376 Intelligence and Miscellaneous Articles. 



P is developed at all points of the contact-layer, acting from with- 

 out inwards upon the cylinder, from within outwards upon the 

 deposit. It is easy to demonstrate the formula 



p= __JL_ (i) 



1/ 8E 2 \ 



m+ 3 



in which m represents the unit diminution of external volume of 

 the cylinder under an external pressure equal to unity, Jc the com- 

 pressibility-coefficient of the metal. 



(1) If the deposition is produced by a current of constant inten- 

 sity distributed uniformly over the whole surface of the cylinder, 

 the weight of copper deposited upon unit length has for its expres- 

 sion (D designating the density of the copper, and p a constant) 



^ = tt(R' 2 -B 2 )D, (2) 



whence a . 



T>_ m + jj-fc M_ .on 



8 h 7rD Ba -H-B { } 



3 m-f--J& p 



I have verified that not only my experiments, but also those of 

 Prof. Mills, are very exactly represented by empiric expressions of 

 this form. 



(2) The limit A towards which the pressure for a deposit of in- 

 definite thickness tends is independent of J& ; but B is not so : the 

 shorter the radius B,, the more rapidly does the pressure approach 

 its limit. Experiment shows, in fact, that the contraction of an 

 almost linear thermometer is very rapid ; while I have observed 

 only a trifling contraction of a large alcohol thermometer of 3 cen- 

 tims. diameter, although it had an extremely capillary stem. 



A thermometer, the cross section of which is a very flat ellipse, 

 will be submitted to pressures rapidly increasing at the extremities 

 of the major axis of the ellipse, where the curvature is considerable ; 

 and its section will become more nearly circular ; the mercury will 

 descend in the stem, while it would rise if the same thermometer 

 had been compressed in a piezometer. 



(3) I have had made, by M. Alvergniat, some cylindrical ther- 

 mometers with much-elongated reservoirs, of known internal and 

 external radii, and swollen at the origin of the stem, so that they 

 could be fitted, in place of the gas-reservoir, into the apparatus 

 constructed by M. Ducretet for the experiments of M. Cailletet. 

 After determining experimentally their internal, from which I de- 

 termined by calculation their external compressibility m, I sub- 

 mitted them to coppering in the centre of a Daniell's cell of the 

 same height as the reservoir. Then observing from hour to hour 

 their excess, I was able to determine empirically the coefficients A 

 and B of the formula (3), and hence to deduce Jc. The mean of 

 fifteen series of experiments, made with three different thermome- 

 ters, gave : — 



