Velocity of Transmission of Disturbances through Sea-water. 507 



and similarly A'= 



A- P -° 

 P'-O' 



Q'-O" 



if the rate of the pendulum be supposed constant during one fork- 

 beat ; in practice this is very nearly attained, for the firing-key is so 

 set as to use only the middle or maximum velocity part of the stroke 

 for scribing. In some earlier measurements the lengths between 

 successive fork-crests were measured, with the view of applying the 

 rigorous correction, but it was found that it differed from the one 

 here given by less than the breadth of a fine scriber line on the 

 smoked glass. It would, moreover, be as likely to be in excess as in 

 defect, according as the fuse was more or less sensitive, and the firing 

 battery stronger or weaker. Hence the whole time to be measured 

 comes to — 



T — WT4-- -T4-— _T. 



Q-0 ^Q'-O' 



In order to eliminate personal peculiarity of observation, the plates 

 were sometimes read by one of us and sometimes by Mr. Pollock, to 

 whom our best thanks are due. The measuring microscope was by 

 the Cambridge Scientific Instrument Co,, and had a respectable 

 screw ; this screw was compared with a standard scale, but found to 

 require no correction for its present purpose. 



It has been stated that observations were always made alternately ; 

 first the shot was fired so that it passed the piles, say, from pile X to 

 pile Y, and then immediately afterwards another similar charge was 

 fired, so that the shock passed from T to X. It is clear on general 

 principles that if the time- constants of the gauges and scribers 

 remain the same from shot to shot, that then, by taking the arith- 

 metical mean of the times obtained from the plates, we shall get the 

 time-value independent of time-constants. In order, however, to 

 obtain additional security, both the gauges, magnets, scribers, &c, 

 were made as much alike as possible, so as to reduce the difference of 

 their time- constants to the least possible amount. Our method of 

 elimination, however, is faulty, if there is any part of the time- 

 constant of the gauges which is reversed by the reversal of the shot. 

 If, for instance, the time-constants of the gauges are functions of the 

 violence of the shock the gauges receive, then there will be outstand- 

 ing errors not eliminated by taking means. In order to test this 

 point thoroughly, a large number of experiments were made during 

 the end of 1886 and beginning of 1887. 



.There may also be small differences of velocity, depending on direc- 

 tion caused by the configuration of the shore or sea-bottom. Finally, 



