MEASURING THE VIBRATORY PERIODS OP TUNING-FORKS. 59 



The divisions on the scale, measured on the axis of ordinates, give the velocity per second of the 

 pellets. One unit on this axis equals 20 feet, and a unit on the axis of abscissas equals one unit of 

 weight of pellet. The weight of a pellet of No. 10 shot is here taken as the unit of weight. The 

 numbers of the shot are written under the axis of abscissas, the velocities along the axis of ordinates- 

 My friend Professor Rice, of the United States Naval Academy, who had previously made sim- 

 ilar experiments with a Le Bouleng^ chronoscope, and who took great interest in these experiments, 

 found that the curve here given is very nearly the curve of secants, and the formula for it is: 



« -1^.7. 



T = sec. — 

 a 



where x is the velocity and y the weight of a pellet, and a h and n undetermined constants. 



So far as the experiments with these two special guns show, there is a marked superiority 

 in the 10 over the 12 gauge, when each is loaded with the same weight of powder and shot- 

 Thus, with the same charges, viz, 4 drams powder and 1^ ounces of shot tired from the 10 gauge, 

 gives a velocity of 100 feet per second more than that given by the 12gauge gun. This fact is 

 conclusively shown in the comparison of the figures in the two tables XVIII and XX, and the 

 ditference in velocities is in favor of the 10 gauge in each of the sixty experiments which were 

 made to get the numbers contained in the lines opposite No. 8 and No. 10. 



With No. 10 shot the mean velocity given by the 10 gauge gun over the first .30 yards is 848 

 feet. With the same charge in the 12 gauge the velocity is 748 feet ; showing a difi'erence of 100 

 feet in favor of the 10 gauge. With No. 8 shot the experiments show a ditierence of 72 feet. The 

 average difference in favor of the 10 gauge in the flight of shot Nos. 8 and 10 over 40 yards amounts 

 to 110 feet. 



If we assume, as we may without grave error, that the penetration of shot varies as the square 

 of its velocity, these experiments will give the relative penetrations of the 10 to the 12 gauge gun 

 about as 9 is to 7. 



That the 10-gauge gun shows such marked superiority over the 12 may be accounted for by 

 the fact that the same charge occupies less length in a 10 than in a 12-gauge, and hence there 

 are fewer pellets in contact with the barrel of the former than of the latter to oppose by their 

 friction the projectile force of the powder. Also, as these choke-bores are contracted two sizes at 

 their muzzles, the action of the choke on the pellets in a 10-gauge, will, I think, be more effective 

 than in the case of a 12, the pellets in the latter being more crowded together and conflicting 

 in their actions than in the case of their discharge from a 10 bore. Also, some effect in favor of 

 the lOgauge may be owing to the fact that in this gun the powder is exploded nearer the center 

 of the charge, and thus there is less chance of it blasting before it unburnt powder contained in 

 the portion of the charge removed from the point of ignition. 



I also venture to predict that with the same weight of barrels the 10-gauge will not heat as 

 much as the 12, because the motion of the shot lost in the 12gauge must appear in the form of 

 heat. 



The simplicity and inexpensiveness of the chronoscope we have described in this paper, its 

 accuracy, and the ease with which it is used must commend it to all who will give it a trial under 

 the conditions of its action which we have endeavored to set forth in this paper. Another of its 

 advantages is that its records on the paper covering the cylinder are easily rendered permanent by 

 drawing the uusmoked side of the paper over the surface of a dilute solution of photographic 

 negative varnish contained in a wide shallow dish. On the records may be written with a blunt 

 style the nature of the experiments they i-ecord before the carbon is fixed by the varnish, and 

 *hen they can be bound togetner in book-form for preservation and reference. 



