to accomplish that end. If 
other bodies would cordially unite with him, particularly his 
noble friend next him, than whom no luminary possessed greater 
weight 

JUPITER rose to order. He conceived his noble friend had no 
right to allude to him in that manner, and was much surprised at 
his proposal, considering the matters which remained in dispute 
between them. In the present state of affairs, he would take 
care never to be in conjunction with his hon. neighbour one 
moment longer than he could help. (Cries of ' Order, order, no 
long inequalities,' during which he sat down.) 

SATURN proceeded to say, that he did not know till then that a 
planet with a ring could affront one who had only a belt, by pro- 
posing mutual co-operation. He would now come to the subject 
under discussion. He should think meanly of his hon. col- 
leagues if they consented to bestow their approbation upon a 
mere astronomical production. Had they forgotten that they 
once were considered the arbiters of fate, and the prognosticators 
of man's destiny ? What had lost them that proud position ? 
Was it not the infernal march of intellect, which, after having 
turned the earth topsy-turvy, was now disturbing the very 
universe. For himself (others might do as they pleased), but he 
stuck to the venerable Partridge, and the Stationers' Company, 
and trusted that they would outlive infidels and anarchists, whether 
of Astronomical or Diffusion of Knowledge Societies. (Cries of 
oh! oh!) 

MARS said he had been told, for he must confess he had not 
seen the work, that the places of the planets were given for 
Sundays. This, he must be allowed to say, was an indecorum 
he had not expected ; and he was convinced the Lords of the 
Admiralty had given no orders to that effect. He hoped this 
point would be considered in the measure which had been intro- 
duced in another place, and that some one would move that the 
prohibition against travelling on Sundays extend to the heavenly 
as well as earthly bodies. 

Several of the stars here declared, that they had been much 
annoyed by being observed on Sunday evenings, during the hours 
of divine service. 



COUNCIL OF THE SOLAE SYSTEM. 185 

The room was then cleared for a division, but we are unable to 
state what took place. Several comets-at-arms were sent for, and 
we heard rumours of a personal collision having taken place 
between two luminaries in opposition. We were afterwards told, 
that the resolution was carried by a majority, and the luminaries 
elongated at 2 h. 15 m. 33,41 s. sidereal time. 



* * 
* 



It is reported, but we hope without foundation, that 
Saturn, and several other discontented planets, have accepted an 
invitation from Sirius to join his system, on the most liberal 
appointments. We believe the report to have originated in 
nothing more than the discovery of the annual parallax of Sirius 
from the orbit of Saturn ; but we may safely assure our readers 
that no steps have as yet been taken to open any communica- 
tion. 

We are also happy to state, that there is no truth in the 
rumour of the laws of gravitation being about to be repealed. 
We have traced this report, and find it originated with a gentle- 
man living near Bath (Captain Forman, E.N.), whose name we 
forbear to mention. 

A great excitement has been observed among the nebulae, 
visible to the earth's southern hemisphere, particularly among 
those which have not yet been discovered from thence. We are 
at a loss to conjecture the cause, but we shall not fail to report 
to our readers the news of any movement which may take place. 
(Sir J. Herschel's visit. He could just see this before he went 
out.) 

A Treatise on the Divine System of the Universe, by Captain 
Woodley, B.N., and as demonstrated by his Universal Time- 
piece, and universal method of determining a ship's longitude 
by the apparent true place of the moon ; with an introduction 
refuting the solar system of Copernicus, the Newtonian philo- 
sophy, and mathematics. 1834. 8vo. 

Description of the Universal Time-piece. (4 pp. 12mo.) 

I think this divine system was published several years before, 
and was republished with an introduction in 1834. Capt. 
Woodley was very sure that the earth does not move : he pointed 
out to me, in a conversation I had with him, something I forget 
what in the motion of the Great Bear, visible to any eye, which 
could not possibly be if the earth moved. He was exceedingly 
ignorant, as the following quotation from his account of the usual 
opinion will show : 



186 A BUDGET OF PARADOXES. 

The north pole of the Earth's axis deserts, they say, the north star 
or pole of the Heavens, at the rate of 1 in 71| years . . . The fact is, 
nothing can be more certain than that the Stars have not changed 
their latitudes or decimations one degree in the last 71 f years. 

