158 Royal Society : — 



and therefore the expression for the rate of heating becomes 



1-69 x-jr. 



Now, by using a sufficiently large single cell, we may make the 

 electromotive force, E, between S and T', be as little short as we 

 please of the whole electromotive force of the cell. We might then, 

 in testing by equality, with a standard and a tested conductor each 

 three inches or so long, and using a single cell, have nearly as much 

 as half the electromotive force of one cell acting per quarter foot of 

 these conductors, or two cells per foot. Hence if either is of best 

 conductive copper, its temperature would commence rising at the 

 rate of 4 X 169° or 67t>° Cent, per second. It would be almost im- 

 possible to work with so high a heating effect as this. But if we 

 use only -^th of the supposed electromotive force, that is to say -^th 

 of a cell per foot of the copper conductor, the rate of heating will be 

 reduced to y^-, that is to say, will be 6°'76 per second. By using 

 only very brief battery applications, it would be possible to work with 

 so high a rate of heating as that, without having the results much 

 vitiated by it. But -^ of a cell per foot will give only *0676° of 

 heating effect per second, and will be quite a sufficient battery power 

 to use in most cases. In the case we have supposed, for instance, 

 of conductors only three inches long, the electromotive force on each 

 would then be about -j^tj of the electromotive force of the cell. What 

 we denoted above by e and f in equations (7) would therefore each 

 have this value. Hence, by equation (4), we see that the effect of a 

 difference of yoVo between SS' and TT' would be to give q-p the 

 value youVon °f tne electromotive force of a single cell. Now one 

 of the light mirror* galvanometers, which I commonly use, re- 

 flecting the image of a gas or paraffine lamp to a scale 25 inches 

 distant, would, if made with a coil of 50 yards of copper wire of 

 moderate quality, weighing 5 grains per foot, give a deflection of 

 half a division of -^ of an inch on this scale, with an electromotive 

 force of 4- ~oWo °f a sm g^ e cellf . Hence by using such a galvano- 



* The mirror is a circle of thin " microscope glass " about three-eighths of an 

 inch in diameter, silvered in the ordinary manner ; and a small piece of fiat file 

 steel of equal length, attached to its back by lac varnish, constitutes the " needle" 

 of the galvanometer. The whole weight of mirror and needle amounts to from 

 1 to Itj grain. It is suspended inside the galvanometer coil by single silk fibre 

 about -i inch long. It is necessary to try many mirrors thus prepared, each 

 with its magnet attached, before one is found giving a good enough image. I 

 am much indebted to Mr. White, optician, Glasgow, for the skill and patience 

 which he has applied to the very troublesome processes involved. 



f In this state of sensibility the needle is under Glasgow horizontal magnetic 

 force of the earth alone ; and, with its mirror, it makes a vibration one way in 

 about "7 of a second. In many uses of my form of mirror galvanometer, both 

 for telegraphic and for experimental purposes, I find it convenient to make its 

 indications still more rapid, though, of course, less sensitive, by increasing the 

 dhective force by means of fixed steel magnets. On the other hand, I use fixed 

 steel magnets to diminish the earth's directing force and make the needle more 

 sensitive, when very high sensibility is wanted ; but this would be inconvenient 

 for the application described in the text, because effects of thermo-electric ac- 

 tion would be made too prominent. 



