Optica promota seu abdita radiorum reflexorum et refrac. 
_ torum mysteria, geometrice enucleata, cui abun dp 
aE » subtilissimorum astronomia problematum resolutio- 
exhibens, Lond. 1663. It was dedicated to Charles 
II. and was completed with the assistance and encou- 
: t of his er David, after he had been stop- 
aos long time at the twenty-sixth problem.* This 
work is remarkable, as containing the description of a 
new reflecting telescope, and the deduction of the true 
law of refraction. The method in which he has inves- 
tigated this law, is remarkable for its elegance and ori- 
ginality ; and, in his experimental demonstration of it, 
we are furnished with a striking proof of the accu 
of his observations. In comparing the refractions cal- 
culated by the law, with the experiments of Vitellio on 
the refractions of water and. glass, the greatest error 
amounts to 61’ in water, and 94’ in refractions from 
into water. When com with the experi- 
ments of Athanasius Kircher, the greatest error in wa- 
ter is 89’, in wine 110’, in oil 104’, and in glass 93’ ; 
but in:comparing them with his own observations, the 
guns error is only 15’; and it is remarkable, that 
made the index of refraction for water 1.3347, dif- 
fering only 0.0018 from 1.3358 the most accurate mea- 
sure, whereas Vitellio made it 1.306. Before the publica- 
tion of the Oplica Promota, Gregory was informed, that 
"he was anticipated in the discovery of the law of refrac- 
tion by Descartes, and he thus alludes to it in his pre- 
face :—Et ex analogiis in prima hujus tractatuli: propo- 
sitione declaratis, inveni primam hujus optice partem, de 
Cay ys refractionum hypothest et mensura nescius sci- 
icet (propter inopiam novorum librorum Mathematice- 
rum in alias inclyta Bibliotheca Abredonensi) hac ea- 
dem a Cartesio fuisse inventa. 
__.. The invention of the reflecting telescope formed an 
epoch in optics and astronomy. Gregory was not ac- 
‘quainted, with the errors in dioptric instruments, ari- 
fat from the unequal refrangybility of the rays of 
light ; and his TS oc in proposing this new 
instrument, was to avoid the error arising from the 
. spherical figure of the lenses. It consisted of a para- 
_ bolic concave mirror, near whose focus is placed a small 
concave elliptic speculum, having a common focus with 
_ the parabolic one. This instrument gave rise to the New- 
tonian telescope, in which the pre arti is plane, and 
reflects the image to the side of the tube where the eye- 
is placed ; and also to the € inian telescope, 
which differs only from that of Gregory, in having the 
small speculum convex instead of concave. The Gre- 
gorian principle has been almost universally used for 
a i absgey tice The Newtonian form 
n in the magnificent instruments used 
Meri Ciechel sienitts ectoanal probable, that the 
fe. telescope, in which the rays never cross 
each other at a focus, + will hereafter be -considered as 
the most valuable of the reflecting telescopes. The 
Optica Promota is terminated by a collection of astra- 
_ 
nis considerationem, &c.” Pref: ad Optic. Promot. 
(See Treatise on, New Philosophical Instruments, p. 44s and 193:) 
GREGORY. 
507 
nomical lems. The object of one of these, is to 
determine the of two planets from their con- 
junction ; and, in a scholium to this problem, he points 
out the great use of the transits of Venus and Mercury, 
in determining the sun’s parallax. {| This happy idea, 
which has since been of such service to astronomy, has 
always been ascribed to Dr Halley. 
Mr Gregory went to London about the year 1664 or 
1665, and was introduced to Mr Collins, the 
to the Royal Society, who introduced him to some of 
the best practical opticians, for the purpose of having 
his reflecting telescope executed, A Mr Rives was em- 
ployed for this purpose, but he could not polish the spe- 
culum upon the tool, and was therefore obliged todo it 
with a cloth and putty. The success of this trial was so 
little, that Gregory was discouraged from making any 
farther attempts, and a tube was never even made to 
hold the mirrors. He afterwards, however, made some 
trials with a little concave and convex speculum ; but, 
to use his own words, “ they wer but rude, seeing & 
had but transient views of the object ; being so 8S< 
ed with the fancie of the defective figure, that I wold not 
be at the pains to fix every thing in its due distance.” 
After these unsuccessful attempts to construct a re» 
flecting telescope, Gregory left England, and fixed 
his residence at Padua, which was then in high repute 
as a seat of mathematical learning. Here he published, 
in 1667, 1668, his work, entitled, Vera Circuli et Hy» 
perbole Quadratura in propria. sua proportionis specie 
inventa, ct demonstrata, which contains his discovery of 
an infinitely converging series for the areas of the circle, 
ellipsis, and hyperbola. A copy of this work was laid 
before the Royal Seciety by his friend Mr Collins, and 
was honoured with the approbation of Lord Brounckes 
and Mr Wallis. In the following year he reprinted it 
at Venice, and added a new work, entitled, Geometrica 
pars universalis quantitatum curvarum transmutalioni et 
mensure, inserviens, which contains a new method for 
the transmutation of curves. This work had previ- 
ously appeared at Padua in 1668 ; and, upon its arrival 
in England, was read by Mr Collins to the Royal So« 
ciety. 
In the year 1670, Mr Gregory received, in a letter 
from Mr Collins, a series for the area of the zone of a 
circle, and being informed that Newton had invented 
an universal method by which he could square all 
curves ical and mechanical by infinite series of 
that kind, Gregory applied himself to the investigation 
of the subject, and discovered an universal method of 
series, which he communicated to Newton, and the 
other English mathematicians, by a letter to Collins, 
dated February 1671. His brother David urged him 
to publish this method without delay ; but he declined 
this from the most honourable motives; for Newton 
having been the. first inventor, he thought himself 
bound to wait till his method should be published. 
Upon Mr Gregory’s return to: London, we believe in 
* © Ubi diu hasi omni spe progrediendi orbatus; sed cantinuis hortatibus et auxiliis fratris mei Davidis Gregorii in mathematicis 
non parum versati (cui siquid in hisce scientiis prestitero, me iliud debere non inficias ibo) animatus tandem incidi in seriam imagi- 
+ The effect of the collision of the rays in the focus was first noticed’by Dr Brewster, in the most perfect achromatic tetescopes + 
; It was afterwards: observed in reflecting telescopes by Mr Kater, 
who has examined the subject with much attention and.success : (See Phil. Trans, 1813,.1814.). We have found from-experiment, that 
_, the heat of a burning lens, as well as the light, is more intense within than without the focus, and that radiant heat is also most in- 
_ tense within the focus. Mr Leslie had long before obtained the same result with regard to radiant heat. 
that this diminution of effect must arise from the collision of the luminous as well as of the calorific rays.. We tray therefore lay it 
down as a principle in the construction of optical instruments, that the rays should, if possible, never be brought to a positive focus. 
$°** Hoc Problema pulcherrimum habet usum, sed forsan laboriosum in observationibus Veneris vel Mercurii particulam solis ob- 
Scurantis ; ex talibus enim solis parallaxis investigari poterit.” Optic. Promot. schol. prop. 87. 
Tt is therefore. certain, 
Gregory, 
James. 
—_—o 
