to the Motion of Vortex-rings. 209 



the velocity of the ring at its different points is approximately 

 found. 



A second projection is made in which the abscissae are the 

 ranges and the ordinates are the velocities ; the points thus de- 

 termined 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 accurate value having been determined by the method 

 of least squares, the results are embodied in the following Table, 

 of which a description is first given. 



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 

 arrival of the ring at a point 4 feet from the orifice is 65 chro- 

 noscopic units, or about 0*93 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 chro- 

 noscope corrected by this amount. 



IV. When the ranges are taken as abscissae and the corre- 

 sponding times as ordinates, it is found that a curve can be 

 drawn through or near all the points thus produced. To iden- 

 tify the points with the curve, small corrections are in some cases 

 required. These corrections are shown in column IV. In 

 the case of No. 5 the correction amounts to 0*7. This is about 

 0*09 second. The magnitude of this error appears to show that 

 some derangement, owing perhaps to a current of air or other 

 source of irregularity, has vitiated this result. For the sake of 

 uniformity, 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 revo- 

 lutions is 



0-1288 second, 



with a probable error of 0*0002 second. 



By means of this factor the corrected means in column V. are 

 evaluated in seconds in column VI. 



VII. This column contains the time calculated on the hypo- 

 thesis 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 



*=9-016-6-251og (27-7-5). 

 Phil Mag. S. 4. Vol. 42. No. 279. Sept. 1871. P 



