LAUNCHING DATA FOR A BATTLESHIP. 95 



is moving rapidly; that places them in a position where they cannot properly ob- 

 serve the instant that motion starts. The origin for time, for these observations, 

 is therefore subject to considerable uncertainty; it was adjusted as described for 

 the moving-picture curve observations. 



The points -|- and X lie surprisingly near the accurate curve, except for ob- 

 servations near the origin. 



The remaining curves were derived by the usual methods, the differentiation 

 being performed numerically on measured ordinates, rather than by drawing tan- 

 gents. As a final check the whole set of curves were reintegrated and adjusted, 

 so as to be correct and consistent for individual parts as well as for the curve as 

 a whole. It will be noted that the derived curves are plotted on a very large scale. 



The position of the ship entering the water at point of maximum velocity 

 after lOO feet travel is worthy of note. 



Pivoting would occur at "E" after 459 feet travel on the assumption of static 

 conditions (see Plate ^y). It actually occurred at "F" after about 569 feet travel. 

 The over-run due to vertical component of velocity is estimated as 10 to 12 feet, 

 leaving about 100 feet to be accounted for by the difference in static and dynamic 

 conditions. 



The coefficient of friction and resistance was obtained by differentiation, as 

 previously explained. It was also noted that the vessel did not start promptly, but 

 hung for several seconds. The coefficient of "starting" or "sticking" friction was 

 estimated from that fact, and the known inclination of the ways, and is plotted at 

 "G." That the curve does not begin at "G" is due to the sensible origin of time and 

 motion not corresponding to the actual origin. They would correspond, no doubt, 

 were we able to observe minute movements at the start. 



A portion of the distance curve "cd" is reproduced to a greatly enlarged scale 

 "CD" at the top of the sheet. The seven double spots represent two determina- 

 tions of travel from each of seven pictures, on which two stations on the ship 

 show in positions to be read on the scales. If the determination of travel is 

 exact, including reading of film, formula, constant distances, co-ordinates for loca- 

 tion of camera, and the numerical calculations, then the difference for the pair on 

 any one picture should be the exact known distance between the stations on the 

 ship, and the spots corrected for that distance would plot one on the other. The 

 variations for the seven pairs "C" to "D," disregarding signs, are, in feet, 0.21, 

 0.31, o.i.o, 0.07, 0.03, 0.34 and 0.31. Considering the above quantities as errors, we 

 find the probable error of a single observation to be 0.16 feet, or 2 inches; that is, 

 by method of least squares, the error that it is an even chance that any error ex- 

 ceeds or falls under. 



In all twenty pairs of readings were made similar to the above, and the prob- 

 able error determined from the whole twenty, including the seven on portion of 

 curve "CD," is 0.21 feet or 2^ inches. 



The distance the vessel moved before lifting was much greater than expected; 

 in fact it was assumed, without very much consideration, that as the differ- 



