352 
DR. P. E. SHAW ON THE NEWTONIAN CONSTANT OP 
k being any number and f any function expansible by Taylor’s theorem which 
vanishes with m/M. For on expanding by Maclaurin’s theorem we have 
acceleration = M k ~]f' ( 0 ) i. 
This is independent of m and therefore satisfies the experimental facts. There is 
an application of Yicaire’s principle to the present subject ; for k might vary 
according to the temperature of the large attracting body. It need only be constant 
as long as all the physical conditions (other than mass) are constant. 
II. Indirect Experimental Evidence. 
1 . It was pointed out by Poynting and Phillips (see paper quoted) that as regards 
small changes in temperature near, say, 15° C., there can be no great variation in weight 
with temperature as shown from various common experiments of great precision : 
(l) pendulum experiments give an appreciably constant value of gravity ( g ) regardless 
of the small temperature differences occurring at different times; (2) the value found 
for the expansibility of a liquid, say, mercury, is appreciably the same whether the 
dilatometer method or weight thermometer method be used. But the temperature 
range is very small, and we must not conclude from this or from the experiments of 
Poynting and Phillips on weight, that there would be no temperature influence on 
weight if the range of temperature were great. 
2 . A survey of previous researches on gravitation affords some slight information as 
to temperature effect :—- 
(1) The temperature of mountain masses and of superficial shells of the earth’s 
surface to a depth of, say, half-a-mile, is well above ordinary laboratory temperatures. 
Hence values of G or of earth’s mean density, A, obtained by these “ earth ” methods 
might differ from those obtained by laboratory methods. The most accurate earth 
methods, say those of Mendenhall, Preston, Yon Sterneck, give a rounded average 
for A of 5'4 c.g.s., whereas the best laboratory methods, say, by Boys, Braun, 
Poynting, Richarz, and Krigar-Menzel, give a mean of 5'51. As the numbers 
stand they show a plus temperature coefficient for G (for G varies inversely as A). 
But inasmuch as the differences between the various “ earth ” results are much greater 
than between the numbers 5'4 and 5'51, no sure inference can be drawn. 
( 2 ) It has been pointed out by Prof. W. M. Hicks that Baily’s results for A show 
a fall in value as temperature rises. This again indicates a plus temperature coefficient 
for G. 
(3) From Cornu’s researches* the mean value of A from winter work was 5'50, 
from summer work 5'56. But in the absence of recorded temperatures we can deduce 
nothing. The apparatus in a laboratory may have a higher temperature in winter 
than in summer. 
* ‘ Comptes Rendus,’ vols. 76 and 86. 