This is a strong specimen of a class of men by whom all ac- 
cessible persons who have made any name in science are hunted. 
It is a pity that they cannot be admitted into scientific societies, 
and allowed fairly to state their cases, and stand quiet cross- 
examination, being kept in their answers very close to the 
questions, and the answers written down. I am perfectly satisfied 
that if one meeting in the year were devoted to the hearing of 
those who chose to come forward on such conditions, much good 
would be done. But I strongly suspect few would come forward 
at first, and none in a little while : and I have had some ex- 
perience of the method I recommend, privately tried. Capt. 
Woodley was proposed, a little after 1834, as a Fellow of the 
Astronomical Society ; and, not caring whether he moved the sun 
or the earth, or both I could not have stood neither I signed 
the proposal. I always had a sneaking kindness for paradoxers, 
such a one, perhaps, as Petit Andre had for his lambs, as he called 
them. There was so little feeling against his opinions, that he 
only failed by a fraction of a ball. Had I myself voted, he would 
have been elected ; but being engaged in conversation, and not 
having heard the slightest objection to him, I did not think it 
worth while to cross the room for the purpose. I regretted this 
at the time, but had I known how ignorant he was I should not 
have supported him. Probably those who voted against him 
knew more of his books than I then did. 

I remember no other instance of exclusion from a scientific 
society on the ground of opinion, eves, if this be one ; of which it 
may be that ignorance had more to do with it than paradoxy. 
Mr. Frend, a strong anti-Newtonian, was a Fellow of the Astro- 
nomical Society, and for some years in the Council. Lieut. 
Kerigan was elected to the Eoyal Society at a time when his 
proposers must have known that his immediate object was to put 
F.E.S. on the title-page of a work against the tides. To give all 
I know, I may add that the editor of some very ignorant bombast 
about the ' forehead of the solar sky, : who did not know the 
difference between Bailly and Baily, received hints which induced 
him to withdraw his proposal for election into the Astronomical 
Society. But this was an act of kindness ; for if he had seen Mr. 
Baily in the chair, with his head on, he might have been political 
historian enough to faint away. 



FRANCIS BAILY FLAMSTEED. 187 



De la formation des Corps. Par Paul Laurent. Nancy, 1834, 8vo. 

Atoms, and ether, and ovules or eggs, which are planets, and 
their eggs, which are satellites. These speculators can create 
worlds, in which they cannot be refuted ; but none of them dare 
attack the problem of a grain of wheat, and its passage from a 
seed to a plant, bearing scores of seeds like what it was itself. 

An account of the Rev. John Flamsteed, the First Astronomer- 
Royal ... By Francis Baily, Esq. London, 1835, 4to. Supple- 
ment, London, 1837, 4to. 

My friend Francis Baily was a paradoxer : he brought forward 
things counter to universal opinion. That Newton was impeccable 
in every point was the national creed ; and failings of temper and 
conduct would have been utterly disbelieved, if the paradox had 
not come supported by very unusual evidence. Anybody who 
impeached Newton on existing evidence might as well have been 
squaring the circle, for any attention he would have got. About 
this book I will tell a story. It was published by the Admiralty 
for distribution ; and the distribution was entrusted to Mr. Baily. 
On the eve of its appearance, rumours of its extraordinary reve- 
lations got about, and persons of influence applied to the Admiralty 
for copies. The Lords were in a difficulty : but on looking at 
the list they saw names, as they thought, which were so obscure 
that they had a right to assume Mr. Baily had included persons 
who had no claim to such a compliment as presentation from the 
Admiralty. The Secretary requested Mr. Baily to call upon him. 
'Mr. Baily, my Lords are inclined to think that some of the 
persons in this list are perhaps not of that note which would 
justify their Lordships in presenting this work.' ' To whom does 
your observation apply, Mr. Secretary ? ' ' Well, now, let us 
examine the list ; let me see ; now, now, now, come I here's 
Gauss who's Gauss ? ' ' Gauss, Mr. Secretary, is the oldest 
mathematician now living, and is generally thought to be the 
greatest.' ' 0-o-oh ! Well, Mr. Baily, we will see about it, and I 
will write you a letter.' The letter expressed their Lordships' 
perfect satisfaction with the list. 

