1815.] Philosophical Transactions, 1814, Part IT. 135 
the different forces which act upon a ship when sailing, and the 
effects apt to be produced by these’ forces. He then examines the- 
different arrangements of Mr. Seppings, and shows that ihey are 
all improvements; though, if we understand him right, he seems 
to state that several of them are not new. 
Ill. Some further Observations on Aimospherical Refraction. By 
Stephen Groombridge, Esq.; F.R.S.—In a preceding volume of 
the Transactions Mr. Groombridge published a paper on this im- 
portant suoject, giving a formula for the mean refraction down to 
80° from the zenith, deduced from his own observations. He has 
since continued his observations and determined the refraction as 
low down as 87°, the trees in Greenwich Park preventing him 
from observing stars any nearer the horison. He has made some 
alterations in his preceding formula. ‘The paper concludes witha 
table of the mean refraction from the zenith to the horizon. 
IV. Propositions containing some Properties of Tangents to 
Circles ; and of Trapexiums inscribed in Circles, and non-inscribed. 
Together with Propositions on the Elliptic Representations of Circles 
upon a Plane Surface by Perspective. By Richard Hey, LL.Q. 
late Fellow of Sidney Sussex, and Magdalen Colleges in the Uni- 
versity of Cambridge.—It is not in our power to give any intel- 
ligible account of this curious paper to our readers without the 
assistance of figures, and without introducing demonstrations not 
quite consistent with the nature of a review. We must therefore 
refer those who wish to study the subject to the paper itself. 
V. On the new Properties of Light exhibited in the Optical 
Phenomena of Mother-of-Pearl and other Bodies, to which the 
superficial Structure of that Substance can ble communicated. By 
David Brewster, LL.D. F.R.S. Edin. and F.S.A. Edin.—The 
beautiful play of colours exhibited by mother-of-pearl, has been 
always ascribed to its laminated structure. Dr. Brewster, however, 
observed that the same property was communicated to wax, gum, 
tin, lead, &c., merely by pressing them against the surface of 
mother-of-pearl. Hence it is obvious, that the property is owing 
to the configuration of the surface. Dr Brewster found by means 
of the microscope, that the surface of mother-of-pearl was com- 
posed of waving lines, something like the skin at the point of an 
infant’s finger. These lines could not be obliterated by grinding or 
polishing. ‘They vary considerably in fineness in different speci- 
mens. Sometimes they may be seen with the naked eye, while at 
others more than 3000 may be reckoned within the space of an 
inch. ‘To this configuration of the surface Dr. Brewster ascribes 
the property of mother-of-pearl to reflect various tints of splendid 
colours. Dr. Brewster found likewise, that when a ray of light 
falls obliquely upon mother-of-pearl, both the portion refleeted and 
the portion transmitted are polarized, and both in the same manner. 
This is different from what happens either in crystallized or un- 
crystallized bodies, 
V1. An improved Method of dividing Astronomical Circles and 
