2 REPORT — 1842. 



clock, an image of the lower end of the other. Then the coincidences of both pendu- 

 lums may be very accurately observed with a telescope, placed in the straight line 

 with both, at a convenient distance. A similar contrivance has been described in the 

 account of pendulum experiments made at Kbnigsberg; and I may here be permitted 

 to add, that the accuracy of the method is such, that the relative rate of both pendu- 

 lums may be ascertained with the required accuracy in a time of ten or twenty minutes. 

 This arrangement supposed, it will be very easy to adjust tbe isochronal piece of Mr. 

 Frodsham. After this has been effected, the rate of the pendulum is to be tried in dif- 

 ferent temperatures. A box, having at its lower end an opening covered with glass, 

 may be fastened to the wall, so that the pendulum swings within it. A couple of 

 metal tubes pass through this box, and may be heated by boiling water or steam, in 

 order to heat the air within the box. Previously to the heating, the air is to be de- 

 prived of its moisture. Two or three thermometers will show whether the heat within 

 is pretty uniform. The pendulum being swung before and after the heating, it will 

 be easy to correct the compensation for heat. 



I believe that not only the readiness with which both these experiments may be 

 made, but also the perfect isolation of the pendulum will recommend this method to 

 artists and astronomers. I have indeed been desirous of trying it myself before pro- 

 posing it to others, but having been delayed beyond expectation with the construction 

 of a pendulum provided with Mr. Frodsham's isochronal piece, I am obliged to leave 

 the experiment to others. 



With respect to the construction of the pendulum, I believe that attention should 

 be paid to one point of view, which hitherto seems to have been overlooked. It often 

 happens that thermometers fixed at the top and at the foot of the case of a clock do 

 not agree ; whence it is evident that a compensation acting only below will not always 

 compensate the variation of the length of the whole rod. I should prefer, for this 

 reason, the gridiron pendulum to the mercurial pendulum, especially if the former is 

 constructed in such a manner that the several rods begin as little as possible below the 

 point of suspension, and end at the centre of gravity of the lens. I should also think 

 proper to make the several rods of equal diameter, and to coat them uniformly. Per- 

 haps the application of galvanism, which the deservedly famed Mr. Dent has made 

 for coating the balance-spring of chronometers with gold, would best answer the pur- 

 pose. I finally believe that the utmost care in the construction of the pendulum is 

 very essential, in order to remove every danger of its derangement by the spring of 

 the metals. 



Supposing a pendulum perfectly regulated, as well with respect to the heat as to 

 the arc of vibrations, only one cause will interfere with the regularity of its vibration 

 time ; this is the effect of that part of the buoyancy of the air which depends upon 

 the variations of the height of the barometer. The other part, depending upon the 

 variations of the thermometer, is comprised in the adjustment of the compensation for 

 heat, if made by the above-described process. There is indeed the possibility to com- 

 pensate the former part too, by fastening a barometer-tube to the pendulum ; and it 

 would not be difficult to find the suitable diameter of this tube ; but I am aware that 

 this complication of the pendulum would be rather inconvenient. At all events, the 

 effect of the variations of the barometer is not very great, especially if the specific 

 gravity of the pendulum is made as great as possible. 



The pendulum of a clock being carefully adjusted, every variation of the rate of the 

 clock, not explicable by a variation of the barometer, will originate in the escapement 

 or the wheels. Though the uniformity of the rate of many clocks is more to be won- 

 dered at than their occasional small variations, yet I believe that further improve- 

 ments are possible, and that they only will be obtained by the separation of the causes 

 of perturbations. From this point of view I might consider it as very desirable severely 

 to test the isolated pendulum by the method which I have submitted to the judgement 

 of the celebrated artists, whose admired works have lately so greatly contributed to the 

 accuracy, as well of astronomical observations as of the determination of longitudes. 



On a New General Principle of Analytical Mechanics. By M. Jacobi of 



Kbnigsberg. 

 In the different problems relative to the motion of a system of material points which 

 have been hitherto considered, one may make an important and curious remark, " that 



