STEWART. 
order of these propositions, added to the 
clearness and simplicity of the demonstra- 
tions, renders this tract perhaps the best 
elementary treatise of physical astronomy 
(hat is any where to be found. 
In the three remaining tracts, our author 
had it in view to determine the effect of 
those forces tvhich disturb the motions of a 
Secondary planet. From this he proposed 
to deduce, not only a theory of the moon, 
but a determination of the sun’s distance 
from the earth. The former, it is well 
known, is the most difficult subject to 
■which mathematics have been applied, and 
the solution required and merited all the 
clearness and simplicity which our author 
possessed in so eminent a degree. It must 
be regretted therefore that the decline of 
Dr. Stewart’s health, which began soon af- 
ter the publication of the tracts, did not 
permit him to pursue this investigation. 
The other object of the tracts was, to de- 
termine the distance of tlie sun, from his ef- 
fect in disturbing the motions of the moon ; 
and his inquiries into the lunar irregularities 
had ffimished him with the means of accom- 
plishing it as he supposed : and in 1763, he 
published his “ Essay on the Sun’s Dis- 
tance,” where the computation being ac- 
tually made, the pai-allax of the sun was 
found to be no more than 6" 9"', and conse- 
quently his distance almost 29,875 semidia- 
meters of the earth, or nearly 119 millions 
of miles. A determination of the sun’s dis- 
tance, that so far exceeded all former esti- 
mation of it, was received with surprise, 
and the reasoning on which it was founded 
was likely to undergo a severe examination. 
But, even among astronomers, it was not 
every one who could judge in a matter of 
such difficult discussion. Accordingly, it 
was not till about rive years after the pub- 
lication of Dr. Stewart’s work that there 
appeared a pamphlet, under the title of 
“ Four Propositions,” intended to point out 
certain errors in Dr. Stewart’s investiga- 
tion, which had given a result much greater 
than the truth. From his desire of simpli- 
fying, and of employing only the geometri- 
cal method of reasoning, he was reduced to 
the necessity of rejecting quantities, which 
were considerable enough to have a great 
effect on the last result. An error was thus 
introduced, which, had it not been for cer- 
tain compensations, would have become 
immediately obvious, by giving the sun’s 
distance near three times as great .as that 
which has been mentioned. 
The “ Sun’s Distance” was the last work 
which Dr. Stewart published ; and though 
he lived to see the animadversions made on 
it, he declined entering into any contro- 
versy. His di.sposition was far from pole- 
mical ; and he knew the value of that quiet, 
which a literary man, should rarely suffer 
his antagonists to interrupt. He used to 
say, that tlie decision of the point in ques- 
tion was now before the public ; that if his 
investigation was right, it would never be 
overturned, and that if it was wrong, it 
ought not to be defended. 
A few months before he published the 
Essay just mentioned, he gave to the world 
another work, entitled, “ Propositiones 
More Veterum Demonstratae.” It consists 
of a series of geometrical theorems, mostly 
new; investigated, first by an analysis, and 
afterwards synthetically demonstrated by 
the inversion of the same analysis. This 
method made an important part in the ana- 
lysis of the ancient geometricians ; but few 
examples of it have been preserved in their 
writings, and those in the “ PropOsitiones 
Geometricae” are therefore the more valu- 
able. 
Doctor Stewart’s constant use of the 
geometrical analysis had put him in posses- 
sion of many valuable propositions, which 
did not enter into the plan of any of the 
works that have been enumerated. Of 
these, not a few have found a place in the 
writings of Dr. Simson, where they will for 
ever remain, to mark the friendship of these 
two mathematicians, and to, evince the 
esteem which Dr. Simson entertained for 
the abilities of his pupil. Many of these 
are in the work upon the Porisms, and 
ethers in the Conic Sections, viz, marked 
with the letter a; ; also a theorem in the edi- 
tion of Euclid’s Data. 
Soon after the publication of the “ Sun’s 
Distance,” Dr. Stewart’s health began to 
decline, and the duties of his office became 
burdensome to him. In the year 1772, he 
retired to the country, where he afterwards 
spent the greater part of his life, and never 
resumed his labours in the university. He 
was however so fortunate as to have a son 
to whom, though very young, he could 
commit the care of them with the greatest 
confidence. Mr. Dugald Stewart, having 
begun to give lectures for his father from 
the period above mentioned, was elected 
joint professor with him in 1775, and gave 
an early specimen of those abilities, which 
have not been confined to a single science. 
After mathematical studies (on account 
of the bad state of health into which Dr. 
