MANUAL OF TIDE OBSERVATIONS 31 



the tide house for the purpose. The measured distance added to the 

 tape graduation to which the measurement was made, together with 

 an allowance for any detached section of tape, will give the plane 

 of flotation as referred to the tape graduations extended. It is also 

 the distance which the tape gage datum is below the reading mark 

 of the gage. The result, however, is subject to a small correction, 

 described in the following paragraph. 



84. Correction to plane of flotation. — The necessity for this cor- 

 rection arises from the fact that the shifting of the tape from one 

 side of the supporting pulley to the other may make a slight differ- 

 ence in the plane of flotation. Although the variation is too small 

 to be of material importance in taking readings during the normal 

 operation of the gage, it is desirable that in a careful determination 

 of the plane of flotation under conditions differing from the normal, 

 a' correction shall be applied to reduce the measurement to a mean 

 sea level reading. The correction will depend upon the weight of 

 the tape, the diameter of the float, and whether the counterpoise is 

 attached directly to the end of the tape or supported by a movable 

 pulley, 



85. In order to make this reduction, the tape reading .taken at the 

 reading mark at the time the measurements are made should be 

 noted. In taking this reading it is assumed that the looped portion 

 of the tape is below the reading mark. 



Let ^'= tape reading at time of measurement. 



R =tape reading corresponding to mean sea level. 

 D = diameter of float in inches. 

 t = weight of tape per linear foot. 

 IF = weight of a cubic foot of water at tide station. 



7rD2 

 The cross section of the float is -r^g square feet and the buoy- 

 ancy due to an immersion of 1 foot of a cylinder of the same diameter 



is ~576~ pounds. Therefore, when the float is operating under 



normal conditions, an application of a force of 1 pound wo aid change 



576 

 the plane of flotation by ^^jji feet. When the apparatus is ar- 

 ranged as in figure 2 with the counterpoise supported by a movable 

 pulley, the shifting of 1 linear foot of tape from one side of the 

 supporting pulley to the other side will cause a change of V-/2 t 

 pounds in the pull on the float and the plane of flotation will be 



864 < 

 changed by _ wj[)2 foot. The total correction to be applied to the 



plane of flotation as obtained by direct measurement, in order to 



864 t 

 reduce to the mean sea level value, is — WW^ {R—R') foot. 



86. Taking the average weight of sea water as 64 pounds j)er cubic 

 foot, the weight of steel and phosphor-bronze tape, respectively, as 

 O.OOtl pound and 0.011 pound per linear foot, and assuming the 

 diameter of the float to be either 8^ or 314 inches, there have been 



