May 1, 1888.] 



♦ KNOWLEDGE ♦ 



153 



All the four weights to be used in a given set of experi- 

 ments are to be first cai-efully weighed against each other, in 

 pairs, above A B and below D E. every pau- being thus 

 tested, each weight in each test being put on one side of M 

 in one trial and on the other side in another, and the indica- 

 tions of the long light-pointer cai-efully noted in each of the 

 twenty-four trials thus made. [Six pairs of weights can be 

 selected from the four ; and taking any pair, v: and vj' , these 

 can bo weighed against each other in two ways in the upper 

 weight-holders, and in two ways in the lower, or four ways 

 in all. Thus twenty-four weighings must be made to 

 eliminate all errors arising from differences — however 

 minute — between the weights.] Next each pair of weights 

 must be balanced against each other, one being above and 

 the other below. One such trial is illustrated in iig. 2. 

 The weight w above A, which should exactly balance the 

 weight w' set in the scale-holder above B, will not balance 



here:. ON THESCALEOF THIS FIGURE. A 

 WRTICk. DISTANCE OF ABOUT 13 INCHES IfJTERVENEi 



Fig. 3. 



w' set^below E. For while each is drawn downwards with 

 equarforce by the earth's mass — or with only such minute 

 and calculable difterence as results from the distance of w 

 from the earth's centre being greater than the distance of 

 w' — to is drawn towards C, or downwards, by the attraction 

 of the great globe A BD, while w' is drawn towards C, or 

 upivards, by the same attraction. The amount of deflection, 

 as indicated by the light-pointer, is to be carefully noted ; 

 then the weight iv is to be transferred to B and the weight w' 

 to D, when an opposite deflection will take place, which is 

 to be similarly noted. Next the two experiments are 

 to be repeated, the weight iv' being above and the 

 weight w below. Corresponding experiments are to be 

 made with each of the six pairs of weights which can be 

 formed out of the four. The mean of the observed de- 

 flections compared with the mean of the twenty-four pre- 

 ceding observations (in all of which the beam is approximately 

 horizontal) will supply the means of compax-ing the attrac- 

 tion of the earth with the atti-action of the globe A B D. 

 Of course many details must be taken into account : as, the 

 weight of the wires or cords along A D and B E ; the 

 angles such as C tn D and C iv'B when w and lu' are in 

 equilibrium ; the difference of the distances of w and w' 

 from the earth's centre ; and the like. But all such matters 

 are readiU' calculable from the original data and the indica- 

 tions of the ray- index. 



Here is a rough calculation of the effects we may expect 

 to recognise in such experiments : — 



Supposing the globe A B D to be of lead, and therefore of 

 twice the mean density of the earth, and i feet in diameter, 

 its mass compared with that of the eai-th is as 2(2)^ to 

 (10,500,000)3; but the weights w and to', neglecting theii- 

 distance from the surface of the large globe and from the 

 vertiaxl diameter, are only 2 feet from the centre of the 

 globe, while they are 10,500,000 feet from the centre of the 

 eai-th. On this account the attraction of the globe is greater 

 than the attraction of the e<xrth as (10,500,000)- is greater 

 than (2)2 ; and since the attraction of the globe is exerted 

 upwartls on one weight and downwards on the other, we 

 must regard it as doubled, and this doubled attmction as 

 practiailly again doubled by the interchange of the ends of 

 the balance from which the upper and lower weights are 

 severally suspended. It follows that while the attraction of 

 the upper globe, so far as it depends on mass, is less than 

 the earth's in the ratio 



2 (2-') to (10,500,000)* 

 it is increased, through the diminution of distance and the 

 adjustment and interchange of the weights, in the ratio 



4(10,500,000)= to (2)2. 

 Hence, finally, the eflect of the leaden globe's pull, 

 quadi-upled as in the experiments, bears to the effect of the 

 earth's pull the ratio compounded of these two, viz., the 

 ratio 



1(5 to 10,500,000. 

 So that if our balance, with its ray-index, is delicate enough 

 to measure a difterence of weights amounting to about 

 s-suWij of tli^ weight used, we may expect this plan to 

 afford a direct, and in that respect satisfactory, comparison 

 between the mass of the earth and that of a globe of known 

 size and den.'^ity. 



[It might seem as though the shght difference of distance 

 of the two small weights from the earth's centre might be 

 neglected. Lord Brougham incurred some just ridicule for 

 the rather strange mistake of asserting that a man can 

 carry a weight more easily over his shoulder than in his 

 hand, because in the former position the weight is farther 

 from the earth's centre. But in delicate experiments such 

 as we are considering in the text, the difference due even to 

 a few feet of distance must be taken into account. Thus, 

 suppose A C to be 2 feet, or iv rather more than -1 feet 

 farther from the earth's centre than w' ; then, since the 

 eai'th's radius contains in round numbers 21 millions of feet, 

 we may take c/ to be -jij (Toinru nearer the earth's centre than 

 w, by which difference the attraction of the earth on lo' is 

 increased by ^-s uonos V^^'^' This, though minute, is appre- 

 ciable, even considerable, in relation to the quantities we 

 are de;iling with in these experiments.] 



ELECTRIC LAMPS FOR COAL MINES. 



By Wm. Lant Carpenter. 



X an article on miners' lamps and colliery 

 explosions in the April number of Kxow- 

 LEDcE, Mr. W. Mattieu Williams alludes at 

 the end in veiy brief terms to the electric 

 lighting of mines. This may be, and is, done 

 in two ways. In some cases the main thorough- 

 fares, and many of the branch ones, are lighted 

 by glow lamps, which are {)erniaiieully fixed, and supplied 

 with current from a dynamo machine, sometimes above, and 

 sometimes underground, driven usually by a steam-engine. 

 The greatest progress made lately, however, is in the con- 

 struction of portable lamps, containing either primary 



