401 



the means of destroying both kinds of aberration in a large focal 

 pencil, and of thus surmounting what has hitherto been a chief ob- 

 stacle to the perfection of the microscope. 



On the Pendulum. By J. W. Lubbock, Esq. F.R.S. Read March 

 11, 1830. [Phil. Trans. 1830, p. 201.] 



The ingenious and beautiful application, made by Capt. Kater, of 

 Huygens's theorem respecting the convertibility of the centres of 

 suspension and oscillation, to the determination of the length of the 

 simple pendulum, is to be considered as a first approximation to the 

 solution of this problem. The accuracy of this determination, how- 

 ever, may be affected by many circumstances which the theory does 

 not take into account ; and the object of the author in this paper is 

 to investigate the limits of the errors that may arise from neglecting 

 them. Laplace and Whewell have shown that when the knife-edges 

 are considered as cylinders of small but of equal radii of curvature, 

 their distance is still equal to the length of the simple pendulum. 

 The author treats the question with the utmost generality, and dis- 

 cusses all the circumstances which may affect the accuracy of Capt. 

 Kater's method, including all possible deviations and positions of the 

 axes. He takes, as an example, the pendulum used by Mr. Baily, 

 and described by him in the Philosophical Magazine of last February; 

 and investigates the errors which would arise in the length of the 

 simple pendulum corresponding to given deviations of the knife-edges. 

 He also considers the case in which the agate planes are fixed on the 

 pendulum, and vibrate on a fixed knife-edge ; and finds that the 

 length of the simple pendulum is here also equal to the distance be- 

 tween the planes. 



On the Theoretical Investigation of the Velocity of Sound, as corrected 

 from M. Dulong's recent Experiments, compared with the Results 

 of the Observations of Dr. Moll and Dr. Van Beek. By Dr. Simons, 

 Assistant at the Observatory of the University of Utrecht. Com- 

 municated by Captain Henry Kater, Vice- President. Read March 

 18, 1830. \Phil. Trans. 1830, p. 209.] 



Laplace has demonstrated that Sir Isaac Newton's formula for 

 obtaining the velocity of sound, requires, in order to render it cor- 

 rect, that it be multiplied by a certain co-efiicient, depending on the 

 ratio between the specific heats of atmospheric air under a constant 

 pressure, and under a constant volume. Laplace has endeavoured to 

 deduce this coefficient, first from the experiments of MM. De la 

 Roche and Berard ; secondly, from those of MM. Clement and De- 

 sormes ; and lastly, from the more accurate investigations of MM. 

 Gay-Lussac and Welter. By applying this correction, the velocity 

 of sound, deduced from calculation, corresponded very nearly with 

 the results of actual experiment. Still, however, a degree of dis- 

 cordance was always found to take place. With a view to perfect 



