Aatronomical Sociely. 467 



very few coi-ds, pulleys, and winches. The diameter of the 

 speculum is fifteen inches, and the focal length twenty-five feet. 

 The eye-pieces, which are adapted to magnify the image, 

 possess powers varying from 100 to 1500 ; and there are pro- 

 per diaphragms to modify the redundancy of light. The mode 

 of observing is by the " front view." 



Mr. Ramage exhibited to the Society, besides a neat model 

 of the tube and apparatus, two speculums ; one of fifteen inches 

 diameter, belonging to the telescope described, and another of 

 twenty-one inches diameter and fifty-four feet focus. 



There was next read a paper on the subject of Parallaxes, 

 taking the word in an enlarged sense, by M. Littrow. It was 

 in the excellent treatise of Lagi'ange on the determination of 

 the solar parallax, from the observed transits of the inferior 

 planets over the sun's disc, where the rectangular co-ordinates 

 were first employed, instead of the less convenient expressions 

 of spherical trigonometry, for the purpose of deducing the ap- 

 parent station of a planet from its longitude and latitude. The 

 process has been since improved by Olbers, Bessel, Rhode, &c. 

 But M. Littrow regards it as susceptible of still further im- 

 provements, which he has here exhibited. He gives the ana- 

 lytical solution of several problems ; viz. 



1 . To determine the apparent longitude and latitude of a 

 star, from the true geocentric longitude and latitude. 



2. To solve the inverse problem. 



3. and 4. The solution of the preceding problems by series. 



5. To find the apparent right ascension and declination, 

 from their true magnitudes, and vice versa. 



6. To determine the apparent azimuth and altitude, from 

 their true magnitudes, and vice versa. 



7. and 8. To find the true place of the star, from its appa- 

 rent place, and vice versa, without any reference to the hori- 

 zon, the ecliptic, and the equator, which is often useful in 

 computing the occultation of fixed stars by the moon. 



9. A general problem, to find the apparent azimuth and 

 apparent altitude, from the true longitude and the true latitude 

 of a star. 



The resulting expressions for these several solutions are ana- 

 lytically simple. Those which are deduced in series are usually 

 of this kind, namely, 



log c = log6 — (^—^ cos 5 — i(y} ^^^ 2 ^ 



-^(■fX cos 3fl, &c. 



in which the law is evident. 



M. Littrow concludes his paper by suggesting the applica- 

 3 N 2 tiou 



