TRACT 37.

OF GUNNERY.

231

pitted from the formula "00003146*!/ —'008 d or (*03146^ — 8)X*001*z>, which agree nearly with the true resistances as taras to the velocity 1700, after which they arc in excess, havingin the 1800 velocity 2 in excess, or the 43rd part; in the1900 velocity, 4 in excess, or the 24th part; and at the 2000velocity, 7 in excess, or the 15th part. Further, the 5th co-lumn contains the resistances as computed from the theorem*00002906t) J — *006v, or Q02906v — 6) X *001 v, being themedium between the two preceding ones; and these numbersare nearer the truth than either of the former, the greatesterror, in defect, being, at 1700 velocity, between 3 and 4,or about the 20th part. Also, in the 6th column are exhibit-ed the resistances as computed by the theorem *00003026^*— *007w or (*03026w —7)x "001 v, being the medium betweenthe two preceding it, which may be esteemed sufficientlynear the truth, varying but by two or three units in the lasttwo velocities.

But, it must still be understood that for the first three orfour velocities, the foregoing simple rule *0000l76v% willalways give the nearest value of the true resistance.

32. Lastly, another theorem may be found still a littlenearer the experiments, on this principle, viz, in three terms,containing the square of the velocity, and the velocity, anda constant quantity, as xv z + yv + z. Now, expounding vseverally by the three velocities 600, 1200, and 1800, andmaking the results equal to their correspondent resistances,we obtain tiie following near values of the coefficients, viz,x= *00003023, and y = — *00716, and z = u* 3 ; by whichthe assumed theorem becomes *00003028*!/ — •007-jty + 0'3,nearly. Then the resistances computed by this formula, forall the velocities, or values of v, they are as arranged in the7th or last column, and are mostly nearer than the precedingones, being only a littte too small in the first two or threenumbers, and too large in the last two numbers. Indeedmost of these theorems exhibit the last two numbers as largerthan the experimented ones; whence it may be suspected,