Velocity of Transmission of Disturbances through Sea-water. 515 



and a mean taken, and each, angle was read off a different part of the 

 graduated circle each time, so that any error due to eccentricity was 

 entirely eliminated, and any errors due to imperfect graduation were 

 reduced to a minimum. In repeating an angle on the graduated circle, 

 not only is the second measures of the angle given on a different part 

 of the circle, but an angular quantity, which perhaps the vernier is 

 incapable of showing, has been doubled, and may therefore become 

 apparent. 



As an example, suppose the instrument carefully set over the point 

 A (see Plate 3) and levelled, and observing to D as an initial point, 

 the two verniers are read off, and their position recorded in the field- 

 book. Leaving the lower clamp fast, and releasing the milled-headed 

 screw clamping the vernier plate and that carrying the graduated 

 circle, the point E is then observed to, and the readings recorded, and 

 so on to the point F. Then leaving the upper clamp fast and releasing 

 the lower, the point D is again referred to, and the operation repeated 

 three times, thus getting four measures for the angles, taking care 

 after the second round to reverse the telescope. This movement will 

 bring the vernier originally on the left hand side of the instrument 

 to the right hand. A mean of the verniers and all the readings is 

 the required angle. Tripods with fine steel points and heavy plum- 

 mets were used as reference marks carefully set over the ends of the 

 base-line. 



The alignment of the points B and C was very carefully performed, 

 using the telescope in reversed positions, both from the ends of the 

 line and at the points themselves. 



The triangles obtained by the above operations for fixing E and E 

 were too small to make it necessary to go into the equation of their 

 conditions. 



Part II. — Reductions of Observations and Calculation of the 

 Theoretical Velocity of Sound through Water. 



Distance over which Disturbance Travelled. 



The distance between the gauges was at first 15,410 cm., it was 

 afterwards 15,840 cm., minus a correction made for the slope of the 

 pile which had been driven slightly out of the vertical. This correc- 

 tion varied between 51 cm. and 59 cm., and depended on the depth 

 of the gauge below the top of the pile. Finally in the third position 

 the distance was 18,210 cm. 



Time Measurements. 



Let t be the epoch of arrival of the disturbance at gauge A, and 

 let t 1} a Y be the time constant of the gauge and of the scriber attached 

 to it respectively, then the record on the smoked plate occurs at 



