443 



number of angles P S Q, Q S Q be also taken, each equal to M S P, 

 the angle which the first drawn radius makes with the axis, then will 

 the continued product of all the radii S P be equal to the last S Q, 

 multiplied by the latus rectum raised to the power of n 1, n being 

 the number of angles taken. 



The author thence proceeds to deduce other theorems that would 

 be for the most part complicated and unintelligible when geometri- 

 cally enunciated, though sufficiently simple in their algebraic expres- 

 sions. They are indeed, as the author observes, properties rather of 

 the equations of the conic sections, than of the curves themselves ; 

 properties of a limited number of disjoined points, determined ac- 

 cording to a certain law, rather than of a series of consecutive points 

 composing a line. 



In the course of this investigation the author employs one species 

 of notation, which is new, and for which he apologizes, by explaining 

 its advantage in point of simplicity. 



Observation of the Summer Solstice, 1812, at the Royal Observatory. 

 By John Pond, Esq. Astronomer Royal, F.R.S. Read November 

 12,1812. [Phil. Trans. 1813, ;>. 27.] 



Since a minute description of the new circular instrument, which 

 has been lately put up at Greenwich, is intended to be given to the 

 Society as soon as it is completed in every respect, the Astronomer 

 Royal takes no further notice of its construction than is necessary to 

 show by what means the results of his observations of the sun at the' 

 last solstice was obtained. 



In other instruments, which take their point of departure from a 

 plumb-line or level, the zenith distance of the sun is the primary ob- 

 ject of investigation ; and the polar distance of the sun, which is the 

 ultimate object, is obtained by adding the co-latitude of the place, 

 which completes the entire arc. 



But by the mural circle at Greenwich, to which there is neither 

 level nor plumb-line, the total arc may be measured without any 

 exact knowledge of the zenith point ; and the co-latitude, which in 

 all other cases it is so essential to know correctly, becomes an object 

 of mere curiosity, rather than of real necessity. 



It is, however, convenient to assume some imaginary point near 

 the zenith, the position of which, with respect to the fixed stars, may 

 be determined within one tenth of a second ; and from this imaginary 

 point Mr. Pond measures the distances of the sun southward, and of 

 the pole northward, as the best means of obtaining the entire arc ; 

 but he also adds a computation of the same solstitial place of the 

 sun, as obtained by direct measurement from the pole without the 

 aid of his imaginary intermediate point, and the difference is found 

 to be only 0'15 of a second. 



In the determination of this arc, it is evident that, however accu- 

 rately it may have been mechanically determined, it must still be 