There was a controversy about the revelations made in this 
work ; but as the eccentric anomalies took no part in it, there is 
nothing for my purpose. The following valentine from Mrs. 
Flamsteed, which I found among Baily's papers, illustrates some 
of the points : 



188 A BUDGET OF PAEADOXES. 



'3 Astronomers' Row, Paradise : February 14, 1836. 

* Dear Sir, I suppose you hardly expected to receive a letter from 
me, dated from this place ; but the truth is, a gentleman from our 
street was appointed guardian angel to the American Treaty, in which 
there is some astronomical question about boundaries. He has got 
leave to go back to fetch some instruments which he left behind, and 
I take this opportunity of making your acquaintance. That America 
has become a wonderful place since I was down among you ; you have 
no idea how grand the fire at New York looked up here. Poor dear 
Mr. Flamsteed does not know I am writing a letter to a gentleman on 
Valentine's day ; he is walked out with Sir Isaac Newton (they are 
pretty good friends now, though they do squabble a little sometimes) 
and Sir William Herschel, to see a new nebula. Sir Isaac says he 
can't make out at all how it is managed ; and I am sure I cannot help 
him. I never bothered my head about those things down below, and 
I don't intend to begin here. 

I have just received the news of your having written a book about 
my poor dear man. It's a chance that I heard it at all ; for the truth 
is, the scientific gentlemen are somehow or other become so wicked, 
and go so little to church, that very few of them are considered fit 
company for this place. If it had not been for Dr. Brinkley, who 
came here of course, I should not have heard about it. He seems a 
nice man, but is not yet used to our ways. As to Mr. Halley, he is of 
course not here ; which is lucky for him, for Mr. Flamsteed swore the 
moment he caught him in a place where there are no magistrates, he 
would make a sacrifice of him to heavenly truth. It was very generous 
in Mr. F. not appearing against Sir Isaac when he came up, for I am 
told that if he had, Sir Isaac would not have been allowed to come in 
at all. I should have been sorry for that, for he is a companionable 
man enough, only holds his head rather higher than he should do. I 
met him the other pay walking with Mr. Whiston, and disputing about 
the deluge. " Well, Mrs. Flamsteed," says he, " does old Poke-the- 
Stars understand gravitation yet ? " Now you must know'that is rather 
a sore point with poor dear Mr. Flamsteed. He says that Sir Isaac is 
as crochetty about the moon as ever ; and as to what some people say 
about what has been done since his time, he says he should like to see 
somebody who knows something about it of himself. For it is very 
singular that none of the people who have carried on Sir Isaac's notions 
have been allowed to come here. 

I hope you have not forgotten to tell how badly Sir Isaac used 
Mr. Flamsteed about that book. I have never quite forgiven him ; as 
for Mr. Flamsteed, he says that as long as he does not come for ob- 
servations, he does not care about it, and that he will never trust him 
with any papers again as long as he lives. I shall never forget what 
a rage he came home in when Sir Isaac had called him a puppy. He 
struck the stairs all the way up with his crutch, and said puppy at 



MRS. FLAMSTE ED'S VALENTINE. 189 

every step, and all the evening, as soon as ever a star appeared in the 
telescope, he called it puppy. I could not think what was the matter, 
and when I asked, he only called me puppy. 

I shall be very glad to see you if you come our way, Pray keep up 
some appearances, and go to church a little. St. Peter is always 
uncommonly civil to astronomers, and indeed to all scientific persons, 
and never bothers them with many questions. If they can make any- 
thing out of a case, he is sure to let them in. Indeed, he says, it is 
perfectly out of the question expecting a mathematician to be as 
religious as an apostle, but that it is as much as his place is worth to 
let in the greater number of those who come. So try if yon cannot 
manage it, for I am very curious to know whether you found all the 
letters. I remain, dear sir, your faithful servant, 

MARGARET FLAMSTEED. 

