TRANSACTIONS OF THE SECTIONS. 5 



'^ willow-leaves," and therefore can afford no corroboration of IVIr. Nasmyth's 

 " discovery" ; or secondly, if they are the same, they are so easily seen as to have 

 been well known to Sir W. Herschel seventy years ago, and to others more 

 recently. 



On tlie Possihillty of constructing Ellipsoidal Lenses. 

 By the Eev, Thomas Fuelong. 

 If a circular disk be put in a convenient position, and a line be supposed pro- 

 ceeding- from its centre, and pei-pendicular to its plane, an eye placed in that line 

 vdll see the dislc as a circle. If the plate be made to revolve on one of its dia- 

 meters through a right angle, it will be seen edgeways as a line ; as the disk so 

 moves through 90°, the eye will perceive it assimie eveiy form of ellipse, from the 

 circle, its limit on the one hand, to the right line, its limit on the other. The 

 elements of those elliptic forms are easily foimd ; for the radius of the disk is 

 always the semiaxis major, and the uatiu-al cosine of the angle through which 

 the disk (or the eye) moves midtiplied by the number of inches or feet in the 

 radius of the disk will be the semiaxis minor, from which, if the focus be given, 

 the angle of revolution can be foimd, or, if the angle be given, the focus may be 

 found ; or, easier still, to the tto ^^ ^^ ^^ inch, by measuring off those numbers on 

 the legs of a right angle on a scale of equal parts. The common slide-rest has 

 two motions, one parallel to the bed of the lathe, the other at right angles to it ; 

 and if a cutting-tool be an-anged as for boring a cylinder, that cutter will produce 

 a cylindrical groove if the work attached to the slide-rest be moved parallel to the 

 bed, or a line (like the cut of a circular saw) if moved across the bed. Now if 

 the upper part of the slide-rest be made capable of moving in azimuth 90°, the 

 cutting point, moving in a circle, can be made to produce grooves corresponding 

 to the small end of the ellipse, or, by a vertical arrangement to the flatter side, ot 

 any eccentricity required. Crossed lenses, gTOund and polished in circidar grooves 

 (the discovery of a French gentleman, he believed), are well known and valued for 

 flatness of field and good definition. His strong impression is that elliptic lenses 

 could be produced in the same way. The only point of difference is that, while 

 the circular groove permits the glass to be worked in it in various positions, the 

 elliptic groove must have the glass worked in it always in the same plane. The 

 aper read was not intended for the learned, but for a plain workman, and in the 

 ope that some one would try the experiment. The author feels confident that, if 

 ellipsoidal curves were introduced, gi'eat advantages are likely to arise. 



hi 



On the possible Connexion hetween the Ellipticity of Mars and the general 

 Appearatice of its Surface. By Professor Hennesst, F.It.S., M.B.I.A. 

 The physical characters of Mars have attracted considerable notice, on account 

 of the supposed resemblance of that planet to our earth, and at the same tirne one 

 of the most prominent of these characters presents a striking contrast with its 

 terrestrial counterpart, namely, its ellipticity, which is estimated by most astro- 

 nomers at a higher value than mechanical theory would assign, if the planet had 

 been originally in a fluid state. In accordance with hydrostatical laws, a planet 

 similar to Mars, and rotatory around its axis in the same period of time, should 

 have an ellipticity very nearly approaching to that of our earth. Two observers 

 of great eminence, Bessel and Johnson, seem to have arrived at a similar con- 

 clusion. The observations made by the former were fully discussed by M. Oude- 

 manns in the ' Astronomische Nachrichten,' No. 838, p. 352. After combining 

 the results of different observed diameters with various angles of position, by the 

 method of least squares, Oudemanns came to the conclusion that the observations 

 gave varied and uncertain values for the diameters; and therefore that it was 

 permissible to regard the planet as approximately spherical. Johnson, in the 

 Kadcliffe Obsen'ations for 1850 and 1853, discussed the results of measurements 

 made with the heliometer, and arrived at substantiallj^ the same result. Although 

 the late M. Arago referred to some of the author's views regarding terrestrial 

 physics, as probably affording explanation for the anomaly of the large ellipticity 

 which he assigned to Mars, in his posthumous publication on the structure of the 



