164 KEPORT— 1898. 



For o, P, X, and yu write 



The equation is unaltered ; this shows that it is a translatant. If the 

 first term only in the right-hand member had to be considered, the homo- 

 logue would be a straight line, making an angle of 45° with the increas- 

 ing direction of the axis of A, on the chart ; if the second term only were 

 present this also would be represented by a straight line sloping in the 

 opposite direction and to the same extent. To put these lines in the chart 

 it is only necessary to calculate one point on each, and to draw through 

 this point the line in the proper direction. 



These lines are drawn on the chart for the case when £'=6x10'", 

 </ = 981, e=100, p=s=l. They are marked 'Short Wave Gravity and 

 Elasticity Lines.' (See fig. 2.) 



18. Short Wave Curve. — To represent the united eflfect of gravity and 

 elasticity these two lines must be joined by a curve. The whole will then 

 be the homologue of the equation 



The curve is asymptotic to the short wave lines ; it very soon becomes 

 practically identical with them. It is symmetrical about a line parallel 

 to the axis of u drawn through the point of intersection of the straight 

 lines ; only half need be computed, the other half being put in by geo- 

 metry. The curve may conveniently be drawn by the method of § 11. 



19. It must next be shown how to adapt this curve to any values of a 

 and /?. It has been already shown that it is a translatant, and thus the 

 curve will not have to be redrawn, but merely shifted about. 



' Most of the experimental investigations into the physics of ice have been con- 

 cerned with the viscosity and not the elasticity. Professor Greenliill, in the paper 

 already cited, remarks that ' ice was the first substance for which an experimental 

 determination of E was attempted, as described in Young's Lectures on Natural 

 Philosophy' Morgan {Natvre, May 7, 1885) points out that the value quoted in 

 Thomson and Tait's ISat. Phil., Art. 686, is ten times too great. McConnel {Proc. 

 Hoy. Soc, March 1891, p. 343) gives the following values for E : — 



92,700 kilos per sq. cm. (Moseley), Phil. Trans., 1871 

 23,632 „ (Reusch), Nature, xxi. 504 



60,000 „ (Sevan) 



The last value is, presumably, computed from Bevan, Phil. Trans., 182C, Part ?, 

 Paper 21. Turning these values into c.g.s. units we obtain, to the nearest sing'e 

 significant figure — 



9 X lO'o (Moseley) 

 2 X lO" (Reusch) 

 6 X lO'" (Bevan) 



McConnel considers Moseley's value too great, and implies that Reusch's method 

 was unreliable. By recomputing Bevan 's value I obtain 5 x 10'°. 



From this it seems that the value of E for ice is somewhere about 6 x 10'° in c.g.s. 

 units ; in drawing the first short wave elasticity line on the chart it appeared unne- 

 cessary from a physical standpoint to allow for the density of ice and water when 

 the value of E was so uncertain. 