Francis Baily, Esq. 

P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding 
cockhorse upon the nebula, and poring over it as if it were a book. 
He has brought in his old acquaintance Ozanam, who says that it was 
always his maxim on earth, that " il appartient aux docteurs de 
Sorbonne de disputer, au Pape de prononcer, et au mathematicien 
d'aller en Paradis en ligne perpendiculaire." ' 

The Secretary of the Admiralty was completely extinguished. 
I can recall but two instances of demolition as complete, though 
no doubt there are many others. The first is in 

Simon Stevin and M. Dumortier. Nieuport, 1845, 12mo. 

M. Dumortier was a member of the Academy of Brussels : there 
was a discussion, I believe, about a national Pantheon for Bel- 
gium. The name of Stevinus suggested itself as naturally as 
that of Newton to an Englishman ; probably no Belgian is better 
known to foreigners as illustrious in science. Stevinus is great 
in the Mecanique Analytique of Lagrange ; Stevinus is great in 
the Tristram, Shandy of Sterne. M. Dumortier, who believed 
that not one Belgian in a thousand knew Stevinus, and who 
confesses with ironical shame that he was not the odd man, 
protested against placing the statue of an obscure man in the 
Pantheon, to give foreigners the notion that Belgium could show 
nothing greater. Tbe work above named is a slashing retort : 
any one who knows the history of science ever so little may 
imagine what a dressing was given, by mere extract from foreign 
writers. The tract is a letter signed J. du Fan, but this is a 
pseudonym of Mr. Van de Weyer. The Academician says 
Stevinus was a man who was not without merit for the time at 



190 A BUDGET OF PARADOXES. 

which he lived : Sir ! is the answer, he was as much before his 
own time as you are behind yours. How came a man who 
had never heard of Stevinus to be a member of the Brussels 
Academy ? 

The second story was told me by Mr. Crabb Eobinson, who was 
long connected with the Times, and intimately acquainted with 
Mr. W***. When W*** was an undergraduate at Cambridge, 
taking a walk, he came to a stile, on which sat a bumpkin who 
did not make way for him : the gown in that day looked down 
on the town. ' Why do you not make way for a gentleman ? ' 
' Eh ? ' ' Yes, why do you not move ? You deserve a good 
hiding, and you shall get it if you don't take care ? ' The 
bumpkin raised his muscular figure on its feet, patted his 
menacer on the head, and said, very quietly, 'Young man ! I'm 
Cribb.' W*** seized the great pugilist's hand, and shook it 
warmly, got him to his own rooms in college, collected some 
friends, and had a symposium which lasted until the large end of 
the small hours. 

God's Creation of the Universe as it is, in support of the Scriptures. 
By Mr. Finleyson. Sixth Edition, 1835, 8vo. 

This writer, by his own account, succeeded in delivering the 
famous Lieut. Richard Brothers from the lunatic asylum, and 
tending him, not as a keeper but as a disciple, till he died. 
Brothers was, by his own account, the nephew of the Almighty, 
and Finleyson ought to have been the nephew of Brothers. For 
Napoleon came to him in a vision, with a broken sword and an 
arrow in his side, beseeching help: Finleyson pulled out the 
arrow, but refused to give a new sword ; whereby poor Napoleon, 
though he got off with life, lost the battle of Waterloo. This 
story was written to the Duke of Wellington, ending with ' I 
pulled out the arrow, but left the broken sword. Your Grace 
can supply the rest, and what followed is amply recorded in 
history.' The book contains a long account of applications to 
Government to do three things : to pay 2,000. for care taken of 
Brothers, to pay 10,000. for discovery of the longitude, and to 
prohibit the teaching of the Newtonian system, which makes God 
a liar. The successive administrations were threatened that they 
would have to turn out if they refused, which, it is remarked, 
came to pass in every case. I have heard of a joke of Lord 
Macaulay, that the House of Commons must be the Beast of the 
Revelations, since 658 members, with the officers necessary for 
the action of the House, make 666. Macaulay read most things, 



