TRANSACTIONS OF THK SECTIONS. 11 



Now by a well-known method, it is easy to find that z = 8'48252 

 will very nearly satisfy this equation ; so nearly that the change of a 

 unit in the fifth decimal place will make the side of the equation 

 upon which z lies differ from the other constant side in the fourth 

 decimal place by nearly two units. This is an accuracy quite un- 

 necessary in practice, but Mr. Stevelly resorted to it, lest in quan- 

 tities depending for their values upon such minute fractions as dp, 

 ds, and dm, there should be any source of fallacy in the mode of 

 calculating which did not readily appear ; and this course he was the 

 rather led to adopt as the length of z which he arrived at differs so 

 materially ft'om that assigned by Captain Kater, and also by Mr. 

 Baily, if the latter be correctly quoted by Kater, in Lardner's Me- 

 chanics. Mr. Baily's paper in the Astronomical Memoirs, Mr. 

 Stevelly had no opportunity of seeing. The length oi 2 z according 

 to Kater should be 14'44 inches, and according to Baily, as quoted 

 by him 14"3. Now if either of these values be assigned to2 z; z will 

 be far from satisfying the equation (c) which has been above de- 

 duced. 



The dimensions of the several parts of the pendulum according to 

 Mr. Stevelly will be as follows : — A steel spring two inches long, 

 measured from the cock to the upper edge of the (iron) rivet which 

 attaches it to the deal rod ; a deal rod furnished with a circular bracket 

 at the bottom, diameter of deal rod = 0*6 inch. ; length from upper 

 edge of the rivet above, to the upper surface of the bracket upon which 

 the leaden tube rests, = 44'995 inches. Tlie bracket may be easily 

 made of such a shape, while its upper circumference is nearly equal 

 to that of the leaden tube, as that the wooden part of the pendulum 

 alone shall swing in a second. The leaden tube is then to be 16-965 

 inches long; external diameter = 1"5 inch; diameter of the space 

 along its axis, through which the deal rod passes, six tenths of 

 an inch : the leaden tube wiU weigh about ten pounds avoir- 

 dupois. 



If the numbers assigned by Kater be more correct than these, it 

 can only arise from the values olds, dp, and dm not having been as 

 yet ascertained with sufficient accuracy, and perhaps an examination 

 of the rates of pendulums made of tubes and rods of various mate- 

 rials would furnish the best possible method of examining the re- 

 lative expansibilities of bodies under various temperatures. 



Mr. SteveUy thinks a bracket of wood firmly attached to the 

 lower part of the pendulum rod a method of suspending the 

 leaden tube much to be preferred to the method in use by a nut and 

 screw, for many reasons ; and thus mounted it becomes necessary to 

 have, at the upper part or suspension of the pendulum, some con- 

 trivance for adjusting its length, so as to make the rate correct. Mr. 

 Stevelly exhibited to the section a nut and screw worked by a mi- 

 crometer screw, the index of which may come out at the side of the 

 clock-case, and there point to a graduated circle ; and he stated that 

 so nice an adjustment may be effected by this, that upon a circle of 

 about three inches in diameter, each division ; being the tenth of an 

 inch in length ; would correspond to an alteration of the length of the 



