264 Professors W. E. Ayrton and J. Perry on 



with the largest value of E which would allow us with run- 

 ning water to keep the outside temperature approximately 

 constant, the radius of an experimental ball to determine the 

 conductivity of copper would need to be greater than 500 cen- 

 tims., and hence impracticable ; but if a more effective method 

 could be employed of keeping the outside temperature con- 

 stant, then, making E, say, O'Ol, the radius of the copper ball, 

 to give satisfactory results, ought to be between 50 and 400 

 centims. It is quite evident, from such considerations, that 

 our method of experimenting can only be used with substances 

 having a heat-conductivity between 0'0003 and 0*03. 



At the commencement of our investigation we chose rather 

 vaguely balls of 5*5 and 6*9 centims. radius, being guided only 

 by former experience in numerical calculations under SirW. 

 Thomson, not having at the beginning of our experiments 

 worked out Fourier's formula, and being quite unable to obtain 

 either Fourier's treatise De la Chaleur, or any mathematical 

 assistance in Japan. 



Now we see that in order that a should equal 120°, 



Er 



-^ should equal 2*21 ; 



that is, for the smaller ball, 

 E 



and for the larger, 



z should equal 0*4 ; 



jt should equal 0'32: 



and we had reason to believe, as our investigation has since 



E 



proved to be correct, that ^- had about these values. If, how- 



F 

 ever, we had found that ^ was very different from 0'4, then 



we should have been compelled either to have made new stone 

 balls, or to have varied E either by coating the surface of the 

 ball, or by using, instead of the flowing water, the method of 

 radiating to an enclosure. 



IX. As this is perhaps the first time that any series of ob- 

 servations have been made illustrating Fourier's mathematical 

 results, we think that students will be glad to get the obser- 

 vations as they were obtained, without any correction whatever, 

 from which the curves AAA, a a a (fig. 2) were drawn. 

 They are as follows: — 