RICHARD BROTHERS, PROPHET AND POET. 101 

and the greater part of the rest : so that he might be suspected 
of having appropriated as a joke one of Finleyson's serious points 
'I wrote Earl Grey upon the 13th of July, 1831, informing 
him that his Reform Bill could not be carried, as it reduced the 
members below the present amount of 658, which, with the 
eight principal clerks or officers of the House, make the number 
666.' But a witness has informed me that Macaulay's joke was 
made in his hearing a great many years before the Reform Bill 
was proposed ; in fact, when both were students at Cambridge. 
Earl Grey was, according to Finleyson, a descendant of Uriah 
the Hittite. For a specimen of Lieut. Brothers, this book would 
be worth picking up. Perhaps a specimen of the Lieutenant's 
poetry may be acceptable : Brothers loquitur, remember : 

Jerusalem ! Jerusalem ! shall be built again ! 

More rich, more grand than ever ; 
And through it shall Jordan flow ! (!) 

My people's favourite river. 
There I'll erect a splendid throne, 

And build on the wasted place ; 
To fulfil my ancient covenant 

To King David and his race. 
****** 

Euphrates' stream shall flow with ships, 

And also my wedded Nile ; 
And on my coast shall cities rise, 

Each one distant but a mile. 

****** 

My friends the Russians on the north 

With Persees and Arabs round, 
Do show the limits of my land, 

Here ! Here ! then I mark the ground. 

Among the paradoxers are some of the theologians who in 
their own organs of the press venture to criticise science. These 
may hold their ground when they confine themselves to the 
geology of long past periods and to general cosmogony : for it is 
the tug of Greek against Greek ; and both sides deal much in 
what is grand when called hypothesis, petty when called supposi- 
tion. And very often they are not conspicuous when they 
venture upon things within knowledge ; wrong, but not quite 
wrong enough for a Budget of Paradoxes. One case, however, 
is destined to live, as an instance of a school which finds writers, 
editors, and readers. The double stars have been seen from the 
seventeenth century, and diligently observed by many from the 



192 A BUDGET OF PAEADOXES. 

time of Wm. Herschel, who first devoted continuous attention to 
them. The year 1836 was that of a remarkable triumph of 
astronomical prediction. The theory of gravitation had been 
applied to the motion of binary stars about each other, in elliptic 
orbits, and in that year the two stars of 7 Virginis, as had been 
predicted should happen within a few years of that time for 
years are small quantities in such long revolutions the two 
stars came to their nearest : in fact, they appeared to be one as 
much with the telescope as without it. This remarkable turn- 
ing-point of the history of a long and widely-known branch of 
astronomy was followed by an article in the Church of England 
Quarterly Review for April 1837, written against the Useful 
Knowledge Society. The notion that there are any such things 
as double stars is (p. 460) implied to be imposture or delusion, 
as in the following extract. I suspect that I myself am the 
Sidrophel, and that my companion to the maps of the stars, 
written for the Society and published in 1 836, is the work to 
which the writer refers : 

We have forgotten the name of that Sidrophel who lately discovered 
that the fixed stars were not single stars, but appear in the heavens, 
like soles at Billingsgate, in pairs ; while a second astronomer, under 
the influence of that competition in trade which the political economists 
tell us is so advantageous to the public, professes to show us, through 
his superior telescope, that the apparently single stars are really three. 
Before such wondrous mandarins of science, how continually must 
homunculi like ourselves keep in the background, lest we come between 
the wind and their nobility. 

If the homunculus who wrote this be still above ground, how 
devoutly must he hope he may be able to keep in the back- 
ground ! But the chief blame falls on the editor. The title of 
the article is 

The new school of superficial pantology ; a speech intended to be 
delivered before a defunct Mechanics' Institute. By Swallow Swift, 
late M.P. for the Borough, of Cockney- Cloud, Witsbury : reprinted 
Balloon Island, Bubble year, month Ventose. Long live Charlatan ! 

