TKANSACTIONS OF THE SECTIONS. 27 



paper by Sir William Thomson, Phil. Mag. July 1867 ; also a paper by the 

 Author, Phil. Mag. July 1868). The blo'svs were delivered by means of a pendulum 

 called the striker, which, falling from a constant height, ensiu-ed that the rings 

 were projected with a constant velocity. In the experiments described in the 

 present series, this velocity was somewhat over 10 feet per second. The pendulum 

 was released to deliver the blow from a pair of forceps, each jaw of which was in 

 connexion with a pole of a battery. After the ring had traversed a range varied 

 from 2 inches to 20 feet, it impinged upon a target. The blows upon the target 

 closed the circuit, which had been opened at the release of the striker. An 

 electric chronoscope (devised, it is oelieved, by Wheatstone) measured the 

 interval of time between the release of the striker and the impact upon the 

 target. 



The target was placed successively at distances of 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 

 feet from the orifice of the box. Not less than ten observations of the time were taken 

 at each range. The probable error of the mean time at each range is in every 

 case less than 1 per cent, of the whole amount. A special series of experiments, 

 which need not be described, determined the value of the chronoscope readings in 

 seconds. 



The observations are next represented in a cui-ve, of which the abscissae are the 

 ranges, and the ordinates the corresponding mean chronoscope readings. By 

 drawing tangents to this curve, the velocity of the ring at its different points ia 

 approximately foimd. 



A second projection is made in which the abscissEe are the ranges and the or- 

 dinates are the velocities ; the points thus determined are approximately in a straight 

 line. 



It follows that the rings are retarded as if acted upon by a force proportional 

 to the velocity, and an approximate value of the numerical coefficient becomes 

 known. 



A more accm-ate value having been determined by the method of least squares, 

 the results are embodied in the following Table (p. 28), of which a description 

 is first given. The Roman letters refer to the several columns of the Table. 



I. contains a series of numbers for convenience of reference. 



II. It was found that the motion of the ring in the immediate vicinity of the 

 box was influenced by some disturbing element. The zero of range was therefore 

 taken at a point 4 feet distant from the orifice. This column contains the ranges. 



III. The interval between the release of the striker and the anival of the ring 

 at a point 4 feet from the orifice is 6-5 chronoscopic units, or about 0-9.3 second. 

 This constant must be subtracted from the mean readings of the time, in order 

 to reduce the zero epoch to the instant when the ring is 4 feet from the orifice. 

 This column contains the mean readings of the chronoscope corrected by this 

 amount. 



IV. When the ranges are taken as abscissae, and the corresponding times as 

 ordinates, it is found that a cui'\e can be drawn through or near all the points 

 thus produced. To identify the points with the cun-e, small corrections are in some 

 cases required. These con-ections are shown in column IV. In the case of experi- 

 ment 5 the con-ection amounts to 07 ; this is about 0-09 second. The magnitude 

 of this error appears to show that some derangement, owing possibly to a current 

 of air or other som-ce of irregularity, has vitiated this result. For the sake of 

 imiformity, however, the corrected value has been retained. 



V. This column merely contains the corrected means, as read off upon the curve 

 determined by the points. 



VI. The value of the chronoscope unit after the first few revolutions is 



. 0-1288 second, 



with a probable error of 0-0002 second. By means of this factor the coiTected 

 means in column V. are evaluated in seconds in column VI. 



VII. This column contains the time calculated on the hypothesis that the rings 

 are retarded as if acted upon by a force proportional to the velocity, the coefficients 

 being determined by the method of least squares ; the formula is 



t=9016-6-25 log (27-7-s). 



