516 Prof. R. Threlfall and Mr. J. F. Adair. On the 



time fe+ Ti + Gi- Similarly if T be the time required for the transmis- 

 sion of tbe disturbance, tben tbe second record on tbe smoked plate 

 occurs at time T + £ + T 2 + <r 2 , where t 2 , <r 2 are tbe time-constants of 

 tbe second gauge and its attached scriber respectively. 



Thus tbe observed interval as recorded on the smoked plate is — 



t = T + t 2 + <r 3 — Tj— a v 



Similarly for a disturbance in the opposite direction tbe recorded 

 interval is — 



7 = r ^ + r 1 + ff 1 — r 2 —ff 2l 



provided that tbe time of transmission is the same in both directions.- 

 and that the time constants of the gauges and scribers have not 

 altered between tbe two observations, and that the scribers are 

 attached to the same gauges in tbe two observations. 



t + t' 



Hence time of transmission of disturbance = — — . 



Li 



The velocity of transmission calculated on the supposition that 

 the fork has an exact frequency of 100 must be multiplied by 

 1-002622— 0-0001472 t, to get tbe correct velocity. 



The velocities bad been originally deduced on the supposition that 

 the fork was correct ; these uncorrected velocities are given in 

 Column 9 of the Table ; tbe correction arising from tbe decimal parts- 

 of the above factor, viz., from 0'002622 — 0*0001472 t, are given in- 

 Column 10, and the corrected velocities in Column 11. 



Tbe complete formula for V the velocity is thus — 



V = — ?L_ {1-002622-0-0001472^, 



where S is the distance between the gauges and t is tbe temperature 

 of the fork. This gives the velocity at the temperature of the sea- 

 water during tbe observation. 



Theoretical Calculation of the Velocity. 



In Column 12 of the Table is given the velocity of sound, calculated 

 theoretically as follows. The formula giving the velocity of sound- 

 through water is taken to be — 



where is the adiabatic resilience of volume, and D is the density 

 at the temperature considered. 