As a rule, orthodox theologians should avoid humour, a weapon 
which all history shows to be very difficult to employ in favour 
of establishment, and which, nine times out of ten, leaves its 
wielder fighting on the side of heterodoxy. Theological argu- 
ment, when not enlivened by bigotry, is seldom worse than 
narcotic : but theological fun, when not covert heresy, is almost 
always sialagogue. The article in question is a craze, which no 
editor should have admitted, except after severe inspection by 



SATIRICAL CRITICISM. 193 

qualified persons. The author of this wit committed a mistake 
which occurs now and then in old satire, the confusion between 
himself and the party aimed at. He ought to be reviewing this 
fictitious book, but every now and then the article becomes the 
book itself; not by quotation, but by the writer forgetting that 
he is not Mr. Swallow Swift, but his reviewer. In fact, he and 
Mr. S, Swift had each had a dose of the Devil's Elixir. A novel 
so called, published about forty years ago, proceeds upon a 
legend of this kind. If two parties both drink of the elixir, 
their identities get curiously intermingled ; each turns up in 
the character of the other throughout the three volumes, without 
having his ideas clear as to whether he be himself or the other. 
There is a similar confusion in the answer made to the famous 
Epistolce Obscurorum Virorum: it is headed Lamentationes 
Obscurorum Virorum. This is not a retort of the writer, throw- 
ing back the imputation : the obscure men who had been 
satirized are themselves made, by name, to wince under the 
disapprobation which the Pope had expressed at the satire upon 
themselves. 

Of course the book here reviewed is a transparent forgery. 
But I do not know how often it may have happened that the 
book, in the journals which always put a title at the head, may 
have been written after the review. About the year 1830 a 
friend showed me the proof of an article of his on the malt tax, 
for the next number of the Edinburgh Review. Nothing was 
wanting except the title of the book reviewed ; I asked what it 
was. He sat down, and wrote as follows at the head, ' The 
Maltster's Guide (pp. 124),' and said that would do as well as 
anything. 

But I myself, it will be remarked, have employed such humour 
as I can command 'in favour of establishment.' What it is 
worth I am not to judge ; as usual in such cases, those who are of 
my cabal pronounce it good, but cyclometers and other paradoxers 
either call it very poor, or commend it as sheer buffoonery. Be 
it one or the other, I observe that all the effective ridicule is, in 
this subject, on the side of establishment. This is partly due to 
the difficulty of quizzing plain and sober demonstration ; but so 
much, if not more, to the ignorance of the paradoxers. For that 
which cannot be ridiculed, can be turned into ridicule by those 
who know how. But by the time a person is deep enough in 
negative quantities, and impossible quantities, to be able to satirise 
them, he is^caught, and being inclined to become a user, sli rinks 
from being an abuser. Imagine a person with a gift of ridicule, 

o 



194 A BUDGET OF PARADOXES. 

and knowledge enough, trying his hand on the junction of the 
assertions which he will find in various books of algebra. First, 
that a negative quantity has no logarithm; secondly, that a 
negative quantity has no square root ; thirdly, that the first non- 
existent is to the second as the circumference of a circle to its 
diameter. One great reason of the allowance of such unsound 
modes of expression is the confidence felt by the writers that V 1 
and log (-1) will make their way, however inaccurately described. 
I heartily wish that the cyclometers had knowledge enough to 
attack the weak points of algebraical diction : they would soon 
work a beneficial change. 

Recueil de ma vie, mes ouvrages et mes pensees. Par Thomas 

Ignace Marie Forster. Brussels, 1836, 12mo. 
Mr. Forster, an Englishman settled at Bruges, was an observer 
in many subjects, but especially in meteorology. He communi- 
cated to the Astronomical Society, in 1848, the information that, 
in the registers kept by his grandfather, his father, and himself, 
beginning in 1767, new moon on Saturday was followed, nineteen 
times out of twenty, by twenty days of rain and wind. This 
statement being published in the Athenceum, a cluster of corres- 
pondents averred that the belief is common among seamen, in all 
parts of the world, and among landsmen too. Some one quoted 
a distich 

' Saturday's moon and Sunday's full 
Never were fine and never wull.' 
Another brought forward 

' If a Saturday's moon 
Comes once in seven years it comes too soon.' 

