Space- Time Man/folds and Gravitational Fields. 703 



Summary. 



1. The hydrodynamic basis of convection of heat .suggests 

 study by means of models. 



2. We have the formulae: 



Natural convection . . h = (k0/l)F(c 2 gl 3 a6/k 2 ), 

 Forced convection . . h= (k-0/lj F(lvc/k). 



3. Graphs drawn with /t-f- (/■#//) as ordinate and either 

 {c 2 yPaO /-) or (Ivc/k) as abscissa should be independent 

 of the size of the object; consequently, to ascertain the 

 heat-loss for any particular body it should be necessary 

 only to perform the appropriate experiment with a model. 



4. For natural convection Peclet's data have been analysed 

 with promising result. The formula would not be applicable 

 to bodies where the fluid expansion caused was no longer 

 negligible as a mere volume change. 



5. For forced convection the formula, tested by data 

 given by Hughes^ is very promising. The cooling fluid 

 is not heated so much as in natural convection, and can 

 still be regarded as incompressible for smaller bodies at 

 higher temperatures. The formula is good, even for thin 

 wires, and it is satisfactory to trace in it the hydrodynamic 

 variable determining turbulence. 



6. Evidence available in published data indicates that, for 

 1 1 cat-loss from a body, an excellent first approximation can 

 be obtained from experiments with a model. The principle 

 of similitude affords a convenient method of expressing 

 experimental results. 



March 1020. 



LXXXI1. Space-Tune Manifolds and correspondin j Gravita- 

 tional Fields. B;i WlLFRTD WlLSON, B.&c, Northampton 

 Polytechnic Institute # . 



rpHE main purpose of the present paper is the investigation 

 X of the gravitational Held of an infinite uniform recti- 

 linear distribution of mass or, more precisely stated, the 

 determination of the equations of the geodesies in a space- 

 time manifold in which the square of the element of length 

 has the form 



<W = -f 1 d**-fJz*-f**dp+f A d*t . . (1) 

 where the /"s are functions of r only |. 



* Communicated by Or. Wm. Wilson. 



+ When f y —f 2 = f :s —f i =\ } r ~ and </> ore the ordinary cylindrical 

 space co-ordinates. 



