1884.] of the Mean Density of the Earth. 161 



(8) The Expansion of the lead mass will produce a similar 

 effect. Its radius was C in., consequently the reading will be 

 too small by 6/3^, where /3 is the coefficient of expansion for lead, 

 and t x is the excess of temperature over that at which the radius is 

 6 inches. Now allowance is made for the variation of distance from 

 11 inches. If the temperatures are measured from the temperature 

 at which the radii were measured, the whole appareut diminution 

 of distance due to causes (7) and (8) will be (5a + 6/3)t, that is, the 

 distance instead of being 8 as in Baily's formula, will be 



8 - (5a + 6/3) t, 



Baily calculates the mean density for a distance of 11 inches, and 

 corrects by multiplying the result by (8/1 1) 2 . The correction to 

 this multiplier will be therefore — 28 (ox + 6/3) t/11 2 , or since 8 = 11 

 very nearly = — 2 (5a + 6/3) t/11. Substituting numbers and tak- 

 ing the mean density to be 5"67, the correction is 



A, - A - - -000063 t. 



The difference between two of the mean densities obtained, 

 without taking account of corrections /3, 7, 8, at temperatures 

 whose difference is t, is therefore — '000122 t, that at the higher 

 temperature being the greater. These corrections would make the 

 table above show still more striking results ; e.g. increasing the 

 difference at 68° over that at 36° by about -0036. No other 

 possible cause to produce temperature effects occurs to me. Is it 

 possible that Baily's personal equation was a function of the 

 temperature ? If his judgment became more bountiful as the air 

 became warmer, the error in the mean densities would be in the 

 direction indicated by the table given above. 



(2) On Possible Systems of Jointed Wickerwork, and their 

 Degrees of Internal Freedom. By J. Larmor, M. A. 



If the two sets of generating lines of a hyperboloid of one 

 sheet be constructed by rods jointed where they cross one another, 

 the system so formed will not be stiff. This statement is verified 

 by the simplest examination of an ordinary paper-basket, or — 

 much better — of one of the jointed frameworks of wooden rods 

 that are sometimes placed round flower-pots. 



Mr A. G. Greenhill has remarked (Math. Tripos, 1879) that the 

 forms assumed by the framework on deformation are those of a 

 confocal system of hyperboloids. This result may be proved syn- 

 thetically as follows. Consider such a confocal system in position ; 

 to the points which lie on a straight line on one of them there 

 correspond (in Ivory's manner) points on any other, which also lie 



vol. v. pt. 11. 11 