Mr. Forster did not say he was aware of the proverbial character 
of the phenomenon. He was a very eccentric man. He treated 
his dogs as friends, and buried them with ceremony. He quar- 
relled with the cure of his parish, who remarked that he could 
not take his dogs to heaven with him. I will go nowhere, said 
he, where I cannot take my dog. He was a sincere Catholic : but 
there is a point beyond which even churches have no influence. 

The following is some account of the announcement of 1849. 
The Athenceum (Feb. 17), giving an account of the meeting of 
the Astronomical Society in December, 1858, says: 

' Dr. Forster of Bruges, who is well known as a meteorologist, made 
a communication at which our readers will stare : he declares that by 
journals of the weather kept by his grandfather, father, and himself, 
ever since 1767, to the present time, whenever the new moon has fallen 
on a Saturday i the following twenty days have been wet and windy, in 



A SATURDAY'S MOON. 195 

nineteen cases out of twenty. In spite of our friend Zadkiel and the 
others who declare that we would smother every truth that does not 
happen to agree with us, we are glad to see that the Society had 
the sense to publish this communication, coming, as it does, from a 
veteran observer, and one whose love of truth is undoubted. It must 
be that the fact is so set down in the journals, because Dr. Forster 
says it : and whether it be only a fact of the journals, or one of the 
heavens, can soon be tried. The new moon of March next, falls on 
Saturday the 24th, at 2 in the afternoon. We shall certainly look out.' 

The following appeared in the number of March 31 : 

* The first Saturday Moon since Dr. Forster's announcement came off 
a week ago. We had previously received a number of letters from 
different correspondents all to the effect that the notion of new moon 
on Saturday bringing wet weather is one of widely extended currency. 
One correspondent (who gives his name) states that he has constantly 
heard it at sea, and among the farmers and peasantry in Scotland, 
Ireland, and the North of England. He proceeds thus : " Since 1826, 
nineteen years of the time I have spent in a seafaring life. I have 
constantly observed, though unable to account for, the phenomenon. 
I have also heard the stormy qualities of a Saturday's moon remarked 
by American, French, and Spanish seamen ; and, still more distant, 
a Chinese pilot, who was once doing duty on board my vessel seemed 
to be perfectly cognizant of the fact." So that it seems we have, in 
giving currency to what we only knew as a very curious communica- 
tion from an earnest meteorologist, been repeating what is common 
enough among sailors and farmers. Another correspondent affirms 
that the thing is most devoutly believed in by seamen ; who would as 
soon sail on a Friday as be in the Channel after a Saturday moon. 
After a tolerable course of dry weather, there was some snow, accom- 
panied by wind on Saturday last, here in London ; there were also 
heavy louring clouds. Sunday was cloudy and cold, with a little rain ; 
Monday was louring ; Tuesday unsettled ; Wednesday quite over- 
clouded, with rain in the morning. The present occasion shows only 
a general change of weather, with a tendency towards rain. If Dr. 
Forster's theory be true, it is decidedly one of the minor instances, 
as far as London weather is concerned. It will take a good deal of 
evidence to make us believe in the omen of a Saturday Moon. But, 
as we have said of the Poughkeepsie Seer, the thing is very curious 
whether true or false. Whence comes this universal proverb and a 
hundred others while the meteorological observer cannot, when he 
puts down a long series of results, detect any weather cycles at all ? 
One of our correspondents wrote us something of a lecture for en- 
couraging, he said, the notion that names could influence the weather. 
He mistakes the question. If there be any weather cycles depending 
on the moon, it is possible that one of them may be so related to the 
k cycle of seven days, as to show recurrences which are of the kind 

o 2 



196 A BUDGET OF PARADOXES. 

stated, or any other. For example, we know that if the new moon of 
March fall on a Saturday iu this year, it will most probably fall on 
a Saturday nineteen years hence. This is not connected with the 
spelling of Saturday but with the connexion between the motions of 
the sun and moon. Nothing but the Moon can settle the question 
and we are willing to wait on her for further information. If the 
adage be true, then the philosopher has missed what lies before his 
eyes ; if false, then the world can be led by the nose in spite of the 
eyes. Both these things happen sometimes; and we are willing to 
take whichever of the two solutions is borne out by future facts. In 
the mean time, we announce the next Saturday Moon for the 18th 
of August.' 

