( 439 ) 



of sympathy may appear have been investigated theoretically and experi- 

 mentally; among others by Euler ^) the case of two scales of a balance 

 of which Daniel Bernoulli^) had observed that they in turns took over 

 each other's oscillations; by Poisson '), by Savart") and by Riésal^) 

 -the case of two pendulums fastened with Poisson to the extremities 

 of a liorizontal elastic rod, or with Savart and Résal to the horizontal 

 arms of a ~J"-shaped elastic spring ; by W. Dumas ") the case of a 

 pendulum, beating seconds, with movable horizontal cross rails, on 

 whicii other pendulums were hung; by Lucien de la Rive') and 

 Everp:tt ^) the case of two pendulums joined by an elastic string; 

 whilst finally Cëllérier, Furtw angler and others developed the theory 

 of the motion of two pendulums of about equal length of pendulum, 

 placed on a common elastic stand, in order to determine experimen- 

 tally, and to take into account in this way the influence exercised 

 by the small motions of such a stand on the period of the oscillations "). 

 However, we see that the more recent investigations, with the 

 exception of the work of W. Dumas, who does not purposely mention 

 the phenomena of sympathy, relate to mechanisms where elasticity 

 plays a part; whilst it seems probable that this was not the case 

 or at least in only a slight degree in the experiments of Huygens 

 and Ellicott. 



1) Novi commeniarii Ac. Sc. Imp. Petro])olitanae, T. 19, 1774, p. 325—339. 

 RouTH, Dynamics of ct system of riyid bodies, Advmiced part, Chapt. l\, Art. 9i, 

 giving the right solution, has justly pointed out an error in Euler's solution and 

 likewise in the one signed D. G. S. appearing in The Cambridge math. Journ. of 

 May 1840, Vol. 2, p. 120—128. Euler's treatment of the phenomenon of the trans- 

 mission of energy is also defective, as he does not lay stress upon the necessity 

 of the two almost equal periods, in this case of his quadratic equation admitting 

 a root nearly equal to the length of the mathematical pendulum by which he 

 replaces the scales. 



2) Nov. Comm. 1. c. preceding note, p. 281. 



3; Connaissance des terns pour Van 1833, Additions, p. 3—40. Theoretical. 

 This memoir was indicated to me after the publication of the Dutch version of 

 this paper. 



^) VInstitut, I*- Section, 7« Année, 1839, p. 462—464. Experimental. 



6) Compt. Rend. T. 76, 1873, p. 75—76 ; Ann. Éc. Norm. (2), II, p. 455—460. 

 Theoretical. 



^) "Ueber Schwingungen verbundener Pendel", Festschrift zur dritten Sdcular- 

 feier des Berlinischen Gymnasiums zum grauen Kloster. Berlin, WEmniANN'sche 

 Buchhandlung. 1874. The investigations themselves are according to this paper 

 from the year 1867. Theoretical and experimental. 



7) ComjJt. Rend. T. 118, 1894, p. 401—404; 522-525; Journ. de j^hys. (3), 

 III, p. 537 — 565. Experimental and theoretical. 



8) Phil. Mag. Vol. 46, 1898, p. 236—238. Theoretical. 



^) See for this the Encyclopadie der mathematischen Wissenschaften, Leipzig, 

 Teubner, Band IV, 1^, Heft 1, § 7, p. 20—22. 



