36 Prof. A. Gray on the "Waste Space 



and 



Let 



\ y dx = h v a Y + h 2 a 2 + . . . + h n a n , 



where 



ai + fla + . . . H-a«=A. 

 Then 



j>*(j:0- 



— (<Ji + a 2 + ... + a„) 3 

 = 4- 2 (| +2 \/|- 3 )} 



I \ \Jh 2 h 3 *JhJi x s/h-Ji 2 y J 



It may be easily shown that the coefficients of a 1 a 2 2 and a^^ 

 are positive. Hence Dis greater than H, unless y is constant, 

 To obtain a numerical estimate of the inequality between 

 D and H, I have taken the case of a cylindrical ocean-bed, 

 whose right section is a parabola, the breadth of the ocean 

 1200 miles, its greatest depth 4 miles, and (for simplicity) I 

 supposed the tide-gauge and the epicentre of the earthquake 

 to be equidistant from the axis of the parabola, the depth of 

 water at each place being one quarter of a mile. The true 

 mean depth of the ocean along the path of the sea-wave is 

 then 2420 fathoms, and the mean depth as calculated from 

 the velocity of the sea-wave is 1900 fathoms, the latter number 

 being about three quarters of the former. 



VI. On the Estimation of " Waste Space round the Needle of a 

 Galvanometer." By Andkew Gkay, LL.D., F.R.S., Pro- 

 fessor of Physics in the University College of North Wales*. 



MY attention has been recalled to Professor Holman's 

 paper in the Philosophical Magazine for December 

 1895 by the reply from Professor Ayrton and Mr. Mather 

 which appeared in the November number of 1896. In that 



* Communicated by the Author. 