How many coincidences are required to establish a law of 
connexion ? It depends on the way in which the mind views the 
matter in question. Many of the paradoxers are quite set up by 
a very few instances. I will now tell a story about myself, and 
then ask them a question. 

So far as instances can prove a law, the following is proved : no 
failure has occurred. Let a clergyman be known to me, whether 
by personal acquaintance or correspondence, or by being frequently 
brought before me by those with whom I am connected in private 
life : that clergyman does not, except in few cases, become a 
bishop ; but, if he become a bishop, h<e is sure, first or last, to 
become an arch-bishop. This has happened in every case. As 
follows : 

1. My last schoolmaster, a former Fellow of Oriel, was a very 
intimate college friend of Eichard Whately, a younger man. 
Struck by his friend's talents, he used to talk of him perpetually, 
and predict his future eminence. Before I was sixteen, and 
before Whately had even given his Barnpton Lectures, I was very 
familiar with his name, and some of his sayings. I need not say 
that he became Archbishop of Dublin. 

2. When I was a child, a first cousin of John Bird Sumner 
married a sister of my mother. I cannot remember the time 
when I first heard his name, but it was made very familiar to me. 
In time he became Bishop of Chester, and then, Archbishop of 
Canterbury. My reader may say that Dr. C. R. Sumner, Bishop 
of Winchester, has just as good a claim : but it is not so : those 
connected with me had more knowledge of Dr. J. B. Sumner ; 
and said nothing, or next to nothing, of the other. Rumour says 
that the Bishop of Winchester has declined an Archbishopric : if 
so, my rule is a rule of gradations. 

3. Thomas Musgrave, Fellow of Trinity College, Cambridge, 
was Dean of the college when I was an undergraduate : this 



ACCIDENT, OR LAW? 197 

brought me into connexion with him, he giving impositions for 
not going to chapel, I writing them out according. We had 
also friendly intercourse in after life ; I forgiving, he probably 
forgetting. Honest Tom Musgrave, as he used to be called, 
became Bishop of Hereford, and Archbishop of York. 

4. About the time when I went to Cambridge, I heard a great 
deal about Mr. C. T. Longley, of Christchurch, from a cousin 
of my own of the same college, long since deceased, who spoke of 
him much, and most affectionately. Dr. Longley passed from 
Durham to York, and thence to Canterbury. I cannot quite make 
out the two Archbishoprics ; I do not remember any other private 
channel through which the name came to me : perhaps Dr. 
Longley, having two strings to his bow, would have been one 
Archbishop if I had never heard of him. 

5. When Dr. Win. Thomson was appointed to the see of 
Gloucester in 1861, he and I had been correspondents on the 
subject of logic on which we had both written for about 
fourteen years. On his elevation I wrote to him, giving the pre- 
ceding instances, and informing him that he would certainly be 
an Archbishop. The case was a strong one, and the law acted 
rapidly; for Dr. Thomson's elevation to the see of York took 
place in 1862. 

Here are five cases ; and there is no opposing instance. I have 
searched the almanacs since 1828, and can find no instance of a 
Bishop not finally Archbishop of whom I had known through 
private sources, direct or indirect. Now what do my paradoxers 
say ? Is this a pre-established harmony, or a chain of coinci- 
dences ? And how many instances will it require to establish a 
law? 

Some account of the great astronomical discoveries lately made 
by Sir John Herschel at the Cape of Good Hope. Second 
Edition. London, 12mo. 1836. 

This is a curious hoax, evidently written by a perso